Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (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: | \(8.04892052375\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(0.939693 + 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.h.673.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.11334 | + | 1.32683i | 0.642788 | + | 0.766044i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.439693 | − | 0.761570i | 0.196637 | − | 0.340584i | −0.750799 | − | 0.660530i | \(-0.770331\pi\) |
0.947436 | + | 0.319946i | \(0.103665\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.520945 | + | 2.95442i | −0.173648 | + | 0.984808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.93969 | + | 3.35965i | 0.584839 | + | 1.01297i | 0.994895 | + | 0.100911i | \(0.0321758\pi\) |
−0.410056 | + | 0.912060i | \(0.634491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.72668 | − | 4.72275i | 0.756245 | − | 1.30986i | −0.188507 | − | 0.982072i | \(-0.560365\pi\) |
0.944753 | − | 0.327784i | \(-0.106302\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 0.264490i | 0.387298 | − | 0.0682911i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.65270 | 0.400840 | 0.200420 | − | 0.979710i | \(-0.435769\pi\) | ||||
0.200420 | + | 0.979710i | \(0.435769\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.41147 | −0.553230 | −0.276615 | − | 0.960981i | \(-0.589213\pi\) | ||||
−0.276615 | + | 0.960981i | \(0.589213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.592396 | + | 1.62760i | −0.129271 | + | 0.355170i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.58125 | − | 2.73881i | 0.329714 | − | 0.571081i | −0.652741 | − | 0.757581i | \(-0.726381\pi\) |
0.982455 | + | 0.186500i | \(0.0597144\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.11334 | + | 3.66041i | 0.422668 | + | 0.732083i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.50000 | + | 2.59808i | −0.866025 | + | 0.500000i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.02481 | + | 5.23913i | 0.561694 | + | 0.972883i | 0.997349 | + | 0.0727688i | \(0.0231835\pi\) |
−0.435655 | + | 0.900114i | \(0.643483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.27719 | + | 3.94421i | −0.408995 | + | 0.708400i | −0.994777 | − | 0.102068i | \(-0.967454\pi\) |
0.585782 | + | 0.810468i | \(0.300787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.29813 | + | 6.31407i | −0.400054 | + | 1.09914i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.879385 | 0.148643 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.55438 | −0.748735 | −0.374368 | − | 0.927280i | \(-0.622140\pi\) | ||||
−0.374368 | + | 0.927280i | \(0.622140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.30200 | − | 1.64019i | 1.48951 | − | 0.262641i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.592396 | − | 1.02606i | 0.0925168 | − | 0.160244i | −0.816053 | − | 0.577977i | \(-0.803842\pi\) |
0.908570 | + | 0.417734i | \(0.137175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0923963 | + | 0.160035i | 0.0140903 | + | 0.0244051i | 0.872985 | − | 0.487748i | \(-0.162181\pi\) |
−0.858894 | + | 0.512153i | \(0.828848\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.02094 | + | 1.69577i | 0.301265 | + | 0.252791i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −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 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.84002 | + | 2.19285i | 0.257655 | + | 0.307061i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.29086 | 1.00148 | 0.500738 | − | 0.865599i | \(-0.333062\pi\) | ||||
0.500738 | + | 0.865599i | \(0.333062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41147 | 0.460003 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.68479 | − | 3.19961i | −0.355609 | − | 0.423799i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | \(0.780181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.81908 | + | 1.02606i | −0.355170 | + | 0.129271i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.39780 | − | 4.15312i | −0.297411 | − | 0.515131i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.47906 | + | 2.56180i | −0.180695 | + | 0.312974i | −0.942118 | − | 0.335283i | \(-0.891168\pi\) |
0.761422 | + | 0.648256i | \(0.224501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.39440 | − | 0.951178i | 0.649409 | − | 0.114508i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68004 | 0.436741 | 0.218370 | − | 0.975866i | \(-0.429926\pi\) | ||||
0.218370 | + | 0.975866i | \(0.429926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.7811 | −1.49591 | −0.747955 | − | 0.663750i | \(-0.768964\pi\) | ||||
−0.747955 | + | 0.663750i | \(0.768964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.50387 | + | 6.87933i | −0.289122 | + | 0.794356i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.93969 | + | 3.35965i | −0.221048 | + | 0.382867i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.97906 | − | 5.15988i | −0.335170 | − | 0.580531i | 0.648348 | − | 0.761345i | \(-0.275460\pi\) |
−0.983517 | + | 0.180813i | \(0.942127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.45723 | − | 3.07818i | −0.939693 | − | 0.342020i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.109470 | − | 0.189608i | −0.0120159 | − | 0.0208122i | 0.859955 | − | 0.510370i | \(-0.170492\pi\) |
−0.871971 | + | 0.489558i | \(0.837158\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.726682 | − | 1.25865i | 0.0788197 | − | 0.136520i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.58378 | + | 9.84635i | −0.384221 | + | 1.05564i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0273 | 1.16890 | 0.584448 | − | 0.811431i | \(-0.301311\pi\) | ||||
0.584448 | + | 0.811431i | \(0.301311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.45336 | 0.571668 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.76857 | + | 1.36981i | −0.805563 | + | 0.142043i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.06031 | + | 1.83651i | −0.108785 | + | 0.188422i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.25150 | − | 10.8279i | −0.634743 | − | 1.09941i | −0.986569 | − | 0.163342i | \(-0.947773\pi\) |
0.351826 | − | 0.936065i | \(-0.385561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.9363 | + | 3.98048i | −1.09914 | + | 0.400054i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.85844 | + | 8.41507i | 0.483433 | + | 0.837330i | 0.999819 | − | 0.0190255i | \(-0.00605638\pi\) |
−0.516386 | + | 0.856356i | \(0.672723\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.29813 | − | 5.71253i | 0.324975 | − | 0.562873i | −0.656533 | − | 0.754298i | \(-0.727978\pi\) |
0.981507 | + | 0.191425i | \(0.0613109\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.979055 | + | 1.16679i | 0.0955460 | + | 0.113867i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.38919 | −0.230971 | −0.115486 | − | 0.993309i | \(-0.536842\pi\) | ||||
−0.115486 | + | 0.993309i | \(0.536842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.95811 | 0.379118 | 0.189559 | − | 0.981869i | \(-0.439294\pi\) | ||||
0.189559 | + | 0.981869i | \(0.439294\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.07057 | − | 6.04288i | −0.481278 | − | 0.573564i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.22668 | + | 14.2490i | −0.773901 | + | 1.34044i | 0.161509 | + | 0.986871i | \(0.448364\pi\) |
−0.935410 | + | 0.353565i | \(0.884969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.39053 | − | 2.40847i | −0.129668 | − | 0.224591i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.5326 | + | 10.5161i | 1.15864 | + | 0.972210i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.826352 | + | 1.43128i | 0.0757515 | + | 0.131206i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.02481 | + | 3.50708i | −0.184074 | + | 0.318826i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.02094 | − | 0.356347i | 0.182222 | − | 0.0321307i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.11381 | 0.725721 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.6536 | −1.56651 | −0.783253 | − | 0.621702i | \(-0.786441\pi\) | ||||
−0.783253 | + | 0.621702i | \(0.786441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.109470 | + | 0.300767i | −0.00963833 | + | 0.0264811i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.59879 | + | 16.6256i | −0.838650 | + | 1.45259i | 0.0523729 | + | 0.998628i | \(0.483322\pi\) |
−0.891023 | + | 0.453958i | \(0.850012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.20574 | − | 2.08840i | −0.104551 | − | 0.181087i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.56942i | 0.393273i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.07785 | − | 15.7233i | −0.775573 | − | 1.34333i | −0.934472 | − | 0.356037i | \(-0.884128\pi\) |
0.158899 | − | 0.987295i | \(-0.449206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0287 | − | 19.1022i | 0.935441 | − | 1.62023i | 0.161595 | − | 0.986857i | \(-0.448336\pi\) |
0.773846 | − | 0.633374i | \(-0.218330\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.605600 | − | 1.66387i | 0.0510007 | − | 0.140123i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.1557 | 1.76913 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.31996 | 0.441798 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.70574 | + | 0.300767i | −0.140687 | + | 0.0248069i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.57785 | − | 13.1252i | 0.620802 | − | 1.07526i | −0.368535 | − | 0.929614i | \(-0.620141\pi\) |
0.989337 | − | 0.145646i | \(-0.0465261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.47818 | − | 16.4167i | −0.771323 | − | 1.33597i | −0.936838 | − | 0.349764i | \(-0.886262\pi\) |
0.165515 | − | 0.986207i | \(-0.447071\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.860967 | + | 4.88279i | −0.0696051 | + | 0.394750i | ||||
\(154\) | 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 | \(-0.0894520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.11721 | + | 9.67372i | 0.643737 | + | 0.767176i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.16250 | 0.249240 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.958111 | −0.0750450 | −0.0375225 | − | 0.999296i | \(-0.511947\pi\) | ||||
−0.0375225 | + | 0.999296i | \(0.511947\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.79813 | + | 4.52644i | 0.295684 | + | 0.352383i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.91921 | − | 17.1806i | 0.767572 | − | 1.32947i | −0.171304 | − | 0.985218i | \(-0.554798\pi\) |
0.938876 | − | 0.344255i | \(-0.111869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.36959 | − | 14.4965i | −0.643814 | − | 1.11512i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.25624 | − | 7.12452i | 0.0960674 | − | 0.544825i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3414 | − | 19.6438i | −0.862268 | − | 1.49349i | −0.869734 | − | 0.493520i | \(-0.835710\pi\) |
0.00746626 | − | 0.999972i | \(-0.497623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.11334 | + | 3.66041i | −0.159754 | + | 0.276701i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.3610 | − | 2.00324i | 0.853943 | − | 0.150573i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.34730 | 0.549163 | 0.274581 | − | 0.961564i | \(-0.411461\pi\) | ||||
0.274581 | + | 0.961564i | \(0.411461\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.44562 | −0.256111 | −0.128056 | − | 0.991767i | \(-0.540874\pi\) | ||||
−0.128056 | + | 0.991767i | \(0.540874\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.53802 | + | 4.22567i | −0.113694 | + | 0.312371i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00253 | + | 3.46848i | −0.147229 | + | 0.255008i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.20574 | + | 5.55250i | 0.234427 | + | 0.406039i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | − | 2.59808i | −0.327327 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | \(0.278916\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.84090 | − | 7.80531i | 0.203441 | − | 0.558950i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.31996 | 0.592772 | 0.296386 | − | 0.955068i | \(-0.404218\pi\) | ||||
0.296386 | + | 0.955068i | \(0.404218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.59627 | −0.467597 | −0.233798 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233798 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.04576 | + | 0.889704i | −0.355900 | + | 0.0627548i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.02481 | + | 5.23913i | −0.212300 | + | 0.367715i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.520945 | − | 0.902302i | −0.0363843 | − | 0.0630195i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.26786 | + | 6.09845i | 0.505151 | + | 0.423872i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.67752 | − | 8.10170i | −0.323551 | − | 0.560406i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68479 | + | 2.91815i | −0.115986 | + | 0.200893i | −0.918173 | − | 0.396179i | \(-0.870336\pi\) |
0.802188 | + | 0.597072i | \(0.203669\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.09714 | + | 4.88279i | 0.280732 | + | 0.334563i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.162504 | 0.0110827 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.55438 | −0.309171 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.2297 | − | 16.9583i | −0.961552 | − | 1.14593i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.50640 | − | 7.80531i | 0.303133 | − | 0.525042i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.13816 | − | 5.43545i | −0.210146 | − | 0.363984i | 0.741614 | − | 0.670827i | \(-0.234061\pi\) |
−0.951760 | + | 0.306843i | \(0.900727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.9153 | + | 4.33683i | −0.794356 | + | 0.289122i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.08125 | − | 5.33688i | −0.204510 | − | 0.354221i | 0.745467 | − | 0.666543i | \(-0.232227\pi\) |
−0.949976 | + | 0.312322i | \(0.898893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6925 | + | 20.2521i | −0.772664 | + | 1.33829i | 0.163434 | + | 0.986554i | \(0.447743\pi\) |
−0.936098 | + | 0.351740i | \(0.885590\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.61721 | + | 1.16679i | −0.435381 | + | 0.0767693i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.52528 | −0.558510 | −0.279255 | − | 0.960217i | \(-0.590087\pi\) | ||||
−0.279255 | + | 0.960217i | \(0.590087\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.898986 | −0.0586434 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.52956 | − | 9.69739i | 0.229270 | − | 0.629913i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.28106 | − | 12.6112i | 0.470973 | − | 0.815748i | −0.528476 | − | 0.848948i | \(-0.677236\pi\) |
0.999449 | + | 0.0331997i | \(0.0105697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.70187 | + | 4.67977i | 0.174043 | + | 0.301451i | 0.939830 | − | 0.341644i | \(-0.110984\pi\) |
−0.765787 | + | 0.643094i | \(0.777650\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.33157 | − | 14.6484i | −0.342020 | − | 0.939693i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.439693 | + | 0.761570i | 0.0280909 | + | 0.0486549i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.57532 | + | 11.3888i | −0.418378 | + | 0.724651i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.129700 | − | 0.356347i | 0.00821939 | − | 0.0225826i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.47906 | − | 0.437124i | 0.155244 | − | 0.0273738i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.28312 | + | 9.15063i | −0.329552 | + | 0.570801i | −0.982423 | − | 0.186668i | \(-0.940231\pi\) |
0.652871 | + | 0.757469i | \(0.273564\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.27719 | − | 3.94421i | −0.141498 | − | 0.245081i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.0544 | + | 6.20729i | −1.05564 | + | 0.384221i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.1766 | − | 24.5547i | −0.874169 | − | 1.51411i | −0.857645 | − | 0.514242i | \(-0.828073\pi\) |
−0.0165240 | − | 0.999863i | \(-0.505260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.20574 | − | 5.55250i | 0.196927 | − | 0.341087i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.2772 | + | 14.6314i | 0.751352 | + | 0.895426i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.48339 | 0.456271 | 0.228135 | − | 0.973629i | \(-0.426737\pi\) | ||||
0.228135 | + | 0.973629i | \(0.426737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6382 | −0.828459 | −0.414229 | − | 0.910172i | \(-0.635949\pi\) | ||||
−0.414229 | + | 0.910172i | \(0.635949\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.07145 | + | 7.23567i | 0.367461 | + | 0.437923i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.19846 | + | 14.2002i | −0.494386 | + | 0.856302i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.07532 | + | 5.32661i | 0.184778 | + | 0.320045i | 0.943502 | − | 0.331368i | \(-0.107510\pi\) |
−0.758724 | + | 0.651413i | \(0.774177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4666 | − | 8.78249i | −0.626617 | − | 0.525794i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.65611 | − | 2.86846i | −0.0987951 | − | 0.171118i | 0.812391 | − | 0.583113i | \(-0.198165\pi\) |
−0.911186 | + | 0.411995i | \(0.864832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.5116 | − | 25.1348i | 0.862626 | − | 1.49411i | −0.00675974 | − | 0.999977i | \(-0.502152\pi\) |
0.869385 | − | 0.494134i | \(-0.164515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.61721 | + | 0.637812i | −0.214265 | + | 0.0377807i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.18479 | 0.0699361 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2686 | −0.839328 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.40673 | − | 20.3498i | 0.434190 | − | 1.19293i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.20961 | − | 7.29125i | 0.245928 | − | 0.425960i | −0.716464 | − | 0.697624i | \(-0.754241\pi\) |
0.962392 | + | 0.271664i | \(0.0875740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.92855 | − | 5.07239i | −0.170507 | − | 0.295326i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.4572 | − | 10.0789i | −1.01297 | − | 0.584839i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.62314 | − | 14.9357i | −0.498689 | − | 0.863755i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0923963 | + | 0.160035i | −0.00532563 | + | 0.00922427i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.75624 | + | 15.8152i | −0.330688 | + | 0.908557i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.28312 | 0.130731 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6878 | 0.724130 | 0.362065 | − | 0.932153i | \(-0.382072\pi\) | ||||
0.362065 | + | 0.932153i | \(0.382072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.2515 | − | 1.98394i | 0.640075 | − | 0.112863i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(-0.465028\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.458111 | + | 2.59808i | −0.0258116 | + | 0.146385i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.9474 | + | 22.4256i | 0.727200 | + | 1.25955i | 0.958062 | + | 0.286561i | \(0.0925122\pi\) |
−0.230862 | + | 0.972987i | \(0.574154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.7344 | + | 20.3246i | −0.657002 | + | 1.13796i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.65998 | − | 3.17004i | −0.148465 | − | 0.176934i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.98545 | −0.221756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.0496 | 1.27856 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.40673 | + | 5.25173i | 0.243693 | + | 0.290421i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.511144 | − | 0.885328i | 0.0281803 | − | 0.0488097i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.10947 | + | 7.11781i | 0.225877 | + | 0.391230i | 0.956582 | − | 0.291463i | \(-0.0941419\pi\) |
−0.730705 | + | 0.682693i | \(0.760809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.37258 | − | 13.4556i | 0.130016 | − | 0.737360i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.30066 | + | 2.25281i | 0.0710626 | + | 0.123084i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.28564 | + | 3.95885i | −0.124507 | + | 0.215652i | −0.921540 | − | 0.388283i | \(-0.873068\pi\) |
0.797033 | + | 0.603936i | \(0.206402\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.0651 | + | 4.94864i | −1.52429 | + | 0.268773i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.6682 | −0.956786 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.64749 | − | 4.52644i | 0.0886978 | − | 0.243695i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 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 | −0.968976 | − | 0.247155i | \(-0.920504\pi\) |
0.270445 | − | 0.962735i | \(-0.412829\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.3365i | 1.51249i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.177519 | + | 0.307471i | 0.00944836 | + | 0.0163650i | 0.870711 | − | 0.491795i | \(-0.163659\pi\) |
−0.861263 | + | 0.508160i | \(0.830326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.61809 | − | 2.80261i | 0.0858792 | − | 0.148747i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.979055 | + | 2.68993i | −0.0518171 | + | 0.142366i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.45605 | −0.287959 | −0.143980 | − | 0.989581i | \(-0.545990\pi\) | ||||
−0.143980 | + | 0.989581i | \(0.545990\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1848 | −0.693936 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.90760 | + | 1.21800i | −0.362555 | + | 0.0639283i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.61974 | + | 9.73367i | −0.294150 | + | 0.509484i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.46198 | + | 9.46043i | 0.285113 | + | 0.493830i | 0.972637 | − | 0.232332i | \(-0.0746355\pi\) |
−0.687523 | + | 0.726162i | \(0.741302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.72281 | + | 2.28471i | 0.141744 | + | 0.118937i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.64543 | + | 6.31407i | 0.189261 | + | 0.327810i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.865715 | + | 1.49946i | −0.0448250 | + | 0.0776392i | −0.887567 | − | 0.460678i | \(-0.847606\pi\) |
0.842742 | + | 0.538317i | \(0.180940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.03343 | + | 10.7656i | 0.466484 | + | 0.555935i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.9908 | 1.69911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.1334 | 0.623251 | 0.311626 | − | 0.950205i | \(-0.399127\pi\) | ||||
0.311626 | + | 0.950205i | \(0.399127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.6545 | − | 23.4233i | −1.00693 | − | 1.20001i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.35591 | + | 7.54467i | −0.222577 | + | 0.385514i | −0.955590 | − | 0.294700i | \(-0.904780\pi\) |
0.733013 | + | 0.680215i | \(0.238113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.70574 | + | 2.95442i | 0.0869324 | + | 0.150571i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.520945 | + | 0.189608i | −0.0264811 | + | 0.00963833i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.82160 | − | 3.15511i | −0.0923590 | − | 0.159970i | 0.816144 | − | 0.577848i | \(-0.196107\pi\) |
−0.908503 | + | 0.417878i | \(0.862774\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.61334 | − | 4.52644i | 0.132162 | − | 0.228912i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.7460 | + | 5.77401i | −1.65182 | + | 0.291260i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.23947 | −0.263627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4456 | −0.775194 | −0.387597 | − | 0.921829i | \(-0.626695\pi\) | ||||
−0.387597 | + | 0.921829i | \(0.626695\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.42855 | − | 3.92490i | 0.0715169 | − | 0.196491i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.21095 | + | 15.9538i | −0.459973 | + | 0.796697i | −0.998959 | − | 0.0456182i | \(-0.985474\pi\) |
0.538986 | + | 0.842315i | \(0.318808\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.4183 | + | 21.5092i | 0.618601 | + | 1.07145i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.06283 | + | 5.08732i | −0.301265 | + | 0.252791i | ||||
\(406\) | 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 | \(-0.0837309\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.7554 | − | 29.5501i | 0.530523 | − | 1.45760i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.66044 | 0.327739 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.192533 | −0.00945109 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.6241 | − | 6.63414i | 1.84246 | − | 0.324875i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3478 | + | 30.0472i | −0.847494 | + | 1.46790i | 0.0359442 | + | 0.999354i | \(0.488556\pi\) |
−0.883438 | + | 0.468548i | \(0.844777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7010 | + | 23.7308i | 0.667745 | + | 1.15657i | 0.978533 | + | 0.206090i | \(0.0660738\pi\) |
−0.310788 | + | 0.950479i | \(0.600593\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.88191 | − | 1.04893i | 0.140123 | − | 0.0510007i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.49273 | + | 6.04958i | 0.169422 | + | 0.293448i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.29813 | + | 2.24843i | −0.0628211 | + | 0.108809i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.5535 | + | 28.0700i | 1.13717 | + | 1.35523i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.5921 | −1.28090 | −0.640449 | − | 0.768000i | \(-0.721252\pi\) | ||||
−0.640449 | + | 0.768000i | \(0.721252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.1830 | 1.78690 | 0.893451 | − | 0.449160i | \(-0.148277\pi\) | ||||
0.893451 | + | 0.449160i | \(0.148277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.92292 | + | 7.05866i | 0.283982 | + | 0.338437i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.81315 | + | 6.60457i | −0.182408 | + | 0.315939i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5373 | + | 21.7152i | 0.598373 | + | 1.03641i | 0.993061 | + | 0.117597i | \(0.0375192\pi\) |
−0.394689 | + | 0.918815i | \(0.629147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.29813 | − | 1.92836i | −0.109435 | − | 0.0918268i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.8516 | − | 4.55834i | 1.22274 | − | 0.215602i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.2344 | −0.482992 | −0.241496 | − | 0.970402i | \(-0.577638\pi\) | ||||
−0.241496 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.59627 | 0.216430 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.2297 | − | 30.8533i | 0.527616 | − | 1.44961i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.39780 | − | 4.15312i | 0.112411 | − | 0.194701i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.2973 | + | 36.8879i | 0.996244 | + | 1.72554i | 0.573115 | + | 0.819475i | \(0.305735\pi\) |
0.423129 | + | 0.906070i | \(0.360932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.43717 | + | 4.29385i | −0.347137 | + | 0.200420i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.252374 | − | 0.437124i | −0.0117542 | − | 0.0203589i | 0.860088 | − | 0.510145i | \(-0.170408\pi\) |
−0.871843 | + | 0.489786i | \(0.837075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.34002 | − | 2.32099i | 0.0622761 | − | 0.107865i | −0.833206 | − | 0.552962i | \(-0.813497\pi\) |
0.895482 | + | 0.445097i | \(0.146831\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.37258 | + | 6.51860i | −0.110026 | + | 0.302293i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.4165 | 1.45378 | 0.726892 | − | 0.686752i | \(-0.240964\pi\) | ||||
0.726892 | + | 0.686752i | \(0.240964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.95811 | −0.136593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.8011 | − | 5.43107i | 1.41924 | − | 0.250250i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.358441 | + | 0.620838i | −0.0164811 | + | 0.0285461i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.09627 | − | 8.82699i | −0.233833 | − | 0.405010i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.79813 | + | 21.5403i | −0.173905 | + | 0.986262i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.22028 | − | 14.2380i | −0.375594 | − | 0.650549i | 0.614821 | − | 0.788666i | \(-0.289228\pi\) |
−0.990416 | + | 0.138118i | \(0.955895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.4183 | + | 21.5092i | −0.566227 | + | 0.980735i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.52094 | + | 4.19610i | 0.160209 | + | 0.190929i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.9949 | −0.499255 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.97535 | 0.134826 | 0.0674129 | − | 0.997725i | \(-0.478526\pi\) | ||||
0.0674129 | + | 0.997725i | \(0.478526\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.06670 | − | 1.27125i | −0.0482380 | − | 0.0574878i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.2430 | + | 22.9376i | −0.597650 | + | 1.03516i | 0.395517 | + | 0.918459i | \(0.370565\pi\) |
−0.993167 | + | 0.116702i | \(0.962768\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.99912 | + | 8.65873i | 0.225149 | + | 0.389970i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.77719 | + | 10.0789i | −0.0798787 | + | 0.453015i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.84002 | + | 3.18701i | 0.0825363 | + | 0.142957i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.72193 | + | 11.6427i | −0.300915 | + | 0.521200i | −0.976343 | − | 0.216225i | \(-0.930625\pi\) |
0.675428 | + | 0.737426i | \(0.263959\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.8391 | − | 5.96675i | 1.51182 | − | 0.266575i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.91622 | − | 27.2446i | 0.440395 | − | 1.20997i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.77379 | + | 8.26844i | −0.211594 | + | 0.366492i | −0.952214 | − | 0.305433i | \(-0.901199\pi\) |
0.740619 | + | 0.671925i | \(0.234532\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.39053 | − | 11.0687i | −0.282700 | − | 0.489651i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.8516 | − | 6.26519i | 0.479111 | − | 0.276615i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.90033 | − | 5.02352i | −0.127804 | − | 0.221363i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.98293 | − | 3.43453i | 0.0872090 | − | 0.151050i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.4372 | − | 36.9183i | 0.589826 | − | 1.62053i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.11287 | −0.136377 | −0.0681887 | − | 0.997672i | \(-0.521722\pi\) | ||||
−0.0681887 | + | 0.997672i | \(0.521722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.1489 | 0.706142 | 0.353071 | − | 0.935597i | \(-0.385137\pi\) | ||||
0.353071 | + | 0.935597i | \(0.385137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.20961 | + | 1.27125i | −0.314653 | + | 0.0554818i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.76352 | + | 6.51860i | −0.163941 | + | 0.283955i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.49928 | + | 11.2571i | 0.282578 | + | 0.489439i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.3066 | + | 12.8438i | 0.664249 | + | 0.557371i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.23055 | − | 5.59548i | −0.139931 | − | 0.242367i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.05051 | + | 1.81953i | −0.0454174 | + | 0.0786652i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.18004 | + | 9.74860i | 0.352995 | + | 0.420683i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.87939 | −0.167097 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.01548 | −0.215632 | −0.107816 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107816 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.83615 | − | 4.57175i | −0.164625 | − | 0.196192i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.74035 | − | 3.01438i | 0.0745485 | − | 0.129122i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.23901 | + | 14.2704i | 0.352275 | + | 0.610157i | 0.986648 | − | 0.162870i | \(-0.0520750\pi\) |
−0.634373 | + | 0.773027i | \(0.718742\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.31908 | + | 2.66393i | −0.312371 | + | 0.113694i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.29426 | − | 12.6340i | −0.310746 | − | 0.538228i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.97906 | − | 5.15988i | 0.126682 | − | 0.219420i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.83157 | + | 1.20459i | −0.289984 | + | 0.0511320i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.5631 | −1.46448 | −0.732242 | − | 0.681045i | \(-0.761526\pi\) | ||||
−0.732242 | + | 0.681045i | \(0.761526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.00774 | 0.0426229 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.79813 | + | 10.4353i | −0.160357 | + | 0.440578i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −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 | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.56283 | − | 8.86327i | −0.0656328 | − | 0.372222i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.202333 | − | 0.350452i | −0.00848226 | − | 0.0146917i | 0.861753 | − | 0.507328i | \(-0.169367\pi\) |
−0.870235 | + | 0.492636i | \(0.836033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8897 | + | 32.7178i | −0.790507 | + | 1.36920i | 0.135146 | + | 0.990826i | \(0.456850\pi\) |
−0.925653 | + | 0.378373i | \(0.876484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.35163 | + | 9.20854i | −0.140017 | + | 0.384692i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.3669 | 0.557438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.21120 | −0.0920535 | −0.0460267 | − | 0.998940i | \(-0.514656\pi\) | ||||
−0.0460267 | + | 0.998940i | \(0.514656\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.3687 | + | 2.88624i | −0.680260 | + | 0.119948i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.109470 | − | 0.189608i | 0.00454160 | − | 0.00786628i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1420 | + | 24.4947i | 0.585703 | + | 1.01447i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.5192 | − | 4.92058i | 0.558950 | − | 0.203441i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.1049 | + | 20.9663i | 0.499622 | + | 0.865371i | 1.00000 | 0.000436347i | \(-0.000138894\pi\) | |
−0.500378 | + | 0.865807i | \(0.666806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.49138 | − | 9.51135i | 0.226268 | − | 0.391908i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.26295 | + | 11.0391i | 0.381027 | + | 0.454090i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.2385 | 0.502577 | 0.251288 | − | 0.967912i | \(-0.419146\pi\) | ||||
0.251288 | + | 0.967912i | \(0.419146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.45336 | 0.0595821 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.34389 | − | 8.75211i | −0.300566 | − | 0.358200i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | 0.990899 | + | 0.134605i | \(0.0429764\pi\) |
−0.378879 | + | 0.925446i | \(0.623690\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.79813 | − | 5.70431i | −0.276841 | − | 0.232298i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.78059 | + | 3.08408i | 0.0723914 | + | 0.125386i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.74216 | + | 16.8739i | −0.395422 | + | 0.684891i | −0.993155 | − | 0.116804i | \(-0.962735\pi\) |
0.597733 | + | 0.801695i | \(0.296068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3191 | + | 1.81953i | −0.418150 | + | 0.0737312i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.57491 | −0.225537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.5276 | −0.748325 | −0.374162 | − | 0.927363i | \(-0.622070\pi\) | ||||
−0.374162 | + | 0.927363i | \(0.622070\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.617211 | − | 1.69577i | 0.0248884 | − | 0.0683802i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.9201 | + | 24.1103i | −0.560402 | + | 0.970644i | 0.437059 | + | 0.899433i | \(0.356020\pi\) |
−0.997461 | + | 0.0712118i | \(0.977313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.4907 | − | 38.9550i | −0.903976 | − | 1.56573i | −0.822286 | − | 0.569075i | \(-0.807301\pi\) |
−0.0816906 | − | 0.996658i | \(-0.526032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.4329i | 0.659428i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.51367 | + | 9.54996i | 0.220901 | + | 0.382611i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.99912 | + | 12.1228i | −0.279965 | + | 0.484913i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.54189 | − | 15.2262i | 0.221322 | − | 0.608076i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.52704 | −0.300123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.43613 | −0.375646 | −0.187823 | − | 0.982203i | \(-0.560143\pi\) | ||||
−0.187823 | + | 0.982203i | \(0.560143\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.74763 | + | 1.01346i | −0.228448 | + | 0.0402815i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.76217 | + | 13.4445i | −0.308032 | + | 0.533528i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.72668 | + | 4.72275i | 0.108035 | + | 0.187122i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.91710 | + | 10.8724i | −0.0758393 | + | 0.430106i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.6951 | − | 32.3808i | −0.738410 | − | 1.27896i | −0.953211 | − | 0.302306i | \(-0.902243\pi\) |
0.214800 | − | 0.976658i | \(-0.431090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.805874 | − | 1.39581i | 0.0317806 | − | 0.0550456i | −0.849698 | − | 0.527270i | \(-0.823216\pi\) |
0.881478 | + | 0.472225i | \(0.156549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.180922 | + | 0.215615i | 0.00712380 | + | 0.00848982i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.1762 | 1.61880 | 0.809402 | − | 0.587255i | \(-0.199791\pi\) | ||||
0.809402 | + | 0.587255i | \(0.199791\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.8384 | 1.01425 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.07057 | − | 6.04288i | −0.198731 | − | 0.236839i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.52600 | + | 2.64310i | −0.0597169 | + | 0.103433i | −0.894338 | − | 0.447391i | \(-0.852353\pi\) |
0.834621 | + | 0.550824i | \(0.185686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.44104 | + | 14.6203i | 0.329819 | + | 0.571263i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.65822 | − | 37.7607i | 0.259762 | − | 1.47318i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8175 | + | 36.0569i | 0.810934 | + | 1.40458i | 0.912211 | + | 0.409721i | \(0.134374\pi\) |
−0.101277 | + | 0.994858i | \(0.532293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1505 | + | 17.5812i | −0.394808 | + | 0.683828i | −0.993077 | − | 0.117468i | \(-0.962522\pi\) |
0.598269 | + | 0.801296i | \(0.295856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.3735 | − | 2.71075i | 0.597056 | − | 0.105277i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.12061 | −0.0822339 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.1320 | 0.740793 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.71806 | − | 10.2153i | 0.143749 | − | 0.394946i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.03596 | + | 8.72254i | −0.194411 | + | 0.336730i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.415345 | + | 0.719398i | 0.0160104 | + | 0.0277307i | 0.873920 | − | 0.486071i | \(-0.161570\pi\) |
−0.857909 | + | 0.513801i | \(0.828237\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.0201 | − | 10.9812i | −0.732083 | − | 0.422668i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.43360 | − | 9.41127i | −0.208830 | − | 0.361705i | 0.742516 | − | 0.669828i | \(-0.233632\pi\) |
−0.951346 | + | 0.308124i | \(0.900299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.25150 | − | 10.8279i | 0.239910 | − | 0.415537i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.65064 | − | 10.0301i | 0.139893 | − | 0.384353i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.6946 | −1.25102 | −0.625512 | − | 0.780215i | \(-0.715110\pi\) | ||||
−0.625512 | + | 0.780215i | \(0.715110\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.9659 | −0.610024 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.8888 | + | 7.03347i | −1.52185 | + | 0.268344i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.8799 | − | 34.4329i | 0.757362 | − | 1.31179i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.49912 | + | 12.9889i | 0.285280 | + | 0.494120i | 0.972677 | − | 0.232162i | \(-0.0745801\pi\) |
−0.687397 | + | 0.726282i | \(0.741247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.91534 | − | 7.48086i | −0.338666 | − | 0.284174i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.69846 | − | 16.7982i | −0.367884 | − | 0.637193i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.979055 | − | 1.69577i | 0.0370844 | − | 0.0642320i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.49154 | − | 11.3116i | −0.359003 | − | 0.427843i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.4688 | 0.999714 | 0.499857 | − | 0.866108i | \(-0.333386\pi\) | ||||
0.499857 | + | 0.866108i | \(0.333386\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9828 | 0.414223 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.00088 | − | 1.19280i | −0.0376952 | − | 0.0449234i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.85844 | + | 8.41507i | −0.182720 | + | 0.316481i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.68004 | − | 13.3022i | −0.288430 | − | 0.499576i | 0.685005 | − | 0.728538i | \(-0.259800\pi\) |
−0.973435 | + | 0.228963i | \(0.926467\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.7964 | − | 6.11338i | 0.629913 | − | 0.229270i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.20162 | + | 12.4736i | 0.269703 | + | 0.467139i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.30200 | − | 16.1115i | 0.347875 | − | 0.602538i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.8391 | − | 4.37981i | 0.927635 | − | 0.163567i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.7306 | −0.996883 | −0.498442 | − | 0.866923i | \(-0.666094\pi\) | ||||
−0.498442 | + | 0.866923i | \(0.666094\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.59627 | 0.245658 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.20115 | + | 8.79509i | −0.119052 | + | 0.327093i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.7849 | + | 22.1441i | −0.474820 | + | 0.822413i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.8221 | − | 39.5290i | −0.846424 | − | 1.46605i | −0.884379 | − | 0.466770i | \(-0.845418\pi\) |
0.0379552 | − | 0.999279i | \(-0.487916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5000 | − | 23.3827i | 0.500000 | − | 0.866025i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.152704 | + | 0.264490i | 0.00564795 | + | 0.00978253i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.98751 | + | 5.17452i | −0.110346 | + | 0.191125i | −0.915910 | − | 0.401384i | \(-0.868529\pi\) |
0.805564 | + | 0.592509i | \(0.201863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.520945 | + | 1.43128i | −0.0192153 | + | 0.0527937i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.4757 | −0.422711 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.5963 | 1.30943 | 0.654715 | − | 0.755876i | \(-0.272789\pi\) | ||||
0.654715 | + | 0.755876i | \(0.272789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.4315 | + | 3.95529i | −0.824043 | + | 0.145301i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.6544 | + | 25.3821i | −0.537616 | + | 0.931178i | 0.461416 | + | 0.887184i | \(0.347342\pi\) |
−0.999032 | + | 0.0439943i | \(0.985992\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.66385 | − | 11.5421i | −0.244145 | − | 0.422871i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.617211 | − | 0.224647i | 0.0225826 | − | 0.00821939i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.19459 | − | 2.06910i | −0.0436495 | − | 0.0756031i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.66684 | + | 15.0114i | −0.316258 | + | 0.547774i | −0.979704 | − | 0.200450i | \(-0.935760\pi\) |
0.663446 | + | 0.748224i | \(0.269093\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4345 | + | 16.0107i | 0.489582 | + | 0.583461i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6699 | −0.606681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.77156 | −0.100734 | −0.0503671 | − | 0.998731i | \(-0.516039\pi\) | ||||
−0.0503671 | + | 0.998731i | \(0.516039\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.6591 | + | 16.2783i | 0.495794 | + | 0.590864i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.75372 | + | 6.50163i | −0.136072 | + | 0.235684i | −0.926007 | − | 0.377508i | \(-0.876781\pi\) |
0.789934 | + | 0.613191i | \(0.210115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.97906 | + | 3.42782i | 0.0716466 | + | 0.124096i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.34002 | + | 2.80261i | 0.120759 | + | 0.101329i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.1609 | − | 31.4556i | −0.655752 | − | 1.13580i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.02182 | + | 1.76985i | −0.0368478 | + | 0.0638223i | −0.883861 | − | 0.467749i | \(-0.845065\pi\) |
0.847013 | + | 0.531572i | \(0.178398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0232 | + | 3.17798i | −0.649090 | + | 0.114452i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −24.9418 | −0.897094 | −0.448547 | − | 0.893759i | \(-0.648058\pi\) | ||||
−0.448547 | + | 0.893759i | \(0.648058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.2499 | −0.691477 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.69800 | − | 7.41268i | 0.0967901 | − | 0.265929i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.42855 | + | 2.47432i | −0.0511831 | + | 0.0886516i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.13816 | + | 12.3636i | 0.255423 | + | 0.442406i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.2233 | − | 15.7174i | −0.972883 | − | 0.561694i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.93969 | − | 13.7520i | −0.283380 | − | 0.490828i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.55350 | − | 6.15484i | 0.126669 | − | 0.219396i | −0.795715 | − | 0.605671i | \(-0.792905\pi\) |
0.922384 | + | 0.386274i | \(0.126238\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.7964 | − | 46.1477i | 0.597967 | − | 1.64290i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4534 | −0.585014 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1584 | 0.502779 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.9363 | − | 1.92836i | 0.387870 | − | 0.0683920i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.8314 | + | 29.1528i | −0.596199 | + | 1.03265i | 0.397178 | + | 0.917742i | \(0.369990\pi\) |
−0.993376 | + | 0.114905i | \(0.963344\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.844770 | − | 1.46318i | −0.0298858 | − | 0.0517638i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.74463 | + | 32.5794i | −0.202977 | + | 1.15114i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.7913 | − | 42.9398i | −0.874867 | − | 1.51531i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.39053 | − | 2.40847i | 0.0490097 | − | 0.0848873i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.33157 | + | 9.92917i | 0.293285 | + | 0.349523i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.8161 | −0.450592 | −0.225296 | − | 0.974290i | \(-0.572335\pi\) | ||||
−0.225296 | + | 0.974290i | \(0.572335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1239 | 0.917335 | 0.458667 | − | 0.888608i | \(-0.348327\pi\) | ||||
0.458667 | + | 0.888608i | \(0.348327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.1839 | − | 18.0955i | −0.532523 | − | 0.634636i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.421274 | + | 0.729669i | −0.0147566 | + | 0.0255592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.222811 | − | 0.385920i | −0.00779518 | − | 0.0135016i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.84090 | + | 16.1115i | −0.0992691 | + | 0.562983i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.8320 | − | 23.9578i | −0.482741 | − | 0.836132i | 0.517062 | − | 0.855948i | \(-0.327026\pi\) |
−0.999804 | + | 0.0198153i | \(0.993692\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.9162 | − | 24.1036i | 0.485089 | − | 0.840199i | −0.514764 | − | 0.857332i | \(-0.672121\pi\) |
0.999853 | + | 0.0171330i | \(0.00545387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.9688 | + | 4.93166i | −0.973750 | + | 0.171698i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.65507 | −0.161873 | −0.0809363 | − | 0.996719i | \(-0.525791\pi\) | ||||
−0.0809363 | + | 0.996719i | \(0.525791\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.97359 | −0.346397 | −0.173199 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173199 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.64362 | + | 10.0108i | −0.126396 | + | 0.347269i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.826352 | + | 1.43128i | −0.0286314 | + | 0.0495910i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.72281 | − | 15.1084i | −0.301865 | − | 0.522846i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 23.6652i | − | 0.817990i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.36484 | − | 5.82807i | −0.116167 | − | 0.201207i | 0.802079 | − | 0.597218i | \(-0.203727\pi\) |
−0.918246 | + | 0.396011i | \(0.870394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.79901 | + | 6.58008i | −0.131000 | + | 0.226899i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.96214 | − | 5.39094i | 0.0675798 | − | 0.185674i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.7202 | −0.506390 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.04963 | −0.139147 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.5060 | − | 8.72924i | 1.69904 | − | 0.299587i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.20162 | + | 12.4736i | −0.246868 | + | 0.427588i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.89528 | − | 5.01477i | −0.0991324 | − | 0.171702i | 0.812193 | − | 0.583388i | \(-0.198273\pi\) |
−0.911326 | + | 0.411686i | \(0.864940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.87346 | − | 4.08931i | −0.166669 | − | 0.139852i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.4538 | + | 30.2309i | 0.596211 | + | 1.03267i | 0.993375 | + | 0.114921i | \(0.0366614\pi\) |
−0.397163 | + | 0.917748i | \(0.630005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.30747 | + | 10.9249i | −0.215208 | + | 0.372751i | −0.953337 | − | 0.301909i | \(-0.902376\pi\) |
0.738129 | + | 0.674660i | \(0.235710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.31908 | + | 1.57202i | 0.0449541 | + | 0.0535742i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.2053 | 0.823959 | 0.411979 | − | 0.911193i | \(-0.364838\pi\) | ||||
0.411979 | + | 0.911193i | \(0.364838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.9469 | −0.678214 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.8858 | − | 18.9319i | −0.539509 | − | 0.642962i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.5569 | − | 20.0171i | 0.392041 | − | 0.679035i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.06583 | + | 13.9704i | 0.273300 | + | 0.473370i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.2469 | − | 12.8288i | 1.19293 | − | 0.434190i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.05690 | + | 7.02676i | 0.137148 | + | 0.237548i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.562834 | − | 0.974856i | 0.0190055 | − | 0.0329186i | −0.856366 | − | 0.516369i | \(-0.827283\pi\) |
0.875372 | + | 0.483450i | \(0.160617\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.3610 | − | 2.53223i | 0.484383 | − | 0.0854099i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.38331 | −0.147678 | −0.0738388 | − | 0.997270i | \(-0.523525\pi\) | ||||
−0.0738388 | + | 0.997270i | \(0.523525\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.88949 | 0.231850 | 0.115925 | − | 0.993258i | \(-0.463017\pi\) | ||||
0.115925 | + | 0.993258i | \(0.463017\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.46972 | − | 9.53298i | 0.116633 | − | 0.320448i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5376 | − | 33.8401i | 0.656009 | − | 1.13624i | −0.325631 | − | 0.945497i | \(-0.605577\pi\) |
0.981640 | − | 0.190744i | \(-0.0610899\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.82682 | − | 15.2885i | −0.296042 | − | 0.512760i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.06283 | − | 34.3840i | −0.203113 | − | 1.15191i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.23261 | + | 2.13495i | 0.0412478 | + | 0.0714432i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.23055 | − | 5.59548i | 0.107985 | − | 0.187036i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.2166 | − | 28.0700i | 0.341123 | − | 0.937229i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.5523 | −0.918921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0496 | 0.401431 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.315207 | + | 0.0555796i | −0.0104894 | + | 0.00184957i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.51501 | + | 2.62408i | −0.0503608 | + | 0.0872275i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.2469 | + | 36.8007i | 0.705492 | + | 1.22195i | 0.966514 | + | 0.256615i | \(0.0826073\pi\) |
−0.261022 | + | 0.965333i | \(0.584059\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.3926 | + | 9.97011i | −0.908557 | + | 0.330688i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.74675 | − | 13.4178i | −0.256661 | − | 0.444550i | 0.708684 | − | 0.705526i | \(-0.249289\pi\) |
−0.965345 | + | 0.260976i | \(0.915956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.424678 | − | 0.735564i | 0.0140548 | − | 0.0243436i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.54189 | + | 3.02931i | 0.0840323 | + | 0.100146i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.1976 | −0.633960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.52940 | −0.215385 | −0.107693 | − | 0.994184i | \(-0.534346\pi\) | ||||
−0.107693 | + | 0.994184i | \(0.534346\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.1258 | + | 16.8345i | 0.465462 | + | 0.554716i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0343 | − | 17.3799i | 0.330283 | − | 0.572068i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.62495 | − | 16.6709i | −0.316466 | − | 0.548136i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.1591 | + | 12.7200i | 0.497890 | + | 0.417779i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.1386 | − | 50.4696i | −0.956007 | − | 1.65585i | −0.732046 | − | 0.681255i | \(-0.761435\pi\) |
−0.223961 | − | 0.974598i | \(-0.571899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.20574 | − | 2.08840i | 0.0395164 | − | 0.0684445i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.1279 | + | 4.95972i | −0.920868 | + | 0.162374i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.63816 | 0.184387 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.4175 | 1.05903 | 0.529516 | − | 0.848300i | \(-0.322374\pi\) | ||||
0.529516 | + | 0.848300i | \(0.322374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.8942 | − | 46.4165i | 0.551323 | − | 1.51475i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.6613 | − | 23.6621i | 0.445346 | − | 0.771363i | −0.552730 | − | 0.833360i | \(-0.686414\pi\) |
0.998076 | + | 0.0619979i | \(0.0197472\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.87346 | − | 3.24492i | −0.0610081 | − | 0.105669i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.95723 | + | 2.28471i | −0.128729 | + | 0.0743216i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.3400 | + | 42.1464i | −0.497434 | + | 1.36669i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.9377 | 1.90918 | 0.954590 | − | 0.297924i | \(-0.0962943\pi\) | ||||
0.954590 | + | 0.297924i | \(0.0962943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.97535 | 0.160998 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −40.0317 | + | 7.05866i | −1.29404 | + | 0.228174i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.07785 | − | 15.7233i | 0.293139 | − | 0.507732i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.12882 | + | 8.88338i | 0.165446 | + | 0.286561i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.24463 | − | 7.05866i | 0.0401077 | − | 0.227462i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.21941 | + | 7.30823i | 0.135828 | + | 0.235260i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.3594 | − | 21.4071i | 0.397451 | − | 0.688405i | −0.595960 | − | 0.803014i | \(-0.703228\pi\) |
0.993411 | + | 0.114609i | \(0.0365616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.43717 | − | 5.28801i | −0.142542 | − | 0.169875i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.17623 | −0.262388 | −0.131194 | − | 0.991357i | \(-0.541881\pi\) | ||||
−0.131194 | + | 0.991357i | \(0.541881\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.0574 | 0.707127 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.6621 | + | 30.5829i | 0.821845 | + | 0.979436i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.92427 | − | 13.7252i | 0.253520 | − | 0.439109i | −0.710973 | − | 0.703220i | \(-0.751745\pi\) |
0.964492 | + | 0.264111i | \(0.0850784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.3897 | + | 37.0480i | 0.683616 | + | 1.18406i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.06196 | + | 11.6939i | −0.0658332 | + | 0.373359i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.6532 | + | 46.1646i | 0.850104 | + | 1.47242i | 0.881114 | + | 0.472904i | \(0.156794\pi\) |
−0.0310096 | + | 0.999519i | \(0.509872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.65822 | − | 6.33623i | 0.116561 | − | 0.201889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.74376 | − | 0.307471i | 0.0555044 | − | 0.00978692i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.584407 | 0.0185831 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.2094 | −1.27730 | −0.638648 | − | 0.769499i | \(-0.720506\pi\) | ||||
−0.638648 | + | 0.769499i | \(0.720506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.86887 | + | 13.3771i | −0.154509 | + | 0.424510i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.90033 | + | 5.02352i | −0.0919466 | + | 0.159256i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.3601 | − | 24.8724i | −0.454789 | − | 0.787717i | 0.543887 | − | 0.839158i | \(-0.316952\pi\) |
−0.998676 | + | 0.0514412i | \(0.983619\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.4947 | − | 11.8326i | 0.648424 | − | 0.374368i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))