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 | 533.12 | ||
Character | \(\chi\) | \(=\) | 570.533 |
Dual form | 570.2.k.b.77.12 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | −0.687407 | − | 0.726272i | \(-0.741251\pi\) |
0.726272 | + | 0.687407i | \(0.241251\pi\) | |||||||
\(8\) | −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 | \(0.374700\pi\) | ||||
−0.383553 | + | 0.923519i | \(0.625300\pi\) | |||||||
\(12\) | 1.63140 | − | 0.581841i | 0.470944 | − | 0.167963i | ||||
\(13\) | −0.754312 | − | 0.754312i | −0.209209 | − | 0.209209i | 0.594722 | − | 0.803931i | \(-0.297262\pi\) |
−0.803931 | + | 0.594722i | \(0.797262\pi\) | |||||||
\(14\) | 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 | 0.930955 | − | 0.365134i | \(-0.118977\pi\) |
−0.365134 | + | 0.930955i | \(0.618977\pi\) | |||||||
\(18\) | −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 | 0.364604 | − | 0.931163i | \(-0.381204\pi\) |
0.931163 | − | 0.364604i | \(-0.118796\pi\) | |||||||
\(24\) | 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 | −0.940823 | − | 0.338897i | \(-0.889946\pi\) |
0.338897 | + | 0.940823i | \(0.389946\pi\) | |||||||
\(38\) | −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 | \(-0.702278\pi\) | ||
0.593561 | − | 0.804789i | \(-0.297722\pi\) | |||||||
\(42\) | −0.0846123 | − | 0.237241i | −0.0130560 | − | 0.0366070i | ||||
\(43\) | −0.994803 | − | 0.994803i | −0.151706 | − | 0.151706i | 0.627174 | − | 0.778880i | \(-0.284212\pi\) |
−0.778880 | + | 0.627174i | \(0.784212\pi\) | |||||||
\(44\) | −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 | 0.967088 | − | 0.254443i | \(-0.0818922\pi\) |
−0.254443 | + | 0.967088i | \(0.581892\pi\) | |||||||
\(48\) | 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 | −0.875927 | − | 0.482443i | \(-0.839749\pi\) |
0.482443 | + | 0.875927i | \(0.339749\pi\) | |||||||
\(54\) | 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 | −0.387289 | − | 0.921958i | \(-0.626589\pi\) |
0.921958 | + | 0.387289i | \(0.126589\pi\) | |||||||
\(68\) | −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 | \(0.00587497\pi\) | ||||
−0.999830 | + | 0.0184557i | \(0.994125\pi\) | |||||||
\(72\) | 0.300162 | − | 2.98495i | 0.0353745 | − | 0.351779i | ||||
\(73\) | 0.755853 | + | 0.755853i | 0.0884659 | + | 0.0884659i | 0.749955 | − | 0.661489i | \(-0.230075\pi\) |
−0.661489 | + | 0.749955i | \(0.730075\pi\) | |||||||
\(74\) | −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 | \(-0.702143\pi\) | ||
0.593218 | − | 0.805042i | \(-0.297857\pi\) | |||||||
\(80\) | −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 | 0.263337 | − | 0.964704i | \(-0.415177\pi\) |
0.964704 | − | 0.263337i | \(-0.0848230\pi\) | |||||||
\(84\) | 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 | −0.736689 | − | 0.676231i | \(-0.763612\pi\) |
0.676231 | + | 0.736689i | \(0.263612\pi\) | |||||||
\(98\) | −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 | \(-0.874001\pi\) | ||
0.922674 | − | 0.385580i | \(-0.125999\pi\) | |||||||
\(102\) | 5.38243 | − | 1.91965i | 0.532940 | − | 0.190074i | ||||
\(103\) | −11.2131 | − | 11.2131i | −1.10486 | − | 1.10486i | −0.993816 | − | 0.111042i | \(-0.964581\pi\) |
−0.111042 | − | 0.993816i | \(-0.535419\pi\) | |||||||
\(104\) | 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 | −0.998457 | − | 0.0555308i | \(-0.982315\pi\) |
−0.0555308 | − | 0.998457i | \(-0.517685\pi\) | |||||||
\(108\) | −2.68503 | + | 4.44866i | −0.258367 | + | 0.428073i | ||||
\(109\) | − | 0.958181i | − | 0.0917771i | −0.998947 | − | 0.0458886i | \(-0.985388\pi\) | ||
0.998947 | − | 0.0458886i | \(-0.0146119\pi\) | |||||||
\(110\) | −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 | −0.900262 | − | 0.435348i | \(-0.856625\pi\) |
0.435348 | + | 0.900262i | \(0.356625\pi\) | |||||||
\(114\) | 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 | −0.198938 | − | 0.980012i | \(-0.563749\pi\) |
0.980012 | + | 0.198938i | \(0.0637492\pi\) | |||||||
\(128\) | 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 | \(0.416365\pi\) | ||||
−0.259735 | + | 0.965680i | \(0.583635\pi\) | |||||||
\(132\) | 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 | 0.771611 | − | 0.636095i | \(-0.219451\pi\) |
−0.636095 | + | 0.771611i | \(0.719451\pi\) | |||||||
\(138\) | −5.11340 | − | 14.3373i | −0.435282 | − | 1.22047i | ||||
\(139\) | − | 11.1773i | − | 0.948045i | −0.880513 | − | 0.474022i | \(-0.842802\pi\) | ||
0.880513 | − | 0.474022i | \(-0.157198\pi\) | |||||||
\(140\) | −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 | −0.531018 | − | 0.847360i | \(-0.678190\pi\) |
0.847360 | + | 0.531018i | \(0.178190\pi\) | |||||||
\(158\) | 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 | 0.910645 | − | 0.413189i | \(-0.135585\pi\) |
−0.413189 | + | 0.910645i | \(0.635585\pi\) | |||||||
\(164\) | 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 | 0.985674 | + | 0.168664i | \(0.0539453\pi\) |
0.168664 | + | 0.985674i | \(0.446055\pi\) | |||||||
\(168\) | 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 | −0.431395 | − | 0.902163i | \(-0.641978\pi\) |
0.902163 | + | 0.431395i | \(0.141978\pi\) | |||||||
\(174\) | −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 | \(-0.812273\pi\) | ||
0.831073 | − | 0.556164i | \(-0.187727\pi\) | |||||||
\(192\) | −1.63140 | + | 0.581841i | −0.117736 | + | 0.0419907i | ||||
\(193\) | 16.5440 | + | 16.5440i | 1.19087 | + | 1.19087i | 0.976824 | + | 0.214042i | \(0.0686629\pi\) |
0.214042 | + | 0.976824i | \(0.431337\pi\) | |||||||
\(194\) | −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 | 0.806690 | − | 0.590974i | \(-0.201257\pi\) |
−0.590974 | + | 0.806690i | \(0.701257\pi\) | |||||||
\(198\) | 1.83877 | − | 18.2856i | 0.130676 | − | 1.29950i | ||||
\(199\) | 8.01713i | 0.568319i | 0.958777 | + | 0.284160i | \(0.0917146\pi\) | ||||
−0.958777 | + | 0.284160i | \(0.908285\pi\) | |||||||
\(200\) | −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 | 0.931303 | − | 0.364246i | \(-0.118673\pi\) |
−0.364246 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(224\) | −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 | 0.882307 | − | 0.470674i | \(-0.155989\pi\) |
−0.470674 | + | 0.882307i | \(0.655989\pi\) | |||||||
\(228\) | 0.581841 | + | 1.63140i | 0.0385334 | + | 0.108042i | ||||
\(229\) | 11.8117i | 0.780536i | 0.920701 | + | 0.390268i | \(0.127618\pi\) | ||||
−0.920701 | + | 0.390268i | \(0.872382\pi\) | |||||||
\(230\) | 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 | −0.271783 | − | 0.962358i | \(-0.587613\pi\) |
0.962358 | + | 0.271783i | \(0.0876134\pi\) | |||||||
\(234\) | 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 | \(0.320541\pi\) | ||||
−0.534392 | + | 0.845237i | \(0.679459\pi\) | |||||||
\(252\) | −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 | 0.873581 | − | 0.486679i | \(-0.161792\pi\) |
−0.486679 | + | 0.873581i | \(0.661792\pi\) | |||||||
\(258\) | −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 | −0.295181 | − | 0.955442i | \(-0.595380\pi\) |
0.955442 | + | 0.295181i | \(0.0953798\pi\) | |||||||
\(264\) | −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 | −0.697559 | − | 0.716528i | \(-0.745730\pi\) |
0.716528 | + | 0.697559i | \(0.245730\pi\) | |||||||
\(278\) | 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 | \(0.0214659\pi\) | ||||
−0.997727 | + | 0.0673860i | \(0.978534\pi\) | |||||||
\(282\) | 11.2719 | − | 4.02014i | 0.671232 | − | 0.239396i | ||||
\(283\) | −17.3455 | − | 17.3455i | −1.03109 | − | 1.03109i | −0.999501 | − | 0.0315844i | \(-0.989945\pi\) |
−0.0315844 | − | 0.999501i | \(-0.510055\pi\) | |||||||
\(284\) | −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 | −0.746122 | − | 0.665809i | \(-0.768087\pi\) |
0.665809 | + | 0.746122i | \(0.268087\pi\) | |||||||
\(294\) | 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 | −0.632765 | − | 0.774343i | \(-0.718080\pi\) |
0.774343 | + | 0.632765i | \(0.218080\pi\) | |||||||
\(308\) | −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 | \(-0.984091\pi\) | ||
0.998751 | − | 0.0499579i | \(-0.0159087\pi\) | |||||||
\(312\) | −0.620684 | − | 1.74031i | −0.0351393 | − | 0.0985256i | ||||
\(313\) | −9.58013 | − | 9.58013i | −0.541501 | − | 0.541501i | 0.382468 | − | 0.923969i | \(-0.375074\pi\) |
−0.923969 | + | 0.382468i | \(0.875074\pi\) | |||||||
\(314\) | 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 | 0.452364 | − | 0.891833i | \(-0.350581\pi\) |
−0.891833 | + | 0.452364i | \(0.850581\pi\) | |||||||
\(318\) | 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 | −0.432958 | − | 0.901414i | \(-0.642530\pi\) |
0.901414 | + | 0.432958i | \(0.142530\pi\) | |||||||
\(338\) | 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 | 0.462158 | − | 0.886797i | \(-0.347075\pi\) |
−0.886797 | + | 0.462158i | \(0.847075\pi\) | |||||||
\(348\) | −3.92846 | + | 1.40109i | −0.210587 | + | 0.0751064i | ||||
\(349\) | − | 18.5835i | − | 0.994752i | −0.867535 | − | 0.497376i | \(-0.834297\pi\) | ||
0.867535 | − | 0.497376i | \(-0.165703\pi\) | |||||||
\(350\) | −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 | −0.600333 | − | 0.799750i | \(-0.704965\pi\) |
0.799750 | + | 0.600333i | \(0.204965\pi\) | |||||||
\(354\) | 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 | 0.350218 | − | 0.936668i | \(-0.386108\pi\) |
0.936668 | − | 0.350218i | \(-0.113892\pi\) | |||||||
\(368\) | −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 | 0.363247 | − | 0.931693i | \(-0.381668\pi\) |
−0.931693 | + | 0.363247i | \(0.881668\pi\) | |||||||
\(374\) | −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 | \(0.305452\pi\) | ||||
−0.573843 | + | 0.818966i | \(0.694548\pi\) | |||||||
\(380\) | −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 | −0.605693 | − | 0.795698i | \(-0.707104\pi\) |
0.795698 | + | 0.605693i | \(0.207104\pi\) | |||||||
\(384\) | −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 | −0.723180 | − | 0.690659i | \(-0.757321\pi\) |
0.690659 | + | 0.723180i | \(0.257321\pi\) | |||||||
\(398\) | −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 | \(0.256954\pi\) | ||||
−0.691491 | + | 0.722385i | \(0.743046\pi\) | |||||||
\(402\) | −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 | \(0.125405\pi\) | ||||
−0.923392 | + | 0.383859i | \(0.874595\pi\) | |||||||
\(410\) | 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 | \(-0.842840\pi\) | ||
0.880570 | − | 0.473917i | \(-0.157160\pi\) | |||||||
\(432\) | −4.44866 | − | 2.68503i | −0.214036 | − | 0.129184i | ||||
\(433\) | −22.2656 | − | 22.2656i | −1.07002 | − | 1.07002i | −0.997357 | − | 0.0726615i | \(-0.976851\pi\) |
−0.0726615 | − | 0.997357i | \(-0.523149\pi\) | |||||||
\(434\) | 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 | \(-0.985067\pi\) | ||
0.998900 | − | 0.0468950i | \(-0.0149326\pi\) | |||||||
\(440\) | 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 | −0.907642 | − | 0.419746i | \(-0.862119\pi\) |
0.419746 | + | 0.907642i | \(0.362119\pi\) | |||||||
\(444\) | −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 | −0.332030 | − | 0.943269i | \(-0.607733\pi\) |
0.943269 | + | 0.332030i | \(0.107733\pi\) | |||||||
\(458\) | −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 | \(0.312412\pi\) | ||||
−0.555800 | + | 0.831316i | \(0.687588\pi\) | |||||||
\(462\) | 1.45332 | − | 0.518329i | 0.0676146 | − | 0.0241148i | ||||
\(463\) | −18.7714 | − | 18.7714i | −0.872381 | − | 0.872381i | 0.120350 | − | 0.992731i | \(-0.461598\pi\) |
−0.992731 | + | 0.120350i | \(0.961598\pi\) | |||||||
\(464\) | 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 | 0.813588 | − | 0.581442i | \(-0.197511\pi\) |
−0.581442 | + | 0.813588i | \(0.697511\pi\) | |||||||
\(468\) | −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 | −0.916654 | − | 0.399681i | \(-0.869121\pi\) |
0.399681 | + | 0.916654i | \(0.369121\pi\) | |||||||
\(488\) | 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 | \(0.0744738\pi\) | ||||
−0.972754 | + | 0.231838i | \(0.925526\pi\) | |||||||
\(492\) | −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 | \(-0.799363\pi\) | ||
0.807839 | − | 0.589404i | \(-0.200637\pi\) | |||||||
\(500\) | −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 | −0.986847 | − | 0.161658i | \(-0.948316\pi\) |
0.161658 | + | 0.986847i | \(0.448316\pi\) | |||||||
\(504\) | −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 | \(0.195046\pi\) | ||||
−0.818066 | + | 0.575125i | \(0.804954\pi\) | |||||||
\(522\) | 7.18784 | + | 0.722800i | 0.314603 | + | 0.0316361i | ||||
\(523\) | 12.9426 | + | 12.9426i | 0.565942 | + | 0.565942i | 0.930989 | − | 0.365047i | \(-0.118947\pi\) |
−0.365047 | + | 0.930989i | \(0.618947\pi\) | |||||||
\(524\) | −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 | −0.692182 | − | 0.721723i | \(-0.743350\pi\) |
0.721723 | + | 0.692182i | \(0.243350\pi\) | |||||||
\(548\) | −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 | 0.970305 | − | 0.241886i | \(-0.0777660\pi\) |
−0.241886 | + | 0.970305i | \(0.577766\pi\) | |||||||
\(558\) | −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 | −0.948500 | − | 0.316777i | \(-0.897399\pi\) |
0.316777 | + | 0.948500i | \(0.397399\pi\) | |||||||
\(564\) | 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 | −0.545046 | − | 0.838406i | \(-0.683488\pi\) |
0.838406 | + | 0.545046i | \(0.183488\pi\) | |||||||
\(578\) | 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 | −0.992873 | − | 0.119179i | \(-0.961974\pi\) |
−0.119179 | − | 0.992873i | \(-0.538026\pi\) | |||||||
\(588\) | 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 | −0.140822 | − | 0.990035i | \(-0.544974\pi\) |
0.990035 | + | 0.140822i | \(0.0449744\pi\) | |||||||
\(594\) | −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 | −0.267752 | − | 0.963488i | \(-0.586281\pi\) |
0.963488 | + | 0.267752i | \(0.0862806\pi\) | |||||||
\(608\) | 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 | 0.902427 | − | 0.430843i | \(-0.141784\pi\) |
−0.430843 | + | 0.902427i | \(0.641784\pi\) | |||||||
\(614\) | 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 | −0.998644 | − | 0.0520498i | \(-0.983425\pi\) |
−0.0520498 | − | 0.998644i | \(-0.516575\pi\) | |||||||
\(618\) | −25.8702 | + | 9.22665i | −1.04065 | + | 0.371150i | ||||
\(619\) | 23.5922i | 0.948249i | 0.880458 | + | 0.474124i | \(0.157235\pi\) | ||||
−0.880458 | + | 0.474124i | \(0.842765\pi\) | |||||||
\(620\) | −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 | \(-0.978410\pi\) | ||
0.997701 | − | 0.0677764i | \(-0.0215904\pi\) | |||||||
\(642\) | −25.1537 | + | 8.97112i | −0.992739 | + | 0.354062i | ||||
\(643\) | 14.6003 | + | 14.6003i | 0.575778 | + | 0.575778i | 0.933737 | − | 0.357959i | \(-0.116527\pi\) |
−0.357959 | + | 0.933737i | \(0.616527\pi\) | |||||||
\(644\) | 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 | −0.951496 | − | 0.307662i | \(-0.900453\pi\) |
−0.307662 | − | 0.951496i | \(-0.599547\pi\) | |||||||
\(648\) | 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 | −0.990906 | − | 0.134559i | \(-0.957038\pi\) |
0.134559 | + | 0.990906i | \(0.457038\pi\) | |||||||
\(654\) | −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 | 0.920065 | − | 0.391765i | \(-0.128135\pi\) |
−0.391765 | + | 0.920065i | \(0.628135\pi\) | |||||||
\(674\) | 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 | 0.710826 | − | 0.703368i | \(-0.248321\pi\) |
−0.703368 | + | 0.710826i | \(0.748321\pi\) | |||||||
\(678\) | 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 | −0.850796 | − | 0.525495i | \(-0.823880\pi\) |
0.525495 | + | 0.850796i | \(0.323880\pi\) | |||||||
\(684\) | 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 | \(0.0398711\pi\) | ||||
−0.992165 | + | 0.124931i | \(0.960129\pi\) | |||||||
\(702\) | 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 | \(0.104919\pi\) | ||||
−0.946168 | + | 0.323675i | \(0.895081\pi\) | |||||||
\(710\) | −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 | −0.301871 | + | 0.953349i | \(0.597611\pi\) |
−0.953349 | + | 0.301871i | \(0.902389\pi\) | |||||||
\(728\) | 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 | 0.534266 | − | 0.845316i | \(-0.320588\pi\) |
−0.845316 | + | 0.534266i | \(0.820588\pi\) | |||||||
\(734\) | 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 | \(-0.889947\pi\) | ||
0.940825 | − | 0.338894i | \(-0.110053\pi\) | |||||||
\(740\) | 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 | 0.000307644 | − | 1.00000i | \(-0.499902\pi\) |
1.00000 | 0.000307644i | \(-9.79262e-5\pi\) | ||||||||
\(744\) | 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 | −0.399766 | − | 0.916617i | \(-0.630909\pi\) |
0.916617 | + | 0.399766i | \(0.130909\pi\) | |||||||
\(758\) | −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 | \(0.155312\pi\) | ||||
−0.883307 | + | 0.468795i | \(0.844688\pi\) | |||||||
\(762\) | −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 | \(0.0219237\pi\) | ||||
−0.997629 | + | 0.0688208i | \(0.978076\pi\) | |||||||
\(770\) | −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 | −0.905405 | − | 0.424549i | \(-0.860433\pi\) |
0.424549 | + | 0.905405i | \(0.360433\pi\) | |||||||
\(774\) | 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 | −0.984567 | − | 0.175006i | \(-0.944005\pi\) |
0.175006 | + | 0.984567i | \(0.444005\pi\) | |||||||
\(788\) | −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 | 0.646007 | − | 0.763332i | \(-0.276438\pi\) |
−0.763332 | + | 0.646007i | \(0.776438\pi\) | |||||||
\(798\) | 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 | \(0.112309\pi\) | ||||
−0.938399 | + | 0.345553i | \(0.887691\pi\) | |||||||
\(822\) | 3.65954 | − | 1.30518i | 0.127641 | − | 0.0455234i | ||||
\(823\) | −26.0210 | − | 26.0210i | −0.907036 | − | 0.907036i | 0.0889960 | − | 0.996032i | \(-0.471634\pi\) |
−0.996032 | + | 0.0889960i | \(0.971634\pi\) | |||||||
\(824\) | 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 | 0.572749 | − | 0.819731i | \(-0.305877\pi\) |
−0.819731 | + | 0.572749i | \(0.805877\pi\) | |||||||
\(828\) | −26.2327 | − | 2.63792i | −0.911648 | − | 0.0916742i | ||||
\(829\) | 40.2350i | 1.39742i | 0.715406 | + | 0.698709i | \(0.246242\pi\) | ||||
−0.715406 | + | 0.698709i | \(0.753758\pi\) | |||||||
\(830\) | 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 | 0.0555025 | − | 0.998459i | \(-0.482324\pi\) |
−0.998459 | + | 0.0555025i | \(0.982324\pi\) | |||||||
\(854\) | −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 | 0.464817 | − | 0.885407i | \(-0.346120\pi\) |
−0.885407 | + | 0.464817i | \(0.846120\pi\) | |||||||
\(858\) | −3.80227 | − | 10.6610i | −0.129807 | − | 0.363961i | ||||
\(859\) | − | 6.21722i | − | 0.212129i | −0.994359 | − | 0.106064i | \(-0.966175\pi\) | ||
0.994359 | − | 0.106064i | \(-0.0338250\pi\) | |||||||
\(860\) | 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 | 0.0748042 | − | 0.997198i | \(-0.476167\pi\) |
0.997198 | − | 0.0748042i | \(-0.0238332\pi\) | |||||||
\(864\) | −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 | −0.943458 | − | 0.331493i | \(-0.892448\pi\) |
0.331493 | + | 0.943458i | \(0.392448\pi\) | |||||||
\(878\) | 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 | \(0.0625915\pi\) | ||||
−0.980729 | + | 0.195372i | \(0.937409\pi\) | |||||||
\(882\) | 2.09479 | − | 20.8315i | 0.0705352 | − | 0.701433i | ||||
\(883\) | −9.62477 | − | 9.62477i | −0.323899 | − | 0.323899i | 0.526362 | − | 0.850261i | \(-0.323556\pi\) |
−0.850261 | + | 0.526362i | \(0.823556\pi\) | |||||||
\(884\) | 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 | 0.0404558 | − | 0.999181i | \(-0.487119\pi\) |
−0.999181 | + | 0.0404558i | \(0.987119\pi\) | |||||||
\(888\) | −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 | 0.170470 | − | 0.985363i | \(-0.445471\pi\) |
0.985363 | − | 0.170470i | \(-0.0545287\pi\) | |||||||
\(908\) | −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 | \(-0.773002\pi\) | ||
0.756315 | − | 0.654208i | \(-0.226998\pi\) | |||||||
\(912\) | −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 | \(0.249741\pi\) | ||||
−0.707683 | + | 0.706530i | \(0.750259\pi\) | |||||||
\(920\) | −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 | −0.166000 | + | 0.986126i | \(0.553085\pi\) |
−0.986126 | + | 0.166000i | \(0.946915\pi\) | |||||||
\(938\) | 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 | \(0.106157\pi\) | ||||
−0.944901 | + | 0.327355i | \(0.893843\pi\) | |||||||
\(942\) | −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 | 0.532834 | − | 0.846220i | \(-0.321127\pi\) |
−0.846220 | + | 0.532834i | \(0.821127\pi\) | |||||||
\(948\) | −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 | −0.299616 | + | 0.954060i | \(0.596858\pi\) |
−0.954060 | + | 0.299616i | \(0.903142\pi\) | |||||||
\(954\) | 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 | −0.917160 | − | 0.398519i | \(-0.869524\pi\) |
0.398519 | + | 0.917160i | \(0.369524\pi\) | |||||||
\(968\) | 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 | \(-0.819772\pi\) | ||
0.843943 | − | 0.536432i | \(-0.180228\pi\) | |||||||
\(972\) | −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 | 0.0827686 | − | 0.996569i | \(-0.473624\pi\) |
−0.996569 | + | 0.0827686i | \(0.973624\pi\) | |||||||
\(978\) | 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 | −0.972687 | − | 0.232119i | \(-0.925434\pi\) |
0.232119 | + | 0.972687i | \(0.425434\pi\) | |||||||
\(984\) | 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 | −0.457703 | − | 0.889105i | \(-0.651328\pi\) |
0.889105 | + | 0.457703i | \(0.151328\pi\) | |||||||
\(998\) | 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.533.12 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.533.2 | yes | 36 | |
5.2 | odd | 4 | inner | 570.2.k.b.77.2 | ✓ | 36 | |
15.2 | even | 4 | inner | 570.2.k.b.77.12 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.2 | ✓ | 36 | 5.2 | odd | 4 | inner | |
570.2.k.b.77.12 | yes | 36 | 15.2 | even | 4 | inner | |
570.2.k.b.533.2 | yes | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.533.12 | yes | 36 | 1.1 | even | 1 | trivial |