Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(226,1323)]
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, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.h (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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 802.1 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.802 |
Dual form | 1323.2.h.e.226.1 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.69963 | −1.20182 | −0.600909 | − | 0.799317i | \(-0.705195\pi\) | ||||
−0.600909 | + | 0.799317i | \(0.705195\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.888736 | 0.444368 | ||||||||
\(5\) | 1.79418 | − | 3.10761i | 0.802383 | − | 1.38977i | −0.115661 | − | 0.993289i | \(-0.536899\pi\) |
0.918044 | − | 0.396479i | \(-0.129768\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.88874 | 0.667769 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.04944 | + | 5.28179i | −0.964318 | + | 1.67025i | ||||
\(11\) | −1.40545 | − | 2.43430i | −0.423758 | − | 0.733970i | 0.572546 | − | 0.819873i | \(-0.305956\pi\) |
−0.996304 | + | 0.0859026i | \(0.972623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | 0.926995 | − | 0.375073i | \(-0.122382\pi\) |
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98762 | −1.24691 | ||||||||
\(17\) | 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 | ||||
\(23\) | 2.93818 | − | 5.08907i | 0.612652 | − | 1.06115i | −0.378139 | − | 0.925749i | \(-0.623436\pi\) |
0.990792 | − | 0.135396i | \(-0.0432308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.93818 | − | 6.82112i | −0.787636 | − | 1.36422i | ||||
\(26\) | −0.849814 | − | 1.47192i | −0.166662 | − | 0.288667i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.849814 | + | 1.47192i | −0.157807 | + | 0.273329i | −0.934077 | − | 0.357071i | \(-0.883776\pi\) |
0.776271 | + | 0.630399i | \(0.217109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.98762 | 1.25501 | 0.627507 | − | 0.778611i | \(-0.284075\pi\) | ||||
0.627507 | + | 0.778611i | \(0.284075\pi\) | |||||||
\(32\) | 4.69963 | 0.830785 | ||||||||
\(33\) | 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 | \(0.961442\pi\) | |||||||
\(38\) | 0.755260 | + | 1.30815i | 0.122519 | + | 0.212210i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.38874 | − | 5.86946i | 0.535806 | − | 0.928044i | ||||
\(41\) | 2.70582 | + | 4.68661i | 0.422578 | + | 0.731926i | 0.996191 | − | 0.0872002i | \(-0.0277920\pi\) |
−0.573613 | + | 0.819126i | \(0.694459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.60507 | + | 4.51212i | −0.397270 | + | 0.688092i | −0.993388 | − | 0.114805i | \(-0.963376\pi\) |
0.596118 | + | 0.802897i | \(0.296709\pi\) | |||||||
\(44\) | −1.24907 | − | 2.16345i | −0.188304 | − | 0.326153i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.99381 | + | 8.64953i | −0.736297 | + | 1.27530i | ||||
\(47\) | −2.66621 | −0.388906 | −0.194453 | − | 0.980912i | \(-0.562293\pi\) | ||||
−0.194453 | + | 0.980912i | \(0.562293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.69344 | + | 11.5934i | 0.946595 | + | 1.63955i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.444368 | + | 0.769668i | 0.0616227 | + | 0.106734i | ||||
\(53\) | −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 | ||||||||
\(58\) | 1.44437 | − | 2.50172i | 0.189655 | − | 0.328492i | ||||
\(59\) | −8.87636 | −1.15560 | −0.577802 | − | 0.816177i | \(-0.696089\pi\) | ||||
−0.577802 | + | 0.816177i | \(0.696089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.87636 | −0.496317 | −0.248158 | − | 0.968720i | \(-0.579825\pi\) | ||||
−0.248158 | + | 0.968720i | \(0.579825\pi\) | |||||||
\(62\) | −11.8764 | −1.50830 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98762 | 0.248453 | ||||||||
\(65\) | 3.58836 | 0.445082 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3090 | 1.50379 | 0.751894 | − | 0.659284i | \(-0.229141\pi\) | ||||
0.751894 | + | 0.659284i | \(0.229141\pi\) | |||||||
\(68\) | 1.82691 | − | 3.16431i | 0.221546 | − | 0.383729i | ||||
\(69\) | 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 | \(0.952685\pi\) | |||||||
\(74\) | 4.04944 | + | 7.01384i | 0.470738 | + | 0.815342i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.394926 | − | 0.684031i | −0.0453011 | − | 0.0784638i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.08650 | −0.797294 | −0.398647 | − | 0.917104i | \(-0.630520\pi\) | ||||
−0.398647 | + | 0.917104i | \(0.630520\pi\) | |||||||
\(80\) | −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 | −0.730875 | − | 0.682512i | \(-0.760888\pi\) |
0.956510 | + | 0.291700i | \(0.0942210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.37636 | − | 12.7762i | −0.800078 | − | 1.38578i | ||||
\(86\) | 4.42766 | − | 7.66893i | 0.477447 | − | 0.826962i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.65452 | − | 4.59776i | −0.282972 | − | 0.490123i | ||||
\(89\) | −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 | ||||||||
\(94\) | 4.53156 | 0.467395 | ||||||||
\(95\) | −3.18911 | −0.327196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.66071 | − | 6.34053i | 0.371688 | − | 0.643783i | −0.618137 | − | 0.786070i | \(-0.712112\pi\) |
0.989825 | + | 0.142287i | \(0.0454456\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.50000 | − | 6.06218i | −0.350000 | − | 0.606218i | ||||
\(101\) | −1.73236 | − | 3.00054i | −0.172376 | − | 0.298564i | 0.766874 | − | 0.641798i | \(-0.221811\pi\) |
−0.939250 | + | 0.343233i | \(0.888478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.93818 | + | 13.7493i | −0.782172 | + | 1.35476i | 0.148502 | + | 0.988912i | \(0.452555\pi\) |
−0.930674 | + | 0.365849i | \(0.880779\pi\) | |||||||
\(104\) | 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 | \(-0.192286\pi\) | |||||||
\(110\) | 17.1433 | 1.63455 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.27561 | − | 16.0658i | −0.872576 | − | 1.51135i | −0.859322 | − | 0.511434i | \(-0.829114\pi\) |
−0.0132538 | − | 0.999912i | \(-0.504219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.5433 | − | 18.2614i | −0.983163 | − | 1.70289i | ||||
\(116\) | −0.755260 | + | 1.30815i | −0.0701242 | + | 0.121459i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0865 | 1.38883 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.54944 | − | 2.68371i | 0.140858 | − | 0.243974i | ||||
\(122\) | 6.58836 | 0.596482 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.21015 | 0.557688 | ||||||||
\(125\) | −10.3214 | −0.923175 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.98762 | 0.886258 | 0.443129 | − | 0.896458i | \(-0.353868\pi\) | ||||
0.443129 | + | 0.896458i | \(0.353868\pi\) | |||||||
\(128\) | −12.7775 | −1.12938 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.09888 | −0.534908 | ||||||||
\(131\) | −8.02654 | + | 13.9024i | −0.701282 | + | 1.21466i | 0.266734 | + | 0.963770i | \(0.414055\pi\) |
−0.968017 | + | 0.250886i | \(0.919278\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −20.9208 | −1.80728 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.88255 | − | 6.72477i | 0.332926 | − | 0.576644i | ||||
\(137\) | −6.49381 | − | 11.2476i | −0.554804 | − | 0.960948i | −0.997919 | − | 0.0644834i | \(-0.979460\pi\) |
0.443115 | − | 0.896465i | \(-0.353873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.555632 | + | 0.962383i | 0.0471281 | + | 0.0816283i | 0.888627 | − | 0.458630i | \(-0.151660\pi\) |
−0.841499 | + | 0.540259i | \(0.818326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.88874 | −0.410254 | ||||||||
\(143\) | 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 | ||||
\(149\) | 4.21634 | − | 7.30291i | 0.345416 | − | 0.598278i | −0.640013 | − | 0.768364i | \(-0.721071\pi\) |
0.985429 | + | 0.170086i | \(0.0544045\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.42580 | + | 12.8619i | 0.604303 | + | 1.04668i | 0.992161 | + | 0.124964i | \(0.0398816\pi\) |
−0.387858 | + | 0.921719i | \(0.626785\pi\) | |||||||
\(152\) | −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 | ||||||||
\(157\) | −2.88874 | −0.230546 | −0.115273 | − | 0.993334i | \(-0.536774\pi\) | ||||
−0.115273 | + | 0.993334i | \(0.536774\pi\) | |||||||
\(158\) | 12.0444 | 0.958203 | ||||||||
\(159\) | 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 | \(0.701046\pi\) | |||||||
\(164\) | 2.40476 | + | 4.16516i | 0.187780 | + | 0.325245i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.49381 | + | 6.05146i | −0.271172 | + | 0.469684i | ||||
\(167\) | −6.07598 | − | 10.5239i | −0.470174 | − | 0.814365i | 0.529244 | − | 0.848469i | \(-0.322475\pi\) |
−0.999418 | + | 0.0341045i | \(0.989142\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −6.60940 | −0.502504 | −0.251252 | − | 0.967922i | \(-0.580842\pi\) | ||||
−0.251252 | + | 0.967922i | \(0.580842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.00983 | + | 12.1414i | 0.528386 | + | 0.915191i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.16621 | + | 14.1443i | 0.612083 | + | 1.06016i | ||||
\(179\) | −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 | ||||||||
\(184\) | 5.54944 | − | 9.61192i | 0.409110 | − | 0.708600i | ||||
\(185\) | −17.0989 | −1.25713 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.5563 | −0.845082 | ||||||||
\(188\) | −2.36955 | −0.172818 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.42030 | 0.393230 | ||||||||
\(191\) | −4.63416 | −0.335316 | −0.167658 | − | 0.985845i | \(-0.553620\pi\) | ||||
−0.167658 | + | 0.985845i | \(0.553620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.2967 | −1.82089 | −0.910446 | − | 0.413627i | \(-0.864262\pi\) | ||||
−0.910446 | + | 0.413627i | \(0.864262\pi\) | |||||||
\(194\) | −6.22184 | + | 10.7765i | −0.446702 | + | 0.773711i | ||||
\(195\) | 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 | \(0.267237\pi\) | |||||||
\(200\) | −7.43818 | − | 12.8833i | −0.525959 | − | 0.910987i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.94437 | + | 5.09979i | 0.207165 | + | 0.358820i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.4189 | 1.35628 | ||||||||
\(206\) | 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 | 0.625902 | − | 0.779902i | \(-0.284731\pi\) |
−0.988366 | + | 0.152096i | \(0.951398\pi\) | |||||||
\(212\) | −0.0549434 | + | 0.0951647i | −0.00377353 | + | 0.00653594i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.54944 | + | 7.87987i | 0.310993 | + | 0.538656i | ||||
\(215\) | 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 | ||||||||
\(220\) | −8.96424 | −0.604369 | ||||||||
\(221\) | 4.11126 | 0.276554 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83379 | + | 4.90827i | −0.189765 | + | 0.328682i | −0.945172 | − | 0.326574i | \(-0.894106\pi\) |
0.755407 | + | 0.655256i | \(0.227439\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.7651 | + | 27.3059i | 1.04868 | + | 1.81636i | ||||
\(227\) | 5.54944 | + | 9.61192i | 0.368329 | + | 0.637965i | 0.989304 | − | 0.145865i | \(-0.0465965\pi\) |
−0.620975 | + | 0.783830i | \(0.713263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.82141 | − | 17.0112i | 0.649017 | − | 1.12413i | −0.334341 | − | 0.942452i | \(-0.608514\pi\) |
0.983358 | − | 0.181679i | \(-0.0581530\pi\) | |||||||
\(230\) | 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 | ||||
\(236\) | −7.88874 | −0.513513 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.61126 | + | 9.71899i | 0.362963 | + | 0.628670i | 0.988447 | − | 0.151567i | \(-0.0484320\pi\) |
−0.625484 | + | 0.780237i | \(0.715099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.49312 | − | 6.05026i | −0.225012 | − | 0.389732i | 0.731311 | − | 0.682044i | \(-0.238909\pi\) |
−0.956323 | + | 0.292312i | \(0.905575\pi\) | |||||||
\(242\) | −2.63348 | + | 4.56131i | −0.169286 | + | 0.293212i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.44506 | −0.220547 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.444368 | − | 0.769668i | 0.0282745 | − | 0.0489728i | ||||
\(248\) | 13.1978 | 0.838059 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 17.5426 | 1.10949 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | −16.9752 | −1.06512 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.7417 | 1.10886 | ||||||||
\(257\) | 0.712008 | − | 1.23323i | 0.0444138 | − | 0.0769270i | −0.842964 | − | 0.537970i | \(-0.819191\pi\) |
0.887378 | + | 0.461043i | \(0.152525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.18911 | 0.197780 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.6421 | − | 23.6289i | 0.842814 | − | 1.45980i | ||||
\(263\) | 8.13162 | + | 14.0844i | 0.501417 | + | 0.868480i | 0.999999 | + | 0.00163692i | \(0.000521048\pi\) |
−0.498582 | + | 0.866843i | \(0.666146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.221840 | + | 0.384237i | 0.0136275 | + | 0.0236035i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.9395 | 0.668235 | ||||||||
\(269\) | 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 | ||||
\(275\) | −11.0698 | + | 19.1734i | −0.667534 | + | 1.15620i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16690 | + | 2.02112i | 0.0701120 | + | 0.121438i | 0.898950 | − | 0.438051i | \(-0.144331\pi\) |
−0.828838 | + | 0.559488i | \(0.810998\pi\) | |||||||
\(278\) | −0.944368 | − | 1.63569i | −0.0566394 | − | 0.0981024i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9975 | − | 24.2443i | 0.835018 | − | 1.44629i | −0.0589978 | − | 0.998258i | \(-0.518790\pi\) |
0.894016 | − | 0.448035i | \(-0.147876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3200 | −0.613462 | −0.306731 | − | 0.951796i | \(-0.599235\pi\) | ||||
−0.306731 | + | 0.951796i | \(0.599235\pi\) | |||||||
\(284\) | 2.55632 | 0.151690 | ||||||||
\(285\) | 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 | ||||
\(290\) | −5.18292 | − | 8.97708i | −0.304351 | − | 0.527152i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.72872 | + | 8.19038i | −0.276727 | + | 0.479306i | ||||
\(293\) | 15.3480 | + | 26.5834i | 0.896637 | + | 1.55302i | 0.831765 | + | 0.555127i | \(0.187330\pi\) |
0.0648718 | + | 0.997894i | \(0.479336\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | 5.87636 | 0.339838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −12.6211 | − | 21.8604i | −0.726262 | − | 1.25792i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.21634 | + | 3.83881i | 0.127116 | + | 0.220171i | ||||
\(305\) | −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 | ||||||||
\(310\) | −21.3083 | + | 36.9071i | −1.21023 | + | 2.09618i | ||||
\(311\) | 11.9629 | 0.678352 | 0.339176 | − | 0.940723i | \(-0.389852\pi\) | ||||
0.339176 | + | 0.940723i | \(0.389852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5439 | 0.765549 | 0.382774 | − | 0.923842i | \(-0.374969\pi\) | ||||
0.382774 | + | 0.923842i | \(0.374969\pi\) | |||||||
\(314\) | 4.90978 | 0.277075 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.29803 | −0.354292 | ||||||||
\(317\) | 29.9629 | 1.68288 | 0.841441 | − | 0.540349i | \(-0.181708\pi\) | ||||
0.841441 | + | 0.540349i | \(0.181708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.77747 | 0.267487 | ||||||||
\(320\) | 3.56615 | − | 6.17676i | 0.199354 | − | 0.345291i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.65383 | −0.203304 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.93818 | − | 6.82112i | 0.218451 | − | 0.378368i | ||||
\(326\) | −8.76076 | − | 15.1741i | −0.485214 | − | 0.840415i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.11058 | + | 8.85178i | 0.282184 | + | 0.488758i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.08650 | 0.114685 | 0.0573423 | − | 0.998355i | \(-0.481737\pi\) | ||||
0.0573423 | + | 0.998355i | \(0.481737\pi\) | |||||||
\(332\) | 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 | 0.997799 | − | 0.0663093i | \(-0.0211224\pi\) |
−0.556325 | + | 0.830965i | \(0.687789\pi\) | |||||||
\(338\) | −10.1978 | + | 17.6631i | −0.554686 | + | 0.960743i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.55563 | − | 11.3547i | −0.355529 | − | 0.615794i | ||||
\(341\) | −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 | ||||||||
\(346\) | 11.2335 | 0.603918 | ||||||||
\(347\) | −11.2670 | −0.604842 | −0.302421 | − | 0.953175i | \(-0.597795\pi\) | ||||
−0.302421 | + | 0.953175i | \(0.597795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.0988844 | + | 0.171273i | −0.00529316 | + | 0.00916803i | −0.868660 | − | 0.495409i | \(-0.835018\pi\) |
0.863367 | + | 0.504577i | \(0.168352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.60507 | − | 11.4403i | −0.352052 | − | 0.609771i | ||||
\(353\) | 6.25093 | + | 10.8269i | 0.332703 | + | 0.576259i | 0.983041 | − | 0.183386i | \(-0.0587059\pi\) |
−0.650338 | + | 0.759645i | \(0.725373\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16071 | − | 8.93861i | 0.273902 | − | 0.474412i | ||||
\(356\) | −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 | ||||
\(362\) | 31.5155 | 1.65642 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0927 | + | 33.0695i | 0.999357 | + | 1.73094i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0364 | + | 26.0438i | 0.784892 | + | 1.35947i | 0.929063 | + | 0.369921i | \(0.120615\pi\) |
−0.144171 | + | 0.989553i | \(0.546052\pi\) | |||||||
\(368\) | −14.6545 | + | 25.3824i | −0.763919 | + | 1.32315i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.0617 | 1.51085 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.50619 | + | 6.07290i | −0.181544 | + | 0.314443i | −0.942406 | − | 0.334470i | \(-0.891443\pi\) |
0.760863 | + | 0.648913i | \(0.224776\pi\) | |||||||
\(374\) | 19.6414 | 1.01564 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.03576 | −0.259700 | ||||||||
\(377\) | −1.69963 | −0.0875353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0741 | −0.979772 | −0.489886 | − | 0.871787i | \(-0.662962\pi\) | ||||
−0.489886 | + | 0.871787i | \(0.662962\pi\) | |||||||
\(380\) | −2.83427 | −0.145395 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.87636 | 0.402989 | ||||||||
\(383\) | −1.60507 | + | 2.78007i | −0.0820155 | + | 0.142055i | −0.904116 | − | 0.427288i | \(-0.859469\pi\) |
0.822100 | + | 0.569343i | \(0.192802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 42.9949 | 2.18838 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.25340 | − | 5.63506i | 0.165166 | − | 0.286077i | ||||
\(389\) | 2.56801 | + | 4.44793i | 0.130203 | + | 0.225519i | 0.923755 | − | 0.382984i | \(-0.125104\pi\) |
−0.793552 | + | 0.608503i | \(0.791770\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0796 | − | 20.9225i | −0.610893 | − | 1.05810i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.2212 | 0.917968 | ||||||||
\(395\) | −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 | ||||
\(401\) | −9.10507 | + | 15.7705i | −0.454686 | + | 0.787539i | −0.998670 | − | 0.0515566i | \(-0.983582\pi\) |
0.543984 | + | 0.839095i | \(0.316915\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.49381 | + | 6.05146i | 0.174039 | + | 0.301445i | ||||
\(404\) | −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 | ||||||||
\(409\) | 15.3324 | 0.758139 | 0.379070 | − | 0.925368i | \(-0.376244\pi\) | ||||
0.379070 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(410\) | −33.0049 | −1.63000 | ||||||||
\(411\) | 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 | ||||
\(416\) | 2.34981 | + | 4.07000i | 0.115209 | + | 0.199548i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.12296 | − | 3.67707i | 0.103837 | − | 0.179851i | ||||
\(419\) | −5.28435 | − | 9.15276i | −0.258157 | − | 0.447142i | 0.707591 | − | 0.706622i | \(-0.249782\pi\) |
−0.965748 | + | 0.259481i | \(0.916449\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0858 | − | 31.3256i | 0.881449 | − | 1.52671i | 0.0317181 | − | 0.999497i | \(-0.489902\pi\) |
0.849731 | − | 0.527217i | \(-0.176765\pi\) | |||||||
\(422\) | 8.94870 | + | 15.4996i | 0.435616 | + | 0.754509i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.116765 | + | 0.202243i | −0.00567062 | + | 0.00982181i | ||||
\(425\) | −32.3818 | −1.57075 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.37890 | − | 4.12038i | −0.114989 | − | 0.199166i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.8880 | − | 27.5189i | −0.766190 | − | 1.32708i | ||||
\(431\) | 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 | ||||||||
\(436\) | 8.38255 | − | 14.5190i | 0.401451 | − | 0.695334i | ||||
\(437\) | −5.22253 | −0.249827 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.67859 | 0.223297 | 0.111648 | − | 0.993748i | \(-0.464387\pi\) | ||||
0.111648 | + | 0.993748i | \(0.464387\pi\) | |||||||
\(440\) | −19.0507 | −0.908209 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.98762 | −0.332367 | ||||||||
\(443\) | −30.1730 | −1.43356 | −0.716781 | − | 0.697298i | \(-0.754385\pi\) | ||||
−0.716781 | + | 0.697298i | \(0.754385\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.4820 | −1.63461 | ||||||||
\(446\) | 4.81639 | − | 8.34224i | 0.228063 | − | 0.395016i | ||||
\(447\) | 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 | ||||
\(452\) | −8.24357 | − | 14.2783i | −0.387745 | − | 0.671594i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.43199 | − | 16.3367i | −0.442665 | − | 0.766719i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.3090 | −0.903238 | −0.451619 | − | 0.892211i | \(-0.649153\pi\) | ||||
−0.451619 | + | 0.892211i | \(0.649153\pi\) | |||||||
\(458\) | −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 | −0.0976463 | + | 0.995221i | \(0.531131\pi\) |
−0.813064 | + | 0.582175i | \(0.802202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9382 | − | 18.9455i | −0.508340 | − | 0.880471i | −0.999953 | − | 0.00965741i | \(-0.996926\pi\) |
0.491613 | − | 0.870814i | \(-0.336407\pi\) | |||||||
\(464\) | 4.23855 | − | 7.34138i | 0.196770 | − | 0.340815i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.61677 | − | 13.1926i | −0.352840 | − | 0.611137i | ||||
\(467\) | 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 | ||||||||
\(472\) | −16.7651 | −0.771676 | ||||||||
\(473\) | 14.6452 | 0.673385 | ||||||||
\(474\) | 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 | ||||
\(479\) | −6.74474 | − | 11.6822i | −0.308175 | − | 0.533775i | 0.669788 | − | 0.742552i | \(-0.266385\pi\) |
−0.977963 | + | 0.208777i | \(0.933052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.38255 | − | 4.12669i | 0.108635 | − | 0.188161i | ||||
\(482\) | 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 | \(0.221342\pi\) | |||||||
\(488\) | −7.32141 | −0.331425 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.06979 | − | 13.9773i | −0.364185 | − | 0.630786i | 0.624460 | − | 0.781057i | \(-0.285319\pi\) |
−0.988645 | + | 0.150270i | \(0.951986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.49381 | + | 6.05146i | 0.157353 | + | 0.272544i | ||||
\(494\) | −0.755260 | + | 1.30815i | −0.0339808 | + | 0.0588564i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.8516 | −1.56488 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.4327 | − | 26.7302i | 0.690862 | − | 1.19661i | −0.280694 | − | 0.959797i | \(-0.590565\pi\) |
0.971556 | − | 0.236810i | \(-0.0761019\pi\) | |||||||
\(500\) | −9.17301 | −0.410229 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.85297 | −0.350495 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 28.0741 | 1.24805 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.87636 | 0.393825 | ||||||||
\(509\) | −6.79487 | + | 11.7691i | −0.301177 | + | 0.521654i | −0.976403 | − | 0.215957i | \(-0.930713\pi\) |
0.675226 | + | 0.737611i | \(0.264046\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4.59937 | −0.203265 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.21015 | + | 2.09604i | −0.0533774 | + | 0.0924523i | ||||
\(515\) | 28.4851 | + | 49.3376i | 1.25520 | + | 2.17407i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.74721 | + | 6.49036i | 0.164802 | + | 0.285446i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.77747 | 0.297212 | ||||||||
\(521\) | 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 | ||||
\(527\) | 14.3640 | − | 24.8791i | 0.625705 | − | 1.08375i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.76578 | − | 9.98663i | −0.250686 | − | 0.434201i | ||||
\(530\) | −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 | ||||||||
\(535\) | −19.2101 | −0.830527 | ||||||||
\(536\) | 23.2485 | 1.00418 | ||||||||
\(537\) | 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 | \(0.850655\pi\) | |||||||
\(542\) | −3.36769 | − | 5.83302i | −0.144655 | − | 0.250550i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.66071 | − | 16.7328i | 0.414199 | − | 0.717414i | ||||
\(545\) | −33.8454 | − | 58.6220i | −1.44978 | − | 2.51109i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.92580 | + | 15.4599i | −0.381640 | + | 0.661019i | −0.991297 | − | 0.131646i | \(-0.957974\pi\) |
0.609657 | + | 0.792665i | \(0.291307\pi\) | |||||||
\(548\) | −5.77128 | − | 9.99615i | −0.246537 | − | 0.427015i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.8145 | − | 32.5877i | 0.802254 | − | 1.38955i | ||||
\(551\) | 1.51052 | 0.0643503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.98329 | − | 3.43516i | −0.0842619 | − | 0.145946i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.493810 | + | 0.855304i | 0.0209422 | + | 0.0362730i | ||||
\(557\) | 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 | ||||||||
\(562\) | −23.7905 | + | 41.2063i | −1.00354 | + | 1.73818i | ||||
\(563\) | −20.7366 | −0.873944 | −0.436972 | − | 0.899475i | \(-0.643949\pi\) | ||||
−0.436972 | + | 0.899475i | \(0.643949\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −66.5685 | −2.80056 | ||||||||
\(566\) | 17.5402 | 0.737271 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.43268 | 0.227950 | ||||||||
\(569\) | 0.268329 | 0.0112489 | 0.00562446 | − | 0.999984i | \(-0.498210\pi\) | ||||
0.00562446 | + | 0.999984i | \(0.498210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.9367 | 1.50391 | 0.751953 | − | 0.659217i | \(-0.229112\pi\) | ||||
0.751953 | + | 0.659217i | \(0.229112\pi\) | |||||||
\(572\) | 1.24907 | − | 2.16345i | 0.0522263 | − | 0.0904585i | ||||
\(573\) | 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 | \(0.130603\pi\) | |||||||
\(578\) | −0.0828628 | − | 0.143523i | −0.00344664 | − | 0.00596976i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.71015 | + | 4.69412i | 0.112533 | + | 0.194913i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.347550 | 0.0143940 | ||||||||
\(584\) | −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 | 0.232994 | + | 0.972478i | \(0.425148\pi\) |
−0.958688 | + | 0.284461i | \(0.908185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.10507 | − | 5.37815i | −0.127942 | − | 0.221603i | ||||
\(590\) | 27.0679 | − | 46.8830i | 1.11437 | − | 1.93014i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.8832 | + | 20.5824i | 0.488398 | + | 0.845930i | ||||
\(593\) | 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 | ||||||||
\(598\) | −9.98762 | −0.408424 | ||||||||
\(599\) | −6.24729 | −0.255257 | −0.127629 | − | 0.991822i | \(-0.540737\pi\) | ||||
−0.127629 | + | 0.991822i | \(0.540737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2040 | − | 19.4058i | 0.457019 | − | 0.791580i | −0.541783 | − | 0.840519i | \(-0.682250\pi\) |
0.998802 | + | 0.0489384i | \(0.0155838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.59957 | + | 11.4308i | 0.268533 | + | 0.465112i | ||||
\(605\) | −5.55996 | − | 9.63014i | −0.226045 | − | 0.391521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.47524 | − | 12.9475i | 0.303411 | − | 0.525523i | −0.673496 | − | 0.739191i | \(-0.735208\pi\) |
0.976906 | + | 0.213669i | \(0.0685413\pi\) | |||||||
\(608\) | −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 | \(0.914994\pi\) | |||||||
\(614\) | −19.4500 | −0.784938 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.00619 | − | 1.74277i | −0.0405077 | − | 0.0701614i | 0.845061 | − | 0.534670i | \(-0.179564\pi\) |
−0.885568 | + | 0.464509i | \(0.846231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6909 | + | 34.1056i | 0.791444 | + | 1.37082i | 0.925073 | + | 0.379789i | \(0.124004\pi\) |
−0.133629 | + | 0.991031i | \(0.542663\pi\) | |||||||
\(620\) | 11.1421 | − | 19.2987i | 0.447479 | − | 0.775056i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.3324 | −0.815256 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.17240 | − | 2.03065i | 0.0468959 | − | 0.0812261i | ||||
\(626\) | −23.0197 | −0.920051 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.56732 | −0.102447 | ||||||||
\(629\) | −19.5906 | −0.781126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.3832 | 1.76687 | 0.883433 | − | 0.468558i | \(-0.155226\pi\) | ||||
0.883433 | + | 0.468558i | \(0.155226\pi\) | |||||||
\(632\) | −13.3845 | −0.532408 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −50.9257 | −2.02252 | ||||||||
\(635\) | 17.9196 | − | 31.0377i | 0.711118 | − | 1.23169i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.11993 | −0.321471 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −22.9251 | + | 39.7075i | −0.906195 | + | 1.56957i | ||||
\(641\) | −7.49312 | − | 12.9785i | −0.295961 | − | 0.512619i | 0.679247 | − | 0.733909i | \(-0.262306\pi\) |
−0.975208 | + | 0.221291i | \(0.928973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.32691 | − | 9.22649i | −0.210073 | − | 0.363857i | 0.741664 | − | 0.670771i | \(-0.234037\pi\) |
−0.951737 | + | 0.306914i | \(0.900703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.21015 | 0.244335 | ||||||||
\(647\) | −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 | ||||
\(653\) | 5.58582 | − | 9.67492i | 0.218590 | − | 0.378609i | −0.735787 | − | 0.677213i | \(-0.763188\pi\) |
0.954377 | + | 0.298604i | \(0.0965210\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.8022 | + | 49.8868i | 1.12539 | + | 1.94924i | ||||
\(656\) | −13.4956 | − | 23.3751i | −0.526914 | − | 0.912642i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.65452 | + | 9.79391i | −0.220269 | + | 0.381517i | −0.954890 | − | 0.296961i | \(-0.904027\pi\) |
0.734621 | + | 0.678478i | \(0.237360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.3570 | −1.25854 | −0.629271 | − | 0.777186i | \(-0.716646\pi\) | ||||
−0.629271 | + | 0.777186i | \(0.716646\pi\) | |||||||
\(662\) | −3.54628 | −0.137830 | ||||||||
\(663\) | 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 | ||||
\(668\) | −5.39995 | − | 9.35298i | −0.208930 | − | 0.361878i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −37.5357 | + | 65.0137i | −1.45013 | + | 2.51170i | ||||
\(671\) | 5.44801 | + | 9.43623i | 0.210318 | + | 0.364282i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0803 | − | 20.9237i | 0.465662 | − | 0.806550i | −0.533569 | − | 0.845756i | \(-0.679150\pi\) |
0.999231 | + | 0.0392063i | \(0.0124830\pi\) | |||||||
\(674\) | −13.7744 | − | 23.8580i | −0.530572 | − | 0.918977i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.33242 | − | 9.23601i | 0.205093 | − | 0.355231i | ||||
\(677\) | 25.0741 | 0.963677 | 0.481838 | − | 0.876260i | \(-0.339969\pi\) | ||||
0.481838 | + | 0.876260i | \(0.339969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −13.9320 | − | 24.1309i | −0.534267 | − | 0.925378i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.6916 | + | 28.9107i | 0.639154 | + | 1.10705i | ||||
\(683\) | −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 | ||||||||
\(688\) | 12.9931 | − | 22.5047i | 0.495358 | − | 0.857985i | ||||
\(689\) | −0.123644 | −0.00471046 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6800 | 0.938870 | 0.469435 | − | 0.882967i | \(-0.344458\pi\) | ||||
0.469435 | + | 0.882967i | \(0.344458\pi\) | |||||||
\(692\) | −5.87402 | −0.223297 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1496 | 0.726910 | ||||||||
\(695\) | 3.98762 | 0.151259 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2487 | 0.842728 | ||||||||
\(698\) | 0.168067 | − | 0.291100i | 0.00636142 | − | 0.0110183i | ||||
\(699\) | 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 | ||||
\(704\) | −2.79349 | − | 4.83847i | −0.105284 | − | 0.182357i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6243 | − | 18.4018i | −0.399849 | − | 0.692559i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.2581 | −1.09881 | −0.549406 | − | 0.835555i | \(-0.685146\pi\) | ||||
−0.549406 | + | 0.835555i | \(0.685146\pi\) | |||||||
\(710\) | −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 | ||||
\(716\) | −1.70768 | + | 2.95778i | −0.0638189 | + | 0.110538i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.0130 | − | 29.4674i | −0.634919 | − | 1.09971i | ||||
\(719\) | −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 | ||||||||
\(724\) | −16.4794 | −0.612454 | ||||||||
\(725\) | 13.3869 | 0.497176 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7163 | − | 22.0253i | 0.471623 | − | 0.816875i | −0.527850 | − | 0.849338i | \(-0.677002\pi\) |
0.999473 | + | 0.0324628i | \(0.0103350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32.4505 | − | 56.2059i | −1.20105 | − | 2.08027i | ||||
\(731\) | 10.7101 | + | 18.5505i | 0.396129 | + | 0.686116i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.69777 | + | 9.86883i | −0.210452 | + | 0.364513i | −0.951856 | − | 0.306545i | \(-0.900827\pi\) |
0.741404 | + | 0.671059i | \(0.234160\pi\) | |||||||
\(734\) | −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 | \(-0.0189613\pi\) | |||||||
\(740\) | −15.1964 | −0.558630 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.50069 | − | 16.4557i | −0.348546 | − | 0.603700i | 0.637445 | − | 0.770496i | \(-0.279991\pi\) |
−0.985991 | + | 0.166796i | \(0.946658\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1298 | − | 26.2055i | −0.554311 | − | 0.960096i | ||||
\(746\) | 5.95922 | − | 10.3217i | 0.218183 | − | 0.377903i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.2705 | −0.375527 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0130684 | + | 0.0226352i | −0.000476873 | + | 0.000825969i | −0.866264 | − | 0.499587i | \(-0.833485\pi\) |
0.865787 | + | 0.500413i | \(0.166818\pi\) | |||||||
\(752\) | 13.2980 | 0.484929 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.88874 | 0.105202 | ||||||||
\(755\) | 53.2929 | 1.93953 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6910 | −0.497607 | −0.248803 | − | 0.968554i | \(-0.580037\pi\) | ||||
−0.248803 | + | 0.968554i | \(0.580037\pi\) | |||||||
\(758\) | 32.4189 | 1.17751 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.02338 | −0.218491 | ||||||||
\(761\) | 7.32141 | − | 12.6811i | 0.265401 | − | 0.459688i | −0.702268 | − | 0.711913i | \(-0.747829\pi\) |
0.967669 | + | 0.252225i | \(0.0811623\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.11855 | −0.149004 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.72803 | − | 4.72509i | 0.0985677 | − | 0.170724i | ||||
\(767\) | −4.43818 | − | 7.68715i | −0.160253 | − | 0.277567i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5672 | + | 42.5517i | 0.885918 | + | 1.53445i | 0.844658 | + | 0.535306i | \(0.179804\pi\) |
0.0412592 | + | 0.999148i | \(0.486863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.4820 | −0.809146 | ||||||||
\(773\) | −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 | ||||
\(779\) | 2.40476 | − | 4.16516i | 0.0861594 | − | 0.149232i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.04256 | − | 7.00193i | −0.144654 | − | 0.250549i | ||||
\(782\) | 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 | ||||||||
\(787\) | 32.9133 | 1.17323 | 0.586617 | − | 0.809865i | \(-0.300459\pi\) | ||||
0.586617 | + | 0.809865i | \(0.300459\pi\) | |||||||
\(788\) | −9.52784 | −0.339415 | ||||||||
\(789\) | 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 | ||||
\(794\) | −19.4931 | − | 33.7631i | −0.691785 | − | 1.19821i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.89554 | + | 6.74727i | −0.138074 | + | 0.239151i | ||||
\(797\) | −13.1989 | − | 22.8612i | −0.467530 | − | 0.809786i | 0.531781 | − | 0.846882i | \(-0.321523\pi\) |
−0.999312 | + | 0.0370953i | \(0.988189\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | 29.9120 | 1.05557 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.93818 | − | 10.2852i | −0.209163 | − | 0.362282i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.27197 | − | 5.66722i | −0.115108 | − | 0.199372i | ||||
\(809\) | 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 | ||||||||
\(814\) | 11.3825 | − | 19.7151i | 0.398958 | − | 0.691016i | ||||
\(815\) | 36.9926 | 1.29579 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.63045 | 0.161999 | ||||||||
\(818\) | −26.0594 | −0.911146 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.2583 | 0.602686 | ||||||||
\(821\) | 18.3128 | 0.639119 | 0.319560 | − | 0.947566i | \(-0.396465\pi\) | ||||
0.319560 | + | 0.947566i | \(0.396465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.0000 | −1.25488 | −0.627441 | − | 0.778664i | \(-0.715897\pi\) | ||||
−0.627441 | + | 0.778664i | \(0.715897\pi\) | |||||||
\(824\) | −14.9931 | + | 25.9688i | −0.522310 | + | 0.904668i | ||||
\(825\) | 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 | \(0.229449\pi\) | |||||||
\(830\) | 12.5371 | + | 21.7148i | 0.435168 | + | 0.753733i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.993810 | + | 1.72133i | 0.0344542 | + | 0.0596764i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.6057 | −1.50904 | ||||||||
\(836\) | −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 | −0.847853 | − | 0.530231i | \(-0.822105\pi\) |
0.883120 | + | 0.469147i | \(0.155439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0556 | + | 22.6130i | 0.450194 | + | 0.779759i | ||||
\(842\) | −30.7392 | + | 53.2418i | −1.05934 | + | 1.83483i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.67928 | − | 8.10474i | −0.161067 | − | 0.278977i | ||||
\(845\) | −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 | ||||||||
\(850\) | 55.0370 | 1.88775 | ||||||||
\(851\) | −28.0014 | −0.959875 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.2960 | + | 42.0818i | −0.831878 | + | 1.44085i | 0.0646692 | + | 0.997907i | \(0.479401\pi\) |
−0.896547 | + | 0.442948i | \(0.853933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.05563 | − | 8.75661i | −0.172798 | − | 0.299295i | ||||
\(857\) | 22.4487 | + | 38.8823i | 0.766833 | + | 1.32819i | 0.939272 | + | 0.343173i | \(0.111502\pi\) |
−0.172439 | + | 0.985020i | \(0.555165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9065 | − | 25.8189i | 0.508605 | − | 0.880929i | −0.491346 | − | 0.870965i | \(-0.663495\pi\) |
0.999950 | − | 0.00996438i | \(-0.00317181\pi\) | |||||||
\(860\) | 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 | ||||
\(866\) | −69.9788 | −2.37798 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.95970 | + | 17.2507i | 0.337860 | + | 0.585190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.15452 | + | 10.6599i | 0.208538 | + | 0.361198i | ||||
\(872\) | 17.8145 | − | 30.8557i | 0.603276 | − | 1.04491i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.87636 | 0.300247 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.2658 | − | 26.4411i | 0.515489 | − | 0.892853i | −0.484350 | − | 0.874875i | \(-0.660944\pi\) |
0.999838 | − | 0.0179782i | \(-0.00572295\pi\) | |||||||
\(878\) | −7.95186 | −0.268362 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 50.3077 | 1.69587 | ||||||||
\(881\) | −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 | \(0.576384\pi\) | |||||||
\(884\) | 3.65383 | 0.122892 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 51.2829 | 1.72288 | ||||||||
\(887\) | 19.9716 | − | 34.5918i | 0.670581 | − | 1.16148i | −0.307159 | − | 0.951658i | \(-0.599378\pi\) |
0.977740 | − | 0.209822i | \(-0.0672883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 58.6067 | 1.96450 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.51849 | + | 4.36216i | −0.0843254 | + | 0.146056i | ||||
\(893\) | 1.18478 | + | 2.05209i | 0.0396471 | + | 0.0686707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.89493 | + | 11.9424i | 0.230472 | + | 0.399189i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.567323 | 0.0189318 | ||||||||
\(899\) | −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 | ||||
\(905\) | −33.2687 | + | 57.6231i | −1.10589 | + | 1.91546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7101 | − | 35.8710i | −0.687669 | − | 1.19108i | −0.972590 | − | 0.232527i | \(-0.925301\pi\) |
0.284921 | − | 0.958551i | \(-0.408033\pi\) | |||||||
\(908\) | 4.93199 | + | 8.54245i | 0.163674 | + | 0.283491i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.894237 | − | 1.54886i | 0.0296274 | − | 0.0513162i | −0.850832 | − | 0.525439i | \(-0.823901\pi\) |
0.880459 | + | 0.474122i | \(0.157235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.5563 | −0.382458 | ||||||||
\(914\) | 32.8182 | 1.08553 | ||||||||
\(915\) | 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 | \(0.436583\pi\) | |||||||
\(920\) | −19.9134 | − | 34.4911i | −0.656526 | − | 1.13714i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.2341 | − | 57.5632i | 1.09451 | − | 1.89574i | ||||
\(923\) | 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 | ||||
\(929\) | 34.7352 | 1.13963 | 0.569813 | − | 0.821774i | \(-0.307016\pi\) | ||||
0.569813 | + | 0.821774i | \(0.307016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.98281 | + | 6.89843i | 0.130461 | + | 0.225965i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.4697 | − | 18.1341i | −0.342580 | − | 0.593367i | ||||
\(935\) | −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 | ||||||||
\(940\) | −4.25141 | + | 7.36366i | −0.138666 | + | 0.240176i | ||||
\(941\) | −50.3374 | −1.64095 | −0.820475 | − | 0.571682i | \(-0.806291\pi\) | ||||
−0.820475 | + | 0.571682i | \(0.806291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.8007 | 1.03557 | ||||||||
\(944\) | 44.2719 | 1.44093 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.8913 | −0.809287 | ||||||||
\(947\) | 32.3883 | 1.05248 | 0.526238 | − | 0.850337i | \(-0.323602\pi\) | ||||
0.526238 | + | 0.850337i | \(0.323602\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.6414 | −0.345436 | ||||||||
\(950\) | 5.94870 | − | 10.3034i | 0.193001 | − | 0.334288i | ||||
\(951\) | 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 | ||||
\(956\) | 4.98693 | + | 8.63762i | 0.161289 | + | 0.279361i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.4635 | + | 19.8555i | 0.370370 | + | 0.641500i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.8268 | 0.575059 | ||||||||
\(962\) | −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 | 0.779248 | + | 0.626715i | \(0.215601\pi\) |
0.153127 | + | 0.988206i | \(0.451065\pi\) | |||||||
\(968\) | 2.92649 | − | 5.06882i | 0.0940609 | − | 0.162918i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.3262 | + | 38.6702i | 0.716852 | + | 1.24162i | ||||
\(971\) | −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 | ||||||||
\(976\) | 19.3338 | 0.618860 | ||||||||
\(977\) | −9.84059 | −0.314829 | −0.157414 | − | 0.987533i | \(-0.550316\pi\) | ||||
−0.157414 | + | 0.987533i | \(0.550316\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | 24.3447 | + | 42.1663i | 0.776476 | + | 1.34490i | 0.933961 | + | 0.357374i | \(0.116328\pi\) |
−0.157485 | + | 0.987521i | \(0.550339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2348 | + | 33.3157i | −0.612873 | + | 1.06153i | ||||
\(986\) | −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 | \(0.181151\pi\) | |||||||
\(992\) | 32.8392 | 1.04265 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.7286 | + | 27.2428i | 0.498631 | + | 0.863655i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.4203 | − | 44.0292i | −0.805069 | − | 1.39442i | −0.916245 | − | 0.400619i | \(-0.868795\pi\) |
0.111176 | − | 0.993801i | \(-0.464538\pi\) | |||||||
\(998\) | −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 \(a_p\))