Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
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([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 557.8 | ||
Character | \(\chi\) | \(=\) | 784.557 |
Dual form | 784.2.x.o.373.8 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.262311 | + | 1.38967i | 0.185482 | + | 0.982648i | ||||
\(3\) | −2.91496 | + | 0.781062i | −1.68295 | + | 0.450946i | −0.968557 | − | 0.248794i | \(-0.919966\pi\) |
−0.714398 | + | 0.699740i | \(0.753299\pi\) | |||||||
\(4\) | −1.86239 | + | 0.729053i | −0.931193 | + | 0.364526i | ||||
\(5\) | 0.745506 | + | 0.199758i | 0.333400 | + | 0.0893344i | 0.421636 | − | 0.906765i | \(-0.361456\pi\) |
−0.0882353 | + | 0.996100i | \(0.528123\pi\) | |||||||
\(6\) | −1.85005 | − | 3.84597i | −0.755279 | − | 1.57011i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.50167 | − | 2.39687i | −0.530920 | − | 0.847422i | ||||
\(9\) | 5.28887 | − | 3.05353i | 1.76296 | − | 1.01784i | ||||
\(10\) | −0.0820438 | + | 1.08841i | −0.0259445 | + | 0.344185i | ||||
\(11\) | −0.333193 | − | 1.24349i | −0.100462 | − | 0.374928i | 0.897329 | − | 0.441362i | \(-0.145504\pi\) |
−0.997791 | + | 0.0664342i | \(0.978838\pi\) | |||||||
\(12\) | 4.85935 | − | 3.57980i | 1.40277 | − | 1.03340i | ||||
\(13\) | 0.919058 | + | 0.919058i | 0.254901 | + | 0.254901i | 0.822976 | − | 0.568076i | \(-0.192312\pi\) |
−0.568076 | + | 0.822976i | \(0.692312\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.32914 | −0.601383 | ||||||||
\(16\) | 2.93696 | − | 2.71556i | 0.734241 | − | 0.678889i | ||||
\(17\) | 3.95601 | − | 6.85200i | 0.959473 | − | 1.66186i | 0.235688 | − | 0.971829i | \(-0.424266\pi\) |
0.723784 | − | 0.690026i | \(-0.242401\pi\) | |||||||
\(18\) | 5.63074 | + | 6.54883i | 1.32718 | + | 1.54357i | ||||
\(19\) | −0.478380 | + | 1.78534i | −0.109748 | + | 0.409585i | −0.998840 | − | 0.0481427i | \(-0.984670\pi\) |
0.889093 | + | 0.457727i | \(0.151336\pi\) | |||||||
\(20\) | −1.53405 | + | 0.171487i | −0.343025 | + | 0.0383457i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.64065 | − | 0.789212i | 0.349788 | − | 0.168261i | ||||
\(23\) | 3.33211 | − | 1.92380i | 0.694793 | − | 0.401139i | −0.110612 | − | 0.993864i | \(-0.535281\pi\) |
0.805405 | + | 0.592725i | \(0.201948\pi\) | |||||||
\(24\) | 6.24941 | + | 5.81389i | 1.27566 | + | 1.18676i | ||||
\(25\) | −3.81425 | − | 2.20216i | −0.762850 | − | 0.440432i | ||||
\(26\) | −1.03611 | + | 1.51827i | −0.203198 | + | 0.297757i | ||||
\(27\) | −6.63016 | + | 6.63016i | −1.27598 | + | 1.27598i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.25154 | + | 5.25154i | 0.975187 | + | 0.975187i | 0.999700 | − | 0.0245125i | \(-0.00780335\pi\) |
−0.0245125 | + | 0.999700i | \(0.507803\pi\) | |||||||
\(30\) | −0.610960 | − | 3.23675i | −0.111546 | − | 0.590947i | ||||
\(31\) | −2.44642 | + | 4.23733i | −0.439391 | + | 0.761047i | −0.997643 | − | 0.0686244i | \(-0.978139\pi\) |
0.558252 | + | 0.829672i | \(0.311472\pi\) | |||||||
\(32\) | 4.54413 | + | 3.36910i | 0.803297 | + | 0.595579i | ||||
\(33\) | 1.94249 | + | 3.36449i | 0.338144 | + | 0.585683i | ||||
\(34\) | 10.5598 | + | 3.70020i | 1.81098 | + | 0.634580i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.62373 | + | 9.54272i | −1.27062 | + | 1.59045i | ||||
\(37\) | −1.28190 | − | 0.343485i | −0.210743 | − | 0.0564685i | 0.151903 | − | 0.988395i | \(-0.451460\pi\) |
−0.362646 | + | 0.931927i | \(0.618127\pi\) | |||||||
\(38\) | −2.60652 | − | 0.196478i | −0.422834 | − | 0.0318730i | ||||
\(39\) | −3.39686 | − | 1.96118i | −0.543933 | − | 0.314040i | ||||
\(40\) | −0.640710 | − | 2.08685i | −0.101305 | − | 0.329960i | ||||
\(41\) | − | 2.84345i | − | 0.444072i | −0.975039 | − | 0.222036i | \(-0.928730\pi\) | ||
0.975039 | − | 0.222036i | \(-0.0712702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.585764 | − | 0.585764i | 0.0893282 | − | 0.0893282i | −0.661031 | − | 0.750359i | \(-0.729881\pi\) |
0.750359 | + | 0.661031i | \(0.229881\pi\) | |||||||
\(44\) | 1.52711 | + | 2.07295i | 0.230220 | + | 0.312509i | ||||
\(45\) | 4.55285 | − | 1.21993i | 0.678699 | − | 0.181857i | ||||
\(46\) | 3.54750 | + | 4.12591i | 0.523050 | + | 0.608333i | ||||
\(47\) | 2.86095 | + | 4.95532i | 0.417313 | + | 0.722807i | 0.995668 | − | 0.0929777i | \(-0.0296385\pi\) |
−0.578355 | + | 0.815785i | \(0.696305\pi\) | |||||||
\(48\) | −6.44012 | + | 10.2097i | −0.929551 | + | 1.47364i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.05976 | − | 5.87821i | 0.291294 | − | 0.831305i | ||||
\(51\) | −6.17977 | + | 23.0632i | −0.865341 | + | 3.22950i | ||||
\(52\) | −2.38168 | − | 1.04160i | −0.330280 | − | 0.144444i | ||||
\(53\) | 2.54947 | + | 9.51475i | 0.350197 | + | 1.30695i | 0.886422 | + | 0.462877i | \(0.153183\pi\) |
−0.536226 | + | 0.844075i | \(0.680150\pi\) | |||||||
\(54\) | −10.9529 | − | 7.47460i | −1.49050 | − | 1.01716i | ||||
\(55\) | − | 0.993590i | − | 0.133976i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.57784i | − | 0.738803i | ||||||
\(58\) | −5.92039 | + | 8.67547i | −0.777386 | + | 1.13914i | ||||
\(59\) | −2.39390 | − | 8.93417i | −0.311660 | − | 1.16313i | −0.927059 | − | 0.374915i | \(-0.877672\pi\) |
0.615400 | − | 0.788215i | \(-0.288995\pi\) | |||||||
\(60\) | 4.33777 | − | 1.69807i | 0.560003 | − | 0.219220i | ||||
\(61\) | 1.71139 | − | 6.38698i | 0.219121 | − | 0.817769i | −0.765555 | − | 0.643371i | \(-0.777535\pi\) |
0.984675 | − | 0.174398i | \(-0.0557980\pi\) | |||||||
\(62\) | −6.53023 | − | 2.28823i | −0.829340 | − | 0.290606i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.48998 | + | 7.19862i | −0.436247 | + | 0.899827i | ||||
\(65\) | 0.501575 | + | 0.868753i | 0.0622127 | + | 0.107755i | ||||
\(66\) | −4.16601 | + | 3.58197i | −0.512801 | + | 0.440910i | ||||
\(67\) | 5.94825 | − | 1.59383i | 0.726695 | − | 0.194717i | 0.123538 | − | 0.992340i | \(-0.460576\pi\) |
0.603157 | + | 0.797623i | \(0.293909\pi\) | |||||||
\(68\) | −2.37214 | + | 15.6452i | −0.287664 | + | 1.89726i | ||||
\(69\) | −8.21037 | + | 8.21037i | −0.988413 | + | 0.988413i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.99534i | − | 0.236803i | −0.992966 | − | 0.118402i | \(-0.962223\pi\) | ||
0.992966 | − | 0.118402i | \(-0.0377770\pi\) | |||||||
\(72\) | −15.2611 | − | 8.09134i | −1.79853 | − | 0.953574i | ||||
\(73\) | 6.69237 | + | 3.86384i | 0.783283 | + | 0.452229i | 0.837592 | − | 0.546296i | \(-0.183962\pi\) |
−0.0543096 | + | 0.998524i | \(0.517296\pi\) | |||||||
\(74\) | 0.141075 | − | 1.87153i | 0.0163996 | − | 0.217560i | ||||
\(75\) | 12.8384 | + | 3.44004i | 1.48245 | + | 0.397222i | ||||
\(76\) | −0.410678 | − | 3.67375i | −0.0471080 | − | 0.421408i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.83437 | − | 5.23497i | 0.207701 | − | 0.592743i | ||||
\(79\) | −4.63378 | − | 8.02594i | −0.521341 | − | 0.902989i | −0.999692 | − | 0.0248202i | \(-0.992099\pi\) |
0.478351 | − | 0.878169i | \(-0.341235\pi\) | |||||||
\(80\) | 2.73198 | − | 1.43778i | 0.305444 | − | 0.160749i | ||||
\(81\) | 4.98751 | − | 8.63862i | 0.554168 | − | 0.959847i | ||||
\(82\) | 3.95146 | − | 0.745866i | 0.436366 | − | 0.0823672i | ||||
\(83\) | 4.78537 | + | 4.78537i | 0.525263 | + | 0.525263i | 0.919156 | − | 0.393893i | \(-0.128872\pi\) |
−0.393893 | + | 0.919156i | \(0.628872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.31797 | − | 4.31797i | 0.468349 | − | 0.468349i | ||||
\(86\) | 0.967673 | + | 0.660369i | 0.104347 | + | 0.0712094i | ||||
\(87\) | −19.4098 | − | 11.2063i | −2.08095 | − | 1.20144i | ||||
\(88\) | −2.48015 | + | 2.66594i | −0.264385 | + | 0.284190i | ||||
\(89\) | 1.84016 | − | 1.06242i | 0.195057 | − | 0.112616i | −0.399291 | − | 0.916824i | \(-0.630744\pi\) |
0.594348 | + | 0.804208i | \(0.297410\pi\) | |||||||
\(90\) | 2.88957 | + | 6.00698i | 0.304588 | + | 0.633191i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.80313 | + | 6.01213i | −0.500761 | + | 0.626808i | ||||
\(93\) | 3.82162 | − | 14.2625i | 0.396283 | − | 1.47895i | ||||
\(94\) | −6.13582 | + | 5.27563i | −0.632861 | + | 0.544139i | ||||
\(95\) | −0.713270 | + | 1.23542i | −0.0731800 | + | 0.126751i | ||||
\(96\) | −15.8775 | − | 6.27155i | −1.62049 | − | 0.640088i | ||||
\(97\) | 9.01961 | 0.915802 | 0.457901 | − | 0.889003i | \(-0.348601\pi\) | ||||
0.457901 | + | 0.889003i | \(0.348601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.55926 | − | 5.55926i | −0.558727 | − | 0.558727i | ||||
\(100\) | 8.70910 | + | 1.32048i | 0.870910 | + | 0.132048i | ||||
\(101\) | 1.29142 | + | 4.81966i | 0.128501 | + | 0.479574i | 0.999940 | − | 0.0109304i | \(-0.00347933\pi\) |
−0.871439 | + | 0.490504i | \(0.836813\pi\) | |||||||
\(102\) | −33.6714 | − | 2.53813i | −3.33396 | − | 0.251313i | ||||
\(103\) | 10.1524 | − | 5.86151i | 1.00035 | − | 0.577551i | 0.0919971 | − | 0.995759i | \(-0.470675\pi\) |
0.908351 | + | 0.418208i | \(0.137342\pi\) | |||||||
\(104\) | 0.822742 | − | 3.58299i | 0.0806765 | − | 0.351341i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.5536 | + | 6.03875i | −1.21932 | + | 0.586536i | ||||
\(107\) | 6.97171 | + | 1.86807i | 0.673981 | + | 0.180593i | 0.579547 | − | 0.814938i | \(-0.303229\pi\) |
0.0944336 | + | 0.995531i | \(0.469896\pi\) | |||||||
\(108\) | 7.51418 | − | 17.1817i | 0.723052 | − | 1.65331i | ||||
\(109\) | 10.9026 | − | 2.92133i | 1.04428 | − | 0.279813i | 0.304391 | − | 0.952547i | \(-0.401547\pi\) |
0.739884 | + | 0.672734i | \(0.234880\pi\) | |||||||
\(110\) | 1.38077 | − | 0.260629i | 0.131651 | − | 0.0248500i | ||||
\(111\) | 4.00498 | 0.380136 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.15066 | 0.860821 | 0.430411 | − | 0.902633i | \(-0.358369\pi\) | ||||
0.430411 | + | 0.902633i | \(0.358369\pi\) | |||||||
\(114\) | 7.75137 | − | 1.46313i | 0.725983 | − | 0.137034i | ||||
\(115\) | 2.86840 | − | 0.768586i | 0.267480 | − | 0.0716710i | ||||
\(116\) | −13.6091 | − | 5.95175i | −1.26357 | − | 0.552606i | ||||
\(117\) | 7.66715 | + | 2.05441i | 0.708829 | + | 0.189930i | ||||
\(118\) | 11.7876 | − | 5.67027i | 1.08514 | − | 0.521991i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.49761 | + | 5.58266i | 0.319286 | + | 0.509625i | ||||
\(121\) | 8.09102 | − | 4.67135i | 0.735547 | − | 0.424668i | ||||
\(122\) | 9.32473 | + | 0.702894i | 0.844222 | + | 0.0636371i | ||||
\(123\) | 2.22091 | + | 8.28853i | 0.200252 | + | 0.747352i | ||||
\(124\) | 1.46695 | − | 9.67512i | 0.131736 | − | 0.868852i | ||||
\(125\) | −5.13239 | − | 5.13239i | −0.459055 | − | 0.459055i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4281 | 1.54649 | 0.773245 | − | 0.634108i | \(-0.218632\pi\) | ||||
0.773245 | + | 0.634108i | \(0.218632\pi\) | |||||||
\(128\) | −10.9192 | − | 2.96165i | −0.965129 | − | 0.261776i | ||||
\(129\) | −1.24996 | + | 2.16500i | −0.110053 | + | 0.190617i | ||||
\(130\) | −1.07571 | + | 0.924908i | −0.0943464 | + | 0.0811198i | ||||
\(131\) | −2.71575 | + | 10.1353i | −0.237276 | + | 0.885527i | 0.739833 | + | 0.672790i | \(0.234904\pi\) |
−0.977110 | + | 0.212737i | \(0.931762\pi\) | |||||||
\(132\) | −6.07056 | − | 4.84981i | −0.528375 | − | 0.422121i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.77520 | + | 7.84805i | 0.326127 | + | 0.677969i | ||||
\(135\) | −6.26725 | + | 3.61840i | −0.539399 | + | 0.311422i | ||||
\(136\) | −22.3640 | + | 0.807413i | −1.91770 | + | 0.0692351i | ||||
\(137\) | −5.24143 | − | 3.02614i | −0.447806 | − | 0.258541i | 0.259097 | − | 0.965851i | \(-0.416575\pi\) |
−0.706903 | + | 0.707310i | \(0.749908\pi\) | |||||||
\(138\) | −13.5634 | − | 9.25607i | −1.15459 | − | 0.787929i | ||||
\(139\) | 4.50305 | − | 4.50305i | 0.381944 | − | 0.381944i | −0.489858 | − | 0.871802i | \(-0.662952\pi\) |
0.871802 | + | 0.489858i | \(0.162952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.2100 | − | 12.2100i | −1.02827 | − | 1.02827i | ||||
\(142\) | 2.77287 | − | 0.523399i | 0.232694 | − | 0.0439227i | ||||
\(143\) | 0.836620 | − | 1.44907i | 0.0699616 | − | 0.121177i | ||||
\(144\) | 7.24119 | − | 23.3303i | 0.603432 | − | 1.94419i | ||||
\(145\) | 2.86602 | + | 4.96409i | 0.238010 | + | 0.412245i | ||||
\(146\) | −3.61400 | + | 10.3137i | −0.299097 | + | 0.853571i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.63782 | − | 0.294874i | 0.216827 | − | 0.0242385i | ||||
\(149\) | −14.6597 | − | 3.92804i | −1.20097 | − | 0.321798i | −0.397754 | − | 0.917492i | \(-0.630210\pi\) |
−0.803211 | + | 0.595694i | \(0.796877\pi\) | |||||||
\(150\) | −1.41288 | + | 18.7436i | −0.115361 | + | 1.53041i | ||||
\(151\) | −12.8763 | − | 7.43412i | −1.04786 | − | 0.604980i | −0.125808 | − | 0.992055i | \(-0.540152\pi\) |
−0.922049 | + | 0.387074i | \(0.873486\pi\) | |||||||
\(152\) | 4.99759 | − | 1.53437i | 0.405358 | − | 0.124454i | ||||
\(153\) | − | 48.3192i | − | 3.90637i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.67026 | + | 2.67026i | −0.214481 | + | 0.214481i | ||||
\(156\) | 7.75607 | + | 1.17598i | 0.620983 | + | 0.0941538i | ||||
\(157\) | 10.9861 | − | 2.94372i | 0.876786 | − | 0.234934i | 0.207766 | − | 0.978178i | \(-0.433381\pi\) |
0.669020 | + | 0.743244i | \(0.266714\pi\) | |||||||
\(158\) | 9.93795 | − | 8.54473i | 0.790621 | − | 0.679782i | ||||
\(159\) | −14.8632 | − | 25.7439i | −1.17873 | − | 2.04162i | ||||
\(160\) | 2.71468 | + | 3.41941i | 0.214614 | + | 0.270328i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 13.3131 | + | 4.66501i | 1.04598 | + | 0.366518i | ||||
\(163\) | 2.61713 | − | 9.76727i | 0.204990 | − | 0.765032i | −0.784463 | − | 0.620176i | \(-0.787061\pi\) |
0.989453 | − | 0.144856i | \(-0.0462720\pi\) | |||||||
\(164\) | 2.07302 | + | 5.29559i | 0.161876 | + | 0.413516i | ||||
\(165\) | 0.776055 | + | 2.89628i | 0.0604158 | + | 0.225475i | ||||
\(166\) | −5.39485 | + | 7.90536i | −0.418721 | + | 0.613575i | ||||
\(167\) | − | 2.61575i | − | 0.202413i | −0.994865 | − | 0.101207i | \(-0.967730\pi\) | ||
0.994865 | − | 0.101207i | \(-0.0322703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.3107i | − | 0.870051i | ||||||
\(170\) | 7.13322 | + | 4.86792i | 0.547093 | + | 0.373352i | ||||
\(171\) | 2.92150 | + | 10.9032i | 0.223412 | + | 0.833786i | ||||
\(172\) | −0.663866 | + | 1.51797i | −0.0506193 | + | 0.115744i | ||||
\(173\) | −2.64600 | + | 9.87502i | −0.201172 | + | 0.750784i | 0.789410 | + | 0.613866i | \(0.210386\pi\) |
−0.990582 | + | 0.136918i | \(0.956280\pi\) | |||||||
\(174\) | 10.4816 | − | 29.9129i | 0.794612 | − | 2.26769i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.35535 | − | 2.74729i | −0.328297 | − | 0.207085i | ||||
\(177\) | 13.9563 | + | 24.1730i | 1.04902 | + | 1.81695i | ||||
\(178\) | 1.95911 | + | 2.27854i | 0.146841 | + | 0.170784i | ||||
\(179\) | −15.0929 | + | 4.04414i | −1.12810 | + | 0.302273i | −0.774156 | − | 0.632994i | \(-0.781826\pi\) |
−0.353942 | + | 0.935267i | \(0.615159\pi\) | |||||||
\(180\) | −7.58977 | + | 5.59126i | −0.565708 | + | 0.416748i | ||||
\(181\) | −12.8671 | + | 12.8671i | −0.956407 | + | 0.956407i | −0.999089 | − | 0.0426817i | \(-0.986410\pi\) |
0.0426817 | + | 0.999089i | \(0.486410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.9545i | 1.47508i | ||||||||
\(184\) | −9.61482 | − | 5.09773i | −0.708814 | − | 0.375810i | ||||
\(185\) | −0.887052 | − | 0.512140i | −0.0652174 | − | 0.0376533i | ||||
\(186\) | 20.8226 | + | 1.56960i | 1.52679 | + | 0.115089i | ||||
\(187\) | −9.83854 | − | 2.63623i | −0.719465 | − | 0.192780i | ||||
\(188\) | −8.94089 | − | 7.14293i | −0.652081 | − | 0.520952i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.90393 | − | 0.667149i | −0.138126 | − | 0.0484001i | ||||
\(191\) | 0.254497 | + | 0.440801i | 0.0184147 | + | 0.0318952i | 0.875086 | − | 0.483968i | \(-0.160805\pi\) |
−0.856671 | + | 0.515863i | \(0.827471\pi\) | |||||||
\(192\) | 4.55058 | − | 23.7096i | 0.328410 | − | 1.71109i | ||||
\(193\) | −2.41417 | + | 4.18147i | −0.173776 | + | 0.300989i | −0.939737 | − | 0.341898i | \(-0.888930\pi\) |
0.765961 | + | 0.642887i | \(0.222264\pi\) | |||||||
\(194\) | 2.36594 | + | 12.5343i | 0.169865 | + | 0.899911i | ||||
\(195\) | −2.14062 | − | 2.14062i | −0.153293 | − | 0.153293i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.02638 | − | 3.02638i | 0.215621 | − | 0.215621i | −0.591029 | − | 0.806650i | \(-0.701278\pi\) |
0.806650 | + | 0.591029i | \(0.201278\pi\) | |||||||
\(198\) | 6.26731 | − | 9.18382i | 0.445398 | − | 0.652665i | ||||
\(199\) | 6.56029 | + | 3.78758i | 0.465046 | + | 0.268495i | 0.714164 | − | 0.699979i | \(-0.246807\pi\) |
−0.249117 | + | 0.968473i | \(0.580140\pi\) | |||||||
\(200\) | 0.449456 | + | 12.4492i | 0.0317813 | + | 0.880290i | ||||
\(201\) | −16.0941 | + | 9.29191i | −1.13519 | + | 0.655401i | ||||
\(202\) | −6.35900 | + | 3.05890i | −0.447417 | + | 0.215224i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.30519 | − | 47.4580i | −0.371438 | − | 3.32272i | ||||
\(205\) | 0.568000 | − | 2.11981i | 0.0396709 | − | 0.148054i | ||||
\(206\) | 10.8087 | + | 12.5710i | 0.753076 | + | 0.875865i | ||||
\(207\) | 11.7487 | − | 20.3494i | 0.816594 | − | 1.41438i | ||||
\(208\) | 5.19500 | + | 0.203486i | 0.360208 | + | 0.0141092i | ||||
\(209\) | 2.37945 | 0.164590 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.60935 | + | 6.60935i | 0.455006 | + | 0.455006i | 0.897012 | − | 0.442006i | \(-0.145733\pi\) |
−0.442006 | + | 0.897012i | \(0.645733\pi\) | |||||||
\(212\) | −11.6849 | − | 15.8614i | −0.802519 | − | 1.08937i | ||||
\(213\) | 1.55848 | + | 5.81634i | 0.106785 | + | 0.398529i | ||||
\(214\) | −0.767245 | + | 10.1784i | −0.0524478 | + | 0.695783i | ||||
\(215\) | 0.553701 | − | 0.319680i | 0.0377621 | − | 0.0218020i | ||||
\(216\) | 25.8479 | + | 5.93532i | 1.75873 | + | 0.403848i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.91955 | + | 14.3847i | 0.468651 | + | 0.974254i | ||||
\(219\) | −22.5259 | − | 6.03580i | −1.52216 | − | 0.407862i | ||||
\(220\) | 0.724380 | + | 1.85045i | 0.0488377 | + | 0.124757i | ||||
\(221\) | 9.93319 | − | 2.66159i | 0.668179 | − | 0.179038i | ||||
\(222\) | 1.05055 | + | 5.56561i | 0.0705083 | + | 0.373540i | ||||
\(223\) | 20.4381 | 1.36864 | 0.684319 | − | 0.729183i | \(-0.260100\pi\) | ||||
0.684319 | + | 0.729183i | \(0.260100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.8974 | −1.79316 | ||||||||
\(226\) | 2.40032 | + | 12.7164i | 0.159667 | + | 0.845884i | ||||
\(227\) | 11.3952 | − | 3.05333i | 0.756326 | − | 0.202657i | 0.140004 | − | 0.990151i | \(-0.455289\pi\) |
0.616322 | + | 0.787494i | \(0.288622\pi\) | |||||||
\(228\) | 4.06654 | + | 10.3881i | 0.269313 | + | 0.687968i | ||||
\(229\) | −13.1330 | − | 3.51899i | −0.867856 | − | 0.232541i | −0.202696 | − | 0.979242i | \(-0.564970\pi\) |
−0.665160 | + | 0.746700i | \(0.731637\pi\) | |||||||
\(230\) | 1.82050 | + | 3.78453i | 0.120040 | + | 0.249545i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.70118 | − | 20.4734i | 0.308648 | − | 1.34414i | ||||
\(233\) | −18.6628 | + | 10.7750i | −1.22264 | + | 0.705893i | −0.965481 | − | 0.260475i | \(-0.916121\pi\) |
−0.257162 | + | 0.966368i | \(0.582787\pi\) | |||||||
\(234\) | −0.843779 | + | 11.1937i | −0.0551595 | + | 0.731757i | ||||
\(235\) | 1.14300 | + | 4.26572i | 0.0745608 | + | 0.278265i | ||||
\(236\) | 10.9719 | + | 14.8936i | 0.714207 | + | 0.969490i | ||||
\(237\) | 19.7760 | + | 19.7760i | 1.28459 | + | 1.28459i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5125 | 0.938733 | 0.469366 | − | 0.883004i | \(-0.344482\pi\) | ||||
0.469366 | + | 0.883004i | \(0.344482\pi\) | |||||||
\(240\) | −6.84061 | + | 6.32492i | −0.441560 | + | 0.408272i | ||||
\(241\) | −4.59046 | + | 7.95090i | −0.295697 | + | 0.512163i | −0.975147 | − | 0.221560i | \(-0.928885\pi\) |
0.679450 | + | 0.733722i | \(0.262219\pi\) | |||||||
\(242\) | 8.61402 | + | 10.0185i | 0.553730 | + | 0.644016i | ||||
\(243\) | −0.510685 | + | 1.90590i | −0.0327604 | + | 0.122264i | ||||
\(244\) | 1.46919 | + | 13.1427i | 0.0940549 | + | 0.841376i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.9358 | + | 5.26051i | −0.697241 | + | 0.335398i | ||||
\(247\) | −2.08049 | + | 1.20117i | −0.132378 | + | 0.0764287i | ||||
\(248\) | 13.8301 | − | 0.499310i | 0.878210 | − | 0.0317062i | ||||
\(249\) | −17.6868 | − | 10.2115i | −1.12086 | − | 0.647128i | ||||
\(250\) | 5.78607 | − | 8.47863i | 0.365943 | − | 0.536236i | ||||
\(251\) | −9.13628 | + | 9.13628i | −0.576677 | + | 0.576677i | −0.933986 | − | 0.357309i | \(-0.883694\pi\) |
0.357309 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.50246 | − | 3.50246i | −0.220198 | − | 0.220198i | ||||
\(254\) | 4.57157 | + | 24.2193i | 0.286846 | + | 1.51965i | ||||
\(255\) | −9.21411 | + | 15.9593i | −0.577010 | + | 0.999411i | ||||
\(256\) | 1.25151 | − | 15.9510i | 0.0782194 | − | 0.996936i | ||||
\(257\) | −4.85503 | − | 8.40916i | −0.302849 | − | 0.524549i | 0.673931 | − | 0.738794i | \(-0.264604\pi\) |
−0.976780 | + | 0.214245i | \(0.931271\pi\) | |||||||
\(258\) | −3.33652 | − | 1.16914i | −0.207723 | − | 0.0727873i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.56749 | − | 1.25228i | −0.0972117 | − | 0.0776630i | ||||
\(261\) | 43.8105 | + | 11.7390i | 2.71180 | + | 0.726625i | ||||
\(262\) | −14.7972 | − | 1.11540i | −0.914172 | − | 0.0689098i | ||||
\(263\) | 9.24140 | + | 5.33552i | 0.569849 | + | 0.329002i | 0.757089 | − | 0.653312i | \(-0.226621\pi\) |
−0.187240 | + | 0.982314i | \(0.559954\pi\) | |||||||
\(264\) | 5.14727 | − | 9.70826i | 0.316793 | − | 0.597502i | ||||
\(265\) | 7.60258i | 0.467023i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.53418 | + | 4.53418i | −0.277487 | + | 0.277487i | ||||
\(268\) | −9.91596 | + | 7.30492i | −0.605714 | + | 0.446219i | ||||
\(269\) | −7.31835 | + | 1.96094i | −0.446207 | + | 0.119561i | −0.474924 | − | 0.880027i | \(-0.657525\pi\) |
0.0287169 | + | 0.999588i | \(0.490858\pi\) | |||||||
\(270\) | −6.67236 | − | 7.76029i | −0.406067 | − | 0.472276i | ||||
\(271\) | −5.62243 | − | 9.73834i | −0.341538 | − | 0.591562i | 0.643180 | − | 0.765715i | \(-0.277615\pi\) |
−0.984719 | + | 0.174153i | \(0.944281\pi\) | |||||||
\(272\) | −6.98836 | − | 30.8668i | −0.423731 | − | 1.87158i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.83047 | − | 8.07767i | 0.170995 | − | 0.487990i | ||||
\(275\) | −1.46749 | + | 5.47674i | −0.0884929 | + | 0.330260i | ||||
\(276\) | 9.30509 | − | 21.2767i | 0.560101 | − | 1.28071i | ||||
\(277\) | 5.50691 | + | 20.5521i | 0.330878 | + | 1.23485i | 0.908269 | + | 0.418386i | \(0.137404\pi\) |
−0.577391 | + | 0.816467i | \(0.695929\pi\) | |||||||
\(278\) | 7.43897 | + | 5.07657i | 0.446160 | + | 0.304472i | ||||
\(279\) | 29.8809i | 1.78892i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0973i | 1.19891i | 0.800410 | + | 0.599453i | \(0.204615\pi\) | ||||
−0.800410 | + | 0.599453i | \(0.795385\pi\) | |||||||
\(282\) | 13.7651 | − | 20.1707i | 0.819699 | − | 1.20115i | ||||
\(283\) | −5.29502 | − | 19.7613i | −0.314756 | − | 1.17469i | −0.924216 | − | 0.381869i | \(-0.875281\pi\) |
0.609460 | − | 0.792816i | \(-0.291386\pi\) | |||||||
\(284\) | 1.45471 | + | 3.71609i | 0.0863210 | + | 0.220509i | ||||
\(285\) | 1.11422 | − | 4.15831i | 0.0660005 | − | 0.246317i | ||||
\(286\) | 2.23319 | + | 0.782522i | 0.132051 | + | 0.0462715i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 34.3210 | + | 3.94309i | 2.02238 | + | 0.232349i | ||||
\(289\) | −22.8000 | − | 39.4907i | −1.34117 | − | 2.32298i | ||||
\(290\) | −6.14668 | + | 5.28497i | −0.360946 | + | 0.310344i | ||||
\(291\) | −26.2918 | + | 7.04487i | −1.54125 | + | 0.412978i | ||||
\(292\) | −15.2807 | − | 2.31687i | −0.894237 | − | 0.135585i | ||||
\(293\) | 10.4368 | − | 10.4368i | 0.609726 | − | 0.609726i | −0.333148 | − | 0.942875i | \(-0.608111\pi\) |
0.942875 | + | 0.333148i | \(0.108111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.13868i | − | 0.415630i | ||||||
\(296\) | 1.10171 | + | 3.58835i | 0.0640353 | + | 0.208569i | ||||
\(297\) | 10.4537 | + | 6.03544i | 0.606585 | + | 0.350212i | ||||
\(298\) | 1.61331 | − | 21.4025i | 0.0934566 | − | 1.23981i | ||||
\(299\) | 4.83048 | + | 1.29432i | 0.279354 | + | 0.0748527i | ||||
\(300\) | −26.4181 | + | 2.95320i | −1.52525 | + | 0.170503i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.95342 | − | 19.8439i | 0.400124 | − | 1.14189i | ||||
\(303\) | −7.52890 | − | 13.0404i | −0.432524 | − | 0.749153i | ||||
\(304\) | 3.44320 | + | 6.54254i | 0.197481 | + | 0.375240i | ||||
\(305\) | 2.55170 | − | 4.41967i | 0.146110 | − | 0.253070i | ||||
\(306\) | 67.1479 | − | 12.6746i | 3.83859 | − | 0.724561i | ||||
\(307\) | −4.72698 | − | 4.72698i | −0.269783 | − | 0.269783i | 0.559230 | − | 0.829013i | \(-0.311097\pi\) |
−0.829013 | + | 0.559230i | \(0.811097\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.0157 | + | 25.0157i | −1.42310 | + | 1.42310i | ||||
\(310\) | −4.41124 | − | 3.01036i | −0.250541 | − | 0.170977i | ||||
\(311\) | 4.82684 | + | 2.78678i | 0.273705 | + | 0.158024i | 0.630570 | − | 0.776132i | \(-0.282821\pi\) |
−0.356865 | + | 0.934156i | \(0.616154\pi\) | |||||||
\(312\) | 0.400273 | + | 11.0869i | 0.0226610 | + | 0.627671i | ||||
\(313\) | −10.2429 | + | 5.91372i | −0.578961 | + | 0.334263i | −0.760720 | − | 0.649080i | \(-0.775154\pi\) |
0.181760 | + | 0.983343i | \(0.441821\pi\) | |||||||
\(314\) | 6.97258 | + | 14.4949i | 0.393485 | + | 0.817996i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4812 | + | 11.5691i | 0.814632 | + | 0.650814i | ||||
\(317\) | −1.17054 | + | 4.36851i | −0.0657441 | + | 0.245360i | −0.990976 | − | 0.134043i | \(-0.957204\pi\) |
0.925231 | + | 0.379403i | \(0.123871\pi\) | |||||||
\(318\) | 31.8768 | − | 27.4079i | 1.78756 | − | 1.53696i | ||||
\(319\) | 4.78048 | − | 8.28004i | 0.267656 | − | 0.463593i | ||||
\(320\) | −4.03978 | + | 4.66946i | −0.225830 | + | 0.261031i | ||||
\(321\) | −21.7814 | −1.21572 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3407 | + | 10.3407i | 0.575370 | + | 0.575370i | ||||
\(324\) | −2.99066 | + | 19.7246i | −0.166148 | + | 1.09581i | ||||
\(325\) | −1.48161 | − | 5.52943i | −0.0821848 | − | 0.306718i | ||||
\(326\) | 14.2598 | + | 1.07490i | 0.789779 | + | 0.0595332i | ||||
\(327\) | −29.4988 | + | 17.0311i | −1.63129 | + | 0.941824i | ||||
\(328\) | −6.81537 | + | 4.26992i | −0.376316 | + | 0.235767i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.82131 | + | 1.83819i | −0.210356 | + | 0.101189i | ||||
\(331\) | 22.2142 | + | 5.95228i | 1.22100 | + | 0.327167i | 0.811071 | − | 0.584948i | \(-0.198885\pi\) |
0.409934 | + | 0.912115i | \(0.365552\pi\) | |||||||
\(332\) | −12.4010 | − | 5.42342i | −0.680593 | − | 0.297649i | ||||
\(333\) | −7.82866 | + | 2.09768i | −0.429008 | + | 0.114952i | ||||
\(334\) | 3.63505 | − | 0.686141i | 0.198901 | − | 0.0375440i | ||||
\(335\) | 4.75284 | 0.259675 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.6077 | −0.904682 | −0.452341 | − | 0.891845i | \(-0.649411\pi\) | ||||
−0.452341 | + | 0.891845i | \(0.649411\pi\) | |||||||
\(338\) | 15.7181 | − | 2.96691i | 0.854954 | − | 0.161379i | ||||
\(339\) | −26.6738 | + | 7.14723i | −1.44872 | + | 0.388184i | ||||
\(340\) | −4.89370 | + | 11.1897i | −0.265398 | + | 0.606849i | ||||
\(341\) | 6.08423 | + | 1.63026i | 0.329479 | + | 0.0882838i | ||||
\(342\) | −14.3855 | + | 6.91995i | −0.777879 | + | 0.374188i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.28362 | − | 0.524376i | −0.123125 | − | 0.0282725i | ||||
\(345\) | −7.76097 | + | 4.48080i | −0.417837 | + | 0.241238i | ||||
\(346\) | −14.4171 | − | 1.08676i | −0.775070 | − | 0.0584244i | ||||
\(347\) | −4.00465 | − | 14.9456i | −0.214981 | − | 0.802320i | −0.986173 | − | 0.165718i | \(-0.947006\pi\) |
0.771192 | − | 0.636602i | \(-0.219661\pi\) | |||||||
\(348\) | 44.3186 | + | 6.71961i | 2.37572 | + | 0.360209i | ||||
\(349\) | −13.7065 | − | 13.7065i | −0.733694 | − | 0.733694i | 0.237656 | − | 0.971349i | \(-0.423621\pi\) |
−0.971349 | + | 0.237656i | \(0.923621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.1870 | −0.650494 | ||||||||
\(352\) | 2.67538 | − | 6.77317i | 0.142598 | − | 0.361011i | ||||
\(353\) | −1.15032 | + | 1.99241i | −0.0612252 | + | 0.106045i | −0.895013 | − | 0.446039i | \(-0.852834\pi\) |
0.833788 | + | 0.552085i | \(0.186167\pi\) | |||||||
\(354\) | −29.9317 | + | 25.7355i | −1.59085 | + | 1.36783i | ||||
\(355\) | 0.398584 | − | 1.48754i | 0.0211547 | − | 0.0789503i | ||||
\(356\) | −2.65253 | + | 3.32020i | −0.140584 | + | 0.175970i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.57907 | − | 19.9134i | −0.506270 | − | 1.05246i | ||||
\(359\) | 6.28570 | − | 3.62905i | 0.331747 | − | 0.191534i | −0.324870 | − | 0.945759i | \(-0.605320\pi\) |
0.656616 | + | 0.754225i | \(0.271987\pi\) | |||||||
\(360\) | −9.76090 | − | 9.08066i | −0.514445 | − | 0.478593i | ||||
\(361\) | 13.4959 | + | 7.79186i | 0.710310 | + | 0.410098i | ||||
\(362\) | −21.2563 | − | 14.5059i | −1.11721 | − | 0.762415i | ||||
\(363\) | −19.9364 | + | 19.9364i | −1.04639 | + | 1.04639i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.21737 | + | 4.21737i | 0.220747 | + | 0.220747i | ||||
\(366\) | −27.7303 | + | 5.23428i | −1.44948 | + | 0.273600i | ||||
\(367\) | 13.4406 | − | 23.2797i | 0.701591 | − | 1.21519i | −0.266316 | − | 0.963886i | \(-0.585807\pi\) |
0.967908 | − | 0.251306i | \(-0.0808601\pi\) | |||||||
\(368\) | 4.56211 | − | 14.6987i | 0.237817 | − | 0.766220i | ||||
\(369\) | −8.68255 | − | 15.0386i | −0.451995 | − | 0.782879i | ||||
\(370\) | 0.479024 | − | 1.36705i | 0.0249033 | − | 0.0710697i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.28077 | + | 29.3484i | 0.170100 | + | 1.52164i | ||||
\(373\) | 1.29586 | + | 0.347226i | 0.0670973 | + | 0.0179787i | 0.292212 | − | 0.956354i | \(-0.405609\pi\) |
−0.225114 | + | 0.974332i | \(0.572276\pi\) | |||||||
\(374\) | 1.08274 | − | 14.3639i | 0.0559873 | − | 0.742738i | ||||
\(375\) | 18.9694 | + | 10.9520i | 0.979578 | + | 0.565559i | ||||
\(376\) | 7.58105 | − | 14.2986i | 0.390963 | − | 0.737393i | ||||
\(377\) | 9.65295i | 0.497152i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3095 | + | 15.3095i | −0.786396 | + | 0.786396i | −0.980901 | − | 0.194506i | \(-0.937690\pi\) |
0.194506 | + | 0.980901i | \(0.437690\pi\) | |||||||
\(380\) | 0.427698 | − | 2.82084i | 0.0219404 | − | 0.144706i | ||||
\(381\) | −50.8021 | + | 13.6124i | −2.60267 | + | 0.697384i | ||||
\(382\) | −0.545812 | + | 0.469294i | −0.0279262 | + | 0.0240112i | ||||
\(383\) | 4.04897 | + | 7.01302i | 0.206893 | + | 0.358348i | 0.950734 | − | 0.310008i | \(-0.100332\pi\) |
−0.743842 | + | 0.668356i | \(0.766998\pi\) | |||||||
\(384\) | 34.1422 | + | 0.104547i | 1.74231 | + | 0.00533513i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.44415 | − | 2.25807i | −0.327998 | − | 0.114933i | ||||
\(387\) | 1.30938 | − | 4.88668i | 0.0665596 | − | 0.248404i | ||||
\(388\) | −16.7980 | + | 6.57577i | −0.852789 | + | 0.333834i | ||||
\(389\) | −4.79714 | − | 17.9032i | −0.243225 | − | 0.907727i | −0.974267 | − | 0.225395i | \(-0.927633\pi\) |
0.731043 | − | 0.682332i | \(-0.239034\pi\) | |||||||
\(390\) | 2.41326 | − | 3.53627i | 0.122200 | − | 0.179066i | ||||
\(391\) | − | 30.4422i | − | 1.53953i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 31.6652i | − | 1.59730i | ||||||
\(394\) | 4.99953 | + | 3.41183i | 0.251873 | + | 0.171885i | ||||
\(395\) | −1.85127 | − | 6.90902i | −0.0931473 | − | 0.347631i | ||||
\(396\) | 14.4065 | + | 6.30050i | 0.723953 | + | 0.316612i | ||||
\(397\) | 4.35104 | − | 16.2383i | 0.218372 | − | 0.814977i | −0.766580 | − | 0.642149i | \(-0.778043\pi\) |
0.984952 | − | 0.172828i | \(-0.0552904\pi\) | |||||||
\(398\) | −3.54267 | + | 10.1102i | −0.177578 | + | 0.506778i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.1824 | + | 3.89015i | −0.859120 | + | 0.194508i | ||||
\(401\) | −2.18786 | − | 3.78949i | −0.109257 | − | 0.189238i | 0.806213 | − | 0.591626i | \(-0.201514\pi\) |
−0.915469 | + | 0.402388i | \(0.868180\pi\) | |||||||
\(402\) | −17.1344 | − | 19.9281i | −0.854585 | − | 0.993924i | ||||
\(403\) | −6.14276 | + | 1.64595i | −0.305993 | + | 0.0819905i | ||||
\(404\) | −5.91891 | − | 8.03454i | −0.294477 | − | 0.399734i | ||||
\(405\) | 5.44385 | − | 5.44385i | 0.270507 | − | 0.270507i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70848i | 0.0846864i | ||||||||
\(408\) | 64.5595 | − | 19.8212i | 3.19617 | − | 0.981297i | ||||
\(409\) | 0.103105 | + | 0.0595279i | 0.00509823 | + | 0.00294347i | 0.502547 | − | 0.864550i | \(-0.332396\pi\) |
−0.497449 | + | 0.867493i | \(0.665730\pi\) | |||||||
\(410\) | 3.09483 | + | 0.233287i | 0.152843 | + | 0.0115212i | ||||
\(411\) | 17.6422 | + | 4.72721i | 0.870225 | + | 0.233176i | ||||
\(412\) | −14.6344 | + | 18.3180i | −0.720985 | + | 0.902465i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 31.3609 | + | 10.9890i | 1.54130 | + | 0.540082i | ||||
\(415\) | 2.61161 | + | 4.52344i | 0.128199 | + | 0.222047i | ||||
\(416\) | 1.07992 | + | 7.27273i | 0.0529476 | + | 0.356575i | ||||
\(417\) | −9.60906 | + | 16.6434i | −0.470558 | + | 0.815030i | ||||
\(418\) | 0.624156 | + | 3.30666i | 0.0305284 | + | 0.161734i | ||||
\(419\) | −21.5456 | − | 21.5456i | −1.05257 | − | 1.05257i | −0.998539 | − | 0.0540333i | \(-0.982792\pi\) |
−0.0540333 | − | 0.998539i | \(-0.517208\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.254915 | + | 0.254915i | −0.0124238 | + | 0.0124238i | −0.713291 | − | 0.700868i | \(-0.752796\pi\) |
0.700868 | + | 0.713291i | \(0.252796\pi\) | |||||||
\(422\) | −7.45113 | + | 10.9185i | −0.362716 | + | 0.531506i | ||||
\(423\) | 30.2624 | + | 17.4720i | 1.47141 | + | 0.849519i | ||||
\(424\) | 18.9772 | − | 20.3988i | 0.921613 | − | 0.990652i | ||||
\(425\) | −30.1784 | + | 17.4235i | −1.46387 | + | 0.845164i | ||||
\(426\) | −7.67400 | + | 3.69147i | −0.371807 | + | 0.178852i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.3459 | + | 1.60369i | −0.693437 | + | 0.0775173i | ||||
\(429\) | −1.30690 | + | 4.87743i | −0.0630979 | + | 0.235484i | ||||
\(430\) | 0.589492 | + | 0.685609i | 0.0284278 | + | 0.0330630i | ||||
\(431\) | −12.1470 | + | 21.0393i | −0.585101 | + | 1.01343i | 0.409762 | + | 0.912193i | \(0.365612\pi\) |
−0.994863 | + | 0.101232i | \(0.967721\pi\) | |||||||
\(432\) | −1.46797 | + | 37.4771i | −0.0706276 | + | 1.80312i | ||||
\(433\) | −19.6797 | −0.945744 | −0.472872 | − | 0.881131i | \(-0.656783\pi\) | ||||
−0.472872 | + | 0.881131i | \(0.656783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2316 | − | 12.2316i | −0.586461 | − | 0.586461i | ||||
\(436\) | −18.1750 | + | 13.3892i | −0.870423 | + | 0.641226i | ||||
\(437\) | 1.84061 | + | 6.86925i | 0.0880483 | + | 0.328601i | ||||
\(438\) | 2.47900 | − | 32.8869i | 0.118451 | − | 1.57140i | ||||
\(439\) | 26.3901 | − | 15.2363i | 1.25953 | − | 0.727190i | 0.286548 | − | 0.958066i | \(-0.407492\pi\) |
0.972983 | + | 0.230876i | \(0.0741590\pi\) | |||||||
\(440\) | −2.38151 | + | 1.49204i | −0.113534 | + | 0.0711304i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.30433 | + | 13.1057i | 0.299866 | + | 0.623376i | ||||
\(443\) | 3.77526 | + | 1.01158i | 0.179368 | + | 0.0480615i | 0.347385 | − | 0.937723i | \(-0.387070\pi\) |
−0.168017 | + | 0.985784i | \(0.553736\pi\) | |||||||
\(444\) | −7.45882 | + | 2.91984i | −0.353980 | + | 0.138570i | ||||
\(445\) | 1.58408 | − | 0.424452i | 0.0750924 | − | 0.0201209i | ||||
\(446\) | 5.36114 | + | 28.4023i | 0.253857 | + | 1.34489i | ||||
\(447\) | 45.8004 | 2.16628 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.0210 | 1.79432 | 0.897161 | − | 0.441704i | \(-0.145626\pi\) | ||||
0.897161 | + | 0.441704i | \(0.145626\pi\) | |||||||
\(450\) | −7.05549 | − | 37.3787i | −0.332599 | − | 1.76205i | ||||
\(451\) | −3.53581 | + | 0.947417i | −0.166495 | + | 0.0446121i | ||||
\(452\) | −17.0421 | + | 6.67131i | −0.801591 | + | 0.313792i | ||||
\(453\) | 43.3404 | + | 11.6130i | 2.03631 | + | 0.545627i | ||||
\(454\) | 7.23222 | + | 15.0347i | 0.339425 | + | 0.705613i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.3694 | + | 8.37607i | −0.626077 | + | 0.392245i | ||||
\(457\) | −15.0844 | + | 8.70896i | −0.705616 | + | 0.407388i | −0.809436 | − | 0.587208i | \(-0.800227\pi\) |
0.103819 | + | 0.994596i | \(0.466894\pi\) | |||||||
\(458\) | 1.44531 | − | 19.1737i | 0.0675347 | − | 0.895929i | ||||
\(459\) | 19.2009 | + | 71.6588i | 0.896223 | + | 3.34475i | ||||
\(460\) | −4.78173 | + | 3.52262i | −0.222949 | + | 0.164243i | ||||
\(461\) | 27.4189 | + | 27.4189i | 1.27703 | + | 1.27703i | 0.942324 | + | 0.334701i | \(0.108635\pi\) |
0.334701 | + | 0.942324i | \(0.391365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.5988 | −1.88679 | −0.943394 | − | 0.331674i | \(-0.892387\pi\) | ||||
−0.943394 | + | 0.331674i | \(0.892387\pi\) | |||||||
\(464\) | 29.6844 | + | 1.16273i | 1.37807 | + | 0.0539784i | ||||
\(465\) | 5.69808 | − | 9.86936i | 0.264242 | − | 0.457681i | ||||
\(466\) | −19.8692 | − | 23.1089i | −0.920422 | − | 1.07050i | ||||
\(467\) | 2.38296 | − | 8.89334i | 0.110270 | − | 0.411535i | −0.888619 | − | 0.458646i | \(-0.848335\pi\) |
0.998890 | + | 0.0471109i | \(0.0150014\pi\) | |||||||
\(468\) | −15.7770 | + | 1.76366i | −0.729291 | + | 0.0815253i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.62813 | + | 2.70733i | −0.259606 | + | 0.124880i | ||||
\(471\) | −29.7248 | + | 17.1616i | −1.36965 | + | 0.790767i | ||||
\(472\) | −17.8192 | + | 19.1540i | −0.820195 | + | 0.881637i | ||||
\(473\) | −0.923566 | − | 0.533221i | −0.0424656 | − | 0.0245175i | ||||
\(474\) | −22.2948 | + | 32.6697i | −1.02403 | + | 1.50057i | ||||
\(475\) | 5.75626 | − | 5.75626i | 0.264115 | − | 0.264115i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 42.5374 | + | 42.5374i | 1.94765 | + | 1.94765i | ||||
\(478\) | 3.80677 | + | 20.1676i | 0.174118 | + | 0.922444i | ||||
\(479\) | −3.73955 | + | 6.47710i | −0.170865 | + | 0.295946i | −0.938722 | − | 0.344674i | \(-0.887989\pi\) |
0.767858 | + | 0.640620i | \(0.221323\pi\) | |||||||
\(480\) | −10.5839 | − | 7.84713i | −0.483089 | − | 0.358171i | ||||
\(481\) | −0.862460 | − | 1.49383i | −0.0393248 | − | 0.0681126i | ||||
\(482\) | −12.2533 | − | 4.29363i | −0.558122 | − | 0.195569i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.6629 | + | 14.5986i | −0.530134 | + | 0.663575i | ||||
\(485\) | 6.72417 | + | 1.80174i | 0.305329 | + | 0.0818126i | ||||
\(486\) | −2.78254 | − | 0.209746i | −0.126218 | − | 0.00951429i | ||||
\(487\) | 17.8451 | + | 10.3029i | 0.808640 | + | 0.466868i | 0.846483 | − | 0.532415i | \(-0.178716\pi\) |
−0.0378436 | + | 0.999284i | \(0.512049\pi\) | |||||||
\(488\) | −17.8787 | + | 5.48916i | −0.809331 | + | 0.248483i | ||||
\(489\) | 30.5154i | 1.37995i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.13401 | − | 1.13401i | 0.0511771 | − | 0.0511771i | −0.681055 | − | 0.732232i | \(-0.738479\pi\) |
0.732232 | + | 0.681055i | \(0.238479\pi\) | |||||||
\(492\) | −10.1790 | − | 13.8173i | −0.458903 | − | 0.622932i | ||||
\(493\) | 56.7587 | − | 15.2085i | 2.55628 | − | 0.684954i | ||||
\(494\) | −2.21497 | − | 2.57612i | −0.0996562 | − | 0.115905i | ||||
\(495\) | −3.03396 | − | 5.25497i | −0.136366 | − | 0.236193i | ||||
\(496\) | 4.32165 | + | 19.0883i | 0.194048 | + | 0.857090i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 9.55121 | − | 27.2575i | 0.428000 | − | 1.22144i | ||||
\(499\) | 8.63159 | − | 32.2136i | 0.386403 | − | 1.44208i | −0.449540 | − | 0.893260i | \(-0.648412\pi\) |
0.835943 | − | 0.548816i | \(-0.184921\pi\) | |||||||
\(500\) | 13.3003 | + | 5.81671i | 0.594806 | + | 0.260131i | ||||
\(501\) | 2.04307 | + | 7.62483i | 0.0912775 | + | 0.340652i | ||||
\(502\) | −15.0930 | − | 10.2999i | −0.673633 | − | 0.459707i | ||||
\(503\) | 20.7931i | 0.927117i | 0.886066 | + | 0.463558i | \(0.153428\pi\) | ||||
−0.886066 | + | 0.463558i | \(0.846572\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.85105i | 0.171370i | ||||||||
\(506\) | 3.94855 | − | 5.78602i | 0.175534 | − | 0.257220i | ||||
\(507\) | 8.83433 | + | 32.9702i | 0.392346 | + | 1.46426i | ||||
\(508\) | −32.4578 | + | 12.7060i | −1.44008 | + | 0.563736i | ||||
\(509\) | 10.3474 | − | 38.6171i | 0.458641 | − | 1.71167i | −0.218515 | − | 0.975834i | \(-0.570121\pi\) |
0.677156 | − | 0.735839i | \(-0.263212\pi\) | |||||||
\(510\) | −24.5952 | − | 8.61831i | −1.08909 | − | 0.381625i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.4949 | − | 2.44492i | 0.994145 | − | 0.108051i | ||||
\(513\) | −8.66534 | − | 15.0088i | −0.382584 | − | 0.662655i | ||||
\(514\) | 10.4125 | − | 8.95273i | 0.459274 | − | 0.394888i | ||||
\(515\) | 8.73958 | − | 2.34176i | 0.385112 | − | 0.103190i | ||||
\(516\) | 0.749514 | − | 4.94335i | 0.0329955 | − | 0.217619i | ||||
\(517\) | 5.20866 | − | 5.20866i | 0.229076 | − | 0.229076i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 30.8520i | − | 1.35425i | ||||||
\(520\) | 1.32909 | − | 2.50679i | 0.0582844 | − | 0.109930i | ||||
\(521\) | 16.0339 | + | 9.25715i | 0.702456 | + | 0.405563i | 0.808262 | − | 0.588824i | \(-0.200409\pi\) |
−0.105805 | + | 0.994387i | \(0.533742\pi\) | |||||||
\(522\) | −4.82139 | + | 63.9615i | −0.211027 | + | 2.79952i | ||||
\(523\) | −35.2333 | − | 9.44073i | −1.54064 | − | 0.412814i | −0.614170 | − | 0.789174i | \(-0.710509\pi\) |
−0.926474 | + | 0.376360i | \(0.877176\pi\) | |||||||
\(524\) | −2.33141 | − | 20.8558i | −0.101848 | − | 0.911090i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.99052 | + | 14.2421i | −0.217597 | + | 0.620985i | ||||
\(527\) | 19.3561 | + | 33.5258i | 0.843167 | + | 1.46041i | ||||
\(528\) | 14.8415 | + | 4.60645i | 0.645893 | + | 0.200470i | ||||
\(529\) | −4.09802 | + | 7.09799i | −0.178175 | + | 0.308608i | ||||
\(530\) | −10.5651 | + | 1.99424i | −0.458919 | + | 0.0866242i | ||||
\(531\) | −39.9418 | − | 39.9418i | −1.73333 | − | 1.73333i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.61329 | − | 2.61329i | 0.113194 | − | 0.113194i | ||||
\(534\) | −7.49040 | − | 5.11167i | −0.324141 | − | 0.221204i | ||||
\(535\) | 4.82429 | + | 2.78531i | 0.208572 | + | 0.120419i | ||||
\(536\) | −12.7525 | − | 11.8638i | −0.550825 | − | 0.512438i | ||||
\(537\) | 40.8366 | − | 23.5770i | 1.76223 | − | 1.01742i | ||||
\(538\) | −4.64475 | − | 9.65574i | −0.200250 | − | 0.416288i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.03404 | − | 11.3080i | 0.388763 | − | 0.486619i | ||||
\(541\) | 0.613332 | − | 2.28899i | 0.0263692 | − | 0.0984112i | −0.951487 | − | 0.307689i | \(-0.900444\pi\) |
0.977856 | + | 0.209277i | \(0.0671112\pi\) | |||||||
\(542\) | 12.0583 | − | 10.3678i | 0.517948 | − | 0.445336i | ||||
\(543\) | 27.4572 | − | 47.5573i | 1.17830 | − | 2.04088i | ||||
\(544\) | 41.0617 | − | 17.8082i | 1.76051 | − | 0.763522i | ||||
\(545\) | 8.71148 | 0.373159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.8419 | − | 15.8419i | −0.677351 | − | 0.677351i | 0.282049 | − | 0.959400i | \(-0.408986\pi\) |
−0.959400 | + | 0.282049i | \(0.908986\pi\) | |||||||
\(548\) | 11.9678 | + | 1.81456i | 0.511239 | + | 0.0775143i | ||||
\(549\) | −10.4515 | − | 39.0057i | −0.446061 | − | 1.66472i | ||||
\(550\) | −7.99582 | − | 0.602722i | −0.340943 | − | 0.0257001i | ||||
\(551\) | −11.8880 | + | 6.86355i | −0.506446 | + | 0.292397i | ||||
\(552\) | 32.0085 | + | 7.34993i | 1.36237 | + | 0.312834i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27.1161 | + | 13.0438i | −1.15205 | + | 0.554179i | ||||
\(555\) | 2.98574 | + | 0.800026i | 0.126737 | + | 0.0339592i | ||||
\(556\) | −5.10345 | + | 11.6694i | −0.216435 | + | 0.494892i | ||||
\(557\) | 42.9377 | − | 11.5051i | 1.81933 | − | 0.487488i | 0.822622 | − | 0.568588i | \(-0.192510\pi\) |
0.996706 | + | 0.0811008i | \(0.0258436\pi\) | |||||||
\(558\) | −41.5247 | + | 7.83809i | −1.75788 | + | 0.331813i | ||||
\(559\) | 1.07670 | 0.0455397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.7380 | 1.29776 | ||||||||
\(562\) | −27.9287 | + | 5.27175i | −1.17810 | + | 0.222375i | ||||
\(563\) | −5.19184 | + | 1.39115i | −0.218810 | + | 0.0586299i | −0.366558 | − | 0.930395i | \(-0.619464\pi\) |
0.147749 | + | 0.989025i | \(0.452797\pi\) | |||||||
\(564\) | 31.6414 | + | 13.8380i | 1.33234 | + | 0.582684i | ||||
\(565\) | 6.82187 | + | 1.82791i | 0.286998 | + | 0.0769009i | ||||
\(566\) | 26.0728 | − | 12.5419i | 1.09592 | − | 0.527177i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.78257 | + | 2.99634i | −0.200672 | + | 0.125724i | ||||
\(569\) | 4.37176 | − | 2.52404i | 0.183274 | − | 0.105813i | −0.405556 | − | 0.914070i | \(-0.632922\pi\) |
0.588830 | + | 0.808257i | \(0.299589\pi\) | |||||||
\(570\) | 6.07097 | + | 0.457627i | 0.254285 | + | 0.0191679i | ||||
\(571\) | −9.72141 | − | 36.2808i | −0.406828 | − | 1.51830i | −0.800658 | − | 0.599121i | \(-0.795517\pi\) |
0.393830 | − | 0.919183i | \(-0.371150\pi\) | |||||||
\(572\) | −0.501662 | + | 3.30866i | −0.0209755 | + | 0.138342i | ||||
\(573\) | −1.08614 | − | 1.08614i | −0.0453742 | − | 0.0453742i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9460 | −0.706697 | ||||||||
\(576\) | 3.52317 | + | 48.7293i | 0.146799 | + | 2.03039i | ||||
\(577\) | −9.36395 | + | 16.2188i | −0.389826 | + | 0.675199i | −0.992426 | − | 0.122845i | \(-0.960798\pi\) |
0.602599 | + | 0.798044i | \(0.294132\pi\) | |||||||
\(578\) | 48.8985 | − | 42.0434i | 2.03391 | − | 1.74877i | ||||
\(579\) | 3.77124 | − | 14.0745i | 0.156727 | − | 0.584914i | ||||
\(580\) | −8.95672 | − | 7.15558i | −0.371908 | − | 0.297119i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −16.6867 | − | 34.6891i | −0.691686 | − | 1.43791i | ||||
\(583\) | 10.9821 | − | 6.34050i | 0.454831 | − | 0.262597i | ||||
\(584\) | −0.788602 | − | 21.8430i | −0.0326326 | − | 0.903868i | ||||
\(585\) | 5.30553 | + | 3.06315i | 0.219356 | + | 0.126646i | ||||
\(586\) | 17.2415 | + | 11.7661i | 0.712239 | + | 0.486053i | ||||
\(587\) | −5.57210 | + | 5.57210i | −0.229985 | + | 0.229985i | −0.812686 | − | 0.582701i | \(-0.801996\pi\) |
0.582701 | + | 0.812686i | \(0.301996\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.39475 | − | 6.39475i | −0.263491 | − | 0.263491i | ||||
\(590\) | 9.92043 | − | 1.87255i | 0.408418 | − | 0.0770918i | ||||
\(591\) | −6.45799 | + | 11.1856i | −0.265646 | + | 0.460113i | ||||
\(592\) | −4.69765 | + | 2.47228i | −0.193072 | + | 0.101610i | ||||
\(593\) | 6.09225 | + | 10.5521i | 0.250179 | + | 0.433322i | 0.963575 | − | 0.267439i | \(-0.0861773\pi\) |
−0.713396 | + | 0.700761i | \(0.752844\pi\) | |||||||
\(594\) | −5.64518 | + | 16.1104i | −0.231624 | + | 0.661017i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.1657 | − | 3.37213i | 1.23563 | − | 0.138128i | ||||
\(597\) | −22.0813 | − | 5.91667i | −0.903728 | − | 0.242153i | ||||
\(598\) | −0.531600 | + | 7.05231i | −0.0217387 | + | 0.288391i | ||||
\(599\) | 16.2977 | + | 9.40947i | 0.665905 | + | 0.384461i | 0.794523 | − | 0.607234i | \(-0.207721\pi\) |
−0.128618 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(600\) | −11.0337 | − | 35.9378i | −0.450450 | − | 1.46716i | ||||
\(601\) | − | 11.3877i | − | 0.464514i | −0.972654 | − | 0.232257i | \(-0.925389\pi\) | ||
0.972654 | − | 0.232257i | \(-0.0746111\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.5927 | − | 26.5927i | 1.08294 | − | 1.08294i | ||||
\(604\) | 29.4005 | + | 4.45772i | 1.19629 | + | 0.181382i | ||||
\(605\) | 6.96504 | − | 1.86628i | 0.283169 | − | 0.0758750i | ||||
\(606\) | 16.1470 | − | 13.8834i | 0.655929 | − | 0.563973i | ||||
\(607\) | 16.9140 | + | 29.2959i | 0.686519 | + | 1.18909i | 0.972957 | + | 0.230986i | \(0.0741953\pi\) |
−0.286438 | + | 0.958099i | \(0.592471\pi\) | |||||||
\(608\) | −8.18881 | + | 6.50111i | −0.332100 | + | 0.263655i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.81124 | + | 2.38670i | 0.275779 | + | 0.0966346i | ||||
\(611\) | −1.92484 | + | 7.18361i | −0.0778708 | + | 0.290618i | ||||
\(612\) | 35.2272 | + | 89.9889i | 1.42398 | + | 3.63759i | ||||
\(613\) | −0.444885 | − | 1.66033i | −0.0179687 | − | 0.0670602i | 0.956359 | − | 0.292193i | \(-0.0943850\pi\) |
−0.974328 | + | 0.225133i | \(0.927718\pi\) | |||||||
\(614\) | 5.32902 | − | 7.80890i | 0.215062 | − | 0.315142i | ||||
\(615\) | 6.62280i | 0.267057i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.15102i | 0.328148i | 0.986448 | + | 0.164074i | \(0.0524636\pi\) | ||||
−0.986448 | + | 0.164074i | \(0.947536\pi\) | |||||||
\(618\) | −41.3256 | − | 28.2018i | −1.66236 | − | 1.13444i | ||||
\(619\) | 8.73907 | + | 32.6147i | 0.351253 | + | 1.31089i | 0.885135 | + | 0.465335i | \(0.154066\pi\) |
−0.533882 | + | 0.845559i | \(0.679267\pi\) | |||||||
\(620\) | 3.02630 | − | 6.91983i | 0.121539 | − | 0.277907i | ||||
\(621\) | −9.33736 | + | 34.8475i | −0.374695 | + | 1.39838i | ||||
\(622\) | −2.60658 | + | 7.43874i | −0.104514 | + | 0.298266i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.3022 | + | 3.46446i | −0.612576 | + | 0.138689i | ||||
\(625\) | 8.20980 | + | 14.2198i | 0.328392 | + | 0.568792i | ||||
\(626\) | −10.9050 | − | 12.6830i | −0.435850 | − | 0.506915i | ||||
\(627\) | −6.93601 | + | 1.85850i | −0.276997 | + | 0.0742212i | ||||
\(628\) | −18.3142 | + | 13.4918i | −0.730818 | + | 0.538381i | ||||
\(629\) | −7.42477 | + | 7.42477i | −0.296045 | + | 0.296045i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 24.8235i | − | 0.988206i | −0.869403 | − | 0.494103i | \(-0.835496\pi\) | ||
0.869403 | − | 0.494103i | \(-0.164504\pi\) | |||||||
\(632\) | −12.2787 | + | 23.1589i | −0.488422 | + | 0.921211i | ||||
\(633\) | −24.4283 | − | 14.1037i | −0.970938 | − | 0.560571i | ||||
\(634\) | −6.37786 | − | 0.480760i | −0.253297 | − | 0.0190934i | ||||
\(635\) | 12.9927 | + | 3.48139i | 0.515600 | + | 0.138155i | ||||
\(636\) | 46.4497 | + | 37.1089i | 1.84185 | + | 1.47146i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.7605 | + | 4.47137i | 0.505194 | + | 0.177023i | ||||
\(639\) | −6.09283 | − | 10.5531i | −0.241029 | − | 0.417474i | ||||
\(640\) | −7.54871 | − | 4.38912i | −0.298389 | − | 0.173495i | ||||
\(641\) | −15.4186 | + | 26.7058i | −0.608998 | + | 1.05482i | 0.382408 | + | 0.923994i | \(0.375095\pi\) |
−0.991406 | + | 0.130822i | \(0.958238\pi\) | |||||||
\(642\) | −5.71349 | − | 30.2690i | −0.225493 | − | 1.19462i | ||||
\(643\) | −7.86848 | − | 7.86848i | −0.310302 | − | 0.310302i | 0.534724 | − | 0.845027i | \(-0.320416\pi\) |
−0.845027 | + | 0.534724i | \(0.820416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.36433 | + | 1.36433i | −0.0537204 | + | 0.0537204i | ||||
\(646\) | −11.6577 | + | 17.0826i | −0.458666 | + | 0.672107i | ||||
\(647\) | −33.1866 | − | 19.1603i | −1.30470 | − | 0.753268i | −0.323492 | − | 0.946231i | \(-0.604857\pi\) |
−0.981206 | + | 0.192963i | \(0.938190\pi\) | |||||||
\(648\) | −28.1952 | + | 1.01794i | −1.10761 | + | 0.0399885i | ||||
\(649\) | −10.3120 | + | 5.95361i | −0.404780 | + | 0.233700i | ||||
\(650\) | 7.29546 | − | 3.50938i | 0.286152 | − | 0.137649i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.24675 | + | 20.0985i | 0.0879894 | + | 0.787116i | ||||
\(653\) | −3.62018 | + | 13.5107i | −0.141669 | + | 0.528714i | 0.858213 | + | 0.513294i | \(0.171575\pi\) |
−0.999881 | + | 0.0154198i | \(0.995092\pi\) | |||||||
\(654\) | −31.4056 | − | 36.5262i | −1.22805 | − | 1.42829i | ||||
\(655\) | −4.04922 | + | 7.01345i | −0.158216 | + | 0.274038i | ||||
\(656\) | −7.72153 | − | 8.35109i | −0.301475 | − | 0.326055i | ||||
\(657\) | 47.1935 | 1.84119 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0981 | − | 18.0981i | −0.705003 | − | 0.705003i | 0.260477 | − | 0.965480i | \(-0.416120\pi\) |
−0.965480 | + | 0.260477i | \(0.916120\pi\) | |||||||
\(660\) | −3.55685 | − | 4.82820i | −0.138450 | − | 0.187938i | ||||
\(661\) | −7.80014 | − | 29.1105i | −0.303390 | − | 1.13227i | −0.934322 | − | 0.356430i | \(-0.883994\pi\) |
0.630932 | − | 0.775838i | \(-0.282673\pi\) | |||||||
\(662\) | −2.44470 | + | 32.4319i | −0.0950160 | + | 1.26050i | ||||
\(663\) | −26.8760 | + | 15.5169i | −1.04378 | + | 0.602625i | ||||
\(664\) | 4.28387 | − | 18.6560i | 0.166246 | − | 0.723992i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.96863 | − | 10.3290i | −0.192531 | − | 0.400242i | ||||
\(667\) | 27.6016 | + | 7.39583i | 1.06874 | + | 0.286368i | ||||
\(668\) | 1.90702 | + | 4.87155i | 0.0737850 | + | 0.188486i | ||||
\(669\) | −59.5763 | + | 15.9634i | −2.30335 | + | 0.617182i | ||||
\(670\) | 1.24672 | + | 6.60490i | 0.0481650 | + | 0.255169i | ||||
\(671\) | −8.51239 | −0.328617 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9832 | −0.423371 | −0.211686 | − | 0.977338i | \(-0.567895\pi\) | ||||
−0.211686 | + | 0.977338i | \(0.567895\pi\) | |||||||
\(674\) | −4.35639 | − | 23.0793i | −0.167802 | − | 0.888983i | ||||
\(675\) | 39.8898 | − | 10.6884i | 1.53536 | − | 0.411398i | ||||
\(676\) | 8.24607 | + | 21.0648i | 0.317157 | + | 0.810185i | ||||
\(677\) | −42.5236 | − | 11.3942i | −1.63431 | − | 0.437913i | −0.679153 | − | 0.733997i | \(-0.737653\pi\) |
−0.955162 | + | 0.296084i | \(0.904319\pi\) | |||||||
\(678\) | −16.9291 | − | 35.1931i | −0.650160 | − | 1.35158i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16.8338 | − | 3.86545i | −0.645546 | − | 0.148233i | ||||
\(681\) | −30.8317 | + | 17.8007i | −1.18147 | + | 0.682125i | ||||
\(682\) | −0.669576 | + | 8.88273i | −0.0256394 | + | 0.340137i | ||||
\(683\) | −6.60660 | − | 24.6562i | −0.252794 | − | 0.943441i | −0.969304 | − | 0.245864i | \(-0.920928\pi\) |
0.716510 | − | 0.697577i | \(-0.245738\pi\) | |||||||
\(684\) | −13.3899 | − | 18.1760i | −0.511977 | − | 0.694976i | ||||
\(685\) | −3.30302 | − | 3.30302i | −0.126202 | − | 0.126202i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.0309 | 1.56543 | ||||||||
\(688\) | 0.129692 | − | 3.31104i | 0.00494448 | − | 0.126232i | ||||
\(689\) | −6.40150 | + | 11.0877i | −0.243878 | + | 0.422409i | ||||
\(690\) | −8.26263 | − | 9.60985i | −0.314553 | − | 0.365841i | ||||
\(691\) | −11.6155 | + | 43.3496i | −0.441875 | + | 1.64910i | 0.282184 | + | 0.959360i | \(0.408941\pi\) |
−0.724059 | + | 0.689738i | \(0.757726\pi\) | |||||||
\(692\) | −2.27153 | − | 20.3202i | −0.0863507 | − | 0.772457i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.7190 | − | 9.48555i | 0.748523 | − | 0.360066i | ||||
\(695\) | 4.25657 | − | 2.45753i | 0.161461 | − | 0.0932195i | ||||
\(696\) | 2.28718 | + | 63.3510i | 0.0866952 | + | 2.40131i | ||||
\(697\) | −19.4833 | − | 11.2487i | −0.737983 | − | 0.426074i | ||||
\(698\) | 15.4522 | − | 22.6430i | 0.584876 | − | 0.857049i | ||||
\(699\) | 45.9855 | − | 45.9855i | 1.73933 | − | 1.73933i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.8486 | − | 34.8486i | −1.31621 | − | 1.31621i | −0.916748 | − | 0.399466i | \(-0.869196\pi\) |
−0.399466 | − | 0.916748i | \(-0.630804\pi\) | |||||||
\(702\) | −3.19678 | − | 16.9360i | −0.120655 | − | 0.639207i | ||||
\(703\) | 1.22647 | − | 2.12431i | 0.0462573 | − | 0.0801200i | ||||
\(704\) | 10.1143 | + | 1.94123i | 0.381196 | + | 0.0731630i | ||||
\(705\) | −6.66358 | − | 11.5417i | −0.250965 | − | 0.434684i | ||||
\(706\) | −3.07054 | − | 1.07594i | −0.115561 | − | 0.0404934i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −43.6154 | − | 34.8446i | −1.63917 | − | 1.30954i | ||||
\(709\) | 33.8583 | + | 9.07232i | 1.27158 | + | 0.340718i | 0.830635 | − | 0.556818i | \(-0.187978\pi\) |
0.440942 | + | 0.897536i | \(0.354644\pi\) | |||||||
\(710\) | 2.17174 | + | 0.163705i | 0.0815041 | + | 0.00614374i | ||||
\(711\) | −49.0149 | − | 28.2988i | −1.83820 | − | 1.06129i | ||||
\(712\) | −5.30979 | − | 2.81523i | −0.198993 | − | 0.105505i | ||||
\(713\) | 18.8257i | 0.705027i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.913167 | − | 0.913167i | 0.0341505 | − | 0.0341505i | ||||
\(716\) | 25.1605 | − | 18.5353i | 0.940291 | − | 0.692696i | ||||
\(717\) | −42.3033 | + | 11.3351i | −1.57984 | + | 0.423318i | ||||
\(718\) | 6.69200 | + | 7.78313i | 0.249743 | + | 0.290464i | ||||
\(719\) | 19.3564 | + | 33.5263i | 0.721872 | + | 1.25032i | 0.960249 | + | 0.279146i | \(0.0900514\pi\) |
−0.238377 | + | 0.971173i | \(0.576615\pi\) | |||||||
\(720\) | 10.0588 | − | 15.9464i | 0.374868 | − | 0.594288i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.28802 | + | 20.7988i | −0.271232 | + | 0.774051i | ||||
\(723\) | 7.17086 | − | 26.7620i | 0.266687 | − | 0.995290i | ||||
\(724\) | 14.5828 | − | 33.3444i | 0.541964 | − | 1.23924i | ||||
\(725\) | −8.46597 | − | 31.5954i | −0.314418 | − | 1.17342i | ||||
\(726\) | −32.9346 | − | 22.4756i | −1.22232 | − | 0.834146i | ||||
\(727\) | − | 11.1458i | − | 0.413375i | −0.978407 | − | 0.206688i | \(-0.933732\pi\) | ||
0.978407 | − | 0.206688i | \(-0.0662684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.9706i | 0.887798i | ||||||||
\(730\) | −4.75451 | + | 6.96703i | −0.175972 | + | 0.257861i | ||||
\(731\) | −1.69637 | − | 6.33094i | −0.0627425 | − | 0.234158i | ||||
\(732\) | −14.5479 | − | 37.1630i | −0.537706 | − | 1.37358i | ||||
\(733\) | −2.45813 | + | 9.17387i | −0.0907931 | + | 0.338845i | −0.996348 | − | 0.0853844i | \(-0.972788\pi\) |
0.905555 | + | 0.424229i | \(0.139455\pi\) | |||||||
\(734\) | 35.8768 | + | 12.5715i | 1.32424 | + | 0.464021i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.6230 | + | 2.48424i | 0.797035 | + | 0.0915701i | ||||
\(737\) | −3.96384 | − | 6.86557i | −0.146010 | − | 0.252896i | ||||
\(738\) | 18.6212 | − | 16.0107i | 0.685457 | − | 0.589362i | ||||
\(739\) | 31.8880 | − | 8.54437i | 1.17302 | − | 0.314310i | 0.380865 | − | 0.924630i | \(-0.375626\pi\) |
0.792154 | + | 0.610321i | \(0.208959\pi\) | |||||||
\(740\) | 2.02541 | + | 0.307094i | 0.0744556 | + | 0.0112890i | ||||
\(741\) | 5.12636 | − | 5.12636i | 0.188321 | − | 0.188321i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.1538i | 1.69322i | 0.532214 | + | 0.846610i | \(0.321360\pi\) | ||||
−0.532214 | + | 0.846610i | \(0.678640\pi\) | |||||||
\(744\) | −39.9241 | + | 12.2576i | −1.46369 | + | 0.449385i | ||||
\(745\) | −10.1442 | − | 5.85676i | −0.371655 | − | 0.214575i | ||||
\(746\) | −0.142611 | + | 1.89191i | −0.00522137 | + | 0.0692677i | ||||
\(747\) | 39.9215 | + | 10.6969i | 1.46065 | + | 0.391380i | ||||
\(748\) | 20.2451 | − | 2.26314i | 0.740235 | − | 0.0827486i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −10.2438 | + | 29.2342i | −0.374052 | + | 1.06748i | ||||
\(751\) | −8.69900 | − | 15.0671i | −0.317431 | − | 0.549807i | 0.662520 | − | 0.749044i | \(-0.269487\pi\) |
−0.979951 | + | 0.199237i | \(0.936154\pi\) | |||||||
\(752\) | 21.8590 | + | 6.78451i | 0.797114 | + | 0.247405i | ||||
\(753\) | 19.4959 | − | 33.7679i | 0.710470 | − | 1.23057i | ||||
\(754\) | −13.4144 | + | 2.53207i | −0.488525 | + | 0.0922127i | ||||
\(755\) | −8.11432 | − | 8.11432i | −0.295310 | − | 0.295310i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.24720 | − | 3.24720i | 0.118021 | − | 0.118021i | −0.645629 | − | 0.763651i | \(-0.723405\pi\) |
0.763651 | + | 0.645629i | \(0.223405\pi\) | |||||||
\(758\) | −25.2910 | − | 17.2594i | −0.918612 | − | 0.626888i | ||||
\(759\) | 12.9452 | + | 7.47391i | 0.469881 | + | 0.271286i | ||||
\(760\) | 4.03224 | − | 0.145577i | 0.146265 | − | 0.00528063i | ||||
\(761\) | −7.91882 | + | 4.57193i | −0.287057 | + | 0.165732i | −0.636614 | − | 0.771183i | \(-0.719665\pi\) |
0.349557 | + | 0.936915i | \(0.386332\pi\) | |||||||
\(762\) | −32.2427 | − | 67.0277i | −1.16803 | − | 2.42816i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.795338 | − | 0.635400i | −0.0287743 | − | 0.0229880i | ||||
\(765\) | 9.65212 | − | 36.0222i | 0.348973 | − | 1.30239i | ||||
\(766\) | −8.68372 | + | 7.46633i | −0.313755 | + | 0.269770i | ||||
\(767\) | 6.01089 | − | 10.4112i | 0.217041 | − | 0.375925i | ||||
\(768\) | 8.81060 | + | 47.4740i | 0.317925 | + | 1.71307i | ||||
\(769\) | −26.8105 | −0.966812 | −0.483406 | − | 0.875396i | \(-0.660600\pi\) | ||||
−0.483406 | + | 0.875396i | \(0.660600\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.7203 | + | 20.7203i | 0.746224 | + | 0.746224i | ||||
\(772\) | 1.44761 | − | 9.54758i | 0.0521006 | − | 0.343625i | ||||
\(773\) | −1.37206 | − | 5.12058i | −0.0493494 | − | 0.184175i | 0.936851 | − | 0.349727i | \(-0.113726\pi\) |
−0.986201 | + | 0.165553i | \(0.947059\pi\) | |||||||
\(774\) | 7.13435 | + | 0.537784i | 0.256439 | + | 0.0193303i | ||||
\(775\) | 18.6626 | − | 10.7748i | 0.670379 | − | 0.387043i | ||||
\(776\) | −13.5445 | − | 21.6188i | −0.486218 | − | 0.776071i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.6212 | − | 11.3627i | 0.846862 | − | 0.407371i | ||||
\(779\) | 5.07651 | + | 1.36025i | 0.181885 | + | 0.0487359i | ||||
\(780\) | 5.54729 | + | 2.42604i | 0.198625 | + | 0.0868660i | ||||
\(781\) | −2.48119 | + | 0.664833i | −0.0887840 | + | 0.0237896i | ||||
\(782\) | 42.3047 | − | 7.98532i | 1.51281 | − | 0.285554i | ||||
\(783\) | −69.6371 | −2.48863 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.77824 | 0.313309 | ||||||||
\(786\) | 44.0044 | − | 8.30614i | 1.56958 | − | 0.296270i | ||||
\(787\) | 37.5883 | − | 10.0718i | 1.33988 | − | 0.359020i | 0.483490 | − | 0.875350i | \(-0.339369\pi\) |
0.856389 | + | 0.516331i | \(0.172702\pi\) | |||||||
\(788\) | −3.42990 | + | 7.84268i | −0.122185 | + | 0.279384i | ||||
\(789\) | −31.1057 | − | 8.33474i | −1.10739 | − | 0.296725i | ||||
\(790\) | 9.11568 | − | 4.38497i | 0.324321 | − | 0.156010i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.97666 | + | 21.6730i | −0.176838 | + | 0.770117i | ||||
\(793\) | 7.44287 | − | 4.29714i | 0.264304 | − | 0.152596i | ||||
\(794\) | 23.7073 | + | 1.78704i | 0.841339 | + | 0.0634198i | ||||
\(795\) | −5.93809 | − | 22.1612i | −0.210602 | − | 0.785978i | ||||
\(796\) | −14.9791 | − | 2.27115i | −0.530921 | − | 0.0804986i | ||||
\(797\) | −4.08133 | − | 4.08133i | −0.144568 | − | 0.144568i | 0.631118 | − | 0.775686i | \(-0.282596\pi\) |
−0.775686 | + | 0.631118i | \(0.782596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.2718 | 1.60160 | ||||||||
\(800\) | −9.91317 | − | 22.8575i | −0.350484 | − | 0.808135i | ||||
\(801\) | 6.48824 | − | 11.2380i | 0.229251 | − | 0.397074i | ||||
\(802\) | 4.69225 | − | 4.03444i | 0.165689 | − | 0.142461i | ||||
\(803\) | 2.57481 | − | 9.60933i | 0.0908631 | − | 0.339106i | ||||
\(804\) | 23.1991 | − | 29.0385i | 0.818168 | − | 1.02411i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.89864 | − | 8.10469i | −0.137324 | − | 0.285475i | ||||
\(807\) | 19.8011 | − | 11.4322i | 0.697031 | − | 0.402431i | ||||
\(808\) | 9.61280 | − | 10.3329i | 0.338177 | − | 0.363510i | ||||
\(809\) | −18.4321 | − | 10.6418i | −0.648037 | − | 0.374144i | 0.139667 | − | 0.990199i | \(-0.455397\pi\) |
−0.787704 | + | 0.616054i | \(0.788730\pi\) | |||||||
\(810\) | 8.99316 | + | 6.13719i | 0.315987 | + | 0.215639i | ||||
\(811\) | −12.6569 | + | 12.6569i | −0.444442 | + | 0.444442i | −0.893502 | − | 0.449060i | \(-0.851759\pi\) |
0.449060 | + | 0.893502i | \(0.351759\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.9954 | + | 23.9954i | 0.841556 | + | 0.841556i | ||||
\(814\) | −2.37424 | + | 0.448154i | −0.0832169 | + | 0.0157078i | ||||
\(815\) | 3.90218 | − | 6.75877i | 0.136687 | − | 0.236749i | ||||
\(816\) | 44.4797 | + | 84.5173i | 1.55710 | + | 2.95870i | ||||
\(817\) | 0.765569 | + | 1.32600i | 0.0267839 | + | 0.0463910i | ||||
\(818\) | −0.0556787 | + | 0.158898i | −0.00194676 | + | 0.00555573i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.487615 | + | 4.36200i | 0.0170282 | + | 0.152328i | ||||
\(821\) | −49.6916 | − | 13.3148i | −1.73425 | − | 0.464691i | −0.753094 | − | 0.657912i | \(-0.771440\pi\) |
−0.981155 | + | 0.193222i | \(0.938106\pi\) | |||||||
\(822\) | −1.94154 | + | 25.7569i | −0.0677190 | + | 0.898374i | ||||
\(823\) | −21.8000 | − | 12.5862i | −0.759899 | − | 0.438728i | 0.0693606 | − | 0.997592i | \(-0.477904\pi\) |
−0.829259 | + | 0.558864i | \(0.811237\pi\) | |||||||
\(824\) | −29.2949 | − | 15.5320i | −1.02054 | − | 0.541083i | ||||
\(825\) | − | 17.1107i | − | 0.595718i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.76090 | + | 3.76090i | −0.130779 | + | 0.130779i | −0.769466 | − | 0.638687i | \(-0.779478\pi\) |
0.638687 | + | 0.769466i | \(0.279478\pi\) | |||||||
\(828\) | −7.04489 | + | 46.4639i | −0.244827 | + | 1.61473i | ||||
\(829\) | −4.47469 | + | 1.19899i | −0.155412 | + | 0.0416426i | −0.335686 | − | 0.941974i | \(-0.608968\pi\) |
0.180274 | + | 0.983616i | \(0.442302\pi\) | |||||||
\(830\) | −5.60105 | + | 4.81583i | −0.194415 | + | 0.167160i | ||||
\(831\) | −32.1048 | − | 55.6072i | −1.11370 | − | 1.92899i | ||||
\(832\) | −9.82344 | + | 3.40846i | −0.340566 | + | 0.118167i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −25.6494 | − | 8.98772i | −0.888167 | − | 0.311219i | ||||
\(835\) | 0.522517 | − | 1.95006i | 0.0180825 | − | 0.0674846i | ||||
\(836\) | −4.43145 | + | 1.73475i | −0.153265 | + | 0.0599974i | ||||
\(837\) | −11.8740 | − | 44.3144i | −0.410426 | − | 1.53173i | ||||
\(838\) | 24.2897 | − | 35.5930i | 0.839075 | − | 1.22954i | ||||
\(839\) | − | 31.7342i | − | 1.09559i | −0.836614 | − | 0.547793i | \(-0.815468\pi\) | ||
0.836614 | − | 0.547793i | \(-0.184532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.1574i | 0.901979i | ||||||||
\(842\) | −0.421115 | − | 0.287381i | −0.0145126 | − | 0.00990381i | ||||
\(843\) | −15.6973 | − | 58.5830i | −0.540642 | − | 2.01771i | ||||
\(844\) | −17.1277 | − | 7.49059i | −0.589561 | − | 0.257837i | ||||
\(845\) | 2.25939 | − | 8.43217i | 0.0777255 | − | 0.290075i | ||||
\(846\) | −16.3422 | + | 46.6380i | −0.561858 | + | 1.60345i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 33.3255 | + | 21.0213i | 1.14440 | + | 0.721873i | ||||
\(849\) | 30.8695 | + | 53.4676i | 1.05944 | + | 1.83500i | ||||
\(850\) | −32.1291 | − | 37.3678i | −1.10202 | − | 1.28170i | ||||
\(851\) | −4.93223 | + | 1.32159i | −0.169075 | + | 0.0453035i | ||||
\(852\) | −7.14291 | − | 9.69605i | −0.244712 | − | 0.332181i | ||||
\(853\) | −25.3410 | + | 25.3410i | −0.867661 | + | 0.867661i | −0.992213 | − | 0.124552i | \(-0.960251\pi\) |
0.124552 | + | 0.992213i | \(0.460251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.71197i | 0.297943i | ||||||||
\(856\) | −5.99170 | − | 19.5155i | −0.204792 | − | 0.667027i | ||||
\(857\) | −39.6000 | − | 22.8631i | −1.35271 | − | 0.780987i | −0.364082 | − | 0.931367i | \(-0.618617\pi\) |
−0.988628 | + | 0.150380i | \(0.951950\pi\) | |||||||
\(858\) | −7.12085 | − | 0.536766i | −0.243102 | − | 0.0183249i | ||||
\(859\) | −35.5511 | − | 9.52588i | −1.21299 | − | 0.325019i | −0.405053 | − | 0.914293i | \(-0.632747\pi\) |
−0.807933 | + | 0.589274i | \(0.799414\pi\) | |||||||
\(860\) | −0.798142 | + | 0.999045i | −0.0272164 | + | 0.0340671i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.4240 | − | 11.3616i | −1.10437 | − | 0.386977i | ||||
\(863\) | −2.15212 | − | 3.72758i | −0.0732590 | − | 0.126888i | 0.827069 | − | 0.562101i | \(-0.190007\pi\) |
−0.900328 | + | 0.435212i | \(0.856673\pi\) | |||||||
\(864\) | −52.4660 | + | 7.79066i | −1.78493 | + | 0.265044i | ||||
\(865\) | −3.94522 | + | 6.83333i | −0.134142 | + | 0.232340i | ||||
\(866\) | −5.16219 | − | 27.3483i | −0.175418 | − | 0.929333i | ||||
\(867\) | 97.3057 | + | 97.3057i | 3.30468 | + | 3.30468i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.43627 | + | 8.43627i | −0.286181 | + | 0.286181i | ||||
\(870\) | 13.7895 | − | 20.2064i | 0.467506 | − | 0.685062i | ||||
\(871\) | 6.93162 | + | 4.00197i | 0.234869 | + | 0.135602i | ||||
\(872\) | −23.3741 | − | 21.7451i | −0.791546 | − | 0.736383i | ||||
\(873\) | 47.7035 | − | 27.5416i | 1.61452 | − | 0.932143i | ||||
\(874\) | −9.06320 | + | 4.35973i | −0.306567 | + | 0.147470i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 46.3524 | − | 5.18159i | 1.56610 | − | 0.175070i | ||||
\(877\) | −14.7923 | + | 55.2056i | −0.499500 | + | 1.86416i | 0.00370287 | + | 0.999993i | \(0.498821\pi\) |
−0.503203 | + | 0.864168i | \(0.667845\pi\) | |||||||
\(878\) | 28.0959 | + | 32.6770i | 0.948192 | + | 1.10279i | ||||
\(879\) | −22.2712 | + | 38.5748i | −0.751188 | + | 1.30110i | ||||
\(880\) | −2.69815 | − | 2.91814i | −0.0909546 | − | 0.0983704i | ||||
\(881\) | 46.7407 | 1.57474 | 0.787368 | − | 0.616484i | \(-0.211443\pi\) | ||||
0.787368 | + | 0.616484i | \(0.211443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.66705 | − | 1.66705i | −0.0561007 | − | 0.0561007i | 0.678500 | − | 0.734601i | \(-0.262630\pi\) |
−0.734601 | + | 0.678500i | \(0.762630\pi\) | |||||||
\(884\) | −16.5590 | + | 12.1987i | −0.556939 | + | 0.410288i | ||||
\(885\) | 5.57575 | + | 20.8090i | 0.187427 | + | 0.699486i | ||||
\(886\) | −0.415471 | + | 5.51172i | −0.0139580 | + | 0.185170i | ||||
\(887\) | 14.2716 | − | 8.23972i | 0.479194 | − | 0.276663i | −0.240887 | − | 0.970553i | \(-0.577438\pi\) |
0.720081 | + | 0.693890i | \(0.244105\pi\) | |||||||
\(888\) | −6.01416 | − | 9.59942i | −0.201822 | − | 0.322135i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.00537 | + | 2.09001i | 0.0337001 | + | 0.0700573i | ||||
\(891\) | −12.4039 | − | 3.32361i | −0.415545 | − | 0.111345i | ||||
\(892\) | −38.0637 | + | 14.9005i | −1.27447 | + | 0.498905i | ||||
\(893\) | −10.2155 | + | 2.73725i | −0.341850 | + | 0.0915984i | ||||
\(894\) | 12.0139 | + | 63.6476i | 0.401806 | + | 2.12869i | ||||
\(895\) | −12.0597 | −0.403112 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.0916 | −0.503895 | ||||||||
\(898\) | 9.97332 | + | 52.8368i | 0.332814 | + | 1.76319i | ||||
\(899\) | −35.1000 | + | 9.40503i | −1.17065 | + | 0.313675i | ||||
\(900\) | 50.0934 | − | 19.6097i | 1.66978 | − | 0.653655i | ||||
\(901\) | 75.2808 | + | 20.1714i | 2.50797 | + | 0.672008i | ||||
\(902\) | −2.24408 | − | 4.66510i | −0.0747197 | − | 0.155331i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.7413 | − | 21.9329i | −0.457028 | − | 0.729479i | ||||
\(905\) | −12.1628 | + | 7.02222i | −0.404307 | + | 0.233426i | ||||
\(906\) | −4.76966 | + | 63.2752i | −0.158461 | + | 2.10218i | ||||
\(907\) | −1.14578 | − | 4.27611i | −0.0380450 | − | 0.141986i | 0.944291 | − | 0.329112i | \(-0.106749\pi\) |
−0.982336 | + | 0.187126i | \(0.940083\pi\) | |||||||
\(908\) | −18.9962 | + | 13.9942i | −0.630412 | + | 0.464414i | ||||
\(909\) | 21.5471 | + | 21.5471i | 0.714673 | + | 0.714673i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.42550 | −0.0803605 | −0.0401802 | − | 0.999192i | \(-0.512793\pi\) | ||||
−0.0401802 | + | 0.999192i | \(0.512793\pi\) | |||||||
\(912\) | −15.1469 | − | 16.3819i | −0.501565 | − | 0.542459i | ||||
\(913\) | 4.35613 | − | 7.54503i | 0.144167 | − | 0.249704i | ||||
\(914\) | −16.0594 | − | 18.6779i | −0.531198 | − | 0.617809i | ||||
\(915\) | −3.98607 | + | 14.8762i | −0.131775 | + | 0.491792i | ||||
\(916\) | 27.0243 | − | 3.02097i | 0.892909 | − | 0.0998157i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −94.5458 | + | 45.4799i | −3.12048 | + | 1.50106i | ||||
\(919\) | 35.0592 | − | 20.2414i | 1.15650 | − | 0.667703i | 0.206034 | − | 0.978545i | \(-0.433944\pi\) |
0.950462 | + | 0.310842i | \(0.100611\pi\) | |||||||
\(920\) | −6.14959 | − | 5.72103i | −0.202746 | − | 0.188617i | ||||
\(921\) | 17.4710 | + | 10.0869i | 0.575690 | + | 0.332375i | ||||
\(922\) | −30.9111 | + | 45.2956i | −1.01800 | + | 1.49173i | ||||
\(923\) | 1.83383 | − | 1.83383i | 0.0603613 | − | 0.0603613i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.13309 | + | 4.13309i | 0.135895 | + | 0.135895i | ||||
\(926\) | −10.6495 | − | 56.4191i | −0.349965 | − | 1.85405i | ||||
\(927\) | 35.7966 | − | 62.0015i | 1.17571 | − | 2.03640i | ||||
\(928\) | 6.17074 | + | 41.5567i | 0.202564 | + | 1.36417i | ||||
\(929\) | 13.6726 | + | 23.6816i | 0.448583 | + | 0.776969i | 0.998294 | − | 0.0583859i | \(-0.0185954\pi\) |
−0.549711 | + | 0.835355i | \(0.685262\pi\) | |||||||
\(930\) | 15.2099 | + | 5.32963i | 0.498751 | + | 0.174765i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.9019 | − | 33.6734i | 0.881200 | − | 1.10301i | ||||
\(933\) | −16.2467 | − | 4.35329i | −0.531893 | − | 0.142520i | ||||
\(934\) | 12.9839 | + | 0.978722i | 0.424847 | + | 0.0320248i | ||||
\(935\) | −6.80808 | − | 3.93065i | −0.222648 | − | 0.128546i | ||||
\(936\) | −6.58938 | − | 21.4622i | −0.215381 | − | 0.701515i | ||||
\(937\) | 6.30987i | 0.206135i | 0.994674 | + | 0.103067i | \(0.0328657\pi\) | ||||
−0.994674 | + | 0.103067i | \(0.967134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.2386 | − | 25.2386i | 0.823630 | − | 0.823630i | ||||
\(940\) | −5.23863 | − | 7.11111i | −0.170865 | − | 0.231939i | ||||
\(941\) | −26.3055 | + | 7.04854i | −0.857535 | + | 0.229776i | −0.660690 | − | 0.750659i | \(-0.729736\pi\) |
−0.196845 | + | 0.980435i | \(0.563070\pi\) | |||||||
\(942\) | −31.6462 | − | 36.8062i | −1.03109 | − | 1.19921i | ||||
\(943\) | −5.47021 | − | 9.47467i | −0.178134 | − | 0.308538i | ||||
\(944\) | −31.2920 | − | 19.7386i | −1.01847 | − | 0.642435i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.498742 | − | 1.42333i | 0.0162155 | − | 0.0462763i | ||||
\(947\) | −5.93030 | + | 22.1322i | −0.192709 | + | 0.719200i | 0.800139 | + | 0.599815i | \(0.204759\pi\) |
−0.992848 | + | 0.119385i | \(0.961908\pi\) | |||||||
\(948\) | −51.2484 | − | 22.4128i | −1.66447 | − | 0.727935i | ||||
\(949\) | 2.59958 | + | 9.70178i | 0.0843860 | + | 0.314933i | ||||
\(950\) | 9.50925 | + | 6.48939i | 0.308521 | + | 0.210544i | ||||
\(951\) | − | 13.6483i | − | 0.442577i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.9914i | − | 1.10109i | −0.834806 | − | 0.550545i | \(-0.814420\pi\) | ||
0.834806 | − | 0.550545i | \(-0.185580\pi\) | |||||||
\(954\) | −47.9551 | + | 70.2711i | −1.55260 | + | 2.27511i | ||||
\(955\) | 0.101675 | + | 0.379457i | 0.00329014 | + | 0.0122790i | ||||
\(956\) | −27.0278 | + | 10.5803i | −0.874141 | + | 0.342193i | ||||
\(957\) | −7.46771 | + | 27.8699i | −0.241397 | + | 0.900905i | ||||
\(958\) | −9.98197 | − | 3.49775i | −0.322503 | − | 0.113007i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.12866 | − | 16.7666i | 0.262351 | − | 0.541140i | ||||
\(961\) | 3.53001 | + | 6.11416i | 0.113871 | + | 0.197231i | ||||
\(962\) | 1.84970 | − | 1.59039i | 0.0596366 | − | 0.0512761i | ||||
\(963\) | 42.5767 | − | 11.4084i | 1.37201 | − | 0.367630i | ||||
\(964\) | 2.75257 | − | 18.1543i | 0.0886544 | − | 0.584712i | ||||
\(965\) | −2.63506 | + | 2.63506i | −0.0848257 | + | 0.0848257i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.2769i | − | 1.61680i | −0.588635 | − | 0.808399i | \(-0.700335\pi\) | ||
0.588635 | − | 0.808399i | \(-0.299665\pi\) | |||||||
\(968\) | −23.3467 | − | 12.3783i | −0.750390 | − | 0.397854i | ||||
\(969\) | −38.2194 | − | 22.0660i | −1.22778 | − | 0.708861i | ||||
\(970\) | −0.740002 | + | 9.81702i | −0.0237600 | + | 0.315205i | ||||
\(971\) | 30.0778 | + | 8.05932i | 0.965243 | + | 0.258636i | 0.706818 | − | 0.707395i | \(-0.250130\pi\) |
0.258425 | + | 0.966031i | \(0.416797\pi\) | |||||||
\(972\) | −0.438411 | − | 3.92184i | −0.0140620 | − | 0.125793i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.63668 | + | 27.5015i | −0.308779 | + | 0.881203i | ||||
\(975\) | 8.63766 | + | 14.9609i | 0.276626 | + | 0.479131i | ||||
\(976\) | −12.3179 | − | 23.4057i | −0.394287 | − | 0.749198i | ||||
\(977\) | 22.6866 | − | 39.2943i | 0.725808 | − | 1.25714i | −0.232832 | − | 0.972517i | \(-0.574799\pi\) |
0.958640 | − | 0.284620i | \(-0.0918674\pi\) | |||||||
\(978\) | −42.4064 | + | 8.00451i | −1.35601 | + | 0.255956i | ||||
\(979\) | −1.93424 | − | 1.93424i | −0.0618185 | − | 0.0618185i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.7418 | − | 48.7418i | 1.55621 | − | 1.55621i | ||||
\(982\) | 1.87337 | + | 1.27844i | 0.0597815 | + | 0.0407967i | ||||
\(983\) | 39.3690 | + | 22.7297i | 1.25568 | + | 0.724966i | 0.972231 | − | 0.234022i | \(-0.0751889\pi\) |
0.283446 | + | 0.958988i | \(0.408522\pi\) | |||||||
\(984\) | 16.5315 | − | 17.7699i | 0.527004 | − | 0.566483i | ||||
\(985\) | 2.86073 | − | 1.65164i | 0.0911504 | − | 0.0526257i | ||||
\(986\) | 36.0232 | + | 74.8868i | 1.14721 | + | 2.38488i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.99896 | − | 3.75383i | 0.0954095 | − | 0.119425i | ||||
\(989\) | 0.824941 | − | 3.07872i | 0.0262316 | − | 0.0978976i | ||||
\(990\) | 6.50685 | − | 5.59465i | 0.206801 | − | 0.177810i | ||||
\(991\) | −12.9817 | + | 22.4850i | −0.412379 | + | 0.714261i | −0.995149 | − | 0.0983759i | \(-0.968635\pi\) |
0.582771 | + | 0.812637i | \(0.301969\pi\) | |||||||
\(992\) | −25.3929 | + | 11.0128i | −0.806225 | + | 0.349655i | ||||
\(993\) | −69.4027 | −2.20243 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.13413 | + | 4.13413i | 0.131061 | + | 0.131061i | ||||
\(996\) | 40.3845 | + | 6.12312i | 1.27963 | + | 0.194018i | ||||
\(997\) | 11.7799 | + | 43.9631i | 0.373073 | + | 1.39233i | 0.856141 | + | 0.516743i | \(0.172856\pi\) |
−0.483068 | + | 0.875583i | \(0.660478\pi\) | |||||||
\(998\) | 47.0305 | + | 3.54514i | 1.48872 | + | 0.112219i | ||||
\(999\) | 10.7766 | − | 6.22186i | 0.340956 | − | 0.196851i |
(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.x.o.557.8 | 48 | ||
7.2 | even | 3 | inner | 784.2.x.o.765.11 | 48 | ||
7.3 | odd | 6 | 784.2.m.j.589.2 | 24 | |||
7.4 | even | 3 | 784.2.m.k.589.2 | 24 | |||
7.5 | odd | 6 | 112.2.w.c.93.11 | yes | 48 | ||
7.6 | odd | 2 | 112.2.w.c.109.8 | yes | 48 | ||
16.5 | even | 4 | inner | 784.2.x.o.165.11 | 48 | ||
28.19 | even | 6 | 448.2.ba.c.401.12 | 48 | |||
28.27 | even | 2 | 448.2.ba.c.81.1 | 48 | |||
56.5 | odd | 6 | 896.2.ba.f.289.12 | 48 | |||
56.13 | odd | 2 | 896.2.ba.f.417.1 | 48 | |||
56.19 | even | 6 | 896.2.ba.e.289.1 | 48 | |||
56.27 | even | 2 | 896.2.ba.e.417.12 | 48 | |||
112.5 | odd | 12 | 112.2.w.c.37.8 | ✓ | 48 | ||
112.13 | odd | 4 | 896.2.ba.f.865.12 | 48 | |||
112.19 | even | 12 | 896.2.ba.e.737.12 | 48 | |||
112.27 | even | 4 | 448.2.ba.c.305.12 | 48 | |||
112.37 | even | 12 | inner | 784.2.x.o.373.8 | 48 | ||
112.53 | even | 12 | 784.2.m.k.197.2 | 24 | |||
112.61 | odd | 12 | 896.2.ba.f.737.1 | 48 | |||
112.69 | odd | 4 | 112.2.w.c.53.11 | yes | 48 | ||
112.75 | even | 12 | 448.2.ba.c.177.1 | 48 | |||
112.83 | even | 4 | 896.2.ba.e.865.1 | 48 | |||
112.101 | odd | 12 | 784.2.m.j.197.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.8 | ✓ | 48 | 112.5 | odd | 12 | ||
112.2.w.c.53.11 | yes | 48 | 112.69 | odd | 4 | ||
112.2.w.c.93.11 | yes | 48 | 7.5 | odd | 6 | ||
112.2.w.c.109.8 | yes | 48 | 7.6 | odd | 2 | ||
448.2.ba.c.81.1 | 48 | 28.27 | even | 2 | |||
448.2.ba.c.177.1 | 48 | 112.75 | even | 12 | |||
448.2.ba.c.305.12 | 48 | 112.27 | even | 4 | |||
448.2.ba.c.401.12 | 48 | 28.19 | even | 6 | |||
784.2.m.j.197.2 | 24 | 112.101 | odd | 12 | |||
784.2.m.j.589.2 | 24 | 7.3 | odd | 6 | |||
784.2.m.k.197.2 | 24 | 112.53 | even | 12 | |||
784.2.m.k.589.2 | 24 | 7.4 | even | 3 | |||
784.2.x.o.165.11 | 48 | 16.5 | even | 4 | inner | ||
784.2.x.o.373.8 | 48 | 112.37 | even | 12 | inner | ||
784.2.x.o.557.8 | 48 | 1.1 | even | 1 | trivial | ||
784.2.x.o.765.11 | 48 | 7.2 | even | 3 | inner | ||
896.2.ba.e.289.1 | 48 | 56.19 | even | 6 | |||
896.2.ba.e.417.12 | 48 | 56.27 | even | 2 | |||
896.2.ba.e.737.12 | 48 | 112.19 | even | 12 | |||
896.2.ba.e.865.1 | 48 | 112.83 | even | 4 | |||
896.2.ba.f.289.12 | 48 | 56.5 | odd | 6 | |||
896.2.ba.f.417.1 | 48 | 56.13 | odd | 2 | |||
896.2.ba.f.737.1 | 48 | 112.61 | odd | 12 | |||
896.2.ba.f.865.12 | 48 | 112.13 | odd | 4 |