Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(101,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bn (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 173.8 | ||
Character | \(\chi\) | \(=\) | 546.173 |
Dual form | 546.2.bn.e.101.8 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.320103 | + | 1.70221i | −0.184812 | + | 0.982774i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.62172 | − | 0.936303i | −0.725257 | − | 0.418728i | 0.0914273 | − | 0.995812i | \(-0.470857\pi\) |
−0.816685 | + | 0.577084i | \(0.804190\pi\) | |||||||
\(6\) | 1.63421 | − | 0.573890i | 0.667164 | − | 0.234290i | ||||
\(7\) | 2.47749 | − | 0.928453i | 0.936405 | − | 0.350922i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.79507 | − | 1.08977i | −0.931689 | − | 0.363256i | ||||
\(10\) | 1.87261i | 0.592170i | ||||||||
\(11\) | −5.09987 | −1.53767 | −0.768835 | − | 0.639447i | \(-0.779163\pi\) | ||||
−0.768835 | + | 0.639447i | \(0.779163\pi\) | |||||||
\(12\) | −1.31411 | − | 1.12832i | −0.379351 | − | 0.325719i | ||||
\(13\) | 3.20727 | − | 1.64725i | 0.889536 | − | 0.456865i | ||||
\(14\) | −2.04281 | − | 1.68135i | −0.545964 | − | 0.449359i | ||||
\(15\) | 2.11291 | − | 2.46081i | 0.545550 | − | 0.635378i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.48106 | − | 2.56527i | 0.359210 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497127\pi\) | |||||||
\(18\) | 0.453768 | + | 2.96548i | 0.106954 | + | 0.698971i | ||||
\(19\) | −2.60154 | −0.596835 | −0.298417 | − | 0.954435i | \(-0.596459\pi\) | ||||
−0.298417 | + | 0.954435i | \(0.596459\pi\) | |||||||
\(20\) | 1.62172 | − | 0.936303i | 0.362629 | − | 0.209364i | ||||
\(21\) | 0.787372 | + | 4.51443i | 0.171819 | + | 0.985129i | ||||
\(22\) | 2.54994 | + | 4.41662i | 0.543648 | + | 0.941627i | ||||
\(23\) | 5.25634 | − | 3.03475i | 1.09602 | − | 0.632789i | 0.160850 | − | 0.986979i | \(-0.448577\pi\) |
0.935174 | + | 0.354190i | \(0.115243\pi\) | |||||||
\(24\) | −0.320103 | + | 1.70221i | −0.0653407 | + | 0.347463i | ||||
\(25\) | −0.746672 | − | 1.29327i | −0.149334 | − | 0.258655i | ||||
\(26\) | −3.03019 | − | 1.95395i | −0.594270 | − | 0.383201i | ||||
\(27\) | 2.74973 | − | 4.40897i | 0.529185 | − | 0.848506i | ||||
\(28\) | −0.434683 | + | 2.60980i | −0.0821475 | + | 0.493206i | ||||
\(29\) | 7.30144 | + | 4.21549i | 1.35584 | + | 0.782796i | 0.989060 | − | 0.147511i | \(-0.0471261\pi\) |
0.366782 | + | 0.930307i | \(0.380459\pi\) | |||||||
\(30\) | −3.18758 | − | 0.599427i | −0.581969 | − | 0.109440i | ||||
\(31\) | −4.09797 | − | 7.09789i | −0.736017 | − | 1.27482i | −0.954276 | − | 0.298928i | \(-0.903371\pi\) |
0.218258 | − | 0.975891i | \(-0.429962\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.63248 | − | 8.68108i | 0.284179 | − | 1.51118i | ||||
\(34\) | −2.96212 | −0.508000 | ||||||||
\(35\) | −4.88713 | − | 0.813991i | −0.826075 | − | 0.137590i | ||||
\(36\) | 2.34130 | − | 1.87572i | 0.390217 | − | 0.312619i | ||||
\(37\) | 5.52226 | − | 3.18828i | 0.907854 | − | 0.524150i | 0.0281141 | − | 0.999605i | \(-0.491050\pi\) |
0.879740 | + | 0.475455i | \(0.157716\pi\) | |||||||
\(38\) | 1.30077 | + | 2.25300i | 0.211013 | + | 0.365485i | ||||
\(39\) | 1.77732 | + | 5.98675i | 0.284599 | + | 0.958647i | ||||
\(40\) | −1.62172 | − | 0.936303i | −0.256417 | − | 0.148043i | ||||
\(41\) | −4.85500 | − | 2.80304i | −0.758223 | − | 0.437761i | 0.0704341 | − | 0.997516i | \(-0.477562\pi\) |
−0.828658 | + | 0.559756i | \(0.810895\pi\) | |||||||
\(42\) | 3.51592 | − | 2.93910i | 0.542519 | − | 0.453513i | ||||
\(43\) | −4.87733 | − | 8.44778i | −0.743786 | − | 1.28827i | −0.950760 | − | 0.309928i | \(-0.899695\pi\) |
0.206974 | − | 0.978346i | \(-0.433638\pi\) | |||||||
\(44\) | 2.54994 | − | 4.41662i | 0.384417 | − | 0.665831i | ||||
\(45\) | 3.51248 | + | 4.38433i | 0.523609 | + | 0.653578i | ||||
\(46\) | −5.25634 | − | 3.03475i | −0.775006 | − | 0.447450i | ||||
\(47\) | −2.70708 | − | 1.56293i | −0.394868 | − | 0.227977i | 0.289400 | − | 0.957208i | \(-0.406544\pi\) |
−0.684267 | + | 0.729232i | \(0.739878\pi\) | |||||||
\(48\) | 1.63421 | − | 0.573890i | 0.235878 | − | 0.0828339i | ||||
\(49\) | 5.27595 | − | 4.60047i | 0.753707 | − | 0.657210i | ||||
\(50\) | −0.746672 | + | 1.29327i | −0.105595 | + | 0.182897i | ||||
\(51\) | 3.89256 | + | 3.34224i | 0.545067 | + | 0.468007i | ||||
\(52\) | −0.177072 | + | 3.60120i | −0.0245555 | + | 0.499397i | ||||
\(53\) | 8.21797 | − | 4.74465i | 1.12883 | − | 0.651728i | 0.185186 | − | 0.982703i | \(-0.440711\pi\) |
0.943639 | + | 0.330976i | \(0.107378\pi\) | |||||||
\(54\) | −5.19314 | − | 0.176850i | −0.706697 | − | 0.0240663i | ||||
\(55\) | 8.27059 | + | 4.77503i | 1.11521 | + | 0.643865i | ||||
\(56\) | 2.47749 | − | 0.928453i | 0.331069 | − | 0.124070i | ||||
\(57\) | 0.832761 | − | 4.42838i | 0.110302 | − | 0.586554i | ||||
\(58\) | − | 8.43097i | − | 1.10704i | ||||||
\(59\) | 1.90771 | + | 1.10141i | 0.248362 | + | 0.143392i | 0.619014 | − | 0.785380i | \(-0.287532\pi\) |
−0.370652 | + | 0.928772i | \(0.620866\pi\) | |||||||
\(60\) | 1.07467 | + | 3.06024i | 0.138739 | + | 0.395075i | ||||
\(61\) | 5.90230i | 0.755712i | 0.925864 | + | 0.377856i | \(0.123339\pi\) | ||||
−0.925864 | + | 0.377856i | \(0.876661\pi\) | |||||||
\(62\) | −4.09797 | + | 7.09789i | −0.520443 | + | 0.901433i | ||||
\(63\) | −7.93656 | − | 0.104805i | −0.999913 | − | 0.0132042i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.74363 | − | 0.331587i | −0.836445 | − | 0.0411283i | ||||
\(66\) | −8.33428 | + | 2.92677i | −1.02588 | + | 0.360260i | ||||
\(67\) | 11.0457i | 1.34944i | 0.738073 | + | 0.674721i | \(0.235736\pi\) | ||||
−0.738073 | + | 0.674721i | \(0.764264\pi\) | |||||||
\(68\) | 1.48106 | + | 2.56527i | 0.179605 | + | 0.311085i | ||||
\(69\) | 3.48323 | + | 9.91886i | 0.419331 | + | 1.19409i | ||||
\(70\) | 1.73863 | + | 4.63937i | 0.207806 | + | 0.554511i | ||||
\(71\) | −7.27923 | − | 12.6080i | −0.863886 | − | 1.49629i | −0.868149 | − | 0.496303i | \(-0.834690\pi\) |
0.00426326 | − | 0.999991i | \(-0.498643\pi\) | |||||||
\(72\) | −2.79507 | − | 1.08977i | −0.329402 | − | 0.128430i | ||||
\(73\) | −1.99779 | − | 3.46027i | −0.233823 | − | 0.404994i | 0.725107 | − | 0.688636i | \(-0.241790\pi\) |
−0.958930 | + | 0.283643i | \(0.908457\pi\) | |||||||
\(74\) | −5.52226 | − | 3.18828i | −0.641950 | − | 0.370630i | ||||
\(75\) | 2.44044 | − | 0.857016i | 0.281798 | − | 0.0989596i | ||||
\(76\) | 1.30077 | − | 2.25300i | 0.149209 | − | 0.258437i | ||||
\(77\) | −12.6349 | + | 4.73499i | −1.43988 | + | 0.539602i | ||||
\(78\) | 4.29602 | − | 4.53258i | 0.486428 | − | 0.513213i | ||||
\(79\) | −5.14630 | + | 8.91365i | −0.579004 | + | 1.00286i | 0.416590 | + | 0.909094i | \(0.363225\pi\) |
−0.995594 | + | 0.0937696i | \(0.970108\pi\) | |||||||
\(80\) | 1.87261i | 0.209364i | ||||||||
\(81\) | 6.62481 | + | 6.09195i | 0.736090 | + | 0.676883i | ||||
\(82\) | 5.60607i | 0.619087i | ||||||||
\(83\) | 9.63409i | 1.05748i | 0.848784 | + | 0.528739i | \(0.177335\pi\) | ||||
−0.848784 | + | 0.528739i | \(0.822665\pi\) | |||||||
\(84\) | −4.30329 | − | 1.57533i | −0.469528 | − | 0.171882i | ||||
\(85\) | −4.80375 | + | 2.77345i | −0.521040 | + | 0.300823i | ||||
\(86\) | −4.87733 | + | 8.44778i | −0.525936 | + | 0.910948i | ||||
\(87\) | −9.51287 | + | 11.0792i | −1.01989 | + | 1.18782i | ||||
\(88\) | −5.09987 | −0.543648 | ||||||||
\(89\) | −12.7850 | + | 7.38141i | −1.35520 | + | 0.782428i | −0.988973 | − | 0.148096i | \(-0.952686\pi\) |
−0.366232 | + | 0.930524i | \(0.619352\pi\) | |||||||
\(90\) | 2.04071 | − | 5.23406i | 0.215109 | − | 0.551719i | ||||
\(91\) | 6.41659 | − | 7.05885i | 0.672642 | − | 0.739969i | ||||
\(92\) | 6.06950i | 0.632789i | ||||||||
\(93\) | 13.3939 | − | 4.70357i | 1.38888 | − | 0.487737i | ||||
\(94\) | 3.12586i | 0.322408i | ||||||||
\(95\) | 4.21899 | + | 2.43583i | 0.432859 | + | 0.249911i | ||||
\(96\) | −1.31411 | − | 1.12832i | −0.134121 | − | 0.115159i | ||||
\(97\) | −5.83860 | − | 10.1127i | −0.592820 | − | 1.02679i | −0.993851 | − | 0.110729i | \(-0.964681\pi\) |
0.401031 | − | 0.916065i | \(-0.368652\pi\) | |||||||
\(98\) | −6.62210 | − | 2.26887i | −0.668933 | − | 0.229191i | ||||
\(99\) | 14.2545 | + | 5.55768i | 1.43263 | + | 0.558568i | ||||
\(100\) | 1.49334 | 0.149334 | ||||||||
\(101\) | −6.30051 | −0.626924 | −0.313462 | − | 0.949601i | \(-0.601489\pi\) | ||||
−0.313462 | + | 0.949601i | \(0.601489\pi\) | |||||||
\(102\) | 0.948185 | − | 5.04217i | 0.0938843 | − | 0.499249i | ||||
\(103\) | 4.99182 | + | 2.88203i | 0.491859 | + | 0.283975i | 0.725345 | − | 0.688385i | \(-0.241680\pi\) |
−0.233486 | + | 0.972360i | \(0.575013\pi\) | |||||||
\(104\) | 3.20727 | − | 1.64725i | 0.314498 | − | 0.161526i | ||||
\(105\) | 2.94997 | − | 8.05838i | 0.287888 | − | 0.786417i | ||||
\(106\) | −8.21797 | − | 4.74465i | −0.798200 | − | 0.460841i | ||||
\(107\) | 5.32321 | − | 3.07336i | 0.514614 | − | 0.297113i | −0.220114 | − | 0.975474i | \(-0.570643\pi\) |
0.734728 | + | 0.678362i | \(0.237310\pi\) | |||||||
\(108\) | 2.44341 | + | 4.58582i | 0.235118 | + | 0.441271i | ||||
\(109\) | 10.8967 | − | 6.29124i | 1.04372 | − | 0.602591i | 0.122834 | − | 0.992427i | \(-0.460802\pi\) |
0.920884 | + | 0.389836i | \(0.127468\pi\) | |||||||
\(110\) | − | 9.55006i | − | 0.910562i | ||||||
\(111\) | 3.65944 | + | 10.4207i | 0.347339 | + | 0.989084i | ||||
\(112\) | −2.04281 | − | 1.68135i | −0.193027 | − | 0.158872i | ||||
\(113\) | 1.92741 | − | 1.11279i | 0.181316 | − | 0.104683i | −0.406595 | − | 0.913609i | \(-0.633284\pi\) |
0.587911 | + | 0.808926i | \(0.299951\pi\) | |||||||
\(114\) | −4.25147 | + | 1.49300i | −0.398187 | + | 0.139832i | ||||
\(115\) | −11.3658 | −1.05987 | ||||||||
\(116\) | −7.30144 | + | 4.21549i | −0.677921 | + | 0.391398i | ||||
\(117\) | −10.7597 | + | 1.10900i | −0.994730 | + | 0.102527i | ||||
\(118\) | − | 2.20283i | − | 0.202787i | ||||||
\(119\) | 1.28759 | − | 7.73055i | 0.118033 | − | 0.708658i | ||||
\(120\) | 2.11291 | − | 2.46081i | 0.192881 | − | 0.224640i | ||||
\(121\) | 15.0087 | 1.36443 | ||||||||
\(122\) | 5.11154 | − | 2.95115i | 0.462777 | − | 0.267185i | ||||
\(123\) | 6.32547 | − | 7.36699i | 0.570348 | − | 0.664259i | ||||
\(124\) | 8.19594 | 0.736017 | ||||||||
\(125\) | 12.1595i | 1.08758i | ||||||||
\(126\) | 3.87752 | + | 6.92567i | 0.345437 | + | 0.616987i | ||||
\(127\) | −3.67232 | + | 6.36064i | −0.325866 | + | 0.564416i | −0.981687 | − | 0.190500i | \(-0.938989\pi\) |
0.655822 | + | 0.754916i | \(0.272322\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 15.9412 | − | 5.59810i | 1.40354 | − | 0.492885i | ||||
\(130\) | 3.08465 | + | 6.00595i | 0.270542 | + | 0.526757i | ||||
\(131\) | 0.465541 | − | 0.806340i | 0.0406745 | − | 0.0704503i | −0.844971 | − | 0.534811i | \(-0.820383\pi\) |
0.885646 | + | 0.464361i | \(0.153716\pi\) | |||||||
\(132\) | 6.70179 | + | 5.75431i | 0.583316 | + | 0.500849i | ||||
\(133\) | −6.44531 | + | 2.41541i | −0.558879 | + | 0.209443i | ||||
\(134\) | 9.56582 | − | 5.52283i | 0.826361 | − | 0.477100i | ||||
\(135\) | −8.58743 | + | 4.57555i | −0.739089 | + | 0.393801i | ||||
\(136\) | 1.48106 | − | 2.56527i | 0.127000 | − | 0.219970i | ||||
\(137\) | −1.07857 | + | 1.86814i | −0.0921483 | + | 0.159606i | −0.908415 | − | 0.418070i | \(-0.862707\pi\) |
0.816267 | + | 0.577675i | \(0.196040\pi\) | |||||||
\(138\) | 6.84837 | − | 7.97599i | 0.582972 | − | 0.678961i | ||||
\(139\) | −7.18997 | + | 4.15113i | −0.609845 | + | 0.352094i | −0.772905 | − | 0.634522i | \(-0.781197\pi\) |
0.163060 | + | 0.986616i | \(0.447864\pi\) | |||||||
\(140\) | 3.14850 | − | 3.82538i | 0.266097 | − | 0.323304i | ||||
\(141\) | 3.52699 | − | 4.10772i | 0.297026 | − | 0.345933i | ||||
\(142\) | −7.27923 | + | 12.6080i | −0.610860 | + | 1.05804i | ||||
\(143\) | −16.3567 | + | 8.40077i | −1.36781 | + | 0.702508i | ||||
\(144\) | 0.453768 | + | 2.96548i | 0.0378140 | + | 0.247124i | ||||
\(145\) | −7.89395 | − | 13.6727i | −0.655557 | − | 1.13546i | ||||
\(146\) | −1.99779 | + | 3.46027i | −0.165338 | + | 0.286374i | ||||
\(147\) | 6.14214 | + | 10.4534i | 0.506595 | + | 0.862184i | ||||
\(148\) | 6.37656i | 0.524150i | ||||||||
\(149\) | 3.95824 | 0.324271 | 0.162136 | − | 0.986768i | \(-0.448162\pi\) | ||||
0.162136 | + | 0.986768i | \(0.448162\pi\) | |||||||
\(150\) | −1.96242 | − | 1.68498i | −0.160231 | − | 0.137578i | ||||
\(151\) | −4.82241 | + | 2.78422i | −0.392442 | + | 0.226576i | −0.683218 | − | 0.730215i | \(-0.739420\pi\) |
0.290776 | + | 0.956791i | \(0.406087\pi\) | |||||||
\(152\) | −2.60154 | −0.211013 | ||||||||
\(153\) | −6.93522 | + | 5.55610i | −0.560680 | + | 0.449184i | ||||
\(154\) | 10.4181 | + | 8.57465i | 0.839512 | + | 0.690965i | ||||
\(155\) | 15.3478i | 1.23276i | ||||||||
\(156\) | −6.07333 | − | 1.45417i | −0.486256 | − | 0.116427i | ||||
\(157\) | 6.31098 | − | 3.64365i | 0.503671 | − | 0.290795i | −0.226557 | − | 0.973998i | \(-0.572747\pi\) |
0.730228 | + | 0.683203i | \(0.239414\pi\) | |||||||
\(158\) | 10.2926 | 0.818835 | ||||||||
\(159\) | 5.44581 | + | 15.5075i | 0.431881 | + | 1.22983i | ||||
\(160\) | 1.62172 | − | 0.936303i | 0.128209 | − | 0.0740213i | ||||
\(161\) | 10.2049 | − | 12.3988i | 0.804262 | − | 0.977166i | ||||
\(162\) | 1.96338 | − | 8.78323i | 0.154257 | − | 0.690076i | ||||
\(163\) | 19.8091i | 1.55157i | 0.630997 | + | 0.775785i | \(0.282646\pi\) | ||||
−0.630997 | + | 0.775785i | \(0.717354\pi\) | |||||||
\(164\) | 4.85500 | − | 2.80304i | 0.379112 | − | 0.218880i | ||||
\(165\) | −10.7756 | + | 12.5498i | −0.838876 | + | 0.977002i | ||||
\(166\) | 8.34337 | − | 4.81704i | 0.647571 | − | 0.373875i | ||||
\(167\) | 13.0891 | + | 7.55698i | 1.01286 | + | 0.584777i | 0.912029 | − | 0.410126i | \(-0.134515\pi\) |
0.100834 | + | 0.994903i | \(0.467849\pi\) | |||||||
\(168\) | 0.787372 | + | 4.51443i | 0.0607471 | + | 0.348296i | ||||
\(169\) | 7.57313 | − | 10.5663i | 0.582548 | − | 0.812796i | ||||
\(170\) | 4.80375 | + | 2.77345i | 0.368431 | + | 0.212714i | ||||
\(171\) | 7.27149 | + | 2.83508i | 0.556065 | + | 0.216804i | ||||
\(172\) | 9.75466 | 0.743786 | ||||||||
\(173\) | −19.2543 | −1.46387 | −0.731937 | − | 0.681372i | \(-0.761384\pi\) | ||||
−0.731937 | + | 0.681372i | \(0.761384\pi\) | |||||||
\(174\) | 14.3513 | + | 2.69878i | 1.08797 | + | 0.204594i | ||||
\(175\) | −3.05062 | − | 2.51083i | −0.230605 | − | 0.189801i | ||||
\(176\) | 2.54994 | + | 4.41662i | 0.192209 | + | 0.332915i | ||||
\(177\) | −2.48551 | + | 2.89476i | −0.186822 | + | 0.217583i | ||||
\(178\) | 12.7850 | + | 7.38141i | 0.958275 | + | 0.553260i | ||||
\(179\) | 5.37303i | 0.401599i | 0.979632 | + | 0.200800i | \(0.0643540\pi\) | ||||
−0.979632 | + | 0.200800i | \(0.935646\pi\) | |||||||
\(180\) | −5.55318 | + | 0.849728i | −0.413910 | + | 0.0633350i | ||||
\(181\) | − | 11.3131i | − | 0.840893i | −0.907317 | − | 0.420446i | \(-0.861874\pi\) | ||
0.907317 | − | 0.420446i | \(-0.138126\pi\) | |||||||
\(182\) | −9.32144 | − | 2.02751i | −0.690951 | − | 0.150289i | ||||
\(183\) | −10.0470 | − | 1.88934i | −0.742694 | − | 0.139664i | ||||
\(184\) | 5.25634 | − | 3.03475i | 0.387503 | − | 0.223725i | ||||
\(185\) | −11.9408 | −0.877904 | ||||||||
\(186\) | −10.7704 | − | 9.24768i | −0.789721 | − | 0.678073i | ||||
\(187\) | −7.55323 | + | 13.0826i | −0.552347 | + | 0.956693i | ||||
\(188\) | 2.70708 | − | 1.56293i | 0.197434 | − | 0.113988i | ||||
\(189\) | 2.71892 | − | 13.4762i | 0.197772 | − | 0.980248i | ||||
\(190\) | − | 4.87167i | − | 0.353428i | ||||||
\(191\) | − | 3.17384i | − | 0.229651i | −0.993386 | − | 0.114826i | \(-0.963369\pi\) | ||
0.993386 | − | 0.114826i | \(-0.0366309\pi\) | |||||||
\(192\) | −0.320103 | + | 1.70221i | −0.0231014 | + | 0.122847i | ||||
\(193\) | 0.209316i | 0.0150669i | 0.999972 | + | 0.00753344i | \(0.00239799\pi\) | ||||
−0.999972 | + | 0.00753344i | \(0.997602\pi\) | |||||||
\(194\) | −5.83860 | + | 10.1127i | −0.419187 | + | 0.726053i | ||||
\(195\) | 2.72309 | − | 11.3730i | 0.195004 | − | 0.814435i | ||||
\(196\) | 1.34615 | + | 6.86934i | 0.0961535 | + | 0.490667i | ||||
\(197\) | 9.71998 | − | 16.8355i | 0.692520 | − | 1.19948i | −0.278490 | − | 0.960439i | \(-0.589834\pi\) |
0.971010 | − | 0.239040i | \(-0.0768328\pi\) | |||||||
\(198\) | −2.31416 | − | 15.1236i | −0.164460 | − | 1.07479i | ||||
\(199\) | −12.5175 | − | 7.22696i | −0.887339 | − | 0.512306i | −0.0142681 | − | 0.999898i | \(-0.504542\pi\) |
−0.873071 | + | 0.487593i | \(0.837875\pi\) | |||||||
\(200\) | −0.746672 | − | 1.29327i | −0.0527977 | − | 0.0914483i | ||||
\(201\) | −18.8021 | − | 3.53575i | −1.32620 | − | 0.249392i | ||||
\(202\) | 3.15026 | + | 5.45640i | 0.221651 | + | 0.383911i | ||||
\(203\) | 22.0031 | + | 3.66480i | 1.54432 | + | 0.257219i | ||||
\(204\) | −4.84074 | + | 1.69993i | −0.338920 | + | 0.119019i | ||||
\(205\) | 5.24898 | + | 9.09150i | 0.366605 | + | 0.634978i | ||||
\(206\) | − | 5.76406i | − | 0.401601i | ||||||
\(207\) | −17.9990 | + | 2.75414i | −1.25102 | + | 0.191426i | ||||
\(208\) | −3.03019 | − | 1.95395i | −0.210106 | − | 0.135482i | ||||
\(209\) | 13.2675 | 0.917735 | ||||||||
\(210\) | −8.45374 | + | 1.47444i | −0.583364 | + | 0.101746i | ||||
\(211\) | 5.78954 | − | 10.0278i | 0.398568 | − | 0.690341i | −0.594981 | − | 0.803740i | \(-0.702840\pi\) |
0.993550 | + | 0.113399i | \(0.0361738\pi\) | |||||||
\(212\) | 9.48930i | 0.651728i | ||||||||
\(213\) | 23.7916 | − | 8.35496i | 1.63018 | − | 0.572472i | ||||
\(214\) | −5.32321 | − | 3.07336i | −0.363887 | − | 0.210090i | ||||
\(215\) | 18.2666i | 1.24577i | ||||||||
\(216\) | 2.74973 | − | 4.40897i | 0.187095 | − | 0.299992i | ||||
\(217\) | −16.7428 | − | 13.7802i | −1.13657 | − | 0.935462i | ||||
\(218\) | −10.8967 | − | 6.29124i | −0.738020 | − | 0.426096i | ||||
\(219\) | 6.52962 | − | 2.29302i | 0.441231 | − | 0.154948i | ||||
\(220\) | −8.27059 | + | 4.77503i | −0.557603 | + | 0.321932i | ||||
\(221\) | 0.524511 | − | 10.6672i | 0.0352824 | − | 0.717554i | ||||
\(222\) | 7.19483 | − | 8.37950i | 0.482885 | − | 0.562395i | ||||
\(223\) | 3.33759 | − | 5.78088i | 0.223502 | − | 0.387116i | −0.732367 | − | 0.680910i | \(-0.761584\pi\) |
0.955869 | + | 0.293794i | \(0.0949178\pi\) | |||||||
\(224\) | −0.434683 | + | 2.60980i | −0.0290435 | + | 0.174375i | ||||
\(225\) | 0.677631 | + | 4.42849i | 0.0451754 | + | 0.295233i | ||||
\(226\) | −1.92741 | − | 1.11279i | −0.128210 | − | 0.0740219i | ||||
\(227\) | −16.0059 | − | 9.24099i | −1.06235 | − | 0.613346i | −0.136266 | − | 0.990672i | \(-0.543510\pi\) |
−0.926080 | + | 0.377327i | \(0.876843\pi\) | |||||||
\(228\) | 3.41871 | + | 2.93538i | 0.226410 | + | 0.194401i | ||||
\(229\) | 0.100542 | − | 0.174145i | 0.00664403 | − | 0.0115078i | −0.862684 | − | 0.505743i | \(-0.831218\pi\) |
0.869328 | + | 0.494235i | \(0.164552\pi\) | |||||||
\(230\) | 5.68289 | + | 9.84306i | 0.374719 | + | 0.649032i | ||||
\(231\) | −4.01550 | − | 23.0230i | −0.264200 | − | 1.51480i | ||||
\(232\) | 7.30144 | + | 4.21549i | 0.479363 | + | 0.276760i | ||||
\(233\) | 11.1073 | + | 6.41280i | 0.727663 | + | 0.420116i | 0.817567 | − | 0.575834i | \(-0.195323\pi\) |
−0.0899037 | + | 0.995950i | \(0.528656\pi\) | |||||||
\(234\) | 6.34025 | + | 8.76363i | 0.414475 | + | 0.572896i | ||||
\(235\) | 2.92675 | + | 5.06929i | 0.190920 | + | 0.330684i | ||||
\(236\) | −1.90771 | + | 1.10141i | −0.124181 | + | 0.0716960i | ||||
\(237\) | −13.5256 | − | 11.6134i | −0.878582 | − | 0.754371i | ||||
\(238\) | −7.33864 | + | 2.75019i | −0.475694 | + | 0.178268i | ||||
\(239\) | 30.2795 | 1.95862 | 0.979311 | − | 0.202363i | \(-0.0648621\pi\) | ||||
0.979311 | + | 0.202363i | \(0.0648621\pi\) | |||||||
\(240\) | −3.18758 | − | 0.599427i | −0.205757 | − | 0.0386928i | ||||
\(241\) | 4.17255 | − | 7.22708i | 0.268778 | − | 0.465537i | −0.699769 | − | 0.714370i | \(-0.746714\pi\) |
0.968546 | + | 0.248833i | \(0.0800469\pi\) | |||||||
\(242\) | −7.50436 | − | 12.9979i | −0.482398 | − | 0.835538i | ||||
\(243\) | −12.4904 | + | 9.32680i | −0.801261 | + | 0.598315i | ||||
\(244\) | −5.11154 | − | 2.95115i | −0.327233 | − | 0.188928i | ||||
\(245\) | −12.8636 | + | 2.52081i | −0.821824 | + | 0.161048i | ||||
\(246\) | −9.54273 | − | 1.79452i | −0.608422 | − | 0.114414i | ||||
\(247\) | −8.34384 | + | 4.28539i | −0.530906 | + | 0.272673i | ||||
\(248\) | −4.09797 | − | 7.09789i | −0.260221 | − | 0.450717i | ||||
\(249\) | −16.3993 | − | 3.08390i | −1.03926 | − | 0.195434i | ||||
\(250\) | 10.5304 | − | 6.07974i | 0.666002 | − | 0.384517i | ||||
\(251\) | −0.325183 | − | 0.563233i | −0.0205253 | − | 0.0355509i | 0.855580 | − | 0.517670i | \(-0.173201\pi\) |
−0.876106 | + | 0.482119i | \(0.839867\pi\) | |||||||
\(252\) | 4.05904 | − | 6.82086i | 0.255696 | − | 0.429674i | ||||
\(253\) | −26.8067 | + | 15.4768i | −1.68532 | + | 0.973021i | ||||
\(254\) | 7.34464 | 0.460844 | ||||||||
\(255\) | −3.18331 | − | 9.06480i | −0.199346 | − | 0.567660i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.70925 | − | 6.42461i | −0.231377 | − | 0.400756i | 0.726837 | − | 0.686810i | \(-0.240990\pi\) |
−0.958213 | + | 0.286054i | \(0.907656\pi\) | |||||||
\(258\) | −12.8187 | − | 11.0064i | −0.798057 | − | 0.685230i | ||||
\(259\) | 10.7212 | − | 13.0261i | 0.666183 | − | 0.809403i | ||||
\(260\) | 3.65898 | − | 5.67436i | 0.226920 | − | 0.351909i | ||||
\(261\) | −15.8141 | − | 19.7394i | −0.978869 | − | 1.22184i | ||||
\(262\) | −0.931081 | −0.0575224 | ||||||||
\(263\) | − | 20.0513i | − | 1.23642i | −0.786013 | − | 0.618209i | \(-0.787858\pi\) | ||
0.786013 | − | 0.618209i | \(-0.212142\pi\) | |||||||
\(264\) | 1.63248 | − | 8.68108i | 0.100472 | − | 0.534283i | ||||
\(265\) | −17.7697 | −1.09159 | ||||||||
\(266\) | 5.31446 | + | 4.37409i | 0.325850 | + | 0.268193i | ||||
\(267\) | −8.47223 | − | 24.1256i | −0.518492 | − | 1.47646i | ||||
\(268\) | −9.56582 | − | 5.52283i | −0.584325 | − | 0.337360i | ||||
\(269\) | 6.24251 | − | 10.8123i | 0.380612 | − | 0.659240i | −0.610538 | − | 0.791987i | \(-0.709047\pi\) |
0.991150 | + | 0.132747i | \(0.0423799\pi\) | |||||||
\(270\) | 8.25626 | + | 5.14916i | 0.502460 | + | 0.313368i | ||||
\(271\) | −1.43966 | − | 2.49356i | −0.0874530 | − | 0.151473i | 0.818981 | − | 0.573821i | \(-0.194539\pi\) |
−0.906434 | + | 0.422348i | \(0.861206\pi\) | |||||||
\(272\) | −2.96212 | −0.179605 | ||||||||
\(273\) | 9.96171 | + | 13.1820i | 0.602910 | + | 0.797809i | ||||
\(274\) | 2.15714 | 0.130317 | ||||||||
\(275\) | 3.80794 | + | 6.59554i | 0.229627 | + | 0.397726i | ||||
\(276\) | −10.3316 | − | 1.94287i | −0.621889 | − | 0.116947i | ||||
\(277\) | −4.00146 | + | 6.93073i | −0.240424 | + | 0.416427i | −0.960835 | − | 0.277120i | \(-0.910620\pi\) |
0.720411 | + | 0.693548i | \(0.243953\pi\) | |||||||
\(278\) | 7.18997 | + | 4.15113i | 0.431226 | + | 0.248968i | ||||
\(279\) | 3.71905 | + | 24.3049i | 0.222654 | + | 1.45510i | ||||
\(280\) | −4.88713 | − | 0.813991i | −0.292062 | − | 0.0486453i | ||||
\(281\) | −6.16209 | −0.367599 | −0.183800 | − | 0.982964i | \(-0.558840\pi\) | ||||
−0.183800 | + | 0.982964i | \(0.558840\pi\) | |||||||
\(282\) | −5.32089 | − | 1.00060i | −0.316854 | − | 0.0595847i | ||||
\(283\) | 13.7428i | 0.816926i | 0.912775 | + | 0.408463i | \(0.133935\pi\) | ||||
−0.912775 | + | 0.408463i | \(0.866065\pi\) | |||||||
\(284\) | 14.5585 | 0.863886 | ||||||||
\(285\) | −5.49682 | + | 6.40190i | −0.325604 | + | 0.379216i | ||||
\(286\) | 15.4536 | + | 9.96490i | 0.913791 | + | 0.589237i | ||||
\(287\) | −14.6307 | − | 2.43687i | −0.863624 | − | 0.143844i | ||||
\(288\) | 2.34130 | − | 1.87572i | 0.137962 | − | 0.110528i | ||||
\(289\) | 4.11291 | + | 7.12377i | 0.241936 | + | 0.419045i | ||||
\(290\) | −7.89395 | + | 13.6727i | −0.463549 | + | 0.802890i | ||||
\(291\) | 19.0830 | − | 6.70142i | 1.11867 | − | 0.392844i | ||||
\(292\) | 3.99557 | 0.233823 | ||||||||
\(293\) | 4.43117 | − | 2.55834i | 0.258872 | − | 0.149460i | −0.364948 | − | 0.931028i | \(-0.618913\pi\) |
0.623820 | + | 0.781568i | \(0.285580\pi\) | |||||||
\(294\) | 5.98186 | − | 10.5460i | 0.348869 | − | 0.615053i | ||||
\(295\) | −2.06252 | − | 3.57238i | −0.120084 | − | 0.207992i | ||||
\(296\) | 5.52226 | − | 3.18828i | 0.320975 | − | 0.185315i | ||||
\(297\) | −14.0233 | + | 22.4852i | −0.813712 | + | 1.30472i | ||||
\(298\) | −1.97912 | − | 3.42793i | −0.114647 | − | 0.198575i | ||||
\(299\) | 11.8595 | − | 18.3918i | 0.685853 | − | 1.06362i | ||||
\(300\) | −0.478024 | + | 2.54199i | −0.0275987 | + | 0.146762i | ||||
\(301\) | −19.9269 | − | 16.4010i | −1.14857 | − | 0.945335i | ||||
\(302\) | 4.82241 | + | 2.78422i | 0.277498 | + | 0.160214i | ||||
\(303\) | 2.01681 | − | 10.7248i | 0.115863 | − | 0.616125i | ||||
\(304\) | 1.30077 | + | 2.25300i | 0.0746044 | + | 0.129219i | ||||
\(305\) | 5.52634 | − | 9.57191i | 0.316437 | − | 0.548086i | ||||
\(306\) | 8.27934 | + | 3.22803i | 0.473298 | + | 0.184534i | ||||
\(307\) | −1.12751 | −0.0643502 | −0.0321751 | − | 0.999482i | \(-0.510243\pi\) | ||||
−0.0321751 | + | 0.999482i | \(0.510243\pi\) | |||||||
\(308\) | 2.21683 | − | 13.3096i | 0.126316 | − | 0.758387i | ||||
\(309\) | −6.50373 | + | 7.57461i | −0.369984 | + | 0.430904i | ||||
\(310\) | 13.2916 | − | 7.67389i | 0.754910 | − | 0.435847i | ||||
\(311\) | 5.59744 | + | 9.69505i | 0.317402 | + | 0.549756i | 0.979945 | − | 0.199268i | \(-0.0638563\pi\) |
−0.662543 | + | 0.749023i | \(0.730523\pi\) | |||||||
\(312\) | 1.77732 | + | 5.98675i | 0.100621 | + | 0.338933i | ||||
\(313\) | 28.1564 | + | 16.2561i | 1.59150 | + | 0.918850i | 0.993051 | + | 0.117686i | \(0.0375475\pi\) |
0.598444 | + | 0.801165i | \(0.295786\pi\) | |||||||
\(314\) | −6.31098 | − | 3.64365i | −0.356149 | − | 0.205623i | ||||
\(315\) | 12.7728 | + | 7.60099i | 0.719665 | + | 0.428267i | ||||
\(316\) | −5.14630 | − | 8.91365i | −0.289502 | − | 0.501432i | ||||
\(317\) | −12.7161 | + | 22.0249i | −0.714206 | + | 1.23704i | 0.249058 | + | 0.968488i | \(0.419879\pi\) |
−0.963265 | + | 0.268553i | \(0.913454\pi\) | |||||||
\(318\) | 10.7070 | − | 12.4700i | 0.600419 | − | 0.699282i | ||||
\(319\) | −37.2364 | − | 21.4984i | −2.08484 | − | 1.20368i | ||||
\(320\) | −1.62172 | − | 0.936303i | −0.0906572 | − | 0.0523409i | ||||
\(321\) | 3.52754 | + | 10.0450i | 0.196888 | + | 0.560659i | ||||
\(322\) | −15.8402 | − | 2.63831i | −0.882739 | − | 0.147027i | ||||
\(323\) | −3.85305 | + | 6.67367i | −0.214389 | + | 0.371333i | ||||
\(324\) | −8.58819 | + | 2.69128i | −0.477122 | + | 0.149516i | ||||
\(325\) | −4.52513 | − | 2.91792i | −0.251009 | − | 0.161857i | ||||
\(326\) | 17.1552 | − | 9.90456i | 0.950139 | − | 0.548563i | ||||
\(327\) | 7.22095 | + | 20.5624i | 0.399320 | + | 1.13711i | ||||
\(328\) | −4.85500 | − | 2.80304i | −0.268072 | − | 0.154772i | ||||
\(329\) | −8.15787 | − | 1.35876i | −0.449758 | − | 0.0749109i | ||||
\(330\) | 16.2562 | + | 3.05700i | 0.894877 | + | 0.168282i | ||||
\(331\) | 7.18613i | 0.394985i | 0.980304 | + | 0.197493i | \(0.0632798\pi\) | ||||
−0.980304 | + | 0.197493i | \(0.936720\pi\) | |||||||
\(332\) | −8.34337 | − | 4.81704i | −0.457902 | − | 0.264370i | ||||
\(333\) | −18.9096 | + | 2.89348i | −1.03624 | + | 0.158561i | ||||
\(334\) | − | 15.1140i | − | 0.826999i | ||||||
\(335\) | 10.3421 | − | 17.9130i | 0.565048 | − | 0.978692i | ||||
\(336\) | 3.51592 | − | 2.93910i | 0.191809 | − | 0.160341i | ||||
\(337\) | 19.2711 | 1.04976 | 0.524882 | − | 0.851175i | \(-0.324109\pi\) | ||||
0.524882 | + | 0.851175i | \(0.324109\pi\) | |||||||
\(338\) | −12.9373 | − | 1.27535i | −0.703696 | − | 0.0693697i | ||||
\(339\) | 1.27724 | + | 3.63708i | 0.0693703 | + | 0.197539i | ||||
\(340\) | − | 5.54689i | − | 0.300823i | ||||||
\(341\) | 20.8991 | + | 36.1984i | 1.13175 | + | 1.96025i | ||||
\(342\) | −1.18050 | − | 7.71483i | −0.0638339 | − | 0.417170i | ||||
\(343\) | 8.79982 | − | 16.2961i | 0.475146 | − | 0.879907i | ||||
\(344\) | −4.87733 | − | 8.44778i | −0.262968 | − | 0.455474i | ||||
\(345\) | 3.63822 | − | 19.3470i | 0.195875 | − | 1.04161i | ||||
\(346\) | 9.62713 | + | 16.6747i | 0.517558 | + | 0.896436i | ||||
\(347\) | −6.75144 | − | 3.89795i | −0.362436 | − | 0.209253i | 0.307713 | − | 0.951479i | \(-0.400436\pi\) |
−0.670149 | + | 0.742227i | \(0.733770\pi\) | |||||||
\(348\) | −4.83845 | − | 13.7780i | −0.259368 | − | 0.738578i | ||||
\(349\) | −7.17103 | + | 12.4206i | −0.383857 | + | 0.664859i | −0.991610 | − | 0.129267i | \(-0.958738\pi\) |
0.607753 | + | 0.794126i | \(0.292071\pi\) | |||||||
\(350\) | −0.649132 | + | 3.89733i | −0.0346976 | + | 0.208321i | ||||
\(351\) | 1.55644 | − | 18.6702i | 0.0830764 | − | 0.996543i | ||||
\(352\) | 2.54994 | − | 4.41662i | 0.135912 | − | 0.235407i | ||||
\(353\) | − | 25.4388i | − | 1.35397i | −0.735997 | − | 0.676985i | \(-0.763286\pi\) | ||
0.735997 | − | 0.676985i | \(-0.236714\pi\) | |||||||
\(354\) | 3.74969 | + | 0.705132i | 0.199294 | + | 0.0374773i | ||||
\(355\) | 27.2623i | 1.44693i | ||||||||
\(356\) | − | 14.7628i | − | 0.782428i | ||||||
\(357\) | 12.7469 | + | 4.66632i | 0.674637 | + | 0.246968i | ||||
\(358\) | 4.65318 | − | 2.68651i | 0.245928 | − | 0.141987i | ||||
\(359\) | 4.87490 | − | 8.44358i | 0.257288 | − | 0.445635i | −0.708227 | − | 0.705985i | \(-0.750505\pi\) |
0.965514 | + | 0.260350i | \(0.0838379\pi\) | |||||||
\(360\) | 3.51248 | + | 4.38433i | 0.185124 | + | 0.231075i | ||||
\(361\) | −12.2320 | −0.643788 | ||||||||
\(362\) | −9.79739 | + | 5.65653i | −0.514939 | + | 0.297300i | ||||
\(363\) | −4.80433 | + | 25.5481i | −0.252162 | + | 1.34092i | ||||
\(364\) | 2.90485 | + | 9.08636i | 0.152255 | + | 0.476254i | ||||
\(365\) | 7.48214i | 0.391633i | ||||||||
\(366\) | 3.38727 | + | 9.64561i | 0.177055 | + | 0.504184i | ||||
\(367\) | 14.5427i | 0.759120i | 0.925167 | + | 0.379560i | \(0.123925\pi\) | ||||
−0.925167 | + | 0.379560i | \(0.876075\pi\) | |||||||
\(368\) | −5.25634 | − | 3.03475i | −0.274006 | − | 0.158197i | ||||
\(369\) | 10.5154 | + | 13.1255i | 0.547410 | + | 0.683286i | ||||
\(370\) | 5.97039 | + | 10.3410i | 0.310386 | + | 0.537604i | ||||
\(371\) | 15.9548 | − | 19.3848i | 0.828332 | − | 1.00641i | ||||
\(372\) | −2.62354 | + | 13.9512i | −0.136024 | + | 0.723339i | ||||
\(373\) | −13.7536 | −0.712133 | −0.356067 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356067 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(374\) | 15.1065 | 0.781136 | ||||||||
\(375\) | −20.6980 | − | 3.89229i | −1.06884 | − | 0.200997i | ||||
\(376\) | −2.70708 | − | 1.56293i | −0.139607 | − | 0.0806020i | ||||
\(377\) | 30.3616 | + | 1.49289i | 1.56370 | + | 0.0768879i | ||||
\(378\) | −13.0302 | + | 4.38344i | −0.670200 | + | 0.225460i | ||||
\(379\) | 25.1138 | + | 14.4995i | 1.29001 | + | 0.744788i | 0.978656 | − | 0.205505i | \(-0.0658838\pi\) |
0.311355 | + | 0.950294i | \(0.399217\pi\) | |||||||
\(380\) | −4.21899 | + | 2.43583i | −0.216429 | + | 0.124956i | ||||
\(381\) | −9.65166 | − | 8.28714i | −0.494470 | − | 0.424563i | ||||
\(382\) | −2.74863 | + | 1.58692i | −0.140632 | + | 0.0811939i | ||||
\(383\) | − | 5.59893i | − | 0.286092i | −0.989716 | − | 0.143046i | \(-0.954310\pi\) | ||
0.989716 | − | 0.143046i | \(-0.0456897\pi\) | |||||||
\(384\) | 1.63421 | − | 0.573890i | 0.0833956 | − | 0.0292862i | ||||
\(385\) | 24.9237 | + | 4.15125i | 1.27023 | + | 0.211567i | ||||
\(386\) | 0.181273 | − | 0.104658i | 0.00922654 | − | 0.00532695i | ||||
\(387\) | 4.42635 | + | 28.9273i | 0.225004 | + | 1.47046i | ||||
\(388\) | 11.6772 | 0.592820 | ||||||||
\(389\) | 4.31018 | − | 2.48848i | 0.218535 | − | 0.126171i | −0.386737 | − | 0.922190i | \(-0.626398\pi\) |
0.605272 | + | 0.796019i | \(0.293065\pi\) | |||||||
\(390\) | −11.2108 | + | 3.32822i | −0.567682 | + | 0.168531i | ||||
\(391\) | − | 17.9786i | − | 0.909218i | ||||||
\(392\) | 5.27595 | − | 4.60047i | 0.266476 | − | 0.232359i | ||||
\(393\) | 1.22354 | + | 1.05056i | 0.0617196 | + | 0.0529938i | ||||
\(394\) | −19.4400 | −0.979371 | ||||||||
\(395\) | 16.6918 | − | 9.63699i | 0.839854 | − | 0.484890i | ||||
\(396\) | −11.9403 | + | 9.56592i | −0.600025 | + | 0.480705i | ||||
\(397\) | 16.2382 | 0.814974 | 0.407487 | − | 0.913211i | \(-0.366405\pi\) | ||||
0.407487 | + | 0.913211i | \(0.366405\pi\) | |||||||
\(398\) | 14.4539i | 0.724510i | ||||||||
\(399\) | −2.04838 | − | 11.7445i | −0.102547 | − | 0.587959i | ||||
\(400\) | −0.746672 | + | 1.29327i | −0.0373336 | + | 0.0646637i | ||||
\(401\) | 3.46023 | + | 5.99329i | 0.172795 | + | 0.299290i | 0.939396 | − | 0.342834i | \(-0.111387\pi\) |
−0.766601 | + | 0.642124i | \(0.778053\pi\) | |||||||
\(402\) | 6.33899 | + | 18.0509i | 0.316160 | + | 0.900299i | ||||
\(403\) | −24.8353 | − | 16.0145i | −1.23713 | − | 0.797737i | ||||
\(404\) | 3.15026 | − | 5.45640i | 0.156731 | − | 0.271466i | ||||
\(405\) | −5.03971 | − | 16.0823i | −0.250425 | − | 0.799136i | ||||
\(406\) | −7.82776 | − | 20.8877i | −0.388485 | − | 1.03664i | ||||
\(407\) | −28.1628 | + | 16.2598i | −1.39598 | + | 0.805970i | ||||
\(408\) | 3.89256 | + | 3.34224i | 0.192710 | + | 0.165465i | ||||
\(409\) | 5.69146 | − | 9.85790i | 0.281425 | − | 0.487442i | −0.690311 | − | 0.723513i | \(-0.742526\pi\) |
0.971736 | + | 0.236071i | \(0.0758597\pi\) | |||||||
\(410\) | 5.24898 | − | 9.09150i | 0.259229 | − | 0.448997i | ||||
\(411\) | −2.83471 | − | 2.43395i | −0.139826 | − | 0.120058i | ||||
\(412\) | −4.99182 | + | 2.88203i | −0.245930 | + | 0.141987i | ||||
\(413\) | 5.74894 | + | 0.957533i | 0.282887 | + | 0.0471171i | ||||
\(414\) | 11.3847 | + | 14.2105i | 0.559526 | + | 0.698409i | ||||
\(415\) | 9.02043 | − | 15.6238i | 0.442795 | − | 0.766944i | ||||
\(416\) | −0.177072 | + | 3.60120i | −0.00868169 | + | 0.176563i | ||||
\(417\) | −4.76458 | − | 13.5677i | −0.233323 | − | 0.664411i | ||||
\(418\) | −6.63377 | − | 11.4900i | −0.324468 | − | 0.561996i | ||||
\(419\) | −4.51941 | + | 7.82784i | −0.220788 | + | 0.382415i | −0.955047 | − | 0.296453i | \(-0.904196\pi\) |
0.734260 | + | 0.678869i | \(0.237529\pi\) | |||||||
\(420\) | 5.50377 | + | 6.58394i | 0.268557 | + | 0.321263i | ||||
\(421\) | 3.07453i | 0.149844i | 0.997189 | + | 0.0749218i | \(0.0238707\pi\) | ||||
−0.997189 | + | 0.0749218i | \(0.976129\pi\) | |||||||
\(422\) | −11.5791 | −0.563661 | ||||||||
\(423\) | 5.86323 | + | 7.31858i | 0.285080 | + | 0.355842i | ||||
\(424\) | 8.21797 | − | 4.74465i | 0.399100 | − | 0.230421i | ||||
\(425\) | −4.42347 | −0.214570 | ||||||||
\(426\) | −19.1314 | − | 16.4267i | −0.926920 | − | 0.795875i | ||||
\(427\) | 5.48000 | + | 14.6229i | 0.265196 | + | 0.707652i | ||||
\(428\) | 6.14671i | 0.297113i | ||||||||
\(429\) | −9.06410 | − | 30.5317i | −0.437619 | − | 1.47408i | ||||
\(430\) | 15.8194 | − | 9.13332i | 0.762878 | − | 0.440448i | ||||
\(431\) | 23.2809 | 1.12140 | 0.560700 | − | 0.828019i | \(-0.310532\pi\) | ||||
0.560700 | + | 0.828019i | \(0.310532\pi\) | |||||||
\(432\) | −5.19314 | − | 0.176850i | −0.249855 | − | 0.00850872i | ||||
\(433\) | 23.9459 | − | 13.8252i | 1.15077 | − | 0.664396i | 0.201693 | − | 0.979449i | \(-0.435356\pi\) |
0.949074 | + | 0.315053i | \(0.102022\pi\) | |||||||
\(434\) | −3.56264 | + | 21.3898i | −0.171012 | + | 1.02674i | ||||
\(435\) | 25.8008 | − | 9.06051i | 1.23705 | − | 0.434418i | ||||
\(436\) | 12.5825i | 0.602591i | ||||||||
\(437\) | −13.6746 | + | 7.89503i | −0.654145 | + | 0.377671i | ||||
\(438\) | −5.25062 | − | 4.50830i | −0.250884 | − | 0.215415i | ||||
\(439\) | −3.78672 | + | 2.18627i | −0.180731 | + | 0.104345i | −0.587636 | − | 0.809126i | \(-0.699941\pi\) |
0.406905 | + | 0.913470i | \(0.366608\pi\) | |||||||
\(440\) | 8.27059 | + | 4.77503i | 0.394285 | + | 0.227641i | ||||
\(441\) | −19.7601 | + | 7.10907i | −0.940957 | + | 0.338527i | ||||
\(442\) | −9.50032 | + | 4.87936i | −0.451884 | + | 0.232088i | ||||
\(443\) | −2.31071 | − | 1.33409i | −0.109785 | − | 0.0633846i | 0.444102 | − | 0.895976i | \(-0.353523\pi\) |
−0.553887 | + | 0.832592i | \(0.686856\pi\) | |||||||
\(444\) | −10.8543 | − | 2.04116i | −0.515121 | − | 0.0968689i | ||||
\(445\) | 27.6450 | 1.31050 | ||||||||
\(446\) | −6.67519 | −0.316079 | ||||||||
\(447\) | −1.26704 | + | 6.73777i | −0.0599291 | + | 0.318685i | ||||
\(448\) | 2.47749 | − | 0.928453i | 0.117051 | − | 0.0438653i | ||||
\(449\) | 7.64162 | + | 13.2357i | 0.360630 | + | 0.624630i | 0.988065 | − | 0.154039i | \(-0.0492282\pi\) |
−0.627434 | + | 0.778670i | \(0.715895\pi\) | |||||||
\(450\) | 3.49637 | − | 2.80109i | 0.164820 | − | 0.132045i | ||||
\(451\) | 24.7599 | + | 14.2951i | 1.16590 | + | 0.673131i | ||||
\(452\) | 2.22559i | 0.104683i | ||||||||
\(453\) | −3.19567 | − | 9.10000i | −0.150146 | − | 0.427555i | ||||
\(454\) | 18.4820i | 0.867402i | ||||||||
\(455\) | −17.0152 | + | 5.43964i | −0.797683 | + | 0.255014i | ||||
\(456\) | 0.832761 | − | 4.42838i | 0.0389976 | − | 0.207378i | ||||
\(457\) | 6.00766 | − | 3.46853i | 0.281027 | − | 0.162251i | −0.352861 | − | 0.935676i | \(-0.614791\pi\) |
0.633888 | + | 0.773425i | \(0.281458\pi\) | |||||||
\(458\) | −0.201085 | −0.00939607 | ||||||||
\(459\) | −7.23770 | − | 13.5838i | −0.337827 | − | 0.634036i | ||||
\(460\) | 5.68289 | − | 9.84306i | 0.264966 | − | 0.458935i | ||||
\(461\) | −17.6491 | + | 10.1897i | −0.822001 | + | 0.474582i | −0.851106 | − | 0.524994i | \(-0.824068\pi\) |
0.0291053 | + | 0.999576i | \(0.490734\pi\) | |||||||
\(462\) | −17.9308 | + | 14.9890i | −0.834214 | + | 0.697353i | ||||
\(463\) | − | 22.4244i | − | 1.04215i | −0.853511 | − | 0.521075i | \(-0.825531\pi\) | ||
0.853511 | − | 0.521075i | \(-0.174469\pi\) | |||||||
\(464\) | − | 8.43097i | − | 0.391398i | ||||||
\(465\) | −26.1252 | − | 4.91287i | −1.21153 | − | 0.227829i | ||||
\(466\) | − | 12.8256i | − | 0.594134i | ||||||
\(467\) | 9.83436 | − | 17.0336i | 0.455080 | − | 0.788221i | −0.543613 | − | 0.839336i | \(-0.682944\pi\) |
0.998693 | + | 0.0511146i | \(0.0162774\pi\) | |||||||
\(468\) | 4.41940 | − | 9.87263i | 0.204287 | − | 0.456363i | ||||
\(469\) | 10.2554 | + | 27.3655i | 0.473549 | + | 1.26362i | ||||
\(470\) | 2.92675 | − | 5.06929i | 0.135001 | − | 0.233829i | ||||
\(471\) | 4.18211 | + | 11.9090i | 0.192701 | + | 0.548737i | ||||
\(472\) | 1.90771 | + | 1.10141i | 0.0878093 | + | 0.0506967i | ||||
\(473\) | 24.8738 | + | 43.0826i | 1.14370 | + | 1.98094i | ||||
\(474\) | −3.29469 | + | 17.5202i | −0.151330 | + | 0.804730i | ||||
\(475\) | 1.94250 | + | 3.36451i | 0.0891280 | + | 0.154374i | ||||
\(476\) | 6.05106 | + | 4.98036i | 0.277350 | + | 0.228274i | ||||
\(477\) | −28.1404 | + | 4.30594i | −1.28846 | + | 0.197155i | ||||
\(478\) | −15.1398 | − | 26.2229i | −0.692477 | − | 1.19941i | ||||
\(479\) | 19.0205i | 0.869070i | 0.900655 | + | 0.434535i | \(0.143087\pi\) | ||||
−0.900655 | + | 0.434535i | \(0.856913\pi\) | |||||||
\(480\) | 1.07467 | + | 3.06024i | 0.0490518 | + | 0.139680i | ||||
\(481\) | 12.4595 | − | 19.3222i | 0.568103 | − | 0.881017i | ||||
\(482\) | −8.34511 | −0.380109 | ||||||||
\(483\) | 17.8389 | + | 21.3399i | 0.811696 | + | 0.970999i | ||||
\(484\) | −7.50436 | + | 12.9979i | −0.341107 | + | 0.590815i | ||||
\(485\) | 21.8668i | 0.992920i | ||||||||
\(486\) | 14.3225 | + | 6.15363i | 0.649680 | + | 0.279134i | ||||
\(487\) | 19.4629 | + | 11.2369i | 0.881947 | + | 0.509192i | 0.871300 | − | 0.490751i | \(-0.163277\pi\) |
0.0106472 | + | 0.999943i | \(0.496611\pi\) | |||||||
\(488\) | 5.90230i | 0.267185i | ||||||||
\(489\) | −33.7194 | − | 6.34096i | −1.52484 | − | 0.286748i | ||||
\(490\) | 8.61487 | + | 9.87978i | 0.389180 | + | 0.446323i | ||||
\(491\) | 25.7148 | + | 14.8464i | 1.16049 | + | 0.670010i | 0.951422 | − | 0.307891i | \(-0.0996233\pi\) |
0.209069 | + | 0.977901i | \(0.432957\pi\) | |||||||
\(492\) | 3.21727 | + | 9.16151i | 0.145046 | + | 0.413033i | ||||
\(493\) | 21.6278 | − | 12.4868i | 0.974065 | − | 0.562377i | ||||
\(494\) | 7.88318 | + | 5.08328i | 0.354681 | + | 0.228708i | ||||
\(495\) | −17.9132 | − | 22.3596i | −0.805138 | − | 1.00499i | ||||
\(496\) | −4.09797 | + | 7.09789i | −0.184004 | + | 0.318705i | ||||
\(497\) | −29.7402 | − | 24.4778i | −1.33403 | − | 1.09798i | ||||
\(498\) | 5.52891 | + | 15.7441i | 0.247756 | + | 0.705512i | ||||
\(499\) | −6.50477 | − | 3.75553i | −0.291193 | − | 0.168121i | 0.347287 | − | 0.937759i | \(-0.387103\pi\) |
−0.638480 | + | 0.769638i | \(0.720436\pi\) | |||||||
\(500\) | −10.5304 | − | 6.07974i | −0.470935 | − | 0.271894i | ||||
\(501\) | −17.0535 | + | 19.8614i | −0.761892 | + | 0.887342i | ||||
\(502\) | −0.325183 | + | 0.563233i | −0.0145136 | + | 0.0251383i | ||||
\(503\) | 14.6024 | + | 25.2921i | 0.651089 | + | 1.12772i | 0.982859 | + | 0.184358i | \(0.0590207\pi\) |
−0.331770 | + | 0.943360i | \(0.607646\pi\) | |||||||
\(504\) | −7.93656 | − | 0.104805i | −0.353523 | − | 0.00466837i | ||||
\(505\) | 10.2177 | + | 5.89919i | 0.454682 | + | 0.262511i | ||||
\(506\) | 26.8067 | + | 15.4768i | 1.19170 | + | 0.688030i | ||||
\(507\) | 15.5620 | + | 16.2734i | 0.691133 | + | 0.722727i | ||||
\(508\) | −3.67232 | − | 6.36064i | −0.162933 | − | 0.282208i | ||||
\(509\) | 33.1098 | − | 19.1160i | 1.46757 | − | 0.847301i | 0.468227 | − | 0.883608i | \(-0.344893\pi\) |
0.999341 | + | 0.0363071i | \(0.0115594\pi\) | |||||||
\(510\) | −6.25870 | + | 7.28922i | −0.277140 | + | 0.322772i | ||||
\(511\) | −8.16220 | − | 6.71794i | −0.361075 | − | 0.297184i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.15353 | + | 11.4701i | −0.315836 | + | 0.506418i | ||||
\(514\) | −3.70925 | + | 6.42461i | −0.163608 | + | 0.283377i | ||||
\(515\) | −5.39691 | − | 9.34772i | −0.237816 | − | 0.411910i | ||||
\(516\) | −3.12249 | + | 16.6045i | −0.137460 | + | 0.730973i | ||||
\(517\) | 13.8057 | + | 7.97075i | 0.607176 | + | 0.350553i | ||||
\(518\) | −16.6415 | − | 2.77178i | −0.731187 | − | 0.121785i | ||||
\(519\) | 6.16335 | − | 32.7749i | 0.270541 | − | 1.43866i | ||||
\(520\) | −6.74363 | − | 0.331587i | −0.295728 | − | 0.0145411i | ||||
\(521\) | −1.01347 | − | 1.75537i | −0.0444008 | − | 0.0769044i | 0.842971 | − | 0.537959i | \(-0.180805\pi\) |
−0.887372 | + | 0.461055i | \(0.847471\pi\) | |||||||
\(522\) | −9.18780 | + | 23.5651i | −0.402139 | + | 1.03142i | ||||
\(523\) | −12.9768 | + | 7.49219i | −0.567438 | + | 0.327610i | −0.756125 | − | 0.654427i | \(-0.772910\pi\) |
0.188687 | + | 0.982037i | \(0.439577\pi\) | |||||||
\(524\) | 0.465541 | + | 0.806340i | 0.0203372 | + | 0.0352251i | ||||
\(525\) | 5.25048 | − | 4.38909i | 0.229150 | − | 0.191555i | ||||
\(526\) | −17.3650 | + | 10.0257i | −0.757149 | + | 0.437140i | ||||
\(527\) | −24.2774 | −1.05754 | ||||||||
\(528\) | −8.33428 | + | 2.92677i | −0.362703 | + | 0.127371i | ||||
\(529\) | 6.91943 | − | 11.9848i | 0.300845 | − | 0.521078i | ||||
\(530\) | 8.88486 | + | 15.3890i | 0.385934 | + | 0.668457i | ||||
\(531\) | −4.13188 | − | 5.15748i | −0.179308 | − | 0.223816i | ||||
\(532\) | 1.13085 | − | 6.78950i | 0.0490285 | − | 0.294362i | ||||
\(533\) | −20.1886 | − | 0.992681i | −0.874465 | − | 0.0429978i | ||||
\(534\) | −16.6573 | + | 19.4000i | −0.720830 | + | 0.839518i | ||||
\(535\) | −11.5104 | −0.497637 | ||||||||
\(536\) | 11.0457i | 0.477100i | ||||||||
\(537\) | −9.14605 | − | 1.71992i | −0.394681 | − | 0.0742201i | ||||
\(538\) | −12.4850 | −0.538267 | ||||||||
\(539\) | −26.9067 | + | 23.4618i | −1.15895 | + | 1.01057i | ||||
\(540\) | 0.331171 | − | 9.72471i | 0.0142513 | − | 0.418485i | ||||
\(541\) | 0.930484 | + | 0.537215i | 0.0400046 | + | 0.0230967i | 0.519869 | − | 0.854246i | \(-0.325981\pi\) |
−0.479864 | + | 0.877343i | \(0.659314\pi\) | |||||||
\(542\) | −1.43966 | + | 2.49356i | −0.0618386 | + | 0.107108i | ||||
\(543\) | 19.2572 | + | 3.62134i | 0.826407 | + | 0.155407i | ||||
\(544\) | 1.48106 | + | 2.56527i | 0.0635000 | + | 0.109985i | ||||
\(545\) | −23.5620 | −1.00929 | ||||||||
\(546\) | 6.43507 | − | 15.2181i | 0.275396 | − | 0.651274i | ||||
\(547\) | −26.8765 | −1.14916 | −0.574578 | − | 0.818450i | \(-0.694834\pi\) | ||||
−0.574578 | + | 0.818450i | \(0.694834\pi\) | |||||||
\(548\) | −1.07857 | − | 1.86814i | −0.0460742 | − | 0.0798028i | ||||
\(549\) | 6.43214 | − | 16.4973i | 0.274517 | − | 0.704089i | ||||
\(550\) | 3.80794 | − | 6.59554i | 0.162371 | − | 0.281235i | ||||
\(551\) | −18.9950 | − | 10.9668i | −0.809214 | − | 0.467200i | ||||
\(552\) | 3.48323 | + | 9.91886i | 0.148256 | + | 0.422175i | ||||
\(553\) | −4.47402 | + | 26.8616i | −0.190255 | + | 1.14227i | ||||
\(554\) | 8.00292 | 0.340011 | ||||||||
\(555\) | 3.82228 | − | 20.3258i | 0.162247 | − | 0.862781i | ||||
\(556\) | − | 8.30226i | − | 0.352094i | ||||||
\(557\) | 27.1489 | 1.15033 | 0.575167 | − | 0.818036i | \(-0.304937\pi\) | ||||
0.575167 | + | 0.818036i | \(0.304937\pi\) | |||||||
\(558\) | 19.1892 | − | 15.3733i | 0.812342 | − | 0.650802i | ||||
\(559\) | −29.5585 | − | 19.0601i | −1.25019 | − | 0.806157i | ||||
\(560\) | 1.73863 | + | 4.63937i | 0.0734704 | + | 0.196049i | ||||
\(561\) | −19.8515 | − | 17.0450i | −0.838133 | − | 0.719640i | ||||
\(562\) | 3.08104 | + | 5.33653i | 0.129966 | + | 0.225108i | ||||
\(563\) | 8.15434 | − | 14.1237i | 0.343664 | − | 0.595244i | −0.641446 | − | 0.767168i | \(-0.721665\pi\) |
0.985110 | + | 0.171924i | \(0.0549985\pi\) | |||||||
\(564\) | 1.79390 | + | 5.10832i | 0.0755368 | + | 0.215099i | ||||
\(565\) | −4.16765 | −0.175334 | ||||||||
\(566\) | 11.9016 | − | 6.87141i | 0.500263 | − | 0.288827i | ||||
\(567\) | 22.0690 | + | 8.94195i | 0.926812 | + | 0.375526i | ||||
\(568\) | −7.27923 | − | 12.6080i | −0.305430 | − | 0.529020i | ||||
\(569\) | 22.6413 | − | 13.0720i | 0.949172 | − | 0.548005i | 0.0563486 | − | 0.998411i | \(-0.482054\pi\) |
0.892824 | + | 0.450406i | \(0.148721\pi\) | |||||||
\(570\) | 8.29262 | + | 1.55943i | 0.347340 | + | 0.0653175i | ||||
\(571\) | −0.114124 | − | 0.197668i | −0.00477593 | − | 0.00827215i | 0.863628 | − | 0.504130i | \(-0.168187\pi\) |
−0.868403 | + | 0.495858i | \(0.834854\pi\) | |||||||
\(572\) | 0.903047 | − | 18.3657i | 0.0377583 | − | 0.767907i | ||||
\(573\) | 5.40256 | + | 1.01596i | 0.225695 | + | 0.0424422i | ||||
\(574\) | 5.20497 | + | 13.8890i | 0.217251 | + | 0.579716i | ||||
\(575\) | −7.84953 | − | 4.53193i | −0.327348 | − | 0.188995i | ||||
\(576\) | −2.79507 | − | 1.08977i | −0.116461 | − | 0.0454070i | ||||
\(577\) | 8.82331 | + | 15.2824i | 0.367319 | + | 0.636215i | 0.989145 | − | 0.146940i | \(-0.0469424\pi\) |
−0.621826 | + | 0.783155i | \(0.713609\pi\) | |||||||
\(578\) | 4.11291 | − | 7.12377i | 0.171075 | − | 0.296310i | ||||
\(579\) | −0.356300 | − | 0.0670026i | −0.0148073 | − | 0.00278453i | ||||
\(580\) | 15.7879 | 0.655557 | ||||||||
\(581\) | 8.94479 | + | 23.8684i | 0.371093 | + | 0.990228i | ||||
\(582\) | −15.3451 | − | 13.1757i | −0.636075 | − | 0.546149i | ||||
\(583\) | −41.9106 | + | 24.1971i | −1.73576 | + | 1.00214i | ||||
\(584\) | −1.99779 | − | 3.46027i | −0.0826690 | − | 0.143187i | ||||
\(585\) | 18.4876 | + | 8.27580i | 0.764366 | + | 0.342162i | ||||
\(586\) | −4.43117 | − | 2.55834i | −0.183050 | − | 0.105684i | ||||
\(587\) | −13.2115 | − | 7.62767i | −0.545298 | − | 0.314828i | 0.201926 | − | 0.979401i | \(-0.435280\pi\) |
−0.747223 | + | 0.664573i | \(0.768613\pi\) | |||||||
\(588\) | −12.1240 | + | 0.0925368i | −0.499985 | + | 0.00381615i | ||||
\(589\) | 10.6610 | + | 18.4655i | 0.439281 | + | 0.760857i | ||||
\(590\) | −2.06252 | + | 3.57238i | −0.0849124 | + | 0.147073i | ||||
\(591\) | 25.5462 | + | 21.9346i | 1.05083 | + | 0.902268i | ||||
\(592\) | −5.52226 | − | 3.18828i | −0.226964 | − | 0.131037i | ||||
\(593\) | 0.0222995 | + | 0.0128746i | 0.000915730 | + | 0.000528697i | 0.500458 | − | 0.865761i | \(-0.333165\pi\) |
−0.499542 | + | 0.866290i | \(0.666498\pi\) | |||||||
\(594\) | 26.4844 | + | 0.901915i | 1.08667 | + | 0.0370060i | ||||
\(595\) | −9.32625 | + | 11.3313i | −0.382339 | + | 0.464536i | ||||
\(596\) | −1.97912 | + | 3.42793i | −0.0810678 | + | 0.140414i | ||||
\(597\) | 16.3087 | − | 18.9940i | 0.667471 | − | 0.777374i | ||||
\(598\) | −21.8575 | − | 1.07474i | −0.893819 | − | 0.0439495i | ||||
\(599\) | −21.8300 | + | 12.6035i | −0.891949 | + | 0.514967i | −0.874579 | − | 0.484882i | \(-0.838862\pi\) |
−0.0173692 | + | 0.999849i | \(0.505529\pi\) | |||||||
\(600\) | 2.44044 | − | 0.857016i | 0.0996307 | − | 0.0349875i | ||||
\(601\) | 15.4945 | + | 8.94574i | 0.632033 | + | 0.364904i | 0.781539 | − | 0.623856i | \(-0.214435\pi\) |
−0.149506 | + | 0.988761i | \(0.547768\pi\) | |||||||
\(602\) | −4.24019 | + | 25.4577i | −0.172817 | + | 1.03758i | ||||
\(603\) | 12.0372 | − | 30.8734i | 0.490192 | − | 1.25726i | ||||
\(604\) | − | 5.56843i | − | 0.226576i | ||||||
\(605\) | −24.3400 | − | 14.0527i | −0.989562 | − | 0.571324i | ||||
\(606\) | −10.2964 | + | 3.61580i | −0.418262 | + | 0.146882i | ||||
\(607\) | − | 26.4339i | − | 1.07292i | −0.843926 | − | 0.536459i | \(-0.819761\pi\) | ||
0.843926 | − | 0.536459i | \(-0.180239\pi\) | |||||||
\(608\) | 1.30077 | − | 2.25300i | 0.0527532 | − | 0.0913713i | ||||
\(609\) | −13.2816 | + | 36.2810i | −0.538196 | + | 1.47018i | ||||
\(610\) | −11.0527 | −0.447510 | ||||||||
\(611\) | −11.2569 | − | 0.553504i | −0.455404 | − | 0.0223924i | ||||
\(612\) | −1.34412 | − | 8.78413i | −0.0543327 | − | 0.355077i | ||||
\(613\) | − | 8.25058i | − | 0.333238i | −0.986021 | − | 0.166619i | \(-0.946715\pi\) | ||
0.986021 | − | 0.166619i | \(-0.0532850\pi\) | |||||||
\(614\) | 0.563753 | + | 0.976449i | 0.0227512 | + | 0.0394063i | ||||
\(615\) | −17.1559 | + | 6.02468i | −0.691793 | + | 0.242938i | ||||
\(616\) | −12.6349 | + | 4.73499i | −0.509075 | + | 0.190778i | ||||
\(617\) | 2.53770 | + | 4.39542i | 0.102164 | + | 0.176953i | 0.912576 | − | 0.408907i | \(-0.134090\pi\) |
−0.810412 | + | 0.585860i | \(0.800757\pi\) | |||||||
\(618\) | 9.81167 | + | 1.84509i | 0.394683 | + | 0.0742205i | ||||
\(619\) | −14.6995 | − | 25.4603i | −0.590822 | − | 1.02333i | −0.994122 | − | 0.108266i | \(-0.965470\pi\) |
0.403300 | − | 0.915068i | \(-0.367863\pi\) | |||||||
\(620\) | −13.2916 | − | 7.67389i | −0.533802 | − | 0.308191i | ||||
\(621\) | 1.07339 | − | 31.5198i | 0.0430738 | − | 1.26485i | ||||
\(622\) | 5.59744 | − | 9.69505i | 0.224437 | − | 0.388736i | ||||
\(623\) | −24.8214 | + | 30.1576i | −0.994449 | + | 1.20824i | ||||
\(624\) | 4.29602 | − | 4.53258i | 0.171978 | − | 0.181448i | ||||
\(625\) | 7.65160 | − | 13.2530i | 0.306064 | − | 0.530118i | ||||
\(626\) | − | 32.5122i | − | 1.29945i | ||||||
\(627\) | −4.24698 | + | 22.5842i | −0.169608 | + | 0.901926i | ||||
\(628\) | 7.28729i | 0.290795i | ||||||||
\(629\) | − | 18.8882i | − | 0.753120i | ||||||
\(630\) | 0.196258 | − | 14.8621i | 0.00781911 | − | 0.592119i | ||||
\(631\) | 31.4596 | − | 18.1632i | 1.25239 | − | 0.723066i | 0.280804 | − | 0.959765i | \(-0.409399\pi\) |
0.971583 | + | 0.236699i | \(0.0760655\pi\) | |||||||
\(632\) | −5.14630 | + | 8.91365i | −0.204709 | + | 0.354566i | ||||
\(633\) | 15.2162 | + | 13.0650i | 0.604789 | + | 0.519286i | ||||
\(634\) | 25.4322 | 1.01004 | ||||||||
\(635\) | 11.9110 | − | 6.87681i | 0.472673 | − | 0.272898i | ||||
\(636\) | −16.1528 | − | 3.03755i | −0.640501 | − | 0.120447i | ||||
\(637\) | 9.34326 | − | 23.4458i | 0.370193 | − | 0.928955i | ||||
\(638\) | 42.9969i | 1.70226i | ||||||||
\(639\) | 6.60616 | + | 43.1729i | 0.261336 | + | 1.70789i | ||||
\(640\) | 1.87261i | 0.0740213i | ||||||||
\(641\) | −0.640544 | − | 0.369818i | −0.0253000 | − | 0.0146069i | 0.487297 | − | 0.873236i | \(-0.337983\pi\) |
−0.512597 | + | 0.858630i | \(0.671316\pi\) | |||||||
\(642\) | 6.93549 | − | 8.07745i | 0.273722 | − | 0.318792i | ||||
\(643\) | 2.41482 | + | 4.18259i | 0.0952313 | + | 0.164945i | 0.909705 | − | 0.415255i | \(-0.136308\pi\) |
−0.814474 | + | 0.580200i | \(0.802974\pi\) | |||||||
\(644\) | 5.63524 | + | 15.0372i | 0.222060 | + | 0.592547i | ||||
\(645\) | −31.0937 | − | 5.84720i | −1.22431 | − | 0.230233i | ||||
\(646\) | 7.70609 | 0.303192 | ||||||||
\(647\) | 4.04141 | 0.158884 | 0.0794422 | − | 0.996839i | \(-0.474686\pi\) | ||||
0.0794422 | + | 0.996839i | \(0.474686\pi\) | |||||||
\(648\) | 6.62481 | + | 6.09195i | 0.260247 | + | 0.239314i | ||||
\(649\) | −9.72906 | − | 5.61707i | −0.381899 | − | 0.220489i | ||||
\(650\) | −0.264430 | + | 5.37783i | −0.0103718 | + | 0.210936i | ||||
\(651\) | 28.8163 | − | 24.0887i | 1.12940 | − | 0.944109i | ||||
\(652\) | −17.1552 | − | 9.90456i | −0.671849 | − | 0.387892i | ||||
\(653\) | 40.4464 | − | 23.3518i | 1.58279 | − | 0.913825i | 0.588342 | − | 0.808612i | \(-0.299781\pi\) |
0.994450 | − | 0.105213i | \(-0.0335524\pi\) | |||||||
\(654\) | 14.1971 | − | 16.5347i | 0.555151 | − | 0.646560i | ||||
\(655\) | −1.50996 | + | 0.871775i | −0.0589989 | + | 0.0340631i | ||||
\(656\) | 5.60607i | 0.218880i | ||||||||
\(657\) | 1.81306 | + | 11.8488i | 0.0707343 | + | 0.462266i | ||||
\(658\) | 2.90221 | + | 7.74430i | 0.113140 | + | 0.301904i | ||||
\(659\) | −40.3288 | + | 23.2838i | −1.57099 | + | 0.907009i | −0.574937 | + | 0.818198i | \(0.694973\pi\) |
−0.996048 | + | 0.0888111i | \(0.971693\pi\) | |||||||
\(660\) | −5.48068 | − | 15.6068i | −0.213335 | − | 0.607495i | ||||
\(661\) | −44.5873 | −1.73424 | −0.867122 | − | 0.498095i | \(-0.834033\pi\) | ||||
−0.867122 | + | 0.498095i | \(0.834033\pi\) | |||||||
\(662\) | 6.22337 | − | 3.59306i | 0.241878 | − | 0.139648i | ||||
\(663\) | 17.9900 | + | 4.30743i | 0.698673 | + | 0.167287i | ||||
\(664\) | 9.63409i | 0.373875i | ||||||||
\(665\) | 12.7141 | + | 2.11763i | 0.493030 | + | 0.0821183i | ||||
\(666\) | 11.9606 | + | 14.9294i | 0.463464 | + | 0.578504i | ||||
\(667\) | 51.1718 | 1.98138 | ||||||||
\(668\) | −13.0891 | + | 7.55698i | −0.506432 | + | 0.292388i | ||||
\(669\) | 8.77193 | + | 7.53178i | 0.339142 | + | 0.291195i | ||||
\(670\) | −20.6842 | −0.799099 | ||||||||
\(671\) | − | 30.1010i | − | 1.16204i | ||||||
\(672\) | −4.30329 | − | 1.57533i | −0.166003 | − | 0.0607696i | ||||
\(673\) | −7.92610 | + | 13.7284i | −0.305529 | + | 0.529191i | −0.977379 | − | 0.211496i | \(-0.932166\pi\) |
0.671850 | + | 0.740687i | \(0.265500\pi\) | |||||||
\(674\) | −9.63555 | − | 16.6893i | −0.371148 | − | 0.642847i | ||||
\(675\) | −7.75515 | − | 0.264099i | −0.298496 | − | 0.0101652i | ||||
\(676\) | 5.36416 | + | 11.8417i | 0.206314 | + | 0.455450i | ||||
\(677\) | 2.65460 | − | 4.59790i | 0.102024 | − | 0.176711i | −0.810494 | − | 0.585747i | \(-0.800801\pi\) |
0.912519 | + | 0.409035i | \(0.134135\pi\) | |||||||
\(678\) | 2.51118 | − | 2.92466i | 0.0964415 | − | 0.112321i | ||||
\(679\) | −23.8543 | − | 19.6334i | −0.915444 | − | 0.753461i | ||||
\(680\) | −4.80375 | + | 2.77345i | −0.184215 | + | 0.106357i | ||||
\(681\) | 20.8537 | − | 24.2873i | 0.799114 | − | 0.930693i | ||||
\(682\) | 20.8991 | − | 36.1984i | 0.800269 | − | 1.38611i | ||||
\(683\) | −5.98567 | + | 10.3675i | −0.229035 | + | 0.396701i | −0.957522 | − | 0.288359i | \(-0.906890\pi\) |
0.728487 | + | 0.685059i | \(0.240224\pi\) | |||||||
\(684\) | −6.09099 | + | 4.87976i | −0.232895 | + | 0.186582i | ||||
\(685\) | 3.49828 | − | 2.01973i | 0.133662 | − | 0.0771701i | ||||
\(686\) | −18.5128 | + | 0.527188i | −0.706820 | + | 0.0201281i | ||||
\(687\) | 0.264247 | + | 0.226889i | 0.0100817 | + | 0.00865635i | ||||
\(688\) | −4.87733 | + | 8.44778i | −0.185946 | + | 0.322069i | ||||
\(689\) | 18.5416 | − | 28.7544i | 0.706379 | − | 1.09546i | ||||
\(690\) | −18.5741 | + | 6.52271i | −0.707104 | + | 0.248315i | ||||
\(691\) | 19.4945 | + | 33.7655i | 0.741608 | + | 1.28450i | 0.951763 | + | 0.306834i | \(0.0992696\pi\) |
−0.210156 | + | 0.977668i | \(0.567397\pi\) | |||||||
\(692\) | 9.62713 | − | 16.6747i | 0.365969 | − | 0.633876i | ||||
\(693\) | 40.4755 | + | 0.534491i | 1.53754 | + | 0.0203036i | ||||
\(694\) | 7.79589i | 0.295928i | ||||||||
\(695\) | 15.5469 | 0.589726 | ||||||||
\(696\) | −9.51287 | + | 11.0792i | −0.360585 | + | 0.419957i | ||||
\(697\) | −14.3811 | + | 8.30294i | −0.544723 | + | 0.314496i | ||||
\(698\) | 14.3421 | 0.542855 | ||||||||
\(699\) | −14.4714 | + | 16.8542i | −0.547360 | + | 0.637486i | ||||
\(700\) | 3.69975 | − | 1.38650i | 0.139838 | − | 0.0524048i | ||||
\(701\) | 41.8339i | 1.58005i | 0.613078 | + | 0.790023i | \(0.289931\pi\) | ||||
−0.613078 | + | 0.790023i | \(0.710069\pi\) | |||||||
\(702\) | −16.9471 | + | 7.98720i | −0.639628 | + | 0.301458i | ||||
\(703\) | −14.3664 | + | 8.29444i | −0.541839 | + | 0.312831i | ||||
\(704\) | −5.09987 | −0.192209 | ||||||||
\(705\) | −9.56588 | + | 3.35927i | −0.360272 | + | 0.126517i | ||||
\(706\) | −22.0306 | + | 12.7194i | −0.829134 | + | 0.478701i | ||||
\(707\) | −15.6095 | + | 5.84973i | −0.587055 | + | 0.220002i | ||||
\(708\) | −1.26418 | − | 3.59989i | −0.0475108 | − | 0.135292i | ||||
\(709\) | − | 11.4460i | − | 0.429864i | −0.976629 | − | 0.214932i | \(-0.931047\pi\) | ||
0.976629 | − | 0.214932i | \(-0.0689530\pi\) | |||||||
\(710\) | 23.6098 | − | 13.6311i | 0.886061 | − | 0.511567i | ||||
\(711\) | 24.0981 | − | 19.3060i | 0.903748 | − | 0.724031i | ||||
\(712\) | −12.7850 | + | 7.38141i | −0.479137 | + | 0.276630i | ||||
\(713\) | −43.0807 | − | 24.8726i | −1.61338 | − | 0.931488i | ||||
\(714\) | −2.33229 | − | 13.3723i | −0.0872839 | − | 0.500445i | ||||
\(715\) | 34.3917 | + | 1.69105i | 1.28618 | + | 0.0632418i | ||||
\(716\) | −4.65318 | − | 2.68651i | −0.173897 | − | 0.100400i | ||||
\(717\) | −9.69257 | + | 51.5423i | −0.361976 | + | 1.92488i | ||||
\(718\) | −9.74981 | −0.363860 | ||||||||
\(719\) | −32.2996 | −1.20457 | −0.602286 | − | 0.798280i | \(-0.705743\pi\) | ||||
−0.602286 | + | 0.798280i | \(0.705743\pi\) | |||||||
\(720\) | 2.04071 | − | 5.23406i | 0.0760526 | − | 0.195062i | ||||
\(721\) | 15.0430 | + | 2.50554i | 0.560232 | + | 0.0933113i | ||||
\(722\) | 6.11599 | + | 10.5932i | 0.227614 | + | 0.394238i | ||||
\(723\) | 10.9664 | + | 9.41599i | 0.407844 | + | 0.350184i | ||||
\(724\) | 9.79739 | + | 5.65653i | 0.364117 | + | 0.210223i | ||||
\(725\) | − | 12.5904i | − | 0.467594i | ||||||
\(726\) | 24.5274 | − | 8.61335i | 0.910298 | − | 0.319671i | ||||
\(727\) | 35.0984i | 1.30173i | 0.759195 | + | 0.650863i | \(0.225593\pi\) | ||||
−0.759195 | + | 0.650863i | \(0.774407\pi\) | |||||||
\(728\) | 6.41659 | − | 7.05885i | 0.237815 | − | 0.261618i | ||||
\(729\) | −11.8780 | − | 24.2469i | −0.439926 | − | 0.898034i | ||||
\(730\) | 6.47972 | − | 3.74107i | 0.239825 | − | 0.138463i | ||||
\(731\) | −28.8945 | −1.06870 | ||||||||
\(732\) | 6.65971 | − | 7.75627i | 0.246150 | − | 0.286680i | ||||
\(733\) | −1.14358 | + | 1.98073i | −0.0422389 | + | 0.0731600i | −0.886372 | − | 0.462974i | \(-0.846782\pi\) |
0.844133 | + | 0.536134i | \(0.180116\pi\) | |||||||
\(734\) | 12.5943 | − | 7.27133i | 0.464864 | − | 0.268390i | ||||
\(735\) | −0.173285 | − | 22.7035i | −0.00639171 | − | 0.837431i | ||||
\(736\) | 6.06950i | 0.223725i | ||||||||
\(737\) | − | 56.3314i | − | 2.07500i | ||||||
\(738\) | 6.10931 | − | 15.6693i | 0.224887 | − | 0.576797i | ||||
\(739\) | − | 6.51596i | − | 0.239693i | −0.992792 | − | 0.119847i | \(-0.961760\pi\) | ||
0.992792 | − | 0.119847i | \(-0.0382403\pi\) | |||||||
\(740\) | 5.97039 | − | 10.3410i | 0.219476 | − | 0.380144i | ||||
\(741\) | −4.62377 | − | 15.5748i | −0.169858 | − | 0.572154i | ||||
\(742\) | −24.7652 | − | 4.12484i | −0.909158 | − | 0.151428i | ||||
\(743\) | 14.5039 | − | 25.1215i | 0.532097 | − | 0.921620i | −0.467201 | − | 0.884151i | \(-0.654737\pi\) |
0.999298 | − | 0.0374682i | \(-0.0119293\pi\) | |||||||
\(744\) | 13.3939 | − | 4.70357i | 0.491045 | − | 0.172441i | ||||
\(745\) | −6.41917 | − | 3.70611i | −0.235180 | − | 0.135781i | ||||
\(746\) | 6.87679 | + | 11.9109i | 0.251777 | + | 0.436091i | ||||
\(747\) | 10.4989 | − | 26.9279i | 0.384135 | − | 0.985242i | ||||
\(748\) | −7.55323 | − | 13.0826i | −0.276173 | − | 0.478346i | ||||
\(749\) | 10.3348 | − | 12.5566i | 0.377624 | − | 0.458807i | ||||
\(750\) | 6.97820 | + | 19.8712i | 0.254808 | + | 0.725593i | ||||
\(751\) | −15.4217 | − | 26.7111i | −0.562744 | − | 0.974701i | −0.997256 | − | 0.0740350i | \(-0.976412\pi\) |
0.434512 | − | 0.900666i | \(-0.356921\pi\) | |||||||
\(752\) | 3.12586i | 0.113988i | ||||||||
\(753\) | 1.06283 | − | 0.373238i | 0.0387318 | − | 0.0136015i | ||||
\(754\) | −13.8879 | − | 27.0404i | −0.505769 | − | 0.984753i | ||||
\(755\) | 10.4275 | 0.379495 | ||||||||
\(756\) | 10.3113 | + | 9.09274i | 0.375017 | + | 0.330700i | ||||
\(757\) | −10.6357 | + | 18.4215i | −0.386560 | + | 0.669542i | −0.991984 | − | 0.126361i | \(-0.959670\pi\) |
0.605424 | + | 0.795903i | \(0.293004\pi\) | |||||||
\(758\) | − | 28.9990i | − | 1.05329i | ||||||
\(759\) | −17.7640 | − | 50.5849i | −0.644793 | − | 1.83612i | ||||
\(760\) | 4.21899 | + | 2.43583i | 0.153039 | + | 0.0883569i | ||||
\(761\) | 24.6519i | 0.893632i | 0.894626 | + | 0.446816i | \(0.147442\pi\) | ||||
−0.894626 | + | 0.446816i | \(0.852558\pi\) | |||||||
\(762\) | −2.35104 | + | 12.5022i | −0.0851692 | + | 0.452905i | ||||
\(763\) | 21.1555 | − | 25.7036i | 0.765880 | − | 0.930533i | ||||
\(764\) | 2.74863 | + | 1.58692i | 0.0994418 | + | 0.0574128i | ||||
\(765\) | 16.4492 | − | 2.51700i | 0.594723 | − | 0.0910023i | ||||
\(766\) | −4.84882 | + | 2.79947i | −0.175195 | + | 0.101149i | ||||
\(767\) | 7.93283 | + | 0.390060i | 0.286438 | + | 0.0140843i | ||||
\(768\) | −1.31411 | − | 1.12832i | −0.0474188 | − | 0.0407149i | ||||
\(769\) | −6.30372 | + | 10.9184i | −0.227318 | + | 0.393726i | −0.957012 | − | 0.290047i | \(-0.906329\pi\) |
0.729694 | + | 0.683773i | \(0.239662\pi\) | |||||||
\(770\) | −8.86677 | − | 23.6602i | −0.319536 | − | 0.852655i | ||||
\(771\) | 12.1234 | − | 4.25740i | 0.436614 | − | 0.153327i | ||||
\(772\) | −0.181273 | − | 0.104658i | −0.00652415 | − | 0.00376672i | ||||
\(773\) | 17.4926 | + | 10.0993i | 0.629164 | + | 0.363248i | 0.780428 | − | 0.625245i | \(-0.215001\pi\) |
−0.151264 | + | 0.988493i | \(0.548334\pi\) | |||||||
\(774\) | 22.8386 | − | 18.2970i | 0.820916 | − | 0.657671i | ||||
\(775\) | −6.11968 | + | 10.5996i | −0.219826 | + | 0.380749i | ||||
\(776\) | −5.83860 | − | 10.1127i | −0.209593 | − | 0.363026i | ||||
\(777\) | 18.7413 | + | 22.4195i | 0.672341 | + | 0.804294i | ||||
\(778\) | −4.31018 | − | 2.48848i | −0.154527 | − | 0.0892164i | ||||
\(779\) | 12.6305 | + | 7.29222i | 0.452534 | + | 0.261271i | ||||
\(780\) | 8.48773 | + | 8.04475i | 0.303910 | + | 0.288048i | ||||
\(781\) | 37.1232 | + | 64.2992i | 1.32837 | + | 2.30081i | ||||
\(782\) | −15.5699 | + | 8.98931i | −0.556780 | + | 0.321457i | ||||
\(783\) | 38.6629 | − | 20.6004i | 1.38170 | − | 0.736197i | ||||
\(784\) | −6.62210 | − | 2.26887i | −0.236504 | − | 0.0810312i | ||||
\(785\) | −13.6462 | −0.487055 | ||||||||
\(786\) | 0.298042 | − | 1.58490i | 0.0106308 | − | 0.0565315i | ||||
\(787\) | 8.76709 | − | 15.1850i | 0.312513 | − | 0.541288i | −0.666393 | − | 0.745601i | \(-0.732163\pi\) |
0.978906 | + | 0.204313i | \(0.0654959\pi\) | |||||||
\(788\) | 9.71998 | + | 16.8355i | 0.346260 | + | 0.599740i | ||||
\(789\) | 34.1317 | + | 6.41849i | 1.21512 | + | 0.228504i | ||||
\(790\) | −16.6918 | − | 9.63699i | −0.593866 | − | 0.342869i | ||||
\(791\) | 3.74198 | − | 4.54645i | 0.133050 | − | 0.161653i | ||||
\(792\) | 14.2545 | + | 5.55768i | 0.506511 | + | 0.197483i | ||||
\(793\) | 9.72257 | + | 18.9303i | 0.345259 | + | 0.672233i | ||||
\(794\) | −8.11912 | − | 14.0627i | −0.288137 | − | 0.499068i | ||||
\(795\) | 5.68814 | − | 30.2479i | 0.201738 | − | 1.07278i | ||||
\(796\) | 12.5175 | − | 7.22696i | 0.443670 | − | 0.256153i | ||||
\(797\) | −24.3061 | − | 42.0995i | −0.860968 | − | 1.49124i | −0.870996 | − | 0.491290i | \(-0.836525\pi\) |
0.0100279 | − | 0.999950i | \(-0.496808\pi\) | |||||||
\(798\) | −9.14682 | + | 7.64619i | −0.323794 | + | 0.270672i | ||||
\(799\) | −8.01869 | + | 4.62959i | −0.283681 | + | 0.163783i | ||||
\(800\) | 1.49334 | 0.0527977 | ||||||||
\(801\) | 43.7789 | − | 6.69889i | 1.54685 | − | 0.236694i | ||||
\(802\) | 3.46023 | − | 5.99329i | 0.122185 | − | 0.211630i | ||||
\(803\) | 10.1885 | + | 17.6469i | 0.359543 | + | 0.622747i | ||||
\(804\) | 12.4631 | − | 14.5152i | 0.439539 | − | 0.511912i | ||||
\(805\) | −28.1587 | + | 10.5526i | −0.992463 | + | 0.371930i | ||||
\(806\) | −1.45128 | + | 29.5152i | −0.0511190 | + | 1.03963i | ||||
\(807\) | 16.4067 | + | 14.0871i | 0.577542 | + | 0.495891i | ||||
\(808\) | −6.30051 | −0.221651 | ||||||||
\(809\) | 8.32150i | 0.292568i | 0.989243 | + | 0.146284i | \(0.0467314\pi\) | ||||
−0.989243 | + | 0.146284i | \(0.953269\pi\) | |||||||
\(810\) | −11.4078 | + | 12.4057i | −0.400830 | + | 0.435891i | ||||
\(811\) | −21.9549 | −0.770941 | −0.385470 | − | 0.922720i | \(-0.625961\pi\) | ||||
−0.385470 | + | 0.922720i | \(0.625961\pi\) | |||||||
\(812\) | −14.1754 | + | 17.2229i | −0.497459 | + | 0.604405i | ||||
\(813\) | 4.70541 | − | 1.65241i | 0.165026 | − | 0.0579525i | ||||
\(814\) | 28.1628 | + | 16.2598i | 0.987107 | + | 0.569907i | ||||
\(815\) | 18.5473 | − | 32.1249i | 0.649685 | − | 1.12529i | ||||
\(816\) | 0.948185 | − | 5.04217i | 0.0331931 | − | 0.176511i | ||||
\(817\) | 12.6886 | + | 21.9773i | 0.443917 | + | 0.768887i | ||||
\(818\) | −11.3829 | −0.397995 | ||||||||
\(819\) | −25.6273 | + | 12.7374i | −0.895491 | + | 0.445080i | ||||
\(820\) | −10.4980 | −0.366605 | ||||||||
\(821\) | 13.6665 | + | 23.6711i | 0.476964 | + | 0.826127i | 0.999652 | − | 0.0263980i | \(-0.00840371\pi\) |
−0.522687 | + | 0.852525i | \(0.675070\pi\) | |||||||
\(822\) | −0.690506 | + | 3.67191i | −0.0240842 | + | 0.128073i | ||||
\(823\) | −6.37963 | + | 11.0498i | −0.222380 | + | 0.385173i | −0.955530 | − | 0.294894i | \(-0.904716\pi\) |
0.733150 | + | 0.680067i | \(0.238049\pi\) | |||||||
\(824\) | 4.99182 | + | 2.88203i | 0.173898 | + | 0.100400i | ||||
\(825\) | −12.4460 | + | 4.37067i | −0.433312 | + | 0.152167i | ||||
\(826\) | −2.04522 | − | 5.45749i | −0.0711624 | − | 0.189891i | ||||
\(827\) | −43.7556 | −1.52153 | −0.760766 | − | 0.649027i | \(-0.775176\pi\) | ||||
−0.760766 | + | 0.649027i | \(0.775176\pi\) | |||||||
\(828\) | 6.61435 | − | 16.9647i | 0.229864 | − | 0.589563i | ||||
\(829\) | 41.0957i | 1.42731i | 0.700496 | + | 0.713656i | \(0.252962\pi\) | ||||
−0.700496 | + | 0.713656i | \(0.747038\pi\) | |||||||
\(830\) | −18.0409 | −0.626207 | ||||||||
\(831\) | −10.5167 | − | 9.02989i | −0.364821 | − | 0.313243i | ||||
\(832\) | 3.20727 | − | 1.64725i | 0.111192 | − | 0.0571082i | ||||
\(833\) | −3.98746 | − | 20.3478i | −0.138157 | − | 0.705011i | ||||
\(834\) | −9.36764 | + | 10.9101i | −0.324375 | + | 0.377785i | ||||
\(835\) | −14.1513 | − | 24.5107i | −0.489724 | − | 0.848227i | ||||
\(836\) | −6.63377 | + | 11.4900i | −0.229434 | + | 0.397391i | ||||
\(837\) | −42.5627 | − | 1.44946i | −1.47118 | − | 0.0501005i | ||||
\(838\) | 9.03882 | 0.312241 | ||||||||
\(839\) | 19.7685 | − | 11.4133i | 0.682484 | − | 0.394032i | −0.118306 | − | 0.992977i | \(-0.537747\pi\) |
0.800790 | + | 0.598945i | \(0.204413\pi\) | |||||||
\(840\) | 2.94997 | − | 8.05838i | 0.101784 | − | 0.278040i | ||||
\(841\) | 21.0407 | + | 36.4435i | 0.725540 | + | 1.25667i | ||||
\(842\) | 2.66263 | − | 1.53727i | 0.0917601 | − | 0.0529777i | ||||
\(843\) | 1.97250 | − | 10.4892i | 0.0679366 | − | 0.361267i | ||||
\(844\) | 5.78954 | + | 10.0278i | 0.199284 | + | 0.345170i | ||||
\(845\) | −22.1748 | + | 10.0450i | −0.762838 | + | 0.345557i | ||||
\(846\) | 3.40646 | − | 8.73700i | 0.117117 | − | 0.300384i | ||||
\(847\) | 37.1840 | − | 13.9349i | 1.27766 | − | 0.478808i | ||||
\(848\) | −8.21797 | − | 4.74465i | −0.282206 | − | 0.162932i | ||||
\(849\) | −23.3932 | − | 4.39912i | −0.802853 | − | 0.150977i | ||||
\(850\) | 2.21174 | + | 3.83084i | 0.0758619 | + | 0.131397i | ||||
\(851\) | 19.3513 | − | 33.5174i | 0.663353 | − | 1.14896i | ||||
\(852\) | −4.66021 | + | 24.7816i | −0.159656 | + | 0.849005i | ||||
\(853\) | 4.19858 | 0.143757 | 0.0718783 | − | 0.997413i | \(-0.477101\pi\) | ||||
0.0718783 | + | 0.997413i | \(0.477101\pi\) | |||||||
\(854\) | 9.92381 | − | 12.0573i | 0.339586 | − | 0.412592i | ||||
\(855\) | −9.13786 | − | 11.4060i | −0.312508 | − | 0.390078i | ||||
\(856\) | 5.32321 | − | 3.07336i | 0.181944 | − | 0.105045i | ||||
\(857\) | 4.09187 | + | 7.08733i | 0.139776 | + | 0.242099i | 0.927412 | − | 0.374042i | \(-0.122028\pi\) |
−0.787636 | + | 0.616141i | \(0.788695\pi\) | |||||||
\(858\) | −21.9091 | + | 23.1156i | −0.747966 | + | 0.789153i | ||||
\(859\) | −42.2454 | − | 24.3904i | −1.44139 | − | 0.832189i | −0.443451 | − | 0.896299i | \(-0.646246\pi\) |
−0.997943 | + | 0.0641096i | \(0.979579\pi\) | |||||||
\(860\) | −15.8194 | − | 9.13332i | −0.539436 | − | 0.311444i | ||||
\(861\) | 8.83140 | − | 24.1246i | 0.300973 | − | 0.822163i | ||||
\(862\) | −11.6404 | − | 20.1618i | −0.396475 | − | 0.686714i | ||||
\(863\) | −0.899862 | + | 1.55861i | −0.0306316 | + | 0.0530556i | −0.880935 | − | 0.473238i | \(-0.843085\pi\) |
0.850303 | + | 0.526293i | \(0.176419\pi\) | |||||||
\(864\) | 2.44341 | + | 4.58582i | 0.0831266 | + | 0.156013i | ||||
\(865\) | 31.2251 | + | 18.0278i | 1.06169 | + | 0.612964i | ||||
\(866\) | −23.9459 | − | 13.8252i | −0.813715 | − | 0.469799i | ||||
\(867\) | −13.4427 | + | 4.72072i | −0.456539 | + | 0.160324i | ||||
\(868\) | 20.3054 | − | 7.60954i | 0.689210 | − | 0.258285i | ||||
\(869\) | 26.2455 | − | 45.4585i | 0.890317 | − | 1.54207i | ||||
\(870\) | −20.7470 | − | 17.8139i | −0.703390 | − | 0.603947i | ||||
\(871\) | 18.1950 | + | 35.4264i | 0.616513 | + | 1.20038i | ||||
\(872\) | 10.8967 | − | 6.29124i | 0.369010 | − | 0.213048i | ||||
\(873\) | 5.29873 | + | 34.6285i | 0.179335 | + | 1.17200i | ||||
\(874\) | 13.6746 | + | 7.89503i | 0.462550 | + | 0.267054i | ||||
\(875\) | 11.2895 | + | 30.1250i | 0.381655 | + | 1.01841i | ||||
\(876\) | −1.27900 | + | 6.80132i | −0.0432132 | + | 0.229795i | ||||
\(877\) | 40.0226i | 1.35147i | 0.737146 | + | 0.675733i | \(0.236173\pi\) | ||||
−0.737146 | + | 0.675733i | \(0.763827\pi\) | |||||||
\(878\) | 3.78672 | + | 2.18627i | 0.127796 | + | 0.0737829i | ||||
\(879\) | 2.93641 | + | 8.36174i | 0.0990426 | + | 0.282034i | ||||
\(880\) | − | 9.55006i | − | 0.321932i | ||||||
\(881\) | −1.57402 | + | 2.72629i | −0.0530302 | + | 0.0918510i | −0.891322 | − | 0.453371i | \(-0.850221\pi\) |
0.838292 | + | 0.545222i | \(0.183555\pi\) | |||||||
\(882\) | 16.0367 | + | 13.5582i | 0.539983 | + | 0.456529i | ||||
\(883\) | −5.79510 | −0.195021 | −0.0975103 | − | 0.995235i | \(-0.531088\pi\) | ||||
−0.0975103 | + | 0.995235i | \(0.531088\pi\) | |||||||
\(884\) | 8.97581 | + | 5.78784i | 0.301889 | + | 0.194666i | ||||
\(885\) | 6.74118 | − | 2.36731i | 0.226602 | − | 0.0795764i | ||||
\(886\) | 2.66818i | 0.0896393i | ||||||||
\(887\) | 24.4055 | + | 42.2716i | 0.819458 | + | 1.41934i | 0.906082 | + | 0.423102i | \(0.139059\pi\) |
−0.0866241 | + | 0.996241i | \(0.527608\pi\) | |||||||
\(888\) | 3.65944 | + | 10.4207i | 0.122803 | + | 0.349694i | ||||
\(889\) | −3.19259 | + | 19.1680i | −0.107076 | + | 0.642875i | ||||
\(890\) | −13.8225 | − | 23.9412i | −0.463330 | − | 0.802512i | ||||
\(891\) | −33.7857 | − | 31.0682i | −1.13186 | − | 1.04082i | ||||
\(892\) | 3.33759 | + | 5.78088i | 0.111751 | + | 0.193558i | ||||
\(893\) | 7.04257 | + | 4.06603i | 0.235671 | + | 0.136065i | ||||
\(894\) | 6.46860 | − | 2.27159i | 0.216342 | − | 0.0759734i | ||||
\(895\) | 5.03078 | − | 8.71357i | 0.168161 | − | 0.291263i | ||||
\(896\) | −2.04281 | − | 1.68135i | −0.0682455 | − | 0.0561698i | ||||
\(897\) | 27.5105 | + | 26.0747i | 0.918548 | + | 0.870608i | ||||
\(898\) | 7.64162 | − | 13.2357i | 0.255004 | − | 0.441680i | ||||
\(899\) | − | 69.0998i | − | 2.30461i | ||||||
\(900\) | −4.17400 | − | 1.62740i | −0.139133 | − | 0.0542466i | ||||
\(901\) | − | 28.1085i | − | 0.936429i | ||||||
\(902\) | − | 28.5903i | − | 0.951951i | ||||||
\(903\) | 34.2966 | − | 28.6699i | 1.14132 | − | 0.954074i | ||||
\(904\) | 1.92741 | − | 1.11279i | 0.0641049 | − | 0.0370110i | ||||
\(905\) | −10.5924 | + | 18.3467i | −0.352105 | + | 0.609864i | ||||
\(906\) | −6.28300 | + | 7.31753i | −0.208739 | + | 0.243109i | ||||
\(907\) | −23.9518 | −0.795307 | −0.397653 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397653 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(908\) | 16.0059 | − | 9.24099i | 0.531173 | − | 0.306673i | ||||
\(909\) | 17.6104 | + | 6.86609i | 0.584099 | + | 0.227734i | ||||
\(910\) | 13.2184 | + | 12.0157i | 0.438187 | + | 0.398318i | ||||
\(911\) | 51.9614i | 1.72156i | 0.508979 | + | 0.860779i | \(0.330023\pi\) | ||||
−0.508979 | + | 0.860779i | \(0.669977\pi\) | |||||||
\(912\) | −4.25147 | + | 1.49300i | −0.140780 | + | 0.0494381i | ||||
\(913\) | − | 49.1326i | − | 1.62605i | ||||||
\(914\) | −6.00766 | − | 3.46853i | −0.198716 | − | 0.114729i | ||||
\(915\) | 14.5244 | + | 12.4710i | 0.480163 | + | 0.412279i | ||||
\(916\) | 0.100542 | + | 0.174145i | 0.00332201 | + | 0.00575390i | ||||
\(917\) | 0.404726 | − | 2.42994i | 0.0133652 | − | 0.0802435i | ||||
\(918\) | −8.14504 | + | 13.0599i | −0.268826 | + | 0.431041i | ||||
\(919\) | −37.7303 | −1.24461 | −0.622303 | − | 0.782776i | \(-0.713803\pi\) | ||||
−0.622303 | + | 0.782776i | \(0.713803\pi\) | |||||||
\(920\) | −11.3658 | −0.374719 | ||||||||
\(921\) | 0.360918 | − | 1.91926i | 0.0118926 | − | 0.0632417i | ||||
\(922\) | 17.6491 | + | 10.1897i | 0.581242 | + | 0.335580i | ||||
\(923\) | −44.1150 | − | 28.4465i | −1.45206 | − | 0.936328i | ||||
\(924\) | 21.9463 | + | 8.03398i | 0.721979 | + | 0.264298i | ||||
\(925\) | −8.24664 | − | 4.76120i | −0.271148 | − | 0.156547i | ||||
\(926\) | −19.4201 | + | 11.2122i | −0.638184 | + | 0.368456i | ||||
\(927\) | −10.8117 | − | 13.4954i | −0.355104 | − | 0.443247i | ||||
\(928\) | −7.30144 | + | 4.21549i | −0.239681 | + | 0.138380i | ||||
\(929\) | − | 24.2142i | − | 0.794441i | −0.917723 | − | 0.397220i | \(-0.869975\pi\) | ||
0.917723 | − | 0.397220i | \(-0.130025\pi\) | |||||||
\(930\) | 8.80793 | + | 25.0815i | 0.288823 | + | 0.822455i | ||||
\(931\) | −13.7256 | + | 11.9683i | −0.449839 | + | 0.392246i | ||||
\(932\) | −11.1073 | + | 6.41280i | −0.363831 | + | 0.210058i | ||||
\(933\) | −18.2948 | + | 6.42463i | −0.598945 | + | 0.210333i | ||||
\(934\) | −19.6687 | −0.643580 | ||||||||
\(935\) | 24.4985 | − | 14.1442i | 0.801187 | − | 0.462566i | ||||
\(936\) | −10.7597 | + | 1.10900i | −0.351690 | + | 0.0362489i | ||||
\(937\) | − | 25.9178i | − | 0.846698i | −0.905967 | − | 0.423349i | \(-0.860854\pi\) | ||
0.905967 | − | 0.423349i | \(-0.139146\pi\) | |||||||
\(938\) | 18.5716 | − | 22.5642i | 0.606383 | − | 0.736746i | ||||
\(939\) | −36.6844 | + | 42.7246i | −1.19715 | + | 1.39427i | ||||
\(940\) | −5.85351 | −0.190920 | ||||||||
\(941\) | −51.6878 | + | 29.8420i | −1.68498 | + | 0.972821i | −0.726709 | + | 0.686946i | \(0.758951\pi\) |
−0.958267 | + | 0.285875i | \(0.907716\pi\) | |||||||
\(942\) | 8.22243 | − | 9.57630i | 0.267901 | − | 0.312013i | ||||
\(943\) | −34.0261 | −1.10804 | ||||||||
\(944\) | − | 2.20283i | − | 0.0716960i | ||||||
\(945\) | −17.0271 | + | 19.3089i | −0.553893 | + | 0.628119i | ||||
\(946\) | 24.8738 | − | 43.0826i | 0.808716 | − | 1.40074i | ||||
\(947\) | −10.9482 | − | 18.9628i | −0.355769 | − | 0.616210i | 0.631480 | − | 0.775392i | \(-0.282448\pi\) |
−0.987249 | + | 0.159182i | \(0.949114\pi\) | |||||||
\(948\) | 16.8203 | − | 5.90682i | 0.546298 | − | 0.191845i | ||||
\(949\) | −12.1074 | − | 7.80715i | −0.393022 | − | 0.253431i | ||||
\(950\) | 1.94250 | − | 3.36451i | 0.0630230 | − | 0.109159i | ||||
\(951\) | −33.4207 | − | 28.6957i | −1.08374 | − | 0.930523i | ||||
\(952\) | 1.28759 | − | 7.73055i | 0.0417309 | − | 0.250549i | ||||
\(953\) | −5.23975 | + | 3.02517i | −0.169732 | + | 0.0979949i | −0.582459 | − | 0.812860i | \(-0.697910\pi\) |
0.412727 | + | 0.910855i | \(0.364576\pi\) | |||||||
\(954\) | 17.7992 | + | 22.2173i | 0.576271 | + | 0.719312i | ||||
\(955\) | −2.97168 | + | 5.14710i | −0.0961612 | + | 0.166556i | ||||
\(956\) | −15.1398 | + | 26.2229i | −0.489655 | + | 0.848108i | ||||
\(957\) | 48.5145 | − | 56.5026i | 1.56825 | − | 1.82647i | ||||
\(958\) | 16.4723 | − | 9.51026i | 0.532195 | − | 0.307263i | ||||
\(959\) | −0.937672 | + | 5.62969i | −0.0302790 | + | 0.181792i | ||||
\(960\) | 2.11291 | − | 2.46081i | 0.0681938 | − | 0.0794223i | ||||
\(961\) | −18.0867 | + | 31.3271i | −0.583443 | + | 1.01055i | ||||
\(962\) | −22.9633 | − | 1.12911i | −0.740365 | − | 0.0364041i | ||||
\(963\) | −18.2280 | + | 2.78918i | −0.587388 | + | 0.0898800i | ||||
\(964\) | 4.17255 | + | 7.22708i | 0.134389 | + | 0.232768i | ||||
\(965\) | 0.195983 | − | 0.339453i | 0.00630892 | − | 0.0109274i | ||||
\(966\) | 9.56146 | − | 26.1189i | 0.307635 | − | 0.840360i | ||||
\(967\) | − | 17.1921i | − | 0.552862i | −0.961034 | − | 0.276431i | \(-0.910848\pi\) | ||
0.961034 | − | 0.276431i | \(-0.0891518\pi\) | |||||||
\(968\) | 15.0087 | 0.482398 | ||||||||
\(969\) | −10.1266 | − | 8.69497i | −0.325315 | − | 0.279323i | ||||
\(970\) | 18.9372 | − | 10.9334i | 0.608037 | − | 0.351050i | ||||
\(971\) | 41.3879 | 1.32820 | 0.664100 | − | 0.747644i | \(-0.268815\pi\) | ||||
0.664100 | + | 0.747644i | \(0.268815\pi\) | |||||||
\(972\) | −1.83203 | − | 15.4804i | −0.0587625 | − | 0.496535i | ||||
\(973\) | −13.9590 | + | 16.9599i | −0.447504 | + | 0.543711i | ||||
\(974\) | − | 22.4738i | − | 0.720107i | ||||||
\(975\) | 6.41543 | − | 6.76870i | 0.205458 | − | 0.216772i | ||||
\(976\) | 5.11154 | − | 2.95115i | 0.163616 | − | 0.0944640i | ||||
\(977\) | −39.9425 | −1.27787 | −0.638937 | − | 0.769259i | \(-0.720626\pi\) | ||||
−0.638937 | + | 0.769259i | \(0.720626\pi\) | |||||||
\(978\) | 11.3683 | + | 32.3723i | 0.363517 | + | 1.03515i | ||||
\(979\) | 65.2018 | − | 37.6443i | 2.08386 | − | 1.20312i | ||||
\(980\) | 4.24871 | − | 12.4006i | 0.135720 | − | 0.396122i | ||||
\(981\) | −37.3131 | + | 5.70952i | −1.19132 | + | 0.182291i | ||||
\(982\) | − | 29.6928i | − | 0.947537i | ||||||
\(983\) | 3.96116 | − | 2.28698i | 0.126342 | − | 0.0729433i | −0.435497 | − | 0.900190i | \(-0.643427\pi\) |
0.561839 | + | 0.827247i | \(0.310094\pi\) | |||||||
\(984\) | 6.32547 | − | 7.36699i | 0.201649 | − | 0.234851i | ||||
\(985\) | −31.5263 | + | 18.2017i | −1.00451 | + | 0.579954i | ||||
\(986\) | −21.6278 | − | 12.4868i | −0.688768 | − | 0.397661i | ||||
\(987\) | 4.92426 | − | 13.4515i | 0.156741 | − | 0.428166i | ||||
\(988\) | 0.460662 | − | 9.36868i | 0.0146556 | − | 0.298057i | ||||
\(989\) | −51.2738 | − | 29.6030i | −1.63041 | − | 0.941319i | ||||
\(990\) | −10.4073 | + | 26.6931i | −0.330767 | + | 0.848361i | ||||
\(991\) | −18.0537 | −0.573493 | −0.286747 | − | 0.958006i | \(-0.592574\pi\) | ||||
−0.286747 | + | 0.958006i | \(0.592574\pi\) | |||||||
\(992\) | 8.19594 | 0.260221 | ||||||||
\(993\) | −12.2323 | − | 2.30030i | −0.388181 | − | 0.0729978i | ||||
\(994\) | −6.32832 | + | 37.9947i | −0.200722 | + | 1.20512i | ||||
\(995\) | 13.5333 | + | 23.4403i | 0.429033 | + | 0.743107i | ||||
\(996\) | 10.8704 | − | 12.6602i | 0.344441 | − | 0.401155i | ||||
\(997\) | −36.7143 | − | 21.1970i | −1.16275 | − | 0.671316i | −0.210791 | − | 0.977531i | \(-0.567604\pi\) |
−0.951962 | + | 0.306215i | \(0.900937\pi\) | |||||||
\(998\) | 7.51106i | 0.237758i | ||||||||
\(999\) | 1.12770 | − | 33.1144i | 0.0356788 | − | 1.04769i |
(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 | 546.2.bn.e.173.8 | yes | 34 | |
3.2 | odd | 2 | 546.2.bn.f.173.10 | yes | 34 | ||
7.3 | odd | 6 | 546.2.bi.f.17.3 | yes | 34 | ||
13.10 | even | 6 | 546.2.bi.e.257.4 | yes | 34 | ||
21.17 | even | 6 | 546.2.bi.e.17.4 | ✓ | 34 | ||
39.23 | odd | 6 | 546.2.bi.f.257.3 | yes | 34 | ||
91.10 | odd | 6 | 546.2.bn.f.101.10 | yes | 34 | ||
273.101 | even | 6 | inner | 546.2.bn.e.101.8 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bi.e.17.4 | ✓ | 34 | 21.17 | even | 6 | ||
546.2.bi.e.257.4 | yes | 34 | 13.10 | even | 6 | ||
546.2.bi.f.17.3 | yes | 34 | 7.3 | odd | 6 | ||
546.2.bi.f.257.3 | yes | 34 | 39.23 | odd | 6 | ||
546.2.bn.e.101.8 | yes | 34 | 273.101 | even | 6 | inner | |
546.2.bn.e.173.8 | yes | 34 | 1.1 | even | 1 | trivial | |
546.2.bn.f.101.10 | yes | 34 | 91.10 | odd | 6 | ||
546.2.bn.f.173.10 | yes | 34 | 3.2 | odd | 2 |