Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), 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: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.12 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.b.533.12 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.581841 | + | 1.63140i | −0.335926 | + | 0.941888i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.36872 | − | 1.76822i | 0.612110 | − | 0.790773i | ||||
\(6\) | 0.742149 | + | 1.56500i | 0.302981 | + | 0.638907i | ||||
\(7\) | 0.102829 | + | 0.102829i | 0.0388656 | + | 0.0388656i | 0.726272 | − | 0.687407i | \(-0.241251\pi\) |
−0.687407 | + | 0.726272i | \(0.741251\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.32292 | − | 1.89843i | −0.774307 | − | 0.632810i | ||||
\(10\) | −0.282491 | − | 2.21815i | −0.0893316 | − | 0.701441i | ||||
\(11\) | − | 6.12593i | − | 1.84704i | −0.383553 | − | 0.923519i | \(-0.625300\pi\) | ||
0.383553 | − | 0.923519i | \(-0.374700\pi\) | |||||||
\(12\) | 1.63140 | + | 0.581841i | 0.470944 | + | 0.167963i | ||||
\(13\) | −0.754312 | + | 0.754312i | −0.209209 | + | 0.209209i | −0.803931 | − | 0.594722i | \(-0.797262\pi\) |
0.594722 | + | 0.803931i | \(0.297262\pi\) | |||||||
\(14\) | 0.145422 | 0.0388656 | ||||||||
\(15\) | 2.08830 | + | 3.26175i | 0.539196 | + | 0.842180i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.33294 | − | 2.33294i | 0.565820 | − | 0.565820i | −0.365134 | − | 0.930955i | \(-0.618977\pi\) |
0.930955 | + | 0.365134i | \(0.118977\pi\) | |||||||
\(18\) | −2.98495 | + | 0.300162i | −0.703559 | + | 0.0707490i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −1.76822 | − | 1.36872i | −0.395386 | − | 0.306055i | ||||
\(21\) | −0.227584 | + | 0.107925i | −0.0496630 | + | 0.0235511i | ||||
\(22\) | −4.33169 | − | 4.33169i | −0.923519 | − | 0.923519i | ||||
\(23\) | 6.21428 | + | 6.21428i | 1.29577 | + | 1.29577i | 0.931163 | + | 0.364604i | \(0.118796\pi\) |
0.364604 | + | 0.931163i | \(0.381204\pi\) | |||||||
\(24\) | 1.56500 | − | 0.742149i | 0.319454 | − | 0.151491i | ||||
\(25\) | −1.25322 | − | 4.84040i | −0.250644 | − | 0.968079i | ||||
\(26\) | 1.06676i | 0.209209i | ||||||||
\(27\) | 4.44866 | − | 2.68503i | 0.856146 | − | 0.516734i | ||||
\(28\) | 0.102829 | − | 0.102829i | 0.0194328 | − | 0.0194328i | ||||
\(29\) | −2.40803 | −0.447160 | −0.223580 | − | 0.974686i | \(-0.571774\pi\) | ||||
−0.223580 | + | 0.974686i | \(0.571774\pi\) | |||||||
\(30\) | 3.78306 | + | 0.829756i | 0.690688 | + | 0.151492i | ||||
\(31\) | 3.69470 | 0.663588 | 0.331794 | − | 0.943352i | \(-0.392346\pi\) | ||||
0.331794 | + | 0.943352i | \(0.392346\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 9.99383 | + | 3.56432i | 1.73970 | + | 0.620468i | ||||
\(34\) | − | 3.29927i | − | 0.565820i | ||||||
\(35\) | 0.322567 | − | 0.0410804i | 0.0545238 | − | 0.00694385i | ||||
\(36\) | −1.89843 | + | 2.32292i | −0.316405 | + | 0.387154i | ||||
\(37\) | −3.66137 | − | 3.66137i | −0.601926 | − | 0.601926i | 0.338897 | − | 0.940823i | \(-0.389946\pi\) |
−0.940823 | + | 0.338897i | \(0.889946\pi\) | |||||||
\(38\) | −0.707107 | − | 0.707107i | −0.114708 | − | 0.114708i | ||||
\(39\) | −0.791694 | − | 1.66947i | −0.126773 | − | 0.267330i | ||||
\(40\) | −2.21815 | + | 0.282491i | −0.350721 | + | 0.0446658i | ||||
\(41\) | 10.3063i | 1.60958i | 0.593561 | + | 0.804789i | \(0.297722\pi\) | ||||
−0.593561 | + | 0.804789i | \(0.702278\pi\) | |||||||
\(42\) | −0.0846123 | + | 0.237241i | −0.0130560 | + | 0.0366070i | ||||
\(43\) | −0.994803 | + | 0.994803i | −0.151706 | + | 0.151706i | −0.778880 | − | 0.627174i | \(-0.784212\pi\) |
0.627174 | + | 0.778880i | \(0.284212\pi\) | |||||||
\(44\) | −6.12593 | −0.923519 | ||||||||
\(45\) | −6.53627 | + | 1.50903i | −0.974370 | + | 0.224952i | ||||
\(46\) | 8.78832 | 1.29577 | ||||||||
\(47\) | 4.88564 | − | 4.88564i | 0.712645 | − | 0.712645i | −0.254443 | − | 0.967088i | \(-0.581892\pi\) |
0.967088 | + | 0.254443i | \(0.0818922\pi\) | |||||||
\(48\) | 0.581841 | − | 1.63140i | 0.0839815 | − | 0.235472i | ||||
\(49\) | − | 6.97885i | − | 0.996979i | ||||||
\(50\) | −4.30884 | − | 2.53652i | −0.609361 | − | 0.358718i | ||||
\(51\) | 2.44855 | + | 5.16335i | 0.342866 | + | 0.723014i | ||||
\(52\) | 0.754312 | + | 0.754312i | 0.104604 | + | 0.104604i | ||||
\(53\) | −2.86461 | − | 2.86461i | −0.393484 | − | 0.393484i | 0.482443 | − | 0.875927i | \(-0.339749\pi\) |
−0.875927 | + | 0.482443i | \(0.839749\pi\) | |||||||
\(54\) | 1.24708 | − | 5.04428i | 0.169706 | − | 0.686440i | ||||
\(55\) | −10.8320 | − | 8.38468i | −1.46059 | − | 1.13059i | ||||
\(56\) | − | 0.145422i | − | 0.0194328i | ||||||
\(57\) | 1.63140 | + | 0.581841i | 0.216084 | + | 0.0770667i | ||||
\(58\) | −1.70274 | + | 1.70274i | −0.223580 | + | 0.223580i | ||||
\(59\) | 7.12402 | 0.927469 | 0.463734 | − | 0.885974i | \(-0.346509\pi\) | ||||
0.463734 | + | 0.885974i | \(0.346509\pi\) | |||||||
\(60\) | 3.26175 | − | 2.08830i | 0.421090 | − | 0.269598i | ||||
\(61\) | −10.3444 | −1.32446 | −0.662230 | − | 0.749301i | \(-0.730390\pi\) | ||||
−0.662230 | + | 0.749301i | \(0.730390\pi\) | |||||||
\(62\) | 2.61255 | − | 2.61255i | 0.331794 | − | 0.331794i | ||||
\(63\) | −0.0436501 | − | 0.434076i | −0.00549940 | − | 0.0546884i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.301350 | + | 2.36623i | 0.0373779 | + | 0.293495i | ||||
\(66\) | 9.58706 | − | 4.54636i | 1.18009 | − | 0.559618i | ||||
\(67\) | 4.37645 | + | 4.37645i | 0.534669 | + | 0.534669i | 0.921958 | − | 0.387289i | \(-0.126589\pi\) |
−0.387289 | + | 0.921958i | \(0.626589\pi\) | |||||||
\(68\) | −2.33294 | − | 2.33294i | −0.282910 | − | 0.282910i | ||||
\(69\) | −13.7537 | + | 6.52225i | −1.65575 | + | 0.785186i | ||||
\(70\) | 0.199041 | − | 0.257138i | 0.0237900 | − | 0.0307338i | ||||
\(71\) | − | 0.311021i | − | 0.0369114i | −0.999830 | − | 0.0184557i | \(-0.994125\pi\) | ||
0.999830 | − | 0.0184557i | \(-0.00587497\pi\) | |||||||
\(72\) | 0.300162 | + | 2.98495i | 0.0353745 | + | 0.351779i | ||||
\(73\) | 0.755853 | − | 0.755853i | 0.0884659 | − | 0.0884659i | −0.661489 | − | 0.749955i | \(-0.730075\pi\) |
0.749955 | + | 0.661489i | \(0.230075\pi\) | |||||||
\(74\) | −5.17797 | −0.601926 | ||||||||
\(75\) | 8.62579 | + | 0.771844i | 0.996020 | + | 0.0891248i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.629921 | − | 0.629921i | 0.0717862 | − | 0.0717862i | ||||
\(78\) | −1.74031 | − | 0.620684i | −0.197051 | − | 0.0702786i | ||||
\(79\) | 14.3107i | 1.61008i | 0.593218 | + | 0.805042i | \(0.297857\pi\) | ||||
−0.593218 | + | 0.805042i | \(0.702143\pi\) | |||||||
\(80\) | −1.36872 | + | 1.76822i | −0.153027 | + | 0.197693i | ||||
\(81\) | 1.79194 | + | 8.81981i | 0.199104 | + | 0.979978i | ||||
\(82\) | 7.28768 | + | 7.28768i | 0.804789 | + | 0.804789i | ||||
\(83\) | 11.1880 | + | 11.1880i | 1.22804 | + | 1.22804i | 0.964704 | + | 0.263337i | \(0.0848230\pi\) |
0.263337 | + | 0.964704i | \(0.415177\pi\) | |||||||
\(84\) | 0.107925 | + | 0.227584i | 0.0117755 | + | 0.0248315i | ||||
\(85\) | −0.932016 | − | 7.31829i | −0.101091 | − | 0.793780i | ||||
\(86\) | 1.40686i | 0.151706i | ||||||||
\(87\) | 1.40109 | − | 3.92846i | 0.150213 | − | 0.421175i | ||||
\(88\) | −4.33169 | + | 4.33169i | −0.461759 | + | 0.461759i | ||||
\(89\) | −2.30981 | −0.244840 | −0.122420 | − | 0.992478i | \(-0.539065\pi\) | ||||
−0.122420 | + | 0.992478i | \(0.539065\pi\) | |||||||
\(90\) | −3.55480 | + | 5.68888i | −0.374709 | + | 0.599661i | ||||
\(91\) | −0.155130 | −0.0162620 | ||||||||
\(92\) | 6.21428 | − | 6.21428i | 0.647883 | − | 0.647883i | ||||
\(93\) | −2.14973 | + | 6.02753i | −0.222917 | + | 0.625026i | ||||
\(94\) | − | 6.90934i | − | 0.712645i | ||||||
\(95\) | −1.76822 | − | 1.36872i | −0.181416 | − | 0.140428i | ||||
\(96\) | −0.742149 | − | 1.56500i | −0.0757453 | − | 0.159727i | ||||
\(97\) | −0.595441 | − | 0.595441i | −0.0604579 | − | 0.0604579i | 0.676231 | − | 0.736689i | \(-0.263612\pi\) |
−0.736689 | + | 0.676231i | \(0.763612\pi\) | |||||||
\(98\) | −4.93479 | − | 4.93479i | −0.498489 | − | 0.498489i | ||||
\(99\) | −11.6296 | + | 14.2301i | −1.16882 | + | 1.43018i | ||||
\(100\) | −4.84040 | + | 1.25322i | −0.484040 | + | 0.125322i | ||||
\(101\) | 7.75006i | 0.771160i | 0.922674 | + | 0.385580i | \(0.125999\pi\) | ||||
−0.922674 | + | 0.385580i | \(0.874001\pi\) | |||||||
\(102\) | 5.38243 | + | 1.91965i | 0.532940 | + | 0.190074i | ||||
\(103\) | −11.2131 | + | 11.2131i | −1.10486 | + | 1.10486i | −0.111042 | + | 0.993816i | \(0.535419\pi\) |
−0.993816 | + | 0.111042i | \(0.964581\pi\) | |||||||
\(104\) | 1.06676 | 0.104604 | ||||||||
\(105\) | −0.120664 | + | 0.550138i | −0.0117756 | + | 0.0536880i | ||||
\(106\) | −4.05117 | −0.393484 | ||||||||
\(107\) | −10.9025 | + | 10.9025i | −1.05399 | + | 1.05399i | −0.0555308 | + | 0.998457i | \(0.517685\pi\) |
−0.998457 | + | 0.0555308i | \(0.982315\pi\) | |||||||
\(108\) | −2.68503 | − | 4.44866i | −0.258367 | − | 0.428073i | ||||
\(109\) | 0.958181i | 0.0917771i | 0.998947 | + | 0.0458886i | \(0.0146119\pi\) | ||||
−0.998947 | + | 0.0458886i | \(0.985388\pi\) | |||||||
\(110\) | −13.5882 | + | 1.73052i | −1.29559 | + | 0.164999i | ||||
\(111\) | 8.10350 | − | 3.84282i | 0.769150 | − | 0.364745i | ||||
\(112\) | −0.102829 | − | 0.102829i | −0.00971639 | − | 0.00971639i | ||||
\(113\) | −4.94211 | − | 4.94211i | −0.464915 | − | 0.464915i | 0.435348 | − | 0.900262i | \(-0.356625\pi\) |
−0.900262 | + | 0.435348i | \(0.856625\pi\) | |||||||
\(114\) | 1.56500 | − | 0.742149i | 0.146575 | − | 0.0695087i | ||||
\(115\) | 19.4938 | − | 2.48262i | 1.81781 | − | 0.231506i | ||||
\(116\) | 2.40803i | 0.223580i | ||||||||
\(117\) | 3.18422 | − | 0.320201i | 0.294381 | − | 0.0296026i | ||||
\(118\) | 5.03744 | − | 5.03744i | 0.463734 | − | 0.463734i | ||||
\(119\) | 0.479786 | 0.0439819 | ||||||||
\(120\) | 0.829756 | − | 3.78306i | 0.0757460 | − | 0.345344i | ||||
\(121\) | −26.5270 | −2.41155 | ||||||||
\(122\) | −7.31457 | + | 7.31457i | −0.662230 | + | 0.662230i | ||||
\(123\) | −16.8137 | − | 5.99664i | −1.51604 | − | 0.540699i | ||||
\(124\) | − | 3.69470i | − | 0.331794i | ||||||
\(125\) | −10.2742 | − | 4.40918i | −0.918952 | − | 0.394369i | ||||
\(126\) | −0.337803 | − | 0.276073i | −0.0300939 | − | 0.0245945i | ||||
\(127\) | 8.80226 | + | 8.80226i | 0.781074 | + | 0.781074i | 0.980012 | − | 0.198938i | \(-0.0637492\pi\) |
−0.198938 | + | 0.980012i | \(0.563749\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −1.04410 | − | 2.20174i | −0.0919281 | − | 0.193852i | ||||
\(130\) | 1.88627 | + | 1.46009i | 0.165436 | + | 0.128059i | ||||
\(131\) | − | 22.1054i | − | 1.93136i | −0.259735 | − | 0.965680i | \(-0.583635\pi\) | ||
0.259735 | − | 0.965680i | \(-0.416365\pi\) | |||||||
\(132\) | 3.56432 | − | 9.99383i | 0.310234 | − | 0.869852i | ||||
\(133\) | 0.102829 | − | 0.102829i | 0.00891637 | − | 0.00891637i | ||||
\(134\) | 6.18924 | 0.534669 | ||||||||
\(135\) | 1.34124 | − | 11.5413i | 0.115436 | − | 0.993315i | ||||
\(136\) | −3.29927 | −0.282910 | ||||||||
\(137\) | 1.58617 | − | 1.58617i | 0.135516 | − | 0.135516i | −0.636095 | − | 0.771611i | \(-0.719451\pi\) |
0.771611 | + | 0.636095i | \(0.219451\pi\) | |||||||
\(138\) | −5.11340 | + | 14.3373i | −0.435282 | + | 1.22047i | ||||
\(139\) | 11.1773i | 0.948045i | 0.880513 | + | 0.474022i | \(0.157198\pi\) | ||||
−0.880513 | + | 0.474022i | \(0.842802\pi\) | |||||||
\(140\) | −0.0410804 | − | 0.322567i | −0.00347192 | − | 0.0272619i | ||||
\(141\) | 5.12777 | + | 10.8131i | 0.431836 | + | 0.910627i | ||||
\(142\) | −0.219925 | − | 0.219925i | −0.0184557 | − | 0.0184557i | ||||
\(143\) | 4.62086 | + | 4.62086i | 0.386416 | + | 0.386416i | ||||
\(144\) | 2.32292 | + | 1.89843i | 0.193577 | + | 0.158202i | ||||
\(145\) | −3.29592 | + | 4.25793i | −0.273711 | + | 0.353602i | ||||
\(146\) | − | 1.06894i | − | 0.0884659i | ||||||
\(147\) | 11.3853 | + | 4.06058i | 0.939043 | + | 0.334911i | ||||
\(148\) | −3.66137 | + | 3.66137i | −0.300963 | + | 0.300963i | ||||
\(149\) | 9.86195 | 0.807922 | 0.403961 | − | 0.914776i | \(-0.367633\pi\) | ||||
0.403961 | + | 0.914776i | \(0.367633\pi\) | |||||||
\(150\) | 6.64513 | − | 5.55358i | 0.542573 | − | 0.453448i | ||||
\(151\) | −7.90117 | −0.642988 | −0.321494 | − | 0.946912i | \(-0.604185\pi\) | ||||
−0.321494 | + | 0.946912i | \(0.604185\pi\) | |||||||
\(152\) | −0.707107 | + | 0.707107i | −0.0573539 | + | 0.0573539i | ||||
\(153\) | −9.84815 | + | 0.990317i | −0.796176 | + | 0.0800624i | ||||
\(154\) | − | 0.890843i | − | 0.0717862i | ||||||
\(155\) | 5.05701 | − | 6.53306i | 0.406189 | − | 0.524748i | ||||
\(156\) | −1.66947 | + | 0.791694i | −0.133665 | + | 0.0633863i | ||||
\(157\) | 3.96376 | + | 3.96376i | 0.316342 | + | 0.316342i | 0.847360 | − | 0.531018i | \(-0.178190\pi\) |
−0.531018 | + | 0.847360i | \(0.678190\pi\) | |||||||
\(158\) | 10.1192 | + | 10.1192i | 0.805042 | + | 0.805042i | ||||
\(159\) | 6.34006 | − | 3.00657i | 0.502800 | − | 0.238437i | ||||
\(160\) | 0.282491 | + | 2.21815i | 0.0223329 | + | 0.175360i | ||||
\(161\) | 1.27801i | 0.100721i | ||||||||
\(162\) | 7.50363 | + | 4.96945i | 0.589541 | + | 0.390437i | ||||
\(163\) | 6.35109 | − | 6.35109i | 0.497456 | − | 0.497456i | −0.413189 | − | 0.910645i | \(-0.635585\pi\) |
0.910645 | + | 0.413189i | \(0.135585\pi\) | |||||||
\(164\) | 10.3063 | 0.804789 | ||||||||
\(165\) | 19.9813 | − | 12.7928i | 1.55554 | − | 0.995916i | ||||
\(166\) | 15.8222 | 1.22804 | ||||||||
\(167\) | 14.9173 | − | 14.9173i | 1.15434 | − | 1.15434i | 0.168664 | − | 0.985674i | \(-0.446055\pi\) |
0.985674 | − | 0.168664i | \(-0.0539453\pi\) | |||||||
\(168\) | 0.237241 | + | 0.0846123i | 0.0183035 | + | 0.00652798i | ||||
\(169\) | 11.8620i | 0.912464i | ||||||||
\(170\) | −5.83385 | − | 4.51578i | −0.447435 | − | 0.346344i | ||||
\(171\) | −1.89843 | + | 2.32292i | −0.145176 | + | 0.177638i | ||||
\(172\) | 0.994803 | + | 0.994803i | 0.0758530 | + | 0.0758530i | ||||
\(173\) | 6.19199 | + | 6.19199i | 0.470769 | + | 0.470769i | 0.902163 | − | 0.431395i | \(-0.141978\pi\) |
−0.431395 | + | 0.902163i | \(0.641978\pi\) | |||||||
\(174\) | −1.78712 | − | 3.76856i | −0.135481 | − | 0.285694i | ||||
\(175\) | 0.368865 | − | 0.626598i | 0.0278836 | − | 0.0473664i | ||||
\(176\) | 6.12593i | 0.461759i | ||||||||
\(177\) | −4.14505 | + | 11.6221i | −0.311561 | + | 0.873572i | ||||
\(178\) | −1.63328 | + | 1.63328i | −0.122420 | + | 0.122420i | ||||
\(179\) | −8.96071 | −0.669755 | −0.334877 | − | 0.942262i | \(-0.608695\pi\) | ||||
−0.334877 | + | 0.942262i | \(0.608695\pi\) | |||||||
\(180\) | 1.50903 | + | 6.53627i | 0.112476 | + | 0.487185i | ||||
\(181\) | 8.58326 | 0.637989 | 0.318994 | − | 0.947757i | \(-0.396655\pi\) | ||||
0.318994 | + | 0.947757i | \(0.396655\pi\) | |||||||
\(182\) | −0.109693 | + | 0.109693i | −0.00813101 | + | 0.00813101i | ||||
\(183\) | 6.01877 | − | 16.8758i | 0.444920 | − | 1.24749i | ||||
\(184\) | − | 8.78832i | − | 0.647883i | ||||||
\(185\) | −11.4855 | + | 1.46273i | −0.844432 | + | 0.107542i | ||||
\(186\) | 2.74202 | + | 5.78220i | 0.201055 | + | 0.423971i | ||||
\(187\) | −14.2914 | − | 14.2914i | −1.04509 | − | 1.04509i | ||||
\(188\) | −4.88564 | − | 4.88564i | −0.356322 | − | 0.356322i | ||||
\(189\) | 0.733548 | + | 0.181352i | 0.0533578 | + | 0.0131914i | ||||
\(190\) | −2.21815 | + | 0.282491i | −0.160922 | + | 0.0204941i | ||||
\(191\) | 15.3727i | 1.11233i | 0.831073 | + | 0.556164i | \(0.187727\pi\) | ||||
−0.831073 | + | 0.556164i | \(0.812273\pi\) | |||||||
\(192\) | −1.63140 | − | 0.581841i | −0.117736 | − | 0.0419907i | ||||
\(193\) | 16.5440 | − | 16.5440i | 1.19087 | − | 1.19087i | 0.214042 | − | 0.976824i | \(-0.431337\pi\) |
0.976824 | − | 0.214042i | \(-0.0686629\pi\) | |||||||
\(194\) | −0.842081 | −0.0604579 | ||||||||
\(195\) | −4.03561 | − | 0.885149i | −0.288996 | − | 0.0633868i | ||||
\(196\) | −6.97885 | −0.498489 | ||||||||
\(197\) | 3.02772 | − | 3.02772i | 0.215716 | − | 0.215716i | −0.590974 | − | 0.806690i | \(-0.701257\pi\) |
0.806690 | + | 0.590974i | \(0.201257\pi\) | |||||||
\(198\) | 1.83877 | + | 18.2856i | 0.130676 | + | 1.29950i | ||||
\(199\) | − | 8.01713i | − | 0.568319i | −0.958777 | − | 0.284160i | \(-0.908285\pi\) | ||
0.958777 | − | 0.284160i | \(-0.0917146\pi\) | |||||||
\(200\) | −2.53652 | + | 4.30884i | −0.179359 | + | 0.304681i | ||||
\(201\) | −9.68614 | + | 4.59334i | −0.683208 | + | 0.323989i | ||||
\(202\) | 5.48012 | + | 5.48012i | 0.385580 | + | 0.385580i | ||||
\(203\) | −0.247615 | − | 0.247615i | −0.0173791 | − | 0.0173791i | ||||
\(204\) | 5.16335 | − | 2.44855i | 0.361507 | − | 0.171433i | ||||
\(205\) | 18.2239 | + | 14.1065i | 1.27281 | + | 0.985238i | ||||
\(206\) | 15.8577i | 1.10486i | ||||||||
\(207\) | −2.63792 | − | 26.2327i | −0.183348 | − | 1.82330i | ||||
\(208\) | 0.754312 | − | 0.754312i | 0.0523021 | − | 0.0523021i | ||||
\(209\) | −6.12593 | −0.423740 | ||||||||
\(210\) | 0.303684 | + | 0.474329i | 0.0209562 | + | 0.0327318i | ||||
\(211\) | −4.50891 | −0.310406 | −0.155203 | − | 0.987883i | \(-0.549603\pi\) | ||||
−0.155203 | + | 0.987883i | \(0.549603\pi\) | |||||||
\(212\) | −2.86461 | + | 2.86461i | −0.196742 | + | 0.196742i | ||||
\(213\) | 0.507400 | + | 0.180965i | 0.0347664 | + | 0.0123995i | ||||
\(214\) | 15.4185i | 1.05399i | ||||||||
\(215\) | 0.397427 | + | 3.12064i | 0.0271043 | + | 0.212826i | ||||
\(216\) | −5.04428 | − | 1.24708i | −0.343220 | − | 0.0848530i | ||||
\(217\) | 0.379921 | + | 0.379921i | 0.0257907 | + | 0.0257907i | ||||
\(218\) | 0.677536 | + | 0.677536i | 0.0458886 | + | 0.0458886i | ||||
\(219\) | 0.793312 | + | 1.67288i | 0.0536070 | + | 0.113043i | ||||
\(220\) | −8.38468 | + | 10.8320i | −0.565295 | + | 0.730294i | ||||
\(221\) | 3.51953i | 0.236749i | ||||||||
\(222\) | 3.01275 | − | 8.44733i | 0.202203 | − | 0.566947i | ||||
\(223\) | 8.46796 | − | 8.46796i | 0.567057 | − | 0.567057i | −0.364246 | − | 0.931303i | \(-0.618673\pi\) |
0.931303 | + | 0.364246i | \(0.118673\pi\) | |||||||
\(224\) | −0.145422 | −0.00971639 | ||||||||
\(225\) | −6.27802 | + | 13.6230i | −0.418535 | + | 0.908201i | ||||
\(226\) | −6.98920 | −0.464915 | ||||||||
\(227\) | 6.20188 | − | 6.20188i | 0.411633 | − | 0.411633i | −0.470674 | − | 0.882307i | \(-0.655989\pi\) |
0.882307 | + | 0.470674i | \(0.155989\pi\) | |||||||
\(228\) | 0.581841 | − | 1.63140i | 0.0385334 | − | 0.108042i | ||||
\(229\) | − | 11.8117i | − | 0.780536i | −0.920701 | − | 0.390268i | \(-0.872382\pi\) | ||
0.920701 | − | 0.390268i | \(-0.127618\pi\) | |||||||
\(230\) | 12.0287 | − | 15.5397i | 0.793151 | − | 1.02466i | ||||
\(231\) | 0.661138 | + | 1.39417i | 0.0434997 | + | 0.0917294i | ||||
\(232\) | 1.70274 | + | 1.70274i | 0.111790 | + | 0.111790i | ||||
\(233\) | 10.5412 | + | 10.5412i | 0.690575 | + | 0.690575i | 0.962358 | − | 0.271783i | \(-0.0876134\pi\) |
−0.271783 | + | 0.962358i | \(0.587613\pi\) | |||||||
\(234\) | 2.02517 | − | 2.47800i | 0.132389 | − | 0.161992i | ||||
\(235\) | −1.95183 | − | 15.3260i | −0.127323 | − | 0.999757i | ||||
\(236\) | − | 7.12402i | − | 0.463734i | ||||||
\(237\) | −23.3465 | − | 8.32658i | −1.51652 | − | 0.540869i | ||||
\(238\) | 0.339260 | − | 0.339260i | 0.0219909 | − | 0.0219909i | ||||
\(239\) | 6.27313 | 0.405775 | 0.202887 | − | 0.979202i | \(-0.434967\pi\) | ||||
0.202887 | + | 0.979202i | \(0.434967\pi\) | |||||||
\(240\) | −2.08830 | − | 3.26175i | −0.134799 | − | 0.210545i | ||||
\(241\) | 13.3425 | 0.859466 | 0.429733 | − | 0.902956i | \(-0.358608\pi\) | ||||
0.429733 | + | 0.902956i | \(0.358608\pi\) | |||||||
\(242\) | −18.7574 | + | 18.7574i | −1.20577 | + | 1.20577i | ||||
\(243\) | −15.4312 | − | 2.20836i | −0.989914 | − | 0.141666i | ||||
\(244\) | 10.3444i | 0.662230i | ||||||||
\(245\) | −12.3402 | − | 9.55209i | −0.788384 | − | 0.610260i | ||||
\(246\) | −16.1294 | + | 7.64884i | −1.02837 | + | 0.487672i | ||||
\(247\) | 0.754312 | + | 0.754312i | 0.0479957 | + | 0.0479957i | ||||
\(248\) | −2.61255 | − | 2.61255i | −0.165897 | − | 0.165897i | ||||
\(249\) | −24.7617 | + | 11.7424i | −1.56921 | + | 0.744146i | ||||
\(250\) | −10.3827 | + | 4.14720i | −0.656661 | + | 0.262292i | ||||
\(251\) | − | 26.7821i | − | 1.69047i | −0.534392 | − | 0.845237i | \(-0.679459\pi\) | ||
0.534392 | − | 0.845237i | \(-0.320541\pi\) | |||||||
\(252\) | −0.434076 | + | 0.0436501i | −0.0273442 | + | 0.00274970i | ||||
\(253\) | 38.0682 | − | 38.0682i | 2.39333 | − | 2.39333i | ||||
\(254\) | 12.4483 | 0.781074 | ||||||||
\(255\) | 12.4813 | + | 2.73759i | 0.781611 | + | 0.171434i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.20250 | − | 6.20250i | 0.386901 | − | 0.386901i | −0.486679 | − | 0.873581i | \(-0.661792\pi\) |
0.873581 | + | 0.486679i | \(0.161792\pi\) | |||||||
\(258\) | −2.29516 | − | 0.818571i | −0.142890 | − | 0.0509620i | ||||
\(259\) | − | 0.752988i | − | 0.0467884i | ||||||
\(260\) | 2.36623 | − | 0.301350i | 0.146748 | − | 0.0186889i | ||||
\(261\) | 5.59367 | + | 4.57148i | 0.346239 | + | 0.282967i | ||||
\(262\) | −15.6309 | − | 15.6309i | −0.965680 | − | 0.965680i | ||||
\(263\) | 10.7076 | + | 10.7076i | 0.660261 | + | 0.660261i | 0.955442 | − | 0.295181i | \(-0.0953798\pi\) |
−0.295181 | + | 0.955442i | \(0.595380\pi\) | |||||||
\(264\) | −4.54636 | − | 9.58706i | −0.279809 | − | 0.590043i | ||||
\(265\) | −8.98610 | + | 1.14442i | −0.552012 | + | 0.0703011i | ||||
\(266\) | − | 0.145422i | − | 0.00891637i | ||||||
\(267\) | 1.34394 | − | 3.76823i | 0.0822480 | − | 0.230612i | ||||
\(268\) | 4.37645 | − | 4.37645i | 0.267335 | − | 0.267335i | ||||
\(269\) | 7.39882 | 0.451114 | 0.225557 | − | 0.974230i | \(-0.427580\pi\) | ||||
0.225557 | + | 0.974230i | \(0.427580\pi\) | |||||||
\(270\) | −7.21251 | − | 9.10932i | −0.438939 | − | 0.554375i | ||||
\(271\) | −32.2520 | −1.95917 | −0.979585 | − | 0.201030i | \(-0.935571\pi\) | ||||
−0.979585 | + | 0.201030i | \(0.935571\pi\) | |||||||
\(272\) | −2.33294 | + | 2.33294i | −0.141455 | + | 0.141455i | ||||
\(273\) | 0.0902608 | − | 0.253078i | 0.00546283 | − | 0.0153170i | ||||
\(274\) | − | 2.24319i | − | 0.135516i | ||||||
\(275\) | −29.6519 | + | 7.67712i | −1.78808 | + | 0.462948i | ||||
\(276\) | 6.52225 | + | 13.7537i | 0.392593 | + | 0.827875i | ||||
\(277\) | 0.315711 | + | 0.315711i | 0.0189693 | + | 0.0189693i | 0.716528 | − | 0.697559i | \(-0.245730\pi\) |
−0.697559 | + | 0.716528i | \(0.745730\pi\) | |||||||
\(278\) | 7.90353 | + | 7.90353i | 0.474022 | + | 0.474022i | ||||
\(279\) | −8.58251 | − | 7.01413i | −0.513821 | − | 0.419925i | ||||
\(280\) | −0.257138 | − | 0.199041i | −0.0153669 | − | 0.0118950i | ||||
\(281\) | − | 2.25919i | − | 0.134772i | −0.997727 | − | 0.0673860i | \(-0.978534\pi\) | ||
0.997727 | − | 0.0673860i | \(-0.0214659\pi\) | |||||||
\(282\) | 11.2719 | + | 4.02014i | 0.671232 | + | 0.239396i | ||||
\(283\) | −17.3455 | + | 17.3455i | −1.03109 | + | 1.03109i | −0.0315844 | + | 0.999501i | \(0.510055\pi\) |
−0.999501 | + | 0.0315844i | \(0.989945\pi\) | |||||||
\(284\) | −0.311021 | −0.0184557 | ||||||||
\(285\) | 3.26175 | − | 2.08830i | 0.193209 | − | 0.123700i | ||||
\(286\) | 6.53489 | 0.386416 | ||||||||
\(287\) | −1.05979 | + | 1.05979i | −0.0625572 | + | 0.0625572i | ||||
\(288\) | 2.98495 | − | 0.300162i | 0.175890 | − | 0.0176872i | ||||
\(289\) | 6.11480i | 0.359694i | ||||||||
\(290\) | 0.680248 | + | 5.34138i | 0.0399455 | + | 0.313657i | ||||
\(291\) | 1.31785 | − | 0.624950i | 0.0772539 | − | 0.0366352i | ||||
\(292\) | −0.755853 | − | 0.755853i | −0.0442330 | − | 0.0442330i | ||||
\(293\) | −1.37475 | − | 1.37475i | −0.0803135 | − | 0.0803135i | 0.665809 | − | 0.746122i | \(-0.268087\pi\) |
−0.746122 | + | 0.665809i | \(0.768087\pi\) | |||||||
\(294\) | 10.9219 | − | 5.17935i | 0.636977 | − | 0.302066i | ||||
\(295\) | 9.75078 | − | 12.5969i | 0.567712 | − | 0.733417i | ||||
\(296\) | 5.17797i | 0.300963i | ||||||||
\(297\) | −16.4483 | − | 27.2522i | −0.954427 | − | 1.58133i | ||||
\(298\) | 6.97345 | − | 6.97345i | 0.403961 | − | 0.403961i | ||||
\(299\) | −9.37501 | −0.542171 | ||||||||
\(300\) | 0.771844 | − | 8.62579i | 0.0445624 | − | 0.498010i | ||||
\(301\) | −0.204588 | −0.0117923 | ||||||||
\(302\) | −5.58697 | + | 5.58697i | −0.321494 | + | 0.321494i | ||||
\(303\) | −12.6434 | − | 4.50930i | −0.726346 | − | 0.259053i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | −14.1585 | + | 18.2911i | −0.810715 | + | 1.04735i | ||||
\(306\) | −6.26343 | + | 7.66395i | −0.358057 | + | 0.438119i | ||||
\(307\) | 2.48065 | + | 2.48065i | 0.141578 | + | 0.141578i | 0.774343 | − | 0.632765i | \(-0.218080\pi\) |
−0.632765 | + | 0.774343i | \(0.718080\pi\) | |||||||
\(308\) | −0.629921 | − | 0.629921i | −0.0358931 | − | 0.0358931i | ||||
\(309\) | −11.7688 | − | 24.8172i | −0.669502 | − | 1.41180i | ||||
\(310\) | −1.04372 | − | 8.19542i | −0.0592794 | − | 0.465468i | ||||
\(311\) | 1.76203i | 0.0999158i | 0.998751 | + | 0.0499579i | \(0.0159087\pi\) | ||||
−0.998751 | + | 0.0499579i | \(0.984091\pi\) | |||||||
\(312\) | −0.620684 | + | 1.74031i | −0.0351393 | + | 0.0985256i | ||||
\(313\) | −9.58013 | + | 9.58013i | −0.541501 | + | 0.541501i | −0.923969 | − | 0.382468i | \(-0.875074\pi\) |
0.382468 | + | 0.923969i | \(0.375074\pi\) | |||||||
\(314\) | 5.60560 | 0.316342 | ||||||||
\(315\) | −0.827287 | − | 0.516945i | −0.0466123 | − | 0.0291265i | ||||
\(316\) | 14.3107 | 0.805042 | ||||||||
\(317\) | −7.82453 | + | 7.82453i | −0.439469 | + | 0.439469i | −0.891833 | − | 0.452364i | \(-0.850581\pi\) |
0.452364 | + | 0.891833i | \(0.350581\pi\) | |||||||
\(318\) | 2.35713 | − | 6.60907i | 0.132182 | − | 0.370618i | ||||
\(319\) | 14.7514i | 0.825922i | ||||||||
\(320\) | 1.76822 | + | 1.36872i | 0.0988466 | + | 0.0765137i | ||||
\(321\) | −11.4428 | − | 24.1299i | −0.638677 | − | 1.34680i | ||||
\(322\) | 0.903691 | + | 0.903691i | 0.0503607 | + | 0.0503607i | ||||
\(323\) | −2.33294 | − | 2.33294i | −0.129808 | − | 0.129808i | ||||
\(324\) | 8.81981 | − | 1.79194i | 0.489989 | − | 0.0995521i | ||||
\(325\) | 4.59649 | + | 2.70585i | 0.254967 | + | 0.150094i | ||||
\(326\) | − | 8.98180i | − | 0.497456i | ||||||
\(327\) | −1.56318 | − | 0.557509i | −0.0864438 | − | 0.0308303i | ||||
\(328\) | 7.28768 | − | 7.28768i | 0.402395 | − | 0.402395i | ||||
\(329\) | 1.00477 | 0.0553947 | ||||||||
\(330\) | 5.08303 | − | 23.1747i | 0.279811 | − | 1.27573i | ||||
\(331\) | −10.1328 | −0.556947 | −0.278473 | − | 0.960444i | \(-0.589828\pi\) | ||||
−0.278473 | + | 0.960444i | \(0.589828\pi\) | |||||||
\(332\) | 11.1880 | − | 11.1880i | 0.614020 | − | 0.614020i | ||||
\(333\) | 1.55423 | + | 15.4559i | 0.0851713 | + | 0.846981i | ||||
\(334\) | − | 21.0963i | − | 1.15434i | ||||||
\(335\) | 13.7287 | − | 1.74841i | 0.750078 | − | 0.0955257i | ||||
\(336\) | 0.227584 | − | 0.107925i | 0.0124157 | − | 0.00588777i | ||||
\(337\) | 8.59971 | + | 8.59971i | 0.468456 | + | 0.468456i | 0.901414 | − | 0.432958i | \(-0.142530\pi\) |
−0.432958 | + | 0.901414i | \(0.642530\pi\) | |||||||
\(338\) | 8.38772 | + | 8.38772i | 0.456232 | + | 0.456232i | ||||
\(339\) | 10.9381 | − | 5.18703i | 0.594075 | − | 0.281721i | ||||
\(340\) | −7.31829 | + | 0.932016i | −0.396890 | + | 0.0505457i | ||||
\(341\) | − | 22.6335i | − | 1.22567i | ||||||
\(342\) | 0.300162 | + | 2.98495i | 0.0162309 | + | 0.161407i | ||||
\(343\) | 1.43743 | − | 1.43743i | 0.0776137 | − | 0.0776137i | ||||
\(344\) | 1.40686 | 0.0758530 | ||||||||
\(345\) | −7.29216 | + | 33.2467i | −0.392597 | + | 1.78994i | ||||
\(346\) | 8.75680 | 0.470769 | ||||||||
\(347\) | −7.91015 | + | 7.91015i | −0.424639 | + | 0.424639i | −0.886797 | − | 0.462158i | \(-0.847075\pi\) |
0.462158 | + | 0.886797i | \(0.347075\pi\) | |||||||
\(348\) | −3.92846 | − | 1.40109i | −0.210587 | − | 0.0751064i | ||||
\(349\) | 18.5835i | 0.994752i | 0.867535 | + | 0.497376i | \(0.165703\pi\) | ||||
−0.867535 | + | 0.497376i | \(0.834297\pi\) | |||||||
\(350\) | −0.182245 | − | 0.703899i | −0.00974140 | − | 0.0376250i | ||||
\(351\) | −1.33033 | + | 5.38103i | −0.0710079 | + | 0.287218i | ||||
\(352\) | 4.33169 | + | 4.33169i | 0.230880 | + | 0.230880i | ||||
\(353\) | 3.74671 | + | 3.74671i | 0.199417 | + | 0.199417i | 0.799750 | − | 0.600333i | \(-0.204965\pi\) |
−0.600333 | + | 0.799750i | \(0.704965\pi\) | |||||||
\(354\) | 5.28709 | + | 11.1491i | 0.281006 | + | 0.592566i | ||||
\(355\) | −0.549955 | − | 0.425701i | −0.0291886 | − | 0.0225938i | ||||
\(356\) | 2.30981i | 0.122420i | ||||||||
\(357\) | −0.279159 | + | 0.782721i | −0.0147747 | + | 0.0414260i | ||||
\(358\) | −6.33618 | + | 6.33618i | −0.334877 | + | 0.334877i | ||||
\(359\) | 17.1601 | 0.905676 | 0.452838 | − | 0.891593i | \(-0.350412\pi\) | ||||
0.452838 | + | 0.891593i | \(0.350412\pi\) | |||||||
\(360\) | 5.68888 | + | 3.55480i | 0.299831 | + | 0.187354i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 6.06928 | − | 6.06928i | 0.318994 | − | 0.318994i | ||||
\(363\) | 15.4345 | − | 43.2762i | 0.810102 | − | 2.27141i | ||||
\(364\) | 0.155130i | 0.00813101i | ||||||||
\(365\) | −0.301966 | − | 2.37107i | −0.0158056 | − | 0.124107i | ||||
\(366\) | −7.67706 | − | 16.1889i | −0.401286 | − | 0.846207i | ||||
\(367\) | 24.6532 | + | 24.6532i | 1.28689 | + | 1.28689i | 0.936668 | + | 0.350218i | \(0.113892\pi\) |
0.350218 | + | 0.936668i | \(0.386108\pi\) | |||||||
\(368\) | −6.21428 | − | 6.21428i | −0.323942 | − | 0.323942i | ||||
\(369\) | 19.5658 | − | 23.9408i | 1.01856 | − | 1.24631i | ||||
\(370\) | −7.08718 | + | 9.15579i | −0.368445 | + | 0.475987i | ||||
\(371\) | − | 0.589127i | − | 0.0305860i | ||||||
\(372\) | 6.02753 | + | 2.14973i | 0.312513 | + | 0.111458i | ||||
\(373\) | −10.9785 | + | 10.9785i | −0.568446 | + | 0.568446i | −0.931693 | − | 0.363247i | \(-0.881668\pi\) |
0.363247 | + | 0.931693i | \(0.381668\pi\) | |||||||
\(374\) | −20.2111 | −1.04509 | ||||||||
\(375\) | 13.1711 | − | 14.1959i | 0.680151 | − | 0.733072i | ||||
\(376\) | −6.90934 | −0.356322 | ||||||||
\(377\) | 1.81641 | − | 1.81641i | 0.0935497 | − | 0.0935497i | ||||
\(378\) | 0.646932 | − | 0.390461i | 0.0332746 | − | 0.0200832i | ||||
\(379\) | − | 31.8871i | − | 1.63793i | −0.573843 | − | 0.818966i | \(-0.694548\pi\) | ||
0.573843 | − | 0.818966i | \(-0.305452\pi\) | |||||||
\(380\) | −1.36872 | + | 1.76822i | −0.0702138 | + | 0.0907079i | ||||
\(381\) | −19.4815 | + | 9.23848i | −0.998068 | + | 0.473302i | ||||
\(382\) | 10.8701 | + | 10.8701i | 0.556164 | + | 0.556164i | ||||
\(383\) | 3.71847 | + | 3.71847i | 0.190005 | + | 0.190005i | 0.795698 | − | 0.605693i | \(-0.207104\pi\) |
−0.605693 | + | 0.795698i | \(0.707104\pi\) | |||||||
\(384\) | −1.56500 | + | 0.742149i | −0.0798634 | + | 0.0378727i | ||||
\(385\) | −0.251655 | − | 1.97603i | −0.0128255 | − | 0.100708i | ||||
\(386\) | − | 23.3968i | − | 1.19087i | ||||||
\(387\) | 4.19941 | − | 0.422288i | 0.213468 | − | 0.0214661i | ||||
\(388\) | −0.595441 | + | 0.595441i | −0.0302289 | + | 0.0302289i | ||||
\(389\) | 27.6876 | 1.40382 | 0.701908 | − | 0.712268i | \(-0.252332\pi\) | ||||
0.701908 | + | 0.712268i | \(0.252332\pi\) | |||||||
\(390\) | −3.47950 | + | 2.22771i | −0.176191 | + | 0.112804i | ||||
\(391\) | 28.9951 | 1.46634 | ||||||||
\(392\) | −4.93479 | + | 4.93479i | −0.249245 | + | 0.249245i | ||||
\(393\) | 36.0628 | + | 12.8618i | 1.81913 | + | 0.648794i | ||||
\(394\) | − | 4.28184i | − | 0.215716i | ||||||
\(395\) | 25.3046 | + | 19.5874i | 1.27321 | + | 0.985548i | ||||
\(396\) | 14.2301 | + | 11.6296i | 0.715088 | + | 0.584412i | ||||
\(397\) | −0.647982 | − | 0.647982i | −0.0325213 | − | 0.0325213i | 0.690659 | − | 0.723180i | \(-0.257321\pi\) |
−0.723180 | + | 0.690659i | \(0.757321\pi\) | |||||||
\(398\) | −5.66897 | − | 5.66897i | −0.284160 | − | 0.284160i | ||||
\(399\) | 0.107925 | + | 0.227584i | 0.00540299 | + | 0.0113935i | ||||
\(400\) | 1.25322 | + | 4.84040i | 0.0626609 | + | 0.242020i | ||||
\(401\) | − | 28.9315i | − | 1.44477i | −0.691491 | − | 0.722385i | \(-0.743046\pi\) | ||
0.691491 | − | 0.722385i | \(-0.256954\pi\) | |||||||
\(402\) | −3.60115 | + | 10.0971i | −0.179609 | + | 0.503599i | ||||
\(403\) | −2.78696 | + | 2.78696i | −0.138828 | + | 0.138828i | ||||
\(404\) | 7.75006 | 0.385580 | ||||||||
\(405\) | 18.0480 | + | 8.90329i | 0.896814 | + | 0.442408i | ||||
\(406\) | −0.350180 | −0.0173791 | ||||||||
\(407\) | −22.4293 | + | 22.4293i | −1.11178 | + | 1.11178i | ||||
\(408\) | 1.91965 | − | 5.38243i | 0.0950369 | − | 0.266470i | ||||
\(409\) | − | 15.5261i | − | 0.767717i | −0.923392 | − | 0.383859i | \(-0.874595\pi\) | ||
0.923392 | − | 0.383859i | \(-0.125405\pi\) | |||||||
\(410\) | 22.8610 | − | 2.91145i | 1.12902 | − | 0.143786i | ||||
\(411\) | 1.66478 | + | 3.51058i | 0.0821176 | + | 0.173164i | ||||
\(412\) | 11.2131 | + | 11.2131i | 0.552429 | + | 0.552429i | ||||
\(413\) | 0.732553 | + | 0.732553i | 0.0360466 | + | 0.0360466i | ||||
\(414\) | −20.4146 | − | 16.6840i | −1.00332 | − | 0.819974i | ||||
\(415\) | 35.0960 | − | 4.46963i | 1.72280 | − | 0.219406i | ||||
\(416\) | − | 1.06676i | − | 0.0523021i | ||||||
\(417\) | −18.2346 | − | 6.50340i | −0.892953 | − | 0.318473i | ||||
\(418\) | −4.33169 | + | 4.33169i | −0.211870 | + | 0.211870i | ||||
\(419\) | 6.96160 | 0.340096 | 0.170048 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170048 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(420\) | 0.550138 | + | 0.120664i | 0.0268440 | + | 0.00588782i | ||||
\(421\) | −29.4232 | −1.43400 | −0.717000 | − | 0.697073i | \(-0.754485\pi\) | ||||
−0.717000 | + | 0.697073i | \(0.754485\pi\) | |||||||
\(422\) | −3.18828 | + | 3.18828i | −0.155203 | + | 0.155203i | ||||
\(423\) | −20.6240 | + | 2.07393i | −1.00277 | + | 0.100838i | ||||
\(424\) | 4.05117i | 0.196742i | ||||||||
\(425\) | −14.2160 | − | 8.36867i | −0.689578 | − | 0.405940i | ||||
\(426\) | 0.486747 | − | 0.230824i | 0.0235830 | − | 0.0111835i | ||||
\(427\) | −1.06370 | − | 1.06370i | −0.0514759 | − | 0.0514759i | ||||
\(428\) | 10.9025 | + | 10.9025i | 0.526994 | + | 0.526994i | ||||
\(429\) | −10.2271 | + | 4.84986i | −0.493768 | + | 0.234154i | ||||
\(430\) | 2.48765 | + | 1.92560i | 0.119965 | + | 0.0928607i | ||||
\(431\) | 19.6775i | 0.947834i | 0.880570 | + | 0.473917i | \(0.157160\pi\) | ||||
−0.880570 | + | 0.473917i | \(0.842840\pi\) | |||||||
\(432\) | −4.44866 | + | 2.68503i | −0.214036 | + | 0.129184i | ||||
\(433\) | −22.2656 | + | 22.2656i | −1.07002 | + | 1.07002i | −0.0726615 | + | 0.997357i | \(0.523149\pi\) |
−0.997357 | + | 0.0726615i | \(0.976851\pi\) | |||||||
\(434\) | 0.537290 | 0.0257907 | ||||||||
\(435\) | −5.02869 | − | 7.85439i | −0.241107 | − | 0.376589i | ||||
\(436\) | 0.958181 | 0.0458886 | ||||||||
\(437\) | 6.21428 | − | 6.21428i | 0.297269 | − | 0.297269i | ||||
\(438\) | 1.74386 | + | 0.621952i | 0.0833250 | + | 0.0297180i | ||||
\(439\) | 1.96512i | 0.0937899i | 0.998900 | + | 0.0468950i | \(0.0149326\pi\) | ||||
−0.998900 | + | 0.0468950i | \(0.985067\pi\) | |||||||
\(440\) | 1.73052 | + | 13.5882i | 0.0824994 | + | 0.647794i | ||||
\(441\) | −13.2489 | + | 16.2113i | −0.630898 | + | 0.771968i | ||||
\(442\) | 2.48868 | + | 2.48868i | 0.118374 | + | 0.118374i | ||||
\(443\) | −10.2690 | − | 10.2690i | −0.487896 | − | 0.487896i | 0.419746 | − | 0.907642i | \(-0.362119\pi\) |
−0.907642 | + | 0.419746i | \(0.862119\pi\) | |||||||
\(444\) | −3.84282 | − | 8.10350i | −0.182372 | − | 0.384575i | ||||
\(445\) | −3.16148 | + | 4.08426i | −0.149869 | + | 0.193613i | ||||
\(446\) | − | 11.9755i | − | 0.567057i | ||||||
\(447\) | −5.73809 | + | 16.0888i | −0.271402 | + | 0.760973i | ||||
\(448\) | −0.102829 | + | 0.102829i | −0.00485820 | + | 0.00485820i | ||||
\(449\) | −28.7172 | −1.35525 | −0.677623 | − | 0.735409i | \(-0.736990\pi\) | ||||
−0.677623 | + | 0.735409i | \(0.736990\pi\) | |||||||
\(450\) | 5.19369 | + | 14.0722i | 0.244833 | + | 0.663368i | ||||
\(451\) | 63.1359 | 2.97295 | ||||||||
\(452\) | −4.94211 | + | 4.94211i | −0.232457 | + | 0.232457i | ||||
\(453\) | 4.59722 | − | 12.8900i | 0.215996 | − | 0.605623i | ||||
\(454\) | − | 8.77078i | − | 0.411633i | ||||||
\(455\) | −0.212329 | + | 0.274304i | −0.00995414 | + | 0.0128596i | ||||
\(456\) | −0.742149 | − | 1.56500i | −0.0347543 | − | 0.0732877i | ||||
\(457\) | 13.0668 | + | 13.0668i | 0.611239 | + | 0.611239i | 0.943269 | − | 0.332030i | \(-0.107733\pi\) |
−0.332030 | + | 0.943269i | \(0.607733\pi\) | |||||||
\(458\) | −8.35210 | − | 8.35210i | −0.390268 | − | 0.390268i | ||||
\(459\) | 4.11445 | − | 16.6425i | 0.192046 | − | 0.776804i | ||||
\(460\) | −2.48262 | − | 19.4938i | −0.115753 | − | 0.908904i | ||||
\(461\) | − | 35.6982i | − | 1.66263i | −0.555800 | − | 0.831316i | \(-0.687588\pi\) | ||
0.555800 | − | 0.831316i | \(-0.312412\pi\) | |||||||
\(462\) | 1.45332 | + | 0.518329i | 0.0676146 | + | 0.0241148i | ||||
\(463\) | −18.7714 | + | 18.7714i | −0.872381 | + | 0.872381i | −0.992731 | − | 0.120350i | \(-0.961598\pi\) |
0.120350 | + | 0.992731i | \(0.461598\pi\) | |||||||
\(464\) | 2.40803 | 0.111790 | ||||||||
\(465\) | 7.71564 | + | 12.0512i | 0.357804 | + | 0.558861i | ||||
\(466\) | 14.9075 | 0.690575 | ||||||||
\(467\) | 5.01672 | − | 5.01672i | 0.232146 | − | 0.232146i | −0.581442 | − | 0.813588i | \(-0.697511\pi\) |
0.813588 | + | 0.581442i | \(0.197511\pi\) | |||||||
\(468\) | −0.320201 | − | 3.18422i | −0.0148013 | − | 0.147190i | ||||
\(469\) | 0.900050i | 0.0415604i | ||||||||
\(470\) | −12.2173 | − | 9.45695i | −0.563540 | − | 0.436217i | ||||
\(471\) | −8.77274 | + | 4.16019i | −0.404227 | + | 0.191692i | ||||
\(472\) | −5.03744 | − | 5.03744i | −0.231867 | − | 0.231867i | ||||
\(473\) | 6.09409 | + | 6.09409i | 0.280207 | + | 0.280207i | ||||
\(474\) | −22.3963 | + | 10.6207i | −1.02869 | + | 0.487825i | ||||
\(475\) | −4.84040 | + | 1.25322i | −0.222093 | + | 0.0575016i | ||||
\(476\) | − | 0.479786i | − | 0.0219909i | ||||||
\(477\) | 1.21601 | + | 12.0925i | 0.0556772 | + | 0.553678i | ||||
\(478\) | 4.43577 | − | 4.43577i | 0.202887 | − | 0.202887i | ||||
\(479\) | −6.25041 | −0.285589 | −0.142794 | − | 0.989752i | \(-0.545609\pi\) | ||||
−0.142794 | + | 0.989752i | \(0.545609\pi\) | |||||||
\(480\) | −3.78306 | − | 0.829756i | −0.172672 | − | 0.0378730i | ||||
\(481\) | 5.52364 | 0.251856 | ||||||||
\(482\) | 9.43457 | − | 9.43457i | 0.429733 | − | 0.429733i | ||||
\(483\) | −2.08495 | − | 0.743599i | −0.0948683 | − | 0.0338349i | ||||
\(484\) | 26.5270i | 1.20577i | ||||||||
\(485\) | −1.86786 | + | 0.237880i | −0.0848153 | + | 0.0108016i | ||||
\(486\) | −12.4731 | + | 9.34999i | −0.565790 | + | 0.424124i | ||||
\(487\) | −11.4086 | − | 11.4086i | −0.516973 | − | 0.516973i | 0.399681 | − | 0.916654i | \(-0.369121\pi\) |
−0.916654 | + | 0.399681i | \(0.869121\pi\) | |||||||
\(488\) | 7.31457 | + | 7.31457i | 0.331115 | + | 0.331115i | ||||
\(489\) | 6.66584 | + | 14.0565i | 0.301439 | + | 0.635656i | ||||
\(490\) | −15.4802 | + | 1.97147i | −0.699322 | + | 0.0890617i | ||||
\(491\) | − | 10.2744i | − | 0.463675i | −0.972754 | − | 0.231838i | \(-0.925526\pi\) | ||
0.972754 | − | 0.231838i | \(-0.0744738\pi\) | |||||||
\(492\) | −5.99664 | + | 16.8137i | −0.270350 | + | 0.758022i | ||||
\(493\) | −5.61779 | + | 5.61779i | −0.253012 | + | 0.253012i | ||||
\(494\) | 1.06676 | 0.0479957 | ||||||||
\(495\) | 9.24420 | + | 40.0407i | 0.415496 | + | 1.79970i | ||||
\(496\) | −3.69470 | −0.165897 | ||||||||
\(497\) | 0.0319819 | − | 0.0319819i | 0.00143458 | − | 0.00143458i | ||||
\(498\) | −9.20600 | + | 25.8123i | −0.412531 | + | 1.15668i | ||||
\(499\) | 26.3326i | 1.17881i | 0.807839 | + | 0.589404i | \(0.200637\pi\) | ||||
−0.807839 | + | 0.589404i | \(0.799363\pi\) | |||||||
\(500\) | −4.40918 | + | 10.2742i | −0.197184 | + | 0.459476i | ||||
\(501\) | 15.6566 | + | 33.0156i | 0.699485 | + | 1.47503i | ||||
\(502\) | −18.9378 | − | 18.9378i | −0.845237 | − | 0.845237i | ||||
\(503\) | −18.5070 | − | 18.5070i | −0.825188 | − | 0.825188i | 0.161658 | − | 0.986847i | \(-0.448316\pi\) |
−0.986847 | + | 0.161658i | \(0.948316\pi\) | |||||||
\(504\) | −0.276073 | + | 0.337803i | −0.0122973 | + | 0.0150469i | ||||
\(505\) | 13.7038 | + | 10.6077i | 0.609812 | + | 0.472034i | ||||
\(506\) | − | 53.8366i | − | 2.39333i | ||||||
\(507\) | −19.3517 | − | 6.90181i | −0.859439 | − | 0.306520i | ||||
\(508\) | 8.80226 | − | 8.80226i | 0.390537 | − | 0.390537i | ||||
\(509\) | 40.9795 | 1.81638 | 0.908191 | − | 0.418555i | \(-0.137463\pi\) | ||||
0.908191 | + | 0.418555i | \(0.137463\pi\) | |||||||
\(510\) | 10.7614 | − | 6.88986i | 0.476523 | − | 0.305088i | ||||
\(511\) | 0.155447 | 0.00687656 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.68503 | − | 4.44866i | −0.118547 | − | 0.196413i | ||||
\(514\) | − | 8.77166i | − | 0.386901i | ||||||
\(515\) | 4.47966 | + | 35.1748i | 0.197397 | + | 1.54999i | ||||
\(516\) | −2.20174 | + | 1.04410i | −0.0969261 | + | 0.0459641i | ||||
\(517\) | −29.9291 | − | 29.9291i | −1.31628 | − | 1.31628i | ||||
\(518\) | −0.532443 | − | 0.532443i | −0.0233942 | − | 0.0233942i | ||||
\(519\) | −13.7044 | + | 6.49886i | −0.601555 | + | 0.285268i | ||||
\(520\) | 1.46009 | − | 1.88627i | 0.0640293 | − | 0.0827182i | ||||
\(521\) | − | 26.2549i | − | 1.15025i | −0.818066 | − | 0.575125i | \(-0.804954\pi\) | ||
0.818066 | − | 0.575125i | \(-0.195046\pi\) | |||||||
\(522\) | 7.18784 | − | 0.722800i | 0.314603 | − | 0.0316361i | ||||
\(523\) | 12.9426 | − | 12.9426i | 0.565942 | − | 0.565942i | −0.365047 | − | 0.930989i | \(-0.618947\pi\) |
0.930989 | + | 0.365047i | \(0.118947\pi\) | |||||||
\(524\) | −22.1054 | −0.965680 | ||||||||
\(525\) | 0.807611 | + | 0.966346i | 0.0352470 | + | 0.0421748i | ||||
\(526\) | 15.1429 | 0.660261 | ||||||||
\(527\) | 8.61951 | − | 8.61951i | 0.375472 | − | 0.375472i | ||||
\(528\) | −9.99383 | − | 3.56432i | −0.434926 | − | 0.155117i | ||||
\(529\) | 54.2345i | 2.35802i | ||||||||
\(530\) | −5.54491 | + | 7.16336i | −0.240855 | + | 0.311156i | ||||
\(531\) | −16.5485 | − | 13.5244i | −0.718146 | − | 0.586911i | ||||
\(532\) | −0.102829 | − | 0.102829i | −0.00445819 | − | 0.00445819i | ||||
\(533\) | −7.77419 | − | 7.77419i | −0.336738 | − | 0.336738i | ||||
\(534\) | −1.71423 | − | 3.61485i | −0.0741818 | − | 0.156430i | ||||
\(535\) | 4.35560 | + | 34.2006i | 0.188309 | + | 1.47862i | ||||
\(536\) | − | 6.18924i | − | 0.267335i | ||||||
\(537\) | 5.21371 | − | 14.6185i | 0.224988 | − | 0.630834i | ||||
\(538\) | 5.23176 | − | 5.23176i | 0.225557 | − | 0.225557i | ||||
\(539\) | −42.7520 | −1.84146 | ||||||||
\(540\) | −11.5413 | − | 1.34124i | −0.496657 | − | 0.0577180i | ||||
\(541\) | 17.1469 | 0.737202 | 0.368601 | − | 0.929588i | \(-0.379837\pi\) | ||||
0.368601 | + | 0.929588i | \(0.379837\pi\) | |||||||
\(542\) | −22.8056 | + | 22.8056i | −0.979585 | + | 0.979585i | ||||
\(543\) | −4.99409 | + | 14.0027i | −0.214317 | + | 0.600914i | ||||
\(544\) | 3.29927i | 0.141455i | ||||||||
\(545\) | 1.69428 | + | 1.31148i | 0.0725749 | + | 0.0561777i | ||||
\(546\) | −0.115129 | − | 0.242778i | −0.00492709 | − | 0.0103899i | ||||
\(547\) | 0.690907 | + | 0.690907i | 0.0295410 | + | 0.0295410i | 0.721723 | − | 0.692182i | \(-0.243350\pi\) |
−0.692182 | + | 0.721723i | \(0.743350\pi\) | |||||||
\(548\) | −1.58617 | − | 1.58617i | −0.0677580 | − | 0.0677580i | ||||
\(549\) | 24.0292 | + | 19.6380i | 1.02554 | + | 0.838131i | ||||
\(550\) | −15.5385 | + | 26.3956i | −0.662566 | + | 1.12551i | ||||
\(551\) | 2.40803i | 0.102586i | ||||||||
\(552\) | 14.3373 | + | 5.11340i | 0.610234 | + | 0.217641i | ||||
\(553\) | −1.47155 | + | 1.47155i | −0.0625768 | + | 0.0625768i | ||||
\(554\) | 0.446483 | 0.0189693 | ||||||||
\(555\) | 4.29645 | − | 19.5885i | 0.182374 | − | 0.831487i | ||||
\(556\) | 11.1773 | 0.474022 | ||||||||
\(557\) | 17.1913 | − | 17.1913i | 0.728419 | − | 0.728419i | −0.241886 | − | 0.970305i | \(-0.577766\pi\) |
0.970305 | + | 0.241886i | \(0.0777660\pi\) | |||||||
\(558\) | −11.0285 | + | 1.10901i | −0.466873 | + | 0.0469482i | ||||
\(559\) | − | 1.50078i | − | 0.0634764i | ||||||
\(560\) | −0.322567 | + | 0.0410804i | −0.0136310 | + | 0.00173596i | ||||
\(561\) | 31.6303 | − | 14.9997i | 1.33543 | − | 0.633286i | ||||
\(562\) | −1.59749 | − | 1.59749i | −0.0673860 | − | 0.0673860i | ||||
\(563\) | −14.9893 | − | 14.9893i | −0.631723 | − | 0.631723i | 0.316777 | − | 0.948500i | \(-0.397399\pi\) |
−0.948500 | + | 0.316777i | \(0.897399\pi\) | |||||||
\(564\) | 10.8131 | − | 5.12777i | 0.455314 | − | 0.215918i | ||||
\(565\) | −15.5031 | + | 1.97439i | −0.652221 | + | 0.0830632i | ||||
\(566\) | 24.5303i | 1.03109i | ||||||||
\(567\) | −0.722666 | + | 1.09119i | −0.0303491 | + | 0.0458257i | ||||
\(568\) | −0.219925 | + | 0.219925i | −0.00922786 | + | 0.00922786i | ||||
\(569\) | −35.8239 | −1.50181 | −0.750907 | − | 0.660408i | \(-0.770383\pi\) | ||||
−0.750907 | + | 0.660408i | \(0.770383\pi\) | |||||||
\(570\) | 0.829756 | − | 3.78306i | 0.0347546 | − | 0.158455i | ||||
\(571\) | −5.53111 | −0.231470 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(572\) | 4.62086 | − | 4.62086i | 0.193208 | − | 0.193208i | ||||
\(573\) | −25.0790 | − | 8.94445i | −1.04769 | − | 0.373660i | ||||
\(574\) | 1.49876i | 0.0625572i | ||||||||
\(575\) | 22.2917 | − | 37.8674i | 0.929630 | − | 1.57918i | ||||
\(576\) | 1.89843 | − | 2.32292i | 0.0791012 | − | 0.0967884i | ||||
\(577\) | 7.04676 | + | 7.04676i | 0.293360 | + | 0.293360i | 0.838406 | − | 0.545046i | \(-0.183488\pi\) |
−0.545046 | + | 0.838406i | \(0.683488\pi\) | |||||||
\(578\) | 4.32382 | + | 4.32382i | 0.179847 | + | 0.179847i | ||||
\(579\) | 17.3639 | + | 36.6159i | 0.721620 | + | 1.52171i | ||||
\(580\) | 4.25793 | + | 3.29592i | 0.176801 | + | 0.136856i | ||||
\(581\) | 2.30089i | 0.0954570i | ||||||||
\(582\) | 0.489957 | − | 1.37377i | 0.0203094 | − | 0.0569446i | ||||
\(583\) | −17.5484 | + | 17.5484i | −0.726780 | + | 0.726780i | ||||
\(584\) | −1.06894 | −0.0442330 | ||||||||
\(585\) | 3.79211 | − | 6.06867i | 0.156785 | − | 0.250908i | ||||
\(586\) | −1.94418 | −0.0803135 | ||||||||
\(587\) | −26.9429 | + | 26.9429i | −1.11205 | + | 1.11205i | −0.119179 | + | 0.992873i | \(0.538026\pi\) |
−0.992873 | + | 0.119179i | \(0.961974\pi\) | |||||||
\(588\) | 4.06058 | − | 11.3853i | 0.167456 | − | 0.469521i | ||||
\(589\) | − | 3.69470i | − | 0.152238i | ||||||
\(590\) | −2.01247 | − | 15.8022i | −0.0828523 | − | 0.650565i | ||||
\(591\) | 3.17776 | + | 6.70106i | 0.130716 | + | 0.275645i | ||||
\(592\) | 3.66137 | + | 3.66137i | 0.150482 | + | 0.150482i | ||||
\(593\) | 20.6797 | + | 20.6797i | 0.849213 | + | 0.849213i | 0.990035 | − | 0.140822i | \(-0.0449744\pi\) |
−0.140822 | + | 0.990035i | \(0.544974\pi\) | |||||||
\(594\) | −30.9009 | − | 7.63952i | −1.26788 | − | 0.313453i | ||||
\(595\) | 0.656692 | − | 0.848367i | 0.0269217 | − | 0.0347797i | ||||
\(596\) | − | 9.86195i | − | 0.403961i | ||||||
\(597\) | 13.0791 | + | 4.66470i | 0.535293 | + | 0.190913i | ||||
\(598\) | −6.62914 | + | 6.62914i | −0.271086 | + | 0.271086i | ||||
\(599\) | 43.6578 | 1.78381 | 0.891904 | − | 0.452225i | \(-0.149369\pi\) | ||||
0.891904 | + | 0.452225i | \(0.149369\pi\) | |||||||
\(600\) | −5.55358 | − | 6.64513i | −0.226724 | − | 0.271286i | ||||
\(601\) | −34.9857 | −1.42710 | −0.713548 | − | 0.700606i | \(-0.752913\pi\) | ||||
−0.713548 | + | 0.700606i | \(0.752913\pi\) | |||||||
\(602\) | −0.144666 | + | 0.144666i | −0.00589614 | + | 0.00589614i | ||||
\(603\) | −1.85778 | − | 18.4746i | −0.0756546 | − | 0.752342i | ||||
\(604\) | 7.90117i | 0.321494i | ||||||||
\(605\) | −36.3080 | + | 46.9057i | −1.47613 | + | 1.90699i | ||||
\(606\) | −12.1288 | + | 5.75170i | −0.492699 | + | 0.233647i | ||||
\(607\) | 17.1411 | + | 17.1411i | 0.695736 | + | 0.695736i | 0.963488 | − | 0.267752i | \(-0.0862806\pi\) |
−0.267752 | + | 0.963488i | \(0.586281\pi\) | |||||||
\(608\) | 0.707107 | + | 0.707107i | 0.0286770 | + | 0.0286770i | ||||
\(609\) | 0.548030 | − | 0.259886i | 0.0222073 | − | 0.0105311i | ||||
\(610\) | 2.92219 | + | 22.9454i | 0.118316 | + | 0.929031i | ||||
\(611\) | 7.37060i | 0.298183i | ||||||||
\(612\) | 0.990317 | + | 9.84815i | 0.0400312 | + | 0.398088i | ||||
\(613\) | 11.6759 | − | 11.6759i | 0.471584 | − | 0.471584i | −0.430843 | − | 0.902427i | \(-0.641784\pi\) |
0.902427 | + | 0.430843i | \(0.141784\pi\) | |||||||
\(614\) | 3.50817 | 0.141578 | ||||||||
\(615\) | −33.6167 | + | 21.5227i | −1.35555 | + | 0.867879i | ||||
\(616\) | −0.890843 | −0.0358931 | ||||||||
\(617\) | −26.0987 | + | 26.0987i | −1.05069 | + | 1.05069i | −0.0520498 | + | 0.998644i | \(0.516575\pi\) |
−0.998644 | + | 0.0520498i | \(0.983425\pi\) | |||||||
\(618\) | −25.8702 | − | 9.22665i | −1.04065 | − | 0.371150i | ||||
\(619\) | − | 23.5922i | − | 0.948249i | −0.880458 | − | 0.474124i | \(-0.842765\pi\) | ||
0.880458 | − | 0.474124i | \(-0.157235\pi\) | |||||||
\(620\) | −6.53306 | − | 5.05701i | −0.262374 | − | 0.203094i | ||||
\(621\) | 44.3308 | + | 10.9597i | 1.77893 | + | 0.439799i | ||||
\(622\) | 1.24595 | + | 1.24595i | 0.0499579 | + | 0.0499579i | ||||
\(623\) | −0.237515 | − | 0.237515i | −0.00951583 | − | 0.00951583i | ||||
\(624\) | 0.791694 | + | 1.66947i | 0.0316931 | + | 0.0668324i | ||||
\(625\) | −21.8589 | + | 12.1321i | −0.874356 | + | 0.485286i | ||||
\(626\) | 13.5483i | 0.541501i | ||||||||
\(627\) | 3.56432 | − | 9.99383i | 0.142345 | − | 0.399115i | ||||
\(628\) | 3.96376 | − | 3.96376i | 0.158171 | − | 0.158171i | ||||
\(629\) | −17.0835 | −0.681164 | ||||||||
\(630\) | −0.950515 | + | 0.219445i | −0.0378694 | + | 0.00874291i | ||||
\(631\) | 33.3627 | 1.32815 | 0.664075 | − | 0.747666i | \(-0.268826\pi\) | ||||
0.664075 | + | 0.747666i | \(0.268826\pi\) | |||||||
\(632\) | 10.1192 | − | 10.1192i | 0.402521 | − | 0.402521i | ||||
\(633\) | 2.62347 | − | 7.35584i | 0.104274 | − | 0.292368i | ||||
\(634\) | 11.0656i | 0.439469i | ||||||||
\(635\) | 27.6122 | − | 3.51653i | 1.09576 | − | 0.139549i | ||||
\(636\) | −3.00657 | − | 6.34006i | −0.119218 | − | 0.251400i | ||||
\(637\) | 5.26423 | + | 5.26423i | 0.208577 | + | 0.208577i | ||||
\(638\) | 10.4308 | + | 10.4308i | 0.412961 | + | 0.412961i | ||||
\(639\) | −0.590452 | + | 0.722478i | −0.0233579 | + | 0.0285808i | ||||
\(640\) | 2.21815 | − | 0.282491i | 0.0876802 | − | 0.0111665i | ||||
\(641\) | 3.43192i | 0.135553i | 0.997701 | + | 0.0677764i | \(0.0215904\pi\) | ||||
−0.997701 | + | 0.0677764i | \(0.978410\pi\) | |||||||
\(642\) | −25.1537 | − | 8.97112i | −0.992739 | − | 0.354062i | ||||
\(643\) | 14.6003 | − | 14.6003i | 0.575778 | − | 0.575778i | −0.357959 | − | 0.933737i | \(-0.616527\pi\) |
0.933737 | + | 0.357959i | \(0.116527\pi\) | |||||||
\(644\) | 1.27801 | 0.0503607 | ||||||||
\(645\) | −5.32224 | − | 1.16735i | −0.209563 | − | 0.0459645i | ||||
\(646\) | −3.29927 | −0.129808 | ||||||||
\(647\) | −32.0282 | + | 32.0282i | −1.25916 | + | 1.25916i | −0.307662 | + | 0.951496i | \(0.599547\pi\) |
−0.951496 | + | 0.307662i | \(0.900453\pi\) | |||||||
\(648\) | 4.96945 | − | 7.50363i | 0.195219 | − | 0.294771i | ||||
\(649\) | − | 43.6413i | − | 1.71307i | ||||||
\(650\) | 5.16354 | − | 1.33688i | 0.202531 | − | 0.0524368i | ||||
\(651\) | −0.840857 | + | 0.398749i | −0.0329558 | + | 0.0156282i | ||||
\(652\) | −6.35109 | − | 6.35109i | −0.248728 | − | 0.248728i | ||||
\(653\) | −21.8830 | − | 21.8830i | −0.856346 | − | 0.856346i | 0.134559 | − | 0.990906i | \(-0.457038\pi\) |
−0.990906 | + | 0.134559i | \(0.957038\pi\) | |||||||
\(654\) | −1.49955 | + | 0.711114i | −0.0586371 | + | 0.0278067i | ||||
\(655\) | −39.0873 | − | 30.2561i | −1.52727 | − | 1.18220i | ||||
\(656\) | − | 10.3063i | − | 0.402395i | ||||||
\(657\) | −3.19072 | + | 0.320855i | −0.124482 | + | 0.0125177i | ||||
\(658\) | 0.710478 | − | 0.710478i | 0.0276973 | − | 0.0276973i | ||||
\(659\) | 9.03239 | 0.351852 | 0.175926 | − | 0.984403i | \(-0.443708\pi\) | ||||
0.175926 | + | 0.984403i | \(0.443708\pi\) | |||||||
\(660\) | −12.7928 | − | 19.9813i | −0.497958 | − | 0.777769i | ||||
\(661\) | −29.1658 | −1.13442 | −0.567210 | − | 0.823573i | \(-0.691977\pi\) | ||||
−0.567210 | + | 0.823573i | \(0.691977\pi\) | |||||||
\(662\) | −7.16494 | + | 7.16494i | −0.278473 | + | 0.278473i | ||||
\(663\) | −5.74175 | − | 2.04780i | −0.222991 | − | 0.0795301i | ||||
\(664\) | − | 15.8222i | − | 0.614020i | ||||||
\(665\) | −0.0410804 | − | 0.322567i | −0.00159303 | − | 0.0125086i | ||||
\(666\) | 12.0280 | + | 9.83000i | 0.466076 | + | 0.380905i | ||||
\(667\) | −14.9642 | − | 14.9642i | −0.579415 | − | 0.579415i | ||||
\(668\) | −14.9173 | − | 14.9173i | −0.577169 | − | 0.577169i | ||||
\(669\) | 8.88761 | + | 18.7416i | 0.343615 | + | 0.724593i | ||||
\(670\) | 8.47133 | − | 10.9440i | 0.327276 | − | 0.422802i | ||||
\(671\) | 63.3688i | 2.44633i | ||||||||
\(672\) | 0.0846123 | − | 0.237241i | 0.00326399 | − | 0.00915176i | ||||
\(673\) | 13.7053 | − | 13.7053i | 0.528300 | − | 0.528300i | −0.391765 | − | 0.920065i | \(-0.628135\pi\) |
0.920065 | + | 0.391765i | \(0.128135\pi\) | |||||||
\(674\) | 12.1618 | 0.468456 | ||||||||
\(675\) | −18.5718 | − | 18.1684i | −0.714827 | − | 0.699301i | ||||
\(676\) | 11.8620 | 0.456232 | ||||||||
\(677\) | 0.194042 | − | 0.194042i | 0.00745766 | − | 0.00745766i | −0.703368 | − | 0.710826i | \(-0.748321\pi\) |
0.710826 | + | 0.703368i | \(0.248321\pi\) | |||||||
\(678\) | 4.06660 | − | 11.4022i | 0.156177 | − | 0.437898i | ||||
\(679\) | − | 0.122457i | − | 0.00469946i | ||||||
\(680\) | −4.51578 | + | 5.83385i | −0.173172 | + | 0.223718i | ||||
\(681\) | 6.50923 | + | 13.7262i | 0.249434 | + | 0.525991i | ||||
\(682\) | −16.0043 | − | 16.0043i | −0.612836 | − | 0.612836i | ||||
\(683\) | −8.50150 | − | 8.50150i | −0.325301 | − | 0.325301i | 0.525495 | − | 0.850796i | \(-0.323880\pi\) |
−0.850796 | + | 0.525495i | \(0.823880\pi\) | |||||||
\(684\) | 2.32292 | + | 1.89843i | 0.0888192 | + | 0.0725882i | ||||
\(685\) | −0.633682 | − | 4.97574i | −0.0242117 | − | 0.190113i | ||||
\(686\) | − | 2.03283i | − | 0.0776137i | ||||||
\(687\) | 19.2695 | + | 6.87251i | 0.735178 | + | 0.262202i | ||||
\(688\) | 0.994803 | − | 0.994803i | 0.0379265 | − | 0.0379265i | ||||
\(689\) | 4.32162 | 0.164640 | ||||||||
\(690\) | 18.3526 | + | 28.6653i | 0.698673 | + | 1.09127i | ||||
\(691\) | −34.6840 | −1.31944 | −0.659721 | − | 0.751511i | \(-0.729325\pi\) | ||||
−0.659721 | + | 0.751511i | \(0.729325\pi\) | |||||||
\(692\) | 6.19199 | − | 6.19199i | 0.235384 | − | 0.235384i | ||||
\(693\) | −2.65912 | + | 0.267398i | −0.101012 | + | 0.0101576i | ||||
\(694\) | 11.1866i | 0.424639i | ||||||||
\(695\) | 19.7639 | + | 15.2986i | 0.749688 | + | 0.580307i | ||||
\(696\) | −3.76856 | + | 1.78712i | −0.142847 | + | 0.0677406i | ||||
\(697\) | 24.0440 | + | 24.0440i | 0.910732 | + | 0.910732i | ||||
\(698\) | 13.1405 | + | 13.1405i | 0.497376 | + | 0.497376i | ||||
\(699\) | −23.3301 | + | 11.0636i | −0.882427 | + | 0.418462i | ||||
\(700\) | −0.626598 | − | 0.368865i | −0.0236832 | − | 0.0139418i | ||||
\(701\) | − | 6.61547i | − | 0.249863i | −0.992165 | − | 0.124931i | \(-0.960129\pi\) | ||
0.992165 | − | 0.124931i | \(-0.0398711\pi\) | |||||||
\(702\) | 2.86428 | + | 4.74565i | 0.108105 | + | 0.179113i | ||||
\(703\) | −3.66137 | + | 3.66137i | −0.138091 | + | 0.138091i | ||||
\(704\) | 6.12593 | 0.230880 | ||||||||
\(705\) | 26.1384 | + | 5.73307i | 0.984430 | + | 0.215920i | ||||
\(706\) | 5.29865 | 0.199417 | ||||||||
\(707\) | −0.796928 | + | 0.796928i | −0.0299716 | + | 0.0299716i | ||||
\(708\) | 11.6221 | + | 4.14505i | 0.436786 | + | 0.155780i | ||||
\(709\) | − | 17.2370i | − | 0.647351i | −0.946168 | − | 0.323675i | \(-0.895081\pi\) | ||
0.946168 | − | 0.323675i | \(-0.104919\pi\) | |||||||
\(710\) | −0.689892 | + | 0.0878608i | −0.0258912 | + | 0.00329736i | ||||
\(711\) | 27.1679 | − | 33.2427i | 1.01888 | − | 1.24670i | ||||
\(712\) | 1.63328 | + | 1.63328i | 0.0612099 | + | 0.0612099i | ||||
\(713\) | 22.9599 | + | 22.9599i | 0.859856 | + | 0.859856i | ||||
\(714\) | 0.356073 | + | 0.750863i | 0.0133257 | + | 0.0281003i | ||||
\(715\) | 14.4954 | − | 1.84605i | 0.542096 | − | 0.0690383i | ||||
\(716\) | 8.96071i | 0.334877i | ||||||||
\(717\) | −3.64996 | + | 10.2340i | −0.136310 | + | 0.382195i | ||||
\(718\) | 12.1340 | − | 12.1340i | 0.452838 | − | 0.452838i | ||||
\(719\) | −16.3498 | −0.609746 | −0.304873 | − | 0.952393i | \(-0.598614\pi\) | ||||
−0.304873 | + | 0.952393i | \(0.598614\pi\) | |||||||
\(720\) | 6.53627 | − | 1.50903i | 0.243592 | − | 0.0562381i | ||||
\(721\) | −2.30605 | −0.0858819 | ||||||||
\(722\) | −0.707107 | + | 0.707107i | −0.0263158 | + | 0.0263158i | ||||
\(723\) | −7.76321 | + | 21.7669i | −0.288717 | + | 0.809521i | ||||
\(724\) | − | 8.58326i | − | 0.318994i | ||||||
\(725\) | 3.01779 | + | 11.6558i | 0.112078 | + | 0.432887i | ||||
\(726\) | −19.6870 | − | 41.5147i | −0.730654 | − | 1.54076i | ||||
\(727\) | −33.8444 | − | 33.8444i | −1.25522 | − | 1.25522i | −0.953349 | − | 0.301871i | \(-0.902389\pi\) |
−0.301871 | − | 0.953349i | \(-0.597611\pi\) | |||||||
\(728\) | 0.109693 | + | 0.109693i | 0.00406550 | + | 0.00406550i | ||||
\(729\) | 12.5812 | − | 23.8896i | 0.465972 | − | 0.884800i | ||||
\(730\) | −1.89012 | − | 1.46308i | −0.0699565 | − | 0.0541509i | ||||
\(731\) | 4.64163i | 0.171677i | ||||||||
\(732\) | −16.8758 | − | 6.01877i | −0.623747 | − | 0.222460i | ||||
\(733\) | −8.42136 | + | 8.42136i | −0.311050 | + | 0.311050i | −0.845316 | − | 0.534266i | \(-0.820588\pi\) |
0.534266 | + | 0.845316i | \(0.320588\pi\) | |||||||
\(734\) | 34.8649 | 1.28689 | ||||||||
\(735\) | 22.7633 | − | 14.5739i | 0.839636 | − | 0.537567i | ||||
\(736\) | −8.78832 | −0.323942 | ||||||||
\(737\) | 26.8099 | − | 26.8099i | 0.987554 | − | 0.987554i | ||||
\(738\) | −3.09357 | − | 30.7638i | −0.113876 | − | 1.13243i | ||||
\(739\) | 18.4254i | 0.677788i | 0.940825 | + | 0.338894i | \(0.110053\pi\) | ||||
−0.940825 | + | 0.338894i | \(0.889947\pi\) | |||||||
\(740\) | 1.46273 | + | 11.4855i | 0.0537710 | + | 0.422216i | ||||
\(741\) | −1.66947 | + | 0.791694i | −0.0613296 | + | 0.0290836i | ||||
\(742\) | −0.416576 | − | 0.416576i | −0.0152930 | − | 0.0152930i | ||||
\(743\) | 27.2664 | + | 27.2664i | 1.00031 | + | 1.00031i | 1.00000 | 0.000307644i | \(9.79262e-5\pi\) | |
0.000307644 | 1.00000i | \(0.499902\pi\) | ||||||||
\(744\) | 5.78220 | − | 2.74202i | 0.211986 | − | 0.100527i | ||||
\(745\) | 13.4982 | − | 17.4381i | 0.494537 | − | 0.638883i | ||||
\(746\) | 15.5260i | 0.568446i | ||||||||
\(747\) | −4.74923 | − | 47.2284i | −0.173765 | − | 1.72800i | ||||
\(748\) | −14.2914 | + | 14.2914i | −0.522546 | + | 0.522546i | ||||
\(749\) | −2.24219 | −0.0819277 | ||||||||
\(750\) | −0.724644 | − | 19.3514i | −0.0264603 | − | 0.706612i | ||||
\(751\) | 29.9776 | 1.09390 | 0.546949 | − | 0.837166i | \(-0.315789\pi\) | ||||
0.546949 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(752\) | −4.88564 | + | 4.88564i | −0.178161 | + | 0.178161i | ||||
\(753\) | 43.6923 | + | 15.5829i | 1.59224 | + | 0.567874i | ||||
\(754\) | − | 2.56879i | − | 0.0935497i | ||||||
\(755\) | −10.8145 | + | 13.9710i | −0.393579 | + | 0.508458i | ||||
\(756\) | 0.181352 | − | 0.733548i | 0.00659572 | − | 0.0266789i | ||||
\(757\) | 14.2204 | + | 14.2204i | 0.516851 | + | 0.516851i | 0.916617 | − | 0.399766i | \(-0.130909\pi\) |
−0.399766 | + | 0.916617i | \(0.630909\pi\) | |||||||
\(758\) | −22.5476 | − | 22.5476i | −0.818966 | − | 0.818966i | ||||
\(759\) | 39.9548 | + | 84.2541i | 1.45027 | + | 3.05823i | ||||
\(760\) | 0.282491 | + | 2.21815i | 0.0102470 | + | 0.0804608i | ||||
\(761\) | − | 25.8646i | − | 0.937590i | −0.883307 | − | 0.468795i | \(-0.844688\pi\) | ||
0.883307 | − | 0.468795i | \(-0.155312\pi\) | |||||||
\(762\) | −7.24291 | + | 20.3081i | −0.262383 | + | 0.735685i | ||||
\(763\) | −0.0985285 | + | 0.0985285i | −0.00356697 | + | 0.00356697i | ||||
\(764\) | 15.3727 | 0.556164 | ||||||||
\(765\) | −11.7282 | + | 18.7692i | −0.424036 | + | 0.678601i | ||||
\(766\) | 5.25871 | 0.190005 | ||||||||
\(767\) | −5.37374 | + | 5.37374i | −0.194034 | + | 0.194034i | ||||
\(768\) | −0.581841 | + | 1.63140i | −0.0209954 | + | 0.0588680i | ||||
\(769\) | − | 3.81692i | − | 0.137642i | −0.997629 | − | 0.0688208i | \(-0.978076\pi\) | ||
0.997629 | − | 0.0688208i | \(-0.0219237\pi\) | |||||||
\(770\) | −1.57521 | − | 1.21931i | −0.0567666 | − | 0.0439410i | ||||
\(771\) | 6.50988 | + | 13.7276i | 0.234448 | + | 0.494388i | ||||
\(772\) | −16.5440 | − | 16.5440i | −0.595433 | − | 0.595433i | ||||
\(773\) | −13.3692 | − | 13.3692i | −0.480857 | − | 0.480857i | 0.424549 | − | 0.905405i | \(-0.360433\pi\) |
−0.905405 | + | 0.424549i | \(0.860433\pi\) | |||||||
\(774\) | 2.67083 | − | 3.26804i | 0.0960010 | − | 0.117467i | ||||
\(775\) | −4.63027 | − | 17.8838i | −0.166324 | − | 0.642406i | ||||
\(776\) | 0.842081i | 0.0302289i | ||||||||
\(777\) | 1.22842 | + | 0.438119i | 0.0440695 | + | 0.0157174i | ||||
\(778\) | 19.5781 | − | 19.5781i | 0.701908 | − | 0.701908i | ||||
\(779\) | 10.3063 | 0.369263 | ||||||||
\(780\) | −0.885149 | + | 4.03561i | −0.0316934 | + | 0.144498i | ||||
\(781\) | −1.90529 | −0.0681768 | ||||||||
\(782\) | 20.5026 | − | 20.5026i | 0.733171 | − | 0.733171i | ||||
\(783\) | −10.7125 | + | 6.46563i | −0.382834 | + | 0.231063i | ||||
\(784\) | 6.97885i | 0.249245i | ||||||||
\(785\) | 12.4341 | − | 1.58353i | 0.443791 | − | 0.0565187i | ||||
\(786\) | 34.5949 | − | 16.4055i | 1.23396 | − | 0.585166i | ||||
\(787\) | −22.7110 | − | 22.7110i | −0.809561 | − | 0.809561i | 0.175006 | − | 0.984567i | \(-0.444005\pi\) |
−0.984567 | + | 0.175006i | \(0.944005\pi\) | |||||||
\(788\) | −3.02772 | − | 3.02772i | −0.107858 | − | 0.107858i | ||||
\(789\) | −23.6986 | + | 11.2383i | −0.843691 | + | 0.400093i | ||||
\(790\) | 31.7434 | − | 4.04266i | 1.12938 | − | 0.143831i | ||||
\(791\) | − | 1.01638i | − | 0.0361384i | ||||||
\(792\) | 18.2856 | − | 1.83877i | 0.649750 | − | 0.0653380i | ||||
\(793\) | 7.80288 | − | 7.80288i | 0.277088 | − | 0.277088i | ||||
\(794\) | −0.916384 | −0.0325213 | ||||||||
\(795\) | 3.36148 | − | 15.3258i | 0.119219 | − | 0.543550i | ||||
\(796\) | −8.01713 | −0.284160 | ||||||||
\(797\) | −3.31221 | + | 3.31221i | −0.117325 | + | 0.117325i | −0.763332 | − | 0.646007i | \(-0.776438\pi\) |
0.646007 | + | 0.763332i | \(0.276438\pi\) | |||||||
\(798\) | 0.237241 | + | 0.0846123i | 0.00839823 | + | 0.00299524i | ||||
\(799\) | − | 22.7958i | − | 0.806458i | ||||||
\(800\) | 4.30884 | + | 2.53652i | 0.152340 | + | 0.0896795i | ||||
\(801\) | 5.36552 | + | 4.38502i | 0.189581 | + | 0.154937i | ||||
\(802\) | −20.4577 | − | 20.4577i | −0.722385 | − | 0.722385i | ||||
\(803\) | −4.63031 | − | 4.63031i | −0.163400 | − | 0.163400i | ||||
\(804\) | 4.59334 | + | 9.68614i | 0.161995 | + | 0.341604i | ||||
\(805\) | 2.25981 | + | 1.74924i | 0.0796478 | + | 0.0616526i | ||||
\(806\) | 3.94136i | 0.138828i | ||||||||
\(807\) | −4.30494 | + | 12.0704i | −0.151541 | + | 0.424899i | ||||
\(808\) | 5.48012 | − | 5.48012i | 0.192790 | − | 0.192790i | ||||
\(809\) | −7.82368 | −0.275066 | −0.137533 | − | 0.990497i | \(-0.543917\pi\) | ||||
−0.137533 | + | 0.990497i | \(0.543917\pi\) | |||||||
\(810\) | 19.0575 | − | 6.46631i | 0.669611 | − | 0.227203i | ||||
\(811\) | 0.275979 | 0.00969094 | 0.00484547 | − | 0.999988i | \(-0.498458\pi\) | ||||
0.00484547 | + | 0.999988i | \(0.498458\pi\) | |||||||
\(812\) | −0.247615 | + | 0.247615i | −0.00868957 | + | 0.00868957i | ||||
\(813\) | 18.7655 | − | 52.6159i | 0.658136 | − | 1.84532i | ||||
\(814\) | 31.7199i | 1.11178i | ||||||||
\(815\) | −2.53728 | − | 19.9230i | −0.0888770 | − | 0.697872i | ||||
\(816\) | −2.44855 | − | 5.16335i | −0.0857165 | − | 0.180753i | ||||
\(817\) | 0.994803 | + | 0.994803i | 0.0348037 | + | 0.0348037i | ||||
\(818\) | −10.9786 | − | 10.9786i | −0.383859 | − | 0.383859i | ||||
\(819\) | 0.360354 | + | 0.294503i | 0.0125918 | + | 0.0102908i | ||||
\(820\) | 14.1065 | − | 18.2239i | 0.492619 | − | 0.636405i | ||||
\(821\) | − | 19.8023i | − | 0.691106i | −0.938399 | − | 0.345553i | \(-0.887691\pi\) | ||
0.938399 | − | 0.345553i | \(-0.112309\pi\) | |||||||
\(822\) | 3.65954 | + | 1.30518i | 0.127641 | + | 0.0455234i | ||||
\(823\) | −26.0210 | + | 26.0210i | −0.907036 | + | 0.907036i | −0.996032 | − | 0.0889960i | \(-0.971634\pi\) |
0.0889960 | + | 0.996032i | \(0.471634\pi\) | |||||||
\(824\) | 15.8577 | 0.552429 | ||||||||
\(825\) | 4.72826 | − | 52.8410i | 0.164617 | − | 1.83969i | ||||
\(826\) | 1.03599 | 0.0360466 | ||||||||
\(827\) | −7.10260 | + | 7.10260i | −0.246982 | + | 0.246982i | −0.819731 | − | 0.572749i | \(-0.805877\pi\) |
0.572749 | + | 0.819731i | \(0.305877\pi\) | |||||||
\(828\) | −26.2327 | + | 2.63792i | −0.911648 | + | 0.0916742i | ||||
\(829\) | − | 40.2350i | − | 1.39742i | −0.715406 | − | 0.698709i | \(-0.753758\pi\) | ||
0.715406 | − | 0.698709i | \(-0.246242\pi\) | |||||||
\(830\) | 21.6561 | − | 27.9772i | 0.751696 | − | 0.971101i | ||||
\(831\) | −0.698745 | + | 0.331357i | −0.0242392 | + | 0.0114947i | ||||
\(832\) | −0.754312 | − | 0.754312i | −0.0261511 | − | 0.0261511i | ||||
\(833\) | −16.2812 | − | 16.2812i | −0.564111 | − | 0.564111i | ||||
\(834\) | −17.4924 | + | 8.29521i | −0.605713 | + | 0.287240i | ||||
\(835\) | −5.95952 | − | 46.7948i | −0.206238 | − | 1.61940i | ||||
\(836\) | 6.12593i | 0.211870i | ||||||||
\(837\) | 16.4365 | − | 9.92039i | 0.568129 | − | 0.342899i | ||||
\(838\) | 4.92259 | − | 4.92259i | 0.170048 | − | 0.170048i | ||||
\(839\) | 7.79127 | 0.268984 | 0.134492 | − | 0.990915i | \(-0.457060\pi\) | ||||
0.134492 | + | 0.990915i | \(0.457060\pi\) | |||||||
\(840\) | 0.474329 | − | 0.303684i | 0.0163659 | − | 0.0104781i | ||||
\(841\) | −23.2014 | −0.800048 | ||||||||
\(842\) | −20.8054 | + | 20.8054i | −0.717000 | + | 0.717000i | ||||
\(843\) | 3.68564 | + | 1.31449i | 0.126940 | + | 0.0452734i | ||||
\(844\) | 4.50891i | 0.155203i | ||||||||
\(845\) | 20.9747 | + | 16.2358i | 0.721551 | + | 0.558528i | ||||
\(846\) | −13.1169 | + | 16.0499i | −0.450968 | + | 0.551806i | ||||
\(847\) | −2.72774 | − | 2.72774i | −0.0937262 | − | 0.0937262i | ||||
\(848\) | 2.86461 | + | 2.86461i | 0.0983710 | + | 0.0983710i | ||||
\(849\) | −18.2051 | − | 38.3898i | −0.624799 | − | 1.31754i | ||||
\(850\) | −15.9698 | + | 4.13471i | −0.547759 | + | 0.141819i | ||||
\(851\) | − | 45.5056i | − | 1.55991i | ||||||
\(852\) | 0.180965 | − | 0.507400i | 0.00619975 | − | 0.0173832i | ||||
\(853\) | −27.5401 | + | 27.5401i | −0.942956 | + | 0.942956i | −0.998459 | − | 0.0555025i | \(-0.982324\pi\) |
0.0555025 | + | 0.998459i | \(0.482324\pi\) | |||||||
\(854\) | −1.50429 | −0.0514759 | ||||||||
\(855\) | 1.50903 | + | 6.53627i | 0.0516076 | + | 0.223536i | ||||
\(856\) | 15.4185 | 0.526994 | ||||||||
\(857\) | −12.3126 | + | 12.3126i | −0.420590 | + | 0.420590i | −0.885407 | − | 0.464817i | \(-0.846120\pi\) |
0.464817 | + | 0.885407i | \(0.346120\pi\) | |||||||
\(858\) | −3.80227 | + | 10.6610i | −0.129807 | + | 0.363961i | ||||
\(859\) | 6.21722i | 0.212129i | 0.994359 | + | 0.106064i | \(0.0338250\pi\) | ||||
−0.994359 | + | 0.106064i | \(0.966175\pi\) | |||||||
\(860\) | 3.12064 | − | 0.397427i | 0.106413 | − | 0.0135521i | ||||
\(861\) | −1.11231 | − | 2.34556i | −0.0379073 | − | 0.0799365i | ||||
\(862\) | 13.9141 | + | 13.9141i | 0.473917 | + | 0.473917i | ||||
\(863\) | 31.4921 | + | 31.4921i | 1.07200 | + | 1.07200i | 0.997198 | + | 0.0748042i | \(0.0238332\pi\) |
0.0748042 | + | 0.997198i | \(0.476167\pi\) | |||||||
\(864\) | −1.24708 | + | 5.04428i | −0.0424265 | + | 0.171610i | ||||
\(865\) | 19.4239 | − | 2.47372i | 0.660433 | − | 0.0841090i | ||||
\(866\) | 31.4884i | 1.07002i | ||||||||
\(867\) | −9.97568 | − | 3.55784i | −0.338792 | − | 0.120831i | ||||
\(868\) | 0.379921 | − | 0.379921i | 0.0128954 | − | 0.0128954i | ||||
\(869\) | 87.6666 | 2.97389 | ||||||||
\(870\) | −9.10971 | − | 1.99808i | −0.308848 | − | 0.0677412i | ||||
\(871\) | −6.60243 | −0.223715 | ||||||||
\(872\) | 0.677536 | − | 0.677536i | 0.0229443 | − | 0.0229443i | ||||
\(873\) | 0.252761 | + | 2.51357i | 0.00855466 | + | 0.0850713i | ||||
\(874\) | − | 8.78832i | − | 0.297269i | ||||||
\(875\) | −0.603092 | − | 1.50987i | −0.0203882 | − | 0.0510430i | ||||
\(876\) | 1.67288 | − | 0.793312i | 0.0565215 | − | 0.0268035i | ||||
\(877\) | −18.1228 | − | 18.1228i | −0.611965 | − | 0.611965i | 0.331493 | − | 0.943458i | \(-0.392448\pi\) |
−0.943458 | + | 0.331493i | \(0.892448\pi\) | |||||||
\(878\) | 1.38955 | + | 1.38955i | 0.0468950 | + | 0.0468950i | ||||
\(879\) | 3.04264 | − | 1.44287i | 0.102626 | − | 0.0486670i | ||||
\(880\) | 10.8320 | + | 8.38468i | 0.365147 | + | 0.282647i | ||||
\(881\) | − | 11.5979i | − | 0.390744i | −0.980729 | − | 0.195372i | \(-0.937409\pi\) | ||
0.980729 | − | 0.195372i | \(-0.0625915\pi\) | |||||||
\(882\) | 2.09479 | + | 20.8315i | 0.0705352 | + | 0.701433i | ||||
\(883\) | −9.62477 | + | 9.62477i | −0.323899 | + | 0.323899i | −0.850261 | − | 0.526362i | \(-0.823556\pi\) |
0.526362 | + | 0.850261i | \(0.323556\pi\) | |||||||
\(884\) | 3.51953 | 0.118374 | ||||||||
\(885\) | 14.8771 | + | 23.2368i | 0.500088 | + | 0.781096i | ||||
\(886\) | −14.5226 | −0.487896 | ||||||||
\(887\) | −28.5533 | + | 28.5533i | −0.958726 | + | 0.958726i | −0.999181 | − | 0.0404558i | \(-0.987119\pi\) |
0.0404558 | + | 0.999181i | \(0.487119\pi\) | |||||||
\(888\) | −8.44733 | − | 3.01275i | −0.283474 | − | 0.101101i | ||||
\(889\) | 1.81025i | 0.0607138i | ||||||||
\(890\) | 0.652502 | + | 5.12352i | 0.0218719 | + | 0.171741i | ||||
\(891\) | 54.0295 | − | 10.9773i | 1.81006 | − | 0.367753i | ||||
\(892\) | −8.46796 | − | 8.46796i | −0.283528 | − | 0.283528i | ||||
\(893\) | −4.88564 | − | 4.88564i | −0.163492 | − | 0.163492i | ||||
\(894\) | 7.31904 | + | 15.4339i | 0.244785 | + | 0.516187i | ||||
\(895\) | −12.2647 | + | 15.8445i | −0.409963 | + | 0.529624i | ||||
\(896\) | 0.145422i | 0.00485820i | ||||||||
\(897\) | 5.45477 | − | 15.2944i | 0.182129 | − | 0.510665i | ||||
\(898\) | −20.3061 | + | 20.3061i | −0.677623 | + | 0.677623i | ||||
\(899\) | −8.89696 | −0.296730 | ||||||||
\(900\) | 13.6230 | + | 6.27802i | 0.454100 | + | 0.209267i | ||||
\(901\) | −13.3659 | −0.445283 | ||||||||
\(902\) | 44.6438 | − | 44.6438i | 1.48648 | − | 1.48648i | ||||
\(903\) | 0.119038 | − | 0.333765i | 0.00396133 | − | 0.0111070i | ||||
\(904\) | 6.98920i | 0.232457i | ||||||||
\(905\) | 11.7481 | − | 15.1771i | 0.390519 | − | 0.504504i | ||||
\(906\) | −5.86385 | − | 12.3653i | −0.194813 | − | 0.410810i | ||||
\(907\) | 34.8096 | + | 34.8096i | 1.15583 | + | 1.15583i | 0.985363 | + | 0.170470i | \(0.0545287\pi\) |
0.170470 | + | 0.985363i | \(0.445471\pi\) | |||||||
\(908\) | −6.20188 | − | 6.20188i | −0.205817 | − | 0.205817i | ||||
\(909\) | 14.7129 | − | 18.0028i | 0.487997 | − | 0.597115i | ||||
\(910\) | 0.0438228 | + | 0.344101i | 0.00145271 | + | 0.0114069i | ||||
\(911\) | 39.4916i | 1.30842i | 0.756315 | + | 0.654208i | \(0.226998\pi\) | ||||
−0.756315 | + | 0.654208i | \(0.773002\pi\) | |||||||
\(912\) | −1.63140 | − | 0.581841i | −0.0540210 | − | 0.0192667i | ||||
\(913\) | 68.5368 | − | 68.5368i | 2.26824 | − | 2.26824i | ||||
\(914\) | 18.4793 | 0.611239 | ||||||||
\(915\) | −21.6021 | − | 33.7407i | −0.714144 | − | 1.11543i | ||||
\(916\) | −11.8117 | −0.390268 | ||||||||
\(917\) | 2.27307 | − | 2.27307i | 0.0750634 | − | 0.0750634i | ||||
\(918\) | −8.85864 | − | 14.6774i | −0.292379 | − | 0.484425i | ||||
\(919\) | − | 42.8370i | − | 1.41306i | −0.707683 | − | 0.706530i | \(-0.750259\pi\) | ||
0.707683 | − | 0.706530i | \(-0.249741\pi\) | |||||||
\(920\) | −15.5397 | − | 12.0287i | −0.512329 | − | 0.396576i | ||||
\(921\) | −5.49027 | + | 2.60358i | −0.180910 | + | 0.0857910i | ||||
\(922\) | −25.2425 | − | 25.2425i | −0.831316 | − | 0.831316i | ||||
\(923\) | 0.234607 | + | 0.234607i | 0.00772219 | + | 0.00772219i | ||||
\(924\) | 1.39417 | − | 0.661138i | 0.0458647 | − | 0.0217499i | ||||
\(925\) | −13.1340 | + | 22.3110i | −0.431844 | + | 0.733581i | ||||
\(926\) | 26.5468i | 0.872381i | ||||||||
\(927\) | 47.3344 | − | 4.75988i | 1.55466 | − | 0.156335i | ||||
\(928\) | 1.70274 | − | 1.70274i | 0.0558950 | − | 0.0558950i | ||||
\(929\) | 15.7833 | 0.517832 | 0.258916 | − | 0.965900i | \(-0.416635\pi\) | ||||
0.258916 | + | 0.965900i | \(0.416635\pi\) | |||||||
\(930\) | 13.9773 | + | 3.06570i | 0.458333 | + | 0.100528i | ||||
\(931\) | −6.97885 | −0.228723 | ||||||||
\(932\) | 10.5412 | − | 10.5412i | 0.345287 | − | 0.345287i | ||||
\(933\) | −2.87458 | − | 1.02522i | −0.0941095 | − | 0.0335643i | ||||
\(934\) | − | 7.09471i | − | 0.232146i | ||||||
\(935\) | −44.8313 | + | 5.70946i | −1.46614 | + | 0.186719i | ||||
\(936\) | −2.47800 | − | 2.02517i | −0.0809959 | − | 0.0661946i | ||||
\(937\) | −35.2671 | − | 35.2671i | −1.15213 | − | 1.15213i | −0.986126 | − | 0.166000i | \(-0.946915\pi\) |
−0.166000 | − | 0.986126i | \(-0.553085\pi\) | |||||||
\(938\) | 0.636431 | + | 0.636431i | 0.0207802 | + | 0.0207802i | ||||
\(939\) | −10.0549 | − | 21.2031i | −0.328129 | − | 0.691938i | ||||
\(940\) | −15.3260 | + | 1.95183i | −0.499878 | + | 0.0636617i | ||||
\(941\) | − | 20.0837i | − | 0.654710i | −0.944901 | − | 0.327355i | \(-0.893843\pi\) | ||
0.944901 | − | 0.327355i | \(-0.106157\pi\) | |||||||
\(942\) | −3.26157 | + | 9.14497i | −0.106268 | + | 0.297959i | ||||
\(943\) | −64.0464 | + | 64.0464i | −2.08564 | + | 2.08564i | ||||
\(944\) | −7.12402 | −0.231867 | ||||||||
\(945\) | 1.32469 | − | 1.04886i | 0.0430922 | − | 0.0341193i | ||||
\(946\) | 8.61835 | 0.280207 | ||||||||
\(947\) | −9.64395 | + | 9.64395i | −0.313386 | + | 0.313386i | −0.846220 | − | 0.532834i | \(-0.821127\pi\) |
0.532834 | + | 0.846220i | \(0.321127\pi\) | |||||||
\(948\) | −8.32658 | + | 23.3465i | −0.270435 | + | 0.758260i | ||||
\(949\) | 1.14030i | 0.0370157i | ||||||||
\(950\) | −2.53652 | + | 4.30884i | −0.0822955 | + | 0.139797i | ||||
\(951\) | −8.21229 | − | 17.3176i | −0.266302 | − | 0.561560i | ||||
\(952\) | −0.339260 | − | 0.339260i | −0.0109955 | − | 0.0109955i | ||||
\(953\) | −38.7018 | − | 38.7018i | −1.25368 | − | 1.25368i | −0.954060 | − | 0.299616i | \(-0.903142\pi\) |
−0.299616 | − | 0.954060i | \(-0.596858\pi\) | |||||||
\(954\) | 9.41054 | + | 7.69085i | 0.304678 | + | 0.249000i | ||||
\(955\) | 27.1823 | + | 21.0409i | 0.879599 | + | 0.680867i | ||||
\(956\) | − | 6.27313i | − | 0.202887i | ||||||
\(957\) | −24.0655 | − | 8.58299i | −0.777926 | − | 0.277449i | ||||
\(958\) | −4.41971 | + | 4.41971i | −0.142794 | + | 0.142794i | ||||
\(959\) | 0.326208 | 0.0105338 | ||||||||
\(960\) | −3.26175 | + | 2.08830i | −0.105273 | + | 0.0673995i | ||||
\(961\) | −17.3492 | −0.559650 | ||||||||
\(962\) | 3.90580 | − | 3.90580i | 0.125928 | − | 0.125928i | ||||
\(963\) | 46.0234 | − | 4.62806i | 1.48308 | − | 0.149137i | ||||
\(964\) | − | 13.3425i | − | 0.429733i | ||||||
\(965\) | −6.60940 | − | 51.8977i | −0.212764 | − | 1.67065i | ||||
\(966\) | −2.00008 | + | 0.948476i | −0.0643516 | + | 0.0305167i | ||||
\(967\) | −16.1280 | − | 16.1280i | −0.518642 | − | 0.518642i | 0.398519 | − | 0.917160i | \(-0.369524\pi\) |
−0.917160 | + | 0.398519i | \(0.869524\pi\) | |||||||
\(968\) | 18.7574 | + | 18.7574i | 0.602887 | + | 0.602887i | ||||
\(969\) | 5.16335 | − | 2.44855i | 0.165871 | − | 0.0786588i | ||||
\(970\) | −1.15257 | + | 1.48899i | −0.0370068 | + | 0.0478084i | ||||
\(971\) | 33.4314i | 1.07286i | 0.843943 | + | 0.536432i | \(0.180228\pi\) | ||||
−0.843943 | + | 0.536432i | \(0.819772\pi\) | |||||||
\(972\) | −2.20836 | + | 15.4312i | −0.0708332 | + | 0.494957i | ||||
\(973\) | −1.14934 | + | 1.14934i | −0.0368463 | + | 0.0368463i | ||||
\(974\) | −16.1342 | −0.516973 | ||||||||
\(975\) | −7.08875 | + | 5.92433i | −0.227022 | + | 0.189730i | ||||
\(976\) | 10.3444 | 0.331115 | ||||||||
\(977\) | −28.5627 | + | 28.5627i | −0.913800 | + | 0.913800i | −0.996569 | − | 0.0827686i | \(-0.973624\pi\) |
0.0827686 | + | 0.996569i | \(0.473624\pi\) | |||||||
\(978\) | 14.6529 | + | 5.22598i | 0.468548 | + | 0.167108i | ||||
\(979\) | 14.1498i | 0.452228i | ||||||||
\(980\) | −9.55209 | + | 12.3402i | −0.305130 | + | 0.394192i | ||||
\(981\) | 1.81904 | − | 2.22578i | 0.0580774 | − | 0.0710637i | ||||
\(982\) | −7.26507 | − | 7.26507i | −0.231838 | − | 0.231838i | ||||
\(983\) | −23.2189 | − | 23.2189i | −0.740569 | − | 0.740569i | 0.232119 | − | 0.972687i | \(-0.425434\pi\) |
−0.972687 | + | 0.232119i | \(0.925434\pi\) | |||||||
\(984\) | 7.64884 | + | 16.1294i | 0.243836 | + | 0.514186i | ||||
\(985\) | −1.20958 | − | 9.49777i | −0.0385405 | − | 0.302624i | ||||
\(986\) | 7.94475i | 0.253012i | ||||||||
\(987\) | −0.584615 | + | 1.63918i | −0.0186085 | + | 0.0521756i | ||||
\(988\) | 0.754312 | − | 0.754312i | 0.0239979 | − | 0.0239979i | ||||
\(989\) | −12.3640 | −0.393151 | ||||||||
\(990\) | 34.8497 | + | 21.7764i | 1.10760 | + | 0.692101i | ||||
\(991\) | −8.55119 | −0.271638 | −0.135819 | − | 0.990734i | \(-0.543366\pi\) | ||||
−0.135819 | + | 0.990734i | \(0.543366\pi\) | |||||||
\(992\) | −2.61255 | + | 2.61255i | −0.0829486 | + | 0.0829486i | ||||
\(993\) | 5.89565 | − | 16.5306i | 0.187093 | − | 0.524582i | ||||
\(994\) | − | 0.0452292i | − | 0.00143458i | ||||||
\(995\) | −14.1761 | − | 10.9732i | −0.449412 | − | 0.347874i | ||||
\(996\) | 11.7424 | + | 24.7617i | 0.372073 | + | 0.784604i | ||||
\(997\) | 13.6217 | + | 13.6217i | 0.431402 | + | 0.431402i | 0.889105 | − | 0.457703i | \(-0.151328\pi\) |
−0.457703 | + | 0.889105i | \(0.651328\pi\) | |||||||
\(998\) | 18.6199 | + | 18.6199i | 0.589404 | + | 0.589404i | ||||
\(999\) | −26.1191 | − | 6.45733i | −0.826373 | − | 0.204301i |
(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.k.b.77.12 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.77.2 | ✓ | 36 | |
5.3 | odd | 4 | inner | 570.2.k.b.533.2 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.b.533.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.2 | ✓ | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.77.12 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.533.2 | yes | 36 | 5.3 | odd | 4 | inner | |
570.2.k.b.533.12 | yes | 36 | 15.8 | even | 4 | inner |