Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(221,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.s (of order \(6\), degree \(2\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.7 | ||
Character | \(\chi\) | \(=\) | 570.521 |
Dual form | 570.2.s.a.221.7 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.362568 | − | 1.69368i | 0.209329 | − | 0.977845i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 1.28548 | + | 1.16083i | 0.524797 | + | 0.473908i | ||||
\(7\) | −0.535070 | −0.202237 | −0.101119 | − | 0.994874i | \(-0.532242\pi\) | ||||
−0.101119 | + | 0.994874i | \(0.532242\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.73709 | − | 1.22815i | −0.912363 | − | 0.409382i | ||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | − | 5.20870i | − | 1.57048i | −0.619191 | − | 0.785240i | \(-0.712539\pi\) | ||
0.619191 | − | 0.785240i | \(-0.287461\pi\) | |||||||
\(12\) | −1.64805 | + | 0.532846i | −0.475752 | + | 0.153819i | ||||
\(13\) | 1.58889 | − | 0.917346i | 0.440679 | − | 0.254426i | −0.263207 | − | 0.964739i | \(-0.584780\pi\) |
0.703885 | + | 0.710314i | \(0.251447\pi\) | |||||||
\(14\) | 0.267535 | − | 0.463384i | 0.0715017 | − | 0.123845i | ||||
\(15\) | 1.16083 | − | 1.28548i | 0.299726 | − | 0.331911i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.93717 | − | 2.27312i | −0.954903 | − | 0.551313i | −0.0603023 | − | 0.998180i | \(-0.519206\pi\) |
−0.894601 | + | 0.446867i | \(0.852540\pi\) | |||||||
\(18\) | 2.43215 | − | 1.75631i | 0.573263 | − | 0.413967i | ||||
\(19\) | −1.25777 | + | 4.17349i | −0.288553 | + | 0.957464i | ||||
\(20\) | − | 1.00000i | − | 0.223607i | ||||||
\(21\) | −0.193999 | + | 0.906236i | −0.0423341 | + | 0.197757i | ||||
\(22\) | 4.51086 | + | 2.60435i | 0.961719 | + | 0.555249i | ||||
\(23\) | 5.55808 | − | 3.20896i | 1.15894 | − | 0.669114i | 0.207890 | − | 0.978152i | \(-0.433340\pi\) |
0.951050 | + | 0.309038i | \(0.100007\pi\) | |||||||
\(24\) | 0.362568 | − | 1.69368i | 0.0740089 | − | 0.345721i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 1.83469i | 0.359813i | ||||||||
\(27\) | −3.07247 | + | 4.19046i | −0.591296 | + | 0.806454i | ||||
\(28\) | 0.267535 | + | 0.463384i | 0.0505593 | + | 0.0875713i | ||||
\(29\) | −4.19776 | − | 7.27074i | −0.779505 | − | 1.35014i | −0.932227 | − | 0.361873i | \(-0.882137\pi\) |
0.152722 | − | 0.988269i | \(-0.451196\pi\) | |||||||
\(30\) | 0.532846 | + | 1.64805i | 0.0972839 | + | 0.300892i | ||||
\(31\) | 4.17904i | 0.750577i | 0.926908 | + | 0.375289i | \(0.122456\pi\) | ||||
−0.926908 | + | 0.375289i | \(0.877544\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −8.82185 | − | 1.88851i | −1.53569 | − | 0.328747i | ||||
\(34\) | 3.93717 | − | 2.27312i | 0.675218 | − | 0.389837i | ||||
\(35\) | −0.463384 | − | 0.267535i | −0.0783262 | − | 0.0452216i | ||||
\(36\) | 0.304938 | + | 2.98446i | 0.0508229 | + | 0.497410i | ||||
\(37\) | − | 5.32678i | − | 0.875718i | −0.899044 | − | 0.437859i | \(-0.855737\pi\) | ||
0.899044 | − | 0.437859i | \(-0.144263\pi\) | |||||||
\(38\) | −2.98546 | − | 3.17601i | −0.484306 | − | 0.515216i | ||||
\(39\) | −0.977607 | − | 3.02367i | −0.156542 | − | 0.484174i | ||||
\(40\) | 0.866025 | + | 0.500000i | 0.136931 | + | 0.0790569i | ||||
\(41\) | 2.33917 | − | 4.05157i | 0.365318 | − | 0.632749i | −0.623509 | − | 0.781816i | \(-0.714294\pi\) |
0.988827 | + | 0.149067i | \(0.0476271\pi\) | |||||||
\(42\) | −0.687824 | − | 0.621126i | −0.106133 | − | 0.0958418i | ||||
\(43\) | 4.21877 | − | 7.30712i | 0.643356 | − | 1.11433i | −0.341322 | − | 0.939946i | \(-0.610875\pi\) |
0.984679 | − | 0.174379i | \(-0.0557919\pi\) | |||||||
\(44\) | −4.51086 | + | 2.60435i | −0.680038 | + | 0.392620i | ||||
\(45\) | −1.75631 | − | 2.43215i | −0.261816 | − | 0.362564i | ||||
\(46\) | 6.41792i | 0.946271i | ||||||||
\(47\) | 3.52343 | − | 2.03425i | 0.513945 | − | 0.296726i | −0.220509 | − | 0.975385i | \(-0.570772\pi\) |
0.734454 | + | 0.678659i | \(0.237438\pi\) | |||||||
\(48\) | 1.28548 | + | 1.16083i | 0.185544 | + | 0.167552i | ||||
\(49\) | −6.71370 | −0.959100 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −5.27743 | + | 5.84413i | −0.738988 | + | 0.818341i | ||||
\(52\) | −1.58889 | − | 0.917346i | −0.220339 | − | 0.127213i | ||||
\(53\) | −3.26957 | − | 5.66307i | −0.449110 | − | 0.777882i | 0.549218 | − | 0.835679i | \(-0.314926\pi\) |
−0.998328 | + | 0.0577971i | \(0.981592\pi\) | |||||||
\(54\) | −2.09281 | − | 4.75606i | −0.284795 | − | 0.647218i | ||||
\(55\) | 2.60435 | − | 4.51086i | 0.351170 | − | 0.608245i | ||||
\(56\) | −0.535070 | −0.0715017 | ||||||||
\(57\) | 6.61252 | + | 3.64344i | 0.875849 | + | 0.482585i | ||||
\(58\) | 8.39553 | 1.10239 | ||||||||
\(59\) | −3.47483 | + | 6.01858i | −0.452384 | + | 0.783552i | −0.998534 | − | 0.0541355i | \(-0.982760\pi\) |
0.546149 | + | 0.837688i | \(0.316093\pi\) | |||||||
\(60\) | −1.69368 | − | 0.362568i | −0.218653 | − | 0.0468073i | ||||
\(61\) | 4.11360 | + | 7.12497i | 0.526693 | + | 0.912259i | 0.999516 | + | 0.0311016i | \(0.00990154\pi\) |
−0.472823 | + | 0.881157i | \(0.656765\pi\) | |||||||
\(62\) | −3.61915 | − | 2.08952i | −0.459633 | − | 0.265369i | ||||
\(63\) | 1.46453 | + | 0.657144i | 0.184514 | + | 0.0827924i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.83469 | 0.227565 | ||||||||
\(66\) | 6.04642 | − | 6.69569i | 0.744263 | − | 0.824183i | ||||
\(67\) | −0.445224 | + | 0.257050i | −0.0543927 | + | 0.0314037i | −0.526950 | − | 0.849896i | \(-0.676664\pi\) |
0.472557 | + | 0.881300i | \(0.343331\pi\) | |||||||
\(68\) | 4.54625i | 0.551313i | ||||||||
\(69\) | −3.41976 | − | 10.5771i | −0.411691 | − | 1.27333i | ||||
\(70\) | 0.463384 | − | 0.267535i | 0.0553850 | − | 0.0319765i | ||||
\(71\) | 3.29907 | − | 5.71415i | 0.391527 | − | 0.678145i | −0.601124 | − | 0.799156i | \(-0.705280\pi\) |
0.992651 | + | 0.121011i | \(0.0386135\pi\) | |||||||
\(72\) | −2.73709 | − | 1.22815i | −0.322569 | − | 0.144739i | ||||
\(73\) | 3.05629 | − | 5.29365i | 0.357712 | − | 0.619575i | −0.629866 | − | 0.776704i | \(-0.716890\pi\) |
0.987578 | + | 0.157128i | \(0.0502236\pi\) | |||||||
\(74\) | 4.61313 | + | 2.66339i | 0.536265 | + | 0.309613i | ||||
\(75\) | 1.64805 | − | 0.532846i | 0.190301 | − | 0.0615277i | ||||
\(76\) | 4.24323 | − | 0.997481i | 0.486732 | − | 0.114419i | ||||
\(77\) | 2.78702i | 0.317610i | ||||||||
\(78\) | 3.10738 | + | 0.665201i | 0.351841 | + | 0.0753191i | ||||
\(79\) | 7.65758 | + | 4.42110i | 0.861545 | + | 0.497413i | 0.864529 | − | 0.502582i | \(-0.167617\pi\) |
−0.00298455 | + | 0.999996i | \(0.500950\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | 5.98331 | + | 6.72310i | 0.664812 | + | 0.747011i | ||||
\(82\) | 2.33917 | + | 4.05157i | 0.258319 | + | 0.447421i | ||||
\(83\) | 13.2159i | 1.45063i | 0.688416 | + | 0.725316i | \(0.258306\pi\) | ||||
−0.688416 | + | 0.725316i | \(0.741694\pi\) | |||||||
\(84\) | 0.881823 | − | 0.285110i | 0.0962148 | − | 0.0311080i | ||||
\(85\) | −2.27312 | − | 3.93717i | −0.246555 | − | 0.427046i | ||||
\(86\) | 4.21877 | + | 7.30712i | 0.454922 | + | 0.787947i | ||||
\(87\) | −13.8363 | + | 4.47352i | −1.48340 | + | 0.479612i | ||||
\(88\) | − | 5.20870i | − | 0.555249i | ||||||
\(89\) | 8.15273 | + | 14.1209i | 0.864187 | + | 1.49682i | 0.867852 | + | 0.496823i | \(0.165500\pi\) |
−0.00366426 | + | 0.999993i | \(0.501166\pi\) | |||||||
\(90\) | 2.98446 | − | 0.304938i | 0.314590 | − | 0.0321433i | ||||
\(91\) | −0.850166 | + | 0.490844i | −0.0891217 | + | 0.0514544i | ||||
\(92\) | −5.55808 | − | 3.20896i | −0.579470 | − | 0.334557i | ||||
\(93\) | 7.07794 | + | 1.51519i | 0.733948 | + | 0.157117i | ||||
\(94\) | 4.06851i | 0.419635i | ||||||||
\(95\) | −3.17601 | + | 2.98546i | −0.325851 | + | 0.306302i | ||||
\(96\) | −1.64805 | + | 0.532846i | −0.168204 | + | 0.0543833i | ||||
\(97\) | 0.567737 | + | 0.327783i | 0.0576449 | + | 0.0332813i | 0.528545 | − | 0.848905i | \(-0.322738\pi\) |
−0.470901 | + | 0.882186i | \(0.656071\pi\) | |||||||
\(98\) | 3.35685 | − | 5.81424i | 0.339093 | − | 0.587326i | ||||
\(99\) | −6.39704 | + | 14.2567i | −0.642927 | + | 1.43285i | ||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −10.5737 | + | 6.10474i | −1.05212 | + | 0.607444i | −0.923243 | − | 0.384216i | \(-0.874472\pi\) |
−0.128881 | + | 0.991660i | \(0.541139\pi\) | |||||||
\(102\) | −2.42245 | − | 7.49245i | −0.239858 | − | 0.741863i | ||||
\(103\) | 10.0328i | 0.988561i | 0.869303 | + | 0.494280i | \(0.164568\pi\) | ||||
−0.869303 | + | 0.494280i | \(0.835432\pi\) | |||||||
\(104\) | 1.58889 | − | 0.917346i | 0.155803 | − | 0.0899531i | ||||
\(105\) | −0.621126 | + | 0.687824i | −0.0606157 | + | 0.0671247i | ||||
\(106\) | 6.53915 | 0.635138 | ||||||||
\(107\) | 19.9736 | 1.93092 | 0.965459 | − | 0.260554i | \(-0.0839052\pi\) | ||||
0.965459 | + | 0.260554i | \(0.0839052\pi\) | |||||||
\(108\) | 5.16528 | + | 0.565605i | 0.497029 | + | 0.0544253i | ||||
\(109\) | −6.94887 | − | 4.01193i | −0.665581 | − | 0.384273i | 0.128819 | − | 0.991668i | \(-0.458881\pi\) |
−0.794400 | + | 0.607395i | \(0.792215\pi\) | |||||||
\(110\) | 2.60435 | + | 4.51086i | 0.248315 | + | 0.430094i | ||||
\(111\) | −9.02185 | − | 1.93132i | −0.856317 | − | 0.183313i | ||||
\(112\) | 0.267535 | − | 0.463384i | 0.0252797 | − | 0.0437857i | ||||
\(113\) | 16.8013 | 1.58054 | 0.790269 | − | 0.612760i | \(-0.209941\pi\) | ||||
0.790269 | + | 0.612760i | \(0.209941\pi\) | |||||||
\(114\) | −6.46157 | + | 3.90489i | −0.605181 | + | 0.365726i | ||||
\(115\) | 6.41792 | 0.598474 | ||||||||
\(116\) | −4.19776 | + | 7.27074i | −0.389753 | + | 0.675071i | ||||
\(117\) | −5.47557 | + | 0.559466i | −0.506216 | + | 0.0517227i | ||||
\(118\) | −3.47483 | − | 6.01858i | −0.319884 | − | 0.554055i | ||||
\(119\) | 2.10666 | + | 1.21628i | 0.193117 | + | 0.111496i | ||||
\(120\) | 1.16083 | − | 1.28548i | 0.105969 | − | 0.117348i | ||||
\(121\) | −16.1305 | −1.46641 | ||||||||
\(122\) | −8.22721 | −0.744856 | ||||||||
\(123\) | −6.01394 | − | 5.43078i | −0.542259 | − | 0.489677i | ||||
\(124\) | 3.61915 | − | 2.08952i | 0.325009 | − | 0.187644i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.30137 | + | 0.939751i | −0.115935 | + | 0.0837197i | ||||
\(127\) | 7.49011 | − | 4.32442i | 0.664640 | − | 0.383730i | −0.129403 | − | 0.991592i | \(-0.541306\pi\) |
0.794043 | + | 0.607862i | \(0.207973\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −10.8463 | − | 9.79456i | −0.954965 | − | 0.862363i | ||||
\(130\) | −0.917346 | + | 1.58889i | −0.0804565 | + | 0.139355i | ||||
\(131\) | −16.6710 | − | 9.62499i | −1.45655 | − | 0.840939i | −0.457710 | − | 0.889102i | \(-0.651330\pi\) |
−0.998840 | + | 0.0481626i | \(0.984663\pi\) | |||||||
\(132\) | 2.77543 | + | 8.58420i | 0.241570 | + | 0.747159i | ||||
\(133\) | 0.672996 | − | 2.23311i | 0.0583562 | − | 0.193635i | ||||
\(134\) | − | 0.514100i | − | 0.0444115i | ||||||
\(135\) | −4.75606 | + | 2.09281i | −0.409337 | + | 0.180120i | ||||
\(136\) | −3.93717 | − | 2.27312i | −0.337609 | − | 0.194919i | ||||
\(137\) | −1.62271 | + | 0.936869i | −0.138637 | + | 0.0800421i | −0.567714 | − | 0.823226i | \(-0.692172\pi\) |
0.429077 | + | 0.903268i | \(0.358839\pi\) | |||||||
\(138\) | 10.8699 | + | 2.32693i | 0.925306 | + | 0.198082i | ||||
\(139\) | 3.33569 | + | 5.77758i | 0.282929 | + | 0.490048i | 0.972105 | − | 0.234546i | \(-0.0753604\pi\) |
−0.689176 | + | 0.724594i | \(0.742027\pi\) | |||||||
\(140\) | 0.535070i | 0.0452216i | ||||||||
\(141\) | −2.16789 | − | 6.70511i | −0.182569 | − | 0.564672i | ||||
\(142\) | 3.29907 | + | 5.71415i | 0.276852 | + | 0.479521i | ||||
\(143\) | −4.77817 | − | 8.27604i | −0.399571 | − | 0.692077i | ||||
\(144\) | 2.43215 | − | 1.75631i | 0.202679 | − | 0.146360i | ||||
\(145\) | − | 8.39553i | − | 0.697211i | ||||||
\(146\) | 3.05629 | + | 5.29365i | 0.252941 | + | 0.438106i | ||||
\(147\) | −2.43417 | + | 11.3708i | −0.200767 | + | 0.937851i | ||||
\(148\) | −4.61313 | + | 2.66339i | −0.379197 | + | 0.218929i | ||||
\(149\) | −3.13836 | − | 1.81193i | −0.257104 | − | 0.148439i | 0.365909 | − | 0.930651i | \(-0.380758\pi\) |
−0.623013 | + | 0.782211i | \(0.714092\pi\) | |||||||
\(150\) | −0.362568 | + | 1.69368i | −0.0296036 | + | 0.138288i | ||||
\(151\) | 19.7459i | 1.60690i | 0.595371 | + | 0.803451i | \(0.297005\pi\) | ||||
−0.595371 | + | 0.803451i | \(0.702995\pi\) | |||||||
\(152\) | −1.25777 | + | 4.17349i | −0.102019 | + | 0.338515i | ||||
\(153\) | 7.98464 | + | 11.0572i | 0.645520 | + | 0.893918i | ||||
\(154\) | −2.41363 | − | 1.39351i | −0.194496 | − | 0.112292i | ||||
\(155\) | −2.08952 | + | 3.61915i | −0.167834 | + | 0.290697i | ||||
\(156\) | −2.12977 | + | 2.35847i | −0.170518 | + | 0.188828i | ||||
\(157\) | 2.03388 | − | 3.52278i | 0.162321 | − | 0.281149i | −0.773380 | − | 0.633943i | \(-0.781435\pi\) |
0.935701 | + | 0.352795i | \(0.114769\pi\) | |||||||
\(158\) | −7.65758 | + | 4.42110i | −0.609204 | + | 0.351724i | ||||
\(159\) | −10.7769 | + | 3.48436i | −0.854660 | + | 0.276327i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | −2.97396 | + | 1.71702i | −0.234381 | + | 0.135320i | ||||
\(162\) | −8.81403 | + | 1.82015i | −0.692495 | + | 0.143004i | ||||
\(163\) | 6.73334 | 0.527396 | 0.263698 | − | 0.964605i | \(-0.415058\pi\) | ||||
0.263698 | + | 0.964605i | \(0.415058\pi\) | |||||||
\(164\) | −4.67835 | −0.365318 | ||||||||
\(165\) | −6.69569 | − | 6.04642i | −0.521259 | − | 0.470713i | ||||
\(166\) | −11.4453 | − | 6.60794i | −0.888327 | − | 0.512876i | ||||
\(167\) | 3.32598 | + | 5.76077i | 0.257372 | + | 0.445782i | 0.965537 | − | 0.260265i | \(-0.0838101\pi\) |
−0.708165 | + | 0.706047i | \(0.750477\pi\) | |||||||
\(168\) | −0.193999 | + | 0.906236i | −0.0149674 | + | 0.0699176i | ||||
\(169\) | −4.81695 | + | 8.34321i | −0.370535 | + | 0.641785i | ||||
\(170\) | 4.54625 | 0.348681 | ||||||||
\(171\) | 8.56829 | − | 9.87848i | 0.655234 | − | 0.755426i | ||||
\(172\) | −8.43754 | −0.643356 | ||||||||
\(173\) | 1.61948 | − | 2.80502i | 0.123127 | − | 0.213262i | −0.797872 | − | 0.602826i | \(-0.794041\pi\) |
0.920999 | + | 0.389565i | \(0.127374\pi\) | |||||||
\(174\) | 3.04395 | − | 14.2193i | 0.230761 | − | 1.07796i | ||||
\(175\) | −0.267535 | − | 0.463384i | −0.0202237 | − | 0.0350285i | ||||
\(176\) | 4.51086 | + | 2.60435i | 0.340019 | + | 0.196310i | ||||
\(177\) | 8.93367 | + | 8.06738i | 0.671496 | + | 0.606382i | ||||
\(178\) | −16.3055 | −1.22215 | ||||||||
\(179\) | 13.4218 | 1.00319 | 0.501597 | − | 0.865101i | \(-0.332746\pi\) | ||||
0.501597 | + | 0.865101i | \(0.332746\pi\) | |||||||
\(180\) | −1.22815 | + | 2.73709i | −0.0915407 | + | 0.204011i | ||||
\(181\) | −5.80040 | + | 3.34886i | −0.431140 | + | 0.248919i | −0.699832 | − | 0.714307i | \(-0.746742\pi\) |
0.268692 | + | 0.963226i | \(0.413409\pi\) | |||||||
\(182\) | − | 0.981688i | − | 0.0727675i | ||||||
\(183\) | 13.5589 | − | 4.38383i | 1.00230 | − | 0.324062i | ||||
\(184\) | 5.55808 | − | 3.20896i | 0.409747 | − | 0.236568i | ||||
\(185\) | 2.66339 | − | 4.61313i | 0.195816 | − | 0.339164i | ||||
\(186\) | −4.85116 | + | 5.37208i | −0.355704 | + | 0.393900i | ||||
\(187\) | −11.8400 | + | 20.5075i | −0.865827 | + | 1.49966i | ||||
\(188\) | −3.52343 | − | 2.03425i | −0.256973 | − | 0.148363i | ||||
\(189\) | 1.64398 | − | 2.24219i | 0.119582 | − | 0.163095i | ||||
\(190\) | −0.997481 | − | 4.24323i | −0.0723649 | − | 0.307837i | ||||
\(191\) | − | 9.59528i | − | 0.694290i | −0.937811 | − | 0.347145i | \(-0.887151\pi\) | ||
0.937811 | − | 0.347145i | \(-0.112849\pi\) | |||||||
\(192\) | 0.362568 | − | 1.69368i | 0.0261661 | − | 0.122231i | ||||
\(193\) | 8.36220 | + | 4.82792i | 0.601924 | + | 0.347521i | 0.769798 | − | 0.638287i | \(-0.220357\pi\) |
−0.167874 | + | 0.985808i | \(0.553690\pi\) | |||||||
\(194\) | −0.567737 | + | 0.327783i | −0.0407611 | + | 0.0235334i | ||||
\(195\) | 0.665201 | − | 3.10738i | 0.0476360 | − | 0.222524i | ||||
\(196\) | 3.35685 | + | 5.81424i | 0.239775 | + | 0.415303i | ||||
\(197\) | 3.26552i | 0.232659i | 0.993211 | + | 0.116329i | \(0.0371128\pi\) | ||||
−0.993211 | + | 0.116329i | \(0.962887\pi\) | |||||||
\(198\) | −9.14811 | − | 12.6683i | −0.650128 | − | 0.900299i | ||||
\(199\) | −0.305926 | − | 0.529880i | −0.0216865 | − | 0.0375622i | 0.854978 | − | 0.518663i | \(-0.173570\pi\) |
−0.876665 | + | 0.481101i | \(0.840237\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 0.273936 | + | 0.847263i | 0.0193220 | + | 0.0597614i | ||||
\(202\) | − | 12.2095i | − | 0.859056i | ||||||
\(203\) | 2.24610 | + | 3.89035i | 0.157645 | + | 0.273049i | ||||
\(204\) | 7.69988 | + | 1.64832i | 0.539099 | + | 0.115406i | ||||
\(205\) | 4.05157 | − | 2.33917i | 0.282974 | − | 0.163375i | ||||
\(206\) | −8.68866 | − | 5.01640i | −0.605367 | − | 0.349509i | ||||
\(207\) | −19.1540 | + | 1.95707i | −1.33130 | + | 0.136025i | ||||
\(208\) | 1.83469i | 0.127213i | ||||||||
\(209\) | 21.7384 | + | 6.55135i | 1.50368 | + | 0.453167i | ||||
\(210\) | −0.285110 | − | 0.881823i | −0.0196744 | − | 0.0608516i | ||||
\(211\) | −4.21436 | − | 2.43316i | −0.290129 | − | 0.167506i | 0.347871 | − | 0.937542i | \(-0.386905\pi\) |
−0.638000 | + | 0.770037i | \(0.720238\pi\) | |||||||
\(212\) | −3.26957 | + | 5.66307i | −0.224555 | + | 0.388941i | ||||
\(213\) | −8.48180 | − | 7.65933i | −0.581163 | − | 0.524808i | ||||
\(214\) | −9.98679 | + | 17.2976i | −0.682683 | + | 1.18244i | ||||
\(215\) | 7.30712 | − | 4.21877i | 0.498342 | − | 0.287718i | ||||
\(216\) | −3.07247 | + | 4.19046i | −0.209055 | + | 0.285125i | ||||
\(217\) | − | 2.23608i | − | 0.151795i | ||||||
\(218\) | 6.94887 | − | 4.01193i | 0.470637 | − | 0.271722i | ||||
\(219\) | −7.85763 | − | 7.09569i | −0.530969 | − | 0.479482i | ||||
\(220\) | −5.20870 | −0.351170 | ||||||||
\(221\) | −8.34096 | −0.561074 | ||||||||
\(222\) | 6.18350 | − | 6.84749i | 0.415009 | − | 0.459574i | ||||
\(223\) | 4.74349 | + | 2.73866i | 0.317648 | + | 0.183394i | 0.650344 | − | 0.759640i | \(-0.274625\pi\) |
−0.332696 | + | 0.943034i | \(0.607958\pi\) | |||||||
\(224\) | 0.267535 | + | 0.463384i | 0.0178754 | + | 0.0309611i | ||||
\(225\) | −0.304938 | − | 2.98446i | −0.0203292 | − | 0.198964i | ||||
\(226\) | −8.40067 | + | 14.5504i | −0.558805 | + | 0.967878i | ||||
\(227\) | 12.2736 | 0.814630 | 0.407315 | − | 0.913288i | \(-0.366465\pi\) | ||||
0.407315 | + | 0.913288i | \(0.366465\pi\) | |||||||
\(228\) | −0.150951 | − | 7.54833i | −0.00999696 | − | 0.499900i | ||||
\(229\) | 25.2326 | 1.66742 | 0.833708 | − | 0.552205i | \(-0.186214\pi\) | ||||
0.833708 | + | 0.552205i | \(0.186214\pi\) | |||||||
\(230\) | −3.20896 | + | 5.55808i | −0.211593 | + | 0.366489i | ||||
\(231\) | 4.72031 | + | 1.01048i | 0.310573 | + | 0.0664849i | ||||
\(232\) | −4.19776 | − | 7.27074i | −0.275597 | − | 0.477347i | ||||
\(233\) | −15.1283 | − | 8.73433i | −0.991088 | − | 0.572205i | −0.0854886 | − | 0.996339i | \(-0.527245\pi\) |
−0.905599 | + | 0.424134i | \(0.860578\pi\) | |||||||
\(234\) | 2.25327 | − | 5.02171i | 0.147301 | − | 0.328280i | ||||
\(235\) | 4.06851 | 0.265400 | ||||||||
\(236\) | 6.94966 | 0.452384 | ||||||||
\(237\) | 10.2643 | − | 11.3665i | 0.666739 | − | 0.738335i | ||||
\(238\) | −2.10666 | + | 1.21628i | −0.136554 | + | 0.0788397i | ||||
\(239\) | 27.8911i | 1.80413i | 0.431603 | + | 0.902063i | \(0.357948\pi\) | ||||
−0.431603 | + | 0.902063i | \(0.642052\pi\) | |||||||
\(240\) | 0.532846 | + | 1.64805i | 0.0343950 | + | 0.106381i | ||||
\(241\) | 21.8025 | − | 12.5877i | 1.40442 | − | 0.810843i | 0.409579 | − | 0.912275i | \(-0.365676\pi\) |
0.994842 | + | 0.101432i | \(0.0323424\pi\) | |||||||
\(242\) | 8.06525 | − | 13.9694i | 0.518454 | − | 0.897989i | ||||
\(243\) | 13.5561 | − | 7.69622i | 0.869625 | − | 0.493713i | ||||
\(244\) | 4.11360 | − | 7.12497i | 0.263346 | − | 0.456129i | ||||
\(245\) | −5.81424 | − | 3.35685i | −0.371458 | − | 0.214461i | ||||
\(246\) | 7.71016 | − | 2.49284i | 0.491582 | − | 0.158938i | ||||
\(247\) | 1.83007 | + | 7.78502i | 0.116445 | + | 0.495349i | ||||
\(248\) | 4.17904i | 0.265369i | ||||||||
\(249\) | 22.3834 | + | 4.79166i | 1.41849 | + | 0.303659i | ||||
\(250\) | −0.866025 | − | 0.500000i | −0.0547723 | − | 0.0316228i | ||||
\(251\) | −15.5790 | + | 8.99456i | −0.983340 | + | 0.567732i | −0.903277 | − | 0.429058i | \(-0.858846\pi\) |
−0.0800634 | + | 0.996790i | \(0.525512\pi\) | |||||||
\(252\) | −0.163163 | − | 1.59690i | −0.0102783 | − | 0.100595i | ||||
\(253\) | −16.7145 | − | 28.9504i | −1.05083 | − | 1.82009i | ||||
\(254\) | 8.64884i | 0.542676i | ||||||||
\(255\) | −7.49245 | + | 2.42245i | −0.469196 | + | 0.151700i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.62204 | + | 13.2018i | 0.475450 | + | 0.823503i | 0.999605 | − | 0.0281201i | \(-0.00895207\pi\) |
−0.524155 | + | 0.851623i | \(0.675619\pi\) | |||||||
\(258\) | 13.9055 | − | 4.49591i | 0.865719 | − | 0.279903i | ||||
\(259\) | 2.85020i | 0.177103i | ||||||||
\(260\) | −0.917346 | − | 1.58889i | −0.0568914 | − | 0.0985387i | ||||
\(261\) | 2.56011 | + | 25.0561i | 0.158467 | + | 1.55094i | ||||
\(262\) | 16.6710 | − | 9.62499i | 1.02994 | − | 0.594634i | ||||
\(263\) | −19.9274 | − | 11.5051i | −1.22878 | − | 0.709436i | −0.262004 | − | 0.965067i | \(-0.584383\pi\) |
−0.966774 | + | 0.255631i | \(0.917717\pi\) | |||||||
\(264\) | −8.82185 | − | 1.88851i | −0.542947 | − | 0.116230i | ||||
\(265\) | − | 6.53915i | − | 0.401697i | ||||||
\(266\) | 1.59743 | + | 1.69939i | 0.0979447 | + | 0.104196i | ||||
\(267\) | 26.8722 | − | 8.68829i | 1.64455 | − | 0.531715i | ||||
\(268\) | 0.445224 | + | 0.257050i | 0.0271964 | + | 0.0157018i | ||||
\(269\) | 11.9188 | − | 20.6440i | 0.726702 | − | 1.25868i | −0.231567 | − | 0.972819i | \(-0.574385\pi\) |
0.958270 | − | 0.285866i | \(-0.0922813\pi\) | |||||||
\(270\) | 0.565605 | − | 5.16528i | 0.0344216 | − | 0.314349i | ||||
\(271\) | 10.8992 | − | 18.8780i | 0.662082 | − | 1.14676i | −0.317986 | − | 0.948095i | \(-0.603006\pi\) |
0.980068 | − | 0.198664i | \(-0.0636602\pi\) | |||||||
\(272\) | 3.93717 | − | 2.27312i | 0.238726 | − | 0.137828i | ||||
\(273\) | 0.523088 | + | 1.61787i | 0.0316587 | + | 0.0979181i | ||||
\(274\) | − | 1.87374i | − | 0.113197i | ||||||
\(275\) | 4.51086 | − | 2.60435i | 0.272015 | − | 0.157048i | ||||
\(276\) | −7.45013 | + | 8.25013i | −0.448445 | + | 0.496600i | ||||
\(277\) | −6.33971 | −0.380916 | −0.190458 | − | 0.981695i | \(-0.560997\pi\) | ||||
−0.190458 | + | 0.981695i | \(0.560997\pi\) | |||||||
\(278\) | −6.67138 | −0.400123 | ||||||||
\(279\) | 5.13247 | − | 11.4384i | 0.307273 | − | 0.684799i | ||||
\(280\) | −0.463384 | − | 0.267535i | −0.0276925 | − | 0.0159883i | ||||
\(281\) | −11.6032 | − | 20.0973i | −0.692188 | − | 1.19890i | −0.971120 | − | 0.238594i | \(-0.923314\pi\) |
0.278932 | − | 0.960311i | \(-0.410020\pi\) | |||||||
\(282\) | 6.89074 | + | 1.47511i | 0.410338 | + | 0.0878416i | ||||
\(283\) | 8.02179 | − | 13.8941i | 0.476846 | − | 0.825921i | −0.522802 | − | 0.852454i | \(-0.675113\pi\) |
0.999648 | + | 0.0265330i | \(0.00844670\pi\) | |||||||
\(284\) | −6.59813 | −0.391527 | ||||||||
\(285\) | 3.90489 | + | 6.46157i | 0.231306 | + | 0.382750i | ||||
\(286\) | 9.55635 | 0.565079 | ||||||||
\(287\) | −1.25162 | + | 2.16787i | −0.0738809 | + | 0.127965i | ||||
\(288\) | 0.304938 | + | 2.98446i | 0.0179686 | + | 0.175861i | ||||
\(289\) | 1.83418 | + | 3.17689i | 0.107893 | + | 0.186876i | ||||
\(290\) | 7.27074 | + | 4.19776i | 0.426953 | + | 0.246501i | ||||
\(291\) | 0.761002 | − | 0.842719i | 0.0446107 | − | 0.0494011i | ||||
\(292\) | −6.11259 | −0.357712 | ||||||||
\(293\) | −20.9324 | −1.22288 | −0.611441 | − | 0.791290i | \(-0.709410\pi\) | ||||
−0.611441 | + | 0.791290i | \(0.709410\pi\) | |||||||
\(294\) | −8.63035 | − | 7.79348i | −0.503332 | − | 0.454525i | ||||
\(295\) | −6.01858 | + | 3.47483i | −0.350415 | + | 0.202312i | ||||
\(296\) | − | 5.32678i | − | 0.309613i | ||||||
\(297\) | 21.8268 | + | 16.0035i | 1.26652 | + | 0.928620i | ||||
\(298\) | 3.13836 | − | 1.81193i | 0.181800 | − | 0.104962i | ||||
\(299\) | 5.88745 | − | 10.1974i | 0.340480 | − | 0.589729i | ||||
\(300\) | −1.28548 | − | 1.16083i | −0.0742174 | − | 0.0670207i | ||||
\(301\) | −2.25734 | + | 3.90982i | −0.130111 | + | 0.225358i | ||||
\(302\) | −17.1005 | − | 9.87297i | −0.984022 | − | 0.568126i | ||||
\(303\) | 6.50577 | + | 20.1219i | 0.373747 | + | 1.15597i | ||||
\(304\) | −2.98546 | − | 3.17601i | −0.171228 | − | 0.182157i | ||||
\(305\) | 8.22721i | 0.471088i | ||||||||
\(306\) | −13.5681 | + | 1.38632i | −0.775637 | + | 0.0792508i | ||||
\(307\) | −9.83298 | − | 5.67707i | −0.561198 | − | 0.324008i | 0.192428 | − | 0.981311i | \(-0.438364\pi\) |
−0.753626 | + | 0.657303i | \(0.771697\pi\) | |||||||
\(308\) | 2.41363 | − | 1.39351i | 0.137529 | − | 0.0794025i | ||||
\(309\) | 16.9923 | + | 3.63757i | 0.966660 | + | 0.206934i | ||||
\(310\) | −2.08952 | − | 3.61915i | −0.118677 | − | 0.205554i | ||||
\(311\) | − | 6.21309i | − | 0.352312i | −0.984362 | − | 0.176156i | \(-0.943634\pi\) | ||
0.984362 | − | 0.176156i | \(-0.0563663\pi\) | |||||||
\(312\) | −0.977607 | − | 3.02367i | −0.0553461 | − | 0.171181i | ||||
\(313\) | −5.11268 | − | 8.85542i | −0.288986 | − | 0.500538i | 0.684582 | − | 0.728936i | \(-0.259985\pi\) |
−0.973568 | + | 0.228398i | \(0.926651\pi\) | |||||||
\(314\) | 2.03388 | + | 3.52278i | 0.114778 | + | 0.198802i | ||||
\(315\) | 0.939751 | + | 1.30137i | 0.0529490 | + | 0.0733239i | ||||
\(316\) | − | 8.84221i | − | 0.497413i | ||||||
\(317\) | −5.46022 | − | 9.45738i | −0.306677 | − | 0.531179i | 0.670957 | − | 0.741497i | \(-0.265884\pi\) |
−0.977633 | + | 0.210317i | \(0.932550\pi\) | |||||||
\(318\) | 2.37089 | − | 11.0752i | 0.132953 | − | 0.621067i | ||||
\(319\) | −37.8711 | + | 21.8649i | −2.12037 | + | 1.22420i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | 7.24178 | − | 33.8288i | 0.404197 | − | 1.88814i | ||||
\(322\) | − | 3.43403i | − | 0.191371i | ||||||
\(323\) | 14.4389 | − | 13.5726i | 0.803403 | − | 0.755202i | ||||
\(324\) | 2.83072 | − | 8.54325i | 0.157262 | − | 0.474625i | ||||
\(325\) | 1.58889 | + | 0.917346i | 0.0881357 | + | 0.0508852i | ||||
\(326\) | −3.36667 | + | 5.83124i | −0.186463 | + | 0.322963i | ||||
\(327\) | −9.31435 | + | 10.3145i | −0.515085 | + | 0.570396i | ||||
\(328\) | 2.33917 | − | 4.05157i | 0.129159 | − | 0.223710i | ||||
\(329\) | −1.88528 | + | 1.08847i | −0.103939 | + | 0.0600092i | ||||
\(330\) | 8.58420 | − | 2.77543i | 0.472545 | − | 0.152782i | ||||
\(331\) | 5.24791i | 0.288451i | 0.989545 | + | 0.144226i | \(0.0460691\pi\) | ||||
−0.989545 | + | 0.144226i | \(0.953931\pi\) | |||||||
\(332\) | 11.4453 | − | 6.60794i | 0.628142 | − | 0.362658i | ||||
\(333\) | −6.54207 | + | 14.5799i | −0.358503 | + | 0.798972i | ||||
\(334\) | −6.65196 | −0.363979 | ||||||||
\(335\) | −0.514100 | −0.0280883 | ||||||||
\(336\) | −0.687824 | − | 0.621126i | −0.0375239 | − | 0.0338852i | ||||
\(337\) | 10.1877 | + | 5.88185i | 0.554957 | + | 0.320405i | 0.751119 | − | 0.660167i | \(-0.229514\pi\) |
−0.196162 | + | 0.980572i | \(0.562848\pi\) | |||||||
\(338\) | −4.81695 | − | 8.34321i | −0.262008 | − | 0.453811i | ||||
\(339\) | 6.09163 | − | 28.4561i | 0.330852 | − | 1.54552i | ||||
\(340\) | −2.27312 | + | 3.93717i | −0.123277 | + | 0.213523i | ||||
\(341\) | 21.7673 | 1.17877 | ||||||||
\(342\) | 4.27087 | + | 12.3596i | 0.230942 | + | 0.668331i | ||||
\(343\) | 7.33779 | 0.396203 | ||||||||
\(344\) | 4.21877 | − | 7.30712i | 0.227461 | − | 0.393974i | ||||
\(345\) | 2.32693 | − | 10.8699i | 0.125278 | − | 0.585215i | ||||
\(346\) | 1.61948 | + | 2.80502i | 0.0870638 | + | 0.150799i | ||||
\(347\) | −18.1066 | − | 10.4539i | −0.972015 | − | 0.561193i | −0.0721651 | − | 0.997393i | \(-0.522991\pi\) |
−0.899850 | + | 0.436200i | \(0.856324\pi\) | |||||||
\(348\) | 10.7923 | + | 9.74580i | 0.578529 | + | 0.522430i | ||||
\(349\) | 3.49912 | 0.187304 | 0.0936518 | − | 0.995605i | \(-0.470146\pi\) | ||||
0.0936518 | + | 0.995605i | \(0.470146\pi\) | |||||||
\(350\) | 0.535070 | 0.0286007 | ||||||||
\(351\) | −1.03771 | + | 9.47669i | −0.0553888 | + | 0.505828i | ||||
\(352\) | −4.51086 | + | 2.60435i | −0.240430 | + | 0.138812i | ||||
\(353\) | 0.0613213i | 0.00326380i | 0.999999 | + | 0.00163190i | \(0.000519451\pi\) | ||||
−0.999999 | + | 0.00163190i | \(0.999481\pi\) | |||||||
\(354\) | −11.4534 | + | 3.70309i | −0.608741 | + | 0.196817i | ||||
\(355\) | 5.71415 | − | 3.29907i | 0.303276 | − | 0.175096i | ||||
\(356\) | 8.15273 | − | 14.1209i | 0.432094 | − | 0.748408i | ||||
\(357\) | 2.82379 | − | 3.12702i | 0.149451 | − | 0.165499i | ||||
\(358\) | −6.71091 | + | 11.6236i | −0.354683 | + | 0.614328i | ||||
\(359\) | 15.0843 | + | 8.70894i | 0.796120 | + | 0.459640i | 0.842113 | − | 0.539302i | \(-0.181312\pi\) |
−0.0459927 | + | 0.998942i | \(0.514645\pi\) | |||||||
\(360\) | −1.75631 | − | 2.43215i | −0.0925659 | − | 0.128186i | ||||
\(361\) | −15.8360 | − | 10.4986i | −0.833475 | − | 0.552558i | ||||
\(362\) | − | 6.69773i | − | 0.352025i | ||||||
\(363\) | −5.84841 | + | 27.3199i | −0.306962 | + | 1.43392i | ||||
\(364\) | 0.850166 | + | 0.490844i | 0.0445608 | + | 0.0257272i | ||||
\(365\) | 5.29365 | − | 3.05629i | 0.277083 | − | 0.159974i | ||||
\(366\) | −2.98292 | + | 13.9342i | −0.155920 | + | 0.728354i | ||||
\(367\) | −1.34926 | − | 2.33699i | −0.0704309 | − | 0.121990i | 0.828659 | − | 0.559753i | \(-0.189104\pi\) |
−0.899090 | + | 0.437763i | \(0.855771\pi\) | |||||||
\(368\) | 6.41792i | 0.334557i | ||||||||
\(369\) | −11.3784 | + | 8.21665i | −0.592338 | + | 0.427742i | ||||
\(370\) | 2.66339 | + | 4.61313i | 0.138463 | + | 0.239825i | ||||
\(371\) | 1.74945 | + | 3.03014i | 0.0908269 | + | 0.157317i | ||||
\(372\) | −2.22678 | − | 6.88727i | −0.115453 | − | 0.357088i | ||||
\(373\) | 10.4311i | 0.540101i | 0.962846 | + | 0.270051i | \(0.0870405\pi\) | ||||
−0.962846 | + | 0.270051i | \(0.912960\pi\) | |||||||
\(374\) | −11.8400 | − | 20.5075i | −0.612232 | − | 1.06042i | ||||
\(375\) | 1.69368 | + | 0.362568i | 0.0874611 | + | 0.0187229i | ||||
\(376\) | 3.52343 | − | 2.03425i | 0.181707 | − | 0.104909i | ||||
\(377\) | −13.3396 | − | 7.70160i | −0.687022 | − | 0.396653i | ||||
\(378\) | 1.11980 | + | 2.54483i | 0.0575963 | + | 0.130892i | ||||
\(379\) | − | 9.19756i | − | 0.472447i | −0.971699 | − | 0.236223i | \(-0.924090\pi\) | ||
0.971699 | − | 0.236223i | \(-0.0759097\pi\) | |||||||
\(380\) | 4.17349 | + | 1.25777i | 0.214095 | + | 0.0645224i | ||||
\(381\) | −4.60850 | − | 14.2537i | −0.236100 | − | 0.730241i | ||||
\(382\) | 8.30976 | + | 4.79764i | 0.425164 | + | 0.245469i | ||||
\(383\) | −5.34538 | + | 9.25846i | −0.273136 | + | 0.473085i | −0.969663 | − | 0.244445i | \(-0.921394\pi\) |
0.696527 | + | 0.717530i | \(0.254728\pi\) | |||||||
\(384\) | 1.28548 | + | 1.16083i | 0.0655996 | + | 0.0592385i | ||||
\(385\) | −1.39351 | + | 2.41363i | −0.0710197 | + | 0.123010i | ||||
\(386\) | −8.36220 | + | 4.82792i | −0.425625 | + | 0.245735i | ||||
\(387\) | −20.5214 | + | 14.8190i | −1.04316 | + | 0.753291i | ||||
\(388\) | − | 0.655566i | − | 0.0332813i | ||||||
\(389\) | 20.5861 | − | 11.8854i | 1.04376 | − | 0.602614i | 0.122863 | − | 0.992424i | \(-0.460793\pi\) |
0.920895 | + | 0.389810i | \(0.127459\pi\) | |||||||
\(390\) | 2.35847 | + | 2.12977i | 0.119426 | + | 0.107845i | ||||
\(391\) | −29.1774 | −1.47557 | ||||||||
\(392\) | −6.71370 | −0.339093 | ||||||||
\(393\) | −22.3460 | + | 24.7455i | −1.12721 | + | 1.24825i | ||||
\(394\) | −2.82802 | − | 1.63276i | −0.142474 | − | 0.0822572i | ||||
\(395\) | 4.42110 | + | 7.65758i | 0.222450 | + | 0.385295i | ||||
\(396\) | 15.5452 | − | 1.58833i | 0.781173 | − | 0.0798165i | ||||
\(397\) | 11.0077 | − | 19.0660i | 0.552463 | − | 0.956893i | −0.445633 | − | 0.895216i | \(-0.647022\pi\) |
0.998096 | − | 0.0616779i | \(-0.0196452\pi\) | |||||||
\(398\) | 0.611852 | 0.0306694 | ||||||||
\(399\) | −3.53816 | − | 1.94949i | −0.177129 | − | 0.0975967i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | −2.08815 | + | 3.61678i | −0.104277 | + | 0.180614i | −0.913443 | − | 0.406967i | \(-0.866586\pi\) |
0.809165 | + | 0.587581i | \(0.199920\pi\) | |||||||
\(402\) | −0.870720 | − | 0.186396i | −0.0434276 | − | 0.00929660i | ||||
\(403\) | 3.83362 | + | 6.64003i | 0.190966 | + | 0.330763i | ||||
\(404\) | 10.5737 | + | 6.10474i | 0.526062 | + | 0.303722i | ||||
\(405\) | 1.82015 | + | 8.81403i | 0.0904440 | + | 0.437972i | ||||
\(406\) | −4.49219 | −0.222944 | ||||||||
\(407\) | −27.7456 | −1.37530 | ||||||||
\(408\) | −5.27743 | + | 5.84413i | −0.261272 | + | 0.289327i | ||||
\(409\) | 5.63570 | − | 3.25377i | 0.278667 | − | 0.160889i | −0.354153 | − | 0.935188i | \(-0.615231\pi\) |
0.632820 | + | 0.774299i | \(0.281897\pi\) | |||||||
\(410\) | 4.67835i | 0.231047i | ||||||||
\(411\) | 0.998413 | + | 3.08802i | 0.0492481 | + | 0.152321i | ||||
\(412\) | 8.68866 | − | 5.01640i | 0.428059 | − | 0.247140i | ||||
\(413\) | 1.85928 | − | 3.22036i | 0.0914890 | − | 0.158464i | ||||
\(414\) | 7.88215 | − | 17.5664i | 0.387387 | − | 0.863342i | ||||
\(415\) | −6.60794 | + | 11.4453i | −0.324371 | + | 0.561827i | ||||
\(416\) | −1.58889 | − | 0.917346i | −0.0779017 | − | 0.0449766i | ||||
\(417\) | 10.9948 | − | 3.55481i | 0.538417 | − | 0.174080i | ||||
\(418\) | −16.5429 | + | 15.5504i | −0.809137 | + | 0.760593i | ||||
\(419\) | 32.4656i | 1.58605i | 0.609189 | + | 0.793025i | \(0.291495\pi\) | ||||
−0.609189 | + | 0.793025i | \(0.708505\pi\) | |||||||
\(420\) | 0.906236 | + | 0.193999i | 0.0442198 | + | 0.00946619i | ||||
\(421\) | 22.1581 | + | 12.7930i | 1.07992 | + | 0.623491i | 0.930874 | − | 0.365339i | \(-0.119047\pi\) |
0.149044 | + | 0.988831i | \(0.452380\pi\) | |||||||
\(422\) | 4.21436 | − | 2.43316i | 0.205152 | − | 0.118444i | ||||
\(423\) | −12.1423 | + | 1.24064i | −0.590379 | + | 0.0603220i | ||||
\(424\) | −3.26957 | − | 5.66307i | −0.158785 | − | 0.275023i | ||||
\(425\) | − | 4.54625i | − | 0.220525i | ||||||
\(426\) | 10.8741 | − | 3.51579i | 0.526850 | − | 0.170340i | ||||
\(427\) | −2.20106 | − | 3.81236i | −0.106517 | − | 0.184493i | ||||
\(428\) | −9.98679 | − | 17.2976i | −0.482730 | − | 0.836112i | ||||
\(429\) | −15.7494 | + | 5.09206i | −0.760386 | + | 0.245847i | ||||
\(430\) | 8.43754i | 0.406894i | ||||||||
\(431\) | −4.97293 | − | 8.61337i | −0.239538 | − | 0.414892i | 0.721044 | − | 0.692889i | \(-0.243663\pi\) |
−0.960582 | + | 0.277998i | \(0.910329\pi\) | |||||||
\(432\) | −2.09281 | − | 4.75606i | −0.100690 | − | 0.228826i | ||||
\(433\) | −21.0832 | + | 12.1724i | −1.01319 | + | 0.584968i | −0.912125 | − | 0.409911i | \(-0.865560\pi\) |
−0.101069 | + | 0.994879i | \(0.532226\pi\) | |||||||
\(434\) | 1.93650 | + | 1.11804i | 0.0929549 | + | 0.0536675i | ||||
\(435\) | −14.2193 | − | 3.04395i | −0.681764 | − | 0.145946i | ||||
\(436\) | 8.02386i | 0.384273i | ||||||||
\(437\) | 6.40176 | + | 27.2327i | 0.306237 | + | 1.30272i | ||||
\(438\) | 10.0739 | − | 3.25706i | 0.481348 | − | 0.155629i | ||||
\(439\) | −32.3043 | − | 18.6509i | −1.54180 | − | 0.890159i | −0.998725 | − | 0.0504744i | \(-0.983927\pi\) |
−0.543075 | − | 0.839684i | \(-0.682740\pi\) | |||||||
\(440\) | 2.60435 | − | 4.51086i | 0.124157 | − | 0.215047i | ||||
\(441\) | 18.3760 | + | 8.24541i | 0.875047 | + | 0.392639i | ||||
\(442\) | 4.17048 | − | 7.22348i | 0.198369 | − | 0.343586i | ||||
\(443\) | 14.9279 | − | 8.61861i | 0.709244 | − | 0.409482i | −0.101537 | − | 0.994832i | \(-0.532376\pi\) |
0.810781 | + | 0.585349i | \(0.199043\pi\) | |||||||
\(444\) | 2.83835 | + | 8.77882i | 0.134702 | + | 0.416624i | ||||
\(445\) | 16.3055i | 0.772953i | ||||||||
\(446\) | −4.74349 | + | 2.73866i | −0.224611 | + | 0.129679i | ||||
\(447\) | −4.20670 | + | 4.65842i | −0.198970 | + | 0.220336i | ||||
\(448\) | −0.535070 | −0.0252797 | ||||||||
\(449\) | 14.5905 | 0.688568 | 0.344284 | − | 0.938865i | \(-0.388122\pi\) | ||||
0.344284 | + | 0.938865i | \(0.388122\pi\) | |||||||
\(450\) | 2.73709 | + | 1.22815i | 0.129028 | + | 0.0578954i | ||||
\(451\) | −21.1034 | − | 12.1840i | −0.993719 | − | 0.573724i | ||||
\(452\) | −8.40067 | − | 14.5504i | −0.395134 | − | 0.684393i | ||||
\(453\) | 33.4433 | + | 7.15925i | 1.57130 | + | 0.336371i | ||||
\(454\) | −6.13682 | + | 10.6293i | −0.288015 | + | 0.498857i | ||||
\(455\) | −0.981688 | −0.0460222 | ||||||||
\(456\) | 6.61252 | + | 3.64344i | 0.309659 | + | 0.170619i | ||||
\(457\) | −35.8465 | −1.67683 | −0.838414 | − | 0.545034i | \(-0.816517\pi\) | ||||
−0.838414 | + | 0.545034i | \(0.816517\pi\) | |||||||
\(458\) | −12.6163 | + | 21.8521i | −0.589521 | + | 1.02108i | ||||
\(459\) | 21.6222 | − | 9.51443i | 1.00924 | − | 0.444096i | ||||
\(460\) | −3.20896 | − | 5.55808i | −0.149619 | − | 0.259147i | ||||
\(461\) | −12.6225 | − | 7.28761i | −0.587889 | − | 0.339418i | 0.176373 | − | 0.984323i | \(-0.443563\pi\) |
−0.764262 | + | 0.644905i | \(0.776897\pi\) | |||||||
\(462\) | −3.23526 | + | 3.58266i | −0.150518 | + | 0.166681i | ||||
\(463\) | 20.1328 | 0.935649 | 0.467825 | − | 0.883821i | \(-0.345038\pi\) | ||||
0.467825 | + | 0.883821i | \(0.345038\pi\) | |||||||
\(464\) | 8.39553 | 0.389753 | ||||||||
\(465\) | 5.37208 | + | 4.85116i | 0.249124 | + | 0.224967i | ||||
\(466\) | 15.1283 | − | 8.73433i | 0.700805 | − | 0.404610i | ||||
\(467\) | 0.535926i | 0.0247997i | 0.999923 | + | 0.0123999i | \(0.00394710\pi\) | ||||
−0.999923 | + | 0.0123999i | \(0.996053\pi\) | |||||||
\(468\) | 3.22229 | + | 4.46225i | 0.148951 | + | 0.206267i | ||||
\(469\) | 0.238226 | − | 0.137540i | 0.0110002 | − | 0.00635099i | ||||
\(470\) | −2.03425 | + | 3.52343i | −0.0938331 | + | 0.162524i | ||||
\(471\) | −5.22904 | − | 4.72198i | −0.240941 | − | 0.217578i | ||||
\(472\) | −3.47483 | + | 6.01858i | −0.159942 | + | 0.277028i | ||||
\(473\) | −38.0606 | − | 21.9743i | −1.75003 | − | 1.01038i | ||||
\(474\) | 4.71153 | + | 14.5724i | 0.216408 | + | 0.669333i | ||||
\(475\) | −4.24323 | + | 0.997481i | −0.194693 | + | 0.0457676i | ||||
\(476\) | − | 2.43256i | − | 0.111496i | ||||||
\(477\) | 1.99403 | + | 19.5158i | 0.0913005 | + | 0.893569i | ||||
\(478\) | −24.1544 | − | 13.9456i | −1.10480 | − | 0.637855i | ||||
\(479\) | −21.8777 | + | 12.6311i | −0.999618 | + | 0.577130i | −0.908135 | − | 0.418677i | \(-0.862494\pi\) |
−0.0914830 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(480\) | −1.69368 | − | 0.362568i | −0.0773055 | − | 0.0165489i | ||||
\(481\) | −4.88650 | − | 8.46367i | −0.222805 | − | 0.385910i | ||||
\(482\) | 25.1753i | 1.14670i | ||||||||
\(483\) | 1.82981 | + | 5.65947i | 0.0832593 | + | 0.257515i | ||||
\(484\) | 8.06525 | + | 13.9694i | 0.366602 | + | 0.634974i | ||||
\(485\) | 0.327783 | + | 0.567737i | 0.0148839 | + | 0.0257796i | ||||
\(486\) | −0.112938 | + | 15.5880i | −0.00512296 | + | 0.707088i | ||||
\(487\) | 27.4924i | 1.24580i | 0.782302 | + | 0.622899i | \(0.214045\pi\) | ||||
−0.782302 | + | 0.622899i | \(0.785955\pi\) | |||||||
\(488\) | 4.11360 | + | 7.12497i | 0.186214 | + | 0.322532i | ||||
\(489\) | 2.44129 | − | 11.4041i | 0.110399 | − | 0.515711i | ||||
\(490\) | 5.81424 | − | 3.35685i | 0.262660 | − | 0.151647i | ||||
\(491\) | 9.52214 | + | 5.49761i | 0.429728 | + | 0.248104i | 0.699231 | − | 0.714896i | \(-0.253526\pi\) |
−0.269503 | + | 0.963000i | \(0.586859\pi\) | |||||||
\(492\) | −1.69622 | + | 7.92361i | −0.0764715 | + | 0.357224i | ||||
\(493\) | 38.1681i | 1.71901i | ||||||||
\(494\) | −7.65706 | − | 2.30762i | −0.344508 | − | 0.103825i | ||||
\(495\) | −12.6683 | + | 9.14811i | −0.569399 | + | 0.411177i | ||||
\(496\) | −3.61915 | − | 2.08952i | −0.162505 | − | 0.0938221i | ||||
\(497\) | −1.76523 | + | 3.05747i | −0.0791814 | + | 0.137146i | ||||
\(498\) | −15.3414 | + | 16.9888i | −0.687465 | + | 0.761286i | ||||
\(499\) | 7.16095 | − | 12.4031i | 0.320568 | − | 0.555241i | −0.660037 | − | 0.751233i | \(-0.729459\pi\) |
0.980605 | + | 0.195992i | \(0.0627928\pi\) | |||||||
\(500\) | 0.866025 | − | 0.500000i | 0.0387298 | − | 0.0223607i | ||||
\(501\) | 10.9628 | − | 3.54447i | 0.489781 | − | 0.158355i | ||||
\(502\) | − | 17.9891i | − | 0.802894i | ||||||
\(503\) | 0.853524 | − | 0.492782i | 0.0380567 | − | 0.0219721i | −0.480851 | − | 0.876802i | \(-0.659672\pi\) |
0.518908 | + | 0.854830i | \(0.326339\pi\) | |||||||
\(504\) | 1.46453 | + | 0.657144i | 0.0652355 | + | 0.0292715i | ||||
\(505\) | −12.2095 | −0.543315 | ||||||||
\(506\) | 33.4290 | 1.48610 | ||||||||
\(507\) | 12.3842 | + | 11.1834i | 0.550003 | + | 0.496670i | ||||
\(508\) | −7.49011 | − | 4.32442i | −0.332320 | − | 0.191865i | ||||
\(509\) | −9.01611 | − | 15.6164i | −0.399632 | − | 0.692183i | 0.594048 | − | 0.804429i | \(-0.297529\pi\) |
−0.993680 | + | 0.112246i | \(0.964195\pi\) | |||||||
\(510\) | 1.64832 | − | 7.69988i | 0.0729890 | − | 0.340956i | ||||
\(511\) | −1.63533 | + | 2.83247i | −0.0723427 | + | 0.125301i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.6244 | − | 18.0935i | −0.601531 | − | 0.798850i | ||||
\(514\) | −15.2441 | −0.672387 | ||||||||
\(515\) | −5.01640 | + | 8.68866i | −0.221049 | + | 0.382868i | ||||
\(516\) | −3.05918 | + | 14.2905i | −0.134673 | + | 0.629103i | ||||
\(517\) | −10.5958 | − | 18.3525i | −0.466003 | − | 0.807141i | ||||
\(518\) | −2.46835 | − | 1.42510i | −0.108453 | − | 0.0626153i | ||||
\(519\) | −4.16363 | − | 3.75989i | −0.182763 | − | 0.165041i | ||||
\(520\) | 1.83469 | 0.0804565 | ||||||||
\(521\) | 31.2308 | 1.36825 | 0.684124 | − | 0.729366i | \(-0.260185\pi\) | ||||
0.684124 | + | 0.729366i | \(0.260185\pi\) | |||||||
\(522\) | −22.9793 | − | 10.3109i | −1.00578 | − | 0.451298i | ||||
\(523\) | 30.0065 | − | 17.3243i | 1.31209 | − | 0.757538i | 0.329651 | − | 0.944103i | \(-0.393069\pi\) |
0.982443 | + | 0.186565i | \(0.0597355\pi\) | |||||||
\(524\) | 19.2500i | 0.840939i | ||||||||
\(525\) | −0.881823 | + | 0.285110i | −0.0384859 | + | 0.0124432i | ||||
\(526\) | 19.9274 | − | 11.5051i | 0.868878 | − | 0.501647i | ||||
\(527\) | 9.49947 | − | 16.4536i | 0.413803 | − | 0.716728i | ||||
\(528\) | 6.04642 | − | 6.69569i | 0.263137 | − | 0.291393i | ||||
\(529\) | 9.09485 | − | 15.7527i | 0.395428 | − | 0.684902i | ||||
\(530\) | 5.66307 | + | 3.26957i | 0.245988 | + | 0.142021i | ||||
\(531\) | 16.9026 | − | 12.2058i | 0.733511 | − | 0.529686i | ||||
\(532\) | −2.27043 | + | 0.533722i | −0.0984354 | + | 0.0231398i | ||||
\(533\) | − | 8.58332i | − | 0.371785i | ||||||
\(534\) | −5.91184 | + | 27.6162i | −0.255830 | + | 1.19507i | ||||
\(535\) | 17.2976 | + | 9.98679i | 0.747842 | + | 0.431767i | ||||
\(536\) | −0.445224 | + | 0.257050i | −0.0192307 | + | 0.0111029i | ||||
\(537\) | 4.86633 | − | 22.7322i | 0.209997 | − | 0.980969i | ||||
\(538\) | 11.9188 | + | 20.6440i | 0.513856 | + | 0.890025i | ||||
\(539\) | 34.9696i | 1.50625i | ||||||||
\(540\) | 4.19046 | + | 3.07247i | 0.180329 | + | 0.132218i | ||||
\(541\) | −18.2442 | − | 31.5999i | −0.784379 | − | 1.35858i | −0.929369 | − | 0.369151i | \(-0.879648\pi\) |
0.144990 | − | 0.989433i | \(-0.453685\pi\) | |||||||
\(542\) | 10.8992 | + | 18.8780i | 0.468163 | + | 0.810881i | ||||
\(543\) | 3.56885 | + | 11.0382i | 0.153154 | + | 0.473694i | ||||
\(544\) | 4.54625i | 0.194919i | ||||||||
\(545\) | −4.01193 | − | 6.94887i | −0.171852 | − | 0.297657i | ||||
\(546\) | −1.66266 | − | 0.355929i | −0.0711554 | − | 0.0152323i | ||||
\(547\) | 32.3959 | − | 18.7038i | 1.38515 | − | 0.799716i | 0.392385 | − | 0.919801i | \(-0.371650\pi\) |
0.992764 | + | 0.120085i | \(0.0383167\pi\) | |||||||
\(548\) | 1.62271 | + | 0.936869i | 0.0693185 | + | 0.0400211i | ||||
\(549\) | −2.50879 | − | 24.5538i | −0.107072 | − | 1.04793i | ||||
\(550\) | 5.20870i | 0.222100i | ||||||||
\(551\) | 35.6242 | − | 8.37438i | 1.51764 | − | 0.356761i | ||||
\(552\) | −3.41976 | − | 10.5771i | −0.145555 | − | 0.450190i | ||||
\(553\) | −4.09734 | − | 2.36560i | −0.174237 | − | 0.100596i | ||||
\(554\) | 3.16986 | − | 5.49035i | 0.134674 | − | 0.233263i | ||||
\(555\) | −6.84749 | − | 6.18350i | −0.290660 | − | 0.262475i | ||||
\(556\) | 3.33569 | − | 5.77758i | 0.141465 | − | 0.245024i | ||||
\(557\) | −17.6536 | + | 10.1923i | −0.748005 | + | 0.431861i | −0.824973 | − | 0.565173i | \(-0.808810\pi\) |
0.0769675 | + | 0.997034i | \(0.475476\pi\) | |||||||
\(558\) | 7.33970 | + | 10.1640i | 0.310714 | + | 0.430278i | ||||
\(559\) | − | 15.4803i | − | 0.654746i | ||||||
\(560\) | 0.463384 | − | 0.267535i | 0.0195815 | − | 0.0113054i | ||||
\(561\) | 30.4403 | + | 27.4885i | 1.28519 | + | 1.16057i | ||||
\(562\) | 23.2064 | 0.978901 | ||||||||
\(563\) | −4.90484 | −0.206714 | −0.103357 | − | 0.994644i | \(-0.532958\pi\) | ||||
−0.103357 | + | 0.994644i | \(0.532958\pi\) | |||||||
\(564\) | −4.72285 | + | 5.23000i | −0.198868 | + | 0.220223i | ||||
\(565\) | 14.5504 | + | 8.40067i | 0.612140 | + | 0.353419i | ||||
\(566\) | 8.02179 | + | 13.8941i | 0.337181 | + | 0.584014i | ||||
\(567\) | −3.20149 | − | 3.59733i | −0.134450 | − | 0.151073i | ||||
\(568\) | 3.29907 | − | 5.71415i | 0.138426 | − | 0.239760i | ||||
\(569\) | −16.9616 | −0.711068 | −0.355534 | − | 0.934663i | \(-0.615701\pi\) | ||||
−0.355534 | + | 0.934663i | \(0.615701\pi\) | |||||||
\(570\) | −7.54833 | + | 0.150951i | −0.316165 | + | 0.00632263i | ||||
\(571\) | −13.9462 | −0.583632 | −0.291816 | − | 0.956474i | \(-0.594260\pi\) | ||||
−0.291816 | + | 0.956474i | \(0.594260\pi\) | |||||||
\(572\) | −4.77817 | + | 8.27604i | −0.199785 | + | 0.346039i | ||||
\(573\) | −16.2513 | − | 3.47894i | −0.678908 | − | 0.145335i | ||||
\(574\) | −1.25162 | − | 2.16787i | −0.0522417 | − | 0.0904852i | ||||
\(575\) | 5.55808 | + | 3.20896i | 0.231788 | + | 0.133823i | ||||
\(576\) | −2.73709 | − | 1.22815i | −0.114045 | − | 0.0511728i | ||||
\(577\) | −4.90123 | −0.204041 | −0.102020 | − | 0.994782i | \(-0.532531\pi\) | ||||
−0.102020 | + | 0.994782i | \(0.532531\pi\) | |||||||
\(578\) | −3.66836 | −0.152584 | ||||||||
\(579\) | 11.2088 | − | 12.4124i | 0.465822 | − | 0.515843i | ||||
\(580\) | −7.27074 | + | 4.19776i | −0.301901 | + | 0.174303i | ||||
\(581\) | − | 7.07142i | − | 0.293372i | ||||||
\(582\) | 0.349315 | + | 1.08041i | 0.0144796 | + | 0.0447843i | ||||
\(583\) | −29.4972 | + | 17.0302i | −1.22165 | + | 0.705319i | ||||
\(584\) | 3.05629 | − | 5.29365i | 0.126470 | − | 0.219053i | ||||
\(585\) | −5.02171 | − | 2.25327i | −0.207622 | − | 0.0931613i | ||||
\(586\) | 10.4662 | − | 18.1280i | 0.432354 | − | 0.748859i | ||||
\(587\) | 39.6685 | + | 22.9026i | 1.63730 | + | 0.945293i | 0.981759 | + | 0.190130i | \(0.0608910\pi\) |
0.655537 | + | 0.755163i | \(0.272442\pi\) | |||||||
\(588\) | 11.0645 | − | 3.57737i | 0.456293 | − | 0.147528i | ||||
\(589\) | −17.4412 | − | 5.25628i | −0.718651 | − | 0.216581i | ||||
\(590\) | − | 6.94966i | − | 0.286113i | ||||||
\(591\) | 5.53074 | + | 1.18397i | 0.227504 | + | 0.0487021i | ||||
\(592\) | 4.61313 | + | 2.66339i | 0.189598 | + | 0.109465i | ||||
\(593\) | −23.0106 | + | 13.2852i | −0.944933 | + | 0.545557i | −0.891503 | − | 0.453014i | \(-0.850349\pi\) |
−0.0534296 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(594\) | −24.7729 | + | 10.9008i | −1.01644 | + | 0.447266i | ||||
\(595\) | 1.21628 | + | 2.10666i | 0.0498626 | + | 0.0863646i | ||||
\(596\) | 3.62387i | 0.148439i | ||||||||
\(597\) | −1.00836 | + | 0.326023i | −0.0412696 | + | 0.0133432i | ||||
\(598\) | 5.88745 | + | 10.1974i | 0.240756 | + | 0.417001i | ||||
\(599\) | 18.2454 | + | 31.6020i | 0.745488 | + | 1.29122i | 0.949967 | + | 0.312352i | \(0.101117\pi\) |
−0.204479 | + | 0.978871i | \(0.565550\pi\) | |||||||
\(600\) | 1.64805 | − | 0.532846i | 0.0672814 | − | 0.0217533i | ||||
\(601\) | 5.57468i | 0.227396i | 0.993515 | + | 0.113698i | \(0.0362696\pi\) | ||||
−0.993515 | + | 0.113698i | \(0.963730\pi\) | |||||||
\(602\) | −2.25734 | − | 3.90982i | −0.0920021 | − | 0.159352i | ||||
\(603\) | 1.53431 | − | 0.156768i | 0.0624820 | − | 0.00638411i | ||||
\(604\) | 17.1005 | − | 9.87297i | 0.695809 | − | 0.401725i | ||||
\(605\) | −13.9694 | − | 8.06525i | −0.567938 | − | 0.327899i | ||||
\(606\) | −20.6789 | − | 4.42677i | −0.840024 | − | 0.179825i | ||||
\(607\) | − | 7.25553i | − | 0.294493i | −0.989100 | − | 0.147246i | \(-0.952959\pi\) | ||
0.989100 | − | 0.147246i | \(-0.0470410\pi\) | |||||||
\(608\) | 4.24323 | − | 0.997481i | 0.172086 | − | 0.0404532i | ||||
\(609\) | 7.40337 | − | 2.39365i | 0.300000 | − | 0.0969954i | ||||
\(610\) | −7.12497 | − | 4.11360i | −0.288482 | − | 0.166555i | ||||
\(611\) | 3.73223 | − | 6.46441i | 0.150990 | − | 0.261522i | ||||
\(612\) | 5.58346 | − | 12.4435i | 0.225698 | − | 0.502998i | ||||
\(613\) | −3.18359 | + | 5.51414i | −0.128584 | + | 0.222714i | −0.923128 | − | 0.384492i | \(-0.874377\pi\) |
0.794544 | + | 0.607206i | \(0.207710\pi\) | |||||||
\(614\) | 9.83298 | − | 5.67707i | 0.396827 | − | 0.229108i | ||||
\(615\) | −2.49284 | − | 7.71016i | −0.100521 | − | 0.310904i | ||||
\(616\) | 2.78702i | 0.112292i | ||||||||
\(617\) | 7.70794 | − | 4.45018i | 0.310310 | − | 0.179158i | −0.336755 | − | 0.941592i | \(-0.609329\pi\) |
0.647065 | + | 0.762435i | \(0.275996\pi\) | |||||||
\(618\) | −11.6464 | + | 12.8970i | −0.468487 | + | 0.518793i | ||||
\(619\) | −9.83923 | −0.395472 | −0.197736 | − | 0.980255i | \(-0.563359\pi\) | ||||
−0.197736 | + | 0.980255i | \(0.563359\pi\) | |||||||
\(620\) | 4.17904 | 0.167834 | ||||||||
\(621\) | −3.63001 | + | 33.1503i | −0.145667 | + | 1.33028i | ||||
\(622\) | 5.38070 | + | 3.10655i | 0.215746 | + | 0.124561i | ||||
\(623\) | −4.36228 | − | 7.55569i | −0.174771 | − | 0.302712i | ||||
\(624\) | 3.10738 | + | 0.665201i | 0.124395 | + | 0.0266293i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 10.2254 | 0.408688 | ||||||||
\(627\) | 18.9775 | − | 34.4426i | 0.757890 | − | 1.37550i | ||||
\(628\) | −4.06776 | −0.162321 | ||||||||
\(629\) | −12.1084 | + | 20.9724i | −0.482795 | + | 0.836225i | ||||
\(630\) | −1.59690 | + | 0.163163i | −0.0636218 | + | 0.00650057i | ||||
\(631\) | 8.42353 | + | 14.5900i | 0.335335 | + | 0.580818i | 0.983549 | − | 0.180641i | \(-0.0578171\pi\) |
−0.648214 | + | 0.761458i | \(0.724484\pi\) | |||||||
\(632\) | 7.65758 | + | 4.42110i | 0.304602 | + | 0.175862i | ||||
\(633\) | −5.64898 | + | 6.25558i | −0.224527 | + | 0.248637i | ||||
\(634\) | 10.9204 | 0.433706 | ||||||||
\(635\) | 8.64884 | 0.343219 | ||||||||
\(636\) | 8.40597 | + | 7.59085i | 0.333318 | + | 0.300997i | ||||
\(637\) | −10.6673 | + | 6.15878i | −0.422655 | + | 0.244020i | ||||
\(638\) | − | 43.7297i | − | 1.73128i | ||||||
\(639\) | −16.0477 | + | 11.5884i | −0.634836 | + | 0.458430i | ||||
\(640\) | −0.866025 | + | 0.500000i | −0.0342327 | + | 0.0197642i | ||||
\(641\) | −18.3162 | + | 31.7246i | −0.723446 | + | 1.25305i | 0.236164 | + | 0.971713i | \(0.424110\pi\) |
−0.959610 | + | 0.281333i | \(0.909224\pi\) | |||||||
\(642\) | 25.6757 | + | 23.1860i | 1.01334 | + | 0.915077i | ||||
\(643\) | −16.7131 | + | 28.9479i | −0.659099 | + | 1.14159i | 0.321750 | + | 0.946825i | \(0.395729\pi\) |
−0.980849 | + | 0.194769i | \(0.937604\pi\) | |||||||
\(644\) | 2.97396 | + | 1.71702i | 0.117190 | + | 0.0676600i | ||||
\(645\) | −4.49591 | − | 13.9055i | −0.177026 | − | 0.547529i | ||||
\(646\) | 4.53480 | + | 19.2908i | 0.178419 | + | 0.758986i | ||||
\(647\) | − | 23.6956i | − | 0.931570i | −0.884898 | − | 0.465785i | \(-0.845772\pi\) | ||
0.884898 | − | 0.465785i | \(-0.154228\pi\) | |||||||
\(648\) | 5.98331 | + | 6.72310i | 0.235047 | + | 0.264108i | ||||
\(649\) | 31.3489 | + | 18.0993i | 1.23055 | + | 0.710461i | ||||
\(650\) | −1.58889 | + | 0.917346i | −0.0623214 | + | 0.0359813i | ||||
\(651\) | −3.78719 | − | 0.810730i | −0.148432 | − | 0.0317750i | ||||
\(652\) | −3.36667 | − | 5.83124i | −0.131849 | − | 0.228369i | ||||
\(653\) | 35.0646i | 1.37218i | 0.727515 | + | 0.686092i | \(0.240675\pi\) | ||||
−0.727515 | + | 0.686092i | \(0.759325\pi\) | |||||||
\(654\) | −4.27548 | − | 13.2237i | −0.167184 | − | 0.517089i | ||||
\(655\) | −9.62499 | − | 16.6710i | −0.376079 | − | 0.651389i | ||||
\(656\) | 2.33917 | + | 4.05157i | 0.0913294 | + | 0.158187i | ||||
\(657\) | −14.8667 | + | 10.7356i | −0.580006 | + | 0.418837i | ||||
\(658\) | − | 2.17694i | − | 0.0848658i | ||||||
\(659\) | −7.25327 | − | 12.5630i | −0.282547 | − | 0.489386i | 0.689464 | − | 0.724320i | \(-0.257846\pi\) |
−0.972011 | + | 0.234934i | \(0.924513\pi\) | |||||||
\(660\) | −1.88851 | + | 8.82185i | −0.0735100 | + | 0.343390i | ||||
\(661\) | 40.0197 | − | 23.1054i | 1.55658 | − | 0.898695i | 0.559005 | − | 0.829164i | \(-0.311183\pi\) |
0.997580 | − | 0.0695304i | \(-0.0221501\pi\) | |||||||
\(662\) | −4.54482 | − | 2.62396i | −0.176640 | − | 0.101983i | ||||
\(663\) | −3.02417 | + | 14.1269i | −0.117449 | + | 0.548643i | ||||
\(664\) | 13.2159i | 0.512876i | ||||||||
\(665\) | 1.69939 | − | 1.59743i | 0.0658993 | − | 0.0619457i | ||||
\(666\) | −9.35551 | − | 12.9555i | −0.362519 | − | 0.502017i | ||||
\(667\) | −46.6630 | − | 26.9409i | −1.80680 | − | 1.04316i | ||||
\(668\) | 3.32598 | − | 5.76077i | 0.128686 | − | 0.222891i | ||||
\(669\) | 6.35824 | − | 7.04100i | 0.245824 | − | 0.272221i | ||||
\(670\) | 0.257050 | − | 0.445224i | 0.00993071 | − | 0.0172005i | ||||
\(671\) | 37.1118 | − | 21.4265i | 1.43268 | − | 0.827161i | ||||
\(672\) | 0.881823 | − | 0.285110i | 0.0340171 | − | 0.0109983i | ||||
\(673\) | 16.5098i | 0.636405i | 0.948023 | + | 0.318202i | \(0.103079\pi\) | ||||
−0.948023 | + | 0.318202i | \(0.896921\pi\) | |||||||
\(674\) | −10.1877 | + | 5.88185i | −0.392414 | + | 0.226560i | ||||
\(675\) | −5.16528 | − | 0.565605i | −0.198812 | − | 0.0217701i | ||||
\(676\) | 9.63391 | 0.370535 | ||||||||
\(677\) | −35.1622 | −1.35139 | −0.675696 | − | 0.737181i | \(-0.736157\pi\) | ||||
−0.675696 | + | 0.737181i | \(0.736157\pi\) | |||||||
\(678\) | 21.5979 | + | 19.5035i | 0.829461 | + | 0.749029i | ||||
\(679\) | −0.303779 | − | 0.175387i | −0.0116580 | − | 0.00673072i | ||||
\(680\) | −2.27312 | − | 3.93717i | −0.0871703 | − | 0.150983i | ||||
\(681\) | 4.45003 | − | 20.7876i | 0.170525 | − | 0.796582i | ||||
\(682\) | −10.8837 | + | 18.8511i | −0.416757 | + | 0.721844i | ||||
\(683\) | 37.8100 | 1.44676 | 0.723380 | − | 0.690450i | \(-0.242587\pi\) | ||||
0.723380 | + | 0.690450i | \(0.242587\pi\) | |||||||
\(684\) | −12.8392 | − | 2.48112i | −0.490918 | − | 0.0948680i | ||||
\(685\) | −1.87374 | −0.0715919 | ||||||||
\(686\) | −3.66889 | + | 6.35471i | −0.140079 | + | 0.242624i | ||||
\(687\) | 9.14853 | − | 42.7359i | 0.349038 | − | 1.63048i | ||||
\(688\) | 4.21877 | + | 7.30712i | 0.160839 | + | 0.278581i | ||||
\(689\) | −10.3900 | − | 5.99866i | −0.395827 | − | 0.228531i | ||||
\(690\) | 8.25013 | + | 7.45013i | 0.314077 | + | 0.283622i | ||||
\(691\) | 32.1235 | 1.22203 | 0.611017 | − | 0.791617i | \(-0.290761\pi\) | ||||
0.611017 | + | 0.791617i | \(0.290761\pi\) | |||||||
\(692\) | −3.23896 | −0.123127 | ||||||||
\(693\) | 3.42286 | − | 7.62831i | 0.130024 | − | 0.289775i | ||||
\(694\) | 18.1066 | − | 10.4539i | 0.687318 | − | 0.396823i | ||||
\(695\) | 6.67138i | 0.253060i | ||||||||
\(696\) | −13.8363 | + | 4.47352i | −0.524462 | + | 0.169568i | ||||
\(697\) | −18.4194 | + | 10.6345i | −0.697686 | + | 0.402809i | ||||
\(698\) | −1.74956 | + | 3.03033i | −0.0662218 | + | 0.114700i | ||||
\(699\) | −20.2782 | + | 22.4557i | −0.766991 | + | 0.849352i | ||||
\(700\) | −0.267535 | + | 0.463384i | −0.0101119 | + | 0.0175143i | ||||
\(701\) | −23.8066 | − | 13.7447i | −0.899161 | − | 0.519131i | −0.0222334 | − | 0.999753i | \(-0.507078\pi\) |
−0.876928 | + | 0.480622i | \(0.840411\pi\) | |||||||
\(702\) | −7.68820 | − | 5.63703i | −0.290172 | − | 0.212756i | ||||
\(703\) | 22.2313 | + | 6.69988i | 0.838468 | + | 0.252691i | ||||
\(704\) | − | 5.20870i | − | 0.196310i | ||||||
\(705\) | 1.47511 | − | 6.89074i | 0.0555559 | − | 0.259520i | ||||
\(706\) | −0.0531058 | − | 0.0306607i | −0.00199866 | − | 0.00115393i | ||||
\(707\) | 5.65768 | − | 3.26646i | 0.212779 | − | 0.122848i | ||||
\(708\) | 2.51972 | − | 11.7705i | 0.0946970 | − | 0.442362i | ||||
\(709\) | 2.73932 | + | 4.74464i | 0.102877 | + | 0.178189i | 0.912869 | − | 0.408253i | \(-0.133862\pi\) |
−0.809992 | + | 0.586441i | \(0.800528\pi\) | |||||||
\(710\) | 6.59813i | 0.247624i | ||||||||
\(711\) | −15.5297 | − | 21.5056i | −0.582409 | − | 0.806522i | ||||
\(712\) | 8.15273 | + | 14.1209i | 0.305536 | + | 0.529205i | ||||
\(713\) | 13.4104 | + | 23.2274i | 0.502222 | + | 0.869874i | ||||
\(714\) | 1.29618 | + | 4.00898i | 0.0485083 | + | 0.150032i | ||||
\(715\) | − | 9.55635i | − | 0.357387i | ||||||
\(716\) | −6.71091 | − | 11.6236i | −0.250799 | − | 0.434396i | ||||
\(717\) | 47.2386 | + | 10.1124i | 1.76416 | + | 0.377656i | ||||
\(718\) | −15.0843 | + | 8.70894i | −0.562942 | + | 0.325015i | ||||
\(719\) | −39.6746 | − | 22.9061i | −1.47961 | − | 0.854254i | −0.479878 | − | 0.877335i | \(-0.659319\pi\) |
−0.999734 | + | 0.0230807i | \(0.992653\pi\) | |||||||
\(720\) | 2.98446 | − | 0.304938i | 0.111224 | − | 0.0113644i | ||||
\(721\) | − | 5.36825i | − | 0.199924i | ||||||
\(722\) | 17.0101 | − | 8.46509i | 0.633049 | − | 0.315038i | ||||
\(723\) | −13.4146 | − | 41.4903i | −0.498893 | − | 1.54304i | ||||
\(724\) | 5.80040 | + | 3.34886i | 0.215570 | + | 0.124459i | ||||
\(725\) | 4.19776 | − | 7.27074i | 0.155901 | − | 0.270028i | ||||
\(726\) | −20.7355 | − | 18.7248i | −0.769567 | − | 0.694943i | ||||
\(727\) | 4.46581 | − | 7.73500i | 0.165628 | − | 0.286875i | −0.771250 | − | 0.636532i | \(-0.780368\pi\) |
0.936878 | + | 0.349657i | \(0.113702\pi\) | |||||||
\(728\) | −0.850166 | + | 0.490844i | −0.0315093 | + | 0.0181919i | ||||
\(729\) | −8.11990 | − | 25.7501i | −0.300737 | − | 0.953707i | ||||
\(730\) | 6.11259i | 0.226237i | ||||||||
\(731\) | −33.2200 | + | 19.1796i | −1.22869 | + | 0.709382i | ||||
\(732\) | −10.5759 | − | 9.55040i | −0.390898 | − | 0.352993i | ||||
\(733\) | −9.80467 | −0.362144 | −0.181072 | − | 0.983470i | \(-0.557957\pi\) | ||||
−0.181072 | + | 0.983470i | \(0.557957\pi\) | |||||||
\(734\) | 2.69852 | 0.0996043 | ||||||||
\(735\) | −7.79348 | + | 8.63035i | −0.287467 | + | 0.318335i | ||||
\(736\) | −5.55808 | − | 3.20896i | −0.204874 | − | 0.118284i | ||||
\(737\) | 1.33890 | + | 2.31903i | 0.0493188 | + | 0.0854227i | ||||
\(738\) | −1.42660 | − | 13.9624i | −0.0525140 | − | 0.513961i | ||||
\(739\) | 21.8672 | − | 37.8751i | 0.804397 | − | 1.39326i | −0.112300 | − | 0.993674i | \(-0.535822\pi\) |
0.916697 | − | 0.399582i | \(-0.130845\pi\) | |||||||
\(740\) | −5.32678 | −0.195816 | ||||||||
\(741\) | 13.8488 | − | 0.276948i | 0.508750 | − | 0.0101739i | ||||
\(742\) | −3.49890 | −0.128449 | ||||||||
\(743\) | 16.1731 | − | 28.0126i | 0.593332 | − | 1.02768i | −0.400448 | − | 0.916319i | \(-0.631146\pi\) |
0.993780 | − | 0.111361i | \(-0.0355211\pi\) | |||||||
\(744\) | 7.07794 | + | 1.51519i | 0.259490 | + | 0.0555494i | ||||
\(745\) | −1.81193 | − | 3.13836i | −0.0663841 | − | 0.114981i | ||||
\(746\) | −9.03359 | − | 5.21555i | −0.330743 | − | 0.190955i | ||||
\(747\) | 16.2310 | − | 36.1730i | 0.593863 | − | 1.32350i | ||||
\(748\) | 23.6800 | 0.865827 | ||||||||
\(749\) | −10.6873 | −0.390504 | ||||||||
\(750\) | −1.16083 | + | 1.28548i | −0.0423876 | + | 0.0469392i | ||||
\(751\) | −9.87219 | + | 5.69971i | −0.360241 | + | 0.207985i | −0.669187 | − | 0.743094i | \(-0.733357\pi\) |
0.308945 | + | 0.951080i | \(0.400024\pi\) | |||||||
\(752\) | 4.06851i | 0.148363i | ||||||||
\(753\) | 9.58543 | + | 29.6470i | 0.349312 | + | 1.08040i | ||||
\(754\) | 13.3396 | − | 7.70160i | 0.485798 | − | 0.280476i | ||||
\(755\) | −9.87297 | + | 17.1005i | −0.359314 | + | 0.622350i | ||||
\(756\) | −2.76378 | − | 0.302638i | −0.100518 | − | 0.0110068i | ||||
\(757\) | −8.74057 | + | 15.1391i | −0.317682 | + | 0.550241i | −0.980004 | − | 0.198978i | \(-0.936238\pi\) |
0.662322 | + | 0.749219i | \(0.269571\pi\) | |||||||
\(758\) | 7.96532 | + | 4.59878i | 0.289313 | + | 0.167035i | ||||
\(759\) | −55.0927 | + | 17.8125i | −1.99974 | + | 0.646552i | ||||
\(760\) | −3.17601 | + | 2.98546i | −0.115206 | + | 0.108294i | ||||
\(761\) | 34.6889i | 1.25747i | 0.777620 | + | 0.628735i | \(0.216427\pi\) | ||||
−0.777620 | + | 0.628735i | \(0.783573\pi\) | |||||||
\(762\) | 14.6483 | + | 3.13579i | 0.530653 | + | 0.113598i | ||||
\(763\) | 3.71813 | + | 2.14666i | 0.134605 | + | 0.0777144i | ||||
\(764\) | −8.30976 | + | 4.79764i | −0.300636 | + | 0.173573i | ||||
\(765\) | 1.38632 | + | 13.5681i | 0.0501226 | + | 0.490556i | ||||
\(766\) | −5.34538 | − | 9.25846i | −0.193136 | − | 0.334522i | ||||
\(767\) | 12.7505i | 0.460393i | ||||||||
\(768\) | −1.64805 | + | 0.532846i | −0.0594690 | + | 0.0192274i | ||||
\(769\) | 27.5176 | + | 47.6619i | 0.992310 | + | 1.71873i | 0.603352 | + | 0.797475i | \(0.293831\pi\) |
0.388958 | + | 0.921256i | \(0.372835\pi\) | |||||||
\(770\) | −1.39351 | − | 2.41363i | −0.0502185 | − | 0.0869810i | ||||
\(771\) | 25.1230 | − | 8.12274i | 0.904784 | − | 0.292533i | ||||
\(772\) | − | 9.65584i | − | 0.347521i | ||||||
\(773\) | −17.5536 | − | 30.4038i | −0.631360 | − | 1.09355i | −0.987274 | − | 0.159029i | \(-0.949164\pi\) |
0.355914 | − | 0.934519i | \(-0.384170\pi\) | |||||||
\(774\) | −2.57292 | − | 25.1815i | −0.0924818 | − | 0.905131i | ||||
\(775\) | −3.61915 | + | 2.08952i | −0.130004 | + | 0.0750577i | ||||
\(776\) | 0.567737 | + | 0.327783i | 0.0203806 | + | 0.0117667i | ||||
\(777\) | 4.82732 | + | 1.03339i | 0.173179 | + | 0.0370727i | ||||
\(778\) | 23.7708i | 0.852225i | ||||||||
\(779\) | 13.9670 | + | 14.8585i | 0.500421 | + | 0.532360i | ||||
\(780\) | −3.02367 | + | 0.977607i | −0.108265 | + | 0.0350040i | ||||
\(781\) | −29.7633 | − | 17.1838i | −1.06501 | − | 0.614886i | ||||
\(782\) | 14.5887 | − | 25.2684i | 0.521692 | − | 0.903597i | ||||
\(783\) | 43.3652 | + | 4.74855i | 1.54975 | + | 0.169699i | ||||
\(784\) | 3.35685 | − | 5.81424i | 0.119888 | − | 0.207651i | ||||
\(785\) | 3.52278 | − | 2.03388i | 0.125733 | − | 0.0725923i | ||||
\(786\) | −10.2573 | − | 31.7250i | −0.365865 | − | 1.13159i | ||||
\(787\) | 10.2958i | 0.367007i | 0.983019 | + | 0.183504i | \(0.0587439\pi\) | ||||
−0.983019 | + | 0.183504i | \(0.941256\pi\) | |||||||
\(788\) | 2.82802 | − | 1.63276i | 0.100744 | − | 0.0581646i | ||||
\(789\) | −26.7110 | + | 29.5793i | −0.950937 | + | 1.05305i | ||||
\(790\) | −8.84221 | −0.314592 | ||||||||
\(791\) | −8.98989 | −0.319644 | ||||||||
\(792\) | −6.39704 | + | 14.2567i | −0.227309 | + | 0.506588i | ||||
\(793\) | 13.0721 | + | 7.54719i | 0.464205 | + | 0.268009i | ||||
\(794\) | 11.0077 | + | 19.0660i | 0.390650 | + | 0.676626i | ||||
\(795\) | −11.0752 | − | 2.37089i | −0.392797 | − | 0.0840867i | ||||
\(796\) | −0.305926 | + | 0.529880i | −0.0108433 | + | 0.0187811i | ||||
\(797\) | 0.450354 | 0.0159524 | 0.00797618 | − | 0.999968i | \(-0.497461\pi\) | ||||
0.00797618 | + | 0.999968i | \(0.497461\pi\) | |||||||
\(798\) | 3.45739 | − | 2.08939i | 0.122390 | − | 0.0739635i | ||||
\(799\) | −18.4964 | −0.654357 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −4.97215 | − | 48.6630i | −0.175682 | − | 1.71942i | ||||
\(802\) | −2.08815 | − | 3.61678i | −0.0737352 | − | 0.127713i | ||||
\(803\) | −27.5730 | − | 15.9193i | −0.973031 | − | 0.561780i | ||||
\(804\) | 0.596784 | − | 0.660867i | 0.0210469 | − | 0.0233070i | ||||
\(805\) | −3.43403 | −0.121034 | ||||||||
\(806\) | −7.66724 | −0.270067 | ||||||||
\(807\) | −30.6429 | − | 27.6715i | −1.07868 | − | 0.974081i | ||||
\(808\) | −10.5737 | + | 6.10474i | −0.371982 | + | 0.214764i | ||||
\(809\) | 14.3150i | 0.503289i | 0.967820 | + | 0.251644i | \(0.0809713\pi\) | ||||
−0.967820 | + | 0.251644i | \(0.919029\pi\) | |||||||
\(810\) | −8.54325 | − | 2.83072i | −0.300179 | − | 0.0994613i | ||||
\(811\) | 16.6190 | − | 9.59499i | 0.583572 | − | 0.336926i | −0.178980 | − | 0.983853i | \(-0.557280\pi\) |
0.762552 | + | 0.646927i | \(0.223946\pi\) | |||||||
\(812\) | 2.24610 | − | 3.89035i | 0.0788225 | − | 0.136525i | ||||
\(813\) | −28.0216 | − | 25.3044i | −0.982760 | − | 0.887463i | ||||
\(814\) | 13.8728 | − | 24.0284i | 0.486241 | − | 0.842195i | ||||
\(815\) | 5.83124 | + | 3.36667i | 0.204260 | + | 0.117929i | ||||
\(816\) | −2.42245 | − | 7.49245i | −0.0848026 | − | 0.262288i | ||||
\(817\) | 25.1899 | + | 26.7977i | 0.881284 | + | 0.937532i | ||||
\(818\) | 6.50754i | 0.227531i | ||||||||
\(819\) | 2.92981 | − | 0.299354i | 0.102376 | − | 0.0104603i | ||||
\(820\) | −4.05157 | − | 2.33917i | −0.141487 | − | 0.0816875i | ||||
\(821\) | −24.1859 | + | 13.9638i | −0.844095 | + | 0.487338i | −0.858654 | − | 0.512556i | \(-0.828699\pi\) |
0.0145591 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(822\) | −3.17351 | − | 0.679358i | −0.110689 | − | 0.0236953i | ||||
\(823\) | −23.4718 | − | 40.6544i | −0.818176 | − | 1.41712i | −0.907024 | − | 0.421078i | \(-0.861652\pi\) |
0.0888479 | − | 0.996045i | \(-0.471681\pi\) | |||||||
\(824\) | 10.0328i | 0.349509i | ||||||||
\(825\) | −2.77543 | − | 8.58420i | −0.0966281 | − | 0.298864i | ||||
\(826\) | 1.85928 | + | 3.22036i | 0.0646925 | + | 0.112051i | ||||
\(827\) | −25.4082 | − | 44.0083i | −0.883531 | − | 1.53032i | −0.847388 | − | 0.530974i | \(-0.821826\pi\) |
−0.0361424 | − | 0.999347i | \(-0.511507\pi\) | |||||||
\(828\) | 11.2719 | + | 15.6094i | 0.391725 | + | 0.542462i | ||||
\(829\) | − | 30.6365i | − | 1.06405i | −0.846729 | − | 0.532024i | \(-0.821431\pi\) | ||
0.846729 | − | 0.532024i | \(-0.178569\pi\) | |||||||
\(830\) | −6.60794 | − | 11.4453i | −0.229365 | − | 0.397272i | ||||
\(831\) | −2.29858 | + | 10.7374i | −0.0797368 | + | 0.372477i | ||||
\(832\) | 1.58889 | − | 0.917346i | 0.0550848 | − | 0.0318032i | ||||
\(833\) | 26.4329 | + | 15.2611i | 0.915847 | + | 0.528765i | ||||
\(834\) | −2.41883 | + | 11.2992i | −0.0837572 | + | 0.391258i | ||||
\(835\) | 6.65196i | 0.230201i | ||||||||
\(836\) | −5.19558 | − | 22.1017i | −0.179693 | − | 0.764404i | ||||
\(837\) | −17.5121 | − | 12.8400i | −0.605306 | − | 0.443814i | ||||
\(838\) | −28.1161 | − | 16.2328i | −0.971254 | − | 0.560754i | ||||
\(839\) | −3.32523 | + | 5.75947i | −0.114800 | + | 0.198839i | −0.917700 | − | 0.397275i | \(-0.869956\pi\) |
0.802900 | + | 0.596114i | \(0.203289\pi\) | |||||||
\(840\) | −0.621126 | + | 0.687824i | −0.0214309 | + | 0.0237322i | ||||
\(841\) | −20.7424 | + | 35.9270i | −0.715256 | + | 1.23886i | ||||
\(842\) | −22.1581 | + | 12.7930i | −0.763618 | + | 0.440875i | ||||
\(843\) | −38.2453 | + | 12.3654i | −1.31724 | + | 0.425887i | ||||
\(844\) | 4.86632i | 0.167506i | ||||||||
\(845\) | −8.34321 | + | 4.81695i | −0.287015 | + | 0.165708i | ||||
\(846\) | 4.99673 | − | 11.1359i | 0.171791 | − | 0.382859i | ||||
\(847\) | 8.63095 | 0.296563 | ||||||||
\(848\) | 6.53915 | 0.224555 | ||||||||
\(849\) | −20.6238 | − | 18.6239i | −0.707805 | − | 0.639170i | ||||
\(850\) | 3.93717 | + | 2.27312i | 0.135044 | + | 0.0779675i | ||||
\(851\) | −17.0934 | − | 29.6067i | −0.585955 | − | 1.01490i | ||||
\(852\) | −2.39227 | + | 11.1751i | −0.0819579 | + | 0.382853i | ||||
\(853\) | −6.96853 | + | 12.0699i | −0.238598 | + | 0.413264i | −0.960312 | − | 0.278927i | \(-0.910021\pi\) |
0.721714 | + | 0.692191i | \(0.243354\pi\) | |||||||
\(854\) | 4.40213 | 0.150638 | ||||||||
\(855\) | 12.3596 | − | 4.27087i | 0.422689 | − | 0.146061i | ||||
\(856\) | 19.9736 | 0.682683 | ||||||||
\(857\) | 8.48584 | − | 14.6979i | 0.289871 | − | 0.502071i | −0.683908 | − | 0.729568i | \(-0.739721\pi\) |
0.973779 | + | 0.227498i | \(0.0730544\pi\) | |||||||
\(858\) | 3.46483 | − | 16.1854i | 0.118287 | − | 0.552559i | ||||
\(859\) | 5.96482 | + | 10.3314i | 0.203517 | + | 0.352502i | 0.949659 | − | 0.313285i | \(-0.101429\pi\) |
−0.746142 | + | 0.665787i | \(0.768096\pi\) | |||||||
\(860\) | −7.30712 | − | 4.21877i | −0.249171 | − | 0.143859i | ||||
\(861\) | 3.21788 | + | 2.90584i | 0.109665 | + | 0.0990309i | ||||
\(862\) | 9.94587 | 0.338758 | ||||||||
\(863\) | −8.15086 | −0.277458 | −0.138729 | − | 0.990330i | \(-0.544302\pi\) | ||||
−0.138729 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(864\) | 5.16528 | + | 0.565605i | 0.175726 | + | 0.0192423i | ||||
\(865\) | 2.80502 | − | 1.61948i | 0.0953736 | − | 0.0550640i | ||||
\(866\) | − | 24.3448i | − | 0.827270i | ||||||
\(867\) | 6.04565 | − | 1.95467i | 0.205321 | − | 0.0663841i | ||||
\(868\) | −1.93650 | + | 1.11804i | −0.0657291 | + | 0.0379487i | ||||
\(869\) | 23.0282 | − | 39.8860i | 0.781178 | − | 1.35304i | ||||
\(870\) | 9.74580 | − | 10.7923i | 0.330413 | − | 0.365894i | ||||
\(871\) | −0.471607 | + | 0.816848i | −0.0159798 | + | 0.0276778i | ||||
\(872\) | −6.94887 | − | 4.01193i | −0.235318 | − | 0.135861i | ||||
\(873\) | −1.15138 | − | 1.59444i | −0.0389683 | − | 0.0539635i | ||||
\(874\) | −26.7851 | − | 8.07228i | −0.906020 | − | 0.273049i | ||||
\(875\) | − | 0.535070i | − | 0.0180887i | ||||||
\(876\) | −2.21623 | + | 10.3528i | −0.0748794 | + | 0.349787i | ||||
\(877\) | 43.0842 | + | 24.8746i | 1.45485 | + | 0.839957i | 0.998751 | − | 0.0499723i | \(-0.0159133\pi\) |
0.456098 | + | 0.889930i | \(0.349247\pi\) | |||||||
\(878\) | 32.3043 | − | 18.6509i | 1.09022 | − | 0.629437i | ||||
\(879\) | −7.58941 | + | 35.4527i | −0.255984 | + | 1.19579i | ||||
\(880\) | 2.60435 | + | 4.51086i | 0.0877925 | + | 0.152061i | ||||
\(881\) | 25.2877i | 0.851964i | 0.904732 | + | 0.425982i | \(0.140071\pi\) | ||||
−0.904732 | + | 0.425982i | \(0.859929\pi\) | |||||||
\(882\) | −16.3287 | + | 11.7914i | −0.549817 | + | 0.397036i | ||||
\(883\) | 15.1793 | + | 26.2913i | 0.510823 | + | 0.884772i | 0.999921 | + | 0.0125430i | \(0.00399266\pi\) |
−0.489098 | + | 0.872229i | \(0.662674\pi\) | |||||||
\(884\) | 4.17048 | + | 7.22348i | 0.140268 | + | 0.242952i | ||||
\(885\) | 3.70309 | + | 11.4534i | 0.124478 | + | 0.385002i | ||||
\(886\) | 17.2372i | 0.579095i | ||||||||
\(887\) | 20.5824 | + | 35.6497i | 0.691089 | + | 1.19700i | 0.971481 | + | 0.237116i | \(0.0762020\pi\) |
−0.280393 | + | 0.959885i | \(0.590465\pi\) | |||||||
\(888\) | −9.02185 | − | 1.93132i | −0.302754 | − | 0.0648109i | ||||
\(889\) | −4.00773 | + | 2.31387i | −0.134415 | + | 0.0776046i | ||||
\(890\) | −14.1209 | − | 8.15273i | −0.473335 | − | 0.273280i | ||||
\(891\) | 35.0186 | − | 31.1652i | 1.17317 | − | 1.04407i | ||||
\(892\) | − | 5.47731i | − | 0.183394i | ||||||
\(893\) | 4.05826 | + | 17.2636i | 0.135805 | + | 0.577705i | ||||
\(894\) | −1.93096 | − | 5.97232i | −0.0645810 | − | 0.199744i | ||||
\(895\) | 11.6236 | + | 6.71091i | 0.388535 | + | 0.224321i | ||||
\(896\) | 0.267535 | − | 0.463384i | 0.00893771 | − | 0.0154806i | ||||
\(897\) | −15.1364 | − | 13.6687i | −0.505391 | − | 0.456384i | ||||
\(898\) | −7.29525 | + | 12.6357i | −0.243446 | + | 0.421660i | ||||
\(899\) | 30.3847 | − | 17.5426i | 1.01339 | − | 0.585079i | ||||
\(900\) | −2.43215 | + | 1.75631i | −0.0810717 | + | 0.0585438i | ||||
\(901\) | 29.7286i | 0.990402i | ||||||||
\(902\) | 21.1034 | − | 12.1840i | 0.702666 | − | 0.405684i | ||||
\(903\) | 5.80354 | + | 5.24078i | 0.193130 | + | 0.174402i | ||||
\(904\) | 16.8013 | 0.558805 | ||||||||
\(905\) | −6.69773 | −0.222640 | ||||||||
\(906\) | −22.9217 | + | 25.3831i | −0.761523 | + | 0.843297i | ||||
\(907\) | 51.4695 | + | 29.7159i | 1.70902 | + | 0.986701i | 0.935780 | + | 0.352583i | \(0.114697\pi\) |
0.773236 | + | 0.634118i | \(0.218637\pi\) | |||||||
\(908\) | −6.13682 | − | 10.6293i | −0.203657 | − | 0.352745i | ||||
\(909\) | 36.4387 | − | 3.72313i | 1.20860 | − | 0.123488i | ||||
\(910\) | 0.490844 | − | 0.850166i | 0.0162713 | − | 0.0281827i | ||||
\(911\) | 36.4247 | 1.20680 | 0.603402 | − | 0.797437i | \(-0.293811\pi\) | ||||
0.603402 | + | 0.797437i | \(0.293811\pi\) | |||||||
\(912\) | −6.46157 | + | 3.90489i | −0.213964 | + | 0.129304i | ||||
\(913\) | 68.8375 | 2.27819 | ||||||||
\(914\) | 17.9232 | − | 31.0440i | 0.592848 | − | 1.02684i | ||||
\(915\) | 13.9342 | + | 2.98292i | 0.460652 | + | 0.0986124i | ||||
\(916\) | −12.6163 | − | 21.8521i | −0.416854 | − | 0.722012i | ||||
\(917\) | 8.92013 | + | 5.15004i | 0.294569 | + | 0.170069i | ||||
\(918\) | −2.57138 | + | 23.4826i | −0.0848681 | + | 0.775042i | ||||
\(919\) | −8.83052 | −0.291292 | −0.145646 | − | 0.989337i | \(-0.546526\pi\) | ||||
−0.145646 | + | 0.989337i | \(0.546526\pi\) | |||||||
\(920\) | 6.41792 | 0.211593 | ||||||||
\(921\) | −13.1803 | + | 14.5956i | −0.434304 | + | 0.480940i | ||||
\(922\) | 12.6225 | − | 7.28761i | 0.415700 | − | 0.240005i | ||||
\(923\) | − | 12.1055i | − | 0.398459i | ||||||
\(924\) | −1.48505 | − | 4.59315i | −0.0488545 | − | 0.151103i | ||||
\(925\) | 4.61313 | − | 2.66339i | 0.151679 | − | 0.0875718i | ||||
\(926\) | −10.0664 | + | 17.4355i | −0.330802 | + | 0.572966i | ||||
\(927\) | 12.3218 | − | 27.4607i | 0.404699 | − | 0.901926i | ||||
\(928\) | −4.19776 | + | 7.27074i | −0.137798 | + | 0.238674i | ||||
\(929\) | −4.83299 | − | 2.79033i | −0.158565 | − | 0.0915477i | 0.418618 | − | 0.908163i | \(-0.362515\pi\) |
−0.577183 | + | 0.816615i | \(0.695848\pi\) | |||||||
\(930\) | −6.88727 | + | 2.22678i | −0.225842 | + | 0.0730190i | ||||
\(931\) | 8.44431 | − | 28.0196i | 0.276751 | − | 0.918304i | ||||
\(932\) | 17.4687i | 0.572205i | ||||||||
\(933\) | −10.5230 | − | 2.25267i | −0.344507 | − | 0.0737491i | ||||
\(934\) | −0.464126 | − | 0.267963i | −0.0151867 | − | 0.00876802i | ||||
\(935\) | −20.5075 | + | 11.8400i | −0.670667 | + | 0.387210i | ||||
\(936\) | −5.47557 | + | 0.559466i | −0.178974 | + | 0.0182867i | ||||
\(937\) | −27.7201 | − | 48.0126i | −0.905576 | − | 1.56850i | −0.820143 | − | 0.572159i | \(-0.806106\pi\) |
−0.0854328 | − | 0.996344i | \(-0.527227\pi\) | |||||||
\(938\) | 0.275079i | 0.00898166i | ||||||||
\(939\) | −16.8519 | + | 5.44854i | −0.549942 | + | 0.177806i | ||||
\(940\) | −2.03425 | − | 3.52343i | −0.0663500 | − | 0.114922i | ||||
\(941\) | −17.5976 | − | 30.4799i | −0.573665 | − | 0.993616i | −0.996185 | − | 0.0872631i | \(-0.972188\pi\) |
0.422521 | − | 0.906353i | \(-0.361145\pi\) | |||||||
\(942\) | 6.70388 | − | 2.16749i | 0.218424 | − | 0.0706206i | ||||
\(943\) | − | 30.0253i | − | 0.977757i | ||||||
\(944\) | −3.47483 | − | 6.01858i | −0.113096 | − | 0.195888i | ||||
\(945\) | 2.54483 | − | 1.11980i | 0.0827832 | − | 0.0364271i | ||||
\(946\) | 38.0606 | − | 21.9743i | 1.23746 | − | 0.714446i | ||||
\(947\) | 1.44559 | + | 0.834610i | 0.0469753 | + | 0.0271212i | 0.523304 | − | 0.852146i | \(-0.324699\pi\) |
−0.476328 | + | 0.879267i | \(0.658033\pi\) | |||||||
\(948\) | −14.9759 | − | 3.20590i | −0.486393 | − | 0.104123i | ||||
\(949\) | − | 11.2147i | − | 0.364045i | ||||||
\(950\) | 1.25777 | − | 4.17349i | 0.0408075 | − | 0.135406i | ||||
\(951\) | −17.9975 | + | 5.81891i | −0.583607 | + | 0.188691i | ||||
\(952\) | 2.10666 | + | 1.21628i | 0.0682772 | + | 0.0394198i | ||||
\(953\) | −18.5367 | + | 32.1065i | −0.600462 | + | 1.04003i | 0.392289 | + | 0.919842i | \(0.371683\pi\) |
−0.992751 | + | 0.120189i | \(0.961650\pi\) | |||||||
\(954\) | −17.8982 | − | 8.03103i | −0.579476 | − | 0.260014i | ||||
\(955\) | 4.79764 | − | 8.30976i | 0.155248 | − | 0.268897i | ||||
\(956\) | 24.1544 | − | 13.9456i | 0.781210 | − | 0.451032i | ||||
\(957\) | 23.3012 | + | 72.0689i | 0.753221 | + | 2.32966i | ||||
\(958\) | − | 25.2622i | − | 0.816185i | ||||||
\(959\) | 0.868260 | − | 0.501290i | 0.0280376 | − | 0.0161875i | ||||
\(960\) | 1.16083 | − | 1.28548i | 0.0374657 | − | 0.0414888i | ||||
\(961\) | 13.5357 | 0.436634 | ||||||||
\(962\) | 9.77300 | 0.315094 | ||||||||
\(963\) | −54.6695 | − | 24.5305i | −1.76170 | − | 0.790484i | ||||
\(964\) | −21.8025 | − | 12.5877i | −0.702211 | − | 0.405421i | ||||
\(965\) | 4.82792 | + | 8.36220i | 0.155416 | + | 0.269189i | ||||
\(966\) | −5.81615 | − | 1.24507i | −0.187132 | − | 0.0400595i | ||||
\(967\) | −6.19162 | + | 10.7242i | −0.199109 | + | 0.344867i | −0.948240 | − | 0.317555i | \(-0.897138\pi\) |
0.749131 | + | 0.662422i | \(0.230471\pi\) | |||||||
\(968\) | −16.1305 | −0.518454 | ||||||||
\(969\) | −17.7526 | − | 29.3759i | −0.570295 | − | 0.943689i | ||||
\(970\) | −0.655566 | −0.0210490 | ||||||||
\(971\) | −12.0657 | + | 20.8984i | −0.387207 | + | 0.670662i | −0.992073 | − | 0.125666i | \(-0.959893\pi\) |
0.604866 | + | 0.796327i | \(0.293227\pi\) | |||||||
\(972\) | −13.4432 | − | 7.89183i | −0.431190 | − | 0.253131i | ||||
\(973\) | −1.78483 | − | 3.09141i | −0.0572189 | − | 0.0991060i | ||||
\(974\) | −23.8091 | − | 13.7462i | −0.762893 | − | 0.440456i | ||||
\(975\) | 2.12977 | − | 2.35847i | 0.0682072 | − | 0.0755314i | ||||
\(976\) | −8.22721 | −0.263346 | ||||||||
\(977\) | 10.4531 | 0.334423 | 0.167212 | − | 0.985921i | \(-0.446524\pi\) | ||||
0.167212 | + | 0.985921i | \(0.446524\pi\) | |||||||
\(978\) | 8.65560 | + | 7.81628i | 0.276776 | + | 0.249937i | ||||
\(979\) | 73.5517 | − | 42.4651i | 2.35072 | − | 1.35719i | ||||
\(980\) | 6.71370i | 0.214461i | ||||||||
\(981\) | 14.0924 | + | 19.5152i | 0.449936 | + | 0.623074i | ||||
\(982\) | −9.52214 | + | 5.49761i | −0.303864 | + | 0.175436i | ||||
\(983\) | 0.0140700 | − | 0.0243700i | 0.000448764 | − | 0.000777282i | −0.865801 | − | 0.500389i | \(-0.833190\pi\) |
0.866250 | + | 0.499611i | \(0.166524\pi\) | |||||||
\(984\) | −6.01394 | − | 5.43078i | −0.191717 | − | 0.173127i | ||||
\(985\) | −1.63276 | + | 2.82802i | −0.0520240 | + | 0.0901083i | ||||
\(986\) | −33.0546 | − | 19.0841i | −1.05267 | − | 0.607761i | ||||
\(987\) | 1.15997 | + | 3.58770i | 0.0369223 | + | 0.114198i | ||||
\(988\) | 5.82699 | − | 5.47740i | 0.185381 | − | 0.174259i | ||||
\(989\) | − | 54.1514i | − | 1.72192i | ||||||
\(990\) | −1.58833 | − | 15.5452i | −0.0504804 | − | 0.494057i | ||||
\(991\) | −44.6814 | − | 25.7968i | −1.41935 | − | 0.819462i | −0.423108 | − | 0.906079i | \(-0.639061\pi\) |
−0.996242 | + | 0.0866170i | \(0.972394\pi\) | |||||||
\(992\) | 3.61915 | − | 2.08952i | 0.114908 | − | 0.0663423i | ||||
\(993\) | 8.88827 | + | 1.90273i | 0.282061 | + | 0.0603812i | ||||
\(994\) | −1.76523 | − | 3.05747i | −0.0559897 | − | 0.0969771i | ||||
\(995\) | − | 0.611852i | − | 0.0193970i | ||||||
\(996\) | −7.04202 | − | 21.7805i | −0.223135 | − | 0.690140i | ||||
\(997\) | 30.5747 | + | 52.9569i | 0.968311 | + | 1.67716i | 0.700445 | + | 0.713707i | \(0.252985\pi\) |
0.267866 | + | 0.963456i | \(0.413682\pi\) | |||||||
\(998\) | 7.16095 | + | 12.4031i | 0.226676 | + | 0.392614i | ||||
\(999\) | 22.3217 | + | 16.3664i | 0.706226 | + | 0.517809i |
(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 | 570.2.s.a.521.7 | yes | 24 | |
3.2 | odd | 2 | 570.2.s.b.521.4 | yes | 24 | ||
19.12 | odd | 6 | 570.2.s.b.221.4 | yes | 24 | ||
57.50 | even | 6 | inner | 570.2.s.a.221.7 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.s.a.221.7 | ✓ | 24 | 57.50 | even | 6 | inner | |
570.2.s.a.521.7 | yes | 24 | 1.1 | even | 1 | trivial | |
570.2.s.b.221.4 | yes | 24 | 19.12 | odd | 6 | ||
570.2.s.b.521.4 | yes | 24 | 3.2 | odd | 2 |