Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(22,507)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 484.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.484 |
Dual form | 507.2.e.h.22.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.207107 | − | 0.358719i | −0.146447 | − | 0.253653i | 0.783465 | − | 0.621436i | \(-0.213450\pi\) |
−0.929912 | + | 0.367783i | \(0.880117\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.914214 | − | 1.58346i | 0.457107 | − | 0.791732i | ||||
\(5\) | −2.82843 | −1.26491 | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | −0.207107 | + | 0.358719i | −0.0845510 | + | 0.146447i | ||||
\(7\) | −1.41421 | + | 2.44949i | −0.534522 | + | 0.925820i | 0.464664 | + | 0.885487i | \(0.346175\pi\) |
−0.999186 | + | 0.0403329i | \(0.987158\pi\) | |||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0.585786 | + | 1.01461i | 0.185242 | + | 0.320848i | ||||
\(11\) | 1.00000 | + | 1.73205i | 0.301511 | + | 0.522233i | 0.976478 | − | 0.215615i | \(-0.0691756\pi\) |
−0.674967 | + | 0.737848i | \(0.735842\pi\) | |||||||
\(12\) | −1.82843 | −0.527821 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.17157 | 0.313116 | ||||||||
\(15\) | 1.41421 | + | 2.44949i | 0.365148 | + | 0.632456i | ||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −3.82843 | + | 6.63103i | −0.928530 | + | 1.60826i | −0.142747 | + | 0.989759i | \(0.545593\pi\) |
−0.785783 | + | 0.618502i | \(0.787740\pi\) | |||||||
\(18\) | 0.414214 | 0.0976311 | ||||||||
\(19\) | 1.41421 | − | 2.44949i | 0.324443 | − | 0.561951i | −0.656957 | − | 0.753928i | \(-0.728157\pi\) |
0.981399 | + | 0.191977i | \(0.0614899\pi\) | |||||||
\(20\) | −2.58579 | + | 4.47871i | −0.578199 | + | 1.00147i | ||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0.414214 | − | 0.717439i | 0.0883106 | − | 0.152958i | ||||
\(23\) | 2.00000 | + | 3.46410i | 0.417029 | + | 0.722315i | 0.995639 | − | 0.0932891i | \(-0.0297381\pi\) |
−0.578610 | + | 0.815604i | \(0.696405\pi\) | |||||||
\(24\) | 0.792893 | + | 1.37333i | 0.161849 | + | 0.280330i | ||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.58579 | + | 4.47871i | 0.488668 | + | 0.846397i | ||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 0.585786 | − | 1.01461i | 0.106949 | − | 0.185242i | ||||
\(31\) | −1.17157 | −0.210421 | −0.105210 | − | 0.994450i | \(-0.533552\pi\) | ||||
−0.105210 | + | 0.994450i | \(0.533552\pi\) | |||||||
\(32\) | −2.20711 | + | 3.82282i | −0.390165 | + | 0.675786i | ||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 3.17157 | 0.543920 | ||||||||
\(35\) | 4.00000 | − | 6.92820i | 0.676123 | − | 1.17108i | ||||
\(36\) | 0.914214 | + | 1.58346i | 0.152369 | + | 0.263911i | ||||
\(37\) | 3.82843 | + | 6.63103i | 0.629390 | + | 1.09013i | 0.987674 | + | 0.156522i | \(0.0500283\pi\) |
−0.358285 | + | 0.933612i | \(0.616638\pi\) | |||||||
\(38\) | −1.17157 | −0.190054 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.48528 | 0.709185 | ||||||||
\(41\) | −2.58579 | − | 4.47871i | −0.403832 | − | 0.699458i | 0.590353 | − | 0.807145i | \(-0.298989\pi\) |
−0.994185 | + | 0.107688i | \(0.965655\pi\) | |||||||
\(42\) | −0.585786 | − | 1.01461i | −0.0903888 | − | 0.156558i | ||||
\(43\) | 0.828427 | − | 1.43488i | 0.126334 | − | 0.218817i | −0.795920 | − | 0.605402i | \(-0.793012\pi\) |
0.922254 | + | 0.386585i | \(0.126346\pi\) | |||||||
\(44\) | 3.65685 | 0.551292 | ||||||||
\(45\) | 1.41421 | − | 2.44949i | 0.210819 | − | 0.365148i | ||||
\(46\) | 0.828427 | − | 1.43488i | 0.122145 | − | 0.211561i | ||||
\(47\) | −11.6569 | −1.70033 | −0.850163 | − | 0.526519i | \(-0.823497\pi\) | ||||
−0.850163 | + | 0.526519i | \(0.823497\pi\) | |||||||
\(48\) | −1.50000 | + | 2.59808i | −0.216506 | + | 0.375000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −0.621320 | − | 1.07616i | −0.0878680 | − | 0.152192i | ||||
\(51\) | 7.65685 | 1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | −0.207107 | − | 0.358719i | −0.0281837 | − | 0.0488155i | ||||
\(55\) | −2.82843 | − | 4.89898i | −0.381385 | − | 0.660578i | ||||
\(56\) | 2.24264 | − | 3.88437i | 0.299685 | − | 0.519070i | ||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | −0.414214 | + | 0.717439i | −0.0543889 | + | 0.0942043i | ||||
\(59\) | −3.82843 | + | 6.63103i | −0.498419 | + | 0.863287i | −0.999998 | − | 0.00182490i | \(-0.999419\pi\) |
0.501580 | + | 0.865112i | \(0.332752\pi\) | |||||||
\(60\) | 5.17157 | 0.667647 | ||||||||
\(61\) | −6.65685 | + | 11.5300i | −0.852323 | + | 1.47627i | 0.0267837 | + | 0.999641i | \(0.491473\pi\) |
−0.879107 | + | 0.476625i | \(0.841860\pi\) | |||||||
\(62\) | 0.242641 | + | 0.420266i | 0.0308154 | + | 0.0533738i | ||||
\(63\) | −1.41421 | − | 2.44949i | −0.178174 | − | 0.308607i | ||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | −3.41421 | − | 5.91359i | −0.417113 | − | 0.722460i | 0.578535 | − | 0.815657i | \(-0.303625\pi\) |
−0.995648 | + | 0.0931973i | \(0.970291\pi\) | |||||||
\(68\) | 7.00000 | + | 12.1244i | 0.848875 | + | 1.47029i | ||||
\(69\) | 2.00000 | − | 3.46410i | 0.240772 | − | 0.417029i | ||||
\(70\) | −3.31371 | −0.396064 | ||||||||
\(71\) | −1.00000 | + | 1.73205i | −0.118678 | + | 0.205557i | −0.919244 | − | 0.393688i | \(-0.871199\pi\) |
0.800566 | + | 0.599245i | \(0.204532\pi\) | |||||||
\(72\) | 0.792893 | − | 1.37333i | 0.0934434 | − | 0.161849i | ||||
\(73\) | 0.343146 | 0.0401622 | 0.0200811 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200811 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(74\) | 1.58579 | − | 2.74666i | 0.184344 | − | 0.319293i | ||||
\(75\) | −1.50000 | − | 2.59808i | −0.173205 | − | 0.300000i | ||||
\(76\) | −2.58579 | − | 4.47871i | −0.296610 | − | 0.513744i | ||||
\(77\) | −5.65685 | −0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3137 | −1.27289 | −0.636446 | − | 0.771321i | \(-0.719596\pi\) | ||||
−0.636446 | + | 0.771321i | \(0.719596\pi\) | |||||||
\(80\) | 4.24264 | + | 7.34847i | 0.474342 | + | 0.821584i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.07107 | + | 1.85514i | −0.118280 | + | 0.204866i | ||||
\(83\) | 3.65685 | 0.401392 | 0.200696 | − | 0.979654i | \(-0.435680\pi\) | ||||
0.200696 | + | 0.979654i | \(0.435680\pi\) | |||||||
\(84\) | 2.58579 | − | 4.47871i | 0.282132 | − | 0.488668i | ||||
\(85\) | 10.8284 | − | 18.7554i | 1.17451 | − | 2.03431i | ||||
\(86\) | −0.686292 | −0.0740047 | ||||||||
\(87\) | −1.00000 | + | 1.73205i | −0.107211 | + | 0.185695i | ||||
\(88\) | −1.58579 | − | 2.74666i | −0.169045 | − | 0.292795i | ||||
\(89\) | −7.41421 | − | 12.8418i | −0.785905 | − | 1.36123i | −0.928457 | − | 0.371440i | \(-0.878864\pi\) |
0.142552 | − | 0.989787i | \(-0.454469\pi\) | |||||||
\(90\) | −1.17157 | −0.123495 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.31371 | 0.762507 | ||||||||
\(93\) | 0.585786 | + | 1.01461i | 0.0607432 | + | 0.105210i | ||||
\(94\) | 2.41421 | + | 4.18154i | 0.249007 | + | 0.431293i | ||||
\(95\) | −4.00000 | + | 6.92820i | −0.410391 | + | 0.710819i | ||||
\(96\) | 4.41421 | 0.450524 | ||||||||
\(97\) | −1.82843 | + | 3.16693i | −0.185649 | + | 0.321553i | −0.943795 | − | 0.330532i | \(-0.892772\pi\) |
0.758146 | + | 0.652085i | \(0.226105\pi\) | |||||||
\(98\) | −0.207107 | + | 0.358719i | −0.0209209 | + | 0.0362361i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 2.74264 | − | 4.75039i | 0.274264 | − | 0.475039i | ||||
\(101\) | −3.82843 | − | 6.63103i | −0.380943 | − | 0.659812i | 0.610255 | − | 0.792205i | \(-0.291067\pi\) |
−0.991197 | + | 0.132393i | \(0.957734\pi\) | |||||||
\(102\) | −1.58579 | − | 2.74666i | −0.157016 | − | 0.271960i | ||||
\(103\) | 2.34315 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | −0.780720 | ||||||||
\(106\) | 0.414214 | + | 0.717439i | 0.0402320 | + | 0.0696838i | ||||
\(107\) | 5.65685 | + | 9.79796i | 0.546869 | + | 0.947204i | 0.998487 | + | 0.0549930i | \(0.0175137\pi\) |
−0.451618 | + | 0.892211i | \(0.649153\pi\) | |||||||
\(108\) | 0.914214 | − | 1.58346i | 0.0879702 | − | 0.152369i | ||||
\(109\) | 5.31371 | 0.508961 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(110\) | −1.17157 | + | 2.02922i | −0.111705 | + | 0.193479i | ||||
\(111\) | 3.82843 | − | 6.63103i | 0.363378 | − | 0.629390i | ||||
\(112\) | 8.48528 | 0.801784 | ||||||||
\(113\) | 2.65685 | − | 4.60181i | 0.249936 | − | 0.432902i | −0.713572 | − | 0.700582i | \(-0.752924\pi\) |
0.963508 | + | 0.267680i | \(0.0862571\pi\) | |||||||
\(114\) | 0.585786 | + | 1.01461i | 0.0548639 | + | 0.0950271i | ||||
\(115\) | −5.65685 | − | 9.79796i | −0.527504 | − | 0.913664i | ||||
\(116\) | −3.65685 | −0.339530 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.17157 | 0.291967 | ||||||||
\(119\) | −10.8284 | − | 18.7554i | −0.992640 | − | 1.71930i | ||||
\(120\) | −2.24264 | − | 3.88437i | −0.204724 | − | 0.354593i | ||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 5.51472 | 0.499279 | ||||||||
\(123\) | −2.58579 | + | 4.47871i | −0.233153 | + | 0.403832i | ||||
\(124\) | −1.07107 | + | 1.85514i | −0.0961847 | + | 0.166597i | ||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | −0.585786 | + | 1.01461i | −0.0521860 | + | 0.0903888i | ||||
\(127\) | −2.82843 | − | 4.89898i | −0.250982 | − | 0.434714i | 0.712814 | − | 0.701353i | \(-0.247420\pi\) |
−0.963797 | + | 0.266639i | \(0.914087\pi\) | |||||||
\(128\) | 5.27817 | + | 9.14207i | 0.466529 | + | 0.808052i | ||||
\(129\) | −1.65685 | −0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | −1.82843 | − | 3.16693i | −0.159144 | − | 0.275646i | ||||
\(133\) | 4.00000 | + | 6.92820i | 0.346844 | + | 0.600751i | ||||
\(134\) | −1.41421 | + | 2.44949i | −0.122169 | + | 0.211604i | ||||
\(135\) | −2.82843 | −0.243432 | ||||||||
\(136\) | 6.07107 | − | 10.5154i | 0.520590 | − | 0.901688i | ||||
\(137\) | 5.41421 | − | 9.37769i | 0.462567 | − | 0.801190i | −0.536521 | − | 0.843887i | \(-0.680262\pi\) |
0.999088 | + | 0.0426968i | \(0.0135950\pi\) | |||||||
\(138\) | −1.65685 | −0.141041 | ||||||||
\(139\) | 3.65685 | − | 6.33386i | 0.310170 | − | 0.537231i | −0.668229 | − | 0.743956i | \(-0.732947\pi\) |
0.978399 | + | 0.206725i | \(0.0662806\pi\) | |||||||
\(140\) | −7.31371 | − | 12.6677i | −0.618121 | − | 1.07062i | ||||
\(141\) | 5.82843 | + | 10.0951i | 0.490842 | + | 0.850163i | ||||
\(142\) | 0.828427 | 0.0695201 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 2.82843 | + | 4.89898i | 0.234888 | + | 0.406838i | ||||
\(146\) | −0.0710678 | − | 0.123093i | −0.00588161 | − | 0.0101873i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | 14.0000 | 1.15079 | ||||||||
\(149\) | 4.58579 | − | 7.94282i | 0.375682 | − | 0.650701i | −0.614747 | − | 0.788725i | \(-0.710742\pi\) |
0.990429 | + | 0.138024i | \(0.0440751\pi\) | |||||||
\(150\) | −0.621320 | + | 1.07616i | −0.0507306 | + | 0.0878680i | ||||
\(151\) | −3.51472 | −0.286024 | −0.143012 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143012 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(152\) | −2.24264 | + | 3.88437i | −0.181902 | + | 0.315064i | ||||
\(153\) | −3.82843 | − | 6.63103i | −0.309510 | − | 0.536087i | ||||
\(154\) | 1.17157 | + | 2.02922i | 0.0944080 | + | 0.163520i | ||||
\(155\) | 3.31371 | 0.266163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 2.34315 | + | 4.05845i | 0.186411 | + | 0.322873i | ||||
\(159\) | 1.00000 | + | 1.73205i | 0.0793052 | + | 0.137361i | ||||
\(160\) | 6.24264 | − | 10.8126i | 0.493524 | − | 0.854809i | ||||
\(161\) | −11.3137 | −0.891645 | ||||||||
\(162\) | −0.207107 | + | 0.358719i | −0.0162718 | + | 0.0281837i | ||||
\(163\) | −9.41421 | + | 16.3059i | −0.737378 | + | 1.27718i | 0.216294 | + | 0.976328i | \(0.430603\pi\) |
−0.953672 | + | 0.300848i | \(0.902730\pi\) | |||||||
\(164\) | −9.45584 | −0.738377 | ||||||||
\(165\) | −2.82843 | + | 4.89898i | −0.220193 | + | 0.381385i | ||||
\(166\) | −0.757359 | − | 1.31178i | −0.0587825 | − | 0.101814i | ||||
\(167\) | 1.82843 | + | 3.16693i | 0.141488 | + | 0.245064i | 0.928057 | − | 0.372438i | \(-0.121478\pi\) |
−0.786569 | + | 0.617502i | \(0.788145\pi\) | |||||||
\(168\) | −4.48528 | −0.346047 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8.97056 | −0.688011 | ||||||||
\(171\) | 1.41421 | + | 2.44949i | 0.108148 | + | 0.187317i | ||||
\(172\) | −1.51472 | − | 2.62357i | −0.115496 | − | 0.200045i | ||||
\(173\) | 5.82843 | − | 10.0951i | 0.443127 | − | 0.767519i | −0.554793 | − | 0.831989i | \(-0.687202\pi\) |
0.997920 | + | 0.0644701i | \(0.0205357\pi\) | |||||||
\(174\) | 0.828427 | 0.0628029 | ||||||||
\(175\) | −4.24264 | + | 7.34847i | −0.320713 | + | 0.555492i | ||||
\(176\) | 3.00000 | − | 5.19615i | 0.226134 | − | 0.391675i | ||||
\(177\) | 7.65685 | 0.575524 | ||||||||
\(178\) | −3.07107 | + | 5.31925i | −0.230186 | + | 0.398694i | ||||
\(179\) | 11.6569 | + | 20.1903i | 0.871274 | + | 1.50909i | 0.860679 | + | 0.509147i | \(0.170039\pi\) |
0.0105948 | + | 0.999944i | \(0.496628\pi\) | |||||||
\(180\) | −2.58579 | − | 4.47871i | −0.192733 | − | 0.333824i | ||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3137 | 0.984178 | ||||||||
\(184\) | −3.17157 | − | 5.49333i | −0.233811 | − | 0.404973i | ||||
\(185\) | −10.8284 | − | 18.7554i | −0.796122 | − | 1.37892i | ||||
\(186\) | 0.242641 | − | 0.420266i | 0.0177913 | − | 0.0308154i | ||||
\(187\) | −15.3137 | −1.11985 | ||||||||
\(188\) | −10.6569 | + | 18.4582i | −0.777231 | + | 1.34620i | ||||
\(189\) | −1.41421 | + | 2.44949i | −0.102869 | + | 0.178174i | ||||
\(190\) | 3.31371 | 0.240402 | ||||||||
\(191\) | −1.65685 | + | 2.86976i | −0.119886 | + | 0.207648i | −0.919722 | − | 0.392570i | \(-0.871586\pi\) |
0.799836 | + | 0.600218i | \(0.204919\pi\) | |||||||
\(192\) | 2.08579 | + | 3.61269i | 0.150529 | + | 0.260723i | ||||
\(193\) | −2.65685 | − | 4.60181i | −0.191245 | − | 0.331245i | 0.754418 | − | 0.656394i | \(-0.227919\pi\) |
−0.945663 | + | 0.325149i | \(0.894586\pi\) | |||||||
\(194\) | 1.51472 | 0.108750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.82843 | −0.130602 | ||||||||
\(197\) | −0.242641 | − | 0.420266i | −0.0172874 | − | 0.0299427i | 0.857252 | − | 0.514897i | \(-0.172170\pi\) |
−0.874540 | + | 0.484954i | \(0.838836\pi\) | |||||||
\(198\) | 0.414214 | + | 0.717439i | 0.0294369 | + | 0.0509862i | ||||
\(199\) | −10.8284 | + | 18.7554i | −0.767607 | + | 1.32953i | 0.171250 | + | 0.985228i | \(0.445219\pi\) |
−0.938857 | + | 0.344307i | \(0.888114\pi\) | |||||||
\(200\) | −4.75736 | −0.336396 | ||||||||
\(201\) | −3.41421 | + | 5.91359i | −0.240820 | + | 0.417113i | ||||
\(202\) | −1.58579 | + | 2.74666i | −0.111576 | + | 0.193255i | ||||
\(203\) | 5.65685 | 0.397033 | ||||||||
\(204\) | 7.00000 | − | 12.1244i | 0.490098 | − | 0.848875i | ||||
\(205\) | 7.31371 | + | 12.6677i | 0.510812 | + | 0.884752i | ||||
\(206\) | −0.485281 | − | 0.840532i | −0.0338112 | − | 0.0585626i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.65685 | 0.391293 | ||||||||
\(210\) | 1.65685 | + | 2.86976i | 0.114334 | + | 0.198032i | ||||
\(211\) | 6.00000 | + | 10.3923i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976347i | \(-0.0311277\pi\) |
−0.582165 | + | 0.813070i | \(0.697794\pi\) | |||||||
\(212\) | −1.82843 | + | 3.16693i | −0.125577 | + | 0.217506i | ||||
\(213\) | 2.00000 | 0.137038 | ||||||||
\(214\) | 2.34315 | − | 4.05845i | 0.160174 | − | 0.277430i | ||||
\(215\) | −2.34315 | + | 4.05845i | −0.159801 | + | 0.276784i | ||||
\(216\) | −1.58579 | −0.107899 | ||||||||
\(217\) | 1.65685 | − | 2.86976i | 0.112475 | − | 0.194812i | ||||
\(218\) | −1.10051 | − | 1.90613i | −0.0745356 | − | 0.129099i | ||||
\(219\) | −0.171573 | − | 0.297173i | −0.0115938 | − | 0.0200811i | ||||
\(220\) | −10.3431 | −0.697335 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.17157 | −0.212862 | ||||||||
\(223\) | 6.24264 | + | 10.8126i | 0.418038 | + | 0.724063i | 0.995742 | − | 0.0921831i | \(-0.0293845\pi\) |
−0.577704 | + | 0.816246i | \(0.696051\pi\) | |||||||
\(224\) | −6.24264 | − | 10.8126i | −0.417104 | − | 0.722445i | ||||
\(225\) | −1.50000 | + | 2.59808i | −0.100000 | + | 0.173205i | ||||
\(226\) | −2.20101 | −0.146409 | ||||||||
\(227\) | 8.65685 | − | 14.9941i | 0.574576 | − | 0.995194i | −0.421512 | − | 0.906823i | \(-0.638500\pi\) |
0.996088 | − | 0.0883713i | \(-0.0281662\pi\) | |||||||
\(228\) | −2.58579 | + | 4.47871i | −0.171248 | + | 0.296610i | ||||
\(229\) | −1.31371 | −0.0868123 | −0.0434062 | − | 0.999058i | \(-0.513821\pi\) | ||||
−0.0434062 | + | 0.999058i | \(0.513821\pi\) | |||||||
\(230\) | −2.34315 | + | 4.05845i | −0.154502 | + | 0.267606i | ||||
\(231\) | 2.82843 | + | 4.89898i | 0.186097 | + | 0.322329i | ||||
\(232\) | 1.58579 | + | 2.74666i | 0.104112 | + | 0.180327i | ||||
\(233\) | 6.97056 | 0.456657 | 0.228328 | − | 0.973584i | \(-0.426674\pi\) | ||||
0.228328 | + | 0.973584i | \(0.426674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.9706 | 2.15076 | ||||||||
\(236\) | 7.00000 | + | 12.1244i | 0.455661 | + | 0.789228i | ||||
\(237\) | 5.65685 | + | 9.79796i | 0.367452 | + | 0.636446i | ||||
\(238\) | −4.48528 | + | 7.76874i | −0.290738 | + | 0.503572i | ||||
\(239\) | 2.00000 | 0.129369 | 0.0646846 | − | 0.997906i | \(-0.479396\pi\) | ||||
0.0646846 | + | 0.997906i | \(0.479396\pi\) | |||||||
\(240\) | 4.24264 | − | 7.34847i | 0.273861 | − | 0.474342i | ||||
\(241\) | −0.171573 | + | 0.297173i | −0.0110520 | + | 0.0191426i | −0.871499 | − | 0.490398i | \(-0.836851\pi\) |
0.860447 | + | 0.509541i | \(0.170185\pi\) | |||||||
\(242\) | −2.89949 | −0.186387 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 12.1716 | + | 21.0818i | 0.779205 | + | 1.34962i | ||||
\(245\) | 1.41421 | + | 2.44949i | 0.0903508 | + | 0.156492i | ||||
\(246\) | 2.14214 | 0.136578 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.85786 | 0.117975 | ||||||||
\(249\) | −1.82843 | − | 3.16693i | −0.115872 | − | 0.200696i | ||||
\(250\) | −1.17157 | − | 2.02922i | −0.0740968 | − | 0.128339i | ||||
\(251\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(252\) | −5.17157 | −0.325778 | ||||||||
\(253\) | −4.00000 | + | 6.92820i | −0.251478 | + | 0.435572i | ||||
\(254\) | −1.17157 | + | 2.02922i | −0.0735110 | + | 0.127325i | ||||
\(255\) | −21.6569 | −1.35620 | ||||||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | 2.17157 | + | 3.76127i | 0.135459 | + | 0.234622i | 0.925773 | − | 0.378081i | \(-0.123416\pi\) |
−0.790314 | + | 0.612702i | \(0.790082\pi\) | |||||||
\(258\) | 0.343146 | + | 0.594346i | 0.0213633 | + | 0.0370024i | ||||
\(259\) | −21.6569 | −1.34569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 1.65685 | + | 2.86976i | 0.102361 | + | 0.177294i | ||||
\(263\) | −6.00000 | − | 10.3923i | −0.369976 | − | 0.640817i | 0.619586 | − | 0.784929i | \(-0.287301\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(264\) | −1.58579 | + | 2.74666i | −0.0975984 | + | 0.169045i | ||||
\(265\) | 5.65685 | 0.347498 | ||||||||
\(266\) | 1.65685 | − | 2.86976i | 0.101588 | − | 0.175956i | ||||
\(267\) | −7.41421 | + | 12.8418i | −0.453743 | + | 0.785905i | ||||
\(268\) | −12.4853 | −0.762660 | ||||||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 0.585786 | + | 1.01461i | 0.0356498 | + | 0.0617473i | ||||
\(271\) | 13.8995 | + | 24.0746i | 0.844334 | + | 1.46243i | 0.886198 | + | 0.463306i | \(0.153337\pi\) |
−0.0418640 | + | 0.999123i | \(0.513330\pi\) | |||||||
\(272\) | 22.9706 | 1.39279 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.48528 | −0.270966 | ||||||||
\(275\) | 3.00000 | + | 5.19615i | 0.180907 | + | 0.313340i | ||||
\(276\) | −3.65685 | − | 6.33386i | −0.220117 | − | 0.381253i | ||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | −3.02944 | −0.181694 | ||||||||
\(279\) | 0.585786 | − | 1.01461i | 0.0350701 | − | 0.0607432i | ||||
\(280\) | −6.34315 | + | 10.9867i | −0.379075 | + | 0.656578i | ||||
\(281\) | 21.1716 | 1.26299 | 0.631495 | − | 0.775380i | \(-0.282442\pi\) | ||||
0.631495 | + | 0.775380i | \(0.282442\pi\) | |||||||
\(282\) | 2.41421 | − | 4.18154i | 0.143764 | − | 0.249007i | ||||
\(283\) | −14.4853 | − | 25.0892i | −0.861061 | − | 1.49140i | −0.870906 | − | 0.491449i | \(-0.836467\pi\) |
0.00984565 | − | 0.999952i | \(-0.496866\pi\) | |||||||
\(284\) | 1.82843 | + | 3.16693i | 0.108497 | + | 0.187923i | ||||
\(285\) | 8.00000 | 0.473879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6274 | 0.863429 | ||||||||
\(288\) | −2.20711 | − | 3.82282i | −0.130055 | − | 0.225262i | ||||
\(289\) | −20.8137 | − | 36.0504i | −1.22434 | − | 2.12061i | ||||
\(290\) | 1.17157 | − | 2.02922i | 0.0687971 | − | 0.119160i | ||||
\(291\) | 3.65685 | 0.214369 | ||||||||
\(292\) | 0.313708 | − | 0.543359i | 0.0183584 | − | 0.0317977i | ||||
\(293\) | −1.07107 | + | 1.85514i | −0.0625724 | + | 0.108379i | −0.895615 | − | 0.444831i | \(-0.853264\pi\) |
0.833042 | + | 0.553210i | \(0.186597\pi\) | |||||||
\(294\) | 0.414214 | 0.0241574 | ||||||||
\(295\) | 10.8284 | − | 18.7554i | 0.630455 | − | 1.09198i | ||||
\(296\) | −6.07107 | − | 10.5154i | −0.352874 | − | 0.611195i | ||||
\(297\) | 1.00000 | + | 1.73205i | 0.0580259 | + | 0.100504i | ||||
\(298\) | −3.79899 | −0.220070 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.48528 | −0.316693 | ||||||||
\(301\) | 2.34315 | + | 4.05845i | 0.135057 | + | 0.233925i | ||||
\(302\) | 0.727922 | + | 1.26080i | 0.0418872 | + | 0.0725508i | ||||
\(303\) | −3.82843 | + | 6.63103i | −0.219937 | + | 0.380943i | ||||
\(304\) | −8.48528 | −0.486664 | ||||||||
\(305\) | 18.8284 | − | 32.6118i | 1.07811 | − | 1.86735i | ||||
\(306\) | −1.58579 | + | 2.74666i | −0.0906534 | + | 0.157016i | ||||
\(307\) | −22.8284 | −1.30289 | −0.651444 | − | 0.758697i | \(-0.725836\pi\) | ||||
−0.651444 | + | 0.758697i | \(0.725836\pi\) | |||||||
\(308\) | −5.17157 | + | 8.95743i | −0.294678 | + | 0.510397i | ||||
\(309\) | −1.17157 | − | 2.02922i | −0.0666485 | − | 0.115439i | ||||
\(310\) | −0.686292 | − | 1.18869i | −0.0389787 | − | 0.0675132i | ||||
\(311\) | −10.6274 | −0.602626 | −0.301313 | − | 0.953525i | \(-0.597425\pi\) | ||||
−0.301313 | + | 0.953525i | \(0.597425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.00000 | 0.339140 | 0.169570 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169570 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(314\) | 2.07107 | + | 3.58719i | 0.116877 | + | 0.202437i | ||||
\(315\) | 4.00000 | + | 6.92820i | 0.225374 | + | 0.390360i | ||||
\(316\) | −10.3431 | + | 17.9149i | −0.581847 | + | 1.00779i | ||||
\(317\) | 8.48528 | 0.476581 | 0.238290 | − | 0.971194i | \(-0.423413\pi\) | ||||
0.238290 | + | 0.971194i | \(0.423413\pi\) | |||||||
\(318\) | 0.414214 | − | 0.717439i | 0.0232279 | − | 0.0402320i | ||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | 11.7990 | 0.659584 | ||||||||
\(321\) | 5.65685 | − | 9.79796i | 0.315735 | − | 0.546869i | ||||
\(322\) | 2.34315 | + | 4.05845i | 0.130578 | + | 0.226168i | ||||
\(323\) | 10.8284 | + | 18.7554i | 0.602510 | + | 1.04358i | ||||
\(324\) | −1.82843 | −0.101579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.79899 | 0.431946 | ||||||||
\(327\) | −2.65685 | − | 4.60181i | −0.146924 | − | 0.254480i | ||||
\(328\) | 4.10051 | + | 7.10228i | 0.226413 | + | 0.392158i | ||||
\(329\) | 16.4853 | − | 28.5533i | 0.908863 | − | 1.57420i | ||||
\(330\) | 2.34315 | 0.128986 | ||||||||
\(331\) | −13.0711 | + | 22.6398i | −0.718451 | + | 1.24439i | 0.243163 | + | 0.969986i | \(0.421815\pi\) |
−0.961613 | + | 0.274408i | \(0.911518\pi\) | |||||||
\(332\) | 3.34315 | − | 5.79050i | 0.183479 | − | 0.317795i | ||||
\(333\) | −7.65685 | −0.419593 | ||||||||
\(334\) | 0.757359 | − | 1.31178i | 0.0414409 | − | 0.0717777i | ||||
\(335\) | 9.65685 | + | 16.7262i | 0.527610 | + | 0.913848i | ||||
\(336\) | −4.24264 | − | 7.34847i | −0.231455 | − | 0.400892i | ||||
\(337\) | 9.31371 | 0.507350 | 0.253675 | − | 0.967290i | \(-0.418361\pi\) | ||||
0.253675 | + | 0.967290i | \(0.418361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.31371 | −0.288601 | ||||||||
\(340\) | −19.7990 | − | 34.2929i | −1.07375 | − | 1.85979i | ||||
\(341\) | −1.17157 | − | 2.02922i | −0.0634442 | − | 0.109889i | ||||
\(342\) | 0.585786 | − | 1.01461i | 0.0316757 | − | 0.0548639i | ||||
\(343\) | −16.9706 | −0.916324 | ||||||||
\(344\) | −1.31371 | + | 2.27541i | −0.0708304 | + | 0.122682i | ||||
\(345\) | −5.65685 | + | 9.79796i | −0.304555 | + | 0.527504i | ||||
\(346\) | −4.82843 | −0.259578 | ||||||||
\(347\) | 4.34315 | − | 7.52255i | 0.233152 | − | 0.403832i | −0.725582 | − | 0.688136i | \(-0.758429\pi\) |
0.958734 | + | 0.284304i | \(0.0917626\pi\) | |||||||
\(348\) | 1.82843 | + | 3.16693i | 0.0980140 | + | 0.169765i | ||||
\(349\) | −1.82843 | − | 3.16693i | −0.0978735 | − | 0.169522i | 0.812931 | − | 0.582360i | \(-0.197871\pi\) |
−0.910804 | + | 0.412839i | \(0.864537\pi\) | |||||||
\(350\) | 3.51472 | 0.187870 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.82843 | −0.470557 | ||||||||
\(353\) | 16.7279 | + | 28.9736i | 0.890337 | + | 1.54211i | 0.839471 | + | 0.543404i | \(0.182865\pi\) |
0.0508663 | + | 0.998705i | \(0.483802\pi\) | |||||||
\(354\) | −1.58579 | − | 2.74666i | −0.0842836 | − | 0.145983i | ||||
\(355\) | 2.82843 | − | 4.89898i | 0.150117 | − | 0.260011i | ||||
\(356\) | −27.1127 | −1.43697 | ||||||||
\(357\) | −10.8284 | + | 18.7554i | −0.573101 | + | 0.992640i | ||||
\(358\) | 4.82843 | − | 8.36308i | 0.255190 | − | 0.442003i | ||||
\(359\) | 34.9706 | 1.84568 | 0.922838 | − | 0.385189i | \(-0.125864\pi\) | ||||
0.922838 | + | 0.385189i | \(0.125864\pi\) | |||||||
\(360\) | −2.24264 | + | 3.88437i | −0.118198 | + | 0.204724i | ||||
\(361\) | 5.50000 | + | 9.52628i | 0.289474 | + | 0.501383i | ||||
\(362\) | −2.89949 | − | 5.02207i | −0.152394 | − | 0.263954i | ||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.970563 | −0.0508016 | ||||||||
\(366\) | −2.75736 | − | 4.77589i | −0.144129 | − | 0.249640i | ||||
\(367\) | 12.0000 | + | 20.7846i | 0.626395 | + | 1.08495i | 0.988269 | + | 0.152721i | \(0.0488036\pi\) |
−0.361874 | + | 0.932227i | \(0.617863\pi\) | |||||||
\(368\) | 6.00000 | − | 10.3923i | 0.312772 | − | 0.541736i | ||||
\(369\) | 5.17157 | 0.269221 | ||||||||
\(370\) | −4.48528 | + | 7.76874i | −0.233179 | + | 0.403877i | ||||
\(371\) | 2.82843 | − | 4.89898i | 0.146845 | − | 0.254342i | ||||
\(372\) | 2.14214 | 0.111065 | ||||||||
\(373\) | −5.00000 | + | 8.66025i | −0.258890 | + | 0.448411i | −0.965945 | − | 0.258748i | \(-0.916690\pi\) |
0.707055 | + | 0.707159i | \(0.250023\pi\) | |||||||
\(374\) | 3.17157 | + | 5.49333i | 0.163998 | + | 0.284053i | ||||
\(375\) | −2.82843 | − | 4.89898i | −0.146059 | − | 0.252982i | ||||
\(376\) | 18.4853 | 0.953306 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.17157 | 0.0602592 | ||||||||
\(379\) | −0.242641 | − | 0.420266i | −0.0124636 | − | 0.0215876i | 0.859726 | − | 0.510755i | \(-0.170634\pi\) |
−0.872190 | + | 0.489167i | \(0.837301\pi\) | |||||||
\(380\) | 7.31371 | + | 12.6677i | 0.375185 | + | 0.649840i | ||||
\(381\) | −2.82843 | + | 4.89898i | −0.144905 | + | 0.250982i | ||||
\(382\) | 1.37258 | 0.0702275 | ||||||||
\(383\) | −15.4853 | + | 26.8213i | −0.791261 | + | 1.37050i | 0.133926 | + | 0.990991i | \(0.457242\pi\) |
−0.925187 | + | 0.379513i | \(0.876092\pi\) | |||||||
\(384\) | 5.27817 | − | 9.14207i | 0.269351 | − | 0.466529i | ||||
\(385\) | 16.0000 | 0.815436 | ||||||||
\(386\) | −1.10051 | + | 1.90613i | −0.0560142 | + | 0.0970195i | ||||
\(387\) | 0.828427 | + | 1.43488i | 0.0421113 | + | 0.0729389i | ||||
\(388\) | 3.34315 | + | 5.79050i | 0.169723 | + | 0.293968i | ||||
\(389\) | −26.9706 | −1.36746 | −0.683731 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683731 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.6274 | −1.54890 | ||||||||
\(392\) | 0.792893 | + | 1.37333i | 0.0400472 | + | 0.0693637i | ||||
\(393\) | 4.00000 | + | 6.92820i | 0.201773 | + | 0.349482i | ||||
\(394\) | −0.100505 | + | 0.174080i | −0.00506337 | + | 0.00877002i | ||||
\(395\) | 32.0000 | 1.61009 | ||||||||
\(396\) | −1.82843 | + | 3.16693i | −0.0918819 | + | 0.159144i | ||||
\(397\) | −15.4853 | + | 26.8213i | −0.777184 | + | 1.34612i | 0.156375 | + | 0.987698i | \(0.450019\pi\) |
−0.933559 | + | 0.358424i | \(0.883314\pi\) | |||||||
\(398\) | 8.97056 | 0.449654 | ||||||||
\(399\) | 4.00000 | − | 6.92820i | 0.200250 | − | 0.346844i | ||||
\(400\) | −4.50000 | − | 7.79423i | −0.225000 | − | 0.389711i | ||||
\(401\) | −13.0711 | − | 22.6398i | −0.652738 | − | 1.13058i | −0.982456 | − | 0.186496i | \(-0.940287\pi\) |
0.329718 | − | 0.944080i | \(-0.393046\pi\) | |||||||
\(402\) | 2.82843 | 0.141069 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 1.41421 | + | 2.44949i | 0.0702728 | + | 0.121716i | ||||
\(406\) | −1.17157 | − | 2.02922i | −0.0581442 | − | 0.100709i | ||||
\(407\) | −7.65685 | + | 13.2621i | −0.379536 | + | 0.657376i | ||||
\(408\) | −12.1421 | −0.601125 | ||||||||
\(409\) | 17.4853 | − | 30.2854i | 0.864592 | − | 1.49752i | −0.00286068 | − | 0.999996i | \(-0.500911\pi\) |
0.867452 | − | 0.497521i | \(-0.165756\pi\) | |||||||
\(410\) | 3.02944 | − | 5.24714i | 0.149613 | − | 0.259138i | ||||
\(411\) | −10.8284 | −0.534127 | ||||||||
\(412\) | 2.14214 | − | 3.71029i | 0.105535 | − | 0.182793i | ||||
\(413\) | −10.8284 | − | 18.7554i | −0.532832 | − | 0.922892i | ||||
\(414\) | 0.828427 | + | 1.43488i | 0.0407150 | + | 0.0705204i | ||||
\(415\) | −10.3431 | −0.507725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.31371 | −0.358154 | ||||||||
\(418\) | −1.17157 | − | 2.02922i | −0.0573035 | − | 0.0992526i | ||||
\(419\) | −7.31371 | − | 12.6677i | −0.357298 | − | 0.618858i | 0.630210 | − | 0.776424i | \(-0.282969\pi\) |
−0.987508 | + | 0.157566i | \(0.949635\pi\) | |||||||
\(420\) | −7.31371 | + | 12.6677i | −0.356872 | + | 0.618121i | ||||
\(421\) | 37.3137 | 1.81856 | 0.909279 | − | 0.416186i | \(-0.136634\pi\) | ||||
0.909279 | + | 0.416186i | \(0.136634\pi\) | |||||||
\(422\) | 2.48528 | − | 4.30463i | 0.120982 | − | 0.209546i | ||||
\(423\) | 5.82843 | − | 10.0951i | 0.283388 | − | 0.490842i | ||||
\(424\) | 3.17157 | 0.154025 | ||||||||
\(425\) | −11.4853 | + | 19.8931i | −0.557118 | + | 0.964957i | ||||
\(426\) | −0.414214 | − | 0.717439i | −0.0200687 | − | 0.0347600i | ||||
\(427\) | −18.8284 | − | 32.6118i | −0.911171 | − | 1.57820i | ||||
\(428\) | 20.6863 | 0.999910 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.94113 | 0.0936094 | ||||||||
\(431\) | −4.17157 | − | 7.22538i | −0.200938 | − | 0.348034i | 0.747893 | − | 0.663819i | \(-0.231066\pi\) |
−0.948831 | + | 0.315785i | \(0.897732\pi\) | |||||||
\(432\) | −1.50000 | − | 2.59808i | −0.0721688 | − | 0.125000i | ||||
\(433\) | 10.6569 | − | 18.4582i | 0.512136 | − | 0.887045i | −0.487765 | − | 0.872975i | \(-0.662188\pi\) |
0.999901 | − | 0.0140703i | \(-0.00447886\pi\) | |||||||
\(434\) | −1.37258 | −0.0658861 | ||||||||
\(435\) | 2.82843 | − | 4.89898i | 0.135613 | − | 0.234888i | ||||
\(436\) | 4.85786 | − | 8.41407i | 0.232650 | − | 0.402961i | ||||
\(437\) | 11.3137 | 0.541208 | ||||||||
\(438\) | −0.0710678 | + | 0.123093i | −0.00339575 | + | 0.00588161i | ||||
\(439\) | −8.48528 | − | 14.6969i | −0.404980 | − | 0.701447i | 0.589339 | − | 0.807886i | \(-0.299388\pi\) |
−0.994319 | + | 0.106439i | \(0.966055\pi\) | |||||||
\(440\) | 4.48528 | + | 7.76874i | 0.213827 | + | 0.370360i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9411 | −1.23250 | −0.616250 | − | 0.787551i | \(-0.711349\pi\) | ||||
−0.616250 | + | 0.787551i | \(0.711349\pi\) | |||||||
\(444\) | −7.00000 | − | 12.1244i | −0.332205 | − | 0.575396i | ||||
\(445\) | 20.9706 | + | 36.3221i | 0.994100 | + | 1.72183i | ||||
\(446\) | 2.58579 | − | 4.47871i | 0.122441 | − | 0.212073i | ||||
\(447\) | −9.17157 | −0.433801 | ||||||||
\(448\) | 5.89949 | − | 10.2182i | 0.278725 | − | 0.482766i | ||||
\(449\) | 15.8995 | − | 27.5387i | 0.750344 | − | 1.29963i | −0.197313 | − | 0.980341i | \(-0.563221\pi\) |
0.947656 | − | 0.319293i | \(-0.103445\pi\) | |||||||
\(450\) | 1.24264 | 0.0585786 | ||||||||
\(451\) | 5.17157 | − | 8.95743i | 0.243520 | − | 0.421789i | ||||
\(452\) | −4.85786 | − | 8.41407i | −0.228495 | − | 0.395764i | ||||
\(453\) | 1.75736 | + | 3.04384i | 0.0825679 | + | 0.143012i | ||||
\(454\) | −7.17157 | −0.336579 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.48528 | 0.210043 | ||||||||
\(457\) | 3.82843 | + | 6.63103i | 0.179086 | + | 0.310187i | 0.941568 | − | 0.336823i | \(-0.109353\pi\) |
−0.762482 | + | 0.647010i | \(0.776019\pi\) | |||||||
\(458\) | 0.272078 | + | 0.471253i | 0.0127134 | + | 0.0220202i | ||||
\(459\) | −3.82843 | + | 6.63103i | −0.178696 | + | 0.309510i | ||||
\(460\) | −20.6863 | −0.964503 | ||||||||
\(461\) | −2.58579 | + | 4.47871i | −0.120432 | + | 0.208594i | −0.919938 | − | 0.392064i | \(-0.871761\pi\) |
0.799506 | + | 0.600658i | \(0.205095\pi\) | |||||||
\(462\) | 1.17157 | − | 2.02922i | 0.0545065 | − | 0.0944080i | ||||
\(463\) | −24.4853 | −1.13793 | −0.568964 | − | 0.822363i | \(-0.692656\pi\) | ||||
−0.568964 | + | 0.822363i | \(0.692656\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | −1.65685 | − | 2.86976i | −0.0768348 | − | 0.133082i | ||||
\(466\) | −1.44365 | − | 2.50048i | −0.0668758 | − | 0.115832i | ||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3137 | 0.891824 | ||||||||
\(470\) | −6.82843 | − | 11.8272i | −0.314972 | − | 0.545547i | ||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 6.07107 | − | 10.5154i | 0.279444 | − | 0.484010i | ||||
\(473\) | 3.31371 | 0.152364 | ||||||||
\(474\) | 2.34315 | − | 4.05845i | 0.107624 | − | 0.186411i | ||||
\(475\) | 4.24264 | − | 7.34847i | 0.194666 | − | 0.337171i | ||||
\(476\) | −39.5980 | −1.81497 | ||||||||
\(477\) | 1.00000 | − | 1.73205i | 0.0457869 | − | 0.0793052i | ||||
\(478\) | −0.414214 | − | 0.717439i | −0.0189457 | − | 0.0328149i | ||||
\(479\) | −12.6569 | − | 21.9223i | −0.578306 | − | 1.00166i | −0.995674 | − | 0.0929182i | \(-0.970380\pi\) |
0.417367 | − | 0.908738i | \(-0.362953\pi\) | |||||||
\(480\) | −12.4853 | −0.569873 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.142136 | 0.00647410 | ||||||||
\(483\) | 5.65685 | + | 9.79796i | 0.257396 | + | 0.445823i | ||||
\(484\) | −6.39949 | − | 11.0843i | −0.290886 | − | 0.503830i | ||||
\(485\) | 5.17157 | − | 8.95743i | 0.234829 | − | 0.406736i | ||||
\(486\) | 0.414214 | 0.0187891 | ||||||||
\(487\) | 3.89949 | − | 6.75412i | 0.176703 | − | 0.306059i | −0.764046 | − | 0.645161i | \(-0.776790\pi\) |
0.940749 | + | 0.339103i | \(0.110123\pi\) | |||||||
\(488\) | 10.5563 | − | 18.2841i | 0.477863 | − | 0.827684i | ||||
\(489\) | 18.8284 | 0.851451 | ||||||||
\(490\) | 0.585786 | − | 1.01461i | 0.0264631 | − | 0.0458355i | ||||
\(491\) | −15.3137 | − | 26.5241i | −0.691098 | − | 1.19702i | −0.971478 | − | 0.237128i | \(-0.923794\pi\) |
0.280380 | − | 0.959889i | \(-0.409539\pi\) | |||||||
\(492\) | 4.72792 | + | 8.18900i | 0.213151 | + | 0.369189i | ||||
\(493\) | 15.3137 | 0.689695 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | 1.75736 | + | 3.04384i | 0.0789078 | + | 0.136672i | ||||
\(497\) | −2.82843 | − | 4.89898i | −0.126872 | − | 0.219749i | ||||
\(498\) | −0.757359 | + | 1.31178i | −0.0339381 | + | 0.0587825i | ||||
\(499\) | 26.1421 | 1.17028 | 0.585141 | − | 0.810931i | \(-0.301039\pi\) | ||||
0.585141 | + | 0.810931i | \(0.301039\pi\) | |||||||
\(500\) | 5.17157 | − | 8.95743i | 0.231280 | − | 0.400588i | ||||
\(501\) | 1.82843 | − | 3.16693i | 0.0816881 | − | 0.141488i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.65685 | − | 6.33386i | 0.163051 | − | 0.282413i | −0.772910 | − | 0.634515i | \(-0.781200\pi\) |
0.935961 | + | 0.352102i | \(0.114533\pi\) | |||||||
\(504\) | 2.24264 | + | 3.88437i | 0.0998952 | + | 0.173023i | ||||
\(505\) | 10.8284 | + | 18.7554i | 0.481859 | + | 0.834604i | ||||
\(506\) | 3.31371 | 0.147312 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.3431 | −0.458903 | ||||||||
\(509\) | −5.89949 | − | 10.2182i | −0.261491 | − | 0.452915i | 0.705148 | − | 0.709060i | \(-0.250881\pi\) |
−0.966638 | + | 0.256146i | \(0.917547\pi\) | |||||||
\(510\) | 4.48528 | + | 7.76874i | 0.198612 | + | 0.344005i | ||||
\(511\) | −0.485281 | + | 0.840532i | −0.0214676 | + | 0.0371829i | ||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | 1.41421 | − | 2.44949i | 0.0624391 | − | 0.108148i | ||||
\(514\) | 0.899495 | − | 1.55797i | 0.0396750 | − | 0.0687192i | ||||
\(515\) | −6.62742 | −0.292039 | ||||||||
\(516\) | −1.51472 | + | 2.62357i | −0.0666818 | + | 0.115496i | ||||
\(517\) | −11.6569 | − | 20.1903i | −0.512668 | − | 0.887967i | ||||
\(518\) | 4.48528 | + | 7.76874i | 0.197072 | + | 0.341339i | ||||
\(519\) | −11.6569 | −0.511679 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3137 | 1.10901 | 0.554507 | − | 0.832179i | \(-0.312907\pi\) | ||||
0.554507 | + | 0.832179i | \(0.312907\pi\) | |||||||
\(522\) | −0.414214 | − | 0.717439i | −0.0181296 | − | 0.0314014i | ||||
\(523\) | 7.65685 | + | 13.2621i | 0.334811 | + | 0.579909i | 0.983448 | − | 0.181188i | \(-0.0579942\pi\) |
−0.648638 | + | 0.761097i | \(0.724661\pi\) | |||||||
\(524\) | −7.31371 | + | 12.6677i | −0.319501 | + | 0.553392i | ||||
\(525\) | 8.48528 | 0.370328 | ||||||||
\(526\) | −2.48528 | + | 4.30463i | −0.108363 | + | 0.187691i | ||||
\(527\) | 4.48528 | − | 7.76874i | 0.195382 | − | 0.338411i | ||||
\(528\) | −6.00000 | −0.261116 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −1.17157 | − | 2.02922i | −0.0508899 | − | 0.0881438i | ||||
\(531\) | −3.82843 | − | 6.63103i | −0.166140 | − | 0.287762i | ||||
\(532\) | 14.6274 | 0.634179 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.14214 | 0.265796 | ||||||||
\(535\) | −16.0000 | − | 27.7128i | −0.691740 | − | 1.19813i | ||||
\(536\) | 5.41421 | + | 9.37769i | 0.233858 | + | 0.405055i | ||||
\(537\) | 11.6569 | − | 20.1903i | 0.503030 | − | 0.871274i | ||||
\(538\) | 7.45584 | 0.321444 | ||||||||
\(539\) | 1.00000 | − | 1.73205i | 0.0430730 | − | 0.0746047i | ||||
\(540\) | −2.58579 | + | 4.47871i | −0.111275 | + | 0.192733i | ||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 5.75736 | − | 9.97204i | 0.247300 | − | 0.428336i | ||||
\(543\) | −7.00000 | − | 12.1244i | −0.300399 | − | 0.520306i | ||||
\(544\) | −16.8995 | − | 29.2708i | −0.724560 | − | 1.25497i | ||||
\(545\) | −15.0294 | −0.643790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.3137 | 0.996822 | 0.498411 | − | 0.866941i | \(-0.333917\pi\) | ||||
0.498411 | + | 0.866941i | \(0.333917\pi\) | |||||||
\(548\) | −9.89949 | − | 17.1464i | −0.422885 | − | 0.732459i | ||||
\(549\) | −6.65685 | − | 11.5300i | −0.284108 | − | 0.492089i | ||||
\(550\) | 1.24264 | − | 2.15232i | 0.0529864 | − | 0.0917751i | ||||
\(551\) | −5.65685 | −0.240990 | ||||||||
\(552\) | −3.17157 | + | 5.49333i | −0.134991 | + | 0.233811i | ||||
\(553\) | 16.0000 | − | 27.7128i | 0.680389 | − | 1.17847i | ||||
\(554\) | −0.828427 | −0.0351965 | ||||||||
\(555\) | −10.8284 | + | 18.7554i | −0.459641 | + | 0.796122i | ||||
\(556\) | −6.68629 | − | 11.5810i | −0.283562 | − | 0.491144i | ||||
\(557\) | 3.89949 | + | 6.75412i | 0.165227 | + | 0.286181i | 0.936736 | − | 0.350037i | \(-0.113831\pi\) |
−0.771509 | + | 0.636218i | \(0.780498\pi\) | |||||||
\(558\) | −0.485281 | −0.0205436 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −24.0000 | −1.01419 | ||||||||
\(561\) | 7.65685 | + | 13.2621i | 0.323273 | + | 0.559925i | ||||
\(562\) | −4.38478 | − | 7.59466i | −0.184961 | − | 0.320361i | ||||
\(563\) | −2.00000 | + | 3.46410i | −0.0842900 | + | 0.145994i | −0.905088 | − | 0.425223i | \(-0.860196\pi\) |
0.820798 | + | 0.571218i | \(0.193529\pi\) | |||||||
\(564\) | 21.3137 | 0.897469 | ||||||||
\(565\) | −7.51472 | + | 13.0159i | −0.316147 | + | 0.547582i | ||||
\(566\) | −6.00000 | + | 10.3923i | −0.252199 | + | 0.436821i | ||||
\(567\) | 2.82843 | 0.118783 | ||||||||
\(568\) | 1.58579 | − | 2.74666i | 0.0665381 | − | 0.115247i | ||||
\(569\) | 21.4853 | + | 37.2136i | 0.900710 | + | 1.56008i | 0.826575 | + | 0.562827i | \(0.190286\pi\) |
0.0741351 | + | 0.997248i | \(0.476380\pi\) | |||||||
\(570\) | −1.65685 | − | 2.86976i | −0.0693980 | − | 0.120201i | ||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.31371 | 0.138432 | ||||||||
\(574\) | −3.02944 | − | 5.24714i | −0.126446 | − | 0.219011i | ||||
\(575\) | 6.00000 | + | 10.3923i | 0.250217 | + | 0.433389i | ||||
\(576\) | 2.08579 | − | 3.61269i | 0.0869078 | − | 0.150529i | ||||
\(577\) | −31.9411 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(578\) | −8.62132 | + | 14.9326i | −0.358600 | + | 0.621113i | ||||
\(579\) | −2.65685 | + | 4.60181i | −0.110415 | + | 0.191245i | ||||
\(580\) | 10.3431 | 0.429476 | ||||||||
\(581\) | −5.17157 | + | 8.95743i | −0.214553 | + | 0.371617i | ||||
\(582\) | −0.757359 | − | 1.31178i | −0.0313936 | − | 0.0543752i | ||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | −0.544156 | −0.0225173 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.887302 | 0.0366541 | ||||||||
\(587\) | 5.48528 | + | 9.50079i | 0.226402 | + | 0.392139i | 0.956739 | − | 0.290947i | \(-0.0939704\pi\) |
−0.730337 | + | 0.683087i | \(0.760637\pi\) | |||||||
\(588\) | 0.914214 | + | 1.58346i | 0.0377015 | + | 0.0653010i | ||||
\(589\) | −1.65685 | + | 2.86976i | −0.0682695 | + | 0.118246i | ||||
\(590\) | −8.97056 | −0.369312 | ||||||||
\(591\) | −0.242641 | + | 0.420266i | −0.00998090 | + | 0.0172874i | ||||
\(592\) | 11.4853 | − | 19.8931i | 0.472042 | − | 0.817601i | ||||
\(593\) | −20.4853 | −0.841230 | −0.420615 | − | 0.907239i | \(-0.638186\pi\) | ||||
−0.420615 | + | 0.907239i | \(0.638186\pi\) | |||||||
\(594\) | 0.414214 | − | 0.717439i | 0.0169954 | − | 0.0294369i | ||||
\(595\) | 30.6274 | + | 53.0482i | 1.25560 | + | 2.17477i | ||||
\(596\) | −8.38478 | − | 14.5229i | −0.343454 | − | 0.594879i | ||||
\(597\) | 21.6569 | 0.886356 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3137 | −0.952572 | −0.476286 | − | 0.879290i | \(-0.658017\pi\) | ||||
−0.476286 | + | 0.879290i | \(0.658017\pi\) | |||||||
\(600\) | 2.37868 | + | 4.11999i | 0.0971092 | + | 0.168198i | ||||
\(601\) | 0.313708 | + | 0.543359i | 0.0127964 | + | 0.0221641i | 0.872353 | − | 0.488877i | \(-0.162593\pi\) |
−0.859556 | + | 0.511041i | \(0.829260\pi\) | |||||||
\(602\) | 0.970563 | − | 1.68106i | 0.0395572 | − | 0.0685151i | ||||
\(603\) | 6.82843 | 0.278075 | ||||||||
\(604\) | −3.21320 | + | 5.56543i | −0.130743 | + | 0.226454i | ||||
\(605\) | −9.89949 | + | 17.1464i | −0.402472 | + | 0.697101i | ||||
\(606\) | 3.17157 | 0.128836 | ||||||||
\(607\) | −20.9706 | + | 36.3221i | −0.851169 | + | 1.47427i | 0.0289853 | + | 0.999580i | \(0.490772\pi\) |
−0.880154 | + | 0.474688i | \(0.842561\pi\) | |||||||
\(608\) | 6.24264 | + | 10.8126i | 0.253173 | + | 0.438508i | ||||
\(609\) | −2.82843 | − | 4.89898i | −0.114614 | − | 0.198517i | ||||
\(610\) | −15.5980 | −0.631544 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 23.8284 | + | 41.2720i | 0.962421 | + | 1.66696i | 0.716390 | + | 0.697700i | \(0.245793\pi\) |
0.246031 | + | 0.969262i | \(0.420873\pi\) | |||||||
\(614\) | 4.72792 | + | 8.18900i | 0.190803 | + | 0.330481i | ||||
\(615\) | 7.31371 | − | 12.6677i | 0.294917 | − | 0.510812i | ||||
\(616\) | 8.97056 | 0.361434 | ||||||||
\(617\) | 17.4142 | − | 30.1623i | 0.701070 | − | 1.21429i | −0.267021 | − | 0.963691i | \(-0.586039\pi\) |
0.968091 | − | 0.250598i | \(-0.0806272\pi\) | |||||||
\(618\) | −0.485281 | + | 0.840532i | −0.0195209 | + | 0.0338112i | ||||
\(619\) | 23.7990 | 0.956562 | 0.478281 | − | 0.878207i | \(-0.341260\pi\) | ||||
0.478281 | + | 0.878207i | \(0.341260\pi\) | |||||||
\(620\) | 3.02944 | − | 5.24714i | 0.121665 | − | 0.210730i | ||||
\(621\) | 2.00000 | + | 3.46410i | 0.0802572 | + | 0.139010i | ||||
\(622\) | 2.20101 | + | 3.81226i | 0.0882525 | + | 0.152858i | ||||
\(623\) | 41.9411 | 1.68034 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | −1.24264 | − | 2.15232i | −0.0496659 | − | 0.0860239i | ||||
\(627\) | −2.82843 | − | 4.89898i | −0.112956 | − | 0.195646i | ||||
\(628\) | −9.14214 | + | 15.8346i | −0.364811 | + | 0.631871i | ||||
\(629\) | −58.6274 | −2.33763 | ||||||||
\(630\) | 1.65685 | − | 2.86976i | 0.0660107 | − | 0.114334i | ||||
\(631\) | −21.5563 | + | 37.3367i | −0.858145 | + | 1.48635i | 0.0155519 | + | 0.999879i | \(0.495049\pi\) |
−0.873697 | + | 0.486471i | \(0.838284\pi\) | |||||||
\(632\) | 17.9411 | 0.713660 | ||||||||
\(633\) | 6.00000 | − | 10.3923i | 0.238479 | − | 0.413057i | ||||
\(634\) | −1.75736 | − | 3.04384i | −0.0697937 | − | 0.120886i | ||||
\(635\) | 8.00000 | + | 13.8564i | 0.317470 | + | 0.549875i | ||||
\(636\) | 3.65685 | 0.145004 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.65685 | −0.0655955 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | −14.9289 | − | 25.8577i | −0.590118 | − | 1.02211i | ||||
\(641\) | −15.1421 | + | 26.2269i | −0.598078 | + | 1.03590i | 0.395026 | + | 0.918670i | \(0.370736\pi\) |
−0.993105 | + | 0.117232i | \(0.962598\pi\) | |||||||
\(642\) | −4.68629 | −0.184953 | ||||||||
\(643\) | −11.4142 | + | 19.7700i | −0.450133 | + | 0.779653i | −0.998394 | − | 0.0566545i | \(-0.981957\pi\) |
0.548261 | + | 0.836307i | \(0.315290\pi\) | |||||||
\(644\) | −10.3431 | + | 17.9149i | −0.407577 | + | 0.705944i | ||||
\(645\) | 4.68629 | 0.184523 | ||||||||
\(646\) | 4.48528 | − | 7.76874i | 0.176471 | − | 0.305657i | ||||
\(647\) | −5.65685 | − | 9.79796i | −0.222394 | − | 0.385198i | 0.733140 | − | 0.680077i | \(-0.238054\pi\) |
−0.955534 | + | 0.294880i | \(0.904720\pi\) | |||||||
\(648\) | 0.792893 | + | 1.37333i | 0.0311478 | + | 0.0539496i | ||||
\(649\) | −15.3137 | −0.601116 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.31371 | −0.129874 | ||||||||
\(652\) | 17.2132 | + | 29.8141i | 0.674121 | + | 1.16761i | ||||
\(653\) | 12.6569 | + | 21.9223i | 0.495301 | + | 0.857886i | 0.999985 | − | 0.00541749i | \(-0.00172445\pi\) |
−0.504684 | + | 0.863304i | \(0.668391\pi\) | |||||||
\(654\) | −1.10051 | + | 1.90613i | −0.0430332 | + | 0.0745356i | ||||
\(655\) | 22.6274 | 0.884126 | ||||||||
\(656\) | −7.75736 | + | 13.4361i | −0.302874 | + | 0.524593i | ||||
\(657\) | −0.171573 | + | 0.297173i | −0.00669370 | + | 0.0115938i | ||||
\(658\) | −13.6569 | −0.532400 | ||||||||
\(659\) | 23.6569 | − | 40.9749i | 0.921540 | − | 1.59615i | 0.124507 | − | 0.992219i | \(-0.460265\pi\) |
0.797033 | − | 0.603936i | \(-0.206402\pi\) | |||||||
\(660\) | 5.17157 | + | 8.95743i | 0.201303 | + | 0.348667i | ||||
\(661\) | 17.4853 | + | 30.2854i | 0.680099 | + | 1.17797i | 0.974950 | + | 0.222422i | \(0.0713964\pi\) |
−0.294852 | + | 0.955543i | \(0.595270\pi\) | |||||||
\(662\) | 10.8284 | 0.420859 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.79899 | −0.225044 | ||||||||
\(665\) | −11.3137 | − | 19.5959i | −0.438727 | − | 0.759897i | ||||
\(666\) | 1.58579 | + | 2.74666i | 0.0614480 | + | 0.106431i | ||||
\(667\) | 4.00000 | − | 6.92820i | 0.154881 | − | 0.268261i | ||||
\(668\) | 6.68629 | 0.258700 | ||||||||
\(669\) | 6.24264 | − | 10.8126i | 0.241354 | − | 0.418038i | ||||
\(670\) | 4.00000 | − | 6.92820i | 0.154533 | − | 0.267660i | ||||
\(671\) | −26.6274 | −1.02794 | ||||||||
\(672\) | −6.24264 | + | 10.8126i | −0.240815 | + | 0.417104i | ||||
\(673\) | −8.31371 | − | 14.3998i | −0.320470 | − | 0.555070i | 0.660115 | − | 0.751164i | \(-0.270507\pi\) |
−0.980585 | + | 0.196094i | \(0.937174\pi\) | |||||||
\(674\) | −1.92893 | − | 3.34101i | −0.0742997 | − | 0.128691i | ||||
\(675\) | 3.00000 | 0.115470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.6863 | 1.02564 | 0.512819 | − | 0.858497i | \(-0.328601\pi\) | ||||
0.512819 | + | 0.858497i | \(0.328601\pi\) | |||||||
\(678\) | 1.10051 | + | 1.90613i | 0.0422646 | + | 0.0732045i | ||||
\(679\) | −5.17157 | − | 8.95743i | −0.198467 | − | 0.343754i | ||||
\(680\) | −17.1716 | + | 29.7420i | −0.658500 | + | 1.14056i | ||||
\(681\) | −17.3137 | −0.663463 | ||||||||
\(682\) | −0.485281 | + | 0.840532i | −0.0185824 | + | 0.0321856i | ||||
\(683\) | −23.9706 | + | 41.5182i | −0.917208 | + | 1.58865i | −0.113572 | + | 0.993530i | \(0.536229\pi\) |
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(684\) | 5.17157 | 0.197740 | ||||||||
\(685\) | −15.3137 | + | 26.5241i | −0.585107 | + | 1.01343i | ||||
\(686\) | 3.51472 | + | 6.08767i | 0.134193 | + | 0.232428i | ||||
\(687\) | 0.656854 | + | 1.13770i | 0.0250606 | + | 0.0434062i | ||||
\(688\) | −4.97056 | −0.189501 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.68629 | 0.178404 | ||||||||
\(691\) | 2.92893 | + | 5.07306i | 0.111422 | + | 0.192988i | 0.916344 | − | 0.400392i | \(-0.131126\pi\) |
−0.804922 | + | 0.593381i | \(0.797793\pi\) | |||||||
\(692\) | −10.6569 | − | 18.4582i | −0.405113 | − | 0.701676i | ||||
\(693\) | 2.82843 | − | 4.89898i | 0.107443 | − | 0.186097i | ||||
\(694\) | −3.59798 | −0.136577 | ||||||||
\(695\) | −10.3431 | + | 17.9149i | −0.392338 | + | 0.679549i | ||||
\(696\) | 1.58579 | − | 2.74666i | 0.0601091 | − | 0.104112i | ||||
\(697\) | 39.5980 | 1.49988 | ||||||||
\(698\) | −0.757359 | + | 1.31178i | −0.0286665 | + | 0.0496518i | ||||
\(699\) | −3.48528 | − | 6.03668i | −0.131825 | − | 0.228328i | ||||
\(700\) | 7.75736 | + | 13.4361i | 0.293201 | + | 0.507838i | ||||
\(701\) | 5.02944 | 0.189959 | 0.0949796 | − | 0.995479i | \(-0.469721\pi\) | ||||
0.0949796 | + | 0.995479i | \(0.469721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.6569 | 0.816804 | ||||||||
\(704\) | −4.17157 | − | 7.22538i | −0.157222 | − | 0.272317i | ||||
\(705\) | −16.4853 | − | 28.5533i | −0.620872 | − | 1.07538i | ||||
\(706\) | 6.92893 | − | 12.0013i | 0.260774 | − | 0.451673i | ||||
\(707\) | 21.6569 | 0.814490 | ||||||||
\(708\) | 7.00000 | − | 12.1244i | 0.263076 | − | 0.455661i | ||||
\(709\) | 2.31371 | − | 4.00746i | 0.0868931 | − | 0.150503i | −0.819303 | − | 0.573360i | \(-0.805639\pi\) |
0.906196 | + | 0.422857i | \(0.138973\pi\) | |||||||
\(710\) | −2.34315 | −0.0879367 | ||||||||
\(711\) | 5.65685 | − | 9.79796i | 0.212149 | − | 0.367452i | ||||
\(712\) | 11.7574 | + | 20.3643i | 0.440626 | + | 0.763186i | ||||
\(713\) | −2.34315 | − | 4.05845i | −0.0877515 | − | 0.151990i | ||||
\(714\) | 8.97056 | 0.335715 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.6274 | 1.59306 | ||||||||
\(717\) | −1.00000 | − | 1.73205i | −0.0373457 | − | 0.0646846i | ||||
\(718\) | −7.24264 | − | 12.5446i | −0.270293 | − | 0.468161i | ||||
\(719\) | 14.9706 | − | 25.9298i | 0.558308 | − | 0.967017i | −0.439330 | − | 0.898326i | \(-0.644784\pi\) |
0.997638 | − | 0.0686918i | \(-0.0218825\pi\) | |||||||
\(720\) | −8.48528 | −0.316228 | ||||||||
\(721\) | −3.31371 | + | 5.73951i | −0.123409 | + | 0.213751i | ||||
\(722\) | 2.27817 | − | 3.94591i | 0.0847849 | − | 0.146852i | ||||
\(723\) | 0.343146 | 0.0127617 | ||||||||
\(724\) | 12.7990 | − | 22.1685i | 0.475671 | − | 0.823886i | ||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | 1.44975 | + | 2.51104i | 0.0538052 | + | 0.0931933i | ||||
\(727\) | −10.3431 | −0.383606 | −0.191803 | − | 0.981433i | \(-0.561433\pi\) | ||||
−0.191803 | + | 0.981433i | \(0.561433\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.201010 | + | 0.348160i | 0.00743972 | + | 0.0128860i | ||||
\(731\) | 6.34315 | + | 10.9867i | 0.234610 | + | 0.406356i | ||||
\(732\) | 12.1716 | − | 21.0818i | 0.449874 | − | 0.779205i | ||||
\(733\) | −36.6274 | −1.35286 | −0.676432 | − | 0.736505i | \(-0.736475\pi\) | ||||
−0.676432 | + | 0.736505i | \(0.736475\pi\) | |||||||
\(734\) | 4.97056 | − | 8.60927i | 0.183467 | − | 0.317774i | ||||
\(735\) | 1.41421 | − | 2.44949i | 0.0521641 | − | 0.0903508i | ||||
\(736\) | −17.6569 | −0.650840 | ||||||||
\(737\) | 6.82843 | − | 11.8272i | 0.251528 | − | 0.435660i | ||||
\(738\) | −1.07107 | − | 1.85514i | −0.0394266 | − | 0.0682888i | ||||
\(739\) | 9.07107 | + | 15.7116i | 0.333685 | + | 0.577959i | 0.983231 | − | 0.182363i | \(-0.0583746\pi\) |
−0.649547 | + | 0.760322i | \(0.725041\pi\) | |||||||
\(740\) | −39.5980 | −1.45565 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.34315 | −0.0860196 | ||||||||
\(743\) | −1.00000 | − | 1.73205i | −0.0366864 | − | 0.0635428i | 0.847099 | − | 0.531435i | \(-0.178347\pi\) |
−0.883786 | + | 0.467892i | \(0.845014\pi\) | |||||||
\(744\) | −0.928932 | − | 1.60896i | −0.0340563 | − | 0.0589873i | ||||
\(745\) | −12.9706 | + | 22.4657i | −0.475205 | + | 0.823079i | ||||
\(746\) | 4.14214 | 0.151654 | ||||||||
\(747\) | −1.82843 | + | 3.16693i | −0.0668987 | + | 0.115872i | ||||
\(748\) | −14.0000 | + | 24.2487i | −0.511891 | + | 0.886621i | ||||
\(749\) | −32.0000 | −1.16925 | ||||||||
\(750\) | −1.17157 | + | 2.02922i | −0.0427798 | + | 0.0740968i | ||||
\(751\) | 0.485281 | + | 0.840532i | 0.0177082 | + | 0.0306714i | 0.874744 | − | 0.484586i | \(-0.161030\pi\) |
−0.857036 | + | 0.515257i | \(0.827696\pi\) | |||||||
\(752\) | 17.4853 | + | 30.2854i | 0.637623 | + | 1.10439i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.94113 | 0.361795 | ||||||||
\(756\) | 2.58579 | + | 4.47871i | 0.0940441 | + | 0.162889i | ||||
\(757\) | −25.9706 | − | 44.9823i | −0.943916 | − | 1.63491i | −0.757907 | − | 0.652363i | \(-0.773778\pi\) |
−0.186009 | − | 0.982548i | \(-0.559555\pi\) | |||||||
\(758\) | −0.100505 | + | 0.174080i | −0.00365051 | + | 0.00632287i | ||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 6.34315 | − | 10.9867i | 0.230090 | − | 0.398528i | ||||
\(761\) | −16.2426 | + | 28.1331i | −0.588795 | + | 1.01982i | 0.405595 | + | 0.914053i | \(0.367064\pi\) |
−0.994391 | + | 0.105771i | \(0.966269\pi\) | |||||||
\(762\) | 2.34315 | 0.0848832 | ||||||||
\(763\) | −7.51472 | + | 13.0159i | −0.272051 | + | 0.471206i | ||||
\(764\) | 3.02944 | + | 5.24714i | 0.109601 | + | 0.189835i | ||||
\(765\) | 10.8284 | + | 18.7554i | 0.391503 | + | 0.678102i | ||||
\(766\) | 12.8284 | 0.463510 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.97056 | 0.143275 | ||||||||
\(769\) | −21.0000 | − | 36.3731i | −0.757279 | − | 1.31165i | −0.944233 | − | 0.329278i | \(-0.893195\pi\) |
0.186954 | − | 0.982369i | \(-0.440139\pi\) | |||||||
\(770\) | −3.31371 | − | 5.73951i | −0.119418 | − | 0.206838i | ||||
\(771\) | 2.17157 | − | 3.76127i | 0.0782073 | − | 0.135459i | ||||
\(772\) | −9.71573 | −0.349677 | ||||||||
\(773\) | −17.0711 | + | 29.5680i | −0.614004 | + | 1.06349i | 0.376555 | + | 0.926394i | \(0.377109\pi\) |
−0.990558 | + | 0.137091i | \(0.956225\pi\) | |||||||
\(774\) | 0.343146 | − | 0.594346i | 0.0123341 | − | 0.0213633i | ||||
\(775\) | −3.51472 | −0.126252 | ||||||||
\(776\) | 2.89949 | − | 5.02207i | 0.104086 | − | 0.180282i | ||||
\(777\) | 10.8284 | + | 18.7554i | 0.388468 | + | 0.672846i | ||||
\(778\) | 5.58579 | + | 9.67487i | 0.200260 | + | 0.346861i | ||||
\(779\) | −14.6274 | −0.524082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 6.34315 | + | 10.9867i | 0.226830 | + | 0.392882i | ||||
\(783\) | −1.00000 | − | 1.73205i | −0.0357371 | − | 0.0618984i | ||||
\(784\) | −1.50000 | + | 2.59808i | −0.0535714 | + | 0.0927884i | ||||
\(785\) | 28.2843 | 1.00951 | ||||||||
\(786\) | 1.65685 | − | 2.86976i | 0.0590980 | − | 0.102361i | ||||
\(787\) | 20.3848 | − | 35.3075i | 0.726639 | − | 1.25858i | −0.231657 | − | 0.972798i | \(-0.574415\pi\) |
0.958296 | − | 0.285778i | \(-0.0922519\pi\) | |||||||
\(788\) | −0.887302 | −0.0316088 | ||||||||
\(789\) | −6.00000 | + | 10.3923i | −0.213606 | + | 0.369976i | ||||
\(790\) | −6.62742 | − | 11.4790i | −0.235793 | − | 0.408405i | ||||
\(791\) | 7.51472 | + | 13.0159i | 0.267193 | + | 0.462791i | ||||
\(792\) | 3.17157 | 0.112697 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.8284 | 0.455264 | ||||||||
\(795\) | −2.82843 | − | 4.89898i | −0.100314 | − | 0.173749i | ||||
\(796\) | 19.7990 | + | 34.2929i | 0.701757 | + | 1.21548i | ||||
\(797\) | −12.1716 | + | 21.0818i | −0.431139 | + | 0.746755i | −0.996972 | − | 0.0777652i | \(-0.975222\pi\) |
0.565832 | + | 0.824520i | \(0.308555\pi\) | |||||||
\(798\) | −3.31371 | −0.117304 | ||||||||
\(799\) | 44.6274 | − | 77.2970i | 1.57880 | − | 2.73457i | ||||
\(800\) | −6.62132 | + | 11.4685i | −0.234099 | + | 0.405471i | ||||
\(801\) | 14.8284 | 0.523937 | ||||||||
\(802\) | −5.41421 | + | 9.37769i | −0.191183 | + | 0.331138i | ||||
\(803\) | 0.343146 | + | 0.594346i | 0.0121094 | + | 0.0209740i | ||||
\(804\) | 6.24264 | + | 10.8126i | 0.220161 | + | 0.381330i | ||||
\(805\) | 32.0000 | 1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | 6.07107 | + | 10.5154i | 0.213579 | + | 0.369930i | ||||
\(809\) | −9.34315 | − | 16.1828i | −0.328488 | − | 0.568957i | 0.653724 | − | 0.756733i | \(-0.273206\pi\) |
−0.982212 | + | 0.187776i | \(0.939872\pi\) | |||||||
\(810\) | 0.585786 | − | 1.01461i | 0.0205824 | − | 0.0356498i | ||||
\(811\) | −30.1421 | −1.05843 | −0.529217 | − | 0.848487i | \(-0.677514\pi\) | ||||
−0.529217 | + | 0.848487i | \(0.677514\pi\) | |||||||
\(812\) | 5.17157 | − | 8.95743i | 0.181487 | − | 0.314344i | ||||
\(813\) | 13.8995 | − | 24.0746i | 0.487477 | − | 0.844334i | ||||
\(814\) | 6.34315 | 0.222327 | ||||||||
\(815\) | 26.6274 | − | 46.1200i | 0.932718 | − | 1.61551i | ||||
\(816\) | −11.4853 | − | 19.8931i | −0.402065 | − | 0.696397i | ||||
\(817\) | −2.34315 | − | 4.05845i | −0.0819763 | − | 0.141987i | ||||
\(818\) | −14.4853 | −0.506466 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 26.7452 | 0.933982 | ||||||||
\(821\) | 11.8995 | + | 20.6105i | 0.415295 | + | 0.719312i | 0.995459 | − | 0.0951871i | \(-0.0303449\pi\) |
−0.580164 | + | 0.814500i | \(0.697012\pi\) | |||||||
\(822\) | 2.24264 | + | 3.88437i | 0.0782211 | + | 0.135483i | ||||
\(823\) | −7.51472 | + | 13.0159i | −0.261947 | + | 0.453705i | −0.966759 | − | 0.255689i | \(-0.917698\pi\) |
0.704813 | + | 0.709394i | \(0.251031\pi\) | |||||||
\(824\) | −3.71573 | −0.129444 | ||||||||
\(825\) | 3.00000 | − | 5.19615i | 0.104447 | − | 0.180907i | ||||
\(826\) | −4.48528 | + | 7.76874i | −0.156063 | + | 0.270309i | ||||
\(827\) | −26.0000 | −0.904109 | −0.452054 | − | 0.891990i | \(-0.649309\pi\) | ||||
−0.452054 | + | 0.891990i | \(0.649309\pi\) | |||||||
\(828\) | −3.65685 | + | 6.33386i | −0.127084 | + | 0.220117i | ||||
\(829\) | 8.65685 | + | 14.9941i | 0.300665 | + | 0.520767i | 0.976287 | − | 0.216481i | \(-0.0694581\pi\) |
−0.675622 | + | 0.737248i | \(0.736125\pi\) | |||||||
\(830\) | 2.14214 | + | 3.71029i | 0.0743546 | + | 0.128786i | ||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65685 | 0.265294 | ||||||||
\(834\) | 1.51472 | + | 2.62357i | 0.0524504 | + | 0.0908468i | ||||
\(835\) | −5.17157 | − | 8.95743i | −0.178970 | − | 0.309985i | ||||
\(836\) | 5.17157 | − | 8.95743i | 0.178863 | − | 0.309799i | ||||
\(837\) | −1.17157 | −0.0404955 | ||||||||
\(838\) | −3.02944 | + | 5.24714i | −0.104650 | + | 0.181259i | ||||
\(839\) | −21.6274 | + | 37.4598i | −0.746661 | + | 1.29326i | 0.202753 | + | 0.979230i | \(0.435011\pi\) |
−0.949415 | + | 0.314026i | \(0.898322\pi\) | |||||||
\(840\) | 12.6863 | 0.437719 | ||||||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | −7.72792 | − | 13.3852i | −0.266322 | − | 0.461283i | ||||
\(843\) | −10.5858 | − | 18.3351i | −0.364594 | − | 0.631495i | ||||
\(844\) | 21.9411 | 0.755245 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.82843 | −0.166005 | ||||||||
\(847\) | 9.89949 | + | 17.1464i | 0.340151 | + | 0.589158i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | −14.4853 | + | 25.0892i | −0.497134 | + | 0.861061i | ||||
\(850\) | 9.51472 | 0.326352 | ||||||||
\(851\) | −15.3137 | + | 26.5241i | −0.524947 | + | 0.909235i | ||||
\(852\) | 1.82843 | − | 3.16693i | 0.0626409 | − | 0.108497i | ||||
\(853\) | 3.65685 | 0.125208 | 0.0626042 | − | 0.998038i | \(-0.480059\pi\) | ||||
0.0626042 | + | 0.998038i | \(0.480059\pi\) | |||||||
\(854\) | −7.79899 | + | 13.5082i | −0.266876 | + | 0.462243i | ||||
\(855\) | −4.00000 | − | 6.92820i | −0.136797 | − | 0.236940i | ||||
\(856\) | −8.97056 | − | 15.5375i | −0.306608 | − | 0.531060i | ||||
\(857\) | −49.5980 | −1.69423 | −0.847117 | − | 0.531406i | \(-0.821664\pi\) | ||||
−0.847117 | + | 0.531406i | \(0.821664\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.686292 | −0.0234160 | −0.0117080 | − | 0.999931i | \(-0.503727\pi\) | ||||
−0.0117080 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(860\) | 4.28427 | + | 7.42058i | 0.146092 | + | 0.253040i | ||||
\(861\) | −7.31371 | − | 12.6677i | −0.249251 | − | 0.431715i | ||||
\(862\) | −1.72792 | + | 2.99285i | −0.0588533 | + | 0.101937i | ||||
\(863\) | −28.3431 | −0.964812 | −0.482406 | − | 0.875948i | \(-0.660237\pi\) | ||||
−0.482406 | + | 0.875948i | \(0.660237\pi\) | |||||||
\(864\) | −2.20711 | + | 3.82282i | −0.0750873 | + | 0.130055i | ||||
\(865\) | −16.4853 | + | 28.5533i | −0.560516 | + | 0.970843i | ||||
\(866\) | −8.82843 | −0.300002 | ||||||||
\(867\) | −20.8137 | + | 36.0504i | −0.706871 | + | 1.22434i | ||||
\(868\) | −3.02944 | − | 5.24714i | −0.102826 | − | 0.178100i | ||||
\(869\) | −11.3137 | − | 19.5959i | −0.383791 | − | 0.664746i | ||||
\(870\) | −2.34315 | −0.0794401 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.42641 | −0.285354 | ||||||||
\(873\) | −1.82843 | − | 3.16693i | −0.0618829 | − | 0.107184i | ||||
\(874\) | −2.34315 | − | 4.05845i | −0.0792581 | − | 0.137279i | ||||
\(875\) | −8.00000 | + | 13.8564i | −0.270449 | + | 0.468432i | ||||
\(876\) | −0.627417 | −0.0211985 | ||||||||
\(877\) | −21.1421 | + | 36.6193i | −0.713919 | + | 1.23654i | 0.249456 | + | 0.968386i | \(0.419748\pi\) |
−0.963375 | + | 0.268158i | \(0.913585\pi\) | |||||||
\(878\) | −3.51472 | + | 6.08767i | −0.118616 | + | 0.205449i | ||||
\(879\) | 2.14214 | 0.0722524 | ||||||||
\(880\) | −8.48528 | + | 14.6969i | −0.286039 | + | 0.495434i | ||||
\(881\) | 12.7990 | + | 22.1685i | 0.431209 | + | 0.746876i | 0.996978 | − | 0.0776882i | \(-0.0247539\pi\) |
−0.565769 | + | 0.824564i | \(0.691421\pi\) | |||||||
\(882\) | −0.207107 | − | 0.358719i | −0.00697365 | − | 0.0120787i | ||||
\(883\) | 27.5980 | 0.928746 | 0.464373 | − | 0.885640i | \(-0.346280\pi\) | ||||
0.464373 | + | 0.885640i | \(0.346280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.6569 | −0.727987 | ||||||||
\(886\) | 5.37258 | + | 9.30559i | 0.180495 | + | 0.312627i | ||||
\(887\) | 4.00000 | + | 6.92820i | 0.134307 | + | 0.232626i | 0.925332 | − | 0.379157i | \(-0.123786\pi\) |
−0.791026 | + | 0.611783i | \(0.790453\pi\) | |||||||
\(888\) | −6.07107 | + | 10.5154i | −0.203732 | + | 0.352874i | ||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 8.68629 | − | 15.0451i | 0.291165 | − | 0.504313i | ||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 22.8284 | 0.764352 | ||||||||
\(893\) | −16.4853 | + | 28.5533i | −0.551659 | + | 0.955501i | ||||
\(894\) | 1.89949 | + | 3.29002i | 0.0635286 | + | 0.110035i | ||||
\(895\) | −32.9706 | − | 57.1067i | −1.10208 | − | 1.90887i | ||||
\(896\) | −29.8579 | −0.997481 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.1716 | −0.439541 | ||||||||
\(899\) | 1.17157 | + | 2.02922i | 0.0390741 | + | 0.0676784i | ||||
\(900\) | 2.74264 | + | 4.75039i | 0.0914214 | + | 0.158346i | ||||
\(901\) | 7.65685 | − | 13.2621i | 0.255087 | − | 0.441823i | ||||
\(902\) | −4.28427 | −0.142651 | ||||||||
\(903\) | 2.34315 | − | 4.05845i | 0.0779750 | − | 0.135057i | ||||
\(904\) | −4.21320 | + | 7.29748i | −0.140129 | + | 0.242711i | ||||
\(905\) | −39.5980 | −1.31628 | ||||||||
\(906\) | 0.727922 | − | 1.26080i | 0.0241836 | − | 0.0418872i | ||||
\(907\) | 6.48528 | + | 11.2328i | 0.215340 | + | 0.372980i | 0.953378 | − | 0.301779i | \(-0.0975806\pi\) |
−0.738038 | + | 0.674760i | \(0.764247\pi\) | |||||||
\(908\) | −15.8284 | − | 27.4156i | −0.525285 | − | 0.909820i | ||||
\(909\) | 7.65685 | 0.253962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.0000 | −1.32526 | −0.662630 | − | 0.748947i | \(-0.730560\pi\) | ||||
−0.662630 | + | 0.748947i | \(0.730560\pi\) | |||||||
\(912\) | 4.24264 | + | 7.34847i | 0.140488 | + | 0.243332i | ||||
\(913\) | 3.65685 | + | 6.33386i | 0.121024 | + | 0.209620i | ||||
\(914\) | 1.58579 | − | 2.74666i | 0.0524532 | − | 0.0908515i | ||||
\(915\) | −37.6569 | −1.24490 | ||||||||
\(916\) | −1.20101 | + | 2.08021i | −0.0396825 | + | 0.0687321i | ||||
\(917\) | 11.3137 | − | 19.5959i | 0.373612 | − | 0.647114i | ||||
\(918\) | 3.17157 | 0.104678 | ||||||||
\(919\) | −1.65685 | + | 2.86976i | −0.0546546 | + | 0.0946645i | −0.892058 | − | 0.451920i | \(-0.850739\pi\) |
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(920\) | 8.97056 | + | 15.5375i | 0.295751 | + | 0.512255i | ||||
\(921\) | 11.4142 | + | 19.7700i | 0.376111 | + | 0.651444i | ||||
\(922\) | 2.14214 | 0.0705475 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 10.3431 | 0.340265 | ||||||||
\(925\) | 11.4853 | + | 19.8931i | 0.377634 | + | 0.654081i | ||||
\(926\) | 5.07107 | + | 8.78335i | 0.166646 | + | 0.288639i | ||||
\(927\) | −1.17157 | + | 2.02922i | −0.0384795 | + | 0.0666485i | ||||
\(928\) | 8.82843 | 0.289807 | ||||||||
\(929\) | −5.89949 | + | 10.2182i | −0.193556 | + | 0.335249i | −0.946426 | − | 0.322920i | \(-0.895336\pi\) |
0.752870 | + | 0.658169i | \(0.228669\pi\) | |||||||
\(930\) | −0.686292 | + | 1.18869i | −0.0225044 | + | 0.0389787i | ||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 6.37258 | − | 11.0376i | 0.208741 | − | 0.361550i | ||||
\(933\) | 5.31371 | + | 9.20361i | 0.173963 | + | 0.301313i | ||||
\(934\) | 1.65685 | + | 2.86976i | 0.0542139 | + | 0.0939013i | ||||
\(935\) | 43.3137 | 1.41651 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.3137 | −0.696289 | −0.348144 | − | 0.937441i | \(-0.613188\pi\) | ||||
−0.348144 | + | 0.937441i | \(0.613188\pi\) | |||||||
\(938\) | −4.00000 | − | 6.92820i | −0.130605 | − | 0.226214i | ||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | 30.1421 | − | 52.2077i | 0.983128 | − | 1.70283i | ||||
\(941\) | 34.1421 | 1.11300 | 0.556501 | − | 0.830847i | \(-0.312144\pi\) | ||||
0.556501 | + | 0.830847i | \(0.312144\pi\) | |||||||
\(942\) | 2.07107 | − | 3.58719i | 0.0674790 | − | 0.116877i | ||||
\(943\) | 10.3431 | − | 17.9149i | 0.336819 | − | 0.583388i | ||||
\(944\) | 22.9706 | 0.747628 | ||||||||
\(945\) | 4.00000 | − | 6.92820i | 0.130120 | − | 0.225374i | ||||
\(946\) | −0.686292 | − | 1.18869i | −0.0223133 | − | 0.0386477i | ||||
\(947\) | 10.5147 | + | 18.2120i | 0.341682 | + | 0.591811i | 0.984745 | − | 0.174002i | \(-0.0556699\pi\) |
−0.643063 | + | 0.765813i | \(0.722337\pi\) | |||||||
\(948\) | 20.6863 | 0.671860 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −3.51472 | −0.114033 | ||||||||
\(951\) | −4.24264 | − | 7.34847i | −0.137577 | − | 0.238290i | ||||
\(952\) | 17.1716 | + | 29.7420i | 0.556534 | + | 0.963945i | ||||
\(953\) | −20.1716 | + | 34.9382i | −0.653421 | + | 1.13176i | 0.328866 | + | 0.944377i | \(0.393334\pi\) |
−0.982287 | + | 0.187382i | \(0.940000\pi\) | |||||||
\(954\) | −0.828427 | −0.0268213 | ||||||||
\(955\) | 4.68629 | − | 8.11689i | 0.151645 | − | 0.262657i | ||||
\(956\) | 1.82843 | − | 3.16693i | 0.0591356 | − | 0.102426i | ||||
\(957\) | −4.00000 | −0.129302 | ||||||||
\(958\) | −5.24264 | + | 9.08052i | −0.169382 | + | 0.293378i | ||||
\(959\) | 15.3137 | + | 26.5241i | 0.494505 | + | 0.856509i | ||||
\(960\) | −5.89949 | − | 10.2182i | −0.190405 | − | 0.329792i | ||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.3137 | −0.364579 | ||||||||
\(964\) | 0.313708 | + | 0.543359i | 0.0101039 | + | 0.0175004i | ||||
\(965\) | 7.51472 | + | 13.0159i | 0.241907 | + | 0.418996i | ||||
\(966\) | 2.34315 | − | 4.05845i | 0.0753895 | − | 0.130578i | ||||
\(967\) | 18.1421 | 0.583412 | 0.291706 | − | 0.956508i | \(-0.405777\pi\) | ||||
0.291706 | + | 0.956508i | \(0.405777\pi\) | |||||||
\(968\) | −5.55025 | + | 9.61332i | −0.178392 | + | 0.308984i | ||||
\(969\) | 10.8284 | − | 18.7554i | 0.347859 | − | 0.602510i | ||||
\(970\) | −4.28427 | −0.137560 | ||||||||
\(971\) | 7.65685 | − | 13.2621i | 0.245720 | − | 0.425600i | −0.716614 | − | 0.697470i | \(-0.754309\pi\) |
0.962334 | + | 0.271871i | \(0.0876422\pi\) | |||||||
\(972\) | 0.914214 | + | 1.58346i | 0.0293234 | + | 0.0507896i | ||||
\(973\) | 10.3431 | + | 17.9149i | 0.331586 | + | 0.574324i | ||||
\(974\) | −3.23045 | −0.103510 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.9411 | 1.27848 | ||||||||
\(977\) | −21.0711 | − | 36.4962i | −0.674123 | − | 1.16762i | −0.976724 | − | 0.214498i | \(-0.931188\pi\) |
0.302601 | − | 0.953117i | \(-0.402145\pi\) | |||||||
\(978\) | −3.89949 | − | 6.75412i | −0.124692 | − | 0.215973i | ||||
\(979\) | 14.8284 | − | 25.6836i | 0.473919 | − | 0.820851i | ||||
\(980\) | 5.17157 | 0.165200 | ||||||||
\(981\) | −2.65685 | + | 4.60181i | −0.0848268 | + | 0.146924i | ||||
\(982\) | −6.34315 | + | 10.9867i | −0.202418 | + | 0.350598i | ||||
\(983\) | 25.3137 | 0.807382 | 0.403691 | − | 0.914895i | \(-0.367727\pi\) | ||||
0.403691 | + | 0.914895i | \(0.367727\pi\) | |||||||
\(984\) | 4.10051 | − | 7.10228i | 0.130719 | − | 0.226413i | ||||
\(985\) | 0.686292 | + | 1.18869i | 0.0218671 | + | 0.0378749i | ||||
\(986\) | −3.17157 | − | 5.49333i | −0.101003 | − | 0.174943i | ||||
\(987\) | −32.9706 | −1.04946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.62742 | 0.210740 | ||||||||
\(990\) | −1.17157 | − | 2.02922i | −0.0372350 | − | 0.0644930i | ||||
\(991\) | −2.34315 | − | 4.05845i | −0.0744325 | − | 0.128921i | 0.826407 | − | 0.563073i | \(-0.190381\pi\) |
−0.900839 | + | 0.434153i | \(0.857048\pi\) | |||||||
\(992\) | 2.58579 | − | 4.47871i | 0.0820988 | − | 0.142199i | ||||
\(993\) | 26.1421 | 0.829596 | ||||||||
\(994\) | −1.17157 | + | 2.02922i | −0.0371600 | + | 0.0643631i | ||||
\(995\) | 30.6274 | − | 53.0482i | 0.970954 | − | 1.68174i | ||||
\(996\) | −6.68629 | −0.211863 | ||||||||
\(997\) | 19.6274 | − | 33.9957i | 0.621607 | − | 1.07665i | −0.367580 | − | 0.929992i | \(-0.619814\pi\) |
0.989187 | − | 0.146662i | \(-0.0468530\pi\) | |||||||
\(998\) | −5.41421 | − | 9.37769i | −0.171384 | − | 0.296846i | ||||
\(999\) | 3.82843 | + | 6.63103i | 0.121126 | + | 0.209797i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))