Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1872,2,Mod(289,1872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1872, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1872.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.t (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: | \(14.9479952584\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-0.780776 - 1.35234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1872.289 |
Dual form | 1872.2.t.r.1153.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.561553 | −0.251134 | −0.125567 | − | 0.992085i | \(-0.540075\pi\) | ||||
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78078 | + | 3.08440i | −0.673070 | + | 1.16579i | 0.303959 | + | 0.952685i | \(0.401692\pi\) |
−0.977029 | + | 0.213107i | \(0.931642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 3.57071i | 0.138675 | + | 0.990338i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.28078 | − | 2.21837i | 0.310634 | − | 0.538034i | −0.667866 | − | 0.744282i | \(-0.732792\pi\) |
0.978500 | + | 0.206248i | \(0.0661254\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.561553 | + | 0.972638i | −0.128829 | + | 0.223138i | −0.923223 | − | 0.384264i | \(-0.874455\pi\) |
0.794394 | + | 0.607403i | \(0.207789\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | − | 1.73205i | −0.208514 | − | 0.361158i | 0.742732 | − | 0.669588i | \(-0.233529\pi\) |
−0.951247 | + | 0.308431i | \(0.900196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.84233 | − | 4.92306i | −0.527807 | − | 0.914189i | −0.999475 | − | 0.0324124i | \(-0.989681\pi\) |
0.471667 | − | 0.881777i | \(-0.343652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56155 | 0.280463 | 0.140232 | − | 0.990119i | \(-0.455215\pi\) | ||||
0.140232 | + | 0.990119i | \(0.455215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.71922 | − | 2.97778i | −0.282639 | − | 0.489544i | 0.689395 | − | 0.724385i | \(-0.257876\pi\) |
−0.972034 | + | 0.234841i | \(0.924543\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.28078 | + | 2.21837i | 0.200024 | + | 0.346451i | 0.948536 | − | 0.316670i | \(-0.102565\pi\) |
−0.748512 | + | 0.663121i | \(0.769231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.219224 | − | 0.379706i | 0.0334313 | − | 0.0579047i | −0.848826 | − | 0.528673i | \(-0.822690\pi\) |
0.882257 | + | 0.470768i | \(0.156023\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.24621 | −1.20283 | −0.601417 | − | 0.798935i | \(-0.705397\pi\) | ||||
−0.601417 | + | 0.798935i | \(0.705397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.84233 | − | 4.92306i | −0.406047 | − | 0.703294i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6847 | −1.60501 | −0.802506 | − | 0.596645i | \(-0.796500\pi\) | ||||
−0.802506 | + | 0.596645i | \(0.796500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.561553 | − | 0.972638i | −0.0757198 | − | 0.131150i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.56155 | − | 9.63289i | 0.724053 | − | 1.25410i | −0.235310 | − | 0.971920i | \(-0.575611\pi\) |
0.959363 | − | 0.282175i | \(-0.0910560\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.06155 | + | 10.4989i | −0.776102 | + | 1.34425i | 0.158071 | + | 0.987428i | \(0.449473\pi\) |
−0.934173 | + | 0.356821i | \(0.883861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.280776 | − | 2.00514i | −0.0348260 | − | 0.248708i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.219224 | + | 0.379706i | 0.0267824 | + | 0.0463885i | 0.879106 | − | 0.476626i | \(-0.158141\pi\) |
−0.852324 | + | 0.523015i | \(0.824807\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.00000 | + | 12.1244i | −0.830747 | + | 1.43890i | 0.0666994 | + | 0.997773i | \(0.478753\pi\) |
−0.897447 | + | 0.441123i | \(0.854580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.87689 | −0.219674 | −0.109837 | − | 0.993950i | \(-0.535033\pi\) | ||||
−0.109837 | + | 0.993950i | \(0.535033\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.12311 | −0.811753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.56155 | −1.07576 | −0.537879 | − | 0.843022i | \(-0.680774\pi\) | ||||
−0.537879 | + | 0.843022i | \(0.680774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.12311 | −1.00139 | −0.500695 | − | 0.865624i | \(-0.666922\pi\) | ||||
−0.500695 | + | 0.865624i | \(0.666922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.719224 | + | 1.24573i | −0.0780108 | + | 0.135119i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.56155 | + | 11.3649i | 0.695523 | + | 1.20468i | 0.970004 | + | 0.243089i | \(0.0781607\pi\) |
−0.274481 | + | 0.961593i | \(0.588506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.9039 | − | 4.81645i | −1.24787 | − | 0.504901i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.315342 | − | 0.546188i | 0.0323534 | − | 0.0560377i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.21922 | − | 3.84381i | 0.225328 | − | 0.390280i | −0.731090 | − | 0.682281i | \(-0.760988\pi\) |
0.956418 | + | 0.292002i | \(0.0943213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.71922 | − | 2.97778i | −0.171069 | − | 0.296300i | 0.767725 | − | 0.640780i | \(-0.221389\pi\) |
−0.938794 | + | 0.344479i | \(0.888055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.56155 | 0.745062 | 0.372531 | − | 0.928020i | \(-0.378490\pi\) | ||||
0.372531 | + | 0.928020i | \(0.378490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.12311 | − | 7.14143i | −0.398596 | − | 0.690388i | 0.594957 | − | 0.803757i | \(-0.297169\pi\) |
−0.993553 | + | 0.113369i | \(0.963836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8078 | 1.70567 | 0.852837 | − | 0.522177i | \(-0.174880\pi\) | ||||
0.852837 | + | 0.522177i | \(0.174880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.40388 | + | 12.8239i | −0.696499 | + | 1.20637i | 0.273174 | + | 0.961965i | \(0.411926\pi\) |
−0.969673 | + | 0.244406i | \(0.921407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.561553 | + | 0.972638i | 0.0523651 | + | 0.0906990i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.56155 | + | 7.90084i | 0.418157 | + | 0.724269i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.43845 | 0.486430 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.78078 | + | 8.28055i | 0.424225 | + | 0.734780i | 0.996348 | − | 0.0853884i | \(-0.0272131\pi\) |
−0.572122 | + | 0.820168i | \(0.693880\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3693 | −1.51756 | −0.758782 | − | 0.651345i | \(-0.774205\pi\) | ||||
−0.758782 | + | 0.651345i | \(0.774205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.719224 | + | 1.24573i | −0.0614474 | + | 0.106430i | −0.895113 | − | 0.445840i | \(-0.852905\pi\) |
0.833665 | + | 0.552270i | \(0.186238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.46543 | − | 9.46641i | 0.463572 | − | 0.802930i | −0.535564 | − | 0.844495i | \(-0.679901\pi\) |
0.999136 | + | 0.0415643i | \(0.0132342\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.68466 | + | 4.43674i | −0.475375 | + | 0.371019i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.59612 | + | 2.76456i | 0.132550 | + | 0.229584i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.28078 | + | 5.68247i | −0.268772 | + | 0.465526i | −0.968545 | − | 0.248839i | \(-0.919951\pi\) |
0.699773 | + | 0.714365i | \(0.253284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3693 | −1.25074 | −0.625369 | − | 0.780329i | \(-0.715051\pi\) | ||||
−0.625369 | + | 0.780329i | \(0.715051\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.876894 | −0.0704339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.36932 | −0.348709 | −0.174355 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174355 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.12311 | 0.561379 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.90388 | − | 13.6899i | 0.619080 | − | 1.07228i | −0.370574 | − | 0.928803i | \(-0.620839\pi\) |
0.989654 | − | 0.143475i | \(-0.0458276\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.12311 | + | 5.40938i | 0.241673 | + | 0.418590i | 0.961191 | − | 0.275884i | \(-0.0889705\pi\) |
−0.719518 | + | 0.694474i | \(0.755637\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5000 | + | 3.57071i | −0.961538 | + | 0.274670i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.87689 | − | 3.25088i | 0.142698 | − | 0.247160i | −0.785814 | − | 0.618463i | \(-0.787756\pi\) |
0.928512 | + | 0.371303i | \(0.121089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.34233 | − | 14.4493i | 0.630621 | − | 1.09227i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.56155 | + | 11.3649i | 0.490433 | + | 0.849456i | 0.999939 | − | 0.0110115i | \(-0.00350513\pi\) |
−0.509506 | + | 0.860467i | \(0.670172\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.68466 | 0.719855 | 0.359927 | − | 0.932980i | \(-0.382801\pi\) | ||||
0.359927 | + | 0.932980i | \(0.382801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.965435 | + | 1.67218i | 0.0709802 | + | 0.122941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.12311 | 0.374639 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.438447 | − | 0.759413i | 0.0317249 | − | 0.0549492i | −0.849727 | − | 0.527223i | \(-0.823233\pi\) |
0.881452 | + | 0.472274i | \(0.156567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.74621 | − | 16.8809i | −0.701548 | − | 1.21512i | −0.967923 | − | 0.251247i | \(-0.919159\pi\) |
0.266375 | − | 0.963869i | \(-0.414174\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.68466 | − | 9.84612i | −0.405015 | − | 0.701507i | 0.589308 | − | 0.807908i | \(-0.299400\pi\) |
−0.994323 | + | 0.106402i | \(0.966067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5885 | + | 20.0719i | −0.821490 | + | 1.42286i | 0.0830828 | + | 0.996543i | \(0.473523\pi\) |
−0.904573 | + | 0.426320i | \(0.859810\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.2462 | 1.42101 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.719224 | − | 1.24573i | −0.0502328 | − | 0.0870057i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.24621 | −0.155374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.65767 | + | 6.33527i | 0.251804 | + | 0.436138i | 0.964023 | − | 0.265820i | \(-0.0856427\pi\) |
−0.712218 | + | 0.701958i | \(0.752309\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.123106 | + | 0.213225i | −0.00839573 | + | 0.0145418i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.78078 | + | 4.81645i | −0.188771 | + | 0.326962i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.56155 | + | 3.46410i | 0.575912 | + | 0.233021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | + | 6.92820i | 0.267860 | + | 0.463947i | 0.968309 | − | 0.249756i | \(-0.0803503\pi\) |
−0.700449 | + | 0.713702i | \(0.747017\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.561553 | − | 0.972638i | 0.0372716 | − | 0.0645563i | −0.846788 | − | 0.531931i | \(-0.821467\pi\) |
0.884059 | + | 0.467374i | \(0.154800\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.246211 | 0.0162701 | 0.00813505 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813505 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.0000 | −1.70332 | −0.851658 | − | 0.524097i | \(-0.824403\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.63068 | 0.302072 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.630683 | −0.0407955 | −0.0203977 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203977 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.40388 | + | 2.43160i | −0.0904320 | + | 0.156633i | −0.907693 | − | 0.419635i | \(-0.862158\pi\) |
0.817261 | + | 0.576268i | \(0.195491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.59612 | + | 2.76456i | 0.101972 | + | 0.176621i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.75379 | − | 1.51883i | −0.238848 | − | 0.0966406i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3693 | − | 26.6204i | 0.970103 | − | 1.68027i | 0.274871 | − | 0.961481i | \(-0.411365\pi\) |
0.695231 | − | 0.718786i | \(-0.255302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | − | 3.46410i | 0.125739 | − | 0.217786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.08854 | − | 14.0098i | −0.504549 | − | 0.873905i | −0.999986 | − | 0.00526106i | \(-0.998325\pi\) |
0.495437 | − | 0.868644i | \(-0.335008\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.2462 | 0.760943 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.68466 | + | 13.3102i | 0.473856 | + | 0.820743i | 0.999552 | − | 0.0299295i | \(-0.00952826\pi\) |
−0.525696 | + | 0.850673i | \(0.676195\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.56155 | 0.403073 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.68466 | − | 2.91791i | 0.102715 | − | 0.177908i | −0.810087 | − | 0.586310i | \(-0.800580\pi\) |
0.912803 | + | 0.408401i | \(0.133914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.534565 | − | 0.925894i | −0.0324725 | − | 0.0562441i | 0.849332 | − | 0.527858i | \(-0.177005\pi\) |
−0.881805 | + | 0.471614i | \(0.843671\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.68466 | − | 8.11407i | −0.282496 | − | 0.489297i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.84233 | + | 15.3154i | −0.531284 | + | 0.920211i | 0.468049 | + | 0.883702i | \(0.344957\pi\) |
−0.999333 | + | 0.0365086i | \(0.988376\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.80776 | 0.167497 | 0.0837486 | − | 0.996487i | \(-0.473311\pi\) | ||||
0.0837486 | + | 0.996487i | \(0.473311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.657671 | − | 1.13912i | −0.0390945 | − | 0.0677136i | 0.845816 | − | 0.533475i | \(-0.179114\pi\) |
−0.884911 | + | 0.465761i | \(0.845781\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.12311 | −0.538520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.21922 | + | 9.03996i | 0.307013 | + | 0.531762i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.2808 | − | 21.2709i | 0.717451 | − | 1.24266i | −0.244556 | − | 0.969635i | \(-0.578642\pi\) |
0.962007 | − | 0.273026i | \(-0.0880244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.12311 | + | 5.40938i | −0.181834 | + | 0.314946i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.68466 | − | 4.43674i | 0.328752 | − | 0.256583i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.780776 | + | 1.35234i | 0.0450032 | + | 0.0779478i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.40388 | − | 5.89570i | 0.194906 | − | 0.337587i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.1922 | −0.581702 | −0.290851 | − | 0.956768i | \(-0.593938\pi\) | ||||
−0.290851 | + | 0.956768i | \(0.593938\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.8769 | −0.616772 | −0.308386 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.31534 | −0.0743475 | −0.0371738 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371738 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0540 | 1.29484 | 0.647420 | − | 0.762133i | \(-0.275848\pi\) | ||||
0.647420 | + | 0.762133i | \(0.275848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.68466 | − | 9.84612i | 0.318280 | − | 0.551277i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.43845 | + | 2.49146i | 0.0800373 | + | 0.138629i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.34233 | − | 16.7276i | −0.129929 | − | 0.927879i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.6847 | − | 25.4346i | 0.809591 | − | 1.40225i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9039 | + | 20.6181i | −0.654297 | + | 1.13327i | 0.327773 | + | 0.944756i | \(0.393702\pi\) |
−0.982070 | + | 0.188518i | \(0.939631\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.123106 | − | 0.213225i | −0.00672598 | − | 0.0116497i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.12311 | 0.115653 | 0.0578265 | − | 0.998327i | \(-0.481583\pi\) | ||||
0.0578265 | + | 0.998327i | \(0.481583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.56155 | + | 2.70469i | 0.0845628 | + | 0.146467i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.68466 | −0.252948 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.80776 | − | 11.7914i | 0.365460 | − | 0.632995i | −0.623390 | − | 0.781911i | \(-0.714245\pi\) |
0.988850 | + | 0.148916i | \(0.0475784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.90388 | + | 11.9579i | 0.369556 | + | 0.640090i | 0.989496 | − | 0.144559i | \(-0.0461763\pi\) |
−0.619940 | + | 0.784649i | \(0.712843\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.84233 | + | 15.3154i | 0.470630 | + | 0.815155i | 0.999436 | − | 0.0335881i | \(-0.0106934\pi\) |
−0.528806 | + | 0.848743i | \(0.677360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.93087 | − | 6.80847i | 0.208629 | − | 0.361356i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.3693 | 0.811162 | 0.405581 | − | 0.914059i | \(-0.367069\pi\) | ||||
0.405581 | + | 0.914059i | \(0.367069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.86932 | + | 15.3621i | 0.466806 | + | 0.808532i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05398 | 0.0551676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0270 | + | 17.3673i | 0.523404 | + | 0.906563i | 0.999629 | + | 0.0272394i | \(0.00867165\pi\) |
−0.476224 | + | 0.879324i | \(0.657995\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.8078 | − | 36.0401i | 1.08029 | − | 1.87111i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.81534 | + | 3.14426i | −0.0939948 | + | 0.162804i | −0.909189 | − | 0.416384i | \(-0.863297\pi\) |
0.815194 | + | 0.579188i | \(0.196630\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.1577 | − | 12.6107i | 0.832162 | − | 0.649483i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.65767 | + | 9.79937i | 0.290615 | + | 0.503360i | 0.973955 | − | 0.226740i | \(-0.0728068\pi\) |
−0.683340 | + | 0.730100i | \(0.739473\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.3693 | + | 23.1563i | −0.683140 | + | 1.18323i | 0.290877 | + | 0.956760i | \(0.406053\pi\) |
−0.974017 | + | 0.226473i | \(0.927280\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.05398 | 0.154843 | 0.0774213 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774213 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.12311 | −0.259087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.36932 | 0.270160 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.02699 | − | 10.4390i | 0.302486 | − | 0.523921i | −0.674213 | − | 0.738537i | \(-0.735517\pi\) |
0.976698 | + | 0.214617i | \(0.0688502\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.28078 | + | 16.0748i | 0.463460 | + | 0.802736i | 0.999131 | − | 0.0416909i | \(-0.0132745\pi\) |
−0.535671 | + | 0.844427i | \(0.679941\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.780776 | + | 5.57586i | 0.0388932 | + | 0.277753i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.43845 | − | 5.95557i | 0.170437 | − | 0.295206i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.18466 | − | 15.9083i | 0.454152 | − | 0.786615i | −0.544487 | − | 0.838769i | \(-0.683276\pi\) |
0.998639 | + | 0.0521548i | \(0.0166089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.8078 | + | 34.3081i | 0.974676 | + | 1.68819i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.12311 | 0.251483 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.87689 | + | 15.3752i | 0.433665 | + | 0.751129i | 0.997186 | − | 0.0749725i | \(-0.0238869\pi\) |
−0.563521 | + | 0.826102i | \(0.690554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7538 | 0.719056 | 0.359528 | − | 0.933134i | \(-0.382938\pi\) | ||||
0.359528 | + | 0.933134i | \(0.382938\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.5885 | − | 37.3924i | −1.04474 | − | 1.80955i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.43845 | + | 2.49146i | 0.0692876 | + | 0.120010i | 0.898588 | − | 0.438794i | \(-0.144594\pi\) |
−0.829300 | + | 0.558803i | \(0.811261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.6231 | + | 21.8639i | −0.606628 | + | 1.05071i | 0.385164 | + | 0.922848i | \(0.374145\pi\) |
−0.991792 | + | 0.127862i | \(0.959189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.24621 | 0.107451 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.657671 | − | 1.13912i | −0.0313889 | − | 0.0543672i | 0.849904 | − | 0.526937i | \(-0.176660\pi\) |
−0.881293 | + | 0.472570i | \(0.843326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.7386 | 0.700254 | 0.350127 | − | 0.936702i | \(-0.386138\pi\) | ||||
0.350127 | + | 0.936702i | \(0.386138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.68466 | − | 6.38202i | −0.174670 | − | 0.302537i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.12311 | − | 7.14143i | 0.194581 | − | 0.337025i | −0.752182 | − | 0.658956i | \(-0.770998\pi\) |
0.946763 | + | 0.321931i | \(0.104332\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.56155 | + | 4.43674i | −0.120619 | + | 0.208918i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.68466 | + | 2.70469i | 0.313382 | + | 0.126798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3078 | + | 24.7818i | 0.669289 | + | 1.15924i | 0.978103 | + | 0.208120i | \(0.0667345\pi\) |
−0.308814 | + | 0.951122i | \(0.599932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.4039 | + | 31.8765i | −0.857154 | + | 1.48463i | 0.0174778 | + | 0.999847i | \(0.494436\pi\) |
−0.874632 | + | 0.484787i | \(0.838897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.6847 | 1.24014 | 0.620071 | − | 0.784546i | \(-0.287104\pi\) | ||||
0.620071 | + | 0.784546i | \(0.287104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.0000 | −1.20314 | −0.601568 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.56155 | −0.0721058 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.876894 | 0.0403196 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.63068 | − | 4.55648i | 0.120704 | − | 0.209065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.12311 | + | 5.40938i | 0.142698 | + | 0.247161i | 0.928512 | − | 0.371303i | \(-0.121089\pi\) |
−0.785814 | + | 0.618463i | \(0.787755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.77320 | − | 7.62775i | 0.445620 | − | 0.347795i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.24621 | + | 2.15850i | −0.0565875 | + | 0.0980125i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.561553 | + | 0.972638i | −0.0254464 | + | 0.0440744i | −0.878468 | − | 0.477801i | \(-0.841434\pi\) |
0.853022 | + | 0.521875i | \(0.174767\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.87689 | + | 17.1073i | 0.445738 | + | 0.772041i | 0.998103 | − | 0.0615613i | \(-0.0196080\pi\) |
−0.552365 | + | 0.833602i | \(0.686275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.5616 | −0.655819 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.9309 | − | 43.1815i | −1.11830 | − | 1.93696i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.4924 | 1.27550 | 0.637748 | − | 0.770245i | \(-0.279866\pi\) | ||||
0.637748 | + | 0.770245i | \(0.279866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.87689 | − | 10.1791i | 0.262038 | − | 0.453863i | −0.704746 | − | 0.709460i | \(-0.748939\pi\) |
0.966783 | + | 0.255597i | \(0.0822722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.965435 | + | 1.67218i | 0.0429613 | + | 0.0744111i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.40388 | + | 5.89570i | 0.150874 | + | 0.261322i | 0.931549 | − | 0.363615i | \(-0.118458\pi\) |
−0.780675 | + | 0.624938i | \(0.785124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.34233 | − | 5.78908i | 0.147856 | − | 0.256094i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.24621 | −0.187110 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.24621 | − | 14.2829i | −0.362668 | − | 0.628159i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.9309 | 1.66178 | 0.830891 | − | 0.556436i | \(-0.187831\pi\) | ||||
0.830891 | + | 0.556436i | \(0.187831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9309 | − | 20.6649i | −0.521701 | − | 0.903612i | −0.999681 | − | 0.0252415i | \(-0.991965\pi\) |
0.477981 | − | 0.878370i | \(-0.341369\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | − | 3.46410i | 0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.50000 | − | 16.4545i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.28078 | + | 5.68247i | −0.315365 | + | 0.246135i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.31534 | + | 4.01029i | 0.100101 | + | 0.173380i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.68466 | − | 9.84612i | 0.244856 | − | 0.424102i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7386 | −1.27856 | −0.639282 | − | 0.768972i | \(-0.720768\pi\) | ||||
−0.639282 | + | 0.768972i | \(0.720768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.9309 | 1.06597 | 0.532984 | − | 0.846126i | \(-0.321071\pi\) | ||||
0.532984 | + | 0.846126i | \(0.321071\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.38447 | 0.271988 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.0270 | − | 29.4916i | 0.724061 | − | 1.25411i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.03457 | − | 12.1842i | −0.298064 | − | 0.516262i | 0.677629 | − | 0.735404i | \(-0.263008\pi\) |
−0.975693 | + | 0.219142i | \(0.929674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.46543 | + | 0.592932i | 0.0619813 | + | 0.0250783i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.684658 | + | 1.18586i | −0.0288549 | + | 0.0499782i | −0.880092 | − | 0.474803i | \(-0.842519\pi\) |
0.851237 | + | 0.524781i | \(0.175853\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.15767 | − | 7.20130i | 0.174915 | − | 0.302961i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.3693 | + | 35.2807i | 0.853926 | + | 1.47904i | 0.877638 | + | 0.479325i | \(0.159118\pi\) |
−0.0237115 | + | 0.999719i | \(0.507548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.3693 | −0.810581 | −0.405290 | − | 0.914188i | \(-0.632830\pi\) | ||||
−0.405290 | + | 0.914188i | \(0.632830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.68466 | + | 8.11407i | 0.195364 | + | 0.338380i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.6847 | −1.23579 | −0.617894 | − | 0.786261i | \(-0.712014\pi\) | ||||
−0.617894 | + | 0.786261i | \(0.712014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.2462 | − | 28.1393i | 0.674006 | − | 1.16741i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6847 | − | 20.2384i | −0.483929 | − | 0.838190i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.31534 | − | 12.6705i | −0.301936 | − | 0.522969i | 0.674638 | − | 0.738149i | \(-0.264300\pi\) |
−0.976575 | + | 0.215179i | \(0.930966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.876894 | + | 1.51883i | −0.0361318 | + | 0.0625821i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −44.4233 | −1.82425 | −0.912123 | − | 0.409917i | \(-0.865558\pi\) | ||||
−0.912123 | + | 0.409917i | \(0.865558\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.56155 | − | 4.43674i | −0.105013 | − | 0.181889i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.384472 | −0.0157091 | −0.00785455 | − | 0.999969i | \(-0.502500\pi\) | ||||
−0.00785455 | + | 0.999969i | \(0.502500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9654 | + | 31.1170i | 0.732825 | + | 1.26929i | 0.955671 | + | 0.294437i | \(0.0951321\pi\) |
−0.222846 | + | 0.974854i | \(0.571535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.96543 | + | 3.40423i | −0.0799063 | + | 0.138402i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | + | 13.8564i | −0.324710 | + | 0.562414i | −0.981454 | − | 0.191700i | \(-0.938600\pi\) |
0.656744 | + | 0.754114i | \(0.271933\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.12311 | − | 29.4449i | −0.166803 | − | 1.19121i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.4309 | − | 19.7988i | −0.461688 | − | 0.799668i | 0.537357 | − | 0.843355i | \(-0.319423\pi\) |
−0.999045 | + | 0.0436871i | \(0.986090\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.40388 | + | 9.35980i | −0.217552 | + | 0.376811i | −0.954059 | − | 0.299619i | \(-0.903141\pi\) |
0.736507 | + | 0.676430i | \(0.236474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.3002 | 0.976707 | 0.488353 | − | 0.872646i | \(-0.337598\pi\) | ||||
0.488353 | + | 0.872646i | \(0.337598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.7386 | −1.87254 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.80776 | −0.351189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.21922 | + | 12.5041i | −0.287393 | + | 0.497779i | −0.973187 | − | 0.230017i | \(-0.926122\pi\) |
0.685794 | + | 0.727796i | \(0.259455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.68466 | − | 4.64996i | −0.106537 | − | 0.184528i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.1577 | − | 12.6107i | 0.640190 | − | 0.499653i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0885 | − | 22.6700i | 0.516966 | − | 0.895412i | −0.482840 | − | 0.875709i | \(-0.660395\pi\) |
0.999806 | − | 0.0197030i | \(-0.00627208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2732 | − | 33.3822i | 0.760061 | − | 1.31646i | −0.182758 | − | 0.983158i | \(-0.558502\pi\) |
0.942819 | − | 0.333306i | \(-0.108164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.8078 | + | 41.2363i | 0.935980 | + | 1.62116i | 0.772877 | + | 0.634555i | \(0.218817\pi\) |
0.163102 | + | 0.986609i | \(0.447850\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.2462 | 0.873240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.43845 | + | 12.8838i | 0.291089 | + | 0.504181i | 0.974068 | − | 0.226258i | \(-0.0726491\pi\) |
−0.682979 | + | 0.730438i | \(0.739316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.75379 | 0.381112 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.12311 | + | 12.3376i | −0.277477 | + | 0.480604i | −0.970757 | − | 0.240064i | \(-0.922831\pi\) |
0.693280 | + | 0.720668i | \(0.256165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.1847 | − | 26.3006i | −0.590615 | − | 1.02297i | −0.994150 | − | 0.108011i | \(-0.965552\pi\) |
0.403535 | − | 0.914964i | \(-0.367781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.12311 | + | 1.94528i | 0.0435522 | + | 0.0754346i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.68466 | + | 9.84612i | −0.220111 | + | 0.381243i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.2462 | −0.936015 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.37689 | + | 5.84895i | 0.130170 | + | 0.225461i | 0.923742 | − | 0.383016i | \(-0.125114\pi\) |
−0.793572 | + | 0.608476i | \(0.791781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.6155 | −0.984485 | −0.492242 | − | 0.870458i | \(-0.663823\pi\) | ||||
−0.492242 | + | 0.870458i | \(0.663823\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.90388 | + | 13.6899i | 0.303323 | + | 0.525371i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.0540 | + | 31.2704i | −0.690816 | + | 1.19653i | 0.280755 | + | 0.959780i | \(0.409415\pi\) |
−0.971571 | + | 0.236749i | \(0.923918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.403882 | − | 0.699544i | 0.0154315 | − | 0.0267282i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.84233 | − | 41.7226i | −0.222575 | − | 1.58950i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.15009 | + | 1.99202i | 0.0437516 | + | 0.0757800i | 0.887072 | − | 0.461631i | \(-0.152736\pi\) |
−0.843320 | + | 0.537411i | \(0.819402\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.06913 | + | 5.31589i | −0.116419 | + | 0.201643i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.56155 | 0.248537 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.3693 | −0.731569 | −0.365785 | − | 0.930700i | \(-0.619199\pi\) | ||||
−0.365785 | + | 0.930700i | \(0.619199\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.86174 | 0.145648 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2462 | 0.460566 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.7462 | + | 22.0771i | −0.478694 | + | 0.829122i | −0.999702 | − | 0.0244297i | \(-0.992223\pi\) |
0.521008 | + | 0.853552i | \(0.325556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.56155 | − | 2.70469i | −0.0584806 | − | 0.101291i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.19224 | − | 2.49146i | 0.119383 | − | 0.0931755i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.684658 | + | 1.18586i | −0.0255335 | + | 0.0442252i | −0.878510 | − | 0.477724i | \(-0.841462\pi\) |
0.852976 | + | 0.521950i | \(0.174795\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4654 | + | 23.3228i | −0.501479 | + | 0.868587i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.3153 | + | 23.0628i | 0.494519 | + | 0.856533i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.6695 | −1.47126 | −0.735630 | − | 0.677383i | \(-0.763114\pi\) | ||||
−0.735630 | + | 0.677383i | \(0.763114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.561553 | − | 0.972638i | −0.0207698 | − | 0.0359743i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 53.4924 | 1.97579 | 0.987894 | − | 0.155131i | \(-0.0495801\pi\) | ||||
0.987894 | + | 0.155131i | \(0.0495801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.438447 | + | 0.759413i | −0.0161504 | + | 0.0279733i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.12311 | − | 5.40938i | −0.114885 | − | 0.198987i | 0.802849 | − | 0.596183i | \(-0.203317\pi\) |
−0.917734 | + | 0.397196i | \(0.869983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.6847 | + | 32.3628i | 0.685474 | + | 1.18728i | 0.973288 | + | 0.229589i | \(0.0737382\pi\) |
−0.287814 | + | 0.957686i | \(0.592929\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.84233 | − | 3.19101i | 0.0674977 | − | 0.116909i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.3693 | 1.07313 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0540 | − | 26.0743i | −0.549327 | − | 0.951463i | −0.998321 | − | 0.0579278i | \(-0.981551\pi\) |
0.448993 | − | 0.893535i | \(-0.351783\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.63068 | 0.314103 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0000 | − | 25.9808i | −0.545184 | − | 0.944287i | −0.998595 | − | 0.0529853i | \(-0.983126\pi\) |
0.453411 | − | 0.891302i | \(-0.350207\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.68466 | + | 13.3102i | −0.278569 | + | 0.482495i | −0.971029 | − | 0.238961i | \(-0.923193\pi\) |
0.692461 | + | 0.721456i | \(0.256527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.7116 | + | 54.9262i | −1.14804 | + | 1.98846i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 37.1771 | + | 15.0423i | 1.34239 | + | 0.543145i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.00000 | + | 15.5885i | 0.324548 | + | 0.562134i | 0.981421 | − | 0.191867i | \(-0.0614544\pi\) |
−0.656873 | + | 0.754002i | \(0.728121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.87689 | + | 6.71498i | −0.139442 | + | 0.241521i | −0.927286 | − | 0.374355i | \(-0.877864\pi\) |
0.787843 | + | 0.615876i | \(0.211198\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.31534 | −0.262775 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.87689 | −0.103075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0000 | −1.00192 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.45360 | 0.0875728 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.588540 | + | 1.01938i | −0.0209792 | + | 0.0363370i | −0.876324 | − | 0.481721i | \(-0.840012\pi\) |
0.855345 | + | 0.518058i | \(0.173345\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.3693 | − | 45.6730i | −0.937585 | − | 1.62394i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.5194 | − | 16.3946i | −1.43889 | − | 0.582190i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.8078 | + | 36.0401i | −0.737049 | + | 1.27661i | 0.216770 | + | 0.976223i | \(0.430448\pi\) |
−0.953819 | + | 0.300383i | \(0.902885\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.5616 | + | 18.2931i | −0.373641 | + | 0.647165i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.87689 | − | 3.25088i | −0.0662342 | − | 0.114721i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.6501 | + | 32.3029i | 0.655702 | + | 1.13571i | 0.981717 | + | 0.190345i | \(0.0609607\pi\) |
−0.326015 | + | 0.945365i | \(0.605706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.56155 | 0.0548335 | 0.0274168 | − | 0.999624i | \(-0.491272\pi\) | ||||
0.0274168 | + | 0.999624i | \(0.491272\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.43845 | + | 7.68762i | −0.155472 | + | 0.269285i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.246211 | + | 0.426450i | 0.00861384 | + | 0.0149196i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2462 | − | 22.9431i | −0.462296 | − | 0.800720i | 0.536779 | − | 0.843723i | \(-0.319641\pi\) |
−0.999075 | + | 0.0430028i | \(0.986308\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000 | − | 6.92820i | 0.139431 | − | 0.241502i | −0.787850 | − | 0.615867i | \(-0.788806\pi\) |
0.927281 | + | 0.374365i | \(0.122139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.7386 | 1.20798 | 0.603990 | − | 0.796992i | \(-0.293577\pi\) | ||||
0.603990 | + | 0.796992i | \(0.293577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.74621 | + | 16.8809i | 0.338500 | + | 0.586299i | 0.984151 | − | 0.177334i | \(-0.0567472\pi\) |
−0.645651 | + | 0.763633i | \(0.723414\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.5616 | −0.504528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.75379 | − | 3.03765i | −0.0606924 | − | 0.105122i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.80776 | − | 16.9875i | 0.338602 | − | 0.586475i | −0.645568 | − | 0.763703i | \(-0.723379\pi\) |
0.984170 | + | 0.177227i | \(0.0567128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65767 | + | 2.87117i | −0.0571611 | + | 0.0990059i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.01941 | − | 2.00514i | 0.241475 | − | 0.0689791i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.4654 | + | 21.5908i | 0.428317 | + | 0.741868i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.43845 | + | 5.95557i | −0.117868 | + | 0.204154i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.12311 | −0.209651 | −0.104826 | − | 0.994491i | \(-0.533428\pi\) | ||||
−0.104826 | + | 0.994491i | \(0.533428\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.4384 | −1.07392 | −0.536958 | − | 0.843609i | \(-0.680427\pi\) | ||||
−0.536958 | + | 0.843609i | \(0.680427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.4384 | −0.697351 | −0.348675 | − | 0.937244i | \(-0.613368\pi\) | ||||
−0.348675 | + | 0.937244i | \(0.613368\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.49242 | −0.0848430 | −0.0424215 | − | 0.999100i | \(-0.513507\pi\) | ||||
−0.0424215 | + | 0.999100i | \(0.513507\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.05398 | + | 1.82554i | −0.0358362 | + | 0.0620702i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.56155 | − | 16.5611i | −0.324353 | − | 0.561797i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.24621 | + | 0.972638i | −0.0422263 | + | 0.0329566i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.68466 | + | 16.7743i | −0.327401 | + | 0.567076i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.71922 | + | 16.8342i | −0.328195 | + | 0.568450i | −0.982154 | − | 0.188080i | \(-0.939774\pi\) |
0.653959 | + | 0.756530i | \(0.273107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.9654 | − | 32.8491i | −0.638962 | − | 1.10671i | −0.985661 | − | 0.168738i | \(-0.946031\pi\) |
0.346699 | − | 0.937976i | \(-0.387302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.8078 | 0.397363 | 0.198681 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198681 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.6847 | − | 42.7551i | −0.828830 | − | 1.43558i | −0.898957 | − | 0.438037i | \(-0.855674\pi\) |
0.0701272 | − | 0.997538i | \(-0.477659\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.0540 | −1.14213 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.63068 | − | 8.02058i | 0.154960 | − | 0.268398i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.68466 | − | 6.38202i | −0.123165 | − | 0.213327i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.43845 | − | 7.68762i | −0.148031 | − | 0.256396i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.9654 | + | 25.9209i | −0.498571 | + | 0.863550i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.43845 | −0.180780 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0000 | + | 24.2487i | 0.464862 | + | 0.805165i | 0.999195 | − | 0.0401089i | \(-0.0127705\pi\) |
−0.534333 | + | 0.845274i | \(0.679437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.7386 | −0.355787 | −0.177893 | − | 0.984050i | \(-0.556928\pi\) | ||||
−0.177893 | + | 0.984050i | \(0.556928\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.12311 | − | 15.8017i | −0.301931 | − | 0.522959i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.9309 | − | 53.5738i | 1.02143 | − | 1.76916i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2462 | − | 38.5316i | 0.733835 | − | 1.27104i | −0.221398 | − | 0.975184i | \(-0.571062\pi\) |
0.955233 | − | 0.295856i | \(-0.0956047\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −46.7926 | − | 18.9328i | −1.54020 | − | 0.623181i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.05398 | + | 13.9499i | 0.264813 | + | 0.458670i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.40388 | − | 11.0918i | 0.210105 | − | 0.363912i | −0.741643 | − | 0.670795i | \(-0.765953\pi\) |
0.951747 | + | 0.306884i | \(0.0992862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.38447 | 0.209243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.87689 | −0.0940845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.43845 | −0.112329 | −0.0561646 | − | 0.998422i | \(-0.517887\pi\) | ||||
−0.0561646 | + | 0.998422i | \(0.517887\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.49242 | 0.0812507 | 0.0406253 | − | 0.999174i | \(-0.487065\pi\) | ||||
0.0406253 | + | 0.999174i | \(0.487065\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.56155 | − | 4.43674i | 0.0834156 | − | 0.144480i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.36932 | − | 9.29993i | −0.174479 | − | 0.302207i | 0.765502 | − | 0.643434i | \(-0.222491\pi\) |
−0.939981 | + | 0.341227i | \(0.889158\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.938447 | − | 6.70185i | −0.0304633 | − | 0.217551i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.4924 | + | 30.2978i | −0.566635 | + | 0.981441i | 0.430260 | + | 0.902705i | \(0.358422\pi\) |
−0.996896 | + | 0.0787360i | \(0.974912\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.246211 | + | 0.426450i | −0.00796721 | + | 0.0137996i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.56155 | − | 4.43674i | −0.0827169 | − | 0.143270i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5616 | −0.921340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.47301 | + | 9.47954i | 0.176183 | + | 0.305157i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.12311 | 0.293379 | 0.146690 | − | 0.989183i | \(-0.453138\pi\) | ||||
0.146690 | + | 0.989183i | \(0.453138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.4924 | + | 45.8862i | −0.850182 | + | 1.47256i | 0.0308612 | + | 0.999524i | \(0.490175\pi\) |
−0.881043 | + | 0.473035i | \(0.843158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.4654 | + | 33.7151i | 0.624033 | + | 1.08086i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.91146 | + | 13.7030i | 0.253110 | + | 0.438399i | 0.964380 | − | 0.264519i | \(-0.0852132\pi\) |
−0.711270 | + | 0.702918i | \(0.751880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.1231 | + | 22.7299i | −0.419416 | + | 0.726450i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.6155 | −0.880799 | −0.440399 | − | 0.897802i | \(-0.645163\pi\) | ||||
−0.440399 | + | 0.897802i | \(0.645163\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.19224 | + | 5.52911i | 0.101713 | + | 0.176172i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.876894 | −0.0278836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.1771 | + | 34.9477i | 0.640946 | + | 1.11015i | 0.985222 | + | 0.171283i | \(0.0547911\pi\) |
−0.344276 | + | 0.938869i | \(0.611876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.50758 | − | 11.2715i | 0.206304 | − | 0.357329i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.3078 | + | 17.8536i | −0.326450 | + | 0.565428i | −0.981805 | − | 0.189893i | \(-0.939186\pi\) |
0.655355 | + | 0.755321i | \(0.272519\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))