Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.3 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.316 |
Dual form | 507.2.j.f.361.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.358719 | + | 0.207107i | 0.253653 | + | 0.146447i | 0.621436 | − | 0.783465i | \(-0.286550\pi\) |
−0.367783 | + | 0.929912i | \(0.619883\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.914214 | − | 1.58346i | −0.457107 | − | 0.791732i | ||||
\(5\) | 2.82843i | 1.26491i | 0.774597 | + | 0.632456i | \(0.217953\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | −0.358719 | + | 0.207107i | −0.146447 | + | 0.0845510i | ||||
\(7\) | 2.44949 | − | 1.41421i | 0.925820 | − | 0.534522i | 0.0403329 | − | 0.999186i | \(-0.487158\pi\) |
0.885487 | + | 0.464664i | \(0.153825\pi\) | |||||||
\(8\) | − | 1.58579i | − | 0.560660i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.585786 | + | 1.01461i | −0.185242 | + | 0.320848i | ||||
\(11\) | 1.73205 | + | 1.00000i | 0.522233 | + | 0.301511i | 0.737848 | − | 0.674967i | \(-0.235842\pi\) |
−0.215615 | + | 0.976478i | \(0.569176\pi\) | |||||||
\(12\) | 1.82843 | 0.527821 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.17157 | 0.313116 | ||||||||
\(15\) | −2.44949 | − | 1.41421i | −0.632456 | − | 0.365148i | ||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | 3.82843 | + | 6.63103i | 0.928530 | + | 1.60826i | 0.785783 | + | 0.618502i | \(0.212260\pi\) |
0.142747 | + | 0.989759i | \(0.454407\pi\) | |||||||
\(18\) | − | 0.414214i | − | 0.0976311i | ||||||
\(19\) | 2.44949 | − | 1.41421i | 0.561951 | − | 0.324443i | −0.191977 | − | 0.981399i | \(-0.561490\pi\) |
0.753928 | + | 0.656957i | \(0.228157\pi\) | |||||||
\(20\) | 4.47871 | − | 2.58579i | 1.00147 | − | 0.578199i | ||||
\(21\) | 2.82843i | 0.617213i | ||||||||
\(22\) | 0.414214 | + | 0.717439i | 0.0883106 | + | 0.152958i | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 1.37333 | + | 0.792893i | 0.280330 | + | 0.161849i | ||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.47871 | − | 2.58579i | −0.846397 | − | 0.488668i | ||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | −0.585786 | − | 1.01461i | −0.106949 | − | 0.185242i | ||||
\(31\) | 1.17157i | 0.210421i | 0.994450 | + | 0.105210i | \(0.0335516\pi\) | ||||
−0.994450 | + | 0.105210i | \(0.966448\pi\) | |||||||
\(32\) | −3.82282 | + | 2.20711i | −0.675786 | + | 0.390165i | ||||
\(33\) | −1.73205 | + | 1.00000i | −0.301511 | + | 0.174078i | ||||
\(34\) | 3.17157i | 0.543920i | ||||||||
\(35\) | 4.00000 | + | 6.92820i | 0.676123 | + | 1.17108i | ||||
\(36\) | −0.914214 | + | 1.58346i | −0.152369 | + | 0.263911i | ||||
\(37\) | 6.63103 | + | 3.82843i | 1.09013 | + | 0.629390i | 0.933612 | − | 0.358285i | \(-0.116638\pi\) |
0.156522 | + | 0.987674i | \(0.449972\pi\) | |||||||
\(38\) | 1.17157 | 0.190054 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.48528 | 0.709185 | ||||||||
\(41\) | 4.47871 | + | 2.58579i | 0.699458 | + | 0.403832i | 0.807145 | − | 0.590353i | \(-0.201011\pi\) |
−0.107688 | + | 0.994185i | \(0.534345\pi\) | |||||||
\(42\) | −0.585786 | + | 1.01461i | −0.0903888 | + | 0.156558i | ||||
\(43\) | −0.828427 | − | 1.43488i | −0.126334 | − | 0.218817i | 0.795920 | − | 0.605402i | \(-0.206988\pi\) |
−0.922254 | + | 0.386585i | \(0.873654\pi\) | |||||||
\(44\) | − | 3.65685i | − | 0.551292i | ||||||
\(45\) | 2.44949 | − | 1.41421i | 0.365148 | − | 0.210819i | ||||
\(46\) | −1.43488 | + | 0.828427i | −0.211561 | + | 0.122145i | ||||
\(47\) | − | 11.6569i | − | 1.70033i | −0.526519 | − | 0.850163i | \(-0.676503\pi\) | ||
0.526519 | − | 0.850163i | \(-0.323497\pi\) | |||||||
\(48\) | −1.50000 | − | 2.59808i | −0.216506 | − | 0.375000i | ||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | −1.07616 | − | 0.621320i | −0.152192 | − | 0.0878680i | ||||
\(51\) | −7.65685 | −1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0.358719 | + | 0.207107i | 0.0488155 | + | 0.0281837i | ||||
\(55\) | −2.82843 | + | 4.89898i | −0.381385 | + | 0.660578i | ||||
\(56\) | −2.24264 | − | 3.88437i | −0.299685 | − | 0.519070i | ||||
\(57\) | 2.82843i | 0.374634i | ||||||||
\(58\) | −0.717439 | + | 0.414214i | −0.0942043 | + | 0.0543889i | ||||
\(59\) | 6.63103 | − | 3.82843i | 0.863287 | − | 0.498419i | −0.00182490 | − | 0.999998i | \(-0.500581\pi\) |
0.865112 | + | 0.501580i | \(0.167248\pi\) | |||||||
\(60\) | 5.17157i | 0.667647i | ||||||||
\(61\) | −6.65685 | − | 11.5300i | −0.852323 | − | 1.47627i | −0.879107 | − | 0.476625i | \(-0.841860\pi\) |
0.0267837 | − | 0.999641i | \(-0.491473\pi\) | |||||||
\(62\) | −0.242641 | + | 0.420266i | −0.0308154 | + | 0.0533738i | ||||
\(63\) | −2.44949 | − | 1.41421i | −0.308607 | − | 0.178174i | ||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | 5.91359 | + | 3.41421i | 0.722460 | + | 0.417113i | 0.815657 | − | 0.578535i | \(-0.196375\pi\) |
−0.0931973 | + | 0.995648i | \(0.529709\pi\) | |||||||
\(68\) | 7.00000 | − | 12.1244i | 0.848875 | − | 1.47029i | ||||
\(69\) | −2.00000 | − | 3.46410i | −0.240772 | − | 0.417029i | ||||
\(70\) | 3.31371i | 0.396064i | ||||||||
\(71\) | −1.73205 | + | 1.00000i | −0.205557 | + | 0.118678i | −0.599245 | − | 0.800566i | \(-0.704532\pi\) |
0.393688 | + | 0.919244i | \(0.371199\pi\) | |||||||
\(72\) | −1.37333 | + | 0.792893i | −0.161849 | + | 0.0934434i | ||||
\(73\) | 0.343146i | 0.0401622i | 0.999798 | + | 0.0200811i | \(0.00639244\pi\) | ||||
−0.999798 | + | 0.0200811i | \(0.993608\pi\) | |||||||
\(74\) | 1.58579 | + | 2.74666i | 0.184344 | + | 0.319293i | ||||
\(75\) | 1.50000 | − | 2.59808i | 0.173205 | − | 0.300000i | ||||
\(76\) | −4.47871 | − | 2.58579i | −0.513744 | − | 0.296610i | ||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | −7.34847 | − | 4.24264i | −0.821584 | − | 0.474342i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.07107 | + | 1.85514i | 0.118280 | + | 0.204866i | ||||
\(83\) | − | 3.65685i | − | 0.401392i | −0.979654 | − | 0.200696i | \(-0.935680\pi\) | ||
0.979654 | − | 0.200696i | \(-0.0643203\pi\) | |||||||
\(84\) | 4.47871 | − | 2.58579i | 0.488668 | − | 0.282132i | ||||
\(85\) | −18.7554 | + | 10.8284i | −2.03431 | + | 1.17451i | ||||
\(86\) | − | 0.686292i | − | 0.0740047i | ||||||
\(87\) | −1.00000 | − | 1.73205i | −0.107211 | − | 0.185695i | ||||
\(88\) | 1.58579 | − | 2.74666i | 0.169045 | − | 0.292795i | ||||
\(89\) | −12.8418 | − | 7.41421i | −1.36123 | − | 0.785905i | −0.371440 | − | 0.928457i | \(-0.621136\pi\) |
−0.989787 | + | 0.142552i | \(0.954469\pi\) | |||||||
\(90\) | 1.17157 | 0.123495 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.31371 | 0.762507 | ||||||||
\(93\) | −1.01461 | − | 0.585786i | −0.105210 | − | 0.0607432i | ||||
\(94\) | 2.41421 | − | 4.18154i | 0.249007 | − | 0.431293i | ||||
\(95\) | 4.00000 | + | 6.92820i | 0.410391 | + | 0.710819i | ||||
\(96\) | − | 4.41421i | − | 0.450524i | ||||||
\(97\) | −3.16693 | + | 1.82843i | −0.321553 | + | 0.185649i | −0.652085 | − | 0.758146i | \(-0.726105\pi\) |
0.330532 | + | 0.943795i | \(0.392772\pi\) | |||||||
\(98\) | 0.358719 | − | 0.207107i | 0.0362361 | − | 0.0209209i | ||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 2.74264 | + | 4.75039i | 0.274264 | + | 0.475039i | ||||
\(101\) | 3.82843 | − | 6.63103i | 0.380943 | − | 0.659812i | −0.610255 | − | 0.792205i | \(-0.708933\pi\) |
0.991197 | + | 0.132393i | \(0.0422662\pi\) | |||||||
\(102\) | −2.74666 | − | 1.58579i | −0.271960 | − | 0.157016i | ||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | −0.717439 | − | 0.414214i | −0.0696838 | − | 0.0402320i | ||||
\(107\) | 5.65685 | − | 9.79796i | 0.546869 | − | 0.947204i | −0.451618 | − | 0.892211i | \(-0.649153\pi\) |
0.998487 | − | 0.0549930i | \(-0.0175137\pi\) | |||||||
\(108\) | −0.914214 | − | 1.58346i | −0.0879702 | − | 0.152369i | ||||
\(109\) | − | 5.31371i | − | 0.508961i | −0.967078 | − | 0.254480i | \(-0.918096\pi\) | ||
0.967078 | − | 0.254480i | \(-0.0819045\pi\) | |||||||
\(110\) | −2.02922 | + | 1.17157i | −0.193479 | + | 0.111705i | ||||
\(111\) | −6.63103 | + | 3.82843i | −0.629390 | + | 0.363378i | ||||
\(112\) | 8.48528i | 0.801784i | ||||||||
\(113\) | 2.65685 | + | 4.60181i | 0.249936 | + | 0.432902i | 0.963508 | − | 0.267680i | \(-0.0862571\pi\) |
−0.713572 | + | 0.700582i | \(0.752924\pi\) | |||||||
\(114\) | −0.585786 | + | 1.01461i | −0.0548639 | + | 0.0950271i | ||||
\(115\) | −9.79796 | − | 5.65685i | −0.913664 | − | 0.527504i | ||||
\(116\) | 3.65685 | 0.339530 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | 18.7554 | + | 10.8284i | 1.71930 | + | 0.992640i | ||||
\(120\) | −2.24264 | + | 3.88437i | −0.204724 | + | 0.354593i | ||||
\(121\) | −3.50000 | − | 6.06218i | −0.318182 | − | 0.551107i | ||||
\(122\) | − | 5.51472i | − | 0.499279i | ||||||
\(123\) | −4.47871 | + | 2.58579i | −0.403832 | + | 0.233153i | ||||
\(124\) | 1.85514 | − | 1.07107i | 0.166597 | − | 0.0961847i | ||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | −0.585786 | − | 1.01461i | −0.0521860 | − | 0.0903888i | ||||
\(127\) | 2.82843 | − | 4.89898i | 0.250982 | − | 0.434714i | −0.712814 | − | 0.701353i | \(-0.752580\pi\) |
0.963797 | + | 0.266639i | \(0.0859131\pi\) | |||||||
\(128\) | 9.14207 | + | 5.27817i | 0.808052 | + | 0.466529i | ||||
\(129\) | 1.65685 | 0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 3.16693 | + | 1.82843i | 0.275646 | + | 0.159144i | ||||
\(133\) | 4.00000 | − | 6.92820i | 0.346844 | − | 0.600751i | ||||
\(134\) | 1.41421 | + | 2.44949i | 0.122169 | + | 0.211604i | ||||
\(135\) | 2.82843i | 0.243432i | ||||||||
\(136\) | 10.5154 | − | 6.07107i | 0.901688 | − | 0.520590i | ||||
\(137\) | −9.37769 | + | 5.41421i | −0.801190 | + | 0.462567i | −0.843887 | − | 0.536521i | \(-0.819738\pi\) |
0.0426968 | + | 0.999088i | \(0.486405\pi\) | |||||||
\(138\) | − | 1.65685i | − | 0.141041i | ||||||
\(139\) | 3.65685 | + | 6.33386i | 0.310170 | + | 0.537231i | 0.978399 | − | 0.206725i | \(-0.0662806\pi\) |
−0.668229 | + | 0.743956i | \(0.732947\pi\) | |||||||
\(140\) | 7.31371 | − | 12.6677i | 0.618121 | − | 1.07062i | ||||
\(141\) | 10.0951 | + | 5.82843i | 0.850163 | + | 0.490842i | ||||
\(142\) | −0.828427 | −0.0695201 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −4.89898 | − | 2.82843i | −0.406838 | − | 0.234888i | ||||
\(146\) | −0.0710678 | + | 0.123093i | −0.00588161 | + | 0.0101873i | ||||
\(147\) | 0.500000 | + | 0.866025i | 0.0412393 | + | 0.0714286i | ||||
\(148\) | − | 14.0000i | − | 1.15079i | ||||||
\(149\) | 7.94282 | − | 4.58579i | 0.650701 | − | 0.375682i | −0.138024 | − | 0.990429i | \(-0.544075\pi\) |
0.788725 | + | 0.614747i | \(0.210742\pi\) | |||||||
\(150\) | 1.07616 | − | 0.621320i | 0.0878680 | − | 0.0507306i | ||||
\(151\) | − | 3.51472i | − | 0.286024i | −0.989721 | − | 0.143012i | \(-0.954321\pi\) | ||
0.989721 | − | 0.143012i | \(-0.0456787\pi\) | |||||||
\(152\) | −2.24264 | − | 3.88437i | −0.181902 | − | 0.315064i | ||||
\(153\) | 3.82843 | − | 6.63103i | 0.309510 | − | 0.536087i | ||||
\(154\) | 2.02922 | + | 1.17157i | 0.163520 | + | 0.0944080i | ||||
\(155\) | −3.31371 | −0.266163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | −4.05845 | − | 2.34315i | −0.322873 | − | 0.186411i | ||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | −6.24264 | − | 10.8126i | −0.493524 | − | 0.854809i | ||||
\(161\) | 11.3137i | 0.891645i | ||||||||
\(162\) | −0.358719 | + | 0.207107i | −0.0281837 | + | 0.0162718i | ||||
\(163\) | 16.3059 | − | 9.41421i | 1.27718 | − | 0.737378i | 0.300848 | − | 0.953672i | \(-0.402730\pi\) |
0.976328 | + | 0.216294i | \(0.0693970\pi\) | |||||||
\(164\) | − | 9.45584i | − | 0.738377i | ||||||
\(165\) | −2.82843 | − | 4.89898i | −0.220193 | − | 0.381385i | ||||
\(166\) | 0.757359 | − | 1.31178i | 0.0587825 | − | 0.101814i | ||||
\(167\) | 3.16693 | + | 1.82843i | 0.245064 | + | 0.141488i | 0.617502 | − | 0.786569i | \(-0.288145\pi\) |
−0.372438 | + | 0.928057i | \(0.621478\pi\) | |||||||
\(168\) | 4.48528 | 0.346047 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.97056 | −0.688011 | ||||||||
\(171\) | −2.44949 | − | 1.41421i | −0.187317 | − | 0.108148i | ||||
\(172\) | −1.51472 | + | 2.62357i | −0.115496 | + | 0.200045i | ||||
\(173\) | −5.82843 | − | 10.0951i | −0.443127 | − | 0.767519i | 0.554793 | − | 0.831989i | \(-0.312798\pi\) |
−0.997920 | + | 0.0644701i | \(0.979464\pi\) | |||||||
\(174\) | − | 0.828427i | − | 0.0628029i | ||||||
\(175\) | −7.34847 | + | 4.24264i | −0.555492 | + | 0.320713i | ||||
\(176\) | −5.19615 | + | 3.00000i | −0.391675 | + | 0.226134i | ||||
\(177\) | 7.65685i | 0.575524i | ||||||||
\(178\) | −3.07107 | − | 5.31925i | −0.230186 | − | 0.398694i | ||||
\(179\) | −11.6569 | + | 20.1903i | −0.871274 | + | 1.50909i | −0.0105948 | + | 0.999944i | \(0.503372\pi\) |
−0.860679 | + | 0.509147i | \(0.829961\pi\) | |||||||
\(180\) | −4.47871 | − | 2.58579i | −0.333824 | − | 0.192733i | ||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3137 | 0.984178 | ||||||||
\(184\) | 5.49333 | + | 3.17157i | 0.404973 | + | 0.233811i | ||||
\(185\) | −10.8284 | + | 18.7554i | −0.796122 | + | 1.37892i | ||||
\(186\) | −0.242641 | − | 0.420266i | −0.0177913 | − | 0.0308154i | ||||
\(187\) | 15.3137i | 1.11985i | ||||||||
\(188\) | −18.4582 | + | 10.6569i | −1.34620 | + | 0.777231i | ||||
\(189\) | 2.44949 | − | 1.41421i | 0.178174 | − | 0.102869i | ||||
\(190\) | 3.31371i | 0.240402i | ||||||||
\(191\) | −1.65685 | − | 2.86976i | −0.119886 | − | 0.207648i | 0.799836 | − | 0.600218i | \(-0.204919\pi\) |
−0.919722 | + | 0.392570i | \(0.871586\pi\) | |||||||
\(192\) | −2.08579 | + | 3.61269i | −0.150529 | + | 0.260723i | ||||
\(193\) | −4.60181 | − | 2.65685i | −0.331245 | − | 0.191245i | 0.325149 | − | 0.945663i | \(-0.394586\pi\) |
−0.656394 | + | 0.754418i | \(0.727919\pi\) | |||||||
\(194\) | −1.51472 | −0.108750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.82843 | −0.130602 | ||||||||
\(197\) | 0.420266 | + | 0.242641i | 0.0299427 | + | 0.0172874i | 0.514897 | − | 0.857252i | \(-0.327830\pi\) |
−0.484954 | + | 0.874540i | \(0.661164\pi\) | |||||||
\(198\) | 0.414214 | − | 0.717439i | 0.0294369 | − | 0.0509862i | ||||
\(199\) | 10.8284 | + | 18.7554i | 0.767607 | + | 1.32953i | 0.938857 | + | 0.344307i | \(0.111886\pi\) |
−0.171250 | + | 0.985228i | \(0.554781\pi\) | |||||||
\(200\) | 4.75736i | 0.336396i | ||||||||
\(201\) | −5.91359 | + | 3.41421i | −0.417113 | + | 0.240820i | ||||
\(202\) | 2.74666 | − | 1.58579i | 0.193255 | − | 0.111576i | ||||
\(203\) | 5.65685i | 0.397033i | ||||||||
\(204\) | 7.00000 | + | 12.1244i | 0.490098 | + | 0.848875i | ||||
\(205\) | −7.31371 | + | 12.6677i | −0.510812 | + | 0.884752i | ||||
\(206\) | −0.840532 | − | 0.485281i | −0.0585626 | − | 0.0338112i | ||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | −2.86976 | − | 1.65685i | −0.198032 | − | 0.114334i | ||||
\(211\) | 6.00000 | − | 10.3923i | 0.413057 | − | 0.715436i | −0.582165 | − | 0.813070i | \(-0.697794\pi\) |
0.995222 | + | 0.0976347i | \(0.0311277\pi\) | |||||||
\(212\) | 1.82843 | + | 3.16693i | 0.125577 | + | 0.217506i | ||||
\(213\) | − | 2.00000i | − | 0.137038i | ||||||
\(214\) | 4.05845 | − | 2.34315i | 0.277430 | − | 0.160174i | ||||
\(215\) | 4.05845 | − | 2.34315i | 0.276784 | − | 0.159801i | ||||
\(216\) | − | 1.58579i | − | 0.107899i | ||||||
\(217\) | 1.65685 | + | 2.86976i | 0.112475 | + | 0.194812i | ||||
\(218\) | 1.10051 | − | 1.90613i | 0.0745356 | − | 0.129099i | ||||
\(219\) | −0.297173 | − | 0.171573i | −0.0200811 | − | 0.0115938i | ||||
\(220\) | 10.3431 | 0.697335 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.17157 | −0.212862 | ||||||||
\(223\) | −10.8126 | − | 6.24264i | −0.724063 | − | 0.418038i | 0.0921831 | − | 0.995742i | \(-0.470615\pi\) |
−0.816246 | + | 0.577704i | \(0.803949\pi\) | |||||||
\(224\) | −6.24264 | + | 10.8126i | −0.417104 | + | 0.722445i | ||||
\(225\) | 1.50000 | + | 2.59808i | 0.100000 | + | 0.173205i | ||||
\(226\) | 2.20101i | 0.146409i | ||||||||
\(227\) | 14.9941 | − | 8.65685i | 0.995194 | − | 0.574576i | 0.0883713 | − | 0.996088i | \(-0.471834\pi\) |
0.906823 | + | 0.421512i | \(0.138500\pi\) | |||||||
\(228\) | 4.47871 | − | 2.58579i | 0.296610 | − | 0.171248i | ||||
\(229\) | − | 1.31371i | − | 0.0868123i | −0.999058 | − | 0.0434062i | \(-0.986179\pi\) | ||
0.999058 | − | 0.0434062i | \(-0.0138209\pi\) | |||||||
\(230\) | −2.34315 | − | 4.05845i | −0.154502 | − | 0.267606i | ||||
\(231\) | −2.82843 | + | 4.89898i | −0.186097 | + | 0.322329i | ||||
\(232\) | 2.74666 | + | 1.58579i | 0.180327 | + | 0.104112i | ||||
\(233\) | −6.97056 | −0.456657 | −0.228328 | − | 0.973584i | \(-0.573326\pi\) | ||||
−0.228328 | + | 0.973584i | \(0.573326\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.9706 | 2.15076 | ||||||||
\(236\) | −12.1244 | − | 7.00000i | −0.789228 | − | 0.455661i | ||||
\(237\) | 5.65685 | − | 9.79796i | 0.367452 | − | 0.636446i | ||||
\(238\) | 4.48528 | + | 7.76874i | 0.290738 | + | 0.503572i | ||||
\(239\) | − | 2.00000i | − | 0.129369i | −0.997906 | − | 0.0646846i | \(-0.979396\pi\) | ||
0.997906 | − | 0.0646846i | \(-0.0206041\pi\) | |||||||
\(240\) | 7.34847 | − | 4.24264i | 0.474342 | − | 0.273861i | ||||
\(241\) | 0.297173 | − | 0.171573i | 0.0191426 | − | 0.0110520i | −0.490398 | − | 0.871499i | \(-0.663149\pi\) |
0.509541 | + | 0.860447i | \(0.329815\pi\) | |||||||
\(242\) | − | 2.89949i | − | 0.186387i | ||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −12.1716 | + | 21.0818i | −0.779205 | + | 1.34962i | ||||
\(245\) | 2.44949 | + | 1.41421i | 0.156492 | + | 0.0903508i | ||||
\(246\) | −2.14214 | −0.136578 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.85786 | 0.117975 | ||||||||
\(249\) | 3.16693 | + | 1.82843i | 0.200696 | + | 0.115872i | ||||
\(250\) | −1.17157 | + | 2.02922i | −0.0740968 | + | 0.128339i | ||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 5.17157i | 0.325778i | ||||||||
\(253\) | −6.92820 | + | 4.00000i | −0.435572 | + | 0.251478i | ||||
\(254\) | 2.02922 | − | 1.17157i | 0.127325 | − | 0.0735110i | ||||
\(255\) | − | 21.6569i | − | 1.35620i | ||||||
\(256\) | −1.98528 | − | 3.43861i | −0.124080 | − | 0.214913i | ||||
\(257\) | −2.17157 | + | 3.76127i | −0.135459 | + | 0.234622i | −0.925773 | − | 0.378081i | \(-0.876584\pi\) |
0.790314 | + | 0.612702i | \(0.209918\pi\) | |||||||
\(258\) | 0.594346 | + | 0.343146i | 0.0370024 | + | 0.0213633i | ||||
\(259\) | 21.6569 | 1.34569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −2.86976 | − | 1.65685i | −0.177294 | − | 0.102361i | ||||
\(263\) | −6.00000 | + | 10.3923i | −0.369976 | + | 0.640817i | −0.989561 | − | 0.144112i | \(-0.953967\pi\) |
0.619586 | + | 0.784929i | \(0.287301\pi\) | |||||||
\(264\) | 1.58579 | + | 2.74666i | 0.0975984 | + | 0.169045i | ||||
\(265\) | − | 5.65685i | − | 0.347498i | ||||||
\(266\) | 2.86976 | − | 1.65685i | 0.175956 | − | 0.101588i | ||||
\(267\) | 12.8418 | − | 7.41421i | 0.785905 | − | 0.453743i | ||||
\(268\) | − | 12.4853i | − | 0.762660i | ||||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | −0.585786 | + | 1.01461i | −0.0356498 | + | 0.0617473i | ||||
\(271\) | 24.0746 | + | 13.8995i | 1.46243 | + | 0.844334i | 0.999123 | − | 0.0418640i | \(-0.0133296\pi\) |
0.463306 | + | 0.886198i | \(0.346663\pi\) | |||||||
\(272\) | −22.9706 | −1.39279 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.48528 | −0.270966 | ||||||||
\(275\) | −5.19615 | − | 3.00000i | −0.313340 | − | 0.180907i | ||||
\(276\) | −3.65685 | + | 6.33386i | −0.220117 | + | 0.381253i | ||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | 3.02944i | 0.181694i | ||||||||
\(279\) | 1.01461 | − | 0.585786i | 0.0607432 | − | 0.0350701i | ||||
\(280\) | 10.9867 | − | 6.34315i | 0.656578 | − | 0.379075i | ||||
\(281\) | 21.1716i | 1.26299i | 0.775380 | + | 0.631495i | \(0.217558\pi\) | ||||
−0.775380 | + | 0.631495i | \(0.782442\pi\) | |||||||
\(282\) | 2.41421 | + | 4.18154i | 0.143764 | + | 0.249007i | ||||
\(283\) | 14.4853 | − | 25.0892i | 0.861061 | − | 1.49140i | −0.00984565 | − | 0.999952i | \(-0.503134\pi\) |
0.870906 | − | 0.491449i | \(-0.163533\pi\) | |||||||
\(284\) | 3.16693 | + | 1.82843i | 0.187923 | + | 0.108497i | ||||
\(285\) | −8.00000 | −0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6274 | 0.863429 | ||||||||
\(288\) | 3.82282 | + | 2.20711i | 0.225262 | + | 0.130055i | ||||
\(289\) | −20.8137 | + | 36.0504i | −1.22434 | + | 2.12061i | ||||
\(290\) | −1.17157 | − | 2.02922i | −0.0687971 | − | 0.119160i | ||||
\(291\) | − | 3.65685i | − | 0.214369i | ||||||
\(292\) | 0.543359 | − | 0.313708i | 0.0317977 | − | 0.0183584i | ||||
\(293\) | 1.85514 | − | 1.07107i | 0.108379 | − | 0.0625724i | −0.444831 | − | 0.895615i | \(-0.646736\pi\) |
0.553210 | + | 0.833042i | \(0.313403\pi\) | |||||||
\(294\) | 0.414214i | 0.0241574i | ||||||||
\(295\) | 10.8284 | + | 18.7554i | 0.630455 | + | 1.09198i | ||||
\(296\) | 6.07107 | − | 10.5154i | 0.352874 | − | 0.611195i | ||||
\(297\) | 1.73205 | + | 1.00000i | 0.100504 | + | 0.0580259i | ||||
\(298\) | 3.79899 | 0.220070 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.48528 | −0.316693 | ||||||||
\(301\) | −4.05845 | − | 2.34315i | −0.233925 | − | 0.135057i | ||||
\(302\) | 0.727922 | − | 1.26080i | 0.0418872 | − | 0.0725508i | ||||
\(303\) | 3.82843 | + | 6.63103i | 0.219937 | + | 0.380943i | ||||
\(304\) | 8.48528i | 0.486664i | ||||||||
\(305\) | 32.6118 | − | 18.8284i | 1.86735 | − | 1.07811i | ||||
\(306\) | 2.74666 | − | 1.58579i | 0.157016 | − | 0.0906534i | ||||
\(307\) | − | 22.8284i | − | 1.30289i | −0.758697 | − | 0.651444i | \(-0.774164\pi\) | ||
0.758697 | − | 0.651444i | \(-0.225836\pi\) | |||||||
\(308\) | −5.17157 | − | 8.95743i | −0.294678 | − | 0.510397i | ||||
\(309\) | 1.17157 | − | 2.02922i | 0.0666485 | − | 0.115439i | ||||
\(310\) | −1.18869 | − | 0.686292i | −0.0675132 | − | 0.0389787i | ||||
\(311\) | 10.6274 | 0.602626 | 0.301313 | − | 0.953525i | \(-0.402575\pi\) | ||||
0.301313 | + | 0.953525i | \(0.402575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | −3.58719 | − | 2.07107i | −0.202437 | − | 0.116877i | ||||
\(315\) | 4.00000 | − | 6.92820i | 0.225374 | − | 0.390360i | ||||
\(316\) | 10.3431 | + | 17.9149i | 0.581847 | + | 1.00779i | ||||
\(317\) | − | 8.48528i | − | 0.476581i | −0.971194 | − | 0.238290i | \(-0.923413\pi\) | ||
0.971194 | − | 0.238290i | \(-0.0765870\pi\) | |||||||
\(318\) | 0.717439 | − | 0.414214i | 0.0402320 | − | 0.0232279i | ||||
\(319\) | −3.46410 | + | 2.00000i | −0.193952 | + | 0.111979i | ||||
\(320\) | 11.7990i | 0.659584i | ||||||||
\(321\) | 5.65685 | + | 9.79796i | 0.315735 | + | 0.546869i | ||||
\(322\) | −2.34315 | + | 4.05845i | −0.130578 | + | 0.226168i | ||||
\(323\) | 18.7554 | + | 10.8284i | 1.04358 | + | 0.602510i | ||||
\(324\) | 1.82843 | 0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.79899 | 0.431946 | ||||||||
\(327\) | 4.60181 | + | 2.65685i | 0.254480 | + | 0.146924i | ||||
\(328\) | 4.10051 | − | 7.10228i | 0.226413 | − | 0.392158i | ||||
\(329\) | −16.4853 | − | 28.5533i | −0.908863 | − | 1.57420i | ||||
\(330\) | − | 2.34315i | − | 0.128986i | ||||||
\(331\) | −22.6398 | + | 13.0711i | −1.24439 | + | 0.718451i | −0.969986 | − | 0.243163i | \(-0.921815\pi\) |
−0.274408 | + | 0.961613i | \(0.588482\pi\) | |||||||
\(332\) | −5.79050 | + | 3.34315i | −0.317795 | + | 0.183479i | ||||
\(333\) | − | 7.65685i | − | 0.419593i | ||||||
\(334\) | 0.757359 | + | 1.31178i | 0.0414409 | + | 0.0717777i | ||||
\(335\) | −9.65685 | + | 16.7262i | −0.527610 | + | 0.913848i | ||||
\(336\) | −7.34847 | − | 4.24264i | −0.400892 | − | 0.231455i | ||||
\(337\) | −9.31371 | −0.507350 | −0.253675 | − | 0.967290i | \(-0.581639\pi\) | ||||
−0.253675 | + | 0.967290i | \(0.581639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.31371 | −0.288601 | ||||||||
\(340\) | 34.2929 | + | 19.7990i | 1.85979 | + | 1.07375i | ||||
\(341\) | −1.17157 | + | 2.02922i | −0.0634442 | + | 0.109889i | ||||
\(342\) | −0.585786 | − | 1.01461i | −0.0316757 | − | 0.0548639i | ||||
\(343\) | 16.9706i | 0.916324i | ||||||||
\(344\) | −2.27541 | + | 1.31371i | −0.122682 | + | 0.0708304i | ||||
\(345\) | 9.79796 | − | 5.65685i | 0.527504 | − | 0.304555i | ||||
\(346\) | − | 4.82843i | − | 0.259578i | ||||||
\(347\) | 4.34315 | + | 7.52255i | 0.233152 | + | 0.403832i | 0.958734 | − | 0.284304i | \(-0.0917626\pi\) |
−0.725582 | + | 0.688136i | \(0.758429\pi\) | |||||||
\(348\) | −1.82843 | + | 3.16693i | −0.0980140 | + | 0.169765i | ||||
\(349\) | −3.16693 | − | 1.82843i | −0.169522 | − | 0.0978735i | 0.412839 | − | 0.910804i | \(-0.364537\pi\) |
−0.582360 | + | 0.812931i | \(0.697871\pi\) | |||||||
\(350\) | −3.51472 | −0.187870 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.82843 | −0.470557 | ||||||||
\(353\) | −28.9736 | − | 16.7279i | −1.54211 | − | 0.890337i | −0.998705 | − | 0.0508663i | \(-0.983802\pi\) |
−0.543404 | − | 0.839471i | \(-0.682865\pi\) | |||||||
\(354\) | −1.58579 | + | 2.74666i | −0.0842836 | + | 0.145983i | ||||
\(355\) | −2.82843 | − | 4.89898i | −0.150117 | − | 0.260011i | ||||
\(356\) | 27.1127i | 1.43697i | ||||||||
\(357\) | −18.7554 | + | 10.8284i | −0.992640 | + | 0.573101i | ||||
\(358\) | −8.36308 | + | 4.82843i | −0.442003 | + | 0.255190i | ||||
\(359\) | 34.9706i | 1.84568i | 0.385189 | + | 0.922838i | \(0.374136\pi\) | ||||
−0.385189 | + | 0.922838i | \(0.625864\pi\) | |||||||
\(360\) | −2.24264 | − | 3.88437i | −0.118198 | − | 0.204724i | ||||
\(361\) | −5.50000 | + | 9.52628i | −0.289474 | + | 0.501383i | ||||
\(362\) | −5.02207 | − | 2.89949i | −0.263954 | − | 0.152394i | ||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.970563 | −0.0508016 | ||||||||
\(366\) | 4.77589 | + | 2.75736i | 0.249640 | + | 0.144129i | ||||
\(367\) | 12.0000 | − | 20.7846i | 0.626395 | − | 1.08495i | −0.361874 | − | 0.932227i | \(-0.617863\pi\) |
0.988269 | − | 0.152721i | \(-0.0488036\pi\) | |||||||
\(368\) | −6.00000 | − | 10.3923i | −0.312772 | − | 0.541736i | ||||
\(369\) | − | 5.17157i | − | 0.269221i | ||||||
\(370\) | −7.76874 | + | 4.48528i | −0.403877 | + | 0.233179i | ||||
\(371\) | −4.89898 | + | 2.82843i | −0.254342 | + | 0.146845i | ||||
\(372\) | 2.14214i | 0.111065i | ||||||||
\(373\) | −5.00000 | − | 8.66025i | −0.258890 | − | 0.448411i | 0.707055 | − | 0.707159i | \(-0.250023\pi\) |
−0.965945 | + | 0.258748i | \(0.916690\pi\) | |||||||
\(374\) | −3.17157 | + | 5.49333i | −0.163998 | + | 0.284053i | ||||
\(375\) | −4.89898 | − | 2.82843i | −0.252982 | − | 0.146059i | ||||
\(376\) | −18.4853 | −0.953306 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.17157 | 0.0602592 | ||||||||
\(379\) | 0.420266 | + | 0.242641i | 0.0215876 | + | 0.0124636i | 0.510755 | − | 0.859726i | \(-0.329366\pi\) |
−0.489167 | + | 0.872190i | \(0.662699\pi\) | |||||||
\(380\) | 7.31371 | − | 12.6677i | 0.375185 | − | 0.649840i | ||||
\(381\) | 2.82843 | + | 4.89898i | 0.144905 | + | 0.250982i | ||||
\(382\) | − | 1.37258i | − | 0.0702275i | ||||||
\(383\) | −26.8213 | + | 15.4853i | −1.37050 | + | 0.791261i | −0.990991 | − | 0.133926i | \(-0.957242\pi\) |
−0.379513 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(384\) | −9.14207 | + | 5.27817i | −0.466529 | + | 0.269351i | ||||
\(385\) | 16.0000i | 0.815436i | ||||||||
\(386\) | −1.10051 | − | 1.90613i | −0.0560142 | − | 0.0970195i | ||||
\(387\) | −0.828427 | + | 1.43488i | −0.0421113 | + | 0.0729389i | ||||
\(388\) | 5.79050 | + | 3.34315i | 0.293968 | + | 0.169723i | ||||
\(389\) | 26.9706 | 1.36746 | 0.683731 | − | 0.729734i | \(-0.260356\pi\) | ||||
0.683731 | + | 0.729734i | \(0.260356\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.6274 | −1.54890 | ||||||||
\(392\) | −1.37333 | − | 0.792893i | −0.0693637 | − | 0.0400472i | ||||
\(393\) | 4.00000 | − | 6.92820i | 0.201773 | − | 0.349482i | ||||
\(394\) | 0.100505 | + | 0.174080i | 0.00506337 | + | 0.00877002i | ||||
\(395\) | − | 32.0000i | − | 1.61009i | ||||||
\(396\) | −3.16693 | + | 1.82843i | −0.159144 | + | 0.0918819i | ||||
\(397\) | 26.8213 | − | 15.4853i | 1.34612 | − | 0.777184i | 0.358424 | − | 0.933559i | \(-0.383314\pi\) |
0.987698 | + | 0.156375i | \(0.0499808\pi\) | |||||||
\(398\) | 8.97056i | 0.449654i | ||||||||
\(399\) | 4.00000 | + | 6.92820i | 0.200250 | + | 0.346844i | ||||
\(400\) | 4.50000 | − | 7.79423i | 0.225000 | − | 0.389711i | ||||
\(401\) | −22.6398 | − | 13.0711i | −1.13058 | − | 0.652738i | −0.186496 | − | 0.982456i | \(-0.559713\pi\) |
−0.944080 | + | 0.329718i | \(0.893046\pi\) | |||||||
\(402\) | −2.82843 | −0.141069 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −2.44949 | − | 1.41421i | −0.121716 | − | 0.0702728i | ||||
\(406\) | −1.17157 | + | 2.02922i | −0.0581442 | + | 0.100709i | ||||
\(407\) | 7.65685 | + | 13.2621i | 0.379536 | + | 0.657376i | ||||
\(408\) | 12.1421i | 0.601125i | ||||||||
\(409\) | 30.2854 | − | 17.4853i | 1.49752 | − | 0.864592i | 0.497521 | − | 0.867452i | \(-0.334244\pi\) |
0.999996 | + | 0.00286068i | \(0.000910584\pi\) | |||||||
\(410\) | −5.24714 | + | 3.02944i | −0.259138 | + | 0.149613i | ||||
\(411\) | − | 10.8284i | − | 0.534127i | ||||||
\(412\) | 2.14214 | + | 3.71029i | 0.105535 | + | 0.182793i | ||||
\(413\) | 10.8284 | − | 18.7554i | 0.532832 | − | 0.922892i | ||||
\(414\) | 1.43488 | + | 0.828427i | 0.0705204 | + | 0.0407150i | ||||
\(415\) | 10.3431 | 0.507725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.31371 | −0.358154 | ||||||||
\(418\) | 2.02922 | + | 1.17157i | 0.0992526 | + | 0.0573035i | ||||
\(419\) | −7.31371 | + | 12.6677i | −0.357298 | + | 0.618858i | −0.987508 | − | 0.157566i | \(-0.949635\pi\) |
0.630210 | + | 0.776424i | \(0.282969\pi\) | |||||||
\(420\) | 7.31371 | + | 12.6677i | 0.356872 | + | 0.618121i | ||||
\(421\) | − | 37.3137i | − | 1.81856i | −0.416186 | − | 0.909279i | \(-0.636634\pi\) | ||
0.416186 | − | 0.909279i | \(-0.363366\pi\) | |||||||
\(422\) | 4.30463 | − | 2.48528i | 0.209546 | − | 0.120982i | ||||
\(423\) | −10.0951 | + | 5.82843i | −0.490842 | + | 0.283388i | ||||
\(424\) | 3.17157i | 0.154025i | ||||||||
\(425\) | −11.4853 | − | 19.8931i | −0.557118 | − | 0.964957i | ||||
\(426\) | 0.414214 | − | 0.717439i | 0.0200687 | − | 0.0347600i | ||||
\(427\) | −32.6118 | − | 18.8284i | −1.57820 | − | 0.911171i | ||||
\(428\) | −20.6863 | −0.999910 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.94113 | 0.0936094 | ||||||||
\(431\) | 7.22538 | + | 4.17157i | 0.348034 | + | 0.200938i | 0.663819 | − | 0.747893i | \(-0.268934\pi\) |
−0.315785 | + | 0.948831i | \(0.602268\pi\) | |||||||
\(432\) | −1.50000 | + | 2.59808i | −0.0721688 | + | 0.125000i | ||||
\(433\) | −10.6569 | − | 18.4582i | −0.512136 | − | 0.887045i | −0.999901 | − | 0.0140703i | \(-0.995521\pi\) |
0.487765 | − | 0.872975i | \(-0.337812\pi\) | |||||||
\(434\) | 1.37258i | 0.0658861i | ||||||||
\(435\) | 4.89898 | − | 2.82843i | 0.234888 | − | 0.135613i | ||||
\(436\) | −8.41407 | + | 4.85786i | −0.402961 | + | 0.232650i | ||||
\(437\) | 11.3137i | 0.541208i | ||||||||
\(438\) | −0.0710678 | − | 0.123093i | −0.00339575 | − | 0.00588161i | ||||
\(439\) | 8.48528 | − | 14.6969i | 0.404980 | − | 0.701447i | −0.589339 | − | 0.807886i | \(-0.700612\pi\) |
0.994319 | + | 0.106439i | \(0.0339450\pi\) | |||||||
\(440\) | 7.76874 | + | 4.48528i | 0.370360 | + | 0.213827i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9411 | −1.23250 | −0.616250 | − | 0.787551i | \(-0.711349\pi\) | ||||
−0.616250 | + | 0.787551i | \(0.711349\pi\) | |||||||
\(444\) | 12.1244 | + | 7.00000i | 0.575396 | + | 0.332205i | ||||
\(445\) | 20.9706 | − | 36.3221i | 0.994100 | − | 1.72183i | ||||
\(446\) | −2.58579 | − | 4.47871i | −0.122441 | − | 0.212073i | ||||
\(447\) | 9.17157i | 0.433801i | ||||||||
\(448\) | 10.2182 | − | 5.89949i | 0.482766 | − | 0.278725i | ||||
\(449\) | −27.5387 | + | 15.8995i | −1.29963 | + | 0.750344i | −0.980341 | − | 0.197313i | \(-0.936779\pi\) |
−0.319293 | + | 0.947656i | \(0.603445\pi\) | |||||||
\(450\) | 1.24264i | 0.0585786i | ||||||||
\(451\) | 5.17157 | + | 8.95743i | 0.243520 | + | 0.421789i | ||||
\(452\) | 4.85786 | − | 8.41407i | 0.228495 | − | 0.395764i | ||||
\(453\) | 3.04384 | + | 1.75736i | 0.143012 | + | 0.0825679i | ||||
\(454\) | 7.17157 | 0.336579 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.48528 | 0.210043 | ||||||||
\(457\) | −6.63103 | − | 3.82843i | −0.310187 | − | 0.179086i | 0.336823 | − | 0.941568i | \(-0.390647\pi\) |
−0.647010 | + | 0.762482i | \(0.723981\pi\) | |||||||
\(458\) | 0.272078 | − | 0.471253i | 0.0127134 | − | 0.0220202i | ||||
\(459\) | 3.82843 | + | 6.63103i | 0.178696 | + | 0.309510i | ||||
\(460\) | 20.6863i | 0.964503i | ||||||||
\(461\) | −4.47871 | + | 2.58579i | −0.208594 | + | 0.120432i | −0.600658 | − | 0.799506i | \(-0.705095\pi\) |
0.392064 | + | 0.919938i | \(0.371761\pi\) | |||||||
\(462\) | −2.02922 | + | 1.17157i | −0.0944080 | + | 0.0545065i | ||||
\(463\) | − | 24.4853i | − | 1.13793i | −0.822363 | − | 0.568964i | \(-0.807344\pi\) | ||
0.822363 | − | 0.568964i | \(-0.192656\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 1.65685 | − | 2.86976i | 0.0768348 | − | 0.133082i | ||||
\(466\) | −2.50048 | − | 1.44365i | −0.115832 | − | 0.0668758i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3137 | 0.891824 | ||||||||
\(470\) | 11.8272 | + | 6.82843i | 0.545547 | + | 0.314972i | ||||
\(471\) | 5.00000 | − | 8.66025i | 0.230388 | − | 0.399043i | ||||
\(472\) | −6.07107 | − | 10.5154i | −0.279444 | − | 0.484010i | ||||
\(473\) | − | 3.31371i | − | 0.152364i | ||||||
\(474\) | 4.05845 | − | 2.34315i | 0.186411 | − | 0.107624i | ||||
\(475\) | −7.34847 | + | 4.24264i | −0.337171 | + | 0.194666i | ||||
\(476\) | − | 39.5980i | − | 1.81497i | ||||||
\(477\) | 1.00000 | + | 1.73205i | 0.0457869 | + | 0.0793052i | ||||
\(478\) | 0.414214 | − | 0.717439i | 0.0189457 | − | 0.0328149i | ||||
\(479\) | −21.9223 | − | 12.6569i | −1.00166 | − | 0.578306i | −0.0929182 | − | 0.995674i | \(-0.529620\pi\) |
−0.908738 | + | 0.417367i | \(0.862953\pi\) | |||||||
\(480\) | 12.4853 | 0.569873 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.142136 | 0.00647410 | ||||||||
\(483\) | −9.79796 | − | 5.65685i | −0.445823 | − | 0.257396i | ||||
\(484\) | −6.39949 | + | 11.0843i | −0.290886 | + | 0.503830i | ||||
\(485\) | −5.17157 | − | 8.95743i | −0.234829 | − | 0.406736i | ||||
\(486\) | − | 0.414214i | − | 0.0187891i | ||||||
\(487\) | 6.75412 | − | 3.89949i | 0.306059 | − | 0.176703i | −0.339103 | − | 0.940749i | \(-0.610123\pi\) |
0.645161 | + | 0.764046i | \(0.276790\pi\) | |||||||
\(488\) | −18.2841 | + | 10.5563i | −0.827684 | + | 0.477863i | ||||
\(489\) | 18.8284i | 0.851451i | ||||||||
\(490\) | 0.585786 | + | 1.01461i | 0.0264631 | + | 0.0458355i | ||||
\(491\) | 15.3137 | − | 26.5241i | 0.691098 | − | 1.19702i | −0.280380 | − | 0.959889i | \(-0.590461\pi\) |
0.971478 | − | 0.237128i | \(-0.0762060\pi\) | |||||||
\(492\) | 8.18900 | + | 4.72792i | 0.369189 | + | 0.213151i | ||||
\(493\) | −15.3137 | −0.689695 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | −3.04384 | − | 1.75736i | −0.136672 | − | 0.0789078i | ||||
\(497\) | −2.82843 | + | 4.89898i | −0.126872 | + | 0.219749i | ||||
\(498\) | 0.757359 | + | 1.31178i | 0.0339381 | + | 0.0587825i | ||||
\(499\) | − | 26.1421i | − | 1.17028i | −0.810931 | − | 0.585141i | \(-0.801039\pi\) | ||
0.810931 | − | 0.585141i | \(-0.198961\pi\) | |||||||
\(500\) | 8.95743 | − | 5.17157i | 0.400588 | − | 0.231280i | ||||
\(501\) | −3.16693 | + | 1.82843i | −0.141488 | + | 0.0816881i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.65685 | + | 6.33386i | 0.163051 | + | 0.282413i | 0.935961 | − | 0.352102i | \(-0.114533\pi\) |
−0.772910 | + | 0.634515i | \(0.781200\pi\) | |||||||
\(504\) | −2.24264 | + | 3.88437i | −0.0998952 | + | 0.173023i | ||||
\(505\) | 18.7554 | + | 10.8284i | 0.834604 | + | 0.481859i | ||||
\(506\) | −3.31371 | −0.147312 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.3431 | −0.458903 | ||||||||
\(509\) | 10.2182 | + | 5.89949i | 0.452915 | + | 0.261491i | 0.709060 | − | 0.705148i | \(-0.249119\pi\) |
−0.256146 | + | 0.966638i | \(0.582453\pi\) | |||||||
\(510\) | 4.48528 | − | 7.76874i | 0.198612 | − | 0.344005i | ||||
\(511\) | 0.485281 | + | 0.840532i | 0.0214676 | + | 0.0371829i | ||||
\(512\) | − | 22.7574i | − | 1.00574i | ||||||
\(513\) | 2.44949 | − | 1.41421i | 0.108148 | − | 0.0624391i | ||||
\(514\) | −1.55797 | + | 0.899495i | −0.0687192 | + | 0.0396750i | ||||
\(515\) | − | 6.62742i | − | 0.292039i | ||||||
\(516\) | −1.51472 | − | 2.62357i | −0.0666818 | − | 0.115496i | ||||
\(517\) | 11.6569 | − | 20.1903i | 0.512668 | − | 0.887967i | ||||
\(518\) | 7.76874 | + | 4.48528i | 0.341339 | + | 0.197072i | ||||
\(519\) | 11.6569 | 0.511679 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3137 | 1.10901 | 0.554507 | − | 0.832179i | \(-0.312907\pi\) | ||||
0.554507 | + | 0.832179i | \(0.312907\pi\) | |||||||
\(522\) | 0.717439 | + | 0.414214i | 0.0314014 | + | 0.0181296i | ||||
\(523\) | 7.65685 | − | 13.2621i | 0.334811 | − | 0.579909i | −0.648638 | − | 0.761097i | \(-0.724661\pi\) |
0.983448 | + | 0.181188i | \(0.0579942\pi\) | |||||||
\(524\) | 7.31371 | + | 12.6677i | 0.319501 | + | 0.553392i | ||||
\(525\) | − | 8.48528i | − | 0.370328i | ||||||
\(526\) | −4.30463 | + | 2.48528i | −0.187691 | + | 0.108363i | ||||
\(527\) | −7.76874 | + | 4.48528i | −0.338411 | + | 0.195382i | ||||
\(528\) | − | 6.00000i | − | 0.261116i | ||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 1.17157 | − | 2.02922i | 0.0508899 | − | 0.0881438i | ||||
\(531\) | −6.63103 | − | 3.82843i | −0.287762 | − | 0.166140i | ||||
\(532\) | −14.6274 | −0.634179 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.14214 | 0.265796 | ||||||||
\(535\) | 27.7128 | + | 16.0000i | 1.19813 | + | 0.691740i | ||||
\(536\) | 5.41421 | − | 9.37769i | 0.233858 | − | 0.405055i | ||||
\(537\) | −11.6569 | − | 20.1903i | −0.503030 | − | 0.871274i | ||||
\(538\) | − | 7.45584i | − | 0.321444i | ||||||
\(539\) | 1.73205 | − | 1.00000i | 0.0746047 | − | 0.0430730i | ||||
\(540\) | 4.47871 | − | 2.58579i | 0.192733 | − | 0.111275i | ||||
\(541\) | 10.0000i | 0.429934i | 0.976621 | + | 0.214967i | \(0.0689643\pi\) | ||||
−0.976621 | + | 0.214967i | \(0.931036\pi\) | |||||||
\(542\) | 5.75736 | + | 9.97204i | 0.247300 | + | 0.428336i | ||||
\(543\) | 7.00000 | − | 12.1244i | 0.300399 | − | 0.520306i | ||||
\(544\) | −29.2708 | − | 16.8995i | −1.25497 | − | 0.724560i | ||||
\(545\) | 15.0294 | 0.643790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3137 | 0.996822 | 0.498411 | − | 0.866941i | \(-0.333917\pi\) | ||||
0.498411 | + | 0.866941i | \(0.333917\pi\) | |||||||
\(548\) | 17.1464 | + | 9.89949i | 0.732459 | + | 0.422885i | ||||
\(549\) | −6.65685 | + | 11.5300i | −0.284108 | + | 0.492089i | ||||
\(550\) | −1.24264 | − | 2.15232i | −0.0529864 | − | 0.0917751i | ||||
\(551\) | 5.65685i | 0.240990i | ||||||||
\(552\) | −5.49333 | + | 3.17157i | −0.233811 | + | 0.134991i | ||||
\(553\) | −27.7128 | + | 16.0000i | −1.17847 | + | 0.680389i | ||||
\(554\) | − | 0.828427i | − | 0.0351965i | ||||||
\(555\) | −10.8284 | − | 18.7554i | −0.459641 | − | 0.796122i | ||||
\(556\) | 6.68629 | − | 11.5810i | 0.283562 | − | 0.491144i | ||||
\(557\) | 6.75412 | + | 3.89949i | 0.286181 | + | 0.165227i | 0.636218 | − | 0.771509i | \(-0.280498\pi\) |
−0.350037 | + | 0.936736i | \(0.613831\pi\) | |||||||
\(558\) | 0.485281 | 0.0205436 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.0000 | −1.01419 | ||||||||
\(561\) | −13.2621 | − | 7.65685i | −0.559925 | − | 0.323273i | ||||
\(562\) | −4.38478 | + | 7.59466i | −0.184961 | + | 0.320361i | ||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | − | 21.3137i | − | 0.897469i | ||||||
\(565\) | −13.0159 | + | 7.51472i | −0.547582 | + | 0.316147i | ||||
\(566\) | 10.3923 | − | 6.00000i | 0.436821 | − | 0.252199i | ||||
\(567\) | 2.82843i | 0.118783i | ||||||||
\(568\) | 1.58579 | + | 2.74666i | 0.0665381 | + | 0.115247i | ||||
\(569\) | −21.4853 | + | 37.2136i | −0.900710 | + | 1.56008i | −0.0741351 | + | 0.997248i | \(0.523620\pi\) |
−0.826575 | + | 0.562827i | \(0.809714\pi\) | |||||||
\(570\) | −2.86976 | − | 1.65685i | −0.120201 | − | 0.0693980i | ||||
\(571\) | 12.9706 | 0.542801 | 0.271401 | − | 0.962466i | \(-0.412513\pi\) | ||||
0.271401 | + | 0.962466i | \(0.412513\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.31371 | 0.138432 | ||||||||
\(574\) | 5.24714 | + | 3.02944i | 0.219011 | + | 0.126446i | ||||
\(575\) | 6.00000 | − | 10.3923i | 0.250217 | − | 0.433389i | ||||
\(576\) | −2.08579 | − | 3.61269i | −0.0869078 | − | 0.150529i | ||||
\(577\) | 31.9411i | 1.32973i | 0.746965 | + | 0.664863i | \(0.231510\pi\) | ||||
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(578\) | −14.9326 | + | 8.62132i | −0.621113 | + | 0.358600i | ||||
\(579\) | 4.60181 | − | 2.65685i | 0.191245 | − | 0.110415i | ||||
\(580\) | 10.3431i | 0.429476i | ||||||||
\(581\) | −5.17157 | − | 8.95743i | −0.214553 | − | 0.371617i | ||||
\(582\) | 0.757359 | − | 1.31178i | 0.0313936 | − | 0.0543752i | ||||
\(583\) | −3.46410 | − | 2.00000i | −0.143468 | − | 0.0828315i | ||||
\(584\) | 0.544156 | 0.0225173 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.887302 | 0.0366541 | ||||||||
\(587\) | −9.50079 | − | 5.48528i | −0.392139 | − | 0.226402i | 0.290947 | − | 0.956739i | \(-0.406030\pi\) |
−0.683087 | + | 0.730337i | \(0.739363\pi\) | |||||||
\(588\) | 0.914214 | − | 1.58346i | 0.0377015 | − | 0.0653010i | ||||
\(589\) | 1.65685 | + | 2.86976i | 0.0682695 | + | 0.118246i | ||||
\(590\) | 8.97056i | 0.369312i | ||||||||
\(591\) | −0.420266 | + | 0.242641i | −0.0172874 | + | 0.00998090i | ||||
\(592\) | −19.8931 | + | 11.4853i | −0.817601 | + | 0.472042i | ||||
\(593\) | − | 20.4853i | − | 0.841230i | −0.907239 | − | 0.420615i | \(-0.861814\pi\) | ||
0.907239 | − | 0.420615i | \(-0.138186\pi\) | |||||||
\(594\) | 0.414214 | + | 0.717439i | 0.0169954 | + | 0.0294369i | ||||
\(595\) | −30.6274 | + | 53.0482i | −1.25560 | + | 2.17477i | ||||
\(596\) | −14.5229 | − | 8.38478i | −0.594879 | − | 0.343454i | ||||
\(597\) | −21.6569 | −0.886356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3137 | −0.952572 | −0.476286 | − | 0.879290i | \(-0.658017\pi\) | ||||
−0.476286 | + | 0.879290i | \(0.658017\pi\) | |||||||
\(600\) | −4.11999 | − | 2.37868i | −0.168198 | − | 0.0971092i | ||||
\(601\) | 0.313708 | − | 0.543359i | 0.0127964 | − | 0.0221641i | −0.859556 | − | 0.511041i | \(-0.829260\pi\) |
0.872353 | + | 0.488877i | \(0.162593\pi\) | |||||||
\(602\) | −0.970563 | − | 1.68106i | −0.0395572 | − | 0.0685151i | ||||
\(603\) | − | 6.82843i | − | 0.278075i | ||||||
\(604\) | −5.56543 | + | 3.21320i | −0.226454 | + | 0.130743i | ||||
\(605\) | 17.1464 | − | 9.89949i | 0.697101 | − | 0.402472i | ||||
\(606\) | 3.17157i | 0.128836i | ||||||||
\(607\) | −20.9706 | − | 36.3221i | −0.851169 | − | 1.47427i | −0.880154 | − | 0.474688i | \(-0.842561\pi\) |
0.0289853 | − | 0.999580i | \(-0.490772\pi\) | |||||||
\(608\) | −6.24264 | + | 10.8126i | −0.253173 | + | 0.438508i | ||||
\(609\) | −4.89898 | − | 2.82843i | −0.198517 | − | 0.114614i | ||||
\(610\) | 15.5980 | 0.631544 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | −41.2720 | − | 23.8284i | −1.66696 | − | 0.962421i | −0.969262 | − | 0.246031i | \(-0.920873\pi\) |
−0.697700 | − | 0.716390i | \(-0.745793\pi\) | |||||||
\(614\) | 4.72792 | − | 8.18900i | 0.190803 | − | 0.330481i | ||||
\(615\) | −7.31371 | − | 12.6677i | −0.294917 | − | 0.510812i | ||||
\(616\) | − | 8.97056i | − | 0.361434i | ||||||
\(617\) | 30.1623 | − | 17.4142i | 1.21429 | − | 0.701070i | 0.250598 | − | 0.968091i | \(-0.419373\pi\) |
0.963691 | + | 0.267021i | \(0.0860394\pi\) | |||||||
\(618\) | 0.840532 | − | 0.485281i | 0.0338112 | − | 0.0195209i | ||||
\(619\) | 23.7990i | 0.956562i | 0.878207 | + | 0.478281i | \(0.158740\pi\) | ||||
−0.878207 | + | 0.478281i | \(0.841260\pi\) | |||||||
\(620\) | 3.02944 | + | 5.24714i | 0.121665 | + | 0.210730i | ||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | 3.81226 | + | 2.20101i | 0.152858 | + | 0.0882525i | ||||
\(623\) | −41.9411 | −1.68034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 2.15232 | + | 1.24264i | 0.0860239 | + | 0.0496659i | ||||
\(627\) | −2.82843 | + | 4.89898i | −0.112956 | + | 0.195646i | ||||
\(628\) | 9.14214 | + | 15.8346i | 0.364811 | + | 0.631871i | ||||
\(629\) | 58.6274i | 2.33763i | ||||||||
\(630\) | 2.86976 | − | 1.65685i | 0.114334 | − | 0.0660107i | ||||
\(631\) | 37.3367 | − | 21.5563i | 1.48635 | − | 0.858145i | 0.486471 | − | 0.873697i | \(-0.338284\pi\) |
0.999879 | + | 0.0155519i | \(0.00495053\pi\) | |||||||
\(632\) | 17.9411i | 0.713660i | ||||||||
\(633\) | 6.00000 | + | 10.3923i | 0.238479 | + | 0.413057i | ||||
\(634\) | 1.75736 | − | 3.04384i | 0.0697937 | − | 0.120886i | ||||
\(635\) | 13.8564 | + | 8.00000i | 0.549875 | + | 0.317470i | ||||
\(636\) | −3.65685 | −0.145004 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.65685 | −0.0655955 | ||||||||
\(639\) | 1.73205 | + | 1.00000i | 0.0685189 | + | 0.0395594i | ||||
\(640\) | −14.9289 | + | 25.8577i | −0.590118 | + | 1.02211i | ||||
\(641\) | 15.1421 | + | 26.2269i | 0.598078 | + | 1.03590i | 0.993105 | + | 0.117232i | \(0.0374022\pi\) |
−0.395026 | + | 0.918670i | \(0.629264\pi\) | |||||||
\(642\) | 4.68629i | 0.184953i | ||||||||
\(643\) | −19.7700 | + | 11.4142i | −0.779653 | + | 0.450133i | −0.836307 | − | 0.548261i | \(-0.815290\pi\) |
0.0566545 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(644\) | 17.9149 | − | 10.3431i | 0.705944 | − | 0.407577i | ||||
\(645\) | 4.68629i | 0.184523i | ||||||||
\(646\) | 4.48528 | + | 7.76874i | 0.176471 | + | 0.305657i | ||||
\(647\) | 5.65685 | − | 9.79796i | 0.222394 | − | 0.385198i | −0.733140 | − | 0.680077i | \(-0.761946\pi\) |
0.955534 | + | 0.294880i | \(0.0952796\pi\) | |||||||
\(648\) | 1.37333 | + | 0.792893i | 0.0539496 | + | 0.0311478i | ||||
\(649\) | 15.3137 | 0.601116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.31371 | −0.129874 | ||||||||
\(652\) | −29.8141 | − | 17.2132i | −1.16761 | − | 0.674121i | ||||
\(653\) | 12.6569 | − | 21.9223i | 0.495301 | − | 0.857886i | −0.504684 | − | 0.863304i | \(-0.668391\pi\) |
0.999985 | + | 0.00541749i | \(0.00172445\pi\) | |||||||
\(654\) | 1.10051 | + | 1.90613i | 0.0430332 | + | 0.0745356i | ||||
\(655\) | − | 22.6274i | − | 0.884126i | ||||||
\(656\) | −13.4361 | + | 7.75736i | −0.524593 | + | 0.302874i | ||||
\(657\) | 0.297173 | − | 0.171573i | 0.0115938 | − | 0.00669370i | ||||
\(658\) | − | 13.6569i | − | 0.532400i | ||||||
\(659\) | 23.6569 | + | 40.9749i | 0.921540 | + | 1.59615i | 0.797033 | + | 0.603936i | \(0.206402\pi\) |
0.124507 | + | 0.992219i | \(0.460265\pi\) | |||||||
\(660\) | −5.17157 | + | 8.95743i | −0.201303 | + | 0.348667i | ||||
\(661\) | 30.2854 | + | 17.4853i | 1.17797 | + | 0.680099i | 0.955543 | − | 0.294852i | \(-0.0952703\pi\) |
0.222422 | + | 0.974950i | \(0.428604\pi\) | |||||||
\(662\) | −10.8284 | −0.420859 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.79899 | −0.225044 | ||||||||
\(665\) | 19.5959 | + | 11.3137i | 0.759897 | + | 0.438727i | ||||
\(666\) | 1.58579 | − | 2.74666i | 0.0614480 | − | 0.106431i | ||||
\(667\) | −4.00000 | − | 6.92820i | −0.154881 | − | 0.268261i | ||||
\(668\) | − | 6.68629i | − | 0.258700i | ||||||
\(669\) | 10.8126 | − | 6.24264i | 0.418038 | − | 0.241354i | ||||
\(670\) | −6.92820 | + | 4.00000i | −0.267660 | + | 0.154533i | ||||
\(671\) | − | 26.6274i | − | 1.02794i | ||||||
\(672\) | −6.24264 | − | 10.8126i | −0.240815 | − | 0.417104i | ||||
\(673\) | 8.31371 | − | 14.3998i | 0.320470 | − | 0.555070i | −0.660115 | − | 0.751164i | \(-0.729493\pi\) |
0.980585 | + | 0.196094i | \(0.0628259\pi\) | |||||||
\(674\) | −3.34101 | − | 1.92893i | −0.128691 | − | 0.0742997i | ||||
\(675\) | −3.00000 | −0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.6863 | 1.02564 | 0.512819 | − | 0.858497i | \(-0.328601\pi\) | ||||
0.512819 | + | 0.858497i | \(0.328601\pi\) | |||||||
\(678\) | −1.90613 | − | 1.10051i | −0.0732045 | − | 0.0422646i | ||||
\(679\) | −5.17157 | + | 8.95743i | −0.198467 | + | 0.343754i | ||||
\(680\) | 17.1716 | + | 29.7420i | 0.658500 | + | 1.14056i | ||||
\(681\) | 17.3137i | 0.663463i | ||||||||
\(682\) | −0.840532 | + | 0.485281i | −0.0321856 | + | 0.0185824i | ||||
\(683\) | 41.5182 | − | 23.9706i | 1.58865 | − | 0.917208i | 0.595121 | − | 0.803636i | \(-0.297104\pi\) |
0.993530 | − | 0.113572i | \(-0.0362293\pi\) | |||||||
\(684\) | 5.17157i | 0.197740i | ||||||||
\(685\) | −15.3137 | − | 26.5241i | −0.585107 | − | 1.01343i | ||||
\(686\) | −3.51472 | + | 6.08767i | −0.134193 | + | 0.232428i | ||||
\(687\) | 1.13770 | + | 0.656854i | 0.0434062 | + | 0.0250606i | ||||
\(688\) | 4.97056 | 0.189501 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.68629 | 0.178404 | ||||||||
\(691\) | −5.07306 | − | 2.92893i | −0.192988 | − | 0.111422i | 0.400392 | − | 0.916344i | \(-0.368874\pi\) |
−0.593381 | + | 0.804922i | \(0.702207\pi\) | |||||||
\(692\) | −10.6569 | + | 18.4582i | −0.405113 | + | 0.701676i | ||||
\(693\) | −2.82843 | − | 4.89898i | −0.107443 | − | 0.186097i | ||||
\(694\) | 3.59798i | 0.136577i | ||||||||
\(695\) | −17.9149 | + | 10.3431i | −0.679549 | + | 0.392338i | ||||
\(696\) | −2.74666 | + | 1.58579i | −0.104112 | + | 0.0601091i | ||||
\(697\) | 39.5980i | 1.49988i | ||||||||
\(698\) | −0.757359 | − | 1.31178i | −0.0286665 | − | 0.0496518i | ||||
\(699\) | 3.48528 | − | 6.03668i | 0.131825 | − | 0.228328i | ||||
\(700\) | 13.4361 | + | 7.75736i | 0.507838 | + | 0.293201i | ||||
\(701\) | −5.02944 | −0.189959 | −0.0949796 | − | 0.995479i | \(-0.530279\pi\) | ||||
−0.0949796 | + | 0.995479i | \(0.530279\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.6569 | 0.816804 | ||||||||
\(704\) | 7.22538 | + | 4.17157i | 0.272317 | + | 0.157222i | ||||
\(705\) | −16.4853 | + | 28.5533i | −0.620872 | + | 1.07538i | ||||
\(706\) | −6.92893 | − | 12.0013i | −0.260774 | − | 0.451673i | ||||
\(707\) | − | 21.6569i | − | 0.814490i | ||||||
\(708\) | 12.1244 | − | 7.00000i | 0.455661 | − | 0.263076i | ||||
\(709\) | −4.00746 | + | 2.31371i | −0.150503 | + | 0.0868931i | −0.573360 | − | 0.819303i | \(-0.694361\pi\) |
0.422857 | + | 0.906196i | \(0.361027\pi\) | |||||||
\(710\) | − | 2.34315i | − | 0.0879367i | ||||||
\(711\) | 5.65685 | + | 9.79796i | 0.212149 | + | 0.367452i | ||||
\(712\) | −11.7574 | + | 20.3643i | −0.440626 | + | 0.763186i | ||||
\(713\) | −4.05845 | − | 2.34315i | −0.151990 | − | 0.0877515i | ||||
\(714\) | −8.97056 | −0.335715 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.6274 | 1.59306 | ||||||||
\(717\) | 1.73205 | + | 1.00000i | 0.0646846 | + | 0.0373457i | ||||
\(718\) | −7.24264 | + | 12.5446i | −0.270293 | + | 0.468161i | ||||
\(719\) | −14.9706 | − | 25.9298i | −0.558308 | − | 0.967017i | −0.997638 | − | 0.0686918i | \(-0.978117\pi\) |
0.439330 | − | 0.898326i | \(-0.355216\pi\) | |||||||
\(720\) | 8.48528i | 0.316228i | ||||||||
\(721\) | −5.73951 | + | 3.31371i | −0.213751 | + | 0.123409i | ||||
\(722\) | −3.94591 | + | 2.27817i | −0.146852 | + | 0.0847849i | ||||
\(723\) | 0.343146i | 0.0127617i | ||||||||
\(724\) | 12.7990 | + | 22.1685i | 0.475671 | + | 0.823886i | ||||
\(725\) | 3.00000 | − | 5.19615i | 0.111417 | − | 0.192980i | ||||
\(726\) | 2.51104 | + | 1.44975i | 0.0931933 | + | 0.0538052i | ||||
\(727\) | 10.3431 | 0.383606 | 0.191803 | − | 0.981433i | \(-0.438567\pi\) | ||||
0.191803 | + | 0.981433i | \(0.438567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.348160 | − | 0.201010i | −0.0128860 | − | 0.00743972i | ||||
\(731\) | 6.34315 | − | 10.9867i | 0.234610 | − | 0.406356i | ||||
\(732\) | −12.1716 | − | 21.0818i | −0.449874 | − | 0.779205i | ||||
\(733\) | 36.6274i | 1.35286i | 0.736505 | + | 0.676432i | \(0.236475\pi\) | ||||
−0.736505 | + | 0.676432i | \(0.763525\pi\) | |||||||
\(734\) | 8.60927 | − | 4.97056i | 0.317774 | − | 0.183467i | ||||
\(735\) | −2.44949 | + | 1.41421i | −0.0903508 | + | 0.0521641i | ||||
\(736\) | − | 17.6569i | − | 0.650840i | ||||||
\(737\) | 6.82843 | + | 11.8272i | 0.251528 | + | 0.435660i | ||||
\(738\) | 1.07107 | − | 1.85514i | 0.0394266 | − | 0.0682888i | ||||
\(739\) | 15.7116 | + | 9.07107i | 0.577959 | + | 0.333685i | 0.760322 | − | 0.649547i | \(-0.225041\pi\) |
−0.182363 | + | 0.983231i | \(0.558375\pi\) | |||||||
\(740\) | 39.5980 | 1.45565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.34315 | −0.0860196 | ||||||||
\(743\) | 1.73205 | + | 1.00000i | 0.0635428 | + | 0.0366864i | 0.531435 | − | 0.847099i | \(-0.321653\pi\) |
−0.467892 | + | 0.883786i | \(0.654986\pi\) | |||||||
\(744\) | −0.928932 | + | 1.60896i | −0.0340563 | + | 0.0589873i | ||||
\(745\) | 12.9706 | + | 22.4657i | 0.475205 | + | 0.823079i | ||||
\(746\) | − | 4.14214i | − | 0.151654i | ||||||
\(747\) | −3.16693 | + | 1.82843i | −0.115872 | + | 0.0668987i | ||||
\(748\) | 24.2487 | − | 14.0000i | 0.886621 | − | 0.511891i | ||||
\(749\) | − | 32.0000i | − | 1.16925i | ||||||
\(750\) | −1.17157 | − | 2.02922i | −0.0427798 | − | 0.0740968i | ||||
\(751\) | −0.485281 | + | 0.840532i | −0.0177082 | + | 0.0306714i | −0.874744 | − | 0.484586i | \(-0.838970\pi\) |
0.857036 | + | 0.515257i | \(0.172304\pi\) | |||||||
\(752\) | 30.2854 | + | 17.4853i | 1.10439 | + | 0.637623i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.94113 | 0.361795 | ||||||||
\(756\) | −4.47871 | − | 2.58579i | −0.162889 | − | 0.0940441i | ||||
\(757\) | −25.9706 | + | 44.9823i | −0.943916 | + | 1.63491i | −0.186009 | + | 0.982548i | \(0.559555\pi\) |
−0.757907 | + | 0.652363i | \(0.773778\pi\) | |||||||
\(758\) | 0.100505 | + | 0.174080i | 0.00365051 | + | 0.00632287i | ||||
\(759\) | − | 8.00000i | − | 0.290382i | ||||||
\(760\) | 10.9867 | − | 6.34315i | 0.398528 | − | 0.230090i | ||||
\(761\) | 28.1331 | − | 16.2426i | 1.01982 | − | 0.588795i | 0.105771 | − | 0.994391i | \(-0.466269\pi\) |
0.914053 | + | 0.405595i | \(0.132936\pi\) | |||||||
\(762\) | 2.34315i | 0.0848832i | ||||||||
\(763\) | −7.51472 | − | 13.0159i | −0.272051 | − | 0.471206i | ||||
\(764\) | −3.02944 | + | 5.24714i | −0.109601 | + | 0.189835i | ||||
\(765\) | 18.7554 | + | 10.8284i | 0.678102 | + | 0.391503i | ||||
\(766\) | −12.8284 | −0.463510 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.97056 | 0.143275 | ||||||||
\(769\) | 36.3731 | + | 21.0000i | 1.31165 | + | 0.757279i | 0.982369 | − | 0.186954i | \(-0.0598615\pi\) |
0.329278 | + | 0.944233i | \(0.393195\pi\) | |||||||
\(770\) | −3.31371 | + | 5.73951i | −0.119418 | + | 0.206838i | ||||
\(771\) | −2.17157 | − | 3.76127i | −0.0782073 | − | 0.135459i | ||||
\(772\) | 9.71573i | 0.349677i | ||||||||
\(773\) | −29.5680 | + | 17.0711i | −1.06349 | + | 0.614004i | −0.926394 | − | 0.376555i | \(-0.877109\pi\) |
−0.137091 | + | 0.990558i | \(0.543775\pi\) | |||||||
\(774\) | −0.594346 | + | 0.343146i | −0.0213633 | + | 0.0123341i | ||||
\(775\) | − | 3.51472i | − | 0.126252i | ||||||
\(776\) | 2.89949 | + | 5.02207i | 0.104086 | + | 0.180282i | ||||
\(777\) | −10.8284 | + | 18.7554i | −0.388468 | + | 0.672846i | ||||
\(778\) | 9.67487 | + | 5.58579i | 0.346861 | + | 0.200260i | ||||
\(779\) | 14.6274 | 0.524082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | −10.9867 | − | 6.34315i | −0.392882 | − | 0.226830i | ||||
\(783\) | −1.00000 | + | 1.73205i | −0.0357371 | + | 0.0618984i | ||||
\(784\) | 1.50000 | + | 2.59808i | 0.0535714 | + | 0.0927884i | ||||
\(785\) | − | 28.2843i | − | 1.00951i | ||||||
\(786\) | 2.86976 | − | 1.65685i | 0.102361 | − | 0.0590980i | ||||
\(787\) | −35.3075 | + | 20.3848i | −1.25858 | + | 0.726639i | −0.972798 | − | 0.231657i | \(-0.925585\pi\) |
−0.285778 | + | 0.958296i | \(0.592252\pi\) | |||||||
\(788\) | − | 0.887302i | − | 0.0316088i | ||||||
\(789\) | −6.00000 | − | 10.3923i | −0.213606 | − | 0.369976i | ||||
\(790\) | 6.62742 | − | 11.4790i | 0.235793 | − | 0.408405i | ||||
\(791\) | 13.0159 | + | 7.51472i | 0.462791 | + | 0.267193i | ||||
\(792\) | −3.17157 | −0.112697 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.8284 | 0.455264 | ||||||||
\(795\) | 4.89898 | + | 2.82843i | 0.173749 | + | 0.100314i | ||||
\(796\) | 19.7990 | − | 34.2929i | 0.701757 | − | 1.21548i | ||||
\(797\) | 12.1716 | + | 21.0818i | 0.431139 | + | 0.746755i | 0.996972 | − | 0.0777652i | \(-0.0247784\pi\) |
−0.565832 | + | 0.824520i | \(0.691445\pi\) | |||||||
\(798\) | 3.31371i | 0.117304i | ||||||||
\(799\) | 77.2970 | − | 44.6274i | 2.73457 | − | 1.57880i | ||||
\(800\) | 11.4685 | − | 6.62132i | 0.405471 | − | 0.234099i | ||||
\(801\) | 14.8284i | 0.523937i | ||||||||
\(802\) | −5.41421 | − | 9.37769i | −0.191183 | − | 0.331138i | ||||
\(803\) | −0.343146 | + | 0.594346i | −0.0121094 | + | 0.0209740i | ||||
\(804\) | 10.8126 | + | 6.24264i | 0.381330 | + | 0.220161i | ||||
\(805\) | −32.0000 | −1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −10.5154 | − | 6.07107i | −0.369930 | − | 0.213579i | ||||
\(809\) | −9.34315 | + | 16.1828i | −0.328488 | + | 0.568957i | −0.982212 | − | 0.187776i | \(-0.939872\pi\) |
0.653724 | + | 0.756733i | \(0.273206\pi\) | |||||||
\(810\) | −0.585786 | − | 1.01461i | −0.0205824 | − | 0.0356498i | ||||
\(811\) | 30.1421i | 1.05843i | 0.848487 | + | 0.529217i | \(0.177514\pi\) | ||||
−0.848487 | + | 0.529217i | \(0.822486\pi\) | |||||||
\(812\) | 8.95743 | − | 5.17157i | 0.314344 | − | 0.181487i | ||||
\(813\) | −24.0746 | + | 13.8995i | −0.844334 | + | 0.487477i | ||||
\(814\) | 6.34315i | 0.222327i | ||||||||
\(815\) | 26.6274 | + | 46.1200i | 0.932718 | + | 1.61551i | ||||
\(816\) | 11.4853 | − | 19.8931i | 0.402065 | − | 0.696397i | ||||
\(817\) | −4.05845 | − | 2.34315i | −0.141987 | − | 0.0819763i | ||||
\(818\) | 14.4853 | 0.506466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.7452 | 0.933982 | ||||||||
\(821\) | −20.6105 | − | 11.8995i | −0.719312 | − | 0.415295i | 0.0951871 | − | 0.995459i | \(-0.469655\pi\) |
−0.814500 | + | 0.580164i | \(0.802988\pi\) | |||||||
\(822\) | 2.24264 | − | 3.88437i | 0.0782211 | − | 0.135483i | ||||
\(823\) | 7.51472 | + | 13.0159i | 0.261947 | + | 0.453705i | 0.966759 | − | 0.255689i | \(-0.0823022\pi\) |
−0.704813 | + | 0.709394i | \(0.748969\pi\) | |||||||
\(824\) | 3.71573i | 0.129444i | ||||||||
\(825\) | 5.19615 | − | 3.00000i | 0.180907 | − | 0.104447i | ||||
\(826\) | 7.76874 | − | 4.48528i | 0.270309 | − | 0.156063i | ||||
\(827\) | − | 26.0000i | − | 0.904109i | −0.891990 | − | 0.452054i | \(-0.850691\pi\) | ||
0.891990 | − | 0.452054i | \(-0.149309\pi\) | |||||||
\(828\) | −3.65685 | − | 6.33386i | −0.127084 | − | 0.220117i | ||||
\(829\) | −8.65685 | + | 14.9941i | −0.300665 | + | 0.520767i | −0.976287 | − | 0.216481i | \(-0.930542\pi\) |
0.675622 | + | 0.737248i | \(0.263875\pi\) | |||||||
\(830\) | 3.71029 | + | 2.14214i | 0.128786 | + | 0.0743546i | ||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65685 | 0.265294 | ||||||||
\(834\) | −2.62357 | − | 1.51472i | −0.0908468 | − | 0.0524504i | ||||
\(835\) | −5.17157 | + | 8.95743i | −0.178970 | + | 0.309985i | ||||
\(836\) | −5.17157 | − | 8.95743i | −0.178863 | − | 0.309799i | ||||
\(837\) | 1.17157i | 0.0404955i | ||||||||
\(838\) | −5.24714 | + | 3.02944i | −0.181259 | + | 0.104650i | ||||
\(839\) | 37.4598 | − | 21.6274i | 1.29326 | − | 0.746661i | 0.314026 | − | 0.949415i | \(-0.398322\pi\) |
0.979230 | + | 0.202753i | \(0.0649889\pi\) | |||||||
\(840\) | 12.6863i | 0.437719i | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | 7.72792 | − | 13.3852i | 0.266322 | − | 0.461283i | ||||
\(843\) | −18.3351 | − | 10.5858i | −0.631495 | − | 0.364594i | ||||
\(844\) | −21.9411 | −0.755245 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.82843 | −0.166005 | ||||||||
\(847\) | −17.1464 | − | 9.89949i | −0.589158 | − | 0.340151i | ||||
\(848\) | 3.00000 | − | 5.19615i | 0.103020 | − | 0.178437i | ||||
\(849\) | 14.4853 | + | 25.0892i | 0.497134 | + | 0.861061i | ||||
\(850\) | − | 9.51472i | − | 0.326352i | ||||||
\(851\) | −26.5241 | + | 15.3137i | −0.909235 | + | 0.524947i | ||||
\(852\) | −3.16693 | + | 1.82843i | −0.108497 | + | 0.0626409i | ||||
\(853\) | 3.65685i | 0.125208i | 0.998038 | + | 0.0626042i | \(0.0199406\pi\) | ||||
−0.998038 | + | 0.0626042i | \(0.980059\pi\) | |||||||
\(854\) | −7.79899 | − | 13.5082i | −0.266876 | − | 0.462243i | ||||
\(855\) | 4.00000 | − | 6.92820i | 0.136797 | − | 0.236940i | ||||
\(856\) | −15.5375 | − | 8.97056i | −0.531060 | − | 0.306608i | ||||
\(857\) | 49.5980 | 1.69423 | 0.847117 | − | 0.531406i | \(-0.178336\pi\) | ||||
0.847117 | + | 0.531406i | \(0.178336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.686292 | −0.0234160 | −0.0117080 | − | 0.999931i | \(-0.503727\pi\) | ||||
−0.0117080 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(860\) | −7.42058 | − | 4.28427i | −0.253040 | − | 0.146092i | ||||
\(861\) | −7.31371 | + | 12.6677i | −0.249251 | + | 0.431715i | ||||
\(862\) | 1.72792 | + | 2.99285i | 0.0588533 | + | 0.101937i | ||||
\(863\) | 28.3431i | 0.964812i | 0.875948 | + | 0.482406i | \(0.160237\pi\) | ||||
−0.875948 | + | 0.482406i | \(0.839763\pi\) | |||||||
\(864\) | −3.82282 | + | 2.20711i | −0.130055 | + | 0.0750873i | ||||
\(865\) | 28.5533 | − | 16.4853i | 0.970843 | − | 0.560516i | ||||
\(866\) | − | 8.82843i | − | 0.300002i | ||||||
\(867\) | −20.8137 | − | 36.0504i | −0.706871 | − | 1.22434i | ||||
\(868\) | 3.02944 | − | 5.24714i | 0.102826 | − | 0.178100i | ||||
\(869\) | −19.5959 | − | 11.3137i | −0.664746 | − | 0.383791i | ||||
\(870\) | 2.34315 | 0.0794401 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.42641 | −0.285354 | ||||||||
\(873\) | 3.16693 | + | 1.82843i | 0.107184 | + | 0.0618829i | ||||
\(874\) | −2.34315 | + | 4.05845i | −0.0792581 | + | 0.137279i | ||||
\(875\) | 8.00000 | + | 13.8564i | 0.270449 | + | 0.468432i | ||||
\(876\) | 0.627417i | 0.0211985i | ||||||||
\(877\) | −36.6193 | + | 21.1421i | −1.23654 | + | 0.713919i | −0.968386 | − | 0.249456i | \(-0.919748\pi\) |
−0.268158 | + | 0.963375i | \(0.586415\pi\) | |||||||
\(878\) | 6.08767 | − | 3.51472i | 0.205449 | − | 0.118616i | ||||
\(879\) | 2.14214i | 0.0722524i | ||||||||
\(880\) | −8.48528 | − | 14.6969i | −0.286039 | − | 0.495434i | ||||
\(881\) | −12.7990 | + | 22.1685i | −0.431209 | + | 0.746876i | −0.996978 | − | 0.0776882i | \(-0.975246\pi\) |
0.565769 | + | 0.824564i | \(0.308579\pi\) | |||||||
\(882\) | −0.358719 | − | 0.207107i | −0.0120787 | − | 0.00697365i | ||||
\(883\) | −27.5980 | −0.928746 | −0.464373 | − | 0.885640i | \(-0.653720\pi\) | ||||
−0.464373 | + | 0.885640i | \(0.653720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.6569 | −0.727987 | ||||||||
\(886\) | −9.30559 | − | 5.37258i | −0.312627 | − | 0.180495i | ||||
\(887\) | 4.00000 | − | 6.92820i | 0.134307 | − | 0.232626i | −0.791026 | − | 0.611783i | \(-0.790453\pi\) |
0.925332 | + | 0.379157i | \(0.123786\pi\) | |||||||
\(888\) | 6.07107 | + | 10.5154i | 0.203732 | + | 0.352874i | ||||
\(889\) | − | 16.0000i | − | 0.536623i | ||||||
\(890\) | 15.0451 | − | 8.68629i | 0.504313 | − | 0.291165i | ||||
\(891\) | −1.73205 | + | 1.00000i | −0.0580259 | + | 0.0335013i | ||||
\(892\) | 22.8284i | 0.764352i | ||||||||
\(893\) | −16.4853 | − | 28.5533i | −0.551659 | − | 0.955501i | ||||
\(894\) | −1.89949 | + | 3.29002i | −0.0635286 | + | 0.110035i | ||||
\(895\) | −57.1067 | − | 32.9706i | −1.90887 | − | 1.10208i | ||||
\(896\) | 29.8579 | 0.997481 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.1716 | −0.439541 | ||||||||
\(899\) | −2.02922 | − | 1.17157i | −0.0676784 | − | 0.0390741i | ||||
\(900\) | 2.74264 | − | 4.75039i | 0.0914214 | − | 0.158346i | ||||
\(901\) | −7.65685 | − | 13.2621i | −0.255087 | − | 0.441823i | ||||
\(902\) | 4.28427i | 0.142651i | ||||||||
\(903\) | 4.05845 | − | 2.34315i | 0.135057 | − | 0.0779750i | ||||
\(904\) | 7.29748 | − | 4.21320i | 0.242711 | − | 0.140129i | ||||
\(905\) | − | 39.5980i | − | 1.31628i | ||||||
\(906\) | 0.727922 | + | 1.26080i | 0.0241836 | + | 0.0418872i | ||||
\(907\) | −6.48528 | + | 11.2328i | −0.215340 | + | 0.372980i | −0.953378 | − | 0.301779i | \(-0.902419\pi\) |
0.738038 | + | 0.674760i | \(0.235753\pi\) | |||||||
\(908\) | −27.4156 | − | 15.8284i | −0.909820 | − | 0.525285i | ||||
\(909\) | −7.65685 | −0.253962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | −7.34847 | − | 4.24264i | −0.243332 | − | 0.140488i | ||||
\(913\) | 3.65685 | − | 6.33386i | 0.121024 | − | 0.209620i | ||||
\(914\) | −1.58579 | − | 2.74666i | −0.0524532 | − | 0.0908515i | ||||
\(915\) | 37.6569i | 1.24490i | ||||||||
\(916\) | −2.08021 | + | 1.20101i | −0.0687321 | + | 0.0396825i | ||||
\(917\) | −19.5959 | + | 11.3137i | −0.647114 | + | 0.373612i | ||||
\(918\) | 3.17157i | 0.104678i | ||||||||
\(919\) | −1.65685 | − | 2.86976i | −0.0546546 | − | 0.0946645i | 0.837404 | − | 0.546585i | \(-0.184072\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(920\) | −8.97056 | + | 15.5375i | −0.295751 | + | 0.512255i | ||||
\(921\) | 19.7700 | + | 11.4142i | 0.651444 | + | 0.376111i | ||||
\(922\) | −2.14214 | −0.0705475 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 10.3431 | 0.340265 | ||||||||
\(925\) | −19.8931 | − | 11.4853i | −0.654081 | − | 0.377634i | ||||
\(926\) | 5.07107 | − | 8.78335i | 0.166646 | − | 0.288639i | ||||
\(927\) | 1.17157 | + | 2.02922i | 0.0384795 | + | 0.0666485i | ||||
\(928\) | − | 8.82843i | − | 0.289807i | ||||||
\(929\) | −10.2182 | + | 5.89949i | −0.335249 | + | 0.193556i | −0.658169 | − | 0.752870i | \(-0.728669\pi\) |
0.322920 | + | 0.946426i | \(0.395336\pi\) | |||||||
\(930\) | 1.18869 | − | 0.686292i | 0.0389787 | − | 0.0225044i | ||||
\(931\) | − | 2.82843i | − | 0.0926980i | ||||||
\(932\) | 6.37258 | + | 11.0376i | 0.208741 | + | 0.361550i | ||||
\(933\) | −5.31371 | + | 9.20361i | −0.173963 | + | 0.301313i | ||||
\(934\) | 2.86976 | + | 1.65685i | 0.0939013 | + | 0.0542139i | ||||
\(935\) | −43.3137 | −1.41651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.3137 | −0.696289 | −0.348144 | − | 0.937441i | \(-0.613188\pi\) | ||||
−0.348144 | + | 0.937441i | \(0.613188\pi\) | |||||||
\(938\) | 6.92820 | + | 4.00000i | 0.226214 | + | 0.130605i | ||||
\(939\) | −3.00000 | + | 5.19615i | −0.0979013 | + | 0.169570i | ||||
\(940\) | −30.1421 | − | 52.2077i | −0.983128 | − | 1.70283i | ||||
\(941\) | − | 34.1421i | − | 1.11300i | −0.830847 | − | 0.556501i | \(-0.812144\pi\) | ||
0.830847 | − | 0.556501i | \(-0.187856\pi\) | |||||||
\(942\) | 3.58719 | − | 2.07107i | 0.116877 | − | 0.0674790i | ||||
\(943\) | −17.9149 | + | 10.3431i | −0.583388 | + | 0.336819i | ||||
\(944\) | 22.9706i | 0.747628i | ||||||||
\(945\) | 4.00000 | + | 6.92820i | 0.130120 | + | 0.225374i | ||||
\(946\) | 0.686292 | − | 1.18869i | 0.0223133 | − | 0.0386477i | ||||
\(947\) | 18.2120 | + | 10.5147i | 0.591811 | + | 0.341682i | 0.765813 | − | 0.643063i | \(-0.222337\pi\) |
−0.174002 | + | 0.984745i | \(0.555670\pi\) | |||||||
\(948\) | −20.6863 | −0.671860 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.51472 | −0.114033 | ||||||||
\(951\) | 7.34847 | + | 4.24264i | 0.238290 | + | 0.137577i | ||||
\(952\) | 17.1716 | − | 29.7420i | 0.556534 | − | 0.963945i | ||||
\(953\) | 20.1716 | + | 34.9382i | 0.653421 | + | 1.13176i | 0.982287 | + | 0.187382i | \(0.0600003\pi\) |
−0.328866 | + | 0.944377i | \(0.606666\pi\) | |||||||
\(954\) | 0.828427i | 0.0268213i | ||||||||
\(955\) | 8.11689 | − | 4.68629i | 0.262657 | − | 0.151645i | ||||
\(956\) | −3.16693 | + | 1.82843i | −0.102426 | + | 0.0591356i | ||||
\(957\) | − | 4.00000i | − | 0.129302i | ||||||
\(958\) | −5.24264 | − | 9.08052i | −0.169382 | − | 0.293378i | ||||
\(959\) | −15.3137 | + | 26.5241i | −0.494505 | + | 0.856509i | ||||
\(960\) | −10.2182 | − | 5.89949i | −0.329792 | − | 0.190405i | ||||
\(961\) | 29.6274 | 0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.3137 | −0.364579 | ||||||||
\(964\) | −0.543359 | − | 0.313708i | −0.0175004 | − | 0.0101039i | ||||
\(965\) | 7.51472 | − | 13.0159i | 0.241907 | − | 0.418996i | ||||
\(966\) | −2.34315 | − | 4.05845i | −0.0753895 | − | 0.130578i | ||||
\(967\) | − | 18.1421i | − | 0.583412i | −0.956508 | − | 0.291706i | \(-0.905777\pi\) | ||
0.956508 | − | 0.291706i | \(-0.0942228\pi\) | |||||||
\(968\) | −9.61332 | + | 5.55025i | −0.308984 | + | 0.178392i | ||||
\(969\) | −18.7554 | + | 10.8284i | −0.602510 | + | 0.347859i | ||||
\(970\) | − | 4.28427i | − | 0.137560i | ||||||
\(971\) | 7.65685 | + | 13.2621i | 0.245720 | + | 0.425600i | 0.962334 | − | 0.271871i | \(-0.0876422\pi\) |
−0.716614 | + | 0.697470i | \(0.754309\pi\) | |||||||
\(972\) | −0.914214 | + | 1.58346i | −0.0293234 | + | 0.0507896i | ||||
\(973\) | 17.9149 | + | 10.3431i | 0.574324 | + | 0.331586i | ||||
\(974\) | 3.23045 | 0.103510 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.9411 | 1.27848 | ||||||||
\(977\) | 36.4962 | + | 21.0711i | 1.16762 | + | 0.674123i | 0.953117 | − | 0.302601i | \(-0.0978550\pi\) |
0.214498 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(978\) | −3.89949 | + | 6.75412i | −0.124692 | + | 0.215973i | ||||
\(979\) | −14.8284 | − | 25.6836i | −0.473919 | − | 0.820851i | ||||
\(980\) | − | 5.17157i | − | 0.165200i | ||||||
\(981\) | −4.60181 | + | 2.65685i | −0.146924 | + | 0.0848268i | ||||
\(982\) | 10.9867 | − | 6.34315i | 0.350598 | − | 0.202418i | ||||
\(983\) | 25.3137i | 0.807382i | 0.914895 | + | 0.403691i | \(0.132273\pi\) | ||||
−0.914895 | + | 0.403691i | \(0.867727\pi\) | |||||||
\(984\) | 4.10051 | + | 7.10228i | 0.130719 | + | 0.226413i | ||||
\(985\) | −0.686292 | + | 1.18869i | −0.0218671 | + | 0.0378749i | ||||
\(986\) | −5.49333 | − | 3.17157i | −0.174943 | − | 0.101003i | ||||
\(987\) | 32.9706 | 1.04946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.62742 | 0.210740 | ||||||||
\(990\) | 2.02922 | + | 1.17157i | 0.0644930 | + | 0.0372350i | ||||
\(991\) | −2.34315 | + | 4.05845i | −0.0744325 | + | 0.128921i | −0.900839 | − | 0.434153i | \(-0.857048\pi\) |
0.826407 | + | 0.563073i | \(0.190381\pi\) | |||||||
\(992\) | −2.58579 | − | 4.47871i | −0.0820988 | − | 0.142199i | ||||
\(993\) | − | 26.1421i | − | 0.829596i | ||||||
\(994\) | −2.02922 | + | 1.17157i | −0.0643631 | + | 0.0371600i | ||||
\(995\) | −53.0482 | + | 30.6274i | −1.68174 | + | 0.970954i | ||||
\(996\) | − | 6.68629i | − | 0.211863i | ||||||
\(997\) | 19.6274 | + | 33.9957i | 0.621607 | + | 1.07665i | 0.989187 | + | 0.146662i | \(0.0468530\pi\) |
−0.367580 | + | 0.929992i | \(0.619814\pi\) | |||||||
\(998\) | 5.41421 | − | 9.37769i | 0.171384 | − | 0.296846i | ||||
\(999\) | 6.63103 | + | 3.82843i | 0.209797 | + | 0.121126i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))