Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, 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("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (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: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.2 | ||
Root | \(0.356769 - 0.617942i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.k.177.2 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.356769 | + | 0.617942i | −0.205981 | + | 0.356769i | −0.950445 | − | 0.310894i | \(-0.899372\pi\) |
0.744464 | + | 0.667663i | \(0.232705\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.10220 | − | 1.90907i | −0.492919 | − | 0.853761i | 0.507048 | − | 0.861918i | \(-0.330737\pi\) |
−0.999967 | + | 0.00815703i | \(0.997404\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.10220 | + | 2.40523i | 0.416593 | + | 0.909093i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.24543 | + | 2.15715i | 0.415144 | + | 0.719050i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.28646 | −0.911501 | −0.455750 | − | 0.890108i | \(-0.650629\pi\) | ||||
−0.455750 | + | 0.890108i | \(0.650629\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.57292 | 0.406127 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.745432 | + | 1.29113i | −0.180794 | + | 0.313144i | −0.942151 | − | 0.335189i | \(-0.891200\pi\) |
0.761357 | + | 0.648333i | \(0.224533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.45897 | − | 5.99111i | −0.793542 | − | 1.37446i | −0.923761 | − | 0.382970i | \(-0.874901\pi\) |
0.130219 | − | 0.991485i | \(-0.458432\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.87953 | − | 0.177017i | −0.410146 | − | 0.0386283i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.24543 | + | 5.62125i | 0.676719 | + | 1.17211i | 0.975963 | + | 0.217936i | \(0.0699323\pi\) |
−0.299244 | + | 0.954177i | \(0.596734\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0703069 | − | 0.121775i | 0.0140614 | − | 0.0243550i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.91794 | −0.754008 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.64975 | −0.306351 | −0.153175 | − | 0.988199i | \(-0.548950\pi\) | ||||
−0.153175 | + | 0.988199i | \(0.548950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17512 | + | 2.03538i | −0.211059 | + | 0.365564i | −0.952046 | − | 0.305955i | \(-0.901024\pi\) |
0.740987 | + | 0.671519i | \(0.234358\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.356769 | − | 0.617942i | −0.0621055 | − | 0.107570i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.37691 | − | 4.75523i | 0.570802 | − | 0.803780i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.77733 | + | 4.81047i | 0.456590 | + | 0.790836i | 0.998778 | − | 0.0494206i | \(-0.0157375\pi\) |
−0.542189 | + | 0.840257i | \(0.682404\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.17251 | − | 2.03084i | 0.187751 | − | 0.325195i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2499 | −1.75694 | −0.878471 | − | 0.477796i | \(-0.841436\pi\) | ||||
−0.878471 | + | 0.477796i | \(0.841436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.26819 | −0.803391 | −0.401696 | − | 0.915773i | \(-0.631579\pi\) | ||||
−0.401696 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.74543 | − | 4.75523i | 0.409265 | − | 0.708867i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.745432 | + | 1.29113i | 0.108732 | + | 0.188330i | 0.915257 | − | 0.402871i | \(-0.131988\pi\) |
−0.806525 | + | 0.591201i | \(0.798654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.57031 | + | 5.30210i | −0.652901 | + | 0.757443i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.531894 | − | 0.921267i | −0.0744800 | − | 0.129003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.152367 | + | 0.263908i | −0.0209293 | + | 0.0362506i | −0.876300 | − | 0.481765i | \(-0.839996\pi\) |
0.855371 | + | 0.518016i | \(0.173329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.20440 | 0.297241 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.93621 | 0.653817 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.32936 | + | 10.9628i | −0.824012 | + | 1.42723i | 0.0786592 | + | 0.996902i | \(0.474936\pi\) |
−0.902672 | + | 0.430330i | \(0.858397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.49086 | + | 11.2425i | 0.831070 | + | 1.43946i | 0.897191 | + | 0.441644i | \(0.145604\pi\) |
−0.0661206 | + | 0.997812i | \(0.521062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.81574 | + | 5.37317i | −0.480738 | + | 0.676956i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.62234 | + | 6.27408i | 0.449296 | + | 0.778204i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.28646 | + | 3.96027i | −0.279336 | + | 0.483824i | −0.971220 | − | 0.238185i | \(-0.923448\pi\) |
0.691884 | + | 0.722009i | \(0.256781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.63148 | −0.557564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3267 | −1.34424 | −0.672119 | − | 0.740444i | \(-0.734615\pi\) | ||||
−0.672119 | + | 0.740444i | \(0.734615\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.28384 | − | 7.41984i | 0.501386 | − | 0.868426i | −0.498613 | − | 0.866825i | \(-0.666157\pi\) |
0.999999 | − | 0.00160129i | \(-0.000509706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0501666 | + | 0.0868912i | 0.00579274 | + | 0.0100333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.63409 | − | 0.248083i | −0.300183 | − | 0.0282717i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.31574 | + | 4.01098i | 0.260541 | + | 0.451270i | 0.966386 | − | 0.257096i | \(-0.0827658\pi\) |
−0.705845 | + | 0.708366i | \(0.749432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.33850 | + | 4.05039i | −0.259833 | + | 0.450044i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.93621 | 0.212527 | 0.106263 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106263 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.28646 | 0.356467 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.588580 | − | 1.01945i | 0.0631024 | − | 0.109297i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.60220 | − | 2.77509i | −0.169833 | − | 0.294159i | 0.768528 | − | 0.639816i | \(-0.220989\pi\) |
−0.938361 | + | 0.345657i | \(0.887656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.62234 | − | 7.90471i | −0.379725 | − | 0.828639i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.838496 | − | 1.45232i | −0.0869480 | − | 0.150598i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.62496 | + | 13.2068i | −0.782304 | + | 1.35499i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.85939 | 0.188792 | 0.0943960 | − | 0.995535i | \(-0.469908\pi\) | ||||
0.0943960 | + | 0.995535i | \(0.469908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.49086 | −0.250341 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.02276 | + | 5.23557i | −0.300776 | + | 0.520959i | −0.976312 | − | 0.216368i | \(-0.930579\pi\) |
0.675536 | + | 0.737327i | \(0.263912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.531894 | − | 0.921267i | −0.0524091 | − | 0.0907752i | 0.838631 | − | 0.544700i | \(-0.183357\pi\) |
−0.891040 | + | 0.453925i | \(0.850023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.73368 | + | 3.78325i | 0.169190 | + | 0.369208i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.16599 | − | 5.48365i | −0.306068 | − | 0.530125i | 0.671431 | − | 0.741067i | \(-0.265680\pi\) |
−0.977498 | + | 0.210943i | \(0.932347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.40694 | − | 2.43688i | 0.134760 | − | 0.233411i | −0.790746 | − | 0.612145i | \(-0.790307\pi\) |
0.925506 | + | 0.378734i | \(0.123640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.96345 | −0.376194 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.7538 | −1.19978 | −0.599889 | − | 0.800083i | \(-0.704789\pi\) | ||||
−0.599889 | + | 0.800083i | \(0.704789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.15423 | − | 12.3915i | 0.667136 | − | 1.15551i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.09306 | − | 7.08940i | −0.378404 | − | 0.655415i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.92708 | − | 0.369859i | −0.359994 | − | 0.0339049i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.01362 | − | 6.95180i | 0.361896 | − | 0.626822i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3320 | −1.01356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.3775 | 1.09832 | 0.549162 | − | 0.835716i | \(-0.314947\pi\) | ||||
0.549162 | + | 0.835716i | \(0.314947\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.87953 | − | 3.25544i | 0.165483 | − | 0.286625i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.379526 | + | 0.657359i | 0.0331594 | + | 0.0574337i | 0.882129 | − | 0.471008i | \(-0.156110\pi\) |
−0.848969 | + | 0.528442i | \(0.822776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.5975 | − | 14.9230i | 0.918924 | − | 1.29399i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.31836 | + | 7.47961i | 0.371665 | + | 0.643742i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.92056 | − | 5.05855i | 0.249520 | − | 0.432181i | −0.713873 | − | 0.700275i | \(-0.753060\pi\) |
0.963393 | + | 0.268094i | \(0.0863938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.57292 | 0.472689 | 0.236345 | − | 0.971669i | \(-0.424051\pi\) | ||||
0.236345 | + | 0.971669i | \(0.424051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.06379 | −0.0895871 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.64323 | − | 2.84616i | 0.137414 | − | 0.238008i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.81836 | + | 3.14948i | 0.151006 | + | 0.261550i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.64585 | − | 4.71581i | −0.135747 | − | 0.388953i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | + | 0.866025i | 0.0409616 | + | 0.0709476i | 0.885779 | − | 0.464107i | \(-0.153625\pi\) |
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.42056 | − | 12.8528i | 0.603876 | − | 1.04594i | −0.388352 | − | 0.921511i | \(-0.626955\pi\) |
0.992228 | − | 0.124433i | \(-0.0397113\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.71354 | −0.300222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.18089 | 0.416139 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.19527 | + | 5.53436i | −0.255010 | + | 0.441690i | −0.964898 | − | 0.262624i | \(-0.915412\pi\) |
0.709888 | + | 0.704314i | \(0.248745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.108720 | − | 0.188308i | −0.00862205 | − | 0.0149338i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.94331 | + | 14.0018i | −0.783643 | + | 1.10349i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.97259 | + | 8.61278i | 0.389483 | + | 0.674605i | 0.992380 | − | 0.123214i | \(-0.0393202\pi\) |
−0.602897 | + | 0.797819i | \(0.705987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.786462 | + | 1.36219i | −0.0612260 | + | 0.106047i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.94145 | 0.150234 | 0.0751168 | − | 0.997175i | \(-0.476067\pi\) | ||||
0.0751168 | + | 0.997175i | \(0.476067\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.19917 | −0.169167 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.61582 | − | 14.9230i | 0.658868 | − | 1.14119i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.21616 | − | 5.57054i | −0.244520 | − | 0.423521i | 0.717477 | − | 0.696582i | \(-0.245297\pi\) |
−0.961996 | + | 0.273062i | \(0.911964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.370390 | + | 0.0348840i | 0.0279989 | + | 0.00263698i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.51624 | − | 7.82235i | −0.339461 | − | 0.587964i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.79298 | + | 3.10553i | −0.134014 | + | 0.232119i | −0.925220 | − | 0.379430i | \(-0.876120\pi\) |
0.791207 | + | 0.611549i | \(0.209453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2134 | 0.907813 | 0.453906 | − | 0.891049i | \(-0.350030\pi\) | ||||
0.453906 | + | 0.891049i | \(0.350030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.26295 | −0.684737 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.12234 | − | 10.6042i | 0.450123 | − | 0.779637i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.745432 | − | 1.29113i | −0.0545114 | − | 0.0944165i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.31836 | − | 9.42356i | −0.314114 | − | 0.685463i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.05465 | + | 10.4870i | 0.438099 | + | 0.758810i | 0.997543 | − | 0.0700583i | \(-0.0223185\pi\) |
−0.559444 | + | 0.828868i | \(0.688985\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.96997 | − | 10.3403i | 0.429728 | − | 0.744311i | −0.567121 | − | 0.823635i | \(-0.691943\pi\) |
0.996849 | + | 0.0793237i | \(0.0252761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.16936 | −0.370185 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1626 | 0.866551 | 0.433275 | − | 0.901262i | \(-0.357358\pi\) | ||||
0.433275 | + | 0.901262i | \(0.357358\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.952451 | − | 1.64969i | 0.0675174 | − | 0.116944i | −0.830290 | − | 0.557331i | \(-0.811826\pi\) |
0.897808 | + | 0.440387i | \(0.145159\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.63148 | − | 2.82580i | −0.115076 | − | 0.199317i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.81836 | − | 3.96804i | −0.127624 | − | 0.278502i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3997 | + | 21.4769i | 0.866030 | + | 1.50001i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.08393 | + | 14.0018i | −0.561872 | + | 0.973191i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.91794 | 0.478524 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2447 | 1.11833 | 0.559165 | − | 0.829056i | \(-0.311122\pi\) | ||||
0.559165 | + | 0.829056i | \(0.311122\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.04103 | − | 6.99927i | 0.276887 | − | 0.479582i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.80660 | + | 10.0573i | 0.396007 | + | 0.685904i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.19078 | − | 0.583058i | −0.420258 | − | 0.0395806i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.05669 | + | 5.29434i | 0.206552 | + | 0.357758i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.44983 | − | 4.24324i | 0.164794 | − | 0.285431i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.03655 | −0.203342 | −0.101671 | − | 0.994818i | \(-0.532419\pi\) | ||||
−0.101671 | + | 0.994818i | \(0.532419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.350250 | 0.0233500 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.22454 | − | 15.9774i | 0.612254 | − | 1.06046i | −0.378605 | − | 0.925558i | \(-0.623596\pi\) |
0.990860 | − | 0.134897i | \(-0.0430705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7499 | + | 22.0835i | 0.842538 | + | 1.45932i | 0.887742 | + | 0.460341i | \(0.152273\pi\) |
−0.0452039 | + | 0.998978i | \(0.514394\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.09306 | − | 1.53921i | 0.0719184 | − | 0.101273i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.90880 | − | 3.30614i | −0.125050 | − | 0.216593i | 0.796703 | − | 0.604372i | \(-0.206576\pi\) |
−0.921752 | + | 0.387779i | \(0.873242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.64323 | − | 2.84616i | 0.107193 | − | 0.185663i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.30473 | −0.214666 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0037 | −0.841142 | −0.420571 | − | 0.907260i | \(-0.638170\pi\) | ||||
−0.420571 | + | 0.907260i | \(0.638170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.225292 | − | 0.390216i | 0.0145123 | − | 0.0251360i | −0.858678 | − | 0.512515i | \(-0.828714\pi\) |
0.873190 | + | 0.487379i | \(0.162047\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.54551 | − | 13.0692i | −0.484045 | − | 0.838391i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.1595 | + | 2.88104i | 0.968503 | + | 0.184063i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3678 | + | 19.6896i | 0.723314 | + | 1.25282i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.690780 | + | 1.19647i | −0.0437764 | + | 0.0758230i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.11861 | −0.0706058 | −0.0353029 | − | 0.999377i | \(-0.511240\pi\) | ||||
−0.0353029 | + | 0.999377i | \(0.511240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.49086 | −0.408077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17251 | + | 2.03084i | −0.0734253 | + | 0.127176i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4198 | + | 19.7797i | 0.712348 | + | 1.23382i | 0.963974 | + | 0.265998i | \(0.0857015\pi\) |
−0.251626 | + | 0.967825i | \(0.580965\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.50914 | + | 11.9822i | −0.528732 | + | 0.744539i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.05465 | − | 3.55876i | −0.127180 | − | 0.220282i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.59568 | + | 7.95995i | −0.283382 | + | 0.490832i | −0.972215 | − | 0.234088i | \(-0.924790\pi\) |
0.688834 | + | 0.724919i | \(0.258123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.671758 | 0.0412658 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.28646 | 0.139929 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.80660 | − | 13.5214i | 0.475977 | − | 0.824416i | −0.523644 | − | 0.851937i | \(-0.675428\pi\) |
0.999621 | + | 0.0275208i | \(0.00876123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8723 | + | 24.0275i | 0.842680 | + | 1.45956i | 0.887621 | + | 0.460574i | \(0.152357\pi\) |
−0.0449415 | + | 0.998990i | \(0.514310\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.17699 | + | 0.581759i | 0.373849 | + | 0.0352097i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0703069 | + | 0.121775i | 0.00423967 | + | 0.00734332i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.40619 | + | 12.8279i | −0.444995 | + | 0.770753i | −0.998052 | − | 0.0623900i | \(-0.980128\pi\) |
0.553057 | + | 0.833143i | \(0.313461\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.85415 | −0.350479 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.2227 | 0.908109 | 0.454054 | − | 0.890974i | \(-0.349977\pi\) | ||||
0.454054 | + | 0.890974i | \(0.349977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8586 | − | 18.8077i | 0.645479 | − | 1.11800i | −0.338712 | − | 0.940890i | \(-0.609991\pi\) |
0.984191 | − | 0.177112i | \(-0.0566755\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.44070 | − | 9.42356i | −0.322279 | − | 0.558204i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.3997 | − | 27.0587i | −0.731929 | − | 1.59722i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.38866 | + | 12.7975i | 0.434627 | + | 0.752796i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.663371 | + | 1.14899i | −0.0388875 | + | 0.0673551i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1276 | 0.650080 | 0.325040 | − | 0.945700i | \(-0.394622\pi\) | ||||
0.325040 | + | 0.945700i | \(0.394622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.9049 | 1.62469 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.95897 | − | 3.39304i | 0.113671 | − | 0.196884i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.6660 | − | 18.4740i | −0.616830 | − | 1.06838i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.80660 | − | 12.6712i | −0.334687 | − | 0.730358i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.15685 | − | 3.73578i | −0.123908 | − | 0.214615i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.3085 | − | 24.7830i | 0.819301 | − | 1.41907i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.9855 | −1.42600 | −0.712998 | − | 0.701166i | \(-0.752663\pi\) | ||||
−0.712998 | + | 0.701166i | \(0.752663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.759053 | 0.0431810 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.3704 | − | 30.0864i | 0.984984 | − | 1.70604i | 0.342979 | − | 0.939343i | \(-0.388564\pi\) |
0.642005 | − | 0.766700i | \(-0.278103\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.8547 | − | 20.5330i | −0.670069 | − | 1.16059i | −0.977884 | − | 0.209148i | \(-0.932931\pi\) |
0.307815 | − | 0.951446i | \(-0.400402\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.4635 | + | 1.36219i | 0.814923 | + | 0.0767508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.83850 | − | 17.0408i | −0.552585 | − | 0.957105i | −0.998087 | − | 0.0618244i | \(-0.980308\pi\) |
0.445502 | − | 0.895281i | \(-0.353025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.824875 | − | 1.42873i | 0.0461841 | − | 0.0799933i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.51811 | 0.252176 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3137 | 0.573870 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.231061 | + | 0.400209i | −0.0128170 | + | 0.0221996i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.00390 | + | 1.73881i | 0.0555159 | + | 0.0961564i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.28384 | + | 3.21602i | −0.125912 | + | 0.177305i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0949 | − | 24.4131i | −0.774728 | − | 1.34187i | −0.934947 | − | 0.354786i | \(-0.884554\pi\) |
0.160220 | − | 0.987081i | \(-0.448780\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.91794 | + | 11.9822i | −0.379101 | + | 0.656622i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0806 | 0.550760 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.7460 | 1.18458 | 0.592290 | − | 0.805725i | \(-0.298224\pi\) | ||||
0.592290 | + | 0.805725i | \(0.298224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.55017 | − | 7.88112i | 0.247131 | − | 0.428044i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17512 | − | 2.03538i | −0.0636366 | − | 0.110222i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7902 | − | 5.14868i | −0.960580 | − | 0.278003i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.10482 | + | 8.84180i | 0.274834 | + | 0.476027i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.97072 | + | 3.41339i | −0.105794 | + | 0.183241i | −0.914062 | − | 0.405574i | \(-0.867072\pi\) |
0.808268 | + | 0.588814i | \(0.200405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.1093 | −0.755254 | −0.377627 | − | 0.925958i | \(-0.623260\pi\) | ||||
−0.377627 | + | 0.925958i | \(0.623260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.8762 | 0.687279 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.48434 | − | 4.30301i | 0.132228 | − | 0.229026i | −0.792307 | − | 0.610123i | \(-0.791120\pi\) |
0.924535 | + | 0.381097i | \(0.124453\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4843 | + | 21.6235i | 0.662600 | + | 1.14766i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.62961 | − | 2.29475i | 0.0862481 | − | 0.121451i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.03580 | − | 3.52610i | −0.107445 | − | 0.186101i | 0.807289 | − | 0.590156i | \(-0.200934\pi\) |
−0.914735 | + | 0.404055i | \(0.867600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4289 | + | 24.9917i | −0.759418 | + | 1.31535i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.713538 | 0.0374510 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.8866 | −0.988571 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.01100 | + | 15.6075i | −0.470371 | + | 0.814706i | −0.999426 | − | 0.0338816i | \(-0.989213\pi\) |
0.529055 | + | 0.848587i | \(0.322546\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.0110 | − | 24.2678i | −0.729384 | − | 1.26333i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.802700 | − | 0.0755997i | −0.0416741 | − | 0.00392494i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.4582 | − | 25.0424i | −0.748618 | − | 1.29664i | −0.948485 | − | 0.316822i | \(-0.897384\pi\) |
0.199867 | − | 0.979823i | \(-0.435949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.04290 | − | 7.00250i | 0.208774 | − | 0.361608i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.42184 | 0.279239 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.30847 | −0.221311 | −0.110656 | − | 0.993859i | \(-0.535295\pi\) | ||||
−0.110656 | + | 0.993859i | \(0.535295\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.41591 | + | 7.64857i | −0.226234 | + | 0.391848i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.17438 | − | 10.6943i | −0.315496 | − | 0.546455i | 0.664047 | − | 0.747691i | \(-0.268837\pi\) |
−0.979543 | + | 0.201236i | \(0.935504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.42969 | + | 5.30210i | 0.123829 | + | 0.270220i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.56117 | − | 11.3643i | −0.333523 | − | 0.577679i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.7115 | + | 25.4811i | −0.745903 | + | 1.29194i | 0.203869 | + | 0.978998i | \(0.434648\pi\) |
−0.949772 | + | 0.312943i | \(0.898685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.67699 | −0.489387 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.541613 | −0.0273208 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.10482 | − | 8.84180i | 0.256851 | − | 0.444879i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.64975 | + | 14.9818i | 0.434119 | + | 0.751915i | 0.997223 | − | 0.0744702i | \(-0.0237266\pi\) |
−0.563105 | + | 0.826386i | \(0.690393\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.44070 | + | 11.8727i | 0.272376 | + | 0.594381i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4752 | + | 21.6077i | 0.622982 | + | 1.07904i | 0.988927 | + | 0.148400i | \(0.0474124\pi\) |
−0.365945 | + | 0.930636i | \(0.619254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.86200 | − | 6.68919i | 0.192380 | − | 0.333212i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.3100 | 0.512306 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.55465 | −0.275334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.2792 | − | 33.3925i | 0.953295 | − | 1.65115i | 0.215072 | − | 0.976598i | \(-0.431001\pi\) |
0.738223 | − | 0.674557i | \(-0.235665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.08393 | + | 3.60947i | 0.102793 | + | 0.178042i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.3443 | − | 3.14042i | −1.64076 | − | 0.154530i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.13409 | − | 3.69636i | −0.104759 | − | 0.181447i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.98825 | + | 3.44374i | −0.0973648 | + | 0.168641i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.908970 | −0.0444061 | −0.0222030 | − | 0.999753i | \(-0.507068\pi\) | ||||
−0.0222030 | + | 0.999753i | \(0.507068\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5532 | 0.758014 | 0.379007 | − | 0.925394i | \(-0.376266\pi\) | ||||
0.379007 | + | 0.925394i | \(0.376266\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.85677 | + | 3.21602i | −0.0902792 | + | 0.156368i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.104818 | + | 0.181550i | 0.00508442 | + | 0.00880647i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.8866 | + | 28.0035i | −0.962381 | + | 1.35519i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.17251 | + | 2.03084i | 0.0566092 | + | 0.0980500i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.76819 | − | 3.06259i | 0.0851707 | − | 0.147520i | −0.820293 | − | 0.571943i | \(-0.806190\pi\) |
0.905464 | + | 0.424423i | \(0.139523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6457 | 0.847997 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.59493 | −0.124417 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.4517 | − | 38.8875i | 1.07401 | − | 1.86024i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.51362 | + | 13.0140i | 0.358606 | + | 0.621123i | 0.987728 | − | 0.156183i | \(-0.0499190\pi\) |
−0.629123 | + | 0.777306i | \(0.716586\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.1294 | − | 3.25544i | −0.815688 | − | 0.155021i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.61134 | + | 11.4512i | 0.314114 | + | 0.544062i | 0.979249 | − | 0.202662i | \(-0.0649592\pi\) |
−0.665135 | + | 0.746723i | \(0.731626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.53189 | + | 6.11742i | −0.167428 | + | 0.289994i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.713538 | −0.0337492 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.90864 | −0.467617 | −0.233809 | − | 0.972283i | \(-0.575119\pi\) | ||||
−0.233809 | + | 0.972283i | \(0.575119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.62496 | − | 9.74271i | 0.264869 | − | 0.458766i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.29485 | + | 9.17095i | 0.248774 | + | 0.430889i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.0981 | + | 15.6279i | −0.520286 | + | 0.732646i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.17251 | − | 8.95905i | −0.241960 | − | 0.419087i | 0.719313 | − | 0.694686i | \(-0.244457\pi\) |
−0.961272 | + | 0.275600i | \(0.911124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.92056 | − | 5.05855i | 0.136320 | − | 0.236113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.3372 | −0.714325 | −0.357163 | − | 0.934042i | \(-0.616256\pi\) | ||||
−0.357163 | + | 0.934042i | \(0.616256\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.1313 | 1.16795 | 0.583976 | − | 0.811771i | \(-0.301496\pi\) | ||||
0.583976 | + | 0.811771i | \(0.301496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.84838 | + | 3.20149i | −0.0857167 | + | 0.148466i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.373007 | − | 0.646068i | −0.0172607 | − | 0.0298964i | 0.857266 | − | 0.514874i | \(-0.172161\pi\) |
−0.874527 | + | 0.484977i | \(0.838828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0455 | − | 1.13447i | −0.556210 | − | 0.0523848i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.27994 | − | 3.94898i | −0.105054 | − | 0.181959i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.63409 | − | 4.56239i | 0.121116 | − | 0.209779i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.972758 | −0.0446332 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.759053 | −0.0347546 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0565 | + | 17.4184i | −0.459494 | + | 0.795867i | −0.998934 | − | 0.0461569i | \(-0.985303\pi\) |
0.539440 | + | 0.842024i | \(0.318636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.12758 | − | 15.8094i | −0.416182 | − | 0.720848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.10482 | − | 11.1398i | −0.232277 | − | 0.506878i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.04942 | − | 3.54969i | −0.0930592 | − | 0.161183i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.12496 | + | 3.68054i | −0.0962911 | + | 0.166781i | −0.910147 | − | 0.414286i | \(-0.864031\pi\) |
0.813856 | + | 0.581067i | \(0.197365\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.09626 | −0.320904 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.3279 | −1.36868 | −0.684340 | − | 0.729163i | \(-0.739909\pi\) | ||||
−0.684340 | + | 0.729163i | \(0.739909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.22978 | − | 2.13003i | 0.0553863 | − | 0.0959320i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.74543 | + | 4.75523i | 0.123398 | + | 0.213732i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.4843 | − | 27.2435i | −0.559999 | − | 1.22204i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.22064 | + | 12.5065i | 0.323240 | + | 0.559869i | 0.981155 | − | 0.193224i | \(-0.0618945\pi\) |
−0.657914 | + | 0.753093i | \(0.728561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.692648 | + | 1.19970i | −0.0309452 | + | 0.0535987i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.95822 | 0.131901 | 0.0659503 | − | 0.997823i | \(-0.478992\pi\) | ||||
0.0659503 | + | 0.997823i | \(0.478992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3267 | 0.593032 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.784595 | − | 1.35896i | 0.0348451 | − | 0.0603534i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.4953 | + | 21.6426i | 0.553847 | + | 0.959290i | 0.997992 | + | 0.0633358i | \(0.0201739\pi\) |
−0.444146 | + | 0.895955i | \(0.646493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.5681 | + | 2.12550i | 0.998354 | + | 0.0940267i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.5520 | + | 23.4728i | 0.598337 | + | 1.03635i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.17251 | + | 2.03084i | −0.0516669 | + | 0.0894896i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49086 | −0.0655681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.58970 | 0.201465 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.4316 | + | 24.9962i | −0.632258 | + | 1.09510i | 0.354831 | + | 0.934931i | \(0.384538\pi\) |
−0.987089 | + | 0.160173i | \(0.948795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.236295 | + | 0.409276i | 0.0103325 | + | 0.0178964i | 0.871145 | − | 0.491025i | \(-0.163378\pi\) |
−0.860813 | + | 0.508921i | \(0.830044\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.153700 | + | 0.216434i | −0.00670802 | + | 0.00944596i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.75195 | − | 3.03447i | −0.0763162 | − | 0.132184i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.56566 | + | 16.5682i | −0.415898 | + | 0.720357i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.5311 | −1.36834 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.9724 | 1.60145 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.97911 | + | 12.0882i | −0.301733 | + | 0.522617i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.27936 | − | 2.21592i | −0.0552085 | − | 0.0956239i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.30660 | − | 6.60905i | −0.0993524 | − | 0.284672i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.72978 | − | 13.3884i | −0.332329 | − | 0.575611i | 0.650639 | − | 0.759387i | \(-0.274501\pi\) |
−0.982968 | + | 0.183776i | \(0.941168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.35735 | + | 7.54715i | −0.186992 | + | 0.323879i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.20290 | −0.265703 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.0440 | 1.49837 | 0.749187 | − | 0.662359i | \(-0.230444\pi\) | ||||
0.749187 | + | 0.662359i | \(0.230444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.1679 | + | 28.0035i | −0.690027 | + | 1.19516i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.70644 | + | 9.88384i | 0.243102 | + | 0.421066i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.09493 | + | 9.99080i | −0.301707 | + | 0.424852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.36852 | + | 7.56650i | 0.185433 | + | 0.321180i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.26632 | + | 9.12154i | −0.223141 | + | 0.386492i | −0.955760 | − | 0.294147i | \(-0.904964\pi\) |
0.732619 | + | 0.680639i | \(0.238298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.3137 | 0.732292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06379 | 0.0449132 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.3574 | + | 26.5997i | −0.647235 | + | 1.12104i | 0.336545 | + | 0.941667i | \(0.390742\pi\) |
−0.983780 | + | 0.179377i | \(0.942592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0573 | + | 24.3479i | 0.591394 | + | 1.02432i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.3196 | − | 1.16028i | −0.517376 | − | 0.0487274i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3860 | + | 26.6494i | 0.645017 | + | 1.11720i | 0.984298 | + | 0.176516i | \(0.0564829\pi\) |
−0.339281 | + | 0.940685i | \(0.610184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.75847 | + | 6.50986i | −0.157287 | + | 0.272429i | −0.933889 | − | 0.357562i | \(-0.883608\pi\) |
0.776602 | + | 0.629991i | \(0.216941\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.64045 | −0.360960 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.912705 | 0.0380624 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.8092 | + | 23.9183i | −0.574885 | + | 0.995731i | 0.421169 | + | 0.906982i | \(0.361620\pi\) |
−0.996054 | + | 0.0887483i | \(0.971713\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.25980 | + | 7.37819i | 0.177031 | + | 0.306627i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.13409 | + | 4.65704i | 0.0885372 | + | 0.193207i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.152367 | − | 0.263908i | −0.00631041 | − | 0.0109300i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.02276 | + | 15.6279i | −0.373045 | + | 0.646133i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.9582 | 1.23651 | 0.618254 | − | 0.785978i | \(-0.287840\pi\) | ||||
0.618254 | + | 0.785978i | \(0.287840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.2589 | 0.669936 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.33925 | + | 7.51579i | −0.178493 | + | 0.309158i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.33401 | − | 10.9708i | −0.260107 | − | 0.450518i | 0.706163 | − | 0.708049i | \(-0.250424\pi\) |
−0.966270 | + | 0.257531i | \(0.917091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.62234 | + | 7.90471i | 0.148502 | + | 0.324062i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.679610 | + | 1.17712i | 0.0278146 | + | 0.0481762i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.647133 | − | 1.12087i | 0.0264411 | − | 0.0457974i | −0.852502 | − | 0.522724i | \(-0.824916\pi\) |
0.878943 | + | 0.476926i | \(0.158249\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.0220 | −1.67332 | −0.836661 | − | 0.547721i | \(-0.815496\pi\) | ||||
−0.836661 | + | 0.547721i | \(0.815496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3905 | −0.463858 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.10220 | + | 1.90907i | −0.0448108 | + | 0.0776146i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5884 | − | 18.3397i | −0.429770 | − | 0.744384i | 0.567082 | − | 0.823661i | \(-0.308072\pi\) |
−0.996853 | + | 0.0792770i | \(0.974739\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.10075 | + | 0.292034i | 0.125649 | + | 0.0118338i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.44983 | − | 4.24324i | −0.0991096 | − | 0.171663i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.38156 | + | 5.85704i | −0.136580 | + | 0.236563i | −0.926200 | − | 0.377033i | \(-0.876944\pi\) |
0.789620 | + | 0.613596i | \(0.210278\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.6953 | −0.713542 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.0728 | −1.65353 | −0.826763 | − | 0.562550i | \(-0.809820\pi\) | ||||
−0.826763 | + | 0.562550i | \(0.809820\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2134 | + | 26.3503i | −0.611477 | + | 1.05911i | 0.379515 | + | 0.925186i | \(0.376091\pi\) |
−0.990992 | + | 0.133924i | \(0.957242\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7154 | − | 22.0237i | −0.510252 | − | 0.883782i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.90880 | − | 6.91238i | 0.196667 | − | 0.276939i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1386 | + | 21.0246i | 0.485543 | + | 0.840985i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.46811 | + | 4.27489i | −0.0985667 | + | 0.170722i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.28123 | −0.330194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.3670 | −0.492323 | −0.246162 | − | 0.969229i | \(-0.579169\pi\) | ||||
−0.246162 | + | 0.969229i | \(0.579169\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.79560 | + | 10.0383i | −0.230354 | + | 0.398985i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.6425 | − | 23.6295i | −0.541385 | − | 0.937707i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0201 | − | 17.4252i | 0.595120 | − | 0.690410i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.1067 | − | 24.4335i | −0.558052 | − | 0.966574i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5657 | − | 40.8169i | 0.930787 | − | 1.61217i | 0.148809 | − | 0.988866i | \(-0.452456\pi\) |
0.781979 | − | 0.623305i | \(-0.214211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.87242 | −0.0738412 | −0.0369206 | − | 0.999318i | \(-0.511755\pi\) | ||||
−0.0369206 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.28646 | −0.326279 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.917939 | + | 1.58992i | −0.0360879 | + | 0.0625061i | −0.883505 | − | 0.468421i | \(-0.844823\pi\) |
0.847417 | + | 0.530927i | \(0.178156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.32936 | − | 10.9628i | −0.248449 | − | 0.430326i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.56897 | − | 3.61753i | 0.100686 | − | 0.141782i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.08858 | + | 15.7419i | 0.355664 | + | 0.616027i | 0.987231 | − | 0.159293i | \(-0.0509216\pi\) |
−0.631568 | + | 0.775321i | \(0.717588\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.836629 | − | 1.44908i | 0.0326898 | − | 0.0566204i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.3409 | 0.832590 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8997 | 0.658318 | 0.329159 | − | 0.944275i | \(-0.393235\pi\) | ||||
0.329159 | + | 0.944275i | \(0.393235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6516 | − | 39.2338i | 0.881046 | − | 1.52602i | 0.0308661 | − | 0.999524i | \(-0.490173\pi\) |
0.850180 | − | 0.526493i | \(-0.176493\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.74805 | + | 3.02771i | 0.0678886 | + | 0.117587i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −40.1697 | − | 3.78325i | −1.55772 | − | 0.146708i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.35415 | − | 9.27366i | −0.207314 | − | 0.359078i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.08335 | − | 1.87641i | 0.0418845 | − | 0.0725462i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.9817 | −0.501154 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.5076 | 1.52291 | 0.761454 | − | 0.648219i | \(-0.224486\pi\) | ||||
0.761454 | + | 0.648219i | \(0.224486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.275458 | + | 0.477108i | −0.0106024 | + | 0.0183639i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.0669 | + | 29.5608i | 0.655936 | + | 1.13611i | 0.981658 | + | 0.190649i | \(0.0610591\pi\) |
−0.325723 | + | 0.945465i | \(0.605608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.04942 | + | 4.47226i | 0.0786494 | + | 0.171630i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.58206 | + | 11.4005i | 0.252225 | + | 0.436867i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.8931 | − | 20.5995i | 0.455079 | − | 0.788219i | −0.543614 | − | 0.839335i | \(-0.682944\pi\) |
0.998693 | + | 0.0511160i | \(0.0162778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.8762 | −0.491973 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.1951 | −0.694186 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.500750 | − | 0.867324i | 0.0190770 | − | 0.0330424i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.2812 | − | 17.8076i | −0.391116 | − | 0.677433i | 0.601481 | − | 0.798887i | \(-0.294578\pi\) |
−0.992597 | + | 0.121454i | \(0.961244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.74543 | − | 5.99111i | −0.104290 | − | 0.227584i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.14248 | − | 10.6391i | −0.232998 | − | 0.403564i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.38605 | − | 14.5251i | 0.317644 | − | 0.550176i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.72401 | 0.103031 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.9907 | −0.906116 | −0.453058 | − | 0.891481i | \(-0.649667\pi\) | ||||
−0.453058 | + | 0.891481i | \(0.649667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.2134 | − | 33.2785i | 0.724646 | − | 1.25512i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.17251 | + | 2.03084i | 0.0441592 | + | 0.0764860i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.9245 | − | 1.49979i | −0.598901 | − | 0.0564055i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8559 | + | 44.7836i | 0.971037 | + | 1.68189i | 0.692437 | + | 0.721478i | \(0.256537\pi\) |
0.278599 | + | 0.960407i | \(0.410130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.76819 | + | 9.99080i | −0.216324 | + | 0.374684i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.2552 | −0.571310 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.24468 | −0.270936 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.63933 | − | 8.03555i | 0.173259 | − | 0.300093i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.8926 | + | 22.3306i | 0.480812 | + | 0.832790i | 0.999758 | − | 0.0220170i | \(-0.00700879\pi\) |
−0.518946 | + | 0.854807i | \(0.673675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.62961 | − | 2.29475i | 0.0606898 | − | 0.0854610i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.160754 | + | 0.278434i | 0.00597851 | + | 0.0103551i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.115989 | + | 0.200899i | −0.00430772 | + | 0.00746118i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.7330 | −1.21400 | −0.606999 | − | 0.794702i | \(-0.707627\pi\) | ||||
−0.606999 | + | 0.794702i | \(0.707627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.26295 | −0.120850 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.92708 | − | 6.80189i | 0.145248 | − | 0.251577i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.64136 | + | 8.03908i | 0.171433 | + | 0.296930i | 0.938921 | − | 0.344133i | \(-0.111827\pi\) |
−0.767488 | + | 0.641063i | \(0.778494\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.18875 | + | 8.33981i | −0.265161 | + | 0.307618i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.28646 | − | 3.96027i | −0.0842229 | − | 0.145878i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0466 | + | 43.3820i | −0.921355 | + | 1.59583i | −0.124035 | + | 0.992278i | \(0.539583\pi\) |
−0.797320 | + | 0.603556i | \(0.793750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.2227 | −0.595955 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.1679 | −0.483082 | −0.241541 | − | 0.970391i | \(-0.577653\pi\) | ||||
−0.241541 | + | 0.970391i | \(0.577653\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.10220 | − | 1.90907i | 0.0403815 | − | 0.0699428i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.41142 | + | 4.17670i | 0.0882293 | + | 0.152818i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.69992 | − | 13.6590i | 0.354427 | − | 0.499090i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.6569 | + | 35.7787i | 0.753779 | + | 1.30558i | 0.945979 | + | 0.324228i | \(0.105105\pi\) |
−0.192200 | + | 0.981356i | \(0.561562\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.399084 | − | 0.691234i | 0.0145434 | − | 0.0251900i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.7158 | −1.19065 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.5114 | −1.65414 | −0.827069 | − | 0.562100i | \(-0.809994\pi\) | ||||
−0.827069 | + | 0.562100i | \(0.809994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.31574 | − | 4.01098i | 0.0840560 | − | 0.145589i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.6360 | − | 27.0823i | −0.566803 | − | 0.981732i | −0.996879 | − | 0.0789393i | \(-0.974847\pi\) |
0.430076 | − | 0.902793i | \(-0.358487\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.41200 | + | 0.698075i | 0.268333 | + | 0.0252720i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.09306 | + | 7.08940i | 0.147985 | + | 0.256318i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.8012 | − | 36.0287i | 0.751088 | − | 1.30092i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0467 | 1.51624 | 0.758121 | − | 0.652114i | \(-0.226118\pi\) | ||||
0.758121 | + | 0.652114i | \(0.226118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.2969 | −0.586920 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.82226 | + | 6.62034i | −0.137477 | + | 0.238117i | −0.926541 | − | 0.376194i | \(-0.877233\pi\) |
0.789064 | + | 0.614311i | \(0.210566\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.165239 | + | 0.286202i | 0.00593555 | + | 0.0102807i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.36852 | − | 9.53304i | −0.156720 | − | 0.341996i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.9131 | + | 67.3995i | 1.39421 | + | 2.41484i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.66337 | − | 9.80925i | 0.202651 | − | 0.351002i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.46362 | 0.230991 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0873 | 0.502797 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.9517 | + | 24.1651i | −0.497324 | + | 0.861391i | −0.999995 | − | 0.00308674i | \(-0.999017\pi\) |
0.502671 | + | 0.864478i | \(0.332351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.27919 | − | 5.67973i | −0.116742 | − | 0.202204i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0573 | − | 30.6759i | −0.499819 | − | 1.09071i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.3320 | − | 36.9481i | −0.757521 | − | 1.31206i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.239662 | + | 0.415107i | −0.00849995 | + | 0.0147223i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0560 | 0.356201 | 0.178101 | − | 0.984012i | \(-0.443005\pi\) | ||||
0.178101 | + | 0.984012i | \(0.443005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.22267 | −0.0786326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.99086 | − | 6.91238i | 0.141010 | − | 0.244237i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.28384 | + | 7.41984i | 0.151174 | + | 0.261840i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 37.6899 | + | 3.54969i | 1.32839 | + | 0.125110i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.57031 | + | 9.64805i | 0.196084 | + | 0.339628i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.2863 | + | 33.4048i | −0.678070 | + | 1.17445i | 0.297491 | + | 0.954725i | \(0.403850\pi\) |
−0.975561 | + | 0.219727i | \(0.929483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.3760 | −0.434580 | −0.217290 | − | 0.976107i | \(-0.569722\pi\) | ||||
−0.217290 | + | 0.976107i | \(0.569722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.7968 | −0.694303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.9616 | − | 18.9860i | 0.383968 | − | 0.665051i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.2225 | + | 31.5623i | 0.637525 | + | 1.10423i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.5403 | − | 17.6587i | 0.438193 | − | 0.617046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.8691 | − | 25.7540i | −0.518934 | − | 0.898820i | −0.999758 | − | 0.0220025i | \(-0.992996\pi\) |
0.480824 | − | 0.876817i | \(-0.340338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.3885 | − | 35.3139i | 0.710698 | − | 1.23097i | −0.253897 | − | 0.967231i | \(-0.581712\pi\) |
0.964595 | − | 0.263734i | \(-0.0849542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.100333 | −0.00349316 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.8411 | 0.655170 | 0.327585 | − | 0.944822i | \(-0.393765\pi\) | ||||
0.327585 | + | 0.944822i | \(0.393765\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.5703 | − | 26.9686i | 0.540779 | − | 0.936657i | −0.458080 | − | 0.888911i | \(-0.651463\pi\) |
0.998860 | − | 0.0477461i | \(-0.0152038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.28459 | − | 9.15319i | −0.183321 | − | 0.317521i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.43883 | − | 9.85320i | −0.119148 | − | 0.341393i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.13986 | − | 3.70635i | −0.0740530 | − | 0.128264i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.60407 | − | 7.97448i | 0.159140 | − | 0.275638i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2589 | −0.354176 | −0.177088 | − | 0.984195i | \(-0.556668\pi\) | ||||
−0.177088 | + | 0.984195i | \(0.556668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2783 | −0.906149 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.43098 | + | 9.40673i | −0.187053 | + | 0.323985i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.42392 | + | 4.19836i | 0.0833855 | + | 0.144428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.53189 | − | 2.15715i | 0.0526365 | − | 0.0741206i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.74805 | + | 13.4200i | 0.265912 | + | 0.460574i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.0272 | + | 31.2241i | −0.617966 | + | 1.07035i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.04435 | 0.104237 | 0.0521183 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521183 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −37.9855 | −1.29908 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.7766 | + | 42.9143i | −0.846352 | + | 1.46592i | 0.0380904 | + | 0.999274i | \(0.487873\pi\) |
−0.884442 | + | 0.466650i | \(0.845461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4373 | + | 31.9344i | 0.629074 | + | 1.08959i | 0.987738 | + | 0.156121i | \(0.0498989\pi\) |
−0.358664 | + | 0.933467i | \(0.616768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.1445 | + | 1.99143i | 0.720603 | + | 0.0678676i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.2115 | − | 40.2035i | −0.790129 | − | 1.36854i | −0.925887 | − | 0.377801i | \(-0.876680\pi\) |
0.135758 | − | 0.990742i | \(-0.456653\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.08970 | + | 12.2797i | −0.241057 | + | 0.417523i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.5442 | −0.358099 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.63148 | −0.157112 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.51437 | − | 13.0153i | 0.254615 | − | 0.441006i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.31574 | + | 4.01098i | 0.0783759 | + | 0.135751i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.4901 | − | 27.2561i | −0.422243 | − | 0.921423i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5155 | − | 33.8018i | −0.658991 | − | 1.14141i | −0.980877 | − | 0.194628i | \(-0.937650\pi\) |
0.321886 | − | 0.946778i | \(-0.395683\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.96997 | + | 6.87620i | −0.133904 | + | 0.231928i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.0049 | −1.48256 | −0.741281 | − | 0.671194i | \(-0.765782\pi\) | ||||
−0.741281 | + | 0.671194i | \(0.765782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.3596 | 0.786112 | 0.393056 | − | 0.919515i | \(-0.371418\pi\) | ||||
0.393056 | + | 0.919515i | \(0.371418\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.95560 | + | 17.2436i | −0.334654 | + | 0.579638i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.9588 | + | 36.3017i | 0.703728 | + | 1.21889i | 0.967149 | + | 0.254211i | \(0.0818158\pi\) |
−0.263421 | + | 0.964681i | \(0.584851\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6425 | + | 29.7708i | 0.457554 | + | 0.998480i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.33850 | − | 4.05039i | −0.0783426 | − | 0.135693i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.15685 | − | 8.93193i | 0.172567 | − | 0.298896i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.90490 | 0.264232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.2212 | 0.508220 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.93866 | − | 3.35786i | 0.0646580 | − | 0.111991i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.227159 | − | 0.393451i | −0.00756776 | − | 0.0131078i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.90170 | + | 0.932559i | 0.329508 | + | 0.0310336i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.4616 | − | 23.3162i | −0.447478 | − | 0.775055i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2591 | + | 17.7692i | −0.340646 | + | 0.590017i | −0.984553 | − | 0.175087i | \(-0.943979\pi\) |
0.643907 | + | 0.765104i | \(0.277313\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.0586 | −0.499461 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6755 | −0.916930 | −0.458465 | − | 0.888712i | \(-0.651601\pi\) | ||||
−0.458465 | + | 0.888712i | \(0.651601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.968106 | + | 1.67681i | −0.0320396 | + | 0.0554943i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.2096 | + | 17.6836i | 0.337520 | + | 0.584602i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.16279 | + | 1.63739i | −0.0383987 | + | 0.0540714i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.481727 | + | 0.834376i | 0.0158907 | + | 0.0275235i | 0.873861 | − | 0.486175i | \(-0.161608\pi\) |
−0.857971 | + | 0.513699i | \(0.828275\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.91404 | − | 15.4396i | 0.293728 | − | 0.508751i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.2249 | 1.22527 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.781061 | 0.0256811 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.32488 | − | 2.29475i | 0.0435146 | − | 0.0753695i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.1660 | − | 22.8042i | −0.431962 | − | 0.748180i | 0.565080 | − | 0.825036i | \(-0.308845\pi\) |
−0.997042 | + | 0.0768558i | \(0.975512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.5740 | + | 9.04140i | 1.55918 | + | 0.296320i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.3944 | + | 21.4678i | 0.405775 | + | 0.702824i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.64323 | + | 2.84616i | −0.0537394 | + | 0.0930794i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.3865 | −0.698665 | −0.349333 | − | 0.936999i | \(-0.613592\pi\) | ||||
−0.349333 | + | 0.936999i | \(0.613592\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.9176 | 0.552085 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.41142 | + | 12.8370i | −0.241605 | + | 0.418473i | −0.961172 | − | 0.275951i | \(-0.911007\pi\) |
0.719566 | + | 0.694424i | \(0.244341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.5108 | − | 63.2386i | −1.18896 | − | 2.05933i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.2305 | + | 18.6307i | −0.430389 | + | 0.606056i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.8560 | + | 27.4634i | 0.515251 | + | 0.892442i | 0.999843 | + | 0.0177013i | \(0.00563478\pi\) |
−0.484592 | + | 0.874740i | \(0.661032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.0787 | + | 24.3850i | −0.457014 | + | 0.791571i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.0403 | 0.455287 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.9620 | 1.61843 | 0.809213 | − | 0.587515i | \(-0.199894\pi\) | ||||
0.809213 | + | 0.587515i | \(0.199894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3469 | − | 23.1175i | 0.431895 | − | 0.748064i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.588580 | + | 1.01945i | 0.0190261 | + | 0.0329541i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.3860 | + | 1.44908i | 0.496841 | + | 0.0467933i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7382 | + | 22.0631i | 0.410908 | + | 0.711714i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.88605 | − | 13.6590i | 0.254124 | − | 0.440156i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.3204 | −0.847285 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.4581 | 1.68694 | 0.843469 | − | 0.537178i | \(-0.180510\pi\) | ||||
0.843469 | + | 0.537178i | \(0.180510\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.67961 | + | 6.37327i | −0.118206 | + | 0.204739i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.4133 | + | 26.6966i | 0.494636 | + | 0.856735i | 0.999981 | − | 0.00618284i | \(-0.00196807\pi\) |
−0.505345 | + | 0.862917i | \(0.668635\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.14248 | + | 13.4042i | 0.196919 | + | 0.429719i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.164871 | − | 0.285565i | −0.00528009 | − | 0.00914538i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.3678 | + | 21.4216i | −0.395680 | + | 0.685338i | −0.993188 | − | 0.116525i | \(-0.962824\pi\) |
0.597508 | + | 0.801863i | \(0.296158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.20440 | 0.102413 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.00897 | 0.223779 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.11192 | − | 10.5862i | 0.194940 | − | 0.337646i | −0.751941 | − | 0.659231i | \(-0.770882\pi\) |
0.946881 | + | 0.321585i | \(0.104215\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.4057 | − | 23.2193i | −0.427140 | − | 0.739827i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.17251 | − | 2.55866i | −0.0373213 | − | 0.0814430i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.0975 | − | 29.6138i | −0.543670 | − | 0.941665i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.30008 | − | 3.98386i | 0.0730645 | − | 0.126552i | −0.827178 | − | 0.561939i | \(-0.810055\pi\) |
0.900243 | + | 0.435388i | \(0.143389\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.1145 | 0.638316 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.19917 | −0.133123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.2382 | − | 29.8574i | 0.545938 | − | 0.945593i | −0.452609 | − | 0.891709i | \(-0.649507\pi\) |
0.998547 | − | 0.0538835i | \(-0.0171600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8814 | − | 18.8471i | −0.344272 | − | 0.596297i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))