Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.18 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.18 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | −2.00232 | − | 4.58156i | −0.400464 | − | 0.916313i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −5.25476 | − | 5.25476i | −0.750680 | − | 0.750680i | 0.223926 | − | 0.974606i | \(-0.428113\pi\) |
−0.974606 | + | 0.223926i | \(0.928113\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −2.57924 | + | 6.58388i | −0.257924 | + | 0.658388i | ||||
\(11\) | 3.64219 | 0.331109 | 0.165554 | − | 0.986201i | \(-0.447059\pi\) | ||||
0.165554 | + | 0.986201i | \(0.447059\pi\) | |||||||
\(12\) | 2.44949 | + | 2.44949i | 0.204124 | + | 0.204124i | ||||
\(13\) | −7.35690 | + | 7.35690i | −0.565916 | + | 0.565916i | −0.930982 | − | 0.365066i | \(-0.881046\pi\) |
0.365066 | + | 0.930982i | \(0.381046\pi\) | |||||||
\(14\) | 10.5095i | 0.750680i | ||||||||
\(15\) | −8.06358 | − | 3.15892i | −0.537572 | − | 0.210594i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −14.6562 | − | 14.6562i | −0.862132 | − | 0.862132i | 0.129454 | − | 0.991585i | \(-0.458678\pi\) |
−0.991585 | + | 0.129454i | \(0.958678\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | 3.37356i | 0.177556i | 0.996051 | + | 0.0887779i | \(0.0282961\pi\) | ||||
−0.996051 | + | 0.0887779i | \(0.971704\pi\) | |||||||
\(20\) | 9.16313 | − | 4.00464i | 0.458156 | − | 0.200232i | ||||
\(21\) | −12.8715 | −0.612928 | ||||||||
\(22\) | −3.64219 | − | 3.64219i | −0.165554 | − | 0.165554i | ||||
\(23\) | −3.39116 | + | 3.39116i | −0.147442 | + | 0.147442i | ||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | −16.9814 | + | 18.3475i | −0.679257 | + | 0.733900i | ||||
\(26\) | 14.7138 | 0.565916 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 10.5095 | − | 10.5095i | 0.375340 | − | 0.375340i | ||||
\(29\) | − | 1.23263i | − | 0.0425045i | −0.999774 | − | 0.0212523i | \(-0.993235\pi\) | ||
0.999774 | − | 0.0212523i | \(-0.00676532\pi\) | |||||||
\(30\) | 4.90466 | + | 11.2225i | 0.163489 | + | 0.374083i | ||||
\(31\) | 19.8064 | 0.638917 | 0.319459 | − | 0.947600i | \(-0.396499\pi\) | ||||
0.319459 | + | 0.947600i | \(0.396499\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 4.46076 | − | 4.46076i | 0.135175 | − | 0.135175i | ||||
\(34\) | 29.3125i | 0.862132i | ||||||||
\(35\) | −13.5533 | + | 34.5967i | −0.387237 | + | 0.988478i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −6.16415 | − | 6.16415i | −0.166599 | − | 0.166599i | 0.618884 | − | 0.785482i | \(-0.287585\pi\) |
−0.785482 | + | 0.618884i | \(0.787585\pi\) | |||||||
\(38\) | 3.37356 | − | 3.37356i | 0.0887779 | − | 0.0887779i | ||||
\(39\) | 18.0207i | 0.462068i | ||||||||
\(40\) | −13.1678 | − | 5.15849i | −0.329194 | − | 0.128962i | ||||
\(41\) | 47.2794 | 1.15316 | 0.576579 | − | 0.817042i | \(-0.304387\pi\) | ||||
0.576579 | + | 0.817042i | \(0.304387\pi\) | |||||||
\(42\) | 12.8715 | + | 12.8715i | 0.306464 | + | 0.306464i | ||||
\(43\) | −35.5800 | + | 35.5800i | −0.827442 | + | 0.827442i | −0.987162 | − | 0.159721i | \(-0.948941\pi\) |
0.159721 | + | 0.987162i | \(0.448941\pi\) | |||||||
\(44\) | 7.28439i | 0.165554i | ||||||||
\(45\) | −13.7447 | + | 6.00696i | −0.305438 | + | 0.133488i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | 33.2177 | + | 33.2177i | 0.706760 | + | 0.706760i | 0.965852 | − | 0.259093i | \(-0.0834236\pi\) |
−0.259093 | + | 0.965852i | \(0.583424\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | 6.22501i | 0.127041i | ||||||||
\(50\) | 35.3289 | − | 1.36607i | 0.706579 | − | 0.0273213i | ||||
\(51\) | −35.9003 | −0.703927 | ||||||||
\(52\) | −14.7138 | − | 14.7138i | −0.282958 | − | 0.282958i | ||||
\(53\) | −26.6463 | + | 26.6463i | −0.502760 | + | 0.502760i | −0.912294 | − | 0.409535i | \(-0.865691\pi\) |
0.409535 | + | 0.912294i | \(0.365691\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | −7.29284 | − | 16.6869i | −0.132597 | − | 0.303399i | ||||
\(56\) | −21.0190 | −0.375340 | ||||||||
\(57\) | 4.13175 | + | 4.13175i | 0.0724868 | + | 0.0724868i | ||||
\(58\) | −1.23263 | + | 1.23263i | −0.0212523 | + | 0.0212523i | ||||
\(59\) | 44.0572i | 0.746732i | 0.927684 | + | 0.373366i | \(0.121796\pi\) | ||||
−0.927684 | + | 0.373366i | \(0.878204\pi\) | |||||||
\(60\) | 6.31783 | − | 16.1272i | 0.105297 | − | 0.268786i | ||||
\(61\) | −37.9182 | −0.621609 | −0.310805 | − | 0.950474i | \(-0.600599\pi\) | ||||
−0.310805 | + | 0.950474i | \(0.600599\pi\) | |||||||
\(62\) | −19.8064 | − | 19.8064i | −0.319459 | − | 0.319459i | ||||
\(63\) | −15.7643 | + | 15.7643i | −0.250227 | + | 0.250227i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 48.4370 | + | 18.9752i | 0.745184 | + | 0.291927i | ||||
\(66\) | −8.92152 | −0.135175 | ||||||||
\(67\) | −87.7712 | − | 87.7712i | −1.31002 | − | 1.31002i | −0.921398 | − | 0.388620i | \(-0.872952\pi\) |
−0.388620 | − | 0.921398i | \(-0.627048\pi\) | |||||||
\(68\) | 29.3125 | − | 29.3125i | 0.431066 | − | 0.431066i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | 48.1500 | − | 21.0434i | 0.687858 | − | 0.300620i | ||||
\(71\) | 7.77433 | 0.109498 | 0.0547488 | − | 0.998500i | \(-0.482564\pi\) | ||||
0.0547488 | + | 0.998500i | \(0.482564\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | −58.7976 | + | 58.7976i | −0.805446 | + | 0.805446i | −0.983941 | − | 0.178494i | \(-0.942877\pi\) |
0.178494 | + | 0.983941i | \(0.442877\pi\) | |||||||
\(74\) | 12.3283i | 0.166599i | ||||||||
\(75\) | 1.67308 | + | 43.2689i | 0.0223078 | + | 0.576919i | ||||
\(76\) | −6.74712 | −0.0887779 | ||||||||
\(77\) | −19.1389 | − | 19.1389i | −0.248557 | − | 0.248557i | ||||
\(78\) | 18.0207 | − | 18.0207i | 0.231034 | − | 0.231034i | ||||
\(79\) | − | 26.9312i | − | 0.340901i | −0.985366 | − | 0.170450i | \(-0.945478\pi\) | ||
0.985366 | − | 0.170450i | \(-0.0545222\pi\) | |||||||
\(80\) | 8.00928 | + | 18.3263i | 0.100116 | + | 0.229078i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −47.2794 | − | 47.2794i | −0.576579 | − | 0.576579i | ||||
\(83\) | −1.79597 | + | 1.79597i | −0.0216382 | + | 0.0216382i | −0.717843 | − | 0.696205i | \(-0.754871\pi\) |
0.696205 | + | 0.717843i | \(0.254871\pi\) | |||||||
\(84\) | − | 25.7430i | − | 0.306464i | ||||||
\(85\) | −37.8020 | + | 96.4949i | −0.444729 | + | 1.13523i | ||||
\(86\) | 71.1600 | 0.827442 | ||||||||
\(87\) | −1.50966 | − | 1.50966i | −0.0173524 | − | 0.0173524i | ||||
\(88\) | 7.28439 | − | 7.28439i | 0.0827771 | − | 0.0827771i | ||||
\(89\) | 110.000i | 1.23595i | 0.786197 | + | 0.617976i | \(0.212047\pi\) | ||||
−0.786197 | + | 0.617976i | \(0.787953\pi\) | |||||||
\(90\) | 19.7516 | + | 7.73773i | 0.219463 | + | 0.0859748i | ||||
\(91\) | 77.3175 | 0.849643 | ||||||||
\(92\) | −6.78233 | − | 6.78233i | −0.0737210 | − | 0.0737210i | ||||
\(93\) | 24.2578 | − | 24.2578i | 0.260837 | − | 0.260837i | ||||
\(94\) | − | 66.4354i | − | 0.706760i | ||||||
\(95\) | 15.4562 | − | 6.75494i | 0.162697 | − | 0.0711047i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 1.22444 | + | 1.22444i | 0.0126231 | + | 0.0126231i | 0.713390 | − | 0.700767i | \(-0.247159\pi\) |
−0.700767 | + | 0.713390i | \(0.747159\pi\) | |||||||
\(98\) | 6.22501 | − | 6.22501i | 0.0635205 | − | 0.0635205i | ||||
\(99\) | − | 10.9266i | − | 0.110370i | ||||||
\(100\) | −36.6950 | − | 33.9629i | −0.366950 | − | 0.339629i | ||||
\(101\) | 134.532 | 1.33200 | 0.665999 | − | 0.745953i | \(-0.268006\pi\) | ||||
0.665999 | + | 0.745953i | \(0.268006\pi\) | |||||||
\(102\) | 35.9003 | + | 35.9003i | 0.351964 | + | 0.351964i | ||||
\(103\) | −60.5363 | + | 60.5363i | −0.587731 | + | 0.587731i | −0.937016 | − | 0.349286i | \(-0.886424\pi\) |
0.349286 | + | 0.937016i | \(0.386424\pi\) | |||||||
\(104\) | 29.4276i | 0.282958i | ||||||||
\(105\) | 25.7728 | + | 58.9715i | 0.245455 | + | 0.561633i | ||||
\(106\) | 53.2925 | 0.502760 | ||||||||
\(107\) | 43.6880 | + | 43.6880i | 0.408299 | + | 0.408299i | 0.881145 | − | 0.472846i | \(-0.156773\pi\) |
−0.472846 | + | 0.881145i | \(0.656773\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 4.39089i | 0.0402834i | 0.999797 | + | 0.0201417i | \(0.00641173\pi\) | ||||
−0.999797 | + | 0.0201417i | \(0.993588\pi\) | |||||||
\(110\) | −9.39411 | + | 23.9798i | −0.0854010 | + | 0.217998i | ||||
\(111\) | −15.0990 | −0.136027 | ||||||||
\(112\) | 21.0190 | + | 21.0190i | 0.187670 | + | 0.187670i | ||||
\(113\) | −68.8182 | + | 68.8182i | −0.609011 | + | 0.609011i | −0.942688 | − | 0.333677i | \(-0.891711\pi\) |
0.333677 | + | 0.942688i | \(0.391711\pi\) | |||||||
\(114\) | − | 8.26350i | − | 0.0724868i | ||||||
\(115\) | 22.3270 | + | 8.74664i | 0.194148 | + | 0.0760577i | ||||
\(116\) | 2.46526 | 0.0212523 | ||||||||
\(117\) | 22.0707 | + | 22.0707i | 0.188639 | + | 0.188639i | ||||
\(118\) | 44.0572 | − | 44.0572i | 0.373366 | − | 0.373366i | ||||
\(119\) | 154.030i | 1.29437i | ||||||||
\(120\) | −22.4450 | + | 9.80932i | −0.187042 | + | 0.0817443i | ||||
\(121\) | −107.734 | −0.890367 | ||||||||
\(122\) | 37.9182 | + | 37.9182i | 0.310805 | + | 0.310805i | ||||
\(123\) | 57.9053 | − | 57.9053i | 0.470774 | − | 0.470774i | ||||
\(124\) | 39.6129i | 0.319459i | ||||||||
\(125\) | 118.062 | + | 41.0640i | 0.944500 | + | 0.328512i | ||||
\(126\) | 31.5286 | 0.250227 | ||||||||
\(127\) | −13.4330 | − | 13.4330i | −0.105771 | − | 0.105771i | 0.652241 | − | 0.758012i | \(-0.273829\pi\) |
−0.758012 | + | 0.652241i | \(0.773829\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 87.1528i | 0.675603i | ||||||||
\(130\) | −29.4617 | − | 67.4122i | −0.226629 | − | 0.518556i | ||||
\(131\) | −121.821 | −0.929935 | −0.464967 | − | 0.885328i | \(-0.653934\pi\) | ||||
−0.464967 | + | 0.885328i | \(0.653934\pi\) | |||||||
\(132\) | 8.92152 | + | 8.92152i | 0.0675873 | + | 0.0675873i | ||||
\(133\) | 17.7272 | − | 17.7272i | 0.133288 | − | 0.133288i | ||||
\(134\) | 175.542i | 1.31002i | ||||||||
\(135\) | −9.47675 | + | 24.1907i | −0.0701981 | + | 0.179191i | ||||
\(136\) | −58.6249 | −0.431066 | ||||||||
\(137\) | −122.729 | − | 122.729i | −0.895829 | − | 0.895829i | 0.0992347 | − | 0.995064i | \(-0.468361\pi\) |
−0.995064 | + | 0.0992347i | \(0.968361\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | − | 7.58478i | − | 0.0545668i | −0.999628 | − | 0.0272834i | \(-0.991314\pi\) | ||
0.999628 | − | 0.0272834i | \(-0.00868565\pi\) | |||||||
\(140\) | −69.1934 | − | 27.1066i | −0.494239 | − | 0.193619i | ||||
\(141\) | 81.3664 | 0.577067 | ||||||||
\(142\) | −7.77433 | − | 7.77433i | −0.0547488 | − | 0.0547488i | ||||
\(143\) | −26.7953 | + | 26.7953i | −0.187379 | + | 0.187379i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | −5.64738 | + | 2.46812i | −0.0389474 | + | 0.0170215i | ||||
\(146\) | 117.595 | 0.805446 | ||||||||
\(147\) | 7.62405 | + | 7.62405i | 0.0518643 | + | 0.0518643i | ||||
\(148\) | 12.3283 | − | 12.3283i | 0.0832993 | − | 0.0832993i | ||||
\(149\) | − | 221.285i | − | 1.48514i | −0.669770 | − | 0.742568i | \(-0.733607\pi\) | ||
0.669770 | − | 0.742568i | \(-0.266393\pi\) | |||||||
\(150\) | 41.5959 | − | 44.9420i | 0.277306 | − | 0.299613i | ||||
\(151\) | 4.57858 | 0.0303217 | 0.0151608 | − | 0.999885i | \(-0.495174\pi\) | ||||
0.0151608 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(152\) | 6.74712 | + | 6.74712i | 0.0443889 | + | 0.0443889i | ||||
\(153\) | −43.9687 | + | 43.9687i | −0.287377 | + | 0.287377i | ||||
\(154\) | 38.2777i | 0.248557i | ||||||||
\(155\) | −39.6588 | − | 90.7444i | −0.255863 | − | 0.585448i | ||||
\(156\) | −36.0413 | −0.231034 | ||||||||
\(157\) | −19.5364 | − | 19.5364i | −0.124436 | − | 0.124436i | 0.642146 | − | 0.766582i | \(-0.278044\pi\) |
−0.766582 | + | 0.642146i | \(0.778044\pi\) | |||||||
\(158\) | −26.9312 | + | 26.9312i | −0.170450 | + | 0.170450i | ||||
\(159\) | 65.2697i | 0.410502i | ||||||||
\(160\) | 10.3170 | − | 26.3355i | 0.0644811 | − | 0.164597i | ||||
\(161\) | 35.6395 | 0.221363 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 96.3330 | − | 96.3330i | 0.591000 | − | 0.591000i | −0.346902 | − | 0.937902i | \(-0.612766\pi\) |
0.937902 | + | 0.346902i | \(0.112766\pi\) | |||||||
\(164\) | 94.5589i | 0.576579i | ||||||||
\(165\) | −29.3691 | − | 11.5054i | −0.177995 | − | 0.0697296i | ||||
\(166\) | 3.59195 | 0.0216382 | ||||||||
\(167\) | −161.676 | − | 161.676i | −0.968120 | − | 0.968120i | 0.0313878 | − | 0.999507i | \(-0.490007\pi\) |
−0.999507 | + | 0.0313878i | \(0.990007\pi\) | |||||||
\(168\) | −25.7430 | + | 25.7430i | −0.153232 | + | 0.153232i | ||||
\(169\) | 60.7520i | 0.359479i | ||||||||
\(170\) | 134.297 | − | 58.6929i | 0.789982 | − | 0.345252i | ||||
\(171\) | 10.1207 | 0.0591853 | ||||||||
\(172\) | −71.1600 | − | 71.1600i | −0.413721 | − | 0.413721i | ||||
\(173\) | 171.585 | − | 171.585i | 0.991820 | − | 0.991820i | −0.00814708 | − | 0.999967i | \(-0.502593\pi\) |
0.999967 | + | 0.00814708i | \(0.00259333\pi\) | |||||||
\(174\) | 3.01932i | 0.0173524i | ||||||||
\(175\) | 185.645 | − | 7.17835i | 1.06083 | − | 0.0410191i | ||||
\(176\) | −14.5688 | −0.0827771 | ||||||||
\(177\) | 53.9588 | + | 53.9588i | 0.304852 | + | 0.304852i | ||||
\(178\) | 110.000 | − | 110.000i | 0.617976 | − | 0.617976i | ||||
\(179\) | 178.228i | 0.995688i | 0.867267 | + | 0.497844i | \(0.165875\pi\) | ||||
−0.867267 | + | 0.497844i | \(0.834125\pi\) | |||||||
\(180\) | −12.0139 | − | 27.4894i | −0.0667440 | − | 0.152719i | ||||
\(181\) | −107.395 | −0.593342 | −0.296671 | − | 0.954980i | \(-0.595876\pi\) | ||||
−0.296671 | + | 0.954980i | \(0.595876\pi\) | |||||||
\(182\) | −77.3175 | − | 77.3175i | −0.424821 | − | 0.424821i | ||||
\(183\) | −46.4401 | + | 46.4401i | −0.253771 | + | 0.253771i | ||||
\(184\) | 13.5647i | 0.0737210i | ||||||||
\(185\) | −15.8988 | + | 40.5840i | −0.0859397 | + | 0.219373i | ||||
\(186\) | −48.5157 | −0.260837 | ||||||||
\(187\) | −53.3809 | − | 53.3809i | −0.285459 | − | 0.285459i | ||||
\(188\) | −66.4354 | + | 66.4354i | −0.353380 | + | 0.353380i | ||||
\(189\) | 38.6144i | 0.204309i | ||||||||
\(190\) | −22.2111 | − | 8.70123i | −0.116901 | − | 0.0457960i | ||||
\(191\) | −120.021 | −0.628383 | −0.314191 | − | 0.949360i | \(-0.601733\pi\) | ||||
−0.314191 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(192\) | −9.79796 | − | 9.79796i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 51.5373 | − | 51.5373i | 0.267033 | − | 0.267033i | −0.560871 | − | 0.827903i | \(-0.689534\pi\) |
0.827903 | + | 0.560871i | \(0.189534\pi\) | |||||||
\(194\) | − | 2.44889i | − | 0.0126231i | ||||||
\(195\) | 82.5628 | − | 36.0831i | 0.423399 | − | 0.185042i | ||||
\(196\) | −12.4500 | −0.0635205 | ||||||||
\(197\) | −20.5257 | − | 20.5257i | −0.104192 | − | 0.104192i | 0.653089 | − | 0.757281i | \(-0.273473\pi\) |
−0.757281 | + | 0.653089i | \(0.773473\pi\) | |||||||
\(198\) | −10.9266 | + | 10.9266i | −0.0551848 | + | 0.0551848i | ||||
\(199\) | − | 261.408i | − | 1.31361i | −0.754061 | − | 0.656805i | \(-0.771908\pi\) | ||
0.754061 | − | 0.656805i | \(-0.228092\pi\) | |||||||
\(200\) | 2.73213 | + | 70.6579i | 0.0136607 | + | 0.353289i | ||||
\(201\) | −214.995 | −1.06963 | ||||||||
\(202\) | −134.532 | − | 134.532i | −0.665999 | − | 0.665999i | ||||
\(203\) | −6.47718 | + | 6.47718i | −0.0319073 | + | 0.0319073i | ||||
\(204\) | − | 71.8006i | − | 0.351964i | ||||||
\(205\) | −94.6685 | − | 216.614i | −0.461798 | − | 1.05665i | ||||
\(206\) | 121.073 | 0.587731 | ||||||||
\(207\) | 10.1735 | + | 10.1735i | 0.0491473 | + | 0.0491473i | ||||
\(208\) | 29.4276 | − | 29.4276i | 0.141479 | − | 0.141479i | ||||
\(209\) | 12.2872i | 0.0587902i | ||||||||
\(210\) | 33.1987 | − | 84.7443i | 0.158089 | − | 0.403544i | ||||
\(211\) | −215.468 | −1.02118 | −0.510588 | − | 0.859825i | \(-0.670572\pi\) | ||||
−0.510588 | + | 0.859825i | \(0.670572\pi\) | |||||||
\(212\) | −53.2925 | − | 53.2925i | −0.251380 | − | 0.251380i | ||||
\(213\) | 9.52156 | − | 9.52156i | 0.0447022 | − | 0.0447022i | ||||
\(214\) | − | 87.3760i | − | 0.408299i | ||||||
\(215\) | 234.254 | + | 91.7695i | 1.08956 | + | 0.426835i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −104.078 | − | 104.078i | −0.479622 | − | 0.479622i | ||||
\(218\) | 4.39089 | − | 4.39089i | 0.0201417 | − | 0.0201417i | ||||
\(219\) | 144.024i | 0.657644i | ||||||||
\(220\) | 33.3739 | − | 14.5857i | 0.151699 | − | 0.0662985i | ||||
\(221\) | 215.649 | 0.975787 | ||||||||
\(222\) | 15.0990 | + | 15.0990i | 0.0680136 | + | 0.0680136i | ||||
\(223\) | 165.267 | − | 165.267i | 0.741110 | − | 0.741110i | −0.231682 | − | 0.972792i | \(-0.574423\pi\) |
0.972792 | + | 0.231682i | \(0.0744229\pi\) | |||||||
\(224\) | − | 42.0381i | − | 0.187670i | ||||||
\(225\) | 55.0425 | + | 50.9443i | 0.244633 | + | 0.226419i | ||||
\(226\) | 137.636 | 0.609011 | ||||||||
\(227\) | −178.325 | − | 178.325i | −0.785574 | − | 0.785574i | 0.195191 | − | 0.980765i | \(-0.437467\pi\) |
−0.980765 | + | 0.195191i | \(0.937467\pi\) | |||||||
\(228\) | −8.26350 | + | 8.26350i | −0.0362434 | + | 0.0362434i | ||||
\(229\) | − | 50.6019i | − | 0.220969i | −0.993878 | − | 0.110484i | \(-0.964760\pi\) | ||
0.993878 | − | 0.110484i | \(-0.0352403\pi\) | |||||||
\(230\) | −13.5804 | − | 31.0737i | −0.0590452 | − | 0.135103i | ||||
\(231\) | −46.8804 | −0.202946 | ||||||||
\(232\) | −2.46526 | − | 2.46526i | −0.0106261 | − | 0.0106261i | ||||
\(233\) | 13.2676 | − | 13.2676i | 0.0569423 | − | 0.0569423i | −0.678062 | − | 0.735005i | \(-0.737180\pi\) |
0.735005 | + | 0.678062i | \(0.237180\pi\) | |||||||
\(234\) | − | 44.1414i | − | 0.188639i | ||||||
\(235\) | 85.6765 | − | 218.701i | 0.364581 | − | 0.930644i | ||||
\(236\) | −88.1143 | −0.373366 | ||||||||
\(237\) | −32.9838 | − | 32.9838i | −0.139172 | − | 0.139172i | ||||
\(238\) | 154.030 | − | 154.030i | 0.647185 | − | 0.647185i | ||||
\(239\) | − | 336.857i | − | 1.40944i | −0.709484 | − | 0.704721i | \(-0.751072\pi\) | ||
0.709484 | − | 0.704721i | \(-0.248928\pi\) | |||||||
\(240\) | 32.2543 | + | 12.6357i | 0.134393 | + | 0.0526486i | ||||
\(241\) | −349.220 | −1.44905 | −0.724524 | − | 0.689250i | \(-0.757940\pi\) | ||||
−0.724524 | + | 0.689250i | \(0.757940\pi\) | |||||||
\(242\) | 107.734 | + | 107.734i | 0.445184 | + | 0.445184i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 75.8363i | − | 0.310805i | ||||||
\(245\) | 28.5203 | − | 12.4645i | 0.116409 | − | 0.0508753i | ||||
\(246\) | −115.811 | −0.470774 | ||||||||
\(247\) | −24.8189 | − | 24.8189i | −0.100482 | − | 0.100482i | ||||
\(248\) | 39.6129 | − | 39.6129i | 0.159729 | − | 0.159729i | ||||
\(249\) | 4.39922i | 0.0176676i | ||||||||
\(250\) | −76.9985 | − | 159.126i | −0.307994 | − | 0.636506i | ||||
\(251\) | −410.838 | −1.63680 | −0.818402 | − | 0.574645i | \(-0.805140\pi\) | ||||
−0.818402 | + | 0.574645i | \(0.805140\pi\) | |||||||
\(252\) | −31.5286 | − | 31.5286i | −0.125113 | − | 0.125113i | ||||
\(253\) | −12.3513 | + | 12.3513i | −0.0488193 | + | 0.0488193i | ||||
\(254\) | 26.8659i | 0.105771i | ||||||||
\(255\) | 71.8839 | + | 164.479i | 0.281897 | + | 0.645018i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −113.403 | − | 113.403i | −0.441255 | − | 0.441255i | 0.451179 | − | 0.892434i | \(-0.351004\pi\) |
−0.892434 | + | 0.451179i | \(0.851004\pi\) | |||||||
\(258\) | 87.1528 | − | 87.1528i | 0.337802 | − | 0.337802i | ||||
\(259\) | 64.7822i | 0.250124i | ||||||||
\(260\) | −37.9505 | + | 96.8739i | −0.145963 | + | 0.372592i | ||||
\(261\) | −3.69789 | −0.0141682 | ||||||||
\(262\) | 121.821 | + | 121.821i | 0.464967 | + | 0.464967i | ||||
\(263\) | 290.995 | − | 290.995i | 1.10644 | − | 1.10644i | 0.112829 | − | 0.993614i | \(-0.464009\pi\) |
0.993614 | − | 0.112829i | \(-0.0359911\pi\) | |||||||
\(264\) | − | 17.8430i | − | 0.0675873i | ||||||
\(265\) | 175.436 | + | 68.7272i | 0.662022 | + | 0.259348i | ||||
\(266\) | −35.4545 | −0.133288 | ||||||||
\(267\) | 134.722 | + | 134.722i | 0.504575 | + | 0.504575i | ||||
\(268\) | 175.542 | − | 175.542i | 0.655009 | − | 0.655009i | ||||
\(269\) | 82.3667i | 0.306196i | 0.988211 | + | 0.153098i | \(0.0489250\pi\) | ||||
−0.988211 | + | 0.153098i | \(0.951075\pi\) | |||||||
\(270\) | 33.6675 | − | 14.7140i | 0.124694 | − | 0.0544962i | ||||
\(271\) | −397.792 | −1.46787 | −0.733933 | − | 0.679222i | \(-0.762317\pi\) | ||||
−0.733933 | + | 0.679222i | \(0.762317\pi\) | |||||||
\(272\) | 58.6249 | + | 58.6249i | 0.215533 | + | 0.215533i | ||||
\(273\) | 94.6942 | − | 94.6942i | 0.346865 | − | 0.346865i | ||||
\(274\) | 245.457i | 0.895829i | ||||||||
\(275\) | −61.8497 | + | 66.8252i | −0.224908 | + | 0.243001i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | −103.267 | − | 103.267i | −0.372804 | − | 0.372804i | 0.495693 | − | 0.868498i | \(-0.334914\pi\) |
−0.868498 | + | 0.495693i | \(0.834914\pi\) | |||||||
\(278\) | −7.58478 | + | 7.58478i | −0.0272834 | + | 0.0272834i | ||||
\(279\) | − | 59.4193i | − | 0.212972i | ||||||
\(280\) | 42.0868 | + | 96.3001i | 0.150310 | + | 0.343929i | ||||
\(281\) | 355.895 | 1.26653 | 0.633264 | − | 0.773936i | \(-0.281715\pi\) | ||||
0.633264 | + | 0.773936i | \(0.281715\pi\) | |||||||
\(282\) | −81.3664 | − | 81.3664i | −0.288533 | − | 0.288533i | ||||
\(283\) | 81.4946 | − | 81.4946i | 0.287967 | − | 0.287967i | −0.548309 | − | 0.836276i | \(-0.684728\pi\) |
0.836276 | + | 0.548309i | \(0.184728\pi\) | |||||||
\(284\) | 15.5487i | 0.0547488i | ||||||||
\(285\) | 10.6568 | − | 27.2030i | 0.0373922 | − | 0.0954490i | ||||
\(286\) | 53.5905 | 0.187379 | ||||||||
\(287\) | −248.442 | − | 248.442i | −0.865652 | − | 0.865652i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 140.610i | 0.486541i | ||||||||
\(290\) | 8.11550 | + | 3.17926i | 0.0279845 | + | 0.0109630i | ||||
\(291\) | 2.99926 | 0.0103067 | ||||||||
\(292\) | −117.595 | − | 117.595i | −0.402723 | − | 0.402723i | ||||
\(293\) | −51.2472 | + | 51.2472i | −0.174905 | + | 0.174905i | −0.789131 | − | 0.614226i | \(-0.789469\pi\) |
0.614226 | + | 0.789131i | \(0.289469\pi\) | |||||||
\(294\) | − | 15.2481i | − | 0.0518643i | ||||||
\(295\) | 201.851 | − | 88.2165i | 0.684240 | − | 0.299039i | ||||
\(296\) | −24.6566 | −0.0832993 | ||||||||
\(297\) | −13.3823 | − | 13.3823i | −0.0450582 | − | 0.0450582i | ||||
\(298\) | −221.285 | + | 221.285i | −0.742568 | + | 0.742568i | ||||
\(299\) | − | 49.8969i | − | 0.166879i | ||||||
\(300\) | −86.5379 | + | 3.34617i | −0.288460 | + | 0.0111539i | ||||
\(301\) | 373.929 | 1.24229 | ||||||||
\(302\) | −4.57858 | − | 4.57858i | −0.0151608 | − | 0.0151608i | ||||
\(303\) | 164.767 | − | 164.767i | 0.543786 | − | 0.543786i | ||||
\(304\) | − | 13.4942i | − | 0.0443889i | ||||||
\(305\) | 75.9243 | + | 173.724i | 0.248932 | + | 0.569588i | ||||
\(306\) | 87.9374 | 0.287377 | ||||||||
\(307\) | −134.262 | − | 134.262i | −0.437336 | − | 0.437336i | 0.453778 | − | 0.891115i | \(-0.350076\pi\) |
−0.891115 | + | 0.453778i | \(0.850076\pi\) | |||||||
\(308\) | 38.2777 | − | 38.2777i | 0.124278 | − | 0.124278i | ||||
\(309\) | 148.283i | 0.479880i | ||||||||
\(310\) | −51.0856 | + | 130.403i | −0.164792 | + | 0.420656i | ||||
\(311\) | 287.922 | 0.925795 | 0.462897 | − | 0.886412i | \(-0.346810\pi\) | ||||
0.462897 | + | 0.886412i | \(0.346810\pi\) | |||||||
\(312\) | 36.0413 | + | 36.0413i | 0.115517 | + | 0.115517i | ||||
\(313\) | −115.283 | + | 115.283i | −0.368316 | + | 0.368316i | −0.866863 | − | 0.498547i | \(-0.833867\pi\) |
0.498547 | + | 0.866863i | \(0.333867\pi\) | |||||||
\(314\) | 39.0728i | 0.124436i | ||||||||
\(315\) | 103.790 | + | 40.6599i | 0.329493 | + | 0.129079i | ||||
\(316\) | 53.8623 | 0.170450 | ||||||||
\(317\) | 90.5079 | + | 90.5079i | 0.285514 | + | 0.285514i | 0.835303 | − | 0.549789i | \(-0.185292\pi\) |
−0.549789 | + | 0.835303i | \(0.685292\pi\) | |||||||
\(318\) | 65.2697 | − | 65.2697i | 0.205251 | − | 0.205251i | ||||
\(319\) | − | 4.48948i | − | 0.0140736i | ||||||
\(320\) | −36.6525 | + | 16.0186i | −0.114539 | + | 0.0500580i | ||||
\(321\) | 107.013 | 0.333375 | ||||||||
\(322\) | −35.6395 | − | 35.6395i | −0.110682 | − | 0.110682i | ||||
\(323\) | 49.4437 | − | 49.4437i | 0.153076 | − | 0.153076i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | −10.0500 | − | 259.912i | −0.0309231 | − | 0.799728i | ||||
\(326\) | −192.666 | −0.591000 | ||||||||
\(327\) | 5.37772 | + | 5.37772i | 0.0164456 | + | 0.0164456i | ||||
\(328\) | 94.5589 | − | 94.5589i | 0.288289 | − | 0.288289i | ||||
\(329\) | − | 349.102i | − | 1.06110i | ||||||
\(330\) | 17.8637 | + | 40.8745i | 0.0541325 | + | 0.123862i | ||||
\(331\) | −225.894 | −0.682458 | −0.341229 | − | 0.939980i | \(-0.610843\pi\) | ||||
−0.341229 | + | 0.939980i | \(0.610843\pi\) | |||||||
\(332\) | −3.59195 | − | 3.59195i | −0.0108191 | − | 0.0108191i | ||||
\(333\) | −18.4924 | + | 18.4924i | −0.0555329 | + | 0.0555329i | ||||
\(334\) | 323.352i | 0.968120i | ||||||||
\(335\) | −226.383 | + | 577.875i | −0.675771 | + | 1.72500i | ||||
\(336\) | 51.4859 | 0.153232 | ||||||||
\(337\) | 82.0993 | + | 82.0993i | 0.243618 | + | 0.243618i | 0.818345 | − | 0.574727i | \(-0.194892\pi\) |
−0.574727 | + | 0.818345i | \(0.694892\pi\) | |||||||
\(338\) | 60.7520 | − | 60.7520i | 0.179740 | − | 0.179740i | ||||
\(339\) | 168.570i | 0.497255i | ||||||||
\(340\) | −192.990 | − | 75.6040i | −0.567617 | − | 0.222365i | ||||
\(341\) | 72.1389 | 0.211551 | ||||||||
\(342\) | −10.1207 | − | 10.1207i | −0.0295926 | − | 0.0295926i | ||||
\(343\) | −224.772 | + | 224.772i | −0.655313 | + | 0.655313i | ||||
\(344\) | 142.320i | 0.413721i | ||||||||
\(345\) | 38.0573 | − | 16.6325i | 0.110311 | − | 0.0482102i | ||||
\(346\) | −343.170 | −0.991820 | ||||||||
\(347\) | −164.374 | − | 164.374i | −0.473701 | − | 0.473701i | 0.429409 | − | 0.903110i | \(-0.358722\pi\) |
−0.903110 | + | 0.429409i | \(0.858722\pi\) | |||||||
\(348\) | 3.01932 | − | 3.01932i | 0.00867620 | − | 0.00867620i | ||||
\(349\) | − | 130.319i | − | 0.373408i | −0.982416 | − | 0.186704i | \(-0.940220\pi\) | ||
0.982416 | − | 0.186704i | \(-0.0597805\pi\) | |||||||
\(350\) | −192.823 | − | 178.467i | −0.550924 | − | 0.509905i | ||||
\(351\) | 54.0620 | 0.154023 | ||||||||
\(352\) | 14.5688 | + | 14.5688i | 0.0413886 | + | 0.0413886i | ||||
\(353\) | 184.926 | − | 184.926i | 0.523869 | − | 0.523869i | −0.394868 | − | 0.918738i | \(-0.629210\pi\) |
0.918738 | + | 0.394868i | \(0.129210\pi\) | |||||||
\(354\) | − | 107.918i | − | 0.304852i | ||||||
\(355\) | −15.5667 | − | 35.6186i | −0.0438498 | − | 0.100334i | ||||
\(356\) | −219.999 | −0.617976 | ||||||||
\(357\) | 188.647 | + | 188.647i | 0.528424 | + | 0.528424i | ||||
\(358\) | 178.228 | − | 178.228i | 0.497844 | − | 0.497844i | ||||
\(359\) | 211.235i | 0.588398i | 0.955744 | + | 0.294199i | \(0.0950528\pi\) | ||||
−0.955744 | + | 0.294199i | \(0.904947\pi\) | |||||||
\(360\) | −15.4755 | + | 39.5033i | −0.0429874 | + | 0.109731i | ||||
\(361\) | 349.619 | 0.968474 | ||||||||
\(362\) | 107.395 | + | 107.395i | 0.296671 | + | 0.296671i | ||||
\(363\) | −131.947 | + | 131.947i | −0.363491 | + | 0.363491i | ||||
\(364\) | 154.635i | 0.424821i | ||||||||
\(365\) | 387.116 | + | 151.653i | 1.06059 | + | 0.415489i | ||||
\(366\) | 92.8802 | 0.253771 | ||||||||
\(367\) | −384.033 | − | 384.033i | −1.04641 | − | 1.04641i | −0.998869 | − | 0.0475425i | \(-0.984861\pi\) |
−0.0475425 | − | 0.998869i | \(-0.515139\pi\) | |||||||
\(368\) | 13.5647 | − | 13.5647i | 0.0368605 | − | 0.0368605i | ||||
\(369\) | − | 141.838i | − | 0.384386i | ||||||
\(370\) | 56.4829 | − | 24.6852i | 0.152656 | − | 0.0667167i | ||||
\(371\) | 280.039 | 0.754823 | ||||||||
\(372\) | 48.5157 | + | 48.5157i | 0.130418 | + | 0.130418i | ||||
\(373\) | −208.764 | + | 208.764i | −0.559689 | + | 0.559689i | −0.929219 | − | 0.369530i | \(-0.879519\pi\) |
0.369530 | + | 0.929219i | \(0.379519\pi\) | |||||||
\(374\) | 106.762i | 0.285459i | ||||||||
\(375\) | 194.889 | − | 94.3036i | 0.519705 | − | 0.251476i | ||||
\(376\) | 132.871 | 0.353380 | ||||||||
\(377\) | 9.06835 | + | 9.06835i | 0.0240540 | + | 0.0240540i | ||||
\(378\) | 38.6144 | − | 38.6144i | 0.102155 | − | 0.102155i | ||||
\(379\) | 706.994i | 1.86542i | 0.360629 | + | 0.932709i | \(0.382562\pi\) | ||||
−0.360629 | + | 0.932709i | \(0.617438\pi\) | |||||||
\(380\) | 13.5099 | + | 30.9124i | 0.0355523 | + | 0.0813483i | ||||
\(381\) | −32.9039 | −0.0863620 | ||||||||
\(382\) | 120.021 | + | 120.021i | 0.314191 | + | 0.314191i | ||||
\(383\) | 399.956 | − | 399.956i | 1.04427 | − | 1.04427i | 0.0452983 | − | 0.998974i | \(-0.485576\pi\) |
0.998974 | − | 0.0452983i | \(-0.0144238\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −49.3638 | + | 126.008i | −0.128218 | + | 0.327293i | ||||
\(386\) | −103.075 | −0.267033 | ||||||||
\(387\) | 106.740 | + | 106.740i | 0.275814 | + | 0.275814i | ||||
\(388\) | −2.44889 | + | 2.44889i | −0.00631156 | + | 0.00631156i | ||||
\(389\) | − | 174.609i | − | 0.448867i | −0.974489 | − | 0.224434i | \(-0.927947\pi\) | ||
0.974489 | − | 0.224434i | \(-0.0720532\pi\) | |||||||
\(390\) | −118.646 | − | 46.4797i | −0.304220 | − | 0.119179i | ||||
\(391\) | 99.4034 | 0.254229 | ||||||||
\(392\) | 12.4500 | + | 12.4500i | 0.0317602 | + | 0.0317602i | ||||
\(393\) | −149.200 | + | 149.200i | −0.379644 | + | 0.379644i | ||||
\(394\) | 41.0515i | 0.104192i | ||||||||
\(395\) | −123.387 | + | 53.9248i | −0.312372 | + | 0.136518i | ||||
\(396\) | 21.8532 | 0.0551848 | ||||||||
\(397\) | 180.755 | + | 180.755i | 0.455302 | + | 0.455302i | 0.897110 | − | 0.441808i | \(-0.145663\pi\) |
−0.441808 | + | 0.897110i | \(0.645663\pi\) | |||||||
\(398\) | −261.408 | + | 261.408i | −0.656805 | + | 0.656805i | ||||
\(399\) | − | 43.4227i | − | 0.108829i | ||||||
\(400\) | 67.9257 | − | 73.3900i | 0.169814 | − | 0.183475i | ||||
\(401\) | 48.1197 | 0.119999 | 0.0599997 | − | 0.998198i | \(-0.480890\pi\) | ||||
0.0599997 | + | 0.998198i | \(0.480890\pi\) | |||||||
\(402\) | 214.995 | + | 214.995i | 0.534813 | + | 0.534813i | ||||
\(403\) | −145.714 | + | 145.714i | −0.361573 | + | 0.361573i | ||||
\(404\) | 269.063i | 0.665999i | ||||||||
\(405\) | 18.0209 | + | 41.2341i | 0.0444960 | + | 0.101813i | ||||
\(406\) | 12.9544 | 0.0319073 | ||||||||
\(407\) | −22.4510 | − | 22.4510i | −0.0551622 | − | 0.0551622i | ||||
\(408\) | −71.8006 | + | 71.8006i | −0.175982 | + | 0.175982i | ||||
\(409\) | 690.337i | 1.68787i | 0.536448 | + | 0.843933i | \(0.319766\pi\) | ||||
−0.536448 | + | 0.843933i | \(0.680234\pi\) | |||||||
\(410\) | −121.945 | + | 311.282i | −0.297427 | + | 0.759225i | ||||
\(411\) | −300.623 | −0.731442 | ||||||||
\(412\) | −121.073 | − | 121.073i | −0.293865 | − | 0.293865i | ||||
\(413\) | 231.510 | − | 231.510i | 0.560557 | − | 0.560557i | ||||
\(414\) | − | 20.3470i | − | 0.0491473i | ||||||
\(415\) | 11.8245 | + | 4.63226i | 0.0284927 | + | 0.0111621i | ||||
\(416\) | −58.8552 | −0.141479 | ||||||||
\(417\) | −9.28942 | − | 9.28942i | −0.0222768 | − | 0.0222768i | ||||
\(418\) | 12.2872 | − | 12.2872i | 0.0293951 | − | 0.0293951i | ||||
\(419\) | 377.004i | 0.899770i | 0.893087 | + | 0.449885i | \(0.148535\pi\) | ||||
−0.893087 | + | 0.449885i | \(0.851465\pi\) | |||||||
\(420\) | −117.943 | + | 51.5456i | −0.280817 | + | 0.122728i | ||||
\(421\) | 87.0930 | 0.206872 | 0.103436 | − | 0.994636i | \(-0.467016\pi\) | ||||
0.103436 | + | 0.994636i | \(0.467016\pi\) | |||||||
\(422\) | 215.468 | + | 215.468i | 0.510588 | + | 0.510588i | ||||
\(423\) | 99.6531 | − | 99.6531i | 0.235587 | − | 0.235587i | ||||
\(424\) | 106.585i | 0.251380i | ||||||||
\(425\) | 517.789 | − | 20.0214i | 1.21833 | − | 0.0471092i | ||||
\(426\) | −19.0431 | −0.0447022 | ||||||||
\(427\) | 199.251 | + | 199.251i | 0.466630 | + | 0.466630i | ||||
\(428\) | −87.3760 | + | 87.3760i | −0.204150 | + | 0.204150i | ||||
\(429\) | 65.6347i | 0.152995i | ||||||||
\(430\) | −142.485 | − | 326.024i | −0.331360 | − | 0.758195i | ||||
\(431\) | −669.508 | −1.55338 | −0.776691 | − | 0.629881i | \(-0.783103\pi\) | ||||
−0.776691 | + | 0.629881i | \(0.783103\pi\) | |||||||
\(432\) | 14.6969 | + | 14.6969i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | −526.019 | + | 526.019i | −1.21483 | + | 1.21483i | −0.245404 | + | 0.969421i | \(0.578921\pi\) |
−0.969421 | + | 0.245404i | \(0.921079\pi\) | |||||||
\(434\) | 208.156i | 0.479622i | ||||||||
\(435\) | −3.89378 | + | 9.93942i | −0.00895121 | + | 0.0228492i | ||||
\(436\) | −8.78178 | −0.0201417 | ||||||||
\(437\) | −11.4403 | − | 11.4403i | −0.0261792 | − | 0.0261792i | ||||
\(438\) | 144.024 | − | 144.024i | 0.328822 | − | 0.328822i | ||||
\(439\) | − | 776.442i | − | 1.76866i | −0.466862 | − | 0.884330i | \(-0.654616\pi\) | ||
0.466862 | − | 0.884330i | \(-0.345384\pi\) | |||||||
\(440\) | −47.9596 | − | 18.7882i | −0.108999 | − | 0.0427005i | ||||
\(441\) | 18.6750 | 0.0423470 | ||||||||
\(442\) | −215.649 | − | 215.649i | −0.487894 | − | 0.487894i | ||||
\(443\) | 71.2577 | − | 71.2577i | 0.160853 | − | 0.160853i | −0.622092 | − | 0.782944i | \(-0.713717\pi\) |
0.782944 | + | 0.622092i | \(0.213717\pi\) | |||||||
\(444\) | − | 30.1980i | − | 0.0680136i | ||||||
\(445\) | 503.971 | − | 220.255i | 1.13252 | − | 0.494954i | ||||
\(446\) | −330.535 | −0.741110 | ||||||||
\(447\) | −271.018 | − | 271.018i | −0.606305 | − | 0.606305i | ||||
\(448\) | −42.0381 | + | 42.0381i | −0.0938350 | + | 0.0938350i | ||||
\(449\) | 597.802i | 1.33141i | 0.746217 | + | 0.665703i | \(0.231868\pi\) | ||||
−0.746217 | + | 0.665703i | \(0.768132\pi\) | |||||||
\(450\) | −4.09820 | − | 105.987i | −0.00910711 | − | 0.235526i | ||||
\(451\) | 172.201 | 0.381820 | ||||||||
\(452\) | −137.636 | − | 137.636i | −0.304505 | − | 0.304505i | ||||
\(453\) | 5.60759 | − | 5.60759i | 0.0123788 | − | 0.0123788i | ||||
\(454\) | 356.651i | 0.785574i | ||||||||
\(455\) | −154.814 | − | 354.235i | −0.340251 | − | 0.778539i | ||||
\(456\) | 16.5270 | 0.0362434 | ||||||||
\(457\) | 548.139 | + | 548.139i | 1.19943 | + | 1.19943i | 0.974338 | + | 0.225090i | \(0.0722677\pi\) |
0.225090 | + | 0.974338i | \(0.427732\pi\) | |||||||
\(458\) | −50.6019 | + | 50.6019i | −0.110484 | + | 0.110484i | ||||
\(459\) | 107.701i | 0.234642i | ||||||||
\(460\) | −17.4933 | + | 44.6541i | −0.0380289 | + | 0.0970740i | ||||
\(461\) | −647.631 | −1.40484 | −0.702420 | − | 0.711763i | \(-0.747897\pi\) | ||||
−0.702420 | + | 0.711763i | \(0.747897\pi\) | |||||||
\(462\) | 46.8804 | + | 46.8804i | 0.101473 | + | 0.101473i | ||||
\(463\) | −26.9735 | + | 26.9735i | −0.0582581 | + | 0.0582581i | −0.735636 | − | 0.677377i | \(-0.763116\pi\) |
0.677377 | + | 0.735636i | \(0.263116\pi\) | |||||||
\(464\) | 4.93053i | 0.0106261i | ||||||||
\(465\) | −159.711 | − | 62.5669i | −0.343464 | − | 0.134552i | ||||
\(466\) | −26.5351 | −0.0569423 | ||||||||
\(467\) | −620.663 | − | 620.663i | −1.32904 | − | 1.32904i | −0.906205 | − | 0.422838i | \(-0.861034\pi\) |
−0.422838 | − | 0.906205i | \(-0.638966\pi\) | |||||||
\(468\) | −44.1414 | + | 44.1414i | −0.0943193 | + | 0.0943193i | ||||
\(469\) | 922.433i | 1.96681i | ||||||||
\(470\) | −304.378 | + | 133.025i | −0.647613 | + | 0.283032i | ||||
\(471\) | −47.8543 | −0.101601 | ||||||||
\(472\) | 88.1143 | + | 88.1143i | 0.186683 | + | 0.186683i | ||||
\(473\) | −129.589 | + | 129.589i | −0.273973 | + | 0.273973i | ||||
\(474\) | 65.9676i | 0.139172i | ||||||||
\(475\) | −61.8964 | − | 57.2879i | −0.130308 | − | 0.120606i | ||||
\(476\) | −308.060 | −0.647185 | ||||||||
\(477\) | 79.9388 | + | 79.9388i | 0.167587 | + | 0.167587i | ||||
\(478\) | −336.857 | + | 336.857i | −0.704721 | + | 0.704721i | ||||
\(479\) | − | 270.238i | − | 0.564171i | −0.959389 | − | 0.282085i | \(-0.908974\pi\) | ||
0.959389 | − | 0.282085i | \(-0.0910262\pi\) | |||||||
\(480\) | −19.6186 | − | 44.8900i | −0.0408722 | − | 0.0935208i | ||||
\(481\) | 90.6981 | 0.188561 | ||||||||
\(482\) | 349.220 | + | 349.220i | 0.724524 | + | 0.724524i | ||||
\(483\) | 43.6493 | − | 43.6493i | 0.0903713 | − | 0.0903713i | ||||
\(484\) | − | 215.469i | − | 0.445184i | ||||||
\(485\) | 3.15814 | − | 8.06159i | 0.00651162 | − | 0.0166218i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 124.905 | + | 124.905i | 0.256479 | + | 0.256479i | 0.823621 | − | 0.567141i | \(-0.191951\pi\) |
−0.567141 | + | 0.823621i | \(0.691951\pi\) | |||||||
\(488\) | −75.8363 | + | 75.8363i | −0.155402 | + | 0.155402i | ||||
\(489\) | − | 235.967i | − | 0.482549i | ||||||
\(490\) | −40.9847 | − | 16.0558i | −0.0836423 | − | 0.0327670i | ||||
\(491\) | −598.054 | −1.21803 | −0.609016 | − | 0.793158i | \(-0.708436\pi\) | ||||
−0.609016 | + | 0.793158i | \(0.708436\pi\) | |||||||
\(492\) | 115.811 | + | 115.811i | 0.235387 | + | 0.235387i | ||||
\(493\) | −18.0657 | + | 18.0657i | −0.0366445 | + | 0.0366445i | ||||
\(494\) | 49.6379i | 0.100482i | ||||||||
\(495\) | −50.0608 | + | 21.8785i | −0.101133 | + | 0.0441990i | ||||
\(496\) | −79.2257 | −0.159729 | ||||||||
\(497\) | −40.8522 | − | 40.8522i | −0.0821976 | − | 0.0821976i | ||||
\(498\) | 4.39922 | − | 4.39922i | 0.00883378 | − | 0.00883378i | ||||
\(499\) | 160.709i | 0.322062i | 0.986949 | + | 0.161031i | \(0.0514820\pi\) | ||||
−0.986949 | + | 0.161031i | \(0.948518\pi\) | |||||||
\(500\) | −82.1279 | + | 236.125i | −0.164256 | + | 0.472250i | ||||
\(501\) | −396.024 | −0.790466 | ||||||||
\(502\) | 410.838 | + | 410.838i | 0.818402 | + | 0.818402i | ||||
\(503\) | −369.487 | + | 369.487i | −0.734566 | + | 0.734566i | −0.971521 | − | 0.236955i | \(-0.923851\pi\) |
0.236955 | + | 0.971521i | \(0.423851\pi\) | |||||||
\(504\) | 63.0571i | 0.125113i | ||||||||
\(505\) | −269.375 | − | 616.365i | −0.533417 | − | 1.22053i | ||||
\(506\) | 24.7026 | 0.0488193 | ||||||||
\(507\) | 74.4057 | + | 74.4057i | 0.146757 | + | 0.146757i | ||||
\(508\) | 26.8659 | − | 26.8659i | 0.0528857 | − | 0.0528857i | ||||
\(509\) | 760.982i | 1.49505i | 0.664232 | + | 0.747526i | \(0.268759\pi\) | ||||
−0.664232 | + | 0.747526i | \(0.731241\pi\) | |||||||
\(510\) | 92.5956 | − | 236.363i | 0.181560 | − | 0.463458i | ||||
\(511\) | 617.934 | 1.20927 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 12.3952 | − | 12.3952i | 0.0241623 | − | 0.0241623i | ||||
\(514\) | 226.805i | 0.441255i | ||||||||
\(515\) | 398.564 | + | 156.138i | 0.773910 | + | 0.303180i | ||||
\(516\) | −174.306 | −0.337802 | ||||||||
\(517\) | 120.985 | + | 120.985i | 0.234014 | + | 0.234014i | ||||
\(518\) | 64.7822 | − | 64.7822i | 0.125062 | − | 0.125062i | ||||
\(519\) | − | 420.295i | − | 0.809817i | ||||||
\(520\) | 134.824 | − | 58.9235i | 0.259278 | − | 0.113314i | ||||
\(521\) | 254.214 | 0.487934 | 0.243967 | − | 0.969784i | \(-0.421551\pi\) | ||||
0.243967 | + | 0.969784i | \(0.421551\pi\) | |||||||
\(522\) | 3.69789 | + | 3.69789i | 0.00708409 | + | 0.00708409i | ||||
\(523\) | 4.21088 | − | 4.21088i | 0.00805140 | − | 0.00805140i | −0.703070 | − | 0.711121i | \(-0.748188\pi\) |
0.711121 | + | 0.703070i | \(0.248188\pi\) | |||||||
\(524\) | − | 243.643i | − | 0.464967i | ||||||
\(525\) | 218.576 | − | 236.160i | 0.416336 | − | 0.449828i | ||||
\(526\) | −581.989 | −1.10644 | ||||||||
\(527\) | −290.288 | − | 290.288i | −0.550831 | − | 0.550831i | ||||
\(528\) | −17.8430 | + | 17.8430i | −0.0337936 | + | 0.0337936i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −106.709 | − | 244.163i | −0.201337 | − | 0.460685i | ||||
\(531\) | 132.172 | 0.248911 | ||||||||
\(532\) | 35.4545 | + | 35.4545i | 0.0666438 | + | 0.0666438i | ||||
\(533\) | −347.830 | + | 347.830i | −0.652589 | + | 0.652589i | ||||
\(534\) | − | 269.443i | − | 0.504575i | ||||||
\(535\) | 112.682 | − | 287.637i | 0.210621 | − | 0.537639i | ||||
\(536\) | −351.085 | −0.655009 | ||||||||
\(537\) | 218.284 | + | 218.284i | 0.406488 | + | 0.406488i | ||||
\(538\) | 82.3667 | − | 82.3667i | 0.153098 | − | 0.153098i | ||||
\(539\) | 22.6727i | 0.0420644i | ||||||||
\(540\) | −48.3815 | − | 18.9535i | −0.0895953 | − | 0.0350991i | ||||
\(541\) | 828.433 | 1.53130 | 0.765650 | − | 0.643258i | \(-0.222418\pi\) | ||||
0.765650 | + | 0.643258i | \(0.222418\pi\) | |||||||
\(542\) | 397.792 | + | 397.792i | 0.733933 | + | 0.733933i | ||||
\(543\) | −131.531 | + | 131.531i | −0.242231 | + | 0.242231i | ||||
\(544\) | − | 117.250i | − | 0.215533i | ||||||
\(545\) | 20.1171 | − | 8.79196i | 0.0369122 | − | 0.0161320i | ||||
\(546\) | −189.388 | −0.346865 | ||||||||
\(547\) | 427.144 | + | 427.144i | 0.780885 | + | 0.780885i | 0.979980 | − | 0.199095i | \(-0.0638003\pi\) |
−0.199095 | + | 0.979980i | \(0.563800\pi\) | |||||||
\(548\) | 245.457 | − | 245.457i | 0.447915 | − | 0.447915i | ||||
\(549\) | 113.755i | 0.207203i | ||||||||
\(550\) | 128.675 | − | 4.97548i | 0.233954 | − | 0.00904633i | ||||
\(551\) | 4.15836 | 0.00754692 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | −141.517 | + | 141.517i | −0.255907 | + | 0.255907i | ||||
\(554\) | 206.534i | 0.372804i | ||||||||
\(555\) | 30.2330 | + | 69.1771i | 0.0544740 | + | 0.124643i | ||||
\(556\) | 15.1696 | 0.0272834 | ||||||||
\(557\) | 49.8244 | + | 49.8244i | 0.0894514 | + | 0.0894514i | 0.750417 | − | 0.660965i | \(-0.229853\pi\) |
−0.660965 | + | 0.750417i | \(0.729853\pi\) | |||||||
\(558\) | −59.4193 | + | 59.4193i | −0.106486 | + | 0.106486i | ||||
\(559\) | − | 523.517i | − | 0.936524i | ||||||
\(560\) | 54.2132 | − | 138.387i | 0.0968093 | − | 0.247119i | ||||
\(561\) | −130.756 | −0.233076 | ||||||||
\(562\) | −355.895 | − | 355.895i | −0.633264 | − | 0.633264i | ||||
\(563\) | 669.424 | − | 669.424i | 1.18903 | − | 1.18903i | 0.211695 | − | 0.977336i | \(-0.432102\pi\) |
0.977336 | − | 0.211695i | \(-0.0678983\pi\) | |||||||
\(564\) | 162.733i | 0.288533i | ||||||||
\(565\) | 453.091 | + | 177.499i | 0.801931 | + | 0.314157i | ||||
\(566\) | −162.989 | −0.287967 | ||||||||
\(567\) | 47.2928 | + | 47.2928i | 0.0834089 | + | 0.0834089i | ||||
\(568\) | 15.5487 | − | 15.5487i | 0.0273744 | − | 0.0273744i | ||||
\(569\) | − | 1024.87i | − | 1.80118i | −0.434671 | − | 0.900589i | \(-0.643135\pi\) | ||
0.434671 | − | 0.900589i | \(-0.356865\pi\) | |||||||
\(570\) | −37.8597 | + | 16.5462i | −0.0664206 | + | 0.0290284i | ||||
\(571\) | 900.323 | 1.57675 | 0.788374 | − | 0.615197i | \(-0.210923\pi\) | ||||
0.788374 | + | 0.615197i | \(0.210923\pi\) | |||||||
\(572\) | −53.5905 | − | 53.5905i | −0.0936897 | − | 0.0936897i | ||||
\(573\) | −146.995 | + | 146.995i | −0.256536 | + | 0.256536i | ||||
\(574\) | 496.884i | 0.865652i | ||||||||
\(575\) | −4.63256 | − | 119.806i | −0.00805662 | − | 0.208359i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 509.691 | + | 509.691i | 0.883346 | + | 0.883346i | 0.993873 | − | 0.110527i | \(-0.0352539\pi\) |
−0.110527 | + | 0.993873i | \(0.535254\pi\) | |||||||
\(578\) | 140.610 | − | 140.610i | 0.243271 | − | 0.243271i | ||||
\(579\) | − | 126.240i | − | 0.218031i | ||||||
\(580\) | −4.93624 | − | 11.2948i | −0.00851076 | − | 0.0194737i | ||||
\(581\) | 18.8748 | 0.0324868 | ||||||||
\(582\) | −2.99926 | − | 2.99926i | −0.00515337 | − | 0.00515337i | ||||
\(583\) | −97.0509 | + | 97.0509i | −0.166468 | + | 0.166468i | ||||
\(584\) | 235.190i | 0.402723i | ||||||||
\(585\) | 56.9257 | − | 145.311i | 0.0973089 | − | 0.248395i | ||||
\(586\) | 102.494 | 0.174905 | ||||||||
\(587\) | −240.945 | − | 240.945i | −0.410468 | − | 0.410468i | 0.471433 | − | 0.881902i | \(-0.343737\pi\) |
−0.881902 | + | 0.471433i | \(0.843737\pi\) | |||||||
\(588\) | −15.2481 | + | 15.2481i | −0.0259321 | + | 0.0259321i | ||||
\(589\) | 66.8182i | 0.113443i | ||||||||
\(590\) | −290.067 | − | 113.634i | −0.491639 | − | 0.192600i | ||||
\(591\) | −50.2776 | −0.0850721 | ||||||||
\(592\) | 24.6566 | + | 24.6566i | 0.0416496 | + | 0.0416496i | ||||
\(593\) | −205.486 | + | 205.486i | −0.346519 | + | 0.346519i | −0.858811 | − | 0.512292i | \(-0.828797\pi\) |
0.512292 | + | 0.858811i | \(0.328797\pi\) | |||||||
\(594\) | 26.7646i | 0.0450582i | ||||||||
\(595\) | 705.698 | − | 308.417i | 1.18605 | − | 0.518348i | ||||
\(596\) | 442.571 | 0.742568 | ||||||||
\(597\) | −320.158 | − | 320.158i | −0.536279 | − | 0.536279i | ||||
\(598\) | −49.8969 | + | 49.8969i | −0.0834397 | + | 0.0834397i | ||||
\(599\) | − | 902.715i | − | 1.50704i | −0.657426 | − | 0.753519i | \(-0.728355\pi\) | ||
0.657426 | − | 0.753519i | \(-0.271645\pi\) | |||||||
\(600\) | 89.8840 | + | 83.1917i | 0.149807 | + | 0.138653i | ||||
\(601\) | −267.744 | −0.445497 | −0.222749 | − | 0.974876i | \(-0.571503\pi\) | ||||
−0.222749 | + | 0.974876i | \(0.571503\pi\) | |||||||
\(602\) | −373.929 | − | 373.929i | −0.621144 | − | 0.621144i | ||||
\(603\) | −263.314 | + | 263.314i | −0.436673 | + | 0.436673i | ||||
\(604\) | 9.15715i | 0.0151608i | ||||||||
\(605\) | 215.719 | + | 493.592i | 0.356560 | + | 0.815855i | ||||
\(606\) | −329.534 | −0.543786 | ||||||||
\(607\) | 438.783 | + | 438.783i | 0.722871 | + | 0.722871i | 0.969189 | − | 0.246318i | \(-0.0792207\pi\) |
−0.246318 | + | 0.969189i | \(0.579221\pi\) | |||||||
\(608\) | −13.4942 | + | 13.4942i | −0.0221945 | + | 0.0221945i | ||||
\(609\) | 15.8658i | 0.0260522i | ||||||||
\(610\) | 97.8002 | − | 249.649i | 0.160328 | − | 0.409260i | ||||
\(611\) | −488.759 | −0.799932 | ||||||||
\(612\) | −87.9374 | − | 87.9374i | −0.143689 | − | 0.143689i | ||||
\(613\) | 152.241 | − | 152.241i | 0.248354 | − | 0.248354i | −0.571941 | − | 0.820295i | \(-0.693809\pi\) |
0.820295 | + | 0.571941i | \(0.193809\pi\) | |||||||
\(614\) | 268.524i | 0.437336i | ||||||||
\(615\) | −381.241 | − | 149.352i | −0.619905 | − | 0.242848i | ||||
\(616\) | −76.5554 | −0.124278 | ||||||||
\(617\) | 451.575 | + | 451.575i | 0.731888 | + | 0.731888i | 0.970994 | − | 0.239105i | \(-0.0768541\pi\) |
−0.239105 | + | 0.970994i | \(0.576854\pi\) | |||||||
\(618\) | 148.283 | − | 148.283i | 0.239940 | − | 0.239940i | ||||
\(619\) | − | 579.724i | − | 0.936550i | −0.883583 | − | 0.468275i | \(-0.844876\pi\) | ||
0.883583 | − | 0.468275i | \(-0.155124\pi\) | |||||||
\(620\) | 181.489 | − | 79.3176i | 0.292724 | − | 0.127932i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | −287.922 | − | 287.922i | −0.462897 | − | 0.462897i | ||||
\(623\) | 578.022 | − | 578.022i | 0.927805 | − | 0.927805i | ||||
\(624\) | − | 72.0826i | − | 0.115517i | ||||||
\(625\) | −48.2617 | − | 623.134i | −0.0772187 | − | 0.997014i | ||||
\(626\) | 230.566 | 0.368316 | ||||||||
\(627\) | 15.0486 | + | 15.0486i | 0.0240010 | + | 0.0240010i | ||||
\(628\) | 39.0728 | − | 39.0728i | 0.0622179 | − | 0.0622179i | ||||
\(629\) | 180.686i | 0.287260i | ||||||||
\(630\) | −63.1302 | − | 144.450i | −0.100207 | − | 0.229286i | ||||
\(631\) | −708.881 | −1.12342 | −0.561712 | − | 0.827333i | \(-0.689857\pi\) | ||||
−0.561712 | + | 0.827333i | \(0.689857\pi\) | |||||||
\(632\) | −53.8623 | − | 53.8623i | −0.0852252 | − | 0.0852252i | ||||
\(633\) | −263.894 | + | 263.894i | −0.416894 | + | 0.416894i | ||||
\(634\) | − | 181.016i | − | 0.285514i | ||||||
\(635\) | −34.6469 | + | 88.4411i | −0.0545621 | + | 0.139277i | ||||
\(636\) | −130.539 | −0.205251 | ||||||||
\(637\) | −45.7968 | − | 45.7968i | −0.0718945 | − | 0.0718945i | ||||
\(638\) | −4.48948 | + | 4.48948i | −0.00703681 | + | 0.00703681i | ||||
\(639\) | − | 23.3230i | − | 0.0364992i | ||||||
\(640\) | 52.6711 | + | 20.6339i | 0.0822985 | + | 0.0322405i | ||||
\(641\) | 1062.59 | 1.65770 | 0.828852 | − | 0.559468i | \(-0.188995\pi\) | ||||
0.828852 | + | 0.559468i | \(0.188995\pi\) | |||||||
\(642\) | −107.013 | − | 107.013i | −0.166687 | − | 0.166687i | ||||
\(643\) | −686.400 | + | 686.400i | −1.06750 | + | 1.06750i | −0.0699458 | + | 0.997551i | \(0.522283\pi\) |
−0.997551 | + | 0.0699458i | \(0.977717\pi\) | |||||||
\(644\) | 71.2790i | 0.110682i | ||||||||
\(645\) | 399.296 | − | 174.508i | 0.619064 | − | 0.270555i | ||||
\(646\) | −98.8874 | −0.153076 | ||||||||
\(647\) | −229.470 | − | 229.470i | −0.354668 | − | 0.354668i | 0.507175 | − | 0.861843i | \(-0.330690\pi\) |
−0.861843 | + | 0.507175i | \(0.830690\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 160.465i | 0.247249i | ||||||||
\(650\) | −249.862 | + | 269.962i | −0.384402 | + | 0.415325i | ||||
\(651\) | −254.938 | −0.391610 | ||||||||
\(652\) | 192.666 | + | 192.666i | 0.295500 | + | 0.295500i | ||||
\(653\) | 372.281 | − | 372.281i | 0.570109 | − | 0.570109i | −0.362050 | − | 0.932159i | \(-0.617923\pi\) |
0.932159 | + | 0.362050i | \(0.117923\pi\) | |||||||
\(654\) | − | 10.7554i | − | 0.0164456i | ||||||
\(655\) | 243.925 | + | 558.133i | 0.372405 | + | 0.852111i | ||||
\(656\) | −189.118 | −0.288289 | ||||||||
\(657\) | 176.393 | + | 176.393i | 0.268482 | + | 0.268482i | ||||
\(658\) | −349.102 | + | 349.102i | −0.530550 | + | 0.530550i | ||||
\(659\) | 78.1061i | 0.118522i | 0.998243 | + | 0.0592611i | \(0.0188744\pi\) | ||||
−0.998243 | + | 0.0592611i | \(0.981126\pi\) | |||||||
\(660\) | 23.0108 | − | 58.7382i | 0.0348648 | − | 0.0889973i | ||||
\(661\) | −79.4275 | −0.120163 | −0.0600813 | − | 0.998193i | \(-0.519136\pi\) | ||||
−0.0600813 | + | 0.998193i | \(0.519136\pi\) | |||||||
\(662\) | 225.894 | + | 225.894i | 0.341229 | + | 0.341229i | ||||
\(663\) | 264.115 | − | 264.115i | 0.398363 | − | 0.398363i | ||||
\(664\) | 7.18390i | 0.0108191i | ||||||||
\(665\) | −116.714 | − | 45.7229i | −0.175510 | − | 0.0687562i | ||||
\(666\) | 36.9849 | 0.0555329 | ||||||||
\(667\) | 4.18006 | + | 4.18006i | 0.00626695 | + | 0.00626695i | ||||
\(668\) | 323.352 | − | 323.352i | 0.484060 | − | 0.484060i | ||||
\(669\) | − | 404.821i | − | 0.605113i | ||||||
\(670\) | 804.259 | − | 351.492i | 1.20039 | − | 0.524615i | ||||
\(671\) | −138.105 | −0.205820 | ||||||||
\(672\) | −51.4859 | − | 51.4859i | −0.0766160 | − | 0.0766160i | ||||
\(673\) | −726.361 | + | 726.361i | −1.07929 | + | 1.07929i | −0.0827151 | + | 0.996573i | \(0.526359\pi\) |
−0.996573 | + | 0.0827151i | \(0.973641\pi\) | |||||||
\(674\) | − | 164.199i | − | 0.243618i | ||||||
\(675\) | 129.807 | − | 5.01925i | 0.192306 | − | 0.00743592i | ||||
\(676\) | −121.504 | −0.179740 | ||||||||
\(677\) | 335.914 | + | 335.914i | 0.496180 | + | 0.496180i | 0.910247 | − | 0.414067i | \(-0.135892\pi\) |
−0.414067 | + | 0.910247i | \(0.635892\pi\) | |||||||
\(678\) | 168.570 | − | 168.570i | 0.248628 | − | 0.248628i | ||||
\(679\) | − | 12.8683i | − | 0.0189519i | ||||||
\(680\) | 117.386 | + | 268.594i | 0.172626 | + | 0.394991i | ||||
\(681\) | −436.806 | −0.641419 | ||||||||
\(682\) | −72.1389 | − | 72.1389i | −0.105775 | − | 0.105775i | ||||
\(683\) | −188.131 | + | 188.131i | −0.275448 | + | 0.275448i | −0.831289 | − | 0.555841i | \(-0.812396\pi\) |
0.555841 | + | 0.831289i | \(0.312396\pi\) | |||||||
\(684\) | 20.2414i | 0.0295926i | ||||||||
\(685\) | −316.547 | + | 808.031i | −0.462112 | + | 1.17961i | ||||
\(686\) | 449.545 | 0.655313 | ||||||||
\(687\) | −61.9744 | − | 61.9744i | −0.0902102 | − | 0.0902102i | ||||
\(688\) | 142.320 | − | 142.320i | 0.206860 | − | 0.206860i | ||||
\(689\) | − | 392.068i | − | 0.569039i | ||||||
\(690\) | −54.6898 | − | 21.4248i | −0.0792606 | − | 0.0310504i | ||||
\(691\) | −729.123 | −1.05517 | −0.527585 | − | 0.849502i | \(-0.676902\pi\) | ||||
−0.527585 | + | 0.849502i | \(0.676902\pi\) | |||||||
\(692\) | 343.170 | + | 343.170i | 0.495910 | + | 0.495910i | ||||
\(693\) | −57.4166 | + | 57.4166i | −0.0828522 | + | 0.0828522i | ||||
\(694\) | 328.748i | 0.473701i | ||||||||
\(695\) | −34.7502 | + | 15.1872i | −0.0500002 | + | 0.0218520i | ||||
\(696\) | −6.03864 | −0.00867620 | ||||||||
\(697\) | −692.939 | − | 692.939i | −0.994173 | − | 0.994173i | ||||
\(698\) | −130.319 | + | 130.319i | −0.186704 | + | 0.186704i | ||||
\(699\) | − | 32.4987i | − | 0.0464932i | ||||||
\(700\) | 14.3567 | + | 371.290i | 0.0205096 | + | 0.530415i | ||||
\(701\) | 616.629 | 0.879642 | 0.439821 | − | 0.898085i | \(-0.355042\pi\) | ||||
0.439821 | + | 0.898085i | \(0.355042\pi\) | |||||||
\(702\) | −54.0620 | − | 54.0620i | −0.0770113 | − | 0.0770113i | ||||
\(703\) | 20.7951 | − | 20.7951i | 0.0295805 | − | 0.0295805i | ||||
\(704\) | − | 29.1376i | − | 0.0413886i | ||||||
\(705\) | −162.922 | − | 372.785i | −0.231094 | − | 0.528774i | ||||
\(706\) | −369.852 | −0.523869 | ||||||||
\(707\) | −706.932 | − | 706.932i | −0.999904 | − | 0.999904i | ||||
\(708\) | −107.918 | + | 107.918i | −0.152426 | + | 0.152426i | ||||
\(709\) | 446.810i | 0.630197i | 0.949059 | + | 0.315099i | \(0.102038\pi\) | ||||
−0.949059 | + | 0.315099i | \(0.897962\pi\) | |||||||
\(710\) | −20.0519 | + | 51.1852i | −0.0282421 | + | 0.0720919i | ||||
\(711\) | −80.7935 | −0.113634 | ||||||||
\(712\) | 219.999 | + | 219.999i | 0.308988 | + | 0.308988i | ||||
\(713\) | −67.1669 | + | 67.1669i | −0.0942032 | + | 0.0942032i | ||||
\(714\) | − | 377.295i | − | 0.528424i | ||||||
\(715\) | 176.417 | + | 69.1115i | 0.246737 | + | 0.0966595i | ||||
\(716\) | −356.456 | −0.497844 | ||||||||
\(717\) | −412.564 | − | 412.564i | −0.575403 | − | 0.575403i | ||||
\(718\) | 211.235 | − | 211.235i | 0.294199 | − | 0.294199i | ||||
\(719\) | − | 359.922i | − | 0.500587i | −0.968170 | − | 0.250294i | \(-0.919473\pi\) | ||
0.968170 | − | 0.250294i | \(-0.0805272\pi\) | |||||||
\(720\) | 54.9788 | − | 24.0278i | 0.0763594 | − | 0.0333720i | ||||
\(721\) | 636.207 | 0.882395 | ||||||||
\(722\) | −349.619 | − | 349.619i | −0.484237 | − | 0.484237i | ||||
\(723\) | −427.706 | + | 427.706i | −0.591571 | + | 0.591571i | ||||
\(724\) | − | 214.790i | − | 0.296671i | ||||||
\(725\) | 22.6157 | + | 20.9319i | 0.0311941 | + | 0.0288715i | ||||
\(726\) | 263.894 | 0.363491 | ||||||||
\(727\) | −541.443 | − | 541.443i | −0.744764 | − | 0.744764i | 0.228727 | − | 0.973491i | \(-0.426544\pi\) |
−0.973491 | + | 0.228727i | \(0.926544\pi\) | |||||||
\(728\) | 154.635 | − | 154.635i | 0.212411 | − | 0.212411i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −235.463 | − | 538.770i | −0.322552 | − | 0.738041i | ||||
\(731\) | 1042.94 | 1.42673 | ||||||||
\(732\) | −92.8802 | − | 92.8802i | −0.126885 | − | 0.126885i | ||||
\(733\) | 283.315 | − | 283.315i | 0.386515 | − | 0.386515i | −0.486928 | − | 0.873442i | \(-0.661882\pi\) |
0.873442 | + | 0.486928i | \(0.161882\pi\) | |||||||
\(734\) | 768.066i | 1.04641i | ||||||||
\(735\) | 19.6643 | − | 50.1958i | 0.0267541 | − | 0.0682936i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | −319.680 | − | 319.680i | −0.433758 | − | 0.433758i | ||||
\(738\) | −141.838 | + | 141.838i | −0.192193 | + | 0.192193i | ||||
\(739\) | − | 514.041i | − | 0.695591i | −0.937571 | − | 0.347795i | \(-0.886930\pi\) | ||
0.937571 | − | 0.347795i | \(-0.113070\pi\) | |||||||
\(740\) | −81.1680 | − | 31.7977i | −0.109687 | − | 0.0429698i | ||||
\(741\) | −60.7938 | −0.0820429 | ||||||||
\(742\) | −280.039 | − | 280.039i | −0.377412 | − | 0.377412i | ||||
\(743\) | 229.186 | − | 229.186i | 0.308460 | − | 0.308460i | −0.535852 | − | 0.844312i | \(-0.680009\pi\) |
0.844312 | + | 0.535852i | \(0.180009\pi\) | |||||||
\(744\) | − | 97.0313i | − | 0.130418i | ||||||
\(745\) | −1013.83 | + | 443.084i | −1.36085 | + | 0.594744i | ||||
\(746\) | 417.528 | 0.559689 | ||||||||
\(747\) | 5.38792 | + | 5.38792i | 0.00721275 | + | 0.00721275i | ||||
\(748\) | 106.762 | − | 106.762i | 0.142730 | − | 0.142730i | ||||
\(749\) | − | 459.140i | − | 0.613004i | ||||||
\(750\) | −289.193 | − | 100.586i | −0.385590 | − | 0.134114i | ||||
\(751\) | 208.038 | 0.277014 | 0.138507 | − | 0.990361i | \(-0.455770\pi\) | ||||
0.138507 | + | 0.990361i | \(0.455770\pi\) | |||||||
\(752\) | −132.871 | − | 132.871i | −0.176690 | − | 0.176690i | ||||
\(753\) | −503.172 | + | 503.172i | −0.668223 | + | 0.668223i | ||||
\(754\) | − | 18.1367i | − | 0.0240540i | ||||||
\(755\) | −9.16777 | − | 20.9770i | −0.0121427 | − | 0.0277841i | ||||
\(756\) | −77.2289 | −0.102155 | ||||||||
\(757\) | 630.839 | + | 630.839i | 0.833340 | + | 0.833340i | 0.987972 | − | 0.154632i | \(-0.0494191\pi\) |
−0.154632 | + | 0.987972i | \(0.549419\pi\) | |||||||
\(758\) | 706.994 | − | 706.994i | 0.932709 | − | 0.932709i | ||||
\(759\) | 30.2543i | 0.0398608i | ||||||||
\(760\) | 17.4025 | − | 44.4222i | 0.0228980 | − | 0.0584503i | ||||
\(761\) | −76.3458 | −0.100323 | −0.0501615 | − | 0.998741i | \(-0.515974\pi\) | ||||
−0.0501615 | + | 0.998741i | \(0.515974\pi\) | |||||||
\(762\) | 32.9039 | + | 32.9039i | 0.0431810 | + | 0.0431810i | ||||
\(763\) | 23.0731 | − | 23.0731i | 0.0302399 | − | 0.0302399i | ||||
\(764\) | − | 240.042i | − | 0.314191i | ||||||
\(765\) | 289.485 | + | 113.406i | 0.378411 | + | 0.148243i | ||||
\(766\) | −799.912 | −1.04427 | ||||||||
\(767\) | −324.124 | − | 324.124i | −0.422587 | − | 0.422587i | ||||
\(768\) | 19.5959 | − | 19.5959i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 975.201i | − | 1.26814i | −0.773275 | − | 0.634071i | \(-0.781383\pi\) | ||
0.773275 | − | 0.634071i | \(-0.218617\pi\) | |||||||
\(770\) | 175.372 | − | 76.6442i | 0.227756 | − | 0.0995379i | ||||
\(771\) | −277.778 | −0.360283 | ||||||||
\(772\) | 103.075 | + | 103.075i | 0.133516 | + | 0.133516i | ||||
\(773\) | −660.918 | + | 660.918i | −0.855004 | + | 0.855004i | −0.990744 | − | 0.135740i | \(-0.956659\pi\) |
0.135740 | + | 0.990744i | \(0.456659\pi\) | |||||||
\(774\) | − | 213.480i | − | 0.275814i | ||||||
\(775\) | −336.342 | + | 363.399i | −0.433989 | + | 0.468901i | ||||
\(776\) | 4.89777 | 0.00631156 | ||||||||
\(777\) | 79.3417 | + | 79.3417i | 0.102113 | + | 0.102113i | ||||
\(778\) | −174.609 | + | 174.609i | −0.224434 | + | 0.224434i | ||||
\(779\) | 159.500i | 0.204750i | ||||||||
\(780\) | 72.1662 | + | 165.126i | 0.0925208 | + | 0.211699i | ||||
\(781\) | 28.3156 | 0.0362556 | ||||||||
\(782\) | −99.4034 | − | 99.4034i | −0.127114 | − | 0.127114i | ||||
\(783\) | −4.52898 | + | 4.52898i | −0.00578413 | + | 0.00578413i | ||||
\(784\) | − | 24.9000i | − | 0.0317602i | ||||||
\(785\) | −50.3892 | + | 128.626i | −0.0641901 | + | 0.163854i | ||||
\(786\) | 298.400 | 0.379644 | ||||||||
\(787\) | −62.5711 | − | 62.5711i | −0.0795059 | − | 0.0795059i | 0.666236 | − | 0.745741i | \(-0.267905\pi\) |
−0.745741 | + | 0.666236i | \(0.767905\pi\) | |||||||
\(788\) | 41.0515 | − | 41.0515i | 0.0520958 | − | 0.0520958i | ||||
\(789\) | − | 712.788i | − | 0.903407i | ||||||
\(790\) | 177.312 | + | 69.4620i | 0.224445 | + | 0.0879266i | ||||
\(791\) | 723.246 | 0.914344 | ||||||||
\(792\) | −21.8532 | − | 21.8532i | −0.0275924 | − | 0.0275924i | ||||
\(793\) | 278.960 | − | 278.960i | 0.351778 | − | 0.351778i | ||||
\(794\) | − | 361.510i | − | 0.455302i | ||||||
\(795\) | 299.037 | − | 130.691i | 0.376148 | − | 0.164391i | ||||
\(796\) | 522.817 | 0.656805 | ||||||||
\(797\) | −444.603 | − | 444.603i | −0.557845 | − | 0.557845i | 0.370848 | − | 0.928693i | \(-0.379067\pi\) |
−0.928693 | + | 0.370848i | \(0.879067\pi\) | |||||||
\(798\) | −43.4227 | + | 43.4227i | −0.0544144 | + | 0.0544144i | ||||
\(799\) | − | 973.693i | − | 1.21864i | ||||||
\(800\) | −141.316 | + | 5.46427i | −0.176645 | + | 0.00683033i | ||||
\(801\) | 329.999 | 0.411984 | ||||||||
\(802\) | −48.1197 | − | 48.1197i | −0.0599997 | − | 0.0599997i | ||||
\(803\) | −214.152 | + | 214.152i | −0.266690 | + | 0.266690i | ||||
\(804\) | − | 429.989i | − | 0.534813i | ||||||
\(805\) | −71.3617 | − | 163.285i | −0.0886481 | − | 0.202838i | ||||
\(806\) | 291.428 | 0.361573 | ||||||||
\(807\) | 100.878 | + | 100.878i | 0.125004 | + | 0.125004i | ||||
\(808\) | 269.063 | − | 269.063i | 0.332999 | − | 0.332999i | ||||
\(809\) | − | 28.7800i | − | 0.0355748i | −0.999842 | − | 0.0177874i | \(-0.994338\pi\) | ||
0.999842 | − | 0.0177874i | \(-0.00566220\pi\) | |||||||
\(810\) | 23.2132 | − | 59.2549i | 0.0286583 | − | 0.0731542i | ||||
\(811\) | −396.915 | −0.489415 | −0.244707 | − | 0.969597i | \(-0.578692\pi\) | ||||
−0.244707 | + | 0.969597i | \(0.578692\pi\) | |||||||
\(812\) | −12.9544 | − | 12.9544i | −0.0159537 | − | 0.0159537i | ||||
\(813\) | −487.193 | + | 487.193i | −0.599254 | + | 0.599254i | ||||
\(814\) | 44.9020i | 0.0551622i | ||||||||
\(815\) | −634.245 | − | 248.466i | −0.778215 | − | 0.304867i | ||||
\(816\) | 143.601 | 0.175982 | ||||||||
\(817\) | −120.031 | − | 120.031i | −0.146917 | − | 0.146917i | ||||
\(818\) | 690.337 | − | 690.337i | 0.843933 | − | 0.843933i | ||||
\(819\) | − | 231.953i | − | 0.283214i | ||||||
\(820\) | 433.227 | − | 189.337i | 0.528326 | − | 0.230899i | ||||
\(821\) | −174.164 | −0.212136 | −0.106068 | − | 0.994359i | \(-0.533826\pi\) | ||||
−0.106068 | + | 0.994359i | \(0.533826\pi\) | |||||||
\(822\) | 300.623 | + | 300.623i | 0.365721 | + | 0.365721i | ||||
\(823\) | −416.204 | + | 416.204i | −0.505716 | + | 0.505716i | −0.913209 | − | 0.407492i | \(-0.866403\pi\) |
0.407492 | + | 0.913209i | \(0.366403\pi\) | |||||||
\(824\) | 242.145i | 0.293865i | ||||||||
\(825\) | 6.09369 | + | 157.594i | 0.00738629 | + | 0.191023i | ||||
\(826\) | −463.020 | −0.560557 | ||||||||
\(827\) | −487.969 | − | 487.969i | −0.590047 | − | 0.590047i | 0.347597 | − | 0.937644i | \(-0.386998\pi\) |
−0.937644 | + | 0.347597i | \(0.886998\pi\) | |||||||
\(828\) | −20.3470 | + | 20.3470i | −0.0245737 | + | 0.0245737i | ||||
\(829\) | 195.269i | 0.235548i | 0.993040 | + | 0.117774i | \(0.0375759\pi\) | ||||
−0.993040 | + | 0.117774i | \(0.962424\pi\) | |||||||
\(830\) | −7.19223 | − | 16.4567i | −0.00866534 | − | 0.0198274i | ||||
\(831\) | −252.951 | −0.304393 | ||||||||
\(832\) | 58.8552 | + | 58.8552i | 0.0707394 | + | 0.0707394i | ||||
\(833\) | 91.2352 | − | 91.2352i | 0.109526 | − | 0.109526i | ||||
\(834\) | 18.5788i | 0.0222768i | ||||||||
\(835\) | −417.002 | + | 1064.46i | −0.499403 | + | 1.27480i | ||||
\(836\) | −24.5743 | −0.0293951 | ||||||||
\(837\) | −72.7735 | − | 72.7735i | −0.0869456 | − | 0.0869456i | ||||
\(838\) | 377.004 | − | 377.004i | 0.449885 | − | 0.449885i | ||||
\(839\) | 467.605i | 0.557337i | 0.960387 | + | 0.278668i | \(0.0898930\pi\) | ||||
−0.960387 | + | 0.278668i | \(0.910107\pi\) | |||||||
\(840\) | 169.489 | + | 66.3974i | 0.201772 | + | 0.0790445i | ||||
\(841\) | 839.481 | 0.998193 | ||||||||
\(842\) | −87.0930 | − | 87.0930i | −0.103436 | − | 0.103436i | ||||
\(843\) | 435.880 | − | 435.880i | 0.517058 | − | 0.517058i | ||||
\(844\) | − | 430.937i | − | 0.510588i | ||||||
\(845\) | 278.339 | − | 121.645i | 0.329395 | − | 0.143958i | ||||
\(846\) | −199.306 | −0.235587 | ||||||||
\(847\) | 566.119 | + | 566.119i | 0.668381 | + | 0.668381i | ||||
\(848\) | 106.585 | − | 106.585i | 0.125690 | − | 0.125690i | ||||
\(849\) | − | 199.620i | − | 0.235124i | ||||||
\(850\) | −537.811 | − | 497.768i | −0.632718 | − | 0.585609i | ||||
\(851\) | 41.8073 | 0.0491272 | ||||||||
\(852\) | 19.0431 | + | 19.0431i | 0.0223511 | + | 0.0223511i | ||||
\(853\) | −1051.43 | + | 1051.43i | −1.23262 | + | 1.23262i | −0.269672 | + | 0.962952i | \(0.586915\pi\) |
−0.962952 | + | 0.269672i | \(0.913085\pi\) | |||||||
\(854\) | − | 398.502i | − | 0.466630i | ||||||
\(855\) | −20.2648 | − | 46.3685i | −0.0237016 | − | 0.0542322i | ||||
\(856\) | 174.752 | 0.204150 | ||||||||
\(857\) | 154.417 | + | 154.417i | 0.180183 | + | 0.180183i | 0.791436 | − | 0.611252i | \(-0.209334\pi\) |
−0.611252 | + | 0.791436i | \(0.709334\pi\) | |||||||
\(858\) | 65.6347 | − | 65.6347i | 0.0764974 | − | 0.0764974i | ||||
\(859\) | − | 198.050i | − | 0.230559i | −0.993333 | − | 0.115279i | \(-0.963224\pi\) | ||
0.993333 | − | 0.115279i | \(-0.0367764\pi\) | |||||||
\(860\) | −183.539 | + | 468.509i | −0.213417 | + | 0.544778i | ||||
\(861\) | −608.556 | −0.706802 | ||||||||
\(862\) | 669.508 | + | 669.508i | 0.776691 | + | 0.776691i | ||||
\(863\) | −76.7618 | + | 76.7618i | −0.0889477 | + | 0.0889477i | −0.750181 | − | 0.661233i | \(-0.770033\pi\) |
0.661233 | + | 0.750181i | \(0.270033\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | −1129.69 | − | 442.559i | −1.30600 | − | 0.511629i | ||||
\(866\) | 1052.04 | 1.21483 | ||||||||
\(867\) | 172.212 | + | 172.212i | 0.198630 | + | 0.198630i | ||||
\(868\) | 208.156 | − | 208.156i | 0.239811 | − | 0.239811i | ||||
\(869\) | − | 98.0885i | − | 0.112875i | ||||||
\(870\) | 13.8332 | − | 6.04564i | 0.0159002 | − | 0.00694901i | ||||
\(871\) | 1291.45 | 1.48272 | ||||||||
\(872\) | 8.78178 | + | 8.78178i | 0.0100708 | + | 0.0100708i | ||||
\(873\) | 3.67333 | − | 3.67333i | 0.00420771 | − | 0.00420771i | ||||
\(874\) | 22.8806i | 0.0261792i | ||||||||
\(875\) | −404.609 | − | 836.171i | −0.462410 | − | 0.955624i | ||||
\(876\) | −288.048 | −0.328822 | ||||||||
\(877\) | −442.624 | − | 442.624i | −0.504702 | − | 0.504702i | 0.408193 | − | 0.912896i | \(-0.366159\pi\) |
−0.912896 | + | 0.408193i | \(0.866159\pi\) | |||||||
\(878\) | −776.442 | + | 776.442i | −0.884330 | + | 0.884330i | ||||
\(879\) | 125.529i | 0.142809i | ||||||||
\(880\) | 29.1713 | + | 66.7478i | 0.0331493 | + | 0.0758497i | ||||
\(881\) | −788.149 | −0.894608 | −0.447304 | − | 0.894382i | \(-0.647616\pi\) | ||||
−0.447304 | + | 0.894382i | \(0.647616\pi\) | |||||||
\(882\) | −18.6750 | − | 18.6750i | −0.0211735 | − | 0.0211735i | ||||
\(883\) | −810.401 | + | 810.401i | −0.917782 | + | 0.917782i | −0.996868 | − | 0.0790863i | \(-0.974800\pi\) |
0.0790863 | + | 0.996868i | \(0.474800\pi\) | |||||||
\(884\) | 431.298i | 0.487894i | ||||||||
\(885\) | 139.173 | − | 355.258i | 0.157257 | − | 0.401422i | ||||
\(886\) | −142.515 | −0.160853 | ||||||||
\(887\) | 1076.88 | + | 1076.88i | 1.21407 | + | 1.21407i | 0.969676 | + | 0.244393i | \(0.0785887\pi\) |
0.244393 | + | 0.969676i | \(0.421411\pi\) | |||||||
\(888\) | −30.1980 | + | 30.1980i | −0.0340068 | + | 0.0340068i | ||||
\(889\) | 141.174i | 0.158801i | ||||||||
\(890\) | −724.225 | − | 283.716i | −0.813736 | − | 0.318782i | ||||
\(891\) | −32.7797 | −0.0367898 | ||||||||
\(892\) | 330.535 | + | 330.535i | 0.370555 | + | 0.370555i | ||||
\(893\) | −112.062 | + | 112.062i | −0.125489 | + | 0.125489i | ||||
\(894\) | 542.036i | 0.606305i | ||||||||
\(895\) | 816.564 | − | 356.870i | 0.912362 | − | 0.398737i | ||||
\(896\) | 84.0762 | 0.0938350 | ||||||||
\(897\) | −61.1110 | − | 61.1110i | −0.0681282 | − | 0.0681282i | ||||
\(898\) | 597.802 | − | 597.802i | 0.665703 | − | 0.665703i | ||||
\(899\) | − | 24.4140i | − | 0.0271569i | ||||||
\(900\) | −101.889 | + | 110.085i | −0.113210 | + | 0.122317i | ||||
\(901\) | 781.068 | 0.866890 | ||||||||
\(902\) | −172.201 | − | 172.201i | −0.190910 | − | 0.190910i | ||||
\(903\) | 457.967 | − | 457.967i | 0.507162 | − | 0.507162i | ||||
\(904\) | 275.273i | 0.304505i | ||||||||
\(905\) | 215.039 | + | 492.036i | 0.237612 | + | 0.543686i | ||||
\(906\) | −11.2152 | −0.0123788 | ||||||||
\(907\) | 341.940 | + | 341.940i | 0.377001 | + | 0.377001i | 0.870019 | − | 0.493018i | \(-0.164106\pi\) |
−0.493018 | + | 0.870019i | \(0.664106\pi\) | |||||||
\(908\) | 356.651 | − | 356.651i | 0.392787 | − | 0.392787i | ||||
\(909\) | − | 403.595i | − | 0.443999i | ||||||
\(910\) | −199.421 | + | 509.049i | −0.219144 | + | 0.559395i | ||||
\(911\) | 1250.37 | 1.37252 | 0.686262 | − | 0.727354i | \(-0.259250\pi\) | ||||
0.686262 | + | 0.727354i | \(0.259250\pi\) | |||||||
\(912\) | −16.5270 | − | 16.5270i | −0.0181217 | − | 0.0181217i | ||||
\(913\) | −6.54129 | + | 6.54129i | −0.00716461 | + | 0.00716461i | ||||
\(914\) | − | 1096.28i | − | 1.19943i | ||||||
\(915\) | 305.756 | + | 119.780i | 0.334160 | + | 0.130907i | ||||
\(916\) | 101.204 | 0.110484 | ||||||||
\(917\) | 640.143 | + | 640.143i | 0.698084 | + | 0.698084i | ||||
\(918\) | 107.701 | − | 107.701i | 0.117321 | − | 0.117321i | ||||
\(919\) | 33.3186i | 0.0362552i | 0.999836 | + | 0.0181276i | \(0.00577052\pi\) | ||||
−0.999836 | + | 0.0181276i | \(0.994229\pi\) | |||||||
\(920\) | 62.1473 | − | 27.1608i | 0.0675515 | − | 0.0295226i | ||||
\(921\) | −328.874 | −0.357083 | ||||||||
\(922\) | 647.631 | + | 647.631i | 0.702420 | + | 0.702420i | ||||
\(923\) | −57.1949 | + | 57.1949i | −0.0619664 | + | 0.0619664i | ||||
\(924\) | − | 93.7609i | − | 0.101473i | ||||||
\(925\) | 217.773 | − | 8.42063i | 0.235430 | − | 0.00910339i | ||||
\(926\) | 53.9470 | 0.0582581 | ||||||||
\(927\) | 181.609 | + | 181.609i | 0.195910 | + | 0.195910i | ||||
\(928\) | 4.93053 | − | 4.93053i | 0.00531307 | − | 0.00531307i | ||||
\(929\) | 201.301i | 0.216686i | 0.994114 | + | 0.108343i | \(0.0345545\pi\) | ||||
−0.994114 | + | 0.108343i | \(0.965446\pi\) | |||||||
\(930\) | 97.1438 | + | 222.278i | 0.104456 | + | 0.239008i | ||||
\(931\) | −21.0004 | −0.0225569 | ||||||||
\(932\) | 26.5351 | + | 26.5351i | 0.0284712 | + | 0.0284712i | ||||
\(933\) | 352.631 | − | 352.631i | 0.377954 | − | 0.377954i | ||||
\(934\) | 1241.33i | 1.32904i | ||||||||
\(935\) | −137.682 | + | 351.453i | −0.147254 | + | 0.375886i | ||||
\(936\) | 88.2828 | 0.0943193 | ||||||||
\(937\) | 186.672 | + | 186.672i | 0.199223 | + | 0.199223i | 0.799667 | − | 0.600444i | \(-0.205009\pi\) |
−0.600444 | + | 0.799667i | \(0.705009\pi\) | |||||||
\(938\) | 922.433 | − | 922.433i | 0.983404 | − | 0.983404i | ||||
\(939\) | 282.384i | 0.300729i | ||||||||
\(940\) | 437.403 | + | 171.353i | 0.465322 | + | 0.182291i | ||||
\(941\) | 68.2261 | 0.0725038 | 0.0362519 | − | 0.999343i | \(-0.488458\pi\) | ||||
0.0362519 | + | 0.999343i | \(0.488458\pi\) | |||||||
\(942\) | 47.8543 | + | 47.8543i | 0.0508007 | + | 0.0508007i | ||||
\(943\) | −160.332 | + | 160.332i | −0.170024 | + | 0.170024i | ||||
\(944\) | − | 176.229i | − | 0.186683i | ||||||
\(945\) | 176.914 | − | 77.3184i | 0.187211 | − | 0.0818185i | ||||
\(946\) | 259.178 | 0.273973 | ||||||||
\(947\) | −1118.93 | − | 1118.93i | −1.18156 | − | 1.18156i | −0.979341 | − | 0.202215i | \(-0.935186\pi\) |
−0.202215 | − | 0.979341i | \(-0.564814\pi\) | |||||||
\(948\) | 65.9676 | − | 65.9676i | 0.0695861 | − | 0.0695861i | ||||
\(949\) | − | 865.136i | − | 0.911629i | ||||||
\(950\) | 4.60851 | + | 119.184i | 0.00485106 | + | 0.125457i | ||||
\(951\) | 221.698 | 0.233121 | ||||||||
\(952\) | 308.060 | + | 308.060i | 0.323592 | + | 0.323592i | ||||
\(953\) | 733.458 | − | 733.458i | 0.769630 | − | 0.769630i | −0.208411 | − | 0.978041i | \(-0.566829\pi\) |
0.978041 | + | 0.208411i | \(0.0668292\pi\) | |||||||
\(954\) | − | 159.878i | − | 0.167587i | ||||||
\(955\) | 240.321 | + | 549.884i | 0.251645 | + | 0.575795i | ||||
\(956\) | 673.714 | 0.704721 | ||||||||
\(957\) | −5.49847 | − | 5.49847i | −0.00574553 | − | 0.00574553i | ||||
\(958\) | −270.238 | + | 270.238i | −0.282085 | + | 0.282085i | ||||
\(959\) | 1289.82i | 1.34496i | ||||||||
\(960\) | −25.2713 | + | 64.5086i | −0.0263243 | + | 0.0671965i | ||||
\(961\) | −568.705 | −0.591785 | ||||||||
\(962\) | −90.6981 | − | 90.6981i | −0.0942807 | − | 0.0942807i | ||||
\(963\) | 131.064 | − | 131.064i | 0.136100 | − | 0.136100i | ||||
\(964\) | − | 698.441i | − | 0.724524i | ||||||
\(965\) | −339.316 | − | 132.927i | −0.351622 | − | 0.137749i | ||||
\(966\) | −87.2986 | −0.0903713 | ||||||||
\(967\) | −781.784 | − | 781.784i | −0.808464 | − | 0.808464i | 0.175938 | − | 0.984401i | \(-0.443704\pi\) |
−0.984401 | + | 0.175938i | \(0.943704\pi\) | |||||||
\(968\) | −215.469 | + | 215.469i | −0.222592 | + | 0.222592i | ||||
\(969\) | − | 121.112i | − | 0.124986i | ||||||
\(970\) | −11.2197 | + | 4.90345i | −0.0115667 | + | 0.00505510i | ||||
\(971\) | 1462.26 | 1.50593 | 0.752966 | − | 0.658059i | \(-0.228622\pi\) | ||||
0.752966 | + | 0.658059i | \(0.228622\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −39.8562 | + | 39.8562i | −0.0409622 | + | 0.0409622i | ||||
\(974\) | − | 249.811i | − | 0.256479i | ||||||
\(975\) | −330.634 | − | 306.017i | −0.339112 | − | 0.313863i | ||||
\(976\) | 151.673 | 0.155402 | ||||||||
\(977\) | −210.961 | − | 210.961i | −0.215927 | − | 0.215927i | 0.590852 | − | 0.806780i | \(-0.298792\pi\) |
−0.806780 | + | 0.590852i | \(0.798792\pi\) | |||||||
\(978\) | −235.967 | + | 235.967i | −0.241275 | + | 0.241275i | ||||
\(979\) | 400.640i | 0.409234i | ||||||||
\(980\) | 24.9289 | + | 57.0405i | 0.0254377 | + | 0.0582046i | ||||
\(981\) | 13.1727 | 0.0134278 | ||||||||
\(982\) | 598.054 | + | 598.054i | 0.609016 | + | 0.609016i | ||||
\(983\) | 480.717 | − | 480.717i | 0.489031 | − | 0.489031i | −0.418970 | − | 0.908000i | \(-0.637609\pi\) |
0.908000 | + | 0.418970i | \(0.137609\pi\) | |||||||
\(984\) | − | 231.621i | − | 0.235387i | ||||||
\(985\) | −52.9409 | + | 135.139i | −0.0537471 | + | 0.137197i | ||||
\(986\) | 36.1315 | 0.0366445 | ||||||||
\(987\) | −427.561 | − | 427.561i | −0.433193 | − | 0.433193i | ||||
\(988\) | 49.6379 | − | 49.6379i | 0.0502408 | − | 0.0502408i | ||||
\(989\) | − | 241.315i | − | 0.243999i | ||||||
\(990\) | 71.9393 | + | 28.1823i | 0.0726660 | + | 0.0284670i | ||||
\(991\) | 451.028 | 0.455124 | 0.227562 | − | 0.973764i | \(-0.426925\pi\) | ||||
0.227562 | + | 0.973764i | \(0.426925\pi\) | |||||||
\(992\) | 79.2257 | + | 79.2257i | 0.0798647 | + | 0.0798647i | ||||
\(993\) | −276.662 | + | 276.662i | −0.278612 | + | 0.278612i | ||||
\(994\) | 81.7044i | 0.0821976i | ||||||||
\(995\) | −1197.66 | + | 523.423i | −1.20368 | + | 0.526053i | ||||
\(996\) | −8.79844 | −0.00883378 | ||||||||
\(997\) | 436.783 | + | 436.783i | 0.438097 | + | 0.438097i | 0.891371 | − | 0.453274i | \(-0.149744\pi\) |
−0.453274 | + | 0.891371i | \(0.649744\pi\) | |||||||
\(998\) | 160.709 | − | 160.709i | 0.161031 | − | 0.161031i | ||||
\(999\) | 45.2970i | 0.0453424i |
(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 | 690.3.k.b.277.18 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.18 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.18 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.18 | yes | 48 | 5.3 | odd | 4 | inner |