Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(107,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.u (of order \(30\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 215.3 | ||
Character | \(\chi\) | \(=\) | 891.215 |
Dual form | 891.2.u.c.431.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.460557 | − | 0.511500i | 0.325663 | − | 0.361685i | −0.557974 | − | 0.829859i | \(-0.688421\pi\) |
0.883637 | + | 0.468173i | \(0.155088\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.159537 | + | 1.51789i | 0.0797686 | + | 0.758947i | ||||
\(5\) | 0.0298066 | − | 0.0268380i | 0.0133299 | − | 0.0120023i | −0.662439 | − | 0.749116i | \(-0.730479\pi\) |
0.675769 | + | 0.737114i | \(0.263812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.100402 | − | 0.225507i | 0.0379485 | − | 0.0852336i | −0.893577 | − | 0.448911i | \(-0.851812\pi\) |
0.931525 | + | 0.363677i | \(0.118479\pi\) | |||||||
\(8\) | 1.96356 | + | 1.42661i | 0.694222 | + | 0.504382i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 0.0276065i | − | 0.00872994i | ||||||
\(11\) | 2.53364 | + | 2.14025i | 0.763921 | + | 0.645310i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.478513 | − | 2.25123i | 0.132716 | − | 0.624378i | −0.860632 | − | 0.509227i | \(-0.829931\pi\) |
0.993348 | − | 0.115151i | \(-0.0367353\pi\) | |||||||
\(14\) | −0.0691059 | − | 0.155214i | −0.0184693 | − | 0.0414828i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35177 | + | 0.287327i | −0.337942 | + | 0.0718317i | ||||
\(17\) | 1.32142 | − | 4.06692i | 0.320492 | − | 0.986372i | −0.652943 | − | 0.757407i | \(-0.726466\pi\) |
0.973435 | − | 0.228965i | \(-0.0735342\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.64429 | + | 5.01593i | −0.836057 | + | 1.15073i | 0.150708 | + | 0.988578i | \(0.451845\pi\) |
−0.986765 | + | 0.162156i | \(0.948155\pi\) | |||||||
\(20\) | 0.0454925 | + | 0.0409616i | 0.0101724 | + | 0.00915930i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.26162 | − | 0.310248i | 0.482180 | − | 0.0661451i | ||||
\(23\) | 5.88883 | + | 3.39992i | 1.22791 | + | 0.708932i | 0.966592 | − | 0.256321i | \(-0.0825105\pi\) |
0.261315 | + | 0.965254i | \(0.415844\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.522474 | + | 4.97101i | −0.104495 | + | 0.994202i | ||||
\(26\) | −0.931121 | − | 1.28158i | −0.182608 | − | 0.251338i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.358314 | + | 0.116423i | 0.0677149 | + | 0.0220019i | ||||
\(29\) | 5.11196 | + | 2.27599i | 0.949268 | + | 0.422641i | 0.822166 | − | 0.569248i | \(-0.192766\pi\) |
0.127102 | + | 0.991890i | \(0.459432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.69255 | − | 0.997431i | −0.842806 | − | 0.179144i | −0.233775 | − | 0.972291i | \(-0.575108\pi\) |
−0.609031 | + | 0.793147i | \(0.708441\pi\) | |||||||
\(32\) | −2.90269 | + | 5.02760i | −0.513128 | + | 0.888763i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.47164 | − | 2.54895i | −0.252384 | − | 0.437142i | ||||
\(35\) | −0.00305951 | − | 0.00941619i | −0.000517151 | − | 0.00159163i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.26102 | − | 2.36927i | 0.536109 | − | 0.389506i | −0.286529 | − | 0.958072i | \(-0.592502\pi\) |
0.822638 | + | 0.568566i | \(0.192502\pi\) | |||||||
\(38\) | 0.887248 | + | 4.17418i | 0.143931 | + | 0.677141i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0968143 | − | 0.0101756i | 0.0153077 | − | 0.00160890i | ||||
\(41\) | −8.77271 | + | 3.90586i | −1.37007 | + | 0.609993i | −0.954128 | − | 0.299399i | \(-0.903214\pi\) |
−0.415939 | + | 0.909392i | \(0.636547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.893447 | − | 0.515832i | 0.136249 | − | 0.0786636i | −0.430326 | − | 0.902674i | \(-0.641601\pi\) |
0.566575 | + | 0.824010i | \(0.308268\pi\) | |||||||
\(44\) | −2.84447 | + | 4.18724i | −0.428820 | + | 0.631251i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.45120 | − | 1.44628i | 0.656294 | − | 0.213243i | ||||
\(47\) | 11.0653 | + | 1.16301i | 1.61403 | + | 0.169642i | 0.868104 | − | 0.496382i | \(-0.165339\pi\) |
0.745930 | + | 0.666024i | \(0.232005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.64314 | + | 5.15673i | 0.663306 | + | 0.736676i | ||||
\(50\) | 2.30204 | + | 2.55668i | 0.325558 | + | 0.361569i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.49347 | + | 0.367178i | 0.484457 | + | 0.0509184i | ||||
\(53\) | 8.52885 | − | 2.77119i | 1.17153 | − | 0.380652i | 0.342314 | − | 0.939585i | \(-0.388789\pi\) |
0.829213 | + | 0.558933i | \(0.188789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.132959 | − | 0.00420408i | 0.0179282 | − | 0.000566878i | ||||
\(56\) | 0.518855 | − | 0.299561i | 0.0693350 | − | 0.0400306i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.51852 | − | 1.56655i | 0.462004 | − | 0.205698i | ||||
\(59\) | −2.77304 | + | 0.291459i | −0.361020 | + | 0.0379447i | −0.283302 | − | 0.959031i | \(-0.591430\pi\) |
−0.0777175 | + | 0.996975i | \(0.524763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.76403 | − | 8.29909i | −0.225860 | − | 1.06259i | −0.934209 | − | 0.356727i | \(-0.883893\pi\) |
0.708348 | − | 0.705863i | \(-0.249441\pi\) | |||||||
\(62\) | −2.67137 | + | 1.94086i | −0.339264 | + | 0.246490i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.380665 | + | 1.17156i | 0.0475831 | + | 0.146446i | ||||
\(65\) | −0.0461556 | − | 0.0799438i | −0.00572489 | − | 0.00991581i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.97294 | + | 6.88133i | −0.485372 | + | 0.840689i | −0.999859 | − | 0.0168095i | \(-0.994649\pi\) |
0.514487 | + | 0.857498i | \(0.327982\pi\) | |||||||
\(68\) | 6.38397 | + | 1.35695i | 0.774170 | + | 0.164555i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.00622546 | − | 0.00277175i | −0.000744084 | − | 0.000331288i | ||||
\(71\) | −3.16559 | − | 1.02856i | −0.375687 | − | 0.122068i | 0.115086 | − | 0.993355i | \(-0.463286\pi\) |
−0.490773 | + | 0.871288i | \(0.663286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.96743 | − | 9.58984i | −0.815476 | − | 1.12241i | −0.990455 | − | 0.137834i | \(-0.955986\pi\) |
0.174980 | − | 0.984572i | \(-0.444014\pi\) | |||||||
\(74\) | 0.290003 | − | 2.75920i | 0.0337122 | − | 0.320750i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.19506 | − | 4.73142i | −0.940038 | − | 0.542731i | ||||
\(77\) | 0.737025 | − | 0.356467i | 0.0839917 | − | 0.0406232i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.23761 | + | 2.01475i | 0.251751 | + | 0.226678i | 0.785337 | − | 0.619068i | \(-0.212489\pi\) |
−0.533587 | + | 0.845745i | \(0.679156\pi\) | |||||||
\(80\) | −0.0325803 | + | 0.0448429i | −0.00364259 | + | 0.00501359i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.04248 | + | 6.28611i | −0.225554 | + | 0.694185i | ||||
\(83\) | −5.17811 | + | 1.10064i | −0.568372 | + | 0.120811i | −0.483129 | − | 0.875549i | \(-0.660500\pi\) |
−0.0852426 | + | 0.996360i | \(0.527167\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0697608 | − | 0.156685i | −0.00756662 | − | 0.0169949i | ||||
\(86\) | 0.147635 | − | 0.694568i | 0.0159199 | − | 0.0748972i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.92164 | + | 7.81702i | 0.204848 | + | 0.833297i | ||||
\(89\) | − | 8.54422i | − | 0.905686i | −0.891590 | − | 0.452843i | \(-0.850410\pi\) | ||
0.891590 | − | 0.452843i | \(-0.149590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.459624 | − | 0.333936i | −0.0481817 | − | 0.0350060i | ||||
\(92\) | −4.22123 | + | 9.48104i | −0.440094 | + | 0.988467i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.69106 | − | 5.12425i | 0.586988 | − | 0.528526i | ||||
\(95\) | 0.0259937 | + | 0.247313i | 0.00266690 | + | 0.0253738i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.02629 | + | 2.25042i | −0.205738 | + | 0.228496i | −0.837180 | − | 0.546928i | \(-0.815797\pi\) |
0.631441 | + | 0.775424i | \(0.282464\pi\) | |||||||
\(98\) | 4.77610 | 0.482459 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.62882 | −0.762882 | ||||||||
\(101\) | 4.65178 | − | 5.16633i | 0.462869 | − | 0.514069i | −0.465844 | − | 0.884867i | \(-0.654249\pi\) |
0.928713 | + | 0.370798i | \(0.120916\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.37135 | − | 13.0475i | −0.135123 | − | 1.28561i | −0.826425 | − | 0.563046i | \(-0.809629\pi\) |
0.691302 | − | 0.722566i | \(-0.257037\pi\) | |||||||
\(104\) | 4.15121 | − | 3.73776i | 0.407059 | − | 0.366518i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.51055 | − | 5.63879i | 0.243846 | − | 0.547688i | ||||
\(107\) | 1.10712 | + | 0.804368i | 0.107029 | + | 0.0777612i | 0.640012 | − | 0.768365i | \(-0.278929\pi\) |
−0.532983 | + | 0.846126i | \(0.678929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.34454i | − | 0.703480i | −0.936098 | − | 0.351740i | \(-0.885590\pi\) | ||
0.936098 | − | 0.351740i | \(-0.114410\pi\) | |||||||
\(110\) | 0.0590849 | − | 0.0699448i | 0.00563352 | − | 0.00666898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0709261 | + | 0.333681i | −0.00670189 | + | 0.0315299i | ||||
\(113\) | −0.214978 | − | 0.482848i | −0.0202234 | − | 0.0454225i | 0.903151 | − | 0.429322i | \(-0.141248\pi\) |
−0.923375 | + | 0.383900i | \(0.874581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.266773 | − | 0.0567044i | 0.0248767 | − | 0.00528771i | ||||
\(116\) | −2.63917 | + | 8.12253i | −0.245041 | + | 0.754158i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.12806 | + | 1.55265i | −0.103847 | + | 0.142933i | ||||
\(119\) | −0.784445 | − | 0.706317i | −0.0719099 | − | 0.0647480i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83864 | + | 10.8452i | 0.167149 | + | 0.985932i | ||||
\(122\) | −5.05742 | − | 2.91990i | −0.457877 | − | 0.264355i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.765360 | − | 7.28192i | 0.0687314 | − | 0.653935i | ||||
\(125\) | 0.235715 | + | 0.324434i | 0.0210830 | + | 0.0290183i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.1468 | + | 3.94673i | 1.07785 | + | 0.350215i | 0.793541 | − | 0.608517i | \(-0.208235\pi\) |
0.284311 | + | 0.958732i | \(0.408235\pi\) | |||||||
\(128\) | −9.83238 | − | 4.37766i | −0.869067 | − | 0.386934i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0621485 | − | 0.0132101i | −0.00545078 | − | 0.00115860i | ||||
\(131\) | 9.07668 | − | 15.7213i | 0.793033 | − | 1.37357i | −0.131047 | − | 0.991376i | \(-0.541834\pi\) |
0.924081 | − | 0.382198i | \(-0.124833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.765233 | + | 1.32542i | 0.0663542 | + | 0.114929i | ||||
\(134\) | 1.69004 | + | 5.20140i | 0.145997 | + | 0.449333i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.39658 | − | 6.10048i | 0.720001 | − | 0.523111i | ||||
\(137\) | −3.34176 | − | 15.7217i | −0.285506 | − | 1.34320i | −0.853897 | − | 0.520441i | \(-0.825767\pi\) |
0.568392 | − | 0.822758i | \(-0.307566\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.83617 | + | 0.403198i | −0.325380 | + | 0.0341988i | −0.265810 | − | 0.964025i | \(-0.585639\pi\) |
−0.0595696 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(140\) | 0.0138047 | − | 0.00614624i | 0.00116671 | − | 0.000519452i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.98404 | + | 1.14549i | −0.166497 | + | 0.0961273i | ||||
\(143\) | 6.03057 | − | 4.67966i | 0.504302 | − | 0.391333i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.213453 | − | 0.0693552i | 0.0177263 | − | 0.00575964i | ||||
\(146\) | −8.11410 | − | 0.852826i | −0.671528 | − | 0.0705804i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.11656 | + | 4.57190i | 0.338379 | + | 0.375808i | ||||
\(149\) | −6.87196 | − | 7.63209i | −0.562973 | − | 0.625245i | 0.392703 | − | 0.919665i | \(-0.371540\pi\) |
−0.955676 | + | 0.294420i | \(0.904873\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.72237 | − | 0.916758i | −0.709817 | − | 0.0746047i | −0.257262 | − | 0.966342i | \(-0.582820\pi\) |
−0.452554 | + | 0.891737i | \(0.649487\pi\) | |||||||
\(152\) | −14.3115 | + | 4.65010i | −1.16082 | + | 0.377173i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.157109 | − | 0.541161i | 0.0126602 | − | 0.0436080i | ||||
\(155\) | −0.166638 | + | 0.0962084i | −0.0133847 | + | 0.00772765i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9043 | + | 5.30012i | −0.950064 | + | 0.422996i | −0.822456 | − | 0.568829i | \(-0.807397\pi\) |
−0.127608 | + | 0.991825i | \(0.540730\pi\) | |||||||
\(158\) | 2.06109 | − | 0.216630i | 0.163972 | − | 0.0172341i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.0484115 | + | 0.227758i | 0.00382726 | + | 0.0180059i | ||||
\(161\) | 1.35796 | − | 0.986614i | 0.107022 | − | 0.0777561i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.83608 | − | 8.72855i | −0.222139 | − | 0.683673i | −0.998569 | − | 0.0534700i | \(-0.982972\pi\) |
0.776431 | − | 0.630203i | \(-0.217028\pi\) | |||||||
\(164\) | −7.32826 | − | 12.6929i | −0.572241 | − | 0.991151i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.82184 | + | 3.15551i | −0.141402 | + | 0.244915i | ||||
\(167\) | −7.44305 | − | 1.58207i | −0.575961 | − | 0.122424i | −0.0892837 | − | 0.996006i | \(-0.528458\pi\) |
−0.486677 | + | 0.873582i | \(0.661791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.03704 | + | 3.13309i | 0.541311 | + | 0.241007i | ||||
\(170\) | −0.112273 | − | 0.0364798i | −0.00861097 | − | 0.00279787i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.925516 | + | 1.27386i | 0.0705699 | + | 0.0971312i | ||||
\(173\) | −1.73731 | + | 16.5294i | −0.132085 | + | 1.25670i | 0.704832 | + | 0.709374i | \(0.251022\pi\) |
−0.836917 | + | 0.547330i | \(0.815644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.06854 | + | 0.616922i | 0.0807740 | + | 0.0466349i | ||||
\(176\) | −4.03984 | − | 2.16514i | −0.304514 | − | 0.163204i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.37037 | − | 3.93510i | −0.327573 | − | 0.294948i | ||||
\(179\) | 4.14376 | − | 5.70340i | 0.309719 | − | 0.426292i | −0.625574 | − | 0.780165i | \(-0.715135\pi\) |
0.935294 | + | 0.353872i | \(0.115135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.52756 | + | 20.0898i | −0.485189 | + | 1.49326i | 0.346517 | + | 0.938044i | \(0.387364\pi\) |
−0.831706 | + | 0.555216i | \(0.812636\pi\) | |||||||
\(182\) | −0.382491 | + | 0.0813010i | −0.0283521 | + | 0.00602643i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.71271 | + | 15.0770i | 0.494868 | + | 1.11149i | ||||
\(185\) | 0.0336135 | − | 0.158139i | 0.00247132 | − | 0.0116266i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0522 | − | 7.47592i | 0.881347 | − | 0.546693i | ||||
\(188\) | 16.9814i | 1.23850i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.138472 | + | 0.100606i | 0.0100458 | + | 0.00729873i | ||||
\(191\) | 5.55938 | − | 12.4866i | 0.402263 | − | 0.903497i | −0.592902 | − | 0.805275i | \(-0.702018\pi\) |
0.995165 | − | 0.0982221i | \(-0.0313155\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6045 | − | 16.7516i | 1.33918 | − | 1.20581i | 0.379345 | − | 0.925255i | \(-0.376149\pi\) |
0.959839 | − | 0.280552i | \(-0.0905174\pi\) | |||||||
\(194\) | 0.217870 | + | 2.07289i | 0.0156421 | + | 0.148825i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.08662 | + | 7.87049i | −0.506187 | + | 0.562178i | ||||
\(197\) | −21.0442 | −1.49934 | −0.749668 | − | 0.661814i | \(-0.769787\pi\) | ||||
−0.749668 | + | 0.661814i | \(0.769787\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3709 | −0.735176 | −0.367588 | − | 0.929989i | \(-0.619816\pi\) | ||||
−0.367588 | + | 0.929989i | \(0.619816\pi\) | |||||||
\(200\) | −8.11759 | + | 9.01550i | −0.574000 | + | 0.637492i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.500167 | − | 4.75877i | −0.0351916 | − | 0.334826i | ||||
\(203\) | 1.02650 | − | 0.924269i | 0.0720465 | − | 0.0648710i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.156659 | + | 0.351862i | −0.0109416 | + | 0.0245751i | ||||
\(206\) | −7.30540 | − | 5.30768i | −0.508991 | − | 0.369804i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.18062i | 0.220537i | ||||||||
\(209\) | −19.9687 | + | 4.90886i | −1.38126 | + | 0.339553i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.89702 | − | 18.3340i | 0.268282 | − | 1.26217i | −0.613192 | − | 0.789934i | \(-0.710115\pi\) |
0.881474 | − | 0.472233i | \(-0.156552\pi\) | |||||||
\(212\) | 5.56704 | + | 12.5038i | 0.382346 | + | 0.858763i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.921325 | − | 0.195834i | 0.0629805 | − | 0.0133869i | ||||
\(215\) | 0.0127867 | − | 0.0393535i | 0.000872048 | − | 0.00268389i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.696069 | + | 0.958057i | −0.0472523 | + | 0.0650372i | ||||
\(218\) | −3.75673 | − | 3.38258i | −0.254438 | − | 0.229097i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0275933 | + | 0.201147i | 0.00186034 | + | 0.0135613i | ||||
\(221\) | −8.52324 | − | 4.92090i | −0.573335 | − | 0.331015i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.01068 | + | 9.61597i | −0.0676801 | + | 0.643933i | 0.907123 | + | 0.420866i | \(0.138274\pi\) |
−0.974803 | + | 0.223067i | \(0.928393\pi\) | |||||||
\(224\) | 0.842323 | + | 1.15936i | 0.0562801 | + | 0.0774629i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.345986 | − | 0.112418i | −0.0230146 | − | 0.00747791i | ||||
\(227\) | −10.7033 | − | 4.76540i | −0.710401 | − | 0.316291i | 0.0195325 | − | 0.999809i | \(-0.493782\pi\) |
−0.729933 | + | 0.683518i | \(0.760449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.0326 | − | 4.25807i | −1.32379 | − | 0.281381i | −0.508817 | − | 0.860875i | \(-0.669917\pi\) |
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(230\) | 0.0938599 | − | 0.162570i | 0.00618894 | − | 0.0107196i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.79068 | + | 11.7618i | 0.445830 | + | 0.772201i | ||||
\(233\) | −4.98842 | − | 15.3528i | −0.326802 | − | 1.00579i | −0.970621 | − | 0.240615i | \(-0.922651\pi\) |
0.643818 | − | 0.765178i | \(-0.277349\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.361031 | − | 0.262304i | 0.0235510 | − | 0.0171108i | ||||
\(236\) | −0.884807 | − | 4.16269i | −0.0575960 | − | 0.270968i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.722562 | + | 0.0759444i | −0.0468368 | + | 0.00492274i | ||||
\(239\) | 25.9333 | − | 11.5462i | 1.67749 | − | 0.746865i | 0.677550 | − | 0.735476i | \(-0.263042\pi\) |
0.999935 | − | 0.0113883i | \(-0.00362510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4408 | + | 7.18270i | −0.801383 | + | 0.462679i | −0.843954 | − | 0.536415i | \(-0.819778\pi\) |
0.0425716 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(242\) | 6.39414 | + | 4.05439i | 0.411031 | + | 0.260626i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.3157 | − | 4.00162i | 0.788433 | − | 0.256177i | ||||
\(245\) | 0.276793 | + | 0.0290921i | 0.0176836 | + | 0.00185862i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.54817 | + | 10.6043i | 0.607535 | + | 0.674737i | ||||
\(248\) | −7.79114 | − | 8.65294i | −0.494738 | − | 0.549462i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.274508 | + | 0.0288520i | 0.0173614 | + | 0.00182476i | ||||
\(251\) | −6.60298 | + | 2.14544i | −0.416776 | + | 0.135419i | −0.509896 | − | 0.860236i | \(-0.670316\pi\) |
0.0931196 | + | 0.995655i | \(0.470316\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.64348 | + | 21.2178i | 0.480542 | + | 1.33395i | ||||
\(254\) | 7.61303 | − | 4.39538i | 0.477684 | − | 0.275791i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.01825 | + | 4.01518i | −0.563641 | + | 0.250949i | ||||
\(257\) | −10.3612 | + | 1.08901i | −0.646315 | + | 0.0679305i | −0.422014 | − | 0.906589i | \(-0.638677\pi\) |
−0.224301 | + | 0.974520i | \(0.572010\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.206873 | − | 0.973263i | −0.0128545 | − | 0.0604756i | ||||
\(260\) | 0.113983 | − | 0.0828133i | 0.00706891 | − | 0.00513586i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.86110 | − | 11.8833i | −0.238540 | − | 0.734150i | ||||
\(263\) | −2.13055 | − | 3.69022i | −0.131375 | − | 0.227549i | 0.792832 | − | 0.609441i | \(-0.208606\pi\) |
−0.924207 | + | 0.381892i | \(0.875273\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.179843 | − | 0.311497i | 0.0110477 | − | 0.0191351i | ||||
\(266\) | 1.03039 | + | 0.219016i | 0.0631771 | + | 0.0134287i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.0790 | − | 4.93268i | −0.676756 | − | 0.301311i | ||||
\(269\) | 10.5223 | + | 3.41889i | 0.641553 | + | 0.208453i | 0.611686 | − | 0.791101i | \(-0.290492\pi\) |
0.0298672 | + | 0.999554i | \(0.490492\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.34327 | + | 12.8599i | 0.567563 | + | 0.781184i | 0.992263 | − | 0.124150i | \(-0.0396205\pi\) |
−0.424700 | + | 0.905334i | \(0.639621\pi\) | |||||||
\(272\) | −0.617719 | + | 5.87720i | −0.0374547 | + | 0.356358i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.58074 | − | 5.53144i | −0.578794 | − | 0.334167i | ||||
\(275\) | −11.9630 | + | 11.4765i | −0.721395 | + | 0.692060i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.42804 | − | 7.58864i | −0.506392 | − | 0.455957i | 0.375900 | − | 0.926660i | \(-0.377334\pi\) |
−0.882292 | + | 0.470703i | \(0.844000\pi\) | |||||||
\(278\) | −1.56054 | + | 2.14790i | −0.0935949 | + | 0.128822i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.00742570 | − | 0.0228539i | 0.000443770 | − | 0.00136578i | ||||
\(281\) | 1.52620 | − | 0.324404i | 0.0910454 | − | 0.0193523i | −0.162164 | − | 0.986764i | \(-0.551847\pi\) |
0.253209 | + | 0.967412i | \(0.418514\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8051 | + | 24.2687i | 0.642299 | + | 1.44263i | 0.881750 | + | 0.471718i | \(0.156366\pi\) |
−0.239451 | + | 0.970908i | \(0.576967\pi\) | |||||||
\(284\) | 1.05622 | − | 4.96913i | 0.0626752 | − | 0.294863i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.383777 | − | 5.23989i | 0.0226932 | − | 0.309841i | ||||
\(287\) | 2.37046i | 0.139924i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.04038 | − | 0.755878i | −0.0611986 | − | 0.0444634i | ||||
\(290\) | 0.0628322 | − | 0.141123i | 0.00368963 | − | 0.00828705i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.4448 | − | 12.1058i | 0.786798 | − | 0.708436i | ||||
\(293\) | −2.75271 | − | 26.1903i | −0.160815 | − | 1.53005i | −0.715867 | − | 0.698237i | \(-0.753968\pi\) |
0.555052 | − | 0.831816i | \(-0.312698\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0748329 | + | 0.0831103i | −0.00435694 | + | 0.00483887i | ||||
\(296\) | 9.78322 | 0.568638 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.06874 | −0.409481 | ||||||||
\(299\) | 10.4719 | − | 11.6302i | 0.605604 | − | 0.672592i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0266197 | − | 0.253269i | −0.00153433 | − | 0.0145982i | ||||
\(302\) | −4.48607 | + | 4.03927i | −0.258144 | + | 0.232434i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.48502 | − | 7.82747i | 0.199879 | − | 0.448936i | ||||
\(305\) | −0.275310 | − | 0.200025i | −0.0157642 | − | 0.0114534i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.0083i | − | 1.48437i | −0.670195 | − | 0.742185i | \(-0.733789\pi\) | ||
0.670195 | − | 0.742185i | \(-0.266211\pi\) | |||||||
\(308\) | 0.658662 | + | 1.06186i | 0.0375307 | + | 0.0605048i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0275356 | + | 0.129545i | −0.00156392 | + | 0.00735765i | ||||
\(311\) | 5.41967 | + | 12.1728i | 0.307321 | + | 0.690255i | 0.999505 | − | 0.0314665i | \(-0.0100177\pi\) |
−0.692183 | + | 0.721722i | \(0.743351\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0025 | − | 2.33866i | 0.621899 | − | 0.132189i | 0.113823 | − | 0.993501i | \(-0.463690\pi\) |
0.508076 | + | 0.861312i | \(0.330357\pi\) | |||||||
\(314\) | −2.77158 | + | 8.53004i | −0.156409 | + | 0.481378i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.70120 | + | 3.71788i | −0.151954 | + | 0.209147i | ||||
\(317\) | 8.13939 | + | 7.32874i | 0.457154 | + | 0.411623i | 0.865269 | − | 0.501307i | \(-0.167147\pi\) |
−0.408116 | + | 0.912930i | \(0.633814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.08067 | + | 16.7074i | 0.452430 | + | 0.935437i | ||||
\(320\) | 0.0427888 | + | 0.0247041i | 0.00239196 | + | 0.00138100i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.120763 | − | 1.14899i | 0.00672988 | − | 0.0640305i | ||||
\(323\) | 15.5837 | + | 21.4492i | 0.867103 | + | 1.19346i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9409 | + | 3.55490i | 0.606890 | + | 0.197191i | ||||
\(326\) | −5.77083 | − | 2.56934i | −0.319616 | − | 0.142302i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −22.7979 | − | 4.84583i | −1.25880 | − | 0.267566i | ||||
\(329\) | 1.37324 | − | 2.37852i | 0.0757093 | − | 0.131132i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.11643 | − | 3.66576i | −0.116329 | − | 0.201488i | 0.801981 | − | 0.597349i | \(-0.203779\pi\) |
−0.918310 | + | 0.395861i | \(0.870446\pi\) | |||||||
\(332\) | −2.49676 | − | 7.68424i | −0.137027 | − | 0.421727i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.23718 | + | 3.07849i | −0.231848 | + | 0.168447i | ||||
\(335\) | 0.0662613 | + | 0.311735i | 0.00362024 | + | 0.0170319i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.64780 | − | 0.278295i | 0.144235 | − | 0.0151597i | −0.0321359 | − | 0.999484i | \(-0.510231\pi\) |
0.176371 | + | 0.984324i | \(0.443564\pi\) | |||||||
\(338\) | 4.84353 | − | 2.15648i | 0.263453 | − | 0.117297i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.226702 | − | 0.130887i | 0.0122947 | − | 0.00709832i | ||||
\(341\) | −9.75446 | − | 12.5704i | −0.528233 | − | 0.680723i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.27243 | − | 1.06328i | 0.176694 | − | 0.0574115i | ||||
\(344\) | 2.49022 | + | 0.261733i | 0.134264 | + | 0.0141117i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.65464 | + | 8.50134i | 0.411516 | + | 0.457035i | ||||
\(347\) | 11.1097 | + | 12.3386i | 0.596399 | + | 0.662368i | 0.963467 | − | 0.267826i | \(-0.0863051\pi\) |
−0.367068 | + | 0.930194i | \(0.619638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6993 | + | 1.43985i | 0.733307 | + | 0.0770736i | 0.463819 | − | 0.885930i | \(-0.346479\pi\) |
0.269488 | + | 0.963004i | \(0.413146\pi\) | |||||||
\(350\) | 0.807679 | − | 0.262431i | 0.0431722 | − | 0.0140275i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.1147 | + | 6.52564i | −0.965517 | + | 0.347818i | ||||
\(353\) | 9.54783 | − | 5.51244i | 0.508180 | − | 0.293398i | −0.223905 | − | 0.974611i | \(-0.571881\pi\) |
0.732085 | + | 0.681213i | \(0.238547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.121960 | + | 0.0543001i | −0.00647297 | + | 0.00288195i | ||||
\(356\) | 12.9692 | − | 1.36312i | 0.687368 | − | 0.0722453i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.00885 | − | 4.74627i | −0.0533195 | − | 0.250848i | ||||
\(359\) | 15.3828 | − | 11.1763i | 0.811875 | − | 0.589862i | −0.102499 | − | 0.994733i | \(-0.532684\pi\) |
0.914374 | + | 0.404871i | \(0.132684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00743 | − | 18.4890i | −0.316180 | − | 0.973103i | ||||
\(362\) | 7.26960 | + | 12.5913i | 0.382082 | + | 0.661785i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.433553 | − | 0.750936i | 0.0227243 | − | 0.0393597i | ||||
\(365\) | −0.465047 | − | 0.0988489i | −0.0243417 | − | 0.00517399i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.20463 | − | 2.31725i | −0.271680 | − | 0.120960i | 0.266375 | − | 0.963869i | \(-0.414174\pi\) |
−0.538055 | + | 0.842910i | \(0.680841\pi\) | |||||||
\(368\) | −8.93722 | − | 2.90388i | −0.465885 | − | 0.151375i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0654073 | − | 0.0900254i | −0.00340036 | − | 0.00468020i | ||||
\(371\) | 0.231392 | − | 2.20155i | 0.0120133 | − | 0.114299i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.1906 | − | 11.0797i | −0.993651 | − | 0.573684i | −0.0872871 | − | 0.996183i | \(-0.527820\pi\) |
−0.906364 | + | 0.422499i | \(0.861153\pi\) | |||||||
\(374\) | 1.72680 | − | 9.60780i | 0.0892909 | − | 0.496808i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.0681 | + | 18.0694i | 1.03493 | + | 0.931859i | ||||
\(377\) | 7.56992 | − | 10.4191i | 0.389871 | − | 0.536611i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.117844 | + | 0.362687i | −0.00605325 | + | 0.0186300i | −0.954038 | − | 0.299687i | \(-0.903118\pi\) |
0.947984 | + | 0.318317i | \(0.103118\pi\) | |||||||
\(380\) | −0.371249 | + | 0.0789113i | −0.0190447 | + | 0.00404807i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.82647 | − | 8.59440i | −0.195779 | − | 0.439728i | ||||
\(383\) | −2.63308 | + | 12.3877i | −0.134544 | + | 0.632981i | 0.858258 | + | 0.513218i | \(0.171547\pi\) |
−0.992803 | + | 0.119763i | \(0.961787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0124013 | − | 0.0304053i | 0.000632031 | − | 0.00154960i | ||||
\(386\) | − | 17.2313i | − | 0.877049i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.73917 | − | 2.71667i | −0.189828 | − | 0.137918i | ||||
\(389\) | −9.67976 | + | 21.7411i | −0.490783 | + | 1.10232i | 0.483161 | + | 0.875531i | \(0.339489\pi\) |
−0.973945 | + | 0.226786i | \(0.927178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.6088 | − | 19.4567i | 1.09281 | − | 0.983966i | ||||
\(392\) | 1.76044 | + | 16.7495i | 0.0889157 | + | 0.845976i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.69204 | + | 10.7641i | −0.488278 | + | 0.542288i | ||||
\(395\) | 0.120768 | 0.00607647 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00497 | 0.251192 | 0.125596 | − | 0.992081i | \(-0.459916\pi\) | ||||
0.125596 | + | 0.992081i | \(0.459916\pi\) | |||||||
\(398\) | −4.77641 | + | 5.30474i | −0.239420 | + | 0.265902i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.722042 | − | 6.86977i | −0.0361021 | − | 0.343488i | ||||
\(401\) | −3.15402 | + | 2.83989i | −0.157504 | + | 0.141817i | −0.744115 | − | 0.668052i | \(-0.767129\pi\) |
0.586611 | + | 0.809869i | \(0.300462\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.49089 | + | 10.0867i | −0.223707 | + | 0.502455i | ||||
\(404\) | 8.58407 | + | 6.23669i | 0.427073 | + | 0.310287i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 0.950735i | − | 0.0471842i | ||||||
\(407\) | 13.3331 | + | 0.976535i | 0.660897 | + | 0.0484051i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.45452 | − | 11.5476i | 0.121368 | − | 0.570992i | −0.874872 | − | 0.484354i | \(-0.839055\pi\) |
0.996240 | − | 0.0866372i | \(-0.0276121\pi\) | |||||||
\(410\) | 0.107827 | + | 0.242184i | 0.00532520 | + | 0.0119606i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.5860 | − | 4.16313i | 0.964933 | − | 0.205103i | ||||
\(413\) | −0.212694 | + | 0.654604i | −0.0104660 | + | 0.0322109i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.124803 | + | 0.171777i | −0.00612634 | + | 0.00843218i | ||||
\(416\) | 9.92930 | + | 8.94039i | 0.486824 | + | 0.438338i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.68582 | + | 12.4748i | −0.327014 | + | 0.610162i | ||||
\(419\) | 18.1688 | + | 10.4898i | 0.887604 | + | 0.512459i | 0.873158 | − | 0.487437i | \(-0.162068\pi\) |
0.0144463 | + | 0.999896i | \(0.495401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.290566 | − | 2.76455i | 0.0141613 | − | 0.134736i | −0.985157 | − | 0.171656i | \(-0.945088\pi\) |
0.999318 | + | 0.0369204i | \(0.0117548\pi\) | |||||||
\(422\) | −7.58306 | − | 10.4372i | −0.369137 | − | 0.508074i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 20.7003 | + | 6.72593i | 1.00529 | + | 0.326640i | ||||
\(425\) | 19.5263 | + | 8.69366i | 0.947164 | + | 0.421704i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.04861 | − | 0.435446i | −0.0991394 | − | 0.0210727i | ||||
\(428\) | −1.04432 | + | 1.80881i | −0.0504791 | + | 0.0874324i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0142403 | − | 0.0246649i | −0.000686729 | − | 0.00118945i | ||||
\(431\) | 8.63060 | + | 26.5623i | 0.415722 | + | 1.27946i | 0.911604 | + | 0.411070i | \(0.134845\pi\) |
−0.495882 | + | 0.868390i | \(0.665155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.41714 | − | 5.38887i | 0.356445 | − | 0.258973i | −0.395123 | − | 0.918628i | \(-0.629298\pi\) |
0.751568 | + | 0.659656i | \(0.229298\pi\) | |||||||
\(434\) | 0.169467 | + | 0.797279i | 0.00813467 | + | 0.0382706i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.1482 | − | 1.17173i | 0.533904 | − | 0.0561156i | ||||
\(437\) | −38.5144 | + | 17.1477i | −1.84239 | + | 0.820286i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.53842 | + | 1.46556i | −0.121152 | + | 0.0699472i | −0.559351 | − | 0.828931i | \(-0.688950\pi\) |
0.438199 | + | 0.898878i | \(0.355616\pi\) | |||||||
\(440\) | 0.267071 | + | 0.181426i | 0.0127321 | + | 0.00864913i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.44247 | + | 2.09329i | −0.306437 | + | 0.0995675i | ||||
\(443\) | 35.6451 | + | 3.74645i | 1.69355 | + | 0.177999i | 0.901594 | − | 0.432583i | \(-0.142398\pi\) |
0.791953 | + | 0.610582i | \(0.209064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.229310 | − | 0.254674i | −0.0108703 | − | 0.0120727i | ||||
\(446\) | 4.45309 | + | 4.94566i | 0.210860 | + | 0.234184i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.302416 | + | 0.0317852i | 0.0142878 | + | 0.00150171i | ||||
\(449\) | 13.5184 | − | 4.39241i | 0.637974 | − | 0.207290i | 0.0278700 | − | 0.999612i | \(-0.491128\pi\) |
0.610104 | + | 0.792321i | \(0.291128\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.5864 | − | 8.87978i | −1.44026 | − | 0.418132i | ||||
\(452\) | 0.698615 | − | 0.403345i | 0.0328601 | − | 0.0189718i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.36696 | + | 3.27998i | −0.345749 | + | 0.153937i | ||||
\(455\) | −0.0226620 | + | 0.00238187i | −0.00106241 | + | 0.000111664i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.24125 | − | 19.9535i | −0.198397 | − | 0.933386i | −0.958833 | − | 0.283972i | \(-0.908348\pi\) |
0.760435 | − | 0.649414i | \(-0.224986\pi\) | |||||||
\(458\) | −11.4042 | + | 8.28561i | −0.532882 | + | 0.387161i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.128631 | + | 0.395887i | 0.00599747 | + | 0.0184583i | ||||
\(461\) | −0.385177 | − | 0.667146i | −0.0179395 | − | 0.0310721i | 0.856916 | − | 0.515456i | \(-0.172377\pi\) |
−0.874856 | + | 0.484383i | \(0.839044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.8974 | + | 32.7312i | −0.878236 | + | 1.52115i | −0.0249608 | + | 0.999688i | \(0.507946\pi\) |
−0.853275 | + | 0.521461i | \(0.825387\pi\) | |||||||
\(464\) | −7.56414 | − | 1.60781i | −0.351156 | − | 0.0746406i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.1504 | − | 4.51925i | −0.470208 | − | 0.209350i | ||||
\(467\) | −16.7411 | − | 5.43950i | −0.774684 | − | 0.251710i | −0.105115 | − | 0.994460i | \(-0.533521\pi\) |
−0.669569 | + | 0.742750i | \(0.733521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.15290 | + | 1.58683i | 0.0532358 | + | 0.0732728i | ||||
\(470\) | 0.0321065 | − | 0.305473i | 0.00148096 | − | 0.0140904i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.86083 | − | 3.38375i | −0.269766 | − | 0.155750i | ||||
\(473\) | 3.36768 | + | 0.605271i | 0.154846 | + | 0.0278304i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.0302 | − | 20.7365i | −1.05670 | − | 0.951456i | ||||
\(476\) | 0.946967 | − | 1.30339i | 0.0434042 | − | 0.0597407i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.03785 | − | 18.5826i | 0.276165 | − | 0.849948i | ||||
\(479\) | 2.35329 | − | 0.500206i | 0.107524 | − | 0.0228550i | −0.153835 | − | 0.988097i | \(-0.549162\pi\) |
0.261360 | + | 0.965242i | \(0.415829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.77333 | − | 8.47503i | −0.172049 | − | 0.386428i | ||||
\(482\) | −2.05574 | + | 9.67152i | −0.0936366 | + | 0.440525i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.1686 | + | 4.52108i | −0.734937 | + | 0.205504i | ||||
\(485\) | 0.121459i | 0.00551517i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8099 | − | 8.58039i | −0.535157 | − | 0.388815i | 0.287126 | − | 0.957893i | \(-0.407300\pi\) |
−0.822283 | + | 0.569078i | \(0.807300\pi\) | |||||||
\(488\) | 8.37578 | − | 18.8123i | 0.379154 | − | 0.851593i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.142359 | − | 0.128181i | 0.00643114 | − | 0.00579062i | ||||
\(491\) | 2.61764 | + | 24.9052i | 0.118132 | + | 1.12396i | 0.879587 | + | 0.475737i | \(0.157819\pi\) |
−0.761455 | + | 0.648218i | \(0.775515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0113 | − | 17.7824i | 0.721114 | − | 0.800879i | ||||
\(494\) | 9.82158 | 0.441894 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.62982 | 0.297688 | ||||||||
\(497\) | −0.549780 | + | 0.610593i | −0.0246610 | + | 0.0273888i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.37400 | − | 22.5871i | −0.106275 | − | 1.01114i | −0.909568 | − | 0.415555i | \(-0.863587\pi\) |
0.803293 | − | 0.595584i | \(-0.203079\pi\) | |||||||
\(500\) | −0.454852 | + | 0.409550i | −0.0203416 | + | 0.0183156i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.94365 | + | 4.36552i | −0.0867496 | + | 0.194843i | ||||
\(503\) | 8.41953 | + | 6.11715i | 0.375408 | + | 0.272750i | 0.759450 | − | 0.650566i | \(-0.225468\pi\) |
−0.384042 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.278835i | − | 0.0124080i | ||||||
\(506\) | 14.3731 | + | 5.86234i | 0.638964 | + | 0.260613i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.05285 | + | 19.0672i | −0.179816 | + | 0.845969i | ||||
\(509\) | −3.28867 | − | 7.38647i | −0.145768 | − | 0.327399i | 0.825875 | − | 0.563853i | \(-0.190682\pi\) |
−0.971643 | + | 0.236454i | \(0.924015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.86212 | + | 0.608363i | −0.126613 | + | 0.0269124i | ||||
\(512\) | 4.55217 | − | 14.0102i | 0.201180 | − | 0.619167i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.21490 | + | 5.80132i | −0.185911 | + | 0.255885i | ||||
\(515\) | −0.391045 | − | 0.352098i | −0.0172315 | − | 0.0155153i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.5462 | + | 26.6291i | 1.12352 | + | 1.17115i | ||||
\(518\) | −0.593101 | − | 0.342427i | −0.0260594 | − | 0.0150454i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0234193 | − | 0.222820i | 0.00102701 | − | 0.00977131i | ||||
\(521\) | −20.5846 | − | 28.3323i | −0.901828 | − | 1.24126i | −0.969881 | − | 0.243578i | \(-0.921679\pi\) |
0.0680535 | − | 0.997682i | \(-0.478321\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.1766 | + | 13.3791i | 1.80052 | + | 0.585026i | 0.999900 | − | 0.0141400i | \(-0.00450104\pi\) |
0.800625 | + | 0.599166i | \(0.204501\pi\) | |||||||
\(524\) | 25.3113 | + | 11.2693i | 1.10573 | + | 0.492302i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.86879 | − | 0.609779i | −0.125085 | − | 0.0265876i | ||||
\(527\) | −10.2573 | + | 17.7662i | −0.446815 | + | 0.773906i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.6189 | + | 20.1245i | 0.505170 | + | 0.874980i | ||||
\(530\) | −0.0765028 | − | 0.235452i | −0.00332307 | − | 0.0102274i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.88977 | + | 1.37300i | −0.0819319 | + | 0.0595270i | ||||
\(533\) | 4.59513 | + | 21.6184i | 0.199037 | + | 0.936396i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0545871 | − | 0.00573733i | 0.00236000 | − | 0.000248046i | ||||
\(536\) | −17.6181 | + | 7.84407i | −0.760984 | + | 0.338812i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.59486 | − | 3.80754i | 0.284324 | − | 0.164155i | ||||
\(539\) | 0.727333 | + | 23.0028i | 0.0313284 | + | 0.990800i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.215252 | + | 0.0699396i | −0.00925440 | + | 0.00300694i | −0.313641 | − | 0.949542i | \(-0.601549\pi\) |
0.304386 | + | 0.952549i | \(0.401549\pi\) | |||||||
\(542\) | 10.8809 | + | 1.14363i | 0.467377 | + | 0.0491233i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.6112 | + | 18.4486i | 0.712198 | + | 0.790976i | ||||
\(545\) | −0.197113 | − | 0.218916i | −0.00844338 | − | 0.00937733i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3731 | + | 1.72088i | 0.700062 | + | 0.0735795i | 0.447871 | − | 0.894098i | \(-0.352182\pi\) |
0.252191 | + | 0.967678i | \(0.418849\pi\) | |||||||
\(548\) | 23.3308 | − | 7.58064i | 0.996643 | − | 0.323829i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.360607 | + | 11.4046i | 0.0153763 | + | 0.486296i | ||||
\(551\) | −30.0457 | + | 17.3469i | −1.27999 | + | 0.739003i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.679002 | − | 0.302311i | 0.0288741 | − | 0.0128556i | ||||
\(554\) | −7.76318 | + | 0.815943i | −0.329826 | + | 0.0346661i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.22402 | − | 5.75858i | −0.0519102 | − | 0.244218i | ||||
\(557\) | −21.2624 | + | 15.4481i | −0.900919 | + | 0.654556i | −0.938702 | − | 0.344730i | \(-0.887970\pi\) |
0.0377832 | + | 0.999286i | \(0.487970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.733729 | − | 2.25818i | −0.0310334 | − | 0.0955110i | ||||
\(560\) | 0.00684126 | + | 0.0118494i | 0.000289096 | + | 0.000500729i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.536969 | − | 0.930057i | 0.0226507 | − | 0.0392321i | ||||
\(563\) | 35.5711 | + | 7.56087i | 1.49914 | + | 0.318653i | 0.883147 | − | 0.469097i | \(-0.155421\pi\) |
0.615996 | + | 0.787750i | \(0.288754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0193664 | − | 0.00862248i | −0.000814751 | − | 0.000362750i | ||||
\(566\) | 17.3898 | + | 5.65030i | 0.730949 | + | 0.237500i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.74846 | − | 6.53570i | −0.199241 | − | 0.274232i | ||||
\(569\) | 2.11468 | − | 20.1198i | 0.0886520 | − | 0.843468i | −0.856348 | − | 0.516399i | \(-0.827272\pi\) |
0.945000 | − | 0.327069i | \(-0.106061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.1312 | − | 12.2001i | −0.884313 | − | 0.510558i | −0.0122350 | − | 0.999925i | \(-0.503895\pi\) |
−0.872078 | + | 0.489367i | \(0.837228\pi\) | |||||||
\(572\) | 8.06533 | + | 8.40720i | 0.337228 | + | 0.351523i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.21249 | + | 1.09173i | 0.0506085 | + | 0.0455681i | ||||
\(575\) | −19.9778 | + | 27.4971i | −0.833132 | + | 1.14671i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.96494 | + | 18.3582i | −0.248324 | + | 0.764262i | 0.746748 | + | 0.665107i | \(0.231614\pi\) |
−0.995072 | + | 0.0991553i | \(0.968386\pi\) | |||||||
\(578\) | −0.865784 | + | 0.184028i | −0.0360118 | + | 0.00765455i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.139328 | + | 0.312935i | 0.00578526 | + | 0.0129939i | ||||
\(581\) | −0.271691 | + | 1.27821i | −0.0112717 | + | 0.0530290i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.5401 | + | 11.2327i | 1.14059 | + | 0.465211i | ||||
\(584\) | − | 28.7700i | − | 1.19051i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6641 | − | 10.6541i | −0.605769 | − | 0.440117i | ||||
\(587\) | −7.78344 | + | 17.4819i | −0.321257 | + | 0.721555i | −0.999917 | − | 0.0128978i | \(-0.995894\pi\) |
0.678660 | + | 0.734453i | \(0.262561\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1040 | − | 19.9026i | 0.910781 | − | 0.820071i | ||||
\(590\) | 0.00804615 | + | 0.0765540i | 0.000331255 | + | 0.00315168i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.72739 | + | 4.13968i | −0.153195 | + | 0.170140i | ||||
\(593\) | 14.9885 | 0.615503 | 0.307751 | − | 0.951467i | \(-0.400423\pi\) | ||||
0.307751 | + | 0.951467i | \(0.400423\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0423378 | −0.00173568 | ||||||||
\(596\) | 10.4884 | − | 11.6485i | 0.429620 | − | 0.477142i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.12595 | − | 10.7127i | −0.0460437 | − | 0.438076i | ||||
\(599\) | 24.7771 | − | 22.3094i | 1.01236 | − | 0.911537i | 0.0162732 | − | 0.999868i | \(-0.494820\pi\) |
0.996091 | + | 0.0883306i | \(0.0281532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1940 | + | 38.6183i | −0.701357 | + | 1.57527i | 0.112133 | + | 0.993693i | \(0.464232\pi\) |
−0.813490 | + | 0.581579i | \(0.802435\pi\) | |||||||
\(602\) | −0.141807 | − | 0.103029i | −0.00577962 | − | 0.00419914i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 13.3859i | − | 0.544664i | ||||||
\(605\) | 0.345868 | + | 0.273915i | 0.0140615 | + | 0.0111362i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.42154 | − | 30.2110i | 0.260642 | − | 1.22623i | −0.631824 | − | 0.775112i | \(-0.717694\pi\) |
0.892467 | − | 0.451114i | \(-0.148973\pi\) | |||||||
\(608\) | −14.6399 | − | 32.8817i | −0.593726 | − | 1.33353i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.229109 | + | 0.0486986i | −0.00927634 | + | 0.00197175i | ||||
\(611\) | 7.91306 | − | 24.3539i | 0.320128 | − | 0.985254i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.38958 | + | 12.9237i | −0.379242 | + | 0.521981i | −0.955383 | − | 0.295368i | \(-0.904558\pi\) |
0.576142 | + | 0.817350i | \(0.304558\pi\) | |||||||
\(614\) | −13.3032 | − | 11.9783i | −0.536875 | − | 0.483404i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.95573 | + | 0.351502i | 0.0787985 | + | 0.0141624i | ||||
\(617\) | 2.28088 | + | 1.31687i | 0.0918248 | + | 0.0530151i | 0.545209 | − | 0.838300i | \(-0.316450\pi\) |
−0.453384 | + | 0.891315i | \(0.649784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.11664 | + | 20.1385i | −0.0850751 | + | 0.809436i | 0.865910 | + | 0.500200i | \(0.166740\pi\) |
−0.950985 | + | 0.309236i | \(0.899927\pi\) | |||||||
\(620\) | −0.172619 | − | 0.237590i | −0.00693255 | − | 0.00954184i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.72244 | + | 2.83409i | 0.349738 | + | 0.113637i | ||||
\(623\) | −1.92678 | − | 0.857858i | −0.0771949 | − | 0.0343694i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.4301 | − | 5.19278i | −0.977204 | − | 0.207711i | ||||
\(626\) | 3.87106 | − | 6.70487i | 0.154719 | − | 0.267980i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.94420 | − | 17.2239i | −0.396817 | − | 0.687307i | ||||
\(629\) | −5.32645 | − | 16.3931i | −0.212379 | − | 0.653636i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.82846 | + | 4.96116i | −0.271837 | + | 0.197501i | −0.715349 | − | 0.698767i | \(-0.753732\pi\) |
0.443512 | + | 0.896268i | \(0.353732\pi\) | |||||||
\(632\) | 1.51941 | + | 7.14828i | 0.0604390 | + | 0.284343i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.49730 | − | 0.787998i | 0.297756 | − | 0.0312954i | ||||
\(635\) | 0.467976 | − | 0.208356i | 0.0185711 | − | 0.00826837i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.8308 | − | 7.98521i | 0.547996 | − | 0.316385i | ||||
\(638\) | 12.2675 | + | 3.56146i | 0.485673 | + | 0.141000i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.410557 | + | 0.133398i | −0.0162287 | + | 0.00527302i | ||||
\(641\) | −32.1374 | − | 3.37778i | −1.26935 | − | 0.133414i | −0.554200 | − | 0.832383i | \(-0.686976\pi\) |
−0.715152 | + | 0.698969i | \(0.753643\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.21842 | + | 10.2381i | 0.363539 | + | 0.403751i | 0.896969 | − | 0.442093i | \(-0.145764\pi\) |
−0.533430 | + | 0.845844i | \(0.679097\pi\) | |||||||
\(644\) | 1.71422 | + | 1.90383i | 0.0675497 | + | 0.0750216i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.1485 | + | 1.90748i | 0.714042 | + | 0.0750488i | ||||
\(647\) | −8.11003 | + | 2.63511i | −0.318838 | + | 0.103597i | −0.464064 | − | 0.885802i | \(-0.653609\pi\) |
0.145226 | + | 0.989399i | \(0.453609\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.64968 | − | 5.19656i | −0.300276 | − | 0.203983i | ||||
\(650\) | 6.85722 | − | 3.95902i | 0.268962 | − | 0.155285i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.7966 | − | 5.69739i | 0.501152 | − | 0.223127i | ||||
\(653\) | 1.20137 | − | 0.126269i | 0.0470132 | − | 0.00494129i | −0.0809927 | − | 0.996715i | \(-0.525809\pi\) |
0.128006 | + | 0.991773i | \(0.459142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.151382 | − | 0.712198i | −0.00591499 | − | 0.0278279i | ||||
\(656\) | 10.7364 | − | 7.80045i | 0.419186 | − | 0.304556i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.584160 | − | 1.79786i | −0.0227729 | − | 0.0700878i | ||||
\(659\) | −4.70527 | − | 8.14977i | −0.183291 | − | 0.317470i | 0.759708 | − | 0.650264i | \(-0.225342\pi\) |
−0.942999 | + | 0.332794i | \(0.892009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.55133 | + | 13.0793i | −0.293713 | + | 0.508725i | −0.974685 | − | 0.223584i | \(-0.928224\pi\) |
0.680972 | + | 0.732309i | \(0.261558\pi\) | |||||||
\(662\) | −2.84977 | − | 0.605737i | −0.110759 | − | 0.0235426i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.7377 | − | 5.22596i | −0.455511 | − | 0.202807i | ||||
\(665\) | 0.0583807 | + | 0.0189690i | 0.00226391 | + | 0.000735588i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.3653 | + | 30.7832i | 0.865988 | + | 1.19193i | ||||
\(668\) | 1.21397 | − | 11.5502i | 0.0469700 | − | 0.446889i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.189970 | + | 0.109679i | 0.00733916 | + | 0.00423727i | ||||
\(671\) | 13.2927 | − | 24.8023i | 0.513161 | − | 0.957484i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.9140 | − | 27.8351i | −1.19165 | − | 1.07296i | −0.995727 | − | 0.0923433i | \(-0.970564\pi\) |
−0.195919 | − | 0.980620i | \(-0.562769\pi\) | |||||||
\(674\) | 1.07711 | − | 1.48252i | 0.0414888 | − | 0.0571045i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.63303 | + | 11.1813i | −0.139732 | + | 0.430051i | ||||
\(677\) | −4.42177 | + | 0.939877i | −0.169943 | + | 0.0361224i | −0.292097 | − | 0.956389i | \(-0.594353\pi\) |
0.122154 | + | 0.992511i | \(0.461020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.304042 | + | 0.682890i | 0.0116681 | + | 0.0262069i | ||||
\(680\) | 0.0865492 | − | 0.407182i | 0.00331901 | − | 0.0156147i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.9222 | − | 0.799960i | −0.418233 | − | 0.0306320i | ||||
\(683\) | 34.7783i | 1.33075i | 0.746507 | + | 0.665377i | \(0.231729\pi\) | ||||
−0.746507 | + | 0.665377i | \(0.768271\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.521547 | − | 0.378926i | −0.0199273 | − | 0.0144780i | ||||
\(686\) | 0.963272 | − | 2.16354i | 0.0367779 | − | 0.0826045i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.05952 | + | 0.953996i | −0.0403938 | + | 0.0363707i | ||||
\(689\) | −2.15741 | − | 20.5264i | −0.0821909 | − | 0.781995i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9664 | + | 13.2900i | −0.455223 | + | 0.505576i | −0.926441 | − | 0.376441i | \(-0.877148\pi\) |
0.471218 | + | 0.882017i | \(0.343815\pi\) | |||||||
\(692\) | −25.3670 | −0.964308 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.4278 | 0.433794 | ||||||||
\(695\) | −0.103522 | + | 0.114973i | −0.00392682 | + | 0.00436118i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.29237 | + | 40.8392i | 0.162585 | + | 1.54689i | ||||
\(698\) | 7.04579 | − | 6.34406i | 0.266687 | − | 0.240126i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.765950 | + | 1.72035i | −0.0289502 | + | 0.0650232i | ||||
\(701\) | 14.1345 | + | 10.2693i | 0.533852 | + | 0.387866i | 0.821797 | − | 0.569781i | \(-0.192972\pi\) |
−0.287945 | + | 0.957647i | \(0.592972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.9914i | 0.942568i | ||||||||
\(704\) | −1.54298 | + | 3.78304i | −0.0581532 | + | 0.142579i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.57770 | − | 7.42251i | 0.0593776 | − | 0.279350i | ||||
\(707\) | −0.697994 | − | 1.56772i | −0.0262507 | − | 0.0589601i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.15627 | + | 1.73367i | −0.306315 | + | 0.0651093i | −0.358505 | − | 0.933528i | \(-0.616713\pi\) |
0.0521896 | + | 0.998637i | \(0.483380\pi\) | |||||||
\(710\) | −0.0283950 | + | 0.0873909i | −0.00106565 | + | 0.00327972i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.1893 | − | 16.7771i | 0.456812 | − | 0.628747i | ||||
\(713\) | −24.2424 | − | 21.8280i | −0.907886 | − | 0.817464i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0541584 | − | 0.301333i | 0.00202541 | − | 0.0112692i | ||||
\(716\) | 9.31824 | + | 5.37989i | 0.348239 | + | 0.201056i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.36800 | − | 13.0156i | 0.0510532 | − | 0.485739i | ||||
\(719\) | 13.8736 | + | 19.0953i | 0.517397 | + | 0.712136i | 0.985145 | − | 0.171726i | \(-0.0549344\pi\) |
−0.467748 | + | 0.883862i | \(0.654934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.08000 | − | 1.00075i | −0.114705 | − | 0.0372699i | ||||
\(722\) | −12.2239 | − | 5.44241i | −0.454925 | − | 0.202546i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −31.5355 | − | 6.70308i | −1.17201 | − | 0.249118i | ||||
\(725\) | −13.9849 | + | 24.2225i | −0.519384 | + | 0.899600i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.952312 | − | 1.64945i | −0.0353193 | − | 0.0611748i | 0.847825 | − | 0.530275i | \(-0.177911\pi\) |
−0.883145 | + | 0.469101i | \(0.844578\pi\) | |||||||
\(728\) | −0.426102 | − | 1.31141i | −0.0157924 | − | 0.0486039i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.264742 | + | 0.192346i | −0.00979854 | + | 0.00711905i | ||||
\(731\) | −0.917225 | − | 4.31521i | −0.0339248 | − | 0.159604i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.5153 | − | 1.84093i | 0.646943 | − | 0.0679964i | 0.224626 | − | 0.974445i | \(-0.427884\pi\) |
0.422316 | + | 0.906449i | \(0.361217\pi\) | |||||||
\(734\) | −3.58230 | + | 1.59494i | −0.132225 | + | 0.0588704i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.1869 | + | 19.7378i | −1.26015 | + | 0.727545i | ||||
\(737\) | −24.7938 | + | 8.93171i | −0.913291 | + | 0.329004i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.54355 | + | 1.47629i | −0.167137 | + | 0.0543062i | −0.391390 | − | 0.920225i | \(-0.628006\pi\) |
0.224253 | + | 0.974531i | \(0.428006\pi\) | |||||||
\(740\) | 0.245401 | + | 0.0257927i | 0.00902113 | + | 0.000948159i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.01952 | − | 1.13229i | −0.0374278 | − | 0.0415678i | ||||
\(743\) | −1.22970 | − | 1.36573i | −0.0451135 | − | 0.0501036i | 0.720166 | − | 0.693802i | \(-0.244066\pi\) |
−0.765279 | + | 0.643698i | \(0.777399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.409660 | − | 0.0430570i | −0.0150088 | − | 0.00157749i | ||||
\(746\) | −14.5056 | + | 4.71316i | −0.531088 | + | 0.172561i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.2704 | + | 17.1013i | 0.485215 | + | 0.625287i | ||||
\(749\) | 0.292548 | − | 0.168902i | 0.0106895 | − | 0.00617156i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.6641 | + | 15.4334i | −1.26491 | + | 0.563174i | −0.925957 | − | 0.377629i | \(-0.876740\pi\) |
−0.338953 | + | 0.940803i | \(0.610073\pi\) | |||||||
\(752\) | −15.2918 | + | 1.60723i | −0.557635 | + | 0.0586098i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.84299 | − | 8.67060i | −0.0671179 | − | 0.315765i | ||||
\(755\) | −0.284588 | + | 0.206765i | −0.0103572 | + | 0.00752497i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.46409 | − | 29.1275i | −0.343978 | − | 1.05866i | −0.962128 | − | 0.272596i | \(-0.912118\pi\) |
0.618150 | − | 0.786060i | \(-0.287882\pi\) | |||||||
\(758\) | 0.131240 | + | 0.227315i | 0.00476687 | + | 0.00825646i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.301779 | + | 0.522697i | −0.0109467 | + | 0.0189602i | ||||
\(761\) | −30.1908 | − | 6.41724i | −1.09441 | − | 0.232625i | −0.374874 | − | 0.927076i | \(-0.622314\pi\) |
−0.719540 | + | 0.694451i | \(0.755647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.65625 | − | 0.737408i | −0.0599601 | − | 0.0266960i | ||||
\(764\) | 19.8402 | + | 6.44648i | 0.717794 | + | 0.233225i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.12362 | + | 7.05205i | 0.185124 | + | 0.254801i | ||||
\(767\) | −0.670798 | + | 6.38222i | −0.0242211 | + | 0.230449i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7276 | + | 9.65771i | 0.603214 | + | 0.348266i | 0.770305 | − | 0.637676i | \(-0.220104\pi\) |
−0.167091 | + | 0.985942i | \(0.553437\pi\) | |||||||
\(770\) | −0.00984080 | − | 0.0203467i | −0.000354638 | − | 0.000733243i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.3953 | + | 25.5672i | 1.02197 | + | 0.920185i | ||||
\(773\) | 1.72928 | − | 2.38015i | 0.0621980 | − | 0.0856082i | −0.776785 | − | 0.629766i | \(-0.783151\pi\) |
0.838983 | + | 0.544158i | \(0.183151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.40997 | − | 22.8056i | 0.266174 | − | 0.819200i | ||||
\(776\) | −7.18920 | + | 1.52811i | −0.258077 | + | 0.0548560i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.66249 | + | 14.9642i | 0.238862 | + | 0.536493i | ||||
\(779\) | 12.3787 | − | 58.2374i | 0.443515 | − | 2.08657i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.81908 | − | 9.38117i | −0.208223 | − | 0.335685i | ||||
\(782\) | − | 20.0138i | − | 0.715693i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.75811 | − | 5.63660i | −0.277075 | − | 0.201307i | ||||
\(785\) | −0.212581 | + | 0.477465i | −0.00758735 | + | 0.0170415i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.97911 | − | 5.38362i | 0.213132 | − | 0.191905i | −0.555649 | − | 0.831417i | \(-0.687530\pi\) |
0.768781 | + | 0.639512i | \(0.220863\pi\) | |||||||
\(788\) | −3.35733 | − | 31.9429i | −0.119600 | − | 1.13792i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.0556203 | − | 0.0617726i | 0.00197888 | − | 0.00219777i | ||||
\(791\) | −0.130470 | −0.00463897 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.5272 | −0.693433 | ||||||||
\(794\) | 2.30507 | − | 2.56004i | 0.0818039 | − | 0.0908524i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.65455 | − | 15.7420i | −0.0586440 | − | 0.557960i | ||||
\(797\) | −40.8149 | + | 36.7499i | −1.44574 | + | 1.30175i | −0.567634 | + | 0.823281i | \(0.692141\pi\) |
−0.878105 | + | 0.478468i | \(0.841192\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.3517 | − | 43.4647i | 0.684615 | − | 1.53767i | ||||
\(800\) | −23.4757 | − | 17.0561i | −0.829991 | − | 0.603024i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.92121i | 0.103152i | ||||||||
\(803\) | 2.87174 | − | 39.2092i | 0.101342 | − | 1.38366i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0139974 | − | 0.0658524i | 0.000493342 | − | 0.00232099i | ||||
\(806\) | 3.09104 | + | 6.94259i | 0.108877 | + | 0.244542i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.5044 | − | 3.50811i | 0.580621 | − | 0.123415i | ||||
\(809\) | −7.52538 | + | 23.1607i | −0.264578 | + | 0.814288i | 0.727212 | + | 0.686413i | \(0.240816\pi\) |
−0.991790 | + | 0.127875i | \(0.959184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.2026 | + | 16.7955i | −0.428493 | + | 0.589770i | −0.967607 | − | 0.252463i | \(-0.918759\pi\) |
0.539114 | + | 0.842233i | \(0.318759\pi\) | |||||||
\(812\) | 1.56671 | + | 1.41067i | 0.0549807 | + | 0.0495048i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.64014 | − | 6.37012i | 0.232737 | − | 0.223273i | ||||
\(815\) | −0.318790 | − | 0.184054i | −0.0111667 | − | 0.00644712i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.668601 | + | 6.36131i | −0.0233914 | + | 0.222554i | ||||
\(818\) | −4.77615 | − | 6.57380i | −0.166994 | − | 0.229848i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.559083 | − | 0.181657i | −0.0195240 | − | 0.00634374i | ||||
\(821\) | −26.1615 | − | 11.6478i | −0.913042 | − | 0.406513i | −0.104212 | − | 0.994555i | \(-0.533232\pi\) |
−0.808830 | + | 0.588043i | \(0.799899\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.43348 | − | 0.517251i | −0.0848256 | − | 0.0180302i | 0.165303 | − | 0.986243i | \(-0.447140\pi\) |
−0.250129 | + | 0.968213i | \(0.580473\pi\) | |||||||
\(824\) | 15.9210 | − | 27.5760i | 0.554634 | − | 0.960654i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.236872 | + | 0.410275i | 0.00824184 | + | 0.0142753i | ||||
\(827\) | 7.36490 | + | 22.6668i | 0.256103 | + | 0.788202i | 0.993610 | + | 0.112864i | \(0.0360024\pi\) |
−0.737508 | + | 0.675338i | \(0.763998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.8736 | − | 23.8841i | 1.14175 | − | 0.829528i | 0.154386 | − | 0.988011i | \(-0.450660\pi\) |
0.987362 | + | 0.158482i | \(0.0506601\pi\) | |||||||
\(830\) | 0.0303849 | + | 0.142950i | 0.00105467 | + | 0.00496185i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.81961 | − | 0.296353i | 0.0977525 | − | 0.0102742i | ||||
\(833\) | 27.1075 | − | 12.0691i | 0.939221 | − | 0.418168i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.264312 | + | 0.152600i | −0.00914688 | + | 0.00528096i | ||||
\(836\) | −10.6369 | − | 29.5272i | −0.367884 | − | 1.02122i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.7333 | − | 4.46221i | 0.474408 | − | 0.154145i | ||||
\(839\) | −56.9097 | − | 5.98145i | −1.96474 | − | 0.206503i | −0.966081 | − | 0.258240i | \(-0.916857\pi\) |
−0.998661 | + | 0.0517373i | \(0.983524\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.54724 | + | 1.71839i | 0.0533532 | + | 0.0592548i | ||||
\(842\) | −1.28025 | − | 1.42186i | −0.0441202 | − | 0.0490004i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28.4508 | + | 2.99030i | 0.979318 | + | 0.102930i | ||||
\(845\) | 0.293836 | − | 0.0954731i | 0.0101083 | − | 0.00328438i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.63028 | + | 0.674260i | 0.0903776 | + | 0.0231679i | ||||
\(848\) | −10.7328 | + | 6.19657i | −0.368565 | + | 0.212791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.4398 | − | 5.98377i | 0.460980 | − | 0.205242i | ||||
\(851\) | 27.2589 | − | 2.86503i | 0.934425 | − | 0.0982120i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.34987 | + | 29.8738i | 0.217415 | + | 1.02286i | 0.942502 | + | 0.334201i | \(0.108466\pi\) |
−0.725087 | + | 0.688658i | \(0.758200\pi\) | |||||||
\(854\) | −1.16623 | + | 0.847318i | −0.0399077 | + | 0.0289946i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.02637 | + | 3.15885i | 0.0350807 | + | 0.107967i | ||||
\(857\) | −3.07390 | − | 5.32416i | −0.105003 | − | 0.181870i | 0.808737 | − | 0.588171i | \(-0.200152\pi\) |
−0.913739 | + | 0.406301i | \(0.866818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.7994 | − | 23.9013i | 0.470830 | − | 0.815501i | −0.528614 | − | 0.848863i | \(-0.677288\pi\) |
0.999443 | + | 0.0333614i | \(0.0106212\pi\) | |||||||
\(860\) | 0.0617744 | + | 0.0131306i | 0.00210649 | + | 0.000447748i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.5615 | + | 7.81887i | 0.598146 | + | 0.266312i | ||||
\(863\) | −40.7061 | − | 13.2262i | −1.38565 | − | 0.450226i | −0.481129 | − | 0.876650i | \(-0.659773\pi\) |
−0.904523 | + | 0.426424i | \(0.859773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.391832 | + | 0.539310i | 0.0133227 | + | 0.0183371i | ||||
\(866\) | 0.659608 | − | 6.27575i | 0.0224144 | − | 0.213259i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.56528 | − | 0.903714i | −0.0531290 | − | 0.0306741i | ||||
\(869\) | 1.35721 | + | 9.89371i | 0.0460403 | + | 0.335621i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.5903 | + | 12.2368i | 0.460491 | + | 0.414628i | ||||
\(872\) | 10.4778 | − | 14.4214i | 0.354822 | − | 0.488371i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.96700 | + | 27.5976i | −0.303313 | + | 0.933503i | ||||
\(875\) | 0.0968285 | − | 0.0205815i | 0.00327340 | − | 0.000695783i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.56785 | + | 10.2596i | 0.154245 | + | 0.346441i | 0.974095 | − | 0.226138i | \(-0.0726099\pi\) |
−0.819850 | + | 0.572578i | \(0.805943\pi\) | |||||||
\(878\) | −0.419453 | + | 1.97337i | −0.0141559 | + | 0.0665981i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.178522 | + | 0.0438857i | −0.00601797 | + | 0.00147939i | ||||
\(881\) | 47.3136i | 1.59403i | 0.603957 | + | 0.797017i | \(0.293590\pi\) | ||||
−0.603957 | + | 0.797017i | \(0.706410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.7740 | − | 10.7340i | −0.497186 | − | 0.361227i | 0.310755 | − | 0.950490i | \(-0.399418\pi\) |
−0.807941 | + | 0.589263i | \(0.799418\pi\) | |||||||
\(884\) | 6.10963 | − | 13.7224i | 0.205489 | − | 0.461536i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.3329 | − | 16.5070i | 0.615905 | − | 0.554563i | ||||
\(887\) | 4.25539 | + | 40.4873i | 0.142882 | + | 1.35943i | 0.797430 | + | 0.603411i | \(0.206192\pi\) |
−0.654548 | + | 0.756020i | \(0.727141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.10958 | − | 2.34292i | 0.0707529 | − | 0.0785791i | ||||
\(890\) | −0.235876 | −0.00790658 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.7573 | −0.494110 | ||||||||
\(893\) | −46.1586 | + | 51.2643i | −1.54464 | + | 1.71549i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.0295563 | − | 0.281209i | −0.000987958 | − | 0.00939979i | ||||
\(896\) | −1.97438 | + | 1.77774i | −0.0659595 | + | 0.0593902i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.97929 | − | 8.93763i | 0.132791 | − | 0.298253i | ||||
\(899\) | −21.7180 | − | 15.7790i | −0.724335 | − | 0.526260i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 38.3480i | − | 1.27756i | ||||||
\(902\) | −18.6288 | + | 11.5553i | −0.620270 | + | 0.384750i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.266713 | − | 1.25479i | 0.00887075 | − | 0.0417336i | ||||
\(905\) | 0.344604 | + | 0.773994i | 0.0114550 | + | 0.0257284i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.15589 | + | 0.245691i | −0.0383806 | + | 0.00815804i | −0.227062 | − | 0.973880i | \(-0.572912\pi\) |
0.188681 | + | 0.982038i | \(0.439579\pi\) | |||||||
\(908\) | 5.52581 | − | 17.0067i | 0.183380 | − | 0.564387i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.00921881 | + | 0.0126886i | −0.000305601 | + | 0.000420623i | ||||
\(911\) | 15.7280 | + | 14.1615i | 0.521092 | + | 0.469193i | 0.887204 | − | 0.461378i | \(-0.152645\pi\) |
−0.366112 | + | 0.930571i | \(0.619311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.4751 | − | 8.29384i | −0.512152 | − | 0.274486i | ||||
\(914\) | −12.1596 | − | 7.02032i | −0.402202 | − | 0.232212i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.26735 | − | 31.0867i | 0.107956 | − | 1.02713i | ||||
\(917\) | −2.63394 | − | 3.62530i | −0.0869803 | − | 0.119718i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.4009 | − | 4.35422i | −0.442055 | − | 0.143633i | 0.0795283 | − | 0.996833i | \(-0.474659\pi\) |
−0.521584 | + | 0.853200i | \(0.674659\pi\) | |||||||
\(920\) | 0.604719 | + | 0.269238i | 0.0199370 | + | 0.00887653i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.518641 | − | 0.110241i | −0.0170805 | − | 0.00363058i | ||||
\(923\) | −3.83031 | + | 6.63429i | −0.126076 | + | 0.218370i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0739 | + | 17.4485i | 0.331227 | + | 0.573702i | ||||
\(926\) | 8.03871 | + | 24.7406i | 0.264168 | + | 0.813027i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −26.2812 | + | 19.0944i | −0.862723 | + | 0.626805i | ||||
\(929\) | −7.08681 | − | 33.3408i | −0.232511 | − | 1.09388i | −0.927200 | − | 0.374567i | \(-0.877791\pi\) |
0.694689 | − | 0.719310i | \(-0.255542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.7868 | + | 4.49707i | −1.40228 | + | 0.147386i | ||||
\(932\) | 22.5081 | − | 10.0212i | 0.737276 | − | 0.328256i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.4925 | + | 6.05786i | −0.343326 | + | 0.198219i | ||||
\(935\) | 0.158598 | − | 0.546290i | 0.00518669 | − | 0.0178656i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.41974 | − | 2.08590i | 0.209724 | − | 0.0681434i | −0.202271 | − | 0.979330i | \(-0.564832\pi\) |
0.411995 | + | 0.911186i | \(0.364832\pi\) | |||||||
\(938\) | 1.34264 | + | 0.141117i | 0.0438386 | + | 0.00460763i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.455748 | + | 0.506159i | 0.0148648 | + | 0.0165091i | ||||
\(941\) | −22.2806 | − | 24.7451i | −0.726328 | − | 0.806669i | 0.261004 | − | 0.965338i | \(-0.415946\pi\) |
−0.987332 | + | 0.158669i | \(0.949280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −64.9407 | − | 6.82554i | −2.11476 | − | 0.222270i | ||||
\(944\) | 3.66476 | − | 1.19075i | 0.119278 | − | 0.0387557i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.86060 | − | 1.44381i | 0.0604934 | − | 0.0469422i | ||||
\(947\) | 0.650586 | − | 0.375616i | 0.0211412 | − | 0.0122059i | −0.489392 | − | 0.872064i | \(-0.662781\pi\) |
0.510533 | + | 0.859858i | \(0.329448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.9229 | + | 11.0964i | −0.809032 | + | 0.360204i | ||||
\(950\) | −21.2134 | + | 2.22962i | −0.688255 | + | 0.0723385i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.532664 | − | 2.50599i | −0.0172638 | − | 0.0812196i | ||||
\(953\) | 3.76491 | − | 2.73537i | 0.121957 | − | 0.0886073i | −0.525134 | − | 0.851019i | \(-0.675985\pi\) |
0.647092 | + | 0.762412i | \(0.275985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.169408 | − | 0.521385i | −0.00548192 | − | 0.0168716i | ||||
\(956\) | 21.6633 | + | 37.5220i | 0.700641 | + | 1.21355i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.827966 | − | 1.43408i | 0.0267504 | − | 0.0463330i | ||||
\(959\) | −3.88088 | − | 0.824907i | −0.125320 | − | 0.0266376i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.29480 | − | 3.24785i | −0.235316 | − | 0.104769i | ||||
\(962\) | −6.07281 | − | 1.97318i | −0.195795 | − | 0.0636177i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.8874 | − | 17.7379i | −0.415074 | − | 0.571300i | ||||
\(965\) | 0.104959 | − | 0.998617i | 0.00337875 | − | 0.0321466i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.8385 | − | 10.8764i | −0.605807 | − | 0.349763i | 0.165516 | − | 0.986207i | \(-0.447071\pi\) |
−0.771323 | + | 0.636444i | \(0.780404\pi\) | |||||||
\(968\) | −11.8616 | + | 23.9183i | −0.381248 | + | 0.768763i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.0621263 | + | 0.0559387i | 0.00199475 | + | 0.00179608i | ||||
\(971\) | −3.45215 | + | 4.75147i | −0.110785 | + | 0.152482i | −0.860809 | − | 0.508928i | \(-0.830042\pi\) |
0.750024 | + | 0.661410i | \(0.230042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.294236 | + | 0.905565i | −0.00943277 | + | 0.0290311i | ||||
\(974\) | −9.82799 | + | 2.08900i | −0.314909 | + | 0.0669360i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.76910 | + | 10.7116i | 0.152655 | + | 0.342869i | ||||
\(977\) | −0.191277 | + | 0.899889i | −0.00611950 | + | 0.0287900i | −0.981101 | − | 0.193494i | \(-0.938018\pi\) |
0.974982 | + | 0.222284i | \(0.0713513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2868 | − | 21.6480i | 0.584448 | − | 0.691872i | ||||
\(980\) | 0.424783i | 0.0135692i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.9446 | + | 10.1313i | 0.444989 | + | 0.323304i | ||||
\(983\) | 18.9685 | − | 42.6040i | 0.605002 | − | 1.35886i | −0.308188 | − | 0.951325i | \(-0.599723\pi\) |
0.913191 | − | 0.407532i | \(-0.133611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.627256 | + | 0.564784i | −0.0199860 | + | 0.0179955i | ||||
\(986\) | −1.72157 | − | 16.3796i | −0.0548258 | − | 0.521633i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.5729 | + | 16.1849i | −0.463627 | + | 0.514910i | ||||
\(989\) | 7.01515 | 0.223069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.21090 | 0.197296 | 0.0986478 | − | 0.995122i | \(-0.468548\pi\) | ||||
0.0986478 | + | 0.995122i | \(0.468548\pi\) | |||||||
\(992\) | 18.6357 | − | 20.6970i | 0.591683 | − | 0.657131i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.0591133 | + | 0.562425i | 0.00187496 | + | 0.0178390i | ||||
\(995\) | −0.309123 | + | 0.278335i | −0.00979984 | + | 0.00882382i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.6192 | + | 26.0971i | −0.367982 | + | 0.826502i | 0.630741 | + | 0.775993i | \(0.282751\pi\) |
−0.998724 | + | 0.0505088i | \(0.983916\pi\) | |||||||
\(998\) | −12.6467 | − | 9.18836i | −0.400324 | − | 0.290852i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 891.2.u.c.215.3 | 32 | ||
3.2 | odd | 2 | inner | 891.2.u.c.215.2 | 32 | ||
9.2 | odd | 6 | inner | 891.2.u.c.512.3 | 32 | ||
9.4 | even | 3 | 99.2.j.a.17.3 | yes | 16 | ||
9.5 | odd | 6 | 99.2.j.a.17.2 | ✓ | 16 | ||
9.7 | even | 3 | inner | 891.2.u.c.512.2 | 32 | ||
11.2 | odd | 10 | inner | 891.2.u.c.134.3 | 32 | ||
33.2 | even | 10 | inner | 891.2.u.c.134.2 | 32 | ||
36.23 | even | 6 | 1584.2.cd.c.17.3 | 16 | |||
36.31 | odd | 6 | 1584.2.cd.c.17.2 | 16 | |||
99.2 | even | 30 | inner | 891.2.u.c.431.3 | 32 | ||
99.13 | odd | 30 | 99.2.j.a.35.2 | yes | 16 | ||
99.14 | odd | 30 | 1089.2.d.g.1088.6 | 16 | |||
99.41 | even | 30 | 1089.2.d.g.1088.12 | 16 | |||
99.58 | even | 15 | 1089.2.d.g.1088.11 | 16 | |||
99.68 | even | 30 | 99.2.j.a.35.3 | yes | 16 | ||
99.79 | odd | 30 | inner | 891.2.u.c.431.2 | 32 | ||
99.85 | odd | 30 | 1089.2.d.g.1088.5 | 16 | |||
396.167 | odd | 30 | 1584.2.cd.c.1025.2 | 16 | |||
396.211 | even | 30 | 1584.2.cd.c.1025.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.17.2 | ✓ | 16 | 9.5 | odd | 6 | ||
99.2.j.a.17.3 | yes | 16 | 9.4 | even | 3 | ||
99.2.j.a.35.2 | yes | 16 | 99.13 | odd | 30 | ||
99.2.j.a.35.3 | yes | 16 | 99.68 | even | 30 | ||
891.2.u.c.134.2 | 32 | 33.2 | even | 10 | inner | ||
891.2.u.c.134.3 | 32 | 11.2 | odd | 10 | inner | ||
891.2.u.c.215.2 | 32 | 3.2 | odd | 2 | inner | ||
891.2.u.c.215.3 | 32 | 1.1 | even | 1 | trivial | ||
891.2.u.c.431.2 | 32 | 99.79 | odd | 30 | inner | ||
891.2.u.c.431.3 | 32 | 99.2 | even | 30 | inner | ||
891.2.u.c.512.2 | 32 | 9.7 | even | 3 | inner | ||
891.2.u.c.512.3 | 32 | 9.2 | odd | 6 | inner | ||
1089.2.d.g.1088.5 | 16 | 99.85 | odd | 30 | |||
1089.2.d.g.1088.6 | 16 | 99.14 | odd | 30 | |||
1089.2.d.g.1088.11 | 16 | 99.58 | even | 15 | |||
1089.2.d.g.1088.12 | 16 | 99.41 | even | 30 | |||
1584.2.cd.c.17.2 | 16 | 36.31 | odd | 6 | |||
1584.2.cd.c.17.3 | 16 | 36.23 | even | 6 | |||
1584.2.cd.c.1025.2 | 16 | 396.167 | odd | 30 | |||
1584.2.cd.c.1025.3 | 16 | 396.211 | even | 30 |