Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [312,2,Mod(155,312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("312.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 312.h (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: | \(2.49133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 155.29 | ||
Character | \(\chi\) | \(=\) | 312.155 |
Dual form | 312.2.h.c.155.32 |
$q$-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 \(\left(\mathbb{Z}/312\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(157\) | \(209\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38664 | − | 0.277882i | 0.980505 | − | 0.196493i | ||||
\(3\) | −0.662918 | − | 1.60017i | −0.382736 | − | 0.923858i | ||||
\(4\) | 1.84556 | − | 0.770648i | 0.922781 | − | 0.385324i | ||||
\(5\) | − | 2.38561i | − | 1.06688i | −0.845839 | − | 0.533438i | \(-0.820900\pi\) | ||
0.845839 | − | 0.533438i | \(-0.179100\pi\) | |||||||
\(6\) | −1.36389 | − | 2.03465i | −0.556806 | − | 0.830643i | ||||
\(7\) | −2.63829 | −0.997178 | −0.498589 | − | 0.866839i | \(-0.666148\pi\) | ||||
−0.498589 | + | 0.866839i | \(0.666148\pi\) | |||||||
\(8\) | 2.34499 | − | 1.58146i | 0.829079 | − | 0.559132i | ||||
\(9\) | −2.12108 | + | 2.12156i | −0.707026 | + | 0.707187i | ||||
\(10\) | −0.662918 | − | 3.30799i | −0.209633 | − | 1.04608i | ||||
\(11\) | 0.764084 | 0.230380 | 0.115190 | − | 0.993343i | \(-0.463252\pi\) | ||||
0.115190 | + | 0.993343i | \(0.463252\pi\) | |||||||
\(12\) | −2.45662 | − | 2.44233i | −0.709166 | − | 0.705041i | ||||
\(13\) | 1.05175 | + | 3.44874i | 0.291702 | + | 0.956509i | ||||
\(14\) | −3.65836 | + | 0.733133i | −0.977738 | + | 0.195938i | ||||
\(15\) | −3.81737 | + | 1.58146i | −0.985642 | + | 0.408332i | ||||
\(16\) | 2.81220 | − | 2.84456i | 0.703051 | − | 0.711139i | ||||
\(17\) | 0.584523i | 0.141768i | 0.997485 | + | 0.0708839i | \(0.0225820\pi\) | ||||
−0.997485 | + | 0.0708839i | \(0.977418\pi\) | |||||||
\(18\) | −2.35164 | + | 3.53126i | −0.554286 | + | 0.832326i | ||||
\(19\) | − | 4.28969i | − | 0.984122i | −0.870561 | − | 0.492061i | \(-0.836244\pi\) | ||
0.870561 | − | 0.492061i | \(-0.163756\pi\) | |||||||
\(20\) | −1.83846 | − | 4.40279i | −0.411093 | − | 0.984494i | ||||
\(21\) | 1.74897 | + | 4.22170i | 0.381656 | + | 0.921251i | ||||
\(22\) | 1.05951 | − | 0.212325i | 0.225889 | − | 0.0452679i | ||||
\(23\) | 4.39993 | 0.917449 | 0.458724 | − | 0.888579i | \(-0.348307\pi\) | ||||
0.458724 | + | 0.888579i | \(0.348307\pi\) | |||||||
\(24\) | −4.08514 | − | 2.70400i | −0.833877 | − | 0.551951i | ||||
\(25\) | −0.691126 | −0.138225 | ||||||||
\(26\) | 2.41674 | + | 4.48992i | 0.473962 | + | 0.880545i | ||||
\(27\) | 4.80096 | + | 1.98766i | 0.923945 | + | 0.382525i | ||||
\(28\) | −4.86912 | + | 2.03319i | −0.920177 | + | 0.384237i | ||||
\(29\) | 8.65308 | 1.60684 | 0.803419 | − | 0.595415i | \(-0.203012\pi\) | ||||
0.803419 | + | 0.595415i | \(0.203012\pi\) | |||||||
\(30\) | −4.85388 | + | 3.25371i | −0.886193 | + | 0.594043i | ||||
\(31\) | −7.09996 | −1.27519 | −0.637595 | − | 0.770372i | \(-0.720071\pi\) | ||||
−0.637595 | + | 0.770372i | \(0.720071\pi\) | |||||||
\(32\) | 3.10907 | − | 4.72585i | 0.549612 | − | 0.835420i | ||||
\(33\) | −0.506525 | − | 1.22266i | −0.0881747 | − | 0.212838i | ||||
\(34\) | 0.162429 | + | 0.810526i | 0.0278563 | + | 0.139004i | ||||
\(35\) | 6.29391i | 1.06387i | ||||||||
\(36\) | −2.27961 | + | 5.55008i | −0.379934 | + | 0.925013i | ||||
\(37\) | 7.63475 | 1.25515 | 0.627573 | − | 0.778558i | \(-0.284049\pi\) | ||||
0.627573 | + | 0.778558i | \(0.284049\pi\) | |||||||
\(38\) | −1.19203 | − | 5.94827i | −0.193373 | − | 0.964937i | ||||
\(39\) | 4.82135 | − | 3.96921i | 0.772034 | − | 0.635582i | ||||
\(40\) | −3.77275 | − | 5.59422i | −0.596524 | − | 0.884525i | ||||
\(41\) | 0.139556 | 0.0217949 | 0.0108975 | − | 0.999941i | \(-0.496531\pi\) | ||||
0.0108975 | + | 0.999941i | \(0.496531\pi\) | |||||||
\(42\) | 3.59833 | + | 5.36799i | 0.555235 | + | 0.828299i | ||||
\(43\) | −6.17544 | −0.941746 | −0.470873 | − | 0.882201i | \(-0.656061\pi\) | ||||
−0.470873 | + | 0.882201i | \(0.656061\pi\) | |||||||
\(44\) | 1.41016 | − | 0.588840i | 0.212590 | − | 0.0887709i | ||||
\(45\) | 5.06122 | + | 5.06006i | 0.754482 | + | 0.754309i | ||||
\(46\) | 6.10114 | − | 1.22266i | 0.899563 | − | 0.180272i | ||||
\(47\) | − | 0.889975i | − | 0.129816i | −0.997891 | − | 0.0649081i | \(-0.979325\pi\) | ||
0.997891 | − | 0.0649081i | \(-0.0206754\pi\) | |||||||
\(48\) | −6.41603 | − | 2.61429i | −0.926075 | − | 0.377340i | ||||
\(49\) | −0.0394518 | −0.00563597 | ||||||||
\(50\) | −0.958345 | + | 0.192052i | −0.135530 | + | 0.0271602i | ||||
\(51\) | 0.935336 | − | 0.387491i | 0.130973 | − | 0.0542596i | ||||
\(52\) | 4.59883 | + | 5.55435i | 0.637743 | + | 0.770249i | ||||
\(53\) | −0.803622 | −0.110386 | −0.0551930 | − | 0.998476i | \(-0.517577\pi\) | ||||
−0.0551930 | + | 0.998476i | \(0.517577\pi\) | |||||||
\(54\) | 7.20956 | + | 1.42207i | 0.981096 | + | 0.193520i | ||||
\(55\) | − | 1.82280i | − | 0.245787i | ||||||
\(56\) | −6.18675 | + | 4.17235i | −0.826739 | + | 0.557554i | ||||
\(57\) | −6.86423 | + | 2.84371i | −0.909189 | + | 0.376659i | ||||
\(58\) | 11.9987 | − | 2.40454i | 1.57551 | − | 0.315731i | ||||
\(59\) | −9.13099 | −1.18875 | −0.594377 | − | 0.804187i | \(-0.702601\pi\) | ||||
−0.594377 | + | 0.804187i | \(0.702601\pi\) | |||||||
\(60\) | −5.82645 | + | 5.86054i | −0.752192 | + | 0.756593i | ||||
\(61\) | 9.47787i | 1.21352i | 0.794886 | + | 0.606758i | \(0.207530\pi\) | ||||
−0.794886 | + | 0.606758i | \(0.792470\pi\) | |||||||
\(62\) | −9.84511 | + | 1.97295i | −1.25033 | + | 0.250565i | ||||
\(63\) | 5.59601 | − | 5.59729i | 0.705031 | − | 0.705192i | ||||
\(64\) | 2.99795 | − | 7.41703i | 0.374743 | − | 0.927129i | ||||
\(65\) | 8.22735 | − | 2.50905i | 1.02048 | − | 0.311210i | ||||
\(66\) | −1.04213 | − | 1.55464i | −0.128277 | − | 0.191363i | ||||
\(67\) | 11.5441i | 1.41034i | 0.709040 | + | 0.705168i | \(0.249128\pi\) | ||||
−0.709040 | + | 0.705168i | \(0.750872\pi\) | |||||||
\(68\) | 0.450462 | + | 1.07877i | 0.0546265 | + | 0.130821i | ||||
\(69\) | −2.91679 | − | 7.04063i | −0.351141 | − | 0.847592i | ||||
\(70\) | 1.74897 | + | 8.72742i | 0.209042 | + | 1.04313i | ||||
\(71\) | 2.56670i | 0.304611i | 0.988333 | + | 0.152305i | \(0.0486697\pi\) | ||||
−0.988333 | + | 0.152305i | \(0.951330\pi\) | |||||||
\(72\) | −1.61873 | + | 8.32945i | −0.190769 | + | 0.981635i | ||||
\(73\) | 13.3885i | 1.56700i | 0.621391 | + | 0.783500i | \(0.286568\pi\) | ||||
−0.621391 | + | 0.783500i | \(0.713432\pi\) | |||||||
\(74\) | 10.5867 | − | 2.12156i | 1.23068 | − | 0.246627i | ||||
\(75\) | 0.458160 | + | 1.10592i | 0.0529037 | + | 0.127700i | ||||
\(76\) | −3.30584 | − | 7.91689i | −0.379206 | − | 0.908130i | ||||
\(77\) | −2.01587 | −0.229730 | ||||||||
\(78\) | 5.58252 | − | 6.84364i | 0.632096 | − | 0.774890i | ||||
\(79\) | 10.9069i | 1.22713i | 0.789646 | + | 0.613563i | \(0.210264\pi\) | ||||
−0.789646 | + | 0.613563i | \(0.789736\pi\) | |||||||
\(80\) | −6.78600 | − | 6.70882i | −0.758698 | − | 0.750068i | ||||
\(81\) | −0.00205378 | − | 9.00000i | −0.000228198 | − | 1.00000i | ||||
\(82\) | 0.193514 | − | 0.0387800i | 0.0213700 | − | 0.00428254i | ||||
\(83\) | 14.6776 | 1.61107 | 0.805536 | − | 0.592547i | \(-0.201877\pi\) | ||||
0.805536 | + | 0.592547i | \(0.201877\pi\) | |||||||
\(84\) | 6.48127 | + | 6.44358i | 0.707165 | + | 0.703052i | ||||
\(85\) | 1.39444 | 0.151249 | ||||||||
\(86\) | −8.56313 | + | 1.71605i | −0.923387 | + | 0.185046i | ||||
\(87\) | −5.73629 | − | 13.8464i | −0.614995 | − | 1.48449i | ||||
\(88\) | 1.79177 | − | 1.20837i | 0.191003 | − | 0.128813i | ||||
\(89\) | −5.68613 | −0.602729 | −0.301364 | − | 0.953509i | \(-0.597442\pi\) | ||||
−0.301364 | + | 0.953509i | \(0.597442\pi\) | |||||||
\(90\) | 8.42421 | + | 5.61008i | 0.887989 | + | 0.591354i | ||||
\(91\) | −2.77481 | − | 9.09877i | −0.290879 | − | 0.953810i | ||||
\(92\) | 8.12035 | − | 3.39080i | 0.846605 | − | 0.353515i | ||||
\(93\) | 4.70669 | + | 11.3611i | 0.488061 | + | 1.17809i | ||||
\(94\) | −0.247308 | − | 1.23408i | −0.0255079 | − | 0.127286i | ||||
\(95\) | −10.2335 | −1.04994 | ||||||||
\(96\) | −9.62322 | − | 1.84219i | −0.982166 | − | 0.188017i | ||||
\(97\) | − | 10.4965i | − | 1.06576i | −0.846191 | − | 0.532879i | \(-0.821110\pi\) | ||
0.846191 | − | 0.532879i | \(-0.178890\pi\) | |||||||
\(98\) | −0.0547056 | + | 0.0109630i | −0.00552610 | + | 0.00110743i | ||||
\(99\) | −1.62068 | + | 1.62105i | −0.162885 | + | 0.162922i | ||||
\(100\) | −1.27552 | + | 0.532614i | −0.127552 | + | 0.0532614i | ||||
\(101\) | −15.4371 | −1.53605 | −0.768023 | − | 0.640422i | \(-0.778759\pi\) | ||||
−0.768023 | + | 0.640422i | \(0.778759\pi\) | |||||||
\(102\) | 1.18930 | − | 0.797226i | 0.117758 | − | 0.0789371i | ||||
\(103\) | 4.99712i | 0.492381i | 0.969221 | + | 0.246191i | \(0.0791789\pi\) | ||||
−0.969221 | + | 0.246191i | \(0.920821\pi\) | |||||||
\(104\) | 7.92039 | + | 6.42397i | 0.776659 | + | 0.629922i | ||||
\(105\) | 10.0713 | − | 4.17235i | 0.982860 | − | 0.407180i | ||||
\(106\) | −1.11434 | + | 0.223312i | −0.108234 | + | 0.0216900i | ||||
\(107\) | − | 19.1495i | − | 1.85126i | −0.378434 | − | 0.925628i | \(-0.623537\pi\) | ||
0.378434 | − | 0.925628i | \(-0.376463\pi\) | |||||||
\(108\) | 10.3923 | − | 0.0314979i | 0.999995 | − | 0.00303088i | ||||
\(109\) | −7.05520 | −0.675766 | −0.337883 | − | 0.941188i | \(-0.609711\pi\) | ||||
−0.337883 | + | 0.941188i | \(0.609711\pi\) | |||||||
\(110\) | −0.506525 | − | 2.52758i | −0.0482953 | − | 0.240995i | ||||
\(111\) | −5.06122 | − | 12.2169i | −0.480389 | − | 1.15958i | ||||
\(112\) | −7.41940 | + | 7.50475i | −0.701067 | + | 0.709133i | ||||
\(113\) | 11.2283i | 1.05627i | 0.849160 | + | 0.528136i | \(0.177109\pi\) | ||||
−0.849160 | + | 0.528136i | \(0.822891\pi\) | |||||||
\(114\) | −8.72802 | + | 5.85067i | −0.817454 | + | 0.547965i | ||||
\(115\) | − | 10.4965i | − | 0.978804i | ||||||
\(116\) | 15.9698 | − | 6.66848i | 1.48276 | − | 0.619153i | ||||
\(117\) | −9.54756 | − | 5.08371i | −0.882672 | − | 0.469989i | ||||
\(118\) | −12.6614 | + | 2.53734i | −1.16558 | + | 0.233581i | ||||
\(119\) | − | 1.54214i | − | 0.141368i | ||||||
\(120\) | −6.45067 | + | 9.74555i | −0.588863 | + | 0.889643i | ||||
\(121\) | −10.4162 | −0.946925 | ||||||||
\(122\) | 2.63373 | + | 13.1424i | 0.238447 | + | 1.18986i | ||||
\(123\) | −0.0925140 | − | 0.223312i | −0.00834170 | − | 0.0201354i | ||||
\(124\) | −13.1034 | + | 5.47157i | −1.17672 | + | 0.491361i | ||||
\(125\) | − | 10.2793i | − | 0.919407i | ||||||
\(126\) | 6.20428 | − | 9.31648i | 0.552722 | − | 0.829978i | ||||
\(127\) | − | 3.17432i | − | 0.281675i | −0.990033 | − | 0.140838i | \(-0.955020\pi\) | ||
0.990033 | − | 0.140838i | \(-0.0449795\pi\) | |||||||
\(128\) | 2.09602 | − | 11.1179i | 0.185264 | − | 0.982689i | ||||
\(129\) | 4.09381 | + | 9.88174i | 0.360440 | + | 0.870039i | ||||
\(130\) | 10.7112 | − | 5.76540i | 0.939433 | − | 0.505659i | ||||
\(131\) | − | 6.42017i | − | 0.560933i | −0.959864 | − | 0.280467i | \(-0.909511\pi\) | ||
0.959864 | − | 0.280467i | \(-0.0904892\pi\) | |||||||
\(132\) | −1.87707 | − | 1.86615i | −0.163378 | − | 0.162427i | ||||
\(133\) | 11.3174i | 0.981345i | ||||||||
\(134\) | 3.20790 | + | 16.0075i | 0.277120 | + | 1.38284i | ||||
\(135\) | 4.74178 | − | 11.4532i | 0.408107 | − | 0.985735i | ||||
\(136\) | 0.924402 | + | 1.37070i | 0.0792669 | + | 0.117537i | ||||
\(137\) | 6.69918 | 0.572350 | 0.286175 | − | 0.958177i | \(-0.407616\pi\) | ||||
0.286175 | + | 0.958177i | \(0.407616\pi\) | |||||||
\(138\) | −6.00102 | − | 8.95232i | −0.510841 | − | 0.762072i | ||||
\(139\) | 10.4217 | 0.883957 | 0.441979 | − | 0.897026i | \(-0.354277\pi\) | ||||
0.441979 | + | 0.897026i | \(0.354277\pi\) | |||||||
\(140\) | 4.85039 | + | 11.6158i | 0.409933 | + | 0.981715i | ||||
\(141\) | −1.42411 | + | 0.589981i | −0.119932 | + | 0.0496854i | ||||
\(142\) | 0.713240 | + | 3.55909i | 0.0598538 | + | 0.298673i | ||||
\(143\) | 0.803622 | + | 2.63513i | 0.0672023 | + | 0.220361i | ||||
\(144\) | 0.0700026 | + | 11.9998i | 0.00583355 | + | 0.999983i | ||||
\(145\) | − | 20.6429i | − | 1.71430i | ||||||
\(146\) | 3.72042 | + | 18.5650i | 0.307904 | + | 1.53645i | ||||
\(147\) | 0.0261533 | + | 0.0631295i | 0.00215709 | + | 0.00520683i | ||||
\(148\) | 14.0904 | − | 5.88370i | 1.15822 | − | 0.483637i | ||||
\(149\) | − | 4.48086i | − | 0.367086i | −0.983012 | − | 0.183543i | \(-0.941243\pi\) | ||
0.983012 | − | 0.183543i | \(-0.0587567\pi\) | |||||||
\(150\) | 0.942620 | + | 1.40620i | 0.0769646 | + | 0.114816i | ||||
\(151\) | −5.12597 | −0.417145 | −0.208573 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208573 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(152\) | −6.78399 | − | 10.0593i | −0.550254 | − | 0.815915i | ||||
\(153\) | −1.24010 | − | 1.23982i | −0.100256 | − | 0.100233i | ||||
\(154\) | −2.79530 | + | 0.560175i | −0.225251 | + | 0.0451402i | ||||
\(155\) | 16.9377i | 1.36047i | ||||||||
\(156\) | 5.83924 | − | 11.0410i | 0.467513 | − | 0.883986i | ||||
\(157\) | − | 7.23041i | − | 0.577050i | −0.957472 | − | 0.288525i | \(-0.906835\pi\) | ||
0.957472 | − | 0.288525i | \(-0.0931648\pi\) | |||||||
\(158\) | 3.03085 | + | 15.1240i | 0.241121 | + | 1.20320i | ||||
\(159\) | 0.532736 | + | 1.28593i | 0.0422487 | + | 0.101981i | ||||
\(160\) | −11.2740 | − | 7.41703i | −0.891290 | − | 0.586368i | ||||
\(161\) | −11.6083 | −0.914860 | ||||||||
\(162\) | −2.50379 | − | 12.4792i | −0.196716 | − | 0.980460i | ||||
\(163\) | 14.7862i | 1.15814i | 0.815276 | + | 0.579072i | \(0.196585\pi\) | ||||
−0.815276 | + | 0.579072i | \(0.803415\pi\) | |||||||
\(164\) | 0.257559 | − | 0.107548i | 0.0201119 | − | 0.00839810i | ||||
\(165\) | −2.91679 | + | 1.20837i | −0.227072 | + | 0.0940715i | ||||
\(166\) | 20.3526 | − | 4.07864i | 1.57966 | − | 0.316564i | ||||
\(167\) | 18.3295i | 1.41838i | 0.705019 | + | 0.709189i | \(0.250938\pi\) | ||||
−0.705019 | + | 0.709189i | \(0.749062\pi\) | |||||||
\(168\) | 10.7778 | + | 7.13391i | 0.831523 | + | 0.550393i | ||||
\(169\) | −10.7877 | + | 7.25440i | −0.829820 | + | 0.558031i | ||||
\(170\) | 1.93360 | − | 0.387491i | 0.148300 | − | 0.0297192i | ||||
\(171\) | 9.10084 | + | 9.09877i | 0.695959 | + | 0.695800i | ||||
\(172\) | −11.3972 | + | 4.75909i | −0.869025 | + | 0.362877i | ||||
\(173\) | 15.4371 | 1.17366 | 0.586829 | − | 0.809711i | \(-0.300376\pi\) | ||||
0.586829 | + | 0.809711i | \(0.300376\pi\) | |||||||
\(174\) | −11.8019 | − | 17.6060i | −0.894696 | − | 1.33471i | ||||
\(175\) | 1.82339 | 0.137835 | ||||||||
\(176\) | 2.14876 | − | 2.17348i | 0.161969 | − | 0.163832i | ||||
\(177\) | 6.05310 | + | 14.6111i | 0.454979 | + | 1.09824i | ||||
\(178\) | −7.88464 | + | 1.58008i | −0.590979 | + | 0.118432i | ||||
\(179\) | − | 2.31859i | − | 0.173300i | −0.996239 | − | 0.0866499i | \(-0.972384\pi\) | ||
0.996239 | − | 0.0866499i | \(-0.0276162\pi\) | |||||||
\(180\) | 13.2403 | + | 5.43825i | 0.986875 | + | 0.405343i | ||||
\(181\) | − | 20.4624i | − | 1.52096i | −0.649364 | − | 0.760478i | \(-0.724965\pi\) | ||
0.649364 | − | 0.760478i | \(-0.275035\pi\) | |||||||
\(182\) | −6.37605 | − | 11.8457i | −0.472625 | − | 0.878060i | ||||
\(183\) | 15.1662 | − | 6.28305i | 1.12112 | − | 0.464457i | ||||
\(184\) | 10.3178 | − | 6.95833i | 0.760637 | − | 0.512975i | ||||
\(185\) | − | 18.2135i | − | 1.33908i | ||||||
\(186\) | 9.68356 | + | 14.4459i | 0.710033 | + | 1.05923i | ||||
\(187\) | 0.446625i | 0.0326604i | ||||||||
\(188\) | −0.685858 | − | 1.64251i | −0.0500213 | − | 0.119792i | ||||
\(189\) | −12.6663 | − | 5.24401i | −0.921338 | − | 0.381446i | ||||
\(190\) | −14.1902 | + | 2.84371i | −1.02947 | + | 0.206305i | ||||
\(191\) | −21.7061 | −1.57060 | −0.785299 | − | 0.619117i | \(-0.787491\pi\) | ||||
−0.785299 | + | 0.619117i | \(0.787491\pi\) | |||||||
\(192\) | −13.8559 | + | 0.119666i | −0.999963 | + | 0.00863617i | ||||
\(193\) | 4.36245i | 0.314016i | 0.987597 | + | 0.157008i | \(0.0501849\pi\) | ||||
−0.987597 | + | 0.157008i | \(0.949815\pi\) | |||||||
\(194\) | −2.91679 | − | 14.5549i | −0.209414 | − | 1.04498i | ||||
\(195\) | −9.46897 | − | 11.5018i | −0.678087 | − | 0.823664i | ||||
\(196\) | −0.0728107 | + | 0.0304034i | −0.00520077 | + | 0.00217167i | ||||
\(197\) | − | 23.5782i | − | 1.67988i | −0.542680 | − | 0.839939i | \(-0.682590\pi\) | ||
0.542680 | − | 0.839939i | \(-0.317410\pi\) | |||||||
\(198\) | −1.79685 | + | 2.69818i | −0.127696 | + | 0.191751i | ||||
\(199\) | − | 10.9069i | − | 0.773172i | −0.922253 | − | 0.386586i | \(-0.873654\pi\) | ||
0.922253 | − | 0.386586i | \(-0.126346\pi\) | |||||||
\(200\) | −1.62068 | + | 1.09299i | −0.114600 | + | 0.0772861i | ||||
\(201\) | 18.4725 | − | 7.65279i | 1.30295 | − | 0.539786i | ||||
\(202\) | −21.4057 | + | 4.28969i | −1.50610 | + | 0.301822i | ||||
\(203\) | −22.8293 | −1.60230 | ||||||||
\(204\) | 1.42760 | − | 1.43595i | 0.0999521 | − | 0.100537i | ||||
\(205\) | − | 0.332925i | − | 0.0232525i | ||||||
\(206\) | 1.38861 | + | 6.92923i | 0.0967492 | + | 0.482782i | ||||
\(207\) | −9.33260 | + | 9.33473i | −0.648660 | + | 0.648808i | ||||
\(208\) | 12.7679 | + | 6.70682i | 0.885293 | + | 0.465034i | ||||
\(209\) | − | 3.27768i | − | 0.226722i | ||||||
\(210\) | 12.8059 | − | 8.58421i | 0.883692 | − | 0.592367i | ||||
\(211\) | 19.5978 | 1.34917 | 0.674584 | − | 0.738198i | \(-0.264323\pi\) | ||||
0.674584 | + | 0.738198i | \(0.264323\pi\) | |||||||
\(212\) | −1.48314 | + | 0.619310i | −0.101862 | + | 0.0425344i | ||||
\(213\) | 4.10715 | − | 1.70151i | 0.281417 | − | 0.116586i | ||||
\(214\) | −5.32132 | − | 26.5536i | −0.363758 | − | 1.81517i | ||||
\(215\) | 14.7322i | 1.00473i | ||||||||
\(216\) | 14.4016 | − | 2.93150i | 0.979905 | − | 0.199463i | ||||
\(217\) | 18.7317 | 1.27159 | ||||||||
\(218\) | −9.78306 | + | 1.96052i | −0.662592 | + | 0.132783i | ||||
\(219\) | 21.4238 | − | 8.87546i | 1.44769 | − | 0.599748i | ||||
\(220\) | −1.40474 | − | 3.36410i | −0.0947076 | − | 0.226808i | ||||
\(221\) | −2.01587 | + | 0.614770i | −0.135602 | + | 0.0413539i | ||||
\(222\) | −10.4130 | − | 15.5340i | −0.698872 | − | 1.04258i | ||||
\(223\) | 6.46108 | 0.432666 | 0.216333 | − | 0.976320i | \(-0.430590\pi\) | ||||
0.216333 | + | 0.976320i | \(0.430590\pi\) | |||||||
\(224\) | −8.20262 | + | 12.4681i | −0.548061 | + | 0.833063i | ||||
\(225\) | 1.46593 | − | 1.46627i | 0.0977288 | − | 0.0977511i | ||||
\(226\) | 3.12015 | + | 15.5697i | 0.207549 | + | 1.03568i | ||||
\(227\) | −10.9383 | −0.725998 | −0.362999 | − | 0.931789i | \(-0.618247\pi\) | ||||
−0.362999 | + | 0.931789i | \(0.618247\pi\) | |||||||
\(228\) | −10.4769 | + | 10.5382i | −0.693847 | + | 0.697906i | ||||
\(229\) | −22.2189 | −1.46826 | −0.734132 | − | 0.679007i | \(-0.762410\pi\) | ||||
−0.734132 | + | 0.679007i | \(0.762410\pi\) | |||||||
\(230\) | −2.91679 | − | 14.5549i | −0.192328 | − | 0.959723i | ||||
\(231\) | 1.33636 | + | 3.22573i | 0.0879259 | + | 0.212238i | ||||
\(232\) | 20.2914 | − | 13.6845i | 1.33219 | − | 0.898434i | ||||
\(233\) | 16.4500i | 1.07768i | 0.842409 | + | 0.538839i | \(0.181137\pi\) | ||||
−0.842409 | + | 0.538839i | \(0.818863\pi\) | |||||||
\(234\) | −14.6517 | − | 4.39620i | −0.957814 | − | 0.287388i | ||||
\(235\) | −2.12313 | −0.138498 | ||||||||
\(236\) | −16.8518 | + | 7.03678i | −1.09696 | + | 0.458055i | ||||
\(237\) | 17.4529 | − | 7.23041i | 1.13369 | − | 0.469666i | ||||
\(238\) | −0.428533 | − | 2.13840i | −0.0277777 | − | 0.138612i | ||||
\(239\) | 28.2054i | 1.82446i | 0.409681 | + | 0.912229i | \(0.365640\pi\) | ||||
−0.409681 | + | 0.912229i | \(0.634360\pi\) | |||||||
\(240\) | −6.23667 | + | 15.3061i | −0.402575 | + | 0.988007i | ||||
\(241\) | 8.57938i | 0.552646i | 0.961065 | + | 0.276323i | \(0.0891160\pi\) | ||||
−0.961065 | + | 0.276323i | \(0.910884\pi\) | |||||||
\(242\) | −14.4435 | + | 2.89447i | −0.928465 | + | 0.186064i | ||||
\(243\) | −14.4002 | + | 5.96955i | −0.923770 | + | 0.382947i | ||||
\(244\) | 7.30410 | + | 17.4920i | 0.467597 | + | 1.11981i | ||||
\(245\) | 0.0941165i | 0.00601288i | ||||||||
\(246\) | −0.190339 | − | 0.283947i | −0.0121355 | − | 0.0181038i | ||||
\(247\) | 14.7940 | − | 4.51166i | 0.941322 | − | 0.287070i | ||||
\(248\) | −16.6493 | + | 11.2283i | −1.05723 | + | 0.712999i | ||||
\(249\) | −9.73003 | − | 23.4866i | −0.616615 | − | 1.48840i | ||||
\(250\) | −2.85643 | − | 14.2537i | −0.180657 | − | 0.901484i | ||||
\(251\) | − | 3.97532i | − | 0.250920i | −0.992099 | − | 0.125460i | \(-0.959959\pi\) | ||
0.992099 | − | 0.125460i | \(-0.0400407\pi\) | |||||||
\(252\) | 6.01425 | − | 14.6427i | 0.378862 | − | 0.922403i | ||||
\(253\) | 3.36192 | 0.211362 | ||||||||
\(254\) | −0.882087 | − | 4.40165i | −0.0553471 | − | 0.276184i | ||||
\(255\) | −0.924402 | − | 2.23134i | −0.0578883 | − | 0.139732i | ||||
\(256\) | −0.183019 | − | 15.9990i | −0.0114387 | − | 0.999935i | ||||
\(257\) | − | 13.5763i | − | 0.846868i | −0.905927 | − | 0.423434i | \(-0.860825\pi\) | ||
0.905927 | − | 0.423434i | \(-0.139175\pi\) | |||||||
\(258\) | 8.42262 | + | 12.5649i | 0.524370 | + | 0.782254i | ||||
\(259\) | −20.1426 | −1.25160 | ||||||||
\(260\) | 13.2505 | − | 10.9710i | 0.821761 | − | 0.680393i | ||||
\(261\) | −18.3539 | + | 18.3581i | −1.13608 | + | 1.13633i | ||||
\(262\) | −1.78405 | − | 8.90249i | −0.110219 | − | 0.549998i | ||||
\(263\) | 9.86533 | 0.608322 | 0.304161 | − | 0.952621i | \(-0.401624\pi\) | ||||
0.304161 | + | 0.952621i | \(0.401624\pi\) | |||||||
\(264\) | −3.12139 | − | 2.06608i | −0.192108 | − | 0.127158i | ||||
\(265\) | 1.91713i | 0.117768i | ||||||||
\(266\) | 3.14491 | + | 15.6932i | 0.192827 | + | 0.962214i | ||||
\(267\) | 3.76944 | + | 9.09877i | 0.230686 | + | 0.556836i | ||||
\(268\) | 8.89643 | + | 21.3053i | 0.543436 | + | 1.30143i | ||||
\(269\) | 13.4212 | 0.818305 | 0.409152 | − | 0.912466i | \(-0.365824\pi\) | ||||
0.409152 | + | 0.912466i | \(0.365824\pi\) | |||||||
\(270\) | 3.39251 | − | 17.1992i | 0.206462 | − | 1.04671i | ||||
\(271\) | 10.7867 | 0.655247 | 0.327624 | − | 0.944808i | \(-0.393752\pi\) | ||||
0.327624 | + | 0.944808i | \(0.393752\pi\) | |||||||
\(272\) | 1.66271 | + | 1.64380i | 0.100817 | + | 0.0996699i | ||||
\(273\) | −12.7201 | + | 10.4719i | −0.769855 | + | 0.633788i | ||||
\(274\) | 9.28938 | − | 1.86158i | 0.561192 | − | 0.112462i | ||||
\(275\) | −0.528078 | −0.0318443 | ||||||||
\(276\) | −10.8090 | − | 10.7461i | −0.650624 | − | 0.646839i | ||||
\(277\) | 4.93632i | 0.296594i | 0.988943 | + | 0.148297i | \(0.0473792\pi\) | ||||
−0.988943 | + | 0.148297i | \(0.952621\pi\) | |||||||
\(278\) | 14.4512 | − | 2.89601i | 0.866725 | − | 0.173691i | ||||
\(279\) | 15.0596 | − | 15.0630i | 0.901592 | − | 0.901798i | ||||
\(280\) | 9.95360 | + | 14.7592i | 0.594841 | + | 0.882028i | ||||
\(281\) | −1.15261 | −0.0687587 | −0.0343794 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343794 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(282\) | −1.81079 | + | 1.21383i | −0.107831 | + | 0.0722824i | ||||
\(283\) | −5.16258 | −0.306884 | −0.153442 | − | 0.988158i | \(-0.549036\pi\) | ||||
−0.153442 | + | 0.988158i | \(0.549036\pi\) | |||||||
\(284\) | 1.97802 | + | 4.73700i | 0.117374 | + | 0.281089i | ||||
\(285\) | 6.78399 | + | 16.3754i | 0.401849 | + | 0.969992i | ||||
\(286\) | 1.84659 | + | 3.43067i | 0.109191 | + | 0.202860i | ||||
\(287\) | −0.368187 | −0.0217334 | ||||||||
\(288\) | 3.43160 | + | 16.6200i | 0.202209 | + | 0.979342i | ||||
\(289\) | 16.6583 | 0.979902 | ||||||||
\(290\) | −5.73629 | − | 28.6243i | −0.336846 | − | 1.68088i | ||||
\(291\) | −16.7962 | + | 6.95833i | −0.984610 | + | 0.407904i | ||||
\(292\) | 10.3178 | + | 24.7092i | 0.603803 | + | 1.44600i | ||||
\(293\) | 5.96029i | 0.348204i | 0.984728 | + | 0.174102i | \(0.0557022\pi\) | ||||
−0.984728 | + | 0.174102i | \(0.944298\pi\) | |||||||
\(294\) | 0.0538079 | + | 0.0802706i | 0.00313814 | + | 0.00468147i | ||||
\(295\) | 21.7830i | 1.26825i | ||||||||
\(296\) | 17.9034 | − | 12.0741i | 1.04061 | − | 0.701792i | ||||
\(297\) | 3.66834 | + | 1.51874i | 0.212858 | + | 0.0881262i | ||||
\(298\) | −1.24515 | − | 6.21335i | −0.0721297 | − | 0.359930i | ||||
\(299\) | 4.62761 | + | 15.1742i | 0.267622 | + | 0.877548i | ||||
\(300\) | 1.69784 | + | 1.68796i | 0.0980246 | + | 0.0974544i | ||||
\(301\) | 16.2926 | 0.939088 | ||||||||
\(302\) | −7.10789 | + | 1.42442i | −0.409013 | + | 0.0819659i | ||||
\(303\) | 10.2335 | + | 24.7019i | 0.587900 | + | 1.41909i | ||||
\(304\) | −12.2023 | − | 12.0635i | −0.699848 | − | 0.691888i | ||||
\(305\) | 22.6105 | 1.29467 | ||||||||
\(306\) | −2.06411 | − | 1.37459i | −0.117997 | − | 0.0785798i | ||||
\(307\) | − | 8.30199i | − | 0.473820i | −0.971532 | − | 0.236910i | \(-0.923865\pi\) | ||
0.971532 | − | 0.236910i | \(-0.0761346\pi\) | |||||||
\(308\) | −3.72042 | + | 1.55353i | −0.211990 | + | 0.0885204i | ||||
\(309\) | 7.99624 | − | 3.31268i | 0.454890 | − | 0.188452i | ||||
\(310\) | 4.70669 | + | 23.4866i | 0.267322 | + | 1.33395i | ||||
\(311\) | −5.46540 | −0.309914 | −0.154957 | − | 0.987921i | \(-0.549524\pi\) | ||||
−0.154957 | + | 0.987921i | \(0.549524\pi\) | |||||||
\(312\) | 5.02885 | − | 16.9325i | 0.284703 | − | 0.958616i | ||||
\(313\) | 5.46660 | 0.308991 | 0.154495 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154495 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(314\) | −2.00920 | − | 10.0260i | −0.113386 | − | 0.565800i | ||||
\(315\) | −13.3529 | − | 13.3499i | −0.752352 | − | 0.752181i | ||||
\(316\) | 8.40541 | + | 20.1294i | 0.472841 | + | 1.13237i | ||||
\(317\) | 1.11720i | 0.0627481i | 0.999508 | + | 0.0313741i | \(0.00998831\pi\) | ||||
−0.999508 | + | 0.0313741i | \(0.990012\pi\) | |||||||
\(318\) | 1.09605 | + | 1.63509i | 0.0614636 | + | 0.0916913i | ||||
\(319\) | 6.61168 | 0.370183 | ||||||||
\(320\) | −17.6941 | − | 7.15192i | −0.989132 | − | 0.399805i | ||||
\(321\) | −30.6425 | + | 12.6946i | −1.71030 | + | 0.708543i | ||||
\(322\) | −16.0965 | + | 3.22573i | −0.897025 | + | 0.179763i | ||||
\(323\) | 2.50742 | 0.139517 | ||||||||
\(324\) | −6.93962 | − | 16.6085i | −0.385534 | − | 0.922693i | ||||
\(325\) | −0.726889 | − | 2.38351i | −0.0403205 | − | 0.132214i | ||||
\(326\) | 4.10882 | + | 20.5032i | 0.227567 | + | 1.13557i | ||||
\(327\) | 4.67703 | + | 11.2895i | 0.258640 | + | 0.624312i | ||||
\(328\) | 0.327256 | − | 0.220702i | 0.0180697 | − | 0.0121862i | ||||
\(329\) | 2.34801i | 0.129450i | ||||||||
\(330\) | −3.70877 | + | 2.48611i | −0.204161 | + | 0.136856i | ||||
\(331\) | 21.5940i | 1.18691i | 0.804866 | + | 0.593456i | \(0.202237\pi\) | ||||
−0.804866 | + | 0.593456i | \(0.797763\pi\) | |||||||
\(332\) | 27.0884 | − | 11.3112i | 1.48667 | − | 0.620785i | ||||
\(333\) | −16.1939 | + | 16.1976i | −0.887420 | + | 0.887623i | ||||
\(334\) | 5.09344 | + | 25.4164i | 0.278700 | + | 1.39073i | ||||
\(335\) | 27.5397 | 1.50465 | ||||||||
\(336\) | 16.9273 | + | 6.89724i | 0.923461 | + | 0.376275i | ||||
\(337\) | −23.6501 | −1.28830 | −0.644152 | − | 0.764898i | \(-0.722790\pi\) | ||||
−0.644152 | + | 0.764898i | \(0.722790\pi\) | |||||||
\(338\) | −12.9428 | + | 13.0570i | −0.703994 | + | 0.710206i | ||||
\(339\) | 17.9672 | − | 7.44346i | 0.975845 | − | 0.404273i | ||||
\(340\) | 2.57353 | − | 1.07462i | 0.139569 | − | 0.0582797i | ||||
\(341\) | −5.42496 | −0.293778 | ||||||||
\(342\) | 15.1480 | + | 10.0878i | 0.819111 | + | 0.545485i | ||||
\(343\) | 18.5721 | 1.00280 | ||||||||
\(344\) | −14.4813 | + | 9.76623i | −0.780781 | + | 0.526560i | ||||
\(345\) | −16.7962 | + | 6.95833i | −0.904276 | + | 0.374624i | ||||
\(346\) | 21.4057 | − | 4.28969i | 1.15078 | − | 0.230615i | ||||
\(347\) | 6.66848i | 0.357983i | 0.983851 | + | 0.178991i | \(0.0572834\pi\) | ||||
−0.983851 | + | 0.178991i | \(0.942717\pi\) | |||||||
\(348\) | −21.2574 | − | 21.1337i | −1.13951 | − | 1.13289i | ||||
\(349\) | −34.9112 | −1.86875 | −0.934376 | − | 0.356289i | \(-0.884042\pi\) | ||||
−0.934376 | + | 0.356289i | \(0.884042\pi\) | |||||||
\(350\) | 2.52839 | − | 0.506687i | 0.135148 | − | 0.0270836i | ||||
\(351\) | −1.80554 | + | 18.6478i | −0.0963725 | + | 0.995345i | ||||
\(352\) | 2.37559 | − | 3.61095i | 0.126619 | − | 0.192464i | ||||
\(353\) | −4.70688 | −0.250522 | −0.125261 | − | 0.992124i | \(-0.539977\pi\) | ||||
−0.125261 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(354\) | 12.4537 | + | 18.5784i | 0.661905 | + | 0.987429i | ||||
\(355\) | 6.12313 | 0.324982 | ||||||||
\(356\) | −10.4941 | + | 4.38200i | −0.556187 | + | 0.232246i | ||||
\(357\) | −2.46768 | + | 1.02231i | −0.130604 | + | 0.0541065i | ||||
\(358\) | −0.644297 | − | 3.21506i | −0.0340521 | − | 0.169921i | ||||
\(359\) | − | 17.1329i | − | 0.904242i | −0.891957 | − | 0.452121i | \(-0.850668\pi\) | ||
0.891957 | − | 0.452121i | \(-0.149332\pi\) | |||||||
\(360\) | 19.8708 | + | 3.86166i | 1.04728 | + | 0.203527i | ||||
\(361\) | 0.598561 | 0.0315032 | ||||||||
\(362\) | −5.68613 | − | 28.3740i | −0.298856 | − | 1.49131i | ||||
\(363\) | 6.90508 | + | 16.6676i | 0.362422 | + | 0.874824i | ||||
\(364\) | −12.1330 | − | 14.6539i | −0.635943 | − | 0.768076i | ||||
\(365\) | 31.9396 | 1.67180 | ||||||||
\(366\) | 19.2841 | − | 12.9268i | 1.00800 | − | 0.675693i | ||||
\(367\) | − | 3.48197i | − | 0.181757i | −0.995862 | − | 0.0908787i | \(-0.971032\pi\) | ||
0.995862 | − | 0.0908787i | \(-0.0289676\pi\) | |||||||
\(368\) | 12.3735 | − | 12.5159i | 0.645013 | − | 0.652434i | ||||
\(369\) | −0.296008 | + | 0.296076i | −0.0154096 | + | 0.0154131i | ||||
\(370\) | −5.06122 | − | 25.2557i | −0.263120 | − | 1.31298i | ||||
\(371\) | 2.12018 | 0.110074 | ||||||||
\(372\) | 17.4419 | + | 17.3405i | 0.904322 | + | 0.899061i | ||||
\(373\) | − | 22.5462i | − | 1.16740i | −0.811970 | − | 0.583699i | \(-0.801605\pi\) | ||
0.811970 | − | 0.583699i | \(-0.198395\pi\) | |||||||
\(374\) | 0.124109 | + | 0.619310i | 0.00641753 | + | 0.0320237i | ||||
\(375\) | −16.4486 | + | 6.81433i | −0.849401 | + | 0.351890i | ||||
\(376\) | −1.40746 | − | 2.08698i | −0.0725844 | − | 0.107628i | ||||
\(377\) | 9.10084 | + | 29.8423i | 0.468717 | + | 1.53695i | ||||
\(378\) | −19.0209 | − | 3.75184i | −0.978328 | − | 0.192974i | ||||
\(379\) | 24.4044i | 1.25357i | 0.779193 | + | 0.626784i | \(0.215629\pi\) | ||||
−0.779193 | + | 0.626784i | \(0.784371\pi\) | |||||||
\(380\) | −18.8866 | + | 7.88644i | −0.968862 | + | 0.404566i | ||||
\(381\) | −5.07944 | + | 2.10431i | −0.260228 | + | 0.107807i | ||||
\(382\) | −30.0986 | + | 6.03174i | −1.53998 | + | 0.308611i | ||||
\(383\) | 10.6604i | 0.544722i | 0.962195 | + | 0.272361i | \(0.0878045\pi\) | ||||
−0.962195 | + | 0.272361i | \(0.912196\pi\) | |||||||
\(384\) | −19.1799 | + | 4.01624i | −0.978772 | + | 0.204953i | ||||
\(385\) | 4.80908i | 0.245093i | ||||||||
\(386\) | 1.21225 | + | 6.04917i | 0.0617018 | + | 0.307895i | ||||
\(387\) | 13.0986 | − | 13.1016i | 0.665839 | − | 0.665991i | ||||
\(388\) | −8.08911 | − | 19.3720i | −0.410662 | − | 0.983462i | ||||
\(389\) | −29.1201 | −1.47645 | −0.738224 | − | 0.674555i | \(-0.764335\pi\) | ||||
−0.738224 | + | 0.674555i | \(0.764335\pi\) | |||||||
\(390\) | −16.3263 | − | 13.3177i | −0.826712 | − | 0.674368i | ||||
\(391\) | 2.57186i | 0.130065i | ||||||||
\(392\) | −0.0925140 | + | 0.0623915i | −0.00467266 | + | 0.00315125i | ||||
\(393\) | −10.2734 | + | 4.25605i | −0.518222 | + | 0.214689i | ||||
\(394\) | −6.55197 | − | 32.6946i | −0.330084 | − | 1.64713i | ||||
\(395\) | 26.0197 | 1.30919 | ||||||||
\(396\) | −1.74181 | + | 4.24073i | −0.0875292 | + | 0.213105i | ||||
\(397\) | −6.54151 | −0.328309 | −0.164154 | − | 0.986435i | \(-0.552490\pi\) | ||||
−0.164154 | + | 0.986435i | \(0.552490\pi\) | |||||||
\(398\) | −3.03085 | − | 15.1240i | −0.151923 | − | 0.758100i | ||||
\(399\) | 18.1098 | − | 7.50253i | 0.906623 | − | 0.375596i | ||||
\(400\) | −1.94359 | + | 1.96595i | −0.0971793 | + | 0.0982973i | ||||
\(401\) | −28.2966 | −1.41307 | −0.706533 | − | 0.707681i | \(-0.749742\pi\) | ||||
−0.706533 | + | 0.707681i | \(0.749742\pi\) | |||||||
\(402\) | 23.4882 | − | 15.7449i | 1.17148 | − | 0.785283i | ||||
\(403\) | −7.46735 | − | 24.4859i | −0.371975 | − | 1.21973i | ||||
\(404\) | −28.4901 | + | 11.8965i | −1.41743 | + | 0.591875i | ||||
\(405\) | −21.4705 | + | 0.00489951i | −1.06688 | + | 0.000243459i | ||||
\(406\) | −31.6561 | + | 6.34386i | −1.57107 | + | 0.314840i | ||||
\(407\) | 5.83359 | 0.289160 | ||||||||
\(408\) | 1.58055 | − | 2.38786i | 0.0782488 | − | 0.118217i | ||||
\(409\) | − | 30.6927i | − | 1.51766i | −0.651290 | − | 0.758829i | \(-0.725772\pi\) | ||
0.651290 | − | 0.758829i | \(-0.274228\pi\) | |||||||
\(410\) | −0.0925140 | − | 0.461648i | −0.00456894 | − | 0.0227992i | ||||
\(411\) | −4.44101 | − | 10.7198i | −0.219059 | − | 0.528770i | ||||
\(412\) | 3.85102 | + | 9.22250i | 0.189726 | + | 0.454360i | ||||
\(413\) | 24.0902 | 1.18540 | ||||||||
\(414\) | −10.3470 | + | 15.5373i | −0.508529 | + | 0.763617i | ||||
\(415\) | − | 35.0149i | − | 1.71881i | ||||||
\(416\) | 19.5682 | + | 5.75200i | 0.959410 | + | 0.282015i | ||||
\(417\) | −6.90874 | − | 16.6765i | −0.338322 | − | 0.816651i | ||||
\(418\) | −0.910810 | − | 4.54498i | −0.0445492 | − | 0.222302i | ||||
\(419\) | 4.78509i | 0.233767i | 0.993146 | + | 0.116883i | \(0.0372904\pi\) | ||||
−0.993146 | + | 0.116883i | \(0.962710\pi\) | |||||||
\(420\) | 15.3718 | − | 15.4618i | 0.750069 | − | 0.754458i | ||||
\(421\) | 4.18333 | 0.203883 | 0.101942 | − | 0.994790i | \(-0.467495\pi\) | ||||
0.101942 | + | 0.994790i | \(0.467495\pi\) | |||||||
\(422\) | 27.1752 | − | 5.44589i | 1.32287 | − | 0.265102i | ||||
\(423\) | 1.88814 | + | 1.88771i | 0.0918044 | + | 0.0917835i | ||||
\(424\) | −1.88449 | + | 1.27090i | −0.0915187 | + | 0.0617203i | ||||
\(425\) | − | 0.403979i | − | 0.0195959i | ||||||
\(426\) | 5.22233 | − | 3.50069i | 0.253023 | − | 0.169609i | ||||
\(427\) | − | 25.0053i | − | 1.21009i | ||||||
\(428\) | −14.7576 | − | 35.3417i | −0.713333 | − | 1.70831i | ||||
\(429\) | 3.68391 | − | 3.03281i | 0.177861 | − | 0.146425i | ||||
\(430\) | 4.09381 | + | 20.4283i | 0.197421 | + | 0.985139i | ||||
\(431\) | − | 19.8528i | − | 0.956274i | −0.878285 | − | 0.478137i | \(-0.841312\pi\) | ||
0.878285 | − | 0.478137i | \(-0.158688\pi\) | |||||||
\(432\) | 19.1553 | − | 8.06690i | 0.921609 | − | 0.388119i | ||||
\(433\) | 24.3561 | 1.17048 | 0.585240 | − | 0.810860i | \(-0.301000\pi\) | ||||
0.585240 | + | 0.810860i | \(0.301000\pi\) | |||||||
\(434\) | 25.9742 | − | 5.20521i | 1.24680 | − | 0.249858i | ||||
\(435\) | −33.0321 | + | 13.6845i | −1.58377 | + | 0.656123i | ||||
\(436\) | −13.0208 | + | 5.43708i | −0.623584 | + | 0.260389i | ||||
\(437\) | − | 18.8743i | − | 0.902882i | ||||||
\(438\) | 27.2408 | − | 18.2604i | 1.30162 | − | 0.872515i | ||||
\(439\) | 16.7139i | 0.797712i | 0.917014 | + | 0.398856i | \(0.130593\pi\) | ||||
−0.917014 | + | 0.398856i | \(0.869407\pi\) | |||||||
\(440\) | −2.88270 | − | 4.27446i | −0.137427 | − | 0.203777i | ||||
\(441\) | 0.0836803 | − | 0.0836994i | 0.00398478 | − | 0.00398569i | ||||
\(442\) | −2.62446 | + | 1.41264i | −0.124833 | + | 0.0671925i | ||||
\(443\) | − | 27.4553i | − | 1.30444i | −0.758030 | − | 0.652219i | \(-0.773838\pi\) | ||
0.758030 | − | 0.652219i | \(-0.226162\pi\) | |||||||
\(444\) | −18.7557 | − | 18.6466i | −0.890107 | − | 0.884929i | ||||
\(445\) | 13.5649i | 0.643037i | ||||||||
\(446\) | 8.95921 | − | 1.79542i | 0.424231 | − | 0.0850156i | ||||
\(447\) | −7.17013 | + | 2.97044i | −0.339135 | + | 0.140497i | ||||
\(448\) | −7.90944 | + | 19.5682i | −0.373686 | + | 0.924512i | ||||
\(449\) | 19.3205 | 0.911791 | 0.455895 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455895 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(450\) | 1.62528 | − | 2.44055i | 0.0766162 | − | 0.115048i | ||||
\(451\) | 0.106632 | 0.00502111 | ||||||||
\(452\) | 8.65308 | + | 20.7226i | 0.407007 | + | 0.974708i | ||||
\(453\) | 3.39810 | + | 8.20241i | 0.159657 | + | 0.385383i | ||||
\(454\) | −15.1675 | + | 3.03955i | −0.711845 | + | 0.142653i | ||||
\(455\) | −21.7061 | + | 6.61960i | −1.01760 | + | 0.310332i | ||||
\(456\) | −11.5993 | + | 17.5240i | −0.543187 | + | 0.820637i | ||||
\(457\) | − | 22.5600i | − | 1.05531i | −0.849458 | − | 0.527656i | \(-0.823071\pi\) | ||
0.849458 | − | 0.527656i | \(-0.176929\pi\) | |||||||
\(458\) | −30.8096 | + | 6.17423i | −1.43964 | + | 0.288503i | ||||
\(459\) | −1.16183 | + | 2.80627i | −0.0542297 | + | 0.130986i | ||||
\(460\) | −8.08911 | − | 19.3720i | −0.377157 | − | 0.903222i | ||||
\(461\) | 17.8735i | 0.832451i | 0.909261 | + | 0.416226i | \(0.136647\pi\) | ||||
−0.909261 | + | 0.416226i | \(0.863353\pi\) | |||||||
\(462\) | 2.74943 | + | 4.10159i | 0.127915 | + | 0.190823i | ||||
\(463\) | 4.69526 | 0.218207 | 0.109104 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109104 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(464\) | 24.3342 | − | 24.6142i | 1.12969 | − | 1.14269i | ||||
\(465\) | 27.1032 | − | 11.2283i | 1.25688 | − | 0.520701i | ||||
\(466\) | 4.57117 | + | 22.8103i | 0.211756 | + | 1.05667i | ||||
\(467\) | 11.7976i | 0.545926i | 0.962025 | + | 0.272963i | \(0.0880036\pi\) | ||||
−0.962025 | + | 0.272963i | \(0.911996\pi\) | |||||||
\(468\) | −21.5384 | − | 2.02450i | −0.995612 | − | 0.0935825i | ||||
\(469\) | − | 30.4566i | − | 1.40636i | ||||||
\(470\) | −2.94403 | + | 0.589981i | −0.135798 | + | 0.0272138i | ||||
\(471\) | −11.5699 | + | 4.79317i | −0.533112 | + | 0.220858i | ||||
\(472\) | −21.4121 | + | 14.4403i | −0.985570 | + | 0.664670i | ||||
\(473\) | −4.71855 | −0.216959 | ||||||||
\(474\) | 22.1918 | − | 14.8759i | 1.01930 | − | 0.683271i | ||||
\(475\) | 2.96471i | 0.136030i | ||||||||
\(476\) | −1.18845 | − | 2.84611i | −0.0544723 | − | 0.130451i | ||||
\(477\) | 1.70455 | − | 1.70493i | 0.0780458 | − | 0.0780636i | ||||
\(478\) | 7.83779 | + | 39.1109i | 0.358492 | + | 1.78889i | ||||
\(479\) | − | 33.8258i | − | 1.54554i | −0.634687 | − | 0.772770i | \(-0.718871\pi\) | ||
0.634687 | − | 0.772770i | \(-0.281129\pi\) | |||||||
\(480\) | −4.39474 | + | 22.9572i | −0.200591 | + | 1.04785i | ||||
\(481\) | 8.02982 | + | 26.3303i | 0.366128 | + | 1.20056i | ||||
\(482\) | 2.38406 | + | 11.8965i | 0.108591 | + | 0.541873i | ||||
\(483\) | 7.69534 | + | 18.5752i | 0.350150 | + | 0.845200i | ||||
\(484\) | −19.2237 | + | 8.02720i | −0.873805 | + | 0.364873i | ||||
\(485\) | −25.0406 | −1.13703 | ||||||||
\(486\) | −18.3091 | + | 12.2792i | −0.830516 | + | 0.556995i | ||||
\(487\) | −12.4952 | −0.566211 | −0.283106 | − | 0.959089i | \(-0.591365\pi\) | ||||
−0.283106 | + | 0.959089i | \(0.591365\pi\) | |||||||
\(488\) | 14.9889 | + | 22.2255i | 0.678516 | + | 1.00610i | ||||
\(489\) | 23.6604 | − | 9.80204i | 1.06996 | − | 0.443264i | ||||
\(490\) | 0.0261533 | + | 0.130506i | 0.00118149 | + | 0.00589566i | ||||
\(491\) | − | 11.0921i | − | 0.500582i | −0.968171 | − | 0.250291i | \(-0.919474\pi\) | ||
0.968171 | − | 0.250291i | \(-0.0805262\pi\) | |||||||
\(492\) | −0.342836 | − | 0.340841i | −0.0154562 | − | 0.0153663i | ||||
\(493\) | 5.05793i | 0.227798i | ||||||||
\(494\) | 19.2604 | − | 10.3671i | 0.866564 | − | 0.466437i | ||||
\(495\) | 3.86719 | + | 3.86631i | 0.173817 | + | 0.173778i | ||||
\(496\) | −19.9665 | + | 20.1962i | −0.896523 | + | 0.906838i | ||||
\(497\) | − | 6.77168i | − | 0.303751i | ||||||
\(498\) | −20.0186 | − | 29.8637i | −0.897054 | − | 1.33823i | ||||
\(499\) | − | 8.57057i | − | 0.383671i | −0.981427 | − | 0.191836i | \(-0.938556\pi\) | ||
0.981427 | − | 0.191836i | \(-0.0614441\pi\) | |||||||
\(500\) | −7.92171 | − | 18.9711i | −0.354270 | − | 0.848412i | ||||
\(501\) | 29.3302 | − | 12.1509i | 1.31038 | − | 0.542864i | ||||
\(502\) | −1.10467 | − | 5.51235i | −0.0493039 | − | 0.246028i | ||||
\(503\) | 18.9134 | 0.843307 | 0.421654 | − | 0.906757i | \(-0.361450\pi\) | ||||
0.421654 | + | 0.906757i | \(0.361450\pi\) | |||||||
\(504\) | 4.27068 | − | 21.9755i | 0.190231 | − | 0.978865i | ||||
\(505\) | 36.8268i | 1.63877i | ||||||||
\(506\) | 4.66178 | − | 0.934217i | 0.207241 | − | 0.0415310i | ||||
\(507\) | 18.7596 | + | 12.4530i | 0.833143 | + | 0.553057i | ||||
\(508\) | −2.44628 | − | 5.85840i | −0.108536 | − | 0.259925i | ||||
\(509\) | 21.7567i | 0.964349i | 0.876075 | + | 0.482174i | \(0.160153\pi\) | ||||
−0.876075 | + | 0.482174i | \(0.839847\pi\) | |||||||
\(510\) | −1.90187 | − | 2.83721i | −0.0842161 | − | 0.125634i | ||||
\(511\) | − | 35.3226i | − | 1.56258i | ||||||
\(512\) | −4.69961 | − | 22.1340i | −0.207695 | − | 0.978194i | ||||
\(513\) | 8.52644 | − | 20.5946i | 0.376452 | − | 0.909275i | ||||
\(514\) | −3.77262 | − | 18.8255i | −0.166403 | − | 0.830359i | ||||
\(515\) | 11.9212 | 0.525310 | ||||||||
\(516\) | 15.1707 | + | 15.0825i | 0.667854 | + | 0.663970i | ||||
\(517\) | − | 0.680016i | − | 0.0299071i | ||||||
\(518\) | −27.9307 | + | 5.59729i | −1.22720 | + | 0.245931i | ||||
\(519\) | −10.2335 | − | 24.7019i | −0.449202 | − | 1.08429i | ||||
\(520\) | 15.3251 | − | 18.8950i | 0.672049 | − | 0.828599i | ||||
\(521\) | − | 35.7964i | − | 1.56827i | −0.620591 | − | 0.784134i | \(-0.713107\pi\) | ||
0.620591 | − | 0.784134i | \(-0.286893\pi\) | |||||||
\(522\) | −20.3489 | + | 30.5563i | −0.890647 | + | 1.33741i | ||||
\(523\) | 10.4148 | 0.455406 | 0.227703 | − | 0.973731i | \(-0.426879\pi\) | ||||
0.227703 | + | 0.973731i | \(0.426879\pi\) | |||||||
\(524\) | −4.94769 | − | 11.8488i | −0.216141 | − | 0.517619i | ||||
\(525\) | −1.20876 | − | 2.91773i | −0.0527545 | − | 0.127340i | ||||
\(526\) | 13.6797 | − | 2.74140i | 0.596463 | − | 0.119531i | ||||
\(527\) | − | 4.15009i | − | 0.180781i | ||||||
\(528\) | −4.90239 | − | 1.99754i | −0.213349 | − | 0.0869316i | ||||
\(529\) | −3.64062 | −0.158288 | ||||||||
\(530\) | 0.532736 | + | 2.65837i | 0.0231406 | + | 0.115472i | ||||
\(531\) | 19.3675 | − | 19.3720i | 0.840480 | − | 0.840672i | ||||
\(532\) | 8.72175 | + | 20.8870i | 0.378136 | + | 0.905567i | ||||
\(533\) | 0.146777 | + | 0.481291i | 0.00635762 | + | 0.0208470i | ||||
\(534\) | 7.75526 | + | 11.5693i | 0.335603 | + | 0.500652i | ||||
\(535\) | −45.6833 | −1.97506 | ||||||||
\(536\) | 18.2566 | + | 27.0708i | 0.788563 | + | 1.16928i | ||||
\(537\) | −3.71014 | + | 1.53704i | −0.160104 | + | 0.0663281i | ||||
\(538\) | 18.6104 | − | 3.72951i | 0.802352 | − | 0.160791i | ||||
\(539\) | −0.0301445 | −0.00129841 | ||||||||
\(540\) | −0.0751416 | − | 24.7919i | −0.00323358 | − | 1.06687i | ||||
\(541\) | 42.8351 | 1.84162 | 0.920812 | − | 0.390006i | \(-0.127527\pi\) | ||||
0.920812 | + | 0.390006i | \(0.127527\pi\) | |||||||
\(542\) | 14.9574 | − | 2.99744i | 0.642473 | − | 0.128751i | ||||
\(543\) | −32.7432 | + | 13.5649i | −1.40515 | + | 0.582125i | ||||
\(544\) | 2.76237 | + | 1.81733i | 0.118436 | + | 0.0779172i | ||||
\(545\) | 16.8310i | 0.720959i | ||||||||
\(546\) | −14.7283 | + | 18.0555i | −0.630312 | + | 0.772703i | ||||
\(547\) | −6.86925 | −0.293708 | −0.146854 | − | 0.989158i | \(-0.546915\pi\) | ||||
−0.146854 | + | 0.989158i | \(0.546915\pi\) | |||||||
\(548\) | 12.3638 | − | 5.16271i | 0.528154 | − | 0.220540i | ||||
\(549\) | −20.1079 | − | 20.1033i | −0.858184 | − | 0.857988i | ||||
\(550\) | −0.732256 | + | 0.146744i | −0.0312235 | + | 0.00625717i | ||||
\(551\) | − | 37.1190i | − | 1.58132i | ||||||
\(552\) | −17.9743 | − | 11.8974i | −0.765039 | − | 0.506387i | ||||
\(553\) | − | 28.7756i | − | 1.22366i | ||||||
\(554\) | 1.37172 | + | 6.84491i | 0.0582786 | + | 0.290812i | ||||
\(555\) | −29.1447 | + | 12.0741i | −1.23712 | + | 0.512516i | ||||
\(556\) | 19.2339 | − | 8.03146i | 0.815699 | − | 0.340610i | ||||
\(557\) | − | 31.9362i | − | 1.35318i | −0.736360 | − | 0.676590i | \(-0.763457\pi\) | ||
0.736360 | − | 0.676590i | \(-0.236543\pi\) | |||||||
\(558\) | 16.6965 | − | 25.0718i | 0.706820 | − | 1.06137i | ||||
\(559\) | −6.49499 | − | 21.2975i | −0.274709 | − | 0.900788i | ||||
\(560\) | 17.9034 | + | 17.6998i | 0.756557 | + | 0.747952i | ||||
\(561\) | 0.714675 | − | 0.296076i | 0.0301736 | − | 0.0125003i | ||||
\(562\) | −1.59825 | + | 0.320289i | −0.0674183 | + | 0.0135106i | ||||
\(563\) | 6.16766i | 0.259936i | 0.991518 | + | 0.129968i | \(0.0414874\pi\) | ||||
−0.991518 | + | 0.129968i | \(0.958513\pi\) | |||||||
\(564\) | −2.17362 | + | 2.18633i | −0.0915258 | + | 0.0920613i | ||||
\(565\) | 26.7864 | 1.12691 | ||||||||
\(566\) | −7.15867 | + | 1.43459i | −0.300901 | + | 0.0603004i | ||||
\(567\) | 0.00541845 | + | 23.7446i | 0.000227554 | + | 0.997178i | ||||
\(568\) | 4.05914 | + | 6.01888i | 0.170318 | + | 0.252546i | ||||
\(569\) | − | 0.180544i | − | 0.00756881i | −0.999993 | − | 0.00378441i | \(-0.998795\pi\) | ||
0.999993 | − | 0.00378441i | \(-0.00120462\pi\) | |||||||
\(570\) | 13.9574 | + | 20.8216i | 0.584611 | + | 0.872122i | ||||
\(571\) | 0.551781 | 0.0230913 | 0.0115457 | − | 0.999933i | \(-0.496325\pi\) | ||||
0.0115457 | + | 0.999933i | \(0.496325\pi\) | |||||||
\(572\) | 3.51389 | + | 4.24399i | 0.146923 | + | 0.177450i | ||||
\(573\) | 14.3894 | + | 34.7334i | 0.601125 | + | 1.45101i | ||||
\(574\) | −0.510545 | + | 0.102313i | −0.0213097 | + | 0.00427045i | ||||
\(575\) | −3.04090 | −0.126814 | ||||||||
\(576\) | 9.37681 | + | 22.0924i | 0.390700 | + | 0.920518i | ||||
\(577\) | 32.0177i | 1.33292i | 0.745543 | + | 0.666458i | \(0.232190\pi\) | ||||
−0.745543 | + | 0.666458i | \(0.767810\pi\) | |||||||
\(578\) | 23.0992 | − | 4.62906i | 0.960799 | − | 0.192543i | ||||
\(579\) | 6.98066 | − | 2.89195i | 0.290106 | − | 0.120185i | ||||
\(580\) | −15.9084 | − | 38.0977i | −0.660559 | − | 1.58192i | ||||
\(581\) | −38.7236 | −1.60653 | ||||||||
\(582\) | −21.3567 | + | 14.3161i | −0.885265 | + | 0.593421i | ||||
\(583\) | −0.614035 | −0.0254307 | ||||||||
\(584\) | 21.1734 | + | 31.3958i | 0.876160 | + | 1.29917i | ||||
\(585\) | −12.1277 | + | 22.7767i | −0.501420 | + | 0.941702i | ||||
\(586\) | 1.65626 | + | 8.26480i | 0.0684195 | + | 0.341416i | ||||
\(587\) | −22.7316 | −0.938232 | −0.469116 | − | 0.883137i | \(-0.655427\pi\) | ||||
−0.469116 | + | 0.883137i | \(0.655427\pi\) | |||||||
\(588\) | 0.0969182 | + | 0.0963544i | 0.00399684 | + | 0.00397359i | ||||
\(589\) | 30.4566i | 1.25494i | ||||||||
\(590\) | 6.05310 | + | 30.2052i | 0.249202 | + | 1.24353i | ||||
\(591\) | −37.7291 | + | 15.6304i | −1.55197 | + | 0.642950i | ||||
\(592\) | 21.4705 | − | 21.7175i | 0.882431 | − | 0.892583i | ||||
\(593\) | −13.2588 | −0.544474 | −0.272237 | − | 0.962230i | \(-0.587763\pi\) | ||||
−0.272237 | + | 0.962230i | \(0.587763\pi\) | |||||||
\(594\) | 5.50871 | + | 1.08658i | 0.226025 | + | 0.0445831i | ||||
\(595\) | −3.67894 | −0.150822 | ||||||||
\(596\) | −3.45316 | − | 8.26970i | −0.141447 | − | 0.338740i | ||||
\(597\) | −17.4529 | + | 7.23041i | −0.714301 | + | 0.295921i | ||||
\(598\) | 10.6335 | + | 19.7553i | 0.434836 | + | 0.807855i | ||||
\(599\) | −14.6334 | −0.597906 | −0.298953 | − | 0.954268i | \(-0.596637\pi\) | ||||
−0.298953 | + | 0.954268i | \(0.596637\pi\) | |||||||
\(600\) | 2.82335 | + | 1.86880i | 0.115263 | + | 0.0762935i | ||||
\(601\) | 23.6583 | 0.965044 | 0.482522 | − | 0.875884i | \(-0.339721\pi\) | ||||
0.482522 | + | 0.875884i | \(0.339721\pi\) | |||||||
\(602\) | 22.5920 | − | 4.52742i | 0.920781 | − | 0.184524i | ||||
\(603\) | −24.4915 | − | 24.4859i | −0.997372 | − | 0.997144i | ||||
\(604\) | −9.46030 | + | 3.95032i | −0.384934 | + | 0.160736i | ||||
\(605\) | 24.8489i | 1.01025i | ||||||||
\(606\) | 21.0545 | + | 31.4090i | 0.855279 | + | 1.27591i | ||||
\(607\) | 15.9152i | 0.645977i | 0.946403 | + | 0.322988i | \(0.104687\pi\) | ||||
−0.946403 | + | 0.322988i | \(0.895313\pi\) | |||||||
\(608\) | −20.2724 | − | 13.3370i | −0.822156 | − | 0.540885i | ||||
\(609\) | 15.1340 | + | 36.5307i | 0.613259 | + | 1.48030i | ||||
\(610\) | 31.3527 | − | 6.28305i | 1.26943 | − | 0.254393i | ||||
\(611\) | 3.06930 | − | 0.936028i | 0.124170 | − | 0.0378676i | ||||
\(612\) | −3.24415 | − | 1.33248i | −0.131137 | − | 0.0538624i | ||||
\(613\) | −8.36313 | −0.337784 | −0.168892 | − | 0.985635i | \(-0.554019\pi\) | ||||
−0.168892 | + | 0.985635i | \(0.554019\pi\) | |||||||
\(614\) | −2.30698 | − | 11.5119i | −0.0931020 | − | 0.464583i | ||||
\(615\) | −0.532736 | + | 0.220702i | −0.0214820 | + | 0.00889957i | ||||
\(616\) | −4.72720 | + | 3.18803i | −0.190464 | + | 0.128449i | ||||
\(617\) | −4.84880 | −0.195205 | −0.0976026 | − | 0.995225i | \(-0.531117\pi\) | ||||
−0.0976026 | + | 0.995225i | \(0.531117\pi\) | |||||||
\(618\) | 10.1674 | − | 6.81553i | 0.408993 | − | 0.274161i | ||||
\(619\) | − | 9.89555i | − | 0.397736i | −0.980026 | − | 0.198868i | \(-0.936274\pi\) | ||
0.980026 | − | 0.198868i | \(-0.0637264\pi\) | |||||||
\(620\) | 13.0530 | + | 31.2596i | 0.524222 | + | 1.25542i | ||||
\(621\) | 21.1239 | + | 8.74556i | 0.847672 | + | 0.350947i | ||||
\(622\) | −7.57857 | + | 1.51874i | −0.303873 | + | 0.0608959i | ||||
\(623\) | 15.0016 | 0.601028 | ||||||||
\(624\) | 2.26798 | − | 24.8768i | 0.0907918 | − | 0.995870i | ||||
\(625\) | −27.9780 | −1.11912 | ||||||||
\(626\) | 7.58023 | − | 1.51907i | 0.302967 | − | 0.0607143i | ||||
\(627\) | −5.24484 | + | 2.17284i | −0.209459 | + | 0.0867747i | ||||
\(628\) | −5.57210 | − | 13.3442i | −0.222351 | − | 0.532491i | ||||
\(629\) | 4.46269i | 0.177939i | ||||||||
\(630\) | −22.2255 | − | 14.8010i | −0.885483 | − | 0.589686i | ||||
\(631\) | −13.4569 | −0.535713 | −0.267856 | − | 0.963459i | \(-0.586315\pi\) | ||||
−0.267856 | + | 0.963459i | \(0.586315\pi\) | |||||||
\(632\) | 17.2489 | + | 25.5767i | 0.686125 | + | 1.01738i | ||||
\(633\) | −12.9918 | − | 31.3598i | −0.516376 | − | 1.24644i | ||||
\(634\) | 0.310450 | + | 1.54916i | 0.0123295 | + | 0.0615249i | ||||
\(635\) | −7.57268 | −0.300513 | ||||||||
\(636\) | 1.97420 | + | 1.96271i | 0.0782820 | + | 0.0778267i | ||||
\(637\) | −0.0414932 | − | 0.136059i | −0.00164402 | − | 0.00539086i | ||||
\(638\) | 9.16805 | − | 1.83727i | 0.362966 | − | 0.0727382i | ||||
\(639\) | −5.44541 | − | 5.44416i | −0.215417 | − | 0.215368i | ||||
\(640\) | −26.5228 | − | 5.00029i | −1.04841 | − | 0.197654i | ||||
\(641\) | 0.939589i | 0.0371115i | 0.999828 | + | 0.0185558i | \(0.00590683\pi\) | ||||
−0.999828 | + | 0.0185558i | \(0.994093\pi\) | |||||||
\(642\) | −38.9626 | + | 26.1179i | −1.53773 | + | 1.03079i | ||||
\(643\) | 42.1553i | 1.66244i | 0.555943 | + | 0.831221i | \(0.312357\pi\) | ||||
−0.555943 | + | 0.831221i | \(0.687643\pi\) | |||||||
\(644\) | −21.4238 | + | 8.94589i | −0.844216 | + | 0.352517i | ||||
\(645\) | 23.5740 | − | 9.76623i | 0.928224 | − | 0.384545i | ||||
\(646\) | 3.47690 | − | 0.696769i | 0.136797 | − | 0.0274140i | ||||
\(647\) | −33.5469 | −1.31886 | −0.659432 | − | 0.751765i | \(-0.729203\pi\) | ||||
−0.659432 | + | 0.751765i | \(0.729203\pi\) | |||||||
\(648\) | −14.2380 | − | 21.1017i | −0.559321 | − | 0.828951i | ||||
\(649\) | −6.97684 | −0.273865 | ||||||||
\(650\) | −1.67027 | − | 3.10310i | −0.0655135 | − | 0.121713i | ||||
\(651\) | −12.4176 | − | 29.9739i | −0.486684 | − | 1.17477i | ||||
\(652\) | 11.3950 | + | 27.2889i | 0.446261 | + | 1.06871i | ||||
\(653\) | −11.6194 | −0.454700 | −0.227350 | − | 0.973813i | \(-0.573006\pi\) | ||||
−0.227350 | + | 0.973813i | \(0.573006\pi\) | |||||||
\(654\) | 9.62253 | + | 14.3549i | 0.376271 | + | 0.561320i | ||||
\(655\) | −15.3160 | −0.598446 | ||||||||
\(656\) | 0.392459 | − | 0.396974i | 0.0153229 | − | 0.0154992i | ||||
\(657\) | −28.4044 | − | 28.3980i | −1.10816 | − | 1.10791i | ||||
\(658\) | 0.652470 | + | 3.25585i | 0.0254359 | + | 0.126926i | ||||
\(659\) | − | 17.4797i | − | 0.680912i | −0.940261 | − | 0.340456i | \(-0.889419\pi\) | ||
0.940261 | − | 0.340456i | \(-0.110581\pi\) | |||||||
\(660\) | −4.45190 | + | 4.47795i | −0.173290 | + | 0.174304i | ||||
\(661\) | 41.5530 | 1.61623 | 0.808113 | − | 0.589028i | \(-0.200489\pi\) | ||||
0.808113 | + | 0.589028i | \(0.200489\pi\) | |||||||
\(662\) | 6.00059 | + | 29.9432i | 0.233219 | + | 1.16377i | ||||
\(663\) | 2.32009 | + | 2.81819i | 0.0901050 | + | 0.109449i | ||||
\(664\) | 34.4187 | − | 23.2120i | 1.33571 | − | 0.900802i | ||||
\(665\) | 26.9989 | 1.04697 | ||||||||
\(666\) | −17.9541 | + | 26.9603i | −0.695709 | + | 1.04469i | ||||
\(667\) | 38.0730 | 1.47419 | ||||||||
\(668\) | 14.1256 | + | 33.8282i | 0.546535 | + | 1.30885i | ||||
\(669\) | −4.28317 | − | 10.3388i | −0.165597 | − | 0.399722i | ||||
\(670\) | 38.1877 | − | 7.65279i | 1.47532 | − | 0.295653i | ||||
\(671\) | 7.24189i | 0.279570i | ||||||||
\(672\) | 25.3888 | + | 4.86021i | 0.979394 | + | 0.187487i | ||||
\(673\) | −23.7494 | −0.915473 | −0.457736 | − | 0.889088i | \(-0.651340\pi\) | ||||
−0.457736 | + | 0.889088i | \(0.651340\pi\) | |||||||
\(674\) | −32.7943 | + | 6.57195i | −1.26319 | + | 0.253142i | ||||
\(675\) | −3.31807 | − | 1.37372i | −0.127712 | − | 0.0528746i | ||||
\(676\) | −14.3187 | + | 21.7019i | −0.550720 | + | 0.834690i | ||||
\(677\) | −0.998225 | −0.0383649 | −0.0191824 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191824 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(678\) | 22.8457 | − | 15.3142i | 0.877384 | − | 0.588138i | ||||
\(679\) | 27.6928i | 1.06275i | ||||||||
\(680\) | 3.26995 | − | 2.20526i | 0.125397 | − | 0.0845679i | ||||
\(681\) | 7.25118 | + | 17.5031i | 0.277866 | + | 0.670719i | ||||
\(682\) | −7.52249 | + | 1.50750i | −0.288051 | + | 0.0577252i | ||||
\(683\) | −20.6883 | −0.791615 | −0.395808 | − | 0.918333i | \(-0.629535\pi\) | ||||
−0.395808 | + | 0.918333i | \(0.629535\pi\) | |||||||
\(684\) | 23.8081 | + | 9.77880i | 0.910326 | + | 0.373902i | ||||
\(685\) | − | 15.9816i | − | 0.610626i | ||||||
\(686\) | 25.7529 | − | 5.16085i | 0.983249 | − | 0.197042i | ||||
\(687\) | 14.7293 | + | 35.5539i | 0.561957 | + | 1.35647i | ||||
\(688\) | −17.3666 | + | 17.5664i | −0.662095 | + | 0.669712i | ||||
\(689\) | −0.845206 | − | 2.77149i | −0.0321998 | − | 0.105585i | ||||
\(690\) | −21.3567 | + | 14.3161i | −0.813037 | + | 0.545004i | ||||
\(691\) | 28.8484i | 1.09744i | 0.836005 | + | 0.548722i | \(0.184885\pi\) | ||||
−0.836005 | + | 0.548722i | \(0.815115\pi\) | |||||||
\(692\) | 28.4901 | − | 11.8965i | 1.08303 | − | 0.452239i | ||||
\(693\) | 4.27582 | − | 4.27680i | 0.162425 | − | 0.162462i | ||||
\(694\) | 1.85305 | + | 9.24681i | 0.0703409 | + | 0.351004i | ||||
\(695\) | − | 24.8621i | − | 0.943073i | ||||||
\(696\) | −35.3491 | − | 23.3979i | −1.33990 | − | 0.886895i | ||||
\(697\) | 0.0815735i | 0.00308982i | ||||||||
\(698\) | −48.4094 | + | 9.70120i | −1.83232 | + | 0.367196i | ||||
\(699\) | 26.3228 | − | 10.9050i | 0.995621 | − | 0.412466i | ||||
\(700\) | 3.36517 | − | 1.40519i | 0.127192 | − | 0.0531111i | ||||
\(701\) | 1.46047 | 0.0551611 | 0.0275805 | − | 0.999620i | \(-0.491220\pi\) | ||||
0.0275805 | + | 0.999620i | \(0.491220\pi\) | |||||||
\(702\) | 2.67825 | + | 26.3596i | 0.101084 | + | 0.994878i | ||||
\(703\) | − | 32.7507i | − | 1.23522i | ||||||
\(704\) | 2.29068 | − | 5.66723i | 0.0863333 | − | 0.213592i | ||||
\(705\) | 1.40746 | + | 3.39737i | 0.0530081 | + | 0.127952i | ||||
\(706\) | −6.52676 | + | 1.30796i | −0.245638 | + | 0.0492256i | ||||
\(707\) | 40.7274 | 1.53171 | ||||||||
\(708\) | 22.4314 | + | 22.3009i | 0.843024 | + | 0.838120i | ||||
\(709\) | 21.9297 | 0.823586 | 0.411793 | − | 0.911277i | \(-0.364903\pi\) | ||||
0.411793 | + | 0.911277i | \(0.364903\pi\) | |||||||
\(710\) | 8.49060 | − | 1.70151i | 0.318647 | − | 0.0638566i | ||||
\(711\) | −23.1398 | − | 23.1345i | −0.867809 | − | 0.867611i | ||||
\(712\) | −13.3339 | + | 8.99241i | −0.499710 | + | 0.337005i | ||||
\(713\) | −31.2393 | −1.16992 | ||||||||
\(714\) | −3.13771 | + | 2.10331i | −0.117426 | + | 0.0787144i | ||||
\(715\) | 6.28639 | − | 1.91713i | 0.235097 | − | 0.0716965i | ||||
\(716\) | −1.78682 | − | 4.27911i | −0.0667766 | − | 0.159918i | ||||
\(717\) | 45.1334 | − | 18.6979i | 1.68554 | − | 0.698286i | ||||
\(718\) | −4.76094 | − | 23.7573i | −0.177677 | − | 0.886614i | ||||
\(719\) | 15.0016 | 0.559467 | 0.279733 | − | 0.960078i | \(-0.409754\pi\) | ||||
0.279733 | + | 0.960078i | \(0.409754\pi\) | |||||||
\(720\) | 28.6268 | − | 0.166999i | 1.06686 | − | 0.00622367i | ||||
\(721\) | − | 13.1838i | − | 0.490992i | ||||||
\(722\) | 0.829991 | − | 0.166330i | 0.0308891 | − | 0.00619014i | ||||
\(723\) | 13.7285 | − | 5.68743i | 0.510567 | − | 0.211518i | ||||
\(724\) | −15.7693 | − | 37.7646i | −0.586061 | − | 1.40351i | ||||
\(725\) | −5.98037 | −0.222105 | ||||||||
\(726\) | 14.2065 | + | 21.1933i | 0.527254 | + | 0.786556i | ||||
\(727\) | 24.4156i | 0.905526i | 0.891631 | + | 0.452763i | \(0.149562\pi\) | ||||
−0.891631 | + | 0.452763i | \(0.850438\pi\) | |||||||
\(728\) | −20.8963 | − | 16.9483i | −0.774467 | − | 0.628144i | ||||
\(729\) | 19.0984 | + | 19.0853i | 0.707349 | + | 0.706865i | ||||
\(730\) | 44.2889 | − | 8.87546i | 1.63920 | − | 0.328495i | ||||
\(731\) | − | 3.60969i | − | 0.133509i | ||||||
\(732\) | 23.1481 | − | 23.2836i | 0.855579 | − | 0.860585i | ||||
\(733\) | 12.6996 | 0.469071 | 0.234536 | − | 0.972108i | \(-0.424643\pi\) | ||||
0.234536 | + | 0.972108i | \(0.424643\pi\) | |||||||
\(734\) | −0.967578 | − | 4.82825i | −0.0357140 | − | 0.178214i | ||||
\(735\) | 0.150602 | − | 0.0623915i | 0.00555505 | − | 0.00230135i | ||||
\(736\) | 13.6797 | − | 20.7934i | 0.504240 | − | 0.766455i | ||||
\(737\) | 8.82066i | 0.324913i | ||||||||
\(738\) | −0.328184 | + | 0.492807i | −0.0120806 | + | 0.0181405i | ||||
\(739\) | − | 20.7156i | − | 0.762037i | −0.924567 | − | 0.381018i | \(-0.875573\pi\) | ||
0.924567 | − | 0.381018i | \(-0.124427\pi\) | |||||||
\(740\) | −14.0362 | − | 33.6142i | −0.515981 | − | 1.23568i | ||||
\(741\) | −17.0267 | − | 20.6821i | −0.625490 | − | 0.759776i | ||||
\(742\) | 2.93994 | − | 0.589162i | 0.107929 | − | 0.0216288i | ||||
\(743\) | 31.3626i | 1.15058i | 0.817948 | + | 0.575292i | \(0.195111\pi\) | ||||
−0.817948 | + | 0.575292i | \(0.804889\pi\) | |||||||
\(744\) | 29.0043 | + | 19.1983i | 1.06335 | + | 0.703842i | ||||
\(745\) | −10.6896 | −0.391636 | ||||||||
\(746\) | −6.26519 | − | 31.2635i | −0.229385 | − | 1.14464i | ||||
\(747\) | −31.1323 | + | 31.1394i | −1.13907 | + | 1.13933i | ||||
\(748\) | 0.344191 | + | 0.824274i | 0.0125849 | + | 0.0301385i | ||||
\(749\) | 50.5220i | 1.84603i | ||||||||
\(750\) | −20.9148 | + | 14.0198i | −0.763699 | + | 0.511931i | ||||
\(751\) | − | 37.1565i | − | 1.35586i | −0.735127 | − | 0.677930i | \(-0.762877\pi\) | ||
0.735127 | − | 0.677930i | \(-0.237123\pi\) | |||||||
\(752\) | −2.53159 | − | 2.50279i | −0.0923174 | − | 0.0912674i | ||||
\(753\) | −6.36118 | + | 2.63531i | −0.231814 | + | 0.0960361i | ||||
\(754\) | 20.9123 | + | 38.8516i | 0.761580 | + | 1.41489i | ||||
\(755\) | 12.2286i | 0.445043i | ||||||||
\(756\) | −27.4177 | + | 0.0831004i | −0.997173 | + | 0.00302233i | ||||
\(757\) | − | 10.7590i | − | 0.391043i | −0.980699 | − | 0.195522i | \(-0.937360\pi\) | ||
0.980699 | − | 0.195522i | \(-0.0626400\pi\) | |||||||
\(758\) | 6.78154 | + | 33.8401i | 0.246317 | + | 1.22913i | ||||
\(759\) | −2.22868 | − | 5.37963i | −0.0808958 | − | 0.195268i | ||||
\(760\) | −23.9975 | + | 16.1839i | −0.870480 | + | 0.587053i | ||||
\(761\) | 36.7545 | 1.33235 | 0.666174 | − | 0.745796i | \(-0.267931\pi\) | ||||
0.666174 | + | 0.745796i | \(0.267931\pi\) | |||||||
\(762\) | −6.45863 | + | 4.32942i | −0.233971 | + | 0.156838i | ||||
\(763\) | 18.6136 | 0.673859 | ||||||||
\(764\) | −40.0600 | + | 16.7278i | −1.44932 | + | 0.605189i | ||||
\(765\) | −2.95772 | + | 2.95840i | −0.106937 | + | 0.106961i | ||||
\(766\) | 2.96234 | + | 14.7822i | 0.107034 | + | 0.534103i | ||||
\(767\) | −9.60348 | − | 31.4904i | −0.346762 | − | 1.13705i | ||||
\(768\) | −25.4797 | + | 10.8989i | −0.919419 | + | 0.393279i | ||||
\(769\) | − | 15.7373i | − | 0.567502i | −0.958898 | − | 0.283751i | \(-0.908421\pi\) | ||
0.958898 | − | 0.283751i | \(-0.0915789\pi\) | |||||||
\(770\) | 1.33636 | + | 6.66848i | 0.0481590 | + | 0.240315i | ||||
\(771\) | −21.7244 | + | 9.00000i | −0.782386 | + | 0.324127i | ||||
\(772\) | 3.36192 | + | 8.05118i | 0.120998 | + | 0.289768i | ||||
\(773\) | 11.9057i | 0.428220i | 0.976810 | + | 0.214110i | \(0.0686851\pi\) | ||||
−0.976810 | + | 0.214110i | \(0.931315\pi\) | |||||||
\(774\) | 14.5224 | − | 21.8071i | 0.521996 | − | 0.783840i | ||||
\(775\) | 4.90696 | 0.176263 | ||||||||
\(776\) | −16.5998 | − | 24.6142i | −0.595900 | − | 0.883598i | ||||
\(777\) | 13.3529 | + | 32.2316i | 0.479034 | + | 1.15630i | ||||
\(778\) | −40.3792 | + | 8.09197i | −1.44767 | + | 0.290111i | ||||
\(779\) | − | 0.598650i | − | 0.0214489i | ||||||
\(780\) | −26.3395 | − | 13.9301i | −0.943104 | − | 0.498779i | ||||
\(781\) | 1.96117i | 0.0701762i | ||||||||
\(782\) | 0.714675 | + | 3.56626i | 0.0255567 | + | 0.127529i | ||||
\(783\) | 41.5431 | + | 17.1994i | 1.48463 | + | 0.614656i | ||||
\(784\) | −0.110946 | + | 0.112223i | −0.00396237 | + | 0.00400796i | ||||
\(785\) | −17.2489 | −0.615641 | ||||||||
\(786\) | −13.0628 | + | 8.75641i | −0.465935 | + | 0.312331i | ||||
\(787\) | − | 16.1112i | − | 0.574301i | −0.957885 | − | 0.287151i | \(-0.907292\pi\) | ||
0.957885 | − | 0.287151i | \(-0.0927080\pi\) | |||||||
\(788\) | −18.1705 | − | 43.5151i | −0.647297 | − | 1.55016i | ||||
\(789\) | −6.53991 | − | 15.7862i | −0.232827 | − | 0.562003i | ||||
\(790\) | 36.0800 | − | 7.23041i | 1.28367 | − | 0.257246i | ||||
\(791\) | − | 29.6235i | − | 1.05329i | ||||||
\(792\) | −1.23685 | + | 6.36440i | −0.0439494 | + | 0.226149i | ||||
\(793\) | −32.6867 | + | 9.96831i | −1.16074 | + | 0.353985i | ||||
\(794\) | −9.07075 | + | 1.81777i | −0.321909 | + | 0.0645103i | ||||
\(795\) | 3.06773 | − | 1.27090i | 0.108801 | − | 0.0450741i | ||||
\(796\) | −8.40541 | − | 20.1294i | −0.297922 | − | 0.713469i | ||||
\(797\) | 14.7802 | 0.523542 | 0.261771 | − | 0.965130i | \(-0.415693\pi\) | ||||
0.261771 | + | 0.965130i | \(0.415693\pi\) | |||||||
\(798\) | 23.0270 | − | 15.4357i | 0.815147 | − | 0.546419i | ||||
\(799\) | 0.520211 | 0.0184038 | ||||||||
\(800\) | −2.14876 | + | 3.26616i | −0.0759701 | + | 0.115476i | ||||
\(801\) | 12.0607 | − | 12.0635i | 0.426145 | − | 0.426242i | ||||
\(802\) | −39.2373 | + | 7.86313i | −1.38552 | + | 0.277657i | ||||
\(803\) | 10.2299i | 0.361005i | ||||||||
\(804\) | 28.1945 | − | 28.3595i | 0.994345 | − | 1.00016i | ||||
\(805\) | 27.6928i | 0.976042i | ||||||||
\(806\) | −17.1588 | − | 31.8782i | −0.604392 | − | 1.12286i | ||||
\(807\) | −8.89716 | − | 21.4762i | −0.313195 | − | 0.755997i | ||||
\(808\) | −36.1998 | + | 24.4132i | −1.27350 | + | 0.858852i | ||||
\(809\) | − | 18.0231i | − | 0.633657i | −0.948483 | − | 0.316829i | \(-0.897382\pi\) | ||
0.948483 | − | 0.316829i | \(-0.102618\pi\) | |||||||
\(810\) | −29.7705 | + | 5.97306i | −1.04603 | + | 0.209872i | ||||
\(811\) | − | 45.5754i | − | 1.60037i | −0.599754 | − | 0.800185i | \(-0.704735\pi\) | ||
0.599754 | − | 0.800185i | \(-0.295265\pi\) | |||||||
\(812\) | −42.1329 | + | 17.5933i | −1.47857 | + | 0.617406i | ||||
\(813\) | −7.15072 | − | 17.2606i | −0.250787 | − | 0.605355i | ||||
\(814\) | 8.08911 | − | 1.62105i | 0.283523 | − | 0.0568178i | ||||
\(815\) | 35.2741 | 1.23560 | ||||||||
\(816\) | 1.52811 | − | 3.75032i | 0.0534947 | − | 0.131288i | ||||
\(817\) | 26.4907i | 0.926793i | ||||||||
\(818\) | −8.52897 | − | 42.5599i | −0.298209 | − | 1.48807i | ||||
\(819\) | 25.1892 | + | 13.4123i | 0.880181 | + | 0.468663i | ||||
\(820\) | −0.256568 | − | 0.614434i | −0.00895974 | − | 0.0214570i | ||||
\(821\) | 43.8260i | 1.52954i | 0.644305 | + | 0.764769i | \(0.277147\pi\) | ||||
−0.644305 | + | 0.764769i | \(0.722853\pi\) | |||||||
\(822\) | −9.13695 | − | 13.6305i | −0.318688 | − | 0.475418i | ||||
\(823\) | 41.8348i | 1.45827i | 0.684369 | + | 0.729135i | \(0.260078\pi\) | ||||
−0.684369 | + | 0.729135i | \(0.739922\pi\) | |||||||
\(824\) | 7.90277 | + | 11.7182i | 0.275306 | + | 0.408223i | ||||
\(825\) | 0.350073 | + | 0.845014i | 0.0121880 | + | 0.0294196i | ||||
\(826\) | 33.4045 | − | 6.69423i | 1.16229 | − | 0.232922i | ||||
\(827\) | 32.1625 | 1.11840 | 0.559200 | − | 0.829033i | \(-0.311108\pi\) | ||||
0.559200 | + | 0.829033i | \(0.311108\pi\) | |||||||
\(828\) | −10.0301 | + | 24.4200i | −0.348570 | + | 0.848652i | ||||
\(829\) | 11.0453i | 0.383619i | 0.981432 | + | 0.191810i | \(0.0614356\pi\) | ||||
−0.981432 | + | 0.191810i | \(0.938564\pi\) | |||||||
\(830\) | −9.73003 | − | 48.5532i | −0.337734 | − | 1.68531i | ||||
\(831\) | 7.89894 | − | 3.27237i | 0.274011 | − | 0.113517i | ||||
\(832\) | 28.7325 | + | 2.53832i | 0.996120 | + | 0.0880003i | ||||
\(833\) | − | 0.0230605i | − | 0.000798998i | ||||||
\(834\) | −14.2141 | − | 21.2045i | −0.492193 | − | 0.734253i | ||||
\(835\) | 43.7269 | 1.51323 | ||||||||
\(836\) | −2.52594 | − | 6.04917i | −0.0873614 | − | 0.209215i | ||||
\(837\) | −34.0866 | − | 14.1123i | −1.17821 | − | 0.487792i | ||||
\(838\) | 1.32969 | + | 6.63521i | 0.0459334 | + | 0.229210i | ||||
\(839\) | − | 32.2336i | − | 1.11283i | −0.830905 | − | 0.556415i | \(-0.812177\pi\) | ||
0.830905 | − | 0.556415i | \(-0.187823\pi\) | |||||||
\(840\) | 17.0187 | − | 25.7115i | 0.587202 | − | 0.887133i | ||||
\(841\) | 45.8758 | 1.58193 | ||||||||
\(842\) | 5.80079 | − | 1.16247i | 0.199908 | − | 0.0400615i | ||||
\(843\) | 0.764084 | + | 1.84436i | 0.0263164 | + | 0.0635233i | ||||
\(844\) | 36.1690 | − | 15.1030i | 1.24499 | − | 0.519867i | ||||
\(845\) | 17.3062 | + | 25.7351i | 0.595350 | + | 0.885315i | ||||
\(846\) | 3.14274 | + | 2.09290i | 0.108049 | + | 0.0719553i | ||||
\(847\) | 27.4808 | 0.944253 | ||||||||
\(848\) | −2.25995 | + | 2.28595i | −0.0776070 | + | 0.0784998i | ||||
\(849\) | 3.42237 | + | 8.26100i | 0.117456 | + | 0.283517i | ||||
\(850\) | −0.112259 | − | 0.560175i | −0.00385044 | − | 0.0192138i | ||||
\(851\) | 33.5924 | 1.15153 | ||||||||
\(852\) | 6.26873 | − | 6.30541i | 0.214763 | − | 0.216020i | ||||
\(853\) | −22.1165 | −0.757256 | −0.378628 | − | 0.925549i | \(-0.623604\pi\) | ||||
−0.378628 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(854\) | −6.94854 | − | 34.6735i | −0.237774 | − | 1.18650i | ||||
\(855\) | 21.7061 | − | 21.7110i | 0.742333 | − | 0.742502i | ||||
\(856\) | −30.2843 | − | 44.9055i | −1.03510 | − | 1.53484i | ||||
\(857\) | − | 2.33809i | − | 0.0798678i | −0.999202 | − | 0.0399339i | \(-0.987285\pi\) | ||
0.999202 | − | 0.0399339i | \(-0.0127147\pi\) | |||||||
\(858\) | 4.26551 | − | 5.22912i | 0.145622 | − | 0.178519i | ||||
\(859\) | −43.4057 | −1.48098 | −0.740492 | − | 0.672065i | \(-0.765408\pi\) | ||||
−0.740492 | + | 0.672065i | \(0.765408\pi\) | |||||||
\(860\) | 11.3533 | + | 27.1892i | 0.387145 | + | 0.927142i | ||||
\(861\) | 0.244078 | + | 0.589162i | 0.00831816 | + | 0.0200786i | ||||
\(862\) | −5.51673 | − | 27.5287i | −0.187901 | − | 0.937631i | ||||
\(863\) | 42.1353i | 1.43430i | 0.696917 | + | 0.717152i | \(0.254555\pi\) | ||||
−0.696917 | + | 0.717152i | \(0.745445\pi\) | |||||||
\(864\) | 24.3199 | − | 16.5088i | 0.827380 | − | 0.561642i | ||||
\(865\) | − | 36.8268i | − | 1.25215i | ||||||
\(866\) | 33.7733 | − | 6.76814i | 1.14766 | − | 0.229991i | ||||
\(867\) | −11.0431 | − | 26.6561i | −0.375044 | − | 0.905290i | ||||
\(868\) | 34.5705 | − | 14.4356i | 1.17340 | − | 0.489975i | ||||
\(869\) | 8.33382i | 0.282705i | ||||||||
\(870\) | −42.0010 | + | 28.1546i | −1.42397 | + | 0.954530i | ||||
\(871\) | −39.8126 | + | 12.1415i | −1.34900 | + | 0.411397i | ||||
\(872\) | −16.5444 | + | 11.1575i | −0.560263 | + | 0.377842i | ||||
\(873\) | 22.2690 | + | 22.2639i | 0.753691 | + | 0.753519i | ||||
\(874\) | −5.24484 | − | 26.1720i | −0.177410 | − | 0.885280i | ||||
\(875\) | 27.1197i | 0.916813i | ||||||||
\(876\) | 32.6991 | − | 32.8904i | 1.10480 | − | 1.11126i | ||||
\(877\) | −38.5223 | −1.30080 | −0.650402 | − | 0.759590i | \(-0.725400\pi\) | ||||
−0.650402 | + | 0.759590i | \(0.725400\pi\) | |||||||
\(878\) | 4.64451 | + | 23.1763i | 0.156744 | + | 0.782161i | ||||
\(879\) | 9.53747 | − | 3.95119i | 0.321691 | − | 0.133270i | ||||
\(880\) | −5.18507 | − | 5.12610i | −0.174789 | − | 0.172801i | ||||
\(881\) | − | 3.54012i | − | 0.119270i | −0.998220 | − | 0.0596348i | \(-0.981006\pi\) | ||
0.998220 | − | 0.0596348i | \(-0.0189936\pi\) | |||||||
\(882\) | 0.0927762 | − | 0.139315i | 0.00312394 | − | 0.00469096i | ||||
\(883\) | −24.1271 | −0.811942 | −0.405971 | − | 0.913886i | \(-0.633067\pi\) | ||||
−0.405971 | + | 0.913886i | \(0.633067\pi\) | |||||||
\(884\) | −3.24665 | + | 2.68812i | −0.109196 | + | 0.0904114i | ||||
\(885\) | 34.8564 | − | 14.4403i | 1.17169 | − | 0.485406i | ||||
\(886\) | −7.62933 | − | 38.0707i | −0.256312 | − | 1.27901i | ||||
\(887\) | 34.9805 | 1.17453 | 0.587265 | − | 0.809394i | \(-0.300204\pi\) | ||||
0.587265 | + | 0.809394i | \(0.300204\pi\) | |||||||
\(888\) | −31.1891 | − | 20.6443i | −1.04664 | − | 0.692778i | ||||
\(889\) | 8.37475i | 0.280880i | ||||||||
\(890\) | 3.76944 | + | 18.8097i | 0.126352 | + | 0.630501i | ||||
\(891\) | −0.00156926 | − | 6.87675i | −5.25721e−5 | − | 0.230380i | ||||
\(892\) | 11.9243 | − | 4.97922i | 0.399256 | − | 0.166716i | ||||
\(893\) | −3.81772 | −0.127755 | ||||||||
\(894\) | −9.11698 | + | 6.11140i | −0.304917 | + | 0.204396i | ||||
\(895\) | −5.53126 | −0.184890 | ||||||||
\(896\) | −5.52990 | + | 29.3321i | −0.184741 | + | 0.979916i | ||||
\(897\) | 21.2136 | − | 17.4642i | 0.708301 | − | 0.583114i | ||||
\(898\) | 26.7907 | − | 5.36883i | 0.894016 | − | 0.179160i | ||||
\(899\) | −61.4365 | −2.04902 | ||||||||
\(900\) | 1.57549 | − | 3.83580i | 0.0525165 | − | 0.127860i | ||||
\(901\) | − | 0.469736i | − | 0.0156492i | ||||||
\(902\) | 0.147861 | − | 0.0296312i | 0.00492323 | − | 0.000986611i | ||||
\(903\) | −10.8006 | − | 26.0709i | −0.359423 | − | 0.867584i | ||||
\(904\) | 17.7572 | + | 26.3303i | 0.590595 | + | 0.875732i | ||||
\(905\) | −48.8152 | −1.62267 | ||||||||
\(906\) | 6.99126 | + | 10.4296i | 0.232269 | + | 0.346499i | ||||
\(907\) | −49.1062 | −1.63054 | −0.815272 | − | 0.579078i | \(-0.803413\pi\) | ||||
−0.815272 | + | 0.579078i | \(0.803413\pi\) | |||||||
\(908\) | −20.1873 | + | 8.42955i | −0.669938 | + | 0.279745i | ||||
\(909\) | 32.7432 | − | 32.7507i | 1.08602 | − | 1.08627i | ||||
\(910\) | −28.2592 | + | 15.2108i | −0.936782 | + | 0.504232i | ||||
\(911\) | 29.3415 | 0.972128 | 0.486064 | − | 0.873923i | \(-0.338432\pi\) | ||||
0.486064 | + | 0.873923i | \(0.338432\pi\) | |||||||
\(912\) | −11.2145 | + | 27.5228i | −0.371349 | + | 0.911371i | ||||
\(913\) | 11.2149 | 0.371159 | ||||||||
\(914\) | −6.26902 | − | 31.2827i | −0.207361 | − | 1.03474i | ||||
\(915\) | −14.9889 | − | 36.1806i | −0.495518 | − | 1.19609i | ||||
\(916\) | −41.0063 | + | 17.1229i | −1.35489 | + | 0.565757i | ||||
\(917\) | 16.9382i | 0.559350i | ||||||||
\(918\) | −0.831236 | + | 4.21415i | −0.0274349 | + | 0.139088i | ||||
\(919\) | 30.8671i | 1.01821i | 0.860704 | + | 0.509106i | \(0.170024\pi\) | ||||
−0.860704 | + | 0.509106i | \(0.829976\pi\) | |||||||
\(920\) | −16.5998 | − | 24.6142i | −0.547281 | − | 0.811506i | ||||
\(921\) | −13.2846 | + | 5.50354i | −0.437742 | + | 0.181348i | ||||
\(922\) | 4.96673 | + | 24.7842i | 0.163570 | + | 0.816223i | ||||
\(923\) | −8.85188 | + | 2.69951i | −0.291363 | + | 0.0888556i | ||||
\(924\) | 4.95224 | + | 4.92343i | 0.162917 | + | 0.161969i | ||||
\(925\) | −5.27657 | −0.173493 | ||||||||
\(926\) | 6.51065 | − | 1.30473i | 0.213953 | − | 0.0428761i | ||||
\(927\) | −10.6017 | − | 10.5993i | −0.348206 | − | 0.348126i | ||||
\(928\) | 26.9031 | − | 40.8932i | 0.883136 | − | 1.34238i | ||||
\(929\) | −56.3252 | −1.84797 | −0.923985 | − | 0.382429i | \(-0.875088\pi\) | ||||
−0.923985 | + | 0.382429i | \(0.875088\pi\) | |||||||
\(930\) | 34.4623 | − | 23.1012i | 1.13006 | − | 0.757518i | ||||
\(931\) | 0.169236i | 0.00554648i | ||||||||
\(932\) | 12.6772 | + | 30.3596i | 0.415255 | + | 0.994461i | ||||
\(933\) | 3.62312 | + | 8.74556i | 0.118615 | + | 0.286317i | ||||
\(934\) | 3.27833 | + | 16.3590i | 0.107270 | + | 0.535283i | ||||
\(935\) | 1.06547 | 0.0348447 | ||||||||
\(936\) | −30.4286 | + | 3.17787i | −0.994591 | + | 0.103872i | ||||
\(937\) | −1.08988 | −0.0356047 | −0.0178024 | − | 0.999842i | \(-0.505667\pi\) | ||||
−0.0178024 | + | 0.999842i | \(0.505667\pi\) | |||||||
\(938\) | −8.46336 | − | 42.2325i | −0.276338 | − | 1.37894i | ||||
\(939\) | −3.62391 | − | 8.74748i | −0.118262 | − | 0.285463i | ||||
\(940\) | −3.91837 | + | 1.63619i | −0.127803 | + | 0.0533665i | ||||
\(941\) | 11.8789i | 0.387240i | 0.981077 | + | 0.193620i | \(0.0620229\pi\) | ||||
−0.981077 | + | 0.193620i | \(0.937977\pi\) | |||||||
\(942\) | −14.7114 | + | 9.86149i | −0.479322 | + | 0.321305i | ||||
\(943\) | 0.614035 | 0.0199957 | ||||||||
\(944\) | −25.6782 | + | 25.9736i | −0.835754 | + | 0.845370i | ||||
\(945\) | −12.5102 | + | 30.2168i | −0.406956 | + | 0.982953i | ||||
\(946\) | −6.54295 | + | 1.31120i | −0.212730 | + | 0.0426309i | ||||
\(947\) | −26.2255 | −0.852216 | −0.426108 | − | 0.904672i | \(-0.640116\pi\) | ||||
−0.426108 | + | 0.904672i | \(0.640116\pi\) | |||||||
\(948\) | 26.6384 | − | 26.7942i | 0.865175 | − | 0.870237i | ||||
\(949\) | −46.1734 | + | 14.0813i | −1.49885 | + | 0.457097i | ||||
\(950\) | 0.823842 | + | 4.11100i | 0.0267290 | + | 0.133379i | ||||
\(951\) | 1.78771 | − | 0.740612i | 0.0579703 | − | 0.0240160i | ||||
\(952\) | −2.43884 | − | 3.61630i | −0.0790432 | − | 0.117205i | ||||
\(953\) | 16.4039i | 0.531375i | 0.964059 | + | 0.265687i | \(0.0855989\pi\) | ||||
−0.964059 | + | 0.265687i | \(0.914401\pi\) | |||||||
\(954\) | 1.88983 | − | 2.83780i | 0.0611854 | − | 0.0918772i | ||||
\(955\) | 51.7822i | 1.67563i | ||||||||
\(956\) | 21.7365 | + | 52.0549i | 0.703007 | + | 1.68358i | ||||
\(957\) | −4.38300 | − | 10.5798i | −0.141682 | − | 0.341996i | ||||
\(958\) | −9.39959 | − | 46.9043i | −0.303687 | − | 1.51541i | ||||
\(959\) | −17.6744 | −0.570735 | ||||||||
\(960\) | 0.285477 | + | 33.0547i | 0.00921372 | + | 1.06684i | ||||
\(961\) | 19.4094 | 0.626109 | ||||||||
\(962\) | 18.4512 | + | 34.2794i | 0.594891 | + | 1.10521i | ||||
\(963\) | 40.6270 | + | 40.6177i | 1.30919 | + | 1.30889i | ||||
\(964\) | 6.61168 | + | 15.8338i | 0.212948 | + | 0.509972i | ||||
\(965\) | 10.4071 | 0.335017 | ||||||||
\(966\) | 15.8324 | + | 23.6188i | 0.509399 | + | 0.759921i | ||||
\(967\) | 23.4856 | 0.755245 | 0.377622 | − | 0.925960i | \(-0.376742\pi\) | ||||
0.377622 | + | 0.925960i | \(0.376742\pi\) | |||||||
\(968\) | −24.4258 | + | 16.4728i | −0.785075 | + | 0.529456i | ||||
\(969\) | −1.66222 | − | 4.01230i | −0.0533981 | − | 0.128894i | ||||
\(970\) | −34.7223 | + | 6.95833i | −1.11487 | + | 0.223418i | ||||
\(971\) | 38.7343i | 1.24304i | 0.783397 | + | 0.621521i | \(0.213485\pi\) | ||||
−0.783397 | + | 0.621521i | \(0.786515\pi\) | |||||||
\(972\) | −21.9760 | + | 22.1146i | −0.704879 | + | 0.709327i | ||||
\(973\) | −27.4954 | −0.881463 | ||||||||
\(974\) | −17.3264 | + | 3.47219i | −0.555173 | + | 0.111256i | ||||
\(975\) | −3.33216 | + | 2.74322i | −0.106714 | + | 0.0878533i | ||||
\(976\) | 26.9603 | + | 26.6537i | 0.862980 | + | 0.853164i | ||||
\(977\) | 61.1629 | 1.95677 | 0.978387 | − | 0.206781i | \(-0.0662987\pi\) | ||||
0.978387 | + | 0.206781i | \(0.0662987\pi\) | |||||||
\(978\) | 30.0847 | − | 20.1668i | 0.962004 | − | 0.644862i | ||||
\(979\) | −4.34468 | −0.138857 | ||||||||
\(980\) | 0.0725306 | + | 0.173698i | 0.00231691 | + | 0.00554857i | ||||
\(981\) | 14.9646 | − | 14.9681i | 0.477784 | − | 0.477893i | ||||
\(982\) | −3.08231 | − | 15.3809i | −0.0983605 | − | 0.490823i | ||||
\(983\) | − | 3.87323i | − | 0.123537i | −0.998091 | − | 0.0617684i | \(-0.980326\pi\) | ||
0.998091 | − | 0.0617684i | \(-0.0196740\pi\) | |||||||
\(984\) | −0.570105 | − | 0.377358i | −0.0181743 | − | 0.0120297i | ||||
\(985\) | −56.2484 | −1.79222 | ||||||||
\(986\) | 1.40551 | + | 7.01355i | 0.0447605 | + | 0.223357i | ||||
\(987\) | 3.75721 | − | 1.55654i | 0.119593 | − | 0.0495452i | ||||
\(988\) | 23.8264 | − | 19.7276i | 0.758020 | − | 0.627617i | ||||
\(989\) | −27.1715 | −0.864003 | ||||||||
\(990\) | 6.43680 | + | 4.28657i | 0.204575 | + | 0.136236i | ||||
\(991\) | − | 20.9226i | − | 0.664627i | −0.943169 | − | 0.332313i | \(-0.892171\pi\) | ||
0.943169 | − | 0.332313i | \(-0.107829\pi\) | |||||||
\(992\) | −22.0743 | + | 33.5533i | −0.700859 | + | 1.06532i | ||||
\(993\) | 34.5540 | − | 14.3150i | 1.09654 | − | 0.454274i | ||||
\(994\) | −1.88173 | − | 9.38991i | −0.0596848 | − | 0.297830i | ||||
\(995\) | −26.0197 | −0.824879 | ||||||||
\(996\) | −36.0573 | − | 35.8475i | −1.14252 | − | 1.13587i | ||||
\(997\) | 46.7104i | 1.47933i | 0.672974 | + | 0.739666i | \(0.265016\pi\) | ||||
−0.672974 | + | 0.739666i | \(0.734984\pi\) | |||||||
\(998\) | −2.38161 | − | 11.8843i | −0.0753886 | − | 0.376192i | ||||
\(999\) | 36.6541 | + | 15.1753i | 1.15969 | + | 0.480125i |
(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 | 312.2.h.c.155.29 | yes | 32 | |
3.2 | odd | 2 | inner | 312.2.h.c.155.4 | yes | 32 | |
4.3 | odd | 2 | 1248.2.h.c.623.21 | 32 | |||
8.3 | odd | 2 | inner | 312.2.h.c.155.31 | yes | 32 | |
8.5 | even | 2 | 1248.2.h.c.623.22 | 32 | |||
12.11 | even | 2 | 1248.2.h.c.623.19 | 32 | |||
13.12 | even | 2 | inner | 312.2.h.c.155.3 | yes | 32 | |
24.5 | odd | 2 | 1248.2.h.c.623.20 | 32 | |||
24.11 | even | 2 | inner | 312.2.h.c.155.2 | yes | 32 | |
39.38 | odd | 2 | inner | 312.2.h.c.155.30 | yes | 32 | |
52.51 | odd | 2 | 1248.2.h.c.623.24 | 32 | |||
104.51 | odd | 2 | inner | 312.2.h.c.155.1 | ✓ | 32 | |
104.77 | even | 2 | 1248.2.h.c.623.23 | 32 | |||
156.155 | even | 2 | 1248.2.h.c.623.18 | 32 | |||
312.77 | odd | 2 | 1248.2.h.c.623.17 | 32 | |||
312.155 | even | 2 | inner | 312.2.h.c.155.32 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.h.c.155.1 | ✓ | 32 | 104.51 | odd | 2 | inner | |
312.2.h.c.155.2 | yes | 32 | 24.11 | even | 2 | inner | |
312.2.h.c.155.3 | yes | 32 | 13.12 | even | 2 | inner | |
312.2.h.c.155.4 | yes | 32 | 3.2 | odd | 2 | inner | |
312.2.h.c.155.29 | yes | 32 | 1.1 | even | 1 | trivial | |
312.2.h.c.155.30 | yes | 32 | 39.38 | odd | 2 | inner | |
312.2.h.c.155.31 | yes | 32 | 8.3 | odd | 2 | inner | |
312.2.h.c.155.32 | yes | 32 | 312.155 | even | 2 | inner | |
1248.2.h.c.623.17 | 32 | 312.77 | odd | 2 | |||
1248.2.h.c.623.18 | 32 | 156.155 | even | 2 | |||
1248.2.h.c.623.19 | 32 | 12.11 | even | 2 | |||
1248.2.h.c.623.20 | 32 | 24.5 | odd | 2 | |||
1248.2.h.c.623.21 | 32 | 4.3 | odd | 2 | |||
1248.2.h.c.623.22 | 32 | 8.5 | even | 2 | |||
1248.2.h.c.623.23 | 32 | 104.77 | even | 2 | |||
1248.2.h.c.623.24 | 32 | 52.51 | odd | 2 |