Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(67,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.x (of order \(12\), degree \(4\), 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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 67.5 | ||
Character | \(\chi\) | \(=\) | 980.67 |
Dual form | 980.2.x.j.863.5 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.702038 | + | 1.22766i | −0.496416 | + | 0.868085i | ||||
\(3\) | −2.07451 | + | 0.555863i | −1.19772 | + | 0.320928i | −0.801932 | − | 0.597415i | \(-0.796194\pi\) |
−0.395786 | + | 0.918343i | \(0.629528\pi\) | |||||||
\(4\) | −1.01428 | − | 1.72372i | −0.507142 | − | 0.861862i | ||||
\(5\) | −2.09358 | + | 0.785436i | −0.936279 | + | 0.351257i | ||||
\(6\) | 0.773975 | − | 2.93702i | 0.315974 | − | 1.19903i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.82821 | − | 0.0350723i | 0.999923 | − | 0.0123999i | ||||
\(9\) | 1.39652 | − | 0.806284i | 0.465508 | − | 0.268761i | ||||
\(10\) | 0.505530 | − | 3.12161i | 0.159863 | − | 0.987139i | ||||
\(11\) | 4.97765 | + | 2.87385i | 1.50082 | + | 0.866498i | 1.00000 | 0.000946947i | \(0.000301423\pi\) | |
0.500820 | + | 0.865552i | \(0.333032\pi\) | |||||||
\(12\) | 3.06230 | + | 3.01208i | 0.884009 | + | 0.869512i | ||||
\(13\) | 1.35121 | − | 1.35121i | 0.374758 | − | 0.374758i | −0.494449 | − | 0.869207i | \(-0.664630\pi\) |
0.869207 | + | 0.494449i | \(0.164630\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.90656 | − | 2.79314i | 1.00867 | − | 0.721185i | ||||
\(16\) | −1.94245 | + | 3.49669i | −0.485614 | + | 0.874174i | ||||
\(17\) | −4.35822 | + | 1.16778i | −1.05702 | + | 0.283229i | −0.745151 | − | 0.666895i | \(-0.767623\pi\) |
−0.311872 | + | 0.950124i | \(0.600956\pi\) | |||||||
\(18\) | 0.00942630 | + | 2.28049i | 0.00222180 | + | 0.537518i | ||||
\(19\) | 2.82966 | + | 4.90112i | 0.649170 | + | 1.12439i | 0.983322 | + | 0.181875i | \(0.0582168\pi\) |
−0.334152 | + | 0.942519i | \(0.608450\pi\) | |||||||
\(20\) | 3.47736 | + | 2.81211i | 0.777562 | + | 0.628806i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.02261 | + | 4.09330i | −1.49722 | + | 0.872695i | ||||
\(23\) | −0.721544 | + | 2.69284i | −0.150452 | + | 0.561496i | 0.849000 | + | 0.528393i | \(0.177205\pi\) |
−0.999452 | + | 0.0331023i | \(0.989461\pi\) | |||||||
\(24\) | −5.84765 | + | 1.64485i | −1.19365 | + | 0.335754i | ||||
\(25\) | 3.76618 | − | 3.28875i | 0.753236 | − | 0.657750i | ||||
\(26\) | 0.710221 | + | 2.60742i | 0.139286 | + | 0.511358i | ||||
\(27\) | 2.10702 | − | 2.10702i | 0.405496 | − | 0.405496i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.11400i | 0.949645i | 0.880081 | + | 0.474823i | \(0.157488\pi\) | ||||
−0.880081 | + | 0.474823i | \(0.842512\pi\) | |||||||
\(30\) | 0.686459 | + | 6.75681i | 0.125330 | + | 1.23362i | ||||
\(31\) | 6.52468 | + | 3.76703i | 1.17187 | + | 0.676578i | 0.954119 | − | 0.299427i | \(-0.0967956\pi\) |
0.217748 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(32\) | −2.92906 | − | 4.83948i | −0.517790 | − | 0.855508i | ||||
\(33\) | −11.9237 | − | 3.19493i | −2.07564 | − | 0.556166i | ||||
\(34\) | 1.62600 | − | 6.17023i | 0.278857 | − | 1.05819i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.80628 | − | 1.58942i | −0.467714 | − | 0.264904i | ||||
\(37\) | 0.683717 | − | 2.55167i | 0.112402 | − | 0.419491i | −0.886677 | − | 0.462389i | \(-0.846992\pi\) |
0.999079 | + | 0.0428978i | \(0.0136590\pi\) | |||||||
\(38\) | −8.00343 | + | 0.0330817i | −1.29833 | + | 0.00536657i | ||||
\(39\) | −2.05201 | + | 3.55418i | −0.328584 | + | 0.569125i | ||||
\(40\) | −5.89355 | + | 2.29480i | −0.931851 | + | 0.362840i | ||||
\(41\) | −3.28498 | −0.513027 | −0.256514 | − | 0.966541i | \(-0.582574\pi\) | ||||
−0.256514 | + | 0.966541i | \(0.582574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.72840 | − | 4.72840i | −0.721075 | − | 0.721075i | 0.247749 | − | 0.968824i | \(-0.420309\pi\) |
−0.968824 | + | 0.247749i | \(0.920309\pi\) | |||||||
\(44\) | −0.0950296 | − | 11.4950i | −0.0143263 | − | 1.73294i | ||||
\(45\) | −2.29046 | + | 2.78490i | −0.341441 | + | 0.415149i | ||||
\(46\) | −2.79933 | − | 2.77628i | −0.412739 | − | 0.409341i | ||||
\(47\) | −5.43916 | − | 1.45742i | −0.793383 | − | 0.212586i | −0.160706 | − | 0.987002i | \(-0.551377\pi\) |
−0.632677 | + | 0.774416i | \(0.718044\pi\) | |||||||
\(48\) | 2.08596 | − | 8.33366i | 0.301082 | − | 1.20286i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.39345 | + | 6.93241i | 0.197064 | + | 0.980391i | ||||
\(51\) | 8.39204 | − | 4.84515i | 1.17512 | − | 0.678456i | ||||
\(52\) | −3.69962 | − | 0.958603i | −0.513045 | − | 0.132934i | ||||
\(53\) | 0.224215 | + | 0.836782i | 0.0307983 | + | 0.114941i | 0.979614 | − | 0.200890i | \(-0.0643834\pi\) |
−0.948815 | + | 0.315831i | \(0.897717\pi\) | |||||||
\(54\) | 1.10749 | + | 4.06590i | 0.150710 | + | 0.553299i | ||||
\(55\) | −12.6784 | − | 2.10702i | −1.70955 | − | 0.284110i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.59451 | − | 8.59451i | −1.13837 | − | 1.13837i | ||||
\(58\) | −6.27823 | − | 3.59022i | −0.824373 | − | 0.471419i | ||||
\(59\) | −2.45601 | + | 4.25393i | −0.319745 | + | 0.553814i | −0.980435 | − | 0.196845i | \(-0.936930\pi\) |
0.660690 | + | 0.750659i | \(0.270264\pi\) | |||||||
\(60\) | −8.77696 | − | 3.90080i | −1.13310 | − | 0.503591i | ||||
\(61\) | −7.67737 | − | 13.2976i | −0.982987 | − | 1.70258i | −0.650561 | − | 0.759454i | \(-0.725466\pi\) |
−0.332425 | − | 0.943130i | \(-0.607867\pi\) | |||||||
\(62\) | −9.20519 | + | 5.36547i | −1.16906 | + | 0.681416i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.99754 | − | 0.198384i | 0.999692 | − | 0.0247980i | ||||
\(65\) | −1.76758 | + | 3.89016i | −0.219242 | + | 0.482515i | ||||
\(66\) | 12.2931 | − | 12.3952i | 1.51318 | − | 1.52574i | ||||
\(67\) | −0.0590861 | − | 0.220512i | −0.00721851 | − | 0.0269398i | 0.962223 | − | 0.272264i | \(-0.0877723\pi\) |
−0.969441 | + | 0.245324i | \(0.921106\pi\) | |||||||
\(68\) | 6.43341 | + | 6.32791i | 0.780165 | + | 0.767372i | ||||
\(69\) | − | 5.98740i | − | 0.720798i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.54768i | 0.421032i | 0.977590 | + | 0.210516i | \(0.0675144\pi\) | ||||
−0.977590 | + | 0.210516i | \(0.932486\pi\) | |||||||
\(72\) | 3.92138 | − | 2.32932i | 0.462140 | − | 0.274513i | ||||
\(73\) | 3.22954 | + | 12.0528i | 0.377989 | + | 1.41067i | 0.848929 | + | 0.528507i | \(0.177248\pi\) |
−0.470940 | + | 0.882165i | \(0.656085\pi\) | |||||||
\(74\) | 2.65258 | + | 2.63074i | 0.308356 | + | 0.305817i | ||||
\(75\) | −5.98488 | + | 8.91602i | −0.691075 | + | 1.02953i | ||||
\(76\) | 5.57810 | − | 9.84869i | 0.639852 | − | 1.12972i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.92273 | − | 5.01433i | −0.330934 | − | 0.567762i | ||||
\(79\) | −1.89058 | − | 3.27458i | −0.212707 | − | 0.368419i | 0.739854 | − | 0.672768i | \(-0.234895\pi\) |
−0.952561 | + | 0.304348i | \(0.901561\pi\) | |||||||
\(80\) | 1.32026 | − | 8.84629i | 0.147610 | − | 0.989046i | ||||
\(81\) | −5.61866 | + | 9.73181i | −0.624296 | + | 1.08131i | ||||
\(82\) | 2.30618 | − | 4.03282i | 0.254675 | − | 0.445351i | ||||
\(83\) | 8.12242 | + | 8.12242i | 0.891552 | + | 0.891552i | 0.994669 | − | 0.103117i | \(-0.0328817\pi\) |
−0.103117 | + | 0.994669i | \(0.532882\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.20708 | − | 5.86795i | 0.890183 | − | 0.636468i | ||||
\(86\) | 9.12438 | − | 2.48534i | 0.983907 | − | 0.268001i | ||||
\(87\) | −2.84268 | − | 10.6090i | −0.304767 | − | 1.13741i | ||||
\(88\) | 14.1786 | + | 7.95327i | 1.51145 | + | 0.847822i | ||||
\(89\) | −6.91145 | + | 3.99033i | −0.732613 | + | 0.422974i | −0.819377 | − | 0.573255i | \(-0.805681\pi\) |
0.0867646 | + | 0.996229i | \(0.472347\pi\) | |||||||
\(90\) | −1.81092 | − | 4.76700i | −0.190887 | − | 0.502486i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.37356 | − | 1.48756i | 0.560233 | − | 0.155089i | ||||
\(93\) | −15.6294 | − | 4.18790i | −1.62070 | − | 0.434265i | ||||
\(94\) | 5.60771 | − | 5.65426i | 0.578391 | − | 0.583192i | ||||
\(95\) | −9.77365 | − | 8.03839i | −1.00276 | − | 0.824721i | ||||
\(96\) | 8.76645 | + | 8.41139i | 0.894722 | + | 0.858484i | ||||
\(97\) | −6.28634 | − | 6.28634i | −0.638281 | − | 0.638281i | 0.311850 | − | 0.950131i | \(-0.399051\pi\) |
−0.950131 | + | 0.311850i | \(0.899051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.26855 | 0.931525 | ||||||||
\(100\) | −9.48888 | − | 3.15614i | −0.948888 | − | 0.315614i | ||||
\(101\) | −1.78452 | + | 3.09087i | −0.177566 | + | 0.307553i | −0.941046 | − | 0.338278i | \(-0.890156\pi\) |
0.763480 | + | 0.645831i | \(0.223489\pi\) | |||||||
\(102\) | 0.0566448 | + | 13.7040i | 0.00560867 | + | 1.35690i | ||||
\(103\) | −0.188510 | + | 0.703531i | −0.0185745 | + | 0.0693209i | −0.974591 | − | 0.223992i | \(-0.928091\pi\) |
0.956017 | + | 0.293313i | \(0.0947577\pi\) | |||||||
\(104\) | 3.77411 | − | 3.86889i | 0.370082 | − | 0.379376i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.18469 | − | 0.312194i | −0.115067 | − | 0.0303230i | ||||
\(107\) | −5.60619 | − | 1.50217i | −0.541971 | − | 0.145221i | −0.0225603 | − | 0.999745i | \(-0.507182\pi\) |
−0.519411 | + | 0.854525i | \(0.673848\pi\) | |||||||
\(108\) | −5.76904 | − | 1.49480i | −0.555126 | − | 0.143838i | ||||
\(109\) | −10.0311 | − | 5.79147i | −0.960807 | − | 0.554722i | −0.0643855 | − | 0.997925i | \(-0.520509\pi\) |
−0.896421 | + | 0.443203i | \(0.853842\pi\) | |||||||
\(110\) | 11.4874 | − | 14.0855i | 1.09528 | − | 1.34300i | ||||
\(111\) | 5.67351i | 0.538505i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.10242 | + | 7.10242i | −0.668139 | + | 0.668139i | −0.957285 | − | 0.289146i | \(-0.906629\pi\) |
0.289146 | + | 0.957285i | \(0.406629\pi\) | |||||||
\(114\) | 16.5848 | − | 4.51744i | 1.55331 | − | 0.423097i | ||||
\(115\) | −0.604439 | − | 6.20441i | −0.0563642 | − | 0.578564i | ||||
\(116\) | 8.81512 | − | 5.18705i | 0.818464 | − | 0.481605i | ||||
\(117\) | 0.797539 | − | 2.97645i | 0.0737325 | − | 0.275173i | ||||
\(118\) | −3.49815 | − | 6.00155i | −0.322031 | − | 0.552488i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 10.9506 | − | 8.03659i | 0.999650 | − | 0.733637i | ||||
\(121\) | 11.0180 | + | 19.0838i | 1.00164 | + | 1.73489i | ||||
\(122\) | 21.7147 | − | 0.0897565i | 1.96596 | − | 0.00812617i | ||||
\(123\) | 6.81471 | − | 1.82600i | 0.614462 | − | 0.164645i | ||||
\(124\) | −0.124564 | − | 15.0676i | −0.0111862 | − | 1.35311i | ||||
\(125\) | −5.30172 | + | 9.84336i | −0.474200 | + | 0.880417i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3246 | + | 14.3246i | −1.27110 | + | 1.27110i | −0.325588 | + | 0.945512i | \(0.605562\pi\) |
−0.945512 | + | 0.325588i | \(0.894438\pi\) | |||||||
\(128\) | −5.37103 | + | 9.95751i | −0.474737 | + | 0.880128i | ||||
\(129\) | 12.4375 | + | 7.18077i | 1.09506 | + | 0.632231i | ||||
\(130\) | −3.53487 | − | 4.90102i | −0.310029 | − | 0.429848i | ||||
\(131\) | 13.8113 | − | 7.97397i | 1.20670 | − | 0.696689i | 0.244664 | − | 0.969608i | \(-0.421322\pi\) |
0.962037 | + | 0.272919i | \(0.0879890\pi\) | |||||||
\(132\) | 6.58679 | + | 23.7937i | 0.573306 | + | 2.07097i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.312194 | + | 0.0822706i | 0.0269695 | + | 0.00710709i | ||||
\(135\) | −2.75629 | + | 6.06615i | −0.237224 | + | 0.522091i | ||||
\(136\) | −12.2850 | + | 3.45558i | −1.05343 | + | 0.296314i | ||||
\(137\) | −3.69599 | + | 0.990337i | −0.315770 | + | 0.0846102i | −0.413223 | − | 0.910630i | \(-0.635597\pi\) |
0.0974534 | + | 0.995240i | \(0.468930\pi\) | |||||||
\(138\) | 7.35047 | + | 4.20338i | 0.625713 | + | 0.357816i | ||||
\(139\) | −9.12605 | −0.774061 | −0.387031 | − | 0.922067i | \(-0.626499\pi\) | ||||
−0.387031 | + | 0.922067i | \(0.626499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0937 | 1.01847 | ||||||||
\(142\) | −4.35534 | − | 2.49061i | −0.365492 | − | 0.209007i | ||||
\(143\) | 10.6090 | − | 2.84268i | 0.887171 | − | 0.237717i | ||||
\(144\) | 0.106642 | + | 6.44939i | 0.00888682 | + | 0.537449i | ||||
\(145\) | −4.01671 | − | 10.7066i | −0.333570 | − | 0.889133i | ||||
\(146\) | −17.0640 | − | 4.49676i | −1.41222 | − | 0.372154i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.09185 | + | 1.40958i | −0.418548 | + | 0.115866i | ||||
\(149\) | 12.4830 | − | 7.20708i | 1.02265 | − | 0.590427i | 0.107779 | − | 0.994175i | \(-0.465626\pi\) |
0.914870 | + | 0.403748i | \(0.132293\pi\) | |||||||
\(150\) | −6.74420 | − | 13.6068i | −0.550661 | − | 1.11099i | ||||
\(151\) | −13.0509 | − | 7.53495i | −1.06207 | − | 0.613186i | −0.136065 | − | 0.990700i | \(-0.543446\pi\) |
−0.926004 | + | 0.377514i | \(0.876779\pi\) | |||||||
\(152\) | 8.17478 | + | 13.7622i | 0.663062 | + | 1.11626i | ||||
\(153\) | −5.14480 | + | 5.14480i | −0.415932 | + | 0.415932i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6187 | − | 2.76187i | −1.33485 | − | 0.221838i | ||||
\(156\) | 8.20775 | − | 0.0678537i | 0.657146 | − | 0.00543265i | ||||
\(157\) | −2.18067 | + | 0.584308i | −0.174036 | + | 0.0466328i | −0.344785 | − | 0.938682i | \(-0.612048\pi\) |
0.170749 | + | 0.985315i | \(0.445381\pi\) | |||||||
\(158\) | 5.34733 | − | 0.0221029i | 0.425410 | − | 0.00175841i | ||||
\(159\) | −0.930272 | − | 1.61128i | −0.0737754 | − | 0.127783i | ||||
\(160\) | 9.93334 | + | 7.83127i | 0.785299 | + | 0.619116i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −8.00281 | − | 13.7299i | −0.628760 | − | 1.07872i | ||||
\(163\) | −4.23398 | + | 15.8014i | −0.331631 | + | 1.23766i | 0.575844 | + | 0.817559i | \(0.304673\pi\) |
−0.907475 | + | 0.420105i | \(0.861993\pi\) | |||||||
\(164\) | 3.33190 | + | 5.66240i | 0.260178 | + | 0.442159i | ||||
\(165\) | 27.4726 | − | 2.67640i | 2.13874 | − | 0.208358i | ||||
\(166\) | −15.6738 | + | 4.26930i | −1.21652 | + | 0.331362i | ||||
\(167\) | 12.2631 | − | 12.2631i | 0.948948 | − | 0.948948i | −0.0498110 | − | 0.998759i | \(-0.515862\pi\) |
0.998759 | + | 0.0498110i | \(0.0158619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.34847i | 0.719113i | ||||||||
\(170\) | 1.44214 | + | 14.1950i | 0.110607 | + | 1.08871i | ||||
\(171\) | 7.90339 | + | 4.56302i | 0.604387 | + | 0.348943i | ||||
\(172\) | −3.35452 | + | 12.9464i | −0.255780 | + | 0.987155i | ||||
\(173\) | 12.8971 | + | 3.45575i | 0.980545 | + | 0.262736i | 0.713274 | − | 0.700885i | \(-0.247212\pi\) |
0.267271 | + | 0.963621i | \(0.413878\pi\) | |||||||
\(174\) | 15.0199 | + | 3.95811i | 1.13866 | + | 0.300063i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.7178 | + | 11.8230i | −1.48629 | + | 0.891193i | ||||
\(177\) | 2.73040 | − | 10.1900i | 0.205230 | − | 0.765928i | ||||
\(178\) | −0.0466511 | − | 11.2863i | −0.00349665 | − | 0.845941i | ||||
\(179\) | 4.82253 | − | 8.35287i | 0.360453 | − | 0.624323i | −0.627583 | − | 0.778550i | \(-0.715956\pi\) |
0.988035 | + | 0.154227i | \(0.0492888\pi\) | |||||||
\(180\) | 7.12358 | + | 1.12343i | 0.530960 | + | 0.0837358i | ||||
\(181\) | −2.19951 | −0.163488 | −0.0817440 | − | 0.996653i | \(-0.526049\pi\) | ||||
−0.0817440 | + | 0.996653i | \(0.526049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.3184 | + | 23.3184i | 1.72375 | + | 1.72375i | ||||
\(184\) | −1.94623 | + | 7.64122i | −0.143478 | + | 0.563318i | ||||
\(185\) | 0.572751 | + | 5.87914i | 0.0421095 | + | 0.432243i | ||||
\(186\) | 16.1138 | − | 16.2475i | 1.18152 | − | 1.19133i | ||||
\(187\) | −25.0497 | − | 6.71206i | −1.83182 | − | 0.490834i | ||||
\(188\) | 3.00466 | + | 10.8538i | 0.219138 | + | 0.791598i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.7299 | − | 6.35544i | 1.21371 | − | 0.461072i | ||||
\(191\) | −9.97854 | + | 5.76111i | −0.722022 | + | 0.416860i | −0.815496 | − | 0.578762i | \(-0.803536\pi\) |
0.0934744 | + | 0.995622i | \(0.470203\pi\) | |||||||
\(192\) | −16.4807 | + | 4.85708i | −1.18939 | + | 0.350530i | ||||
\(193\) | −1.06401 | − | 3.97092i | −0.0765888 | − | 0.285833i | 0.917000 | − | 0.398887i | \(-0.130603\pi\) |
−0.993589 | + | 0.113054i | \(0.963937\pi\) | |||||||
\(194\) | 12.1307 | − | 3.30422i | 0.870935 | − | 0.237229i | ||||
\(195\) | 1.50447 | − | 9.05270i | 0.107737 | − | 0.648277i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.24605 | + | 1.24605i | 0.0887772 | + | 0.0887772i | 0.750101 | − | 0.661324i | \(-0.230005\pi\) |
−0.661324 | + | 0.750101i | \(0.730005\pi\) | |||||||
\(198\) | −6.50688 | + | 11.3786i | −0.462424 | + | 0.808642i | ||||
\(199\) | −2.10702 | + | 3.64946i | −0.149363 | + | 0.258704i | −0.930992 | − | 0.365039i | \(-0.881055\pi\) |
0.781629 | + | 0.623743i | \(0.214389\pi\) | |||||||
\(200\) | 10.5362 | − | 9.43336i | 0.745022 | − | 0.667039i | ||||
\(201\) | 0.245149 | + | 0.424610i | 0.0172915 | + | 0.0299497i | ||||
\(202\) | −2.54173 | − | 4.36068i | −0.178836 | − | 0.306817i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.8636 | − | 9.55121i | −1.18069 | − | 0.668718i | ||||
\(205\) | 6.87737 | − | 2.58014i | 0.480336 | − | 0.180205i | ||||
\(206\) | −0.731353 | − | 0.725332i | −0.0509558 | − | 0.0505362i | ||||
\(207\) | 1.16354 | + | 4.34238i | 0.0808715 | + | 0.301817i | ||||
\(208\) | 2.10010 | + | 7.34943i | 0.145616 | + | 0.509591i | ||||
\(209\) | 32.5281i | 2.25002i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.6715i | − | 1.07887i | −0.842028 | − | 0.539434i | \(-0.818638\pi\) | ||
0.842028 | − | 0.539434i | \(-0.181362\pi\) | |||||||
\(212\) | 1.21496 | − | 1.23522i | 0.0834441 | − | 0.0848353i | ||||
\(213\) | −1.97202 | − | 7.35969i | −0.135121 | − | 0.504278i | ||||
\(214\) | 5.77991 | − | 5.82790i | 0.395107 | − | 0.398387i | ||||
\(215\) | 13.6132 | + | 6.18545i | 0.928410 | + | 0.421844i | ||||
\(216\) | 5.88519 | − | 6.03299i | 0.400437 | − | 0.410493i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.1522 | − | 8.24894i | 0.958506 | − | 0.558689i | ||||
\(219\) | −13.3994 | − | 23.2084i | −0.905447 | − | 1.56828i | ||||
\(220\) | 9.22754 | + | 23.9911i | 0.622121 | + | 1.61748i | ||||
\(221\) | −4.31095 | + | 7.46679i | −0.289986 | + | 0.502270i | ||||
\(222\) | −6.96512 | − | 3.98302i | −0.467468 | − | 0.267323i | ||||
\(223\) | 13.8409 | + | 13.8409i | 0.926857 | + | 0.926857i | 0.997502 | − | 0.0706444i | \(-0.0225056\pi\) |
−0.0706444 | + | 0.997502i | \(0.522506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.60790 | − | 7.62943i | 0.173860 | − | 0.508629i | ||||
\(226\) | −3.73316 | − | 13.7055i | −0.248326 | − | 0.911677i | ||||
\(227\) | 1.51560 | + | 5.65628i | 0.100594 | + | 0.375420i | 0.997808 | − | 0.0661747i | \(-0.0210795\pi\) |
−0.897214 | + | 0.441595i | \(0.854413\pi\) | |||||||
\(228\) | −6.09730 | + | 23.5319i | −0.403803 | + | 1.55844i | ||||
\(229\) | 16.6826 | − | 9.63173i | 1.10242 | − | 0.636483i | 0.165565 | − | 0.986199i | \(-0.447055\pi\) |
0.936856 | + | 0.349716i | \(0.113722\pi\) | |||||||
\(230\) | 8.04123 | + | 3.61369i | 0.530223 | + | 0.238280i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.179360 | + | 14.4635i | 0.0117756 | + | 0.949572i | ||||
\(233\) | −25.6962 | − | 6.88528i | −1.68341 | − | 0.451070i | −0.714737 | − | 0.699393i | \(-0.753454\pi\) |
−0.968677 | + | 0.248323i | \(0.920120\pi\) | |||||||
\(234\) | 3.09416 | + | 3.06869i | 0.202272 | + | 0.200606i | ||||
\(235\) | 12.5320 | − | 1.22088i | 0.817500 | − | 0.0796415i | ||||
\(236\) | 9.82369 | − | 0.0812127i | 0.639468 | − | 0.00528650i | ||||
\(237\) | 5.74225 | + | 5.74225i | 0.372999 | + | 0.372999i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.48226 | −0.0958794 | −0.0479397 | − | 0.998850i | \(-0.515266\pi\) | ||||
−0.0479397 | + | 0.998850i | \(0.515266\pi\) | |||||||
\(240\) | 2.17843 | + | 19.0856i | 0.140617 | + | 1.23197i | ||||
\(241\) | −6.80218 | + | 11.7817i | −0.438167 | + | 0.758927i | −0.997548 | − | 0.0699833i | \(-0.977705\pi\) |
0.559381 | + | 0.828910i | \(0.311039\pi\) | |||||||
\(242\) | −31.1634 | + | 0.128812i | −2.00326 | + | 0.00828037i | ||||
\(243\) | 3.93275 | − | 14.6772i | 0.252286 | − | 0.941543i | ||||
\(244\) | −15.1344 | + | 26.7212i | −0.968878 | + | 1.71065i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.54249 | + | 9.64805i | −0.162103 | + | 0.615137i | ||||
\(247\) | 10.4459 | + | 2.79897i | 0.664657 | + | 0.178094i | ||||
\(248\) | 18.5853 | + | 10.4251i | 1.18017 | + | 0.661995i | ||||
\(249\) | −21.3650 | − | 12.3351i | −1.35395 | − | 0.781704i | ||||
\(250\) | −8.36227 | − | 13.4191i | −0.528876 | − | 0.848699i | ||||
\(251\) | 21.2752i | 1.34288i | 0.741059 | + | 0.671440i | \(0.234324\pi\) | ||||
−0.741059 | + | 0.671440i | \(0.765676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3304 | + | 11.3304i | −0.712337 | + | 0.712337i | ||||
\(254\) | −7.52926 | − | 27.6421i | −0.472428 | − | 1.73442i | ||||
\(255\) | −13.7639 | + | 16.7351i | −0.861928 | + | 1.04799i | ||||
\(256\) | −8.45374 | − | 13.5843i | −0.528359 | − | 0.849021i | ||||
\(257\) | −3.55302 | + | 13.2601i | −0.221631 | + | 0.827140i | 0.762095 | + | 0.647466i | \(0.224171\pi\) |
−0.983726 | + | 0.179674i | \(0.942496\pi\) | |||||||
\(258\) | −17.5471 | + | 10.2278i | −1.09243 | + | 0.636752i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.49839 | − | 0.898901i | 0.527048 | − | 0.0557475i | ||||
\(261\) | 4.12333 | + | 7.14182i | 0.255228 | + | 0.442068i | ||||
\(262\) | 0.0932241 | + | 22.5536i | 0.00575940 | + | 1.39337i | ||||
\(263\) | −13.6782 | + | 3.66506i | −0.843434 | + | 0.225998i | −0.654566 | − | 0.756005i | \(-0.727149\pi\) |
−0.188868 | + | 0.982002i | \(0.560482\pi\) | |||||||
\(264\) | −33.8346 | − | 8.61775i | −2.08238 | − | 0.530386i | ||||
\(265\) | −1.12665 | − | 1.57577i | −0.0692097 | − | 0.0967986i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1198 | − | 12.1198i | 0.741719 | − | 0.741719i | ||||
\(268\) | −0.320172 | + | 0.325510i | −0.0195576 | + | 0.0198837i | ||||
\(269\) | −18.0324 | − | 10.4110i | −1.09946 | − | 0.634772i | −0.163379 | − | 0.986563i | \(-0.552239\pi\) |
−0.936078 | + | 0.351792i | \(0.885573\pi\) | |||||||
\(270\) | −5.51212 | − | 7.64245i | −0.335457 | − | 0.465105i | ||||
\(271\) | −10.1496 | + | 5.85987i | −0.616544 | + | 0.355962i | −0.775522 | − | 0.631320i | \(-0.782513\pi\) |
0.158979 | + | 0.987282i | \(0.449180\pi\) | |||||||
\(272\) | 4.38227 | − | 17.5077i | 0.265714 | − | 1.06156i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.37893 | − | 5.23266i | 0.0833043 | − | 0.316117i | ||||
\(275\) | 28.1981 | − | 5.54682i | 1.70041 | − | 0.334486i | ||||
\(276\) | −10.3206 | + | 6.07292i | −0.621228 | + | 0.365547i | ||||
\(277\) | 1.68632 | − | 0.451847i | 0.101321 | − | 0.0271489i | −0.207802 | − | 0.978171i | \(-0.566631\pi\) |
0.309123 | + | 0.951022i | \(0.399964\pi\) | |||||||
\(278\) | 6.40684 | − | 11.2037i | 0.384256 | − | 0.671951i | ||||
\(279\) | 12.1492 | 0.727351 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3578 | 0.975825 | 0.487912 | − | 0.872893i | \(-0.337759\pi\) | ||||
0.487912 | + | 0.872893i | \(0.337759\pi\) | |||||||
\(282\) | −8.49024 | + | 14.8469i | −0.505587 | + | 0.884121i | ||||
\(283\) | 4.63542 | − | 1.24206i | 0.275547 | − | 0.0738327i | −0.118399 | − | 0.992966i | \(-0.537776\pi\) |
0.393946 | + | 0.919133i | \(0.371110\pi\) | |||||||
\(284\) | 6.11523 | − | 3.59836i | 0.362872 | − | 0.213523i | ||||
\(285\) | 24.7438 | + | 11.2429i | 1.46569 | + | 0.665972i | ||||
\(286\) | −3.95811 | + | 15.0199i | −0.234048 | + | 0.888146i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.99250 | − | 4.39680i | −0.470963 | − | 0.259084i | ||||
\(289\) | 2.90794 | − | 1.67890i | 0.171055 | − | 0.0987589i | ||||
\(290\) | 15.9639 | + | 2.58528i | 0.937432 | + | 0.151813i | ||||
\(291\) | 16.5354 | + | 9.54672i | 0.969323 | + | 0.559639i | ||||
\(292\) | 17.5000 | − | 17.7918i | 1.02411 | − | 1.04119i | ||||
\(293\) | 3.45390 | − | 3.45390i | 0.201779 | − | 0.201779i | −0.598983 | − | 0.800762i | \(-0.704428\pi\) |
0.800762 | + | 0.598983i | \(0.204428\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.80067 | − | 10.8350i | 0.104839 | − | 0.630837i | ||||
\(296\) | 1.84420 | − | 7.24063i | 0.107192 | − | 0.420853i | ||||
\(297\) | 16.5433 | − | 4.43275i | 0.959938 | − | 0.257215i | ||||
\(298\) | 0.0842583 | + | 20.3845i | 0.00488095 | + | 1.18084i | ||||
\(299\) | 2.66363 | + | 4.61355i | 0.154042 | + | 0.266808i | ||||
\(300\) | 21.4391 | + | 1.27291i | 1.23779 | + | 0.0734917i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.4126 | − | 10.7322i | 1.05953 | − | 0.617571i | ||||
\(303\) | 1.98389 | − | 7.40398i | 0.113972 | − | 0.425348i | ||||
\(304\) | −22.6342 | + | 0.374261i | −1.29816 | + | 0.0214654i | ||||
\(305\) | 26.5176 | + | 21.8096i | 1.51839 | + | 1.24881i | ||||
\(306\) | −2.70420 | − | 9.92789i | −0.154589 | − | 0.567540i | ||||
\(307\) | 9.46795 | − | 9.46795i | 0.540364 | − | 0.540364i | −0.383271 | − | 0.923636i | \(-0.625203\pi\) |
0.923636 | + | 0.383271i | \(0.125203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.56427i | − | 0.0889880i | ||||||
\(310\) | 15.0576 | − | 18.4631i | 0.855214 | − | 1.04864i | ||||
\(311\) | −20.2933 | − | 11.7163i | −1.15073 | − | 0.664372i | −0.201662 | − | 0.979455i | \(-0.564634\pi\) |
−0.949064 | + | 0.315083i | \(0.897968\pi\) | |||||||
\(312\) | −5.67885 | + | 10.1239i | −0.321502 | + | 0.573155i | ||||
\(313\) | −6.30502 | − | 1.68942i | −0.356381 | − | 0.0954919i | 0.0761865 | − | 0.997094i | \(-0.475726\pi\) |
−0.432567 | + | 0.901602i | \(0.642392\pi\) | |||||||
\(314\) | 0.813582 | − | 3.08732i | 0.0459131 | − | 0.174227i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.72689 | + | 6.58020i | −0.209654 | + | 0.370165i | ||||
\(317\) | 0.411168 | − | 1.53450i | 0.0230935 | − | 0.0861861i | −0.953417 | − | 0.301654i | \(-0.902461\pi\) |
0.976511 | + | 0.215468i | \(0.0691278\pi\) | |||||||
\(318\) | 2.63119 | − | 0.0108759i | 0.147550 | − | 0.000609888i | ||||
\(319\) | −14.6969 | + | 25.4557i | −0.822866 | + | 1.42525i | ||||
\(320\) | −16.5877 | + | 6.69688i | −0.927281 | + | 0.374367i | ||||
\(321\) | 12.4651 | 0.695733 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0557 | − | 18.0557i | −1.00465 | − | 1.00465i | ||||
\(324\) | 22.4739 | − | 0.185792i | 1.24855 | − | 0.0103218i | ||||
\(325\) | 0.645112 | − | 9.53269i | 0.0357844 | − | 0.528778i | ||||
\(326\) | −16.4263 | − | 16.2911i | −0.909771 | − | 0.902281i | ||||
\(327\) | 24.0289 | + | 6.43852i | 1.32880 | + | 0.356051i | ||||
\(328\) | −9.29060 | + | 0.115212i | −0.512988 | + | 0.00636151i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.0011 | + | 35.6058i | −0.880831 | + | 1.96004i | ||||
\(331\) | 16.6210 | − | 9.59616i | 0.913575 | − | 0.527453i | 0.0319954 | − | 0.999488i | \(-0.489814\pi\) |
0.881580 | + | 0.472035i | \(0.156480\pi\) | |||||||
\(332\) | 5.76238 | − | 22.2393i | 0.316252 | − | 1.22054i | ||||
\(333\) | −1.10254 | − | 4.11473i | −0.0604188 | − | 0.225486i | ||||
\(334\) | 6.44572 | + | 23.6641i | 0.352694 | + | 1.29484i | ||||
\(335\) | 0.296900 | + | 0.415252i | 0.0162214 | + | 0.0226877i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1955 | − | 16.1955i | −0.882225 | − | 0.882225i | 0.111535 | − | 0.993760i | \(-0.464423\pi\) |
−0.993760 | + | 0.111535i | \(0.964423\pi\) | |||||||
\(338\) | −11.4767 | − | 6.56298i | −0.624251 | − | 0.356979i | ||||
\(339\) | 10.7861 | − | 18.6820i | 0.585818 | − | 1.01467i | ||||
\(340\) | −18.4390 | − | 8.19498i | −0.999998 | − | 0.444435i | ||||
\(341\) | 21.6517 | + | 37.5019i | 1.17251 | + | 2.03084i | ||||
\(342\) | −11.1503 | + | 6.49924i | −0.602940 | + | 0.351438i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −13.5388 | − | 13.2071i | −0.729961 | − | 0.712078i | ||||
\(345\) | 4.70271 | + | 12.5351i | 0.253186 | + | 0.674868i | ||||
\(346\) | −13.2967 | + | 13.4071i | −0.714835 | + | 0.720769i | ||||
\(347\) | 5.97452 | + | 22.2972i | 0.320729 | + | 1.19698i | 0.918536 | + | 0.395337i | \(0.129372\pi\) |
−0.597807 | + | 0.801640i | \(0.703961\pi\) | |||||||
\(348\) | −15.4038 | + | 15.6606i | −0.825728 | + | 0.839495i | ||||
\(349\) | − | 23.7289i | − | 1.27018i | −0.772439 | − | 0.635089i | \(-0.780963\pi\) | ||
0.772439 | − | 0.635089i | \(-0.219037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.69405i | − | 0.303926i | ||||||
\(352\) | −0.671921 | − | 32.5070i | −0.0358135 | − | 1.73263i | ||||
\(353\) | −6.01837 | − | 22.4609i | −0.320326 | − | 1.19547i | −0.918928 | − | 0.394425i | \(-0.870944\pi\) |
0.598603 | − | 0.801046i | \(-0.295723\pi\) | |||||||
\(354\) | 10.5930 | + | 10.5058i | 0.563011 | + | 0.558376i | ||||
\(355\) | −2.78647 | − | 7.42736i | −0.147891 | − | 0.394204i | ||||
\(356\) | 13.8884 | + | 7.86612i | 0.736084 | + | 0.416903i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.86886 | + | 11.7844i | 0.363030 | + | 0.622827i | ||||
\(359\) | 13.4667 | + | 23.3250i | 0.710745 | + | 1.23105i | 0.964578 | + | 0.263798i | \(0.0849754\pi\) |
−0.253833 | + | 0.967248i | \(0.581691\pi\) | |||||||
\(360\) | −6.38022 | + | 7.95662i | −0.336267 | + | 0.419351i | ||||
\(361\) | −6.51400 | + | 11.2826i | −0.342842 | + | 0.593820i | ||||
\(362\) | 1.54414 | − | 2.70024i | 0.0811581 | − | 0.141922i | ||||
\(363\) | −33.4650 | − | 33.4650i | −1.75646 | − | 1.75646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.2280 | − | 22.6969i | −0.849412 | − | 1.18801i | ||||
\(366\) | −44.9974 | + | 12.2566i | −2.35205 | + | 0.640663i | ||||
\(367\) | 2.30848 | + | 8.61536i | 0.120502 | + | 0.449718i | 0.999639 | − | 0.0268495i | \(-0.00854748\pi\) |
−0.879138 | + | 0.476567i | \(0.841881\pi\) | |||||||
\(368\) | −8.01447 | − | 7.75374i | −0.417783 | − | 0.404191i | ||||
\(369\) | −4.58755 | + | 2.64862i | −0.238818 | + | 0.137882i | ||||
\(370\) | −7.61966 | − | 3.42424i | −0.396127 | − | 0.178018i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.63392 | + | 31.1886i | 0.447648 | + | 1.61705i | ||||
\(373\) | −12.0606 | − | 3.23163i | −0.624475 | − | 0.167328i | −0.0673137 | − | 0.997732i | \(-0.521443\pi\) |
−0.557161 | + | 0.830404i | \(0.688109\pi\) | |||||||
\(374\) | 25.8260 | − | 26.0404i | 1.33543 | − | 1.34652i | ||||
\(375\) | 5.52689 | − | 23.3672i | 0.285407 | − | 1.20668i | ||||
\(376\) | −15.4342 | − | 3.93112i | −0.795958 | − | 0.202732i | ||||
\(377\) | 6.91008 | + | 6.91008i | 0.355887 | + | 0.355887i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.28361 | −0.374134 | −0.187067 | − | 0.982347i | \(-0.559898\pi\) | ||||
−0.187067 | + | 0.982347i | \(0.559898\pi\) | |||||||
\(380\) | −3.94271 | + | 25.0003i | −0.202257 | + | 1.28249i | ||||
\(381\) | 21.7539 | − | 37.6789i | 1.11449 | − | 1.93035i | ||||
\(382\) | −0.0673535 | − | 16.2948i | −0.00344610 | − | 0.833712i | ||||
\(383\) | 3.71220 | − | 13.8541i | 0.189684 | − | 0.707912i | −0.803895 | − | 0.594772i | \(-0.797242\pi\) |
0.993579 | − | 0.113140i | \(-0.0360909\pi\) | |||||||
\(384\) | 5.60724 | − | 23.6425i | 0.286143 | − | 1.20650i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.62190 | + | 1.48151i | 0.286147 | + | 0.0754066i | ||||
\(387\) | −10.4158 | − | 2.79090i | −0.529463 | − | 0.141869i | ||||
\(388\) | −4.45979 | + | 17.2121i | −0.226411 | + | 0.873810i | ||||
\(389\) | −22.5816 | − | 13.0375i | −1.14493 | − | 0.661028i | −0.197287 | − | 0.980346i | \(-0.563213\pi\) |
−0.947648 | + | 0.319318i | \(0.896546\pi\) | |||||||
\(390\) | 10.0574 | + | 8.20231i | 0.509277 | + | 0.415340i | ||||
\(391\) | − | 12.5786i | − | 0.636127i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.2193 | + | 24.2193i | −1.22170 | + | 1.22170i | ||||
\(394\) | −2.40449 | + | 0.654946i | −0.121137 | + | 0.0329957i | ||||
\(395\) | 6.53006 | + | 5.37068i | 0.328563 | + | 0.270228i | ||||
\(396\) | −9.40095 | − | 15.9764i | −0.472415 | − | 0.802846i | ||||
\(397\) | 4.36480 | − | 16.2897i | 0.219063 | − | 0.817555i | −0.765634 | − | 0.643277i | \(-0.777574\pi\) |
0.984697 | − | 0.174277i | \(-0.0557590\pi\) | |||||||
\(398\) | −3.00108 | − | 5.14876i | −0.150431 | − | 0.258084i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.18411 | + | 19.5574i | 0.209206 | + | 0.977872i | ||||
\(401\) | 2.06024 | + | 3.56843i | 0.102883 | + | 0.178199i | 0.912871 | − | 0.408247i | \(-0.133860\pi\) |
−0.809988 | + | 0.586446i | \(0.800527\pi\) | |||||||
\(402\) | −0.693380 | + | 0.00286605i | −0.0345827 | + | 0.000142946i | ||||
\(403\) | 13.9062 | − | 3.72617i | 0.692720 | − | 0.185614i | ||||
\(404\) | 7.13782 | − | 0.0590086i | 0.355120 | − | 0.00293579i | ||||
\(405\) | 4.11943 | − | 24.7875i | 0.204696 | − | 1.23170i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7364 | − | 10.7364i | 0.532184 | − | 0.532184i | ||||
\(408\) | 23.5645 | − | 13.9974i | 1.16662 | − | 0.692975i | ||||
\(409\) | 1.43363 | + | 0.827707i | 0.0708884 | + | 0.0409275i | 0.535025 | − | 0.844836i | \(-0.320302\pi\) |
−0.464137 | + | 0.885764i | \(0.653635\pi\) | |||||||
\(410\) | −1.66066 | + | 10.2544i | −0.0820139 | + | 0.506429i | ||||
\(411\) | 7.11687 | − | 4.10892i | 0.351049 | − | 0.202678i | ||||
\(412\) | 1.40390 | − | 0.388640i | 0.0691650 | − | 0.0191469i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.14781 | − | 1.62009i | −0.302148 | − | 0.0796233i | ||||
\(415\) | −23.3846 | − | 10.6253i | −1.14791 | − | 0.521577i | ||||
\(416\) | −10.4969 | − | 2.58138i | −0.514654 | − | 0.126562i | ||||
\(417\) | 18.9321 | − | 5.07283i | 0.927107 | − | 0.248418i | ||||
\(418\) | −39.9334 | − | 22.8360i | −1.95321 | − | 1.11695i | ||||
\(419\) | −23.4536 | −1.14579 | −0.572893 | − | 0.819630i | \(-0.694179\pi\) | ||||
−0.572893 | + | 0.819630i | \(0.694179\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3030 | 1.18446 | 0.592228 | − | 0.805770i | \(-0.298248\pi\) | ||||
0.592228 | + | 0.805770i | \(0.298248\pi\) | |||||||
\(422\) | 19.2392 | + | 11.0020i | 0.936549 | + | 0.535568i | ||||
\(423\) | −8.77101 | + | 2.35018i | −0.426461 | + | 0.114270i | ||||
\(424\) | 0.663475 | + | 2.35873i | 0.0322212 | + | 0.114550i | ||||
\(425\) | −12.5733 | + | 18.7312i | −0.609895 | + | 0.908595i | ||||
\(426\) | 10.4196 | + | 2.74582i | 0.504832 | + | 0.133035i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.09694 | + | 11.1872i | 0.149696 | + | 0.540752i | ||||
\(429\) | −20.4284 | + | 11.7943i | −0.986291 | + | 0.569435i | ||||
\(430\) | −17.1506 | + | 12.3699i | −0.827074 | + | 0.596528i | ||||
\(431\) | 8.78820 | + | 5.07387i | 0.423313 | + | 0.244400i | 0.696494 | − | 0.717563i | \(-0.254742\pi\) |
−0.273181 | + | 0.961963i | \(0.588076\pi\) | |||||||
\(432\) | 3.27481 | + | 11.4604i | 0.157559 | + | 0.551388i | ||||
\(433\) | 3.32616 | − | 3.32616i | 0.159845 | − | 0.159845i | −0.622653 | − | 0.782498i | \(-0.713945\pi\) |
0.782498 | + | 0.622653i | \(0.213945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.2841 | + | 19.9781i | 0.684870 | + | 0.957879i | ||||
\(436\) | 0.191506 | + | 23.1651i | 0.00917150 | + | 1.10941i | ||||
\(437\) | −15.2397 | + | 4.08345i | −0.729012 | + | 0.195338i | ||||
\(438\) | 37.8989 | − | 0.156653i | 1.81088 | − | 0.00748517i | ||||
\(439\) | −9.87337 | − | 17.1012i | −0.471230 | − | 0.816194i | 0.528228 | − | 0.849102i | \(-0.322857\pi\) |
−0.999458 | + | 0.0329080i | \(0.989523\pi\) | |||||||
\(440\) | −35.9310 | − | 5.51443i | −1.71294 | − | 0.262890i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.14020 | − | 10.5343i | −0.292060 | − | 0.501067i | ||||
\(443\) | −4.03815 | + | 15.0706i | −0.191858 | + | 0.716025i | 0.801199 | + | 0.598398i | \(0.204196\pi\) |
−0.993058 | + | 0.117628i | \(0.962471\pi\) | |||||||
\(444\) | 9.77956 | − | 5.75455i | 0.464118 | − | 0.273099i | ||||
\(445\) | 11.3356 | − | 13.7826i | 0.537357 | − | 0.653357i | ||||
\(446\) | −26.7088 | + | 7.27505i | −1.26470 | + | 0.344484i | ||||
\(447\) | −21.8900 | + | 21.8900i | −1.03536 | + | 1.03536i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.5643i | − | 0.640137i | −0.947394 | − | 0.320069i | \(-0.896294\pi\) | ||
0.947394 | − | 0.320069i | \(-0.103706\pi\) | |||||||
\(450\) | 7.53548 | + | 8.55776i | 0.355226 | + | 0.403417i | ||||
\(451\) | −16.3515 | − | 9.44053i | −0.769961 | − | 0.444537i | ||||
\(452\) | 19.4465 | + | 5.03874i | 0.914686 | + | 0.237003i | ||||
\(453\) | 31.2626 | + | 8.37680i | 1.46885 | + | 0.393576i | ||||
\(454\) | −8.00798 | − | 2.11029i | −0.375833 | − | 0.0990410i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24.6085 | − | 24.0057i | −1.15240 | − | 1.12417i | ||||
\(457\) | 7.01260 | − | 26.1714i | 0.328036 | − | 1.22425i | −0.583189 | − | 0.812336i | \(-0.698195\pi\) |
0.911225 | − | 0.411909i | \(-0.135138\pi\) | |||||||
\(458\) | 0.112605 | + | 27.2424i | 0.00526169 | + | 1.27295i | ||||
\(459\) | −6.72231 | + | 11.6434i | −0.313771 | + | 0.543467i | ||||
\(460\) | −10.0816 | + | 7.33492i | −0.470058 | + | 0.341992i | ||||
\(461\) | 30.4323 | 1.41737 | 0.708686 | − | 0.705524i | \(-0.249288\pi\) | ||||
0.708686 | + | 0.705524i | \(0.249288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5147 | + | 12.5147i | 0.581607 | + | 0.581607i | 0.935345 | − | 0.353737i | \(-0.115089\pi\) |
−0.353737 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(464\) | −17.8821 | − | 9.93371i | −0.830155 | − | 0.461161i | ||||
\(465\) | 36.0109 | − | 3.50821i | 1.66996 | − | 0.162689i | ||||
\(466\) | 26.4925 | − | 26.7124i | 1.22724 | − | 1.23743i | ||||
\(467\) | 18.5089 | + | 4.95944i | 0.856490 | + | 0.229496i | 0.660237 | − | 0.751058i | \(-0.270456\pi\) |
0.196253 | + | 0.980553i | \(0.437123\pi\) | |||||||
\(468\) | −5.93952 | + | 1.64423i | −0.274554 | + | 0.0760047i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7.29915 | + | 16.2422i | −0.336685 | + | 0.749195i | ||||
\(471\) | 4.19901 | − | 2.42430i | 0.193480 | − | 0.111706i | ||||
\(472\) | −6.79690 | + | 12.1171i | −0.312853 | + | 0.557736i | ||||
\(473\) | −9.94764 | − | 37.1251i | −0.457393 | − | 1.70701i | ||||
\(474\) | −11.0808 | + | 3.01823i | −0.508957 | + | 0.138632i | ||||
\(475\) | 26.7756 | + | 9.15246i | 1.22855 | + | 0.419944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.987806 | + | 0.987806i | 0.0452285 | + | 0.0452285i | ||||
\(478\) | 1.04060 | − | 1.81971i | 0.0475961 | − | 0.0832314i | ||||
\(479\) | 1.79254 | − | 3.10476i | 0.0819031 | − | 0.141860i | −0.822164 | − | 0.569250i | \(-0.807234\pi\) |
0.904067 | + | 0.427390i | \(0.140567\pi\) | |||||||
\(480\) | −24.9599 | − | 10.7245i | −1.13926 | − | 0.489502i | ||||
\(481\) | −2.52399 | − | 4.37168i | −0.115084 | − | 0.199331i | ||||
\(482\) | −9.68852 | − | 16.6220i | −0.441300 | − | 0.757109i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.7198 | − | 38.3484i | 0.987263 | − | 1.74311i | ||||
\(485\) | 18.0985 | + | 8.22346i | 0.821810 | + | 0.373408i | ||||
\(486\) | 15.2576 | + | 15.1320i | 0.692101 | + | 0.686403i | ||||
\(487\) | −5.39752 | − | 20.1438i | −0.244585 | − | 0.912804i | −0.973592 | − | 0.228297i | \(-0.926684\pi\) |
0.729006 | − | 0.684507i | \(-0.239982\pi\) | |||||||
\(488\) | −22.1796 | − | 37.3391i | −1.00402 | − | 1.69026i | ||||
\(489\) | − | 35.1337i | − | 1.58880i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2968i | 0.780592i | 0.920689 | + | 0.390296i | \(0.127627\pi\) | ||||
−0.920689 | + | 0.390296i | \(0.872373\pi\) | |||||||
\(492\) | −10.0596 | − | 9.89461i | −0.453520 | − | 0.446083i | ||||
\(493\) | −5.97203 | − | 22.2879i | −0.268967 | − | 1.00380i | ||||
\(494\) | −10.7696 | + | 10.8590i | −0.484548 | + | 0.488570i | ||||
\(495\) | −19.4045 | + | 7.27985i | −0.872167 | + | 0.327205i | ||||
\(496\) | −25.8460 | + | 15.4975i | −1.16052 | + | 0.695860i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 30.1423 | − | 17.5692i | 1.35071 | − | 0.787294i | ||||
\(499\) | 13.0271 | + | 22.5636i | 0.583173 | + | 1.01009i | 0.995100 | + | 0.0988689i | \(0.0315224\pi\) |
−0.411927 | + | 0.911217i | \(0.635144\pi\) | |||||||
\(500\) | 22.3447 | − | 0.845270i | 0.999285 | − | 0.0378016i | ||||
\(501\) | −18.6233 | + | 32.2565i | −0.832028 | + | 1.44111i | ||||
\(502\) | −26.1187 | − | 14.9360i | −1.16573 | − | 0.666627i | ||||
\(503\) | −2.43908 | − | 2.43908i | −0.108753 | − | 0.108753i | 0.650636 | − | 0.759390i | \(-0.274502\pi\) |
−0.759390 | + | 0.650636i | \(0.774502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.30835 | − | 7.87262i | 0.0582209 | − | 0.350327i | ||||
\(506\) | −5.95548 | − | 21.8642i | −0.264753 | − | 0.971984i | ||||
\(507\) | −5.19646 | − | 19.3935i | −0.230783 | − | 0.861294i | ||||
\(508\) | 39.2208 | + | 10.1624i | 1.74014 | + | 0.450885i | ||||
\(509\) | 3.53392 | − | 2.04031i | 0.156638 | − | 0.0904352i | −0.419632 | − | 0.907694i | \(-0.637841\pi\) |
0.576270 | + | 0.817259i | \(0.304508\pi\) | |||||||
\(510\) | −10.8822 | − | 28.6460i | −0.481873 | − | 1.26847i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6118 | − | 0.841564i | 0.999308 | − | 0.0371922i | ||||
\(513\) | 16.2889 | + | 4.36460i | 0.719173 | + | 0.192702i | ||||
\(514\) | −13.7844 | − | 13.6710i | −0.608006 | − | 0.603000i | ||||
\(515\) | −0.157916 | − | 1.62096i | −0.00695859 | − | 0.0714281i | ||||
\(516\) | −0.237446 | − | 28.7221i | −0.0104530 | − | 1.26442i | ||||
\(517\) | −22.8858 | − | 22.8858i | −1.00652 | − | 1.00652i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.6760 | −1.25874 | ||||||||
\(520\) | −4.86265 | + | 11.0642i | −0.213242 | + | 0.485196i | ||||
\(521\) | −3.01201 | + | 5.21696i | −0.131959 | + | 0.228559i | −0.924432 | − | 0.381348i | \(-0.875460\pi\) |
0.792473 | + | 0.609907i | \(0.208793\pi\) | |||||||
\(522\) | −11.6624 | + | 0.0482061i | −0.510451 | + | 0.00210992i | ||||
\(523\) | −9.49137 | + | 35.4223i | −0.415029 | + | 1.54891i | 0.369749 | + | 0.929132i | \(0.379444\pi\) |
−0.784778 | + | 0.619777i | \(0.787223\pi\) | |||||||
\(524\) | −27.7535 | − | 15.7191i | −1.21242 | − | 0.686690i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.10318 | − | 19.3652i | 0.222509 | − | 0.844361i | ||||
\(527\) | −32.8351 | − | 8.79813i | −1.43032 | − | 0.383252i | ||||
\(528\) | 34.3329 | − | 35.4873i | 1.49415 | − | 1.54439i | ||||
\(529\) | 13.1878 | + | 7.61400i | 0.573384 | + | 0.331043i | ||||
\(530\) | 2.72545 | − | 0.276893i | 0.118386 | − | 0.0120275i | ||||
\(531\) | 7.92095i | 0.343740i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.43869 | + | 4.43869i | −0.192261 | + | 0.192261i | ||||
\(534\) | 6.37039 | + | 23.3875i | 0.275674 | + | 1.01208i | ||||
\(535\) | 12.9169 | − | 1.25837i | 0.558446 | − | 0.0544043i | ||||
\(536\) | −0.174842 | − | 0.621582i | −0.00755201 | − | 0.0268483i | ||||
\(537\) | −5.36133 | + | 20.0088i | −0.231358 | + | 0.863442i | ||||
\(538\) | 25.4406 | − | 14.8287i | 1.09682 | − | 0.639311i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 13.2520 | − | 1.40171i | 0.570277 | − | 0.0603199i | ||||
\(541\) | 3.17890 | + | 5.50602i | 0.136672 | + | 0.236722i | 0.926235 | − | 0.376947i | \(-0.123026\pi\) |
−0.789563 | + | 0.613669i | \(0.789693\pi\) | |||||||
\(542\) | −0.0685080 | − | 16.5741i | −0.00294267 | − | 0.711917i | ||||
\(543\) | 4.56290 | − | 1.22262i | 0.195813 | − | 0.0524678i | ||||
\(544\) | 18.4170 | + | 17.6710i | 0.789621 | + | 0.757639i | ||||
\(545\) | 25.5498 | + | 4.24613i | 1.09443 | + | 0.181884i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.38074 | + | 3.38074i | −0.144550 | + | 0.144550i | −0.775678 | − | 0.631128i | \(-0.782592\pi\) |
0.631128 | + | 0.775678i | \(0.282592\pi\) | |||||||
\(548\) | 5.45585 | + | 5.36638i | 0.233062 | + | 0.229241i | ||||
\(549\) | −21.4433 | − | 12.3803i | −0.915177 | − | 0.528377i | ||||
\(550\) | −12.9866 | + | 38.5117i | −0.553750 | + | 1.64214i | ||||
\(551\) | −25.0643 | + | 14.4709i | −1.06778 | + | 0.616481i | ||||
\(552\) | −0.209992 | − | 16.9336i | −0.00893785 | − | 0.720742i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.629146 | + | 2.38743i | −0.0267298 | + | 0.101432i | ||||
\(555\) | −4.45617 | − | 11.8780i | −0.189154 | − | 0.504191i | ||||
\(556\) | 9.25641 | + | 15.7308i | 0.392559 | + | 0.667134i | ||||
\(557\) | 8.85561 | − | 2.37285i | 0.375224 | − | 0.100541i | −0.0662779 | − | 0.997801i | \(-0.521112\pi\) |
0.441502 | + | 0.897260i | \(0.354446\pi\) | |||||||
\(558\) | −8.52918 | + | 14.9150i | −0.361069 | + | 0.631403i | ||||
\(559\) | −12.7781 | −0.540457 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 55.6969 | 2.35152 | ||||||||
\(562\) | −11.4838 | + | 20.0818i | −0.484415 | + | 0.847098i | ||||
\(563\) | −20.3469 | + | 5.45194i | −0.857520 | + | 0.229772i | −0.660684 | − | 0.750664i | \(-0.729734\pi\) |
−0.196837 | + | 0.980436i | \(0.563067\pi\) | |||||||
\(564\) | −12.2664 | − | 20.8462i | −0.516511 | − | 0.877784i | ||||
\(565\) | 9.29101 | − | 20.4480i | 0.390876 | − | 0.860254i | ||||
\(566\) | −1.72942 | + | 6.56269i | −0.0726931 | + | 0.275850i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.124425 | + | 10.0336i | 0.00522078 | + | 0.421000i | ||||
\(569\) | −13.5683 | + | 7.83365i | −0.568812 | + | 0.328404i | −0.756675 | − | 0.653792i | \(-0.773177\pi\) |
0.187863 | + | 0.982195i | \(0.439844\pi\) | |||||||
\(570\) | −31.1735 | + | 22.4839i | −1.30571 | + | 0.941748i | ||||
\(571\) | −5.57733 | − | 3.22007i | −0.233404 | − | 0.134756i | 0.378738 | − | 0.925504i | \(-0.376358\pi\) |
−0.612141 | + | 0.790748i | \(0.709692\pi\) | |||||||
\(572\) | −15.6606 | − | 15.4038i | −0.654801 | − | 0.644064i | ||||
\(573\) | 17.4982 | − | 17.4982i | 0.730997 | − | 0.730997i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.13861 | + | 12.5147i | 0.255998 | + | 0.521899i | ||||
\(576\) | 11.0088 | − | 6.72533i | 0.458700 | − | 0.280222i | ||||
\(577\) | 21.4921 | − | 5.75880i | 0.894729 | − | 0.239742i | 0.217978 | − | 0.975954i | \(-0.430054\pi\) |
0.676751 | + | 0.736212i | \(0.263387\pi\) | |||||||
\(578\) | 0.0196281 | + | 4.74861i | 0.000816422 | + | 0.197516i | ||||
\(579\) | 4.41457 | + | 7.64627i | 0.183463 | + | 0.317768i | ||||
\(580\) | −14.3811 | + | 17.7832i | −0.597143 | + | 0.738408i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −23.3286 | + | 13.5976i | −0.967001 | + | 0.563641i | ||||
\(583\) | −1.28872 | + | 4.80957i | −0.0533734 | + | 0.199192i | ||||
\(584\) | 9.55652 | + | 33.9746i | 0.395452 | + | 1.40588i | ||||
\(585\) | 0.668100 | + | 6.85787i | 0.0276225 | + | 0.283538i | ||||
\(586\) | 1.81544 | + | 6.66498i | 0.0749949 | + | 0.275328i | ||||
\(587\) | −6.67713 | + | 6.67713i | −0.275595 | + | 0.275595i | −0.831348 | − | 0.555753i | \(-0.812430\pi\) |
0.555753 | + | 0.831348i | \(0.312430\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.6377i | 1.75685i | ||||||||
\(590\) | 12.0375 | + | 9.81718i | 0.495576 | + | 0.404167i | ||||
\(591\) | −3.27757 | − | 1.89230i | −0.134821 | − | 0.0778390i | ||||
\(592\) | 7.59431 | + | 7.34725i | 0.312124 | + | 0.301970i | ||||
\(593\) | −18.6723 | − | 5.00324i | −0.766781 | − | 0.205458i | −0.145832 | − | 0.989309i | \(-0.546586\pi\) |
−0.620949 | + | 0.783851i | \(0.713253\pi\) | |||||||
\(594\) | −6.17210 | + | 23.4214i | −0.253244 | + | 0.960993i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.0844 | − | 14.2073i | −1.02750 | − | 0.581953i | ||||
\(597\) | 2.34243 | − | 8.74205i | 0.0958691 | − | 0.357788i | ||||
\(598\) | −7.53382 | + | 0.0311407i | −0.308081 | + | 0.00127344i | ||||
\(599\) | 8.68441 | − | 15.0418i | 0.354835 | − | 0.614593i | −0.632255 | − | 0.774761i | \(-0.717870\pi\) |
0.987090 | + | 0.160168i | \(0.0512036\pi\) | |||||||
\(600\) | −16.6138 | + | 25.4263i | −0.678255 | + | 1.03802i | ||||
\(601\) | −22.5611 | −0.920285 | −0.460142 | − | 0.887845i | \(-0.652202\pi\) | ||||
−0.460142 | + | 0.887845i | \(0.652202\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.260310 | − | 0.260310i | −0.0106007 | − | 0.0106007i | ||||
\(604\) | 0.249158 | + | 30.1388i | 0.0101381 | + | 1.22633i | ||||
\(605\) | −38.0563 | − | 31.2996i | −1.54721 | − | 1.27251i | ||||
\(606\) | 7.69678 | + | 7.63342i | 0.312660 | + | 0.310086i | ||||
\(607\) | 13.7372 | + | 3.68087i | 0.557575 | + | 0.149402i | 0.526592 | − | 0.850118i | \(-0.323470\pi\) |
0.0309832 | + | 0.999520i | \(0.490136\pi\) | |||||||
\(608\) | 15.4306 | − | 28.0498i | 0.625795 | − | 1.13757i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45.3910 | + | 17.2434i | −1.83783 | + | 0.698165i | ||||
\(611\) | −9.31872 | + | 5.38016i | −0.376995 | + | 0.217658i | ||||
\(612\) | 14.0865 | + | 3.64993i | 0.569413 | + | 0.147540i | ||||
\(613\) | 8.25672 | + | 30.8145i | 0.333486 | + | 1.24459i | 0.905501 | + | 0.424344i | \(0.139495\pi\) |
−0.572015 | + | 0.820243i | \(0.693838\pi\) | |||||||
\(614\) | 4.97653 | + | 18.2703i | 0.200836 | + | 0.737328i | ||||
\(615\) | −12.8330 | + | 9.17539i | −0.517475 | + | 0.369987i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1111 | + | 25.1111i | 1.01093 | + | 1.01093i | 0.999940 | + | 0.0109950i | \(0.00349990\pi\) |
0.0109950 | + | 0.999940i | \(0.496500\pi\) | |||||||
\(618\) | 1.92038 | + | 1.09817i | 0.0772491 | + | 0.0441751i | ||||
\(619\) | −17.6742 | + | 30.6126i | −0.710387 | + | 1.23043i | 0.254325 | + | 0.967119i | \(0.418147\pi\) |
−0.964712 | + | 0.263307i | \(0.915187\pi\) | |||||||
\(620\) | 12.0954 | + | 31.4474i | 0.485763 | + | 1.26296i | ||||
\(621\) | 4.15355 | + | 7.19417i | 0.166676 | + | 0.288692i | ||||
\(622\) | 28.6303 | − | 16.6879i | 1.14797 | − | 0.669123i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.44195 | − | 14.0791i | −0.337949 | − | 0.563614i | ||||
\(625\) | 3.36826 | − | 24.7721i | 0.134730 | − | 0.990882i | ||||
\(626\) | 6.50040 | − | 6.55436i | 0.259808 | − | 0.261965i | ||||
\(627\) | −18.0812 | − | 67.4799i | −0.722093 | − | 2.69489i | ||||
\(628\) | 3.21900 | + | 3.16621i | 0.128452 | + | 0.126346i | ||||
\(629\) | 11.9192i | 0.475248i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 21.4460i | − | 0.853752i | −0.904310 | − | 0.426876i | \(-0.859614\pi\) | ||
0.904310 | − | 0.426876i | \(-0.140386\pi\) | |||||||
\(632\) | −5.46181 | − | 9.19490i | −0.217259 | − | 0.365754i | ||||
\(633\) | 8.71119 | + | 32.5106i | 0.346239 | + | 1.29218i | ||||
\(634\) | 1.59518 | + | 1.58205i | 0.0633528 | + | 0.0628313i | ||||
\(635\) | 18.7387 | − | 41.2407i | 0.743621 | − | 1.63659i | ||||
\(636\) | −1.83384 | + | 3.23783i | −0.0727165 | + | 0.128388i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −20.9331 | − | 35.9136i | −0.828750 | − | 1.42183i | ||||
\(639\) | 2.86044 | + | 4.95442i | 0.113157 | + | 0.195994i | ||||
\(640\) | 3.42372 | − | 25.0655i | 0.135334 | − | 0.990800i | ||||
\(641\) | −6.13958 | + | 10.6341i | −0.242499 | + | 0.420020i | −0.961425 | − | 0.275066i | \(-0.911300\pi\) |
0.718927 | + | 0.695086i | \(0.244634\pi\) | |||||||
\(642\) | −8.75097 | + | 15.3029i | −0.345373 | + | 0.603956i | ||||
\(643\) | −8.02266 | − | 8.02266i | −0.316383 | − | 0.316383i | 0.530993 | − | 0.847376i | \(-0.321819\pi\) |
−0.847376 | + | 0.530993i | \(0.821819\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.6789 | − | 5.26472i | −1.24735 | − | 0.207298i | ||||
\(646\) | 34.8421 | − | 9.49044i | 1.37084 | − | 0.373396i | ||||
\(647\) | 8.97722 | + | 33.5034i | 0.352931 | + | 1.31716i | 0.883068 | + | 0.469244i | \(0.155474\pi\) |
−0.530138 | + | 0.847912i | \(0.677860\pi\) | |||||||
\(648\) | −15.5494 | + | 27.7207i | −0.610840 | + | 1.08897i | ||||
\(649\) | −24.4503 | + | 14.1164i | −0.959758 | + | 0.554117i | ||||
\(650\) | 11.2500 | + | 7.48429i | 0.441261 | + | 0.293558i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 31.5318 | − | 8.72893i | 1.23488 | − | 0.341851i | ||||
\(653\) | 25.2083 | + | 6.75454i | 0.986476 | + | 0.264326i | 0.715770 | − | 0.698336i | \(-0.246076\pi\) |
0.270707 | + | 0.962662i | \(0.412743\pi\) | |||||||
\(654\) | −24.7735 | + | 24.9792i | −0.968721 | + | 0.976762i | ||||
\(655\) | −22.6521 | + | 27.5421i | −0.885092 | + | 1.07616i | ||||
\(656\) | 6.38092 | − | 11.4866i | 0.249133 | − | 0.448475i | ||||
\(657\) | 14.2281 | + | 14.2281i | 0.555091 | + | 0.555091i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.8116 | 0.538024 | 0.269012 | − | 0.963137i | \(-0.413303\pi\) | ||||
0.269012 | + | 0.963137i | \(0.413303\pi\) | |||||||
\(660\) | −32.4784 | − | 44.6405i | −1.26422 | − | 1.73763i | ||||
\(661\) | −2.97447 | + | 5.15193i | −0.115693 | + | 0.200387i | −0.918057 | − | 0.396449i | \(-0.870242\pi\) |
0.802363 | + | 0.596836i | \(0.203576\pi\) | |||||||
\(662\) | 0.112189 | + | 27.1418i | 0.00436036 | + | 1.05490i | ||||
\(663\) | 4.79259 | − | 17.8862i | 0.186129 | − | 0.694643i | ||||
\(664\) | 23.2568 | + | 22.6870i | 0.902538 | + | 0.880428i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.82551 | + | 1.53516i | 0.225734 | + | 0.0594863i | ||||
\(667\) | −13.7712 | − | 3.68997i | −0.533222 | − | 0.142876i | ||||
\(668\) | −33.5765 | − | 8.69995i | −1.29911 | − | 0.336611i | ||||
\(669\) | −36.4068 | − | 21.0195i | −1.40757 | − | 0.812659i | ||||
\(670\) | −0.718222 | + | 0.0729679i | −0.0277474 | + | 0.00281900i | ||||
\(671\) | − | 88.2545i | − | 3.40703i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.95231 | − | 2.95231i | 0.113803 | − | 0.113803i | −0.647912 | − | 0.761715i | \(-0.724358\pi\) |
0.761715 | + | 0.647912i | \(0.224358\pi\) | |||||||
\(674\) | 31.2524 | − | 8.51266i | 1.20380 | − | 0.327895i | ||||
\(675\) | 1.00596 | − | 14.8649i | 0.0387194 | − | 0.572149i | ||||
\(676\) | 16.1142 | − | 9.48200i | 0.619776 | − | 0.364692i | ||||
\(677\) | −4.26545 | + | 15.9189i | −0.163934 | + | 0.611812i | 0.834239 | + | 0.551403i | \(0.185907\pi\) |
−0.998174 | + | 0.0604090i | \(0.980759\pi\) | |||||||
\(678\) | 15.3629 | + | 26.3571i | 0.590007 | + | 1.01224i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 23.0055 | − | 16.8836i | 0.882222 | − | 0.647458i | ||||
\(681\) | −6.28823 | − | 10.8915i | −0.240965 | − | 0.417364i | ||||
\(682\) | −61.2398 | + | 0.253131i | −2.34499 | + | 0.00969290i | ||||
\(683\) | −48.5144 | + | 12.9994i | −1.85635 | + | 0.497408i | −0.999825 | − | 0.0186937i | \(-0.994049\pi\) |
−0.856527 | + | 0.516102i | \(0.827383\pi\) | |||||||
\(684\) | −0.150886 | − | 18.2515i | −0.00576925 | − | 0.697863i | ||||
\(685\) | 6.96001 | − | 4.97631i | 0.265928 | − | 0.190135i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.2544 | + | 29.2544i | −1.11612 | + | 1.11612i | ||||
\(688\) | 25.7185 | − | 7.34907i | 0.980508 | − | 0.280181i | ||||
\(689\) | 1.43363 | + | 0.827707i | 0.0546169 | + | 0.0315331i | ||||
\(690\) | −18.6903 | − | 3.02681i | −0.711528 | − | 0.115229i | ||||
\(691\) | −0.185080 | + | 0.106856i | −0.00704078 | + | 0.00406500i | −0.503516 | − | 0.863986i | \(-0.667961\pi\) |
0.496475 | + | 0.868051i | \(0.334627\pi\) | |||||||
\(692\) | −7.12451 | − | 25.7361i | −0.270833 | − | 0.978339i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.5677 | − | 8.31883i | −1.19829 | − | 0.315779i | ||||
\(695\) | 19.1061 | − | 7.16792i | 0.724737 | − | 0.271895i | ||||
\(696\) | −8.41178 | − | 29.9049i | −0.318848 | − | 1.13354i | ||||
\(697\) | 14.3167 | − | 3.83614i | 0.542282 | − | 0.145304i | ||||
\(698\) | 29.1309 | + | 16.6586i | 1.10262 | + | 0.630537i | ||||
\(699\) | 57.1343 | 2.16102 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.4863 | −0.962605 | −0.481303 | − | 0.876554i | \(-0.659836\pi\) | ||||
−0.481303 | + | 0.876554i | \(0.659836\pi\) | |||||||
\(702\) | 6.99034 | + | 3.99744i | 0.263833 | + | 0.150874i | ||||
\(703\) | 14.4407 | − | 3.86938i | 0.544642 | − | 0.145936i | ||||
\(704\) | 40.3791 | + | 21.9962i | 1.52185 | + | 0.829015i | ||||
\(705\) | −25.3192 | + | 9.49882i | −0.953575 | + | 0.357746i | ||||
\(706\) | 31.7994 | + | 8.37989i | 1.19678 | + | 0.315381i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −20.3342 | + | 5.62910i | −0.764205 | + | 0.211554i | ||||
\(709\) | −33.0877 | + | 19.1032i | −1.24264 | + | 0.717436i | −0.969630 | − | 0.244576i | \(-0.921351\pi\) |
−0.273006 | + | 0.962012i | \(0.588018\pi\) | |||||||
\(710\) | 11.0745 | + | 1.79346i | 0.415617 | + | 0.0673074i | ||||
\(711\) | −5.28049 | − | 3.04869i | −0.198034 | − | 0.114335i | ||||
\(712\) | −19.4071 | + | 11.5279i | −0.727311 | + | 0.432026i | ||||
\(713\) | −14.8518 | + | 14.8518i | −0.556206 | + | 0.556206i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9781 | + | 14.2841i | −0.747140 | + | 0.534195i | ||||
\(716\) | −19.2895 | + | 0.159467i | −0.720881 | + | 0.00595955i | ||||
\(717\) | 3.07496 | − | 0.823933i | 0.114836 | − | 0.0307703i | ||||
\(718\) | −38.0892 | + | 0.157440i | −1.42148 | + | 0.00587560i | ||||
\(719\) | −1.79254 | − | 3.10476i | −0.0668503 | − | 0.115788i | 0.830663 | − | 0.556776i | \(-0.187962\pi\) |
−0.897513 | + | 0.440987i | \(0.854628\pi\) | |||||||
\(720\) | −5.28884 | − | 13.4186i | −0.197103 | − | 0.500081i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.27806 | − | 15.9178i | −0.345294 | − | 0.592398i | ||||
\(723\) | 7.56215 | − | 28.2223i | 0.281240 | − | 1.04960i | ||||
\(724\) | 2.23093 | + | 3.79135i | 0.0829117 | + | 0.140904i | ||||
\(725\) | 16.8187 | + | 19.2602i | 0.624629 | + | 0.715307i | ||||
\(726\) | 64.5772 | − | 17.5898i | 2.39668 | − | 0.652819i | ||||
\(727\) | −35.6453 | + | 35.6453i | −1.32201 | + | 1.32201i | −0.409867 | + | 0.912145i | \(0.634425\pi\) |
−0.912145 | + | 0.409867i | \(0.865575\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.07793i | − | 0.0399234i | ||||||
\(730\) | 39.2567 | − | 3.98830i | 1.45296 | − | 0.147613i | ||||
\(731\) | 26.1292 | + | 15.0857i | 0.966422 | + | 0.557964i | ||||
\(732\) | 16.5430 | − | 63.8460i | 0.611448 | − | 2.35982i | ||||
\(733\) | 24.3770 | + | 6.53180i | 0.900386 | + | 0.241258i | 0.679182 | − | 0.733970i | \(-0.262335\pi\) |
0.221204 | + | 0.975228i | \(0.429001\pi\) | |||||||
\(734\) | −12.1973 | − | 3.21429i | −0.450212 | − | 0.118642i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.1454 | − | 4.39560i | 0.558267 | − | 0.162024i | ||||
\(737\) | 0.339609 | − | 1.26744i | 0.0125097 | − | 0.0466867i | ||||
\(738\) | −0.0309652 | − | 7.49137i | −0.00113984 | − | 0.275761i | ||||
\(739\) | 3.57030 | − | 6.18393i | 0.131335 | − | 0.227480i | −0.792856 | − | 0.609409i | \(-0.791407\pi\) |
0.924192 | + | 0.381929i | \(0.124740\pi\) | |||||||
\(740\) | 9.55309 | − | 6.95039i | 0.351179 | − | 0.255501i | ||||
\(741\) | −23.2260 | −0.853228 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.64091 | + | 2.64091i | 0.0968857 | + | 0.0968857i | 0.753888 | − | 0.657003i | \(-0.228176\pi\) |
−0.657003 | + | 0.753888i | \(0.728176\pi\) | |||||||
\(744\) | −44.3502 | − | 11.2961i | −1.62596 | − | 0.414135i | ||||
\(745\) | −20.4736 | + | 24.8932i | −0.750093 | + | 0.912018i | ||||
\(746\) | 12.4344 | − | 12.5376i | 0.455254 | − | 0.459033i | ||||
\(747\) | 17.8921 | + | 4.79418i | 0.654639 | + | 0.175410i | ||||
\(748\) | 13.8378 | + | 49.9868i | 0.505961 | + | 1.82770i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 24.8068 | + | 23.1898i | 0.905815 | + | 0.846771i | ||||
\(751\) | 7.78637 | − | 4.49547i | 0.284129 | − | 0.164042i | −0.351162 | − | 0.936315i | \(-0.614213\pi\) |
0.635291 | + | 0.772273i | \(0.280880\pi\) | |||||||
\(752\) | 15.6615 | − | 16.1881i | 0.571115 | − | 0.590319i | ||||
\(753\) | −11.8261 | − | 44.1356i | −0.430967 | − | 1.60839i | ||||
\(754\) | −13.3344 | + | 3.63207i | −0.485608 | + | 0.132272i | ||||
\(755\) | 33.2414 | + | 5.52440i | 1.20978 | + | 0.201053i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.3874 | − | 32.3874i | −1.17714 | − | 1.17714i | −0.980470 | − | 0.196670i | \(-0.936987\pi\) |
−0.196670 | − | 0.980470i | \(-0.563013\pi\) | |||||||
\(758\) | 5.11338 | − | 8.94178i | 0.185726 | − | 0.324780i | ||||
\(759\) | 17.2069 | − | 29.8032i | 0.624570 | − | 1.08179i | ||||
\(760\) | −27.9239 | − | 22.3915i | −1.01291 | − | 0.812224i | ||||
\(761\) | −10.7235 | − | 18.5737i | −0.388727 | − | 0.673295i | 0.603552 | − | 0.797324i | \(-0.293752\pi\) |
−0.992279 | + | 0.124029i | \(0.960418\pi\) | |||||||
\(762\) | 30.9847 | + | 53.1584i | 1.12246 | + | 1.92573i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.0517 | + | 11.3569i | 0.725443 | + | 0.410877i | ||||
\(765\) | 6.73016 | − | 14.8120i | 0.243329 | − | 0.535528i | ||||
\(766\) | 14.4020 | + | 14.2834i | 0.520365 | + | 0.516081i | ||||
\(767\) | 2.42937 | + | 9.06652i | 0.0877194 | + | 0.327373i | ||||
\(768\) | 25.0884 | + | 23.4817i | 0.905299 | + | 0.847323i | ||||
\(769\) | 25.9795i | 0.936844i | 0.883505 | + | 0.468422i | \(0.155177\pi\) | ||||
−0.883505 | + | 0.468422i | \(0.844823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 29.4831i | − | 1.06181i | ||||||
\(772\) | −5.76557 | + | 5.86169i | −0.207507 | + | 0.210967i | ||||
\(773\) | −4.84222 | − | 18.0714i | −0.174162 | − | 0.649983i | −0.996693 | − | 0.0812619i | \(-0.974105\pi\) |
0.822530 | − | 0.568721i | \(-0.192562\pi\) | |||||||
\(774\) | 10.7385 | − | 10.8277i | 0.385988 | − | 0.389193i | ||||
\(775\) | 36.9619 | − | 7.27073i | 1.32771 | − | 0.261172i | ||||
\(776\) | −17.9996 | − | 17.5586i | −0.646147 | − | 0.630317i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.8588 | − | 18.5697i | 1.14219 | − | 0.665755i | ||||
\(779\) | −9.29538 | − | 16.1001i | −0.333042 | − | 0.576845i | ||||
\(780\) | −17.1303 | + | 6.58872i | −0.613364 | + | 0.235914i | ||||
\(781\) | −10.1955 | + | 17.6591i | −0.364824 | + | 0.631893i | ||||
\(782\) | 15.4422 | + | 8.83065i | 0.552212 | + | 0.315784i | ||||
\(783\) | 10.7753 | + | 10.7753i | 0.385077 | + | 0.385077i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.10647 | − | 2.93607i | 0.146566 | − | 0.104793i | ||||
\(786\) | −12.7301 | − | 46.7358i | −0.454068 | − | 1.66701i | ||||
\(787\) | 4.58242 | + | 17.1018i | 0.163346 | + | 0.609615i | 0.998245 | + | 0.0592125i | \(0.0188590\pi\) |
−0.834900 | + | 0.550402i | \(0.814474\pi\) | |||||||
\(788\) | 0.883997 | − | 3.41169i | 0.0314911 | − | 0.121536i | ||||
\(789\) | 26.3383 | − | 15.2064i | 0.937668 | − | 0.541363i | ||||
\(790\) | −11.1777 | + | 4.24625i | −0.397685 | + | 0.151075i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 26.2134 | − | 0.325070i | 0.931453 | − | 0.0115509i | ||||
\(793\) | −28.3416 | − | 7.59410i | −1.00644 | − | 0.269675i | ||||
\(794\) | 16.9339 | + | 16.7944i | 0.600960 | + | 0.596013i | ||||
\(795\) | 3.21316 | + | 2.64268i | 0.113959 | + | 0.0937261i | ||||
\(796\) | 8.42779 | − | 0.0696728i | 0.298715 | − | 0.00246949i | ||||
\(797\) | 35.3823 | + | 35.3823i | 1.25331 | + | 1.25331i | 0.954229 | + | 0.299076i | \(0.0966785\pi\) |
0.299076 | + | 0.954229i | \(0.403321\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4070 | 0.898835 | ||||||||
\(800\) | −26.9472 | − | 8.59341i | −0.952728 | − | 0.303823i | ||||
\(801\) | −6.43467 | + | 11.1452i | −0.227358 | + | 0.393796i | ||||
\(802\) | −5.82718 | + | 0.0240863i | −0.205765 | + | 0.000850518i | ||||
\(803\) | −18.5624 | + | 69.2758i | −0.655053 | + | 2.44469i | ||||
\(804\) | 0.483261 | − | 0.853245i | 0.0170433 | − | 0.0300916i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.18826 | + | 19.6880i | −0.182749 | + | 0.693481i | ||||
\(807\) | 43.1955 | + | 11.5742i | 1.52055 | + | 0.407431i | ||||
\(808\) | −4.93858 | + | 8.80422i | −0.173739 | + | 0.309731i | ||||
\(809\) | 14.5481 | + | 8.39937i | 0.511485 | + | 0.295306i | 0.733444 | − | 0.679750i | \(-0.237912\pi\) |
−0.221959 | + | 0.975056i | \(0.571245\pi\) | |||||||
\(810\) | 27.5385 | + | 22.4590i | 0.967604 | + | 0.789129i | ||||
\(811\) | 18.6742i | 0.655738i | 0.944723 | + | 0.327869i | \(0.106331\pi\) | ||||
−0.944723 | + | 0.327869i | \(0.893669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7981 | − | 17.7981i | 0.624207 | − | 0.624207i | ||||
\(814\) | 5.64326 | + | 20.7180i | 0.197796 | + | 0.726166i | ||||
\(815\) | −3.54682 | − | 36.4072i | −0.124240 | − | 1.27529i | ||||
\(816\) | 0.640836 | + | 38.7559i | 0.0224337 | + | 1.35673i | ||||
\(817\) | 9.79469 | − | 36.5543i | 0.342673 | − | 1.27887i | ||||
\(818\) | −2.02260 | + | 1.17892i | −0.0707187 | + | 0.0412201i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.4231 | − | 9.23770i | −0.398910 | − | 0.322595i | ||||
\(821\) | −1.90261 | − | 3.29541i | −0.0664014 | − | 0.115011i | 0.830913 | − | 0.556402i | \(-0.187818\pi\) |
−0.897315 | + | 0.441391i | \(0.854485\pi\) | |||||||
\(822\) | 0.0480376 | + | 11.6217i | 0.00167550 | + | 0.405353i | ||||
\(823\) | 37.2403 | − | 9.97850i | 1.29811 | − | 0.347828i | 0.457377 | − | 0.889273i | \(-0.348789\pi\) |
0.840737 | + | 0.541444i | \(0.182122\pi\) | |||||||
\(824\) | −0.508473 | + | 1.99634i | −0.0177135 | + | 0.0695459i | ||||
\(825\) | −55.4140 | + | 27.1812i | −1.92927 | + | 0.946328i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.43350 | − | 2.43350i | 0.0846212 | − | 0.0846212i | −0.663529 | − | 0.748150i | \(-0.730942\pi\) |
0.748150 | + | 0.663529i | \(0.230942\pi\) | |||||||
\(828\) | 6.30492 | − | 6.41003i | 0.219111 | − | 0.222764i | ||||
\(829\) | 33.7071 | + | 19.4608i | 1.17070 | + | 0.675902i | 0.953844 | − | 0.300303i | \(-0.0970876\pi\) |
0.216852 | + | 0.976204i | \(0.430421\pi\) | |||||||
\(830\) | 29.4612 | − | 21.2489i | 1.02261 | − | 0.737560i | ||||
\(831\) | −3.24711 | + | 1.87472i | −0.112641 | + | 0.0650334i | ||||
\(832\) | 10.5383 | − | 11.0744i | 0.365350 | − | 0.383936i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.06334 | + | 26.8034i | −0.244583 | + | 0.928126i | ||||
\(835\) | −16.0420 | + | 35.3057i | −0.555155 | + | 1.22180i | ||||
\(836\) | 56.0695 | − | 32.9928i | 1.93921 | − | 1.14108i | ||||
\(837\) | 21.6848 | − | 5.81043i | 0.749537 | − | 0.200838i | ||||
\(838\) | 16.4654 | − | 28.7930i | 0.568786 | − | 0.994639i | ||||
\(839\) | 50.2557 | 1.73502 | 0.867509 | − | 0.497422i | \(-0.165720\pi\) | ||||
0.867509 | + | 0.497422i | \(0.165720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.84704 | 0.0981737 | ||||||||
\(842\) | −17.0617 | + | 29.8358i | −0.587983 | + | 1.02821i | ||||
\(843\) | −33.9344 | + | 9.09269i | −1.16876 | + | 0.313169i | ||||
\(844\) | −27.0133 | + | 15.8953i | −0.929836 | + | 0.547140i | ||||
\(845\) | −7.34262 | − | 19.5718i | −0.252594 | − | 0.673290i | ||||
\(846\) | 3.27236 | − | 12.4177i | 0.112506 | − | 0.426930i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.36150 | − | 0.841400i | −0.115434 | − | 0.0288938i | ||||
\(849\) | −8.92581 | + | 5.15332i | −0.306333 | + | 0.176861i | ||||
\(850\) | −14.1685 | − | 28.5857i | −0.485976 | − | 0.980482i | ||||
\(851\) | 6.37789 | + | 3.68228i | 0.218631 | + | 0.126227i | ||||
\(852\) | −10.6859 | + | 10.8640i | −0.366093 | + | 0.372196i | ||||
\(853\) | −4.47340 | + | 4.47340i | −0.153166 | + | 0.153166i | −0.779531 | − | 0.626364i | \(-0.784542\pi\) |
0.626364 | + | 0.779531i | \(0.284542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.1304 | − | 3.34547i | −0.688444 | − | 0.114413i | ||||
\(856\) | −15.9082 | − | 4.05184i | −0.543730 | − | 0.138489i | ||||
\(857\) | −25.2566 | + | 6.76748i | −0.862749 | + | 0.231173i | −0.662950 | − | 0.748664i | \(-0.730696\pi\) |
−0.199799 | + | 0.979837i | \(0.564029\pi\) | |||||||
\(858\) | −0.137888 | − | 33.3591i | −0.00470742 | − | 1.13886i | ||||
\(859\) | −6.61087 | − | 11.4504i | −0.225560 | − | 0.390681i | 0.730927 | − | 0.682455i | \(-0.239088\pi\) |
−0.956487 | + | 0.291774i | \(0.905754\pi\) | |||||||
\(860\) | −3.14560 | − | 29.7392i | −0.107264 | − | 1.01410i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.3986 | + | 7.22685i | −0.422299 | + | 0.246147i | ||||
\(863\) | 9.30796 | − | 34.7378i | 0.316847 | − | 1.18249i | −0.605411 | − | 0.795913i | \(-0.706991\pi\) |
0.922258 | − | 0.386575i | \(-0.126342\pi\) | |||||||
\(864\) | −16.3685 | − | 4.02529i | −0.556867 | − | 0.136943i | ||||
\(865\) | −29.7153 | + | 2.89489i | −1.01035 | + | 0.0984293i | ||||
\(866\) | 1.74829 | + | 6.41847i | 0.0594094 | + | 0.218109i | ||||
\(867\) | −5.09931 | + | 5.09931i | −0.173182 | + | 0.173182i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 21.7330i | − | 0.737241i | ||||||
\(870\) | −34.5543 | + | 3.51055i | −1.17150 | + | 0.119019i | ||||
\(871\) | −0.377796 | − | 0.218120i | −0.0128011 | − | 0.00739073i | ||||
\(872\) | −28.5732 | − | 16.0277i | −0.967611 | − | 0.542765i | ||||
\(873\) | −13.8476 | − | 3.71045i | −0.468670 | − | 0.125580i | ||||
\(874\) | 5.68574 | − | 21.5758i | 0.192323 | − | 0.729813i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26.4142 | + | 46.6368i | −0.892452 | + | 1.57571i | ||||
\(877\) | −13.8817 | + | 51.8073i | −0.468752 | + | 1.74941i | 0.175388 | + | 0.984499i | \(0.443882\pi\) |
−0.644140 | + | 0.764907i | \(0.722785\pi\) | |||||||
\(878\) | 27.9259 | − | 0.115430i | 0.942452 | − | 0.00389557i | ||||
\(879\) | −5.24525 | + | 9.08504i | −0.176918 | + | 0.306431i | ||||
\(880\) | 31.9947 | − | 40.2396i | 1.07854 | − | 1.35648i | ||||
\(881\) | −11.3298 | −0.381709 | −0.190855 | − | 0.981618i | \(-0.561126\pi\) | ||||
−0.190855 | + | 0.981618i | \(0.561126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0638 | + | 24.0638i | 0.809810 | + | 0.809810i | 0.984605 | − | 0.174795i | \(-0.0559263\pi\) |
−0.174795 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(884\) | 17.2432 | − | 0.142550i | 0.579952 | − | 0.00479448i | ||||
\(885\) | 2.28727 | + | 23.4782i | 0.0768856 | + | 0.789211i | ||||
\(886\) | −15.6666 | − | 15.5376i | −0.526329 | − | 0.521996i | ||||
\(887\) | −33.4167 | − | 8.95397i | −1.12202 | − | 0.300645i | −0.350320 | − | 0.936630i | \(-0.613927\pi\) |
−0.771701 | + | 0.635985i | \(0.780594\pi\) | |||||||
\(888\) | 0.198983 | + | 16.0459i | 0.00667744 | + | 0.538464i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.96230 | + | 23.5921i | 0.300417 | + | 0.790808i | ||||
\(891\) | −55.9355 | + | 32.2944i | −1.87391 | + | 1.08190i | ||||
\(892\) | 9.81932 | − | 37.8966i | 0.328775 | − | 1.26887i | ||||
\(893\) | −8.24801 | − | 30.7820i | −0.276009 | − | 1.03008i | ||||
\(894\) | −11.5058 | − | 42.2410i | −0.384811 | − | 1.41275i | ||||
\(895\) | −3.53573 | + | 21.2752i | −0.118186 | + | 0.711152i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.09022 | − | 8.09022i | −0.270125 | − | 0.270125i | ||||
\(898\) | 16.6523 | + | 9.52263i | 0.555693 | + | 0.317774i | ||||
\(899\) | −19.2646 | + | 33.3672i | −0.642509 | + | 1.11286i | ||||
\(900\) | −15.7962 | + | 3.24311i | −0.526540 | + | 0.108104i | ||||
\(901\) | −1.95436 | − | 3.38505i | −0.0651091 | − | 0.112772i | ||||
\(902\) | 23.0691 | − | 13.4464i | 0.768117 | − | 0.447716i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.8380 | + | 20.3362i | −0.659803 | + | 0.676373i | ||||
\(905\) | 4.60485 | − | 1.72757i | 0.153070 | − | 0.0574264i | ||||
\(906\) | −32.2314 | + | 32.4990i | −1.07082 | + | 1.07971i | ||||
\(907\) | 13.1830 | + | 49.1996i | 0.437734 | + | 1.63365i | 0.734438 | + | 0.678676i | \(0.237446\pi\) |
−0.296703 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(908\) | 8.21262 | − | 8.34954i | 0.272546 | − | 0.277089i | ||||
\(909\) | 5.75530i | 0.190891i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.9908i | − | 0.761719i | −0.924633 | − | 0.380860i | \(-0.875628\pi\) | ||
0.924633 | − | 0.380860i | \(-0.124372\pi\) | |||||||
\(912\) | 46.7468 | − | 13.3579i | 1.54794 | − | 0.442325i | ||||
\(913\) | 17.0880 | + | 63.7732i | 0.565530 | + | 2.11059i | ||||
\(914\) | 27.2064 | + | 26.9824i | 0.899907 | + | 0.892498i | ||||
\(915\) | −67.1341 | − | 30.5039i | −2.21939 | − | 1.00843i | ||||
\(916\) | −33.5234 | − | 18.9870i | −1.10764 | − | 0.627348i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −9.57477 | − | 16.4268i | −0.316014 | − | 0.542165i | ||||
\(919\) | −2.90036 | − | 5.02358i | −0.0956742 | − | 0.165713i | 0.814216 | − | 0.580563i | \(-0.197167\pi\) |
−0.909890 | + | 0.414850i | \(0.863834\pi\) | |||||||
\(920\) | −1.92708 | − | 17.5262i | −0.0635340 | − | 0.577821i | ||||
\(921\) | −14.3785 | + | 24.9042i | −0.473786 | + | 0.820622i | ||||
\(922\) | −21.3646 | + | 37.3604i | −0.703607 | + | 1.23040i | ||||
\(923\) | 4.79366 | + | 4.79366i | 0.157785 | + | 0.157785i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.81679 | − | 11.8586i | −0.191255 | − | 0.389909i | ||||
\(926\) | −24.1496 | + | 6.57796i | −0.793604 | + | 0.216165i | ||||
\(927\) | 0.303986 | + | 1.13449i | 0.00998420 | + | 0.0372615i | ||||
\(928\) | 24.7491 | − | 14.9792i | 0.812429 | − | 0.491717i | ||||
\(929\) | −36.8435 | + | 21.2716i | −1.20880 | + | 0.697899i | −0.962496 | − | 0.271294i | \(-0.912548\pi\) |
−0.246300 | + | 0.969194i | \(0.579215\pi\) | |||||||
\(930\) | −20.9741 | + | 46.6719i | −0.687769 | + | 1.53043i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.1949 | + | 51.2768i | 0.464971 | + | 1.67963i | ||||
\(933\) | 48.6112 | + | 13.0253i | 1.59146 | + | 0.426431i | ||||
\(934\) | −19.0825 | + | 19.2409i | −0.624397 | + | 0.629580i | ||||
\(935\) | 57.7156 | − | 5.62271i | 1.88750 | − | 0.183882i | ||||
\(936\) | 2.15122 | − | 8.44601i | 0.0703147 | − | 0.276066i | ||||
\(937\) | −2.08780 | − | 2.08780i | −0.0682055 | − | 0.0682055i | 0.672181 | − | 0.740387i | \(-0.265358\pi\) |
−0.740387 | + | 0.672181i | \(0.765358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0189 | 0.457490 | ||||||||
\(940\) | −14.8155 | − | 20.3635i | −0.483229 | − | 0.664183i | ||||
\(941\) | −14.3629 | + | 24.8773i | −0.468217 | + | 0.810976i | −0.999340 | − | 0.0363189i | \(-0.988437\pi\) |
0.531123 | + | 0.847295i | \(0.321770\pi\) | |||||||
\(942\) | 0.0283426 | + | 6.85690i | 0.000923453 | + | 0.223410i | ||||
\(943\) | 2.37025 | − | 8.84591i | 0.0771861 | − | 0.288063i | ||||
\(944\) | −10.1040 | − | 16.8510i | −0.328857 | − | 0.548452i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52.5605 | + | 13.8509i | 1.70889 | + | 0.450333i | ||||
\(947\) | 51.0535 | + | 13.6798i | 1.65902 | + | 0.444532i | 0.962117 | − | 0.272636i | \(-0.0878955\pi\) |
0.696900 | + | 0.717168i | \(0.254562\pi\) | |||||||
\(948\) | 4.07378 | − | 15.7223i | 0.132310 | − | 0.510637i | ||||
\(949\) | 20.6496 | + | 11.9221i | 0.670315 | + | 0.387007i | ||||
\(950\) | −30.0336 | + | 26.4459i | −0.974418 | + | 0.858017i | ||||
\(951\) | 3.41189i | 0.110638i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.91911 | + | 8.91911i | −0.288918 | + | 0.288918i | −0.836652 | − | 0.547734i | \(-0.815491\pi\) |
0.547734 | + | 0.836652i | \(0.315491\pi\) | |||||||
\(954\) | −1.90616 | + | 0.519209i | −0.0617144 | + | 0.0168100i | ||||
\(955\) | 16.3659 | − | 19.8989i | 0.529589 | − | 0.643912i | ||||
\(956\) | 1.50343 | + | 2.55501i | 0.0486245 | + | 0.0826348i | ||||
\(957\) | 16.3389 | − | 60.9775i | 0.528161 | − | 1.97112i | ||||
\(958\) | 2.55316 | + | 4.38028i | 0.0824887 | + | 0.141521i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.6888 | − | 23.1132i | 0.990476 | − | 0.745976i | ||||
\(961\) | 12.8810 | + | 22.3105i | 0.415515 | + | 0.719693i | ||||
\(962\) | 7.13886 | − | 0.0295081i | 0.230166 | − | 0.000951379i | ||||
\(963\) | −9.04036 | + | 2.42236i | −0.291321 | + | 0.0780593i | ||||
\(964\) | 27.2078 | − | 0.224928i | 0.876304 | − | 0.00724443i | ||||
\(965\) | 5.34649 | + | 7.47775i | 0.172109 | + | 0.240717i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.7524 | − | 38.7524i | 1.24619 | − | 1.24619i | 0.288805 | − | 0.957388i | \(-0.406742\pi\) |
0.957388 | − | 0.288805i | \(-0.0932580\pi\) | |||||||
\(968\) | 31.8306 | + | 53.5865i | 1.02307 | + | 1.72234i | ||||
\(969\) | 47.4933 | + | 27.4203i | 1.52570 | + | 0.880866i | ||||
\(970\) | −22.8014 | + | 16.4456i | −0.732110 | + | 0.528035i | ||||
\(971\) | 13.9138 | − | 8.03315i | 0.446516 | − | 0.257796i | −0.259842 | − | 0.965651i | \(-0.583670\pi\) |
0.706358 | + | 0.707855i | \(0.250337\pi\) | |||||||
\(972\) | −29.2884 | + | 8.10789i | −0.939426 | + | 0.260061i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.5190 | + | 7.51543i | 0.913807 | + | 0.240810i | ||||
\(975\) | 3.96058 | + | 20.1342i | 0.126840 | + | 0.644812i | ||||
\(976\) | 61.4106 | − | 1.01544i | 1.96571 | − | 0.0325033i | ||||
\(977\) | 12.1266 | − | 3.24931i | 0.387964 | − | 0.103955i | −0.0595641 | − | 0.998224i | \(-0.518971\pi\) |
0.447528 | + | 0.894270i | \(0.352304\pi\) | |||||||
\(978\) | 43.1322 | + | 24.6652i | 1.37922 | + | 0.788707i | ||||
\(979\) | −45.8704 | −1.46603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6783 | −0.596351 | ||||||||
\(982\) | −21.2345 | − | 12.1430i | −0.677620 | − | 0.387498i | ||||
\(983\) | 9.63621 | − | 2.58201i | 0.307347 | − | 0.0823535i | −0.101849 | − | 0.994800i | \(-0.532476\pi\) |
0.409196 | + | 0.912446i | \(0.365809\pi\) | |||||||
\(984\) | 19.2094 | − | 5.40331i | 0.612373 | − | 0.172251i | ||||
\(985\) | −3.58739 | − | 1.63001i | −0.114304 | − | 0.0519366i | ||||
\(986\) | 31.5545 | + | 8.31537i | 1.00490 | + | 0.264815i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.77046 | − | 20.8448i | −0.183583 | − | 0.663163i | ||||
\(989\) | 16.1446 | − | 9.32108i | 0.513368 | − | 0.296393i | ||||
\(990\) | 4.68553 | − | 28.9328i | 0.148916 | − | 0.919545i | ||||
\(991\) | 45.3896 | + | 26.2057i | 1.44185 | + | 0.832451i | 0.997973 | − | 0.0636385i | \(-0.0202704\pi\) |
0.443874 | + | 0.896089i | \(0.353604\pi\) | |||||||
\(992\) | −0.880749 | − | 42.6099i | −0.0279638 | − | 1.35287i | ||||
\(993\) | −29.1463 | + | 29.1463i | −0.924931 | + | 0.924931i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.54480 | − | 9.29538i | 0.0489735 | − | 0.294683i | ||||
\(996\) | 0.407884 | + | 49.3386i | 0.0129243 | + | 1.56335i | ||||
\(997\) | 0.380238 | − | 0.101885i | 0.0120423 | − | 0.00322672i | −0.252793 | − | 0.967520i | \(-0.581349\pi\) |
0.264835 | + | 0.964294i | \(0.414682\pi\) | |||||||
\(998\) | −36.8459 | + | 0.152300i | −1.16634 | + | 0.00482099i | ||||
\(999\) | −3.93580 | − | 6.81701i | −0.124523 | − | 0.215681i |
(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 | 980.2.x.j.67.5 | 64 | ||
4.3 | odd | 2 | inner | 980.2.x.j.67.10 | 64 | ||
5.3 | odd | 4 | inner | 980.2.x.j.263.13 | 64 | ||
7.2 | even | 3 | inner | 980.2.x.j.667.16 | 64 | ||
7.3 | odd | 6 | 980.2.k.i.687.7 | yes | 32 | ||
7.4 | even | 3 | 980.2.k.i.687.8 | yes | 32 | ||
7.5 | odd | 6 | inner | 980.2.x.j.667.15 | 64 | ||
7.6 | odd | 2 | inner | 980.2.x.j.67.6 | 64 | ||
20.3 | even | 4 | inner | 980.2.x.j.263.16 | 64 | ||
28.3 | even | 6 | 980.2.k.i.687.4 | yes | 32 | ||
28.11 | odd | 6 | 980.2.k.i.687.3 | ✓ | 32 | ||
28.19 | even | 6 | inner | 980.2.x.j.667.14 | 64 | ||
28.23 | odd | 6 | inner | 980.2.x.j.667.13 | 64 | ||
28.27 | even | 2 | inner | 980.2.x.j.67.9 | 64 | ||
35.3 | even | 12 | 980.2.k.i.883.4 | yes | 32 | ||
35.13 | even | 4 | inner | 980.2.x.j.263.14 | 64 | ||
35.18 | odd | 12 | 980.2.k.i.883.3 | yes | 32 | ||
35.23 | odd | 12 | inner | 980.2.x.j.863.10 | 64 | ||
35.33 | even | 12 | inner | 980.2.x.j.863.9 | 64 | ||
140.3 | odd | 12 | 980.2.k.i.883.7 | yes | 32 | ||
140.23 | even | 12 | inner | 980.2.x.j.863.5 | 64 | ||
140.83 | odd | 4 | inner | 980.2.x.j.263.15 | 64 | ||
140.103 | odd | 12 | inner | 980.2.x.j.863.6 | 64 | ||
140.123 | even | 12 | 980.2.k.i.883.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.k.i.687.3 | ✓ | 32 | 28.11 | odd | 6 | ||
980.2.k.i.687.4 | yes | 32 | 28.3 | even | 6 | ||
980.2.k.i.687.7 | yes | 32 | 7.3 | odd | 6 | ||
980.2.k.i.687.8 | yes | 32 | 7.4 | even | 3 | ||
980.2.k.i.883.3 | yes | 32 | 35.18 | odd | 12 | ||
980.2.k.i.883.4 | yes | 32 | 35.3 | even | 12 | ||
980.2.k.i.883.7 | yes | 32 | 140.3 | odd | 12 | ||
980.2.k.i.883.8 | yes | 32 | 140.123 | even | 12 | ||
980.2.x.j.67.5 | 64 | 1.1 | even | 1 | trivial | ||
980.2.x.j.67.6 | 64 | 7.6 | odd | 2 | inner | ||
980.2.x.j.67.9 | 64 | 28.27 | even | 2 | inner | ||
980.2.x.j.67.10 | 64 | 4.3 | odd | 2 | inner | ||
980.2.x.j.263.13 | 64 | 5.3 | odd | 4 | inner | ||
980.2.x.j.263.14 | 64 | 35.13 | even | 4 | inner | ||
980.2.x.j.263.15 | 64 | 140.83 | odd | 4 | inner | ||
980.2.x.j.263.16 | 64 | 20.3 | even | 4 | inner | ||
980.2.x.j.667.13 | 64 | 28.23 | odd | 6 | inner | ||
980.2.x.j.667.14 | 64 | 28.19 | even | 6 | inner | ||
980.2.x.j.667.15 | 64 | 7.5 | odd | 6 | inner | ||
980.2.x.j.667.16 | 64 | 7.2 | even | 3 | inner | ||
980.2.x.j.863.5 | 64 | 140.23 | even | 12 | inner | ||
980.2.x.j.863.6 | 64 | 140.103 | odd | 12 | inner | ||
980.2.x.j.863.9 | 64 | 35.33 | even | 12 | inner | ||
980.2.x.j.863.10 | 64 | 35.23 | odd | 12 | inner |