Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(47,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.144054149089536.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.3 | ||
Root | \(-2.37165 - 1.78079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.47 |
Dual form | 224.2.q.a.143.3 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.416472 | − | 0.240450i | 0.240450 | − | 0.138824i | −0.374933 | − | 0.927052i | \(-0.622334\pi\) |
0.615384 | + | 0.788228i | \(0.289001\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59713 | + | 2.76632i | −0.714260 | + | 1.23714i | 0.248984 | + | 0.968508i | \(0.419903\pi\) |
−0.963244 | + | 0.268628i | \(0.913430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.694153 | + | 2.55307i | 0.262365 | + | 0.964969i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.38437 | + | 2.39779i | −0.461456 | + | 0.799265i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.800840 | − | 1.38709i | −0.241462 | − | 0.418225i | 0.719669 | − | 0.694318i | \(-0.244294\pi\) |
−0.961131 | + | 0.276093i | \(0.910960\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38831 | 0.385047 | 0.192523 | − | 0.981292i | \(-0.438333\pi\) | ||||
0.192523 | + | 0.981292i | \(0.438333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.53613i | 0.396626i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.48605 | − | 2.01267i | 0.845490 | − | 0.488144i | −0.0136363 | − | 0.999907i | \(-0.504341\pi\) |
0.859127 | + | 0.511763i | \(0.171007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.56957 | + | 2.63824i | 1.04833 | + | 0.605255i | 0.922182 | − | 0.386756i | \(-0.126405\pi\) |
0.126150 | + | 0.992011i | \(0.459738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.902982 | + | 0.896373i | 0.197047 | + | 0.195605i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.83044 | − | 2.21151i | −0.798702 | − | 0.461131i | 0.0443149 | − | 0.999018i | \(-0.485890\pi\) |
−0.843017 | + | 0.537887i | \(0.819223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.60168 | − | 4.50624i | −0.520336 | − | 0.901248i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.77419i | 0.533893i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.10613i | − | 0.948185i | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||
0.880475 | − | 0.474093i | \(-0.157224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0579809 | − | 0.100426i | −0.0104137 | − | 0.0180370i | 0.860772 | − | 0.508991i | \(-0.169982\pi\) |
−0.871185 | + | 0.490954i | \(0.836648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.667055 | − | 0.385124i | −0.116119 | − | 0.0670416i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.17125 | − | 2.15734i | −1.38119 | − | 0.364658i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.63087 | + | 2.67363i | 0.761310 | + | 0.439543i | 0.829766 | − | 0.558111i | \(-0.188474\pi\) |
−0.0684556 | + | 0.997654i | \(0.521807\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.578191 | − | 0.333819i | 0.0925847 | − | 0.0534538i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.21689i | 0.658568i | 0.944231 | + | 0.329284i | \(0.106807\pi\) | ||||
−0.944231 | + | 0.329284i | \(0.893193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.42204 | − | 7.65920i | −0.659199 | − | 1.14177i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.05821 | − | 8.76108i | 0.737816 | − | 1.27794i | −0.215660 | − | 0.976468i | \(-0.569190\pi\) |
0.953477 | − | 0.301467i | \(-0.0974763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.03630 | + | 3.54444i | −0.862329 | + | 0.506348i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.967895 | − | 1.67644i | 0.135532 | − | 0.234749i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.13514 | + | 3.54212i | −0.842726 | + | 0.486548i | −0.858190 | − | 0.513332i | \(-0.828411\pi\) |
0.0154638 | + | 0.999880i | \(0.495078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.11619 | 0.689868 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.53747 | 0.336096 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.38856 | − | 2.53374i | 0.571342 | − | 0.329865i | −0.186343 | − | 0.982485i | \(-0.559664\pi\) |
0.757685 | + | 0.652620i | \(0.226330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.21321 | − | 7.29750i | 0.539447 | − | 0.934349i | −0.459487 | − | 0.888184i | \(-0.651967\pi\) |
0.998934 | − | 0.0461646i | \(-0.0146999\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.08269 | − | 1.86995i | −0.892335 | − | 0.235591i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.21731 | + | 3.84050i | −0.275024 | + | 0.476355i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.01815 | − | 8.69169i | −0.613065 | − | 1.06186i | −0.990721 | − | 0.135913i | \(-0.956603\pi\) |
0.377656 | − | 0.925946i | \(-0.376730\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.12703 | −0.256064 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.29150i | − | 0.627986i | −0.949425 | − | 0.313993i | \(-0.898333\pi\) | ||
0.949425 | − | 0.313993i | \(-0.101667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.30504 | − | 5.37227i | 1.08907 | − | 0.628776i | 0.155743 | − | 0.987798i | \(-0.450223\pi\) |
0.933329 | + | 0.359021i | \(0.116890\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.16706 | − | 1.25115i | −0.250230 | − | 0.144470i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.98544 | − | 3.00745i | 0.340223 | − | 0.342731i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3349 | + | 5.96688i | 1.16277 | + | 0.671327i | 0.951967 | − | 0.306201i | \(-0.0990581\pi\) |
0.210805 | + | 0.977528i | \(0.432391\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.48605 | − | 6.03801i | −0.387338 | − | 0.670890i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.9789i | 1.64415i | 0.569382 | + | 0.822073i | \(0.307182\pi\) | ||||
−0.569382 | + | 0.822073i | \(0.692818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8580i | 1.39465i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.22777 | − | 2.12656i | −0.131631 | − | 0.227992i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50000 | + | 0.866025i | 0.159000 | + | 0.0917985i | 0.577389 | − | 0.816469i | \(-0.304072\pi\) |
−0.418389 | + | 0.908268i | \(0.637405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.963697 | + | 3.54444i | 0.101023 | + | 0.371558i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0482949 | − | 0.0278831i | −0.00500795 | − | 0.00289134i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.5965 | + | 8.42726i | −1.49756 | + | 0.864619i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.87198i | 0.291606i | 0.989314 | + | 0.145803i | \(0.0465765\pi\) | ||||
−0.989314 | + | 0.145803i | \(0.953423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.43462 | 0.445696 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.40310 | + | 5.89434i | 0.338621 | + | 0.586509i | 0.984174 | − | 0.177207i | \(-0.0567062\pi\) |
−0.645553 | + | 0.763716i | \(0.723373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.02471 | + | 12.1672i | −0.692165 | + | 1.19887i | 0.278962 | + | 0.960302i | \(0.410010\pi\) |
−0.971127 | + | 0.238563i | \(0.923324\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.92184 | + | 1.06631i | −0.382732 | + | 0.104061i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.56957 | + | 4.45063i | −0.248410 | + | 0.430259i | −0.963085 | − | 0.269198i | \(-0.913241\pi\) |
0.714675 | + | 0.699457i | \(0.246575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.45182 | − | 1.41556i | 0.234842 | − | 0.135586i | −0.377962 | − | 0.925821i | \(-0.623375\pi\) |
0.612804 | + | 0.790235i | \(0.290042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.57151 | 0.244077 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.43695 | −0.135177 | −0.0675887 | − | 0.997713i | \(-0.521531\pi\) | ||||
−0.0675887 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2355 | − | 7.06415i | 1.14096 | − | 0.658735i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.92193 | + | 3.32887i | −0.177682 | + | 0.307754i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.55833 | + | 7.50301i | 0.692871 | + | 0.687800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.21731 | − | 7.30460i | 0.383392 | − | 0.664054i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.01395 | + | 1.75622i | 0.0914251 | + | 0.158353i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.649581 | 0.0581003 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.92077i | 0.436647i | 0.975876 | + | 0.218324i | \(0.0700589\pi\) | ||||
−0.975876 | + | 0.218324i | \(0.929941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.41647 | + | 1.97250i | 0.298499 | + | 0.172338i | 0.641768 | − | 0.766899i | \(-0.278201\pi\) |
−0.343270 | + | 0.939237i | \(0.611534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.56363 | + | 13.4978i | −0.309006 | + | 1.17041i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.67429 | − | 4.43075i | −0.660498 | − | 0.381339i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0514223 | + | 0.0890661i | 0.00439331 | + | 0.00760943i | 0.868214 | − | 0.496190i | \(-0.165268\pi\) |
−0.863820 | + | 0.503800i | \(0.831935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 14.9789i | − | 1.27049i | −0.772310 | − | 0.635246i | \(-0.780899\pi\) | ||
0.772310 | − | 0.635246i | \(-0.219101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.86500i | − | 0.409707i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.11181 | − | 1.92571i | −0.0929743 | − | 0.161036i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1252 | + | 8.15518i | 1.17303 | + | 0.677251i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.66169 | + | 2.92759i | −0.137054 | + | 0.241464i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.79164 | − | 5.65320i | −0.802162 | − | 0.463129i | 0.0420645 | − | 0.999115i | \(-0.486607\pi\) |
−0.844227 | + | 0.535986i | \(0.819940\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8351 | − | 7.41032i | 1.04450 | − | 0.603044i | 0.123397 | − | 0.992357i | \(-0.460621\pi\) |
0.921105 | + | 0.389314i | \(0.127288\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.1451i | 0.901028i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.370413 | 0.0297523 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.369362 | + | 0.639755i | 0.0294783 | + | 0.0510580i | 0.880388 | − | 0.474254i | \(-0.157282\pi\) |
−0.850910 | + | 0.525312i | \(0.823949\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.70341 | + | 2.95039i | −0.135089 | + | 0.233981i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.98721 | − | 11.3145i | 0.235425 | − | 0.891707i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.35226 | + | 7.53834i | −0.340895 | + | 0.590448i | −0.984599 | − | 0.174826i | \(-0.944064\pi\) |
0.643704 | + | 0.765275i | \(0.277397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.13075 | − | 1.23019i | 0.165879 | − | 0.0957703i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.38831 | −0.107430 | −0.0537152 | − | 0.998556i | \(-0.517106\pi\) | ||||
−0.0537152 | + | 0.998556i | \(0.517106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0726 | −0.851739 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.6519 | + | 7.30460i | −0.967518 | + | 0.558597i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.485324 | + | 0.840606i | −0.0368985 | + | 0.0639101i | −0.883885 | − | 0.467704i | \(-0.845081\pi\) |
0.846986 | + | 0.531615i | \(0.178414\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.69877 | − | 9.77028i | 0.733158 | − | 0.738564i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.21848 | − | 2.11046i | 0.0915864 | − | 0.158632i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.13495 | − | 12.3581i | −0.533291 | − | 0.923687i | −0.999244 | − | 0.0388779i | \(-0.987622\pi\) |
0.465953 | − | 0.884810i | \(-0.345712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3218 | 1.13886 | 0.569429 | − | 0.822041i | \(-0.307164\pi\) | ||||
0.569429 | + | 0.822041i | \(0.307164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.05228i | − | 0.299553i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.7922 | + | 8.54031i | −1.08755 | + | 0.627896i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.58353 | − | 3.22365i | −0.408308 | − | 0.235737i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.08269 | + | 1.92571i | −0.515190 | + | 0.140075i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.16564 | + | 1.25033i | 0.156700 | + | 0.0904709i | 0.576300 | − | 0.817238i | \(-0.304496\pi\) |
−0.419599 | + | 0.907709i | \(0.637829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.55026 | + | 2.68512i | 0.111590 | + | 0.193279i | 0.916411 | − | 0.400237i | \(-0.131072\pi\) |
−0.804822 | + | 0.593517i | \(0.797739\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.13261i | 0.152720i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.6891i | − | 1.11780i | −0.829233 | − | 0.558902i | \(-0.811223\pi\) | ||
0.829233 | − | 0.558902i | \(-0.188777\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.91290 | − | 10.2414i | −0.419154 | − | 0.725997i | 0.576700 | − | 0.816956i | \(-0.304340\pi\) |
−0.995855 | + | 0.0909591i | \(0.971007\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.17984 | − | 2.41323i | −0.294823 | − | 0.170216i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.0363 | − | 3.54444i | 0.914969 | − | 0.248771i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.6653 | − | 6.73495i | −0.814738 | − | 0.470389i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.6055 | − | 6.12307i | 0.737131 | − | 0.425583i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.45124i | − | 0.584585i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0726 | −0.693427 | −0.346713 | − | 0.937971i | \(-0.612702\pi\) | ||||
−0.346713 | + | 0.937971i | \(0.612702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.27234 | − | 2.20376i | −0.0871796 | − | 0.150999i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.216146 | − | 0.217740i | 0.0146730 | − | 0.0147812i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.58353 | − | 4.47480i | 0.174579 | − | 0.302379i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.83970 | − | 2.79420i | 0.325553 | − | 0.187958i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.3086 | −1.62783 | −0.813913 | − | 0.580987i | \(-0.802667\pi\) | ||||
−0.813913 | + | 0.580987i | \(0.802667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.4067 | 0.960448 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.4048 | − | 7.16194i | 0.823339 | − | 0.475355i | −0.0282277 | − | 0.999602i | \(-0.508986\pi\) |
0.851566 | + | 0.524247i | \(0.175653\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.32502 | − | 9.22321i | 0.351887 | − | 0.609487i | −0.634693 | − | 0.772765i | \(-0.718873\pi\) |
0.986580 | + | 0.163278i | \(0.0522066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.520210 | − | 1.97037i | 0.0342273 | − | 0.129641i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.318991 | − | 0.552509i | 0.0208978 | − | 0.0361961i | −0.855387 | − | 0.517989i | \(-0.826681\pi\) |
0.876285 | + | 0.481793i | \(0.160014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.1573 | + | 27.9853i | 1.05399 | + | 1.82556i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.73896 | 0.372785 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4.73540i | − | 0.306307i | −0.988202 | − | 0.153154i | \(-0.951057\pi\) | ||
0.988202 | − | 0.153154i | \(-0.0489430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1380 | + | 5.85317i | −0.653045 | + | 0.377036i | −0.789622 | − | 0.613594i | \(-0.789723\pi\) |
0.136577 | + | 0.990629i | \(0.456390\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.1112 | − | 5.83773i | −0.648636 | − | 0.374490i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.164257 | − | 22.3593i | −0.0104940 | − | 1.42848i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.34397 | + | 3.66269i | 0.403657 | + | 0.233051i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.60168 | + | 6.23829i | 0.228247 | + | 0.395336i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.5631i | − | 0.729858i | −0.931035 | − | 0.364929i | \(-0.881093\pi\) | ||
0.931035 | − | 0.364929i | \(-0.118907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.08425i | 0.445383i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.09172 | + | 5.35501i | 0.193611 | + | 0.335344i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.4302 | − | 11.7954i | −1.27440 | − | 0.735777i | −0.298589 | − | 0.954382i | \(-0.596516\pi\) |
−0.975813 | + | 0.218605i | \(0.929849\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.61144 | + | 13.6788i | −0.224404 | + | 0.849961i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2435 | + | 7.06876i | 0.757851 | + | 0.437546i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.24833 | + | 5.33953i | −0.570277 | + | 0.329249i | −0.757260 | − | 0.653114i | \(-0.773462\pi\) |
0.186983 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 22.6290i | − | 1.39009i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.832945 | 0.0509754 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6690 | + | 20.2113i | 0.711471 | + | 1.23230i | 0.964305 | + | 0.264794i | \(0.0853040\pi\) |
−0.252834 | + | 0.967510i | \(0.581363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.81961 | − | 11.8119i | 0.414262 | − | 0.717522i | −0.581089 | − | 0.813840i | \(-0.697373\pi\) |
0.995351 | + | 0.0963179i | \(0.0307066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.25362 | + | 1.24444i | 0.0758722 | + | 0.0753169i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.16706 | + | 7.21755i | −0.251283 | + | 0.435235i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.396180 | − | 0.228735i | 0.0238042 | − | 0.0137433i | −0.488051 | − | 0.872815i | \(-0.662292\pi\) |
0.511855 | + | 0.859072i | \(0.328959\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.321068 | 0.0192218 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.43695 | 0.0857215 | 0.0428608 | − | 0.999081i | \(-0.486353\pi\) | ||||
0.0428608 | + | 0.999081i | \(0.486353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.0428 | + | 15.6132i | −1.60753 | + | 0.928108i | −0.617609 | + | 0.786486i | \(0.711898\pi\) |
−0.989921 | + | 0.141622i | \(0.954768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.05268 | + | 7.01945i | −0.240060 | + | 0.415796i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7660 | + | 2.92717i | −0.635497 | + | 0.172785i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.398321 | + | 0.689912i | −0.0234306 | + | 0.0405831i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.690570 | + | 1.19610i | 0.0404819 | + | 0.0701168i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.3006 | −1.82860 | −0.914299 | − | 0.405040i | \(-0.867258\pi\) | ||||
−0.914299 | + | 0.405040i | \(0.867258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1869i | 0.942437i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.84806 | − | 2.22168i | 0.223287 | − | 0.128915i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.31783 | − | 3.07025i | −0.307538 | − | 0.177557i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.83459 | + | 1.63655i | 0.162843 | + | 0.0940175i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.4581 | + | 23.3102i | 0.770611 | + | 1.33474i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.7215i | − | 0.840202i | −0.907477 | − | 0.420101i | \(-0.861995\pi\) | ||
0.907477 | − | 0.420101i | \(-0.138005\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.75638i | 0.384357i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.79025 | + | 13.4931i | 0.441745 | + | 0.765124i | 0.997819 | − | 0.0660082i | \(-0.0210263\pi\) |
−0.556074 | + | 0.831133i | \(0.687693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.3329 | + | 6.54308i | 0.640576 | + | 0.369837i | 0.784836 | − | 0.619703i | \(-0.212747\pi\) |
−0.144260 | + | 0.989540i | \(0.546080\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.4849 | − | 16.6064i | 0.928818 | − | 0.935666i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.3971 | + | 11.7763i | 1.14562 | + | 0.661422i | 0.947815 | − | 0.318821i | \(-0.103287\pi\) |
0.197801 | + | 0.980242i | \(0.436620\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.08269 | + | 4.08919i | −0.396555 | + | 0.228951i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.47142i | 0.137941i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.2397 | 1.18181 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.61193 | − | 6.25604i | −0.200354 | − | 0.347023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.680744 | − | 1.17908i | 0.0376452 | − | 0.0652035i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.8788 | + | 6.83243i | 1.42674 | + | 0.376684i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5277 | − | 28.6268i | 0.908445 | − | 1.57347i | 0.0922207 | − | 0.995739i | \(-0.470603\pi\) |
0.816225 | − | 0.577735i | \(-0.196063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.8217 | + | 7.40258i | −0.702622 | + | 0.405659i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.0587 | 1.75155 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5096 | −0.844860 | −0.422430 | − | 0.906396i | \(-0.638823\pi\) | ||||
−0.422430 | + | 0.906396i | \(0.638823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.598452 | + | 0.345516i | −0.0325035 | + | 0.0187659i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.0928668 | + | 0.160850i | −0.00502902 | + | 0.00871052i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2393 | − | 12.9507i | −0.714855 | − | 0.699272i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.39716 | − | 5.88405i | 0.182897 | − | 0.316786i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.2494 | + | 19.4846i | 0.603900 | + | 1.04599i | 0.992224 | + | 0.124463i | \(0.0397209\pi\) |
−0.388324 | + | 0.921523i | \(0.626946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4735 | −1.52415 | −0.762077 | − | 0.647486i | \(-0.775820\pi\) | ||||
−0.762077 | + | 0.647486i | \(0.775820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.85142i | 0.205574i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.29108 | + | 4.78686i | −0.441290 | + | 0.254779i | −0.704145 | − | 0.710057i | \(-0.748669\pi\) |
0.262855 | + | 0.964835i | \(0.415336\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.6380 | + | 8.45124i | 0.776903 | + | 0.448545i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.95194 | + | 1.30739i | 0.262084 | + | 0.0691945i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.25225 | + | 1.87769i | 0.171647 | + | 0.0991006i | 0.583362 | − | 0.812212i | \(-0.301737\pi\) |
−0.411715 | + | 0.911313i | \(0.635070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.42067 | + | 7.65683i | 0.232667 | + | 0.402991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.05622i | − | 0.212896i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.3209i | 1.79644i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.41302 | + | 14.5718i | 0.439156 | + | 0.760640i | 0.997625 | − | 0.0688852i | \(-0.0219442\pi\) |
−0.558469 | + | 0.829526i | \(0.688611\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.1112 | − | 5.83773i | −0.526370 | − | 0.303900i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.3020 | − | 13.2046i | −0.690606 | − | 0.685551i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1354 | − | 6.42901i | −0.576568 | − | 0.332882i | 0.183200 | − | 0.983076i | \(-0.441354\pi\) |
−0.759768 | + | 0.650194i | \(0.774688\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.270533 | − | 0.156192i | 0.0139702 | − | 0.00806572i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.08888i | − | 0.365096i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5822 | −1.31407 | −0.657034 | − | 0.753861i | \(-0.728189\pi\) | ||||
−0.657034 | + | 0.753861i | \(0.728189\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.18320 | + | 2.04936i | 0.0606172 | + | 0.104992i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.4846 | + | 23.3561i | −0.689033 | + | 1.19344i | 0.283118 | + | 0.959085i | \(0.408631\pi\) |
−0.972151 | + | 0.234355i | \(0.924702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.55142 | + | 13.0620i | 0.180997 | + | 0.665701i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.7043 | − | 15.9951i | 1.40466 | − | 0.810983i | 0.409796 | − | 0.912177i | \(-0.365600\pi\) |
0.994867 | + | 0.101195i | \(0.0322665\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.8041 | −0.900394 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.89716 | 0.0956988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.0126 | + | 19.0598i | −1.66104 | + | 0.959004i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.51929 | + | 14.7558i | −0.427571 | + | 0.740575i | −0.996657 | − | 0.0817035i | \(-0.973964\pi\) |
0.569086 | + | 0.822278i | \(0.307297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.76139 | + | 6.47833i | 0.0881799 | + | 0.324322i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.94858 | − | 5.10709i | 0.147245 | − | 0.255036i | −0.782963 | − | 0.622068i | \(-0.786293\pi\) |
0.930208 | + | 0.367032i | \(0.119626\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0804953 | − | 0.139422i | −0.00400976 | − | 0.00694510i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.2707 | 1.10664 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.56461i | − | 0.424532i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.207751 | + | 0.119945i | −0.0102726 | + | 0.00593090i | −0.505128 | − | 0.863045i | \(-0.668555\pi\) |
0.494855 | + | 0.868976i | \(0.335221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.0428320 | + | 0.0247290i | 0.00211274 | + | 0.00121979i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.51514 | + | 9.44550i | 0.468210 | + | 0.464783i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.4364 | − | 23.9233i | −2.03403 | − | 1.17435i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.60168 | − | 6.23829i | −0.176375 | − | 0.305490i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.4140i | 1.43697i | 0.695544 | + | 0.718484i | \(0.255163\pi\) | ||||
−0.695544 | + | 0.718484i | \(0.744837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 32.1265i | − | 1.56575i | −0.622180 | − | 0.782874i | \(-0.713753\pi\) | ||
0.622180 | − | 0.782874i | \(-0.286247\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.0049 | + | 24.2571i | 0.680939 | + | 1.17942i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.1391 | − | 10.4726i | −0.879878 | − | 0.507998i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.5556 | + | 5.69103i | 1.04315 | + | 0.275408i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.926077 | − | 0.534671i | −0.0447114 | − | 0.0258141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.7662 | − | 18.9176i | 1.57829 | − | 0.911228i | 0.583196 | − | 0.812332i | \(-0.301802\pi\) |
0.995098 | − | 0.0988962i | \(-0.0315312\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.4835i | − | 1.22466i | −0.790602 | − | 0.612330i | \(-0.790232\pi\) | ||
0.790602 | − | 0.612330i | \(-0.209768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.84367 | 0.376075 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6690 | − | 20.2113i | −0.558204 | − | 0.966837i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9804 | − | 20.7506i | 0.571792 | − | 0.990373i | −0.424590 | − | 0.905386i | \(-0.639582\pi\) |
0.996382 | − | 0.0849871i | \(-0.0270849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.142375 | − | 19.3806i | −0.00677975 | − | 0.922887i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.13495 | − | 8.89399i | 0.243969 | − | 0.422566i | −0.717872 | − | 0.696175i | \(-0.754884\pi\) |
0.961841 | + | 0.273608i | \(0.0882172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.79140 | + | 2.76632i | −0.227134 | + | 0.131136i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.43726 | −0.257174 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5096 | 0.543170 | 0.271585 | − | 0.962414i | \(-0.412452\pi\) | ||||
0.271585 | + | 0.962414i | \(0.412452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.84923 | − | 3.37705i | 0.275429 | − | 0.159019i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.56363 | − | 6.17239i | 0.167434 | − | 0.290004i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3442 | − | 2.99505i | −0.531824 | − | 0.140410i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3050 | + | 26.5091i | −0.715939 | + | 1.24004i | 0.246657 | + | 0.969103i | \(0.420668\pi\) |
−0.962596 | + | 0.270941i | \(0.912665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.58353 | + | 9.67095i | 0.260617 | + | 0.451401i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.3671 | 0.808866 | 0.404433 | − | 0.914568i | \(-0.367469\pi\) | ||||
0.404433 | + | 0.914568i | \(0.367469\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.7288i | − | 1.00983i | −0.863171 | − | 0.504913i | \(-0.831525\pi\) | ||
0.863171 | − | 0.504913i | \(-0.168475\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.154267 | − | 0.0890661i | 0.00715396 | − | 0.00413034i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.585859 | + | 0.338246i | 0.0271103 | + | 0.0156521i | 0.513494 | − | 0.858093i | \(-0.328351\pi\) |
−0.486384 | + | 0.873745i | \(0.661684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7071 | − | 18.8450i | 0.863814 | − | 0.870183i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.307659 | + | 0.177627i | 0.0141762 | + | 0.00818461i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 27.4555i | − | 1.25974i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 19.6144i | − | 0.898082i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.3839 | − | 24.9136i | −0.657217 | − | 1.13833i | −0.981333 | − | 0.192316i | \(-0.938400\pi\) |
0.324116 | − | 0.946017i | \(-0.394933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.42907 | + | 3.71182i | 0.293140 | + | 0.169245i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.47649 | − | 5.43045i | −0.0671824 | − | 0.247094i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.94483 | − | 4.58695i | −0.360756 | − | 0.208283i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.58745 | − | 0.916514i | 0.0719342 | − | 0.0415312i | −0.463602 | − | 0.886044i | \(-0.653443\pi\) |
0.535536 | + | 0.844513i | \(0.320110\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.18601i | 0.189298i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4370 | −0.606401 | −0.303201 | − | 0.952927i | \(-0.598055\pi\) | ||||
−0.303201 | + | 0.952927i | \(0.598055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2770 | − | 17.8002i | −0.462851 | − | 0.801682i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.08269 | + | 12.2676i | −0.318343 | + | 0.551387i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5096 | − | 3.67311i | 0.605987 | − | 0.164762i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.68404 | + | 9.84505i | −0.254453 | + | 0.440725i | −0.964747 | − | 0.263180i | \(-0.915229\pi\) |
0.710294 | + | 0.703905i | \(0.248562\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.578191 | + | 0.333819i | −0.0258317 | + | 0.0149139i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.2022 | 0.588656 | 0.294328 | − | 0.955704i | \(-0.404904\pi\) | ||||
0.294328 | + | 0.955704i | \(0.404904\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.7408 | −0.967454 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.61144 | + | 2.66241i | −0.204801 | + | 0.118242i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2178 | + | 22.8940i | −0.585870 | + | 1.01476i | 0.408896 | + | 0.912581i | \(0.365914\pi\) |
−0.994766 | + | 0.102176i | \(0.967420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.1749 | + | 20.0272i | 0.892484 | + | 0.885952i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.31899 | + | 12.6769i | −0.323141 | + | 0.559697i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.4388 | − | 38.8652i | −0.988773 | − | 1.71260i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.2033 | −0.712619 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.466786i | 0.0204896i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.4163 | + | 6.01384i | −0.456345 | + | 0.263471i | −0.710506 | − | 0.703691i | \(-0.751534\pi\) |
0.254161 | + | 0.967162i | \(0.418201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.43276 | − | 1.40455i | −0.106377 | − | 0.0614168i | 0.445868 | − | 0.895099i | \(-0.352895\pi\) |
−0.552245 | + | 0.833682i | \(0.686229\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.69000 | − | 6.40113i | 0.0737577 | − | 0.279368i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.404248 | − | 0.233393i | −0.0176093 | − | 0.0101668i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.71848 | − | 2.97649i | −0.0747164 | − | 0.129413i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.0305i | 0.608872i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.85434i | 0.253580i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.20791 | − | 14.2165i | −0.354859 | − | 0.614634i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.94302 | − | 3.43120i | −0.256460 | − | 0.148067i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.75058 | + | 5.53440i | 0.419987 | + | 0.238383i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.68628 | + | 0.973573i | 0.0724988 | + | 0.0418572i | 0.535811 | − | 0.844338i | \(-0.320006\pi\) |
−0.463312 | + | 0.886195i | \(0.653339\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.38109 | − | 3.68413i | 0.273839 | − | 0.158101i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.04336i | 0.387375i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.4561 | −1.21669 | −0.608347 | − | 0.793671i | \(-0.708167\pi\) | ||||
−0.608347 | + | 0.793671i | \(0.708167\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.6653 | + | 20.2048i | 0.497862 | + | 0.862321i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.4712 | − | 23.3329i | 0.573894 | − | 0.994013i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.05982 | + | 30.5277i | −0.342738 | + | 1.29817i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.10704 | + | 7.11361i | −0.174334 | + | 0.301956i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.96630 | − | 4.59935i | 0.337543 | − | 0.194881i | −0.321642 | − | 0.946861i | \(-0.604235\pi\) |
0.659185 | + | 0.751981i | \(0.270901\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.10051 | −0.130904 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.5533 | − | 13.5985i | 0.992653 | − | 0.573108i | 0.0865866 | − | 0.996244i | \(-0.472404\pi\) |
0.906066 | + | 0.423136i | \(0.139071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.29501 | − | 3.97508i | 0.0965518 | − | 0.167233i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.9956 | − | 13.0914i | 0.545764 | − | 0.549788i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.7699 | − | 20.3861i | 0.493420 | − | 0.854628i | −0.506551 | − | 0.862210i | \(-0.669080\pi\) |
0.999971 | + | 0.00758149i | \(0.00241329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.1713 | + | 26.2774i | 0.634897 | + | 1.09967i | 0.986537 | + | 0.163539i | \(0.0522909\pi\) |
−0.351640 | + | 0.936135i | \(0.614376\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.20257 | 0.0502382 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.0145i | 0.959772i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7760 | − | 14.3044i | 1.03144 | − | 0.595500i | 0.114041 | − | 0.993476i | \(-0.463620\pi\) |
0.917396 | + | 0.397976i | \(0.130287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.29128 | + | 0.745520i | 0.0536637 | + | 0.0309828i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.2421 | + | 10.3976i | −1.58655 | + | 0.431367i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.82652 | + | 5.67335i | 0.406973 | + | 0.234966i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.13915 | − | 10.6333i | −0.253823 | − | 0.439634i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 15.2362i | − | 0.628867i | −0.949280 | − | 0.314433i | \(-0.898186\pi\) | ||
0.949280 | − | 0.314433i | \(-0.101814\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.611872i | − | 0.0252117i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.77246 | − | 6.53409i | −0.155178 | − | 0.268777i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.2934 | + | 10.5617i | 0.751221 | + | 0.433717i | 0.826135 | − | 0.563473i | \(-0.190535\pi\) |
−0.0749142 | + | 0.997190i | \(0.523868\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.8274 | + | 8.92543i | −1.34579 | + | 0.365907i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.92512 | − | 2.84352i | −0.201572 | − | 0.116378i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.1795 | + | 16.8468i | −1.19224 | + | 0.688341i | −0.958814 | − | 0.284033i | \(-0.908327\pi\) |
−0.233427 | + | 0.972374i | \(0.574994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.3960i | 0.995132i | 0.867426 | + | 0.497566i | \(0.165773\pi\) | ||||
−0.867426 | + | 0.497566i | \(0.834227\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.7879 | 1.13161 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4712 | + | 23.3329i | 0.547683 | + | 0.948616i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.08757 | + | 7.07987i | −0.165909 | + | 0.287363i | −0.936978 | − | 0.349389i | \(-0.886389\pi\) |
0.771069 | + | 0.636752i | \(0.219723\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.57700 | − | 4.61075i | 0.185469 | − | 0.186837i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.02235 | − | 12.1631i | 0.284094 | − | 0.492065i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7221 | + | 8.49981i | −0.594620 | + | 0.343304i | −0.766922 | − | 0.641740i | \(-0.778213\pi\) |
0.172302 | + | 0.985044i | \(0.444879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.47768 | −0.261205 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.6548 | 1.59644 | 0.798221 | − | 0.602365i | \(-0.205775\pi\) | ||||
0.798221 | + | 0.602365i | \(0.205775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4719 | − | 7.20065i | 0.501288 | − | 0.289419i | −0.227957 | − | 0.973671i | \(-0.573205\pi\) |
0.729245 | + | 0.684252i | \(0.239871\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.13514 | − | 10.6264i | 0.246195 | − | 0.426422i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.16979 | + | 4.43075i | −0.0468667 | + | 0.177514i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.9709 | − | 20.7343i | 0.478837 | − | 0.829370i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.03211 | − | 3.51971i | −0.0811545 | − | 0.140564i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.5246 | 0.858241 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.6698i | 1.45980i | 0.683553 | + | 0.729900i | \(0.260434\pi\) | ||||
−0.683553 | + | 0.729900i | \(0.739566\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.19496 | + | 2.42196i | −0.166735 | + | 0.0962644i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.6124 | − | 7.85913i | −0.540192 | − | 0.311880i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.38024 | + | 4.92077i | −0.332037 | + | 0.194968i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.6879 | + | 7.32538i | 0.501927 | + | 0.289788i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.13798 | − | 15.8274i | −0.360929 | − | 0.625147i | 0.627185 | − | 0.778870i | \(-0.284207\pi\) |
−0.988114 | + | 0.153723i | \(0.950874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.6340i | 0.537671i | 0.963186 | + | 0.268836i | \(0.0866389\pi\) | ||||
−0.963186 | + | 0.268836i | \(0.913361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.74153 | − | 15.1408i | −0.343665 | − | 0.595245i | 0.641445 | − | 0.767169i | \(-0.278335\pi\) |
−0.985110 | + | 0.171923i | \(0.945002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.02907 | − | 4.05824i | −0.275915 | − | 0.159300i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0376633 | − | 0.142655i | 0.00147614 | − | 0.00559110i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.40495 | + | 4.85260i | 0.328911 | + | 0.189897i | 0.655358 | − | 0.755319i | \(-0.272518\pi\) |
−0.326446 | + | 0.945216i | \(0.605851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.9131 | + | 6.30070i | −0.426411 | + | 0.246189i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.7488i | 1.16061i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.9465 | 1.12760 | 0.563798 | − | 0.825913i | \(-0.309340\pi\) | ||||
0.563798 | + | 0.825913i | \(0.309340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.43683 | + | 11.1489i | 0.250364 | + | 0.433643i | 0.963626 | − | 0.267254i | \(-0.0861164\pi\) |
−0.713262 | + | 0.700897i | \(0.752783\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.34373 | − | 2.32742i | 0.0521863 | − | 0.0903893i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −31.6475 | − | 31.4159i | −1.22724 | − | 1.21826i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.2922 | + | 19.5587i | −0.437238 | + | 0.757318i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1239 | + | 5.84502i | −0.391412 | + | 0.225982i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.4964 | −0.521024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.6548 | −0.911825 | −0.455912 | − | 0.890025i | \(-0.650687\pi\) | ||||
−0.455912 | + | 0.890025i | \(0.650687\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.5012 | − | 7.21755i | 0.481170 | − | 0.277804i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.80224 | − | 3.12157i | 0.0692657 | − | 0.119972i | −0.829313 | − | 0.558785i | \(-0.811268\pi\) |
0.898578 | + | 0.438813i | \(0.144601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.33237 | + | 1.99360i | −0.281391 | + | 0.0765072i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.44419 | − | 5.96550i | 0.131981 | − | 0.228599i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.80924 | − | 6.59779i | −0.145756 | − | 0.252457i | 0.783899 | − | 0.620889i | \(-0.213228\pi\) |
−0.929655 | + | 0.368432i | \(0.879895\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.328514 | −0.0125519 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5.12162i | − | 0.195402i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.51745 | + | 4.91755i | −0.324489 | + | 0.187344i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.9707 | + | 25.9639i | 1.71077 | + | 0.987712i | 0.933526 | + | 0.358509i | \(0.116715\pi\) |
0.777241 | + | 0.629203i | \(0.216619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.07831 | + | 11.3219i | 0.116935 | + | 0.430083i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.4364 | + | 23.9233i | 1.57177 | + | 0.907462i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.48721 | + | 14.7003i | 0.321476 | + | 0.556813i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 0.306806i | − | 0.0116045i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.741474i | 0.0280051i | 0.999902 | + | 0.0140025i | \(0.00445729\pi\) | ||||
−0.999902 | + | 0.0140025i | \(0.995543\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1074 | + | 24.4347i | 0.532071 | + | 0.921574i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.4581 | + | 7.77006i | 0.506863 | + | 0.292637i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.6864 | + | 12.7799i | −0.477120 | + | 0.480638i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.6491 | + | 20.5820i | 1.33883 | + | 0.772974i | 0.986634 | − | 0.162952i | \(-0.0521016\pi\) |
0.352196 | + | 0.935926i | \(0.385435\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.6147 | + | 16.5207i | −1.07314 | + | 0.619575i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.512901i | 0.0192083i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.10284 | 0.265631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.13863 | − | 1.97216i | −0.0425229 | − | 0.0736518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.02471 | + | 12.1672i | −0.261978 | + | 0.453758i | −0.966767 | − | 0.255658i | \(-0.917708\pi\) |
0.704790 | + | 0.709416i | \(0.251041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.9398 | − | 9.48869i | −1.33847 | − | 0.353377i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.81479 | + | 4.87536i | −0.104683 | + | 0.181317i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.0095 | + | 13.2845i | −0.854550 | + | 0.493375i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.2022 | −0.489642 | −0.244821 | − | 0.969568i | \(-0.578729\pi\) | ||||
−0.244821 | + | 0.969568i | \(0.578729\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.3015 | 0.566724 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.9797 | − | 43.2661i | 0.922646 | − | 1.59807i | 0.127342 | − | 0.991859i | \(-0.459356\pi\) |
0.795304 | − | 0.606211i | \(-0.207311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.44471 | − | 9.27253i | −0.200831 | − | 0.342022i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.03747 | + | 13.9213i | −0.296064 | + | 0.512798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2718 | − | 31.6476i | −0.672138 | − | 1.16418i | −0.977297 | − | 0.211875i | \(-0.932043\pi\) |
0.305159 | − | 0.952301i | \(-0.401290\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.52278 | 0.129413 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 15.1330i | − | 0.555177i | −0.960700 | − | 0.277589i | \(-0.910465\pi\) | ||
0.960700 | − | 0.277589i | \(-0.0895352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.2771 | − | 18.0579i | 1.14591 | − | 0.661589i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −35.9163 | − | 20.7363i | −1.31411 | − | 0.758701i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.1464 | − | 3.47087i | −0.480360 | − | 0.126823i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.9997 | − | 6.92806i | −0.437877 | − | 0.252808i | 0.264820 | − | 0.964298i | \(-0.414688\pi\) |
−0.702697 | + | 0.711490i | \(0.748021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.78036 | − | 4.81572i | −0.101322 | − | 0.175495i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.3412i | 1.72292i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.6967i | 1.69722i | 0.529019 | + | 0.848610i | \(0.322560\pi\) | ||||
−0.529019 | + | 0.848610i | \(0.677440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.70341 | + | 2.95039i | 0.0618299 | + | 0.107093i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.7899 | + | 23.5501i | 1.47863 | + | 0.853689i | 0.999708 | − | 0.0241662i | \(-0.00769309\pi\) |
0.478925 | + | 0.877856i | \(0.341026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31596 | + | 5.27705i | 0.192451 | + | 0.191042i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.8309 | − | 17.8002i | −1.11469 | − | 0.643568i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.09267 | − | 3.51761i | 0.219994 | − | 0.127013i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.3071i | − | 0.624110i | −0.950064 | − | 0.312055i | \(-0.898983\pi\) | ||
0.950064 | − | 0.312055i | \(-0.101017\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.3448 | −0.408574 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.5389 | − | 23.4501i | −0.486960 | − | 0.843440i | 0.512927 | − | 0.858432i | \(-0.328561\pi\) |
−0.999888 | + | 0.0149920i | \(0.995228\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.301696 | + | 0.522552i | −0.0108372 | + | 0.0187706i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.78502 | + | 6.56523i | 0.0640372 | + | 0.235526i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.1252 | + | 19.2694i | −0.398601 | + | 0.690398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.33982 | + | 4.23764i | −0.262639 | + | 0.151635i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1654 | 0.506230 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.35969 | −0.0842208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.9684 | − | 27.1172i | 1.67424 | − | 0.966624i | 0.709023 | − | 0.705186i | \(-0.249136\pi\) |
0.965220 | − | 0.261439i | \(-0.0841969\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.56778 | + | 4.44753i | −0.0914155 | + | 0.158336i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.997467 | − | 3.66864i | −0.0354658 | − | 0.130442i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.84923 | − | 10.1312i | 0.207712 | − | 0.359768i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.44115 | − | 9.42435i | −0.192978 | − | 0.334247i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.1437 | 0.713527 | 0.356763 | − | 0.934195i | \(-0.383880\pi\) | ||||
0.356763 | + | 0.934195i | \(0.383880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 40.7221i | − | 1.44064i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.15310 | + | 2.39779i | −0.146743 | + | 0.0847219i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.9037 | − | 8.60465i | −0.525940 | − | 0.303651i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.5285 | + | 26.3344i | 0.935008 | + | 0.928164i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.71963 | + | 5.61163i | 0.342147 | + | 0.197539i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.2771 | − | 29.9249i | −0.607432 | − | 1.05210i | −0.991662 | − | 0.128865i | \(-0.958867\pi\) |
0.384231 | − | 0.923237i | \(-0.374467\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.6340i | − | 0.478754i | −0.970927 | − | 0.239377i | \(-0.923057\pi\) | ||
0.970927 | − | 0.239377i | \(-0.0769431\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 6.55911i | − | 0.230038i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.9023 | − | 24.0795i | −0.486976 | − | 0.843468i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.83294 | − | 2.59606i | −0.343591 | − | 0.0907136i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.7311 | − | 16.0106i | −0.967822 | − | 0.558772i | −0.0692505 | − | 0.997599i | \(-0.522061\pi\) |
−0.898572 | + | 0.438827i | \(0.855394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8399 | − | 15.4960i | 0.935580 | − | 0.540158i | 0.0470083 | − | 0.998894i | \(-0.485031\pi\) |
0.888572 | + | 0.458737i | \(0.151698\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00788i | 0.139537i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.0191 | 0.383172 | 0.191586 | − | 0.981476i | \(-0.438637\pi\) | ||||
0.191586 | + | 0.981476i | \(0.438637\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.9836 | − | 32.8806i | −0.659328 | − | 1.14199i | −0.980790 | − | 0.195067i | \(-0.937508\pi\) |
0.321462 | − | 0.946922i | \(-0.395826\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.109999 | − | 0.190524i | 0.00381582 | − | 0.00660919i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.9090 | + | 24.5052i | −0.481920 | + | 0.849054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.21731 | − | 3.84050i | 0.0767332 | − | 0.132906i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.278601 | − | 0.160850i | 0.00962984 | − | 0.00555979i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.32984 | 0.287578 | 0.143789 | − | 0.989608i | \(-0.454071\pi\) | ||||
0.143789 | + | 0.989608i | \(0.454071\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.92739 | 0.100945 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.598452 | − | 0.345516i | 0.0206118 | − | 0.0119002i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.6844 | − | 30.6304i | 0.608363 | − | 1.05372i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5766 | + | 5.69657i | 0.741380 | + | 0.195736i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50840 | + | 13.0049i | −0.257687 | + | 0.446328i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.8255 | − | 20.4824i | −0.405374 | − | 0.702128i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.94153 | −0.237673 | −0.118837 | − | 0.992914i | \(-0.537917\pi\) | ||||
−0.118837 | + | 0.992914i | \(0.537917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 46.6657i | − | 1.59593i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.91744 | − | 1.10704i | 0.0654986 | − | 0.0378156i | −0.466893 | − | 0.884314i | \(-0.654627\pi\) |
0.532392 | + | 0.846498i | \(0.321293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.26337 | − | 3.03881i | −0.179584 | − | 0.103683i | 0.407513 | − | 0.913199i | \(-0.366396\pi\) |
−0.587097 | + | 0.809516i | \(0.699729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.77991 | + | 3.80778i | −0.128819 | + | 0.129769i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.64747 | + | 4.41527i | 0.260323 | + | 0.150298i | 0.624482 | − | 0.781039i | \(-0.285310\pi\) |
−0.364159 | + | 0.931337i | \(0.618643\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.55026 | − | 2.68512i | −0.0527103 | − | 0.0912969i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.383106i | 0.0130110i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 19.1141i | − | 0.648400i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.96673 | − | 12.0667i | −0.236059 | − | 0.408866i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.88643 | − | 3.97588i | −0.233070 | − | 0.134563i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.450909 | + | 1.65842i | 0.0152435 | + | 0.0560650i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3059 | − | 5.95011i | −0.348005 | − | 0.200921i | 0.315801 | − | 0.948825i | \(-0.397727\pi\) |
−0.663806 | + | 0.747905i | \(0.731060\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.0358 | + | 7.52623i | −0.439687 | + | 0.253854i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 53.9142i | 1.81642i | 0.418519 | + | 0.908208i | \(0.362549\pi\) | ||||
−0.418519 | + | 0.908208i | \(0.637451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1987 | −0.376866 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.89215 | + | 6.74139i | 0.130833 | + | 0.226609i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.1832 | + | 31.4942i | −0.610531 | + | 1.05747i | 0.380620 | + | 0.924732i | \(0.375711\pi\) |
−0.991151 | + | 0.132740i | \(0.957623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5630 | + | 3.41576i | −0.421351 | + | 0.114561i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.58353 | + | 9.67095i | −0.187055 | + | 0.323989i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.2278 | − | 26.6896i | 1.54695 | − | 0.893134i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.5819 | 1.52364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.95297 | −0.0985968 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.512788 | + | 0.296058i | −0.0171024 | + | 0.00987410i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.2583 | + | 24.6960i | −0.475011 | + | 0.822744i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.4709 | + | 42.3849i | −0.813441 | + | 1.40892i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.92370 | − | 15.4563i | −0.296307 | − | 0.513218i | 0.678981 | − | 0.734156i | \(-0.262422\pi\) |
−0.975288 | + | 0.220937i | \(0.929088\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.8446 | −0.625034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1458i | 0.369278i | 0.982806 | + | 0.184639i | \(0.0591116\pi\) | ||||
−0.982806 | + | 0.184639i | \(0.940888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7771 | − | 11.9957i | 0.687623 | − | 0.396999i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.2099 | + | 6.47203i | 0.370587 | + | 0.213959i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.66437 | + | 10.0917i | −0.0879854 | + | 0.333257i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.2802 | − | 16.3276i | −0.932879 | − | 0.538598i | −0.0451579 | − | 0.998980i | \(-0.514379\pi\) |
−0.887721 | + | 0.460382i | \(0.847712\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.53980 | − | 6.13111i | −0.116640 | − | 0.202027i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 7.34623i | − | 0.241804i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 27.8238i | − | 0.914839i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.4496 | − | 33.6876i | −0.638807 | − | 1.10645i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.3027 | − | 13.4538i | −0.764537 | − | 0.441406i | 0.0663853 | − | 0.997794i | \(-0.478853\pi\) |
−0.830922 | + | 0.556388i | \(0.812187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.9344 | + | 0.271329i | −1.21048 | + | 0.00889246i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.48885 | + | 3.74634i | 0.212435 | + | 0.122650i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8353 | − | 10.2972i | 0.583276 | − | 0.336755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.6476i | − | 1.06655i | −0.845942 | − | 0.533275i | \(-0.820961\pi\) | ||
0.845942 | − | 0.533275i | \(-0.179039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.29315 | 0.205369 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.32087 | − | 10.9481i | −0.206055 | − | 0.356897i | 0.744414 | − | 0.667719i | \(-0.232729\pi\) |
−0.950468 | + | 0.310822i | \(0.899396\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.32569 | − | 16.1526i | 0.303686 | − | 0.526000i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.98488 | − | 22.6686i | 0.194688 | − | 0.737410i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.1271 | + | 36.5931i | −0.686537 | + | 1.18912i | 0.286414 | + | 0.958106i | \(0.407537\pi\) |
−0.972951 | + | 0.231011i | \(0.925797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9182 | − | 7.45835i | 0.419344 | − | 0.242108i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3264 | 0.367285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.4561 | −1.44007 | −0.720037 | − | 0.693936i | \(-0.755875\pi\) | ||||
−0.720037 | + | 0.693936i | \(0.755875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.91764 | + | 3.99390i | −0.223850 | + | 0.129240i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.96650 | + | 3.40607i | −0.0635678 | + | 0.110103i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.191697 | + | 0.193110i | −0.00619021 | + | 0.00623585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4933 | − | 26.8351i | 0.499783 | − | 0.865650i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.11447 | − | 12.3226i | −0.229261 | − | 0.397091i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.90388 | −0.318817 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7160i | 0.826972i | 0.910510 | + | 0.413486i | \(0.135689\pi\) | ||||
−0.910510 | + | 0.413486i | \(0.864311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.84573 | − | 5.10709i | 0.284166 | − | 0.164063i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.2746 | + | 23.2526i | 1.29247 | + | 0.746210i | 0.979092 | − | 0.203417i | \(-0.0652048\pi\) |
0.313381 | + | 0.949627i | \(0.398538\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.2421 | − | 10.3976i | 1.22599 | − | 0.333333i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.00854 | − | 1.73698i | −0.0963503 | − | 0.0556278i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.1348 | − | 29.6783i | −0.548189 | − | 0.949492i | −0.998399 | − | 0.0565688i | \(-0.981984\pi\) |
0.450209 | − | 0.892923i | \(-0.351349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.77419i | − | 0.0886635i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.83862i | 0.250268i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.777334 | + | 1.34638i | 0.0247931 | + | 0.0429429i | 0.878156 | − | 0.478375i | \(-0.158774\pi\) |
−0.853363 | + | 0.521318i | \(0.825441\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.4012 | + | 25.0577i | 1.38288 | + | 0.798404i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.4207 | − | 3.37705i | 0.395354 | − | 0.107493i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.6482 | + | 13.0759i | −0.719443 | + | 0.415371i | −0.814548 | − | 0.580097i | \(-0.803015\pi\) |
0.0951047 | + | 0.995467i | \(0.469681\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 15.8964i | − | 0.504457i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.7748 | 1.19754 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.1467 | + | 31.4310i | 0.574711 | + | 0.995429i | 0.996073 | + | 0.0885360i | \(0.0282188\pi\) |
−0.421362 | + | 0.906893i | \(0.638448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.41717 | + | 12.8469i | −0.234669 | + | 0.406458i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))