Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(361,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.3 | ||
Root | \(-0.766044 + 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.667 |
Dual form | 1323.2.g.d.361.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26604 | + | 2.19285i | 0.895229 | + | 1.55058i | 0.833521 | + | 0.552487i | \(0.186321\pi\) |
0.0617072 | + | 0.998094i | \(0.480346\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.20574 | + | 3.82045i | −1.10287 | + | 1.91022i | ||||
\(5\) | 0.879385 | 0.393273 | 0.196637 | − | 0.980476i | \(-0.436998\pi\) | ||||
0.196637 | + | 0.980476i | \(0.436998\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.10607 | −2.15882 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.11334 | + | 1.92836i | 0.352069 | + | 0.609802i | ||||
\(11\) | −3.87939 | −1.16968 | −0.584839 | − | 0.811149i | \(-0.698842\pi\) | ||||
−0.584839 | + | 0.811149i | \(0.698842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.72668 | + | 4.72275i | 0.756245 | + | 1.30986i | 0.944753 | + | 0.327784i | \(0.106302\pi\) |
−0.188507 | + | 0.982072i | \(0.560365\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.31908 | − | 5.74881i | −0.829769 | − | 1.43720i | ||||
\(17\) | 0.826352 | + | 1.43128i | 0.200420 | + | 0.347137i | 0.948664 | − | 0.316286i | \(-0.102436\pi\) |
−0.748244 | + | 0.663424i | \(0.769103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.20574 | + | 2.08840i | −0.276615 | + | 0.479111i | −0.970541 | − | 0.240935i | \(-0.922546\pi\) |
0.693926 | + | 0.720046i | \(0.255879\pi\) | |||||||
\(20\) | −1.93969 | + | 3.35965i | −0.433728 | + | 0.751240i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.91147 | − | 8.50692i | −1.04713 | − | 1.81368i | ||||
\(23\) | −3.16250 | −0.659428 | −0.329714 | − | 0.944081i | \(-0.606952\pi\) | ||||
−0.329714 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.22668 | −0.845336 | ||||||||
\(26\) | −6.90420 | + | 11.9584i | −1.35403 | + | 2.34524i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.02481 | + | 5.23913i | −0.561694 | + | 0.972883i | 0.435655 | + | 0.900114i | \(0.356517\pi\) |
−0.997349 | + | 0.0727688i | \(0.976816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.27719 | − | 3.94421i | 0.408995 | − | 0.708400i | −0.585782 | − | 0.810468i | \(-0.699213\pi\) |
0.994777 | + | 0.102068i | \(0.0325459\pi\) | |||||||
\(32\) | 2.29813 | − | 3.98048i | 0.406256 | − | 0.703657i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.09240 | + | 3.62414i | −0.358843 | + | 0.621534i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27719 | − | 3.94421i | 0.374368 | − | 0.648424i | −0.615865 | − | 0.787852i | \(-0.711193\pi\) |
0.990232 | + | 0.139428i | \(0.0445265\pi\) | |||||||
\(38\) | −6.10607 | −0.990535 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.36959 | −0.849006 | ||||||||
\(41\) | −0.592396 | − | 1.02606i | −0.0925168 | − | 0.160244i | 0.816053 | − | 0.577977i | \(-0.196158\pi\) |
−0.908570 | + | 0.417734i | \(0.862825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0923963 | + | 0.160035i | −0.0140903 | + | 0.0244051i | −0.872985 | − | 0.487748i | \(-0.837819\pi\) |
0.858894 | + | 0.512153i | \(0.171152\pi\) | |||||||
\(44\) | 8.55690 | − | 14.8210i | 1.29000 | − | 2.23435i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00387 | − | 6.93491i | −0.590338 | − | 1.02250i | ||||
\(47\) | −0.511144 | − | 0.885328i | −0.0745581 | − | 0.129138i | 0.826336 | − | 0.563178i | \(-0.190421\pi\) |
−0.900894 | + | 0.434039i | \(0.857088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.35117 | − | 9.26849i | −0.756769 | − | 1.31076i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −24.0574 | −3.33616 | ||||||||
\(53\) | 3.64543 | + | 6.31407i | 0.500738 | + | 0.867304i | 1.00000 | 0.000852699i | \(0.000271423\pi\) | |
−0.499261 | + | 0.866451i | \(0.666395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.41147 | −0.460003 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.3182 | −2.01138 | ||||||||
\(59\) | 3.33022 | − | 5.76811i | 0.433558 | − | 0.750944i | −0.563619 | − | 0.826035i | \(-0.690591\pi\) |
0.997177 | + | 0.0750906i | \(0.0239246\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29813 | + | 2.24843i | 0.166209 | + | 0.287882i | 0.937084 | − | 0.349104i | \(-0.113514\pi\) |
−0.770875 | + | 0.636986i | \(0.780181\pi\) | |||||||
\(62\) | 11.5321 | 1.46458 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.63816 | −0.204769 | ||||||||
\(65\) | 2.39780 | + | 4.15312i | 0.297411 | + | 0.515131i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47906 | − | 2.56180i | 0.180695 | − | 0.312974i | −0.761422 | − | 0.648256i | \(-0.775499\pi\) |
0.942118 | + | 0.335283i | \(0.108832\pi\) | |||||||
\(68\) | −7.29086 | −0.884147 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68004 | 0.436741 | 0.218370 | − | 0.975866i | \(-0.429926\pi\) | ||||
0.218370 | + | 0.975866i | \(0.429926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.39053 | + | 11.0687i | 0.747955 | + | 1.29550i | 0.948801 | + | 0.315873i | \(0.102297\pi\) |
−0.200847 | + | 0.979623i | \(0.564369\pi\) | |||||||
\(74\) | 11.5321 | 1.34058 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.31908 | − | 9.21291i | −0.610140 | − | 1.05679i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.97906 | + | 5.15988i | 0.335170 | + | 0.580531i | 0.983517 | − | 0.180813i | \(-0.0578729\pi\) |
−0.648348 | + | 0.761345i | \(0.724540\pi\) | |||||||
\(80\) | −2.91875 | − | 5.05542i | −0.326326 | − | 0.565213i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | −0.109470 | + | 0.189608i | −0.0120159 | + | 0.0208122i | −0.871971 | − | 0.489558i | \(-0.837158\pi\) |
0.859955 | + | 0.510370i | \(0.170492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.726682 | + | 1.25865i | 0.0788197 | + | 0.136520i | ||||
\(86\) | −0.467911 | −0.0504562 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 23.6878 | 2.52513 | ||||||||
\(89\) | 5.51367 | − | 9.54996i | 0.584448 | − | 1.01229i | −0.410496 | − | 0.911862i | \(-0.634644\pi\) |
0.994944 | − | 0.100431i | \(-0.0320222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.97565 | − | 12.0822i | 0.727262 | − | 1.25965i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.29426 | − | 2.24173i | 0.133493 | − | 0.231217i | ||||
\(95\) | −1.06031 | + | 1.83651i | −0.108785 | + | 0.188422i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.25150 | + | 10.8279i | −0.634743 | + | 1.09941i | 0.351826 | + | 0.936065i | \(0.385561\pi\) |
−0.986569 | + | 0.163342i | \(0.947773\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.32295 | − | 16.1478i | 0.932295 | − | 1.61478i | ||||
\(101\) | 9.71688 | 0.966866 | 0.483433 | − | 0.875381i | \(-0.339390\pi\) | ||||
0.483433 | + | 0.875381i | \(0.339390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.59627 | 0.649949 | 0.324975 | − | 0.945723i | \(-0.394644\pi\) | ||||
0.324975 | + | 0.945723i | \(0.394644\pi\) | |||||||
\(104\) | −16.6493 | − | 28.8374i | −1.63260 | − | 2.82774i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.23055 | + | 15.9878i | −0.896550 | + | 1.55287i | ||||
\(107\) | 1.19459 | − | 2.06910i | 0.115486 | − | 0.200027i | −0.802488 | − | 0.596668i | \(-0.796491\pi\) |
0.917974 | + | 0.396641i | \(0.129824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.97906 | − | 3.42782i | −0.189559 | − | 0.328326i | 0.755544 | − | 0.655098i | \(-0.227373\pi\) |
−0.945103 | + | 0.326772i | \(0.894039\pi\) | |||||||
\(110\) | −4.31908 | − | 7.48086i | −0.411808 | − | 0.713272i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.22668 | + | 14.2490i | 0.773901 | + | 1.34044i | 0.935410 | + | 0.353565i | \(0.115031\pi\) |
−0.161509 | + | 0.986871i | \(0.551636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.78106 | −0.259335 | ||||||||
\(116\) | −13.3439 | − | 23.1123i | −1.23895 | − | 2.14592i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.8648 | 1.55253 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.04963 | 0.368148 | ||||||||
\(122\) | −3.28699 | + | 5.69323i | −0.297590 | + | 0.515441i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.0458 | + | 17.3998i | 0.902136 | + | 1.56255i | ||||
\(125\) | −8.11381 | −0.725721 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6536 | 1.56651 | 0.783253 | − | 0.621702i | \(-0.213559\pi\) | ||||
0.783253 | + | 0.621702i | \(0.213559\pi\) | |||||||
\(128\) | −6.67024 | − | 11.5532i | −0.589572 | − | 1.02117i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.07145 | + | 10.5161i | −0.532502 | + | 0.922320i | ||||
\(131\) | 19.1976 | 1.67730 | 0.838650 | − | 0.544670i | \(-0.183345\pi\) | ||||
0.838650 | + | 0.544670i | \(0.183345\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.49020 | 0.647055 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.04576 | − | 8.73951i | −0.432670 | − | 0.749407i | ||||
\(137\) | −18.1557 | −1.55115 | −0.775573 | − | 0.631258i | \(-0.782539\pi\) | ||||
−0.775573 | + | 0.631258i | \(0.782539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0287 | − | 19.1022i | −0.935441 | − | 1.62023i | −0.773846 | − | 0.633374i | \(-0.781670\pi\) |
−0.161595 | − | 0.986857i | \(-0.551664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.65910 | + | 8.06980i | 0.390983 | + | 0.677202i | ||||
\(143\) | −10.5778 | − | 18.3214i | −0.884564 | − | 1.53211i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.65998 | + | 4.60722i | −0.220899 | + | 0.382608i | ||||
\(146\) | −16.1814 | + | 28.0270i | −1.33918 | + | 2.31953i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0458 | + | 17.3998i | 0.825756 | + | 1.43025i | ||||
\(149\) | 15.1557 | 1.24160 | 0.620802 | − | 0.783968i | \(-0.286807\pi\) | ||||
0.620802 | + | 0.783968i | \(0.286807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9564 | −1.54265 | −0.771323 | − | 0.636444i | \(-0.780405\pi\) | ||||
−0.771323 | + | 0.636444i | \(0.780405\pi\) | |||||||
\(152\) | 7.36231 | − | 12.7519i | 0.597162 | − | 1.03432i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00253 | − | 3.46848i | 0.160847 | − | 0.278595i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.02869 | − | 15.6381i | 0.720568 | − | 1.24806i | −0.240205 | − | 0.970722i | \(-0.577215\pi\) |
0.960773 | − | 0.277337i | \(-0.0894520\pi\) | |||||||
\(158\) | −7.54323 | + | 13.0653i | −0.600107 | + | 1.03942i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.02094 | − | 3.50038i | 0.159770 | − | 0.276729i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.479055 | + | 0.829748i | −0.0375225 | + | 0.0649909i | −0.884177 | − | 0.467152i | \(-0.845280\pi\) |
0.846654 | + | 0.532143i | \(0.178613\pi\) | |||||||
\(164\) | 5.22668 | 0.408135 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.554378 | −0.0430280 | ||||||||
\(167\) | 9.91921 | + | 17.1806i | 0.767572 | + | 1.32947i | 0.938876 | + | 0.344255i | \(0.111869\pi\) |
−0.171304 | + | 0.985218i | \(0.554798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.36959 | + | 14.4965i | −0.643814 | + | 1.11512i | ||||
\(170\) | −1.84002 | + | 3.18701i | −0.141123 | + | 0.244433i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.407604 | − | 0.705990i | −0.0310795 | − | 0.0538313i | ||||
\(173\) | 11.3414 | + | 19.6438i | 0.862268 | + | 1.49349i | 0.869734 | + | 0.493520i | \(0.164290\pi\) |
−0.00746626 | + | 0.999972i | \(0.502377\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.8760 | + | 22.3019i | 0.970564 | + | 1.68107i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 27.9222 | 2.09286 | ||||||||
\(179\) | −3.67365 | − | 6.36295i | −0.274581 | − | 0.475589i | 0.695448 | − | 0.718576i | \(-0.255206\pi\) |
−0.970029 | + | 0.242988i | \(0.921873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.44562 | −0.256111 | −0.128056 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128056 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19.3105 | 1.42359 | ||||||||
\(185\) | 2.00253 | − | 3.46848i | 0.147229 | − | 0.255008i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.20574 | − | 5.55250i | −0.234427 | − | 0.406039i | ||||
\(188\) | 4.50980 | 0.328911 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.36959 | −0.389551 | ||||||||
\(191\) | 2.82888 | + | 4.89976i | 0.204690 | + | 0.354534i | 0.950034 | − | 0.312146i | \(-0.101048\pi\) |
−0.745344 | + | 0.666680i | \(0.767715\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.79813 | + | 8.31061i | −0.345377 | + | 0.598211i | −0.985422 | − | 0.170127i | \(-0.945582\pi\) |
0.640045 | + | 0.768337i | \(0.278916\pi\) | |||||||
\(194\) | −31.6587 | −2.27296 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.31996 | −0.592772 | −0.296386 | − | 0.955068i | \(-0.595782\pi\) | ||||
−0.296386 | + | 0.955068i | \(0.595782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.29813 | − | 5.71253i | −0.233798 | − | 0.404951i | 0.725124 | − | 0.688618i | \(-0.241782\pi\) |
−0.958923 | + | 0.283667i | \(0.908449\pi\) | |||||||
\(200\) | 25.8084 | 1.82493 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.3020 | + | 21.3077i | 0.865566 | + | 1.49920i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.520945 | − | 0.902302i | −0.0363843 | − | 0.0630195i | ||||
\(206\) | 8.35117 | + | 14.4646i | 0.581853 | + | 1.00780i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.1001 | − | 31.3504i | 1.25502 | − | 2.17376i | ||||
\(209\) | 4.67752 | − | 8.10170i | 0.323551 | − | 0.560406i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.68479 | + | 2.91815i | 0.115986 | + | 0.200893i | 0.918173 | − | 0.396179i | \(-0.129664\pi\) |
−0.802188 | + | 0.597072i | \(0.796331\pi\) | |||||||
\(212\) | −32.1634 | −2.20899 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.04963 | 0.413544 | ||||||||
\(215\) | −0.0812519 | + | 0.140732i | −0.00554133 | + | 0.00959787i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.01114 | − | 8.67956i | 0.339398 | − | 0.587854i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.52481 | − | 13.0334i | 0.507323 | − | 0.878709i | ||||
\(221\) | −4.50640 | + | 7.80531i | −0.303133 | + | 0.525042i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.13816 | − | 5.43545i | 0.210146 | − | 0.363984i | −0.741614 | − | 0.670827i | \(-0.765939\pi\) |
0.951760 | + | 0.306843i | \(0.0992726\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.8307 | + | 36.0798i | −1.38564 | + | 2.39999i | ||||
\(227\) | 6.16250 | 0.409020 | 0.204510 | − | 0.978865i | \(-0.434440\pi\) | ||||
0.204510 | + | 0.978865i | \(0.434440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.3851 | 1.54533 | 0.772664 | − | 0.634815i | \(-0.218924\pi\) | ||||
0.772664 | + | 0.634815i | \(0.218924\pi\) | |||||||
\(230\) | −3.52094 | − | 6.09845i | −0.232164 | − | 0.402120i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.4697 | − | 31.9905i | 1.21260 | − | 2.10028i | ||||
\(233\) | −4.26264 | + | 7.38311i | −0.279255 | + | 0.483684i | −0.971200 | − | 0.238267i | \(-0.923421\pi\) |
0.691945 | + | 0.721950i | \(0.256754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.449493 | − | 0.778544i | −0.0293217 | − | 0.0507866i | ||||
\(236\) | 14.6912 | + | 25.4459i | 0.956315 | + | 1.65639i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.28106 | + | 12.6112i | 0.470973 | + | 0.815748i | 0.999449 | − | 0.0331997i | \(-0.0105697\pi\) |
−0.528476 | + | 0.848948i | \(0.677236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.40373 | −0.348085 | −0.174043 | − | 0.984738i | \(-0.555683\pi\) | ||||
−0.174043 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(242\) | 5.12701 | + | 8.88024i | 0.329577 | + | 0.570844i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.4534 | −0.733226 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1506 | −0.836755 | ||||||||
\(248\) | −13.9047 | + | 24.0836i | −0.882947 | + | 1.52931i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.2724 | − | 17.7924i | −0.649686 | − | 1.12529i | ||||
\(251\) | 12.0669 | 0.761654 | 0.380827 | − | 0.924646i | \(-0.375639\pi\) | ||||
0.380827 | + | 0.924646i | \(0.375639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2686 | 0.771318 | ||||||||
\(254\) | 22.3503 | + | 38.7118i | 1.40238 | + | 2.42900i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.2515 | − | 26.4164i | 0.953219 | − | 1.65102i | ||||
\(257\) | −10.5662 | −0.659104 | −0.329552 | − | 0.944137i | \(-0.606898\pi\) | ||||
−0.329552 | + | 0.944137i | \(0.606898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −21.1557 | −1.31202 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.3050 | + | 42.0975i | 1.50157 | + | 2.60079i | ||||
\(263\) | 28.3533 | 1.74834 | 0.874169 | − | 0.485622i | \(-0.161407\pi\) | ||||
0.874169 | + | 0.485622i | \(0.161407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.20574 | + | 5.55250i | 0.196927 | + | 0.341087i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.52481 | + | 11.3013i | 0.398567 | + | 0.690337i | ||||
\(269\) | 3.74170 | + | 6.48081i | 0.228135 | + | 0.395142i | 0.957255 | − | 0.289244i | \(-0.0934038\pi\) |
−0.729120 | + | 0.684386i | \(0.760070\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.81908 | + | 11.8110i | −0.414229 | + | 0.717467i | −0.995347 | − | 0.0963530i | \(-0.969282\pi\) |
0.581118 | + | 0.813819i | \(0.302616\pi\) | |||||||
\(272\) | 5.48545 | − | 9.50108i | 0.332604 | − | 0.576088i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.9859 | − | 39.8128i | −1.38863 | − | 2.40518i | ||||
\(275\) | 16.3969 | 0.988772 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.15064 | −0.369556 | −0.184778 | − | 0.982780i | \(-0.559157\pi\) | ||||
−0.184778 | + | 0.982780i | \(0.559157\pi\) | |||||||
\(278\) | 27.9256 | − | 48.3686i | 1.67487 | − | 2.90095i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.65611 | − | 2.86846i | 0.0987951 | − | 0.171118i | −0.812391 | − | 0.583113i | \(-0.801835\pi\) |
0.911186 | + | 0.411995i | \(0.135168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.5116 | + | 25.1348i | −0.862626 | + | 1.49411i | 0.00675974 | + | 0.999977i | \(0.497848\pi\) |
−0.869385 | + | 0.494134i | \(0.835485\pi\) | |||||||
\(284\) | −8.11721 | + | 14.0594i | −0.481668 | + | 0.834273i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.7841 | − | 46.3913i | 1.58377 | − | 2.74318i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.13429 | − | 12.3569i | 0.419664 | − | 0.726879i | ||||
\(290\) | −13.4706 | −0.791021 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −56.3833 | −3.29958 | ||||||||
\(293\) | −4.20961 | − | 7.29125i | −0.245928 | − | 0.425960i | 0.716464 | − | 0.697624i | \(-0.245759\pi\) |
−0.962392 | + | 0.271664i | \(0.912426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.92855 | − | 5.07239i | 0.170507 | − | 0.295326i | ||||
\(296\) | −13.9047 | + | 24.0836i | −0.808192 | + | 1.39983i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 19.1878 | + | 33.2342i | 1.11152 | + | 1.92521i | ||||
\(299\) | −8.62314 | − | 14.9357i | −0.498689 | − | 0.863755i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −23.9996 | − | 41.5685i | −1.38102 | − | 2.39200i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0077 | 0.918107 | ||||||||
\(305\) | 1.14156 | + | 1.97724i | 0.0653655 | + | 0.113216i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.6878 | −0.724130 | −0.362065 | − | 0.932153i | \(-0.617928\pi\) | ||||
−0.362065 | + | 0.932153i | \(0.617928\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.1411 | 0.575979 | ||||||||
\(311\) | −8.24510 | + | 14.2809i | −0.467537 | + | 0.809797i | −0.999312 | − | 0.0370881i | \(-0.988192\pi\) |
0.531775 | + | 0.846886i | \(0.321525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.2592 | − | 24.6977i | −0.805980 | − | 1.39600i | −0.915628 | − | 0.402027i | \(-0.868306\pi\) |
0.109648 | − | 0.993970i | \(-0.465028\pi\) | |||||||
\(314\) | 45.7229 | 2.58029 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.2841 | −1.47859 | ||||||||
\(317\) | −12.9474 | − | 22.4256i | −0.727200 | − | 1.25955i | −0.958062 | − | 0.286561i | \(-0.907488\pi\) |
0.230862 | − | 0.972987i | \(-0.425846\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7344 | − | 20.3246i | 0.657002 | − | 1.13796i | ||||
\(320\) | −1.44057 | −0.0805303 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98545 | −0.221756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.5248 | − | 19.9616i | −0.639282 | − | 1.10727i | ||||
\(326\) | −2.42602 | −0.134365 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.61721 | + | 6.26519i | 0.199727 | + | 0.345937i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.10947 | − | 7.11781i | −0.225877 | − | 0.391230i | 0.730705 | − | 0.682693i | \(-0.239191\pi\) |
−0.956582 | + | 0.291463i | \(0.905858\pi\) | |||||||
\(332\) | −0.482926 | − | 0.836452i | −0.0265040 | − | 0.0459063i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.1163 | + | 43.5028i | −1.37430 | + | 2.38037i | ||||
\(335\) | 1.30066 | − | 2.25281i | 0.0710626 | − | 0.123084i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.28564 | − | 3.95885i | −0.124507 | − | 0.215652i | 0.797033 | − | 0.603936i | \(-0.206402\pi\) |
−0.921540 | + | 0.388283i | \(0.873068\pi\) | |||||||
\(338\) | −42.3851 | −2.30544 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.41147 | −0.347711 | ||||||||
\(341\) | −8.83409 | + | 15.3011i | −0.478393 | + | 0.828601i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.564178 | − | 0.977185i | 0.0304184 | − | 0.0526863i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.7173 | + | 49.7399i | −1.54385 | + | 2.67403i | ||||
\(347\) | 11.2331 | − | 19.4563i | 0.603023 | − | 1.04447i | −0.389337 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123372i | \(-0.0393707\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.0496 | + | 22.6026i | −0.698531 | + | 1.20989i | 0.270445 | + | 0.962735i | \(0.412829\pi\) |
−0.968976 | + | 0.247155i | \(0.920504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.91534 | + | 15.4418i | −0.475189 | + | 0.823052i | ||||
\(353\) | 0.355037 | 0.0188967 | 0.00944836 | − | 0.999955i | \(-0.496992\pi\) | ||||
0.00944836 | + | 0.999955i | \(0.496992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.23618 | 0.171758 | ||||||||
\(356\) | 24.3234 | + | 42.1294i | 1.28914 | + | 2.23285i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.30200 | − | 16.1115i | 0.491626 | − | 0.851522i | ||||
\(359\) | 2.72803 | − | 4.72508i | 0.143980 | − | 0.249380i | −0.785012 | − | 0.619480i | \(-0.787343\pi\) |
0.928992 | + | 0.370100i | \(0.120677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.59240 | + | 11.4184i | 0.346968 | + | 0.600967i | ||||
\(362\) | −4.36231 | − | 7.55574i | −0.229278 | − | 0.397121i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.61974 | + | 9.73367i | 0.294150 | + | 0.509484i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9240 | 0.570226 | 0.285113 | − | 0.958494i | \(-0.407969\pi\) | ||||
0.285113 | + | 0.958494i | \(0.407969\pi\) | |||||||
\(368\) | 10.4966 | + | 18.1806i | 0.547173 | + | 0.947731i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.1411 | 0.527213 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.73143 | 0.0896500 | 0.0448250 | − | 0.998995i | \(-0.485727\pi\) | ||||
0.0448250 | + | 0.998995i | \(0.485727\pi\) | |||||||
\(374\) | 8.11721 | − | 14.0594i | 0.419731 | − | 0.726995i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.12108 | + | 5.40587i | 0.160957 | + | 0.278787i | ||||
\(377\) | −32.9908 | −1.69911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1334 | −0.623251 | −0.311626 | − | 0.950205i | \(-0.600873\pi\) | ||||
−0.311626 | + | 0.950205i | \(0.600873\pi\) | |||||||
\(380\) | −4.67752 | − | 8.10170i | −0.239952 | − | 0.415608i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.16297 | + | 12.4066i | −0.366489 | + | 0.634778i | ||||
\(383\) | 8.71183 | 0.445154 | 0.222577 | − | 0.974915i | \(-0.428553\pi\) | ||||
0.222577 | + | 0.974915i | \(0.428553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.2986 | −1.23677 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.5783 | − | 47.7670i | −1.40008 | − | 2.42500i | ||||
\(389\) | −3.64321 | −0.184718 | −0.0923590 | − | 0.995726i | \(-0.529441\pi\) | ||||
−0.0923590 | + | 0.995726i | \(0.529441\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.61334 | − | 4.52644i | −0.132162 | − | 0.228912i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.5334 | − | 18.2444i | −0.530667 | − | 0.919142i | ||||
\(395\) | 2.61974 | + | 4.53752i | 0.131813 | + | 0.228307i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.72281 | − | 13.3763i | 0.387597 | − | 0.671337i | −0.604529 | − | 0.796583i | \(-0.706639\pi\) |
0.992126 | + | 0.125246i | \(0.0399720\pi\) | |||||||
\(398\) | 8.35117 | − | 14.4646i | 0.418606 | − | 0.725047i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.0287 | + | 24.2984i | 0.701434 | + | 1.21492i | ||||
\(401\) | −18.4219 | −0.919946 | −0.459973 | − | 0.887933i | \(-0.652141\pi\) | ||||
−0.459973 | + | 0.887933i | \(0.652141\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.8367 | 1.23720 | ||||||||
\(404\) | −21.4329 | + | 37.1228i | −1.06633 | + | 1.84693i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.83409 | + | 15.3011i | −0.437890 | + | 0.758447i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3182 | − | 24.7999i | 0.707989 | − | 1.22627i | −0.257612 | − | 0.966248i | \(-0.582936\pi\) |
0.965602 | − | 0.260025i | \(-0.0837309\pi\) | |||||||
\(410\) | 1.31908 | − | 2.28471i | 0.0651446 | − | 0.112834i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.5496 | + | 25.2007i | −0.716809 | + | 1.24155i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0962667 | + | 0.166739i | −0.00472554 | + | 0.00818488i | ||||
\(416\) | 25.0651 | 1.22892 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.6878 | 1.15861 | ||||||||
\(419\) | −17.3478 | − | 30.0472i | −0.847494 | − | 1.46790i | −0.883438 | − | 0.468548i | \(-0.844777\pi\) |
0.0359442 | − | 0.999354i | \(-0.488556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7010 | − | 23.7308i | 0.667745 | − | 1.15657i | −0.310788 | − | 0.950479i | \(-0.600593\pi\) |
0.978533 | − | 0.206090i | \(-0.0660738\pi\) | |||||||
\(422\) | −4.26604 | + | 7.38901i | −0.207668 | + | 0.359691i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.2592 | − | 38.5541i | −1.08100 | − | 1.87235i | ||||
\(425\) | −3.49273 | − | 6.04958i | −0.169422 | − | 0.293448i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.26991 | + | 9.12776i | 0.254731 | + | 0.441207i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.411474 | −0.0198430 | ||||||||
\(431\) | 13.2961 | + | 23.0295i | 0.640449 | + | 1.10929i | 0.985333 | + | 0.170645i | \(0.0545852\pi\) |
−0.344883 | + | 0.938646i | \(0.612081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.1830 | 1.78690 | 0.893451 | − | 0.449160i | \(-0.148277\pi\) | ||||
0.893451 | + | 0.449160i | \(0.148277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.4611 | 0.836235 | ||||||||
\(437\) | 3.81315 | − | 6.60457i | 0.182408 | − | 0.315939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5373 | − | 21.7152i | −0.598373 | − | 1.03641i | −0.993061 | − | 0.117597i | \(-0.962481\pi\) |
0.394689 | − | 0.918815i | \(-0.370853\pi\) | |||||||
\(440\) | 20.8307 | 0.993064 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.8212 | −1.08549 | ||||||||
\(443\) | 1.02229 | + | 1.77066i | 0.0485704 | + | 0.0841264i | 0.889288 | − | 0.457347i | \(-0.151200\pi\) |
−0.840718 | + | 0.541473i | \(0.817867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.84864 | − | 8.39809i | 0.229848 | − | 0.398108i | ||||
\(446\) | 15.8922 | 0.752516 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2344 | 0.482992 | 0.241496 | − | 0.970402i | \(-0.422362\pi\) | ||||
0.241496 | + | 0.970402i | \(0.422362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.29813 | + | 3.98048i | 0.108215 | + | 0.187434i | ||||
\(452\) | −72.5836 | −3.41404 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.80200 | + | 13.5135i | 0.366166 | + | 0.634218i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.2973 | + | 36.8879i | 0.996244 | + | 1.72554i | 0.573115 | + | 0.819475i | \(0.305735\pi\) |
0.423129 | + | 0.906070i | \(0.360932\pi\) | |||||||
\(458\) | 29.6065 | + | 51.2800i | 1.38342 | + | 2.39616i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.13429 | − | 10.6249i | 0.286013 | − | 0.495388i | ||||
\(461\) | 0.252374 | − | 0.437124i | 0.0117542 | − | 0.0203589i | −0.860088 | − | 0.510145i | \(-0.829592\pi\) |
0.871843 | + | 0.489786i | \(0.162925\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.34002 | − | 2.32099i | −0.0622761 | − | 0.107865i | 0.833206 | − | 0.552962i | \(-0.186503\pi\) |
−0.895482 | + | 0.445097i | \(0.853169\pi\) | |||||||
\(464\) | 40.1584 | 1.86431 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.5868 | −0.999988 | ||||||||
\(467\) | −15.7083 | + | 27.2075i | −0.726892 | + | 1.25901i | 0.231299 | + | 0.972883i | \(0.425702\pi\) |
−0.958191 | + | 0.286131i | \(0.907631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.13816 | − | 1.97134i | 0.0524992 | − | 0.0909313i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20.3346 | + | 35.2205i | −0.935974 | + | 1.62115i | ||||
\(473\) | 0.358441 | − | 0.620838i | 0.0164811 | − | 0.0285461i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.09627 | − | 8.82699i | 0.233833 | − | 0.405010i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.4363 | + | 31.9326i | −0.843256 | + | 1.46056i | ||||
\(479\) | 16.4406 | 0.751189 | 0.375594 | − | 0.926784i | \(-0.377439\pi\) | ||||
0.375594 | + | 0.926784i | \(0.377439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.8367 | 1.13245 | ||||||||
\(482\) | −6.84137 | − | 11.8496i | −0.311616 | − | 0.539734i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.93242 | + | 15.4714i | −0.406019 | + | 0.703246i | ||||
\(485\) | −5.49747 | + | 9.52190i | −0.249627 | + | 0.432367i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.48767 | + | 2.57673i | 0.0674129 | + | 0.116763i | 0.897762 | − | 0.440481i | \(-0.145192\pi\) |
−0.830349 | + | 0.557244i | \(0.811859\pi\) | |||||||
\(488\) | −7.92649 | − | 13.7291i | −0.358815 | − | 0.621486i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2430 | − | 22.9376i | −0.597650 | − | 1.03516i | −0.993167 | − | 0.116702i | \(-0.962768\pi\) |
0.395517 | − | 0.918459i | \(-0.370565\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.99825 | −0.450298 | ||||||||
\(494\) | −16.6493 | − | 28.8374i | −0.749087 | − | 1.29746i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.2327 | −1.35749 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4439 | −0.601830 | −0.300915 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300915 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(500\) | 17.8969 | − | 30.9984i | 0.800375 | − | 1.38629i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.2772 | + | 26.4609i | 0.681854 | + | 1.18101i | ||||
\(503\) | 22.6631 | 1.01050 | 0.505250 | − | 0.862973i | \(-0.331400\pi\) | ||||
0.505250 | + | 0.862973i | \(0.331400\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.54488 | 0.380242 | ||||||||
\(506\) | 15.5326 | + | 26.9032i | 0.690506 | + | 1.19599i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −38.9393 | + | 67.4448i | −1.72765 | + | 2.99238i | ||||
\(509\) | −9.54757 | −0.423189 | −0.211594 | − | 0.977358i | \(-0.567866\pi\) | ||||
−0.211594 | + | 0.977358i | \(0.567866\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 50.5553 | 2.23425 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.3773 | − | 23.1702i | −0.590049 | − | 1.02199i | ||||
\(515\) | 5.80066 | 0.255608 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.98293 | + | 3.43453i | 0.0872090 | + | 0.151050i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.6411 | − | 25.3592i | −0.642057 | − | 1.11208i | ||||
\(521\) | −1.55644 | − | 2.69583i | −0.0681887 | − | 0.118106i | 0.829915 | − | 0.557889i | \(-0.188389\pi\) |
−0.898104 | + | 0.439783i | \(0.855055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.07444 | − | 13.9853i | 0.353071 | − | 0.611537i | −0.633715 | − | 0.773567i | \(-0.718471\pi\) |
0.986786 | + | 0.162030i | \(0.0518041\pi\) | |||||||
\(524\) | −42.3448 | + | 73.3434i | −1.84984 | + | 3.20402i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.8965 | + | 62.1746i | 1.56516 | + | 2.71094i | ||||
\(527\) | 7.52704 | 0.327883 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9986 | −0.565155 | ||||||||
\(530\) | −8.11721 | + | 14.0594i | −0.352589 | + | 0.610702i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.23055 | − | 5.59548i | 0.139931 | − | 0.242367i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.05051 | − | 1.81953i | 0.0454174 | − | 0.0786652i | ||||
\(536\) | −9.03121 | + | 15.6425i | −0.390089 | + | 0.675654i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.47431 | + | 16.4100i | −0.408466 | + | 0.707485i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.50774 | − | 4.34353i | 0.107816 | − | 0.186743i | −0.807069 | − | 0.590457i | \(-0.798948\pi\) |
0.914885 | + | 0.403714i | \(0.132281\pi\) | |||||||
\(542\) | −34.5330 | −1.48332 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.59627 | 0.325687 | ||||||||
\(545\) | −1.74035 | − | 3.01438i | −0.0745485 | − | 0.129122i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.23901 | + | 14.2704i | −0.352275 | + | 0.610157i | −0.986648 | − | 0.162870i | \(-0.947925\pi\) |
0.634373 | + | 0.773027i | \(0.281258\pi\) | |||||||
\(548\) | 40.0467 | − | 69.3629i | 1.71071 | − | 2.96304i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.7592 | + | 35.9561i | 0.885177 | + | 1.53317i | ||||
\(551\) | −7.29426 | − | 12.6340i | −0.310746 | − | 0.538228i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.78699 | − | 13.4875i | −0.330837 | − | 0.573027i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 97.3055 | 4.12667 | ||||||||
\(557\) | −17.2815 | − | 29.9325i | −0.732242 | − | 1.26828i | −0.955923 | − | 0.293618i | \(-0.905141\pi\) |
0.223681 | − | 0.974662i | \(-0.428193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.00774 | −0.0426229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.38682 | 0.353777 | ||||||||
\(563\) | −18.6052 | + | 32.2251i | −0.784115 | + | 1.35813i | 0.145411 | + | 0.989371i | \(0.453550\pi\) |
−0.929526 | + | 0.368756i | \(0.879784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.23442 | + | 12.5304i | 0.304354 | + | 0.527157i | ||||
\(566\) | −73.4894 | −3.08899 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.4706 | −0.942845 | ||||||||
\(569\) | 0.202333 | + | 0.350452i | 0.00848226 | + | 0.0146917i | 0.870235 | − | 0.492636i | \(-0.163967\pi\) |
−0.861753 | + | 0.507328i | \(0.830633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.8897 | − | 32.7178i | 0.790507 | − | 1.36920i | −0.135146 | − | 0.990826i | \(-0.543150\pi\) |
0.925653 | − | 0.378373i | \(-0.123516\pi\) | |||||||
\(572\) | 93.3278 | 3.90223 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.3669 | 0.557438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.10560 | + | 1.91496i | 0.0460267 | + | 0.0797206i | 0.888121 | − | 0.459610i | \(-0.152011\pi\) |
−0.842094 | + | 0.539330i | \(0.818677\pi\) | |||||||
\(578\) | 36.1293 | 1.50278 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.7344 | − | 20.3246i | −0.487245 | − | 0.843934i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.1420 | − | 24.4947i | −0.585703 | − | 1.01447i | ||||
\(584\) | −39.0210 | − | 67.5864i | −1.61470 | − | 2.79674i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.6591 | − | 18.4621i | 0.440323 | − | 0.762662i | ||||
\(587\) | 12.1049 | − | 20.9663i | 0.499622 | − | 0.865371i | −0.500378 | − | 0.865807i | \(-0.666806\pi\) |
1.00000 | 0.000436347i | \(0.000138894\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.49138 | + | 9.51135i | 0.226268 | + | 0.391908i | ||||
\(590\) | 14.8307 | 0.610570 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.2327 | −1.24255 | ||||||||
\(593\) | 6.11927 | − | 10.5989i | 0.251288 | − | 0.435244i | −0.712592 | − | 0.701578i | \(-0.752479\pi\) |
0.963881 | + | 0.266334i | \(0.0858124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.4295 | + | 57.9016i | −1.36932 | + | 2.37174i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.8346 | − | 37.8186i | 0.892882 | − | 1.54652i | ||||
\(599\) | 19.8084 | − | 34.3092i | 0.809349 | − | 1.40183i | −0.103966 | − | 0.994581i | \(-0.533153\pi\) |
0.913315 | − | 0.407253i | \(-0.133513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0039 | − | 25.9875i | 0.612021 | − | 1.06005i | −0.378879 | − | 0.925446i | \(-0.623690\pi\) |
0.990899 | − | 0.134605i | \(-0.0429764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 41.8127 | − | 72.4218i | 1.70134 | − | 2.94680i | ||||
\(605\) | 3.56118 | 0.144783 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.4843 | −0.790844 | −0.395422 | − | 0.918499i | \(-0.629402\pi\) | ||||
−0.395422 | + | 0.918499i | \(0.629402\pi\) | |||||||
\(608\) | 5.54189 | + | 9.59883i | 0.224753 | + | 0.389284i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.89053 | + | 5.00654i | −0.117034 | + | 0.202709i | ||||
\(611\) | 2.78746 | − | 4.82802i | 0.112768 | − | 0.195321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.26382 | + | 16.0454i | 0.374162 | + | 0.648068i | 0.990201 | − | 0.139648i | \(-0.0445970\pi\) |
−0.616039 | + | 0.787716i | \(0.711264\pi\) | |||||||
\(614\) | −16.0633 | − | 27.8225i | −0.648262 | − | 1.12282i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.9201 | + | 24.1103i | 0.560402 | + | 0.970644i | 0.997461 | + | 0.0712118i | \(0.0226866\pi\) |
−0.437059 | + | 0.899433i | \(0.643980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.9813 | −1.80795 | −0.903976 | − | 0.427583i | \(-0.859365\pi\) | ||||
−0.903976 | + | 0.427583i | \(0.859365\pi\) | |||||||
\(620\) | 8.83409 | + | 15.3011i | 0.354786 | + | 0.614507i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −41.7547 | −1.67421 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9982 | 0.559930 | ||||||||
\(626\) | 36.1057 | − | 62.5368i | 1.44307 | − | 2.49947i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 39.8298 | + | 68.9873i | 1.58938 | + | 2.75289i | ||||
\(629\) | 7.52704 | 0.300123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.43613 | 0.375646 | 0.187823 | − | 0.982203i | \(-0.439857\pi\) | ||||
0.187823 | + | 0.982203i | \(0.439857\pi\) | |||||||
\(632\) | −18.1903 | − | 31.5065i | −0.723572 | − | 1.25326i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.7841 | − | 56.7836i | 1.30202 | − | 2.25517i | ||||
\(635\) | 15.5243 | 0.616065 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 59.4252 | 2.35267 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.86571 | − | 10.1597i | −0.231863 | − | 0.401598i | ||||
\(641\) | −37.3901 | −1.47682 | −0.738410 | − | 0.674352i | \(-0.764423\pi\) | ||||
−0.738410 | + | 0.674352i | \(0.764423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.805874 | − | 1.39581i | −0.0317806 | − | 0.0550456i | 0.849698 | − | 0.527270i | \(-0.176784\pi\) |
−0.881478 | + | 0.472225i | \(0.843451\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.04576 | − | 8.73951i | −0.198523 | − | 0.343851i | ||||
\(647\) | −20.5881 | − | 35.6597i | −0.809402 | − | 1.40193i | −0.913278 | − | 0.407336i | \(-0.866458\pi\) |
0.103876 | − | 0.994590i | \(-0.466875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.9192 | + | 22.3767i | −0.507124 | + | 0.878364i | ||||
\(650\) | 29.1819 | − | 50.5445i | 1.14461 | − | 1.98252i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.11334 | − | 3.66041i | −0.0827648 | − | 0.143353i | ||||
\(653\) | −3.05199 | −0.119434 | −0.0597169 | − | 0.998215i | \(-0.519020\pi\) | ||||
−0.0597169 | + | 0.998215i | \(0.519020\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.8821 | 0.659637 | ||||||||
\(656\) | −3.93242 | + | 6.81115i | −0.153535 | + | 0.265931i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8175 | − | 36.0569i | 0.810934 | − | 1.40458i | −0.101277 | − | 0.994858i | \(-0.532293\pi\) |
0.912211 | − | 0.409721i | \(-0.134374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1505 | + | 17.5812i | −0.394808 | + | 0.683828i | −0.993077 | − | 0.117468i | \(-0.962522\pi\) |
0.598269 | + | 0.801296i | \(0.295856\pi\) | |||||||
\(662\) | 10.4055 | − | 18.0229i | 0.404423 | − | 0.700481i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.668434 | − | 1.15776i | 0.0259403 | − | 0.0449298i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.56599 | − | 16.5688i | 0.370397 | − | 0.641546i | ||||
\(668\) | −87.5167 | −3.38612 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.58677 | 0.254469 | ||||||||
\(671\) | −5.03596 | − | 8.72254i | −0.194411 | − | 0.336730i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.415345 | − | 0.719398i | 0.0160104 | − | 0.0277307i | −0.857909 | − | 0.513801i | \(-0.828237\pi\) |
0.873920 | + | 0.486071i | \(0.161570\pi\) | |||||||
\(674\) | 5.78746 | − | 10.0242i | 0.222924 | − | 0.386117i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.9222 | − | 63.9511i | −1.42008 | − | 2.45966i | ||||
\(677\) | 5.43360 | + | 9.41127i | 0.208830 | + | 0.361705i | 0.951346 | − | 0.308124i | \(-0.0997011\pi\) |
−0.742516 | + | 0.669828i | \(0.766368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.43717 | − | 7.68540i | −0.170158 | − | 0.294722i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −44.7374 | −1.71308 | ||||||||
\(683\) | 16.3473 | + | 28.3143i | 0.625512 | + | 1.08342i | 0.988442 | + | 0.151602i | \(0.0484432\pi\) |
−0.362930 | + | 0.931817i | \(0.618223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.9659 | −0.610024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.22668 | 0.0467668 | ||||||||
\(689\) | −19.8799 | + | 34.4329i | −0.757362 | + | 1.31179i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.49912 | − | 12.9889i | −0.285280 | − | 0.494120i | 0.687397 | − | 0.726282i | \(-0.258753\pi\) |
−0.972677 | + | 0.232162i | \(0.925420\pi\) | |||||||
\(692\) | −100.064 | −3.80387 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 56.8863 | 2.15937 | ||||||||
\(695\) | −9.69846 | − | 16.7982i | −0.367884 | − | 0.637193i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.979055 | − | 1.69577i | 0.0370844 | − | 0.0642320i | ||||
\(698\) | −66.0856 | −2.50138 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.4688 | −0.999714 | −0.499857 | − | 0.866108i | \(-0.666614\pi\) | ||||
−0.499857 | + | 0.866108i | \(0.666614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.49138 | + | 9.51135i | 0.207111 | + | 0.358727i | ||||
\(704\) | 6.35504 | 0.239514 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.449493 | + | 0.778544i | 0.0169169 | + | 0.0293009i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.68004 | − | 13.3022i | −0.288430 | − | 0.499576i | 0.685005 | − | 0.728538i | \(-0.259800\pi\) |
−0.973435 | + | 0.228963i | \(0.926467\pi\) | |||||||
\(710\) | 4.09714 | + | 7.09646i | 0.153763 | + | 0.266325i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −33.6668 | + | 58.3127i | −1.26172 | + | 2.18536i | ||||
\(713\) | −7.20162 | + | 12.4736i | −0.269703 | + | 0.467139i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.30200 | − | 16.1115i | −0.347875 | − | 0.602538i | ||||
\(716\) | 32.4124 | 1.21131 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.8152 | 0.515579 | ||||||||
\(719\) | 13.3653 | − | 23.1494i | 0.498442 | − | 0.863326i | −0.501557 | − | 0.865125i | \(-0.667239\pi\) |
0.999998 | + | 0.00179839i | \(0.000572447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.6925 | + | 28.9123i | −0.621232 | + | 1.07600i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.60014 | − | 13.1638i | 0.282457 | − | 0.489230i | ||||
\(725\) | 12.7849 | − | 22.1441i | 0.474820 | − | 0.822413i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8221 | − | 39.5290i | 0.846424 | − | 1.46605i | −0.0379552 | − | 0.999279i | \(-0.512084\pi\) |
0.884379 | − | 0.466770i | \(-0.154582\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.2297 | + | 24.6465i | −0.526664 | + | 0.912209i | ||||
\(731\) | −0.305407 | −0.0112959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.97502 | 0.220693 | 0.110346 | − | 0.993893i | \(-0.464804\pi\) | ||||
0.110346 | + | 0.993893i | \(0.464804\pi\) | |||||||
\(734\) | 13.8302 | + | 23.9546i | 0.510483 | + | 0.884182i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.26786 | + | 12.5883i | −0.267897 | + | 0.464011i | ||||
\(737\) | −5.73783 | + | 9.93821i | −0.211356 | + | 0.366079i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7981 | + | 30.8273i | 0.654715 | + | 1.13400i | 0.981965 | + | 0.189062i | \(0.0605447\pi\) |
−0.327250 | + | 0.944938i | \(0.606122\pi\) | |||||||
\(740\) | 8.83409 | + | 15.3011i | 0.324748 | + | 0.562480i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.6544 | − | 25.3821i | −0.537616 | − | 0.931178i | −0.999032 | − | 0.0439943i | \(-0.985992\pi\) |
0.461416 | − | 0.887184i | \(-0.347342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3277 | 0.488289 | ||||||||
\(746\) | 2.19207 | + | 3.79677i | 0.0802573 | + | 0.139010i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.2841 | 1.03417 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3337 | −0.632515 | −0.316258 | − | 0.948673i | \(-0.602426\pi\) | ||||
−0.316258 | + | 0.948673i | \(0.602426\pi\) | |||||||
\(752\) | −3.39306 | + | 5.87695i | −0.123732 | + | 0.214310i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −41.7679 | − | 72.3440i | −1.52110 | − | 2.63461i | ||||
\(755\) | −16.6699 | −0.606681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.77156 | −0.100734 | −0.0503671 | − | 0.998731i | \(-0.516039\pi\) | ||||
−0.0503671 | + | 0.998731i | \(0.516039\pi\) | |||||||
\(758\) | −15.3614 | − | 26.6068i | −0.557952 | − | 0.966402i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.47431 | − | 11.2138i | 0.234848 | − | 0.406768i | ||||
\(761\) | −7.50744 | −0.272144 | −0.136072 | − | 0.990699i | \(-0.543448\pi\) | ||||
−0.136072 | + | 0.990699i | \(0.543448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.9590 | −0.902987 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.0296 | + | 19.1038i | 0.398514 | + | 0.690247i | ||||
\(767\) | 36.3218 | 1.31150 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.02182 | − | 1.76985i | −0.0368478 | − | 0.0638223i | 0.847013 | − | 0.531572i | \(-0.178398\pi\) |
−0.883861 | + | 0.467749i | \(0.845065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.1668 | − | 36.6620i | −0.761811 | − | 1.31950i | ||||
\(773\) | −12.4709 | − | 21.6002i | −0.448547 | − | 0.776907i | 0.549744 | − | 0.835333i | \(-0.314725\pi\) |
−0.998292 | + | 0.0584263i | \(0.981392\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.62495 | + | 16.6709i | −0.345738 | + | 0.598837i | ||||
\(776\) | 38.1721 | − | 66.1159i | 1.37030 | − | 2.37342i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.61246 | − | 7.98902i | −0.165365 | − | 0.286420i | ||||
\(779\) | 2.85710 | 0.102366 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.2763 | −0.510847 | ||||||||
\(782\) | 6.61721 | − | 11.4613i | 0.236631 | − | 0.409857i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.93969 | − | 13.7520i | 0.283380 | − | 0.490828i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.55350 | + | 6.15484i | −0.126669 | + | 0.219396i | −0.922384 | − | 0.386274i | \(-0.873762\pi\) |
0.795715 | + | 0.605671i | \(0.207095\pi\) | |||||||
\(788\) | 18.3516 | − | 31.7860i | 0.653750 | − | 1.13233i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.63341 | + | 11.4894i | −0.236006 | + | 0.408774i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.07919 | + | 12.2615i | −0.251389 | + | 0.435419i | ||||
\(794\) | 39.1097 | 1.38795 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 29.0993 | 1.03140 | ||||||||
\(797\) | 16.8314 | + | 29.1528i | 0.596199 | + | 1.03265i | 0.993376 | + | 0.114905i | \(0.0366564\pi\) |
−0.397178 | + | 0.917742i | \(0.630010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.844770 | − | 1.46318i | 0.0298858 | − | 0.0517638i | ||||
\(800\) | −9.71348 | + | 16.8242i | −0.343423 | + | 0.594827i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.3229 | − | 40.3965i | −0.823562 | − | 1.42645i | ||||
\(803\) | −24.7913 | − | 42.9398i | −0.874867 | − | 1.51531i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.4443 | + | 54.4632i | 1.10758 | + | 1.91838i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −59.3319 | −2.08729 | ||||||||
\(809\) | −6.40807 | − | 11.0991i | −0.225296 | − | 0.390224i | 0.731112 | − | 0.682257i | \(-0.239002\pi\) |
−0.956408 | + | 0.292033i | \(0.905668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.1239 | −0.917335 | −0.458667 | − | 0.888608i | \(-0.651673\pi\) | ||||
−0.458667 | + | 0.888608i | \(0.651673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −44.7374 | −1.56805 | ||||||||
\(815\) | −0.421274 | + | 0.729669i | −0.0147566 | + | 0.0255592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.222811 | − | 0.385920i | −0.00779518 | − | 0.0135016i | ||||
\(818\) | 72.5099 | 2.53525 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.59627 | 0.160509 | ||||||||
\(821\) | 13.8320 | + | 23.9578i | 0.482741 | + | 0.836132i | 0.999804 | − | 0.0198153i | \(-0.00630781\pi\) |
−0.517062 | + | 0.855948i | \(0.672974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.9162 | + | 24.1036i | −0.485089 | + | 0.840199i | −0.999853 | − | 0.0171330i | \(-0.994546\pi\) |
0.514764 | + | 0.857332i | \(0.327879\pi\) | |||||||
\(824\) | −40.2772 | −1.40312 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.65507 | −0.161873 | −0.0809363 | − | 0.996719i | \(-0.525791\pi\) | ||||
−0.0809363 | + | 0.996719i | \(0.525791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.98680 | + | 8.63738i | 0.173199 | + | 0.299989i | 0.939536 | − | 0.342449i | \(-0.111256\pi\) |
−0.766338 | + | 0.642438i | \(0.777923\pi\) | |||||||
\(830\) | −0.487511 | −0.0169218 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.46673 | − | 7.73660i | −0.154856 | − | 0.268218i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.72281 | + | 15.1084i | 0.301865 | + | 0.522846i | ||||
\(836\) | 20.6348 | + | 35.7404i | 0.713668 | + | 1.23611i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 43.9261 | − | 76.0822i | 1.51740 | − | 2.62822i | ||||
\(839\) | −3.36484 | + | 5.82807i | −0.116167 | + | 0.201207i | −0.918246 | − | 0.396011i | \(-0.870394\pi\) |
0.802079 | + | 0.597218i | \(0.203727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.79901 | − | 6.58008i | −0.131000 | − | 0.226899i | ||||
\(842\) | 69.3842 | 2.39114 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.8648 | −0.511669 | ||||||||
\(845\) | −7.36009 | + | 12.7480i | −0.253195 | + | 0.438546i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.1989 | − | 41.9138i | 0.830995 | − | 1.43932i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.84389 | − | 15.3181i | 0.303343 | − | 0.525406i | ||||
\(851\) | −7.20162 | + | 12.4736i | −0.246868 | + | 0.427588i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.89528 | + | 5.01477i | −0.0991324 | + | 0.171702i | −0.911326 | − | 0.411686i | \(-0.864940\pi\) |
0.812193 | + | 0.583388i | \(0.198273\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.29426 | + | 12.6340i | −0.249313 | + | 0.431822i | ||||
\(857\) | 34.9077 | 1.19242 | 0.596211 | − | 0.802827i | \(-0.296672\pi\) | ||||
0.596211 | + | 0.802827i | \(0.296672\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.6149 | −0.430416 | −0.215208 | − | 0.976568i | \(-0.569043\pi\) | ||||
−0.215208 | + | 0.976568i | \(0.569043\pi\) | |||||||
\(860\) | −0.358441 | − | 0.620838i | −0.0122227 | − | 0.0211704i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.6668 | + | 58.3127i | −1.14670 | + | 1.98614i | ||||
\(863\) | −12.1027 | + | 20.9624i | −0.411979 | + | 0.713569i | −0.995106 | − | 0.0988119i | \(-0.968496\pi\) |
0.583127 | + | 0.812381i | \(0.301829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.97343 | + | 17.2745i | 0.339107 | + | 0.587350i | ||||
\(866\) | 47.0754 | + | 81.5369i | 1.59969 | + | 2.77074i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.5569 | − | 20.0171i | −0.392041 | − | 0.679035i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1317 | 0.546600 | ||||||||
\(872\) | 12.0842 | + | 20.9305i | 0.409224 | + | 0.708797i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.3105 | 0.653186 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.12567 | −0.0380111 | −0.0190055 | − | 0.999819i | \(-0.506050\pi\) | ||||
−0.0190055 | + | 0.999819i | \(0.506050\pi\) | |||||||
\(878\) | 31.7456 | − | 54.9849i | 1.07136 | − | 1.85565i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.3229 | + | 19.6119i | 0.381697 | + | 0.661118i | ||||
\(881\) | 4.38331 | 0.147678 | 0.0738388 | − | 0.997270i | \(-0.476475\pi\) | ||||
0.0738388 | + | 0.997270i | \(0.476475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.88949 | −0.231850 | −0.115925 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115925 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(884\) | −19.8799 | − | 34.4329i | −0.668632 | − | 1.15810i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.58853 | + | 4.48346i | −0.0869632 | + | 0.150625i | ||||
\(887\) | −39.0752 | −1.31202 | −0.656009 | − | 0.754753i | \(-0.727757\pi\) | ||||
−0.656009 | + | 0.754753i | \(0.727757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.5544 | 0.823065 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.8439 | + | 23.9783i | 0.463528 | + | 0.802854i | ||||
\(893\) | 2.46522 | 0.0824955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.23055 | − | 5.59548i | −0.107985 | − | 0.187036i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.9572 | + | 22.4426i | 0.432388 | + | 0.748919i | ||||
\(899\) | 13.7761 | + | 23.8610i | 0.459460 | + | 0.795809i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.02481 | + | 10.4353i | −0.200716 | + | 0.347650i | ||||
\(902\) | −5.81908 | + | 10.0789i | −0.193754 | + | 0.335592i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50.2327 | − | 87.0055i | −1.67071 | − | 2.89376i | ||||
\(905\) | −3.03003 | −0.100722 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.4938 | 1.41098 | 0.705492 | − | 0.708718i | \(-0.250726\pi\) | ||||
0.705492 | + | 0.708718i | \(0.250726\pi\) | |||||||
\(908\) | −13.5929 | + | 23.5435i | −0.451095 | + | 0.781319i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.74675 | + | 13.4178i | −0.256661 | + | 0.444550i | −0.965345 | − | 0.260976i | \(-0.915956\pi\) |
0.708684 | + | 0.705526i | \(0.249289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.424678 | − | 0.735564i | 0.0140548 | − | 0.0243436i | ||||
\(914\) | −53.9265 | + | 93.4035i | −1.78373 | + | 3.08951i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.5813 | + | 89.3414i | −1.70429 | + | 2.95192i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.26470 | + | 5.65463i | −0.107693 | + | 0.186529i | −0.914835 | − | 0.403828i | \(-0.867680\pi\) |
0.807143 | + | 0.590357i | \(0.201013\pi\) | |||||||
\(920\) | 16.9813 | 0.559858 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.27807 | 0.0420909 | ||||||||
\(923\) | 10.0343 | + | 17.3799i | 0.330283 | + | 0.572068i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.62495 | + | 16.6709i | −0.316466 | + | 0.548136i | ||||
\(926\) | 3.39306 | − | 5.87695i | 0.111503 | − | 0.193128i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.9029 | + | 24.0805i | 0.456384 | + | 0.790480i | ||||
\(929\) | 29.1386 | + | 50.4696i | 0.956007 | + | 1.65585i | 0.732046 | + | 0.681255i | \(0.238565\pi\) |
0.223961 | + | 0.974598i | \(0.428101\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18.8045 | − | 32.5704i | −0.615963 | − | 1.06688i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −79.5494 | −2.60294 | ||||||||
\(935\) | −2.81908 | − | 4.88279i | −0.0921937 | − | 0.159684i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.4175 | 1.05903 | 0.529516 | − | 0.848300i | \(-0.322374\pi\) | ||||
0.529516 | + | 0.848300i | \(0.322374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.96585 | 0.129352 | ||||||||
\(941\) | −13.6613 | + | 23.6621i | −0.445346 | + | 0.771363i | −0.998076 | − | 0.0619979i | \(-0.980253\pi\) |
0.552730 | + | 0.833360i | \(0.313586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.87346 | + | 3.24492i | 0.0610081 | + | 0.105669i | ||||
\(944\) | −44.2131 | −1.43901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.81521 | 0.0590175 | ||||||||
\(947\) | −19.1065 | − | 33.0935i | −0.620879 | − | 1.07539i | −0.989322 | − | 0.145744i | \(-0.953443\pi\) |
0.368443 | − | 0.929650i | \(-0.379891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.8499 | + | 60.3618i | −1.13127 | + | 1.95943i | ||||
\(950\) | 25.8084 | 0.837335 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.9377 | −1.90918 | −0.954590 | − | 0.297924i | \(-0.903706\pi\) | ||||
−0.954590 | + | 0.297924i | \(0.903706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.48767 | + | 4.30878i | 0.0804992 | + | 0.139429i | ||||
\(956\) | −64.2404 | −2.07768 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.8145 | + | 36.0518i | 0.672486 | + | 1.16478i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.12882 | + | 8.88338i | 0.165446 | + | 0.286561i | ||||
\(962\) | 31.4443 | + | 54.4632i | 1.01381 | + | 1.75596i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.9192 | − | 20.6447i | 0.383892 | − | 0.664921i | ||||
\(965\) | −4.21941 | + | 7.30823i | −0.135828 | + | 0.235260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.3594 | − | 21.4071i | −0.397451 | − | 0.688405i | 0.595960 | − | 0.803014i | \(-0.296772\pi\) |
−0.993411 | + | 0.114609i | \(0.963438\pi\) | |||||||
\(968\) | −24.7273 | −0.794766 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.8402 | −0.893894 | ||||||||
\(971\) | 4.08812 | − | 7.08082i | 0.131194 | − | 0.227234i | −0.792943 | − | 0.609296i | \(-0.791452\pi\) |
0.924137 | + | 0.382061i | \(0.124786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.76692 | + | 6.52450i | −0.120700 | + | 0.209058i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.61721 | − | 14.9254i | 0.275830 | − | 0.477752i | ||||
\(977\) | −7.92427 | + | 13.7252i | −0.253520 | + | 0.439109i | −0.964492 | − | 0.264111i | \(-0.914922\pi\) |
0.710973 | + | 0.703220i | \(0.248255\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.3897 | + | 37.0480i | −0.683616 | + | 1.18406i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.5326 | − | 58.0801i | 1.07007 | − | 1.85341i | ||||
\(983\) | −53.3063 | −1.70021 | −0.850104 | − | 0.526615i | \(-0.823461\pi\) | ||||
−0.850104 | + | 0.526615i | \(0.823461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.31645 | −0.233121 | ||||||||
\(986\) | −12.6582 | − | 21.9247i | −0.403120 | − | 0.698224i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.0069 | − | 50.2414i | 0.922831 | − | 1.59839i | ||||
\(989\) | 0.292204 | − | 0.506111i | 0.00929153 | − | 0.0160934i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.1047 | − | 34.8224i | −0.638648 | − | 1.10617i | −0.985730 | − | 0.168335i | \(-0.946161\pi\) |
0.347082 | − | 0.937835i | \(-0.387172\pi\) | |||||||
\(992\) | −10.4666 | − | 18.1286i | −0.332314 | − | 0.575584i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.90033 | − | 5.02352i | −0.0919466 | − | 0.159256i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.7202 | 0.909577 | 0.454789 | − | 0.890599i | \(-0.349715\pi\) | ||||
0.454789 | + | 0.890599i | \(0.349715\pi\) | |||||||
\(998\) | −17.0205 | − | 29.4804i | −0.538776 | − | 0.933187i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))