Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(193,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.l (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 205.1 | ||
Root | \(-1.73040 - 0.0755709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.205 |
Dual form | 252.2.l.b.193.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.73040 | − | 0.0755709i | −0.999048 | − | 0.0436309i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.967857 | 0.432839 | 0.216419 | − | 0.976300i | \(-0.430562\pi\) | ||||
0.216419 | + | 0.976300i | \(0.430562\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.11482 | + | 2.39941i | −0.421363 | + | 0.906892i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.98858 | + | 0.261536i | 0.996193 | + | 0.0871787i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.728244 | 0.219574 | 0.109787 | − | 0.993955i | \(-0.464983\pi\) | ||||
0.109787 | + | 0.993955i | \(0.464983\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.81066 | + | 3.13615i | 0.502187 | + | 0.869813i | 0.999997 | + | 0.00252677i | \(0.000804296\pi\) |
−0.497810 | + | 0.867286i | \(0.665862\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67478 | − | 0.0731419i | −0.432427 | − | 0.0188851i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.49948 | + | 6.06128i | 0.848749 | + | 1.47008i | 0.882325 | + | 0.470641i | \(0.155977\pi\) |
−0.0335755 | + | 0.999436i | \(0.510689\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.348050 | + | 0.602841i | −0.0798483 | + | 0.138301i | −0.903184 | − | 0.429253i | \(-0.858777\pi\) |
0.823336 | + | 0.567554i | \(0.192110\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.11041 | − | 4.06770i | 0.460530 | − | 0.887644i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.43796 | 1.34241 | 0.671204 | − | 0.741273i | \(-0.265778\pi\) | ||||
0.671204 | + | 0.741273i | \(0.265778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.06325 | −0.812650 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.15168 | − | 0.678412i | −0.991440 | − | 0.130560i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.34727 | − | 5.79764i | 0.621573 | − | 1.07660i | −0.367620 | − | 0.929976i | \(-0.619827\pi\) |
0.989193 | − | 0.146619i | \(-0.0468393\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.58310 | + | 7.93816i | −0.823149 | + | 1.42574i | 0.0801762 | + | 0.996781i | \(0.474452\pi\) |
−0.903326 | + | 0.428956i | \(0.858882\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.26015 | − | 0.0550340i | −0.219365 | − | 0.00958020i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07899 | + | 2.32229i | −0.182382 | + | 0.392538i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.854506 | − | 1.48005i | 0.140480 | − | 0.243318i | −0.787197 | − | 0.616701i | \(-0.788469\pi\) |
0.927677 | + | 0.373383i | \(0.121802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.89617 | − | 5.56364i | −0.463758 | − | 0.890895i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.62444 | − | 6.27771i | −0.566042 | − | 0.980413i | −0.996952 | − | 0.0780185i | \(-0.975141\pi\) |
0.430910 | − | 0.902395i | \(-0.358193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.348050 | + | 0.602841i | −0.0530772 | + | 0.0919324i | −0.891343 | − | 0.453329i | \(-0.850236\pi\) |
0.838266 | + | 0.545261i | \(0.183570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.89252 | + | 0.253130i | 0.431191 | + | 0.0377343i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.83120 | − | 6.63583i | −0.558838 | − | 0.967936i | −0.997594 | − | 0.0693294i | \(-0.977914\pi\) |
0.438756 | − | 0.898606i | \(-0.355419\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.51435 | − | 5.34983i | −0.644907 | − | 0.764261i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.59745 | − | 10.7529i | −0.783800 | − | 1.50571i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.05637 | + | 3.56174i | 0.282465 | + | 0.489243i | 0.971991 | − | 0.235017i | \(-0.0755147\pi\) |
−0.689527 | + | 0.724260i | \(0.742181\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.704836 | 0.0950401 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.647824 | − | 1.01685i | 0.0858064 | − | 0.134686i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.38809 | − | 4.13629i | 0.310903 | − | 0.538500i | −0.667655 | − | 0.744471i | \(-0.732702\pi\) |
0.978558 | + | 0.205971i | \(0.0660353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46287 | − | 4.26582i | −0.315338 | − | 0.546182i | 0.664171 | − | 0.747581i | \(-0.268785\pi\) |
−0.979509 | + | 0.201399i | \(0.935451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.95926 | + | 6.87926i | −0.498820 | + | 0.866705i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.75246 | + | 3.03535i | 0.217366 | + | 0.376489i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.91035 | − | 5.04087i | 0.355556 | − | 0.615841i | −0.631657 | − | 0.775248i | \(-0.717625\pi\) |
0.987213 | + | 0.159407i | \(0.0509583\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.1403 | − | 0.486523i | −1.34113 | − | 0.0585704i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.304424 | 0.0361285 | 0.0180642 | − | 0.999837i | \(-0.494250\pi\) | ||||
0.0180642 | + | 0.999837i | \(0.494250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.33879 | + | 9.24705i | 0.624858 | + | 1.08229i | 0.988568 | + | 0.150773i | \(0.0481763\pi\) |
−0.363711 | + | 0.931512i | \(0.618490\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.03106 | + | 0.307064i | 0.811877 | + | 0.0354567i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.811862 | + | 1.74736i | −0.0925202 | + | 0.199130i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61945 | + | 2.80497i | 0.182203 | + | 0.315584i | 0.942630 | − | 0.333839i | \(-0.108344\pi\) |
−0.760428 | + | 0.649423i | \(0.775011\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.86320 | + | 1.56324i | 0.984800 | + | 0.173694i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.618759 | − | 1.07172i | 0.0679176 | − | 0.117637i | −0.830067 | − | 0.557664i | \(-0.811698\pi\) |
0.897985 | + | 0.440027i | \(0.145031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.38700 | + | 5.86646i | 0.367372 | + | 0.636307i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.23026 | + | 9.77930i | −0.667954 | + | 1.04845i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.78679 | + | 10.0230i | −0.613399 | + | 1.06244i | 0.377264 | + | 0.926106i | \(0.376865\pi\) |
−0.990663 | + | 0.136333i | \(0.956468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.54349 | + | 0.848265i | −1.00043 | + | 0.0889223i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.53050 | − | 13.3899i | 0.884572 | − | 1.38846i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.336863 | + | 0.583464i | −0.0345614 | + | 0.0598622i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.32933 | − | 2.30247i | 0.134973 | − | 0.233780i | −0.790614 | − | 0.612315i | \(-0.790238\pi\) |
0.925587 | + | 0.378534i | \(0.123572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.17641 | + | 0.190462i | 0.218738 | + | 0.0191422i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.61394 | 0.160593 | 0.0802964 | − | 0.996771i | \(-0.474413\pi\) | ||||
0.0802964 | + | 0.996771i | \(0.474413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8401 | 1.06811 | 0.534055 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534055 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.04258 | − | 3.93695i | 0.199335 | − | 0.384207i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.97630 | − | 8.61920i | 0.481077 | − | 0.833249i | −0.518688 | − | 0.854964i | \(-0.673579\pi\) |
0.999764 | + | 0.0217146i | \(0.00691252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.27835 | − | 16.0706i | −0.888705 | − | 1.53928i | −0.841407 | − | 0.540401i | \(-0.818272\pi\) |
−0.0472974 | − | 0.998881i | \(-0.515061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.59049 | + | 2.49650i | −0.150962 | + | 0.236957i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.75824 | + | 9.97356i | 0.541689 | + | 0.938234i | 0.998807 | + | 0.0488275i | \(0.0155485\pi\) |
−0.457118 | + | 0.889406i | \(0.651118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.23103 | 0.581046 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.59108 | + | 9.84620i | 0.424446 | + | 0.910281i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.4448 | + | 1.63945i | −1.69083 | + | 0.150288i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4697 | −0.951787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.79732 | + | 11.1369i | 0.522727 | + | 1.00418i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.77193 | −0.784586 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.06977 | 0.804812 | 0.402406 | − | 0.915461i | \(-0.368174\pi\) | ||||
0.402406 | + | 0.915461i | \(0.368174\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.647824 | − | 1.01685i | 0.0570377 | − | 0.0895291i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.0851 | 1.14325 | 0.571625 | − | 0.820515i | \(-0.306313\pi\) | ||||
0.571625 | + | 0.820515i | \(0.306313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.05845 | − | 1.50718i | −0.0917792 | − | 0.130689i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.98609 | − | 0.656606i | −0.429134 | − | 0.0565116i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.0764 | −1.71525 | −0.857623 | − | 0.514279i | \(-0.828060\pi\) | ||||
−0.857623 | + | 0.514279i | \(0.828060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.337832 | + | 0.585143i | 0.0286546 | + | 0.0496312i | 0.879997 | − | 0.474979i | \(-0.157544\pi\) |
−0.851343 | + | 0.524610i | \(0.824211\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.12804 | + | 11.7722i | 0.516074 | + | 0.991397i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.31860 | + | 2.28388i | 0.110267 | + | 0.190988i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.23968 | − | 5.61129i | 0.269041 | − | 0.465992i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.40734 | + | 9.59851i | 0.610947 | + | 0.791671i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.5088 | 1.76207 | 0.881034 | − | 0.473054i | \(-0.156848\pi\) | ||||
0.881034 | + | 0.473054i | \(0.156848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1705 | 1.15318 | 0.576588 | − | 0.817035i | \(-0.304384\pi\) | ||||
0.576588 | + | 0.817035i | \(0.304384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.87324 | + | 19.0299i | 0.717359 | + | 1.53847i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.43579 | + | 7.68301i | −0.356291 | + | 0.617114i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.99845 | − | 13.8537i | 0.638346 | − | 1.10565i | −0.347450 | − | 0.937699i | \(-0.612952\pi\) |
0.985796 | − | 0.167949i | \(-0.0537143\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.28919 | − | 6.31865i | −0.260850 | − | 0.501101i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.17717 | + | 15.4473i | −0.565641 | + | 1.21742i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0904 | + | 17.4771i | −0.790340 | + | 1.36891i | 0.135417 | + | 0.990789i | \(0.456763\pi\) |
−0.925757 | + | 0.378120i | \(0.876571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.21965 | − | 0.0532651i | −0.0949495 | − | 0.00414668i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2299 | − | 21.1828i | −0.946378 | − | 1.63917i | −0.752968 | − | 0.658057i | \(-0.771379\pi\) |
−0.193410 | − | 0.981118i | \(-0.561955\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0569772 | + | 0.0986874i | −0.00438286 | + | 0.00759134i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.19784 | + | 1.71061i | −0.0916012 | + | 0.130814i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.87800 | − | 17.1092i | −0.751010 | − | 1.30079i | −0.947333 | − | 0.320249i | \(-0.896233\pi\) |
0.196323 | − | 0.980539i | \(-0.437100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.52980 | − | 9.74941i | 0.342421 | − | 0.736986i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.44494 | + | 6.97698i | −0.334102 | + | 0.524422i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.32439 | − | 10.9542i | −0.472707 | − | 0.818753i | 0.526805 | − | 0.849986i | \(-0.323390\pi\) |
−0.999512 | + | 0.0312332i | \(0.990057\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5654 | 0.933975 | 0.466988 | − | 0.884264i | \(-0.345339\pi\) | ||||
0.466988 | + | 0.884264i | \(0.345339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.93938 | + | 7.56770i | 0.291208 | + | 0.559421i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.827040 | − | 1.43248i | 0.0608052 | − | 0.105318i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.54848 | + | 4.41409i | 0.186363 | + | 0.322790i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.37099 | − | 11.6047i | 0.536160 | − | 0.844116i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.70316 | + | 6.41407i | 0.267951 | + | 0.464105i | 0.968333 | − | 0.249663i | \(-0.0803200\pi\) |
−0.700381 | + | 0.713769i | \(0.746987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.813937 | − | 1.40978i | 0.0585885 | − | 0.101478i | −0.835244 | − | 0.549880i | \(-0.814673\pi\) |
0.893832 | + | 0.448402i | \(0.148007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.80308 | − | 5.38481i | −0.200732 | − | 0.385614i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.27125 | −0.589302 | −0.294651 | − | 0.955605i | \(-0.595203\pi\) | ||||
−0.294651 | + | 0.955605i | \(0.595203\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.34411 | + | 9.25627i | 0.378834 | + | 0.656159i | 0.990893 | − | 0.134653i | \(-0.0429919\pi\) |
−0.612059 | + | 0.790812i | \(0.709659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.41702 | + | 8.50279i | −0.382087 | + | 0.599741i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1793 | + | 14.4948i | 0.714448 | + | 1.01734i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.50794 | − | 6.07593i | −0.245005 | − | 0.424361i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.2403 | + | 1.68376i | 1.33730 | + | 0.117029i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.253466 | + | 0.439015i | −0.0175326 | + | 0.0303673i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2725 | − | 19.5246i | −0.776034 | − | 1.34413i | −0.934211 | − | 0.356720i | \(-0.883895\pi\) |
0.158178 | − | 0.987411i | \(-0.449438\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.526776 | − | 0.0230056i | −0.0360941 | − | 0.00157632i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.336863 | + | 0.583464i | −0.0229739 | + | 0.0397919i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.9376 | − | 19.8464i | −0.946145 | − | 1.34726i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.53944 | − | 16.4046i | −0.577042 | − | 1.10852i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.6727 | + | 21.9498i | −0.852461 | + | 1.47651i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.70093 | − | 6.41020i | 0.247832 | − | 0.429258i | −0.715092 | − | 0.699031i | \(-0.753615\pi\) |
0.962924 | + | 0.269772i | \(0.0869484\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.1433 | − | 1.06269i | −0.809556 | − | 0.0708458i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.598173 | −0.0397021 | −0.0198511 | − | 0.999803i | \(-0.506319\pi\) | ||||
−0.0198511 | + | 0.999803i | \(0.506319\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.03717 | −0.266783 | −0.133392 | − | 0.991063i | \(-0.542587\pi\) | ||||
−0.133392 | + | 0.991063i | \(0.542587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.53690 | − | 2.96227i | 0.101120 | − | 0.194903i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.59754 | + | 9.69523i | −0.366707 | + | 0.635155i | −0.989049 | − | 0.147591i | \(-0.952848\pi\) |
0.622341 | + | 0.782746i | \(0.286182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.70805 | − | 6.42254i | −0.241887 | − | 0.418960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.59033 | − | 4.97611i | −0.168260 | − | 0.323233i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.8171 | − | 22.1999i | −0.829069 | − | 1.43599i | −0.898769 | − | 0.438421i | \(-0.855538\pi\) |
0.0697006 | − | 0.997568i | \(-0.477796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.59180 | −0.424615 | −0.212307 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212307 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2188 | − | 3.37484i | −0.976284 | − | 0.216496i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.36924 | − | 5.17787i | −0.279141 | − | 0.330802i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.52080 | −0.160395 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.15169 | + | 1.80775i | −0.0729856 | + | 0.114561i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.0438 | 1.58075 | 0.790374 | − | 0.612624i | \(-0.209886\pi\) | ||||
0.790374 | + | 0.612624i | \(0.209886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.68840 | 0.294757 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.41754 | − | 10.4073i | −0.339259 | − | 0.651729i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1407 | −1.13159 | −0.565794 | − | 0.824547i | \(-0.691430\pi\) | ||||
−0.565794 | + | 0.824547i | \(0.691430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.59862 | + | 3.70030i | 0.161471 | + | 0.229926i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.5199 | − | 16.4513i | 0.713062 | − | 1.01831i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8088 | 0.789822 | 0.394911 | − | 0.918719i | \(-0.370775\pi\) | ||||
0.394911 | + | 0.918719i | \(0.370775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.99028 | + | 3.44726i | 0.122262 | + | 0.211763i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7709 | − | 16.9065i | 0.659170 | − | 1.03466i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4412 | − | 25.0129i | −0.880497 | − | 1.52507i | −0.850789 | − | 0.525507i | \(-0.823876\pi\) |
−0.0297079 | − | 0.999559i | \(-0.509458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.59579 | − | 7.96015i | 0.279175 | − | 0.483544i | −0.692005 | − | 0.721892i | \(-0.743273\pi\) |
0.971180 | + | 0.238348i | \(0.0766059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.5782 | − | 0.746629i | 1.00336 | − | 0.0451880i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.95904 | −0.178437 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.91557 | −0.235264 | −0.117632 | − | 0.993057i | \(-0.537530\pi\) | ||||
−0.117632 | + | 0.993057i | \(0.537530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.7731 | + | 22.5252i | −0.944309 | + | 1.34855i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.64654 | − | 13.2442i | 0.456154 | − | 0.790082i | −0.542600 | − | 0.839991i | \(-0.682560\pi\) |
0.998754 | + | 0.0499093i | \(0.0158932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4890 | + | 21.6315i | −0.742392 | + | 1.28586i | 0.209011 | + | 0.977913i | \(0.432975\pi\) |
−0.951403 | + | 0.307947i | \(0.900358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.627001 | − | 0.984170i | 0.0371404 | − | 0.0582972i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.1034 | − | 1.69799i | 1.12764 | − | 0.100229i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.9928 | + | 27.7003i | −0.940751 | + | 1.62943i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.47428 | + | 3.88374i | −0.145045 | + | 0.227669i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.08092 | − | 7.06835i | −0.238410 | − | 0.412938i | 0.721848 | − | 0.692051i | \(-0.243293\pi\) |
−0.960258 | + | 0.279114i | \(0.909959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.31133 | − | 4.00334i | 0.134571 | − | 0.233084i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.75167 | − | 0.494049i | −0.217694 | − | 0.0286676i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.6570 | + | 20.1904i | 0.674139 | + | 1.16764i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05845 | − | 1.50718i | −0.0610080 | − | 0.0868722i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.79276 | − | 0.121967i | −0.160440 | − | 0.00700681i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.38371 | − | 4.12870i | −0.136491 | − | 0.236409i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0692 | 1.03126 | 0.515631 | − | 0.856811i | \(-0.327558\pi\) | ||||
0.515631 | + | 0.856811i | \(0.327558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.7578 | − | 0.819199i | −1.06709 | − | 0.0466026i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.00384 | − | 8.66691i | 0.283742 | − | 0.491456i | −0.688561 | − | 0.725178i | \(-0.741757\pi\) |
0.972303 | + | 0.233723i | \(0.0750907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.49532 | − | 2.58998i | −0.0845207 | − | 0.146394i | 0.820666 | − | 0.571408i | \(-0.193603\pi\) |
−0.905187 | + | 0.425014i | \(0.860269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.83200 | + | 6.65814i | −0.215909 | + | 0.375144i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9246 | + | 20.6541i | 0.669754 | + | 1.16005i | 0.977973 | + | 0.208732i | \(0.0669336\pi\) |
−0.308219 | + | 0.951315i | \(0.599733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.43763 | − | 4.22210i | 0.136481 | − | 0.236392i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.26235 | + | 14.5386i | −0.516974 | + | 0.811466i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.87199 | −0.271085 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.35717 | − | 12.7430i | −0.408102 | − | 0.706854i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.8408 | + | 28.5097i | 0.820698 | + | 1.57659i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.1932 | − | 1.79486i | 1.11329 | − | 0.0989536i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.01886 | + | 13.8891i | 0.440757 | + | 0.763413i | 0.997746 | − | 0.0671069i | \(-0.0213768\pi\) |
−0.556989 | + | 0.830520i | \(0.688044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.94084 | − | 4.19976i | 0.161157 | − | 0.230145i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.81680 | − | 4.87884i | 0.153898 | − | 0.266560i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8985 | + | 29.2691i | 0.920520 | + | 1.59439i | 0.798613 | + | 0.601845i | \(0.205568\pi\) |
0.121907 | + | 0.992542i | \(0.461099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.21035 | − | 17.6934i | −0.500238 | − | 0.960975i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.33761 | + | 5.78092i | −0.180742 | + | 0.313054i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8691 | − | 4.86767i | 0.964842 | − | 0.262829i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.7822 | − | 0.470884i | −0.580493 | − | 0.0253516i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.6637 | + | 30.5944i | −0.948237 | + | 1.64240i | −0.199102 | + | 0.979979i | \(0.563802\pi\) |
−0.749136 | + | 0.662417i | \(0.769531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.75344 | + | 9.96526i | −0.307975 | + | 0.533428i | −0.977919 | − | 0.208983i | \(-0.932985\pi\) |
0.669944 | + | 0.742411i | \(0.266318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.20033 | − | 17.3848i | −0.384325 | − | 0.927933i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8863 | 1.32457 | 0.662283 | − | 0.749254i | \(-0.269588\pi\) | ||||
0.662283 | + | 0.749254i | \(0.269588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.294639 | 0.0156378 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.0408 | − | 1.44302i | 1.69578 | − | 0.0763726i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.22681 | − | 15.9813i | 0.486972 | − | 0.843461i | −0.512916 | − | 0.858439i | \(-0.671435\pi\) |
0.999888 | + | 0.0149785i | \(0.00476798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.25772 | + | 16.0348i | 0.487249 | + | 0.843939i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.1167 | + | 0.791202i | 0.950881 | + | 0.0415273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.16718 | + | 8.94982i | 0.270463 | + | 0.468455i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.2138 | −0.950750 | −0.475375 | − | 0.879783i | \(-0.657688\pi\) | ||||
−0.475375 | + | 0.879783i | \(0.657688\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.19007 | − | 19.7093i | −0.478416 | − | 1.02603i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.8386 | + | 0.963378i | −0.562711 | + | 0.0500161i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.1999 | −0.942355 | −0.471177 | − | 0.882038i | \(-0.656171\pi\) | ||||
−0.471177 | + | 0.882038i | \(0.656171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.1790 | + | 0.662903i | 0.783839 | + | 0.0342322i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.2431 | 1.24858 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.1061 | −1.23825 | −0.619124 | − | 0.785293i | \(-0.712512\pi\) | ||||
−0.619124 | + | 0.785293i | \(0.712512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6944 | − | 0.685411i | −0.804046 | − | 0.0351147i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.43694 | −0.328912 | −0.164456 | − | 0.986384i | \(-0.552587\pi\) | ||||
−0.164456 | + | 0.986384i | \(0.552587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.785766 | + | 1.69119i | −0.0400463 | + | 0.0861911i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.19784 | + | 1.71061i | −0.0608897 | + | 0.0869552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.8597 | 1.71676 | 0.858379 | − | 0.513017i | \(-0.171472\pi\) | ||||
0.858379 | + | 0.513017i | \(0.171472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.5295 | + | 39.0223i | 1.13937 | + | 1.97344i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.6425 | − | 0.988853i | −1.14216 | − | 0.0498810i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.56740 | + | 2.71481i | 0.0788643 | + | 0.136597i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.808630 | + | 1.40059i | −0.0405840 | + | 0.0702935i | −0.885604 | − | 0.464441i | \(-0.846255\pi\) |
0.845020 | + | 0.534735i | \(0.179588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.71764 | + | 2.68801i | 0.0859897 | + | 0.134569i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.75382 | 0.287332 | 0.143666 | − | 0.989626i | \(-0.454111\pi\) | ||||
0.143666 | + | 0.989626i | \(0.454111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.1937 | −1.65350 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.57831 | + | 1.51300i | 0.426260 | + | 0.0751813i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.622289 | − | 1.07784i | 0.0308457 | − | 0.0534263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.88631 | − | 4.99923i | 0.142719 | − | 0.247196i | −0.785801 | − | 0.618480i | \(-0.787749\pi\) |
0.928520 | + | 0.371284i | \(0.121082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 34.7403 | + | 1.51720i | 1.71361 | + | 0.0748377i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.26237 | + | 10.3412i | 0.357358 | + | 0.508859i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.598871 | − | 1.03727i | 0.0293974 | − | 0.0509178i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.540366 | − | 1.03806i | −0.0264618 | − | 0.0508341i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.29032 | − | 16.0913i | −0.453862 | − | 0.786111i | 0.544760 | − | 0.838592i | \(-0.316621\pi\) |
−0.998622 | + | 0.0524804i | \(0.983287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.05788 | + | 13.9567i | −0.392717 | + | 0.680206i | −0.992807 | − | 0.119727i | \(-0.961798\pi\) |
0.600090 | + | 0.799933i | \(0.295131\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.71433 | − | 20.8337i | −0.472327 | − | 1.01297i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.2193 | − | 24.6285i | −0.689737 | − | 1.19466i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.9811 | − | 1.15382i | 0.628200 | − | 0.0558371i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.10911 | − | 4.05169i | −0.101829 | − | 0.195617i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.82664 | + | 3.16383i | 0.0879860 | + | 0.152396i | 0.906660 | − | 0.421863i | \(-0.138624\pi\) |
−0.818674 | + | 0.574259i | \(0.805290\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6697 | 0.608865 | 0.304432 | − | 0.952534i | \(-0.401533\pi\) | ||||
0.304432 | + | 0.952534i | \(0.401533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.03000 | + | 9.46496i | −0.289116 | + | 0.453810i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.24073 | + | 3.88107i | −0.107189 | + | 0.185657i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.85810 | − | 10.1465i | −0.279592 | − | 0.484267i | 0.691692 | − | 0.722193i | \(-0.256866\pi\) |
−0.971283 | + | 0.237926i | \(0.923532\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.0923 | − | 17.1690i | −0.575824 | − | 0.817574i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.8735 | + | 25.7617i | 0.706661 | + | 1.22397i | 0.966089 | + | 0.258210i | \(0.0831328\pi\) |
−0.259428 | + | 0.965763i | \(0.583534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.60079 | + | 9.70085i | −0.265503 | + | 0.459865i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −37.2188 | − | 1.62544i | −1.76039 | − | 0.0768806i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.0193 | 0.520034 | 0.260017 | − | 0.965604i | \(-0.416272\pi\) | ||||
0.260017 | + | 0.965604i | \(0.416272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.63947 | − | 4.57170i | −0.124288 | − | 0.215273i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.5206 | − | 1.07088i | −1.15208 | − | 0.0503141i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.23673 | + | 0.820999i | −0.433025 | + | 0.0384890i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.258224 | − | 0.447257i | −0.0120792 | − | 0.0209218i | 0.859923 | − | 0.510424i | \(-0.170512\pi\) |
−0.872002 | + | 0.489503i | \(0.837178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.9162 | − | 33.5999i | −0.649550 | − | 1.56831i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.54962 | + | 6.14813i | −0.165322 | + | 0.286347i | −0.936770 | − | 0.349946i | \(-0.886200\pi\) |
0.771447 | + | 0.636293i | \(0.219533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.91148 | − | 8.50693i | −0.228256 | − | 0.395351i | 0.729035 | − | 0.684476i | \(-0.239969\pi\) |
−0.957291 | + | 0.289125i | \(0.906636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.25631 | − | 12.9595i | 0.382877 | − | 0.600981i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.79604 | + | 8.30698i | −0.221934 | + | 0.384401i | −0.955395 | − | 0.295330i | \(-0.904570\pi\) |
0.733461 | + | 0.679731i | \(0.237904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.85061 | + | 12.6028i | 0.408683 | + | 0.581943i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.8875 | + | 23.3681i | −0.685978 | + | 1.07674i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.253466 | + | 0.439015i | −0.0116544 | + | 0.0201859i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.41422 | − | 2.44950i | 0.0648887 | − | 0.112391i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.21411 | + | 11.1824i | 0.238738 | + | 0.512005i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.2724 | 0.743506 | 0.371753 | − | 0.928332i | \(-0.378757\pi\) | ||||
0.371753 | + | 0.928332i | \(0.378757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.18888 | 0.282189 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.5868 | − | 26.1877i | 0.618219 | − | 1.19158i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.28660 | − | 2.22846i | 0.0584217 | − | 0.101189i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.50511 | − | 16.4633i | −0.430718 | − | 0.746025i | 0.566217 | − | 0.824256i | \(-0.308406\pi\) |
−0.996935 | + | 0.0782307i | \(0.975073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.7812 | − | 29.4798i | 0.849314 | − | 1.33312i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.55413 | + | 4.42387i | 0.115266 | + | 0.199647i | 0.917886 | − | 0.396844i | \(-0.129895\pi\) |
−0.802620 | + | 0.596491i | \(0.796561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.8549 | 2.11024 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.10646 | + | 0.184340i | 0.0946782 | + | 0.00828547i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.339378 | + | 0.730439i | −0.0152232 | + | 0.0327646i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.5276 | −1.27707 | −0.638536 | − | 0.769592i | \(-0.720459\pi\) | ||||
−0.638536 | + | 0.769592i | \(0.720459\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.5618 | + | 37.5790i | 0.873958 | + | 1.67891i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.05885 | 0.180975 | 0.0904877 | − | 0.995898i | \(-0.471157\pi\) | ||||
0.0904877 | + | 0.995898i | \(0.471157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.56206 | 0.0695108 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.106051 | − | 0.166463i | 0.00470990 | − | 0.00739288i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2605 | 0.765056 | 0.382528 | − | 0.923944i | \(-0.375054\pi\) | ||||
0.382528 | + | 0.923944i | \(0.375054\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1393 | + | 2.50114i | −1.24481 | + | 0.110644i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.20202 | − | 2.86952i | 0.0972214 | − | 0.126692i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.4917 | 0.462320 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.79005 | − | 4.83250i | −0.122706 | − | 0.212533i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.7999 | + | 30.3523i | 0.693541 | + | 1.33232i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0525 | − | 29.5358i | −0.747083 | − | 1.29399i | −0.949215 | − | 0.314628i | \(-0.898120\pi\) |
0.202132 | − | 0.979358i | \(-0.435213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.44847 | + | 16.3652i | −0.413153 | + | 0.715602i | −0.995233 | − | 0.0975299i | \(-0.968906\pi\) |
0.582080 | + | 0.813132i | \(0.302239\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.57514 | + | 16.5281i | −0.374250 | + | 0.721344i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −64.1539 | −2.79459 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.4473 | 0.802057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.21878 | − | 11.7371i | 0.356665 | − | 0.509345i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.1252 | − | 22.7336i | 0.568517 | − | 0.984701i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.81634 | − | 8.34215i | 0.208229 | − | 0.360663i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.1159 | + | 19.4331i | 0.436534 | + | 0.838598i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.28754 | − | 3.89598i | −0.141605 | − | 0.167812i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.564117 | − | 0.977080i | 0.0242533 | − | 0.0420080i | −0.853644 | − | 0.520857i | \(-0.825613\pi\) |
0.877897 | + | 0.478849i | \(0.158946\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.7431 | − | 0.949575i | −0.933086 | − | 0.0407502i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.98012 | − | 15.5540i | −0.384666 | − | 0.666261i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8427 | − | 27.4404i | 0.677386 | − | 1.17327i | −0.298380 | − | 0.954447i | \(-0.596446\pi\) |
0.975765 | − | 0.218819i | \(-0.0702205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.24482 | − | 13.3929i | −0.266522 | − | 0.571593i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.33004 | + | 4.03575i | 0.0992630 | + | 0.171929i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.53568 | + | 0.758687i | −0.362974 | + | 0.0322626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.53936 | + | 2.41626i | −0.0653424 | + | 0.102564i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.8135 | − | 23.9257i | −0.585298 | − | 1.01377i | −0.994838 | − | 0.101474i | \(-0.967644\pi\) |
0.409540 | − | 0.912292i | \(-0.365689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.52080 | −0.106619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.07631 | − | 7.83074i | −0.172102 | − | 0.330614i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.920685 | + | 1.59467i | −0.0388022 | + | 0.0672074i | −0.884774 | − | 0.466020i | \(-0.845688\pi\) |
0.845972 | + | 0.533227i | \(0.179021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.57315 | + | 9.65298i | 0.234464 | + | 0.406104i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.6317 | + | 19.5237i | −0.572479 | + | 0.819919i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.75524 | + | 9.96837i | 0.241272 | + | 0.417896i | 0.961077 | − | 0.276281i | \(-0.0891020\pi\) |
−0.719805 | + | 0.694177i | \(0.755769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.35262 | − | 7.53896i | 0.182152 | − | 0.315496i | −0.760461 | − | 0.649383i | \(-0.775027\pi\) |
0.942613 | + | 0.333887i | \(0.108361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.92324 | − | 11.3788i | −0.247447 | − | 0.475354i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.1591 | −1.09091 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.24358 | − | 12.5462i | −0.301554 | − | 0.522307i | 0.674934 | − | 0.737878i | \(-0.264172\pi\) |
−0.976488 | + | 0.215571i | \(0.930839\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.51498 | + | 2.37798i | −0.0629603 | + | 0.0988253i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.88170 | + | 2.67944i | 0.0780659 | + | 0.111162i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.49754 | + | 2.59382i | 0.0620218 | + | 0.107425i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.44351 | + | 9.52971i | 0.183717 | + | 0.394005i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.3695 | + | 24.8886i | −0.593091 | + | 1.02726i | 0.400722 | + | 0.916200i | \(0.368759\pi\) |
−0.993813 | + | 0.111065i | \(0.964574\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.19030 | − | 5.52576i | −0.131454 | − | 0.227685i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.3126 | + | 0.625066i | 0.588741 | + | 0.0257118i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.82328 | − | 11.8183i | 0.280199 | − | 0.485318i | −0.691235 | − | 0.722630i | \(-0.742933\pi\) |
0.971434 | + | 0.237312i | \(0.0762663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8519 | + | 1.58676i | −0.731858 | + | 0.0650506i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.54795 | − | 16.4209i | −0.349844 | − | 0.672063i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.64585 | + | 4.58275i | −0.108106 | + | 0.187246i | −0.915003 | − | 0.403447i | \(-0.867812\pi\) |
0.806897 | + | 0.590693i | \(0.201145\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0522 | − | 29.5353i | 0.695574 | − | 1.20477i | −0.274412 | − | 0.961612i | \(-0.588483\pi\) |
0.969987 | − | 0.243158i | \(-0.0781834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0162 | − | 14.3039i | 0.407890 | − | 0.582499i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.1331 | −0.411971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.04464 | −0.367111 | −0.183555 | − | 0.983009i | \(-0.558761\pi\) | ||||
−0.183555 | + | 0.983009i | \(0.558761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.5189 | − | 25.8511i | −0.669381 | − | 1.04754i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.8740 | − | 24.0305i | 0.561282 | − | 0.972169i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.97889 | + | 10.3557i | 0.241485 | + | 0.418264i | 0.961137 | − | 0.276070i | \(-0.0890322\pi\) |
−0.719653 | + | 0.694334i | \(0.755699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.61098 | + | 10.7789i | 0.226256 | + | 0.434647i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.13220 | + | 8.88923i | 0.206615 | + | 0.357867i | 0.950646 | − | 0.310278i | \(-0.100422\pi\) |
−0.744031 | + | 0.668145i | \(0.767089\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.5605 | −1.75085 | −0.875423 | − | 0.483358i | \(-0.839417\pi\) | ||||
−0.875423 | + | 0.483358i | \(0.839417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.1663 | − | 4.36759i | −1.33092 | − | 0.175265i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.5981 | − | 25.0588i | −0.705053 | − | 1.00396i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.8263 | 0.473051 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.471774 | − | 0.740518i | 0.0188408 | − | 0.0295734i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.9613 | 0.476929 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.3703 | 0.771119 | 0.385559 | − | 0.922683i | \(-0.374008\pi\) | ||||
0.385559 | + | 0.922683i | \(0.374008\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0305 | + | 34.6373i | 0.716649 | + | 1.37671i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.77825 | 0.348354 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.60395 | − | 23.8444i | 0.340901 | − | 0.944750i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.909795 | + | 0.0796179i | 0.0359909 | + | 0.00314963i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50016 | 0.177746 | 0.0888728 | − | 0.996043i | \(-0.471674\pi\) | ||||
0.0888728 | + | 0.996043i | \(0.471674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9045 | − | 36.2077i | −0.824394 | − | 1.42789i | −0.902381 | − | 0.430939i | \(-0.858183\pi\) |
0.0779869 | − | 0.996954i | \(-0.475151\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.627001 | − | 0.984170i | 0.0246882 | − | 0.0387517i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.9381 | + | 20.6773i | 0.469334 | + | 0.812910i | 0.999385 | − | 0.0350555i | \(-0.0111608\pi\) |
−0.530052 | + | 0.847965i | \(0.677827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.73911 | − | 3.01223i | 0.0682661 | − | 0.118240i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.6178 | + | 35.3955i | 0.886461 | + | 1.38726i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.33347 | −0.326114 | −0.163057 | − | 0.986617i | \(-0.552135\pi\) | ||||
−0.163057 | + | 0.986617i | \(0.552135\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.6645 | 0.494843 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.5369 | + | 29.0318i | 0.528126 | + | 1.13264i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.2488 | + | 35.0719i | −0.788781 | + | 1.36621i | 0.137933 | + | 0.990442i | \(0.455954\pi\) |
−0.926714 | + | 0.375767i | \(0.877379\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88559 | − | 6.73004i | 0.151132 | − | 0.261768i | −0.780512 | − | 0.625141i | \(-0.785042\pi\) |
0.931644 | + | 0.363373i | \(0.118375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.5877 | − | 37.0243i | 0.916071 | − | 1.43791i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.02443 | − | 1.45873i | −0.0397256 | − | 0.0565672i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.5496 | − | 37.3250i | 0.834404 | − | 1.44523i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.88852 | + | 10.8125i | −0.266325 | + | 0.418037i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.79357 | − | 3.10656i | −0.0692400 | − | 0.119927i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7830 | + | 39.4614i | −0.878221 | + | 1.52112i | −0.0249302 | + | 0.999689i | \(0.507936\pi\) |
−0.853291 | + | 0.521435i | \(0.825397\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.9326 | + | 2.75656i | 0.805694 | + | 0.106100i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.54521 | − | 11.3366i | −0.251553 | − | 0.435702i | 0.712401 | − | 0.701773i | \(-0.247608\pi\) |
−0.963954 | + | 0.266071i | \(0.914275\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.04261 | + | 5.75646i | 0.155141 | + | 0.220913i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.03508 | + | 0.0452045i | 0.0396643 | + | 0.00173224i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.6506 | − | 21.9114i | −0.484060 | − | 0.838417i | 0.515772 | − | 0.856726i | \(-0.327505\pi\) |
−0.999832 | + | 0.0183087i | \(0.994172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.4311 | −0.742425 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.98592 | + | 0.305092i | 0.266529 | + | 0.0116400i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.44679 | + | 12.8982i | −0.283700 | + | 0.491383i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.2016 | + | 21.1337i | 0.464170 | + | 0.803965i | 0.999164 | − | 0.0408905i | \(-0.0130195\pi\) |
−0.534994 | + | 0.844856i | \(0.679686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.88331 | + | 5.00978i | −0.109528 | + | 0.190306i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.326974 | + | 0.566335i | 0.0124028 | + | 0.0214823i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.3673 | − | 43.9375i | 0.960855 | − | 1.66425i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.4187 | − | 16.3536i | 0.394070 | − | 0.618551i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.4137 | −0.695476 | −0.347738 | − | 0.937592i | \(-0.613050\pi\) | ||||
−0.347738 | + | 0.937592i | \(0.613050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.594823 | + | 1.03026i | 0.0224342 | + | 0.0388571i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.93107 | + | 11.3938i | 0.223377 | + | 0.429115i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.79925 | + | 3.87250i | −0.0676679 | + | 0.145640i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.66501 | + | 11.5441i | 0.250310 | + | 0.433549i | 0.963611 | − | 0.267308i | \(-0.0861342\pi\) |
−0.713301 | + | 0.700858i | \(0.752801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.10626 | + | 8.80642i | 0.153997 | + | 0.330267i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.5058 | + | 51.1056i | −1.10500 | + | 1.91392i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.27622 | + | 2.21047i | 0.0477278 | + | 0.0826671i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.5011 | + | 39.3833i | 0.765626 | + | 1.47079i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.84705 | + | 13.5915i | −0.292646 | + | 0.506877i | −0.974434 | − | 0.224672i | \(-0.927869\pi\) |
0.681789 | + | 0.731549i | \(0.261202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.0848 | + | 26.0099i | −0.450062 | + | 0.968660i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.4065 | + | 0.498148i | 0.424211 | + | 0.0185263i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.6008 | + | 23.5573i | −0.505121 | + | 0.874896i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12.8388 | + | 22.2374i | −0.476163 | + | 0.824739i | −0.999627 | − | 0.0273090i | \(-0.991306\pi\) |
0.523464 | + | 0.852048i | \(0.324640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.0795 | + | 6.98992i | 0.965908 | + | 0.258886i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.87199 | −0.180197 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.17308 | 0.0433288 | 0.0216644 | − | 0.999765i | \(-0.493103\pi\) | ||||
0.0216644 | + | 0.999765i | \(0.493103\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.16925 | + | 9.28998i | 0.264442 | + | 0.342666i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.11944 | − | 3.67098i | 0.0780707 | − | 0.135222i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6114 | + | 20.1116i | 0.427133 | + | 0.739816i | 0.996617 | − | 0.0821861i | \(-0.0261902\pi\) |
−0.569484 | + | 0.822003i | \(0.692857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.36200 | + | 0.190499i | 0.160242 | + | 0.00699817i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.7846 | + | 20.4115i | 0.432335 | + | 0.748826i | 0.997074 | − | 0.0764439i | \(-0.0243566\pi\) |
−0.564739 | + | 0.825269i | \(0.691023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.8174 | 0.762691 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.12950 | − | 3.04110i | 0.0779145 | − | 0.111268i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1333 | + | 21.5490i | 0.552959 | + | 0.787385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.1062 | 1.60946 | 0.804728 | − | 0.593643i | \(-0.202311\pi\) | ||||
0.804728 | + | 0.593643i | \(0.202311\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −43.3358 | − | 1.89258i | −1.57924 | − | 0.0689695i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.7150 | 0.499139 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.71020 | −0.0985040 | −0.0492520 | − | 0.998786i | \(-0.515684\pi\) | ||||
−0.0492520 | + | 0.998786i | \(0.515684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.11282 | − | 0.354307i | −0.294477 | − | 0.0128605i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.0496 | 1.05305 | 0.526524 | − | 0.850160i | \(-0.323495\pi\) | ||||
0.526524 | + | 0.850160i | \(0.323495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.9036 | − | 4.34676i | 1.77043 | − | 0.157363i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.58803 | + | 18.4182i | 0.310501 | + | 0.665911i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.2961 | 0.624525 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.25175 | − | 9.09629i | −0.189383 | − | 0.328021i | 0.755662 | − | 0.654962i | \(-0.227315\pi\) |
−0.945045 | + | 0.326941i | \(0.893982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.3907 | + | 1.37091i | 1.13051 | + | 0.0493722i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.9230 | − | 20.6513i | −0.428841 | − | 0.742774i | 0.567930 | − | 0.823077i | \(-0.307745\pi\) |
−0.996771 | + | 0.0803029i | \(0.974411\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.6223 | − | 32.2548i | 0.668933 | − | 1.15863i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.21703 | − | 6.59939i | −0.151285 | − | 0.236752i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.04595 | 0.180790 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.221695 | 0.00793287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.1772 | + | 27.5968i | −0.756813 | + | 0.986227i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.74136 | − | 13.4084i | 0.276301 | − | 0.478567i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.19788 | − | 3.80684i | 0.0783460 | − | 0.135699i | −0.824190 | − | 0.566313i | \(-0.808369\pi\) |
0.902536 | + | 0.430613i | \(0.141703\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.1643 | − | 0.967970i | −0.789070 | − | 0.0344606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.3501 | + | 2.69764i | −1.07912 | + | 0.0959171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.91885 | − | 15.4479i | 0.316717 | − | 0.548571i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.18346 | − | 6.11555i | −0.112906 | − | 0.216896i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.56236 | − | 4.43813i | −0.0907633 | − | 0.157207i | 0.817069 | − | 0.576540i | \(-0.195597\pi\) |
−0.907833 | + | 0.419333i | \(0.862264\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.8144 | − | 46.4440i | 0.948627 | − | 1.64307i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.9157 | + | 28.4411i | −0.703686 | + | 1.00492i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.88794 | + | 6.73410i | 0.137202 | + | 0.237641i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.94648 | + | 14.9508i | −0.244831 | + | 0.526946i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.0989 | + | 44.3738i | 0.813119 | + | 1.56203i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.4612 | − | 28.5116i | −0.578744 | − | 1.00241i | −0.995624 | − | 0.0934519i | \(-0.970210\pi\) |
0.416880 | − | 0.908961i | \(-0.363123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.8830 | −1.11956 | −0.559781 | − | 0.828640i | \(-0.689115\pi\) | ||||
−0.559781 | + | 0.828640i | \(0.689115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.55412 | + | 13.4269i | −0.300006 | + | 0.470903i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.76605 | + | 16.9153i | −0.342090 | + | 0.592517i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.242278 | − | 0.419638i | −0.00847624 | − | 0.0146813i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.7433 | + | 0.0391402i | −1.00437 | + | 0.00136767i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.1139 | − | 29.6421i | −0.597278 | − | 1.03452i | −0.993221 | − | 0.116241i | \(-0.962916\pi\) |
0.395943 | − | 0.918275i | \(-0.370418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.1866 | + | 33.2321i | −0.668802 | + | 1.15840i | 0.309437 | + | 0.950920i | \(0.399859\pi\) |
−0.978239 | + | 0.207480i | \(0.933474\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.12032 | + | 0.223617i | 0.178267 | + | 0.00778535i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.23903 | 0.321273 | 0.160636 | − | 0.987014i | \(-0.448645\pi\) | ||||
0.160636 | + | 0.987014i | \(0.448645\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.8224 | + | 36.0654i | 0.723191 | + | 1.25260i | 0.959714 | + | 0.280978i | \(0.0906589\pi\) |
−0.236523 | + | 0.971626i | \(0.576008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.77551 | + | 0.295903i | 0.235040 | + | 0.0102648i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.6289 | − | 46.0844i | 0.576159 | − | 1.59673i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.8368 | − | 20.5019i | −0.409629 | − | 0.709499i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.9960 | − | 37.7856i | 1.00225 | − | 1.30606i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.4241 | + | 26.7154i | −0.532500 | + | 0.922318i | 0.466780 | + | 0.884374i | \(0.345414\pi\) |
−0.999280 | + | 0.0379439i | \(0.987919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.90845 | − | 13.6978i | −0.272705 | − | 0.472339i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.2325 | + | 22.3399i | −0.490192 | + | 0.769427i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0551458 | + | 0.0955153i | −0.00189707 | + | 0.00328583i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.6718 | − | 25.1210i | 0.401048 | − | 0.863168i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.2456 | − | 36.4874i | 0.797788 | − | 1.25224i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.50128 | − | 9.52849i | 0.188581 | − | 0.326632i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4171 | + | 19.7750i | −0.390913 | + | 0.677082i | −0.992570 | − | 0.121673i | \(-0.961174\pi\) |
0.601657 | + | 0.798755i | \(0.294507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.15934 | + | 1.65563i | −0.0396485 | + | 0.0566212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.3441 | −1.82220 | −0.911100 | − | 0.412186i | \(-0.864765\pi\) | ||||
−0.911100 | + | 0.412186i | \(0.864765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.1757 | −0.790743 | −0.395372 | − | 0.918521i | \(-0.629384\pi\) | ||||
−0.395372 | + | 0.918521i | \(0.629384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.1849 | + | 1.49454i | −1.13094 | + | 0.0509339i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.58456 | − | 7.94069i | 0.156060 | − | 0.270304i | −0.777384 | − | 0.629026i | \(-0.783454\pi\) |
0.933445 | + | 0.358722i | \(0.116787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.56049 | − | 16.5593i | −0.325067 | − | 0.563032i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.7672 | − | 46.7240i | 1.01095 | − | 1.58683i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.17936 | + | 2.04270i | 0.0400069 | + | 0.0692940i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0786 | 0.714221 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.57499 | − | 6.53344i | 0.154840 | − | 0.221124i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.77914 | − | 21.0475i | 0.330595 | − | 0.711535i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.2380 | 1.25744 | 0.628718 | − | 0.777633i | \(-0.283580\pi\) | ||||
0.628718 | + | 0.777633i | \(0.283580\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.52746 | + | 12.5395i | 0.220166 | + | 0.422946i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.15345 | 0.241006 | 0.120503 | − | 0.992713i | \(-0.461549\pi\) | ||||
0.120503 | + | 0.992713i | \(0.461549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.8688 | −1.34169 | −0.670846 | − | 0.741596i | \(-0.734069\pi\) | ||||
−0.670846 | + | 0.741596i | \(0.734069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.30207 | + | 6.75272i | −0.144612 | + | 0.226990i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.3509 | −0.716893 | −0.358447 | − | 0.933550i | \(-0.616694\pi\) | ||||
−0.358447 | + | 0.933550i | \(0.616694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.1112 | + | 21.7621i | −0.339118 | + | 0.729878i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.45457 | + | 1.13842i | 0.216236 | + | 0.0381385i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.33380 | 0.178489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.12111 | − | 10.6021i | −0.204606 | − | 0.354388i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.6454 | − | 35.8185i | −0.622552 | − | 1.19594i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.6818 | + | 53.1424i | 1.02329 | + | 1.77240i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.3925 | + | 24.9285i | −0.479483 | + | 0.830490i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.71764 | + | 2.68801i | 0.0571596 | + | 0.0894513i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.1615 | 0.404261 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6024 | −0.750499 | −0.375250 | − | 0.926924i | \(-0.622443\pi\) | ||||
−0.375250 | + | 0.926924i | \(0.622443\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.82338 | + | 0.422103i | 0.159981 | + | 0.0140003i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.7594 | − | 22.0999i | 0.422738 | − | 0.732203i | −0.573468 | − | 0.819228i | \(-0.694402\pi\) |
0.996206 | + | 0.0870243i | \(0.0277358\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.450607 | − | 0.780475i | 0.0149129 | − | 0.0258300i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.81276 | + | 7.32445i | 0.126046 | + | 0.242139i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.5876 | + | 31.3965i | −0.481723 | + | 1.03681i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.71326 | − | 9.89566i | 0.188463 | − | 0.326428i | −0.756275 | − | 0.654254i | \(-0.772983\pi\) |
0.944738 | + | 0.327826i | \(0.106316\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.2669 | − | 1.36550i | −1.03028 | − | 0.0449949i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.551208 | + | 0.954721i | 0.0181432 | + | 0.0314250i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.47207 | + | 6.01381i | −0.114161 | + | 0.197733i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.3966 | + | 2.83509i | 1.06404 | + | 0.0931164i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.79851 | − | 11.7754i | −0.223052 | − | 0.386337i | 0.732681 | − | 0.680572i | \(-0.238269\pi\) |
−0.955733 | + | 0.294235i | \(0.904935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.79632 | − | 0.859423i | 0.157193 | − | 0.0281665i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.31363 | + | 14.6191i | −0.304914 | + | 0.478608i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.46656 | + | 4.27221i | 0.0806652 | + | 0.139716i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1455 | −0.364109 | −0.182054 | − | 0.983288i | \(-0.558275\pi\) | ||||
−0.182054 | + | 0.983288i | \(0.558275\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.39178 | + | 4.59470i | 0.0780529 | + | 0.149942i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7310 | + | 35.9072i | −0.675813 | + | 1.17054i | 0.300418 | + | 0.953808i | \(0.402874\pi\) |
−0.976231 | + | 0.216734i | \(0.930460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.3340 | − | 40.4156i | −0.759859 | − | 1.31611i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.13406 | − | 11.2317i | 0.232071 | − | 0.365366i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.2784 | − | 36.8552i | −0.691454 | − | 1.19763i | −0.971362 | − | 0.237606i | \(-0.923637\pi\) |
0.279908 | − | 0.960027i | \(-0.409696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.3335 | + | 33.4865i | −0.627590 | + | 1.08702i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.0735 | − | 36.6410i | −0.618502 | − | 1.18816i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2114 | 0.687106 | 0.343553 | − | 0.939133i | \(-0.388370\pi\) | ||||
0.343553 | + | 0.939133i | \(0.388370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.58413 | + | 6.20790i | 0.115980 | + | 0.200883i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.53714 | + | 7.12171i | −0.146665 | + | 0.230212i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.3816 | − | 48.1716i | 0.722741 | − | 1.55554i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5096 | − | 45.9160i | −0.855150 | − | 1.48116i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.1263 | − | 24.4577i | 0.551887 | − | 0.788137i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.787775 | − | 1.36447i | 0.0253594 | − | 0.0439237i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.83257 | − | 17.0305i | −0.316194 | − | 0.547664i | 0.663496 | − | 0.748179i | \(-0.269072\pi\) |
−0.979691 | + | 0.200515i | \(0.935738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.43049 | + | 0.368181i | 0.270826 | + | 0.0118277i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.2892 | + | 21.2855i | −0.394379 | + | 0.683084i | −0.993022 | − | 0.117932i | \(-0.962374\pi\) |
0.598643 | + | 0.801016i | \(0.295707\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78062 | + | 0.158269i | −0.0570841 | + | 0.00507387i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.7679 | + | 22.6065i | 0.376873 | + | 0.723987i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7359 | − | 41.1117i | 0.759378 | − | 1.31528i | −0.183790 | − | 0.982966i | \(-0.558837\pi\) |
0.943168 | − | 0.332316i | \(-0.107830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.21420 | + | 7.29920i | −0.134686 | + | 0.233284i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.5260 | − | 50.4548i | −0.751129 | − | 1.61090i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.5440 | 0.878516 | 0.439258 | − | 0.898361i | \(-0.355241\pi\) | ||||
0.439258 | + | 0.898361i | \(0.355241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.00539 | −0.255073 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.0780 | + | 1.57980i | −1.11654 | + | 0.0502857i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.24073 | + | 3.88107i | −0.0712512 | + | 0.123411i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.2335 | + | 33.3135i | 0.610973 | + | 1.05824i | 0.991077 | + | 0.133293i | \(0.0425551\pi\) |
−0.380103 | + | 0.924944i | \(0.624112\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.8262 | − | 24.6397i | −0.407029 | − | 0.781917i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.17233 | + | 8.95874i | 0.163974 | + | 0.284011i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.4544 | −1.02784 | −0.513921 | − | 0.857837i | \(-0.671808\pi\) | ||||
−0.513921 | + | 0.857837i | \(0.671808\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.40622 | + | 7.04502i | −0.171045 | + | 0.222895i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))