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 | 667.15 | ||
Character | \(\chi\) | \(=\) | 980.667 |
Dual form | 980.2.x.j.263.15 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41420 | − | 0.00584552i | 0.999991 | − | 0.00413341i | ||||
\(3\) | −0.555863 | + | 2.07451i | −0.320928 | + | 1.19772i | 0.597415 | + | 0.801932i | \(0.296194\pi\) |
−0.918343 | + | 0.395786i | \(0.870472\pi\) | |||||||
\(4\) | 1.99993 | − | 0.0165335i | 0.999966 | − | 0.00826675i | ||||
\(5\) | −1.72700 | − | 1.42038i | −0.772337 | − | 0.635213i | ||||
\(6\) | −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 | ||||
\(10\) | −2.45063 | − | 1.99861i | −0.774956 | − | 0.632015i | ||||
\(11\) | −4.97765 | + | 2.87385i | −1.50082 | + | 0.866498i | −0.500820 | + | 0.865552i | \(0.666968\pi\) |
−1.00000 | 0.000946947i | \(0.999699\pi\) | ||||||||
\(12\) | −1.07739 | + | 4.15806i | −0.311015 | + | 1.20033i | ||||
\(13\) | −1.35121 | + | 1.35121i | −0.374758 | + | 0.374758i | −0.869207 | − | 0.494449i | \(-0.835370\pi\) |
0.494449 | + | 0.869207i | \(0.335370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.90656 | − | 2.79314i | 1.00867 | − | 0.721185i | ||||
\(16\) | 3.99945 | − | 0.0661317i | 0.999863 | − | 0.0165329i | ||||
\(17\) | −1.16778 | + | 4.35822i | −0.283229 | + | 1.05702i | 0.666895 | + | 0.745151i | \(0.267623\pi\) |
−0.950124 | + | 0.311872i | \(0.899044\pi\) | |||||||
\(18\) | −1.97968 | − | 1.13208i | −0.466615 | − | 0.266835i | ||||
\(19\) | −2.82966 | + | 4.90112i | −0.649170 | + | 1.12439i | 0.334152 | + | 0.942519i | \(0.391550\pi\) |
−0.983322 | + | 0.181875i | \(0.941783\pi\) | |||||||
\(20\) | −3.47736 | − | 2.81211i | −0.777562 | − | 0.628806i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.02261 | + | 4.09330i | −1.49722 | + | 0.872695i | ||||
\(23\) | 2.69284 | − | 0.721544i | 0.561496 | − | 0.150452i | 0.0331023 | − | 0.999452i | \(-0.489461\pi\) |
0.528393 | + | 0.849000i | \(0.322795\pi\) | |||||||
\(24\) | −1.49934 | + | 5.88664i | −0.306051 | + | 1.20161i | ||||
\(25\) | 0.965049 | + | 4.90598i | 0.193010 | + | 0.981197i | ||||
\(26\) | −1.90298 | + | 1.91878i | −0.373206 | + | 0.376304i | ||||
\(27\) | −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 | \(0.842512\pi\) | |||||||
\(30\) | 5.50834 | − | 3.97289i | 1.00568 | − | 0.725348i | ||||
\(31\) | 6.52468 | − | 3.76703i | 1.17187 | − | 0.676578i | 0.217748 | − | 0.976005i | \(-0.430129\pi\) |
0.954119 | + | 0.299427i | \(0.0967956\pi\) | |||||||
\(32\) | 5.65565 | − | 0.116902i | 0.999786 | − | 0.0206656i | ||||
\(33\) | −3.19493 | − | 11.9237i | −0.556166 | − | 2.07564i | ||||
\(34\) | −1.62600 | + | 6.17023i | −0.278857 | + | 1.05819i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.80628 | − | 1.58942i | −0.467714 | − | 0.264904i | ||||
\(37\) | −2.55167 | + | 0.683717i | −0.419491 | + | 0.112402i | −0.462389 | − | 0.886677i | \(-0.653008\pi\) |
0.0428978 | + | 0.999079i | \(0.486341\pi\) | |||||||
\(38\) | −3.97307 | + | 6.94772i | −0.644516 | + | 1.12707i | ||||
\(39\) | −2.05201 | − | 3.55418i | −0.328584 | − | 0.569125i | ||||
\(40\) | −4.93413 | − | 3.95656i | −0.780155 | − | 0.625587i | ||||
\(41\) | 3.28498 | 0.513027 | 0.256514 | − | 0.966541i | \(-0.417426\pi\) | ||||
0.256514 | + | 0.966541i | \(0.417426\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.72840 | − | 4.72840i | −0.721075 | − | 0.721075i | 0.247749 | − | 0.968824i | \(-0.420309\pi\) |
−0.968824 | + | 0.247749i | \(0.920309\pi\) | |||||||
\(44\) | −9.90745 | + | 5.82980i | −1.49360 | + | 0.878876i | ||||
\(45\) | 1.26657 | + | 3.37604i | 0.188809 | + | 0.503271i | ||||
\(46\) | 3.80400 | − | 1.03615i | 0.560869 | − | 0.152772i | ||||
\(47\) | −1.45742 | − | 5.43916i | −0.212586 | − | 0.793383i | −0.987002 | − | 0.160706i | \(-0.948623\pi\) |
0.774416 | − | 0.632677i | \(-0.218044\pi\) | |||||||
\(48\) | −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 | ||||
\(52\) | −2.67999 | + | 2.72467i | −0.371647 | + | 0.377843i | ||||
\(53\) | −0.836782 | − | 0.224215i | −0.114941 | − | 0.0307983i | 0.200890 | − | 0.979614i | \(-0.435617\pi\) |
−0.315831 | + | 0.948815i | \(0.602283\pi\) | |||||||
\(54\) | −2.96743 | + | 2.99207i | −0.403816 | + | 0.407168i | ||||
\(55\) | 12.6784 | + | 2.10702i | 1.70955 | + | 0.284110i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.59451 | − | 8.59451i | −1.13837 | − | 1.13837i | ||||
\(58\) | 0.0298940 | + | 7.23222i | 0.00392527 | + | 0.949637i | ||||
\(59\) | 2.45601 | + | 4.25393i | 0.319745 | + | 0.553814i | 0.980435 | − | 0.196845i | \(-0.0630695\pi\) |
−0.660690 | + | 0.750659i | \(0.729736\pi\) | |||||||
\(60\) | 7.76667 | − | 5.65067i | 1.00267 | − | 0.729499i | ||||
\(61\) | 7.67737 | − | 13.2976i | 0.982987 | − | 1.70258i | 0.332425 | − | 0.943130i | \(-0.392133\pi\) |
0.650561 | − | 0.759454i | \(-0.274534\pi\) | |||||||
\(62\) | 9.20519 | − | 5.36547i | 1.16906 | − | 0.681416i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.99754 | − | 0.198384i | 0.999692 | − | 0.0247980i | ||||
\(65\) | 4.25277 | − | 0.414308i | 0.527491 | − | 0.0513886i | ||||
\(66\) | −4.58798 | − | 16.8438i | −0.564741 | − | 2.07332i | ||||
\(67\) | 0.220512 | + | 0.0590861i | 0.0269398 | + | 0.00721851i | 0.272264 | − | 0.962223i | \(-0.412228\pi\) |
−0.245324 | + | 0.969441i | \(0.578894\pi\) | |||||||
\(68\) | −2.26343 | + | 8.73545i | −0.274481 | + | 1.05933i | ||||
\(69\) | 5.98740i | 0.720798i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.54768i | 0.421032i | 0.977590 | + | 0.210516i | \(0.0675144\pi\) | ||||
−0.977590 | + | 0.210516i | \(0.932486\pi\) | |||||||
\(72\) | −3.97794 | − | 2.23136i | −0.468805 | − | 0.262968i | ||||
\(73\) | 12.0528 | + | 3.22954i | 1.41067 | + | 0.377989i | 0.882165 | − | 0.470940i | \(-0.156085\pi\) |
0.528507 | + | 0.848929i | \(0.322752\pi\) | |||||||
\(74\) | −3.60457 | + | 0.981829i | −0.419023 | + | 0.114135i | ||||
\(75\) | −10.7139 | − | 0.725051i | −1.23714 | − | 0.0837217i | ||||
\(76\) | −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 | −0.952561 | − | 0.304348i | \(-0.901561\pi\) |
0.739854 | + | 0.672768i | \(0.234895\pi\) | |||||||
\(80\) | −7.00098 | − | 5.56653i | −0.782734 | − | 0.622357i | ||||
\(81\) | −5.61866 | − | 9.73181i | −0.624296 | − | 1.08131i | ||||
\(82\) | 4.64562 | − | 0.0192024i | 0.513023 | − | 0.00212055i | ||||
\(83\) | −8.12242 | − | 8.12242i | −0.891552 | − | 0.891552i | 0.103117 | − | 0.994669i | \(-0.467118\pi\) |
−0.994669 | + | 0.103117i | \(0.967118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.20708 | − | 5.86795i | 0.890183 | − | 0.636468i | ||||
\(86\) | −6.71456 | − | 6.65928i | −0.724049 | − | 0.718088i | ||||
\(87\) | −10.6090 | − | 2.84268i | −1.13741 | − | 0.304767i | ||||
\(88\) | −13.9771 | + | 8.30243i | −1.48996 | + | 0.885042i | ||||
\(89\) | −6.91145 | − | 3.99033i | −0.732613 | − | 0.422974i | 0.0867646 | − | 0.996229i | \(-0.472347\pi\) |
−0.819377 | + | 0.573255i | \(0.805681\pi\) | |||||||
\(90\) | 1.81092 | + | 4.76700i | 0.190887 | + | 0.502486i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.37356 | − | 1.48756i | 0.560233 | − | 0.155089i | ||||
\(93\) | 4.18790 | + | 15.6294i | 0.434265 | + | 1.62070i | ||||
\(94\) | −2.09288 | − | 7.68355i | −0.215864 | − | 0.792497i | ||||
\(95\) | 11.8483 | − | 4.44504i | 1.21561 | − | 0.456051i | ||||
\(96\) | −2.90125 | + | 11.7977i | −0.296107 | + | 1.20409i | ||||
\(97\) | 6.28634 | + | 6.28634i | 0.638281 | + | 0.638281i | 0.950131 | − | 0.311850i | \(-0.100949\pi\) |
−0.311850 | + | 0.950131i | \(0.600949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.26855 | 0.931525 | ||||||||
\(100\) | 2.01115 | + | 9.79568i | 0.201115 | + | 0.979568i | ||||
\(101\) | 1.78452 | + | 3.09087i | 0.177566 | + | 0.307553i | 0.941046 | − | 0.338278i | \(-0.109844\pi\) |
−0.763480 | + | 0.645831i | \(0.776511\pi\) | |||||||
\(102\) | −11.8964 | − | 6.80296i | −1.17791 | − | 0.673593i | ||||
\(103\) | −0.703531 | + | 0.188510i | −0.0693209 | + | 0.0185745i | −0.293313 | − | 0.956017i | \(-0.594758\pi\) |
0.223992 | + | 0.974591i | \(0.428091\pi\) | |||||||
\(104\) | −3.77411 | + | 3.86889i | −0.370082 | + | 0.379376i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.18469 | − | 0.312194i | −0.115067 | − | 0.0303230i | ||||
\(107\) | 1.50217 | + | 5.60619i | 0.145221 | + | 0.541971i | 0.999745 | + | 0.0225603i | \(0.00718177\pi\) |
−0.854525 | + | 0.519411i | \(0.826152\pi\) | |||||||
\(108\) | −4.17906 | + | 4.24873i | −0.402130 | + | 0.408834i | ||||
\(109\) | 10.0311 | − | 5.79147i | 0.960807 | − | 0.554722i | 0.0643855 | − | 0.997925i | \(-0.479491\pi\) |
0.896421 | + | 0.443203i | \(0.146158\pi\) | |||||||
\(110\) | 17.9421 | + | 2.90564i | 1.71071 | + | 0.277042i | ||||
\(111\) | − | 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 | \(0.406629\pi\) | |||||||
\(114\) | −12.2046 | − | 12.1041i | −1.14307 | − | 1.13366i | ||||
\(115\) | −5.67539 | − | 2.57874i | −0.529233 | − | 0.240469i | ||||
\(116\) | 0.0845523 | + | 10.2276i | 0.00785048 | + | 0.949613i | ||||
\(117\) | 2.97645 | − | 0.797539i | 0.275173 | − | 0.0737325i | ||||
\(118\) | 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 | ||||
\(122\) | 10.7796 | − | 18.8504i | 0.975941 | − | 1.70663i | ||||
\(123\) | −1.82600 | + | 6.81471i | −0.164645 | + | 0.614462i | ||||
\(124\) | 12.9866 | − | 7.64167i | 1.16623 | − | 0.686242i | ||||
\(125\) | 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 | \(0.894438\pi\) | |||||||
\(128\) | 11.3090 | − | 0.327305i | 0.999581 | − | 0.0289299i | ||||
\(129\) | 12.4375 | − | 7.18077i | 1.09506 | − | 0.632231i | ||||
\(130\) | 6.01185 | − | 0.610775i | 0.527274 | − | 0.0535685i | ||||
\(131\) | 13.8113 | + | 7.97397i | 1.20670 | + | 0.696689i | 0.962037 | − | 0.272919i | \(-0.0879890\pi\) |
0.244664 | + | 0.969608i | \(0.421322\pi\) | |||||||
\(132\) | −6.58679 | − | 23.7937i | −0.573306 | − | 2.07097i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.312194 | + | 0.0822706i | 0.0269695 | + | 0.00710709i | ||||
\(135\) | 6.63158 | − | 0.646054i | 0.570756 | − | 0.0556035i | ||||
\(136\) | −3.14988 | + | 12.3669i | −0.270100 | + | 1.06045i | ||||
\(137\) | 0.990337 | − | 3.69599i | 0.0846102 | − | 0.315770i | −0.910630 | − | 0.413223i | \(-0.864403\pi\) |
0.995240 | + | 0.0974534i | \(0.0310697\pi\) | |||||||
\(138\) | 0.0349995 | + | 8.46738i | 0.00297935 | + | 0.720792i | ||||
\(139\) | 9.12605 | 0.774061 | 0.387031 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387031 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0937 | 1.01847 | ||||||||
\(142\) | 0.0207381 | + | 5.01714i | 0.00174030 | + | 0.421029i | ||||
\(143\) | 2.84268 | − | 10.6090i | 0.237717 | − | 0.887171i | ||||
\(144\) | −5.63865 | − | 3.13234i | −0.469888 | − | 0.261028i | ||||
\(145\) | 7.26381 | − | 8.83187i | 0.603227 | − | 0.733447i | ||||
\(146\) | 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 | \(-0.534374\pi\) |
−0.914870 | + | 0.403748i | \(0.867707\pi\) | |||||||
\(150\) | −15.1559 | − | 0.962740i | −1.23747 | − | 0.0786074i | ||||
\(151\) | 13.0509 | − | 7.53495i | 1.06207 | − | 0.613186i | 0.136065 | − | 0.990700i | \(-0.456554\pi\) |
0.926004 | + | 0.377514i | \(0.123221\pi\) | |||||||
\(152\) | −7.83099 | + | 13.9606i | −0.635177 | + | 1.13236i | ||||
\(153\) | 5.14480 | − | 5.14480i | 0.415932 | − | 0.415932i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6187 | − | 2.76187i | −1.33485 | − | 0.221838i | ||||
\(156\) | −4.16264 | − | 7.07419i | −0.333278 | − | 0.566389i | ||||
\(157\) | −0.584308 | + | 2.18067i | −0.0466328 | + | 0.174036i | −0.985315 | − | 0.170749i | \(-0.945381\pi\) |
0.938682 | + | 0.344785i | \(0.112048\pi\) | |||||||
\(158\) | −2.65452 | + | 4.64197i | −0.211182 | + | 0.369296i | ||||
\(159\) | 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 | ||||
\(163\) | 15.8014 | − | 4.23398i | 1.23766 | − | 0.331631i | 0.420105 | − | 0.907475i | \(-0.361993\pi\) |
0.817559 | + | 0.575844i | \(0.195327\pi\) | |||||||
\(164\) | 6.56973 | − | 0.0543122i | 0.513010 | − | 0.00424107i | ||||
\(165\) | −11.4185 | + | 25.1301i | −0.888925 | + | 1.95638i | ||||
\(166\) | −11.5342 | − | 11.4393i | −0.895229 | − | 0.887859i | ||||
\(167\) | −12.2631 | + | 12.2631i | −0.948948 | + | 0.948948i | −0.998759 | − | 0.0498110i | \(-0.984138\pi\) |
0.0498110 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.34847i | 0.719113i | ||||||||
\(170\) | 11.5722 | − | 8.34644i | 0.887545 | − | 0.640143i | ||||
\(171\) | 7.90339 | − | 4.56302i | 0.604387 | − | 0.348943i | ||||
\(172\) | −9.53466 | − | 9.37831i | −0.727011 | − | 0.715089i | ||||
\(173\) | 3.45575 | + | 12.8971i | 0.262736 | + | 0.980545i | 0.963621 | + | 0.267271i | \(0.0861218\pi\) |
−0.700885 | + | 0.713274i | \(0.747212\pi\) | |||||||
\(174\) | −15.0199 | − | 3.95811i | −1.13866 | − | 0.300063i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.7178 | + | 11.8230i | −1.48629 | + | 0.891193i | ||||
\(177\) | −10.1900 | + | 2.73040i | −0.765928 | + | 0.205230i | ||||
\(178\) | −9.79751 | − | 5.60273i | −0.734355 | − | 0.419942i | ||||
\(179\) | 4.82253 | + | 8.35287i | 0.360453 | + | 0.624323i | 0.988035 | − | 0.154227i | \(-0.0492888\pi\) |
−0.627583 | + | 0.778550i | \(0.715956\pi\) | |||||||
\(180\) | 2.58887 | + | 6.73092i | 0.192963 | + | 0.501693i | ||||
\(181\) | 2.19951 | 0.163488 | 0.0817440 | − | 0.996653i | \(-0.473951\pi\) | ||||
0.0817440 | + | 0.996653i | \(0.473951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.3184 | + | 23.3184i | 1.72375 | + | 1.72375i | ||||
\(184\) | 7.59061 | − | 2.13512i | 0.559587 | − | 0.157403i | ||||
\(185\) | 5.37786 | + | 2.44355i | 0.395388 | + | 0.179654i | ||||
\(186\) | 6.01389 | + | 22.0787i | 0.440960 | + | 1.61889i | ||||
\(187\) | −6.71206 | − | 25.0497i | −0.490834 | − | 1.83182i | ||||
\(188\) | −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 | \(-0.196464\pi\) |
−0.0934744 | + | 0.995622i | \(0.529797\pi\) | |||||||
\(192\) | −4.03399 | + | 16.7012i | −0.291128 | + | 1.20531i | ||||
\(193\) | 3.97092 | + | 1.06401i | 0.285833 | + | 0.0765888i | 0.398887 | − | 0.917000i | \(-0.369397\pi\) |
−0.113054 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(194\) | 8.92690 | + | 8.85340i | 0.640914 | + | 0.635637i | ||||
\(195\) | −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 | \(0.730005\pi\) | |||||||
\(198\) | 13.1076 | − | 0.0541796i | 0.931517 | − | 0.00385037i | ||||
\(199\) | 2.10702 | + | 3.64946i | 0.149363 | + | 0.258704i | 0.930992 | − | 0.365039i | \(-0.118945\pi\) |
−0.781629 | + | 0.623743i | \(0.785611\pi\) | |||||||
\(200\) | 2.90143 | + | 13.8413i | 0.205162 | + | 0.978728i | ||||
\(201\) | −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 | ||||
\(205\) | −5.67315 | − | 4.66591i | −0.396230 | − | 0.325881i | ||||
\(206\) | −0.993832 | + | 0.270704i | −0.0692436 | + | 0.0188609i | ||||
\(207\) | −4.34238 | − | 1.16354i | −0.301817 | − | 0.0808715i | ||||
\(208\) | −5.31474 | + | 5.49346i | −0.368511 | + | 0.380903i | ||||
\(209\) | − | 32.5281i | − | 2.25002i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.6715i | − | 1.07887i | −0.842028 | − | 0.539434i | \(-0.818638\pi\) | ||
0.842028 | − | 0.539434i | \(-0.181362\pi\) | |||||||
\(212\) | −1.67721 | − | 0.434580i | −0.115192 | − | 0.0298471i | ||||
\(213\) | −7.35969 | − | 1.97202i | −0.504278 | − | 0.135121i | ||||
\(214\) | 2.15715 | + | 7.91950i | 0.147460 | + | 0.541366i | ||||
\(215\) | 1.44982 | + | 14.8821i | 0.0988772 | + | 1.01495i | ||||
\(216\) | −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 | ||||
\(220\) | 25.3907 | + | 4.00427i | 1.71184 | + | 0.269968i | ||||
\(221\) | −4.31095 | − | 7.46679i | −0.289986 | − | 0.502270i | ||||
\(222\) | −0.0331646 | − | 8.02348i | −0.00222586 | − | 0.538501i | ||||
\(223\) | −13.8409 | − | 13.8409i | −0.926857 | − | 0.926857i | 0.0706444 | − | 0.997502i | \(-0.477494\pi\) |
−0.997502 | + | 0.0706444i | \(0.977494\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.60790 | − | 7.62943i | 0.173860 | − | 0.508629i | ||||
\(226\) | −10.0027 | + | 10.0858i | −0.665372 | + | 0.670895i | ||||
\(227\) | 5.65628 | + | 1.51560i | 0.375420 | + | 0.100594i | 0.441595 | − | 0.897214i | \(-0.354413\pi\) |
−0.0661747 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(228\) | −17.3305 | − | 17.0463i | −1.14774 | − | 1.12892i | ||||
\(229\) | 16.6826 | + | 9.63173i | 1.10242 | + | 0.636483i | 0.936856 | − | 0.349716i | \(-0.113722\pi\) |
0.165565 | + | 0.986199i | \(0.447055\pi\) | |||||||
\(230\) | −8.04123 | − | 3.61369i | −0.530223 | − | 0.238280i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.179360 | + | 14.4635i | 0.0117756 | + | 0.949572i | ||||
\(233\) | 6.88528 | + | 25.6962i | 0.451070 | + | 1.68341i | 0.699393 | + | 0.714737i | \(0.253454\pi\) |
−0.248323 | + | 0.968677i | \(0.579880\pi\) | |||||||
\(234\) | 4.20464 | − | 1.14528i | 0.274866 | − | 0.0748692i | ||||
\(235\) | −5.20870 | + | 11.4635i | −0.339778 | + | 0.747796i | ||||
\(236\) | 4.98218 | + | 8.46696i | 0.324312 | + | 0.551152i | ||||
\(237\) | −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 | \(0.515266\pi\) | |||||||
\(240\) | 15.4394 | − | 11.4294i | 0.996609 | − | 0.737763i | ||||
\(241\) | 6.80218 | + | 11.7817i | 0.438167 | + | 0.758927i | 0.997548 | − | 0.0699833i | \(-0.0222946\pi\) |
−0.559381 | + | 0.828910i | \(0.688961\pi\) | |||||||
\(242\) | 15.4702 | − | 27.0527i | 0.994460 | − | 1.73902i | ||||
\(243\) | 14.6772 | − | 3.93275i | 0.941543 | − | 0.252286i | ||||
\(244\) | 15.1344 | − | 26.7212i | 0.968878 | − | 1.71065i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.54249 | + | 9.64805i | −0.162103 | + | 0.615137i | ||||
\(247\) | −2.79897 | − | 10.4459i | −0.178094 | − | 0.664657i | ||||
\(248\) | 18.3210 | − | 10.8828i | 1.16339 | − | 0.691057i | ||||
\(249\) | 21.3650 | − | 12.3351i | 1.35395 | − | 0.781704i | ||||
\(250\) | 7.44015 | − | 13.9515i | 0.470557 | − | 0.882370i | ||||
\(251\) | − | 21.2752i | − | 1.34288i | −0.741059 | − | 0.671440i | \(-0.765676\pi\) | ||
0.741059 | − | 0.671440i | \(-0.234324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.3304 | + | 11.3304i | −0.712337 | + | 0.712337i | ||||
\(254\) | −20.1741 | + | 20.3416i | −1.26583 | + | 1.27634i | ||||
\(255\) | 7.61110 | + | 20.2874i | 0.476625 | + | 1.27045i | ||||
\(256\) | 15.9913 | − | 0.528982i | 0.999453 | − | 0.0330613i | ||||
\(257\) | −13.2601 | + | 3.55302i | −0.827140 | + | 0.221631i | −0.647466 | − | 0.762095i | \(-0.724171\pi\) |
−0.179674 | + | 0.983726i | \(0.557504\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | 19.5786 | + | 11.1961i | 1.20957 | + | 0.691696i | ||||
\(263\) | 3.66506 | − | 13.6782i | 0.225998 | − | 0.843434i | −0.756005 | − | 0.654566i | \(-0.772851\pi\) |
0.982002 | − | 0.188868i | \(-0.0604819\pi\) | |||||||
\(264\) | −9.45413 | − | 33.6105i | −0.581862 | − | 2.06859i | ||||
\(265\) | 1.12665 | + | 1.57577i | 0.0692097 | + | 0.0967986i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1198 | − | 12.1198i | 0.741719 | − | 0.741719i | ||||
\(268\) | 0.441986 | + | 0.114522i | 0.0269986 | + | 0.00699556i | ||||
\(269\) | −18.0324 | + | 10.4110i | −1.09946 | + | 0.634772i | −0.936078 | − | 0.351792i | \(-0.885573\pi\) |
−0.163379 | + | 0.986563i | \(0.552239\pi\) | |||||||
\(270\) | 9.37462 | − | 0.952416i | 0.570521 | − | 0.0579622i | ||||
\(271\) | −10.1496 | − | 5.85987i | −0.616544 | − | 0.355962i | 0.158979 | − | 0.987282i | \(-0.449180\pi\) |
−0.775522 | + | 0.631320i | \(0.782513\pi\) | |||||||
\(272\) | −4.38227 | + | 17.5077i | −0.265714 | + | 1.06156i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.37893 | − | 5.23266i | 0.0833043 | − | 0.316117i | ||||
\(275\) | −18.9027 | − | 21.6469i | −1.13988 | − | 1.30536i | ||||
\(276\) | 0.0989926 | + | 11.9744i | 0.00595865 | + | 0.720773i | ||||
\(277\) | −0.451847 | + | 1.68632i | −0.0271489 | + | 0.101321i | −0.978171 | − | 0.207802i | \(-0.933369\pi\) |
0.951022 | + | 0.309123i | \(0.100036\pi\) | |||||||
\(278\) | 12.9061 | − | 0.0533465i | 0.774055 | − | 0.00319951i | ||||
\(279\) | −12.1492 | −0.727351 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.3578 | 0.975825 | 0.487912 | − | 0.872893i | \(-0.337759\pi\) | ||||
0.487912 | + | 0.872893i | \(0.337759\pi\) | |||||||
\(282\) | 17.1029 | − | 0.0706940i | 1.01846 | − | 0.00420977i | ||||
\(283\) | 1.24206 | − | 4.63542i | 0.0738327 | − | 0.275547i | −0.919133 | − | 0.393946i | \(-0.871110\pi\) |
0.992966 | + | 0.118399i | \(0.0377762\pi\) | |||||||
\(284\) | 0.0586556 | + | 7.09512i | 0.00348057 | + | 0.421018i | ||||
\(285\) | 2.63525 | + | 27.0502i | 0.156099 | + | 1.60231i | ||||
\(286\) | 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 | ||||
\(290\) | 10.2209 | − | 12.5325i | 0.600190 | − | 0.735934i | ||||
\(291\) | −16.5354 | + | 9.54672i | −0.969323 | + | 0.559639i | ||||
\(292\) | 24.1582 | + | 6.25958i | 1.41375 | + | 0.366314i | ||||
\(293\) | −3.45390 | + | 3.45390i | −0.201779 | + | 0.201779i | −0.800762 | − | 0.598983i | \(-0.795572\pi\) |
0.598983 | + | 0.800762i | \(0.295572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.80067 | − | 10.8350i | 0.104839 | − | 0.630837i | ||||
\(296\) | −7.19267 | + | 2.02319i | −0.418065 | + | 0.117595i | ||||
\(297\) | 4.43275 | − | 16.5433i | 0.257215 | − | 0.959938i | ||||
\(298\) | −17.6956 | − | 10.1193i | −1.02508 | − | 0.586195i | ||||
\(299\) | −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 | ||||
\(303\) | −7.40398 | + | 1.98389i | −0.425348 | + | 0.113972i | ||||
\(304\) | −10.9930 | + | 19.7889i | −0.630491 | + | 1.13497i | ||||
\(305\) | −32.1464 | + | 12.0602i | −1.84070 | + | 0.690563i | ||||
\(306\) | 7.24571 | − | 7.30585i | 0.414209 | − | 0.417648i | ||||
\(307\) | −9.46795 | + | 9.46795i | −0.540364 | + | 0.540364i | −0.923636 | − | 0.383271i | \(-0.874797\pi\) |
0.383271 | + | 0.923636i | \(0.374797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.56427i | − | 0.0889880i | ||||||
\(310\) | −23.5184 | − | 3.80869i | −1.33575 | − | 0.216319i | ||||
\(311\) | −20.2933 | + | 11.7163i | −1.15073 | + | 0.664372i | −0.949064 | − | 0.315083i | \(-0.897968\pi\) |
−0.201662 | + | 0.979455i | \(0.564634\pi\) | |||||||
\(312\) | −5.92816 | − | 9.98000i | −0.335616 | − | 0.565006i | ||||
\(313\) | −1.68942 | − | 6.30502i | −0.0954919 | − | 0.356381i | 0.901602 | − | 0.432567i | \(-0.142392\pi\) |
−0.997094 | + | 0.0761865i | \(0.975726\pi\) | |||||||
\(314\) | −0.813582 | + | 3.08732i | −0.0459131 | + | 0.174227i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.72689 | + | 6.58020i | −0.209654 | + | 0.370165i | ||||
\(317\) | −1.53450 | + | 0.411168i | −0.0861861 | + | 0.0230935i | −0.301654 | − | 0.953417i | \(-0.597539\pi\) |
0.215468 | + | 0.976511i | \(0.430872\pi\) | |||||||
\(318\) | 1.30617 | − | 2.28411i | 0.0732466 | − | 0.128087i | ||||
\(319\) | −14.6969 | − | 25.4557i | −0.822866 | − | 1.42525i | ||||
\(320\) | −14.0935 | − | 11.0169i | −0.787852 | − | 0.615865i | ||||
\(321\) | −12.4651 | −0.695733 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0557 | − | 18.0557i | −1.00465 | − | 1.00465i | ||||
\(324\) | −11.3978 | − | 19.3701i | −0.633214 | − | 1.07611i | ||||
\(325\) | −7.93300 | − | 5.32503i | −0.440043 | − | 0.295379i | ||||
\(326\) | 22.3217 | − | 6.08007i | 1.23628 | − | 0.336744i | ||||
\(327\) | 6.43852 | + | 24.0289i | 0.356051 | + | 1.32880i | ||||
\(328\) | 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 | \(-0.510186\pi\) |
−0.881580 | + | 0.472035i | \(0.843520\pi\) | |||||||
\(332\) | −16.3786 | − | 16.1100i | −0.898892 | − | 0.884151i | ||||
\(333\) | 4.11473 | + | 1.10254i | 0.225486 | + | 0.0604188i | ||||
\(334\) | −17.2708 | + | 17.4142i | −0.945017 | + | 0.952862i | ||||
\(335\) | −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 | \(0.964423\pi\) | |||||||
\(338\) | 0.0546467 | + | 13.2206i | 0.00297239 | + | 0.719107i | ||||
\(339\) | −10.7861 | − | 18.6820i | −0.585818 | − | 1.01467i | ||||
\(340\) | 16.3166 | − | 11.8712i | 0.884891 | − | 0.643806i | ||||
\(341\) | −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 | ||||
\(345\) | 8.50437 | − | 10.3402i | 0.457860 | − | 0.556699i | ||||
\(346\) | 4.96252 | + | 18.2188i | 0.266787 | + | 0.979450i | ||||
\(347\) | −22.2972 | − | 5.97452i | −1.19698 | − | 0.320729i | −0.395337 | − | 0.918536i | \(-0.629372\pi\) |
−0.801640 | + | 0.597807i | \(0.796039\pi\) | |||||||
\(348\) | −21.2643 | − | 5.50976i | −1.13989 | − | 0.295354i | ||||
\(349\) | 23.7289i | 1.27018i | 0.772439 | + | 0.635089i | \(0.219037\pi\) | ||||
−0.772439 | + | 0.635089i | \(0.780963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.69405i | − | 0.303926i | ||||||
\(352\) | −27.8159 | + | 16.8354i | −1.48259 | + | 0.897329i | ||||
\(353\) | −22.4609 | − | 6.01837i | −1.19547 | − | 0.320326i | −0.394425 | − | 0.918928i | \(-0.629056\pi\) |
−0.801046 | + | 0.598603i | \(0.795723\pi\) | |||||||
\(354\) | −14.3948 | + | 3.92091i | −0.765073 | + | 0.208394i | ||||
\(355\) | 5.03905 | − | 6.12684i | 0.267445 | − | 0.325179i | ||||
\(356\) | −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 | −0.253833 | − | 0.967248i | \(-0.581691\pi\) |
0.964578 | − | 0.263798i | \(-0.0849754\pi\) | |||||||
\(360\) | 3.70052 | + | 9.50374i | 0.195035 | + | 0.500891i | ||||
\(361\) | −6.51400 | − | 11.2826i | −0.342842 | − | 0.593820i | ||||
\(362\) | 3.11055 | − | 0.0128573i | 0.163487 | − | 0.000675763i | ||||
\(363\) | 33.4650 | + | 33.4650i | 1.75646 | + | 1.75646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.2280 | − | 22.6969i | −0.849412 | − | 1.18801i | ||||
\(366\) | 33.1132 | + | 32.8406i | 1.73086 | + | 1.71661i | ||||
\(367\) | 8.61536 | + | 2.30848i | 0.449718 | + | 0.120502i | 0.476567 | − | 0.879138i | \(-0.341881\pi\) |
−0.0268495 | + | 0.999639i | \(0.508547\pi\) | |||||||
\(368\) | 10.7222 | − | 3.06386i | 0.558932 | − | 0.159715i | ||||
\(369\) | −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 | ||||
\(373\) | 3.23163 | + | 12.0606i | 0.167328 | + | 0.624475i | 0.997732 | + | 0.0673137i | \(0.0214428\pi\) |
−0.830404 | + | 0.557161i | \(0.811891\pi\) | |||||||
\(374\) | −9.63863 | − | 35.3862i | −0.498402 | − | 1.82977i | ||||
\(375\) | 17.4731 | + | 16.4700i | 0.902308 | + | 0.850508i | ||||
\(376\) | −4.31265 | − | 15.3320i | −0.222408 | − | 0.790686i | ||||
\(377\) | −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 | \(0.559898\pi\) | |||||||
\(380\) | 23.6223 | − | 9.08567i | 1.21180 | − | 0.466085i | ||||
\(381\) | −21.7539 | − | 37.6789i | −1.11449 | − | 1.93035i | ||||
\(382\) | 14.1453 | + | 8.08905i | 0.723739 | + | 0.413872i | ||||
\(383\) | 13.8541 | − | 3.71220i | 0.707912 | − | 0.189684i | 0.113140 | − | 0.993579i | \(-0.463909\pi\) |
0.594772 | + | 0.803895i | \(0.297242\pi\) | |||||||
\(384\) | −5.60724 | + | 23.6425i | −0.286143 | + | 1.20650i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.62190 | + | 1.48151i | 0.286147 | + | 0.0754066i | ||||
\(387\) | 2.79090 | + | 10.4158i | 0.141869 | + | 0.529463i | ||||
\(388\) | 12.6762 | + | 12.4683i | 0.643536 | + | 0.632983i | ||||
\(389\) | 22.5816 | − | 13.0375i | 1.14493 | − | 0.661028i | 0.197287 | − | 0.980346i | \(-0.436787\pi\) |
0.947648 | + | 0.319318i | \(0.103454\pi\) | |||||||
\(390\) | −2.07470 | + | 12.8111i | −0.105057 | + | 0.648717i | ||||
\(391\) | 12.5786i | 0.636127i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.2193 | + | 24.2193i | −1.22170 | + | 1.22170i | ||||
\(394\) | 1.76945 | + | 1.75488i | 0.0891434 | + | 0.0884095i | ||||
\(395\) | 7.91618 | − | 2.96986i | 0.398306 | − | 0.149430i | ||||
\(396\) | 18.5365 | − | 0.153242i | 0.931493 | − | 0.00770068i | ||||
\(397\) | 16.2897 | − | 4.36480i | 0.817555 | − | 0.219063i | 0.174277 | − | 0.984697i | \(-0.444241\pi\) |
0.643277 | + | 0.765634i | \(0.277574\pi\) | |||||||
\(398\) | 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 | −0.809988 | − | 0.586446i | \(-0.800527\pi\) |
0.912871 | + | 0.408247i | \(0.133860\pi\) | |||||||
\(402\) | −0.344208 | + | 0.601918i | −0.0171675 | + | 0.0300209i | ||||
\(403\) | −3.72617 | + | 13.9062i | −0.185614 | + | 0.692720i | ||||
\(404\) | 3.62001 | + | 6.15203i | 0.180102 | + | 0.306075i | ||||
\(405\) | −4.11943 | + | 24.7875i | −0.204696 | + | 1.23170i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7364 | − | 10.7364i | 0.532184 | − | 0.532184i | ||||
\(408\) | −23.9044 | − | 13.4088i | −1.18344 | − | 0.663832i | ||||
\(409\) | 1.43363 | − | 0.827707i | 0.0708884 | − | 0.0409275i | −0.464137 | − | 0.885764i | \(-0.653635\pi\) |
0.535025 | + | 0.844836i | \(0.320302\pi\) | |||||||
\(410\) | −8.05025 | − | 6.56537i | −0.397574 | − | 0.324241i | ||||
\(411\) | 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 | ||||
\(415\) | 2.49050 | + | 25.5643i | 0.122254 | + | 1.25490i | ||||
\(416\) | −7.48400 | + | 7.79992i | −0.366933 | + | 0.382423i | ||||
\(417\) | −5.07283 | + | 18.9321i | −0.248418 | + | 0.927107i | ||||
\(418\) | −0.190144 | − | 46.0013i | −0.00930025 | − | 2.25000i | ||||
\(419\) | 23.4536 | 1.14579 | 0.572893 | − | 0.819630i | \(-0.305821\pi\) | ||||
0.572893 | + | 0.819630i | \(0.305821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.3030 | 1.18446 | 0.592228 | − | 0.805770i | \(-0.298248\pi\) | ||||
0.592228 | + | 0.805770i | \(0.298248\pi\) | |||||||
\(422\) | −0.0916080 | − | 22.1626i | −0.00445941 | − | 1.07886i | ||||
\(423\) | −2.35018 | + | 8.77101i | −0.114270 | + | 0.426461i | ||||
\(424\) | −2.37446 | − | 0.604780i | −0.115314 | − | 0.0293707i | ||||
\(425\) | −22.5083 | − | 1.52322i | −1.09181 | − | 0.0738870i | ||||
\(426\) | −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 | ||||
\(430\) | 2.13734 | + | 21.0378i | 0.103072 | + | 1.01453i | ||||
\(431\) | −8.78820 | + | 5.07387i | −0.423313 | + | 0.244400i | −0.696494 | − | 0.717563i | \(-0.745258\pi\) |
0.273181 | + | 0.961963i | \(0.411924\pi\) | |||||||
\(432\) | −8.28758 | + | 8.56626i | −0.398736 | + | 0.412144i | ||||
\(433\) | −3.32616 | + | 3.32616i | −0.159845 | + | 0.159845i | −0.782498 | − | 0.622653i | \(-0.786055\pi\) |
0.622653 | + | 0.782498i | \(0.286055\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.2841 | + | 19.9781i | 0.684870 | + | 0.957879i | ||||
\(436\) | 19.9658 | − | 11.7484i | 0.956188 | − | 0.562646i | ||||
\(437\) | −4.08345 | + | 15.2397i | −0.195338 | + | 0.729012i | ||||
\(438\) | −18.8138 | + | 32.8997i | −0.898957 | + | 1.57201i | ||||
\(439\) | 9.87337 | − | 17.1012i | 0.471230 | − | 0.816194i | −0.528228 | − | 0.849102i | \(-0.677143\pi\) |
0.999458 | + | 0.0329080i | \(0.0104768\pi\) | |||||||
\(440\) | 35.9310 | + | 5.51443i | 1.71294 | + | 0.262890i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.14020 | − | 10.5343i | −0.292060 | − | 0.501067i | ||||
\(443\) | 15.0706 | − | 4.03815i | 0.716025 | − | 0.191858i | 0.117628 | − | 0.993058i | \(-0.462471\pi\) |
0.598398 | + | 0.801199i | \(0.295804\pi\) | |||||||
\(444\) | −0.0938029 | − | 11.3466i | −0.00445169 | − | 0.538487i | ||||
\(445\) | 6.26829 | + | 16.7082i | 0.297146 | + | 0.792043i | ||||
\(446\) | −19.6548 | − | 19.4930i | −0.930680 | − | 0.923018i | ||||
\(447\) | 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 | \(-0.103706\pi\) | |||||||
\(450\) | 3.64350 | − | 10.8048i | 0.171756 | − | 0.509343i | ||||
\(451\) | −16.3515 | + | 9.44053i | −0.769961 | + | 0.444537i | ||||
\(452\) | −14.0869 | + | 14.3218i | −0.662593 | + | 0.673640i | ||||
\(453\) | 8.37680 | + | 31.2626i | 0.393576 | + | 1.46885i | ||||
\(454\) | 8.00798 | + | 2.11029i | 0.375833 | + | 0.0990410i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −24.6085 | − | 24.0057i | −1.15240 | − | 1.12417i | ||||
\(457\) | −26.1714 | + | 7.01260i | −1.22425 | + | 0.328036i | −0.812336 | − | 0.583189i | \(-0.801805\pi\) |
−0.411909 | + | 0.911225i | \(0.635138\pi\) | |||||||
\(458\) | 23.6489 | + | 13.5237i | 1.10504 | + | 0.631921i | ||||
\(459\) | −6.72231 | − | 11.6434i | −0.313771 | − | 0.543467i | ||||
\(460\) | −11.3930 | − | 5.06348i | −0.531203 | − | 0.236086i | ||||
\(461\) | −30.4323 | −1.41737 | −0.708686 | − | 0.705524i | \(-0.750712\pi\) | ||||
−0.708686 | + | 0.705524i | \(0.750712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5147 | + | 12.5147i | 0.581607 | + | 0.581607i | 0.935345 | − | 0.353737i | \(-0.115089\pi\) |
−0.353737 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(464\) | 0.338197 | + | 20.4532i | 0.0157004 | + | 0.949516i | ||||
\(465\) | 14.9672 | − | 32.9404i | 0.694089 | − | 1.52758i | ||||
\(466\) | 9.88738 | + | 36.2994i | 0.458024 | + | 1.68154i | ||||
\(467\) | 4.95944 | + | 18.5089i | 0.229496 | + | 0.856490i | 0.980553 | + | 0.196253i | \(0.0628774\pi\) |
−0.751058 | + | 0.660237i | \(0.770456\pi\) | |||||||
\(468\) | 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 | ||||
\(472\) | 7.09529 | + | 11.9449i | 0.326587 | + | 0.549807i | ||||
\(473\) | 37.1251 | + | 9.94764i | 1.70701 | + | 0.457393i | ||||
\(474\) | −8.15426 | − | 8.08713i | −0.374538 | − | 0.371454i | ||||
\(475\) | −26.7756 | − | 9.15246i | −1.22855 | − | 0.419944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.987806 | + | 0.987806i | 0.0452285 | + | 0.0452285i | ||||
\(478\) | −2.09621 | + | 0.00866458i | −0.0958785 | + | 0.000396309i | ||||
\(479\) | −1.79254 | − | 3.10476i | −0.0819031 | − | 0.141860i | 0.822164 | − | 0.569250i | \(-0.192766\pi\) |
−0.904067 | + | 0.427390i | \(0.859433\pi\) | |||||||
\(480\) | 21.7676 | − | 16.2537i | 0.993551 | − | 0.741876i | ||||
\(481\) | 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 | ||||
\(485\) | −1.92752 | − | 19.7855i | −0.0875241 | − | 0.898413i | ||||
\(486\) | 20.7335 | − | 5.64749i | 0.940492 | − | 0.256175i | ||||
\(487\) | 20.1438 | + | 5.39752i | 0.912804 | + | 0.244585i | 0.684507 | − | 0.729006i | \(-0.260018\pi\) |
0.228297 | + | 0.973592i | \(0.426684\pi\) | |||||||
\(488\) | 21.2468 | − | 37.8777i | 0.961799 | − | 1.71464i | ||||
\(489\) | 35.1337i | 1.58880i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.2968i | 0.780592i | 0.920689 | + | 0.390296i | \(0.127627\pi\) | ||||
−0.920689 | + | 0.390296i | \(0.872373\pi\) | |||||||
\(492\) | −3.53920 | + | 13.6591i | −0.159559 | + | 0.615802i | ||||
\(493\) | −22.2879 | − | 5.97203i | −1.00380 | − | 0.268967i | ||||
\(494\) | −4.01937 | − | 14.7563i | −0.180840 | − | 0.663916i | ||||
\(495\) | −16.0068 | − | 13.1649i | −0.719451 | − | 0.591716i | ||||
\(496\) | 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 | −0.411927 | − | 0.911217i | \(-0.635144\pi\) |
0.995100 | − | 0.0988689i | \(-0.0315224\pi\) | |||||||
\(500\) | 10.4403 | − | 19.7737i | 0.466905 | − | 0.884307i | ||||
\(501\) | −18.6233 | − | 32.2565i | −0.832028 | − | 1.44111i | ||||
\(502\) | −0.124365 | − | 30.0874i | −0.00555067 | − | 1.34287i | ||||
\(503\) | 2.43908 | + | 2.43908i | 0.108753 | + | 0.108753i | 0.759390 | − | 0.650636i | \(-0.225498\pi\) |
−0.650636 | + | 0.759390i | \(0.725498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.30835 | − | 7.87262i | 0.0582209 | − | 0.350327i | ||||
\(506\) | −15.9573 | + | 16.0897i | −0.709386 | + | 0.715275i | ||||
\(507\) | −19.3935 | − | 5.19646i | −0.861294 | − | 0.230783i | ||||
\(508\) | −28.4113 | + | 28.8850i | −1.26055 | + | 1.28156i | ||||
\(509\) | 3.53392 | + | 2.04031i | 0.156638 | + | 0.0904352i | 0.576270 | − | 0.817259i | \(-0.304508\pi\) |
−0.419632 | + | 0.907694i | \(0.637841\pi\) | |||||||
\(510\) | 10.8822 | + | 28.6460i | 0.481873 | + | 1.26847i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6118 | − | 0.841564i | 0.999308 | − | 0.0371922i | ||||
\(513\) | −4.36460 | − | 16.2889i | −0.192702 | − | 0.719173i | ||||
\(514\) | −18.7316 | + | 5.10220i | −0.826217 | + | 0.225048i | ||||
\(515\) | 1.48275 | + | 0.673722i | 0.0653379 | + | 0.0296878i | ||||
\(516\) | 24.7553 | − | 14.5667i | 1.08979 | − | 0.641262i | ||||
\(517\) | 22.8858 | + | 22.8858i | 1.00652 | + | 1.00652i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.6760 | −1.25874 | ||||||||
\(520\) | 12.0132 | − | 1.32090i | 0.526813 | − | 0.0579255i | ||||
\(521\) | 3.01201 | + | 5.21696i | 0.131959 | + | 0.228559i | 0.924432 | − | 0.381348i | \(-0.124540\pi\) |
−0.792473 | + | 0.609907i | \(0.791207\pi\) | |||||||
\(522\) | 5.78947 | − | 10.1241i | 0.253398 | − | 0.443119i | ||||
\(523\) | −35.4223 | + | 9.49137i | −1.54891 | + | 0.415029i | −0.929132 | − | 0.369749i | \(-0.879444\pi\) |
−0.619777 | + | 0.784778i | \(0.712777\pi\) | |||||||
\(524\) | 27.7535 | + | 15.7191i | 1.21242 | + | 0.686690i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.10318 | − | 19.3652i | 0.222509 | − | 0.844361i | ||||
\(527\) | 8.79813 | + | 32.8351i | 0.383252 | + | 1.43032i | ||||
\(528\) | −13.5665 | − | 47.4768i | −0.590407 | − | 2.06616i | ||||
\(529\) | −13.1878 | + | 7.61400i | −0.573384 | + | 0.331043i | ||||
\(530\) | 1.60252 | + | 2.22187i | 0.0696092 | + | 0.0965117i | ||||
\(531\) | − | 7.92095i | − | 0.343740i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.43869 | + | 4.43869i | −0.192261 | + | 0.192261i | ||||
\(534\) | 17.0690 | − | 17.2107i | 0.738647 | − | 0.744779i | ||||
\(535\) | 5.36866 | − | 11.8155i | 0.232107 | − | 0.510830i | ||||
\(536\) | 0.625727 | + | 0.159374i | 0.0270273 | + | 0.00688390i | ||||
\(537\) | −20.0088 | + | 5.36133i | −0.863442 | + | 0.231358i | ||||
\(538\) | −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 | −0.789563 | − | 0.613669i | \(-0.789693\pi\) |
0.926235 | + | 0.376947i | \(0.123026\pi\) | |||||||
\(542\) | −14.3878 | − | 8.22770i | −0.618010 | − | 0.353410i | ||||
\(543\) | −1.22262 | + | 4.56290i | −0.0524678 | + | 0.195813i | ||||
\(544\) | −6.09507 | + | 24.7851i | −0.261324 | + | 1.06265i | ||||
\(545\) | −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 | \(0.282592\pi\) | |||||||
\(548\) | 1.91950 | − | 7.40810i | 0.0819969 | − | 0.316458i | ||||
\(549\) | −21.4433 | + | 12.3803i | −0.915177 | + | 0.528377i | ||||
\(550\) | −26.8588 | − | 30.5026i | −1.14526 | − | 1.30063i | ||||
\(551\) | −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 | ||||
\(555\) | −8.05853 | + | 9.79814i | −0.342065 | + | 0.415908i | ||||
\(556\) | 18.2515 | − | 0.150886i | 0.774035 | − | 0.00639897i | ||||
\(557\) | −2.37285 | + | 8.85561i | −0.100541 | + | 0.375224i | −0.997801 | − | 0.0662779i | \(-0.978888\pi\) |
0.897260 | + | 0.441502i | \(0.145554\pi\) | |||||||
\(558\) | −17.1814 | + | 0.0710182i | −0.727345 | + | 0.00300644i | ||||
\(559\) | 12.7781 | 0.540457 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 55.6969 | 2.35152 | ||||||||
\(562\) | 23.1332 | − | 0.0956199i | 0.975816 | − | 0.00403348i | ||||
\(563\) | −5.45194 | + | 20.3469i | −0.229772 | + | 0.857520i | 0.750664 | + | 0.660684i | \(0.229734\pi\) |
−0.980436 | + | 0.196837i | \(0.936933\pi\) | |||||||
\(564\) | 24.1866 | − | 0.199951i | 1.01844 | − | 0.00841946i | ||||
\(565\) | 22.3540 | − | 2.17774i | 0.940440 | − | 0.0916184i | ||||
\(566\) | 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 | \(-0.226823\pi\) |
−0.187863 | + | 0.982195i | \(0.560156\pi\) | |||||||
\(570\) | 3.88490 | + | 38.2390i | 0.162721 | + | 1.60166i | ||||
\(571\) | 5.57733 | − | 3.22007i | 0.233404 | − | 0.134756i | −0.378738 | − | 0.925504i | \(-0.623642\pi\) |
0.612141 | + | 0.790748i | \(0.290308\pi\) | |||||||
\(572\) | 5.50976 | − | 21.2643i | 0.230375 | − | 0.889106i | ||||
\(573\) | −17.4982 | + | 17.4982i | −0.730997 | + | 0.730997i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.13861 | + | 12.5147i | 0.255998 | + | 0.521899i | ||||
\(576\) | −11.3287 | − | 6.17124i | −0.472030 | − | 0.257135i | ||||
\(577\) | 5.75880 | − | 21.4921i | 0.239742 | − | 0.894729i | −0.736212 | − | 0.676751i | \(-0.763387\pi\) |
0.975954 | − | 0.217978i | \(-0.0699461\pi\) | |||||||
\(578\) | −4.12223 | − | 2.35731i | −0.171462 | − | 0.0980510i | ||||
\(579\) | −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 | ||||
\(583\) | 4.80957 | − | 1.28872i | 0.199192 | − | 0.0533734i | ||||
\(584\) | 34.2011 | + | 8.71109i | 1.41525 | + | 0.360467i | ||||
\(585\) | −6.27314 | − | 2.85034i | −0.259362 | − | 0.117847i | ||||
\(586\) | −4.86432 | + | 4.90470i | −0.200943 | + | 0.202611i | ||||
\(587\) | 6.67713 | − | 6.67713i | 0.275595 | − | 0.275595i | −0.555753 | − | 0.831348i | \(-0.687570\pi\) |
0.831348 | + | 0.555753i | \(0.187570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.6377i | 1.75685i | ||||||||
\(590\) | 2.48317 | − | 15.3334i | 0.102231 | − | 0.631265i | ||||
\(591\) | −3.27757 | + | 1.89230i | −0.134821 | + | 0.0778390i | ||||
\(592\) | −10.1601 | + | 2.90324i | −0.417576 | + | 0.119322i | ||||
\(593\) | −5.00324 | − | 18.6723i | −0.205458 | − | 0.766781i | −0.989309 | − | 0.145832i | \(-0.953414\pi\) |
0.783851 | − | 0.620949i | \(-0.213253\pi\) | |||||||
\(594\) | 6.17210 | − | 23.4214i | 0.253244 | − | 0.960993i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.0844 | − | 14.2073i | −1.02750 | − | 0.581953i | ||||
\(597\) | −8.74205 | + | 2.34243i | −0.357788 | + | 0.0958691i | ||||
\(598\) | −3.73994 | + | 6.54005i | −0.152938 | + | 0.267443i | ||||
\(599\) | 8.68441 | + | 15.0418i | 0.354835 | + | 0.614593i | 0.987090 | − | 0.160168i | \(-0.0512036\pi\) |
−0.632255 | + | 0.774761i | \(0.717870\pi\) | |||||||
\(600\) | −30.3267 | − | 1.67483i | −1.23808 | − | 0.0683748i | ||||
\(601\) | 22.5611 | 0.920285 | 0.460142 | − | 0.887845i | \(-0.347798\pi\) | ||||
0.460142 | + | 0.887845i | \(0.347798\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.260310 | − | 0.260310i | −0.0106007 | − | 0.0106007i | ||||
\(604\) | 25.9764 | − | 15.2852i | 1.05696 | − | 0.621945i | ||||
\(605\) | −46.1343 | + | 17.3079i | −1.87563 | + | 0.703666i | ||||
\(606\) | −10.4591 | + | 2.84890i | −0.424873 | + | 0.115729i | ||||
\(607\) | 3.68087 | + | 13.7372i | 0.149402 | + | 0.557575i | 0.999520 | + | 0.0309832i | \(0.00986383\pi\) |
−0.850118 | + | 0.526592i | \(0.823470\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | 10.2042 | − | 10.3743i | 0.412480 | − | 0.419356i | ||||
\(613\) | −30.8145 | − | 8.25672i | −1.24459 | − | 0.333486i | −0.424344 | − | 0.905501i | \(-0.639495\pi\) |
−0.820243 | + | 0.572015i | \(0.806162\pi\) | |||||||
\(614\) | −13.3342 | + | 13.4449i | −0.538126 | + | 0.542593i | ||||
\(615\) | 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 | \(0.496500\pi\) | |||||||
\(618\) | −0.00914395 | − | 2.21219i | −0.000367824 | − | 0.0889872i | ||||
\(619\) | 17.6742 | + | 30.6126i | 0.710387 | + | 1.23043i | 0.964712 | + | 0.263307i | \(0.0848133\pi\) |
−0.254325 | + | 0.967119i | \(0.581853\pi\) | |||||||
\(620\) | −33.2820 | − | 5.24878i | −1.33664 | − | 0.210796i | ||||
\(621\) | −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 | ||||
\(625\) | −23.1374 | + | 9.46903i | −0.925494 | + | 0.378761i | ||||
\(626\) | −2.42604 | − | 8.90669i | −0.0969642 | − | 0.355983i | ||||
\(627\) | 67.4799 | + | 18.0812i | 2.69489 | + | 0.722093i | ||||
\(628\) | −1.13252 | + | 4.37084i | −0.0451925 | + | 0.174416i | ||||
\(629\) | − | 11.9192i | − | 0.475248i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 21.4460i | − | 0.853752i | −0.904310 | − | 0.426876i | \(-0.859614\pi\) | ||
0.904310 | − | 0.426876i | \(-0.140386\pi\) | |||||||
\(632\) | −5.23211 | + | 9.32752i | −0.208122 | + | 0.371029i | ||||
\(633\) | 32.5106 | + | 8.71119i | 1.29218 | + | 0.346239i | ||||
\(634\) | −2.16769 | + | 0.590444i | −0.0860899 | + | 0.0234495i | ||||
\(635\) | 45.0848 | − | 4.39220i | 1.78914 | − | 0.174299i | ||||
\(636\) | 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 | ||||
\(640\) | −19.9955 | − | 15.4978i | −0.790391 | − | 0.612603i | ||||
\(641\) | −6.13958 | − | 10.6341i | −0.242499 | − | 0.420020i | 0.718927 | − | 0.695086i | \(-0.244634\pi\) |
−0.961425 | + | 0.275066i | \(0.911300\pi\) | |||||||
\(642\) | −17.6281 | + | 0.0728650i | −0.695727 | + | 0.00287575i | ||||
\(643\) | 8.02266 | + | 8.02266i | 0.316383 | + | 0.316383i | 0.847376 | − | 0.530993i | \(-0.178181\pi\) |
−0.530993 | + | 0.847376i | \(0.678181\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.6789 | − | 5.26472i | −1.24735 | − | 0.207298i | ||||
\(646\) | −25.6400 | − | 25.4289i | −1.00879 | − | 1.00049i | ||||
\(647\) | 33.5034 | + | 8.97722i | 1.31716 | + | 0.352931i | 0.847912 | − | 0.530138i | \(-0.177860\pi\) |
0.469244 | + | 0.883068i | \(0.344526\pi\) | |||||||
\(648\) | −16.2321 | − | 27.3265i | −0.637656 | − | 1.07349i | ||||
\(649\) | −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 | ||||
\(653\) | −6.75454 | − | 25.2083i | −0.264326 | − | 0.986476i | −0.962662 | − | 0.270707i | \(-0.912743\pi\) |
0.698336 | − | 0.715770i | \(-0.253924\pi\) | |||||||
\(654\) | 9.24583 | + | 33.9441i | 0.361541 | + | 1.32732i | ||||
\(655\) | −12.5261 | − | 33.3884i | −0.489435 | − | 1.30459i | ||||
\(656\) | 13.1381 | − | 0.217241i | 0.512957 | − | 0.00848184i | ||||
\(657\) | −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 | \(0.413303\pi\) | |||||||
\(660\) | −22.4206 | + | 50.4474i | −0.872722 | + | 1.96366i | ||||
\(661\) | 2.97447 | + | 5.15193i | 0.115693 | + | 0.200387i | 0.918057 | − | 0.396449i | \(-0.129758\pi\) |
−0.802363 | + | 0.596836i | \(0.796424\pi\) | |||||||
\(662\) | −23.5616 | − | 13.4738i | −0.915748 | − | 0.523672i | ||||
\(663\) | 17.8862 | − | 4.79259i | 0.694643 | − | 0.186129i | ||||
\(664\) | −23.2568 | − | 22.6870i | −0.902538 | − | 0.880428i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.82551 | + | 1.53516i | 0.225734 | + | 0.0594863i | ||||
\(667\) | 3.68997 | + | 13.7712i | 0.142876 | + | 0.533222i | ||||
\(668\) | −24.3226 | + | 24.7281i | −0.941071 | + | 0.956760i | ||||
\(669\) | 36.4068 | − | 21.0195i | 1.40757 | − | 0.812659i | ||||
\(670\) | −0.422303 | − | 0.585515i | −0.0163150 | − | 0.0226204i | ||||
\(671\) | 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 | \(0.224358\pi\) | |||||||
\(674\) | −22.9984 | − | 22.8090i | −0.885864 | − | 0.878571i | ||||
\(675\) | −12.3704 | − | 8.30362i | −0.476136 | − | 0.319607i | ||||
\(676\) | 0.154563 | + | 18.6963i | 0.00594472 | + | 0.719088i | ||||
\(677\) | −15.9189 | + | 4.26545i | −0.611812 | + | 0.163934i | −0.551403 | − | 0.834239i | \(-0.685907\pi\) |
−0.0604090 | + | 0.998174i | \(0.519241\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | −30.4007 | + | 53.1618i | −1.16410 | + | 2.03567i | ||||
\(683\) | 12.9994 | − | 48.5144i | 0.497408 | − | 1.85635i | −0.0186937 | − | 0.999825i | \(-0.505951\pi\) |
0.516102 | − | 0.856527i | \(-0.327383\pi\) | |||||||
\(684\) | 15.7308 | − | 9.25641i | 0.601482 | − | 0.353928i | ||||
\(685\) | −6.96001 | + | 4.97631i | −0.265928 | + | 0.190135i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.2544 | + | 29.2544i | −1.11612 | + | 1.11612i | ||||
\(688\) | −19.2237 | − | 18.5983i | −0.732898 | − | 0.709055i | ||||
\(689\) | 1.43363 | − | 0.827707i | 0.0546169 | − | 0.0315331i | ||||
\(690\) | 11.9664 | − | 14.6729i | 0.455555 | − | 0.558587i | ||||
\(691\) | −0.185080 | − | 0.106856i | −0.00704078 | − | 0.00406500i | 0.496475 | − | 0.868051i | \(-0.334627\pi\) |
−0.503516 | + | 0.863986i | \(0.667961\pi\) | |||||||
\(692\) | 7.12451 | + | 25.7361i | 0.270833 | + | 0.978339i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.5677 | − | 8.31883i | −1.19829 | − | 0.315779i | ||||
\(695\) | −15.7607 | − | 12.9624i | −0.597836 | − | 0.491694i | ||||
\(696\) | −30.1043 | − | 7.66761i | −1.14110 | − | 0.290640i | ||||
\(697\) | −3.83614 | + | 14.3167i | −0.145304 | + | 0.542282i | ||||
\(698\) | 0.138708 | + | 33.5574i | 0.00525017 | + | 1.27017i | ||||
\(699\) | −57.1343 | −2.16102 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.4863 | −0.962605 | −0.481303 | − | 0.876554i | \(-0.659836\pi\) | ||||
−0.481303 | + | 0.876554i | \(0.659836\pi\) | |||||||
\(702\) | −0.0332847 | − | 8.05253i | −0.00125625 | − | 0.303923i | ||||
\(703\) | 3.86938 | − | 14.4407i | 0.145936 | − | 0.544642i | ||||
\(704\) | −39.2389 | + | 23.9712i | −1.47887 | + | 0.903449i | ||||
\(705\) | −20.8858 | − | 17.1776i | −0.786605 | − | 0.646947i | ||||
\(706\) | −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 | \(-0.0786489\pi\) |
0.273006 | + | 0.962012i | \(0.411982\pi\) | |||||||
\(710\) | 7.09042 | − | 8.69404i | 0.266099 | − | 0.326282i | ||||
\(711\) | 5.28049 | − | 3.04869i | 0.198034 | − | 0.114335i | ||||
\(712\) | −19.6870 | − | 11.0431i | −0.737801 | − | 0.413857i | ||||
\(713\) | 14.8518 | − | 14.8518i | 0.556206 | − | 0.556206i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.9781 | + | 14.2841i | −0.747140 | + | 0.534195i | ||||
\(716\) | 9.78283 | + | 16.6254i | 0.365602 | + | 0.621322i | ||||
\(717\) | 0.823933 | − | 3.07496i | 0.0307703 | − | 0.114836i | ||||
\(718\) | 18.9083 | − | 33.0650i | 0.705651 | − | 1.23397i | ||||
\(719\) | 1.79254 | − | 3.10476i | 0.0668503 | − | 0.115788i | −0.830663 | − | 0.556776i | \(-0.812038\pi\) |
0.897513 | + | 0.440987i | \(0.145372\pi\) | |||||||
\(720\) | 5.28884 | + | 13.4186i | 0.197103 | + | 0.500081i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.27806 | − | 15.9178i | −0.345294 | − | 0.592398i | ||||
\(723\) | −28.2223 | + | 7.56215i | −1.04960 | + | 0.281240i | ||||
\(724\) | 4.39886 | − | 0.0363655i | 0.163483 | − | 0.00135151i | ||||
\(725\) | −25.0892 | + | 4.93526i | −0.931789 | + | 0.183291i | ||||
\(726\) | 47.5218 | + | 47.1306i | 1.76370 | + | 1.74918i | ||||
\(727\) | 35.6453 | − | 35.6453i | 1.32201 | − | 1.32201i | 0.409867 | − | 0.912145i | \(-0.365575\pi\) |
0.912145 | − | 0.409867i | \(-0.134425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.07793i | − | 0.0399234i | ||||||
\(730\) | −23.0823 | − | 32.0032i | −0.854315 | − | 1.18449i | ||||
\(731\) | 26.1292 | − | 15.0857i | 0.966422 | − | 0.557964i | ||||
\(732\) | 47.0208 | + | 46.2497i | 1.73794 | + | 1.70944i | ||||
\(733\) | 6.53180 | + | 24.3770i | 0.241258 | + | 0.900386i | 0.975228 | + | 0.221204i | \(0.0709986\pi\) |
−0.733970 | + | 0.679182i | \(0.762335\pi\) | |||||||
\(734\) | 12.1973 | + | 3.21429i | 0.450212 | + | 0.118642i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.1454 | − | 4.39560i | 0.558267 | − | 0.162024i | ||||
\(737\) | −1.26744 | + | 0.339609i | −0.0466867 | + | 0.0125097i | ||||
\(738\) | −6.50320 | − | 3.71887i | −0.239386 | − | 0.136893i | ||||
\(739\) | 3.57030 | + | 6.18393i | 0.131335 | + | 0.227480i | 0.924192 | − | 0.381929i | \(-0.124740\pi\) |
−0.792856 | + | 0.609409i | \(0.791407\pi\) | |||||||
\(740\) | 10.7958 | + | 4.79803i | 0.396860 | + | 0.176379i | ||||
\(741\) | 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 | \(0.728176\pi\) | |||||||
\(744\) | 12.3924 | + | 44.0565i | 0.454328 | + | 1.61519i | ||||
\(745\) | 11.3214 | + | 30.1772i | 0.414784 | + | 1.10561i | ||||
\(746\) | 4.64068 | + | 17.0372i | 0.169907 | + | 0.623778i | ||||
\(747\) | 4.79418 | + | 17.8921i | 0.175410 | + | 0.654639i | ||||
\(748\) | −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 | \(-0.385787\pi\) |
−0.635291 | + | 0.772273i | \(0.719120\pi\) | |||||||
\(752\) | −6.18858 | − | 21.6573i | −0.225674 | − | 0.789760i | ||||
\(753\) | 44.1356 | + | 11.8261i | 1.60839 | + | 0.430967i | ||||
\(754\) | −9.81264 | − | 9.73185i | −0.357355 | − | 0.354413i | ||||
\(755\) | −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 | \(-0.563013\pi\) | |||||||
\(758\) | −10.3005 | + | 0.0425765i | −0.374131 | + | 0.00154645i | ||||
\(759\) | −17.2069 | − | 29.8032i | −0.624570 | − | 1.08179i | ||||
\(760\) | 33.3535 | − | 12.9870i | 1.20986 | − | 0.471090i | ||||
\(761\) | 10.7235 | − | 18.5737i | 0.388727 | − | 0.673295i | −0.603552 | − | 0.797324i | \(-0.706248\pi\) |
0.992279 | + | 0.124029i | \(0.0395817\pi\) | |||||||
\(762\) | −30.9847 | − | 53.1584i | −1.12246 | − | 1.92573i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.0517 | + | 11.3569i | 0.725443 | + | 0.410877i | ||||
\(765\) | −16.1926 | + | 1.57750i | −0.585445 | + | 0.0570346i | ||||
\(766\) | 19.5708 | − | 5.33078i | 0.707122 | − | 0.192609i | ||||
\(767\) | −9.06652 | − | 2.42937i | −0.327373 | − | 0.0877194i | ||||
\(768\) | −7.79157 | + | 33.4680i | −0.281154 | + | 1.20767i | ||||
\(769\) | − | 25.9795i | − | 0.936844i | −0.883505 | − | 0.468422i | \(-0.844823\pi\) | ||
0.883505 | − | 0.468422i | \(-0.155177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 29.4831i | − | 1.06181i | ||||||
\(772\) | 7.95916 | + | 2.06228i | 0.286457 | + | 0.0742232i | ||||
\(773\) | −18.0714 | − | 4.84222i | −0.649983 | − | 0.174162i | −0.0812619 | − | 0.996693i | \(-0.525895\pi\) |
−0.568721 | + | 0.822530i | \(0.692562\pi\) | |||||||
\(774\) | 4.00777 | + | 14.7137i | 0.144056 | + | 0.528872i | ||||
\(775\) | 24.7776 | + | 28.3746i | 0.890038 | + | 1.01925i | ||||
\(776\) | 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 | ||||
\(780\) | −2.85916 | + | 18.1296i | −0.102374 | + | 0.649145i | ||||
\(781\) | −10.1955 | − | 17.6591i | −0.364824 | − | 0.631893i | ||||
\(782\) | 0.0735285 | + | 17.7887i | 0.00262937 | + | 0.636121i | ||||
\(783\) | −10.7753 | − | 10.7753i | −0.385077 | − | 0.385077i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.10647 | − | 2.93607i | 0.146566 | − | 0.104793i | ||||
\(786\) | −34.1094 | + | 34.3925i | −1.21664 | + | 1.22674i | ||||
\(787\) | 17.1018 | + | 4.58242i | 0.609615 | + | 0.163346i | 0.550402 | − | 0.834900i | \(-0.314474\pi\) |
0.0592125 | + | 0.998245i | \(0.481141\pi\) | |||||||
\(788\) | 2.51261 | + | 2.47141i | 0.0895081 | + | 0.0880403i | ||||
\(789\) | 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 | ||||
\(793\) | 7.59410 | + | 28.3416i | 0.269675 | + | 1.00644i | ||||
\(794\) | 23.0113 | − | 6.26793i | 0.816642 | − | 0.222440i | ||||
\(795\) | −3.89521 | + | 1.46134i | −0.138149 | + | 0.0518283i | ||||
\(796\) | 4.27423 | + | 7.26384i | 0.151496 | + | 0.257460i | ||||
\(797\) | −35.3823 | − | 35.3823i | −1.25331 | − | 1.25331i | −0.954229 | − | 0.299076i | \(-0.903321\pi\) |
−0.299076 | − | 0.954229i | \(-0.596679\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4070 | 0.898835 | ||||||||
\(800\) | 6.03150 | + | 27.6337i | 0.213246 | + | 0.976999i | ||||
\(801\) | 6.43467 | + | 11.1452i | 0.227358 | + | 0.393796i | ||||
\(802\) | 2.89273 | − | 5.05853i | 0.102146 | − | 0.178623i | ||||
\(803\) | −69.2758 | + | 18.5624i | −2.44469 | + | 0.655053i | ||||
\(804\) | −0.483261 | + | 0.853245i | −0.0170433 | + | 0.0300916i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.18826 | + | 19.6880i | −0.182749 | + | 0.693481i | ||||
\(807\) | −11.5742 | − | 43.1955i | −0.407431 | − | 1.52055i | ||||
\(808\) | 5.15539 | + | 8.67904i | 0.181366 | + | 0.305328i | ||||
\(809\) | −14.5481 | + | 8.39937i | −0.511485 | + | 0.295306i | −0.733444 | − | 0.679750i | \(-0.762088\pi\) |
0.221959 | + | 0.975056i | \(0.428755\pi\) | |||||||
\(810\) | −5.68081 | + | 35.0785i | −0.199603 | + | 1.23253i | ||||
\(811\) | − | 18.6742i | − | 0.655738i | −0.944723 | − | 0.327869i | \(-0.893669\pi\) | ||
0.944723 | − | 0.327869i | \(-0.106331\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7981 | − | 17.7981i | 0.624207 | − | 0.624207i | ||||
\(814\) | 15.1207 | − | 15.2462i | 0.529980 | − | 0.534380i | ||||
\(815\) | −33.3029 | − | 15.1319i | −1.16655 | − | 0.530049i | ||||
\(816\) | −33.8840 | − | 18.8230i | −1.18618 | − | 0.658935i | ||||
\(817\) | 36.5543 | − | 9.79469i | 1.27887 | − | 0.342673i | ||||
\(818\) | 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 | −0.897315 | − | 0.441391i | \(-0.854485\pi\) |
0.830913 | + | 0.556402i | \(0.187818\pi\) | |||||||
\(822\) | 10.0887 | + | 5.76925i | 0.351884 | + | 0.201226i | ||||
\(823\) | −9.97850 | + | 37.2403i | −0.347828 | + | 1.29811i | 0.541444 | + | 0.840737i | \(0.317878\pi\) |
−0.889273 | + | 0.457377i | \(0.848789\pi\) | |||||||
\(824\) | −1.98312 | + | 0.557822i | −0.0690853 | + | 0.0194326i | ||||
\(825\) | 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 | \(0.230942\pi\) | |||||||
\(828\) | −8.70371 | − | 2.25520i | −0.302475 | − | 0.0783737i | ||||
\(829\) | 33.7071 | − | 19.4608i | 1.17070 | − | 0.675902i | 0.216852 | − | 0.976204i | \(-0.430421\pi\) |
0.953844 | + | 0.300303i | \(0.0970876\pi\) | |||||||
\(830\) | 3.67150 | + | 36.1386i | 0.127440 | + | 1.25439i | ||||
\(831\) | −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 | ||||
\(835\) | 38.5966 | − | 3.76012i | 1.33569 | − | 0.130124i | ||||
\(836\) | −0.537804 | − | 65.0540i | −0.0186003 | − | 2.24994i | ||||
\(837\) | −5.81043 | + | 21.6848i | −0.200838 | + | 0.749537i | ||||
\(838\) | 33.1682 | − | 0.137099i | 1.14578 | − | 0.00473600i | ||||
\(839\) | −50.2557 | −1.73502 | −0.867509 | − | 0.497422i | \(-0.834280\pi\) | ||||
−0.867509 | + | 0.497422i | \(0.834280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.84704 | 0.0981737 | ||||||||
\(842\) | 34.3694 | − | 0.142064i | 1.18445 | − | 0.00489585i | ||||
\(843\) | −9.09269 | + | 33.9344i | −0.313169 | + | 1.16876i | ||||
\(844\) | −0.259104 | − | 31.3419i | −0.00891874 | − | 1.07883i | ||||
\(845\) | 13.2784 | − | 16.1448i | 0.456790 | − | 0.555398i | ||||
\(846\) | −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 | ||||
\(850\) | −31.8402 | − | 2.02257i | −1.09211 | − | 0.0693735i | ||||
\(851\) | −6.37789 | + | 3.68228i | −0.218631 | + | 0.126227i | ||||
\(852\) | −14.7515 | − | 3.82223i | −0.505378 | − | 0.130947i | ||||
\(853\) | 4.47340 | − | 4.47340i | 0.153166 | − | 0.153166i | −0.626364 | − | 0.779531i | \(-0.715458\pi\) |
0.779531 | + | 0.626364i | \(0.215458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.1304 | − | 3.34547i | −0.688444 | − | 0.114413i | ||||
\(856\) | 4.44509 | + | 15.8028i | 0.151930 | + | 0.540128i | ||||
\(857\) | −6.76748 | + | 25.2566i | −0.231173 | + | 0.862749i | 0.748664 | + | 0.662950i | \(0.230696\pi\) |
−0.979837 | + | 0.199799i | \(0.935971\pi\) | |||||||
\(858\) | 28.9588 | + | 16.5601i | 0.988636 | + | 0.565354i | ||||
\(859\) | 6.61087 | − | 11.4504i | 0.225560 | − | 0.390681i | −0.730927 | − | 0.682455i | \(-0.760912\pi\) |
0.956487 | + | 0.291774i | \(0.0942455\pi\) | |||||||
\(860\) | 3.14560 | + | 29.7392i | 0.107264 | + | 1.01410i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.3986 | + | 7.22685i | −0.422299 | + | 0.246147i | ||||
\(863\) | −34.7378 | + | 9.30796i | −1.18249 | + | 0.316847i | −0.795913 | − | 0.605411i | \(-0.793009\pi\) |
−0.386575 | + | 0.922258i | \(0.626342\pi\) | |||||||
\(864\) | −11.6702 | + | 12.1629i | −0.397029 | + | 0.413789i | ||||
\(865\) | 12.3506 | − | 27.1817i | 0.419933 | − | 0.924205i | ||||
\(866\) | −4.68442 | + | 4.72330i | −0.159183 | + | 0.160504i | ||||
\(867\) | 5.09931 | − | 5.09931i | 0.173182 | − | 0.173182i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 21.7330i | − | 0.737241i | ||||||
\(870\) | 20.3174 | + | 28.1696i | 0.688823 | + | 0.955040i | ||||
\(871\) | −0.377796 | + | 0.218120i | −0.0128011 | + | 0.00739073i | ||||
\(872\) | 28.1670 | − | 16.7313i | 0.953854 | − | 0.566593i | ||||
\(873\) | −3.71045 | − | 13.8476i | −0.125580 | − | 0.468670i | ||||
\(874\) | −5.68574 | + | 21.5758i | −0.192323 | + | 0.729813i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26.4142 | + | 46.6368i | −0.892452 | + | 1.57571i | ||||
\(877\) | 51.8073 | − | 13.8817i | 1.74941 | − | 0.468752i | 0.764907 | − | 0.644140i | \(-0.222785\pi\) |
0.984499 | + | 0.175388i | \(0.0561181\pi\) | |||||||
\(878\) | 13.8630 | − | 24.2422i | 0.467852 | − | 0.818135i | ||||
\(879\) | −5.24525 | − | 9.08504i | −0.176918 | − | 0.306431i | ||||
\(880\) | 50.8458 | + | 7.58848i | 1.71401 | + | 0.255808i | ||||
\(881\) | 11.3298 | 0.381709 | 0.190855 | − | 0.981618i | \(-0.438874\pi\) | ||||
0.190855 | + | 0.981618i | \(0.438874\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0638 | + | 24.0638i | 0.809810 | + | 0.809810i | 0.984605 | − | 0.174795i | \(-0.0559263\pi\) |
−0.174795 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(884\) | −8.74506 | − | 14.8618i | −0.294128 | − | 0.499856i | ||||
\(885\) | 21.4763 | + | 9.75826i | 0.721919 | + | 0.328020i | ||||
\(886\) | 21.2892 | − | 5.79886i | 0.715226 | − | 0.194816i | ||||
\(887\) | −8.95397 | − | 33.4167i | −0.300645 | − | 1.12202i | −0.936630 | − | 0.350320i | \(-0.886073\pi\) |
0.635985 | − | 0.771701i | \(-0.280594\pi\) | |||||||
\(888\) | −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 | ||||
\(892\) | −27.9098 | − | 27.4521i | −0.934488 | − | 0.919163i | ||||
\(893\) | 30.7820 | + | 8.24801i | 1.03008 | + | 0.276009i | ||||
\(894\) | 30.8289 | − | 31.0848i | 1.03107 | − | 1.03963i | ||||
\(895\) | 3.53573 | − | 21.2752i | 0.118186 | − | 0.711152i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.09022 | − | 8.09022i | −0.270125 | − | 0.270125i | ||||
\(898\) | −0.0792902 | − | 19.1826i | −0.00264595 | − | 0.640132i | ||||
\(899\) | 19.2646 | + | 33.3672i | 0.642509 | + | 1.11286i | ||||
\(900\) | 5.08948 | − | 15.3015i | 0.169649 | − | 0.510048i | ||||
\(901\) | 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 | ||||
\(905\) | −3.79855 | − | 3.12413i | −0.126268 | − | 0.103850i | ||||
\(906\) | 12.0292 | + | 44.1627i | 0.399644 | + | 1.46721i | ||||
\(907\) | −49.1996 | − | 13.1830i | −1.63365 | − | 0.437734i | −0.678676 | − | 0.734438i | \(-0.737446\pi\) |
−0.954970 | + | 0.296703i | \(0.904113\pi\) | |||||||
\(908\) | 11.3372 | + | 2.93757i | 0.376239 | + | 0.0974867i | ||||
\(909\) | − | 5.75530i | − | 0.190891i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.9908i | − | 0.761719i | −0.924633 | − | 0.380860i | \(-0.875628\pi\) | ||
0.924633 | − | 0.380860i | \(-0.124372\pi\) | |||||||
\(912\) | −34.9417 | − | 33.8050i | −1.15704 | − | 1.11939i | ||||
\(913\) | 63.7732 | + | 17.0880i | 2.11059 | + | 0.565530i | ||||
\(914\) | −36.9706 | + | 10.0702i | −1.22288 | + | 0.333093i | ||||
\(915\) | −7.14990 | − | 73.3918i | −0.236368 | − | 2.42626i | ||||
\(916\) | 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 | −0.909890 | − | 0.414850i | \(-0.863834\pi\) |
0.814216 | + | 0.580563i | \(0.197167\pi\) | |||||||
\(920\) | −16.1416 | − | 7.09418i | −0.532174 | − | 0.233888i | ||||
\(921\) | −14.3785 | − | 24.9042i | −0.473786 | − | 0.820622i | ||||
\(922\) | −43.0374 | + | 0.177893i | −1.41736 | + | 0.00585858i | ||||
\(923\) | −4.79366 | − | 4.79366i | −0.157785 | − | 0.157785i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.81679 | − | 11.8586i | −0.191255 | − | 0.389909i | ||||
\(926\) | 17.7715 | + | 17.6252i | 0.584006 | + | 0.579198i | ||||
\(927\) | 1.13449 | + | 0.303986i | 0.0372615 | + | 0.00998420i | ||||
\(928\) | 0.597839 | + | 28.9230i | 0.0196250 | + | 0.949443i | ||||
\(929\) | −36.8435 | − | 21.2716i | −1.20880 | − | 0.697899i | −0.246300 | − | 0.969194i | \(-0.579215\pi\) |
−0.962496 | + | 0.271294i | \(0.912548\pi\) | |||||||
\(930\) | 20.9741 | − | 46.6719i | 0.687769 | − | 1.53043i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.1949 | + | 51.2768i | 0.464971 | + | 1.67963i | ||||
\(933\) | −13.0253 | − | 48.6112i | −0.426431 | − | 1.59146i | ||||
\(934\) | 7.12185 | + | 26.1463i | 0.233034 | + | 0.855534i | ||||
\(935\) | −23.9884 | + | 52.7945i | −0.784505 | + | 1.72657i | ||||
\(936\) | 8.39007 | − | 2.36000i | 0.274238 | − | 0.0771389i | ||||
\(937\) | 2.08780 | + | 2.08780i | 0.0682055 | + | 0.0682055i | 0.740387 | − | 0.672181i | \(-0.234642\pi\) |
−0.672181 | + | 0.740387i | \(0.734642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0189 | 0.457490 | ||||||||
\(940\) | −10.2275 | + | 23.0123i | −0.333585 | + | 0.750580i | ||||
\(941\) | 14.3629 | + | 24.8773i | 0.468217 | + | 0.810976i | 0.999340 | − | 0.0363189i | \(-0.0115632\pi\) |
−0.531123 | + | 0.847295i | \(0.678230\pi\) | |||||||
\(942\) | −5.95242 | − | 3.40391i | −0.193940 | − | 0.110905i | ||||
\(943\) | 8.84591 | − | 2.37025i | 0.288063 | − | 0.0771861i | ||||
\(944\) | 10.1040 | + | 16.8510i | 0.328857 | + | 0.548452i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52.5605 | + | 13.8509i | 1.70889 | + | 0.450333i | ||||
\(947\) | −13.6798 | − | 51.0535i | −0.444532 | − | 1.65902i | −0.717168 | − | 0.696900i | \(-0.754562\pi\) |
0.272636 | − | 0.962117i | \(-0.412104\pi\) | |||||||
\(948\) | −11.5790 | − | 11.3892i | −0.376070 | − | 0.369903i | ||||
\(949\) | −20.6496 | + | 11.9221i | −0.670315 | + | 0.387007i | ||||
\(950\) | −37.9196 | − | 12.7869i | −1.23027 | − | 0.414862i | ||||
\(951\) | − | 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 | \(0.315491\pi\) | |||||||
\(954\) | 1.40273 | + | 1.39118i | 0.0454151 | + | 0.0450412i | ||||
\(955\) | −9.04997 | − | 24.1227i | −0.292850 | − | 0.780594i | ||||
\(956\) | −2.96442 | + | 0.0245069i | −0.0958761 | + | 0.000792611i | ||||
\(957\) | 60.9775 | − | 16.3389i | 1.97112 | − | 0.528161i | ||||
\(958\) | −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 | ||||
\(962\) | 3.54388 | − | 6.19719i | 0.114259 | − | 0.199805i | ||||
\(963\) | 2.42236 | − | 9.04036i | 0.0780593 | − | 0.291321i | ||||
\(964\) | 13.7987 | + | 23.4502i | 0.444426 | + | 0.755279i | ||||
\(965\) | −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 | \(-0.0932580\pi\) | |||||||
\(968\) | 30.4920 | − | 54.3594i | 0.980050 | − | 1.74718i | ||||
\(969\) | 47.4933 | − | 27.4203i | 1.52570 | − | 0.880866i | ||||
\(970\) | −2.84156 | − | 27.9694i | −0.0912369 | − | 0.898043i | ||||
\(971\) | 13.9138 | + | 8.03315i | 0.446516 | + | 0.257796i | 0.706358 | − | 0.707855i | \(-0.250337\pi\) |
−0.259842 | + | 0.965651i | \(0.583670\pi\) | |||||||
\(972\) | 29.2884 | − | 8.10789i | 0.939426 | − | 0.260061i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.5190 | + | 7.51543i | 0.913807 | + | 0.240810i | ||||
\(975\) | 15.4565 | − | 13.4971i | 0.495003 | − | 0.432252i | ||||
\(976\) | 29.8259 | − | 53.6908i | 0.954704 | − | 1.71860i | ||||
\(977\) | −3.24931 | + | 12.1266i | −0.103955 | + | 0.387964i | −0.998224 | − | 0.0595641i | \(-0.981029\pi\) |
0.894270 | + | 0.447528i | \(0.147696\pi\) | |||||||
\(978\) | 0.205375 | + | 49.6862i | 0.00656717 | + | 1.58879i | ||||
\(979\) | 45.8704 | 1.46603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.6783 | −0.596351 | ||||||||
\(982\) | 0.101109 | + | 24.4611i | 0.00322651 | + | 0.780585i | ||||
\(983\) | 2.58201 | − | 9.63621i | 0.0823535 | − | 0.307347i | −0.912446 | − | 0.409196i | \(-0.865809\pi\) |
0.994800 | + | 0.101849i | \(0.0324758\pi\) | |||||||
\(984\) | −4.92529 | + | 19.3375i | −0.157013 | + | 0.616456i | ||||
\(985\) | −0.382063 | − | 3.92178i | −0.0121735 | − | 0.124958i | ||||
\(986\) | −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 | ||||
\(990\) | −22.7138 | − | 18.5242i | −0.721891 | − | 0.588737i | ||||
\(991\) | −45.3896 | + | 26.2057i | −1.44185 | + | 0.832451i | −0.997973 | − | 0.0636385i | \(-0.979730\pi\) |
−0.443874 | + | 0.896089i | \(0.646396\pi\) | |||||||
\(992\) | 36.4609 | − | 22.0677i | 1.15763 | − | 0.700651i | ||||
\(993\) | 29.1463 | − | 29.1463i | 0.924931 | − | 0.924931i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.54480 | − | 9.29538i | 0.0489735 | − | 0.294683i | ||||
\(996\) | 42.5246 | − | 25.0226i | 1.34744 | − | 0.792870i | ||||
\(997\) | 0.101885 | − | 0.380238i | 0.00322672 | − | 0.0120423i | −0.964294 | − | 0.264835i | \(-0.914682\pi\) |
0.967520 | + | 0.252793i | \(0.0813491\pi\) | |||||||
\(998\) | 18.2911 | − | 31.9856i | 0.578993 | − | 1.01249i | ||||
\(999\) | 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.667.15 | 64 | ||
4.3 | odd | 2 | inner | 980.2.x.j.667.14 | 64 | ||
5.3 | odd | 4 | inner | 980.2.x.j.863.9 | 64 | ||
7.2 | even | 3 | 980.2.k.i.687.7 | yes | 32 | ||
7.3 | odd | 6 | inner | 980.2.x.j.67.5 | 64 | ||
7.4 | even | 3 | inner | 980.2.x.j.67.6 | 64 | ||
7.5 | odd | 6 | 980.2.k.i.687.8 | yes | 32 | ||
7.6 | odd | 2 | inner | 980.2.x.j.667.16 | 64 | ||
20.3 | even | 4 | inner | 980.2.x.j.863.6 | 64 | ||
28.3 | even | 6 | inner | 980.2.x.j.67.10 | 64 | ||
28.11 | odd | 6 | inner | 980.2.x.j.67.9 | 64 | ||
28.19 | even | 6 | 980.2.k.i.687.3 | ✓ | 32 | ||
28.23 | odd | 6 | 980.2.k.i.687.4 | yes | 32 | ||
28.27 | even | 2 | inner | 980.2.x.j.667.13 | 64 | ||
35.3 | even | 12 | inner | 980.2.x.j.263.13 | 64 | ||
35.13 | even | 4 | inner | 980.2.x.j.863.10 | 64 | ||
35.18 | odd | 12 | inner | 980.2.x.j.263.14 | 64 | ||
35.23 | odd | 12 | 980.2.k.i.883.4 | yes | 32 | ||
35.33 | even | 12 | 980.2.k.i.883.3 | yes | 32 | ||
140.3 | odd | 12 | inner | 980.2.x.j.263.16 | 64 | ||
140.23 | even | 12 | 980.2.k.i.883.7 | yes | 32 | ||
140.83 | odd | 4 | inner | 980.2.x.j.863.5 | 64 | ||
140.103 | odd | 12 | 980.2.k.i.883.8 | yes | 32 | ||
140.123 | even | 12 | inner | 980.2.x.j.263.15 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.k.i.687.3 | ✓ | 32 | 28.19 | even | 6 | ||
980.2.k.i.687.4 | yes | 32 | 28.23 | odd | 6 | ||
980.2.k.i.687.7 | yes | 32 | 7.2 | even | 3 | ||
980.2.k.i.687.8 | yes | 32 | 7.5 | odd | 6 | ||
980.2.k.i.883.3 | yes | 32 | 35.33 | even | 12 | ||
980.2.k.i.883.4 | yes | 32 | 35.23 | odd | 12 | ||
980.2.k.i.883.7 | yes | 32 | 140.23 | even | 12 | ||
980.2.k.i.883.8 | yes | 32 | 140.103 | odd | 12 | ||
980.2.x.j.67.5 | 64 | 7.3 | odd | 6 | inner | ||
980.2.x.j.67.6 | 64 | 7.4 | even | 3 | inner | ||
980.2.x.j.67.9 | 64 | 28.11 | odd | 6 | inner | ||
980.2.x.j.67.10 | 64 | 28.3 | even | 6 | inner | ||
980.2.x.j.263.13 | 64 | 35.3 | even | 12 | inner | ||
980.2.x.j.263.14 | 64 | 35.18 | odd | 12 | inner | ||
980.2.x.j.263.15 | 64 | 140.123 | even | 12 | inner | ||
980.2.x.j.263.16 | 64 | 140.3 | odd | 12 | inner | ||
980.2.x.j.667.13 | 64 | 28.27 | even | 2 | inner | ||
980.2.x.j.667.14 | 64 | 4.3 | odd | 2 | inner | ||
980.2.x.j.667.15 | 64 | 1.1 | even | 1 | trivial | ||
980.2.x.j.667.16 | 64 | 7.6 | odd | 2 | inner | ||
980.2.x.j.863.5 | 64 | 140.83 | odd | 4 | inner | ||
980.2.x.j.863.6 | 64 | 20.3 | even | 4 | inner | ||
980.2.x.j.863.9 | 64 | 5.3 | odd | 4 | inner | ||
980.2.x.j.863.10 | 64 | 35.13 | even | 4 | inner |