Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(19,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.w (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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 227.5 | ||
Character | \(\chi\) | \(=\) | 784.227 |
Dual form | 784.2.w.e.411.5 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.655294 | + | 1.25323i | 0.463363 | + | 0.886169i | ||||
\(3\) | −3.05239 | + | 0.817885i | −1.76230 | + | 0.472206i | −0.987180 | − | 0.159610i | \(-0.948976\pi\) |
−0.775118 | + | 0.631816i | \(0.782310\pi\) | |||||||
\(4\) | −1.14118 | + | 1.64247i | −0.570590 | + | 0.821235i | ||||
\(5\) | 0.213773 | − | 0.797811i | 0.0956021 | − | 0.356792i | −0.901508 | − | 0.432763i | \(-0.857539\pi\) |
0.997110 | + | 0.0759706i | \(0.0242055\pi\) | |||||||
\(6\) | −3.02521 | − | 3.28940i | −1.23504 | − | 1.34289i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.80620 | − | 0.353863i | −0.992143 | − | 0.125109i | ||||
\(9\) | 6.05007 | − | 3.49301i | 2.01669 | − | 1.16434i | ||||
\(10\) | 1.13993 | − | 0.254894i | 0.360476 | − | 0.0806045i | ||||
\(11\) | 2.73205 | − | 0.732051i | 0.823744 | − | 0.220722i | 0.177762 | − | 0.984074i | \(-0.443114\pi\) |
0.645983 | + | 0.763352i | \(0.276448\pi\) | |||||||
\(12\) | 2.13997 | − | 5.94681i | 0.617757 | − | 1.71670i | ||||
\(13\) | 2.91203 | − | 2.91203i | 0.807651 | − | 0.807651i | −0.176627 | − | 0.984278i | \(-0.556519\pi\) |
0.984278 | + | 0.176627i | \(0.0565185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.61007i | 0.673918i | ||||||||
\(16\) | −1.39542 | − | 3.74871i | −0.348854 | − | 0.937177i | ||||
\(17\) | −2.30469 | − | 1.33061i | −0.558969 | − | 0.322721i | 0.193763 | − | 0.981048i | \(-0.437931\pi\) |
−0.752732 | + | 0.658328i | \(0.771264\pi\) | |||||||
\(18\) | 8.34213 | + | 5.29319i | 1.96626 | + | 1.24762i | ||||
\(19\) | 0.117075 | − | 0.436928i | 0.0268587 | − | 0.100238i | −0.951195 | − | 0.308590i | \(-0.900143\pi\) |
0.978054 | + | 0.208351i | \(0.0668097\pi\) | |||||||
\(20\) | 1.06643 | + | 1.26156i | 0.238461 | + | 0.282094i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.70773 | + | 2.94418i | 0.577289 | + | 0.627702i | ||||
\(23\) | 1.63915 | + | 2.83909i | 0.341786 | + | 0.591991i | 0.984764 | − | 0.173894i | \(-0.0556349\pi\) |
−0.642978 | + | 0.765884i | \(0.722302\pi\) | |||||||
\(24\) | 8.85505 | − | 1.21503i | 1.80753 | − | 0.248016i | ||||
\(25\) | 3.73932 | + | 2.15890i | 0.747865 | + | 0.431780i | ||||
\(26\) | 5.55768 | + | 1.74121i | 1.08995 | + | 0.341480i | ||||
\(27\) | −8.90678 | + | 8.90678i | −1.71411 | + | 1.71411i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.04184 | − | 2.04184i | −0.379160 | − | 0.379160i | 0.491639 | − | 0.870799i | \(-0.336398\pi\) |
−0.870799 | + | 0.491639i | \(0.836398\pi\) | |||||||
\(30\) | −3.27103 | + | 1.71036i | −0.597205 | + | 0.312268i | ||||
\(31\) | −1.26156 | + | 2.18509i | −0.226583 | + | 0.392454i | −0.956793 | − | 0.290769i | \(-0.906089\pi\) |
0.730210 | + | 0.683223i | \(0.239422\pi\) | |||||||
\(32\) | 3.78359 | − | 4.20529i | 0.668851 | − | 0.743396i | ||||
\(33\) | −7.74055 | + | 4.46901i | −1.34746 | + | 0.777955i | ||||
\(34\) | 0.157318 | − | 3.76025i | 0.0269798 | − | 0.644878i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.16706 | + | 13.9232i | −0.194509 | + | 2.32054i | ||||
\(37\) | −2.33280 | − | 0.625071i | −0.383509 | − | 0.102761i | 0.0619131 | − | 0.998082i | \(-0.480280\pi\) |
−0.445422 | + | 0.895321i | \(0.646946\pi\) | |||||||
\(38\) | 0.624291 | − | 0.139595i | 0.101273 | − | 0.0226453i | ||||
\(39\) | −6.50694 | + | 11.2704i | −1.04194 | + | 1.80470i | ||||
\(40\) | −0.882206 | + | 2.16318i | −0.139489 | + | 0.342028i | ||||
\(41\) | 11.9895 | 1.87245 | 0.936224 | − | 0.351405i | \(-0.114296\pi\) | ||||
0.936224 | + | 0.351405i | \(0.114296\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.27830 | − | 3.27830i | −0.499936 | − | 0.499936i | 0.411482 | − | 0.911418i | \(-0.365011\pi\) |
−0.911418 | + | 0.411482i | \(0.865011\pi\) | |||||||
\(44\) | −1.91539 | + | 5.32271i | −0.288756 | + | 0.802429i | ||||
\(45\) | −1.49342 | − | 5.57353i | −0.222626 | − | 0.830852i | ||||
\(46\) | −2.48391 | + | 3.91467i | −0.366233 | + | 0.577187i | ||||
\(47\) | 4.98400 | + | 8.63254i | 0.726991 | + | 1.25918i | 0.958149 | + | 0.286269i | \(0.0924150\pi\) |
−0.231159 | + | 0.972916i | \(0.574252\pi\) | |||||||
\(48\) | 7.32537 | + | 10.3012i | 1.05733 | + | 1.48685i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.255246 | + | 6.10095i | −0.0360972 | + | 0.862805i | ||||
\(51\) | 8.12310 | + | 2.17658i | 1.13746 | + | 0.304782i | ||||
\(52\) | 1.45977 | + | 8.10607i | 0.202434 | + | 1.12411i | ||||
\(53\) | −0.869658 | − | 3.24561i | −0.119457 | − | 0.445818i | 0.880125 | − | 0.474742i | \(-0.157459\pi\) |
−0.999582 | + | 0.0289238i | \(0.990792\pi\) | |||||||
\(54\) | −16.9988 | − | 5.32570i | −2.31325 | − | 0.724737i | ||||
\(55\) | − | 2.33615i | − | 0.315007i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.42943i | 0.189332i | ||||||||
\(58\) | 1.22089 | − | 3.89690i | 0.160311 | − | 0.511688i | ||||
\(59\) | 1.51870 | + | 5.66785i | 0.197717 | + | 0.737891i | 0.991547 | + | 0.129751i | \(0.0414177\pi\) |
−0.793829 | + | 0.608141i | \(0.791916\pi\) | |||||||
\(60\) | −4.28697 | − | 2.97856i | −0.553445 | − | 0.384531i | ||||
\(61\) | 6.18083 | + | 1.65615i | 0.791374 | + | 0.212048i | 0.631793 | − | 0.775137i | \(-0.282319\pi\) |
0.159580 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(62\) | −3.56512 | − | 0.149154i | −0.452770 | − | 0.0189426i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.74956 | + | 1.98602i | 0.968695 | + | 0.248253i | ||||
\(65\) | −1.70074 | − | 2.94576i | −0.210950 | − | 0.365377i | ||||
\(66\) | −10.6730 | − | 6.77219i | −1.31376 | − | 0.833599i | ||||
\(67\) | −1.60085 | − | 5.97447i | −0.195575 | − | 0.729897i | −0.992117 | − | 0.125314i | \(-0.960006\pi\) |
0.796542 | − | 0.604584i | \(-0.206660\pi\) | |||||||
\(68\) | 4.81556 | − | 2.26691i | 0.583972 | − | 0.274904i | ||||
\(69\) | −7.32537 | − | 7.32537i | −0.881871 | − | 0.881871i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.14114 | 0.610141 | 0.305071 | − | 0.952330i | \(-0.401320\pi\) | ||||
0.305071 | + | 0.952330i | \(0.401320\pi\) | |||||||
\(72\) | −18.2138 | + | 7.66121i | −2.14651 | + | 0.902882i | ||||
\(73\) | 3.49607 | − | 6.05536i | 0.409184 | − | 0.708727i | −0.585615 | − | 0.810589i | \(-0.699147\pi\) |
0.994798 | + | 0.101863i | \(0.0324802\pi\) | |||||||
\(74\) | −0.745308 | − | 3.33314i | −0.0866403 | − | 0.387470i | ||||
\(75\) | −13.1796 | − | 3.53146i | −1.52185 | − | 0.407778i | ||||
\(76\) | 0.584038 | + | 0.690905i | 0.0669938 | + | 0.0792523i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −18.3883 | − | 0.769313i | −2.08207 | − | 0.0871076i | ||||
\(79\) | 9.72098 | − | 5.61241i | 1.09370 | − | 0.631445i | 0.159137 | − | 0.987256i | \(-0.449129\pi\) |
0.934558 | + | 0.355811i | \(0.115795\pi\) | |||||||
\(80\) | −3.28906 | + | 0.311907i | −0.367729 | + | 0.0348722i | ||||
\(81\) | 9.42322 | − | 16.3215i | 1.04702 | − | 1.81350i | ||||
\(82\) | 7.85665 | + | 15.0256i | 0.867622 | + | 1.65930i | ||||
\(83\) | −5.39734 | − | 5.39734i | −0.592435 | − | 0.592435i | 0.345854 | − | 0.938288i | \(-0.387589\pi\) |
−0.938288 | + | 0.345854i | \(0.887589\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.55426 | + | 1.55426i | −0.168583 | + | 0.168583i | ||||
\(86\) | 1.96022 | − | 6.25671i | 0.211376 | − | 0.674679i | ||||
\(87\) | 7.90247 | + | 4.56249i | 0.847234 | + | 0.489151i | ||||
\(88\) | −7.92574 | + | 1.08751i | −0.844886 | + | 0.115929i | ||||
\(89\) | 0.528369 | + | 0.915163i | 0.0560071 | + | 0.0970071i | 0.892670 | − | 0.450712i | \(-0.148830\pi\) |
−0.836663 | + | 0.547719i | \(0.815496\pi\) | |||||||
\(90\) | 6.00629 | − | 5.52390i | 0.633119 | − | 0.582270i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.53368 | − | 0.547659i | −0.681183 | − | 0.0570974i | ||||
\(93\) | 2.06363 | − | 7.70156i | 0.213988 | − | 0.798614i | ||||
\(94\) | −7.55259 | + | 11.9030i | −0.778990 | + | 1.22770i | ||||
\(95\) | −0.323559 | − | 0.186807i | −0.0331964 | − | 0.0191660i | ||||
\(96\) | −8.10956 | + | 15.9307i | −0.827678 | + | 1.62592i | ||||
\(97\) | 13.2689i | 1.34726i | 0.739071 | + | 0.673628i | \(0.235265\pi\) | ||||
−0.739071 | + | 0.673628i | \(0.764735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.9720 | − | 13.9720i | 1.40424 | − | 1.40424i | ||||
\(100\) | −7.81317 | + | 3.67803i | −0.781317 | + | 0.367803i | ||||
\(101\) | −0.342603 | + | 0.0918003i | −0.0340903 | + | 0.00913447i | −0.275824 | − | 0.961208i | \(-0.588951\pi\) |
0.241734 | + | 0.970343i | \(0.422284\pi\) | |||||||
\(102\) | 2.59526 | + | 11.6064i | 0.256969 | + | 1.14921i | ||||
\(103\) | 10.8408 | − | 6.25894i | 1.06818 | − | 0.616712i | 0.140494 | − | 0.990082i | \(-0.455131\pi\) |
0.927683 | + | 0.373370i | \(0.121798\pi\) | |||||||
\(104\) | −9.20220 | + | 7.14129i | −0.902350 | + | 0.700261i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.49762 | − | 3.21671i | 0.339718 | − | 0.312434i | ||||
\(107\) | −1.42324 | + | 5.31161i | −0.137590 | + | 0.513493i | 0.862384 | + | 0.506255i | \(0.168971\pi\) |
−0.999974 | + | 0.00723781i | \(0.997696\pi\) | |||||||
\(108\) | −4.46488 | − | 24.7934i | −0.429634 | − | 2.38574i | ||||
\(109\) | 5.82517 | − | 1.56085i | 0.557950 | − | 0.149502i | 0.0311855 | − | 0.999514i | \(-0.490072\pi\) |
0.526764 | + | 0.850011i | \(0.323405\pi\) | |||||||
\(110\) | 2.92774 | − | 1.53087i | 0.279149 | − | 0.145962i | ||||
\(111\) | 7.63184 | 0.724382 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.79072 | 0.732889 | 0.366445 | − | 0.930440i | \(-0.380575\pi\) | ||||
0.366445 | + | 0.930440i | \(0.380575\pi\) | |||||||
\(114\) | −1.79141 | + | 0.936696i | −0.167781 | + | 0.0877296i | ||||
\(115\) | 2.61546 | − | 0.700811i | 0.243893 | − | 0.0653510i | ||||
\(116\) | 5.68376 | − | 1.02355i | 0.527724 | − | 0.0950345i | ||||
\(117\) | 7.44623 | − | 27.7897i | 0.688405 | − | 2.56916i | ||||
\(118\) | −6.10794 | + | 5.61739i | −0.562281 | + | 0.517122i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.923607 | − | 7.32440i | 0.0843134 | − | 0.668623i | ||||
\(121\) | −2.59808 | + | 1.50000i | −0.236189 | + | 0.136364i | ||||
\(122\) | 1.97472 | + | 8.83127i | 0.178783 | + | 0.799546i | ||||
\(123\) | −36.5967 | + | 9.80605i | −3.29981 | + | 0.884182i | ||||
\(124\) | −2.14927 | − | 4.56566i | −0.193011 | − | 0.410008i | ||||
\(125\) | 5.44195 | − | 5.44195i | 0.486743 | − | 0.486743i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.02552i | 0.712150i | 0.934457 | + | 0.356075i | \(0.115885\pi\) | ||||
−0.934457 | + | 0.356075i | \(0.884115\pi\) | |||||||
\(128\) | 2.58929 | + | 11.0134i | 0.228863 | + | 0.973459i | ||||
\(129\) | 12.6879 | + | 7.32537i | 1.11711 | + | 0.644963i | ||||
\(130\) | 2.57724 | − | 4.06176i | 0.226039 | − | 0.356240i | ||||
\(131\) | 3.37718 | − | 12.6038i | 0.295066 | − | 1.10120i | −0.646099 | − | 0.763254i | \(-0.723601\pi\) |
0.941165 | − | 0.337947i | \(-0.109733\pi\) | |||||||
\(132\) | 1.49315 | − | 17.8136i | 0.129962 | − | 1.55047i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.43836 | − | 5.92127i | 0.556190 | − | 0.511520i | ||||
\(135\) | 5.20190 | + | 9.00996i | 0.447709 | + | 0.775454i | ||||
\(136\) | 5.99657 | + | 4.54951i | 0.514202 | + | 0.390118i | ||||
\(137\) | −7.81979 | − | 4.51476i | −0.668089 | − | 0.385722i | 0.127263 | − | 0.991869i | \(-0.459381\pi\) |
−0.795352 | + | 0.606147i | \(0.792714\pi\) | |||||||
\(138\) | 4.38012 | − | 13.9807i | 0.372860 | − | 1.19011i | ||||
\(139\) | 4.33613 | − | 4.33613i | 0.367785 | − | 0.367785i | −0.498884 | − | 0.866669i | \(-0.666256\pi\) |
0.866669 | + | 0.498884i | \(0.166256\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.2735 | − | 22.2735i | −1.87577 | − | 1.87577i | ||||
\(142\) | 3.36896 | + | 6.44304i | 0.282717 | + | 0.540688i | ||||
\(143\) | 5.82406 | − | 10.0876i | 0.487032 | − | 0.843564i | ||||
\(144\) | −21.5366 | − | 17.8058i | −1.79472 | − | 1.48381i | ||||
\(145\) | −2.06549 | + | 1.19251i | −0.171530 | + | 0.0990327i | ||||
\(146\) | 9.87973 | + | 0.413339i | 0.817652 | + | 0.0342082i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.68880 | − | 3.11823i | 0.303218 | − | 0.256317i | ||||
\(149\) | 18.1162 | + | 4.85422i | 1.48414 | + | 0.397673i | 0.907753 | − | 0.419505i | \(-0.137796\pi\) |
0.576384 | + | 0.817179i | \(0.304463\pi\) | |||||||
\(150\) | −4.21077 | − | 18.8312i | −0.343808 | − | 1.53756i | ||||
\(151\) | 5.87561 | − | 10.1769i | 0.478150 | − | 0.828180i | −0.521536 | − | 0.853229i | \(-0.674641\pi\) |
0.999686 | + | 0.0250489i | \(0.00797414\pi\) | |||||||
\(152\) | −0.483148 | + | 1.18468i | −0.0391885 | + | 0.0960904i | ||||
\(153\) | −18.5914 | −1.50302 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.47360 | + | 1.47360i | 0.118362 | + | 0.118362i | ||||
\(156\) | −11.0856 | − | 23.5490i | −0.887560 | − | 1.88543i | ||||
\(157\) | 2.89504 | + | 10.8045i | 0.231050 | + | 0.862289i | 0.979890 | + | 0.199539i | \(0.0639443\pi\) |
−0.748840 | + | 0.662750i | \(0.769389\pi\) | |||||||
\(158\) | 13.4037 | + | 8.50486i | 1.06634 | + | 0.676610i | ||||
\(159\) | 5.30907 | + | 9.19558i | 0.421037 | + | 0.729257i | ||||
\(160\) | −2.54619 | − | 3.91757i | −0.201294 | − | 0.309711i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 26.6296 | + | 1.11410i | 2.09222 | + | 0.0875323i | ||||
\(163\) | −13.1848 | − | 3.53284i | −1.03271 | − | 0.276714i | −0.297621 | − | 0.954684i | \(-0.596193\pi\) |
−0.735089 | + | 0.677971i | \(0.762860\pi\) | |||||||
\(164\) | −13.6822 | + | 19.6924i | −1.06840 | + | 1.53772i | ||||
\(165\) | 1.91071 | + | 7.13085i | 0.148748 | + | 0.555136i | ||||
\(166\) | 3.22727 | − | 10.3010i | 0.250485 | − | 0.799509i | ||||
\(167\) | − | 7.84557i | − | 0.607109i | −0.952814 | − | 0.303554i | \(-0.901827\pi\) | ||
0.952814 | − | 0.303554i | \(-0.0981734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.95982i | − | 0.304601i | ||||||
\(170\) | −2.96634 | − | 0.929350i | −0.227508 | − | 0.0712779i | ||||
\(171\) | −0.817885 | − | 3.05239i | −0.0625453 | − | 0.233422i | ||||
\(172\) | 9.12563 | − | 1.64338i | 0.695823 | − | 0.125306i | ||||
\(173\) | −3.00073 | − | 0.804044i | −0.228141 | − | 0.0611303i | 0.142937 | − | 0.989732i | \(-0.454345\pi\) |
−0.371079 | + | 0.928601i | \(0.621012\pi\) | |||||||
\(174\) | −0.539422 | + | 12.8934i | −0.0408935 | + | 0.977446i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.55659 | − | 9.22015i | −0.494222 | − | 0.694995i | ||||
\(177\) | −9.27131 | − | 16.0584i | −0.696874 | − | 1.20702i | ||||
\(178\) | −0.800674 | + | 1.26187i | −0.0600130 | + | 0.0945811i | ||||
\(179\) | 3.67131 | + | 13.7015i | 0.274406 | + | 1.02410i | 0.956238 | + | 0.292589i | \(0.0945169\pi\) |
−0.681832 | + | 0.731509i | \(0.738816\pi\) | |||||||
\(180\) | 10.8586 | + | 3.90750i | 0.809353 | + | 0.291248i | ||||
\(181\) | −3.03153 | − | 3.03153i | −0.225332 | − | 0.225332i | 0.585407 | − | 0.810739i | \(-0.300935\pi\) |
−0.810739 | + | 0.585407i | \(0.800935\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.2208 | −1.49477 | ||||||||
\(184\) | −3.59514 | − | 8.54709i | −0.265037 | − | 0.630100i | ||||
\(185\) | −0.997377 | + | 1.72751i | −0.0733286 | + | 0.127009i | ||||
\(186\) | 11.0041 | − | 2.46058i | 0.806861 | − | 0.180419i | ||||
\(187\) | −7.27060 | − | 1.94815i | −0.531679 | − | 0.142463i | ||||
\(188\) | −19.8663 | − | 1.66521i | −1.44890 | − | 0.121448i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0220861 | − | 0.527908i | 0.00160229 | − | 0.0382984i | ||||
\(191\) | −12.3049 | + | 7.10425i | −0.890353 | + | 0.514046i | −0.874058 | − | 0.485822i | \(-0.838520\pi\) |
−0.0162951 | + | 0.999867i | \(0.505187\pi\) | |||||||
\(192\) | −25.2790 | + | 0.276141i | −1.82436 | + | 0.0199288i | ||||
\(193\) | 9.64726 | − | 16.7095i | 0.694425 | − | 1.20278i | −0.275950 | − | 0.961172i | \(-0.588992\pi\) |
0.970374 | − | 0.241607i | \(-0.0776744\pi\) | |||||||
\(194\) | −16.6290 | + | 8.69505i | −1.19390 | + | 0.624268i | ||||
\(195\) | 7.60061 | + | 7.60061i | 0.544291 | + | 0.544291i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.454953 | − | 0.454953i | 0.0324140 | − | 0.0324140i | −0.690714 | − | 0.723128i | \(-0.742704\pi\) |
0.723128 | + | 0.690714i | \(0.242704\pi\) | |||||||
\(198\) | 26.6660 | + | 8.35442i | 1.89507 | + | 0.593722i | ||||
\(199\) | −21.3063 | − | 12.3012i | −1.51036 | − | 0.872009i | −0.999927 | − | 0.0120940i | \(-0.996150\pi\) |
−0.510437 | − | 0.859915i | \(-0.670516\pi\) | |||||||
\(200\) | −9.72935 | − | 7.38152i | −0.687969 | − | 0.521952i | ||||
\(201\) | 9.77286 | + | 16.9271i | 0.689324 | + | 1.19394i | ||||
\(202\) | −0.339553 | − | 0.369205i | −0.0238909 | − | 0.0259772i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −12.8449 | + | 10.8581i | −0.899321 | + | 0.760217i | ||||
\(205\) | 2.56303 | − | 9.56537i | 0.179010 | − | 0.668074i | ||||
\(206\) | 14.9478 | + | 9.48459i | 1.04146 | + | 0.660823i | ||||
\(207\) | 19.8339 | + | 11.4511i | 1.37855 | + | 0.795908i | ||||
\(208\) | −14.9798 | − | 6.85285i | −1.03866 | − | 0.475160i | ||||
\(209\) | − | 1.27941i | − | 0.0884990i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1092 | − | 10.1092i | 0.695946 | − | 0.695946i | −0.267588 | − | 0.963534i | \(-0.586226\pi\) |
0.963534 | + | 0.267588i | \(0.0862265\pi\) | |||||||
\(212\) | 6.32325 | + | 2.27543i | 0.434282 | + | 0.156277i | ||||
\(213\) | −15.6928 | + | 4.20487i | −1.07525 | + | 0.288113i | ||||
\(214\) | −7.58932 | + | 1.69701i | −0.518795 | + | 0.116005i | ||||
\(215\) | −3.31627 | + | 1.91465i | −0.226168 | + | 0.130578i | ||||
\(216\) | 28.1460 | − | 21.8425i | 1.91509 | − | 1.48619i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.77330 | + | 6.27747i | 0.391017 | + | 0.425164i | ||||
\(219\) | −5.71876 | + | 21.3427i | −0.386438 | + | 1.44221i | ||||
\(220\) | 3.83706 | + | 2.66597i | 0.258695 | + | 0.179740i | ||||
\(221\) | −10.5861 | + | 2.83654i | −0.712098 | + | 0.190806i | ||||
\(222\) | 5.00110 | + | 9.56447i | 0.335652 | + | 0.641925i | ||||
\(223\) | 15.1035 | 1.01140 | 0.505702 | − | 0.862708i | \(-0.331234\pi\) | ||||
0.505702 | + | 0.862708i | \(0.331234\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 30.1642 | 2.01095 | ||||||||
\(226\) | 5.10521 | + | 9.76357i | 0.339593 | + | 0.649463i | ||||
\(227\) | 9.73295 | − | 2.60794i | 0.645999 | − | 0.173095i | 0.0790797 | − | 0.996868i | \(-0.474802\pi\) |
0.566919 | + | 0.823773i | \(0.308135\pi\) | |||||||
\(228\) | −2.34779 | − | 1.63124i | −0.155486 | − | 0.108031i | ||||
\(229\) | −6.87883 | + | 25.6721i | −0.454566 | + | 1.69646i | 0.234795 | + | 0.972045i | \(0.424558\pi\) |
−0.689361 | + | 0.724418i | \(0.742109\pi\) | |||||||
\(230\) | 2.59217 | + | 2.81854i | 0.170923 | + | 0.185849i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00728 | + | 6.45234i | 0.328744 | + | 0.423617i | ||||
\(233\) | −3.87771 | + | 2.23879i | −0.254037 | + | 0.146668i | −0.621611 | − | 0.783326i | \(-0.713522\pi\) |
0.367574 | + | 0.929994i | \(0.380188\pi\) | |||||||
\(234\) | 39.7064 | − | 8.87858i | 2.59569 | − | 0.580411i | ||||
\(235\) | 7.95258 | − | 2.13089i | 0.518769 | − | 0.139004i | ||||
\(236\) | −11.0424 | − | 3.97363i | −0.718798 | − | 0.258661i | ||||
\(237\) | −25.0819 | + | 25.0819i | −1.62924 | + | 1.62924i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.13871i | 0.591134i | 0.955322 | + | 0.295567i | \(0.0955086\pi\) | ||||
−0.955322 | + | 0.295567i | \(0.904491\pi\) | |||||||
\(240\) | 9.78440 | − | 3.64214i | 0.631580 | − | 0.235099i | ||||
\(241\) | −8.37419 | − | 4.83484i | −0.539429 | − | 0.311440i | 0.205418 | − | 0.978674i | \(-0.434144\pi\) |
−0.744848 | + | 0.667235i | \(0.767478\pi\) | |||||||
\(242\) | −3.58235 | − | 2.27305i | −0.230282 | − | 0.146117i | ||||
\(243\) | −5.63390 | + | 21.0260i | −0.361415 | + | 1.34882i | ||||
\(244\) | −9.77361 | + | 8.26186i | −0.625691 | + | 0.528911i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −36.2708 | − | 39.4383i | −2.31254 | − | 2.51449i | ||||
\(247\) | −0.931423 | − | 1.61327i | −0.0592650 | − | 0.102650i | ||||
\(248\) | 4.31342 | − | 5.68539i | 0.273903 | − | 0.361022i | ||||
\(249\) | 20.8892 | + | 12.0604i | 1.32380 | + | 0.764295i | ||||
\(250\) | 10.3861 | + | 3.25395i | 0.656875 | + | 0.205798i | ||||
\(251\) | 10.9231 | − | 10.9231i | 0.689459 | − | 0.689459i | −0.272653 | − | 0.962112i | \(-0.587901\pi\) |
0.962112 | + | 0.272653i | \(0.0879012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.55659 | + | 6.55659i | 0.412209 | + | 0.412209i | ||||
\(254\) | −10.0578 | + | 5.25908i | −0.631085 | + | 0.329984i | ||||
\(255\) | 3.47300 | − | 6.01541i | 0.217487 | − | 0.376699i | ||||
\(256\) | −12.1056 | + | 10.4620i | −0.756602 | + | 0.653876i | ||||
\(257\) | −20.4285 | + | 11.7944i | −1.27429 | + | 0.735713i | −0.975793 | − | 0.218697i | \(-0.929819\pi\) |
−0.298500 | + | 0.954410i | \(0.596486\pi\) | |||||||
\(258\) | −0.866076 | + | 20.7012i | −0.0539195 | + | 1.28880i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.77917 | + | 0.568236i | 0.420426 | + | 0.0352405i | ||||
\(261\) | −19.4854 | − | 5.22110i | −1.20612 | − | 0.323178i | ||||
\(262\) | 18.0086 | − | 4.02681i | 1.11257 | − | 0.248777i | ||||
\(263\) | −12.6798 | + | 21.9620i | −0.781868 | + | 1.35424i | 0.148984 | + | 0.988840i | \(0.452400\pi\) |
−0.930852 | + | 0.365396i | \(0.880934\pi\) | |||||||
\(264\) | 23.3030 | − | 9.80186i | 1.43420 | − | 0.603263i | ||||
\(265\) | −2.77529 | −0.170485 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.36129 | − | 2.36129i | −0.144508 | − | 0.144508i | ||||
\(268\) | 11.6397 | + | 4.18859i | 0.711011 | + | 0.255859i | ||||
\(269\) | 2.10457 | + | 7.85436i | 0.128318 | + | 0.478889i | 0.999936 | − | 0.0112965i | \(-0.00359586\pi\) |
−0.871618 | + | 0.490185i | \(0.836929\pi\) | |||||||
\(270\) | −7.88280 | + | 12.4234i | −0.479732 | + | 0.756062i | ||||
\(271\) | −8.37841 | − | 14.5118i | −0.508952 | − | 0.881531i | −0.999946 | − | 0.0103684i | \(-0.996700\pi\) |
0.490994 | − | 0.871163i | \(-0.336634\pi\) | |||||||
\(272\) | −1.77208 | + | 10.4964i | −0.107448 | + | 0.636436i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.533778 | − | 12.7585i | 0.0322467 | − | 0.770769i | ||||
\(275\) | 11.7964 | + | 3.16085i | 0.711352 | + | 0.190606i | ||||
\(276\) | 20.3913 | − | 3.67213i | 1.22741 | − | 0.221037i | ||||
\(277\) | −1.99751 | − | 7.45479i | −0.120019 | − | 0.447915i | 0.879595 | − | 0.475724i | \(-0.157814\pi\) |
−0.999613 | + | 0.0278086i | \(0.991147\pi\) | |||||||
\(278\) | 8.27561 | + | 2.59273i | 0.496338 | + | 0.155502i | ||||
\(279\) | 17.6266i | 1.05528i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.11163i | 0.364589i | 0.983244 | + | 0.182295i | \(0.0583525\pi\) | ||||
−0.983244 | + | 0.182295i | \(0.941648\pi\) | |||||||
\(282\) | 13.3182 | − | 42.5096i | 0.793087 | − | 2.53141i | ||||
\(283\) | −1.84251 | − | 6.87634i | −0.109526 | − | 0.408756i | 0.889293 | − | 0.457337i | \(-0.151197\pi\) |
−0.998819 | + | 0.0485811i | \(0.984530\pi\) | |||||||
\(284\) | −5.86697 | + | 8.44417i | −0.348141 | + | 0.501069i | ||||
\(285\) | 1.14041 | + | 0.305573i | 0.0675523 | + | 0.0181006i | ||||
\(286\) | 16.4585 | + | 0.688576i | 0.973213 | + | 0.0407164i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 8.20190 | − | 38.6584i | 0.483302 | − | 2.27797i | ||||
\(289\) | −4.95894 | − | 8.58914i | −0.291702 | − | 0.505243i | ||||
\(290\) | −2.84800 | − | 1.80709i | −0.167240 | − | 0.106116i | ||||
\(291\) | −10.8525 | − | 40.5019i | −0.636183 | − | 2.37427i | ||||
\(292\) | 5.95611 | + | 12.6524i | 0.348555 | + | 0.740428i | ||||
\(293\) | 19.6200 | + | 19.6200i | 1.14621 | + | 1.14621i | 0.987291 | + | 0.158921i | \(0.0508014\pi\) |
0.158921 | + | 0.987291i | \(0.449199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.84653 | 0.282176 | ||||||||
\(296\) | 6.32511 | + | 2.57957i | 0.367640 | + | 0.149934i | ||||
\(297\) | −17.8136 | + | 30.8540i | −1.03365 | + | 1.79033i | ||||
\(298\) | 5.78797 | + | 25.8847i | 0.335288 | + | 1.49946i | ||||
\(299\) | 13.0407 | + | 3.49426i | 0.754166 | + | 0.202078i | ||||
\(300\) | 20.8406 | − | 17.6171i | 1.20323 | − | 1.01712i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 16.6042 | + | 0.694671i | 0.955464 | + | 0.0399738i | ||||
\(303\) | 0.970677 | − | 0.560420i | 0.0557639 | − | 0.0321953i | ||||
\(304\) | −1.80128 | + | 0.170818i | −0.103311 | + | 0.00979710i | ||||
\(305\) | 2.64259 | − | 4.57709i | 0.151314 | − | 0.262084i | ||||
\(306\) | −12.1828 | − | 23.2993i | −0.696445 | − | 1.33193i | ||||
\(307\) | −3.08795 | − | 3.08795i | −0.176238 | − | 0.176238i | 0.613475 | − | 0.789714i | \(-0.289771\pi\) |
−0.789714 | + | 0.613475i | \(0.789771\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.9713 | + | 27.9713i | −1.59123 | + | 1.59123i | ||||
\(310\) | −0.881122 | + | 2.81241i | −0.0500444 | + | 0.159734i | ||||
\(311\) | −17.5043 | − | 10.1061i | −0.992576 | − | 0.573064i | −0.0865328 | − | 0.996249i | \(-0.527579\pi\) |
−0.906043 | + | 0.423185i | \(0.860912\pi\) | |||||||
\(312\) | 22.2480 | − | 29.3243i | 1.25954 | − | 1.66016i | ||||
\(313\) | −7.61557 | − | 13.1906i | −0.430457 | − | 0.745574i | 0.566455 | − | 0.824093i | \(-0.308314\pi\) |
−0.996913 | + | 0.0785183i | \(0.974981\pi\) | |||||||
\(314\) | −11.6434 | + | 10.7083i | −0.657074 | + | 0.604302i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.87517 | + | 22.3712i | −0.105487 | + | 1.25848i | ||||
\(317\) | −7.44788 | + | 27.7959i | −0.418315 | + | 1.56117i | 0.359788 | + | 0.933034i | \(0.382849\pi\) |
−0.778102 | + | 0.628138i | \(0.783817\pi\) | |||||||
\(318\) | −8.04519 | + | 12.6793i | −0.451152 | + | 0.711020i | ||||
\(319\) | −7.07313 | − | 4.08367i | −0.396019 | − | 0.228642i | ||||
\(320\) | 3.24112 | − | 5.75813i | 0.181184 | − | 0.321889i | ||||
\(321\) | − | 17.3772i | − | 0.969898i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.851203 | + | 0.851203i | −0.0473622 | + | 0.0473622i | ||||
\(324\) | 16.0540 | + | 34.1031i | 0.891887 | + | 1.89462i | ||||
\(325\) | 17.1758 | − | 4.60224i | 0.952741 | − | 0.255286i | ||||
\(326\) | −4.21241 | − | 18.8386i | −0.233304 | − | 1.04337i | ||||
\(327\) | −16.5041 | + | 9.52864i | −0.912678 | + | 0.526935i | ||||
\(328\) | −33.6450 | − | 4.24264i | −1.85774 | − | 0.234261i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.68454 | + | 7.06736i | −0.423020 | + | 0.389045i | ||||
\(331\) | 7.62013 | − | 28.4387i | 0.418840 | − | 1.56313i | −0.358177 | − | 0.933654i | \(-0.616602\pi\) |
0.777018 | − | 0.629479i | \(-0.216732\pi\) | |||||||
\(332\) | 15.0243 | − | 2.70563i | 0.824565 | − | 0.148491i | ||||
\(333\) | −16.2970 | + | 4.36676i | −0.893068 | + | 0.239297i | ||||
\(334\) | 9.83232 | − | 5.14116i | 0.538001 | − | 0.281312i | ||||
\(335\) | −5.10872 | −0.279119 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7954 | −0.751483 | −0.375741 | − | 0.926725i | \(-0.622612\pi\) | ||||
−0.375741 | + | 0.926725i | \(0.622612\pi\) | |||||||
\(338\) | 4.96257 | − | 2.59484i | 0.269928 | − | 0.141141i | ||||
\(339\) | −23.7803 | + | 6.37191i | −1.29157 | + | 0.346075i | ||||
\(340\) | −0.779134 | − | 4.32651i | −0.0422545 | − | 0.234638i | ||||
\(341\) | −1.84705 | + | 6.89330i | −0.100024 | + | 0.373293i | ||||
\(342\) | 3.28940 | − | 3.02521i | 0.177870 | − | 0.163585i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.03950 | + | 10.3596i | 0.433461 | + | 0.558554i | ||||
\(345\) | −7.41023 | + | 4.27830i | −0.398953 | + | 0.230336i | ||||
\(346\) | −0.958708 | − | 4.28750i | −0.0515405 | − | 0.230497i | ||||
\(347\) | 5.02347 | − | 1.34603i | 0.269674 | − | 0.0722589i | −0.121448 | − | 0.992598i | \(-0.538754\pi\) |
0.391122 | + | 0.920339i | \(0.372087\pi\) | |||||||
\(348\) | −16.5119 | + | 7.77295i | −0.885131 | + | 0.416674i | ||||
\(349\) | 17.8960 | − | 17.8960i | 0.957951 | − | 0.957951i | −0.0412000 | − | 0.999151i | \(-0.513118\pi\) |
0.999151 | + | 0.0412000i | \(0.0131181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 51.8736i | 2.76881i | ||||||||
\(352\) | 7.25849 | − | 14.2588i | 0.386879 | − | 0.759998i | ||||
\(353\) | −3.79300 | − | 2.18989i | −0.201881 | − | 0.116556i | 0.395652 | − | 0.918401i | \(-0.370519\pi\) |
−0.597533 | + | 0.801845i | \(0.703852\pi\) | |||||||
\(354\) | 14.0494 | − | 22.1421i | 0.746719 | − | 1.17684i | ||||
\(355\) | 1.09904 | − | 4.10166i | 0.0583308 | − | 0.217694i | ||||
\(356\) | −2.10609 | − | 0.176534i | −0.111623 | − | 0.00935631i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.7654 | + | 13.5795i | −0.780374 | + | 0.717699i | ||||
\(359\) | 7.66467 | + | 13.2756i | 0.404526 | + | 0.700659i | 0.994266 | − | 0.106934i | \(-0.0341032\pi\) |
−0.589740 | + | 0.807593i | \(0.700770\pi\) | |||||||
\(360\) | 2.21858 | + | 16.1689i | 0.116930 | + | 0.852177i | ||||
\(361\) | 16.2773 | + | 9.39769i | 0.856699 | + | 0.494615i | ||||
\(362\) | 1.81267 | − | 5.78575i | 0.0952717 | − | 0.304092i | ||||
\(363\) | 6.70351 | − | 6.70351i | 0.351843 | − | 0.351843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.08367 | − | 4.08367i | −0.213749 | − | 0.213749i | ||||
\(366\) | −13.2506 | − | 25.3414i | −0.692619 | − | 1.32462i | ||||
\(367\) | −13.1576 | + | 22.7896i | −0.686821 | + | 1.18961i | 0.286040 | + | 0.958218i | \(0.407661\pi\) |
−0.972861 | + | 0.231391i | \(0.925672\pi\) | |||||||
\(368\) | 8.35562 | − | 10.1064i | 0.435567 | − | 0.526832i | ||||
\(369\) | 72.5374 | − | 41.8795i | 3.77615 | − | 2.18016i | ||||
\(370\) | −2.81854 | − | 0.117920i | −0.146529 | − | 0.00613035i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.2946 | + | 12.1783i | 0.533751 | + | 0.631416i | ||||
\(373\) | −33.7164 | − | 9.03428i | −1.74577 | − | 0.467777i | −0.762053 | − | 0.647514i | \(-0.775809\pi\) |
−0.983715 | + | 0.179737i | \(0.942475\pi\) | |||||||
\(374\) | −2.32289 | − | 10.3884i | −0.120114 | − | 0.537169i | ||||
\(375\) | −12.1601 | + | 21.0619i | −0.627943 | + | 1.08763i | ||||
\(376\) | −10.9314 | − | 25.9883i | −0.563743 | − | 1.34024i | ||||
\(377\) | −11.8918 | −0.612458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8512 | − | 14.8512i | −0.762855 | − | 0.762855i | 0.213982 | − | 0.976838i | \(-0.431356\pi\) |
−0.976838 | + | 0.213982i | \(0.931356\pi\) | |||||||
\(380\) | 0.676064 | − | 0.318256i | 0.0346813 | − | 0.0163262i | ||||
\(381\) | −6.56396 | − | 24.4970i | −0.336282 | − | 1.25502i | ||||
\(382\) | −16.9666 | − | 10.7656i | −0.868088 | − | 0.550814i | ||||
\(383\) | −12.7227 | − | 22.0364i | −0.650100 | − | 1.12601i | −0.983098 | − | 0.183079i | \(-0.941394\pi\) |
0.332998 | − | 0.942927i | \(-0.391940\pi\) | |||||||
\(384\) | −16.9113 | − | 31.4995i | −0.862999 | − | 1.60745i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.2627 | + | 1.14059i | 1.38764 | + | 0.0580546i | ||||
\(387\) | −31.2851 | − | 8.38281i | −1.59031 | − | 0.426122i | ||||
\(388\) | −21.7938 | − | 15.1422i | −1.10641 | − | 0.768730i | ||||
\(389\) | 0.310707 | + | 1.15957i | 0.0157535 | + | 0.0587928i | 0.973355 | − | 0.229303i | \(-0.0736446\pi\) |
−0.957602 | + | 0.288096i | \(0.906978\pi\) | |||||||
\(390\) | −4.54469 | + | 14.5060i | −0.230129 | + | 0.734537i | ||||
\(391\) | − | 8.72428i | − | 0.441206i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.2339i | 2.07998i | ||||||||
\(394\) | 0.868289 | + | 0.272033i | 0.0437438 | + | 0.0137048i | ||||
\(395\) | −2.39956 | − | 8.95529i | −0.120735 | − | 0.450589i | ||||
\(396\) | 7.00405 | + | 38.8933i | 0.351967 | + | 1.95446i | ||||
\(397\) | −21.1153 | − | 5.65782i | −1.05975 | − | 0.283958i | −0.313472 | − | 0.949598i | \(-0.601492\pi\) |
−0.746273 | + | 0.665640i | \(0.768159\pi\) | |||||||
\(398\) | 1.45437 | − | 34.7626i | 0.0729008 | − | 1.74249i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.87517 | − | 17.0302i | 0.143759 | − | 0.851510i | ||||
\(401\) | 10.8674 | + | 18.8229i | 0.542692 | + | 0.939970i | 0.998748 | + | 0.0500194i | \(0.0159283\pi\) |
−0.456056 | + | 0.889951i | \(0.650738\pi\) | |||||||
\(402\) | −14.8095 | + | 23.3399i | −0.738629 | + | 1.16409i | ||||
\(403\) | 2.68934 | + | 10.0367i | 0.133965 | + | 0.499966i | ||||
\(404\) | 0.240193 | − | 0.667476i | 0.0119500 | − | 0.0332082i | ||||
\(405\) | −11.0070 | − | 11.0070i | −0.546944 | − | 0.546944i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.83090 | −0.338595 | ||||||||
\(408\) | −22.0249 | − | 8.98238i | −1.09039 | − | 0.444694i | ||||
\(409\) | 13.5071 | − | 23.3950i | 0.667883 | − | 1.15681i | −0.310612 | − | 0.950537i | \(-0.600534\pi\) |
0.978495 | − | 0.206270i | \(-0.0661326\pi\) | |||||||
\(410\) | 13.6672 | − | 3.05605i | 0.674973 | − | 0.150928i | ||||
\(411\) | 27.5616 | + | 7.38511i | 1.35951 | + | 0.364280i | ||||
\(412\) | −2.09119 | + | 24.9483i | −0.103025 | + | 1.22911i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.35386 | + | 32.3604i | −0.0665387 | + | 1.59043i | ||||
\(415\) | −5.45986 | + | 3.15225i | −0.268014 | + | 0.154738i | ||||
\(416\) | −1.22798 | − | 23.2638i | −0.0602067 | − | 1.14060i | ||||
\(417\) | −9.68909 | + | 16.7820i | −0.474477 | + | 0.821818i | ||||
\(418\) | 1.60340 | − | 0.838392i | 0.0784250 | − | 0.0410071i | ||||
\(419\) | −1.31859 | − | 1.31859i | −0.0644176 | − | 0.0644176i | 0.674164 | − | 0.738582i | \(-0.264504\pi\) |
−0.738582 | + | 0.674164i | \(0.764504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.73490 | + | 9.73490i | −0.474450 | + | 0.474450i | −0.903351 | − | 0.428901i | \(-0.858901\pi\) |
0.428901 | + | 0.903351i | \(0.358901\pi\) | |||||||
\(422\) | 19.2937 | + | 6.04467i | 0.939201 | + | 0.294250i | ||||
\(423\) | 60.3071 | + | 34.8183i | 2.93223 | + | 1.69292i | ||||
\(424\) | 1.29194 | + | 9.41557i | 0.0627420 | + | 0.457261i | ||||
\(425\) | −5.74532 | − | 9.95118i | −0.278689 | − | 0.482703i | ||||
\(426\) | −15.5530 | − | 16.9113i | −0.753548 | − | 0.819353i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.09999 | − | 8.39914i | −0.343191 | − | 0.405988i | ||||
\(429\) | −9.52682 | + | 35.5546i | −0.459959 | + | 1.71659i | ||||
\(430\) | −4.57263 | − | 2.90140i | −0.220512 | − | 0.139918i | ||||
\(431\) | 19.5083 | + | 11.2631i | 0.939680 | + | 0.542525i | 0.889860 | − | 0.456234i | \(-0.150802\pi\) |
0.0498200 | + | 0.998758i | \(0.484135\pi\) | |||||||
\(432\) | 45.8176 | + | 20.9603i | 2.20440 | + | 1.00845i | ||||
\(433\) | − | 7.16594i | − | 0.344373i | −0.985064 | − | 0.172187i | \(-0.944917\pi\) | ||
0.985064 | − | 0.172187i | \(-0.0550832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.32934 | − | 5.32934i | 0.255522 | − | 0.255522i | ||||
\(436\) | −4.08392 | + | 11.3489i | −0.195584 | + | 0.543512i | ||||
\(437\) | 1.43238 | − | 0.383805i | 0.0685200 | − | 0.0183599i | ||||
\(438\) | −30.4948 | + | 6.81881i | −1.45710 | + | 0.325816i | ||||
\(439\) | −12.5170 | + | 7.22667i | −0.597402 | + | 0.344910i | −0.768019 | − | 0.640427i | \(-0.778757\pi\) |
0.170617 | + | 0.985337i | \(0.445424\pi\) | |||||||
\(440\) | −0.826678 | + | 6.55572i | −0.0394103 | + | 0.312532i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.4918 | − | 11.4081i | −0.499046 | − | 0.542627i | ||||
\(443\) | −4.94674 | + | 18.4615i | −0.235027 | + | 0.877132i | 0.743110 | + | 0.669169i | \(0.233350\pi\) |
−0.978137 | + | 0.207963i | \(0.933317\pi\) | |||||||
\(444\) | −8.70930 | + | 12.5351i | −0.413325 | + | 0.594888i | ||||
\(445\) | 0.843078 | − | 0.225902i | 0.0399657 | − | 0.0107088i | ||||
\(446\) | 9.89721 | + | 18.9282i | 0.468647 | + | 0.896274i | ||||
\(447\) | −59.2679 | −2.80328 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.2712 | 0.626306 | 0.313153 | − | 0.949703i | \(-0.398615\pi\) | ||||
0.313153 | + | 0.949703i | \(0.398615\pi\) | |||||||
\(450\) | 19.7664 | + | 37.8028i | 0.931799 | + | 1.78204i | ||||
\(451\) | 32.7560 | − | 8.77693i | 1.54242 | − | 0.413290i | ||||
\(452\) | −8.89061 | + | 12.7960i | −0.418179 | + | 0.601874i | ||||
\(453\) | −9.61115 | + | 35.8693i | −0.451571 | + | 1.68529i | ||||
\(454\) | 9.64629 | + | 10.4887i | 0.452723 | + | 0.492258i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.505822 | − | 4.01127i | 0.0236873 | − | 0.187845i | ||||
\(457\) | 30.3726 | − | 17.5356i | 1.42077 | − | 0.820282i | 0.424405 | − | 0.905472i | \(-0.360483\pi\) |
0.996365 | + | 0.0851904i | \(0.0271498\pi\) | |||||||
\(458\) | −36.6808 | + | 8.20203i | −1.71398 | + | 0.383256i | ||||
\(459\) | 32.3788 | − | 8.67588i | 1.51131 | − | 0.404956i | ||||
\(460\) | −1.83365 | + | 5.09557i | −0.0854945 | + | 0.237582i | ||||
\(461\) | −16.3005 | + | 16.3005i | −0.759188 | + | 0.759188i | −0.976175 | − | 0.216987i | \(-0.930377\pi\) |
0.216987 | + | 0.976175i | \(0.430377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.09532i | 0.0509037i | 0.999676 | + | 0.0254519i | \(0.00810245\pi\) | ||||
−0.999676 | + | 0.0254519i | \(0.991898\pi\) | |||||||
\(464\) | −4.80504 | + | 10.5035i | −0.223068 | + | 0.487611i | ||||
\(465\) | −5.70324 | − | 3.29277i | −0.264482 | − | 0.152698i | ||||
\(466\) | −5.34677 | − | 3.39260i | −0.247684 | − | 0.157159i | ||||
\(467\) | 6.41294 | − | 23.9334i | 0.296755 | − | 1.10751i | −0.643058 | − | 0.765818i | \(-0.722334\pi\) |
0.939813 | − | 0.341689i | \(-0.110999\pi\) | |||||||
\(468\) | 37.1463 | + | 43.9433i | 1.71709 | + | 2.03128i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.88177 | + | 8.57007i | 0.363559 | + | 0.395308i | ||||
\(471\) | −17.6736 | − | 30.6116i | −0.814357 | − | 1.41051i | ||||
\(472\) | −2.25613 | − | 16.4426i | −0.103847 | − | 0.756830i | ||||
\(473\) | −11.3564 | − | 6.55659i | −0.522166 | − | 0.301472i | ||||
\(474\) | −47.8695 | − | 14.9974i | −2.19872 | − | 0.688854i | ||||
\(475\) | 1.38106 | − | 1.38106i | 0.0633675 | − | 0.0633675i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.5984 | − | 16.5984i | −0.759990 | − | 0.759990i | ||||
\(478\) | −11.4529 | + | 5.98854i | −0.523844 | + | 0.273909i | ||||
\(479\) | −3.89155 | + | 6.74037i | −0.177810 | + | 0.307975i | −0.941130 | − | 0.338045i | \(-0.890234\pi\) |
0.763320 | + | 0.646020i | \(0.223568\pi\) | |||||||
\(480\) | 10.9761 | + | 9.87545i | 0.500988 | + | 0.450751i | ||||
\(481\) | −8.61339 | + | 4.97294i | −0.392737 | + | 0.226747i | ||||
\(482\) | 0.571622 | − | 13.6630i | 0.0260367 | − | 0.622335i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.501168 | − | 5.97903i | 0.0227803 | − | 0.271774i | ||||
\(485\) | 10.5861 | + | 2.83654i | 0.480690 | + | 0.128800i | ||||
\(486\) | −30.0423 | + | 6.71762i | −1.36275 | + | 0.304718i | ||||
\(487\) | 13.8477 | − | 23.9848i | 0.627497 | − | 1.08686i | −0.360555 | − | 0.932738i | \(-0.617413\pi\) |
0.988052 | − | 0.154119i | \(-0.0492539\pi\) | |||||||
\(488\) | −16.7586 | − | 6.83465i | −0.758627 | − | 0.309390i | ||||
\(489\) | 43.1345 | 1.95061 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.2667 | + | 20.2667i | 0.914621 | + | 0.914621i | 0.996631 | − | 0.0820102i | \(-0.0261340\pi\) |
−0.0820102 | + | 0.996631i | \(0.526134\pi\) | |||||||
\(492\) | 25.6572 | − | 71.2994i | 1.15672 | − | 3.21443i | ||||
\(493\) | 1.98890 | + | 7.42269i | 0.0895758 | + | 0.334301i | ||||
\(494\) | 1.41145 | − | 2.22446i | 0.0635040 | − | 0.100083i | ||||
\(495\) | −8.16021 | − | 14.1339i | −0.366774 | − | 0.635271i | ||||
\(496\) | 9.95167 | + | 1.68012i | 0.446843 | + | 0.0754396i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.42589 | + | 34.0821i | −0.0638958 | + | 1.52725i | ||||
\(499\) | −27.3003 | − | 7.31511i | −1.22213 | − | 0.327469i | −0.410620 | − | 0.911806i | \(-0.634688\pi\) |
−0.811511 | + | 0.584337i | \(0.801355\pi\) | |||||||
\(500\) | 2.72800 | + | 15.1485i | 0.122000 | + | 0.677461i | ||||
\(501\) | 6.41678 | + | 23.9478i | 0.286681 | + | 1.06991i | ||||
\(502\) | 20.8470 | + | 6.53133i | 0.930447 | + | 0.291507i | ||||
\(503\) | − | 3.04877i | − | 0.135938i | −0.997687 | − | 0.0679689i | \(-0.978348\pi\) | ||
0.997687 | − | 0.0679689i | \(-0.0216519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.292957i | 0.0130364i | ||||||||
\(506\) | −3.92044 | + | 12.5134i | −0.174285 | + | 0.556290i | ||||
\(507\) | 3.23868 | + | 12.0869i | 0.143835 | + | 0.536798i | ||||
\(508\) | −13.1817 | − | 9.15857i | −0.584843 | − | 0.406346i | ||||
\(509\) | 22.4920 | + | 6.02673i | 0.996942 | + | 0.267130i | 0.720164 | − | 0.693804i | \(-0.244067\pi\) |
0.276778 | + | 0.960934i | \(0.410733\pi\) | |||||||
\(510\) | 9.81453 | + | 0.410611i | 0.434595 | + | 0.0181822i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.0441 | − | 8.31546i | −0.930025 | − | 0.367495i | ||||
\(513\) | 2.84887 | + | 4.93438i | 0.125781 | + | 0.217858i | ||||
\(514\) | −28.1677 | − | 17.8728i | −1.24243 | − | 0.788336i | ||||
\(515\) | −2.67598 | − | 9.98691i | −0.117918 | − | 0.440076i | ||||
\(516\) | −26.5109 | + | 12.4799i | −1.16708 | + | 0.549399i | ||||
\(517\) | 19.9360 | + | 19.9360i | 0.876784 | + | 0.876784i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.81702 | 0.430919 | ||||||||
\(520\) | 3.73022 | + | 8.86824i | 0.163581 | + | 0.388898i | ||||
\(521\) | 17.4291 | − | 30.1881i | 0.763584 | − | 1.32257i | −0.177408 | − | 0.984137i | \(-0.556771\pi\) |
0.940992 | − | 0.338429i | \(-0.109896\pi\) | |||||||
\(522\) | −6.22542 | − | 27.8411i | −0.272479 | − | 1.21857i | ||||
\(523\) | 43.6182 | + | 11.6875i | 1.90729 | + | 0.511057i | 0.994786 | + | 0.101989i | \(0.0325205\pi\) |
0.912504 | + | 0.409068i | \(0.134146\pi\) | |||||||
\(524\) | 16.8474 | + | 19.9302i | 0.735983 | + | 0.870653i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −35.8325 | − | 1.49912i | −1.56237 | − | 0.0653649i | ||||
\(527\) | 5.81501 | − | 3.35730i | 0.253306 | − | 0.146246i | ||||
\(528\) | 27.5543 | + | 22.7809i | 1.19915 | + | 0.991413i | ||||
\(529\) | 6.12639 | − | 10.6112i | 0.266365 | − | 0.461357i | ||||
\(530\) | −1.81863 | − | 3.47808i | −0.0789963 | − | 0.151078i | ||||
\(531\) | 28.9861 | + | 28.9861i | 1.25789 | + | 1.25789i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.9138 | − | 34.9138i | 1.51228 | − | 1.51228i | ||||
\(534\) | 1.41190 | − | 4.50658i | 0.0610991 | − | 0.195019i | ||||
\(535\) | 3.93341 | + | 2.27096i | 0.170056 | + | 0.0981820i | ||||
\(536\) | 2.37818 | + | 17.3321i | 0.102722 | + | 0.748631i | ||||
\(537\) | −22.4125 | − | 38.8196i | −0.967171 | − | 1.67519i | ||||
\(538\) | −8.46422 | + | 7.78442i | −0.364918 | + | 0.335610i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −20.7349 | − | 1.73802i | −0.892288 | − | 0.0747923i | ||||
\(541\) | 10.4575 | − | 39.0280i | 0.449604 | − | 1.67794i | −0.253882 | − | 0.967235i | \(-0.581707\pi\) |
0.703486 | − | 0.710709i | \(-0.251626\pi\) | |||||||
\(542\) | 12.6964 | − | 20.0096i | 0.545356 | − | 0.859487i | ||||
\(543\) | 11.7329 | + | 6.77397i | 0.503505 | + | 0.290699i | ||||
\(544\) | −14.3156 | + | 4.65738i | −0.613777 | + | 0.199683i | ||||
\(545\) | − | 4.98105i | − | 0.213365i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.86041 | + | 7.86041i | −0.336087 | + | 0.336087i | −0.854892 | − | 0.518805i | \(-0.826377\pi\) |
0.518805 | + | 0.854892i | \(0.326377\pi\) | |||||||
\(548\) | 16.3391 | − | 7.69162i | 0.697973 | − | 0.328570i | ||||
\(549\) | 43.1794 | − | 11.5699i | 1.84285 | − | 0.493790i | ||||
\(550\) | 3.76886 | + | 16.8550i | 0.160705 | + | 0.718698i | ||||
\(551\) | −1.13118 | + | 0.653089i | −0.0481900 | + | 0.0278225i | ||||
\(552\) | 17.9643 | + | 23.1487i | 0.764612 | + | 0.985272i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.03363 | − | 7.38842i | 0.341316 | − | 0.313904i | ||||
\(555\) | 1.63148 | − | 6.08877i | 0.0692525 | − | 0.258454i | ||||
\(556\) | 2.17366 | + | 12.0703i | 0.0921836 | + | 0.511893i | ||||
\(557\) | −7.65079 | + | 2.05002i | −0.324174 | + | 0.0868622i | −0.417236 | − | 0.908798i | \(-0.637001\pi\) |
0.0930619 | + | 0.995660i | \(0.470335\pi\) | |||||||
\(558\) | −22.0902 | + | 11.5506i | −0.935153 | + | 0.488976i | ||||
\(559\) | −19.0930 | −0.807547 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.7861 | 1.00425 | ||||||||
\(562\) | −7.65929 | + | 4.00491i | −0.323088 | + | 0.168937i | ||||
\(563\) | 3.64243 | − | 0.975986i | 0.153510 | − | 0.0411329i | −0.181246 | − | 0.983438i | \(-0.558013\pi\) |
0.334756 | + | 0.942305i | \(0.391346\pi\) | |||||||
\(564\) | 62.0017 | − | 11.1655i | 2.61074 | − | 0.470152i | ||||
\(565\) | 1.66544 | − | 6.21552i | 0.0700658 | − | 0.261489i | ||||
\(566\) | 7.41026 | − | 6.81512i | 0.311477 | − | 0.286461i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.4271 | − | 1.81926i | −0.605347 | − | 0.0763344i | ||||
\(569\) | −24.5695 | + | 14.1852i | −1.03001 | + | 0.594675i | −0.916987 | − | 0.398918i | \(-0.869386\pi\) |
−0.113020 | + | 0.993593i | \(0.536052\pi\) | |||||||
\(570\) | 0.364353 | + | 1.62944i | 0.0152611 | + | 0.0682499i | ||||
\(571\) | −0.180977 | + | 0.0484925i | −0.00757363 | + | 0.00202935i | −0.262604 | − | 0.964904i | \(-0.584581\pi\) |
0.255030 | + | 0.966933i | \(0.417915\pi\) | |||||||
\(572\) | 9.92222 | + | 21.0776i | 0.414869 | + | 0.881297i | ||||
\(573\) | 31.7490 | − | 31.7490i | 1.32633 | − | 1.32633i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.1550i | 0.590305i | ||||||||
\(576\) | 53.8226 | − | 15.0537i | 2.24261 | − | 0.627239i | ||||
\(577\) | 0.530825 | + | 0.306472i | 0.0220985 | + | 0.0127586i | 0.511009 | − | 0.859576i | \(-0.329272\pi\) |
−0.488910 | + | 0.872334i | \(0.662605\pi\) | |||||||
\(578\) | 7.51462 | − | 11.8431i | 0.312567 | − | 0.492608i | ||||
\(579\) | −15.7807 | + | 58.8944i | −0.655824 | + | 2.44757i | ||||
\(580\) | 0.398432 | − | 4.75338i | 0.0165440 | − | 0.197373i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 43.6468 | − | 40.1413i | 1.80922 | − | 1.66391i | ||||
\(583\) | −4.75190 | − | 8.23053i | −0.196803 | − | 0.340874i | ||||
\(584\) | −11.9534 | + | 15.7555i | −0.494637 | + | 0.651966i | ||||
\(585\) | −20.5792 | − | 11.8814i | −0.850843 | − | 0.491235i | ||||
\(586\) | −11.7315 | + | 37.4453i | −0.484625 | + | 1.54685i | ||||
\(587\) | −21.1197 | + | 21.1197i | −0.871704 | + | 0.871704i | −0.992658 | − | 0.120954i | \(-0.961405\pi\) |
0.120954 | + | 0.992658i | \(0.461405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.807030 | + | 0.807030i | 0.0332531 | + | 0.0332531i | ||||
\(590\) | 3.17590 | + | 6.07383i | 0.130750 | + | 0.250056i | ||||
\(591\) | −1.01659 | + | 1.76079i | −0.0418171 | + | 0.0724293i | ||||
\(592\) | 0.912013 | + | 9.61721i | 0.0374835 | + | 0.395265i | ||||
\(593\) | 3.03239 | − | 1.75075i | 0.124525 | − | 0.0718947i | −0.436443 | − | 0.899732i | \(-0.643762\pi\) |
0.560969 | + | 0.827837i | \(0.310429\pi\) | |||||||
\(594\) | −50.3403 | − | 2.10609i | −2.06549 | − | 0.0864140i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.6468 | + | 24.2158i | −1.17342 | + | 0.991917i | ||||
\(597\) | 75.0961 | + | 20.1219i | 3.07348 | + | 0.823536i | ||||
\(598\) | 4.16641 | + | 18.6328i | 0.170377 | + | 0.761954i | ||||
\(599\) | 7.18793 | − | 12.4499i | 0.293691 | − | 0.508687i | −0.680989 | − | 0.732294i | \(-0.738450\pi\) |
0.974679 | + | 0.223607i | \(0.0717831\pi\) | |||||||
\(600\) | 35.7350 | + | 14.5738i | 1.45888 | + | 0.594972i | ||||
\(601\) | −4.26571 | −0.174002 | −0.0870010 | − | 0.996208i | \(-0.527728\pi\) | ||||
−0.0870010 | + | 0.996208i | \(0.527728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.5542 | − | 30.5542i | −1.24426 | − | 1.24426i | ||||
\(604\) | 10.0100 | + | 21.2641i | 0.407303 | + | 0.865225i | ||||
\(605\) | 0.641319 | + | 2.39343i | 0.0260733 | + | 0.0973069i | ||||
\(606\) | 1.33842 | + | 0.849243i | 0.0543694 | + | 0.0344981i | ||||
\(607\) | −6.52176 | − | 11.2960i | −0.264710 | − | 0.458491i | 0.702778 | − | 0.711410i | \(-0.251943\pi\) |
−0.967488 | + | 0.252918i | \(0.918610\pi\) | |||||||
\(608\) | −1.39445 | − | 2.14549i | −0.0565522 | − | 0.0870111i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.46783 | + | 0.312432i | 0.302364 | + | 0.0126500i | ||||
\(611\) | 39.6517 | + | 10.6246i | 1.60414 | + | 0.429827i | ||||
\(612\) | 21.2161 | − | 30.5358i | 0.857610 | − | 1.23434i | ||||
\(613\) | 10.7310 | + | 40.0487i | 0.433422 | + | 1.61755i | 0.744815 | + | 0.667271i | \(0.232538\pi\) |
−0.311393 | + | 0.950281i | \(0.600795\pi\) | |||||||
\(614\) | 1.84640 | − | 5.89342i | 0.0745146 | − | 0.237839i | ||||
\(615\) | 31.2935i | 1.26188i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19.2992i | − | 0.776956i | −0.921458 | − | 0.388478i | \(-0.873001\pi\) | ||
0.921458 | − | 0.388478i | \(-0.126999\pi\) | |||||||
\(618\) | −53.3839 | − | 16.7251i | −2.14741 | − | 0.672781i | ||||
\(619\) | −0.579917 | − | 2.16428i | −0.0233088 | − | 0.0869897i | 0.953292 | − | 0.302051i | \(-0.0976714\pi\) |
−0.976600 | + | 0.215062i | \(0.931005\pi\) | |||||||
\(620\) | −4.10199 | + | 0.738702i | −0.164740 | + | 0.0296670i | ||||
\(621\) | −39.8867 | − | 10.6876i | −1.60060 | − | 0.428879i | ||||
\(622\) | 1.19484 | − | 28.5594i | 0.0479087 | − | 1.14513i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 51.3291 | + | 8.66579i | 2.05481 | + | 0.346909i | ||||
\(625\) | 7.61619 | + | 13.1916i | 0.304647 | + | 0.527665i | ||||
\(626\) | 11.5404 | − | 18.1878i | 0.461247 | − | 0.726929i | ||||
\(627\) | 1.04641 | + | 3.90527i | 0.0417898 | + | 0.155962i | ||||
\(628\) | −21.0498 | − | 7.57480i | −0.839977 | − | 0.302267i | ||||
\(629\) | 4.54464 | + | 4.54464i | 0.181207 | + | 0.181207i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.7915 | −0.549031 | −0.274515 | − | 0.961583i | \(-0.588517\pi\) | ||||
−0.274515 | + | 0.961583i | \(0.588517\pi\) | |||||||
\(632\) | −29.2651 | + | 12.3097i | −1.16410 | + | 0.489652i | ||||
\(633\) | −22.5890 | + | 39.1254i | −0.897834 | + | 1.55509i | ||||
\(634\) | −39.7152 | + | 8.88054i | −1.57729 | + | 0.352691i | ||||
\(635\) | 6.40285 | + | 1.71564i | 0.254089 | + | 0.0680831i | ||||
\(636\) | −21.1621 | − | 1.77382i | −0.839130 | − | 0.0703366i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.482811 | − | 11.5403i | 0.0191147 | − | 0.456884i | ||||
\(639\) | 31.1043 | − | 17.9581i | 1.23047 | − | 0.710410i | ||||
\(640\) | 9.34016 | + | 0.288603i | 0.369202 | + | 0.0114081i | ||||
\(641\) | −3.41080 | + | 5.90767i | −0.134718 | + | 0.233339i | −0.925490 | − | 0.378772i | \(-0.876346\pi\) |
0.790771 | + | 0.612111i | \(0.209680\pi\) | |||||||
\(642\) | 21.7776 | − | 11.3871i | 0.859494 | − | 0.449415i | ||||
\(643\) | −32.9875 | − | 32.9875i | −1.30090 | − | 1.30090i | −0.927786 | − | 0.373112i | \(-0.878291\pi\) |
−0.373112 | − | 0.927786i | \(-0.621709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.55659 | − | 8.55659i | 0.336916 | − | 0.336916i | ||||
\(646\) | −1.62454 | − | 0.508966i | −0.0639167 | − | 0.0200250i | ||||
\(647\) | −17.7203 | − | 10.2308i | −0.696657 | − | 0.402215i | 0.109444 | − | 0.993993i | \(-0.465093\pi\) |
−0.806101 | + | 0.591778i | \(0.798426\pi\) | |||||||
\(648\) | −32.2190 | + | 42.4669i | −1.26568 | + | 1.66826i | ||||
\(649\) | 8.29831 | + | 14.3731i | 0.325737 | + | 0.564193i | ||||
\(650\) | 17.0229 | + | 18.5094i | 0.667692 | + | 0.725999i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.8488 | − | 17.6240i | 0.816501 | − | 0.690207i | ||||
\(653\) | 1.23483 | − | 4.60844i | 0.0483226 | − | 0.180342i | −0.937547 | − | 0.347860i | \(-0.886908\pi\) |
0.985869 | + | 0.167518i | \(0.0535751\pi\) | |||||||
\(654\) | −22.7566 | − | 14.4394i | −0.889854 | − | 0.564625i | ||||
\(655\) | −9.33352 | − | 5.38871i | −0.364691 | − | 0.210554i | ||||
\(656\) | −16.7304 | − | 44.9452i | −0.653211 | − | 1.75481i | ||||
\(657\) | − | 48.8472i | − | 1.90571i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8983 | + | 17.8983i | −0.697217 | + | 0.697217i | −0.963809 | − | 0.266592i | \(-0.914102\pi\) |
0.266592 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(660\) | −13.8927 | − | 4.99931i | −0.540771 | − | 0.194598i | ||||
\(661\) | −20.9520 | + | 5.61408i | −0.814939 | + | 0.218362i | −0.642133 | − | 0.766593i | \(-0.721950\pi\) |
−0.172807 | + | 0.984956i | \(0.555284\pi\) | |||||||
\(662\) | 40.6337 | − | 9.08592i | 1.57927 | − | 0.353134i | ||||
\(663\) | 29.9929 | − | 17.3164i | 1.16483 | − | 0.672515i | ||||
\(664\) | 13.2361 | + | 17.0559i | 0.513661 | + | 0.661899i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.1519 | − | 17.5624i | −0.625872 | − | 0.680528i | ||||
\(667\) | 2.45008 | − | 9.14383i | 0.0948675 | − | 0.354050i | ||||
\(668\) | 12.8861 | + | 8.95321i | 0.498579 | + | 0.346410i | ||||
\(669\) | −46.1017 | + | 12.3529i | −1.78239 | + | 0.477591i | ||||
\(670\) | −3.34771 | − | 6.40241i | −0.129333 | − | 0.247347i | ||||
\(671\) | 18.0987 | 0.698693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.74723 | −0.260086 | −0.130043 | − | 0.991508i | \(-0.541512\pi\) | ||||
−0.130043 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(674\) | −9.04003 | − | 17.2888i | −0.348209 | − | 0.665940i | ||||
\(675\) | −52.5342 | + | 14.0765i | −2.02204 | + | 0.541805i | ||||
\(676\) | 6.50388 | + | 4.51886i | 0.250149 | + | 0.173802i | ||||
\(677\) | −10.0463 | + | 37.4932i | −0.386110 | + | 1.44098i | 0.450299 | + | 0.892878i | \(0.351317\pi\) |
−0.836410 | + | 0.548105i | \(0.815349\pi\) | |||||||
\(678\) | −23.5686 | − | 25.6268i | −0.905146 | − | 0.984190i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.91156 | − | 3.81157i | 0.188350 | − | 0.146167i | ||||
\(681\) | −27.5758 | + | 15.9209i | −1.05671 | + | 0.610090i | ||||
\(682\) | −9.84927 | + | 2.20235i | −0.377148 | + | 0.0843324i | ||||
\(683\) | −23.3707 | + | 6.26215i | −0.894254 | + | 0.239615i | −0.676547 | − | 0.736400i | \(-0.736524\pi\) |
−0.217707 | + | 0.976014i | \(0.569858\pi\) | |||||||
\(684\) | 5.94681 | + | 2.13997i | 0.227382 | + | 0.0818240i | ||||
\(685\) | −5.27358 | + | 5.27358i | −0.201493 | + | 0.201493i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 83.9875i | − | 3.20432i | ||||||
\(688\) | −7.71479 | + | 16.8640i | −0.294124 | + | 0.642933i | ||||
\(689\) | −11.9838 | − | 6.91883i | −0.456545 | − | 0.263586i | ||||
\(690\) | −10.2176 | − | 6.48319i | −0.388976 | − | 0.246811i | ||||
\(691\) | 4.05677 | − | 15.1401i | 0.154327 | − | 0.575955i | −0.844835 | − | 0.535026i | \(-0.820302\pi\) |
0.999162 | − | 0.0409286i | \(-0.0130316\pi\) | |||||||
\(692\) | 4.74499 | − | 4.01105i | 0.180378 | − | 0.152477i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.97874 | + | 5.41352i | 0.188990 | + | 0.205494i | ||||
\(695\) | −2.53246 | − | 4.38636i | −0.0960618 | − | 0.166384i | ||||
\(696\) | −20.5615 | − | 15.5997i | −0.779380 | − | 0.591304i | ||||
\(697\) | −27.6321 | − | 15.9534i | −1.04664 | − | 0.604278i | ||||
\(698\) | 34.1550 | + | 10.7007i | 1.29278 | + | 0.405027i | ||||
\(699\) | 10.0052 | − | 10.0052i | 0.378431 | − | 0.378431i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.821691 | + | 0.821691i | 0.0310348 | + | 0.0310348i | 0.722454 | − | 0.691419i | \(-0.243014\pi\) |
−0.691419 | + | 0.722454i | \(0.743014\pi\) | |||||||
\(702\) | −65.0097 | + | 33.9925i | −2.45363 | + | 1.28296i | ||||
\(703\) | −0.546222 | + | 0.946085i | −0.0206012 | + | 0.0356823i | ||||
\(704\) | 22.6261 | − | 0.247161i | 0.852752 | − | 0.00931523i | ||||
\(705\) | −22.5315 | + | 13.0086i | −0.848587 | + | 0.489932i | ||||
\(706\) | 0.258910 | − | 6.18853i | 0.00974420 | − | 0.232908i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 36.9556 | + | 3.09765i | 1.38888 | + | 0.116417i | ||||
\(709\) | −11.7719 | − | 3.15427i | −0.442103 | − | 0.118461i | 0.0308989 | − | 0.999523i | \(-0.490163\pi\) |
−0.473002 | + | 0.881061i | \(0.656830\pi\) | |||||||
\(710\) | 5.86052 | − | 1.31045i | 0.219942 | − | 0.0491801i | ||||
\(711\) | 39.2084 | − | 67.9109i | 1.47043 | − | 2.54686i | ||||
\(712\) | −1.15887 | − | 2.75510i | −0.0434305 | − | 0.103252i | ||||
\(713\) | −8.27155 | −0.309772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.80294 | − | 6.80294i | −0.254416 | − | 0.254416i | ||||
\(716\) | −26.6939 | − | 9.60587i | −0.997599 | − | 0.358988i | ||||
\(717\) | −7.47442 | − | 27.8949i | −0.279137 | − | 1.04175i | ||||
\(718\) | −11.6148 | + | 18.3050i | −0.433460 | + | 0.683138i | ||||
\(719\) | 11.4433 | + | 19.8204i | 0.426763 | + | 0.739175i | 0.996583 | − | 0.0825945i | \(-0.0263206\pi\) |
−0.569821 | + | 0.821769i | \(0.692987\pi\) | |||||||
\(720\) | −18.8096 | + | 13.3758i | −0.700992 | + | 0.498486i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.11109 | + | 26.5575i | −0.0413503 | + | 0.988366i | ||||
\(723\) | 29.5157 | + | 7.90870i | 1.09770 | + | 0.294128i | ||||
\(724\) | 8.43872 | − | 1.51968i | 0.313623 | − | 0.0564783i | ||||
\(725\) | −3.22697 | − | 12.0432i | −0.119847 | − | 0.447274i | ||||
\(726\) | 12.7938 | + | 4.00829i | 0.474823 | + | 0.148761i | ||||
\(727\) | 12.6428i | 0.468896i | 0.972129 | + | 0.234448i | \(0.0753283\pi\) | ||||
−0.972129 | + | 0.234448i | \(0.924672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 12.2481i | − | 0.453633i | ||||||
\(730\) | 2.44178 | − | 7.79380i | 0.0903745 | − | 0.288461i | ||||
\(731\) | 3.19331 | + | 11.9176i | 0.118109 | + | 0.440788i | ||||
\(732\) | 23.0756 | − | 33.2121i | 0.852899 | − | 1.22755i | ||||
\(733\) | 23.0882 | + | 6.18646i | 0.852782 | + | 0.228502i | 0.658628 | − | 0.752469i | \(-0.271137\pi\) |
0.194154 | + | 0.980971i | \(0.437804\pi\) | |||||||
\(734\) | −37.1828 | − | 1.55562i | −1.37244 | − | 0.0574189i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.1410 | + | 3.84887i | 0.668688 | + | 0.141871i | ||||
\(737\) | −8.74723 | − | 15.1506i | −0.322208 | − | 0.558081i | ||||
\(738\) | 100.018 | + | 63.4628i | 3.68171 | + | 2.33610i | ||||
\(739\) | −5.40440 | − | 20.1695i | −0.198804 | − | 0.741947i | −0.991249 | − | 0.132004i | \(-0.957859\pi\) |
0.792445 | − | 0.609943i | \(-0.208808\pi\) | |||||||
\(740\) | −1.69919 | − | 3.60956i | −0.0624636 | − | 0.132690i | ||||
\(741\) | 4.16254 | + | 4.16254i | 0.152915 | + | 0.152915i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6332 | −0.390093 | −0.195046 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195046 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(744\) | −8.51625 | + | 20.8819i | −0.312221 | + | 0.765568i | ||||
\(745\) | 7.74551 | − | 13.4156i | 0.283773 | − | 0.491510i | ||||
\(746\) | −10.7721 | − | 48.1745i | −0.394394 | − | 1.76380i | ||||
\(747\) | −51.5072 | − | 13.8013i | −1.88455 | − | 0.504964i | ||||
\(748\) | 11.4968 | − | 9.71855i | 0.420366 | − | 0.355346i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −34.3638 | − | 1.43768i | −1.25479 | − | 0.0524967i | ||||
\(751\) | −9.49457 | + | 5.48169i | −0.346462 | + | 0.200030i | −0.663126 | − | 0.748508i | \(-0.730771\pi\) |
0.316664 | + | 0.948538i | \(0.397437\pi\) | |||||||
\(752\) | 25.4061 | − | 30.7295i | 0.926465 | − | 1.12059i | ||||
\(753\) | −24.4077 | + | 42.2753i | −0.889465 | + | 1.54060i | ||||
\(754\) | −7.79261 | − | 14.9031i | −0.283790 | − | 0.542741i | ||||
\(755\) | −6.86316 | − | 6.86316i | −0.249776 | − | 0.249776i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.8153 | + | 21.8153i | −0.792889 | + | 0.792889i | −0.981963 | − | 0.189073i | \(-0.939452\pi\) |
0.189073 | + | 0.981963i | \(0.439452\pi\) | |||||||
\(758\) | 8.88010 | − | 28.3439i | 0.322540 | − | 1.02950i | ||||
\(759\) | −25.3758 | − | 14.6507i | −0.921084 | − | 0.531788i | ||||
\(760\) | 0.841868 | + | 0.638713i | 0.0305378 | + | 0.0231686i | ||||
\(761\) | −4.75921 | − | 8.24319i | −0.172521 | − | 0.298816i | 0.766779 | − | 0.641911i | \(-0.221858\pi\) |
−0.939301 | + | 0.343095i | \(0.888525\pi\) | |||||||
\(762\) | 26.3991 | − | 24.2789i | 0.956340 | − | 0.879532i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.37361 | − | 28.3177i | 0.0858743 | − | 1.02450i | ||||
\(765\) | −3.97433 | + | 14.8324i | −0.143692 | + | 0.536267i | ||||
\(766\) | 19.2796 | − | 30.3848i | 0.696599 | − | 1.09785i | ||||
\(767\) | 20.9274 | + | 12.0825i | 0.755646 | + | 0.436272i | ||||
\(768\) | 28.3944 | − | 41.8352i | 1.02459 | − | 1.50960i | ||||
\(769\) | 36.0771i | 1.30098i | 0.759517 | + | 0.650488i | \(0.225435\pi\) | ||||
−0.759517 | + | 0.650488i | \(0.774565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.7092 | − | 52.7092i | 1.89827 | − | 1.89827i | ||||
\(772\) | 16.4357 | + | 34.9139i | 0.591532 | + | 1.25658i | ||||
\(773\) | −32.9353 | + | 8.82499i | −1.18460 | + | 0.317413i | −0.796750 | − | 0.604309i | \(-0.793449\pi\) |
−0.387851 | + | 0.921722i | \(0.626783\pi\) | |||||||
\(774\) | −9.99530 | − | 44.7006i | −0.359274 | − | 1.60673i | ||||
\(775\) | −9.43477 | + | 5.44717i | −0.338907 | + | 0.195668i | ||||
\(776\) | 4.69538 | − | 37.2353i | 0.168554 | − | 1.33667i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.24961 | + | 1.14925i | −0.0448007 | + | 0.0412026i | ||||
\(779\) | 1.40367 | − | 5.23856i | 0.0502916 | − | 0.187691i | ||||
\(780\) | −21.1574 | + | 3.81011i | −0.757557 | + | 0.136424i | ||||
\(781\) | 14.0459 | − | 3.76358i | 0.502600 | − | 0.134671i | ||||
\(782\) | 10.9336 | − | 5.71697i | 0.390983 | − | 0.204438i | ||||
\(783\) | 36.3724 | 1.29984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.23879 | 0.329747 | ||||||||
\(786\) | −51.6757 | + | 27.0203i | −1.84321 | + | 0.963784i | ||||
\(787\) | 4.99859 | − | 1.33937i | 0.178180 | − | 0.0477433i | −0.168626 | − | 0.985680i | \(-0.553933\pi\) |
0.346806 | + | 0.937937i | \(0.387266\pi\) | |||||||
\(788\) | 0.228063 | + | 1.26643i | 0.00812442 | + | 0.0451147i | ||||
\(789\) | 20.7412 | − | 77.4072i | 0.738406 | − | 2.75577i | ||||
\(790\) | 9.65063 | − | 8.87555i | 0.343354 | − | 0.315778i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −44.1526 | + | 34.2642i | −1.56889 | + | 1.21753i | ||||
\(793\) | 22.8215 | − | 13.1760i | 0.810415 | − | 0.467893i | ||||
\(794\) | −6.74615 | − | 30.1699i | −0.239412 | − | 1.07069i | ||||
\(795\) | 8.47127 | − | 2.26987i | 0.300445 | − | 0.0805040i | ||||
\(796\) | 44.5187 | − | 20.9571i | 1.57792 | − | 0.742804i | ||||
\(797\) | −8.56228 | + | 8.56228i | −0.303291 | + | 0.303291i | −0.842300 | − | 0.539009i | \(-0.818799\pi\) |
0.539009 | + | 0.842300i | \(0.318799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26.5271i | − | 0.938460i | ||||||
\(800\) | 23.2269 | − | 7.55652i | 0.821194 | − | 0.267163i | ||||
\(801\) | 6.39335 | + | 3.69120i | 0.225898 | + | 0.130422i | ||||
\(802\) | −16.4681 | + | 25.9539i | −0.581509 | + | 0.916464i | ||||
\(803\) | 5.11860 | − | 19.1029i | 0.180631 | − | 0.674125i | ||||
\(804\) | −38.9548 | − | 3.26523i | −1.37383 | − | 0.115156i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.8161 | + | 9.94738i | −0.380980 | + | 0.350382i | ||||
\(807\) | −12.8479 | − | 22.2533i | −0.452268 | − | 0.783352i | ||||
\(808\) | 0.993899 | − | 0.136376i | 0.0349653 | − | 0.00479768i | ||||
\(809\) | −8.21438 | − | 4.74257i | −0.288802 | − | 0.166740i | 0.348599 | − | 0.937272i | \(-0.386657\pi\) |
−0.637402 | + | 0.770532i | \(0.719991\pi\) | |||||||
\(810\) | 6.58153 | − | 21.0072i | 0.231251 | − | 0.738118i | ||||
\(811\) | −8.37320 | + | 8.37320i | −0.294023 | + | 0.294023i | −0.838667 | − | 0.544644i | \(-0.816665\pi\) |
0.544644 | + | 0.838667i | \(0.316665\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.4432 | + | 37.4432i | 1.31319 | + | 1.31319i | ||||
\(814\) | −4.47625 | − | 8.56070i | −0.156892 | − | 0.300052i | ||||
\(815\) | −5.63709 | + | 9.76372i | −0.197459 | + | 0.342008i | ||||
\(816\) | −3.17575 | − | 33.4884i | −0.111173 | − | 1.17233i | ||||
\(817\) | −1.81619 | + | 1.04858i | −0.0635403 | + | 0.0366850i | ||||
\(818\) | 38.1704 | + | 1.59694i | 1.33460 | + | 0.0558357i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.7859 | + | 15.1255i | 0.446505 | + | 0.528206i | ||||
\(821\) | −40.9552 | − | 10.9739i | −1.42934 | − | 0.382992i | −0.540556 | − | 0.841308i | \(-0.681786\pi\) |
−0.888789 | + | 0.458316i | \(0.848453\pi\) | |||||||
\(822\) | 8.80569 | + | 39.3805i | 0.307134 | + | 1.37355i | ||||
\(823\) | 4.62629 | − | 8.01297i | 0.161262 | − | 0.279314i | −0.774059 | − | 0.633113i | \(-0.781777\pi\) |
0.935322 | + | 0.353799i | \(0.115110\pi\) | |||||||
\(824\) | −32.6363 | + | 13.7277i | −1.13694 | + | 0.478227i | ||||
\(825\) | −38.5926 | −1.34362 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2363 | + | 18.2363i | 0.634137 | + | 0.634137i | 0.949103 | − | 0.314966i | \(-0.101993\pi\) |
−0.314966 | + | 0.949103i | \(0.601993\pi\) | |||||||
\(828\) | −41.4422 | + | 19.5088i | −1.44022 | + | 0.677979i | ||||
\(829\) | 11.9775 | + | 44.7008i | 0.415997 | + | 1.55252i | 0.782829 | + | 0.622236i | \(0.213776\pi\) |
−0.366832 | + | 0.930287i | \(0.619558\pi\) | |||||||
\(830\) | −7.52831 | − | 4.77682i | −0.261312 | − | 0.165806i | ||||
\(831\) | 12.1943 | + | 21.1212i | 0.423017 | + | 0.732687i | ||||
\(832\) | 28.3503 | − | 16.7836i | 0.982870 | − | 0.581866i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −27.3809 | − | 1.14554i | −0.948124 | − | 0.0396667i | ||||
\(835\) | −6.25929 | − | 1.67717i | −0.216612 | − | 0.0580409i | ||||
\(836\) | 2.10140 | + | 1.46004i | 0.0726784 | + | 0.0504966i | ||||
\(837\) | −8.22566 | − | 30.6986i | −0.284320 | − | 1.06110i | ||||
\(838\) | 0.788438 | − | 2.51657i | 0.0272361 | − | 0.0869335i | ||||
\(839\) | − | 14.1360i | − | 0.488028i | −0.969772 | − | 0.244014i | \(-0.921536\pi\) | ||
0.969772 | − | 0.244014i | \(-0.0784643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 20.6618i | − | 0.712476i | ||||||
\(842\) | −18.5793 | − | 5.82087i | −0.640285 | − | 0.200600i | ||||
\(843\) | −4.99861 | − | 18.6551i | −0.172161 | − | 0.642515i | ||||
\(844\) | 5.06764 | + | 28.1405i | 0.174435 | + | 0.968635i | ||||
\(845\) | −3.15919 | − | 0.846501i | −0.108679 | − | 0.0291205i | ||||
\(846\) | −4.11656 | + | 98.3950i | −0.141530 | + | 3.38289i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.9533 | + | 7.78906i | −0.376138 | + | 0.267478i | ||||
\(849\) | 11.2481 | + | 19.4823i | 0.386034 | + | 0.668631i | ||||
\(850\) | 8.70627 | − | 13.7212i | 0.298622 | − | 0.470632i | ||||
\(851\) | −2.04917 | − | 7.64760i | −0.0702446 | − | 0.262156i | ||||
\(852\) | 11.0019 | − | 30.5734i | 0.376919 | − | 1.04743i | ||||
\(853\) | −11.3648 | − | 11.3648i | −0.389122 | − | 0.389122i | 0.485252 | − | 0.874374i | \(-0.338728\pi\) |
−0.874374 | + | 0.485252i | \(0.838728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.61007 | −0.0892626 | ||||||||
\(856\) | 5.87349 | − | 14.4018i | 0.200752 | − | 0.492245i | ||||
\(857\) | 7.66444 | − | 13.2752i | 0.261812 | − | 0.453472i | −0.704911 | − | 0.709295i | \(-0.749013\pi\) |
0.966724 | + | 0.255823i | \(0.0823465\pi\) | |||||||
\(858\) | −50.8010 | + | 11.3594i | −1.73432 | + | 0.387803i | ||||
\(859\) | −17.7129 | − | 4.74614i | −0.604355 | − | 0.161936i | −0.0563492 | − | 0.998411i | \(-0.517946\pi\) |
−0.548005 | + | 0.836475i | \(0.684613\pi\) | |||||||
\(860\) | 0.639707 | − | 7.63184i | 0.0218138 | − | 0.260244i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.33163 | + | 31.8290i | −0.0453556 | + | 1.08410i | ||||
\(863\) | 37.0810 | − | 21.4088i | 1.26225 | − | 0.728762i | 0.288744 | − | 0.957406i | \(-0.406763\pi\) |
0.973510 | + | 0.228644i | \(0.0734292\pi\) | |||||||
\(864\) | 3.75592 | + | 71.1552i | 0.127779 | + | 2.42075i | ||||
\(865\) | −1.28295 | + | 2.22214i | −0.0436216 | + | 0.0755549i | ||||
\(866\) | 8.98058 | − | 4.69580i | 0.305173 | − | 0.159570i | ||||
\(867\) | 22.1616 | + | 22.1616i | 0.752646 | + | 0.752646i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.4496 | − | 22.4496i | 0.761552 | − | 0.761552i | ||||
\(870\) | 10.1712 | + | 3.18662i | 0.344836 | + | 0.108036i | ||||
\(871\) | −22.0595 | − | 12.7361i | −0.747459 | − | 0.431546i | ||||
\(872\) | −16.8989 | + | 2.31875i | −0.572270 | + | 0.0785228i | ||||
\(873\) | 46.3485 | + | 80.2780i | 1.56866 | + | 2.71700i | ||||
\(874\) | 1.41963 | + | 1.54360i | 0.0480196 | + | 0.0522130i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −28.5286 | − | 33.7488i | −0.963893 | − | 1.14027i | ||||
\(877\) | −10.4760 | + | 39.0969i | −0.353749 | + | 1.32021i | 0.528302 | + | 0.849056i | \(0.322829\pi\) |
−0.882051 | + | 0.471153i | \(0.843838\pi\) | |||||||
\(878\) | −17.2590 | − | 10.9511i | −0.582462 | − | 0.369580i | ||||
\(879\) | −75.9348 | − | 43.8410i | −2.56122 | − | 1.47872i | ||||
\(880\) | −8.75756 | + | 3.25991i | −0.295217 | + | 0.109891i | ||||
\(881\) | 5.93539i | 0.199969i | 0.994989 | + | 0.0999843i | \(0.0318792\pi\) | ||||
−0.994989 | + | 0.0999843i | \(0.968121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.96040 | − | 2.96040i | 0.0996254 | − | 0.0996254i | −0.655537 | − | 0.755163i | \(-0.727558\pi\) |
0.755163 | + | 0.655537i | \(0.227558\pi\) | |||||||
\(884\) | 7.42172 | − | 20.6244i | 0.249619 | − | 0.693672i | ||||
\(885\) | −14.7935 | + | 3.96391i | −0.497278 | + | 0.133245i | ||||
\(886\) | −26.3781 | + | 5.89829i | −0.886190 | + | 0.198157i | ||||
\(887\) | −10.4423 | + | 6.02888i | −0.350619 | + | 0.202430i | −0.664958 | − | 0.746881i | \(-0.731551\pi\) |
0.314339 | + | 0.949311i | \(0.398217\pi\) | |||||||
\(888\) | −21.4165 | − | 2.70062i | −0.718691 | − | 0.0906270i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.835572 | + | 0.908540i | 0.0280084 | + | 0.0304543i | ||||
\(891\) | 13.7965 | − | 51.4894i | 0.462202 | − | 1.72496i | ||||
\(892\) | −17.2358 | + | 24.8070i | −0.577097 | + | 0.830600i | ||||
\(893\) | 4.35530 | − | 1.16700i | 0.145744 | − | 0.0390521i | ||||
\(894\) | −38.8379 | − | 74.2764i | −1.29893 | − | 2.48418i | ||||
\(895\) | 11.7160 | 0.391624 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.6634 | −1.42449 | ||||||||
\(898\) | 8.69653 | + | 16.6319i | 0.290207 | + | 0.555013i | ||||
\(899\) | 7.03750 | − | 1.88569i | 0.234714 | − | 0.0628914i | ||||
\(900\) | −34.4228 | + | 49.5439i | −1.14743 | + | 1.65146i | ||||
\(901\) | −2.31435 | + | 8.63729i | −0.0771023 | + | 0.287750i | ||||
\(902\) | 32.4643 | + | 35.2993i | 1.08094 | + | 1.17534i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.8623 | − | 2.75684i | −0.727131 | − | 0.0916913i | ||||
\(905\) | −3.06665 | + | 1.77053i | −0.101939 | + | 0.0588544i | ||||
\(906\) | −51.2507 | + | 11.4599i | −1.70269 | + | 0.380731i | ||||
\(907\) | 8.49595 | − | 2.27648i | 0.282103 | − | 0.0755893i | −0.114993 | − | 0.993366i | \(-0.536685\pi\) |
0.397096 | + | 0.917777i | \(0.370018\pi\) | |||||||
\(908\) | −6.82359 | + | 18.9622i | −0.226449 | + | 0.629283i | ||||
\(909\) | −1.75212 | + | 1.75212i | −0.0581140 | + | 0.0581140i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3682i | 0.873617i | 0.899554 | + | 0.436809i | \(0.143891\pi\) | ||||
−0.899554 | + | 0.436809i | \(0.856109\pi\) | |||||||
\(912\) | 5.35851 | − | 1.99465i | 0.177438 | − | 0.0660494i | ||||
\(913\) | −18.6969 | − | 10.7947i | −0.618778 | − | 0.357251i | ||||
\(914\) | 41.8792 | + | 26.5729i | 1.38524 | + | 0.878954i | ||||
\(915\) | −4.32266 | + | 16.1324i | −0.142903 | + | 0.533321i | ||||
\(916\) | −34.3157 | − | 40.5948i | −1.13382 | − | 1.34129i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 32.0905 | + | 34.8929i | 1.05915 | + | 1.15164i | ||||
\(919\) | 30.0247 | + | 52.0044i | 0.990425 | + | 1.71547i | 0.614770 | + | 0.788707i | \(0.289249\pi\) |
0.375655 | + | 0.926759i | \(0.377418\pi\) | |||||||
\(920\) | −7.58751 | + | 1.04110i | −0.250153 | + | 0.0343242i | ||||
\(921\) | 11.9512 | + | 6.90003i | 0.393805 | + | 0.227364i | ||||
\(922\) | −31.1098 | − | 9.74666i | −1.02455 | − | 0.320989i | ||||
\(923\) | 14.9712 | − | 14.9712i | 0.492781 | − | 0.492781i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.37361 | − | 7.37361i | −0.242443 | − | 0.242443i | ||||
\(926\) | −1.37269 | + | 0.717755i | −0.0451093 | + | 0.0235869i | ||||
\(927\) | 43.7251 | − | 75.7341i | 1.43612 | − | 2.48743i | ||||
\(928\) | −16.3120 | + | 0.861027i | −0.535467 | + | 0.0282646i | ||||
\(929\) | −33.0418 | + | 19.0767i | −1.08407 | + | 0.625887i | −0.931991 | − | 0.362482i | \(-0.881929\pi\) |
−0.152077 | + | 0.988369i | \(0.548596\pi\) | |||||||
\(930\) | 0.389303 | − | 9.30522i | 0.0127657 | − | 0.305130i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.748007 | − | 8.92388i | 0.0245018 | − | 0.292312i | ||||
\(933\) | 61.6955 | + | 16.5313i | 2.01982 | + | 0.541209i | ||||
\(934\) | 34.1965 | − | 7.64652i | 1.11894 | − | 0.250202i | ||||
\(935\) | −3.10852 | + | 5.38411i | −0.101659 | + | 0.176079i | ||||
\(936\) | −30.7294 | + | 75.3487i | −1.00442 | + | 2.46285i | ||||
\(937\) | 15.2637 | 0.498643 | 0.249321 | − | 0.968421i | \(-0.419792\pi\) | ||||
0.249321 | + | 0.968421i | \(0.419792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.0341 | + | 34.0341i | 1.11066 | + | 1.11066i | ||||
\(940\) | −5.57541 | + | 15.4936i | −0.181850 | + | 0.505345i | ||||
\(941\) | 13.0736 | + | 48.7913i | 0.426187 | + | 1.59055i | 0.761317 | + | 0.648380i | \(0.224553\pi\) |
−0.335130 | + | 0.942172i | \(0.608780\pi\) | |||||||
\(942\) | 26.7820 | − | 42.2087i | 0.872605 | − | 1.37523i | ||||
\(943\) | 19.6526 | + | 34.0393i | 0.639976 | + | 1.10847i | ||||
\(944\) | 19.1279 | − | 13.6022i | 0.622560 | − | 0.442713i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.775184 | − | 18.5286i | 0.0252034 | − | 0.602418i | ||||
\(947\) | −36.0934 | − | 9.67121i | −1.17288 | − | 0.314272i | −0.380781 | − | 0.924665i | \(-0.624345\pi\) |
−0.792098 | + | 0.610393i | \(0.791011\pi\) | |||||||
\(948\) | −12.5733 | − | 69.8192i | −0.408362 | − | 2.26762i | ||||
\(949\) | −7.45275 | − | 27.8140i | −0.241926 | − | 0.902882i | ||||
\(950\) | 2.63580 | + | 0.825790i | 0.0855165 | + | 0.0267922i | ||||
\(951\) | − | 90.9354i | − | 2.94878i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.2788i | − | 1.69348i | −0.532010 | − | 0.846738i | \(-0.678563\pi\) | ||
0.532010 | − | 0.846738i | \(-0.321437\pi\) | |||||||
\(954\) | 9.92483 | − | 31.6785i | 0.321328 | − | 1.02563i | ||||
\(955\) | 3.03739 | + | 11.3357i | 0.0982877 | + | 0.366815i | ||||
\(956\) | −15.0101 | − | 10.4289i | −0.485460 | − | 0.337295i | ||||
\(957\) | 24.9299 | + | 6.67996i | 0.805870 | + | 0.215932i | ||||
\(958\) | −10.9974 | − | 0.460097i | −0.355308 | − | 0.0148651i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.18366 | + | 20.2269i | −0.167302 | + | 0.652821i | ||||
\(961\) | 12.3169 | + | 21.3335i | 0.397320 | + | 0.688179i | ||||
\(962\) | −11.8766 | − | 7.53584i | −0.382915 | − | 0.242965i | ||||
\(963\) | 9.94280 | + | 37.1070i | 0.320402 | + | 1.19576i | ||||
\(964\) | 17.4975 | − | 8.23694i | 0.563558 | − | 0.265294i | ||||
\(965\) | −11.2687 | − | 11.2687i | −0.362753 | − | 0.362753i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6054 | 0.919888 | 0.459944 | − | 0.887948i | \(-0.347870\pi\) | ||||
0.459944 | + | 0.887948i | \(0.347870\pi\) | |||||||
\(968\) | 7.82153 | − | 3.28994i | 0.251393 | − | 0.105743i | ||||
\(969\) | 1.90202 | − | 3.29439i | 0.0611016 | − | 0.105831i | ||||
\(970\) | 3.38217 | + | 15.1256i | 0.108595 | + | 0.485654i | ||||
\(971\) | −44.7840 | − | 11.9998i | −1.43719 | − | 0.385093i | −0.545639 | − | 0.838020i | \(-0.683713\pi\) |
−0.891548 | + | 0.452927i | \(0.850380\pi\) | |||||||
\(972\) | −28.1053 | − | 33.2479i | −0.901477 | − | 1.06643i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 39.1328 | + | 1.63720i | 1.25390 | + | 0.0524594i | ||||
\(975\) | −48.6631 | + | 28.0957i | −1.55847 | + | 0.899781i | ||||
\(976\) | −2.41641 | − | 25.4811i | −0.0773474 | − | 0.815631i | ||||
\(977\) | −16.6403 | + | 28.8218i | −0.532369 | + | 0.922091i | 0.466916 | + | 0.884301i | \(0.345365\pi\) |
−0.999286 | + | 0.0377892i | \(0.987968\pi\) | |||||||
\(978\) | 28.2658 | + | 54.0575i | 0.903839 | + | 1.72857i | ||||
\(979\) | 2.11348 | + | 2.11348i | 0.0675470 | + | 0.0675470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.7906 | − | 29.7906i | 0.951141 | − | 0.951141i | ||||
\(982\) | −12.1182 | + | 38.6794i | −0.386707 | + | 1.23431i | ||||
\(983\) | 23.5506 | + | 13.5969i | 0.751147 | + | 0.433675i | 0.826108 | − | 0.563511i | \(-0.190550\pi\) |
−0.0749609 | + | 0.997186i | \(0.523883\pi\) | |||||||
\(984\) | 106.168 | − | 14.5676i | 3.38450 | − | 0.464397i | ||||
\(985\) | −0.265710 | − | 0.460223i | −0.00846622 | − | 0.0146639i | ||||
\(986\) | −7.99904 | + | 7.35660i | −0.254741 | + | 0.234282i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.71267 | + | 0.311199i | 0.118116 | + | 0.00990057i | ||||
\(989\) | 3.93376 | − | 14.6810i | 0.125086 | − | 0.466828i | ||||
\(990\) | 12.3657 | − | 19.4885i | 0.393008 | − | 0.619385i | ||||
\(991\) | 36.7867 | + | 21.2388i | 1.16857 | + | 0.674673i | 0.953342 | − | 0.301892i | \(-0.0976182\pi\) |
0.215225 | + | 0.976564i | \(0.430952\pi\) | |||||||
\(992\) | 4.41569 | + | 13.5727i | 0.140198 | + | 0.430934i | ||||
\(993\) | 93.0384i | 2.95248i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.3687 | + | 14.3687i | −0.455520 | + | 0.455520i | ||||
\(996\) | −43.6471 | + | 20.5468i | −1.38301 | + | 0.651050i | ||||
\(997\) | −42.2801 | + | 11.3289i | −1.33902 | + | 0.358791i | −0.856072 | − | 0.516856i | \(-0.827102\pi\) |
−0.482952 | + | 0.875647i | \(0.660436\pi\) | |||||||
\(998\) | −8.72222 | − | 39.0072i | −0.276097 | − | 1.23475i | ||||
\(999\) | 26.3451 | − | 15.2103i | 0.833522 | − | 0.481234i |
(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 | 784.2.w.e.227.5 | 32 | ||
7.2 | even | 3 | inner | 784.2.w.e.19.6 | 32 | ||
7.3 | odd | 6 | 112.2.j.d.83.1 | yes | 16 | ||
7.4 | even | 3 | 112.2.j.d.83.2 | yes | 16 | ||
7.5 | odd | 6 | inner | 784.2.w.e.19.5 | 32 | ||
7.6 | odd | 2 | inner | 784.2.w.e.227.6 | 32 | ||
16.11 | odd | 4 | inner | 784.2.w.e.619.5 | 32 | ||
28.3 | even | 6 | 448.2.j.d.111.8 | 16 | |||
28.11 | odd | 6 | 448.2.j.d.111.1 | 16 | |||
56.3 | even | 6 | 896.2.j.g.223.1 | 16 | |||
56.11 | odd | 6 | 896.2.j.g.223.8 | 16 | |||
56.45 | odd | 6 | 896.2.j.h.223.8 | 16 | |||
56.53 | even | 6 | 896.2.j.h.223.1 | 16 | |||
112.3 | even | 12 | 896.2.j.h.671.1 | 16 | |||
112.11 | odd | 12 | 112.2.j.d.27.1 | ✓ | 16 | ||
112.27 | even | 4 | inner | 784.2.w.e.619.6 | 32 | ||
112.45 | odd | 12 | 896.2.j.g.671.8 | 16 | |||
112.53 | even | 12 | 448.2.j.d.335.8 | 16 | |||
112.59 | even | 12 | 112.2.j.d.27.2 | yes | 16 | ||
112.67 | odd | 12 | 896.2.j.h.671.8 | 16 | |||
112.75 | even | 12 | inner | 784.2.w.e.411.5 | 32 | ||
112.101 | odd | 12 | 448.2.j.d.335.1 | 16 | |||
112.107 | odd | 12 | inner | 784.2.w.e.411.6 | 32 | ||
112.109 | even | 12 | 896.2.j.g.671.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.j.d.27.1 | ✓ | 16 | 112.11 | odd | 12 | ||
112.2.j.d.27.2 | yes | 16 | 112.59 | even | 12 | ||
112.2.j.d.83.1 | yes | 16 | 7.3 | odd | 6 | ||
112.2.j.d.83.2 | yes | 16 | 7.4 | even | 3 | ||
448.2.j.d.111.1 | 16 | 28.11 | odd | 6 | |||
448.2.j.d.111.8 | 16 | 28.3 | even | 6 | |||
448.2.j.d.335.1 | 16 | 112.101 | odd | 12 | |||
448.2.j.d.335.8 | 16 | 112.53 | even | 12 | |||
784.2.w.e.19.5 | 32 | 7.5 | odd | 6 | inner | ||
784.2.w.e.19.6 | 32 | 7.2 | even | 3 | inner | ||
784.2.w.e.227.5 | 32 | 1.1 | even | 1 | trivial | ||
784.2.w.e.227.6 | 32 | 7.6 | odd | 2 | inner | ||
784.2.w.e.411.5 | 32 | 112.75 | even | 12 | inner | ||
784.2.w.e.411.6 | 32 | 112.107 | odd | 12 | inner | ||
784.2.w.e.619.5 | 32 | 16.11 | odd | 4 | inner | ||
784.2.w.e.619.6 | 32 | 112.27 | even | 4 | inner | ||
896.2.j.g.223.1 | 16 | 56.3 | even | 6 | |||
896.2.j.g.223.8 | 16 | 56.11 | odd | 6 | |||
896.2.j.g.671.1 | 16 | 112.109 | even | 12 | |||
896.2.j.g.671.8 | 16 | 112.45 | odd | 12 | |||
896.2.j.h.223.1 | 16 | 56.53 | even | 6 | |||
896.2.j.h.223.8 | 16 | 56.45 | odd | 6 | |||
896.2.j.h.671.1 | 16 | 112.3 | even | 12 | |||
896.2.j.h.671.8 | 16 | 112.67 | odd | 12 |