Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(9,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.j (of order \(10\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 9.3 | ||
Character | \(\chi\) | \(=\) | 605.9 |
Dual form | 605.2.j.k.269.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92380 | − | 0.625081i | −1.36033 | − | 0.441999i | −0.464179 | − | 0.885741i | \(-0.653651\pi\) |
−0.896155 | + | 0.443742i | \(0.853651\pi\) | |||||||
\(3\) | −1.71325 | − | 2.35809i | −0.989145 | − | 1.36144i | −0.931754 | − | 0.363090i | \(-0.881722\pi\) |
−0.0573908 | − | 0.998352i | \(-0.518278\pi\) | |||||||
\(4\) | 1.69226 | + | 1.22950i | 0.846128 | + | 0.614748i | ||||
\(5\) | 2.16467 | + | 0.560538i | 0.968070 | + | 0.250680i | ||||
\(6\) | 1.82196 | + | 5.60741i | 0.743812 | + | 2.28922i | ||||
\(7\) | −1.88754 | + | 2.59798i | −0.713424 | + | 0.981943i | 0.286293 | + | 0.958142i | \(0.407577\pi\) |
−0.999717 | + | 0.0238013i | \(0.992423\pi\) | |||||||
\(8\) | −0.109082 | − | 0.150138i | −0.0385663 | − | 0.0530819i | ||||
\(9\) | −1.69829 | + | 5.22681i | −0.566098 | + | 1.74227i | ||||
\(10\) | −3.81402 | − | 2.43146i | −1.20610 | − | 0.768895i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 6.09692i | − | 1.76003i | ||||||
\(13\) | −0.617001 | − | 0.200476i | −0.171125 | − | 0.0556020i | 0.222201 | − | 0.975001i | \(-0.428676\pi\) |
−0.393327 | + | 0.919399i | \(0.628676\pi\) | |||||||
\(14\) | 5.25521 | − | 3.81813i | 1.40451 | − | 1.02044i | ||||
\(15\) | −2.38682 | − | 6.06482i | −0.616275 | − | 1.56593i | ||||
\(16\) | −1.17677 | − | 3.62171i | −0.294191 | − | 0.905428i | ||||
\(17\) | 1.13030 | − | 0.367258i | 0.274139 | − | 0.0890731i | −0.168721 | − | 0.985664i | \(-0.553964\pi\) |
0.442860 | + | 0.896591i | \(0.353964\pi\) | |||||||
\(18\) | 6.53436 | − | 8.99378i | 1.54016 | − | 2.11985i | ||||
\(19\) | 1.52982 | − | 1.11148i | 0.350964 | − | 0.254990i | −0.398309 | − | 0.917251i | \(-0.630403\pi\) |
0.749273 | + | 0.662261i | \(0.230403\pi\) | |||||||
\(20\) | 2.97400 | + | 3.61003i | 0.665006 | + | 0.807227i | ||||
\(21\) | 9.36008 | 2.04254 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.35986i | − | 0.909095i | −0.890723 | − | 0.454547i | \(-0.849801\pi\) | ||
0.890723 | − | 0.454547i | \(-0.150199\pi\) | |||||||
\(24\) | −0.167155 | + | 0.514449i | −0.0341203 | + | 0.105011i | ||||
\(25\) | 4.37159 | + | 2.42676i | 0.874319 | + | 0.485352i | ||||
\(26\) | 1.06168 | + | 0.771352i | 0.208212 | + | 0.151275i | ||||
\(27\) | 6.91857 | − | 2.24798i | 1.33148 | − | 0.432624i | ||||
\(28\) | −6.38841 | + | 2.07572i | −1.20730 | + | 0.392274i | ||||
\(29\) | −3.36869 | − | 2.44750i | −0.625550 | − | 0.454489i | 0.229306 | − | 0.973354i | \(-0.426355\pi\) |
−0.854856 | + | 0.518866i | \(0.826355\pi\) | |||||||
\(30\) | 0.800770 | + | 13.1595i | 0.146200 | + | 2.40258i | ||||
\(31\) | 2.44118 | − | 7.51319i | 0.438450 | − | 1.34941i | −0.451060 | − | 0.892493i | \(-0.648954\pi\) |
0.889510 | − | 0.456916i | \(-0.151046\pi\) | |||||||
\(32\) | 8.07420i | 1.42733i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.40405 | −0.412291 | ||||||||
\(35\) | −5.54217 | + | 4.56573i | −0.936798 | + | 0.771749i | ||||
\(36\) | −9.30029 | + | 6.75706i | −1.55005 | + | 1.12618i | ||||
\(37\) | −1.20995 | + | 1.66536i | −0.198915 | + | 0.273783i | −0.896809 | − | 0.442418i | \(-0.854121\pi\) |
0.697894 | + | 0.716201i | \(0.254121\pi\) | |||||||
\(38\) | −3.63783 | + | 1.18200i | −0.590134 | + | 0.191746i | ||||
\(39\) | 0.584338 | + | 1.79841i | 0.0935689 | + | 0.287976i | ||||
\(40\) | −0.151968 | − | 0.386145i | −0.0240283 | − | 0.0610548i | ||||
\(41\) | 2.67396 | − | 1.94275i | 0.417602 | − | 0.303406i | −0.359070 | − | 0.933311i | \(-0.616906\pi\) |
0.776672 | + | 0.629905i | \(0.216906\pi\) | |||||||
\(42\) | −18.0070 | − | 5.85081i | −2.77853 | − | 0.902800i | ||||
\(43\) | − | 10.9313i | − | 1.66701i | −0.552509 | − | 0.833507i | \(-0.686330\pi\) | ||
0.552509 | − | 0.833507i | \(-0.313670\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.60607 | + | 10.3624i | −0.984775 | + | 1.54473i | ||||
\(46\) | −2.72527 | + | 8.38752i | −0.401819 | + | 1.23667i | ||||
\(47\) | −1.71325 | − | 2.35809i | −0.249903 | − | 0.343962i | 0.665574 | − | 0.746332i | \(-0.268187\pi\) |
−0.915477 | + | 0.402370i | \(0.868187\pi\) | |||||||
\(48\) | −6.52422 | + | 8.97981i | −0.941689 | + | 1.29612i | ||||
\(49\) | −1.02356 | − | 3.15019i | −0.146223 | − | 0.450027i | ||||
\(50\) | −6.89316 | − | 7.40121i | −0.974840 | − | 1.04669i | ||||
\(51\) | −2.80252 | − | 2.03615i | −0.392431 | − | 0.285118i | ||||
\(52\) | −0.797640 | − | 1.09786i | −0.110613 | − | 0.152245i | ||||
\(53\) | 6.10422 | + | 1.98338i | 0.838479 | + | 0.272438i | 0.696613 | − | 0.717447i | \(-0.254690\pi\) |
0.141866 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(54\) | −14.7151 | −2.00248 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.595953 | 0.0796376 | ||||||||
\(57\) | −5.24191 | − | 1.70320i | −0.694308 | − | 0.225594i | ||||
\(58\) | 4.95081 | + | 6.81421i | 0.650074 | + | 0.894750i | ||||
\(59\) | −3.00659 | − | 2.18442i | −0.391425 | − | 0.284387i | 0.374614 | − | 0.927181i | \(-0.377775\pi\) |
−0.766039 | + | 0.642794i | \(0.777775\pi\) | |||||||
\(60\) | 3.41756 | − | 13.1978i | 0.441205 | − | 1.70383i | ||||
\(61\) | −2.40630 | − | 7.40582i | −0.308095 | − | 0.948218i | −0.978504 | − | 0.206227i | \(-0.933882\pi\) |
0.670410 | − | 0.741991i | \(-0.266118\pi\) | |||||||
\(62\) | −9.39272 | + | 12.9280i | −1.19288 | + | 1.64185i | ||||
\(63\) | −10.3735 | − | 14.2779i | −1.30694 | − | 1.79885i | ||||
\(64\) | 2.69350 | − | 8.28974i | 0.336688 | − | 1.03622i | ||||
\(65\) | −1.22323 | − | 0.779817i | −0.151723 | − | 0.0967244i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.37993i | − | 0.290755i | −0.989376 | − | 0.145377i | \(-0.953560\pi\) | ||
0.989376 | − | 0.145377i | \(-0.0464396\pi\) | |||||||
\(68\) | 2.36431 | + | 0.768210i | 0.286714 | + | 0.0931591i | ||||
\(69\) | −10.2809 | + | 7.46954i | −1.23768 | + | 0.899226i | ||||
\(70\) | 13.5160 | − | 5.31925i | 1.61547 | − | 0.635772i | ||||
\(71\) | 4.85662 | + | 14.9471i | 0.576375 | + | 1.77390i | 0.631450 | + | 0.775417i | \(0.282460\pi\) |
−0.0550754 | + | 0.998482i | \(0.517540\pi\) | |||||||
\(72\) | 0.969998 | − | 0.315171i | 0.114315 | − | 0.0371433i | ||||
\(73\) | 3.35877 | − | 4.62295i | 0.393114 | − | 0.541075i | −0.565885 | − | 0.824484i | \(-0.691465\pi\) |
0.958999 | + | 0.283409i | \(0.0914653\pi\) | |||||||
\(74\) | 3.36869 | − | 2.44750i | 0.391602 | − | 0.284516i | ||||
\(75\) | −1.76712 | − | 14.4662i | −0.204049 | − | 1.67042i | ||||
\(76\) | 3.95540 | 0.453715 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 3.82504i | − | 0.433100i | ||||||
\(79\) | 4.71438 | − | 14.5094i | 0.530410 | − | 1.63243i | −0.222954 | − | 0.974829i | \(-0.571570\pi\) |
0.753364 | − | 0.657604i | \(-0.228430\pi\) | |||||||
\(80\) | −0.517201 | − | 8.49944i | −0.0578248 | − | 0.950266i | ||||
\(81\) | −3.81561 | − | 2.77220i | −0.423956 | − | 0.308022i | ||||
\(82\) | −6.35854 | + | 2.06602i | −0.702184 | + | 0.228153i | ||||
\(83\) | −10.1161 | + | 3.28693i | −1.11039 | + | 0.360787i | −0.806092 | − | 0.591790i | \(-0.798421\pi\) |
−0.304297 | + | 0.952577i | \(0.598421\pi\) | |||||||
\(84\) | 15.8397 | + | 11.5082i | 1.72825 | + | 1.25565i | ||||
\(85\) | 2.65260 | − | 0.161414i | 0.287714 | − | 0.0175078i | ||||
\(86\) | −6.83298 | + | 21.0297i | −0.736819 | + | 2.26770i | ||||
\(87\) | 12.1368i | 1.30121i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 19.1861 | − | 15.8058i | 2.02239 | − | 1.66608i | ||||
\(91\) | 1.68545 | − | 1.22455i | 0.176683 | − | 0.128368i | ||||
\(92\) | 5.36044 | − | 7.37801i | 0.558864 | − | 0.769211i | ||||
\(93\) | −21.8991 | + | 7.11545i | −2.27083 | + | 0.737838i | ||||
\(94\) | 1.82196 | + | 5.60741i | 0.187921 | + | 0.578360i | ||||
\(95\) | 3.93457 | − | 1.54846i | 0.403679 | − | 0.158869i | ||||
\(96\) | 19.0397 | − | 13.8331i | 1.94323 | − | 1.41184i | ||||
\(97\) | 14.3972 | + | 4.67793i | 1.46181 | + | 0.474971i | 0.928623 | − | 0.371025i | \(-0.120994\pi\) |
0.533189 | + | 0.845996i | \(0.320994\pi\) | |||||||
\(98\) | 6.70015i | 0.676817i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.41416 | + | 9.48156i | 0.441416 | + | 0.948156i | ||||
\(101\) | −1.72375 | + | 5.30516i | −0.171519 | + | 0.527883i | −0.999457 | − | 0.0329370i | \(-0.989514\pi\) |
0.827938 | + | 0.560820i | \(0.189514\pi\) | |||||||
\(102\) | 4.11873 | + | 5.66895i | 0.407815 | + | 0.561310i | ||||
\(103\) | 1.87043 | − | 2.57443i | 0.184299 | − | 0.253666i | −0.706864 | − | 0.707350i | \(-0.749891\pi\) |
0.891163 | + | 0.453684i | \(0.149891\pi\) | |||||||
\(104\) | 0.0372046 | + | 0.114504i | 0.00364821 | + | 0.0112280i | ||||
\(105\) | 20.2615 | + | 5.24669i | 1.97732 | + | 0.512024i | ||||
\(106\) | −10.5035 | − | 7.63127i | −1.02019 | − | 0.741214i | ||||
\(107\) | −2.33296 | − | 3.21104i | −0.225536 | − | 0.310423i | 0.681221 | − | 0.732078i | \(-0.261449\pi\) |
−0.906756 | + | 0.421655i | \(0.861449\pi\) | |||||||
\(108\) | 14.4719 | + | 4.70220i | 1.39256 | + | 0.452470i | ||||
\(109\) | 15.4150 | 1.47649 | 0.738243 | − | 0.674535i | \(-0.235656\pi\) | ||||
0.738243 | + | 0.674535i | \(0.235656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 11.6303 | + | 3.77892i | 1.09896 | + | 0.357074i | ||||
\(113\) | −5.95741 | − | 8.19967i | −0.560426 | − | 0.771360i | 0.430955 | − | 0.902374i | \(-0.358177\pi\) |
−0.991381 | + | 0.131014i | \(0.958177\pi\) | |||||||
\(114\) | 9.01977 | + | 6.55325i | 0.844779 | + | 0.613768i | ||||
\(115\) | 2.44387 | − | 9.43767i | 0.227892 | − | 0.880067i | ||||
\(116\) | −2.69150 | − | 8.28359i | −0.249900 | − | 0.769112i | ||||
\(117\) | 2.09570 | − | 2.88448i | 0.193747 | − | 0.266670i | ||||
\(118\) | 4.41865 | + | 6.08175i | 0.406770 | + | 0.559870i | ||||
\(119\) | −1.17937 | + | 3.62972i | −0.108112 | + | 0.332736i | ||||
\(120\) | −0.650203 | + | 1.01992i | −0.0593552 | + | 0.0931052i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 15.7515i | 1.42607i | ||||||||
\(123\) | −9.16232 | − | 2.97702i | −0.826138 | − | 0.268429i | ||||
\(124\) | 13.3686 | − | 9.71282i | 1.20053 | − | 0.872237i | ||||
\(125\) | 8.10277 | + | 7.70358i | 0.724733 | + | 0.689029i | ||||
\(126\) | 11.0318 | + | 33.9523i | 0.982787 | + | 3.02471i | ||||
\(127\) | 15.6382 | − | 5.08117i | 1.38767 | − | 0.450881i | 0.482486 | − | 0.875904i | \(-0.339734\pi\) |
0.905183 | + | 0.425023i | \(0.139734\pi\) | |||||||
\(128\) | −0.871737 | + | 1.19984i | −0.0770514 | + | 0.106052i | ||||
\(129\) | −25.7770 | + | 18.7281i | −2.26954 | + | 1.64892i | ||||
\(130\) | 1.86580 | + | 2.26483i | 0.163642 | + | 0.198639i | ||||
\(131\) | −14.0007 | −1.22325 | −0.611625 | − | 0.791148i | \(-0.709484\pi\) | ||||
−0.611625 | + | 0.791148i | \(0.709484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07239i | 0.526543i | ||||||||
\(134\) | −1.48765 | + | 4.57851i | −0.128513 | + | 0.395523i | ||||
\(135\) | 16.2365 | − | 0.988011i | 1.39742 | − | 0.0850345i | ||||
\(136\) | −0.178435 | − | 0.129641i | −0.0153007 | − | 0.0111166i | ||||
\(137\) | 13.0975 | − | 4.25564i | 1.11900 | − | 0.363584i | 0.309611 | − | 0.950863i | \(-0.399801\pi\) |
0.809384 | + | 0.587280i | \(0.199801\pi\) | |||||||
\(138\) | 24.4476 | − | 7.94349i | 2.08111 | − | 0.676195i | ||||
\(139\) | −5.46468 | − | 3.97032i | −0.463508 | − | 0.336758i | 0.331398 | − | 0.943491i | \(-0.392480\pi\) |
−0.794906 | + | 0.606733i | \(0.792480\pi\) | |||||||
\(140\) | −14.9923 | + | 0.912301i | −1.26708 | + | 0.0771035i | ||||
\(141\) | −2.62534 | + | 8.07998i | −0.221094 | + | 0.680457i | ||||
\(142\) | − | 31.7911i | − | 2.66785i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 20.9285 | 1.74404 | ||||||||
\(145\) | −5.92019 | − | 7.18631i | −0.491645 | − | 0.596790i | ||||
\(146\) | −9.35133 | + | 6.79414i | −0.773922 | + | 0.562287i | ||||
\(147\) | −5.67480 | + | 7.81069i | −0.468050 | + | 0.644215i | ||||
\(148\) | −4.09510 | + | 1.33058i | −0.336615 | + | 0.109373i | ||||
\(149\) | −5.93216 | − | 18.2573i | −0.485982 | − | 1.49570i | −0.830554 | − | 0.556938i | \(-0.811976\pi\) |
0.344572 | − | 0.938760i | \(-0.388024\pi\) | |||||||
\(150\) | −5.64299 | + | 28.9348i | −0.460748 | + | 2.36252i | ||||
\(151\) | −2.66216 | + | 1.93418i | −0.216644 | + | 0.157401i | −0.690815 | − | 0.723032i | \(-0.742748\pi\) |
0.474171 | + | 0.880433i | \(0.342748\pi\) | |||||||
\(152\) | −0.333751 | − | 0.108442i | −0.0270708 | − | 0.00879582i | ||||
\(153\) | 6.53159i | 0.528048i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.49579 | − | 14.8952i | 0.762720 | − | 1.19641i | ||||
\(156\) | −1.22229 | + | 3.76181i | −0.0978612 | + | 0.301186i | ||||
\(157\) | −8.23746 | − | 11.3379i | −0.657421 | − | 0.904863i | 0.341971 | − | 0.939710i | \(-0.388905\pi\) |
−0.999393 | + | 0.0348477i | \(0.988905\pi\) | |||||||
\(158\) | −18.1391 | + | 24.9663i | −1.44307 | + | 1.98621i | ||||
\(159\) | −5.78107 | − | 17.7923i | −0.458469 | − | 1.41102i | ||||
\(160\) | −4.52590 | + | 17.4780i | −0.357804 | + | 1.38176i | ||||
\(161\) | 11.3268 | + | 8.22942i | 0.892679 | + | 0.648570i | ||||
\(162\) | 5.60762 | + | 7.71823i | 0.440577 | + | 0.606402i | ||||
\(163\) | −9.81676 | − | 3.18966i | −0.768908 | − | 0.249833i | −0.101811 | − | 0.994804i | \(-0.532464\pi\) |
−0.667097 | + | 0.744970i | \(0.732464\pi\) | |||||||
\(164\) | 6.91362 | 0.539863 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.5160 | 1.66997 | ||||||||
\(167\) | 13.8909 | + | 4.51344i | 1.07491 | + | 0.349260i | 0.792399 | − | 0.610003i | \(-0.208832\pi\) |
0.282513 | + | 0.959263i | \(0.408832\pi\) | |||||||
\(168\) | −1.02102 | − | 1.40531i | −0.0787731 | − | 0.108422i | ||||
\(169\) | −10.1767 | − | 7.39382i | −0.782825 | − | 0.568755i | ||||
\(170\) | −5.20397 | − | 1.34756i | −0.399126 | − | 0.103353i | ||||
\(171\) | 3.21140 | + | 9.88367i | 0.245582 | + | 0.755823i | ||||
\(172\) | 13.4400 | − | 18.4986i | 1.02479 | − | 1.41051i | ||||
\(173\) | 1.29806 | + | 1.78662i | 0.0986895 | + | 0.135834i | 0.855506 | − | 0.517793i | \(-0.173246\pi\) |
−0.756816 | + | 0.653628i | \(0.773246\pi\) | |||||||
\(174\) | 7.58651 | − | 23.3489i | 0.575132 | − | 1.77007i | ||||
\(175\) | −14.5562 | + | 6.77669i | −1.10035 | + | 0.512270i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.8322i | 0.814201i | ||||||||
\(178\) | 17.3142 | + | 5.62573i | 1.29776 | + | 0.421667i | ||||
\(179\) | 8.74393 | − | 6.35284i | 0.653552 | − | 0.474833i | −0.210927 | − | 0.977502i | \(-0.567648\pi\) |
0.864479 | + | 0.502668i | \(0.167648\pi\) | |||||||
\(180\) | −23.9197 | + | 9.41363i | −1.78287 | + | 0.701651i | ||||
\(181\) | −1.04045 | − | 3.20219i | −0.0773363 | − | 0.238017i | 0.904913 | − | 0.425596i | \(-0.139936\pi\) |
−0.982249 | + | 0.187580i | \(0.939936\pi\) | |||||||
\(182\) | −4.00791 | + | 1.30225i | −0.297086 | + | 0.0965291i | ||||
\(183\) | −13.3410 | + | 18.3623i | −0.986193 | + | 1.35738i | ||||
\(184\) | −0.654583 | + | 0.475582i | −0.0482565 | + | 0.0350604i | ||||
\(185\) | −3.55264 | + | 2.92672i | −0.261195 | + | 0.215177i | ||||
\(186\) | 46.5773 | 3.41521 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 6.09692i | − | 0.444664i | ||||||
\(189\) | −7.21889 | + | 22.2175i | −0.525097 | + | 1.61608i | ||||
\(190\) | −8.53726 | + | 0.519502i | −0.619358 | + | 0.0376887i | ||||
\(191\) | −7.50382 | − | 5.45185i | −0.542957 | − | 0.394482i | 0.282225 | − | 0.959348i | \(-0.408928\pi\) |
−0.825182 | + | 0.564867i | \(0.808928\pi\) | |||||||
\(192\) | −24.1626 | + | 7.85089i | −1.74378 | + | 0.566589i | ||||
\(193\) | −4.62491 | + | 1.50273i | −0.332908 | + | 0.108169i | −0.470702 | − | 0.882293i | \(-0.655999\pi\) |
0.137793 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(194\) | −24.7732 | − | 17.9988i | −1.77862 | − | 1.29224i | ||||
\(195\) | 0.256823 | + | 4.22050i | 0.0183914 | + | 0.302236i | ||||
\(196\) | 2.14102 | − | 6.58939i | 0.152930 | − | 0.470670i | ||||
\(197\) | 11.8747i | 0.846038i | 0.906121 | + | 0.423019i | \(0.139030\pi\) | ||||
−0.906121 | + | 0.423019i | \(0.860970\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.99158 | 0.353844 | 0.176922 | − | 0.984225i | \(-0.443386\pi\) | ||||
0.176922 | + | 0.984225i | \(0.443386\pi\) | |||||||
\(200\) | −0.112512 | − | 0.921060i | −0.00795579 | − | 0.0651288i | ||||
\(201\) | −5.61208 | + | 4.07741i | −0.395845 | + | 0.287598i | ||||
\(202\) | 6.63231 | − | 9.12859i | 0.466648 | − | 0.642285i | ||||
\(203\) | 12.7171 | − | 4.13203i | 0.892565 | − | 0.290012i | ||||
\(204\) | −2.23914 | − | 6.89137i | −0.156771 | − | 0.482492i | ||||
\(205\) | 6.87722 | − | 2.70655i | 0.480326 | − | 0.189033i | ||||
\(206\) | −5.20757 | + | 3.78352i | −0.362828 | + | 0.263610i | ||||
\(207\) | 22.7882 | + | 7.40433i | 1.58389 | + | 0.514636i | ||||
\(208\) | 2.47051i | 0.171299i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −35.6995 | − | 22.7587i | −2.46350 | − | 1.57050i | ||||
\(211\) | −0.486128 | + | 1.49615i | −0.0334665 | + | 0.102999i | −0.966394 | − | 0.257064i | \(-0.917245\pi\) |
0.932928 | + | 0.360063i | \(0.117245\pi\) | |||||||
\(212\) | 7.89135 | + | 10.8615i | 0.541980 | + | 0.745971i | ||||
\(213\) | 26.9260 | − | 37.0605i | 1.84494 | − | 2.53934i | ||||
\(214\) | 2.48099 | + | 7.63570i | 0.169597 | + | 0.521966i | ||||
\(215\) | 6.12743 | − | 23.6627i | 0.417888 | − | 1.61379i | ||||
\(216\) | −1.09220 | − | 0.793530i | −0.0743148 | − | 0.0539928i | ||||
\(217\) | 14.9113 | + | 20.5236i | 1.01224 | + | 1.39323i | ||||
\(218\) | −29.6554 | − | 9.63561i | −2.00852 | − | 0.652606i | ||||
\(219\) | −16.6557 | −1.12549 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.771025 | −0.0518647 | ||||||||
\(222\) | −11.5428 | − | 3.75049i | −0.774703 | − | 0.251716i | ||||
\(223\) | −1.94836 | − | 2.68169i | −0.130472 | − | 0.179579i | 0.738783 | − | 0.673943i | \(-0.235401\pi\) |
−0.869255 | + | 0.494364i | \(0.835401\pi\) | |||||||
\(224\) | −20.9766 | − | 15.2404i | −1.40156 | − | 1.01829i | ||||
\(225\) | −20.1085 | + | 18.7281i | −1.34056 | + | 1.24854i | ||||
\(226\) | 6.33542 | + | 19.4984i | 0.421426 | + | 1.29702i | ||||
\(227\) | 1.66938 | − | 2.29770i | 0.110800 | − | 0.152504i | −0.750015 | − | 0.661421i | \(-0.769954\pi\) |
0.860816 | + | 0.508917i | \(0.169954\pi\) | |||||||
\(228\) | −6.77658 | − | 9.32717i | −0.448790 | − | 0.617707i | ||||
\(229\) | 0.615433 | − | 1.89411i | 0.0406690 | − | 0.125166i | −0.928661 | − | 0.370930i | \(-0.879039\pi\) |
0.969330 | + | 0.245764i | \(0.0790389\pi\) | |||||||
\(230\) | −10.6008 | + | 16.6286i | −0.698999 | + | 1.09646i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.772748i | 0.0507334i | ||||||||
\(233\) | 19.2623 | + | 6.25868i | 1.26191 | + | 0.410020i | 0.862175 | − | 0.506610i | \(-0.169102\pi\) |
0.399737 | + | 0.916630i | \(0.369102\pi\) | |||||||
\(234\) | −5.83474 | + | 4.23919i | −0.381429 | + | 0.277125i | ||||
\(235\) | −2.38682 | − | 6.06482i | −0.155699 | − | 0.395625i | ||||
\(236\) | −2.40219 | − | 7.39318i | −0.156369 | − | 0.481255i | ||||
\(237\) | −42.2913 | + | 13.7413i | −2.74711 | + | 0.892591i | ||||
\(238\) | 4.53774 | − | 6.24566i | 0.294138 | − | 0.404846i | ||||
\(239\) | 1.52982 | − | 1.11148i | 0.0989556 | − | 0.0718954i | −0.537207 | − | 0.843450i | \(-0.680521\pi\) |
0.636163 | + | 0.771555i | \(0.280521\pi\) | |||||||
\(240\) | −19.1563 | + | 15.7813i | −1.23653 | + | 1.01868i | ||||
\(241\) | 4.00503 | 0.257986 | 0.128993 | − | 0.991645i | \(-0.458825\pi\) | ||||
0.128993 | + | 0.991645i | \(0.458825\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 8.07686i | − | 0.518131i | ||||||
\(244\) | 5.03336 | − | 15.4911i | 0.322228 | − | 0.991715i | ||||
\(245\) | −0.449864 | − | 7.39286i | −0.0287408 | − | 0.472312i | ||||
\(246\) | 15.7656 | + | 11.4544i | 1.00518 | + | 0.730305i | ||||
\(247\) | −1.16672 | + | 0.379091i | −0.0742368 | + | 0.0241210i | ||||
\(248\) | −1.39431 | + | 0.453038i | −0.0885386 | + | 0.0287680i | ||||
\(249\) | 25.0823 | + | 18.2234i | 1.58953 | + | 1.15486i | ||||
\(250\) | −10.7728 | − | 19.8851i | −0.681329 | − | 1.25764i | ||||
\(251\) | 7.01714 | − | 21.5965i | 0.442918 | − | 1.36316i | −0.441833 | − | 0.897097i | \(-0.645672\pi\) |
0.884751 | − | 0.466064i | \(-0.154328\pi\) | |||||||
\(252\) | − | 36.9162i | − | 2.32550i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −33.2610 | −2.08698 | ||||||||
\(255\) | −4.92519 | − | 5.97851i | −0.308427 | − | 0.374389i | ||||
\(256\) | −11.6763 | + | 8.48333i | −0.729769 | + | 0.530208i | ||||
\(257\) | 2.38815 | − | 3.28701i | 0.148969 | − | 0.205038i | −0.728011 | − | 0.685566i | \(-0.759555\pi\) |
0.876979 | + | 0.480528i | \(0.159555\pi\) | |||||||
\(258\) | 61.2965 | − | 19.9164i | 3.81616 | − | 1.23994i | ||||
\(259\) | −2.04272 | − | 6.28686i | −0.126929 | − | 0.390646i | ||||
\(260\) | −1.11124 | − | 2.82361i | −0.0689160 | − | 0.175113i | ||||
\(261\) | 18.5136 | − | 13.4509i | 1.14596 | − | 0.832592i | ||||
\(262\) | 26.9347 | + | 8.75160i | 1.66403 | + | 0.540676i | ||||
\(263\) | − | 12.3054i | − | 0.758783i | −0.925236 | − | 0.379391i | \(-0.876133\pi\) | ||
0.925236 | − | 0.379391i | \(-0.123867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1019 | + | 7.71502i | 0.743411 | + | 0.473930i | ||||
\(266\) | 3.79574 | − | 11.6821i | 0.232732 | − | 0.716274i | ||||
\(267\) | 15.4192 | + | 21.2228i | 0.943642 | + | 1.29881i | ||||
\(268\) | 2.92611 | − | 4.02745i | 0.178741 | − | 0.246016i | ||||
\(269\) | 2.38188 | + | 7.33068i | 0.145226 | + | 0.446959i | 0.997040 | − | 0.0768848i | \(-0.0244974\pi\) |
−0.851814 | + | 0.523844i | \(0.824497\pi\) | |||||||
\(270\) | −31.8534 | − | 8.24840i | −1.93854 | − | 0.501982i | ||||
\(271\) | −12.5995 | − | 9.15410i | −0.765367 | − | 0.556072i | 0.135185 | − | 0.990820i | \(-0.456837\pi\) |
−0.900552 | + | 0.434749i | \(0.856837\pi\) | |||||||
\(272\) | −2.66020 | − | 3.66146i | −0.161299 | − | 0.222008i | ||||
\(273\) | −5.77518 | − | 1.87647i | −0.349530 | − | 0.113569i | ||||
\(274\) | −27.8571 | −1.68291 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −26.5817 | −1.60003 | ||||||||
\(277\) | −19.3093 | − | 6.27399i | −1.16019 | − | 0.376967i | −0.335215 | − | 0.942142i | \(-0.608809\pi\) |
−0.824971 | + | 0.565175i | \(0.808809\pi\) | |||||||
\(278\) | 8.03120 | + | 11.0540i | 0.481679 | + | 0.662974i | ||||
\(279\) | 35.1242 | + | 25.5192i | 2.10283 | + | 1.52779i | ||||
\(280\) | 1.29004 | + | 0.334055i | 0.0770947 | + | 0.0199636i | ||||
\(281\) | 7.48425 | + | 23.0342i | 0.446473 | + | 1.37410i | 0.880860 | + | 0.473377i | \(0.156965\pi\) |
−0.434387 | + | 0.900726i | \(0.643035\pi\) | |||||||
\(282\) | 10.1013 | − | 13.9032i | 0.601523 | − | 0.827925i | ||||
\(283\) | 8.48599 | + | 11.6800i | 0.504440 | + | 0.694302i | 0.982969 | − | 0.183770i | \(-0.0588300\pi\) |
−0.478529 | + | 0.878072i | \(0.658830\pi\) | |||||||
\(284\) | −10.1588 | + | 31.2656i | −0.602814 | + | 1.85527i | ||||
\(285\) | −10.3923 | − | 6.62516i | −0.615587 | − | 0.392441i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6139i | 0.626519i | ||||||||
\(288\) | −42.2023 | − | 13.7124i | −2.48679 | − | 0.808008i | ||||
\(289\) | −12.6106 | + | 9.16212i | −0.741799 | + | 0.538948i | ||||
\(290\) | 6.89725 | + | 17.5256i | 0.405021 | + | 1.02914i | ||||
\(291\) | −13.6350 | − | 41.9642i | −0.799298 | − | 2.45999i | ||||
\(292\) | 11.3678 | − | 3.69362i | 0.665250 | − | 0.216153i | ||||
\(293\) | −8.91231 | + | 12.2667i | −0.520663 | + | 0.716631i | −0.985672 | − | 0.168675i | \(-0.946051\pi\) |
0.465009 | + | 0.885306i | \(0.346051\pi\) | |||||||
\(294\) | 15.7995 | − | 11.4790i | 0.921447 | − | 0.669470i | ||||
\(295\) | −5.28383 | − | 6.41385i | −0.307636 | − | 0.373429i | ||||
\(296\) | 0.382018 | 0.0222043 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 38.8316i | 2.24945i | ||||||||
\(299\) | −0.874048 | + | 2.69004i | −0.0505475 | + | 0.155569i | ||||
\(300\) | 14.7958 | − | 26.6533i | 0.854234 | − | 1.53883i | ||||
\(301\) | 28.3994 | + | 20.6334i | 1.63691 | + | 1.18929i | ||||
\(302\) | 6.33050 | − | 2.05690i | 0.364279 | − | 0.118361i | ||||
\(303\) | 15.4632 | − | 5.02431i | 0.888339 | − | 0.288639i | ||||
\(304\) | −5.82568 | − | 4.23261i | −0.334126 | − | 0.242757i | ||||
\(305\) | −1.05759 | − | 17.3800i | −0.0605576 | − | 0.995175i | ||||
\(306\) | 4.08278 | − | 12.5655i | 0.233397 | − | 0.718321i | ||||
\(307\) | 8.04171i | 0.458965i | 0.973313 | + | 0.229482i | \(0.0737033\pi\) | ||||
−0.973313 | + | 0.229482i | \(0.926297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.27523 | −0.527650 | ||||||||
\(310\) | −27.5787 | + | 22.7198i | −1.56637 | + | 1.29040i | ||||
\(311\) | −18.0142 | + | 13.0881i | −1.02149 | + | 0.742158i | −0.966588 | − | 0.256333i | \(-0.917486\pi\) |
−0.0549049 | + | 0.998492i | \(0.517486\pi\) | |||||||
\(312\) | 0.206269 | − | 0.283905i | 0.0116777 | − | 0.0160730i | ||||
\(313\) | −2.23540 | + | 0.726326i | −0.126352 | + | 0.0410543i | −0.371511 | − | 0.928429i | \(-0.621160\pi\) |
0.245158 | + | 0.969483i | \(0.421160\pi\) | |||||||
\(314\) | 8.76015 | + | 26.9610i | 0.494364 | + | 1.52150i | ||||
\(315\) | −14.4519 | − | 36.7218i | −0.814275 | − | 2.06904i | ||||
\(316\) | 25.8172 | − | 18.7573i | 1.45233 | − | 1.05518i | ||||
\(317\) | −17.1412 | − | 5.56952i | −0.962747 | − | 0.312815i | −0.214863 | − | 0.976644i | \(-0.568930\pi\) |
−0.747885 | + | 0.663829i | \(0.768930\pi\) | |||||||
\(318\) | 37.8425i | 2.12210i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 10.4773 | − | 16.4347i | 0.585696 | − | 0.918730i | ||||
\(321\) | −3.57497 | + | 11.0026i | −0.199535 | + | 0.614107i | ||||
\(322\) | −16.6465 | − | 22.9120i | −0.927675 | − | 1.27683i | ||||
\(323\) | 1.32096 | − | 1.81814i | 0.0735001 | − | 0.101164i | ||||
\(324\) | −3.04858 | − | 9.38255i | −0.169365 | − | 0.521253i | ||||
\(325\) | −2.21077 | − | 2.37371i | −0.122632 | − | 0.131670i | ||||
\(326\) | 16.8917 | + | 12.2726i | 0.935546 | + | 0.679714i | ||||
\(327\) | −26.4097 | − | 36.3498i | −1.46046 | − | 2.01015i | ||||
\(328\) | −0.583361 | − | 0.189546i | −0.0322107 | − | 0.0104659i | ||||
\(329\) | 9.36008 | 0.516038 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.09174 | −0.169938 | −0.0849688 | − | 0.996384i | \(-0.527079\pi\) | ||||
−0.0849688 | + | 0.996384i | \(0.527079\pi\) | |||||||
\(332\) | −21.1603 | − | 6.87541i | −1.16132 | − | 0.377337i | ||||
\(333\) | −6.64964 | − | 9.15245i | −0.364398 | − | 0.501551i | ||||
\(334\) | −23.9021 | − | 17.3659i | −1.30787 | − | 0.950221i | ||||
\(335\) | 1.33404 | − | 5.15176i | 0.0728865 | − | 0.281471i | ||||
\(336\) | −11.0146 | − | 33.8995i | −0.600897 | − | 1.84937i | ||||
\(337\) | 21.1284 | − | 29.0807i | 1.15094 | − | 1.58413i | 0.410719 | − | 0.911762i | \(-0.365278\pi\) |
0.740218 | − | 0.672367i | \(-0.234722\pi\) | |||||||
\(338\) | 14.9563 | + | 20.5855i | 0.813514 | + | 1.11971i | ||||
\(339\) | −9.12900 | + | 28.0962i | −0.495819 | + | 1.52597i | ||||
\(340\) | 4.68733 | + | 2.98820i | 0.254206 | + | 0.162058i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 21.0216i | − | 1.13672i | ||||||
\(343\) | −11.2626 | − | 3.65945i | −0.608124 | − | 0.197592i | ||||
\(344\) | −1.64121 | + | 1.19241i | −0.0884883 | + | 0.0642905i | ||||
\(345\) | −26.4418 | + | 10.4062i | −1.42358 | + | 0.560252i | ||||
\(346\) | −1.38042 | − | 4.24850i | −0.0742119 | − | 0.228401i | ||||
\(347\) | −11.6627 | + | 3.78944i | −0.626087 | + | 0.203428i | −0.604841 | − | 0.796346i | \(-0.706763\pi\) |
−0.0212460 | + | 0.999774i | \(0.506763\pi\) | |||||||
\(348\) | −14.9222 | + | 20.5386i | −0.799914 | + | 1.10099i | ||||
\(349\) | 14.2981 | − | 10.3881i | 0.765357 | − | 0.556065i | −0.135192 | − | 0.990819i | \(-0.543165\pi\) |
0.900549 | + | 0.434755i | \(0.143165\pi\) | |||||||
\(350\) | 32.2393 | − | 3.93819i | 1.72326 | − | 0.210505i | ||||
\(351\) | −4.71943 | −0.251905 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.7202i | − | 0.996378i | −0.867068 | − | 0.498189i | \(-0.833999\pi\) | ||
0.867068 | − | 0.498189i | \(-0.166001\pi\) | |||||||
\(354\) | 6.77104 | − | 20.8391i | 0.359876 | − | 1.10759i | ||||
\(355\) | 2.13454 | + | 35.0779i | 0.113289 | + | 1.86174i | ||||
\(356\) | −15.2303 | − | 11.0655i | −0.807205 | − | 0.586469i | ||||
\(357\) | 10.5797 | − | 3.43756i | 0.559939 | − | 0.181935i | ||||
\(358\) | −20.7926 | + | 6.75594i | −1.09893 | + | 0.357062i | ||||
\(359\) | 30.1495 | + | 21.9049i | 1.59123 | + | 1.15610i | 0.902159 | + | 0.431403i | \(0.141981\pi\) |
0.689071 | + | 0.724694i | \(0.258019\pi\) | |||||||
\(360\) | 2.27639 | − | 0.138521i | 0.119976 | − | 0.00730071i | ||||
\(361\) | −4.76637 | + | 14.6694i | −0.250861 | + | 0.772072i | ||||
\(362\) | 6.81074i | 0.357965i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.35779 | 0.228410 | ||||||||
\(365\) | 9.86197 | − | 8.12444i | 0.516199 | − | 0.425253i | ||||
\(366\) | 37.1433 | − | 26.9862i | 1.94151 | − | 1.41059i | ||||
\(367\) | −10.5794 | + | 14.5613i | −0.552242 | + | 0.760096i | −0.990314 | − | 0.138844i | \(-0.955661\pi\) |
0.438072 | + | 0.898940i | \(0.355661\pi\) | |||||||
\(368\) | −15.7902 | + | 5.13054i | −0.823120 | + | 0.267448i | ||||
\(369\) | 5.61319 | + | 17.2756i | 0.292211 | + | 0.899333i | ||||
\(370\) | 8.66402 | − | 3.40974i | 0.450421 | − | 0.177264i | ||||
\(371\) | −16.6748 | + | 12.1149i | −0.865710 | + | 0.628975i | ||||
\(372\) | −45.8073 | − | 14.8837i | −2.37500 | − | 0.771684i | ||||
\(373\) | − | 0.202607i | − | 0.0104906i | −0.999986 | − | 0.00524531i | \(-0.998330\pi\) | ||
0.999986 | − | 0.00524531i | \(-0.00166964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.28365 | − | 32.3052i | 0.221207 | − | 1.66823i | ||||
\(376\) | −0.167155 | + | 0.514449i | −0.00862034 | + | 0.0265307i | ||||
\(377\) | 1.58782 | + | 2.18545i | 0.0817770 | + | 0.112556i | ||||
\(378\) | 27.7754 | − | 38.2296i | 1.42861 | − | 1.96632i | ||||
\(379\) | 10.5014 | + | 32.3199i | 0.539419 | + | 1.66016i | 0.733901 | + | 0.679256i | \(0.237697\pi\) |
−0.194482 | + | 0.980906i | \(0.562303\pi\) | |||||||
\(380\) | 8.56213 | + | 2.21715i | 0.439228 | + | 0.113738i | ||||
\(381\) | −38.7740 | − | 28.1710i | −1.98645 | − | 1.44324i | ||||
\(382\) | 11.0280 | + | 15.1788i | 0.564243 | + | 0.776614i | ||||
\(383\) | −6.79248 | − | 2.20701i | −0.347080 | − | 0.112773i | 0.130289 | − | 0.991476i | \(-0.458409\pi\) |
−0.477369 | + | 0.878703i | \(0.658409\pi\) | |||||||
\(384\) | 4.32284 | 0.220599 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.83675 | 0.500677 | ||||||||
\(387\) | 57.1360 | + | 18.5646i | 2.90439 | + | 0.943692i | ||||
\(388\) | 18.6122 | + | 25.6175i | 0.944893 | + | 1.30053i | ||||
\(389\) | 10.7331 | + | 7.79804i | 0.544189 | + | 0.395376i | 0.825638 | − | 0.564200i | \(-0.190815\pi\) |
−0.281450 | + | 0.959576i | \(0.590815\pi\) | |||||||
\(390\) | 2.14408 | − | 8.27995i | 0.108570 | − | 0.419271i | ||||
\(391\) | −1.60119 | − | 4.92797i | −0.0809759 | − | 0.249218i | ||||
\(392\) | −0.361312 | + | 0.497304i | −0.0182490 | + | 0.0251176i | ||||
\(393\) | 23.9867 | + | 33.0149i | 1.20997 | + | 1.66538i | ||||
\(394\) | 7.42266 | − | 22.8446i | 0.373948 | − | 1.15089i | ||||
\(395\) | 18.3382 | − | 28.7654i | 0.922692 | − | 1.44735i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 33.5614i | − | 1.68440i | −0.539165 | − | 0.842200i | \(-0.681260\pi\) | ||
0.539165 | − | 0.842200i | \(-0.318740\pi\) | |||||||
\(398\) | −9.60282 | − | 3.12015i | −0.481346 | − | 0.156399i | ||||
\(399\) | 14.3192 | − | 10.4035i | 0.716857 | − | 0.520827i | ||||
\(400\) | 3.64469 | − | 18.6884i | 0.182235 | − | 0.934419i | ||||
\(401\) | 10.3802 | + | 31.9469i | 0.518361 | + | 1.59535i | 0.777082 | + | 0.629399i | \(0.216699\pi\) |
−0.258721 | + | 0.965952i | \(0.583301\pi\) | |||||||
\(402\) | 13.3452 | − | 4.33613i | 0.665600 | − | 0.216267i | ||||
\(403\) | −3.01243 | + | 4.14625i | −0.150060 | + | 0.206539i | ||||
\(404\) | −9.43970 | + | 6.85834i | −0.469642 | + | 0.341215i | ||||
\(405\) | −6.70561 | − | 8.13969i | −0.333204 | − | 0.404465i | ||||
\(406\) | −27.0480 | −1.34237 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.642872i | 0.0318269i | ||||||||
\(409\) | −2.52435 | + | 7.76914i | −0.124821 | + | 0.384159i | −0.993868 | − | 0.110569i | \(-0.964733\pi\) |
0.869048 | + | 0.494729i | \(0.164733\pi\) | |||||||
\(410\) | −14.9222 | + | 0.908036i | −0.736957 | + | 0.0448447i | ||||
\(411\) | −32.4745 | − | 23.5941i | −1.60185 | − | 1.16381i | ||||
\(412\) | 6.33050 | − | 2.05690i | 0.311881 | − | 0.101336i | ||||
\(413\) | 11.3501 | − | 3.68788i | 0.558503 | − | 0.181469i | ||||
\(414\) | −39.2117 | − | 28.4889i | −1.92715 | − | 1.40015i | ||||
\(415\) | −23.7405 | + | 1.44464i | −1.16538 | + | 0.0709146i | ||||
\(416\) | 1.61868 | − | 4.98179i | 0.0793624 | − | 0.244252i | ||||
\(417\) | 19.6883i | 0.964142i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.5329 | −0.954243 | −0.477121 | − | 0.878837i | \(-0.658320\pi\) | ||||
−0.477121 | + | 0.878837i | \(0.658320\pi\) | |||||||
\(420\) | 27.8369 | + | 33.7902i | 1.35830 | + | 1.64879i | ||||
\(421\) | 19.3422 | − | 14.0529i | 0.942680 | − | 0.684897i | −0.00638396 | − | 0.999980i | \(-0.502032\pi\) |
0.949064 | + | 0.315082i | \(0.102032\pi\) | |||||||
\(422\) | 1.87043 | − | 2.57443i | 0.0910511 | − | 0.125321i | ||||
\(423\) | 15.2349 | − | 4.95011i | 0.740744 | − | 0.240682i | ||||
\(424\) | −0.368078 | − | 1.13283i | −0.0178755 | − | 0.0550150i | ||||
\(425\) | 5.83247 | + | 1.13747i | 0.282917 | + | 0.0551756i | ||||
\(426\) | −74.9662 | + | 54.4661i | −3.63212 | + | 2.63889i | ||||
\(427\) | 23.7821 | + | 7.72729i | 1.15090 | + | 0.373950i | ||||
\(428\) | − | 8.30227i | − | 0.401306i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.5791 | + | 41.6923i | −1.28176 | + | 2.01058i | ||||
\(431\) | −2.33735 | + | 7.19363i | −0.112586 | + | 0.346505i | −0.991436 | − | 0.130594i | \(-0.958312\pi\) |
0.878850 | + | 0.477099i | \(0.158312\pi\) | |||||||
\(432\) | −16.2831 | − | 22.4117i | −0.783420 | − | 1.07829i | ||||
\(433\) | −15.0587 | + | 20.7265i | −0.723675 | + | 0.996054i | 0.275718 | + | 0.961238i | \(0.411084\pi\) |
−0.999394 | + | 0.0348152i | \(0.988916\pi\) | |||||||
\(434\) | −15.8574 | − | 48.8041i | −0.761181 | − | 2.34267i | ||||
\(435\) | −6.80316 | + | 26.2722i | −0.326187 | + | 1.25966i | ||||
\(436\) | 26.0861 | + | 18.9527i | 1.24930 | + | 0.907668i | ||||
\(437\) | −4.84589 | − | 6.66979i | −0.231810 | − | 0.319059i | ||||
\(438\) | 32.0423 | + | 10.4112i | 1.53104 | + | 0.497466i | ||||
\(439\) | 20.4668 | 0.976827 | 0.488413 | − | 0.872612i | \(-0.337576\pi\) | ||||
0.488413 | + | 0.872612i | \(0.337576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.2037 | 0.866844 | ||||||||
\(442\) | 1.48330 | + | 0.481953i | 0.0705534 | + | 0.0229242i | ||||
\(443\) | 5.97474 | + | 8.22353i | 0.283869 | + | 0.390712i | 0.927010 | − | 0.375035i | \(-0.122369\pi\) |
−0.643142 | + | 0.765747i | \(0.722369\pi\) | |||||||
\(444\) | 10.1535 | + | 7.37698i | 0.481866 | + | 0.350096i | ||||
\(445\) | −19.4820 | − | 5.04485i | −0.923537 | − | 0.239149i | ||||
\(446\) | 2.07199 | + | 6.37692i | 0.0981114 | + | 0.301956i | ||||
\(447\) | −32.8891 | + | 45.2679i | −1.55560 | + | 2.14110i | ||||
\(448\) | 16.4525 | + | 22.6449i | 0.777306 | + | 1.06987i | ||||
\(449\) | 4.54240 | − | 13.9801i | 0.214369 | − | 0.659760i | −0.784829 | − | 0.619713i | \(-0.787249\pi\) |
0.999198 | − | 0.0400475i | \(-0.0127509\pi\) | |||||||
\(450\) | 50.3913 | − | 23.4598i | 2.37547 | − | 1.10591i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 21.2006i | − | 0.997190i | ||||||
\(453\) | 9.12191 | + | 2.96389i | 0.428584 | + | 0.139256i | ||||
\(454\) | −4.64780 | + | 3.37683i | −0.218132 | + | 0.158482i | ||||
\(455\) | 4.33484 | − | 1.70599i | 0.203221 | − | 0.0799779i | ||||
\(456\) | 0.316082 | + | 0.972801i | 0.0148019 | + | 0.0455556i | ||||
\(457\) | −3.19822 | + | 1.03916i | −0.149606 | + | 0.0486101i | −0.382863 | − | 0.923805i | \(-0.625062\pi\) |
0.233256 | + | 0.972415i | \(0.425062\pi\) | |||||||
\(458\) | −2.36794 | + | 3.25919i | −0.110647 | + | 0.152292i | ||||
\(459\) | 6.99450 | − | 5.08180i | 0.326475 | − | 0.237198i | ||||
\(460\) | 15.7392 | − | 12.9662i | 0.733846 | − | 0.604553i | ||||
\(461\) | −1.41424 | −0.0658677 | −0.0329338 | − | 0.999458i | \(-0.510485\pi\) | ||||
−0.0329338 | + | 0.999458i | \(0.510485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4595i | 0.718465i | 0.933248 | + | 0.359232i | \(0.116961\pi\) | ||||
−0.933248 | + | 0.359232i | \(0.883039\pi\) | |||||||
\(464\) | −4.89997 | + | 15.0806i | −0.227475 | + | 0.700098i | ||||
\(465\) | −51.3928 | + | 3.12732i | −2.38329 | + | 0.145026i | ||||
\(466\) | −33.1446 | − | 24.0810i | −1.53539 | − | 1.11553i | ||||
\(467\) | −17.7760 | + | 5.77576i | −0.822574 | + | 0.267270i | −0.689914 | − | 0.723891i | \(-0.742352\pi\) |
−0.132660 | + | 0.991162i | \(0.542352\pi\) | |||||||
\(468\) | 7.09292 | − | 2.30463i | 0.327870 | − | 0.106531i | ||||
\(469\) | 6.18300 | + | 4.49221i | 0.285505 | + | 0.207431i | ||||
\(470\) | 0.800770 | + | 13.1595i | 0.0369368 | + | 0.607001i | ||||
\(471\) | −12.6229 | + | 38.8493i | −0.581633 | + | 1.79008i | ||||
\(472\) | 0.689685i | 0.0317453i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 89.9495 | 4.13152 | ||||||||
\(475\) | 9.38502 | − | 1.14643i | 0.430614 | − | 0.0526016i | ||||
\(476\) | −6.45852 | + | 4.69239i | −0.296026 | + | 0.215075i | ||||
\(477\) | −20.7335 | + | 28.5372i | −0.949322 | + | 1.30663i | ||||
\(478\) | −3.63783 | + | 1.18200i | −0.166390 | + | 0.0540635i | ||||
\(479\) | 9.23235 | + | 28.4142i | 0.421837 | + | 1.29828i | 0.905991 | + | 0.423297i | \(0.139127\pi\) |
−0.484154 | + | 0.874983i | \(0.660873\pi\) | |||||||
\(480\) | 48.9686 | − | 19.2717i | 2.23510 | − | 0.879628i | ||||
\(481\) | 1.08041 | − | 0.784960i | 0.0492622 | − | 0.0357911i | ||||
\(482\) | −7.70488 | − | 2.50347i | −0.350948 | − | 0.114030i | ||||
\(483\) | − | 40.8087i | − | 1.85686i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.5430 | + | 18.1963i | 1.29607 | + | 0.826253i | ||||
\(486\) | −5.04869 | + | 15.5383i | −0.229013 | + | 0.704831i | ||||
\(487\) | −0.549473 | − | 0.756284i | −0.0248990 | − | 0.0342705i | 0.796386 | − | 0.604789i | \(-0.206742\pi\) |
−0.821285 | + | 0.570518i | \(0.806742\pi\) | |||||||
\(488\) | −0.849414 | + | 1.16912i | −0.0384512 | + | 0.0529235i | ||||
\(489\) | 9.29707 | + | 28.6134i | 0.420428 | + | 1.29394i | ||||
\(490\) | −3.75569 | + | 14.5036i | −0.169665 | + | 0.655206i | ||||
\(491\) | 26.6121 | + | 19.3348i | 1.20099 | + | 0.872569i | 0.994382 | − | 0.105855i | \(-0.0337580\pi\) |
0.206607 | + | 0.978424i | \(0.433758\pi\) | |||||||
\(492\) | −11.8448 | − | 16.3029i | −0.534003 | − | 0.734992i | ||||
\(493\) | −4.70651 | − | 1.52924i | −0.211970 | − | 0.0688733i | ||||
\(494\) | 2.48151 | 0.111648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.0833 | −1.35078 | ||||||||
\(497\) | −47.9994 | − | 15.5960i | −2.15307 | − | 0.699574i | ||||
\(498\) | −36.8623 | − | 50.7366i | −1.65184 | − | 2.27356i | ||||
\(499\) | 7.27434 | + | 5.28512i | 0.325644 | + | 0.236594i | 0.738580 | − | 0.674166i | \(-0.235497\pi\) |
−0.412936 | + | 0.910760i | \(0.635497\pi\) | |||||||
\(500\) | 4.24043 | + | 22.9988i | 0.189638 | + | 1.02854i | ||||
\(501\) | −13.1556 | − | 40.4886i | −0.587747 | − | 1.80890i | ||||
\(502\) | −26.9992 | + | 37.1612i | −1.20503 | + | 1.65858i | ||||
\(503\) | −0.717663 | − | 0.987779i | −0.0319990 | − | 0.0440429i | 0.792718 | − | 0.609589i | \(-0.208665\pi\) |
−0.824717 | + | 0.565546i | \(0.808665\pi\) | |||||||
\(504\) | −1.01210 | + | 3.11493i | −0.0450826 | + | 0.138750i | ||||
\(505\) | −6.70509 | + | 10.5177i | −0.298373 | + | 0.468031i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 36.6650i | 1.62835i | ||||||||
\(508\) | 32.7112 | + | 10.6285i | 1.45132 | + | 0.471564i | ||||
\(509\) | 19.5744 | − | 14.2216i | 0.867621 | − | 0.630363i | −0.0623268 | − | 0.998056i | \(-0.519852\pi\) |
0.929947 | + | 0.367692i | \(0.119852\pi\) | |||||||
\(510\) | 5.73803 | + | 14.5801i | 0.254084 | + | 0.645618i | ||||
\(511\) | 5.67051 | + | 17.4520i | 0.250848 | + | 0.772032i | ||||
\(512\) | 30.5867 | − | 9.93821i | 1.35175 | − | 0.439211i | ||||
\(513\) | 8.08557 | − | 11.1288i | 0.356987 | − | 0.491350i | ||||
\(514\) | −6.64897 | + | 4.83076i | −0.293274 | + | 0.213076i | ||||
\(515\) | 5.49193 | − | 4.52434i | 0.242003 | − | 0.199366i | ||||
\(516\) | −66.6475 | −2.93399 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 13.3715i | 0.587512i | ||||||||
\(519\) | 1.98911 | − | 6.12186i | 0.0873124 | − | 0.268720i | ||||
\(520\) | 0.0163518 | + | 0.268718i | 0.000717074 | + | 0.0117841i | ||||
\(521\) | 3.92663 | + | 2.85286i | 0.172029 | + | 0.124986i | 0.670468 | − | 0.741938i | \(-0.266093\pi\) |
−0.498439 | + | 0.866925i | \(0.666093\pi\) | |||||||
\(522\) | −44.0245 | + | 14.3044i | −1.92690 | + | 0.626088i | ||||
\(523\) | −6.97451 | + | 2.26616i | −0.304974 | + | 0.0990921i | −0.457506 | − | 0.889206i | \(-0.651257\pi\) |
0.152532 | + | 0.988299i | \(0.451257\pi\) | |||||||
\(524\) | −23.6928 | − | 17.2139i | −1.03503 | − | 0.751991i | ||||
\(525\) | 40.9185 | + | 22.7147i | 1.78583 | + | 0.991350i | ||||
\(526\) | −7.69187 | + | 23.6731i | −0.335382 | + | 1.03220i | ||||
\(527\) | − | 9.38873i | − | 0.408980i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.99158 | 0.173547 | ||||||||
\(530\) | −18.4591 | − | 22.4068i | −0.801811 | − | 0.973290i | ||||
\(531\) | 16.5236 | − | 12.0051i | 0.717063 | − | 0.520977i | ||||
\(532\) | −7.46598 | + | 10.2760i | −0.323691 | + | 0.445523i | ||||
\(533\) | −2.03931 | + | 0.662612i | −0.0883323 | + | 0.0287009i | ||||
\(534\) | −16.3976 | − | 50.4667i | −0.709595 | − | 2.18391i | ||||
\(535\) | −3.25017 | − | 8.25856i | −0.140517 | − | 0.357049i | ||||
\(536\) | −0.357319 | + | 0.259607i | −0.0154338 | + | 0.0112133i | ||||
\(537\) | −29.9611 | − | 9.73494i | −1.29292 | − | 0.420094i | ||||
\(538\) | − | 15.5917i | − | 0.672204i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 28.6911 | + | 18.2908i | 1.23467 | + | 0.787109i | ||||
\(541\) | 8.67728 | − | 26.7059i | 0.373065 | − | 1.14818i | −0.571710 | − | 0.820456i | \(-0.693720\pi\) |
0.944775 | − | 0.327720i | \(-0.106280\pi\) | |||||||
\(542\) | 18.5170 | + | 25.4864i | 0.795372 | + | 1.09474i | ||||
\(543\) | −5.76847 | + | 7.93962i | −0.247549 | + | 0.340722i | ||||
\(544\) | 2.96531 | + | 9.12629i | 0.127137 | + | 0.391287i | ||||
\(545\) | 33.3683 | + | 8.64068i | 1.42934 | + | 0.370126i | ||||
\(546\) | 9.93737 | + | 7.21992i | 0.425280 | + | 0.308984i | ||||
\(547\) | 13.7323 | + | 18.9009i | 0.587151 | + | 0.808144i | 0.994457 | − | 0.105148i | \(-0.0335316\pi\) |
−0.407306 | + | 0.913292i | \(0.633532\pi\) | |||||||
\(548\) | 27.3966 | + | 8.90171i | 1.17033 | + | 0.380262i | ||||
\(549\) | 42.7954 | 1.82646 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.87382 | −0.335436 | ||||||||
\(552\) | 2.24293 | + | 0.728772i | 0.0954654 | + | 0.0310186i | ||||
\(553\) | 28.7965 | + | 39.6349i | 1.22455 | + | 1.68545i | ||||
\(554\) | 33.2256 | + | 24.1398i | 1.41162 | + | 1.02560i | ||||
\(555\) | 12.9880 | + | 3.36323i | 0.551311 | + | 0.142761i | ||||
\(556\) | −4.36615 | − | 13.4376i | −0.185166 | − | 0.569882i | ||||
\(557\) | −0.0200153 | + | 0.0275487i | −0.000848077 | + | 0.00116728i | −0.809441 | − | 0.587201i | \(-0.800230\pi\) |
0.808593 | + | 0.588369i | \(0.200230\pi\) | |||||||
\(558\) | −51.6204 | − | 71.0494i | −2.18527 | − | 3.00776i | ||||
\(559\) | −2.19147 | + | 6.74465i | −0.0926893 | + | 0.285268i | ||||
\(560\) | 23.0576 | + | 14.6994i | 0.974361 | + | 0.621161i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 48.9915i | − | 2.06658i | ||||||
\(563\) | 22.4995 | + | 7.31054i | 0.948242 | + | 0.308103i | 0.742001 | − | 0.670399i | \(-0.233877\pi\) |
0.206241 | + | 0.978501i | \(0.433877\pi\) | |||||||
\(564\) | −14.3771 | + | 10.4455i | −0.605383 | + | 0.439837i | ||||
\(565\) | −8.29960 | − | 21.0889i | −0.349167 | − | 0.887218i | ||||
\(566\) | −9.02445 | − | 27.7744i | −0.379326 | − | 1.16744i | ||||
\(567\) | 14.4042 | − | 4.68022i | 0.604921 | − | 0.196551i | ||||
\(568\) | 1.71437 | − | 2.35963i | 0.0719334 | − | 0.0990078i | ||||
\(569\) | 24.8653 | − | 18.0657i | 1.04241 | − | 0.757355i | 0.0716547 | − | 0.997429i | \(-0.477172\pi\) |
0.970754 | + | 0.240075i | \(0.0771720\pi\) | |||||||
\(570\) | 15.8515 | + | 19.2415i | 0.663945 | + | 0.805940i | ||||
\(571\) | −28.4768 | −1.19172 | −0.595860 | − | 0.803089i | \(-0.703188\pi\) | ||||
−0.595860 | + | 0.803089i | \(0.703188\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0350i | 1.12940i | ||||||||
\(574\) | 6.63455 | − | 20.4191i | 0.276921 | − | 0.852275i | ||||
\(575\) | 10.5803 | − | 19.0596i | 0.441231 | − | 0.794838i | ||||
\(576\) | 38.7545 | + | 28.1568i | 1.61477 | + | 1.17320i | ||||
\(577\) | 36.7234 | − | 11.9321i | 1.52881 | − | 0.496742i | 0.580550 | − | 0.814225i | \(-0.302838\pi\) |
0.948264 | + | 0.317483i | \(0.102838\pi\) | |||||||
\(578\) | 29.9873 | − | 9.74348i | 1.24731 | − | 0.405275i | ||||
\(579\) | 11.4672 | + | 8.33140i | 0.476560 | + | 0.346241i | ||||
\(580\) | −1.18294 | − | 19.4399i | −0.0491190 | − | 0.807199i | ||||
\(581\) | 10.5552 | − | 32.4857i | 0.437905 | − | 1.34773i | ||||
\(582\) | 89.2539i | 3.69969i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.06046 | −0.0438823 | ||||||||
\(585\) | 6.15336 | − | 5.06923i | 0.254410 | − | 0.209587i | ||||
\(586\) | 24.8132 | − | 18.0279i | 1.02503 | − | 0.744725i | ||||
\(587\) | 8.39465 | − | 11.5542i | 0.346484 | − | 0.476894i | −0.599837 | − | 0.800122i | \(-0.704768\pi\) |
0.946321 | + | 0.323228i | \(0.104768\pi\) | |||||||
\(588\) | −19.2064 | + | 6.24055i | −0.792060 | + | 0.257356i | ||||
\(589\) | −4.61617 | − | 14.2071i | −0.190206 | − | 0.585394i | ||||
\(590\) | 6.15586 | + | 15.6418i | 0.253433 | + | 0.643963i | ||||
\(591\) | 28.0016 | − | 20.3443i | 1.15183 | − | 0.836854i | ||||
\(592\) | 7.45527 | + | 2.42236i | 0.306410 | + | 0.0995585i | ||||
\(593\) | 36.4700i | 1.49764i | 0.662771 | + | 0.748822i | \(0.269380\pi\) | ||||
−0.662771 | + | 0.748822i | \(0.730620\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.58754 | + | 7.19606i | −0.188071 | + | 0.295010i | ||||
\(596\) | 12.4086 | − | 38.1897i | 0.508275 | − | 1.56431i | ||||
\(597\) | −8.55183 | − | 11.7706i | −0.350003 | − | 0.481738i | ||||
\(598\) | 3.36299 | − | 4.62876i | 0.137523 | − | 0.189284i | ||||
\(599\) | −9.37587 | − | 28.8560i | −0.383088 | − | 1.17902i | −0.937858 | − | 0.347019i | \(-0.887194\pi\) |
0.554770 | − | 0.832004i | \(-0.312806\pi\) | |||||||
\(600\) | −1.97918 | + | 1.84332i | −0.0807996 | + | 0.0752531i | ||||
\(601\) | −30.5989 | − | 22.2314i | −1.24816 | − | 0.906839i | −0.250043 | − | 0.968235i | \(-0.580445\pi\) |
−0.998113 | + | 0.0613962i | \(0.980445\pi\) | |||||||
\(602\) | −41.7373 | − | 57.4464i | −1.70108 | − | 2.34134i | ||||
\(603\) | 12.4394 | + | 4.04182i | 0.506573 | + | 0.164595i | ||||
\(604\) | −6.88313 | −0.280071 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −32.8888 | −1.33602 | ||||||||
\(607\) | 29.5616 | + | 9.60513i | 1.19987 | + | 0.389860i | 0.839712 | − | 0.543032i | \(-0.182724\pi\) |
0.360155 | + | 0.932893i | \(0.382724\pi\) | |||||||
\(608\) | 8.97428 | + | 12.3520i | 0.363955 | + | 0.500941i | ||||
\(609\) | −31.5312 | − | 22.9088i | −1.27771 | − | 0.928311i | ||||
\(610\) | −8.82930 | + | 34.0967i | −0.357488 | + | 1.38054i | ||||
\(611\) | 0.584338 | + | 1.79841i | 0.0236398 | + | 0.0727558i | ||||
\(612\) | −8.03057 | + | 11.0531i | −0.324616 | + | 0.446796i | ||||
\(613\) | −21.3175 | − | 29.3410i | −0.861004 | − | 1.18507i | −0.981329 | − | 0.192336i | \(-0.938394\pi\) |
0.120325 | − | 0.992735i | \(-0.461606\pi\) | |||||||
\(614\) | 5.02672 | − | 15.4707i | 0.202862 | − | 0.624345i | ||||
\(615\) | −18.1647 | − | 11.5801i | −0.732470 | − | 0.466954i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.28079i | − | 0.0515626i | −0.999668 | − | 0.0257813i | \(-0.991793\pi\) | ||
0.999668 | − | 0.0257813i | \(-0.00820735\pi\) | |||||||
\(618\) | 17.8437 | + | 5.79778i | 0.717780 | + | 0.233221i | ||||
\(619\) | 6.66694 | − | 4.84382i | 0.267967 | − | 0.194689i | −0.445685 | − | 0.895190i | \(-0.647040\pi\) |
0.713652 | + | 0.700500i | \(0.247040\pi\) | |||||||
\(620\) | 34.3829 | − | 13.5315i | 1.38085 | − | 0.543437i | ||||
\(621\) | −9.80089 | − | 30.1640i | −0.393296 | − | 1.21044i | ||||
\(622\) | 42.8370 | − | 13.9186i | 1.71761 | − | 0.558084i | ||||
\(623\) | 16.9879 | − | 23.3818i | 0.680605 | − | 0.936772i | ||||
\(624\) | 5.82568 | − | 4.23261i | 0.233214 | − | 0.169440i | ||||
\(625\) | 13.2217 | + | 21.2176i | 0.528866 | + | 0.848705i | ||||
\(626\) | 4.75448 | 0.190027 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 29.3146i | − | 1.16978i | ||||||
\(629\) | −0.755998 | + | 2.32672i | −0.0301436 | + | 0.0927725i | ||||
\(630\) | 4.84857 | + | 79.6792i | 0.193172 | + | 3.17449i | ||||
\(631\) | 10.0378 | + | 7.29291i | 0.399600 | + | 0.290326i | 0.769378 | − | 0.638794i | \(-0.220566\pi\) |
−0.369778 | + | 0.929120i | \(0.620566\pi\) | |||||||
\(632\) | −2.69267 | + | 0.874901i | −0.107109 | + | 0.0348017i | ||||
\(633\) | 4.36091 | − | 1.41694i | 0.173331 | − | 0.0563185i | ||||
\(634\) | 29.4949 | + | 21.4293i | 1.17139 | + | 0.851067i | ||||
\(635\) | 36.6998 | − | 2.23323i | 1.45639 | − | 0.0886229i | ||||
\(636\) | 12.0925 | − | 37.2169i | 0.479500 | − | 1.47575i | ||||
\(637\) | 2.14887i | 0.0851412i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −86.3738 | −3.41689 | ||||||||
\(640\) | −2.55958 | + | 2.10862i | −0.101176 | + | 0.0833507i | ||||
\(641\) | 4.39239 | − | 3.19126i | 0.173489 | − | 0.126047i | −0.497652 | − | 0.867377i | \(-0.665804\pi\) |
0.671141 | + | 0.741329i | \(0.265804\pi\) | |||||||
\(642\) | 13.7551 | − | 18.9322i | 0.542870 | − | 0.747196i | ||||
\(643\) | −1.98579 | + | 0.645222i | −0.0783119 | + | 0.0254451i | −0.347911 | − | 0.937528i | \(-0.613109\pi\) |
0.269599 | + | 0.962973i | \(0.413109\pi\) | |||||||
\(644\) | 9.04986 | + | 27.8526i | 0.356614 | + | 1.09755i | ||||
\(645\) | −66.2966 | + | 26.0912i | −2.61043 | + | 1.02734i | ||||
\(646\) | −3.67775 | + | 2.67204i | −0.144699 | + | 0.105130i | ||||
\(647\) | −23.5511 | − | 7.65223i | −0.925891 | − | 0.300840i | −0.193010 | − | 0.981197i | \(-0.561825\pi\) |
−0.732881 | + | 0.680357i | \(0.761825\pi\) | |||||||
\(648\) | 0.875266i | 0.0343837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.76932 | + | 5.94847i | 0.108622 | + | 0.233318i | ||||
\(651\) | 22.8497 | − | 70.3241i | 0.895550 | − | 2.75622i | ||||
\(652\) | −12.6908 | − | 17.4674i | −0.497010 | − | 0.684076i | ||||
\(653\) | −4.05522 | + | 5.58154i | −0.158693 | + | 0.218422i | −0.880958 | − | 0.473194i | \(-0.843101\pi\) |
0.722265 | + | 0.691616i | \(0.243101\pi\) | |||||||
\(654\) | 28.0854 | + | 86.4381i | 1.09823 | + | 3.38000i | ||||
\(655\) | −30.3070 | − | 7.84795i | −1.18419 | − | 0.306645i | ||||
\(656\) | −10.1827 | − | 7.39816i | −0.397567 | − | 0.288849i | ||||
\(657\) | 18.4591 | + | 25.4068i | 0.720158 | + | 0.991213i | ||||
\(658\) | −18.0070 | − | 5.85081i | −0.701984 | − | 0.228089i | ||||
\(659\) | 12.4567 | 0.485246 | 0.242623 | − | 0.970121i | \(-0.421992\pi\) | ||||
0.242623 | + | 0.970121i | \(0.421992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8173 | 0.693012 | 0.346506 | − | 0.938048i | \(-0.387368\pi\) | ||||
0.346506 | + | 0.938048i | \(0.387368\pi\) | |||||||
\(662\) | 5.94791 | + | 1.93259i | 0.231172 | + | 0.0751123i | ||||
\(663\) | 1.32096 | + | 1.81814i | 0.0513018 | + | 0.0706108i | ||||
\(664\) | 1.59698 | + | 1.16027i | 0.0619749 | + | 0.0450274i | ||||
\(665\) | −3.40381 | + | 13.1447i | −0.131994 | + | 0.509730i | ||||
\(666\) | 7.07158 | + | 21.7641i | 0.274018 | + | 0.843341i | ||||
\(667\) | −10.6708 | + | 14.6870i | −0.413173 | + | 0.568684i | ||||
\(668\) | 17.9578 | + | 24.7167i | 0.694807 | + | 0.956320i | ||||
\(669\) | −2.98562 | + | 9.18880i | −0.115431 | + | 0.355259i | ||||
\(670\) | −5.78670 | + | 9.07709i | −0.223560 | + | 0.350679i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 75.5752i | 2.91538i | ||||||||
\(673\) | −27.6539 | − | 8.98531i | −1.06598 | − | 0.346358i | −0.277060 | − | 0.960853i | \(-0.589360\pi\) |
−0.788921 | + | 0.614494i | \(0.789360\pi\) | |||||||
\(674\) | −58.8247 | + | 42.7386i | −2.26584 | + | 1.64623i | ||||
\(675\) | 35.7005 | + | 6.96247i | 1.37411 | + | 0.267985i | ||||
\(676\) | −8.13095 | − | 25.0245i | −0.312729 | − | 0.962480i | ||||
\(677\) | −38.8680 | + | 12.6290i | −1.49382 | + | 0.485371i | −0.938208 | − | 0.346072i | \(-0.887515\pi\) |
−0.555610 | + | 0.831443i | \(0.687515\pi\) | |||||||
\(678\) | 35.1248 | − | 48.3451i | 1.34896 | − | 1.85668i | ||||
\(679\) | −39.3284 | + | 28.5738i | −1.50929 | + | 1.09656i | ||||
\(680\) | −0.313585 | − | 0.380649i | −0.0120254 | − | 0.0145972i | ||||
\(681\) | −8.27824 | −0.317223 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2211i | 0.658948i | 0.944165 | + | 0.329474i | \(0.106871\pi\) | ||||
−0.944165 | + | 0.329474i | \(0.893129\pi\) | |||||||
\(684\) | −6.71743 | + | 20.6741i | −0.256847 | + | 0.790494i | ||||
\(685\) | 30.7372 | − | 1.87040i | 1.17441 | − | 0.0714642i | ||||
\(686\) | 19.3796 | + | 14.0801i | 0.739917 | + | 0.537581i | ||||
\(687\) | −5.52086 | + | 1.79384i | −0.210634 | + | 0.0684391i | ||||
\(688\) | −39.5902 | + | 12.8636i | −1.50936 | + | 0.490421i | ||||
\(689\) | −3.36869 | − | 2.44750i | −0.128337 | − | 0.0932422i | ||||
\(690\) | 57.3735 | − | 3.49125i | 2.18417 | − | 0.132910i | ||||
\(691\) | 6.22380 | − | 19.1549i | 0.236764 | − | 0.728686i | −0.760118 | − | 0.649785i | \(-0.774859\pi\) |
0.996882 | − | 0.0789009i | \(-0.0251411\pi\) | |||||||
\(692\) | 4.61938i | 0.175603i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.8055 | 0.941603 | ||||||||
\(695\) | −9.60372 | − | 11.6576i | −0.364290 | − | 0.442198i | ||||
\(696\) | 1.82221 | − | 1.32391i | 0.0690705 | − | 0.0501827i | ||||
\(697\) | 2.30890 | − | 3.17792i | 0.0874557 | − | 0.120372i | ||||
\(698\) | −34.0001 | + | 11.0473i | −1.28692 | + | 0.418146i | ||||
\(699\) | −18.2425 | − | 56.1447i | −0.689996 | − | 2.12359i | ||||
\(700\) | −32.9648 | − | 6.42894i | −1.24595 | − | 0.242991i | ||||
\(701\) | −17.1242 | + | 12.4414i | −0.646771 | + | 0.469906i | −0.862170 | − | 0.506620i | \(-0.830895\pi\) |
0.215399 | + | 0.976526i | \(0.430895\pi\) | |||||||
\(702\) | 9.07926 | + | 2.95003i | 0.342675 | + | 0.111342i | ||||
\(703\) | 3.89252i | 0.146809i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.2121 | + | 16.0189i | −0.384611 | + | 0.603306i | ||||
\(706\) | −11.7017 | + | 36.0141i | −0.440398 | + | 1.35541i | ||||
\(707\) | −10.5290 | − | 14.4920i | −0.395985 | − | 0.545026i | ||||
\(708\) | −13.3182 | + | 18.3309i | −0.500529 | + | 0.688919i | ||||
\(709\) | −6.35410 | − | 19.5559i | −0.238633 | − | 0.734437i | −0.996619 | − | 0.0821658i | \(-0.973816\pi\) |
0.757986 | − | 0.652271i | \(-0.226184\pi\) | |||||||
\(710\) | 17.8201 | − | 68.8173i | 0.668778 | − | 2.58267i | ||||
\(711\) | 67.8313 | + | 49.2824i | 2.54387 | + | 1.84823i | ||||
\(712\) | 0.981738 | + | 1.35125i | 0.0367922 | + | 0.0506401i | ||||
\(713\) | −32.7565 | − | 10.6432i | −1.22674 | − | 0.398592i | ||||
\(714\) | −22.5021 | −0.842119 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.6078 | 0.844892 | ||||||||
\(717\) | −5.24191 | − | 1.70320i | −0.195763 | − | 0.0636072i | ||||
\(718\) | −44.3094 | − | 60.9866i | −1.65361 | − | 2.27600i | ||||
\(719\) | −14.7645 | − | 10.7271i | −0.550625 | − | 0.400052i | 0.277391 | − | 0.960757i | \(-0.410530\pi\) |
−0.828016 | + | 0.560705i | \(0.810530\pi\) | |||||||
\(720\) | 45.3033 | + | 11.7312i | 1.68835 | + | 0.437197i | ||||
\(721\) | 3.15779 | + | 9.71868i | 0.117602 | + | 0.361942i | ||||
\(722\) | 18.3391 | − | 25.2416i | 0.682510 | − | 0.939395i | ||||
\(723\) | −6.86161 | − | 9.44419i | −0.255186 | − | 0.351233i | ||||
\(724\) | 2.17636 | − | 6.69816i | 0.0808839 | − | 0.248935i | ||||
\(725\) | −8.78706 | − | 18.8745i | −0.326343 | − | 0.700980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 0.218345i | − | 0.00809798i | −0.999992 | − | 0.00404899i | \(-0.998711\pi\) | ||
0.999992 | − | 0.00404899i | \(-0.00128884\pi\) | |||||||
\(728\) | −0.367704 | − | 0.119474i | −0.0136280 | − | 0.00442801i | ||||
\(729\) | −30.4927 | + | 22.1543i | −1.12936 | + | 0.820529i | ||||
\(730\) | −24.0509 | + | 9.46529i | −0.890165 | + | 0.350326i | ||||
\(731\) | −4.01462 | − | 12.3557i | −0.148486 | − | 0.456993i | ||||
\(732\) | −45.1527 | + | 14.6710i | −1.66889 | + | 0.542256i | ||||
\(733\) | 1.02489 | − | 1.41065i | 0.0378553 | − | 0.0521034i | −0.789670 | − | 0.613532i | \(-0.789748\pi\) |
0.827525 | + | 0.561429i | \(0.189748\pi\) | |||||||
\(734\) | 29.4548 | − | 21.4002i | 1.08720 | − | 0.789894i | ||||
\(735\) | −16.6623 | + | 13.7266i | −0.614597 | + | 0.506314i | ||||
\(736\) | 35.2024 | 1.29758 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 36.7436i | − | 1.35255i | ||||||
\(739\) | −9.38909 | + | 28.8966i | −0.345383 | + | 1.06298i | 0.615995 | + | 0.787750i | \(0.288754\pi\) |
−0.961378 | + | 0.275230i | \(0.911246\pi\) | |||||||
\(740\) | −9.61038 | + | 0.584803i | −0.353284 | + | 0.0214978i | ||||
\(741\) | 2.89282 | + | 2.10175i | 0.106270 | + | 0.0772099i | ||||
\(742\) | 39.6517 | − | 12.8836i | 1.45566 | − | 0.472973i | ||||
\(743\) | −32.9687 | + | 10.7122i | −1.20950 | + | 0.392991i | −0.843249 | − | 0.537524i | \(-0.819360\pi\) |
−0.366254 | + | 0.930515i | \(0.619360\pi\) | |||||||
\(744\) | 3.45710 | + | 2.51173i | 0.126743 | + | 0.0920845i | ||||
\(745\) | −2.60725 | − | 42.8463i | −0.0955222 | − | 1.56977i | ||||
\(746\) | −0.126646 | + | 0.389777i | −0.00463684 | + | 0.0142707i | ||||
\(747\) | − | 58.4572i | − | 2.13884i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.7458 | 0.465720 | ||||||||
\(750\) | −28.4343 | + | 59.4712i | −1.03827 | + | 2.17158i | ||||
\(751\) | −7.73330 | + | 5.61857i | −0.282192 | + | 0.205025i | −0.719873 | − | 0.694106i | \(-0.755800\pi\) |
0.437681 | + | 0.899130i | \(0.355800\pi\) | |||||||
\(752\) | −6.52422 | + | 8.97981i | −0.237914 | + | 0.327460i | ||||
\(753\) | −62.9486 | + | 20.4532i | −2.29397 | + | 0.745357i | ||||
\(754\) | −1.68857 | − | 5.19689i | −0.0614942 | − | 0.189260i | ||||
\(755\) | −6.84689 | + | 2.69461i | −0.249184 | + | 0.0980668i | ||||
\(756\) | −39.5325 | + | 28.7220i | −1.43778 | + | 1.04461i | ||||
\(757\) | −5.95480 | − | 1.93483i | −0.216431 | − | 0.0703226i | 0.198795 | − | 0.980041i | \(-0.436297\pi\) |
−0.415225 | + | 0.909719i | \(0.636297\pi\) | |||||||
\(758\) | − | 68.7414i | − | 2.49680i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.661674 | − | 0.421822i | −0.0240014 | − | 0.0153011i | ||||
\(761\) | 8.24025 | − | 25.3609i | 0.298709 | − | 0.919331i | −0.683241 | − | 0.730193i | \(-0.739430\pi\) |
0.981950 | − | 0.189139i | \(-0.0605696\pi\) | |||||||
\(762\) | 56.9844 | + | 78.4324i | 2.06433 | + | 2.84130i | ||||
\(763\) | −29.0964 | + | 40.0478i | −1.05336 | + | 1.44983i | ||||
\(764\) | −5.99537 | − | 18.4518i | −0.216905 | − | 0.667564i | ||||
\(765\) | −3.66121 | + | 14.1387i | −0.132371 | + | 0.511187i | ||||
\(766\) | 11.6878 | + | 8.49171i | 0.422299 | + | 0.306818i | ||||
\(767\) | 1.41715 | + | 1.95054i | 0.0511702 | + | 0.0704298i | ||||
\(768\) | 40.0088 | + | 12.9997i | 1.44369 | + | 0.469085i | ||||
\(769\) | −42.2399 | −1.52321 | −0.761605 | − | 0.648042i | \(-0.775588\pi\) | ||||
−0.761605 | + | 0.648042i | \(0.775588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.8425 | −0.426498 | ||||||||
\(772\) | −9.67414 | − | 3.14332i | −0.348180 | − | 0.113130i | ||||
\(773\) | −27.2115 | − | 37.4535i | −0.978731 | − | 1.34711i | −0.937510 | − | 0.347958i | \(-0.886875\pi\) |
−0.0412213 | − | 0.999150i | \(-0.513125\pi\) | |||||||
\(774\) | −98.3140 | − | 71.4293i | −3.53382 | − | 2.56747i | ||||
\(775\) | 28.9046 | − | 26.9205i | 1.03828 | − | 0.967011i | ||||
\(776\) | −0.868135 | − | 2.67185i | −0.0311642 | − | 0.0959137i | ||||
\(777\) | −11.3252 | + | 15.5879i | −0.406291 | + | 0.559212i | ||||
\(778\) | −15.7739 | − | 21.7109i | −0.565522 | − | 0.778375i | ||||
\(779\) | 1.93135 | − | 5.94409i | 0.0691978 | − | 0.212969i | ||||
\(780\) | −4.75448 | + | 7.45793i | −0.170238 | + | 0.267037i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 10.4813i | 0.374811i | ||||||||
\(783\) | −28.8085 | − | 9.36044i | −1.02953 | − | 0.334515i | ||||
\(784\) | −10.2046 | + | 7.41406i | −0.364449 | + | 0.264788i | ||||
\(785\) | −11.4761 | − | 29.1602i | −0.409598 | − | 1.04077i | ||||
\(786\) | −25.5088 | − | 78.5079i | −0.909867 | − | 2.80028i | ||||
\(787\) | 46.7397 | − | 15.1866i | 1.66609 | − | 0.541345i | 0.683955 | − | 0.729524i | \(-0.260258\pi\) |
0.982135 | + | 0.188178i | \(0.0602583\pi\) | |||||||
\(788\) | −14.5999 | + | 20.0951i | −0.520100 | + | 0.715857i | ||||
\(789\) | −29.0172 | + | 21.0822i | −1.03304 | + | 0.750546i | ||||
\(790\) | −53.2597 | + | 43.8762i | −1.89490 | + | 1.56104i | ||||
\(791\) | 32.5474 | 1.15725 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.05180i | 0.179395i | ||||||||
\(794\) | −20.9786 | + | 64.5656i | −0.744504 | + | 2.29135i | ||||
\(795\) | −2.54084 | − | 41.7550i | −0.0901143 | − | 1.48090i | ||||
\(796\) | 8.44704 | + | 6.13713i | 0.299397 | + | 0.217525i | ||||
\(797\) | −41.5326 | + | 13.4948i | −1.47116 | + | 0.478009i | −0.931459 | − | 0.363847i | \(-0.881463\pi\) |
−0.539702 | + | 0.841856i | \(0.681463\pi\) | |||||||
\(798\) | −34.0504 | + | 11.0636i | −1.20537 | + | 0.391649i | ||||
\(799\) | −2.80252 | − | 2.03615i | −0.0991459 | − | 0.0720337i | ||||
\(800\) | −19.5942 | + | 35.2971i | −0.692758 | + | 1.24794i | ||||
\(801\) | 15.2846 | − | 47.0413i | 0.540056 | − | 1.66212i | ||||
\(802\) | − | 67.9480i | − | 2.39933i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.5102 | −0.511737 | ||||||||
\(805\) | 19.9059 | + | 24.1631i | 0.701592 | + | 0.851638i | ||||
\(806\) | 8.38706 | − | 6.09356i | 0.295422 | − | 0.214636i | ||||
\(807\) | 13.2056 | − | 18.1760i | 0.464860 | − | 0.639824i | ||||
\(808\) | 0.984538 | − | 0.319896i | 0.0346359 | − | 0.0112539i | ||||
\(809\) | 12.2076 | + | 37.5713i | 0.429198 | + | 1.32094i | 0.898917 | + | 0.438120i | \(0.144355\pi\) |
−0.469719 | + | 0.882816i | \(0.655645\pi\) | |||||||
\(810\) | 7.81229 | + | 19.8507i | 0.274496 | + | 0.697483i | ||||
\(811\) | −37.6818 | + | 27.3775i | −1.32319 | + | 0.961352i | −0.323302 | + | 0.946296i | \(0.604793\pi\) |
−0.999887 | + | 0.0150565i | \(0.995207\pi\) | |||||||
\(812\) | 26.6009 | + | 8.64316i | 0.933509 | + | 0.303315i | ||||
\(813\) | 45.3940i | 1.59204i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.4621 | − | 12.4072i | −0.681728 | − | 0.434606i | ||||
\(816\) | −4.07644 | + | 12.5460i | −0.142704 | + | 0.439197i | ||||
\(817\) | −12.1499 | − | 16.7229i | −0.425072 | − | 0.585062i | ||||
\(818\) | 9.71269 | − | 13.3684i | 0.339596 | − | 0.467414i | ||||
\(819\) | 3.53810 | + | 10.8892i | 0.123631 | + | 0.380498i | ||||
\(820\) | 14.9657 | + | 3.87535i | 0.522625 | + | 0.135333i | ||||
\(821\) | −23.6291 | − | 17.1675i | −0.824661 | − | 0.599151i | 0.0933826 | − | 0.995630i | \(-0.470232\pi\) |
−0.918044 | + | 0.396479i | \(0.870232\pi\) | |||||||
\(822\) | 47.7262 | + | 65.6895i | 1.66464 | + | 2.29119i | ||||
\(823\) | −13.2024 | − | 4.28972i | −0.460207 | − | 0.149530i | 0.0697326 | − | 0.997566i | \(-0.477785\pi\) |
−0.529940 | + | 0.848035i | \(0.677785\pi\) | |||||||
\(824\) | −0.590551 | −0.0205728 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.1406 | −0.839960 | ||||||||
\(827\) | 9.08284 | + | 2.95119i | 0.315841 | + | 0.102623i | 0.462648 | − | 0.886542i | \(-0.346899\pi\) |
−0.146806 | + | 0.989165i | \(0.546899\pi\) | |||||||
\(828\) | 29.4599 | + | 40.5480i | 1.02380 | + | 1.40914i | ||||
\(829\) | 30.1958 | + | 21.9386i | 1.04875 | + | 0.761958i | 0.971973 | − | 0.235091i | \(-0.0755387\pi\) |
0.0767717 | + | 0.997049i | \(0.475539\pi\) | |||||||
\(830\) | 46.5751 | + | 12.0606i | 1.61665 | + | 0.418628i | ||||
\(831\) | 18.2871 | + | 56.2820i | 0.634373 | + | 1.95240i | ||||
\(832\) | −3.32379 | + | 4.57480i | −0.115232 | + | 0.158603i | ||||
\(833\) | −2.31386 | − | 3.18476i | −0.0801706 | − | 0.110345i | ||||
\(834\) | 12.3068 | − | 37.8765i | 0.426150 | − | 1.31156i | ||||
\(835\) | 27.5393 | + | 17.5565i | 0.953038 | + | 0.607568i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 57.4683i | − | 1.98640i | ||||||
\(838\) | 37.5774 | + | 12.2096i | 1.29809 | + | 0.421775i | ||||
\(839\) | −1.15908 | + | 0.842119i | −0.0400158 | + | 0.0290732i | −0.607613 | − | 0.794233i | \(-0.707873\pi\) |
0.567598 | + | 0.823306i | \(0.307873\pi\) | |||||||
\(840\) | −1.42243 | − | 3.61435i | −0.0490786 | − | 0.124707i | ||||
\(841\) | −3.60366 | − | 11.0909i | −0.124264 | − | 0.382445i | ||||
\(842\) | −45.9948 | + | 14.9446i | −1.58508 | + | 0.515025i | ||||
\(843\) | 41.4941 | − | 57.1118i | 1.42913 | − | 1.96703i | ||||
\(844\) | −2.66216 | + | 1.93418i | −0.0916355 | + | 0.0665771i | ||||
\(845\) | −17.8847 | − | 21.7096i | −0.615253 | − | 0.746834i | ||||
\(846\) | −32.4031 | −1.11404 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 24.4417i | − | 0.839332i | ||||||
\(849\) | 13.0037 | − | 40.0214i | 0.446287 | − | 1.37353i | ||||
\(850\) | −10.5095 | − | 5.83405i | −0.360473 | − | 0.200106i | ||||
\(851\) | 7.26072 | + | 5.27523i | 0.248894 | + | 0.180832i | ||||
\(852\) | 91.1315 | − | 29.6104i | 3.12211 | − | 1.01444i | ||||
\(853\) | 26.7648 | − | 8.69640i | 0.916408 | − | 0.297759i | 0.187416 | − | 0.982281i | \(-0.439989\pi\) |
0.728993 | + | 0.684522i | \(0.239989\pi\) | |||||||
\(854\) | −40.9220 | − | 29.7315i | −1.40032 | − | 1.01739i | ||||
\(855\) | 1.41144 | + | 23.1950i | 0.0482703 | + | 0.793252i | ||||
\(856\) | −0.227617 | + | 0.700533i | −0.00777979 | + | 0.0239437i | ||||
\(857\) | 4.04561i | 0.138195i | 0.997610 | + | 0.0690977i | \(0.0220120\pi\) | ||||
−0.997610 | + | 0.0690977i | \(0.977988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.2064 | 1.88362 | 0.941808 | − | 0.336151i | \(-0.109125\pi\) | ||||
0.941808 | + | 0.336151i | \(0.109125\pi\) | |||||||
\(860\) | 39.4625 | − | 32.5098i | 1.34566 | − | 1.10857i | ||||
\(861\) | 25.0285 | − | 18.1843i | 0.852968 | − | 0.619718i | ||||
\(862\) | 8.99321 | − | 12.3781i | 0.306310 | − | 0.421599i | ||||
\(863\) | 28.7149 | − | 9.33004i | 0.977467 | − | 0.317598i | 0.223641 | − | 0.974672i | \(-0.428206\pi\) |
0.753827 | + | 0.657073i | \(0.228206\pi\) | |||||||
\(864\) | 18.1506 | + | 55.8619i | 0.617497 | + | 1.90046i | ||||
\(865\) | 1.80840 | + | 4.59506i | 0.0614873 | + | 0.156237i | ||||
\(866\) | 41.9258 | − | 30.4608i | 1.42470 | − | 1.03510i | ||||
\(867\) | 43.2101 | + | 14.0398i | 1.46749 | + | 0.476818i | ||||
\(868\) | 53.0646i | 1.80113i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 29.5102 | − | 46.2901i | 1.00049 | − | 1.56938i | ||||
\(871\) | −0.477118 | + | 1.46842i | −0.0161665 | + | 0.0497555i | ||||
\(872\) | −1.68150 | − | 2.31438i | −0.0569426 | − | 0.0783748i | ||||
\(873\) | −48.9012 | + | 67.3068i | −1.65506 | + | 2.27799i | ||||
\(874\) | 5.15337 | + | 15.8604i | 0.174315 | + | 0.536487i | ||||
\(875\) | −35.3080 | + | 6.50997i | −1.19363 | + | 0.220077i | ||||
\(876\) | −28.1858 | − | 20.4782i | −0.952309 | − | 0.691893i | ||||
\(877\) | 18.1859 | + | 25.0308i | 0.614096 | + | 0.845230i | 0.996906 | − | 0.0785967i | \(-0.0250439\pi\) |
−0.382811 | + | 0.923827i | \(0.625044\pi\) | |||||||
\(878\) | −39.3741 | − | 12.7934i | −1.32881 | − | 0.431757i | ||||
\(879\) | 44.1951 | 1.49066 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.25840 | −0.278233 | −0.139116 | − | 0.990276i | \(-0.544426\pi\) | ||||
−0.139116 | + | 0.990276i | \(0.544426\pi\) | |||||||
\(882\) | −35.0204 | − | 11.3788i | −1.17920 | − | 0.383144i | ||||
\(883\) | 23.5284 | + | 32.3840i | 0.791793 | + | 1.08981i | 0.993883 | + | 0.110442i | \(0.0352267\pi\) |
−0.202090 | + | 0.979367i | \(0.564773\pi\) | |||||||
\(884\) | −1.30477 | − | 0.947972i | −0.0438842 | − | 0.0318838i | ||||
\(885\) | −6.07189 | + | 23.4482i | −0.204104 | + | 0.788204i | ||||
\(886\) | −6.35385 | − | 19.5551i | −0.213462 | − | 0.656968i | ||||
\(887\) | 22.1801 | − | 30.5283i | 0.744735 | − | 1.02504i | −0.253597 | − | 0.967310i | \(-0.581614\pi\) |
0.998332 | − | 0.0577299i | \(-0.0183862\pi\) | |||||||
\(888\) | −0.654492 | − | 0.900831i | −0.0219633 | − | 0.0302299i | ||||
\(889\) | −16.3170 | + | 50.2187i | −0.547256 | + | 1.68428i | ||||
\(890\) | 34.3261 | + | 21.8831i | 1.15062 | + | 0.733525i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 6.93360i | − | 0.232154i | ||||||
\(893\) | −5.24191 | − | 1.70320i | −0.175414 | − | 0.0569955i | ||||
\(894\) | 91.5682 | − | 66.5282i | 3.06250 | − | 2.22504i | ||||
\(895\) | 22.4887 | − | 8.85049i | 0.751716 | − | 0.295839i | ||||
\(896\) | −1.47173 | − | 4.52951i | −0.0491669 | − | 0.151320i | ||||
\(897\) | 7.84081 | − | 2.54763i | 0.261797 | − | 0.0850630i | ||||
\(898\) | −17.4774 | + | 24.0555i | −0.583227 | + | 0.802743i | ||||
\(899\) | −26.6121 | + | 19.3348i | −0.887564 | + | 0.644853i | ||||
\(900\) | −57.0549 | + | 6.96952i | −1.90183 | + | 0.232317i | ||||
\(901\) | 7.62803 | 0.254127 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 102.318i | − | 3.40494i | ||||||
\(904\) | −0.581240 | + | 1.78887i | −0.0193317 | + | 0.0594970i | ||||
\(905\) | −0.457290 | − | 7.51489i | −0.0152008 | − | 0.249803i | ||||
\(906\) | −15.6961 | − | 11.4039i | −0.521467 | − | 0.378868i | ||||
\(907\) | −31.8908 | + | 10.3619i | −1.05892 | + | 0.344063i | −0.786161 | − | 0.618021i | \(-0.787935\pi\) |
−0.272754 | + | 0.962084i | \(0.587935\pi\) | |||||||
\(908\) | 5.65003 | − | 1.83581i | 0.187503 | − | 0.0609234i | ||||
\(909\) | −24.8016 | − | 18.0194i | −0.822617 | − | 0.597666i | ||||
\(910\) | −9.40577 | + | 0.572352i | −0.311798 | + | 0.0189733i | ||||
\(911\) | −4.25913 | + | 13.1083i | −0.141111 | + | 0.434296i | −0.996490 | − | 0.0837064i | \(-0.973324\pi\) |
0.855379 | + | 0.518003i | \(0.173324\pi\) | |||||||
\(912\) | 20.9890i | 0.695014i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 6.80231 | 0.225000 | ||||||||
\(915\) | −39.1716 | + | 32.2701i | −1.29497 | + | 1.06682i | ||||
\(916\) | 3.37027 | − | 2.44864i | 0.111357 | − | 0.0809055i | ||||
\(917\) | 26.4270 | − | 36.3736i | 0.872695 | − | 1.20116i | ||||
\(918\) | −16.6326 | + | 5.40425i | −0.548957 | + | 0.178367i | ||||
\(919\) | −12.9209 | − | 39.7663i | −0.426220 | − | 1.31177i | −0.901821 | − | 0.432109i | \(-0.857769\pi\) |
0.475601 | − | 0.879661i | \(-0.342231\pi\) | |||||||
\(920\) | −1.68354 | + | 0.662560i | −0.0555046 | + | 0.0218440i | ||||
\(921\) | 18.9630 | − | 13.7775i | 0.624853 | − | 0.453982i | ||||
\(922\) | 2.72072 | + | 0.884014i | 0.0896020 | + | 0.0291135i | ||||
\(923\) | − | 10.1960i | − | 0.335607i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.33084 | + | 4.34399i | −0.306796 | + | 0.142830i | ||||
\(926\) | 9.66346 | − | 29.7411i | 0.317561 | − | 0.977352i | ||||
\(927\) | 10.2795 | + | 14.1485i | 0.337623 | + | 0.464698i | ||||
\(928\) | 19.7616 | − | 27.1995i | 0.648706 | − | 0.892867i | ||||
\(929\) | −4.04898 | − | 12.4615i | −0.132843 | − | 0.408848i | 0.862405 | − | 0.506218i | \(-0.168957\pi\) |
−0.995248 | + | 0.0973699i | \(0.968957\pi\) | |||||||
\(930\) | 100.825 | + | 26.1084i | 3.30617 | + | 0.856127i | ||||
\(931\) | −5.06721 | − | 3.68155i | −0.166071 | − | 0.120658i | ||||
\(932\) | 24.9016 | + | 34.2742i | 0.815680 | + | 1.12269i | ||||
\(933\) | 61.7258 | + | 20.0559i | 2.02081 | + | 0.656601i | ||||
\(934\) | 37.8078 | 1.23711 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.661674 | −0.0216275 | ||||||||
\(937\) | −8.32692 | − | 2.70558i | −0.272029 | − | 0.0883875i | 0.169826 | − | 0.985474i | \(-0.445679\pi\) |
−0.441855 | + | 0.897087i | \(0.645679\pi\) | |||||||
\(938\) | −9.08688 | − | 12.5070i | −0.296697 | − | 0.408369i | ||||
\(939\) | 5.54254 | + | 4.02689i | 0.180874 | + | 0.131413i | ||||
\(940\) | 3.41756 | − | 13.1978i | 0.111468 | − | 0.430466i | ||||
\(941\) | −5.45505 | − | 16.7889i | −0.177829 | − | 0.547303i | 0.821922 | − | 0.569600i | \(-0.192902\pi\) |
−0.999751 | + | 0.0222975i | \(0.992902\pi\) | |||||||
\(942\) | 48.5679 | − | 66.8480i | 1.58243 | − | 2.17803i | ||||
\(943\) | −8.47011 | − | 11.6581i | −0.275825 | − | 0.379640i | ||||
\(944\) | −4.37327 | + | 13.4595i | −0.142338 | + | 0.438071i | ||||
\(945\) | −28.0803 | + | 44.0470i | −0.913451 | + | 1.43285i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.2415i | 1.82760i | 0.406159 | + | 0.913802i | \(0.366868\pi\) | ||||
−0.406159 | + | 0.913802i | \(0.633132\pi\) | |||||||
\(948\) | −88.4625 | − | 28.7432i | −2.87313 | − | 0.933537i | ||||
\(949\) | −2.99916 | + | 2.17901i | −0.0973567 | + | 0.0707338i | ||||
\(950\) | −18.7715 | − | 3.66091i | −0.609029 | − | 0.118776i | ||||
\(951\) | 16.2338 | + | 49.9625i | 0.526417 | + | 1.62014i | ||||
\(952\) | 0.673608 | − | 0.218868i | 0.0218318 | − | 0.00709357i | ||||
\(953\) | 2.78838 | − | 3.83788i | 0.0903246 | − | 0.124321i | −0.761463 | − | 0.648208i | \(-0.775519\pi\) |
0.851788 | + | 0.523887i | \(0.175519\pi\) | |||||||
\(954\) | 57.7253 | − | 41.9399i | 1.86892 | − | 1.35785i | ||||
\(955\) | −13.1873 | − | 16.0076i | −0.426732 | − | 0.517995i | ||||
\(956\) | 3.95540 | 0.127927 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 60.4344i | − | 1.95255i | ||||||
\(959\) | −13.6660 | + | 42.0597i | −0.441299 | + | 1.35818i | ||||
\(960\) | −56.7047 | + | 3.45055i | −1.83014 | + | 0.111366i | ||||
\(961\) | −25.4092 | − | 18.4608i | −0.819650 | − | 0.595511i | ||||
\(962\) | −2.56915 | + | 0.834768i | −0.0828327 | + | 0.0269140i | ||||
\(963\) | 20.7456 | − | 6.74064i | 0.668516 | − | 0.217214i | ||||
\(964\) | 6.77753 | + | 4.92416i | 0.218290 | + | 0.158597i | ||||
\(965\) | −10.8537 | + | 0.660464i | −0.349394 | + | 0.0212611i | ||||
\(966\) | −25.5088 | + | 78.5079i | −0.820731 | + | 2.52595i | ||||
\(967\) | 33.8619i | 1.08892i | 0.838785 | + | 0.544462i | \(0.183266\pi\) | ||||
−0.838785 | + | 0.544462i | \(0.816734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.55047 | −0.210431 | ||||||||
\(970\) | −43.5369 | − | 52.8478i | −1.39788 | − | 1.69684i | ||||
\(971\) | 16.0047 | − | 11.6281i | 0.513614 | − | 0.373162i | −0.300579 | − | 0.953757i | \(-0.597180\pi\) |
0.814193 | + | 0.580595i | \(0.197180\pi\) | |||||||
\(972\) | 9.93047 | − | 13.6681i | 0.318520 | − | 0.438405i | ||||
\(973\) | 20.6296 | − | 6.70297i | 0.661356 | − | 0.214887i | ||||
\(974\) | 0.584338 | + | 1.79841i | 0.0187234 | + | 0.0576247i | ||||
\(975\) | −1.80982 | + | 9.27995i | −0.0579605 | + | 0.297196i | ||||
\(976\) | −23.9901 | + | 17.4298i | −0.767904 | + | 0.557915i | ||||
\(977\) | −6.33521 | − | 2.05844i | −0.202681 | − | 0.0658552i | 0.205917 | − | 0.978569i | \(-0.433982\pi\) |
−0.408598 | + | 0.912714i | \(0.633982\pi\) | |||||||
\(978\) | − | 60.8581i | − | 1.94603i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.32821 | − | 13.0637i | 0.266035 | − | 0.417305i | ||||
\(981\) | −26.1791 | + | 80.5711i | −0.835836 | + | 2.57244i | ||||
\(982\) | −39.1106 | − | 53.8312i | −1.24807 | − | 1.71782i | ||||
\(983\) | 3.03421 | − | 4.17623i | 0.0967762 | − | 0.133201i | −0.757883 | − | 0.652391i | \(-0.773766\pi\) |
0.854659 | + | 0.519190i | \(0.173766\pi\) | |||||||
\(984\) | 0.552479 | + | 1.70035i | 0.0176124 | + | 0.0542053i | ||||
\(985\) | −6.65623 | + | 25.7048i | −0.212085 | + | 0.819024i | ||||
\(986\) | 8.09849 | + | 5.88390i | 0.257909 | + | 0.187382i | ||||
\(987\) | −16.0362 | − | 22.0719i | −0.510437 | − | 0.702556i | ||||
\(988\) | −2.44049 | − | 0.792962i | −0.0776422 | − | 0.0252275i | ||||
\(989\) | −47.6592 | −1.51547 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8830 | −0.758669 | −0.379334 | − | 0.925260i | \(-0.623847\pi\) | ||||
−0.379334 | + | 0.925260i | \(0.623847\pi\) | |||||||
\(992\) | 60.6630 | + | 19.7106i | 1.92605 | + | 0.625812i | ||||
\(993\) | 5.29693 | + | 7.29060i | 0.168093 | + | 0.231360i | ||||
\(994\) | 82.5926 | + | 60.0071i | 2.61968 | + | 1.90331i | ||||
\(995\) | 10.8051 | + | 2.79797i | 0.342546 | + | 0.0887017i | ||||
\(996\) | 20.0401 | + | 61.6772i | 0.634996 | + | 1.95432i | ||||
\(997\) | 17.4233 | − | 23.9811i | 0.551801 | − | 0.759489i | −0.438454 | − | 0.898753i | \(-0.644474\pi\) |
0.990255 | + | 0.139265i | \(0.0444739\pi\) | |||||||
\(998\) | −10.6908 | − | 14.7146i | −0.338410 | − | 0.465782i | ||||
\(999\) | −4.62745 | + | 14.2418i | −0.146406 | + | 0.450592i |
(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 | 605.2.j.k.9.3 | 48 | ||
5.4 | even | 2 | inner | 605.2.j.k.9.10 | 48 | ||
11.2 | odd | 10 | inner | 605.2.j.k.124.3 | 48 | ||
11.3 | even | 5 | inner | 605.2.j.k.444.4 | 48 | ||
11.4 | even | 5 | 605.2.b.h.364.4 | yes | 12 | ||
11.5 | even | 5 | inner | 605.2.j.k.269.10 | 48 | ||
11.6 | odd | 10 | inner | 605.2.j.k.269.4 | 48 | ||
11.7 | odd | 10 | 605.2.b.h.364.10 | yes | 12 | ||
11.8 | odd | 10 | inner | 605.2.j.k.444.10 | 48 | ||
11.9 | even | 5 | inner | 605.2.j.k.124.9 | 48 | ||
11.10 | odd | 2 | inner | 605.2.j.k.9.9 | 48 | ||
55.4 | even | 10 | 605.2.b.h.364.9 | yes | 12 | ||
55.7 | even | 20 | 3025.2.a.bo.1.4 | 12 | |||
55.9 | even | 10 | inner | 605.2.j.k.124.4 | 48 | ||
55.14 | even | 10 | inner | 605.2.j.k.444.9 | 48 | ||
55.18 | even | 20 | 3025.2.a.bo.1.9 | 12 | |||
55.19 | odd | 10 | inner | 605.2.j.k.444.3 | 48 | ||
55.24 | odd | 10 | inner | 605.2.j.k.124.10 | 48 | ||
55.29 | odd | 10 | 605.2.b.h.364.3 | ✓ | 12 | ||
55.37 | odd | 20 | 3025.2.a.bo.1.10 | 12 | |||
55.39 | odd | 10 | inner | 605.2.j.k.269.9 | 48 | ||
55.48 | odd | 20 | 3025.2.a.bo.1.3 | 12 | |||
55.49 | even | 10 | inner | 605.2.j.k.269.3 | 48 | ||
55.54 | odd | 2 | inner | 605.2.j.k.9.4 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.h.364.3 | ✓ | 12 | 55.29 | odd | 10 | ||
605.2.b.h.364.4 | yes | 12 | 11.4 | even | 5 | ||
605.2.b.h.364.9 | yes | 12 | 55.4 | even | 10 | ||
605.2.b.h.364.10 | yes | 12 | 11.7 | odd | 10 | ||
605.2.j.k.9.3 | 48 | 1.1 | even | 1 | trivial | ||
605.2.j.k.9.4 | 48 | 55.54 | odd | 2 | inner | ||
605.2.j.k.9.9 | 48 | 11.10 | odd | 2 | inner | ||
605.2.j.k.9.10 | 48 | 5.4 | even | 2 | inner | ||
605.2.j.k.124.3 | 48 | 11.2 | odd | 10 | inner | ||
605.2.j.k.124.4 | 48 | 55.9 | even | 10 | inner | ||
605.2.j.k.124.9 | 48 | 11.9 | even | 5 | inner | ||
605.2.j.k.124.10 | 48 | 55.24 | odd | 10 | inner | ||
605.2.j.k.269.3 | 48 | 55.49 | even | 10 | inner | ||
605.2.j.k.269.4 | 48 | 11.6 | odd | 10 | inner | ||
605.2.j.k.269.9 | 48 | 55.39 | odd | 10 | inner | ||
605.2.j.k.269.10 | 48 | 11.5 | even | 5 | inner | ||
605.2.j.k.444.3 | 48 | 55.19 | odd | 10 | inner | ||
605.2.j.k.444.4 | 48 | 11.3 | even | 5 | inner | ||
605.2.j.k.444.9 | 48 | 55.14 | even | 10 | inner | ||
605.2.j.k.444.10 | 48 | 11.8 | odd | 10 | inner | ||
3025.2.a.bo.1.3 | 12 | 55.48 | odd | 20 | |||
3025.2.a.bo.1.4 | 12 | 55.7 | even | 20 | |||
3025.2.a.bo.1.9 | 12 | 55.18 | even | 20 | |||
3025.2.a.bo.1.10 | 12 | 55.37 | odd | 20 |