Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(209,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.g (of order \(2\), degree \(1\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.3 | ||
Root | \(1.64187 + 0.551597i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.209 |
Dual form | 546.2.g.c.209.9 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −0.551597 | − | 1.64187i | −0.318465 | − | 0.947935i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.124244 | 0.0555638 | 0.0277819 | − | 0.999614i | \(-0.491156\pi\) | ||||
0.0277819 | + | 0.999614i | \(0.491156\pi\) | |||||||
\(6\) | −1.64187 | + | 0.551597i | −0.670291 | + | 0.225188i | ||||
\(7\) | 1.46370 | − | 2.20399i | 0.553226 | − | 0.833031i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.39148 | + | 1.81130i | −0.797161 | + | 0.603767i | ||||
\(10\) | − | 0.124244i | − | 0.0392895i | ||||||
\(11\) | − | 3.15950i | − | 0.952624i | −0.879276 | − | 0.476312i | \(-0.841973\pi\) | ||
0.879276 | − | 0.476312i | \(-0.158027\pi\) | |||||||
\(12\) | 0.551597 | + | 1.64187i | 0.159232 | + | 0.473967i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | −2.20399 | − | 1.46370i | −0.589042 | − | 0.391190i | ||||
\(15\) | −0.0685329 | − | 0.203993i | −0.0176951 | − | 0.0526709i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.18986 | −1.25873 | −0.629364 | − | 0.777111i | \(-0.716684\pi\) | ||||
−0.629364 | + | 0.777111i | \(0.716684\pi\) | |||||||
\(18\) | 1.81130 | + | 2.39148i | 0.426928 | + | 0.563678i | ||||
\(19\) | − | 7.80424i | − | 1.79042i | −0.445649 | − | 0.895208i | \(-0.647027\pi\) | ||
0.445649 | − | 0.895208i | \(-0.352973\pi\) | |||||||
\(20\) | −0.124244 | −0.0277819 | ||||||||
\(21\) | −4.42604 | − | 1.18749i | −0.965842 | − | 0.259131i | ||||
\(22\) | −3.15950 | −0.673607 | ||||||||
\(23\) | 8.49945i | 1.77226i | 0.463440 | + | 0.886128i | \(0.346615\pi\) | ||||
−0.463440 | + | 0.886128i | \(0.653385\pi\) | |||||||
\(24\) | 1.64187 | − | 0.551597i | 0.335146 | − | 0.112594i | ||||
\(25\) | −4.98456 | −0.996913 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 4.29306 | + | 2.92740i | 0.826199 | + | 0.563378i | ||||
\(28\) | −1.46370 | + | 2.20399i | −0.276613 | + | 0.416516i | ||||
\(29\) | 0.988265i | 0.183516i | 0.995781 | + | 0.0917581i | \(0.0292487\pi\) | ||||
−0.995781 | + | 0.0917581i | \(0.970751\pi\) | |||||||
\(30\) | −0.203993 | + | 0.0685329i | −0.0372439 | + | 0.0125123i | ||||
\(31\) | 2.03612i | 0.365697i | 0.983141 | + | 0.182849i | \(0.0585318\pi\) | ||||
−0.983141 | + | 0.182849i | \(0.941468\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −5.18749 | + | 1.74277i | −0.903026 | + | 0.303377i | ||||
\(34\) | 5.18986i | 0.890054i | ||||||||
\(35\) | 0.181856 | − | 0.273834i | 0.0307393 | − | 0.0462864i | ||||
\(36\) | 2.39148 | − | 1.81130i | 0.398580 | − | 0.301884i | ||||
\(37\) | 4.99544 | 0.821245 | 0.410622 | − | 0.911806i | \(-0.365311\pi\) | ||||
0.410622 | + | 0.911806i | \(0.365311\pi\) | |||||||
\(38\) | −7.80424 | −1.26601 | ||||||||
\(39\) | −1.64187 | + | 0.551597i | −0.262910 | + | 0.0883262i | ||||
\(40\) | 0.124244i | 0.0196448i | ||||||||
\(41\) | 0.374977 | 0.0585616 | 0.0292808 | − | 0.999571i | \(-0.490678\pi\) | ||||
0.0292808 | + | 0.999571i | \(0.490678\pi\) | |||||||
\(42\) | −1.18749 | + | 4.42604i | −0.183233 | + | 0.682954i | ||||
\(43\) | 0.643654 | 0.0981564 | 0.0490782 | − | 0.998795i | \(-0.484372\pi\) | ||||
0.0490782 | + | 0.998795i | \(0.484372\pi\) | |||||||
\(44\) | 3.15950i | 0.476312i | ||||||||
\(45\) | −0.297128 | + | 0.225044i | −0.0442933 | + | 0.0335476i | ||||
\(46\) | 8.49945 | 1.25317 | ||||||||
\(47\) | −0.322562 | −0.0470506 | −0.0235253 | − | 0.999723i | \(-0.507489\pi\) | ||||
−0.0235253 | + | 0.999723i | \(0.507489\pi\) | |||||||
\(48\) | −0.551597 | − | 1.64187i | −0.0796161 | − | 0.236984i | ||||
\(49\) | −2.71517 | − | 6.45196i | −0.387882 | − | 0.921709i | ||||
\(50\) | 4.98456i | 0.704924i | ||||||||
\(51\) | 2.86271 | + | 8.52109i | 0.400860 | + | 1.19319i | ||||
\(52\) | 1.00000i | 0.138675i | ||||||||
\(53\) | − | 11.3835i | − | 1.56364i | −0.623505 | − | 0.781819i | \(-0.714292\pi\) | ||
0.623505 | − | 0.781819i | \(-0.285708\pi\) | |||||||
\(54\) | 2.92740 | − | 4.29306i | 0.398368 | − | 0.584211i | ||||
\(55\) | − | 0.392550i | − | 0.0529314i | ||||||
\(56\) | 2.20399 | + | 1.46370i | 0.294521 | + | 0.195595i | ||||
\(57\) | −12.8136 | + | 4.30479i | −1.69720 | + | 0.570184i | ||||
\(58\) | 0.988265 | 0.129766 | ||||||||
\(59\) | −6.22502 | −0.810428 | −0.405214 | − | 0.914222i | \(-0.632803\pi\) | ||||
−0.405214 | + | 0.914222i | \(0.632803\pi\) | |||||||
\(60\) | 0.0685329 | + | 0.203993i | 0.00884755 | + | 0.0263354i | ||||
\(61\) | 9.38452i | 1.20156i | 0.799413 | + | 0.600782i | \(0.205144\pi\) | ||||
−0.799413 | + | 0.600782i | \(0.794856\pi\) | |||||||
\(62\) | 2.03612 | 0.258587 | ||||||||
\(63\) | 0.491689 | + | 7.92201i | 0.0619470 | + | 0.998079i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 0.124244i | − | 0.0154106i | ||||||
\(66\) | 1.74277 | + | 5.18749i | 0.214520 | + | 0.638536i | ||||
\(67\) | 11.0585 | 1.35101 | 0.675504 | − | 0.737356i | \(-0.263926\pi\) | ||||
0.675504 | + | 0.737356i | \(0.263926\pi\) | |||||||
\(68\) | 5.18986 | 0.629364 | ||||||||
\(69\) | 13.9550 | − | 4.68827i | 1.67998 | − | 0.564401i | ||||
\(70\) | −0.273834 | − | 0.181856i | −0.0327294 | − | 0.0217360i | ||||
\(71\) | − | 10.1781i | − | 1.20792i | −0.797014 | − | 0.603961i | \(-0.793588\pi\) | ||
0.797014 | − | 0.603961i | \(-0.206412\pi\) | |||||||
\(72\) | −1.81130 | − | 2.39148i | −0.213464 | − | 0.281839i | ||||
\(73\) | − | 10.3117i | − | 1.20689i | −0.797404 | − | 0.603446i | \(-0.793794\pi\) | ||
0.797404 | − | 0.603446i | \(-0.206206\pi\) | |||||||
\(74\) | − | 4.99544i | − | 0.580708i | ||||||
\(75\) | 2.74947 | + | 8.18401i | 0.317481 | + | 0.945008i | ||||
\(76\) | 7.80424i | 0.895208i | ||||||||
\(77\) | −6.96351 | − | 4.62455i | −0.793566 | − | 0.527017i | ||||
\(78\) | 0.551597 | + | 1.64187i | 0.0624560 | + | 0.185905i | ||||
\(79\) | 0.149958 | 0.0168716 | 0.00843581 | − | 0.999964i | \(-0.497315\pi\) | ||||
0.00843581 | + | 0.999964i | \(0.497315\pi\) | |||||||
\(80\) | 0.124244 | 0.0138910 | ||||||||
\(81\) | 2.43837 | − | 8.66339i | 0.270930 | − | 0.962599i | ||||
\(82\) | − | 0.374977i | − | 0.0414093i | ||||||
\(83\) | −7.17707 | −0.787786 | −0.393893 | − | 0.919156i | \(-0.628872\pi\) | ||||
−0.393893 | + | 0.919156i | \(0.628872\pi\) | |||||||
\(84\) | 4.42604 | + | 1.18749i | 0.482921 | + | 0.129566i | ||||
\(85\) | −0.644812 | −0.0699397 | ||||||||
\(86\) | − | 0.643654i | − | 0.0694070i | ||||||
\(87\) | 1.62260 | − | 0.545124i | 0.173961 | − | 0.0584434i | ||||
\(88\) | 3.15950 | 0.336804 | ||||||||
\(89\) | 6.93771 | 0.735396 | 0.367698 | − | 0.929945i | \(-0.380146\pi\) | ||||
0.367698 | + | 0.929945i | \(0.380146\pi\) | |||||||
\(90\) | 0.225044 | + | 0.297128i | 0.0237217 | + | 0.0313201i | ||||
\(91\) | −2.20399 | − | 1.46370i | −0.231041 | − | 0.153437i | ||||
\(92\) | − | 8.49945i | − | 0.886128i | ||||||
\(93\) | 3.34304 | − | 1.12311i | 0.346657 | − | 0.116462i | ||||
\(94\) | 0.322562i | 0.0332698i | ||||||||
\(95\) | − | 0.969633i | − | 0.0994823i | ||||||
\(96\) | −1.64187 | + | 0.551597i | −0.167573 | + | 0.0562971i | ||||
\(97\) | 4.53137i | 0.460091i | 0.973180 | + | 0.230045i | \(0.0738875\pi\) | ||||
−0.973180 | + | 0.230045i | \(0.926113\pi\) | |||||||
\(98\) | −6.45196 | + | 2.71517i | −0.651747 | + | 0.274274i | ||||
\(99\) | 5.72280 | + | 7.55588i | 0.575163 | + | 0.759395i | ||||
\(100\) | 4.98456 | 0.498456 | ||||||||
\(101\) | 14.8286 | 1.47550 | 0.737751 | − | 0.675073i | \(-0.235888\pi\) | ||||
0.737751 | + | 0.675073i | \(0.235888\pi\) | |||||||
\(102\) | 8.52109 | − | 2.86271i | 0.843714 | − | 0.283451i | ||||
\(103\) | − | 0.578134i | − | 0.0569652i | −0.999594 | − | 0.0284826i | \(-0.990932\pi\) | ||
0.999594 | − | 0.0284826i | \(-0.00906752\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −0.549912 | − | 0.147539i | −0.0536659 | − | 0.0143983i | ||||
\(106\) | −11.3835 | −1.10566 | ||||||||
\(107\) | − | 18.6047i | − | 1.79859i | −0.437344 | − | 0.899294i | \(-0.644081\pi\) | ||
0.437344 | − | 0.899294i | \(-0.355919\pi\) | |||||||
\(108\) | −4.29306 | − | 2.92740i | −0.413100 | − | 0.281689i | ||||
\(109\) | −4.91894 | −0.471149 | −0.235575 | − | 0.971856i | \(-0.575697\pi\) | ||||
−0.235575 | + | 0.971856i | \(0.575697\pi\) | |||||||
\(110\) | −0.392550 | −0.0374282 | ||||||||
\(111\) | −2.75547 | − | 8.20186i | −0.261537 | − | 0.778486i | ||||
\(112\) | 1.46370 | − | 2.20399i | 0.138307 | − | 0.208258i | ||||
\(113\) | − | 13.6446i | − | 1.28358i | −0.766882 | − | 0.641788i | \(-0.778193\pi\) | ||
0.766882 | − | 0.641788i | \(-0.221807\pi\) | |||||||
\(114\) | 4.30479 | + | 12.8136i | 0.403181 | + | 1.20010i | ||||
\(115\) | 1.05601i | 0.0984734i | ||||||||
\(116\) | − | 0.988265i | − | 0.0917581i | ||||||
\(117\) | 1.81130 | + | 2.39148i | 0.167455 | + | 0.221093i | ||||
\(118\) | 6.22502i | 0.573059i | ||||||||
\(119\) | −7.59640 | + | 11.4384i | −0.696361 | + | 1.04856i | ||||
\(120\) | 0.203993 | − | 0.0685329i | 0.0186220 | − | 0.00625616i | ||||
\(121\) | 1.01757 | 0.0925066 | ||||||||
\(122\) | 9.38452 | 0.849634 | ||||||||
\(123\) | −0.206836 | − | 0.615664i | −0.0186498 | − | 0.0555125i | ||||
\(124\) | − | 2.03612i | − | 0.182849i | ||||||
\(125\) | −1.24053 | −0.110956 | ||||||||
\(126\) | 7.92201 | − | 0.491689i | 0.705749 | − | 0.0438031i | ||||
\(127\) | 6.96593 | 0.618126 | 0.309063 | − | 0.951041i | \(-0.399985\pi\) | ||||
0.309063 | + | 0.951041i | \(0.399985\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −0.355038 | − | 1.05680i | −0.0312593 | − | 0.0930459i | ||||
\(130\) | −0.124244 | −0.0108970 | ||||||||
\(131\) | 10.5712 | 0.923606 | 0.461803 | − | 0.886983i | \(-0.347203\pi\) | ||||
0.461803 | + | 0.886983i | \(0.347203\pi\) | |||||||
\(132\) | 5.18749 | − | 1.74277i | 0.451513 | − | 0.151689i | ||||
\(133\) | −17.2005 | − | 11.4231i | −1.49147 | − | 0.990504i | ||||
\(134\) | − | 11.0585i | − | 0.955307i | ||||||
\(135\) | 0.533389 | + | 0.363713i | 0.0459068 | + | 0.0313034i | ||||
\(136\) | − | 5.18986i | − | 0.445027i | ||||||
\(137\) | − | 22.1462i | − | 1.89208i | −0.324049 | − | 0.946040i | \(-0.605044\pi\) | ||
0.324049 | − | 0.946040i | \(-0.394956\pi\) | |||||||
\(138\) | −4.68827 | − | 13.9550i | −0.399092 | − | 1.18793i | ||||
\(139\) | 11.7008i | 0.992451i | 0.868194 | + | 0.496225i | \(0.165281\pi\) | ||||
−0.868194 | + | 0.496225i | \(0.834719\pi\) | |||||||
\(140\) | −0.181856 | + | 0.273834i | −0.0153697 | + | 0.0231432i | ||||
\(141\) | 0.177924 | + | 0.529606i | 0.0149839 | + | 0.0446009i | ||||
\(142\) | −10.1781 | −0.854130 | ||||||||
\(143\) | −3.15950 | −0.264210 | ||||||||
\(144\) | −2.39148 | + | 1.81130i | −0.199290 | + | 0.150942i | ||||
\(145\) | 0.122786i | 0.0101969i | ||||||||
\(146\) | −10.3117 | −0.853402 | ||||||||
\(147\) | −9.09561 | + | 8.01685i | −0.750193 | + | 0.661218i | ||||
\(148\) | −4.99544 | −0.410622 | ||||||||
\(149\) | 24.2302i | 1.98502i | 0.122176 | + | 0.992508i | \(0.461013\pi\) | ||||
−0.122176 | + | 0.992508i | \(0.538987\pi\) | |||||||
\(150\) | 8.18401 | − | 2.74947i | 0.668222 | − | 0.224493i | ||||
\(151\) | 15.4209 | 1.25493 | 0.627466 | − | 0.778644i | \(-0.284092\pi\) | ||||
0.627466 | + | 0.778644i | \(0.284092\pi\) | |||||||
\(152\) | 7.80424 | 0.633007 | ||||||||
\(153\) | 12.4115 | − | 9.40041i | 1.00341 | − | 0.759978i | ||||
\(154\) | −4.62455 | + | 6.96351i | −0.372657 | + | 0.561136i | ||||
\(155\) | 0.252976i | 0.0203195i | ||||||||
\(156\) | 1.64187 | − | 0.551597i | 0.131455 | − | 0.0441631i | ||||
\(157\) | − | 15.5649i | − | 1.24221i | −0.783727 | − | 0.621106i | \(-0.786684\pi\) | ||
0.783727 | − | 0.621106i | \(-0.213316\pi\) | |||||||
\(158\) | − | 0.149958i | − | 0.0119300i | ||||||
\(159\) | −18.6902 | + | 6.27908i | −1.48223 | + | 0.497963i | ||||
\(160\) | − | 0.124244i | − | 0.00982239i | ||||||
\(161\) | 18.7327 | + | 12.4406i | 1.47635 | + | 0.980459i | ||||
\(162\) | −8.66339 | − | 2.43837i | −0.680660 | − | 0.191577i | ||||
\(163\) | 6.45488 | 0.505585 | 0.252792 | − | 0.967521i | \(-0.418651\pi\) | ||||
0.252792 | + | 0.967521i | \(0.418651\pi\) | |||||||
\(164\) | −0.374977 | −0.0292808 | ||||||||
\(165\) | −0.644517 | + | 0.216529i | −0.0501756 | + | 0.0168568i | ||||
\(166\) | 7.17707i | 0.557049i | ||||||||
\(167\) | 22.4303 | 1.73571 | 0.867853 | − | 0.496821i | \(-0.165500\pi\) | ||||
0.867853 | + | 0.496821i | \(0.165500\pi\) | |||||||
\(168\) | 1.18749 | − | 4.42604i | 0.0916167 | − | 0.341477i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0.644812i | 0.0494548i | ||||||||
\(171\) | 14.1358 | + | 18.6637i | 1.08099 | + | 1.42725i | ||||
\(172\) | −0.643654 | −0.0490782 | ||||||||
\(173\) | −11.0835 | −0.842666 | −0.421333 | − | 0.906906i | \(-0.638438\pi\) | ||||
−0.421333 | + | 0.906906i | \(0.638438\pi\) | |||||||
\(174\) | −0.545124 | − | 1.62260i | −0.0413257 | − | 0.123009i | ||||
\(175\) | −7.29590 | + | 10.9859i | −0.551518 | + | 0.830459i | ||||
\(176\) | − | 3.15950i | − | 0.238156i | ||||||
\(177\) | 3.43370 | + | 10.2207i | 0.258093 | + | 0.768233i | ||||
\(178\) | − | 6.93771i | − | 0.520003i | ||||||
\(179\) | 0.910490i | 0.0680532i | 0.999421 | + | 0.0340266i | \(0.0108331\pi\) | ||||
−0.999421 | + | 0.0340266i | \(0.989167\pi\) | |||||||
\(180\) | 0.297128 | − | 0.225044i | 0.0221466 | − | 0.0167738i | ||||
\(181\) | 3.83313i | 0.284915i | 0.989801 | + | 0.142457i | \(0.0455004\pi\) | ||||
−0.989801 | + | 0.142457i | \(0.954500\pi\) | |||||||
\(182\) | −1.46370 | + | 2.20399i | −0.108497 | + | 0.163371i | ||||
\(183\) | 15.4082 | − | 5.17647i | 1.13900 | − | 0.382656i | ||||
\(184\) | −8.49945 | −0.626587 | ||||||||
\(185\) | 0.620655 | 0.0456315 | ||||||||
\(186\) | −1.12311 | − | 3.34304i | −0.0823508 | − | 0.245124i | ||||
\(187\) | 16.3974i | 1.19909i | ||||||||
\(188\) | 0.322562 | 0.0235253 | ||||||||
\(189\) | 12.7357 | − | 5.17705i | 0.926386 | − | 0.376575i | ||||
\(190\) | −0.969633 | −0.0703446 | ||||||||
\(191\) | 4.10415i | 0.296966i | 0.988915 | + | 0.148483i | \(0.0474391\pi\) | ||||
−0.988915 | + | 0.148483i | \(0.952561\pi\) | |||||||
\(192\) | 0.551597 | + | 1.64187i | 0.0398081 | + | 0.118492i | ||||
\(193\) | −8.09615 | −0.582774 | −0.291387 | − | 0.956605i | \(-0.594117\pi\) | ||||
−0.291387 | + | 0.956605i | \(0.594117\pi\) | |||||||
\(194\) | 4.53137 | 0.325333 | ||||||||
\(195\) | −0.203993 | + | 0.0685329i | −0.0146083 | + | 0.00490774i | ||||
\(196\) | 2.71517 | + | 6.45196i | 0.193941 | + | 0.460855i | ||||
\(197\) | 15.0484i | 1.07215i | 0.844170 | + | 0.536076i | \(0.180094\pi\) | ||||
−0.844170 | + | 0.536076i | \(0.819906\pi\) | |||||||
\(198\) | 7.55588 | − | 5.72280i | 0.536973 | − | 0.406702i | ||||
\(199\) | 16.5733i | 1.17485i | 0.809279 | + | 0.587425i | \(0.199858\pi\) | ||||
−0.809279 | + | 0.587425i | \(0.800142\pi\) | |||||||
\(200\) | − | 4.98456i | − | 0.352462i | ||||||
\(201\) | −6.09982 | − | 18.1566i | −0.430248 | − | 1.28067i | ||||
\(202\) | − | 14.8286i | − | 1.04334i | ||||||
\(203\) | 2.17813 | + | 1.44652i | 0.152875 | + | 0.101526i | ||||
\(204\) | −2.86271 | − | 8.52109i | −0.200430 | − | 0.596596i | ||||
\(205\) | 0.0465888 | 0.00325390 | ||||||||
\(206\) | −0.578134 | −0.0402805 | ||||||||
\(207\) | −15.3951 | − | 20.3263i | −1.07003 | − | 1.41277i | ||||
\(208\) | − | 1.00000i | − | 0.0693375i | ||||||
\(209\) | −24.6575 | −1.70559 | ||||||||
\(210\) | −0.147539 | + | 0.549912i | −0.0101811 | + | 0.0379475i | ||||
\(211\) | 23.6447 | 1.62777 | 0.813885 | − | 0.581026i | \(-0.197349\pi\) | ||||
0.813885 | + | 0.581026i | \(0.197349\pi\) | |||||||
\(212\) | 11.3835i | 0.781819i | ||||||||
\(213\) | −16.7112 | + | 5.61422i | −1.14503 | + | 0.384680i | ||||
\(214\) | −18.6047 | −1.27179 | ||||||||
\(215\) | 0.0799705 | 0.00545394 | ||||||||
\(216\) | −2.92740 | + | 4.29306i | −0.199184 | + | 0.292106i | ||||
\(217\) | 4.48759 | + | 2.98026i | 0.304637 | + | 0.202313i | ||||
\(218\) | 4.91894i | 0.333153i | ||||||||
\(219\) | −16.9305 | + | 5.68790i | −1.14405 | + | 0.384352i | ||||
\(220\) | 0.392550i | 0.0264657i | ||||||||
\(221\) | 5.18986i | 0.349108i | ||||||||
\(222\) | −8.20186 | + | 2.75547i | −0.550473 | + | 0.184935i | ||||
\(223\) | − | 20.4113i | − | 1.36684i | −0.730024 | − | 0.683421i | \(-0.760491\pi\) | ||
0.730024 | − | 0.683421i | \(-0.239509\pi\) | |||||||
\(224\) | −2.20399 | − | 1.46370i | −0.147261 | − | 0.0977975i | ||||
\(225\) | 11.9205 | − | 9.02855i | 0.794700 | − | 0.601903i | ||||
\(226\) | −13.6446 | −0.907625 | ||||||||
\(227\) | −8.72027 | −0.578785 | −0.289392 | − | 0.957211i | \(-0.593453\pi\) | ||||
−0.289392 | + | 0.957211i | \(0.593453\pi\) | |||||||
\(228\) | 12.8136 | − | 4.30479i | 0.848598 | − | 0.285092i | ||||
\(229\) | − | 12.6352i | − | 0.834956i | −0.908687 | − | 0.417478i | \(-0.862914\pi\) | ||
0.908687 | − | 0.417478i | \(-0.137086\pi\) | |||||||
\(230\) | 1.05601 | 0.0696312 | ||||||||
\(231\) | −3.75187 | + | 13.9841i | −0.246855 | + | 0.920085i | ||||
\(232\) | −0.988265 | −0.0648828 | ||||||||
\(233\) | 10.1218i | 0.663098i | 0.943438 | + | 0.331549i | \(0.107571\pi\) | ||||
−0.943438 | + | 0.331549i | \(0.892429\pi\) | |||||||
\(234\) | 2.39148 | − | 1.81130i | 0.156336 | − | 0.118409i | ||||
\(235\) | −0.0400766 | −0.00261431 | ||||||||
\(236\) | 6.22502 | 0.405214 | ||||||||
\(237\) | −0.0827165 | − | 0.246212i | −0.00537301 | − | 0.0159932i | ||||
\(238\) | 11.4384 | + | 7.59640i | 0.741443 | + | 0.492401i | ||||
\(239\) | 11.3900i | 0.736756i | 0.929676 | + | 0.368378i | \(0.120087\pi\) | ||||
−0.929676 | + | 0.368378i | \(0.879913\pi\) | |||||||
\(240\) | −0.0685329 | − | 0.203993i | −0.00442378 | − | 0.0131677i | ||||
\(241\) | 10.1714i | 0.655199i | 0.944817 | + | 0.327599i | \(0.106240\pi\) | ||||
−0.944817 | + | 0.327599i | \(0.893760\pi\) | |||||||
\(242\) | − | 1.01757i | − | 0.0654121i | ||||||
\(243\) | −15.5692 | + | 0.775207i | −0.998763 | + | 0.0497296i | ||||
\(244\) | − | 9.38452i | − | 0.600782i | ||||||
\(245\) | −0.337345 | − | 0.801621i | −0.0215522 | − | 0.0512137i | ||||
\(246\) | −0.615664 | + | 0.206836i | −0.0392533 | + | 0.0131874i | ||||
\(247\) | −7.80424 | −0.496572 | ||||||||
\(248\) | −2.03612 | −0.129293 | ||||||||
\(249\) | 3.95885 | + | 11.7838i | 0.250882 | + | 0.746770i | ||||
\(250\) | 1.24053i | 0.0784578i | ||||||||
\(251\) | −22.8458 | −1.44201 | −0.721007 | − | 0.692927i | \(-0.756321\pi\) | ||||
−0.721007 | + | 0.692927i | \(0.756321\pi\) | |||||||
\(252\) | −0.491689 | − | 7.92201i | −0.0309735 | − | 0.499040i | ||||
\(253\) | 26.8540 | 1.68830 | ||||||||
\(254\) | − | 6.96593i | − | 0.437081i | ||||||
\(255\) | 0.355676 | + | 1.05870i | 0.0222733 | + | 0.0662982i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.37630 | 0.210608 | 0.105304 | − | 0.994440i | \(-0.466418\pi\) | ||||
0.105304 | + | 0.994440i | \(0.466418\pi\) | |||||||
\(258\) | −1.05680 | + | 0.355038i | −0.0657934 | + | 0.0221037i | ||||
\(259\) | 7.31181 | − | 11.0099i | 0.454334 | − | 0.684122i | ||||
\(260\) | 0.124244i | 0.00770531i | ||||||||
\(261\) | −1.79005 | − | 2.36342i | −0.110801 | − | 0.146292i | ||||
\(262\) | − | 10.5712i | − | 0.653088i | ||||||
\(263\) | − | 4.54885i | − | 0.280494i | −0.990117 | − | 0.140247i | \(-0.955210\pi\) | ||
0.990117 | − | 0.140247i | \(-0.0447897\pi\) | |||||||
\(264\) | −1.74277 | − | 5.18749i | −0.107260 | − | 0.319268i | ||||
\(265\) | − | 1.41433i | − | 0.0868817i | ||||||
\(266\) | −11.4231 | + | 17.2005i | −0.700392 | + | 1.05463i | ||||
\(267\) | −3.82682 | − | 11.3908i | −0.234197 | − | 0.697107i | ||||
\(268\) | −11.0585 | −0.675504 | ||||||||
\(269\) | 7.73403 | 0.471552 | 0.235776 | − | 0.971807i | \(-0.424237\pi\) | ||||
0.235776 | + | 0.971807i | \(0.424237\pi\) | |||||||
\(270\) | 0.363713 | − | 0.533389i | 0.0221349 | − | 0.0324610i | ||||
\(271\) | − | 6.93234i | − | 0.421110i | −0.977582 | − | 0.210555i | \(-0.932473\pi\) | ||
0.977582 | − | 0.210555i | \(-0.0675271\pi\) | |||||||
\(272\) | −5.18986 | −0.314682 | ||||||||
\(273\) | −1.18749 | + | 4.42604i | −0.0718701 | + | 0.267876i | ||||
\(274\) | −22.1462 | −1.33790 | ||||||||
\(275\) | 15.7487i | 0.949683i | ||||||||
\(276\) | −13.9550 | + | 4.68827i | −0.839992 | + | 0.282201i | ||||
\(277\) | 5.97653 | 0.359095 | 0.179547 | − | 0.983749i | \(-0.442537\pi\) | ||||
0.179547 | + | 0.983749i | \(0.442537\pi\) | |||||||
\(278\) | 11.7008 | 0.701769 | ||||||||
\(279\) | −3.68802 | − | 4.86933i | −0.220796 | − | 0.291519i | ||||
\(280\) | 0.273834 | + | 0.181856i | 0.0163647 | + | 0.0108680i | ||||
\(281\) | − | 12.7998i | − | 0.763574i | −0.924250 | − | 0.381787i | \(-0.875309\pi\) | ||
0.924250 | − | 0.381787i | \(-0.124691\pi\) | |||||||
\(282\) | 0.529606 | − | 0.177924i | 0.0315376 | − | 0.0105952i | ||||
\(283\) | 12.2413i | 0.727668i | 0.931464 | + | 0.363834i | \(0.118532\pi\) | ||||
−0.931464 | + | 0.363834i | \(0.881468\pi\) | |||||||
\(284\) | 10.1781i | 0.603961i | ||||||||
\(285\) | −1.59201 | + | 0.534847i | −0.0943027 | + | 0.0316816i | ||||
\(286\) | 3.15950i | 0.186825i | ||||||||
\(287\) | 0.548853 | − | 0.826447i | 0.0323978 | − | 0.0487836i | ||||
\(288\) | 1.81130 | + | 2.39148i | 0.106732 | + | 0.140919i | ||||
\(289\) | 9.93469 | 0.584394 | ||||||||
\(290\) | 0.122786 | 0.00721027 | ||||||||
\(291\) | 7.43992 | − | 2.49949i | 0.436136 | − | 0.146523i | ||||
\(292\) | 10.3117i | 0.603446i | ||||||||
\(293\) | −24.6407 | −1.43953 | −0.719763 | − | 0.694220i | \(-0.755749\pi\) | ||||
−0.719763 | + | 0.694220i | \(0.755749\pi\) | |||||||
\(294\) | 8.01685 | + | 9.09561i | 0.467552 | + | 0.530467i | ||||
\(295\) | −0.773424 | −0.0450305 | ||||||||
\(296\) | 4.99544i | 0.290354i | ||||||||
\(297\) | 9.24910 | − | 13.5639i | 0.536687 | − | 0.787058i | ||||
\(298\) | 24.2302 | 1.40362 | ||||||||
\(299\) | 8.49945 | 0.491536 | ||||||||
\(300\) | −2.74947 | − | 8.18401i | −0.158741 | − | 0.472504i | ||||
\(301\) | 0.942116 | − | 1.41861i | 0.0543027 | − | 0.0817673i | ||||
\(302\) | − | 15.4209i | − | 0.887371i | ||||||
\(303\) | −8.17942 | − | 24.3467i | −0.469895 | − | 1.39868i | ||||
\(304\) | − | 7.80424i | − | 0.447604i | ||||||
\(305\) | 1.16597i | 0.0667635i | ||||||||
\(306\) | −9.40041 | − | 12.4115i | −0.537386 | − | 0.709516i | ||||
\(307\) | 19.5052i | 1.11322i | 0.830774 | + | 0.556610i | \(0.187898\pi\) | ||||
−0.830774 | + | 0.556610i | \(0.812102\pi\) | |||||||
\(308\) | 6.96351 | + | 4.62455i | 0.396783 | + | 0.263508i | ||||
\(309\) | −0.949221 | + | 0.318897i | −0.0539993 | + | 0.0181414i | ||||
\(310\) | 0.252976 | 0.0143681 | ||||||||
\(311\) | −6.05188 | −0.343170 | −0.171585 | − | 0.985169i | \(-0.554889\pi\) | ||||
−0.171585 | + | 0.985169i | \(0.554889\pi\) | |||||||
\(312\) | −0.551597 | − | 1.64187i | −0.0312280 | − | 0.0929527i | ||||
\(313\) | 23.2819i | 1.31597i | 0.753030 | + | 0.657986i | \(0.228592\pi\) | ||||
−0.753030 | + | 0.657986i | \(0.771408\pi\) | |||||||
\(314\) | −15.5649 | −0.878376 | ||||||||
\(315\) | 0.0610896 | + | 0.984266i | 0.00344201 | + | 0.0554571i | ||||
\(316\) | −0.149958 | −0.00843581 | ||||||||
\(317\) | 2.14295i | 0.120360i | 0.998188 | + | 0.0601800i | \(0.0191675\pi\) | ||||
−0.998188 | + | 0.0601800i | \(0.980833\pi\) | |||||||
\(318\) | 6.27908 | + | 18.6902i | 0.352113 | + | 1.04809i | ||||
\(319\) | 3.12242 | 0.174822 | ||||||||
\(320\) | −0.124244 | −0.00694548 | ||||||||
\(321\) | −30.5466 | + | 10.2623i | −1.70494 | + | 0.572787i | ||||
\(322\) | 12.4406 | − | 18.7327i | 0.693289 | − | 1.04393i | ||||
\(323\) | 40.5029i | 2.25364i | ||||||||
\(324\) | −2.43837 | + | 8.66339i | −0.135465 | + | 0.481300i | ||||
\(325\) | 4.98456i | 0.276494i | ||||||||
\(326\) | − | 6.45488i | − | 0.357503i | ||||||
\(327\) | 2.71327 | + | 8.07627i | 0.150044 | + | 0.446619i | ||||
\(328\) | 0.374977i | 0.0207046i | ||||||||
\(329\) | −0.472134 | + | 0.710925i | −0.0260296 | + | 0.0391946i | ||||
\(330\) | 0.216529 | + | 0.644517i | 0.0119196 | + | 0.0354795i | ||||
\(331\) | 13.3421 | 0.733346 | 0.366673 | − | 0.930350i | \(-0.380497\pi\) | ||||
0.366673 | + | 0.930350i | \(0.380497\pi\) | |||||||
\(332\) | 7.17707 | 0.393893 | ||||||||
\(333\) | −11.9465 | + | 9.04824i | −0.654664 | + | 0.495841i | ||||
\(334\) | − | 22.4303i | − | 1.22733i | ||||||
\(335\) | 1.37395 | 0.0750672 | ||||||||
\(336\) | −4.42604 | − | 1.18749i | −0.241461 | − | 0.0647828i | ||||
\(337\) | −33.1596 | −1.80632 | −0.903160 | − | 0.429304i | \(-0.858759\pi\) | ||||
−0.903160 | + | 0.429304i | \(0.858759\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | −22.4027 | + | 7.52631i | −1.21675 | + | 0.408773i | ||||
\(340\) | 0.644812 | 0.0349698 | ||||||||
\(341\) | 6.43310 | 0.348372 | ||||||||
\(342\) | 18.6637 | − | 14.1358i | 1.00922 | − | 0.764378i | ||||
\(343\) | −18.1943 | − | 3.45950i | −0.982399 | − | 0.186796i | ||||
\(344\) | 0.643654i | 0.0347035i | ||||||||
\(345\) | 1.73383 | − | 0.582491i | 0.0933463 | − | 0.0313603i | ||||
\(346\) | 11.0835i | 0.595855i | ||||||||
\(347\) | 3.53681i | 0.189866i | 0.995484 | + | 0.0949328i | \(0.0302636\pi\) | ||||
−0.995484 | + | 0.0949328i | \(0.969736\pi\) | |||||||
\(348\) | −1.62260 | + | 0.545124i | −0.0869807 | + | 0.0292217i | ||||
\(349\) | 17.8637i | 0.956221i | 0.878300 | + | 0.478110i | \(0.158678\pi\) | ||||
−0.878300 | + | 0.478110i | \(0.841322\pi\) | |||||||
\(350\) | 10.9859 | + | 7.29590i | 0.587223 | + | 0.389982i | ||||
\(351\) | 2.92740 | − | 4.29306i | 0.156253 | − | 0.229146i | ||||
\(352\) | −3.15950 | −0.168402 | ||||||||
\(353\) | 3.37871 | 0.179830 | 0.0899152 | − | 0.995949i | \(-0.471340\pi\) | ||||
0.0899152 | + | 0.995949i | \(0.471340\pi\) | |||||||
\(354\) | 10.2207 | − | 3.43370i | 0.543223 | − | 0.182499i | ||||
\(355\) | − | 1.26458i | − | 0.0671167i | ||||||
\(356\) | −6.93771 | −0.367698 | ||||||||
\(357\) | 22.9706 | + | 6.16290i | 1.21573 | + | 0.326175i | ||||
\(358\) | 0.910490 | 0.0481209 | ||||||||
\(359\) | 0.644499i | 0.0340154i | 0.999855 | + | 0.0170077i | \(0.00541397\pi\) | ||||
−0.999855 | + | 0.0170077i | \(0.994586\pi\) | |||||||
\(360\) | −0.225044 | − | 0.297128i | −0.0118609 | − | 0.0156600i | ||||
\(361\) | −41.9061 | −2.20559 | ||||||||
\(362\) | 3.83313 | 0.201465 | ||||||||
\(363\) | −0.561290 | − | 1.67072i | −0.0294601 | − | 0.0876903i | ||||
\(364\) | 2.20399 | + | 1.46370i | 0.115521 | + | 0.0767186i | ||||
\(365\) | − | 1.28117i | − | 0.0670595i | ||||||
\(366\) | −5.17647 | − | 15.4082i | −0.270578 | − | 0.805398i | ||||
\(367\) | − | 14.7009i | − | 0.767381i | −0.923462 | − | 0.383690i | \(-0.874653\pi\) | ||
0.923462 | − | 0.383690i | \(-0.125347\pi\) | |||||||
\(368\) | 8.49945i | 0.443064i | ||||||||
\(369\) | −0.896751 | + | 0.679196i | −0.0466830 | + | 0.0353576i | ||||
\(370\) | − | 0.620655i | − | 0.0322663i | ||||||
\(371\) | −25.0891 | − | 16.6619i | −1.30256 | − | 0.865045i | ||||
\(372\) | −3.34304 | + | 1.12311i | −0.173329 | + | 0.0582308i | ||||
\(373\) | −20.6490 | −1.06917 | −0.534583 | − | 0.845116i | \(-0.679531\pi\) | ||||
−0.534583 | + | 0.845116i | \(0.679531\pi\) | |||||||
\(374\) | 16.3974 | 0.847888 | ||||||||
\(375\) | 0.684271 | + | 2.03679i | 0.0353356 | + | 0.105179i | ||||
\(376\) | − | 0.322562i | − | 0.0166349i | ||||||
\(377\) | 0.988265 | 0.0508982 | ||||||||
\(378\) | −5.17705 | − | 12.7357i | −0.266278 | − | 0.655054i | ||||
\(379\) | 8.57681 | 0.440561 | 0.220281 | − | 0.975437i | \(-0.429303\pi\) | ||||
0.220281 | + | 0.975437i | \(0.429303\pi\) | |||||||
\(380\) | 0.969633i | 0.0497411i | ||||||||
\(381\) | −3.84239 | − | 11.4372i | −0.196851 | − | 0.585944i | ||||
\(382\) | 4.10415 | 0.209987 | ||||||||
\(383\) | 15.0175 | 0.767356 | 0.383678 | − | 0.923467i | \(-0.374657\pi\) | ||||
0.383678 | + | 0.923467i | \(0.374657\pi\) | |||||||
\(384\) | 1.64187 | − | 0.551597i | 0.0837864 | − | 0.0281486i | ||||
\(385\) | −0.865178 | − | 0.574575i | −0.0440935 | − | 0.0292831i | ||||
\(386\) | 8.09615i | 0.412083i | ||||||||
\(387\) | −1.53929 | + | 1.16585i | −0.0782464 | + | 0.0592636i | ||||
\(388\) | − | 4.53137i | − | 0.230045i | ||||||
\(389\) | − | 29.5429i | − | 1.49788i | −0.662635 | − | 0.748942i | \(-0.730562\pi\) | ||
0.662635 | − | 0.748942i | \(-0.269438\pi\) | |||||||
\(390\) | 0.0685329 | + | 0.203993i | 0.00347030 | + | 0.0103296i | ||||
\(391\) | − | 44.1110i | − | 2.23079i | ||||||
\(392\) | 6.45196 | − | 2.71517i | 0.325873 | − | 0.137137i | ||||
\(393\) | −5.83101 | − | 17.3565i | −0.294136 | − | 0.875518i | ||||
\(394\) | 15.0484 | 0.758125 | ||||||||
\(395\) | 0.0186315 | 0.000937451 | ||||||||
\(396\) | −5.72280 | − | 7.55588i | −0.287582 | − | 0.379697i | ||||
\(397\) | − | 36.8561i | − | 1.84975i | −0.380268 | − | 0.924876i | \(-0.624168\pi\) | ||
0.380268 | − | 0.924876i | \(-0.375832\pi\) | |||||||
\(398\) | 16.5733 | 0.830744 | ||||||||
\(399\) | −9.26744 | + | 34.5419i | −0.463952 | + | 1.72926i | ||||
\(400\) | −4.98456 | −0.249228 | ||||||||
\(401\) | 13.7772i | 0.687998i | 0.938970 | + | 0.343999i | \(0.111782\pi\) | ||||
−0.938970 | + | 0.343999i | \(0.888218\pi\) | |||||||
\(402\) | −18.1566 | + | 6.09982i | −0.905569 | + | 0.304231i | ||||
\(403\) | 2.03612 | 0.101426 | ||||||||
\(404\) | −14.8286 | −0.737751 | ||||||||
\(405\) | 0.302954 | − | 1.07638i | 0.0150539 | − | 0.0534857i | ||||
\(406\) | 1.44652 | − | 2.17813i | 0.0717897 | − | 0.108099i | ||||
\(407\) | − | 15.7831i | − | 0.782338i | ||||||
\(408\) | −8.52109 | + | 2.86271i | −0.421857 | + | 0.141725i | ||||
\(409\) | − | 2.27730i | − | 0.112605i | −0.998414 | − | 0.0563026i | \(-0.982069\pi\) | ||
0.998414 | − | 0.0563026i | \(-0.0179311\pi\) | |||||||
\(410\) | − | 0.0465888i | − | 0.00230086i | ||||||
\(411\) | −36.3613 | + | 12.2158i | −1.79357 | + | 0.602561i | ||||
\(412\) | 0.578134i | 0.0284826i | ||||||||
\(413\) | −9.11155 | + | 13.7199i | −0.448350 | + | 0.675112i | ||||
\(414\) | −20.3263 | + | 15.3951i | −0.998982 | + | 0.756626i | ||||
\(415\) | −0.891711 | −0.0437724 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 19.2112 | − | 6.45414i | 0.940779 | − | 0.316060i | ||||
\(418\) | 24.6575i | 1.20604i | ||||||||
\(419\) | 13.1561 | 0.642718 | 0.321359 | − | 0.946957i | \(-0.395860\pi\) | ||||
0.321359 | + | 0.946957i | \(0.395860\pi\) | |||||||
\(420\) | 0.549912 | + | 0.147539i | 0.0268329 | + | 0.00719916i | ||||
\(421\) | 30.2957 | 1.47652 | 0.738262 | − | 0.674514i | \(-0.235647\pi\) | ||||
0.738262 | + | 0.674514i | \(0.235647\pi\) | |||||||
\(422\) | − | 23.6447i | − | 1.15101i | ||||||
\(423\) | 0.771402 | − | 0.584258i | 0.0375069 | − | 0.0284076i | ||||
\(424\) | 11.3835 | 0.552830 | ||||||||
\(425\) | 25.8692 | 1.25484 | ||||||||
\(426\) | 5.61422 | + | 16.7112i | 0.272010 | + | 0.809659i | ||||
\(427\) | 20.6834 | + | 13.7361i | 1.00094 | + | 0.664737i | ||||
\(428\) | 18.6047i | 0.899294i | ||||||||
\(429\) | 1.74277 | + | 5.18749i | 0.0841417 | + | 0.250454i | ||||
\(430\) | − | 0.0799705i | − | 0.00385652i | ||||||
\(431\) | 3.82945i | 0.184458i | 0.995738 | + | 0.0922291i | \(0.0293992\pi\) | ||||
−0.995738 | + | 0.0922291i | \(0.970601\pi\) | |||||||
\(432\) | 4.29306 | + | 2.92740i | 0.206550 | + | 0.140844i | ||||
\(433\) | 8.62531i | 0.414506i | 0.978287 | + | 0.207253i | \(0.0664523\pi\) | ||||
−0.978287 | + | 0.207253i | \(0.933548\pi\) | |||||||
\(434\) | 2.98026 | − | 4.48759i | 0.143057 | − | 0.215411i | ||||
\(435\) | 0.201600 | − | 0.0677286i | 0.00966596 | − | 0.00324734i | ||||
\(436\) | 4.91894 | 0.235575 | ||||||||
\(437\) | 66.3317 | 3.17308 | ||||||||
\(438\) | 5.68790 | + | 16.9305i | 0.271778 | + | 0.808969i | ||||
\(439\) | − | 8.37200i | − | 0.399574i | −0.979839 | − | 0.199787i | \(-0.935975\pi\) | ||
0.979839 | − | 0.199787i | \(-0.0640250\pi\) | |||||||
\(440\) | 0.392550 | 0.0187141 | ||||||||
\(441\) | 18.1797 | + | 10.5118i | 0.865702 | + | 0.500560i | ||||
\(442\) | 5.18986 | 0.246857 | ||||||||
\(443\) | − | 16.3126i | − | 0.775034i | −0.921863 | − | 0.387517i | \(-0.873333\pi\) | ||
0.921863 | − | 0.387517i | \(-0.126667\pi\) | |||||||
\(444\) | 2.75547 | + | 8.20186i | 0.130769 | + | 0.389243i | ||||
\(445\) | 0.861972 | 0.0408614 | ||||||||
\(446\) | −20.4113 | −0.966503 | ||||||||
\(447\) | 39.7829 | − | 13.3653i | 1.88167 | − | 0.632158i | ||||
\(448\) | −1.46370 | + | 2.20399i | −0.0691533 | + | 0.104129i | ||||
\(449\) | 20.3899i | 0.962258i | 0.876650 | + | 0.481129i | \(0.159773\pi\) | ||||
−0.876650 | + | 0.481129i | \(0.840227\pi\) | |||||||
\(450\) | −9.02855 | − | 11.9205i | −0.425610 | − | 0.561937i | ||||
\(451\) | − | 1.18474i | − | 0.0557872i | ||||||
\(452\) | 13.6446i | 0.641788i | ||||||||
\(453\) | −8.50610 | − | 25.3191i | −0.399651 | − | 1.18959i | ||||
\(454\) | 8.72027i | 0.409263i | ||||||||
\(455\) | −0.273834 | − | 0.181856i | −0.0128375 | − | 0.00852556i | ||||
\(456\) | −4.30479 | − | 12.8136i | −0.201590 | − | 0.600050i | ||||
\(457\) | −18.5156 | −0.866124 | −0.433062 | − | 0.901364i | \(-0.642567\pi\) | ||||
−0.433062 | + | 0.901364i | \(0.642567\pi\) | |||||||
\(458\) | −12.6352 | −0.590403 | ||||||||
\(459\) | −22.2804 | − | 15.1928i | −1.03996 | − | 0.709139i | ||||
\(460\) | − | 1.05601i | − | 0.0492367i | ||||||
\(461\) | 23.9362 | 1.11482 | 0.557410 | − | 0.830237i | \(-0.311795\pi\) | ||||
0.557410 | + | 0.830237i | \(0.311795\pi\) | |||||||
\(462\) | 13.9841 | + | 3.75187i | 0.650598 | + | 0.174553i | ||||
\(463\) | 7.52582 | 0.349754 | 0.174877 | − | 0.984590i | \(-0.444047\pi\) | ||||
0.174877 | + | 0.984590i | \(0.444047\pi\) | |||||||
\(464\) | 0.988265i | 0.0458790i | ||||||||
\(465\) | 0.415354 | − | 0.139541i | 0.0192616 | − | 0.00647105i | ||||
\(466\) | 10.1218 | 0.468881 | ||||||||
\(467\) | 38.4422 | 1.77889 | 0.889447 | − | 0.457038i | \(-0.151090\pi\) | ||||
0.889447 | + | 0.457038i | \(0.151090\pi\) | |||||||
\(468\) | −1.81130 | − | 2.39148i | −0.0837275 | − | 0.110546i | ||||
\(469\) | 16.1863 | − | 24.3728i | 0.747413 | − | 1.12543i | ||||
\(470\) | 0.0400766i | 0.00184860i | ||||||||
\(471\) | −25.5555 | + | 8.58553i | −1.17754 | + | 0.395600i | ||||
\(472\) | − | 6.22502i | − | 0.286530i | ||||||
\(473\) | − | 2.03363i | − | 0.0935062i | ||||||
\(474\) | −0.246212 | + | 0.0827165i | −0.0113089 | + | 0.00379929i | ||||
\(475\) | 38.9007i | 1.78489i | ||||||||
\(476\) | 7.59640 | − | 11.4384i | 0.348180 | − | 0.524279i | ||||
\(477\) | 20.6189 | + | 27.2233i | 0.944074 | + | 1.24647i | ||||
\(478\) | 11.3900 | 0.520965 | ||||||||
\(479\) | −14.2485 | −0.651032 | −0.325516 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325516 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(480\) | −0.203993 | + | 0.0685329i | −0.00931098 | + | 0.00312808i | ||||
\(481\) | − | 4.99544i | − | 0.227772i | ||||||
\(482\) | 10.1714 | 0.463295 | ||||||||
\(483\) | 10.0930 | − | 37.6189i | 0.459247 | − | 1.71172i | ||||
\(484\) | −1.01757 | −0.0462533 | ||||||||
\(485\) | 0.562998i | 0.0255644i | ||||||||
\(486\) | 0.775207 | + | 15.5692i | 0.0351641 | + | 0.706232i | ||||
\(487\) | 2.29079 | 0.103806 | 0.0519028 | − | 0.998652i | \(-0.483471\pi\) | ||||
0.0519028 | + | 0.998652i | \(0.483471\pi\) | |||||||
\(488\) | −9.38452 | −0.424817 | ||||||||
\(489\) | −3.56049 | − | 10.5981i | −0.161011 | − | 0.479262i | ||||
\(490\) | −0.801621 | + | 0.337345i | −0.0362135 | + | 0.0152397i | ||||
\(491\) | 28.2076i | 1.27299i | 0.771281 | + | 0.636495i | \(0.219616\pi\) | ||||
−0.771281 | + | 0.636495i | \(0.780384\pi\) | |||||||
\(492\) | 0.206836 | + | 0.615664i | 0.00932489 | + | 0.0277563i | ||||
\(493\) | − | 5.12896i | − | 0.230997i | ||||||
\(494\) | 7.80424i | 0.351129i | ||||||||
\(495\) | 0.711027 | + | 0.938777i | 0.0319583 | + | 0.0421949i | ||||
\(496\) | 2.03612i | 0.0914243i | ||||||||
\(497\) | −22.4325 | − | 14.8977i | −1.00624 | − | 0.668254i | ||||
\(498\) | 11.7838 | − | 3.95885i | 0.528046 | − | 0.177400i | ||||
\(499\) | 7.25740 | 0.324886 | 0.162443 | − | 0.986718i | \(-0.448063\pi\) | ||||
0.162443 | + | 0.986718i | \(0.448063\pi\) | |||||||
\(500\) | 1.24053 | 0.0554780 | ||||||||
\(501\) | −12.3725 | − | 36.8276i | −0.552761 | − | 1.64534i | ||||
\(502\) | 22.8458i | 1.01966i | ||||||||
\(503\) | −4.44557 | −0.198218 | −0.0991091 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991091 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(504\) | −7.92201 | + | 0.491689i | −0.352874 | + | 0.0219016i | ||||
\(505\) | 1.84237 | 0.0819846 | ||||||||
\(506\) | − | 26.8540i | − | 1.19381i | ||||||
\(507\) | 0.551597 | + | 1.64187i | 0.0244973 | + | 0.0729181i | ||||
\(508\) | −6.96593 | −0.309063 | ||||||||
\(509\) | 5.00425 | 0.221810 | 0.110905 | − | 0.993831i | \(-0.464625\pi\) | ||||
0.110905 | + | 0.993831i | \(0.464625\pi\) | |||||||
\(510\) | 1.05870 | − | 0.355676i | 0.0468799 | − | 0.0157496i | ||||
\(511\) | −22.7269 | − | 15.0932i | −1.00538 | − | 0.667684i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 22.8461 | − | 33.5040i | 1.00868 | − | 1.47924i | ||||
\(514\) | − | 3.37630i | − | 0.148922i | ||||||
\(515\) | − | 0.0718299i | − | 0.00316520i | ||||||
\(516\) | 0.355038 | + | 1.05680i | 0.0156297 | + | 0.0465229i | ||||
\(517\) | 1.01914i | 0.0448215i | ||||||||
\(518\) | −11.0099 | − | 7.31181i | −0.483748 | − | 0.321263i | ||||
\(519\) | 6.11365 | + | 18.1977i | 0.268359 | + | 0.798792i | ||||
\(520\) | 0.124244 | 0.00544848 | ||||||||
\(521\) | −8.60868 | −0.377153 | −0.188577 | − | 0.982058i | \(-0.560387\pi\) | ||||
−0.188577 | + | 0.982058i | \(0.560387\pi\) | |||||||
\(522\) | −2.36342 | + | 1.79005i | −0.103444 | + | 0.0783482i | ||||
\(523\) | − | 2.31380i | − | 0.101175i | −0.998720 | − | 0.0505876i | \(-0.983891\pi\) | ||
0.998720 | − | 0.0505876i | \(-0.0161094\pi\) | |||||||
\(524\) | −10.5712 | −0.461803 | ||||||||
\(525\) | 22.0619 | + | 5.91911i | 0.962860 | + | 0.258331i | ||||
\(526\) | −4.54885 | −0.198339 | ||||||||
\(527\) | − | 10.5672i | − | 0.460313i | ||||||
\(528\) | −5.18749 | + | 1.74277i | −0.225756 | + | 0.0758443i | ||||
\(529\) | −49.2406 | −2.14089 | ||||||||
\(530\) | −1.41433 | −0.0614346 | ||||||||
\(531\) | 14.8870 | − | 11.2754i | 0.646042 | − | 0.489310i | ||||
\(532\) | 17.2005 | + | 11.4231i | 0.745736 | + | 0.495252i | ||||
\(533\) | − | 0.374977i | − | 0.0162421i | ||||||
\(534\) | −11.3908 | + | 3.82682i | −0.492929 | + | 0.165603i | ||||
\(535\) | − | 2.31154i | − | 0.0999365i | ||||||
\(536\) | 11.0585i | 0.477653i | ||||||||
\(537\) | 1.49491 | − | 0.502223i | 0.0645100 | − | 0.0216725i | ||||
\(538\) | − | 7.73403i | − | 0.333438i | ||||||
\(539\) | −20.3850 | + | 8.57859i | −0.878043 | + | 0.369506i | ||||
\(540\) | −0.533389 | − | 0.363713i | −0.0229534 | − | 0.0156517i | ||||
\(541\) | 3.59839 | 0.154707 | 0.0773534 | − | 0.997004i | \(-0.475353\pi\) | ||||
0.0773534 | + | 0.997004i | \(0.475353\pi\) | |||||||
\(542\) | −6.93234 | −0.297770 | ||||||||
\(543\) | 6.29351 | − | 2.11434i | 0.270081 | − | 0.0907352i | ||||
\(544\) | 5.18986i | 0.222514i | ||||||||
\(545\) | −0.611151 | −0.0261789 | ||||||||
\(546\) | 4.42604 | + | 1.18749i | 0.189417 | + | 0.0508198i | ||||
\(547\) | 27.3170 | 1.16799 | 0.583995 | − | 0.811757i | \(-0.301489\pi\) | ||||
0.583995 | + | 0.811757i | \(0.301489\pi\) | |||||||
\(548\) | 22.1462i | 0.946040i | ||||||||
\(549\) | −16.9982 | − | 22.4429i | −0.725465 | − | 0.957840i | ||||
\(550\) | 15.7487 | 0.671528 | ||||||||
\(551\) | 7.71266 | 0.328570 | ||||||||
\(552\) | 4.68827 | + | 13.9550i | 0.199546 | + | 0.593964i | ||||
\(553\) | 0.219494 | − | 0.330507i | 0.00933382 | − | 0.0140546i | ||||
\(554\) | − | 5.97653i | − | 0.253918i | ||||||
\(555\) | −0.342351 | − | 1.01904i | −0.0145320 | − | 0.0432557i | ||||
\(556\) | − | 11.7008i | − | 0.496225i | ||||||
\(557\) | 19.0462i | 0.807015i | 0.914976 | + | 0.403508i | \(0.132209\pi\) | ||||
−0.914976 | + | 0.403508i | \(0.867791\pi\) | |||||||
\(558\) | −4.86933 | + | 3.68802i | −0.206135 | + | 0.156126i | ||||
\(559\) | − | 0.643654i | − | 0.0272237i | ||||||
\(560\) | 0.181856 | − | 0.273834i | 0.00768484 | − | 0.0115716i | ||||
\(561\) | 26.9224 | − | 9.04473i | 1.13666 | − | 0.381869i | ||||
\(562\) | −12.7998 | −0.539928 | ||||||||
\(563\) | −7.29866 | −0.307602 | −0.153801 | − | 0.988102i | \(-0.549151\pi\) | ||||
−0.153801 | + | 0.988102i | \(0.549151\pi\) | |||||||
\(564\) | −0.177924 | − | 0.529606i | −0.00749197 | − | 0.0223004i | ||||
\(565\) | − | 1.69527i | − | 0.0713203i | ||||||
\(566\) | 12.2413 | 0.514539 | ||||||||
\(567\) | −15.5250 | − | 18.0547i | −0.651989 | − | 0.758228i | ||||
\(568\) | 10.1781 | 0.427065 | ||||||||
\(569\) | − | 21.4605i | − | 0.899671i | −0.893112 | − | 0.449835i | \(-0.851483\pi\) | ||
0.893112 | − | 0.449835i | \(-0.148517\pi\) | |||||||
\(570\) | 0.534847 | + | 1.59201i | 0.0224023 | + | 0.0666821i | ||||
\(571\) | 36.6944 | 1.53561 | 0.767806 | − | 0.640682i | \(-0.221348\pi\) | ||||
0.767806 | + | 0.640682i | \(0.221348\pi\) | |||||||
\(572\) | 3.15950 | 0.132105 | ||||||||
\(573\) | 6.73849 | − | 2.26384i | 0.281505 | − | 0.0945732i | ||||
\(574\) | −0.826447 | − | 0.548853i | −0.0344952 | − | 0.0229087i | ||||
\(575\) | − | 42.3660i | − | 1.76679i | ||||||
\(576\) | 2.39148 | − | 1.81130i | 0.0996451 | − | 0.0754709i | ||||
\(577\) | 25.7075i | 1.07022i | 0.844784 | + | 0.535108i | \(0.179729\pi\) | ||||
−0.844784 | + | 0.535108i | \(0.820271\pi\) | |||||||
\(578\) | − | 9.93469i | − | 0.413229i | ||||||
\(579\) | 4.46581 | + | 13.2928i | 0.185593 | + | 0.552431i | ||||
\(580\) | − | 0.122786i | − | 0.00509843i | ||||||
\(581\) | −10.5051 | + | 15.8182i | −0.435824 | + | 0.656250i | ||||
\(582\) | −2.49949 | − | 7.43992i | −0.103607 | − | 0.308395i | ||||
\(583\) | −35.9660 | −1.48956 | ||||||||
\(584\) | 10.3117 | 0.426701 | ||||||||
\(585\) | 0.225044 | + | 0.297128i | 0.00930443 | + | 0.0122847i | ||||
\(586\) | 24.6407i | 1.01790i | ||||||||
\(587\) | −19.4004 | −0.800739 | −0.400369 | − | 0.916354i | \(-0.631118\pi\) | ||||
−0.400369 | + | 0.916354i | \(0.631118\pi\) | |||||||
\(588\) | 9.09561 | − | 8.01685i | 0.375097 | − | 0.330609i | ||||
\(589\) | 15.8903 | 0.654750 | ||||||||
\(590\) | 0.773424i | 0.0318414i | ||||||||
\(591\) | 24.7075 | − | 8.30063i | 1.01633 | − | 0.341442i | ||||
\(592\) | 4.99544 | 0.205311 | ||||||||
\(593\) | 24.0394 | 0.987181 | 0.493591 | − | 0.869694i | \(-0.335684\pi\) | ||||
0.493591 | + | 0.869694i | \(0.335684\pi\) | |||||||
\(594\) | −13.5639 | − | 9.24910i | −0.556534 | − | 0.379495i | ||||
\(595\) | −0.943810 | + | 1.42116i | −0.0386924 | + | 0.0582619i | ||||
\(596\) | − | 24.2302i | − | 0.992508i | ||||||
\(597\) | 27.2112 | − | 9.14178i | 1.11368 | − | 0.374148i | ||||
\(598\) | − | 8.49945i | − | 0.347568i | ||||||
\(599\) | 8.88663i | 0.363098i | 0.983382 | + | 0.181549i | \(0.0581111\pi\) | ||||
−0.983382 | + | 0.181549i | \(0.941889\pi\) | |||||||
\(600\) | −8.18401 | + | 2.74947i | −0.334111 | + | 0.112247i | ||||
\(601\) | 23.8259i | 0.971881i | 0.873992 | + | 0.485940i | \(0.161523\pi\) | ||||
−0.873992 | + | 0.485940i | \(0.838477\pi\) | |||||||
\(602\) | −1.41861 | − | 0.942116i | −0.0578182 | − | 0.0383978i | ||||
\(603\) | −26.4461 | + | 20.0302i | −1.07697 | + | 0.815694i | ||||
\(604\) | −15.4209 | −0.627466 | ||||||||
\(605\) | 0.126428 | 0.00514002 | ||||||||
\(606\) | −24.3467 | + | 8.17942i | −0.989016 | + | 0.332266i | ||||
\(607\) | − | 38.5757i | − | 1.56574i | −0.622187 | − | 0.782869i | \(-0.713755\pi\) | ||
0.622187 | − | 0.782869i | \(-0.286245\pi\) | |||||||
\(608\) | −7.80424 | −0.316504 | ||||||||
\(609\) | 1.17355 | − | 4.37410i | 0.0475548 | − | 0.177248i | ||||
\(610\) | 1.16597 | 0.0472089 | ||||||||
\(611\) | 0.322562i | 0.0130495i | ||||||||
\(612\) | −12.4115 | + | 9.40041i | −0.501704 | + | 0.379989i | ||||
\(613\) | −18.0124 | −0.727515 | −0.363757 | − | 0.931494i | \(-0.618506\pi\) | ||||
−0.363757 | + | 0.931494i | \(0.618506\pi\) | |||||||
\(614\) | 19.5052 | 0.787166 | ||||||||
\(615\) | −0.0256982 | − | 0.0764928i | −0.00103625 | − | 0.00308449i | ||||
\(616\) | 4.62455 | − | 6.96351i | 0.186329 | − | 0.280568i | ||||
\(617\) | − | 15.7284i | − | 0.633203i | −0.948559 | − | 0.316602i | \(-0.897458\pi\) | ||
0.948559 | − | 0.316602i | \(-0.102542\pi\) | |||||||
\(618\) | 0.318897 | + | 0.949221i | 0.0128279 | + | 0.0381833i | ||||
\(619\) | 28.2469i | 1.13534i | 0.823256 | + | 0.567670i | \(0.192155\pi\) | ||||
−0.823256 | + | 0.567670i | \(0.807845\pi\) | |||||||
\(620\) | − | 0.252976i | − | 0.0101598i | ||||||
\(621\) | −24.8812 | + | 36.4886i | −0.998450 | + | 1.46424i | ||||
\(622\) | 6.05188i | 0.242658i | ||||||||
\(623\) | 10.1547 | − | 15.2907i | 0.406840 | − | 0.612608i | ||||
\(624\) | −1.64187 | + | 0.551597i | −0.0657274 | + | 0.0220815i | ||||
\(625\) | 24.7687 | 0.990748 | ||||||||
\(626\) | 23.2819 | 0.930533 | ||||||||
\(627\) | 13.6010 | + | 40.4844i | 0.543171 | + | 1.61679i | ||||
\(628\) | 15.5649i | 0.621106i | ||||||||
\(629\) | −25.9256 | −1.03372 | ||||||||
\(630\) | 0.984266 | − | 0.0610896i | 0.0392141 | − | 0.00243387i | ||||
\(631\) | −18.7479 | −0.746342 | −0.373171 | − | 0.927763i | \(-0.621730\pi\) | ||||
−0.373171 | + | 0.927763i | \(0.621730\pi\) | |||||||
\(632\) | 0.149958i | 0.00596502i | ||||||||
\(633\) | −13.0424 | − | 38.8216i | −0.518387 | − | 1.54302i | ||||
\(634\) | 2.14295 | 0.0851073 | ||||||||
\(635\) | 0.865478 | 0.0343455 | ||||||||
\(636\) | 18.6902 | − | 6.27908i | 0.741114 | − | 0.248982i | ||||
\(637\) | −6.45196 | + | 2.71517i | −0.255636 | + | 0.107579i | ||||
\(638\) | − | 3.12242i | − | 0.123618i | ||||||
\(639\) | 18.4357 | + | 24.3408i | 0.729304 | + | 0.962908i | ||||
\(640\) | 0.124244i | 0.00491119i | ||||||||
\(641\) | 43.5297i | 1.71932i | 0.510867 | + | 0.859660i | \(0.329324\pi\) | ||||
−0.510867 | + | 0.859660i | \(0.670676\pi\) | |||||||
\(642\) | 10.2623 | + | 30.5466i | 0.405021 | + | 1.20558i | ||||
\(643\) | 24.9955i | 0.985724i | 0.870107 | + | 0.492862i | \(0.164049\pi\) | ||||
−0.870107 | + | 0.492862i | \(0.835951\pi\) | |||||||
\(644\) | −18.7327 | − | 12.4406i | −0.738173 | − | 0.490229i | ||||
\(645\) | −0.0441115 | − | 0.131301i | −0.00173689 | − | 0.00516998i | ||||
\(646\) | 40.5029 | 1.59357 | ||||||||
\(647\) | 28.3710 | 1.11538 | 0.557691 | − | 0.830049i | \(-0.311688\pi\) | ||||
0.557691 | + | 0.830049i | \(0.311688\pi\) | |||||||
\(648\) | 8.66339 | + | 2.43837i | 0.340330 | + | 0.0957883i | ||||
\(649\) | 19.6679i | 0.772034i | ||||||||
\(650\) | 4.98456 | 0.195511 | ||||||||
\(651\) | 2.41786 | − | 9.01194i | 0.0947636 | − | 0.353206i | ||||
\(652\) | −6.45488 | −0.252792 | ||||||||
\(653\) | − | 23.4531i | − | 0.917790i | −0.888490 | − | 0.458895i | \(-0.848245\pi\) | ||
0.888490 | − | 0.458895i | \(-0.151755\pi\) | |||||||
\(654\) | 8.07627 | − | 2.71327i | 0.315807 | − | 0.106097i | ||||
\(655\) | 1.31341 | 0.0513191 | ||||||||
\(656\) | 0.374977 | 0.0146404 | ||||||||
\(657\) | 18.6776 | + | 24.6602i | 0.728682 | + | 0.962087i | ||||
\(658\) | 0.710925 | + | 0.472134i | 0.0277148 | + | 0.0184057i | ||||
\(659\) | − | 28.4739i | − | 1.10919i | −0.832122 | − | 0.554593i | \(-0.812874\pi\) | ||
0.832122 | − | 0.554593i | \(-0.187126\pi\) | |||||||
\(660\) | 0.644517 | − | 0.216529i | 0.0250878 | − | 0.00842840i | ||||
\(661\) | 2.92424i | 0.113740i | 0.998382 | + | 0.0568698i | \(0.0181120\pi\) | ||||
−0.998382 | + | 0.0568698i | \(0.981888\pi\) | |||||||
\(662\) | − | 13.3421i | − | 0.518554i | ||||||
\(663\) | 8.52109 | − | 2.86271i | 0.330932 | − | 0.111179i | ||||
\(664\) | − | 7.17707i | − | 0.278524i | ||||||
\(665\) | −2.13707 | − | 1.41925i | −0.0828719 | − | 0.0550362i | ||||
\(666\) | 9.04824 | + | 11.9465i | 0.350612 | + | 0.462917i | ||||
\(667\) | −8.39970 | −0.325238 | ||||||||
\(668\) | −22.4303 | −0.867853 | ||||||||
\(669\) | −33.5127 | + | 11.2588i | −1.29568 | + | 0.435291i | ||||
\(670\) | − | 1.37395i | − | 0.0530805i | ||||||
\(671\) | 29.6504 | 1.14464 | ||||||||
\(672\) | −1.18749 | + | 4.42604i | −0.0458084 | + | 0.170738i | ||||
\(673\) | −49.0052 | −1.88901 | −0.944505 | − | 0.328496i | \(-0.893458\pi\) | ||||
−0.944505 | + | 0.328496i | \(0.893458\pi\) | |||||||
\(674\) | 33.1596i | 1.27726i | ||||||||
\(675\) | −21.3990 | − | 14.5918i | −0.823649 | − | 0.561638i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 7.79695 | 0.299661 | 0.149831 | − | 0.988712i | \(-0.452127\pi\) | ||||
0.149831 | + | 0.988712i | \(0.452127\pi\) | |||||||
\(678\) | 7.52631 | + | 22.4027i | 0.289046 | + | 0.860369i | ||||
\(679\) | 9.98711 | + | 6.63256i | 0.383270 | + | 0.254534i | ||||
\(680\) | − | 0.644812i | − | 0.0247274i | ||||||
\(681\) | 4.81007 | + | 14.3176i | 0.184322 | + | 0.548650i | ||||
\(682\) | − | 6.43310i | − | 0.246336i | ||||||
\(683\) | 16.8062i | 0.643071i | 0.946898 | + | 0.321535i | \(0.104199\pi\) | ||||
−0.946898 | + | 0.321535i | \(0.895801\pi\) | |||||||
\(684\) | −14.1358 | − | 18.6637i | −0.540497 | − | 0.713624i | ||||
\(685\) | − | 2.75155i | − | 0.105131i | ||||||
\(686\) | −3.45950 | + | 18.1943i | −0.132084 | + | 0.694661i | ||||
\(687\) | −20.7453 | + | 6.96952i | −0.791484 | + | 0.265904i | ||||
\(688\) | 0.643654 | 0.0245391 | ||||||||
\(689\) | −11.3835 | −0.433675 | ||||||||
\(690\) | −0.582491 | − | 1.73383i | −0.0221751 | − | 0.0660058i | ||||
\(691\) | − | 34.9724i | − | 1.33041i | −0.746660 | − | 0.665206i | \(-0.768344\pi\) | ||
0.746660 | − | 0.665206i | \(-0.231656\pi\) | |||||||
\(692\) | 11.0835 | 0.421333 | ||||||||
\(693\) | 25.0296 | − | 1.55349i | 0.950795 | − | 0.0590122i | ||||
\(694\) | 3.53681 | 0.134255 | ||||||||
\(695\) | 1.45376i | 0.0551443i | ||||||||
\(696\) | 0.545124 | + | 1.62260i | 0.0206629 | + | 0.0615046i | ||||
\(697\) | −1.94608 | −0.0737130 | ||||||||
\(698\) | 17.8637 | 0.676150 | ||||||||
\(699\) | 16.6186 | − | 5.58313i | 0.628574 | − | 0.211173i | ||||
\(700\) | 7.29590 | − | 10.9859i | 0.275759 | − | 0.415230i | ||||
\(701\) | 35.5652i | 1.34328i | 0.740878 | + | 0.671639i | \(0.234409\pi\) | ||||
−0.740878 | + | 0.671639i | \(0.765591\pi\) | |||||||
\(702\) | −4.29306 | − | 2.92740i | −0.162031 | − | 0.110487i | ||||
\(703\) | − | 38.9856i | − | 1.47037i | ||||||
\(704\) | 3.15950i | 0.119078i | ||||||||
\(705\) | 0.0221061 | + | 0.0658006i | 0.000832565 | + | 0.00247819i | ||||
\(706\) | − | 3.37871i | − | 0.127159i | ||||||
\(707\) | 21.7046 | − | 32.6822i | 0.816286 | − | 1.22914i | ||||
\(708\) | −3.43370 | − | 10.2207i | −0.129046 | − | 0.384117i | ||||
\(709\) | −27.3777 | −1.02819 | −0.514095 | − | 0.857733i | \(-0.671872\pi\) | ||||
−0.514095 | + | 0.857733i | \(0.671872\pi\) | |||||||
\(710\) | −1.26458 | −0.0474587 | ||||||||
\(711\) | −0.358622 | + | 0.271620i | −0.0134494 | + | 0.0101865i | ||||
\(712\) | 6.93771i | 0.260002i | ||||||||
\(713\) | −17.3059 | −0.648109 | ||||||||
\(714\) | 6.16290 | − | 22.9706i | 0.230641 | − | 0.859652i | ||||
\(715\) | −0.392550 | −0.0146805 | ||||||||
\(716\) | − | 0.910490i | − | 0.0340266i | ||||||
\(717\) | 18.7009 | − | 6.28267i | 0.698397 | − | 0.234631i | ||||
\(718\) | 0.644499 | 0.0240525 | ||||||||
\(719\) | 16.6195 | 0.619802 | 0.309901 | − | 0.950769i | \(-0.399704\pi\) | ||||
0.309901 | + | 0.950769i | \(0.399704\pi\) | |||||||
\(720\) | −0.297128 | + | 0.225044i | −0.0110733 | + | 0.00838690i | ||||
\(721\) | −1.27420 | − | 0.846213i | −0.0474538 | − | 0.0315146i | ||||
\(722\) | 41.9061i | 1.55959i | ||||||||
\(723\) | 16.7002 | − | 5.61052i | 0.621086 | − | 0.208658i | ||||
\(724\) | − | 3.83313i | − | 0.142457i | ||||||
\(725\) | − | 4.92607i | − | 0.182950i | ||||||
\(726\) | −1.67072 | + | 0.561290i | −0.0620064 | + | 0.0208314i | ||||
\(727\) | − | 1.30212i | − | 0.0482931i | −0.999708 | − | 0.0241466i | \(-0.992313\pi\) | ||
0.999708 | − | 0.0241466i | \(-0.00768684\pi\) | |||||||
\(728\) | 1.46370 | − | 2.20399i | 0.0542483 | − | 0.0816854i | ||||
\(729\) | 9.86070 | + | 25.1350i | 0.365211 | + | 0.930925i | ||||
\(730\) | −1.28117 | −0.0474182 | ||||||||
\(731\) | −3.34048 | −0.123552 | ||||||||
\(732\) | −15.4082 | + | 5.17647i | −0.569502 | + | 0.191328i | ||||
\(733\) | 33.3250i | 1.23089i | 0.788180 | + | 0.615444i | \(0.211023\pi\) | ||||
−0.788180 | + | 0.615444i | \(0.788977\pi\) | |||||||
\(734\) | −14.7009 | −0.542620 | ||||||||
\(735\) | −1.13008 | + | 0.996049i | −0.0416836 | + | 0.0367398i | ||||
\(736\) | 8.49945 | 0.313294 | ||||||||
\(737\) | − | 34.9392i | − | 1.28700i | ||||||
\(738\) | 0.679196 | + | 0.896751i | 0.0250016 | + | 0.0330098i | ||||
\(739\) | 14.3308 | 0.527167 | 0.263583 | − | 0.964637i | \(-0.415096\pi\) | ||||
0.263583 | + | 0.964637i | \(0.415096\pi\) | |||||||
\(740\) | −0.620655 | −0.0228157 | ||||||||
\(741\) | 4.30479 | + | 12.8136i | 0.158141 | + | 0.470718i | ||||
\(742\) | −16.6619 | + | 25.0891i | −0.611679 | + | 0.921049i | ||||
\(743\) | 16.8346i | 0.617600i | 0.951127 | + | 0.308800i | \(0.0999274\pi\) | ||||
−0.951127 | + | 0.308800i | \(0.900073\pi\) | |||||||
\(744\) | 1.12311 | + | 3.34304i | 0.0411754 | + | 0.122562i | ||||
\(745\) | 3.01047i | 0.110295i | ||||||||
\(746\) | 20.6490i | 0.756014i | ||||||||
\(747\) | 17.1638 | − | 12.9998i | 0.627992 | − | 0.475639i | ||||
\(748\) | − | 16.3974i | − | 0.599547i | ||||||
\(749\) | −41.0047 | − | 27.2317i | −1.49828 | − | 0.995026i | ||||
\(750\) | 2.03679 | − | 0.684271i | 0.0743729 | − | 0.0249860i | ||||
\(751\) | −20.0038 | −0.729949 | −0.364975 | − | 0.931017i | \(-0.618922\pi\) | ||||
−0.364975 | + | 0.931017i | \(0.618922\pi\) | |||||||
\(752\) | −0.322562 | −0.0117626 | ||||||||
\(753\) | 12.6017 | + | 37.5099i | 0.459231 | + | 1.36694i | ||||
\(754\) | − | 0.988265i | − | 0.0359905i | ||||||
\(755\) | 1.91596 | 0.0697288 | ||||||||
\(756\) | −12.7357 | + | 5.17705i | −0.463193 | + | 0.188287i | ||||
\(757\) | −22.8314 | −0.829820 | −0.414910 | − | 0.909862i | \(-0.636187\pi\) | ||||
−0.414910 | + | 0.909862i | \(0.636187\pi\) | |||||||
\(758\) | − | 8.57681i | − | 0.311524i | ||||||
\(759\) | −14.8126 | − | 44.0908i | −0.537662 | − | 1.60039i | ||||
\(760\) | 0.969633 | 0.0351723 | ||||||||
\(761\) | −49.2050 | −1.78368 | −0.891840 | − | 0.452351i | \(-0.850585\pi\) | ||||
−0.891840 | + | 0.452351i | \(0.850585\pi\) | |||||||
\(762\) | −11.4372 | + | 3.84239i | −0.414325 | + | 0.139195i | ||||
\(763\) | −7.19985 | + | 10.8413i | −0.260652 | + | 0.392482i | ||||
\(764\) | − | 4.10415i | − | 0.148483i | ||||||
\(765\) | 1.54206 | − | 1.16795i | 0.0557532 | − | 0.0422273i | ||||
\(766\) | − | 15.0175i | − | 0.542603i | ||||||
\(767\) | 6.22502i | 0.224772i | ||||||||
\(768\) | −0.551597 | − | 1.64187i | −0.0199040 | − | 0.0592459i | ||||
\(769\) | 22.1710i | 0.799506i | 0.916623 | + | 0.399753i | \(0.130904\pi\) | ||||
−0.916623 | + | 0.399753i | \(0.869096\pi\) | |||||||
\(770\) | −0.574575 | + | 0.865178i | −0.0207062 | + | 0.0311788i | ||||
\(771\) | −1.86236 | − | 5.54345i | −0.0670711 | − | 0.199642i | ||||
\(772\) | 8.09615 | 0.291387 | ||||||||
\(773\) | −18.8854 | −0.679262 | −0.339631 | − | 0.940559i | \(-0.610302\pi\) | ||||
−0.339631 | + | 0.940559i | \(0.610302\pi\) | |||||||
\(774\) | 1.16585 | + | 1.53929i | 0.0419057 | + | 0.0553286i | ||||
\(775\) | − | 10.1491i | − | 0.364568i | ||||||
\(776\) | −4.53137 | −0.162667 | ||||||||
\(777\) | −22.1100 | − | 5.93202i | −0.793193 | − | 0.212810i | ||||
\(778\) | −29.5429 | −1.05916 | ||||||||
\(779\) | − | 2.92641i | − | 0.104850i | ||||||
\(780\) | 0.203993 | − | 0.0685329i | 0.00730414 | − | 0.00245387i | ||||
\(781\) | −32.1578 | −1.15070 | ||||||||
\(782\) | −44.1110 | −1.57741 | ||||||||
\(783\) | −2.89304 | + | 4.24268i | −0.103389 | + | 0.151621i | ||||
\(784\) | −2.71517 | − | 6.45196i | −0.0969705 | − | 0.230427i | ||||
\(785\) | − | 1.93385i | − | 0.0690220i | ||||||
\(786\) | −17.3565 | + | 5.83101i | −0.619085 | + | 0.207985i | ||||
\(787\) | 12.4746i | 0.444673i | 0.974970 | + | 0.222336i | \(0.0713683\pi\) | ||||
−0.974970 | + | 0.222336i | \(0.928632\pi\) | |||||||
\(788\) | − | 15.0484i | − | 0.536076i | ||||||
\(789\) | −7.46863 | + | 2.50913i | −0.265890 | + | 0.0893275i | ||||
\(790\) | − | 0.0186315i | − | 0.000662878i | ||||||
\(791\) | −30.0726 | − | 19.9716i | −1.06926 | − | 0.710107i | ||||
\(792\) | −7.55588 | + | 5.72280i | −0.268487 | + | 0.203351i | ||||
\(793\) | 9.38452 | 0.333254 | ||||||||
\(794\) | −36.8561 | −1.30797 | ||||||||
\(795\) | −2.32215 | + | 0.780141i | −0.0823582 | + | 0.0276687i | ||||
\(796\) | − | 16.5733i | − | 0.587425i | ||||||
\(797\) | −2.69149 | −0.0953374 | −0.0476687 | − | 0.998863i | \(-0.515179\pi\) | ||||
−0.0476687 | + | 0.998863i | \(0.515179\pi\) | |||||||
\(798\) | 34.5419 | + | 9.26744i | 1.22277 | + | 0.328064i | ||||
\(799\) | 1.67406 | 0.0592238 | ||||||||
\(800\) | 4.98456i | 0.176231i | ||||||||
\(801\) | −16.5914 | + | 12.5663i | −0.586229 | + | 0.444008i | ||||
\(802\) | 13.7772 | 0.486488 | ||||||||
\(803\) | −32.5798 | −1.14971 | ||||||||
\(804\) | 6.09982 | + | 18.1566i | 0.215124 | + | 0.640334i | ||||
\(805\) | 2.32744 | + | 1.54568i | 0.0820314 | + | 0.0544780i | ||||
\(806\) | − | 2.03612i | − | 0.0717191i | ||||||
\(807\) | −4.26606 | − | 12.6983i | −0.150173 | − | 0.447000i | ||||
\(808\) | 14.8286i | 0.521669i | ||||||||
\(809\) | 3.83361i | 0.134782i | 0.997727 | + | 0.0673912i | \(0.0214676\pi\) | ||||
−0.997727 | + | 0.0673912i | \(0.978532\pi\) | |||||||
\(810\) | −1.07638 | − | 0.302954i | −0.0378201 | − | 0.0106447i | ||||
\(811\) | − | 43.1125i | − | 1.51388i | −0.653482 | − | 0.756942i | \(-0.726692\pi\) | ||
0.653482 | − | 0.756942i | \(-0.273308\pi\) | |||||||
\(812\) | −2.17813 | − | 1.44652i | −0.0764374 | − | 0.0507630i | ||||
\(813\) | −11.3820 | + | 3.82386i | −0.399185 | + | 0.134109i | ||||
\(814\) | −15.7831 | −0.553196 | ||||||||
\(815\) | 0.801983 | 0.0280922 | ||||||||
\(816\) | 2.86271 | + | 8.52109i | 0.100215 | + | 0.298298i | ||||
\(817\) | − | 5.02323i | − | 0.175741i | ||||||
\(818\) | −2.27730 | −0.0796239 | ||||||||
\(819\) | 7.92201 | − | 0.491689i | 0.276817 | − | 0.0171810i | ||||
\(820\) | −0.0465888 | −0.00162695 | ||||||||
\(821\) | − | 42.3073i | − | 1.47653i | −0.674509 | − | 0.738267i | \(-0.735645\pi\) | ||
0.674509 | − | 0.738267i | \(-0.264355\pi\) | |||||||
\(822\) | 12.2158 | + | 36.3613i | 0.426075 | + | 1.26824i | ||||
\(823\) | −31.3358 | −1.09230 | −0.546149 | − | 0.837688i | \(-0.683907\pi\) | ||||
−0.546149 | + | 0.837688i | \(0.683907\pi\) | |||||||
\(824\) | 0.578134 | 0.0201402 | ||||||||
\(825\) | 25.8574 | − | 8.68694i | 0.900238 | − | 0.302441i | ||||
\(826\) | 13.7199 | + | 9.11155i | 0.477376 | + | 0.317031i | ||||
\(827\) | − | 8.39803i | − | 0.292028i | −0.989283 | − | 0.146014i | \(-0.953356\pi\) | ||
0.989283 | − | 0.146014i | \(-0.0466445\pi\) | |||||||
\(828\) | 15.3951 | + | 20.3263i | 0.535015 | + | 0.706387i | ||||
\(829\) | 39.8138i | 1.38279i | 0.722477 | + | 0.691395i | \(0.243004\pi\) | ||||
−0.722477 | + | 0.691395i | \(0.756996\pi\) | |||||||
\(830\) | 0.891711i | 0.0309518i | ||||||||
\(831\) | −3.29663 | − | 9.81269i | −0.114359 | − | 0.340399i | ||||
\(832\) | 1.00000i | 0.0346688i | ||||||||
\(833\) | 14.0914 | + | 33.4848i | 0.488238 | + | 1.16018i | ||||
\(834\) | −6.45414 | − | 19.2112i | −0.223488 | − | 0.665231i | ||||
\(835\) | 2.78684 | 0.0964424 | ||||||||
\(836\) | 24.6575 | 0.852797 | ||||||||
\(837\) | −5.96052 | + | 8.74116i | −0.206026 | + | 0.302139i | ||||
\(838\) | − | 13.1561i | − | 0.454471i | ||||||
\(839\) | −22.7370 | −0.784967 | −0.392484 | − | 0.919759i | \(-0.628384\pi\) | ||||
−0.392484 | + | 0.919759i | \(0.628384\pi\) | |||||||
\(840\) | 0.147539 | − | 0.549912i | 0.00509057 | − | 0.0189738i | ||||
\(841\) | 28.0233 | 0.966322 | ||||||||
\(842\) | − | 30.2957i | − | 1.04406i | ||||||
\(843\) | −21.0157 | + | 7.06035i | −0.723818 | + | 0.243171i | ||||
\(844\) | −23.6447 | −0.813885 | ||||||||
\(845\) | −0.124244 | −0.00427414 | ||||||||
\(846\) | −0.584258 | − | 0.771402i | −0.0200872 | − | 0.0265214i | ||||
\(847\) | 1.48942 | − | 2.24272i | 0.0511771 | − | 0.0770609i | ||||
\(848\) | − | 11.3835i | − | 0.390910i | ||||||
\(849\) | 20.0986 | − | 6.75224i | 0.689782 | − | 0.231736i | ||||
\(850\) | − | 25.8692i | − | 0.887307i | ||||||
\(851\) | 42.4584i | 1.45546i | ||||||||
\(852\) | 16.7112 | − | 5.61422i | 0.572515 | − | 0.192340i | ||||
\(853\) | − | 39.4064i | − | 1.34925i | −0.738160 | − | 0.674625i | \(-0.764305\pi\) | ||
0.738160 | − | 0.674625i | \(-0.235695\pi\) | |||||||
\(854\) | 13.7361 | − | 20.6834i | 0.470040 | − | 0.707772i | ||||
\(855\) | 1.75630 | + | 2.31886i | 0.0600642 | + | 0.0793034i | ||||
\(856\) | 18.6047 | 0.635897 | ||||||||
\(857\) | −41.6581 | −1.42301 | −0.711506 | − | 0.702680i | \(-0.751987\pi\) | ||||
−0.711506 | + | 0.702680i | \(0.751987\pi\) | |||||||
\(858\) | 5.18749 | − | 1.74277i | 0.177098 | − | 0.0594972i | ||||
\(859\) | − | 36.9939i | − | 1.26221i | −0.775696 | − | 0.631107i | \(-0.782601\pi\) | ||
0.775696 | − | 0.631107i | \(-0.217399\pi\) | |||||||
\(860\) | −0.0799705 | −0.00272697 | ||||||||
\(861\) | −1.65966 | − | 0.445281i | −0.0565612 | − | 0.0151751i | ||||
\(862\) | 3.82945 | 0.130432 | ||||||||
\(863\) | 10.0590i | 0.342411i | 0.985235 | + | 0.171205i | \(0.0547662\pi\) | ||||
−0.985235 | + | 0.171205i | \(0.945234\pi\) | |||||||
\(864\) | 2.92740 | − | 4.29306i | 0.0995921 | − | 0.146053i | ||||
\(865\) | −1.37707 | −0.0468217 | ||||||||
\(866\) | 8.62531 | 0.293100 | ||||||||
\(867\) | −5.47995 | − | 16.3115i | −0.186109 | − | 0.553967i | ||||
\(868\) | −4.48759 | − | 2.98026i | −0.152319 | − | 0.101157i | ||||
\(869\) | − | 0.473793i | − | 0.0160723i | ||||||
\(870\) | −0.0677286 | − | 0.201600i | −0.00229622 | − | 0.00683486i | ||||
\(871\) | − | 11.0585i | − | 0.374702i | ||||||
\(872\) | − | 4.91894i | − | 0.166576i | ||||||
\(873\) | −8.20768 | − | 10.8367i | −0.277788 | − | 0.366766i | ||||
\(874\) | − | 66.3317i | − | 2.24370i | ||||||
\(875\) | −1.81576 | + | 2.73411i | −0.0613838 | + | 0.0924299i | ||||
\(876\) | 16.9305 | − | 5.68790i | 0.572027 | − | 0.192176i | ||||
\(877\) | 45.1345 | 1.52408 | 0.762042 | − | 0.647528i | \(-0.224197\pi\) | ||||
0.762042 | + | 0.647528i | \(0.224197\pi\) | |||||||
\(878\) | −8.37200 | −0.282541 | ||||||||
\(879\) | 13.5917 | + | 40.4569i | 0.458438 | + | 1.36458i | ||||
\(880\) | − | 0.392550i | − | 0.0132329i | ||||||
\(881\) | 27.1323 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(882\) | 10.5118 | − | 18.1797i | 0.353949 | − | 0.612144i | ||||
\(883\) | −39.6851 | −1.33551 | −0.667755 | − | 0.744381i | \(-0.732745\pi\) | ||||
−0.667755 | + | 0.744381i | \(0.732745\pi\) | |||||||
\(884\) | − | 5.18986i | − | 0.174554i | ||||||
\(885\) | 0.426618 | + | 1.26986i | 0.0143406 | + | 0.0426860i | ||||
\(886\) | −16.3126 | −0.548032 | ||||||||
\(887\) | −18.9220 | −0.635339 | −0.317670 | − | 0.948201i | \(-0.602900\pi\) | ||||
−0.317670 | + | 0.948201i | \(0.602900\pi\) | |||||||
\(888\) | 8.20186 | − | 2.75547i | 0.275236 | − | 0.0924674i | ||||
\(889\) | 10.1960 | − | 15.3529i | 0.341964 | − | 0.514919i | ||||
\(890\) | − | 0.861972i | − | 0.0288934i | ||||||
\(891\) | −27.3720 | − | 7.70403i | −0.916995 | − | 0.258095i | ||||
\(892\) | 20.4113i | 0.683421i | ||||||||
\(893\) | 2.51735i | 0.0842400i | ||||||||
\(894\) | −13.3653 | − | 39.7829i | −0.447003 | − | 1.33054i | ||||
\(895\) | 0.113123i | 0.00378130i | ||||||||
\(896\) | 2.20399 | + | 1.46370i | 0.0736303 | + | 0.0488987i | ||||
\(897\) | −4.68827 | − | 13.9550i | −0.156537 | − | 0.465944i | ||||
\(898\) | 20.3899 | 0.680419 | ||||||||
\(899\) | −2.01222 | −0.0671113 | ||||||||
\(900\) | −11.9205 | + | 9.02855i | −0.397350 | + | 0.300952i | ||||
\(901\) | 59.0786i | 1.96819i | ||||||||
\(902\) | −1.18474 | −0.0394475 | ||||||||
\(903\) | −2.84884 | − | 0.764332i | −0.0948036 | − | 0.0254354i | ||||
\(904\) | 13.6446 | 0.453812 | ||||||||
\(905\) | 0.476246i | 0.0158309i | ||||||||
\(906\) | −25.3191 | + | 8.50610i | −0.841169 | + | 0.282596i | ||||
\(907\) | 4.14265 | 0.137554 | 0.0687772 | − | 0.997632i | \(-0.478090\pi\) | ||||
0.0687772 | + | 0.997632i | \(0.478090\pi\) | |||||||
\(908\) | 8.72027 | 0.289392 | ||||||||
\(909\) | −35.4624 | + | 26.8591i | −1.17621 | + | 0.890860i | ||||
\(910\) | −0.181856 | + | 0.273834i | −0.00602848 | + | 0.00907751i | ||||
\(911\) | 29.2725i | 0.969843i | 0.874558 | + | 0.484921i | \(0.161152\pi\) | ||||
−0.874558 | + | 0.484921i | \(0.838848\pi\) | |||||||
\(912\) | −12.8136 | + | 4.30479i | −0.424299 | + | 0.142546i | ||||
\(913\) | 22.6759i | 0.750464i | ||||||||
\(914\) | 18.5156i | 0.612442i | ||||||||
\(915\) | 1.91438 | − | 0.643148i | 0.0632874 | − | 0.0212618i | ||||
\(916\) | 12.6352i | 0.417478i | ||||||||
\(917\) | 15.4730 | − | 23.2987i | 0.510963 | − | 0.769392i | ||||
\(918\) | −15.1928 | + | 22.2804i | −0.501437 | + | 0.735362i | ||||
\(919\) | 24.4878 | 0.807779 | 0.403890 | − | 0.914808i | \(-0.367658\pi\) | ||||
0.403890 | + | 0.914808i | \(0.367658\pi\) | |||||||
\(920\) | −1.05601 | −0.0348156 | ||||||||
\(921\) | 32.0250 | − | 10.7590i | 1.05526 | − | 0.354521i | ||||
\(922\) | − | 23.9362i | − | 0.788297i | ||||||
\(923\) | −10.1781 | −0.335017 | ||||||||
\(924\) | 3.75187 | − | 13.9841i | 0.123427 | − | 0.460042i | ||||
\(925\) | −24.9001 | −0.818709 | ||||||||
\(926\) | − | 7.52582i | − | 0.247314i | ||||||
\(927\) | 1.04717 | + | 1.38260i | 0.0343937 | + | 0.0454104i | ||||
\(928\) | 0.988265 | 0.0324414 | ||||||||
\(929\) | −30.0493 | −0.985886 | −0.492943 | − | 0.870062i | \(-0.664079\pi\) | ||||
−0.492943 | + | 0.870062i | \(0.664079\pi\) | |||||||
\(930\) | −0.139541 | − | 0.415354i | −0.00457572 | − | 0.0136200i | ||||
\(931\) | −50.3527 | + | 21.1899i | −1.65024 | + | 0.694470i | ||||
\(932\) | − | 10.1218i | − | 0.331549i | ||||||
\(933\) | 3.33820 | + | 9.93640i | 0.109288 | + | 0.325303i | ||||
\(934\) | − | 38.4422i | − | 1.25787i | ||||||
\(935\) | 2.03728i | 0.0666262i | ||||||||
\(936\) | −2.39148 | + | 1.81130i | −0.0781680 | + | 0.0592043i | ||||
\(937\) | 46.8815i | 1.53155i | 0.643107 | + | 0.765776i | \(0.277645\pi\) | ||||
−0.643107 | + | 0.765776i | \(0.722355\pi\) | |||||||
\(938\) | −24.3728 | − | 16.1863i | −0.795800 | − | 0.528501i | ||||
\(939\) | 38.2259 | − | 12.8422i | 1.24746 | − | 0.419091i | ||||
\(940\) | 0.0400766 | 0.00130715 | ||||||||
\(941\) | −12.7550 | −0.415800 | −0.207900 | − | 0.978150i | \(-0.566663\pi\) | ||||
−0.207900 | + | 0.978150i | \(0.566663\pi\) | |||||||
\(942\) | 8.58553 | + | 25.5555i | 0.279732 | + | 0.832644i | ||||
\(943\) | 3.18710i | 0.103786i | ||||||||
\(944\) | −6.22502 | −0.202607 | ||||||||
\(945\) | 1.58234 | − | 0.643219i | 0.0514736 | − | 0.0209239i | ||||
\(946\) | −2.03363 | −0.0661189 | ||||||||
\(947\) | − | 21.8570i | − | 0.710257i | −0.934817 | − | 0.355129i | \(-0.884437\pi\) | ||
0.934817 | − | 0.355129i | \(-0.115563\pi\) | |||||||
\(948\) | 0.0827165 | + | 0.246212i | 0.00268651 | + | 0.00799660i | ||||
\(949\) | −10.3117 | −0.334732 | ||||||||
\(950\) | 38.9007 | 1.26211 | ||||||||
\(951\) | 3.51844 | − | 1.18204i | 0.114093 | − | 0.0383304i | ||||
\(952\) | −11.4384 | − | 7.59640i | −0.370722 | − | 0.246201i | ||||
\(953\) | − | 21.2742i | − | 0.689137i | −0.938761 | − | 0.344569i | \(-0.888025\pi\) | ||
0.938761 | − | 0.344569i | \(-0.111975\pi\) | |||||||
\(954\) | 27.2233 | − | 20.6189i | 0.881388 | − | 0.667561i | ||||
\(955\) | 0.509919i | 0.0165006i | ||||||||
\(956\) | − | 11.3900i | − | 0.368378i | ||||||
\(957\) | −1.72232 | − | 5.12661i | −0.0556746 | − | 0.165720i | ||||
\(958\) | 14.2485i | 0.460349i | ||||||||
\(959\) | −48.8102 | − | 32.4154i | −1.57616 | − | 1.04675i | ||||
\(960\) | 0.0685329 | + | 0.203993i | 0.00221189 | + | 0.00658386i | ||||
\(961\) | 26.8542 | 0.866266 | ||||||||
\(962\) | −4.99544 | −0.161059 | ||||||||
\(963\) | 33.6988 | + | 44.4929i | 1.08593 | + | 1.43376i | ||||
\(964\) | − | 10.1714i | − | 0.327599i | ||||||
\(965\) | −1.00590 | −0.0323811 | ||||||||
\(966\) | −37.6189 | − | 10.0930i | −1.21037 | − | 0.324737i | ||||
\(967\) | −4.17220 | −0.134169 | −0.0670845 | − | 0.997747i | \(-0.521370\pi\) | ||||
−0.0670845 | + | 0.997747i | \(0.521370\pi\) | |||||||
\(968\) | 1.01757i | 0.0327060i | ||||||||
\(969\) | 66.5006 | − | 22.3413i | 2.13631 | − | 0.717706i | ||||
\(970\) | 0.562998 | 0.0180768 | ||||||||
\(971\) | 47.3425 | 1.51929 | 0.759647 | − | 0.650336i | \(-0.225372\pi\) | ||||
0.759647 | + | 0.650336i | \(0.225372\pi\) | |||||||
\(972\) | 15.5692 | − | 0.775207i | 0.499381 | − | 0.0248648i | ||||
\(973\) | 25.7885 | + | 17.1265i | 0.826742 | + | 0.549050i | ||||
\(974\) | − | 2.29079i | − | 0.0734016i | ||||||
\(975\) | 8.18401 | − | 2.74947i | 0.262098 | − | 0.0880535i | ||||
\(976\) | 9.38452i | 0.300391i | ||||||||
\(977\) | 23.6190i | 0.755640i | 0.925879 | + | 0.377820i | \(0.123326\pi\) | ||||
−0.925879 | + | 0.377820i | \(0.876674\pi\) | |||||||
\(978\) | −10.5981 | + | 3.56049i | −0.338889 | + | 0.113852i | ||||
\(979\) | − | 21.9197i | − | 0.700556i | ||||||
\(980\) | 0.337345 | + | 0.801621i | 0.0107761 | + | 0.0256068i | ||||
\(981\) | 11.7636 | − | 8.90969i | 0.375582 | − | 0.284465i | ||||
\(982\) | 28.2076 | 0.900140 | ||||||||
\(983\) | 36.2816 | 1.15720 | 0.578602 | − | 0.815610i | \(-0.303598\pi\) | ||||
0.578602 | + | 0.815610i | \(0.303598\pi\) | |||||||
\(984\) | 0.615664 | − | 0.206836i | 0.0196266 | − | 0.00659369i | ||||
\(985\) | 1.86968i | 0.0595728i | ||||||||
\(986\) | −5.12896 | −0.163339 | ||||||||
\(987\) | 1.42768 | + | 0.383039i | 0.0454434 | + | 0.0121923i | ||||
\(988\) | 7.80424 | 0.248286 | ||||||||
\(989\) | 5.47071i | 0.173958i | ||||||||
\(990\) | 0.938777 | − | 0.711027i | 0.0298363 | − | 0.0225979i | ||||
\(991\) | −6.84537 | −0.217450 | −0.108725 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108725 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(992\) | 2.03612 | 0.0646467 | ||||||||
\(993\) | −7.35944 | − | 21.9059i | −0.233545 | − | 0.695164i | ||||
\(994\) | −14.8977 | + | 22.4325i | −0.472527 | + | 0.711517i | ||||
\(995\) | 2.05914i | 0.0652791i | ||||||||
\(996\) | −3.95885 | − | 11.7838i | −0.125441 | − | 0.373385i | ||||
\(997\) | 49.2377i | 1.55937i | 0.626169 | + | 0.779687i | \(0.284622\pi\) | ||||
−0.626169 | + | 0.779687i | \(0.715378\pi\) | |||||||
\(998\) | − | 7.25740i | − | 0.229729i | ||||||
\(999\) | 21.4457 | + | 14.6236i | 0.678512 | + | 0.462671i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.g.c.209.3 | ✓ | 12 | |
3.2 | odd | 2 | 546.2.g.d.209.10 | yes | 12 | ||
7.6 | odd | 2 | 546.2.g.d.209.4 | yes | 12 | ||
21.20 | even | 2 | inner | 546.2.g.c.209.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.g.c.209.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
546.2.g.c.209.9 | yes | 12 | 21.20 | even | 2 | inner | |
546.2.g.d.209.4 | yes | 12 | 7.6 | odd | 2 | ||
546.2.g.d.209.10 | yes | 12 | 3.2 | odd | 2 |