Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.361 |
Dual form | 1323.2.g.b.667.3 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.849814 | − | 1.47192i | 0.600909 | − | 1.04081i | −0.391774 | − | 0.920061i | \(-0.628139\pi\) |
0.992684 | − | 0.120744i | \(-0.0385280\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.444368 | − | 0.769668i | −0.222184 | − | 0.384834i | ||||
\(5\) | −3.58836 | −1.60477 | −0.802383 | − | 0.596810i | \(-0.796435\pi\) | ||||
−0.802383 | + | 0.596810i | \(0.796435\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.88874 | 0.667769 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.04944 | + | 5.28179i | −0.964318 | + | 1.67025i | ||||
\(11\) | 2.81089 | 0.847516 | 0.423758 | − | 0.905775i | \(-0.360711\pi\) | ||||
0.423758 | + | 0.905775i | \(0.360711\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49381 | − | 4.31941i | 0.623453 | − | 1.07985i | ||||
\(17\) | 2.05563 | − | 3.56046i | 0.498564 | − | 0.863538i | −0.501435 | − | 0.865196i | \(-0.667194\pi\) |
0.999999 | + | 0.00165734i | \(0.000527549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.444368 | − | 0.769668i | −0.101945 | − | 0.176574i | 0.810541 | − | 0.585682i | \(-0.199173\pi\) |
−0.912486 | + | 0.409108i | \(0.865840\pi\) | |||||||
\(20\) | 1.59455 | + | 2.76185i | 0.356553 | + | 0.617568i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.38874 | − | 4.13741i | 0.509280 | − | 0.882099i | ||||
\(23\) | −5.87636 | −1.22530 | −0.612652 | − | 0.790352i | \(-0.709897\pi\) | ||||
−0.612652 | + | 0.790352i | \(0.709897\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.87636 | 1.57527 | ||||||||
\(26\) | −0.849814 | − | 1.47192i | −0.166662 | − | 0.288667i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.849814 | − | 1.47192i | −0.157807 | − | 0.273329i | 0.776271 | − | 0.630399i | \(-0.217109\pi\) |
−0.934077 | + | 0.357071i | \(0.883776\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.49381 | − | 6.05146i | −0.627507 | − | 1.08687i | −0.988050 | − | 0.154131i | \(-0.950742\pi\) |
0.360544 | − | 0.932742i | \(-0.382591\pi\) | |||||||
\(32\) | −2.34981 | − | 4.07000i | −0.415392 | − | 0.719481i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.49381 | − | 6.05146i | −0.599183 | − | 1.03782i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.38255 | − | 4.12669i | −0.391688 | − | 0.678424i | 0.600984 | − | 0.799261i | \(-0.294775\pi\) |
−0.992672 | + | 0.120837i | \(0.961442\pi\) | |||||||
\(38\) | −1.51052 | −0.245039 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.77747 | −1.07161 | ||||||||
\(41\) | 2.70582 | − | 4.68661i | 0.422578 | − | 0.731926i | −0.573613 | − | 0.819126i | \(-0.694459\pi\) |
0.996191 | + | 0.0872002i | \(0.0277920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.60507 | − | 4.51212i | −0.397270 | − | 0.688092i | 0.596118 | − | 0.802897i | \(-0.296709\pi\) |
−0.993388 | + | 0.114805i | \(0.963376\pi\) | |||||||
\(44\) | −1.24907 | − | 2.16345i | −0.188304 | − | 0.326153i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.99381 | + | 8.64953i | −0.736297 | + | 1.27530i | ||||
\(47\) | 1.33310 | − | 2.30900i | 0.194453 | − | 0.336803i | −0.752268 | − | 0.658857i | \(-0.771040\pi\) |
0.946721 | + | 0.322055i | \(0.104373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.69344 | − | 11.5934i | 0.946595 | − | 1.63955i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.888736 | −0.123245 | ||||||||
\(53\) | −0.0618219 | + | 0.107079i | −0.00849190 | + | 0.0147084i | −0.870240 | − | 0.492628i | \(-0.836036\pi\) |
0.861748 | + | 0.507336i | \(0.169370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0865 | −1.36006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.88874 | −0.379310 | ||||||||
\(59\) | 4.43818 | + | 7.68715i | 0.577802 | + | 1.00078i | 0.995731 | + | 0.0923022i | \(0.0294226\pi\) |
−0.417929 | + | 0.908479i | \(0.637244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.93818 | − | 3.35702i | 0.248158 | − | 0.429823i | −0.714857 | − | 0.699271i | \(-0.753508\pi\) |
0.963015 | + | 0.269448i | \(0.0868414\pi\) | |||||||
\(62\) | −11.8764 | −1.50830 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98762 | 0.248453 | ||||||||
\(65\) | −1.79418 | + | 3.10761i | −0.222541 | + | 0.385452i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.15452 | − | 10.6599i | −0.751894 | − | 1.30232i | −0.946904 | − | 0.321517i | \(-0.895807\pi\) |
0.195010 | − | 0.980801i | \(-0.437526\pi\) | |||||||
\(68\) | −3.65383 | −0.443092 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.87636 | 0.341361 | 0.170680 | − | 0.985326i | \(-0.445403\pi\) | ||||
0.170680 | + | 0.985326i | \(0.445403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.32072 | + | 9.21576i | −0.622744 | + | 1.07862i | 0.366229 | + | 0.930525i | \(0.380649\pi\) |
−0.988973 | + | 0.148099i | \(0.952685\pi\) | |||||||
\(74\) | −8.09888 | −0.941476 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.394926 | + | 0.684031i | −0.0453011 | + | 0.0784638i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.54325 | − | 6.13709i | 0.398647 | − | 0.690477i | −0.594912 | − | 0.803791i | \(-0.702813\pi\) |
0.993559 | + | 0.113314i | \(0.0361465\pi\) | |||||||
\(80\) | −8.94870 | + | 15.4996i | −1.00049 | + | 1.73291i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.59888 | − | 7.96550i | −0.507862 | − | 0.879642i | ||||
\(83\) | 2.05563 | + | 3.56046i | 0.225635 | + | 0.390811i | 0.956510 | − | 0.291700i | \(-0.0942210\pi\) |
−0.730875 | + | 0.682512i | \(0.760888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.37636 | + | 12.7762i | −0.800078 | + | 1.38578i | ||||
\(86\) | −8.85532 | −0.954893 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.30903 | 0.565945 | ||||||||
\(89\) | −4.80470 | − | 8.32199i | −0.509297 | − | 0.882129i | −0.999942 | − | 0.0107692i | \(-0.996572\pi\) |
0.490645 | − | 0.871360i | \(-0.336761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.61126 | + | 4.52284i | 0.272243 | + | 0.471539i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.26578 | − | 3.92445i | −0.233697 | − | 0.404776i | ||||
\(95\) | 1.59455 | + | 2.76185i | 0.163598 | + | 0.283360i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.66071 | + | 6.34053i | 0.371688 | + | 0.643783i | 0.989825 | − | 0.142287i | \(-0.0454456\pi\) |
−0.618137 | + | 0.786070i | \(0.712112\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.50000 | − | 6.06218i | −0.350000 | − | 0.606218i | ||||
\(101\) | 3.46472 | 0.344753 | 0.172376 | − | 0.985031i | \(-0.444856\pi\) | ||||
0.172376 | + | 0.985031i | \(0.444856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8764 | 1.56434 | 0.782172 | − | 0.623063i | \(-0.214112\pi\) | ||||
0.782172 | + | 0.623063i | \(0.214112\pi\) | |||||||
\(104\) | 0.944368 | − | 1.63569i | 0.0926029 | − | 0.160393i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.105074 | + | 0.181994i | 0.0102057 | + | 0.0176768i | ||||
\(107\) | −2.67673 | − | 4.63623i | −0.258769 | − | 0.448201i | 0.707143 | − | 0.707070i | \(-0.249984\pi\) |
−0.965912 | + | 0.258869i | \(0.916650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.43199 | − | 16.3367i | 0.903421 | − | 1.56477i | 0.0803973 | − | 0.996763i | \(-0.474381\pi\) |
0.823023 | − | 0.568008i | \(-0.192286\pi\) | |||||||
\(110\) | −8.57165 | + | 14.8465i | −0.817275 | + | 1.41556i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.27561 | + | 16.0658i | −0.872576 | + | 1.51135i | −0.0132538 | + | 0.999912i | \(0.504219\pi\) |
−0.859322 | + | 0.511434i | \(0.829114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 21.0865 | 1.96633 | ||||||||
\(116\) | −0.755260 | + | 1.30815i | −0.0701242 | + | 0.121459i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0865 | 1.38883 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.09888 | −0.281717 | ||||||||
\(122\) | −3.29418 | − | 5.70569i | −0.298241 | − | 0.516569i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.10507 | + | 5.37815i | −0.278844 | + | 0.482972i | ||||
\(125\) | −10.3214 | −0.923175 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.98762 | 0.886258 | 0.443129 | − | 0.896458i | \(-0.353868\pi\) | ||||
0.443129 | + | 0.896458i | \(0.353868\pi\) | |||||||
\(128\) | 6.38874 | − | 11.0656i | 0.564690 | − | 0.978071i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.04944 | + | 5.28179i | 0.267454 | + | 0.463244i | ||||
\(131\) | 16.0531 | 1.40256 | 0.701282 | − | 0.712884i | \(-0.252611\pi\) | ||||
0.701282 | + | 0.712884i | \(0.252611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.9208 | −1.80728 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.88255 | − | 6.72477i | 0.332926 | − | 0.576644i | ||||
\(137\) | 12.9876 | 1.10961 | 0.554804 | − | 0.831981i | \(-0.312793\pi\) | ||||
0.554804 | + | 0.831981i | \(0.312793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.555632 | − | 0.962383i | 0.0471281 | − | 0.0816283i | −0.841499 | − | 0.540259i | \(-0.818326\pi\) |
0.888627 | + | 0.458630i | \(0.151660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.44437 | − | 4.23377i | 0.205127 | − | 0.355290i | ||||
\(143\) | 1.40545 | − | 2.43430i | 0.117529 | − | 0.203567i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.04944 | + | 5.28179i | 0.253242 | + | 0.438629i | ||||
\(146\) | 9.04325 | + | 15.6634i | 0.748425 | + | 1.29631i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.11745 | + | 3.66754i | −0.174054 | + | 0.301470i | ||||
\(149\) | −8.43268 | −0.690832 | −0.345416 | − | 0.938450i | \(-0.612262\pi\) | ||||
−0.345416 | + | 0.938450i | \(0.612262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.8516 | −1.20861 | −0.604303 | − | 0.796755i | \(-0.706548\pi\) | ||||
−0.604303 | + | 0.796755i | \(0.706548\pi\) | |||||||
\(152\) | −0.839294 | − | 1.45370i | −0.0680757 | − | 0.117911i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.5371 | + | 21.7148i | 1.00700 | + | 1.74418i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.44437 | + | 2.50172i | 0.115273 | + | 0.199659i | 0.917889 | − | 0.396837i | \(-0.129892\pi\) |
−0.802616 | + | 0.596496i | \(0.796559\pi\) | |||||||
\(158\) | −6.02221 | − | 10.4308i | −0.479101 | − | 0.829828i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.43199 | + | 14.6046i | 0.666607 | + | 1.15460i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.15452 | + | 8.92788i | 0.403733 | + | 0.699286i | 0.994173 | − | 0.107796i | \(-0.0343792\pi\) |
−0.590440 | + | 0.807081i | \(0.701046\pi\) | |||||||
\(164\) | −4.80951 | −0.375560 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.98762 | 0.542345 | ||||||||
\(167\) | −6.07598 | + | 10.5239i | −0.470174 | + | 0.814365i | −0.999418 | − | 0.0341045i | \(-0.989142\pi\) |
0.529244 | + | 0.848469i | \(0.322475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 12.5371 | + | 21.7148i | 0.961549 | + | 1.66545i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.31522 | + | 4.01008i | −0.176534 | + | 0.305766i | ||||
\(173\) | 3.30470 | − | 5.72391i | 0.251252 | − | 0.435181i | −0.712619 | − | 0.701551i | \(-0.752491\pi\) |
0.963871 | + | 0.266370i | \(0.0858244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.00983 | − | 12.1414i | 0.528386 | − | 0.915191i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.3324 | −1.22417 | ||||||||
\(179\) | −1.92147 | + | 3.32808i | −0.143617 | + | 0.248752i | −0.928856 | − | 0.370440i | \(-0.879207\pi\) |
0.785239 | + | 0.619193i | \(0.212540\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.5426 | −1.37826 | −0.689129 | − | 0.724639i | \(-0.742007\pi\) | ||||
−0.689129 | + | 0.724639i | \(0.742007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.0989 | −0.818221 | ||||||||
\(185\) | 8.54944 | + | 14.8081i | 0.628567 | + | 1.08871i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.77816 | − | 10.0081i | 0.422541 | − | 0.731862i | ||||
\(188\) | −2.36955 | −0.172818 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.42030 | 0.393230 | ||||||||
\(191\) | 2.31708 | − | 4.01330i | 0.167658 | − | 0.290392i | −0.769938 | − | 0.638119i | \(-0.779713\pi\) |
0.937596 | + | 0.347726i | \(0.113046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6483 | + | 21.9075i | 0.910446 | + | 1.57694i | 0.813435 | + | 0.581656i | \(0.197595\pi\) |
0.0970118 | + | 0.995283i | \(0.469072\pi\) | |||||||
\(194\) | 12.4437 | 0.893404 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7207 | −0.763816 | −0.381908 | − | 0.924200i | \(-0.624733\pi\) | ||||
−0.381908 | + | 0.924200i | \(0.624733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.38323 | + | 7.59199i | −0.310719 | + | 0.538182i | −0.978518 | − | 0.206160i | \(-0.933903\pi\) |
0.667799 | + | 0.744342i | \(0.267237\pi\) | |||||||
\(200\) | 14.8764 | 1.05192 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.94437 | − | 5.09979i | 0.207165 | − | 0.358820i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.70946 | + | 16.8173i | −0.678138 | + | 1.17457i | ||||
\(206\) | 13.4920 | − | 23.3687i | 0.940029 | − | 1.62818i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.49381 | − | 4.31941i | −0.172915 | − | 0.299497i | ||||
\(209\) | −1.24907 | − | 2.16345i | −0.0864000 | − | 0.149649i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.26509 | + | 9.11941i | −0.362464 | + | 0.627806i | −0.988366 | − | 0.152096i | \(-0.951398\pi\) |
0.625902 | + | 0.779902i | \(0.284731\pi\) | |||||||
\(212\) | 0.109887 | 0.00754705 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.09888 | −0.621987 | ||||||||
\(215\) | 9.34795 | + | 16.1911i | 0.637525 | + | 1.10423i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −16.0309 | − | 27.7663i | −1.08575 | − | 1.88057i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.48212 | + | 7.76326i | 0.302184 | + | 0.523399i | ||||
\(221\) | −2.05563 | − | 3.56046i | −0.138277 | − | 0.239502i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83379 | − | 4.90827i | −0.189765 | − | 0.328682i | 0.755407 | − | 0.655256i | \(-0.227439\pi\) |
−0.945172 | + | 0.326574i | \(0.894106\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.7651 | + | 27.3059i | 1.04868 | + | 1.81636i | ||||
\(227\) | −11.0989 | −0.736659 | −0.368329 | − | 0.929695i | \(-0.620070\pi\) | ||||
−0.368329 | + | 0.929695i | \(0.620070\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6428 | −1.29803 | −0.649017 | − | 0.760774i | \(-0.724820\pi\) | ||||
−0.649017 | + | 0.760774i | \(0.724820\pi\) | |||||||
\(230\) | 17.9196 | − | 31.0377i | 1.18158 | − | 2.04656i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.60507 | − | 2.78007i | −0.105378 | − | 0.182521i | ||||
\(233\) | 4.48143 | + | 7.76207i | 0.293588 | + | 0.508510i | 0.974656 | − | 0.223711i | \(-0.0718172\pi\) |
−0.681067 | + | 0.732221i | \(0.738484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.78366 | + | 8.28554i | −0.312052 | + | 0.540489i | ||||
\(236\) | 3.94437 | − | 6.83185i | 0.256756 | − | 0.444715i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.61126 | − | 9.71899i | 0.362963 | − | 0.628670i | −0.625484 | − | 0.780237i | \(-0.715099\pi\) |
0.988447 | + | 0.151567i | \(0.0484320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.98624 | 0.450023 | 0.225012 | − | 0.974356i | \(-0.427758\pi\) | ||||
0.225012 | + | 0.974356i | \(0.427758\pi\) | |||||||
\(242\) | −2.63348 | + | 4.56131i | −0.169286 | + | 0.293212i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.44506 | −0.220547 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.888736 | −0.0565489 | ||||||||
\(248\) | −6.59888 | − | 11.4296i | −0.419030 | − | 0.725781i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.77128 | + | 15.1923i | −0.554745 | + | 0.960846i | ||||
\(251\) | 4.62041 | 0.291638 | 0.145819 | − | 0.989311i | \(-0.453418\pi\) | ||||
0.145819 | + | 0.989311i | \(0.453418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.5178 | −1.03847 | ||||||||
\(254\) | 8.48762 | − | 14.7010i | 0.532561 | − | 0.922422i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.87085 | − | 15.3648i | −0.554428 | − | 0.960298i | ||||
\(257\) | −1.42402 | −0.0888277 | −0.0444138 | − | 0.999013i | \(-0.514142\pi\) | ||||
−0.0444138 | + | 0.999013i | \(0.514142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.18911 | 0.197780 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.6421 | − | 23.6289i | 0.842814 | − | 1.45980i | ||||
\(263\) | −16.2632 | −1.00283 | −0.501417 | − | 0.865206i | \(-0.667188\pi\) | ||||
−0.501417 | + | 0.865206i | \(0.667188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.221840 | − | 0.384237i | 0.0136275 | − | 0.0236035i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.46974 | + | 9.47387i | −0.334118 | + | 0.578709i | ||||
\(269\) | 9.32691 | − | 16.1547i | 0.568672 | − | 0.984969i | −0.428026 | − | 0.903767i | \(-0.640791\pi\) |
0.996698 | − | 0.0812022i | \(-0.0258759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.98143 | + | 3.43194i | 0.120363 | + | 0.208475i | 0.919911 | − | 0.392127i | \(-0.128261\pi\) |
−0.799548 | + | 0.600603i | \(0.794927\pi\) | |||||||
\(272\) | −10.2527 | − | 17.7582i | −0.621662 | − | 1.07675i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0371 | − | 19.1168i | 0.666773 | − | 1.15489i | ||||
\(275\) | 22.1396 | 1.33507 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.33379 | −0.140224 | −0.0701120 | − | 0.997539i | \(-0.522336\pi\) | ||||
−0.0701120 | + | 0.997539i | \(0.522336\pi\) | |||||||
\(278\) | −0.944368 | − | 1.63569i | −0.0566394 | − | 0.0981024i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9975 | + | 24.2443i | 0.835018 | + | 1.44629i | 0.894016 | + | 0.448035i | \(0.147876\pi\) |
−0.0589978 | + | 0.998258i | \(0.518790\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.16002 | + | 8.93741i | 0.306731 | + | 0.531274i | 0.977645 | − | 0.210261i | \(-0.0674314\pi\) |
−0.670914 | + | 0.741535i | \(0.734098\pi\) | |||||||
\(284\) | −1.27816 | − | 2.21384i | −0.0758449 | − | 0.131367i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.38874 | − | 4.13741i | −0.141249 | − | 0.244650i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0487535 | + | 0.0844436i | 0.00286785 | + | 0.00496727i | ||||
\(290\) | 10.3658 | 0.608703 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.45744 | 0.553455 | ||||||||
\(293\) | 15.3480 | − | 26.5834i | 0.896637 | − | 1.55302i | 0.0648718 | − | 0.997894i | \(-0.479336\pi\) |
0.831765 | − | 0.555127i | \(-0.187330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.9258 | − | 27.5843i | −0.927236 | − | 1.60602i | ||||
\(296\) | −4.50000 | − | 7.79423i | −0.261557 | − | 0.453030i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.16621 | + | 12.4122i | −0.415127 | + | 0.719021i | ||||
\(299\) | −2.93818 | + | 5.08907i | −0.169919 | + | 0.294309i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.6211 | + | 21.8604i | −0.726262 | + | 1.25792i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.43268 | −0.254231 | ||||||||
\(305\) | −6.95489 | + | 12.0462i | −0.398236 | + | 0.689765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4437 | 0.653125 | 0.326563 | − | 0.945176i | \(-0.394110\pi\) | ||||
0.326563 | + | 0.945176i | \(0.394110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 42.6167 | 2.42047 | ||||||||
\(311\) | −5.98143 | − | 10.3601i | −0.339176 | − | 0.587470i | 0.645102 | − | 0.764096i | \(-0.276815\pi\) |
−0.984278 | + | 0.176627i | \(0.943481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.77197 | + | 11.7294i | −0.382774 | + | 0.662985i | −0.991458 | − | 0.130429i | \(-0.958365\pi\) |
0.608683 | + | 0.793413i | \(0.291698\pi\) | |||||||
\(314\) | 4.90978 | 0.277075 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.29803 | −0.354292 | ||||||||
\(317\) | −14.9814 | + | 25.9486i | −0.841441 | + | 1.45742i | 0.0472355 | + | 0.998884i | \(0.484959\pi\) |
−0.888676 | + | 0.458535i | \(0.848374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.38874 | − | 4.13741i | −0.133744 | − | 0.231651i | ||||
\(320\) | −7.13231 | −0.398708 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.65383 | −0.203304 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.93818 | − | 6.82112i | 0.218451 | − | 0.378368i | ||||
\(326\) | 17.5215 | 0.970427 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.11058 | − | 8.85178i | 0.282184 | − | 0.488758i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.04325 | + | 1.80697i | −0.0573423 | + | 0.0993198i | −0.893272 | − | 0.449517i | \(-0.851596\pi\) |
0.835929 | + | 0.548837i | \(0.184929\pi\) | |||||||
\(332\) | 1.82691 | − | 3.16431i | 0.100265 | − | 0.173664i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.3269 | + | 17.8867i | 0.565064 | + | 0.978719i | ||||
\(335\) | 22.0846 | + | 38.2517i | 1.20661 | + | 2.08992i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.10439 | − | 14.0372i | 0.441474 | − | 0.764655i | −0.556325 | − | 0.830965i | \(-0.687789\pi\) |
0.997799 | + | 0.0663093i | \(0.0211224\pi\) | |||||||
\(338\) | 20.3955 | 1.10937 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.1113 | 0.711058 | ||||||||
\(341\) | −9.82072 | − | 17.0100i | −0.531822 | − | 0.921143i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.92030 | − | 8.52220i | −0.265285 | − | 0.459486i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.61677 | − | 9.72852i | −0.301959 | − | 0.523009i | ||||
\(347\) | 5.63348 | + | 9.75747i | 0.302421 | + | 0.523808i | 0.976684 | − | 0.214683i | \(-0.0688719\pi\) |
−0.674263 | + | 0.738491i | \(0.735539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.0988844 | − | 0.171273i | −0.00529316 | − | 0.00916803i | 0.863367 | − | 0.504577i | \(-0.168352\pi\) |
−0.868660 | + | 0.495409i | \(0.835018\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.60507 | − | 11.4403i | −0.352052 | − | 0.609771i | ||||
\(353\) | −12.5019 | −0.665407 | −0.332703 | − | 0.943032i | \(-0.607961\pi\) | ||||
−0.332703 | + | 0.943032i | \(0.607961\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.3214 | −0.547804 | ||||||||
\(356\) | −4.27011 | + | 7.39605i | −0.226315 | + | 0.391990i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.26578 | + | 5.65650i | 0.172602 | + | 0.298955i | ||||
\(359\) | 10.0098 | + | 17.3375i | 0.528299 | + | 0.915040i | 0.999456 | + | 0.0329908i | \(0.0105032\pi\) |
−0.471157 | + | 0.882049i | \(0.656163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.10507 | − | 15.7705i | 0.479214 | − | 0.830024i | ||||
\(362\) | −15.7577 | + | 27.2932i | −0.828208 | + | 1.43450i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0927 | − | 33.0695i | 0.999357 | − | 1.73094i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.0727 | −1.56978 | −0.784892 | − | 0.619632i | \(-0.787282\pi\) | ||||
−0.784892 | + | 0.619632i | \(0.787282\pi\) | |||||||
\(368\) | −14.6545 | + | 25.3824i | −0.763919 | + | 1.32315i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.0617 | 1.51085 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.01238 | 0.363087 | 0.181544 | − | 0.983383i | \(-0.441891\pi\) | ||||
0.181544 | + | 0.983383i | \(0.441891\pi\) | |||||||
\(374\) | −9.82072 | − | 17.0100i | −0.507818 | − | 0.879566i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.51788 | − | 4.36110i | 0.129850 | − | 0.224906i | ||||
\(377\) | −1.69963 | −0.0875353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0741 | −0.979772 | −0.489886 | − | 0.871787i | \(-0.662962\pi\) | ||||
−0.489886 | + | 0.871787i | \(0.662962\pi\) | |||||||
\(380\) | 1.41714 | − | 2.45455i | 0.0726976 | − | 0.125916i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.93818 | − | 6.82112i | −0.201495 | − | 0.348999i | ||||
\(383\) | 3.21015 | 0.164031 | 0.0820155 | − | 0.996631i | \(-0.473864\pi\) | ||||
0.0820155 | + | 0.996631i | \(0.473864\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 42.9949 | 2.18838 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.25340 | − | 5.63506i | 0.165166 | − | 0.286077i | ||||
\(389\) | −5.13602 | −0.260407 | −0.130203 | − | 0.991487i | \(-0.541563\pi\) | ||||
−0.130203 | + | 0.991487i | \(0.541563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0796 | + | 20.9225i | −0.610893 | + | 1.05810i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.11058 | + | 15.7800i | −0.458984 | + | 0.794984i | ||||
\(395\) | −12.7145 | + | 22.0221i | −0.639735 | + | 1.10805i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4691 | + | 19.8650i | 0.575615 | + | 0.996995i | 0.995975 | + | 0.0896370i | \(0.0285707\pi\) |
−0.420359 | + | 0.907358i | \(0.638096\pi\) | |||||||
\(398\) | 7.44987 | + | 12.9036i | 0.373428 | + | 0.646797i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.6421 | − | 34.0212i | 0.982107 | − | 1.70106i | ||||
\(401\) | 18.2101 | 0.909371 | 0.454686 | − | 0.890652i | \(-0.349752\pi\) | ||||
0.454686 | + | 0.890652i | \(0.349752\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.98762 | −0.348078 | ||||||||
\(404\) | −1.53961 | − | 2.66668i | −0.0765985 | − | 0.132672i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.69708 | − | 11.5997i | −0.331962 | − | 0.574975i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.66621 | − | 13.2783i | −0.379070 | − | 0.656568i | 0.611858 | − | 0.790968i | \(-0.290423\pi\) |
−0.990927 | + | 0.134400i | \(0.957089\pi\) | |||||||
\(410\) | 16.5025 | + | 28.5831i | 0.814999 | + | 1.41162i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.05494 | − | 12.2195i | −0.347572 | − | 0.602013i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.37636 | − | 12.7762i | −0.362091 | − | 0.627160i | ||||
\(416\) | −4.69963 | −0.230418 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.24591 | −0.207674 | ||||||||
\(419\) | −5.28435 | + | 9.15276i | −0.258157 | + | 0.447142i | −0.965748 | − | 0.259481i | \(-0.916449\pi\) |
0.707591 | + | 0.706622i | \(0.249782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0858 | + | 31.3256i | 0.881449 | + | 1.52671i | 0.849731 | + | 0.527217i | \(0.176765\pi\) |
0.0317181 | + | 0.999497i | \(0.489902\pi\) | |||||||
\(422\) | 8.94870 | + | 15.4996i | 0.435616 | + | 0.754509i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.116765 | + | 0.202243i | −0.00567062 | + | 0.00982181i | ||||
\(425\) | 16.1909 | − | 28.0434i | 0.785374 | − | 1.36031i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.37890 | + | 4.12038i | −0.114989 | + | 0.199166i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.7761 | 1.53238 | ||||||||
\(431\) | 17.5494 | − | 30.3965i | 0.845327 | − | 1.46415i | −0.0400101 | − | 0.999199i | \(-0.512739\pi\) |
0.885337 | − | 0.464950i | \(-0.153928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.1730 | 1.97865 | 0.989324 | − | 0.145731i | \(-0.0465533\pi\) | ||||
0.989324 | + | 0.145731i | \(0.0465533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.7651 | −0.802902 | ||||||||
\(437\) | 2.61126 | + | 4.52284i | 0.124914 | + | 0.216357i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.33929 | + | 4.05178i | −0.111648 | + | 0.193381i | −0.916435 | − | 0.400184i | \(-0.868946\pi\) |
0.804787 | + | 0.593564i | \(0.202280\pi\) | |||||||
\(440\) | −19.0507 | −0.908209 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.98762 | −0.332367 | ||||||||
\(443\) | 15.0865 | − | 26.1306i | 0.716781 | − | 1.24150i | −0.245487 | − | 0.969400i | \(-0.578948\pi\) |
0.962268 | − | 0.272102i | \(-0.0877188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2410 | + | 29.8623i | 0.817303 | + | 1.41561i | ||||
\(446\) | −9.63279 | −0.456126 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.333792 | −0.0157526 | −0.00787632 | − | 0.999969i | \(-0.502507\pi\) | ||||
−0.00787632 | + | 0.999969i | \(0.502507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.60576 | − | 13.1736i | 0.358141 | − | 0.620319i | ||||
\(452\) | 16.4871 | 0.775490 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.43199 | + | 16.3367i | −0.442665 | + | 0.766719i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.65452 | − | 16.7221i | 0.451619 | − | 0.782227i | −0.546868 | − | 0.837219i | \(-0.684180\pi\) |
0.998487 | + | 0.0549917i | \(0.0175132\pi\) | |||||||
\(458\) | −16.6927 | + | 28.9127i | −0.780001 | + | 1.35100i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.37017 | − | 16.2296i | −0.436886 | − | 0.756709i | ||||
\(461\) | −19.5538 | − | 33.8681i | −0.910710 | − | 1.57740i | −0.813064 | − | 0.582175i | \(-0.802202\pi\) |
−0.0976463 | − | 0.995221i | \(-0.531131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9382 | + | 18.9455i | −0.508340 | + | 0.880471i | 0.491613 | + | 0.870814i | \(0.336407\pi\) |
−0.999953 | + | 0.00965741i | \(0.996926\pi\) | |||||||
\(464\) | −8.47710 | −0.393539 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.2335 | 0.705680 | ||||||||
\(467\) | 6.16002 | + | 10.6695i | 0.285052 | + | 0.493724i | 0.972622 | − | 0.232394i | \(-0.0746559\pi\) |
−0.687570 | + | 0.726118i | \(0.741323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.13045 | + | 14.0823i | 0.375029 | + | 0.649570i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.38255 | + | 14.5190i | 0.385838 | + | 0.668291i | ||||
\(473\) | −7.32258 | − | 12.6831i | −0.336693 | − | 0.583169i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | − | 6.06218i | −0.160591 | − | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.53706 | − | 16.5187i | −0.436215 | − | 0.755547i | ||||
\(479\) | 13.4895 | 0.616350 | 0.308175 | − | 0.951330i | \(-0.400282\pi\) | ||||
0.308175 | + | 0.951330i | \(0.400282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.76509 | −0.217269 | ||||||||
\(482\) | 5.93701 | − | 10.2832i | 0.270423 | − | 0.468387i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.37704 | + | 2.38511i | 0.0625929 | + | 0.108414i | ||||
\(485\) | −13.1359 | − | 22.7521i | −0.596473 | − | 1.03312i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.77197 | + | 6.53324i | −0.170924 | + | 0.296050i | −0.938743 | − | 0.344617i | \(-0.888009\pi\) |
0.767819 | + | 0.640667i | \(0.221342\pi\) | |||||||
\(488\) | 3.66071 | − | 6.34053i | 0.165712 | − | 0.287022i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.06979 | + | 13.9773i | −0.364185 | + | 0.630786i | −0.988645 | − | 0.150270i | \(-0.951986\pi\) |
0.624460 | + | 0.781057i | \(0.285319\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.98762 | −0.314707 | ||||||||
\(494\) | −0.755260 | + | 1.30815i | −0.0339808 | + | 0.0588564i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.8516 | −1.56488 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.8654 | −1.38172 | −0.690862 | − | 0.722987i | \(-0.742769\pi\) | ||||
−0.690862 | + | 0.722987i | \(0.742769\pi\) | |||||||
\(500\) | 4.58650 | + | 7.94406i | 0.205115 | + | 0.355269i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.92649 | − | 6.80088i | 0.175248 | − | 0.303538i | ||||
\(503\) | 24.6304 | 1.09822 | 0.549109 | − | 0.835751i | \(-0.314967\pi\) | ||||
0.549109 | + | 0.835751i | \(0.314967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4327 | −0.553247 | ||||||||
\(506\) | −14.0371 | + | 24.3129i | −0.624024 | + | 1.08084i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.43818 | − | 7.68715i | −0.196912 | − | 0.341062i | ||||
\(509\) | 13.5897 | 0.602355 | 0.301177 | − | 0.953568i | \(-0.402620\pi\) | ||||
0.301177 | + | 0.953568i | \(0.402620\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.59937 | −0.203265 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.21015 | + | 2.09604i | −0.0533774 | + | 0.0924523i | ||||
\(515\) | −56.9701 | −2.51040 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.74721 | − | 6.49036i | 0.164802 | − | 0.285446i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.38874 | + | 5.86946i | −0.148606 | + | 0.257393i | ||||
\(521\) | 19.5865 | − | 33.9248i | 0.858100 | − | 1.48627i | −0.0156383 | − | 0.999878i | \(-0.504978\pi\) |
0.873739 | − | 0.486396i | \(-0.161689\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.56182 | + | 16.5616i | 0.418109 | + | 0.724187i | 0.995749 | − | 0.0921051i | \(-0.0293596\pi\) |
−0.577640 | + | 0.816292i | \(0.696026\pi\) | |||||||
\(524\) | −7.13348 | − | 12.3555i | −0.311627 | − | 0.539754i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.8207 | + | 23.9382i | −0.602612 | + | 1.04375i | ||||
\(527\) | −28.7280 | −1.25141 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5316 | 0.501372 | ||||||||
\(530\) | −0.377045 | − | 0.653061i | −0.0163778 | − | 0.0283671i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.70582 | − | 4.68661i | −0.117202 | − | 0.203000i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.60507 | + | 16.6365i | 0.415264 | + | 0.719258i | ||||
\(536\) | −11.6243 | − | 20.1338i | −0.502091 | − | 0.869648i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.8523 | − | 27.4570i | −0.683441 | − | 1.18375i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.26509 | − | 2.19120i | −0.0543906 | − | 0.0942072i | 0.837548 | − | 0.546363i | \(-0.183988\pi\) |
−0.891939 | + | 0.452156i | \(0.850655\pi\) | |||||||
\(542\) | 6.73539 | 0.289310 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −19.3214 | −0.828399 | ||||||||
\(545\) | −33.8454 | + | 58.6220i | −1.44978 | + | 2.51109i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.92580 | − | 15.4599i | −0.381640 | − | 0.661019i | 0.609657 | − | 0.792665i | \(-0.291307\pi\) |
−0.991297 | + | 0.131646i | \(0.957974\pi\) | |||||||
\(548\) | −5.77128 | − | 9.99615i | −0.246537 | − | 0.427015i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.8145 | − | 32.5877i | 0.802254 | − | 1.38955i | ||||
\(551\) | −0.755260 | + | 1.30815i | −0.0321752 | + | 0.0557290i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.98329 | + | 3.43516i | −0.0842619 | + | 0.145946i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.987620 | −0.0418844 | ||||||||
\(557\) | 20.6804 | − | 35.8195i | 0.876255 | − | 1.51772i | 0.0208360 | − | 0.999783i | \(-0.493367\pi\) |
0.855419 | − | 0.517936i | \(-0.173299\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.21015 | −0.220366 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 47.5809 | 2.00708 | ||||||||
\(563\) | 10.3683 | + | 17.9584i | 0.436972 | + | 0.756858i | 0.997454 | − | 0.0713087i | \(-0.0227175\pi\) |
−0.560482 | + | 0.828166i | \(0.689384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.2843 | − | 57.6501i | 1.40028 | − | 2.42536i | ||||
\(566\) | 17.5402 | 0.737271 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.43268 | 0.227950 | ||||||||
\(569\) | −0.134164 | + | 0.232379i | −0.00562446 | + | 0.00974185i | −0.868824 | − | 0.495121i | \(-0.835124\pi\) |
0.863199 | + | 0.504863i | \(0.168457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9684 | − | 31.1221i | −0.751953 | − | 1.30242i | −0.946875 | − | 0.321601i | \(-0.895779\pi\) |
0.194923 | − | 0.980819i | \(-0.437554\pi\) | |||||||
\(572\) | −2.49814 | −0.104453 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −46.2843 | −1.93019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.71565 | − | 4.70364i | 0.113054 | − | 0.195815i | −0.803946 | − | 0.594702i | \(-0.797270\pi\) |
0.917000 | + | 0.398887i | \(0.130603\pi\) | |||||||
\(578\) | 0.165726 | 0.00689328 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.71015 | − | 4.69412i | 0.112533 | − | 0.194913i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.173775 | + | 0.300987i | −0.00719702 | + | 0.0124656i | ||||
\(584\) | −10.0494 | + | 17.4061i | −0.415849 | + | 0.720271i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.0858 | − | 45.1820i | −1.07760 | − | 1.86645i | ||||
\(587\) | −17.5822 | − | 30.4532i | −0.725694 | − | 1.25694i | −0.958688 | − | 0.284461i | \(-0.908185\pi\) |
0.232994 | − | 0.972478i | \(-0.425148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.10507 | + | 5.37815i | −0.127942 | + | 0.221603i | ||||
\(590\) | −54.1359 | −2.22874 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.7665 | −0.976796 | ||||||||
\(593\) | 16.7534 | + | 29.0177i | 0.687980 | + | 1.19162i | 0.972490 | + | 0.232943i | \(0.0748355\pi\) |
−0.284511 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.74721 | + | 6.49036i | 0.153492 | + | 0.265856i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.99381 | + | 8.64953i | 0.204212 | + | 0.353706i | ||||
\(599\) | 3.12364 | + | 5.41031i | 0.127629 | + | 0.221059i | 0.922757 | − | 0.385381i | \(-0.125930\pi\) |
−0.795129 | + | 0.606441i | \(0.792597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2040 | + | 19.4058i | 0.457019 | + | 0.791580i | 0.998802 | − | 0.0489384i | \(-0.0155838\pi\) |
−0.541783 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.59957 | + | 11.4308i | 0.268533 | + | 0.465112i | ||||
\(605\) | 11.1199 | 0.452089 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.9505 | −0.606821 | −0.303411 | − | 0.952860i | \(-0.598125\pi\) | ||||
−0.303411 | + | 0.952860i | \(0.598125\pi\) | |||||||
\(608\) | −2.08836 | + | 3.61715i | −0.0846943 | + | 0.146695i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11.8207 | + | 20.4741i | 0.478607 | + | 0.828972i | ||||
\(611\) | −1.33310 | − | 2.30900i | −0.0539316 | − | 0.0934123i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.5989 | + | 30.4822i | −0.710812 | + | 1.23116i | 0.253740 | + | 0.967272i | \(0.418339\pi\) |
−0.964553 | + | 0.263891i | \(0.914994\pi\) | |||||||
\(614\) | 9.72500 | − | 16.8442i | 0.392469 | − | 0.679776i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.00619 | + | 1.74277i | −0.0405077 | + | 0.0701614i | −0.885568 | − | 0.464509i | \(-0.846231\pi\) |
0.845061 | + | 0.534670i | \(0.179564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.3818 | −1.58289 | −0.791444 | − | 0.611242i | \(-0.790670\pi\) | ||||
−0.791444 | + | 0.611242i | \(0.790670\pi\) | |||||||
\(620\) | 11.1421 | − | 19.2987i | 0.447479 | − | 0.775056i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.3324 | −0.815256 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.34479 | −0.0937918 | ||||||||
\(626\) | 11.5098 | + | 19.9356i | 0.460025 | + | 0.796787i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.28366 | − | 2.22337i | 0.0512237 | − | 0.0887220i | ||||
\(629\) | −19.5906 | −0.781126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.3832 | 1.76687 | 0.883433 | − | 0.468558i | \(-0.155226\pi\) | ||||
0.883433 | + | 0.468558i | \(0.155226\pi\) | |||||||
\(632\) | 6.69227 | − | 11.5913i | 0.266204 | − | 0.461079i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.4629 | + | 44.1030i | 1.01126 | + | 1.75155i | ||||
\(635\) | −35.8392 | −1.42224 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.11993 | −0.321471 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22.9251 | + | 39.7075i | −0.906195 | + | 1.56957i | ||||
\(641\) | 14.9862 | 0.591921 | 0.295961 | − | 0.955200i | \(-0.404360\pi\) | ||||
0.295961 | + | 0.955200i | \(0.404360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.32691 | + | 9.22649i | −0.210073 | + | 0.363857i | −0.951737 | − | 0.306914i | \(-0.900703\pi\) |
0.741664 | + | 0.670771i | \(0.234037\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.10507 | + | 5.37815i | −0.122168 | + | 0.211600i | ||||
\(647\) | −1.06478 | + | 1.84424i | −0.0418606 | + | 0.0725047i | −0.886197 | − | 0.463309i | \(-0.846662\pi\) |
0.844336 | + | 0.535814i | \(0.179995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.4752 | + | 21.6078i | 0.489696 | + | 0.848178i | ||||
\(650\) | −6.69344 | − | 11.5934i | −0.262538 | − | 0.454730i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.58100 | − | 7.93453i | 0.179406 | − | 0.310740i | ||||
\(653\) | −11.1716 | −0.437180 | −0.218590 | − | 0.975817i | \(-0.570146\pi\) | ||||
−0.218590 | + | 0.975817i | \(0.570146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.6043 | −2.25079 | ||||||||
\(656\) | −13.4956 | − | 23.3751i | −0.526914 | − | 0.912642i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.65452 | − | 9.79391i | −0.220269 | − | 0.381517i | 0.734621 | − | 0.678478i | \(-0.237360\pi\) |
−0.954890 | + | 0.296961i | \(0.904027\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1785 | + | 28.0220i | 0.629271 | + | 1.08993i | 0.987698 | + | 0.156372i | \(0.0499798\pi\) |
−0.358427 | + | 0.933558i | \(0.616687\pi\) | |||||||
\(662\) | 1.77314 | + | 3.07117i | 0.0689151 | + | 0.119364i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.88255 | + | 6.72477i | 0.150672 | + | 0.260972i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.99381 | + | 8.64953i | 0.193361 | + | 0.334911i | ||||
\(668\) | 10.7999 | 0.417860 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 75.0714 | 2.90026 | ||||||||
\(671\) | 5.44801 | − | 9.43623i | 0.210318 | − | 0.364282i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0803 | + | 20.9237i | 0.465662 | + | 0.806550i | 0.999231 | − | 0.0392063i | \(-0.0124830\pi\) |
−0.533569 | + | 0.845756i | \(0.679150\pi\) | |||||||
\(674\) | −13.7744 | − | 23.8580i | −0.530572 | − | 0.918977i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.33242 | − | 9.23601i | 0.205093 | − | 0.355231i | ||||
\(677\) | −12.5371 | + | 21.7148i | −0.481838 | + | 0.834569i | −0.999783 | − | 0.0208457i | \(-0.993364\pi\) |
0.517944 | + | 0.855414i | \(0.326697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.9320 | + | 24.1309i | −0.534267 | + | 0.925378i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −33.3832 | −1.27831 | ||||||||
\(683\) | −23.8392 | + | 41.2907i | −0.912182 | + | 1.57995i | −0.101207 | + | 0.994865i | \(0.532271\pi\) |
−0.810975 | + | 0.585081i | \(0.801063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.6043 | −1.78066 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.9862 | −0.990716 | ||||||||
\(689\) | 0.0618219 | + | 0.107079i | 0.00235523 | + | 0.00407937i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3400 | + | 21.3735i | −0.469435 | + | 0.813085i | −0.999389 | − | 0.0349408i | \(-0.988876\pi\) |
0.529954 | + | 0.848026i | \(0.322209\pi\) | |||||||
\(692\) | −5.87402 | −0.223297 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1496 | 0.726910 | ||||||||
\(695\) | −1.99381 | + | 3.45338i | −0.0756295 | + | 0.130994i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1243 | − | 19.2679i | −0.421364 | − | 0.729824i | ||||
\(698\) | −0.336134 | −0.0127228 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.6784 | 1.12094 | 0.560469 | − | 0.828175i | \(-0.310621\pi\) | ||||
0.560469 | + | 0.828175i | \(0.310621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.11745 | + | 3.66754i | −0.0798613 | + | 0.138324i | ||||
\(704\) | 5.58699 | 0.210567 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6243 | + | 18.4018i | −0.399849 | + | 0.692559i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.6291 | − | 25.3383i | 0.549406 | − | 0.951599i | −0.448909 | − | 0.893577i | \(-0.648187\pi\) |
0.998315 | − | 0.0580220i | \(-0.0184794\pi\) | |||||||
\(710\) | −8.77128 | + | 15.1923i | −0.329180 | + | 0.570157i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.07481 | − | 15.7180i | −0.340093 | − | 0.589058i | ||||
\(713\) | 20.5309 | + | 35.5605i | 0.768887 | + | 1.33175i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.04325 | + | 8.73517i | −0.188607 | + | 0.326677i | ||||
\(716\) | 3.41535 | 0.127638 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.0260 | 1.26984 | ||||||||
\(719\) | −0.537063 | − | 0.930220i | −0.0200291 | − | 0.0346913i | 0.855837 | − | 0.517245i | \(-0.173043\pi\) |
−0.875866 | + | 0.482554i | \(0.839709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.4752 | − | 26.8039i | −0.575929 | − | 0.997538i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.23972 | + | 14.2716i | 0.306227 | + | 0.530400i | ||||
\(725\) | −6.69344 | − | 11.5934i | −0.248588 | − | 0.430567i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7163 | + | 22.0253i | 0.471623 | + | 0.816875i | 0.999473 | − | 0.0324628i | \(-0.0103350\pi\) |
−0.527850 | + | 0.849338i | \(0.677002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.4505 | − | 56.2059i | −1.20105 | − | 2.08027i | ||||
\(731\) | −21.4203 | −0.792258 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.3955 | 0.420904 | 0.210452 | − | 0.977604i | \(-0.432506\pi\) | ||||
0.210452 | + | 0.977604i | \(0.432506\pi\) | |||||||
\(734\) | −25.5562 | + | 44.2647i | −0.943298 | + | 1.63384i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.8083 | + | 23.9168i | 0.508982 | + | 0.881583i | ||||
\(737\) | −17.2997 | − | 29.9639i | −0.637242 | − | 1.10374i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.9697 | − | 25.9283i | 0.550671 | − | 0.953790i | −0.447556 | − | 0.894256i | \(-0.647705\pi\) |
0.998226 | − | 0.0595336i | \(-0.0189613\pi\) | |||||||
\(740\) | 7.59820 | − | 13.1605i | 0.279315 | − | 0.483788i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.50069 | + | 16.4557i | −0.348546 | + | 0.603700i | −0.985991 | − | 0.166796i | \(-0.946658\pi\) |
0.637445 | + | 0.770496i | \(0.279991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.2595 | 1.10862 | ||||||||
\(746\) | 5.95922 | − | 10.3217i | 0.218183 | − | 0.377903i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.2705 | −0.375527 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0261368 | 0.000953747 | 0.000476873 | − | 1.00000i | \(-0.499848\pi\) | ||||
0.000476873 | 1.00000i | \(0.499848\pi\) | ||||||||
\(752\) | −6.64902 | − | 11.5164i | −0.242465 | − | 0.419961i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.44437 | + | 2.50172i | −0.0526008 | + | 0.0911072i | ||||
\(755\) | 53.2929 | 1.93953 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6910 | −0.497607 | −0.248803 | − | 0.968554i | \(-0.580037\pi\) | ||||
−0.248803 | + | 0.968554i | \(0.580037\pi\) | |||||||
\(758\) | −16.2095 | + | 28.0756i | −0.588754 | + | 1.01975i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.01169 | + | 5.21640i | 0.109246 | + | 0.189219i | ||||
\(761\) | −14.6428 | −0.530802 | −0.265401 | − | 0.964138i | \(-0.585504\pi\) | ||||
−0.265401 | + | 0.964138i | \(0.585504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.11855 | −0.149004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.72803 | − | 4.72509i | 0.0985677 | − | 0.170724i | ||||
\(767\) | 8.87636 | 0.320507 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5672 | − | 42.5517i | 0.885918 | − | 1.53445i | 0.0412592 | − | 0.999148i | \(-0.486863\pi\) |
0.844658 | − | 0.535306i | \(-0.179804\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.2410 | − | 19.4700i | 0.404573 | − | 0.700741i | ||||
\(773\) | −6.22067 | + | 10.7745i | −0.223742 | + | 0.387532i | −0.955941 | − | 0.293558i | \(-0.905161\pi\) |
0.732199 | + | 0.681090i | \(0.238494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.5185 | − | 47.6634i | −0.988493 | − | 1.71212i | ||||
\(776\) | 6.91411 | + | 11.9756i | 0.248202 | + | 0.429898i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.36467 | + | 7.55982i | −0.156481 | + | 0.271033i | ||||
\(779\) | −4.80951 | −0.172319 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.08513 | 0.289309 | ||||||||
\(782\) | 20.5309 | + | 35.5605i | 0.734183 | + | 1.27164i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.18292 | − | 8.97708i | −0.184986 | − | 0.320406i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4567 | − | 28.5038i | −0.586617 | − | 1.01605i | −0.994672 | − | 0.103093i | \(-0.967126\pi\) |
0.408055 | − | 0.912957i | \(-0.366207\pi\) | |||||||
\(788\) | 4.76392 | + | 8.25135i | 0.169708 | + | 0.293942i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.6099 | + | 37.4294i | 0.768845 | + | 1.33168i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.93818 | − | 3.35702i | −0.0688267 | − | 0.119211i | ||||
\(794\) | 38.9862 | 1.38357 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.79108 | 0.276147 | ||||||||
\(797\) | −13.1989 | + | 22.8612i | −0.467530 | + | 0.809786i | −0.999312 | − | 0.0370953i | \(-0.988189\pi\) |
0.531781 | + | 0.846882i | \(0.321523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.48074 | − | 9.49292i | −0.193895 | − | 0.335835i | ||||
\(800\) | −18.5080 | − | 32.0567i | −0.654356 | − | 1.13338i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.4752 | − | 26.8039i | 0.546450 | − | 0.946479i | ||||
\(803\) | −14.9560 | + | 25.9045i | −0.527785 | + | 0.914151i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.93818 | + | 10.2852i | −0.209163 | + | 0.362282i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.54394 | 0.230215 | ||||||||
\(809\) | 17.7960 | − | 30.8235i | 0.625673 | − | 1.08370i | −0.362738 | − | 0.931891i | \(-0.618158\pi\) |
0.988410 | − | 0.151806i | \(-0.0485088\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8268 | 1.32828 | 0.664140 | − | 0.747608i | \(-0.268798\pi\) | ||||
0.664140 | + | 0.747608i | \(0.268798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.7651 | −0.797916 | ||||||||
\(815\) | −18.4963 | − | 32.0365i | −0.647896 | − | 1.12219i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.31522 | + | 4.01008i | −0.0809994 | + | 0.140295i | ||||
\(818\) | −26.0594 | −0.911146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.2583 | 0.602686 | ||||||||
\(821\) | −9.15638 | + | 15.8593i | −0.319560 | + | 0.553494i | −0.980396 | − | 0.197036i | \(-0.936868\pi\) |
0.660836 | + | 0.750530i | \(0.270202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0000 | + | 31.1769i | 0.627441 | + | 1.08676i | 0.988063 | + | 0.154047i | \(0.0492308\pi\) |
−0.360623 | + | 0.932712i | \(0.617436\pi\) | |||||||
\(824\) | 29.9862 | 1.04462 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.2115 | 0.981011 | 0.490505 | − | 0.871438i | \(-0.336812\pi\) | ||||
0.490505 | + | 0.871438i | \(0.336812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.64214 | + | 9.77247i | −0.195960 | + | 0.339412i | −0.947215 | − | 0.320600i | \(-0.896115\pi\) |
0.751255 | + | 0.660012i | \(0.229449\pi\) | |||||||
\(830\) | −25.0741 | −0.870336 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.993810 | − | 1.72133i | 0.0344542 | − | 0.0596764i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8028 | − | 37.7636i | 0.754519 | − | 1.30686i | ||||
\(836\) | −1.11009 | + | 1.92274i | −0.0383934 | + | 0.0664993i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.98143 | + | 15.5563i | 0.310258 | + | 0.537383i | ||||
\(839\) | 1.02152 | + | 1.76933i | 0.0352669 | + | 0.0610840i | 0.883120 | − | 0.469147i | \(-0.155439\pi\) |
−0.847853 | + | 0.530231i | \(0.822105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0556 | − | 22.6130i | 0.450194 | − | 0.779759i | ||||
\(842\) | 61.4783 | 2.11868 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.35855 | 0.322135 | ||||||||
\(845\) | −21.5302 | − | 37.2914i | −0.740661 | − | 1.28286i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.308344 | + | 0.534068i | 0.0105886 | + | 0.0183400i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −27.5185 | − | 47.6634i | −0.943877 | − | 1.63484i | ||||
\(851\) | 14.0007 | + | 24.2499i | 0.479937 | + | 0.831276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.2960 | − | 42.0818i | −0.831878 | − | 1.44085i | −0.896547 | − | 0.442948i | \(-0.853933\pi\) |
0.0646692 | − | 0.997907i | \(-0.479401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.05563 | − | 8.75661i | −0.172798 | − | 0.299295i | ||||
\(857\) | −44.8974 | −1.53367 | −0.766833 | − | 0.641847i | \(-0.778169\pi\) | ||||
−0.766833 | + | 0.641847i | \(0.778169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.8131 | −1.01721 | −0.508605 | − | 0.861000i | \(-0.669838\pi\) | ||||
−0.508605 | + | 0.861000i | \(0.669838\pi\) | |||||||
\(860\) | 8.30786 | − | 14.3896i | 0.283296 | − | 0.490683i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.8275 | − | 51.6628i | −1.01593 | − | 1.75964i | ||||
\(863\) | −21.1298 | − | 36.5978i | −0.719265 | − | 1.24580i | −0.961291 | − | 0.275534i | \(-0.911145\pi\) |
0.242026 | − | 0.970270i | \(-0.422188\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.8585 | + | 20.5395i | −0.403200 | + | 0.698363i | ||||
\(866\) | 34.9894 | − | 60.6034i | 1.18899 | − | 2.05939i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.95970 | − | 17.2507i | 0.337860 | − | 0.585190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.3090 | −0.417076 | ||||||||
\(872\) | 17.8145 | − | 30.8557i | 0.603276 | − | 1.04491i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.87636 | 0.300247 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.5316 | −1.03098 | −0.515489 | − | 0.856896i | \(-0.672390\pi\) | ||||
−0.515489 | + | 0.856896i | \(0.672390\pi\) | |||||||
\(878\) | 3.97593 | + | 6.88651i | 0.134181 | + | 0.232409i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −25.1538 | + | 43.5677i | −0.847935 | + | 1.46867i | ||||
\(881\) | −13.4079 | −0.451724 | −0.225862 | − | 0.974159i | \(-0.572520\pi\) | ||||
−0.225862 | + | 0.974159i | \(0.572520\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.1250 | −0.475345 | −0.237672 | − | 0.971345i | \(-0.576384\pi\) | ||||
−0.237672 | + | 0.971345i | \(0.576384\pi\) | |||||||
\(884\) | −1.82691 | + | 3.16431i | −0.0614458 | + | 0.106427i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.6414 | − | 44.4123i | −0.861441 | − | 1.49206i | ||||
\(887\) | −39.9432 | −1.34116 | −0.670581 | − | 0.741837i | \(-0.733955\pi\) | ||||
−0.670581 | + | 0.741837i | \(0.733955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 58.6067 | 1.96450 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.51849 | + | 4.36216i | −0.0843254 | + | 0.146056i | ||||
\(893\) | −2.36955 | −0.0792941 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.89493 | − | 11.9424i | 0.230472 | − | 0.399189i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.283662 | + | 0.491316i | −0.00946591 | + | 0.0163954i | ||||
\(899\) | −5.93818 | + | 10.2852i | −0.198049 | + | 0.343031i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.254166 | + | 0.440229i | 0.00846751 | + | 0.0146662i | ||||
\(902\) | −12.9270 | − | 22.3902i | −0.430421 | − | 0.745511i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.5192 | + | 30.3441i | −0.582679 | + | 1.00923i | ||||
\(905\) | 66.5375 | 2.21178 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.4203 | 1.37534 | 0.687669 | − | 0.726024i | \(-0.258634\pi\) | ||||
0.687669 | + | 0.726024i | \(0.258634\pi\) | |||||||
\(908\) | 4.93199 | + | 8.54245i | 0.163674 | + | 0.283491i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.894237 | + | 1.54886i | 0.0296274 | + | 0.0513162i | 0.880459 | − | 0.474122i | \(-0.157235\pi\) |
−0.850832 | + | 0.525439i | \(0.823901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.77816 | + | 10.0081i | 0.191229 | + | 0.331219i | ||||
\(914\) | −16.4091 | − | 28.4214i | −0.542764 | − | 0.940096i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.72864 | + | 15.1185i | 0.288402 | + | 0.499528i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.7341 | + | 49.7690i | 0.947852 | + | 1.64173i | 0.749938 | + | 0.661508i | \(0.230083\pi\) |
0.197914 | + | 0.980219i | \(0.436583\pi\) | |||||||
\(920\) | 39.8268 | 1.31305 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −66.4683 | −2.18902 | ||||||||
\(923\) | 1.43818 | − | 2.49100i | 0.0473382 | − | 0.0819922i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.7658 | − | 32.5033i | −0.617015 | − | 1.06870i | ||||
\(926\) | 18.5908 | + | 32.2003i | 0.610933 | + | 1.05817i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.99381 | + | 6.91748i | −0.131103 | + | 0.227077i | ||||
\(929\) | −17.3676 | + | 30.0816i | −0.569813 | + | 0.986945i | 0.426771 | + | 0.904360i | \(0.359651\pi\) |
−0.996584 | + | 0.0825854i | \(0.973682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.98281 | − | 6.89843i | 0.130461 | − | 0.225965i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.9395 | 0.685161 | ||||||||
\(935\) | −20.7341 | + | 35.9126i | −0.678079 | + | 1.17447i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.6662 | −0.381118 | −0.190559 | − | 0.981676i | \(-0.561030\pi\) | ||||
−0.190559 | + | 0.981676i | \(0.561030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.50282 | 0.277332 | ||||||||
\(941\) | 25.1687 | + | 43.5934i | 0.820475 | + | 1.42111i | 0.905329 | + | 0.424712i | \(0.139625\pi\) |
−0.0848531 | + | 0.996393i | \(0.527042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.9004 | + | 27.5402i | −0.517787 | + | 0.896833i | ||||
\(944\) | 44.2719 | 1.44093 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.8913 | −0.809287 | ||||||||
\(947\) | −16.1941 | + | 28.0491i | −0.526238 | + | 0.911472i | 0.473294 | + | 0.880904i | \(0.343065\pi\) |
−0.999533 | + | 0.0305673i | \(0.990269\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.32072 | + | 9.21576i | 0.172718 | + | 0.299156i | ||||
\(950\) | −11.8974 | −0.386003 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5367 | 0.406102 | 0.203051 | − | 0.979168i | \(-0.434914\pi\) | ||||
0.203051 | + | 0.979168i | \(0.434914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.31453 | + | 14.4012i | −0.269052 | + | 0.466012i | ||||
\(956\) | −9.97386 | −0.322578 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.4635 | − | 19.8555i | 0.370370 | − | 0.641500i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.91342 | + | 15.4385i | −0.287530 | + | 0.498016i | ||||
\(962\) | −4.04944 | + | 7.01384i | −0.130559 | + | 0.226135i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.10446 | − | 5.37709i | −0.0999880 | − | 0.173184i | ||||
\(965\) | −45.3868 | − | 78.6122i | −1.46105 | − | 2.53062i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.9937 | − | 50.2186i | 0.932376 | − | 1.61492i | 0.153127 | − | 0.988206i | \(-0.451065\pi\) |
0.779248 | − | 0.626715i | \(-0.215601\pi\) | |||||||
\(968\) | −5.85297 | −0.188122 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −44.6525 | −1.43370 | ||||||||
\(971\) | −14.0185 | − | 24.2807i | −0.449875 | − | 0.779206i | 0.548503 | − | 0.836149i | \(-0.315198\pi\) |
−0.998377 | + | 0.0569428i | \(0.981865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.41095 | + | 11.1041i | 0.205420 | + | 0.355798i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.66690 | − | 16.7436i | −0.309430 | − | 0.535948i | ||||
\(977\) | 4.92030 | + | 8.52220i | 0.157414 | + | 0.272649i | 0.933935 | − | 0.357442i | \(-0.116351\pi\) |
−0.776521 | + | 0.630091i | \(0.783018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5055 | − | 23.3922i | −0.431638 | − | 0.747618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.7156 | + | 23.7562i | 0.437684 | + | 0.758091i | ||||
\(983\) | −48.6894 | −1.55295 | −0.776476 | − | 0.630147i | \(-0.782995\pi\) | ||||
−0.776476 | + | 0.630147i | \(0.782995\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.4697 | 1.22575 | ||||||||
\(986\) | −5.93818 | + | 10.2852i | −0.189110 | + | 0.327548i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.394926 | + | 0.684031i | 0.0125643 | + | 0.0217619i | ||||
\(989\) | 15.3083 | + | 26.5148i | 0.486777 | + | 0.843123i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.43199 | + | 2.48028i | −0.0454886 | + | 0.0787886i | −0.887873 | − | 0.460088i | \(-0.847818\pi\) |
0.842385 | + | 0.538877i | \(0.181151\pi\) | |||||||
\(992\) | −16.4196 | + | 28.4396i | −0.521323 | + | 0.902958i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.7286 | − | 27.2428i | 0.498631 | − | 0.863655i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.8406 | 1.61014 | 0.805069 | − | 0.593181i | \(-0.202128\pi\) | ||||
0.805069 | + | 0.593181i | \(0.202128\pi\) | |||||||
\(998\) | −26.2298 | + | 45.4314i | −0.830290 | + | 1.43810i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))