Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(271,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bf (of order \(6\), degree \(2\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Character | \(\chi\) | \(=\) | 756.703 |
Dual form | 756.2.bf.c.271.1 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38270 | − | 0.296888i | −0.977716 | − | 0.209932i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.82372 | + | 0.821014i | 0.911858 | + | 0.410507i | ||||
\(5\) | −0.421763 | + | 0.243505i | −0.188618 | + | 0.108899i | −0.591336 | − | 0.806426i | \(-0.701399\pi\) |
0.402717 | + | 0.915324i | \(0.368066\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.250520 | − | 2.63386i | 0.0946876 | − | 0.995507i | ||||
\(8\) | −2.27790 | − | 1.67665i | −0.805359 | − | 0.592787i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.655465 | − | 0.211478i | 0.207276 | − | 0.0668752i | ||||
\(11\) | −2.51153 | − | 1.45003i | −0.757254 | − | 0.437201i | 0.0710549 | − | 0.997472i | \(-0.477363\pi\) |
−0.828309 | + | 0.560272i | \(0.810697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17266i | 0.325239i | 0.986689 | + | 0.162619i | \(0.0519942\pi\) | ||||
−0.986689 | + | 0.162619i | \(0.948006\pi\) | |||||||
\(14\) | −1.12836 | + | 3.56747i | −0.301566 | + | 0.953445i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.65187 | + | 2.99459i | 0.662968 | + | 0.748648i | ||||
\(17\) | −0.0401295 | − | 0.0231688i | −0.00973282 | − | 0.00561925i | 0.495126 | − | 0.868821i | \(-0.335122\pi\) |
−0.504859 | + | 0.863202i | \(0.668455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38246 | − | 4.12654i | −0.546574 | − | 0.946693i | −0.998506 | − | 0.0546412i | \(-0.982598\pi\) |
0.451932 | − | 0.892052i | \(-0.350735\pi\) | |||||||
\(20\) | −0.969097 | + | 0.0978105i | −0.216697 | + | 0.0218711i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.04219 | + | 2.75060i | 0.648597 | + | 0.586430i | ||||
\(23\) | −6.02414 | + | 3.47804i | −1.25612 | + | 0.725221i | −0.972318 | − | 0.233661i | \(-0.924929\pi\) |
−0.283802 | + | 0.958883i | \(0.591596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.38141 | + | 4.12472i | −0.476282 | + | 0.824945i | ||||
\(26\) | 0.348150 | − | 1.62144i | 0.0682779 | − | 0.317991i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.61932 | − | 4.59774i | 0.495004 | − | 0.868891i | ||||
\(29\) | 0.465824 | 0.0865013 | 0.0432506 | − | 0.999064i | \(-0.486229\pi\) | ||||
0.0432506 | + | 0.999064i | \(0.486229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.536070 | + | 0.928500i | −0.0962810 | + | 0.166764i | −0.910142 | − | 0.414295i | \(-0.864028\pi\) |
0.813862 | + | 0.581059i | \(0.197361\pi\) | |||||||
\(32\) | −2.77769 | − | 4.92793i | −0.491030 | − | 0.871143i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0486085 | + | 0.0439494i | 0.00833628 | + | 0.00753726i | ||||
\(35\) | 0.535699 | + | 1.17187i | 0.0905497 | + | 0.198082i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.196198 | + | 0.339825i | 0.0322547 | + | 0.0558668i | 0.881702 | − | 0.471806i | \(-0.156398\pi\) |
−0.849447 | + | 0.527673i | \(0.823065\pi\) | |||||||
\(38\) | 2.06910 | + | 6.41309i | 0.335653 | + | 1.04034i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.36901 | + | 0.152471i | 0.216459 | + | 0.0241077i | ||||
\(41\) | 0.139187i | 0.0217373i | 0.999941 | + | 0.0108686i | \(0.00345967\pi\) | ||||
−0.999941 | + | 0.0108686i | \(0.996540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.47359i | − | 0.987213i | −0.869685 | − | 0.493607i | \(-0.835678\pi\) | ||
0.869685 | − | 0.493607i | \(-0.164322\pi\) | |||||||
\(44\) | −3.38982 | − | 4.70644i | −0.511034 | − | 0.709523i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.36217 | − | 3.02059i | 1.38038 | − | 0.445361i | ||||
\(47\) | −3.81879 | − | 6.61433i | −0.557027 | − | 0.964800i | −0.997743 | − | 0.0671528i | \(-0.978609\pi\) |
0.440715 | − | 0.897647i | \(-0.354725\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.87448 | − | 1.31967i | −0.982069 | − | 0.188524i | ||||
\(50\) | 4.51736 | − | 4.99624i | 0.638851 | − | 0.706575i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.962774 | + | 2.13861i | −0.133513 | + | 0.296571i | ||||
\(53\) | 5.03428 | − | 8.71964i | 0.691512 | − | 1.19773i | −0.279830 | − | 0.960049i | \(-0.590278\pi\) |
0.971342 | − | 0.237685i | \(-0.0763885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41236 | 0.190443 | ||||||||
\(56\) | −4.98674 | + | 5.57964i | −0.666381 | + | 0.745611i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.644094 | − | 0.138297i | −0.0845737 | − | 0.0181593i | ||||
\(59\) | −3.65438 | + | 6.32958i | −0.475760 | + | 0.824041i | −0.999614 | − | 0.0277670i | \(-0.991160\pi\) |
0.523854 | + | 0.851808i | \(0.324494\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0409 | + | 6.95182i | −1.54168 | + | 0.890090i | −0.542948 | + | 0.839767i | \(0.682692\pi\) |
−0.998733 | + | 0.0503231i | \(0.983975\pi\) | |||||||
\(62\) | 1.01688 | − | 1.12468i | 0.129144 | − | 0.142835i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.37766 | + | 7.63850i | 0.297208 | + | 0.954813i | ||||
\(65\) | −0.285550 | − | 0.494587i | −0.0354181 | − | 0.0613459i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.49182 | − | 2.01601i | −0.426594 | − | 0.246294i | 0.271300 | − | 0.962495i | \(-0.412546\pi\) |
−0.697895 | + | 0.716200i | \(0.745880\pi\) | |||||||
\(68\) | −0.0541628 | − | 0.0752000i | −0.00656821 | − | 0.00911934i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.392797 | − | 1.77939i | −0.0469482 | − | 0.212677i | ||||
\(71\) | − | 6.95063i | − | 0.824888i | −0.910983 | − | 0.412444i | \(-0.864675\pi\) | ||
0.910983 | − | 0.412444i | \(-0.135325\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.14246 | − | 4.12370i | −0.835961 | − | 0.482643i | 0.0199280 | − | 0.999801i | \(-0.493656\pi\) |
−0.855889 | + | 0.517159i | \(0.826990\pi\) | |||||||
\(74\) | −0.170393 | − | 0.528124i | −0.0198078 | − | 0.0613932i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.956981 | − | 9.48167i | −0.109773 | − | 1.08762i | ||||
\(77\) | −4.44837 | + | 6.25176i | −0.506939 | + | 0.712454i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0015 | + | 6.92909i | −1.35028 | + | 0.779584i | −0.988288 | − | 0.152598i | \(-0.951236\pi\) |
−0.361990 | + | 0.932182i | \(0.617903\pi\) | |||||||
\(80\) | −1.84766 | − | 0.617263i | −0.206575 | − | 0.0690121i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.0413228 | − | 0.192453i | 0.00456334 | − | 0.0212529i | ||||
\(83\) | 6.34905 | 0.696899 | 0.348450 | − | 0.937328i | \(-0.386708\pi\) | ||||
0.348450 | + | 0.937328i | \(0.386708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0225668 | 0.00244772 | ||||||||
\(86\) | −1.92193 | + | 8.95103i | −0.207247 | + | 0.965214i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.28981 | + | 7.51399i | 0.350695 | + | 0.800994i | ||||
\(89\) | −9.16832 | + | 5.29333i | −0.971840 | + | 0.561092i | −0.899797 | − | 0.436309i | \(-0.856285\pi\) |
−0.0720434 | + | 0.997401i | \(0.522952\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.08864 | + | 0.293776i | 0.323777 | + | 0.0307961i | ||||
\(92\) | −13.8418 | + | 1.39705i | −1.44311 | + | 0.145653i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.31652 | + | 10.2794i | 0.342073 | + | 1.06024i | ||||
\(95\) | 2.00967 | + | 1.16028i | 0.206188 | + | 0.119042i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.51277i | 0.864341i | 0.901792 | + | 0.432171i | \(0.142252\pi\) | ||||
−0.901792 | + | 0.432171i | \(0.857748\pi\) | |||||||
\(98\) | 9.11354 | + | 3.86566i | 0.920607 | + | 0.390490i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.72947 | + | 5.56715i | −0.772947 | + | 0.556715i | ||||
\(101\) | 15.8252 | + | 9.13670i | 1.57467 | + | 0.909136i | 0.995585 | + | 0.0938690i | \(0.0299235\pi\) |
0.579085 | + | 0.815267i | \(0.303410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.99009 | − | 15.5713i | −0.885820 | − | 1.53429i | −0.844771 | − | 0.535128i | \(-0.820263\pi\) |
−0.0410493 | − | 0.999157i | \(-0.513070\pi\) | |||||||
\(104\) | 1.96615 | − | 2.67121i | 0.192797 | − | 0.261934i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.54966 | + | 10.5620i | −0.927545 | + | 1.02587i | ||||
\(107\) | 4.20572 | − | 2.42818i | 0.406583 | − | 0.234741i | −0.282738 | − | 0.959197i | \(-0.591243\pi\) |
0.689320 | + | 0.724457i | \(0.257909\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.83866 | − | 15.3090i | 0.846590 | − | 1.46634i | −0.0376439 | − | 0.999291i | \(-0.511985\pi\) |
0.884234 | − | 0.467045i | \(-0.154681\pi\) | |||||||
\(110\) | −1.95287 | − | 0.419313i | −0.186199 | − | 0.0399799i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.55169 | − | 6.23447i | 0.808059 | − | 0.589102i | ||||
\(113\) | −17.4915 | −1.64546 | −0.822732 | − | 0.568430i | \(-0.807551\pi\) | ||||
−0.822732 | + | 0.568430i | \(0.807551\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.69384 | − | 2.93382i | 0.157951 | − | 0.273580i | ||||
\(116\) | 0.849529 | + | 0.382447i | 0.0788768 | + | 0.0355094i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.93209 | − | 7.66696i | 0.638151 | − | 0.705801i | ||||
\(119\) | −0.0710766 | + | 0.0998913i | −0.00651558 | + | 0.00915702i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29482 | − | 2.24269i | −0.117711 | − | 0.203881i | ||||
\(122\) | 18.7129 | − | 6.03748i | 1.69418 | − | 0.546608i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.73995 | + | 1.25320i | −0.156252 | + | 0.112541i | ||||
\(125\) | − | 4.75459i | − | 0.425264i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.10449i | − | 0.630421i | −0.949022 | − | 0.315211i | \(-0.897925\pi\) | ||
0.949022 | − | 0.315211i | \(-0.102075\pi\) | |||||||
\(128\) | −1.01981 | − | 11.2677i | −0.0901394 | − | 0.995929i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.247993 | + | 0.768641i | 0.0217504 | + | 0.0674143i | ||||
\(131\) | 7.34587 | + | 12.7234i | 0.641812 | + | 1.11165i | 0.985028 | + | 0.172394i | \(0.0551503\pi\) |
−0.343216 | + | 0.939256i | \(0.611516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.4656 | + | 5.24129i | −0.994194 | + | 0.454478i | ||||
\(134\) | 4.22961 | + | 3.82421i | 0.365383 | + | 0.330361i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0525649 | + | 0.120059i | 0.00450741 | + | 0.0102950i | ||||
\(137\) | 5.97043 | − | 10.3411i | 0.510088 | − | 0.883498i | −0.489844 | − | 0.871810i | \(-0.662946\pi\) |
0.999932 | − | 0.0116880i | \(-0.00372050\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.39809 | 0.797135 | 0.398568 | − | 0.917139i | \(-0.369507\pi\) | ||||
0.398568 | + | 0.917139i | \(0.369507\pi\) | |||||||
\(140\) | 0.0148416 | + | 2.57697i | 0.00125435 | + | 0.217794i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.06356 | + | 9.61063i | −0.173170 | + | 0.806506i | ||||
\(143\) | 1.70040 | − | 2.94518i | 0.142195 | − | 0.246288i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.196467 | + | 0.113430i | −0.0163157 | + | 0.00941988i | ||||
\(146\) | 8.65159 | + | 7.82235i | 0.716011 | + | 0.647382i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0788082 | + | 0.780824i | 0.00647800 | + | 0.0641833i | ||||
\(149\) | −6.35996 | − | 11.0158i | −0.521028 | − | 0.902447i | −0.999701 | − | 0.0244538i | \(-0.992215\pi\) |
0.478673 | − | 0.877993i | \(-0.341118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.87775 | + | 1.66147i | 0.234188 | + | 0.135209i | 0.612503 | − | 0.790468i | \(-0.290163\pi\) |
−0.378314 | + | 0.925677i | \(0.623496\pi\) | |||||||
\(152\) | −1.49178 | + | 13.3944i | −0.120999 | + | 1.08643i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.00684 | − | 7.32364i | 0.645209 | − | 0.590156i | ||||
\(155\) | − | 0.522143i | − | 0.0419395i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.22021 | + | 4.74594i | 0.656045 | + | 0.378767i | 0.790768 | − | 0.612116i | \(-0.209681\pi\) |
−0.134724 | + | 0.990883i | \(0.543015\pi\) | |||||||
\(158\) | 18.6517 | − | 6.01774i | 1.48385 | − | 0.478746i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.37150 | + | 1.40204i | 0.187484 | + | 0.110841i | ||||
\(161\) | 7.65152 | + | 16.7381i | 0.603024 | + | 1.31915i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.9144 | + | 6.87876i | −0.933205 | + | 0.538786i | −0.887824 | − | 0.460183i | \(-0.847784\pi\) |
−0.0453814 | + | 0.998970i | \(0.514450\pi\) | |||||||
\(164\) | −0.114274 | + | 0.253837i | −0.00892331 | + | 0.0198213i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.77883 | − | 1.88496i | −0.681369 | − | 0.146301i | ||||
\(167\) | 11.0139 | 0.852280 | 0.426140 | − | 0.904657i | \(-0.359873\pi\) | ||||
0.426140 | + | 0.904657i | \(0.359873\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6249 | 0.894220 | ||||||||
\(170\) | −0.0312032 | − | 0.00669982i | −0.00239317 | − | 0.000513853i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.31491 | − | 11.8060i | 0.405258 | − | 0.900198i | ||||
\(173\) | 15.2097 | − | 8.78130i | 1.15637 | − | 0.667630i | 0.205938 | − | 0.978565i | \(-0.433975\pi\) |
0.950431 | + | 0.310935i | \(0.100642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.2674 | + | 7.30564i | 0.776140 | + | 0.552254i | ||||
\(176\) | −2.31800 | − | 11.3663i | −0.174726 | − | 0.856767i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.2486 | − | 4.59712i | 1.06797 | − | 0.344569i | ||||
\(179\) | 8.95722 | + | 5.17145i | 0.669494 | + | 0.386533i | 0.795885 | − | 0.605448i | \(-0.207006\pi\) |
−0.126391 | + | 0.991981i | \(0.540339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4154i | 0.848503i | 0.905544 | + | 0.424252i | \(0.139463\pi\) | ||||
−0.905544 | + | 0.424252i | \(0.860537\pi\) | |||||||
\(182\) | −4.18344 | − | 1.32318i | −0.310097 | − | 0.0980809i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19.5539 | + | 2.17777i | 1.44153 | + | 0.160548i | ||||
\(185\) | −0.165498 | − | 0.0955503i | −0.0121677 | − | 0.00702500i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0671908 | + | 0.116378i | 0.00491348 | + | 0.00851040i | ||||
\(188\) | −1.53392 | − | 15.1979i | −0.111873 | − | 1.10842i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.43429 | − | 2.20097i | −0.176602 | − | 0.159675i | ||||
\(191\) | 12.6603 | − | 7.30943i | 0.916068 | − | 0.528892i | 0.0336895 | − | 0.999432i | \(-0.489274\pi\) |
0.882379 | + | 0.470540i | \(0.155941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0358245 | − | 0.0620498i | 0.00257870 | − | 0.00446644i | −0.864733 | − | 0.502232i | \(-0.832513\pi\) |
0.867312 | + | 0.497765i | \(0.165846\pi\) | |||||||
\(194\) | 2.52734 | − | 11.7706i | 0.181452 | − | 0.845080i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.4536 | − | 8.05074i | −0.818116 | − | 0.575053i | ||||
\(197\) | 1.90917 | 0.136023 | 0.0680113 | − | 0.997685i | \(-0.478335\pi\) | ||||
0.0680113 | + | 0.997685i | \(0.478335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.291782 | − | 0.505382i | 0.0206839 | − | 0.0358256i | −0.855498 | − | 0.517806i | \(-0.826749\pi\) |
0.876182 | + | 0.481980i | \(0.160082\pi\) | |||||||
\(200\) | 12.3404 | − | 5.40291i | 0.872595 | − | 0.382043i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.1690 | − | 17.3316i | −1.34872 | − | 1.21945i | ||||
\(203\) | 0.116698 | − | 1.22692i | 0.00819060 | − | 0.0861126i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.0338926 | − | 0.0587038i | −0.00236716 | − | 0.00410005i | ||||
\(206\) | 7.80766 | + | 24.1995i | 0.543986 | + | 1.68606i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.51165 | + | 3.10976i | −0.243489 | + | 0.215623i | ||||
\(209\) | 13.8186i | 0.955850i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89200i | 0.336779i | 0.985721 | + | 0.168390i | \(0.0538567\pi\) | ||||
−0.985721 | + | 0.168390i | \(0.946143\pi\) | |||||||
\(212\) | 16.3400 | − | 11.7689i | 1.12224 | − | 0.808292i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.53615 | + | 2.10881i | −0.446802 | + | 0.144155i | ||||
\(215\) | 1.57635 | + | 2.73032i | 0.107506 | + | 0.186206i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.31125 | + | 1.64454i | 0.156898 | + | 0.111639i | ||||
\(218\) | −16.7663 | + | 18.5437i | −1.13555 | + | 1.25593i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.57574 | + | 1.15957i | 0.173656 | + | 0.0781780i | ||||
\(221\) | 0.0271692 | − | 0.0470584i | 0.00182760 | − | 0.00316549i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3383 | 1.22803 | 0.614013 | − | 0.789296i | \(-0.289554\pi\) | ||||
0.614013 | + | 0.789296i | \(0.289554\pi\) | |||||||
\(224\) | −13.6754 | + | 6.08150i | −0.913723 | + | 0.406337i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.1855 | + | 5.19302i | 1.60880 | + | 0.345435i | ||||
\(227\) | 8.05581 | − | 13.9531i | 0.534683 | − | 0.926098i | −0.464496 | − | 0.885575i | \(-0.653764\pi\) |
0.999179 | − | 0.0405227i | \(-0.0129023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0728 | − | 6.97024i | 0.797793 | − | 0.460606i | −0.0449057 | − | 0.998991i | \(-0.514299\pi\) |
0.842699 | + | 0.538385i | \(0.180965\pi\) | |||||||
\(230\) | −3.21309 | + | 3.55371i | −0.211865 | + | 0.234325i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.06110 | − | 0.781025i | −0.0696646 | − | 0.0512768i | ||||
\(233\) | −1.82721 | − | 3.16482i | −0.119704 | − | 0.207334i | 0.799946 | − | 0.600072i | \(-0.204861\pi\) |
−0.919651 | + | 0.392738i | \(0.871528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.22125 | + | 1.85979i | 0.210131 | + | 0.121319i | ||||
\(236\) | −11.8612 | + | 8.54305i | −0.772100 | + | 0.556105i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.127934 | − | 0.117018i | 0.00829273 | − | 0.00758514i | ||||
\(239\) | 16.3218i | 1.05577i | 0.849315 | + | 0.527886i | \(0.177015\pi\) | ||||
−0.849315 | + | 0.527886i | \(0.822985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.32608 | − | 1.34296i | −0.149836 | − | 0.0865079i | 0.423208 | − | 0.906033i | \(-0.360904\pi\) |
−0.573044 | + | 0.819525i | \(0.694237\pi\) | |||||||
\(242\) | 1.12452 | + | 3.48538i | 0.0722867 | + | 0.224049i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −27.6667 | + | 2.79239i | −1.77118 | + | 0.178765i | ||||
\(245\) | 3.22075 | − | 1.11738i | 0.205766 | − | 0.0713869i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.83905 | − | 2.79383i | 0.307901 | − | 0.177767i | ||||
\(248\) | 2.77789 | − | 1.21623i | 0.176396 | − | 0.0772305i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.41158 | + | 6.57417i | −0.0892763 | + | 0.415787i | ||||
\(251\) | −30.3569 | −1.91611 | −0.958055 | − | 0.286585i | \(-0.907480\pi\) | ||||
−0.958055 | + | 0.286585i | \(0.907480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.1731 | 1.26827 | ||||||||
\(254\) | −2.10924 | + | 9.82337i | −0.132345 | + | 0.616373i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.93514 | + | 15.8825i | −0.120946 | + | 0.992659i | ||||
\(257\) | −20.1221 | + | 11.6175i | −1.25518 | + | 0.724678i | −0.972133 | − | 0.234428i | \(-0.924678\pi\) |
−0.283046 | + | 0.959106i | \(0.591345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.944203 | − | 0.431625i | 0.0586699 | − | 0.0268199i | ||||
\(260\) | −0.114699 | − | 1.13643i | −0.00711333 | − | 0.0704781i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.37970 | − | 19.7736i | −0.394139 | − | 1.22162i | ||||
\(263\) | −8.24274 | − | 4.75895i | −0.508269 | − | 0.293449i | 0.223853 | − | 0.974623i | \(-0.428137\pi\) |
−0.732122 | + | 0.681174i | \(0.761470\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.90349i | 0.301219i | ||||||||
\(266\) | 17.4096 | − | 3.84313i | 1.06745 | − | 0.235638i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.71292 | − | 6.54346i | −0.287888 | − | 0.399705i | ||||
\(269\) | 10.0770 | + | 5.81796i | 0.614405 | + | 0.354727i | 0.774688 | − | 0.632344i | \(-0.217907\pi\) |
−0.160282 | + | 0.987071i | \(0.551240\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.94241 | + | 13.7567i | 0.482467 | + | 0.835657i | 0.999797 | − | 0.0201285i | \(-0.00640752\pi\) |
−0.517330 | + | 0.855786i | \(0.673074\pi\) | |||||||
\(272\) | −0.0370373 | − | 0.181612i | −0.00224572 | − | 0.0110118i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.3254 | + | 12.5261i | −0.684195 | + | 0.756727i | ||||
\(275\) | 11.9620 | − | 6.90624i | 0.721333 | − | 0.416462i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.38977 | − | 12.7995i | 0.444008 | − | 0.769045i | −0.553974 | − | 0.832534i | \(-0.686889\pi\) |
0.997983 | + | 0.0634891i | \(0.0202228\pi\) | |||||||
\(278\) | −12.9947 | − | 2.79018i | −0.779372 | − | 0.167344i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.744551 | − | 3.56758i | 0.0444954 | − | 0.213204i | ||||
\(281\) | −24.2255 | −1.44517 | −0.722586 | − | 0.691281i | \(-0.757047\pi\) | ||||
−0.722586 | + | 0.691281i | \(0.757047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.1171 | + | 26.1836i | −0.898619 | + | 1.55645i | −0.0693572 | + | 0.997592i | \(0.522095\pi\) |
−0.829261 | + | 0.558861i | \(0.811239\pi\) | |||||||
\(284\) | 5.70656 | − | 12.6760i | 0.338622 | − | 0.752180i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.22553 | + | 3.56747i | −0.190730 | + | 0.210949i | ||||
\(287\) | 0.366598 | + | 0.0348690i | 0.0216396 | + | 0.00205825i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.49893 | − | 14.7206i | −0.499937 | − | 0.865916i | ||||
\(290\) | 0.305331 | − | 0.0985114i | 0.0179297 | − | 0.00578479i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.64019 | − | 13.3845i | −0.564150 | − | 0.783269i | ||||
\(293\) | − | 27.6085i | − | 1.61290i | −0.591300 | − | 0.806452i | \(-0.701385\pi\) | ||
0.591300 | − | 0.806452i | \(-0.298615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.55944i | − | 0.207239i | ||||||
\(296\) | 0.122849 | − | 1.10304i | 0.00714047 | − | 0.0641130i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.52346 | + | 17.1197i | 0.319965 | + | 0.991717i | ||||
\(299\) | −4.07857 | − | 7.06430i | −0.235870 | − | 0.408539i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0506 | − | 1.62176i | −0.982778 | − | 0.0934769i | ||||
\(302\) | −3.48580 | − | 3.15169i | −0.200585 | − | 0.181359i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.03932 | − | 18.0776i | 0.346379 | − | 1.03682i | ||||
\(305\) | 3.38561 | − | 5.86405i | 0.193859 | − | 0.335774i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.3244 | 1.04583 | 0.522913 | − | 0.852386i | \(-0.324845\pi\) | ||||
0.522913 | + | 0.852386i | \(0.324845\pi\) | |||||||
\(308\) | −13.2453 | + | 7.74926i | −0.754724 | + | 0.441555i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.155018 | + | 0.721966i | −0.00880443 | + | 0.0410049i | ||||
\(311\) | −9.34254 | + | 16.1817i | −0.529767 | + | 0.917583i | 0.469630 | + | 0.882863i | \(0.344387\pi\) |
−0.999397 | + | 0.0347196i | \(0.988946\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3438 | − | 14.0549i | 1.37599 | − | 0.794431i | 0.384320 | − | 0.923200i | \(-0.374436\pi\) |
0.991675 | + | 0.128769i | \(0.0411027\pi\) | |||||||
\(314\) | −9.95707 | − | 9.00270i | −0.561910 | − | 0.508051i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.5763 | + | 2.78326i | −1.55129 | + | 0.156571i | ||||
\(317\) | 3.14099 | + | 5.44035i | 0.176416 | + | 0.305561i | 0.940650 | − | 0.339378i | \(-0.110216\pi\) |
−0.764235 | + | 0.644938i | \(0.776883\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.16993 | − | 0.675459i | −0.0655034 | − | 0.0378184i | ||||
\(320\) | −2.86282 | − | 2.64267i | −0.160037 | − | 0.147730i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.61041 | − | 25.4154i | −0.312656 | − | 1.41634i | ||||
\(323\) | 0.220794i | 0.0122853i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.83692 | − | 2.79260i | −0.268304 | − | 0.154905i | ||||
\(326\) | 18.5162 | − | 5.97403i | 1.02552 | − | 0.330871i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.233368 | − | 0.317053i | 0.0128856 | − | 0.0175063i | ||||
\(329\) | −18.3779 | + | 8.40114i | −1.01321 | + | 0.463170i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.2443 | + | 9.95600i | −0.947832 | + | 0.547231i | −0.892407 | − | 0.451232i | \(-0.850985\pi\) |
−0.0554253 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(332\) | 11.5789 | + | 5.21266i | 0.635473 | + | 0.286082i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.2289 | − | 3.26989i | −0.833288 | − | 0.178920i | ||||
\(335\) | 1.96363 | 0.107285 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.4718 | 1.49649 | 0.748243 | − | 0.663424i | \(-0.230898\pi\) | ||||
0.748243 | + | 0.663424i | \(0.230898\pi\) | |||||||
\(338\) | −16.0737 | − | 3.45128i | −0.874293 | − | 0.187725i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.0411555 | + | 0.0185277i | 0.00223197 | + | 0.00100480i | ||||
\(341\) | 2.69271 | − | 1.55464i | 0.145818 | − | 0.0841882i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.19803 | + | 17.7758i | −0.280667 | + | 0.959805i | ||||
\(344\) | −10.8540 | + | 14.7462i | −0.585207 | + | 0.795062i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.6375 | + | 7.62634i | −1.27076 | + | 0.409994i | ||||
\(347\) | −7.37788 | − | 4.25962i | −0.396065 | − | 0.228668i | 0.288720 | − | 0.957414i | \(-0.406770\pi\) |
−0.684785 | + | 0.728745i | \(0.740104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.53420i | − | 0.296239i | −0.988969 | − | 0.148119i | \(-0.952678\pi\) | ||
0.988969 | − | 0.148119i | \(-0.0473220\pi\) | |||||||
\(350\) | −12.0277 | − | 13.1498i | −0.642909 | − | 0.702884i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.169415 | + | 16.4044i | −0.00902982 | + | 0.874355i | ||||
\(353\) | 14.9667 | + | 8.64101i | 0.796595 | + | 0.459914i | 0.842279 | − | 0.539042i | \(-0.181213\pi\) |
−0.0456841 | + | 0.998956i | \(0.514547\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.69251 | + | 2.93152i | 0.0898293 | + | 0.155589i | ||||
\(356\) | −21.0663 | + | 2.12621i | −1.11651 | + | 0.112689i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8498 | − | 9.80986i | −0.573430 | − | 0.518467i | ||||
\(359\) | −20.8753 | + | 12.0523i | −1.10175 | + | 0.636098i | −0.936681 | − | 0.350183i | \(-0.886119\pi\) |
−0.165073 | + | 0.986281i | \(0.552786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.85223 | + | 3.20815i | −0.0974857 | + | 0.168850i | ||||
\(362\) | 3.38911 | − | 15.7841i | 0.178128 | − | 0.829595i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.39160 | + | 3.07158i | 0.282597 | + | 0.160994i | ||||
\(365\) | 4.01657 | 0.210237 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.54588 | + | 4.40959i | −0.132894 | + | 0.230179i | −0.924791 | − | 0.380476i | \(-0.875760\pi\) |
0.791897 | + | 0.610655i | \(0.209094\pi\) | |||||||
\(368\) | −26.3906 | − | 8.81652i | −1.37570 | − | 0.459593i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.200466 | + | 0.181252i | 0.0104217 | + | 0.00942283i | ||||
\(371\) | −21.7051 | − | 15.4441i | −1.12688 | − | 0.801816i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.30359 | − | 10.9181i | −0.326388 | − | 0.565320i | 0.655405 | − | 0.755278i | \(-0.272498\pi\) |
−0.981792 | + | 0.189958i | \(0.939165\pi\) | |||||||
\(374\) | −0.0583535 | − | 0.180864i | −0.00301739 | − | 0.00935225i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.39113 | + | 21.4696i | −0.123313 | + | 1.10721i | ||||
\(377\) | 0.546255i | 0.0281336i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.1068i | − | 0.621883i | −0.950429 | − | 0.310942i | \(-0.899356\pi\) | ||
0.950429 | − | 0.310942i | \(-0.100644\pi\) | |||||||
\(380\) | 2.71245 | + | 3.76599i | 0.139146 | + | 0.193191i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.6755 | + | 6.34806i | −1.00669 | + | 0.324795i | ||||
\(383\) | −0.646193 | − | 1.11924i | −0.0330189 | − | 0.0571905i | 0.849044 | − | 0.528323i | \(-0.177179\pi\) |
−0.882063 | + | 0.471132i | \(0.843845\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.353824 | − | 3.71996i | 0.0180326 | − | 0.189587i | ||||
\(386\) | −0.0679563 | + | 0.0751604i | −0.00345888 | + | 0.00382556i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.98910 | + | 15.5249i | −0.354818 | + | 0.788156i | ||||
\(389\) | 15.0809 | − | 26.1208i | 0.764630 | − | 1.32438i | −0.175812 | − | 0.984424i | \(-0.556255\pi\) |
0.940442 | − | 0.339954i | \(-0.110412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.322327 | 0.0163008 | ||||||||
\(392\) | 13.4467 | + | 14.5322i | 0.679163 | + | 0.733987i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.63980 | − | 0.566809i | −0.132991 | − | 0.0285554i | ||||
\(395\) | 3.37454 | − | 5.84487i | 0.169791 | − | 0.294087i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.80099 | + | 2.19450i | −0.190766 | + | 0.110139i | −0.592341 | − | 0.805687i | \(-0.701796\pi\) |
0.401575 | + | 0.915826i | \(0.368463\pi\) | |||||||
\(398\) | −0.553489 | + | 0.612165i | −0.0277439 | + | 0.0306850i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.6671 | + | 3.80690i | −0.933353 | + | 0.190345i | ||||
\(401\) | −6.56098 | − | 11.3640i | −0.327640 | − | 0.567489i | 0.654403 | − | 0.756146i | \(-0.272920\pi\) |
−0.982043 | + | 0.188657i | \(0.939587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.08882 | − | 0.628630i | −0.0542379 | − | 0.0313143i | ||||
\(404\) | 21.3594 | + | 29.6555i | 1.06267 | + | 1.47542i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.525615 | + | 1.66181i | −0.0260858 | + | 0.0824742i | ||||
\(407\) | − | 1.13797i | − | 0.0564072i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.8601 | − | 8.00213i | −0.685338 | − | 0.395680i | 0.116525 | − | 0.993188i | \(-0.462824\pi\) |
−0.801863 | + | 0.597508i | \(0.796158\pi\) | |||||||
\(410\) | 0.0294349 | + | 0.0912320i | 0.00145369 | + | 0.00450563i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.61112 | − | 35.7786i | −0.177907 | − | 1.76268i | ||||
\(413\) | 15.7558 | + | 11.2108i | 0.775290 | + | 0.551649i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.67780 | + | 1.54603i | −0.131448 | + | 0.0758914i | ||||
\(416\) | 5.77881 | − | 3.25729i | 0.283329 | − | 0.159702i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.10257 | − | 19.1069i | 0.200663 | − | 0.934550i | ||||
\(419\) | −18.2612 | −0.892119 | −0.446059 | − | 0.895003i | \(-0.647173\pi\) | ||||
−0.446059 | + | 0.895003i | \(0.647173\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6765 | 1.10518 | 0.552592 | − | 0.833452i | \(-0.313639\pi\) | ||||
0.552592 | + | 0.833452i | \(0.313639\pi\) | |||||||
\(422\) | 1.45238 | − | 6.76416i | 0.0707006 | − | 0.329274i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.0874 | + | 11.4217i | −1.26692 | + | 0.554687i | ||||
\(425\) | 0.191129 | − | 0.110349i | 0.00927114 | − | 0.00535270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.2937 | + | 33.4557i | 0.740112 | + | 1.61903i | ||||
\(428\) | 9.66361 | − | 0.975344i | 0.467108 | − | 0.0471450i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.36902 | − | 4.24321i | −0.0660201 | − | 0.204626i | ||||
\(431\) | 20.9603 | + | 12.1015i | 1.00962 | + | 0.582907i | 0.911082 | − | 0.412226i | \(-0.135249\pi\) |
0.0985425 | + | 0.995133i | \(0.468582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.0508i | 1.49221i | 0.665830 | + | 0.746103i | \(0.268078\pi\) | ||||
−0.665830 | + | 0.746103i | \(0.731922\pi\) | |||||||
\(434\) | −2.70751 | − | 2.96009i | −0.129965 | − | 0.142089i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.6881 | − | 20.6626i | 1.37391 | − | 0.989559i | ||||
\(437\) | 28.7045 | + | 16.5726i | 1.37312 | + | 0.792774i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6459 | + | 30.5637i | 0.842195 | + | 1.45872i | 0.888035 | + | 0.459775i | \(0.152070\pi\) |
−0.0458405 | + | 0.998949i | \(0.514597\pi\) | |||||||
\(440\) | −3.21722 | − | 2.36804i | −0.153375 | − | 0.112892i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0515379 | + | 0.0570014i | −0.00245141 | + | 0.00271128i | ||||
\(443\) | −12.9852 | + | 7.49702i | −0.616947 | + | 0.356194i | −0.775679 | − | 0.631127i | \(-0.782593\pi\) |
0.158733 | + | 0.987322i | \(0.449259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.57791 | − | 4.46507i | 0.122205 | − | 0.211664i | ||||
\(446\) | −25.3564 | − | 5.44443i | −1.20066 | − | 0.257801i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7144 | − | 4.34884i | 0.978665 | − | 0.205463i | ||||
\(449\) | −5.15686 | −0.243367 | −0.121684 | − | 0.992569i | \(-0.538829\pi\) | ||||
−0.121684 | + | 0.992569i | \(0.538829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.201825 | − | 0.349571i | 0.00950356 | − | 0.0164607i | ||||
\(452\) | −31.8995 | − | 14.3608i | −1.50043 | − | 0.675474i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.2813 | + | 16.9012i | −0.717185 | + | 0.793214i | ||||
\(455\) | −1.37421 | + | 0.628196i | −0.0644240 | + | 0.0294503i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7402 | − | 22.0666i | −0.595961 | − | 1.03223i | −0.993411 | − | 0.114610i | \(-0.963438\pi\) |
0.397450 | − | 0.917624i | \(-0.369895\pi\) | |||||||
\(458\) | −18.7624 | + | 6.05347i | −0.876711 | + | 0.282860i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.49779 | − | 3.95978i | 0.256336 | − | 0.184626i | ||||
\(461\) | 1.16194i | 0.0541170i | 0.999634 | + | 0.0270585i | \(0.00861403\pi\) | ||||
−0.999634 | + | 0.0270585i | \(0.991386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.3409i | − | 1.08474i | −0.840139 | − | 0.542371i | \(-0.817527\pi\) | ||
0.840139 | − | 0.542371i | \(-0.182473\pi\) | |||||||
\(464\) | 1.23530 | + | 1.39495i | 0.0573476 | + | 0.0647589i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.58688 | + | 4.91847i | 0.0735110 | + | 0.227844i | ||||
\(467\) | −9.08065 | − | 15.7281i | −0.420202 | − | 0.727812i | 0.575757 | − | 0.817621i | \(-0.304708\pi\) |
−0.995959 | + | 0.0898092i | \(0.971374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.18466 | + | 8.69194i | −0.285581 | + | 0.401357i | ||||
\(470\) | −3.90187 | − | 3.52788i | −0.179980 | − | 0.162729i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.9368 | − | 8.29101i | 0.871639 | − | 0.381625i | ||||
\(473\) | −9.38691 | + | 16.2586i | −0.431611 | + | 0.747571i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.6945 | 1.04129 | ||||||||
\(476\) | −0.211636 | + | 0.123818i | −0.00970030 | + | 0.00567521i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.84576 | − | 22.5682i | 0.221640 | − | 1.03225i | ||||
\(479\) | −5.41667 | + | 9.38196i | −0.247494 | + | 0.428672i | −0.962830 | − | 0.270108i | \(-0.912940\pi\) |
0.715336 | + | 0.698781i | \(0.246274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.398500 | + | 0.230074i | −0.0181700 | + | 0.0104905i | ||||
\(482\) | 2.81756 | + | 2.54750i | 0.128336 | + | 0.116036i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.520100 | − | 5.15309i | −0.0236409 | − | 0.234232i | ||||
\(485\) | −2.07290 | − | 3.59037i | −0.0941257 | − | 0.163030i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3315 | − | 8.85162i | −0.694734 | − | 0.401105i | 0.110649 | − | 0.993860i | \(-0.464707\pi\) |
−0.805383 | + | 0.592754i | \(0.798040\pi\) | |||||||
\(488\) | 39.0838 | + | 4.35288i | 1.76924 | + | 0.197046i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.78506 | + | 0.588802i | −0.216167 | + | 0.0265994i | ||||
\(491\) | − | 2.86819i | − | 0.129440i | −0.997903 | − | 0.0647199i | \(-0.979385\pi\) | ||
0.997903 | − | 0.0647199i | \(-0.0206154\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0186932 | − | 0.0107926i | −0.000841901 | − | 0.000486072i | ||||
\(494\) | −7.52040 | + | 2.42637i | −0.338359 | + | 0.109167i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.20207 | + | 0.856955i | −0.188678 | + | 0.0384784i | ||||
\(497\) | −18.3070 | − | 1.74127i | −0.821182 | − | 0.0781067i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5923 | − | 14.1984i | 1.10090 | − | 0.635606i | 0.164444 | − | 0.986386i | \(-0.447417\pi\) |
0.936458 | + | 0.350781i | \(0.114084\pi\) | |||||||
\(500\) | 3.90359 | − | 8.67102i | 0.174574 | − | 0.387780i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.9744 | + | 9.01260i | 1.87341 | + | 0.402252i | ||||
\(503\) | 0.613623 | 0.0273601 | 0.0136800 | − | 0.999906i | \(-0.495645\pi\) | ||||
0.0136800 | + | 0.999906i | \(0.495645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.89933 | −0.396015 | ||||||||
\(506\) | −27.8933 | − | 5.98914i | −1.24001 | − | 0.266250i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.83288 | − | 12.9566i | 0.258792 | − | 0.574854i | ||||
\(509\) | 8.62877 | − | 4.98182i | 0.382464 | − | 0.220816i | −0.296426 | − | 0.955056i | \(-0.595795\pi\) |
0.678890 | + | 0.734240i | \(0.262461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.6506 | + | 17.7792i | −0.559629 | + | 0.786505i | ||||
\(512\) | 7.39105 | − | 21.3863i | 0.326641 | − | 0.945148i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 31.2718 | − | 10.0895i | 1.37934 | − | 0.445028i | ||||
\(515\) | 7.58338 | + | 4.37827i | 0.334164 | + | 0.192929i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.1494i | 0.974131i | ||||||||
\(518\) | −1.43369 | + | 0.316486i | −0.0629929 | + | 0.0139056i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.178797 | + | 1.60539i | −0.00784077 | + | 0.0704009i | ||||
\(521\) | −37.1542 | − | 21.4510i | −1.62776 | − | 0.939786i | −0.984760 | − | 0.173917i | \(-0.944357\pi\) |
−0.642997 | − | 0.765869i | \(-0.722309\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.342559 | − | 0.593329i | −0.0149790 | − | 0.0259445i | 0.858439 | − | 0.512916i | \(-0.171435\pi\) |
−0.873418 | + | 0.486972i | \(0.838101\pi\) | |||||||
\(524\) | 2.95067 | + | 29.2350i | 0.128901 | + | 1.27714i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.98436 | + | 9.02737i | 0.435339 | + | 0.393612i | ||||
\(527\) | 0.0430244 | − | 0.0248401i | 0.00187417 | − | 0.00108205i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6935 | − | 21.9858i | 0.551892 | − | 0.955906i | ||||
\(530\) | 1.45579 | − | 6.78006i | 0.0632354 | − | 0.294507i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25.2132 | + | 0.145211i | −1.09313 | + | 0.00629569i | ||||
\(533\) | −0.163219 | −0.00706981 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.18255 | + | 2.04823i | −0.0511259 | + | 0.0885527i | ||||
\(536\) | 4.57388 | + | 10.4468i | 0.197562 | + | 0.451235i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.2062 | − | 11.0362i | −0.526245 | − | 0.475805i | ||||
\(539\) | 15.3519 | + | 13.2826i | 0.661252 | + | 0.572122i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.951285 | − | 1.64767i | −0.0408989 | − | 0.0708390i | 0.844851 | − | 0.535001i | \(-0.179689\pi\) |
−0.885750 | + | 0.464162i | \(0.846356\pi\) | |||||||
\(542\) | −6.89778 | − | 21.3793i | −0.296285 | − | 0.918321i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.00270692 | + | 0.262111i | −0.000116058 | + | 0.0112379i | ||||
\(545\) | 8.60903i | 0.368770i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.8931i | − | 1.40641i | −0.710989 | − | 0.703203i | \(-0.751753\pi\) | ||
0.710989 | − | 0.703203i | \(-0.248247\pi\) | |||||||
\(548\) | 19.3785 | − | 13.9574i | 0.827810 | − | 0.596230i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −18.5902 | + | 5.99789i | −0.792688 | + | 0.255751i | ||||
\(551\) | −1.10981 | − | 1.92224i | −0.0472793 | − | 0.0818902i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2437 | + | 33.3463i | 0.648226 | + | 1.41803i | ||||
\(554\) | −14.0178 | + | 15.5039i | −0.595561 | + | 0.658696i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.1394 | + | 7.71596i | 0.726874 | + | 0.327230i | ||||
\(557\) | 11.8145 | − | 20.4633i | 0.500596 | − | 0.867058i | −0.499404 | − | 0.866369i | \(-0.666448\pi\) |
1.00000 | 0.000688398i | \(-0.000219124\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.59135 | 0.321080 | ||||||||
\(560\) | −2.08866 | + | 4.71185i | −0.0882621 | + | 0.199112i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.4966 | + | 7.19226i | 1.41297 | + | 0.303387i | ||||
\(563\) | −10.9592 | + | 18.9820i | −0.461877 | + | 0.799994i | −0.999055 | − | 0.0434752i | \(-0.986157\pi\) |
0.537178 | + | 0.843469i | \(0.319490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.37728 | − | 4.25927i | 0.310364 | − | 0.179189i | ||||
\(566\) | 28.6760 | − | 31.7159i | 1.20534 | − | 1.33312i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.6538 | + | 15.8328i | −0.488983 | + | 0.664331i | ||||
\(569\) | 4.15511 | + | 7.19687i | 0.174191 | + | 0.301708i | 0.939881 | − | 0.341502i | \(-0.110936\pi\) |
−0.765690 | + | 0.643210i | \(0.777602\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.1031 | − | 12.7613i | −0.924988 | − | 0.534042i | −0.0397651 | − | 0.999209i | \(-0.512661\pi\) |
−0.885223 | + | 0.465167i | \(0.845994\pi\) | |||||||
\(572\) | 5.51908 | − | 3.97512i | 0.230764 | − | 0.166208i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.496543 | − | 0.157052i | −0.0207253 | − | 0.00655523i | ||||
\(575\) | − | 33.1306i | − | 1.38164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.3610 | + | 8.29131i | 0.597855 | + | 0.345172i | 0.768197 | − | 0.640213i | \(-0.221154\pi\) |
−0.170342 | + | 0.985385i | \(0.554487\pi\) | |||||||
\(578\) | 7.38110 | + | 22.8774i | 0.307013 | + | 0.951573i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.451428 | + | 0.0455624i | −0.0187445 | + | 0.00189188i | ||||
\(581\) | 1.59056 | − | 16.7225i | 0.0659877 | − | 0.693768i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.2875 | + | 14.5997i | −1.04730 | + | 0.604659i | ||||
\(584\) | 9.35579 | + | 21.3688i | 0.387145 | + | 0.884248i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.19662 | + | 38.1742i | −0.338599 | + | 1.57696i | ||||
\(587\) | 27.4851 | 1.13443 | 0.567216 | − | 0.823569i | \(-0.308021\pi\) | ||||
0.567216 | + | 0.823569i | \(0.308021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.10866 | 0.210499 | ||||||||
\(590\) | −1.05676 | + | 4.92164i | −0.0435060 | + | 0.202621i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.497344 | + | 1.48870i | −0.0204407 | + | 0.0611853i | ||||
\(593\) | −31.4732 | + | 18.1711i | −1.29245 | + | 0.746197i | −0.979088 | − | 0.203437i | \(-0.934789\pi\) |
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.00565344 | − | 0.0594380i | 0.000231768 | − | 0.00243672i | ||||
\(596\) | −2.55465 | − | 25.3112i | −0.104643 | − | 1.03679i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.54214 | + | 10.9787i | 0.144849 | + | 0.448952i | ||||
\(599\) | −27.8050 | − | 16.0532i | −1.13608 | − | 0.655918i | −0.190625 | − | 0.981663i | \(-0.561051\pi\) |
−0.945458 | + | 0.325745i | \(0.894385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.7728i | 0.928923i | 0.885593 | + | 0.464462i | \(0.153752\pi\) | ||||
−0.885593 | + | 0.464462i | \(0.846248\pi\) | |||||||
\(602\) | 23.0943 | + | 7.30452i | 0.941254 | + | 0.297710i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.88411 | + | 5.39273i | 0.158042 | + | 0.219427i | ||||
\(605\) | 1.09221 | + | 0.630590i | 0.0444048 | + | 0.0256371i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.4667 | − | 38.9134i | −0.911893 | − | 1.57945i | −0.811387 | − | 0.584509i | \(-0.801287\pi\) |
−0.100506 | − | 0.994936i | \(-0.532046\pi\) | |||||||
\(608\) | −13.7176 | + | 23.2028i | −0.556321 | + | 0.940999i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.42224 | + | 7.10306i | −0.260029 | + | 0.287595i | ||||
\(611\) | 7.75640 | − | 4.47816i | 0.313790 | − | 0.181167i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0988 | + | 26.1519i | −0.609836 | + | 1.05627i | 0.381432 | + | 0.924397i | \(0.375431\pi\) |
−0.991267 | + | 0.131869i | \(0.957902\pi\) | |||||||
\(614\) | −25.3371 | − | 5.44028i | −1.02252 | − | 0.219552i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.6150 | − | 6.78251i | 0.830602 | − | 0.273275i | ||||
\(617\) | 9.76529 | 0.393136 | 0.196568 | − | 0.980490i | \(-0.437020\pi\) | ||||
0.196568 | + | 0.980490i | \(0.437020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.9884 | − | 41.5491i | 0.964174 | − | 1.67000i | 0.252355 | − | 0.967635i | \(-0.418795\pi\) |
0.711819 | − | 0.702363i | \(-0.247872\pi\) | |||||||
\(620\) | 0.428686 | − | 0.952240i | 0.0172165 | − | 0.0382429i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7221 | − | 19.6008i | 0.710591 | − | 0.785921i | ||||
\(623\) | 11.6451 | + | 25.4742i | 0.466550 | + | 1.02060i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.7493 | − | 18.6183i | −0.429971 | − | 0.744732i | ||||
\(626\) | −37.8329 | + | 12.2063i | −1.51211 | + | 0.487863i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.0948 | + | 15.4042i | 0.442732 | + | 0.614693i | ||||
\(629\) | − | 0.0181826i | − | 0.000724989i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.7354i | − | 0.506987i | −0.967337 | − | 0.253493i | \(-0.918420\pi\) | ||
0.967337 | − | 0.253493i | \(-0.0815796\pi\) | |||||||
\(632\) | 38.9560 | + | 4.33865i | 1.54959 | + | 0.172582i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.72787 | − | 8.45489i | −0.108337 | − | 0.335787i | ||||
\(635\) | 1.72998 | + | 2.99641i | 0.0686521 | + | 0.118909i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.54753 | − | 8.06146i | 0.0613154 | − | 0.319407i | ||||
\(638\) | 1.41712 | + | 1.28129i | 0.0561045 | + | 0.0507269i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.17385 | + | 4.50395i | 0.125457 | + | 0.178034i | ||||
\(641\) | −22.4179 | + | 38.8289i | −0.885452 | + | 1.53365i | −0.0402575 | + | 0.999189i | \(0.512818\pi\) |
−0.845195 | + | 0.534459i | \(0.820515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.9324 | −0.983236 | −0.491618 | − | 0.870811i | \(-0.663594\pi\) | ||||
−0.491618 | + | 0.870811i | \(0.663594\pi\) | |||||||
\(644\) | 0.211986 | + | 36.8075i | 0.00835343 | + | 1.45042i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0655512 | − | 0.305292i | 0.00257908 | − | 0.0120116i | ||||
\(647\) | 23.4210 | − | 40.5664i | 0.920775 | − | 1.59483i | 0.122556 | − | 0.992462i | \(-0.460891\pi\) |
0.798219 | − | 0.602367i | \(-0.205776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.3562 | − | 10.5979i | 0.720543 | − | 0.416006i | ||||
\(650\) | 5.85892 | + | 5.29734i | 0.229806 | + | 0.207779i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.3760 | + | 2.76304i | −1.07213 | + | 0.108209i | ||||
\(653\) | 12.1952 | + | 21.1227i | 0.477236 | + | 0.826597i | 0.999660 | − | 0.0260892i | \(-0.00830540\pi\) |
−0.522424 | + | 0.852686i | \(0.674972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.19644 | − | 3.57751i | −0.242115 | − | 0.139785i | ||||
\(656\) | −0.416807 | + | 0.369105i | −0.0162736 | + | 0.0144111i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.9054 | − | 6.16007i | 1.08786 | − | 0.240144i | ||||
\(659\) | 36.2942i | 1.41382i | 0.707302 | + | 0.706911i | \(0.249912\pi\) | ||||
−0.707302 | + | 0.706911i | \(0.750088\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1034 | − | 9.87464i | −0.665244 | − | 0.384079i | 0.129028 | − | 0.991641i | \(-0.458814\pi\) |
−0.794272 | + | 0.607562i | \(0.792148\pi\) | |||||||
\(662\) | 26.7995 | − | 8.64653i | 1.04159 | − | 0.336057i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.4625 | − | 10.6452i | −0.561254 | − | 0.413113i | ||||
\(665\) | 3.55949 | − | 5.00252i | 0.138031 | − | 0.193989i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.80619 | + | 1.62015i | −0.108656 | + | 0.0627326i | ||||
\(668\) | 20.0862 | + | 9.04255i | 0.777158 | + | 0.349867i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.71511 | − | 0.582978i | −0.104894 | − | 0.0225224i | ||||
\(671\) | 40.3214 | 1.55659 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.01232 | −0.347399 | −0.173700 | − | 0.984799i | \(-0.555572\pi\) | ||||
−0.173700 | + | 0.984799i | \(0.555572\pi\) | |||||||
\(674\) | −37.9853 | − | 8.15606i | −1.46314 | − | 0.314160i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.2004 | + | 9.54417i | 0.815401 | + | 0.367083i | ||||
\(677\) | 14.1790 | − | 8.18626i | 0.544944 | − | 0.314624i | −0.202136 | − | 0.979357i | \(-0.564788\pi\) |
0.747080 | + | 0.664734i | \(0.231455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.4215 | + | 2.13262i | 0.860458 | + | 0.0818424i | ||||
\(680\) | −0.0514050 | − | 0.0378368i | −0.00197129 | − | 0.00145097i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.18476 | + | 1.35016i | −0.160243 | + | 0.0517003i | ||||
\(683\) | 18.9098 | + | 10.9176i | 0.723564 | + | 0.417750i | 0.816063 | − | 0.577963i | \(-0.196152\pi\) |
−0.0924991 | + | 0.995713i | \(0.529486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.81532i | 0.222192i | ||||||||
\(686\) | 12.4647 | − | 23.0354i | 0.475906 | − | 0.879496i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.3858 | − | 17.1671i | 0.739075 | − | 0.654491i | ||||
\(689\) | 10.2252 | + | 5.90353i | 0.389549 | + | 0.224906i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.17352 | + | 10.6929i | 0.234852 | + | 0.406775i | 0.959230 | − | 0.282628i | \(-0.0912062\pi\) |
−0.724378 | + | 0.689403i | \(0.757873\pi\) | |||||||
\(692\) | 34.9477 | − | 3.52725i | 1.32851 | − | 0.134086i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.93676 | + | 8.08018i | 0.339235 | + | 0.306719i | ||||
\(695\) | −3.96377 | + | 2.28848i | −0.150354 | + | 0.0868071i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.00322478 | − | 0.00558548i | 0.000122147 | − | 0.000211565i | ||||
\(698\) | −1.64304 | + | 7.65213i | −0.0621898 | + | 0.289637i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.7267 | + | 21.7531i | 0.481025 | + | 0.822188i | ||||
\(701\) | 31.7226 | 1.19815 | 0.599074 | − | 0.800694i | \(-0.295536\pi\) | ||||
0.599074 | + | 0.800694i | \(0.295536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.934867 | − | 1.61924i | 0.0352592 | − | 0.0610707i | ||||
\(704\) | 5.10451 | − | 22.6320i | 0.192383 | − | 0.852975i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.1290 | − | 16.3913i | −0.682293 | − | 0.616896i | ||||
\(707\) | 28.0294 | − | 39.3926i | 1.05415 | − | 1.48151i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7550 | − | 30.7526i | −0.666804 | − | 1.15494i | −0.978793 | − | 0.204852i | \(-0.934329\pi\) |
0.311989 | − | 0.950086i | \(-0.399005\pi\) | |||||||
\(710\) | −1.46990 | − | 4.55590i | −0.0551645 | − | 0.170980i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 29.7596 | + | 3.31442i | 1.11529 | + | 0.124213i | ||||
\(713\) | − | 7.45789i | − | 0.279300i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.65622i | 0.0619393i | ||||||||
\(716\) | 12.0896 | + | 16.7853i | 0.451809 | + | 0.627295i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.4424 | − | 10.4671i | 1.21074 | − | 0.390630i | ||||
\(719\) | 6.27192 | + | 10.8633i | 0.233903 | + | 0.405132i | 0.958953 | − | 0.283564i | \(-0.0915168\pi\) |
−0.725050 | + | 0.688696i | \(0.758183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.2649 | + | 19.7778i | −1.61127 | + | 0.736562i | ||||
\(722\) | 3.51354 | − | 3.88601i | 0.130760 | − | 0.144622i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.37223 | + | 20.8185i | −0.348316 | + | 0.773714i | ||||
\(725\) | −1.10932 | + | 1.92139i | −0.0411990 | + | 0.0713588i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.90679 | 0.330335 | 0.165167 | − | 0.986266i | \(-0.447184\pi\) | ||||
0.165167 | + | 0.986266i | \(0.447184\pi\) | |||||||
\(728\) | −6.54305 | − | 5.84777i | −0.242502 | − | 0.216733i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.55370 | − | 1.19247i | −0.205552 | − | 0.0441353i | ||||
\(731\) | −0.149985 | + | 0.259782i | −0.00554740 | + | 0.00960837i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.4986 | + | 8.37078i | −0.535519 | + | 0.309182i | −0.743261 | − | 0.669002i | \(-0.766722\pi\) |
0.207742 | + | 0.978184i | \(0.433388\pi\) | |||||||
\(734\) | 4.82934 | − | 5.34130i | 0.178254 | − | 0.197151i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33.8727 | + | 20.0256i | 1.24856 | + | 0.738155i | ||||
\(737\) | 5.84654 | + | 10.1265i | 0.215360 | + | 0.373015i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0208 | − | 11.5590i | −0.736476 | − | 0.425205i | 0.0843103 | − | 0.996440i | \(-0.473131\pi\) |
−0.820787 | + | 0.571235i | \(0.806465\pi\) | |||||||
\(740\) | −0.223373 | − | 0.310133i | −0.00821136 | − | 0.0114007i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.4265 | + | 27.7985i | 0.933437 | + | 1.02051i | ||||
\(743\) | − | 25.7365i | − | 0.944181i | −0.881550 | − | 0.472091i | \(-0.843499\pi\) | ||
0.881550 | − | 0.472091i | \(-0.156501\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.36479 | + | 3.09736i | 0.196551 | + | 0.113479i | ||||
\(746\) | 5.47451 | + | 16.9680i | 0.200436 | + | 0.621242i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.0269891 | + | 0.267405i | 0.000986818 | + | 0.00977729i | ||||
\(749\) | −5.34187 | − | 11.6856i | −0.195188 | − | 0.426983i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0832 | − | 11.0177i | 0.696355 | − | 0.402041i | −0.109633 | − | 0.993972i | \(-0.534968\pi\) |
0.805988 | + | 0.591931i | \(0.201634\pi\) | |||||||
\(752\) | 9.68028 | − | 28.9761i | 0.353003 | − | 1.05665i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.162176 | − | 0.755306i | 0.00590612 | − | 0.0275066i | ||||
\(755\) | −1.61831 | −0.0588962 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.29374 | −0.192404 | −0.0962021 | − | 0.995362i | \(-0.530670\pi\) | ||||
−0.0962021 | + | 0.995362i | \(0.530670\pi\) | |||||||
\(758\) | −3.59436 | + | 16.7400i | −0.130553 | + | 0.608025i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.63243 | − | 6.01252i | −0.0954883 | − | 0.218097i | ||||
\(761\) | 36.0460 | − | 20.8112i | 1.30667 | − | 0.754405i | 0.325129 | − | 0.945670i | \(-0.394592\pi\) |
0.981538 | + | 0.191265i | \(0.0612589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.1076 | − | 27.1150i | −1.37959 | − | 0.981630i | ||||
\(764\) | 29.0899 | − | 2.93604i | 1.05244 | − | 0.106222i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.561202 | + | 1.73942i | 0.0202771 | + | 0.0628477i | ||||
\(767\) | −7.42247 | − | 4.28537i | −0.268010 | − | 0.154736i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.29112i | 0.154742i | 0.997002 | + | 0.0773709i | \(0.0246526\pi\) | ||||
−0.997002 | + | 0.0773709i | \(0.975347\pi\) | |||||||
\(770\) | −1.59365 | + | 5.03855i | −0.0574310 | + | 0.181577i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.116277 | − | 0.0837488i | 0.00418491 | − | 0.00301418i | ||||
\(773\) | −40.4039 | − | 23.3272i | −1.45323 | − | 0.839021i | −0.454564 | − | 0.890714i | \(-0.650205\pi\) |
−0.998663 | + | 0.0516925i | \(0.983538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.55320 | − | 4.42228i | −0.0917138 | − | 0.158853i | ||||
\(776\) | 14.2730 | − | 19.3913i | 0.512370 | − | 0.696105i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.6073 | + | 31.6399i | −1.02562 | + | 1.13435i | ||||
\(779\) | 0.574359 | − | 0.331606i | 0.0205785 | − | 0.0118810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0786 | + | 17.4567i | −0.360642 | + | 0.624650i | ||||
\(782\) | −0.445682 | − | 0.0956951i | −0.0159376 | − | 0.00342205i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.2784 | − | 24.0858i | −0.509942 | − | 0.860209i | ||||
\(785\) | −4.62264 | −0.164989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1595 | + | 36.6493i | −0.754254 | + | 1.30641i | 0.191490 | + | 0.981495i | \(0.438668\pi\) |
−0.945744 | + | 0.324912i | \(0.894665\pi\) | |||||||
\(788\) | 3.48178 | + | 1.56745i | 0.124033 | + | 0.0558382i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.40124 | + | 7.07984i | −0.227746 | + | 0.251889i | ||||
\(791\) | −4.38197 | + | 46.0703i | −0.155805 | + | 1.63807i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.15216 | − | 14.1200i | −0.289492 | − | 0.501414i | ||||
\(794\) | 5.90714 | − | 1.90587i | 0.209637 | − | 0.0676367i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.947053 | − | 0.682115i | 0.0335674 | − | 0.0241769i | ||||
\(797\) | 7.72777i | 0.273732i | 0.990590 | + | 0.136866i | \(0.0437029\pi\) | ||||
−0.990590 | + | 0.136866i | \(0.956297\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.353906i | 0.0125203i | ||||||||
\(800\) | 26.9411 | + | 0.278232i | 0.952513 | + | 0.00983700i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.69804 | + | 17.6608i | 0.201205 | + | 0.623625i | ||||
\(803\) | 11.9590 | + | 20.7136i | 0.422023 | + | 0.730966i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.30294 | − | 5.19633i | −0.257395 | − | 0.183146i | ||||
\(806\) | 1.31888 | + | 1.19246i | 0.0464555 | + | 0.0420027i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.7292 | − | 47.3460i | −0.729251 | − | 1.66562i | ||||
\(809\) | 1.09641 | − | 1.89904i | 0.0385477 | − | 0.0667666i | −0.846108 | − | 0.533012i | \(-0.821060\pi\) |
0.884656 | + | 0.466245i | \(0.154394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.83311 | 0.169713 | 0.0848567 | − | 0.996393i | \(-0.472957\pi\) | ||||
0.0848567 | + | 0.996393i | \(0.472957\pi\) | |||||||
\(812\) | 1.22014 | − | 2.14173i | 0.0428185 | − | 0.0751601i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.337850 | + | 1.57347i | −0.0118416 | + | 0.0551502i | ||||
\(815\) | 3.35003 | − | 5.80242i | 0.117346 | − | 0.203250i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.7135 | + | 15.4231i | −0.934589 | + | 0.539585i | ||||
\(818\) | 16.7886 | + | 15.1794i | 0.587000 | + | 0.530737i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0136139 | − | 0.134885i | −0.000475418 | − | 0.00471040i | ||||
\(821\) | −19.6615 | − | 34.0547i | −0.686191 | − | 1.18852i | −0.973061 | − | 0.230548i | \(-0.925948\pi\) |
0.286870 | − | 0.957970i | \(-0.407385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.3558 | − | 7.71099i | −0.465555 | − | 0.268788i | 0.248822 | − | 0.968549i | \(-0.419956\pi\) |
−0.714377 | + | 0.699761i | \(0.753290\pi\) | |||||||
\(824\) | −5.62914 | + | 50.5431i | −0.196101 | + | 1.76075i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.4571 | − | 20.1789i | −0.642205 | − | 0.702114i | ||||
\(827\) | 10.7035i | 0.372196i | 0.982531 | + | 0.186098i | \(0.0595843\pi\) | ||||
−0.982531 | + | 0.186098i | \(0.940416\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.7020 | − | 13.6843i | −0.823203 | − | 0.475276i | 0.0283169 | − | 0.999599i | \(-0.490985\pi\) |
−0.851520 | + | 0.524323i | \(0.824319\pi\) | |||||||
\(830\) | 4.16158 | − | 1.34268i | 0.144451 | − | 0.0466052i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.95740 | + | 2.78820i | −0.310542 | + | 0.0966634i | ||||
\(833\) | 0.245294 | + | 0.212231i | 0.00849893 | + | 0.00735336i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.64525 | + | 2.68194i | −0.160756 | + | 0.0928123i | ||||
\(836\) | −11.3452 | + | 25.2011i | −0.392383 | + | 0.871599i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.2498 | + | 5.42153i | 0.872239 | + | 0.187284i | ||||
\(839\) | 9.67322 | 0.333957 | 0.166978 | − | 0.985961i | \(-0.446599\pi\) | ||||
0.166978 | + | 0.985961i | \(0.446599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7830 | −0.992518 | ||||||||
\(842\) | −31.3547 | − | 6.73237i | −1.08056 | − | 0.232013i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.01640 | + | 8.92161i | −0.138250 | + | 0.307095i | ||||
\(845\) | −4.90294 | + | 2.83071i | −0.168666 | + | 0.0973794i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.23132 | + | 2.84854i | −0.214111 | + | 0.0978769i | ||||
\(848\) | 39.4620 | − | 8.04775i | 1.35513 | − | 0.276361i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.297036 | + | 0.0958349i | −0.0101882 | + | 0.00328711i | ||||
\(851\) | −2.36385 | − | 1.36477i | −0.0810316 | − | 0.0467836i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.8757i | 1.39956i | 0.714359 | + | 0.699779i | \(0.246718\pi\) | ||||
−0.714359 | + | 0.699779i | \(0.753282\pi\) | |||||||
\(854\) | −11.2140 | − | 50.7997i | −0.383734 | − | 1.73833i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.6514 | − | 1.52040i | −0.466596 | − | 0.0519663i | ||||
\(857\) | −21.4624 | − | 12.3913i | −0.733141 | − | 0.423279i | 0.0864289 | − | 0.996258i | \(-0.472454\pi\) |
−0.819570 | + | 0.572979i | \(0.805788\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.84935 | + | 4.93522i | 0.0972185 | + | 0.168387i | 0.910532 | − | 0.413438i | \(-0.135672\pi\) |
−0.813314 | + | 0.581825i | \(0.802339\pi\) | |||||||
\(860\) | 0.633185 | + | 6.27354i | 0.0215914 | + | 0.213926i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.3891 | − | 22.9556i | −0.864755 | − | 0.781869i | ||||
\(863\) | −11.4093 | + | 6.58713i | −0.388375 | + | 0.224229i | −0.681456 | − | 0.731859i | \(-0.738653\pi\) |
0.293081 | + | 0.956088i | \(0.405320\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.27658 | + | 7.40726i | −0.145408 | + | 0.251854i | ||||
\(866\) | 9.21861 | − | 42.9339i | 0.313261 | − | 1.45895i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.86486 | + | 4.89674i | 0.0972398 | + | 0.166206i | ||||
\(869\) | 40.1896 | 1.36334 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.36410 | − | 4.09474i | 0.0801044 | − | 0.138745i | ||||
\(872\) | −45.8015 | + | 20.0530i | −1.55103 | + | 0.679081i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.7696 | − | 31.4369i | −1.17610 | − | 1.06337i | ||||
\(875\) | −12.5230 | − | 1.19112i | −0.423353 | − | 0.0402672i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.6431 | + | 25.3625i | 0.494461 | + | 0.856432i | 0.999980 | − | 0.00638414i | \(-0.00203215\pi\) |
−0.505519 | + | 0.862816i | \(0.668699\pi\) | |||||||
\(878\) | −15.3250 | − | 47.4992i | −0.517195 | − | 1.60302i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.74540 | + | 4.22944i | 0.126257 | + | 0.142574i | ||||
\(881\) | 41.7794i | 1.40758i | 0.710406 | + | 0.703792i | \(0.248511\pi\) | ||||
−0.710406 | + | 0.703792i | \(0.751489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.9004i | − | 0.535090i | −0.963545 | − | 0.267545i | \(-0.913788\pi\) | ||
0.963545 | − | 0.267545i | \(-0.0862124\pi\) | |||||||
\(884\) | 0.0881844 | − | 0.0635148i | 0.00296596 | − | 0.00213624i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.1804 | − | 6.51097i | 0.677975 | − | 0.218740i | ||||
\(887\) | −2.54513 | − | 4.40830i | −0.0854572 | − | 0.148016i | 0.820129 | − | 0.572179i | \(-0.193902\pi\) |
−0.905586 | + | 0.424163i | \(0.860568\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.7123 | − | 1.77982i | −0.627589 | − | 0.0596931i | ||||
\(890\) | −4.89009 | + | 5.40849i | −0.163916 | + | 0.181293i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.4439 | + | 15.0560i | 1.11978 | + | 0.504113i | ||||
\(893\) | −18.1962 | + | 31.5168i | −0.608913 | + | 1.05467i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.03710 | −0.168372 | ||||||||
\(896\) | −29.9329 | − | 0.136728i | −0.999990 | − | 0.00456777i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.13039 | + | 1.53101i | 0.237944 | + | 0.0510905i | ||||
\(899\) | −0.249714 | + | 0.432517i | −0.00832842 | + | 0.0144253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.404046 | + | 0.233276i | −0.0134607 | + | 0.00777156i | ||||
\(902\) | −0.382847 | + | 0.423432i | −0.0127474 | + | 0.0140987i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.8439 | + | 29.3272i | 1.32519 | + | 0.975409i | ||||
\(905\) | −2.77972 | − | 4.81461i | −0.0924009 | − | 0.160043i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.1139 | − | 17.3863i | −0.999916 | − | 0.577302i | −0.0916923 | − | 0.995787i | \(-0.529228\pi\) |
−0.908223 | + | 0.418486i | \(0.862561\pi\) | |||||||
\(908\) | 26.1472 | − | 18.8325i | 0.867724 | − | 0.624978i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.08662 | − | 0.460619i | 0.0691709 | − | 0.0152694i | ||||
\(911\) | − | 26.6242i | − | 0.882098i | −0.897483 | − | 0.441049i | \(-0.854606\pi\) | ||
0.897483 | − | 0.441049i | \(-0.145394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.9458 | − | 9.20632i | −0.527730 | − | 0.304685i | ||||
\(914\) | 11.0645 | + | 34.2939i | 0.365982 | + | 1.13434i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.7400 | − | 2.79979i | 0.916556 | − | 0.0925076i | ||||
\(917\) | 35.3521 | − | 16.1606i | 1.16743 | − | 0.533669i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.74511 | − | 1.00754i | 0.0575659 | − | 0.0332357i | −0.470941 | − | 0.882165i | \(-0.656085\pi\) |
0.528507 | + | 0.848929i | \(0.322752\pi\) | |||||||
\(920\) | −8.77740 | + | 3.84296i | −0.289382 | + | 0.126699i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.344966 | − | 1.60661i | 0.0113609 | − | 0.0529110i | ||||
\(923\) | 8.15076 | 0.268285 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.86891 | −0.0614494 | ||||||||
\(926\) | −6.92963 | + | 32.2734i | −0.227722 | + | 1.06057i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.29391 | − | 2.29554i | −0.0424747 | − | 0.0753549i | ||||
\(929\) | −30.2534 | + | 17.4668i | −0.992581 | + | 0.573067i | −0.906045 | − | 0.423182i | \(-0.860913\pi\) |
−0.0865362 | + | 0.996249i | \(0.527580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.9325 | + | 31.5119i | 0.358298 | + | 1.03276i | ||||
\(932\) | −0.733949 | − | 7.27189i | −0.0240413 | − | 0.238199i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.88631 | + | 24.4432i | 0.258048 | + | 0.799807i | ||||
\(935\) | −0.0566772 | − | 0.0327226i | −0.00185354 | − | 0.00107014i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.1738i | − | 1.47576i | −0.674931 | − | 0.737881i | \(-0.735826\pi\) | ||
0.674931 | − | 0.737881i | \(-0.264174\pi\) | |||||||
\(938\) | 11.1321 | − | 10.1822i | 0.363474 | − | 0.332460i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.34773 | + | 6.03641i | 0.141807 | + | 0.196886i | ||||
\(941\) | −0.227297 | − | 0.131230i | −0.00740966 | − | 0.00427797i | 0.496291 | − | 0.868156i | \(-0.334695\pi\) |
−0.503700 | + | 0.863878i | \(0.668028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.484096 | − | 0.838480i | −0.0157643 | − | 0.0273047i | ||||
\(944\) | −28.6455 | + | 5.84186i | −0.932330 | + | 0.190136i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.8063 | − | 19.6939i | 0.578931 | − | 0.640304i | ||||
\(947\) | 26.5793 | − | 15.3456i | 0.863711 | − | 0.498664i | −0.00154195 | − | 0.999999i | \(-0.500491\pi\) |
0.865253 | + | 0.501335i | \(0.167157\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.83572 | − | 8.37571i | 0.156974 | − | 0.271887i | ||||
\(950\) | −31.3796 | − | 6.73771i | −1.01809 | − | 0.218600i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.329389 | − | 0.108372i | 0.0106755 | − | 0.00351234i | ||||
\(953\) | −33.2031 | −1.07555 | −0.537777 | − | 0.843087i | \(-0.680736\pi\) | ||||
−0.537777 | + | 0.843087i | \(0.680736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.55977 | + | 6.16570i | −0.115191 | + | 0.199517i | ||||
\(956\) | −13.4005 | + | 29.7664i | −0.433402 | + | 0.962714i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.2750 | − | 11.3643i | 0.331971 | − | 0.367163i | ||||
\(959\) | −25.7413 | − | 18.3159i | −0.831230 | − | 0.591453i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9253 | + | 25.8513i | 0.481460 | + | 0.833913i | ||||
\(962\) | 0.619312 | − | 0.199814i | 0.0199674 | − | 0.00644225i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.13952 | − | 4.35893i | −0.101117 | − | 0.140392i | ||||
\(965\) | 0.0348938i | 0.00112327i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.4179i | − | 1.01033i | −0.863022 | − | 0.505166i | \(-0.831431\pi\) | ||
0.863022 | − | 0.505166i | \(-0.168569\pi\) | |||||||
\(968\) | −0.810750 | + | 7.27959i | −0.0260585 | + | 0.233975i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.80026 | + | 5.57983i | 0.0578030 | + | 0.179157i | ||||
\(971\) | −0.674219 | − | 1.16778i | −0.0216367 | − | 0.0374759i | 0.855004 | − | 0.518621i | \(-0.173554\pi\) |
−0.876641 | + | 0.481145i | \(0.840221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.35441 | − | 24.7533i | 0.0754788 | − | 0.793554i | ||||
\(974\) | 18.5709 | + | 16.7909i | 0.595048 | + | 0.538014i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −52.7488 | − | 17.6222i | −1.68845 | − | 0.564074i | ||||
\(977\) | −28.2780 | + | 48.9789i | −0.904694 | + | 1.56698i | −0.0833656 | + | 0.996519i | \(0.526567\pi\) |
−0.821328 | + | 0.570456i | \(0.806766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.7020 | 0.981240 | ||||||||
\(980\) | 6.79111 | + | 0.606492i | 0.216934 | + | 0.0193737i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.851532 | + | 3.96585i | −0.0271735 | + | 0.126555i | ||||
\(983\) | −25.5636 | + | 44.2775i | −0.815353 | + | 1.41223i | 0.0937214 | + | 0.995598i | \(0.470124\pi\) |
−0.909074 | + | 0.416634i | \(0.863210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.805216 | + | 0.464892i | −0.0256563 | + | 0.0148127i | ||||
\(986\) | 0.0226430 | + | 0.0204727i | 0.000721099 | + | 0.000651982i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.1188 | − | 1.12222i | 0.353737 | − | 0.0357025i | ||||
\(989\) | 22.5154 | + | 38.9978i | 0.715948 | + | 1.24006i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.61700 | + | 3.82033i | 0.210196 | + | 0.121357i | 0.601402 | − | 0.798946i | \(-0.294609\pi\) |
−0.391207 | + | 0.920303i | \(0.627942\pi\) | |||||||
\(992\) | 6.06461 | + | 0.0626317i | 0.192552 | + | 0.00198856i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.7961 | + | 7.84279i | 0.786485 | + | 0.248758i | ||||
\(995\) | 0.284202i | 0.00900981i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7883 | − | 7.96070i | −0.436681 | − | 0.252118i | 0.265508 | − | 0.964109i | \(-0.414460\pi\) |
−0.702189 | + | 0.711991i | \(0.747794\pi\) | |||||||
\(998\) | −38.2190 | + | 12.3309i | −1.20980 | + | 0.390328i | ||||
\(999\) | 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 | 756.2.bf.c.703.1 | yes | 32 | |
3.2 | odd | 2 | 756.2.bf.b.703.16 | yes | 32 | ||
4.3 | odd | 2 | 756.2.bf.b.703.11 | yes | 32 | ||
7.5 | odd | 6 | 756.2.bf.b.271.11 | ✓ | 32 | ||
12.11 | even | 2 | inner | 756.2.bf.c.703.6 | yes | 32 | |
21.5 | even | 6 | inner | 756.2.bf.c.271.6 | yes | 32 | |
28.19 | even | 6 | inner | 756.2.bf.c.271.1 | yes | 32 | |
84.47 | odd | 6 | 756.2.bf.b.271.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bf.b.271.11 | ✓ | 32 | 7.5 | odd | 6 | ||
756.2.bf.b.271.16 | yes | 32 | 84.47 | odd | 6 | ||
756.2.bf.b.703.11 | yes | 32 | 4.3 | odd | 2 | ||
756.2.bf.b.703.16 | yes | 32 | 3.2 | odd | 2 | ||
756.2.bf.c.271.1 | yes | 32 | 28.19 | even | 6 | inner | |
756.2.bf.c.271.6 | yes | 32 | 21.5 | even | 6 | inner | |
756.2.bf.c.703.1 | yes | 32 | 1.1 | even | 1 | trivial | |
756.2.bf.c.703.6 | yes | 32 | 12.11 | even | 2 | inner |