Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(32,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.p (of order \(12\), degree \(4\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.3 | ||
Character | \(\chi\) | \(=\) | 225.32 |
Dual form | 225.4.p.b.218.3 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.14355 | − | 1.11026i | −1.46497 | − | 0.392537i | −0.563765 | − | 0.825935i | \(-0.690648\pi\) |
−0.901203 | + | 0.433398i | \(0.857314\pi\) | |||||||
\(3\) | −1.80338 | − | 4.87317i | −0.347060 | − | 0.937843i | ||||
\(4\) | 9.00816 | + | 5.20086i | 1.12602 | + | 0.650108i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.06189 | + | 22.1945i | 0.140294 | + | 1.51014i | ||||
\(7\) | −3.90791 | + | 14.5845i | −0.211007 | + | 0.787490i | 0.776527 | + | 0.630084i | \(0.216980\pi\) |
−0.987534 | + | 0.157406i | \(0.949687\pi\) | |||||||
\(8\) | −7.28515 | − | 7.28515i | −0.321961 | − | 0.321961i | ||||
\(9\) | −20.4957 | + | 17.5763i | −0.759098 | + | 0.650976i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.5632 | − | 24.5739i | 1.16666 | − | 0.673573i | 0.213771 | − | 0.976884i | \(-0.431425\pi\) |
0.952892 | + | 0.303310i | \(0.0980919\pi\) | |||||||
\(12\) | 9.09960 | − | 53.2775i | 0.218902 | − | 1.28166i | ||||
\(13\) | −9.04733 | − | 33.7651i | −0.193021 | − | 0.720366i | −0.992770 | − | 0.120031i | \(-0.961701\pi\) |
0.799749 | − | 0.600335i | \(-0.204966\pi\) | |||||||
\(14\) | 32.3853 | − | 56.0930i | 0.618238 | − | 1.07082i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.5089 | − | 33.7905i | −0.304827 | − | 0.527976i | ||||
\(17\) | 18.9033 | − | 18.9033i | 0.269690 | − | 0.269690i | −0.559285 | − | 0.828975i | \(-0.688924\pi\) |
0.828975 | + | 0.559285i | \(0.188924\pi\) | |||||||
\(18\) | 104.439 | − | 50.0730i | 1.36759 | − | 0.655685i | ||||
\(19\) | 53.7656i | 0.649193i | 0.945853 | + | 0.324596i | \(0.105228\pi\) | ||||
−0.945853 | + | 0.324596i | \(0.894772\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 78.1204 | − | 7.25747i | 0.811774 | − | 0.0754148i | ||||
\(22\) | −203.647 | + | 54.5669i | −1.97353 | + | 0.528805i | ||||
\(23\) | 170.922 | − | 45.7984i | 1.54955 | − | 0.415201i | 0.620214 | − | 0.784432i | \(-0.287046\pi\) |
0.929338 | + | 0.369231i | \(0.120379\pi\) | |||||||
\(24\) | −22.3639 | + | 48.6397i | −0.190209 | + | 0.413689i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 149.952i | 1.13108i | ||||||||
\(27\) | 122.614 | + | 68.1821i | 0.873966 | + | 0.485987i | ||||
\(28\) | −111.055 | + | 111.055i | −0.749552 | + | 0.749552i | ||||
\(29\) | −110.003 | − | 190.531i | −0.704382 | − | 1.22003i | −0.966914 | − | 0.255103i | \(-0.917891\pi\) |
0.262532 | − | 0.964923i | \(-0.415443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.1047 | + | 38.2864i | −0.128068 | + | 0.221821i | −0.922928 | − | 0.384972i | \(-0.874211\pi\) |
0.794860 | + | 0.606793i | \(0.207544\pi\) | |||||||
\(32\) | 64.6525 | + | 241.286i | 0.357158 | + | 1.33293i | ||||
\(33\) | −196.510 | − | 163.102i | −1.03661 | − | 0.860376i | ||||
\(34\) | −99.3145 | + | 57.3392i | −0.500950 | + | 0.289224i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −276.040 | + | 51.7355i | −1.27796 | + | 0.239516i | ||||
\(37\) | −169.138 | − | 169.138i | −0.751516 | − | 0.751516i | 0.223246 | − | 0.974762i | \(-0.428335\pi\) |
−0.974762 | + | 0.223246i | \(0.928335\pi\) | |||||||
\(38\) | 59.6939 | − | 222.781i | 0.254832 | − | 0.951047i | ||||
\(39\) | −148.227 | + | 104.980i | −0.608600 | + | 0.431034i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.1171 | + | 24.3163i | 0.160429 | + | 0.0926237i | 0.578065 | − | 0.815991i | \(-0.303808\pi\) |
−0.417636 | + | 0.908614i | \(0.637141\pi\) | |||||||
\(42\) | −331.754 | − | 56.6624i | −1.21883 | − | 0.208171i | ||||
\(43\) | −344.771 | − | 92.3811i | −1.22272 | − | 0.327628i | −0.410981 | − | 0.911644i | \(-0.634814\pi\) |
−0.811742 | + | 0.584016i | \(0.801480\pi\) | |||||||
\(44\) | 511.222 | 1.75158 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −759.073 | −2.43303 | ||||||||
\(47\) | −512.264 | − | 137.261i | −1.58982 | − | 0.425990i | −0.647870 | − | 0.761751i | \(-0.724340\pi\) |
−0.941947 | + | 0.335761i | \(0.891007\pi\) | |||||||
\(48\) | −129.485 | + | 156.007i | −0.389365 | + | 0.469119i | ||||
\(49\) | 99.6102 | + | 57.5100i | 0.290409 | + | 0.167667i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −126.209 | − | 58.0293i | −0.346525 | − | 0.159328i | ||||
\(52\) | 94.1079 | − | 351.215i | 0.250969 | − | 0.936631i | ||||
\(53\) | 198.516 | + | 198.516i | 0.514496 | + | 0.514496i | 0.915901 | − | 0.401405i | \(-0.131478\pi\) |
−0.401405 | + | 0.915901i | \(0.631478\pi\) | |||||||
\(54\) | −432.358 | − | 418.650i | −1.08956 | − | 1.05502i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 134.720 | − | 77.7807i | 0.321477 | − | 0.185605i | ||||
\(57\) | 262.009 | − | 96.9596i | 0.608841 | − | 0.225309i | ||||
\(58\) | 244.265 | + | 911.609i | 0.552992 | + | 2.06379i | ||||
\(59\) | −64.3921 | + | 111.530i | −0.142087 | + | 0.246102i | −0.928282 | − | 0.371876i | \(-0.878715\pi\) |
0.786195 | + | 0.617978i | \(0.212048\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.4727 | − | 57.9764i | −0.0702581 | − | 0.121691i | 0.828756 | − | 0.559610i | \(-0.189049\pi\) |
−0.899014 | + | 0.437919i | \(0.855716\pi\) | |||||||
\(62\) | 134.100 | − | 134.100i | 0.274689 | − | 0.274689i | ||||
\(63\) | −176.247 | − | 367.606i | −0.352462 | − | 0.735143i | ||||
\(64\) | − | 759.421i | − | 1.48324i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 633.166 | + | 894.000i | 1.18087 | + | 1.66733i | ||||
\(67\) | 69.7613 | − | 18.6925i | 0.127204 | − | 0.0340843i | −0.194655 | − | 0.980872i | \(-0.562359\pi\) |
0.321860 | + | 0.946787i | \(0.395692\pi\) | |||||||
\(68\) | 268.597 | − | 71.9705i | 0.479003 | − | 0.128349i | ||||
\(69\) | −531.420 | − | 750.341i | −0.927181 | − | 1.30914i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1038.75i | − | 1.73629i | −0.496313 | − | 0.868143i | \(-0.665313\pi\) | ||
0.496313 | − | 0.868143i | \(-0.334687\pi\) | |||||||
\(72\) | 277.360 | + | 21.2676i | 0.453989 | + | 0.0348112i | ||||
\(73\) | −339.210 | + | 339.210i | −0.543857 | + | 0.543857i | −0.924657 | − | 0.380800i | \(-0.875649\pi\) |
0.380800 | + | 0.924657i | \(0.375649\pi\) | |||||||
\(74\) | 513.044 | + | 888.619i | 0.805949 | + | 1.39594i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −279.627 | + | 484.329i | −0.422045 | + | 0.731004i | ||||
\(77\) | 192.065 | + | 716.797i | 0.284258 | + | 1.06086i | ||||
\(78\) | 730.744 | − | 270.421i | 1.06078 | − | 0.392553i | ||||
\(79\) | −297.681 | + | 171.866i | −0.423946 | + | 0.244766i | −0.696764 | − | 0.717300i | \(-0.745378\pi\) |
0.272818 | + | 0.962066i | \(0.412044\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 111.144 | − | 720.478i | 0.152461 | − | 0.988310i | ||||
\(82\) | −147.517 | − | 147.517i | −0.198665 | − | 0.198665i | ||||
\(83\) | 225.584 | − | 841.890i | 0.298326 | − | 1.11337i | −0.640214 | − | 0.768196i | \(-0.721155\pi\) |
0.938540 | − | 0.345170i | \(-0.112179\pi\) | |||||||
\(84\) | 741.466 | + | 340.917i | 0.963102 | + | 0.442822i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1326.01 | + | 765.572i | 1.66264 | + | 0.959928i | ||||
\(87\) | −730.114 | + | 879.665i | −0.899730 | + | 1.08402i | ||||
\(88\) | −489.104 | − | 131.055i | −0.592485 | − | 0.158756i | ||||
\(89\) | −230.315 | −0.274307 | −0.137153 | − | 0.990550i | \(-0.543795\pi\) | ||||
−0.137153 | + | 0.990550i | \(0.543795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 527.804 | 0.608010 | ||||||||
\(92\) | 1777.88 | + | 476.383i | 2.01475 | + | 0.539851i | ||||
\(93\) | 226.440 | + | 38.6751i | 0.252481 | + | 0.0431228i | ||||
\(94\) | 1970.20 | + | 1137.50i | 2.16181 | + | 1.24812i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1059.24 | − | 750.193i | 1.12612 | − | 0.797565i | ||||
\(97\) | 148.198 | − | 553.082i | 0.155126 | − | 0.578938i | −0.843969 | − | 0.536393i | \(-0.819787\pi\) |
0.999095 | − | 0.0425454i | \(-0.0135467\pi\) | |||||||
\(98\) | −348.889 | − | 348.889i | −0.359624 | − | 0.359624i | ||||
\(99\) | −440.442 | + | 1251.76i | −0.447132 | + | 1.27078i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −122.461 | + | 70.7028i | −0.120647 | + | 0.0696554i | −0.559109 | − | 0.829094i | \(-0.688857\pi\) |
0.438462 | + | 0.898750i | \(0.355523\pi\) | |||||||
\(102\) | 458.526 | + | 380.572i | 0.445106 | + | 0.369434i | ||||
\(103\) | 31.0089 | + | 115.727i | 0.0296641 | + | 0.110708i | 0.979170 | − | 0.203040i | \(-0.0650821\pi\) |
−0.949506 | + | 0.313748i | \(0.898415\pi\) | |||||||
\(104\) | −180.073 | + | 311.895i | −0.169784 | + | 0.294075i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −602.157 | − | 1042.97i | −0.551761 | − | 0.955678i | ||||
\(107\) | 940.778 | − | 940.778i | 0.849985 | − | 0.849985i | −0.140146 | − | 0.990131i | \(-0.544757\pi\) |
0.990131 | + | 0.140146i | \(0.0447571\pi\) | |||||||
\(108\) | 749.921 | + | 1251.89i | 0.668159 | + | 1.11540i | ||||
\(109\) | − | 1052.78i | − | 0.925121i | −0.886588 | − | 0.462560i | \(-0.846931\pi\) | ||
0.886588 | − | 0.462560i | \(-0.153069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −519.219 | + | 1129.26i | −0.443982 | + | 0.965625i | ||||
\(112\) | 569.057 | − | 152.478i | 0.480097 | − | 0.128642i | ||||
\(113\) | −1132.84 | + | 303.543i | −0.943085 | + | 0.252699i | −0.697425 | − | 0.716657i | \(-0.745671\pi\) |
−0.245659 | + | 0.969356i | \(0.579004\pi\) | |||||||
\(114\) | −1193.30 | + | 110.859i | −0.980374 | + | 0.0910779i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 2288.45i | − | 1.83170i | ||||||
\(117\) | 778.898 | + | 533.019i | 0.615463 | + | 0.421176i | ||||
\(118\) | 390.640 | − | 390.640i | 0.304757 | − | 0.304757i | ||||
\(119\) | 201.823 | + | 349.568i | 0.155471 | + | 0.269284i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 542.252 | − | 939.209i | 0.407402 | − | 0.705641i | ||||
\(122\) | 74.3270 | + | 277.392i | 0.0551578 | + | 0.205852i | ||||
\(123\) | 42.5446 | − | 249.095i | 0.0311880 | − | 0.182603i | ||||
\(124\) | −398.245 | + | 229.927i | −0.288415 | + | 0.166517i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 322.152 | + | 1718.88i | 0.227774 | + | 1.21532i | ||||
\(127\) | −2.78116 | − | 2.78116i | −0.00194321 | − | 0.00194321i | 0.706135 | − | 0.708078i | \(-0.250437\pi\) |
−0.708078 | + | 0.706135i | \(0.750437\pi\) | |||||||
\(128\) | −325.937 | + | 1216.41i | −0.225070 | + | 0.839974i | ||||
\(129\) | 171.563 | + | 1846.73i | 0.117095 | + | 1.26043i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −455.461 | − | 262.961i | −0.303770 | − | 0.175381i | 0.340365 | − | 0.940293i | \(-0.389449\pi\) |
−0.644135 | + | 0.764912i | \(0.722783\pi\) | |||||||
\(132\) | −921.926 | − | 2491.27i | −0.607904 | − | 1.64271i | ||||
\(133\) | −784.145 | − | 210.111i | −0.511233 | − | 0.136984i | ||||
\(134\) | −309.813 | −0.199730 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −275.427 | −0.173659 | ||||||||
\(137\) | −1800.69 | − | 482.495i | −1.12295 | − | 0.300893i | −0.350871 | − | 0.936424i | \(-0.614115\pi\) |
−0.772075 | + | 0.635531i | \(0.780781\pi\) | |||||||
\(138\) | 1368.89 | + | 3699.09i | 0.844406 | + | 2.28180i | ||||
\(139\) | −2076.42 | − | 1198.82i | −1.26705 | − | 0.731531i | −0.292620 | − | 0.956229i | \(-0.594527\pi\) |
−0.974428 | + | 0.224698i | \(0.927860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 254.910 | + | 2743.89i | 0.152250 | + | 1.63884i | ||||
\(142\) | −1153.28 | + | 4304.10i | −0.681557 | + | 2.54360i | ||||
\(143\) | −1214.82 | − | 1214.82i | −0.710410 | − | 0.710410i | ||||
\(144\) | 993.761 | + | 349.662i | 0.575093 | + | 0.202351i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1782.15 | − | 1028.92i | 1.01022 | − | 0.583249i | ||||
\(147\) | 100.621 | − | 589.130i | 0.0564565 | − | 0.330548i | ||||
\(148\) | −643.958 | − | 2403.28i | −0.357655 | − | 1.33479i | ||||
\(149\) | 1086.72 | − | 1882.25i | 0.597498 | − | 1.03490i | −0.395691 | − | 0.918384i | \(-0.629495\pi\) |
0.993189 | − | 0.116513i | \(-0.0371718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1316.04 | − | 2279.46i | −0.709260 | − | 1.22847i | −0.965132 | − | 0.261763i | \(-0.915696\pi\) |
0.255873 | − | 0.966711i | \(-0.417637\pi\) | |||||||
\(152\) | 391.690 | − | 391.690i | 0.209015 | − | 0.209015i | ||||
\(153\) | −55.1846 | + | 719.687i | −0.0291595 | + | 0.380282i | ||||
\(154\) | − | 3183.33i | − | 1.66571i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1881.25 | + | 174.770i | −0.965514 | + | 0.0896974i | ||||
\(157\) | 2798.52 | − | 749.861i | 1.42259 | − | 0.381181i | 0.536186 | − | 0.844100i | \(-0.319865\pi\) |
0.886401 | + | 0.462919i | \(0.153198\pi\) | |||||||
\(158\) | 1424.28 | − | 381.633i | 0.717147 | − | 0.192159i | ||||
\(159\) | 609.404 | − | 1325.40i | 0.303955 | − | 0.661077i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2671.79i | 1.30787i | ||||||||
\(162\) | −1260.45 | + | 2861.94i | −0.611298 | + | 1.38800i | ||||
\(163\) | 1097.25 | − | 1097.25i | 0.527259 | − | 0.527259i | −0.392495 | − | 0.919754i | \(-0.628388\pi\) |
0.919754 | + | 0.392495i | \(0.128388\pi\) | |||||||
\(164\) | 252.932 | + | 438.091i | 0.120431 | + | 0.208592i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1869.44 | + | 3237.96i | −0.874075 | + | 1.51394i | ||||
\(167\) | −900.215 | − | 3359.65i | −0.417130 | − | 1.55675i | −0.780531 | − | 0.625117i | \(-0.785051\pi\) |
0.363401 | − | 0.931633i | \(-0.381616\pi\) | |||||||
\(168\) | −621.990 | − | 516.247i | −0.285640 | − | 0.237079i | ||||
\(169\) | 844.431 | − | 487.532i | 0.384356 | − | 0.221908i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −945.002 | − | 1101.96i | −0.422609 | − | 0.492801i | ||||
\(172\) | −2625.29 | − | 2625.29i | −1.16382 | − | 1.16382i | ||||
\(173\) | −229.047 | + | 854.813i | −0.100659 | + | 0.375666i | −0.997817 | − | 0.0660452i | \(-0.978962\pi\) |
0.897157 | + | 0.441711i | \(0.145628\pi\) | |||||||
\(174\) | 4001.93 | − | 2834.32i | 1.74359 | − | 1.23488i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1660.73 | − | 958.821i | −0.711261 | − | 0.410647i | ||||
\(177\) | 659.631 | + | 112.663i | 0.280118 | + | 0.0478432i | ||||
\(178\) | 954.321 | + | 255.710i | 0.401851 | + | 0.107676i | ||||
\(179\) | −1948.94 | −0.813803 | −0.406901 | − | 0.913472i | \(-0.633391\pi\) | ||||
−0.406901 | + | 0.913472i | \(0.633391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1591.17 | 0.653431 | 0.326716 | − | 0.945123i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945123i | \(0.394058\pi\) | |||||||
\(182\) | −2186.98 | − | 586.001i | −0.890715 | − | 0.238666i | ||||
\(183\) | −222.165 | + | 267.672i | −0.0897428 | + | 0.108125i | ||||
\(184\) | −1578.84 | − | 911.544i | −0.632574 | − | 0.365217i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −895.326 | − | 411.660i | −0.352949 | − | 0.162281i | ||||
\(187\) | 340.058 | − | 1269.11i | 0.132981 | − | 0.496293i | ||||
\(188\) | −3900.68 | − | 3900.68i | −1.51323 | − | 1.51323i | ||||
\(189\) | −1473.57 | + | 1521.82i | −0.567123 | + | 0.585693i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1725.63 | + | 996.295i | −0.653730 | + | 0.377431i | −0.789884 | − | 0.613257i | \(-0.789859\pi\) |
0.136154 | + | 0.990688i | \(0.456526\pi\) | |||||||
\(192\) | −3700.79 | + | 1369.52i | −1.39105 | + | 0.514775i | ||||
\(193\) | 636.807 | + | 2376.60i | 0.237504 | + | 0.886379i | 0.977004 | + | 0.213221i | \(0.0683956\pi\) |
−0.739500 | + | 0.673157i | \(0.764938\pi\) | |||||||
\(194\) | −1228.13 | + | 2127.19i | −0.454509 | + | 0.787233i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 598.203 | + | 1036.12i | 0.218004 | + | 0.377594i | ||||
\(197\) | 497.126 | − | 497.126i | 0.179790 | − | 0.179790i | −0.611474 | − | 0.791265i | \(-0.709423\pi\) |
0.791265 | + | 0.611474i | \(0.209423\pi\) | |||||||
\(198\) | 3214.78 | − | 4697.75i | 1.15386 | − | 1.68613i | ||||
\(199\) | 1269.73i | 0.452305i | 0.974092 | + | 0.226152i | \(0.0726148\pi\) | ||||
−0.974092 | + | 0.226152i | \(0.927385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −216.898 | − | 306.249i | −0.0761133 | − | 0.107468i | ||||
\(202\) | 585.922 | − | 156.997i | 0.204086 | − | 0.0546846i | ||||
\(203\) | 3208.69 | − | 859.766i | 1.10939 | − | 0.297260i | ||||
\(204\) | −835.107 | − | 1179.13i | −0.286614 | − | 0.404685i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 513.949i | − | 0.173828i | ||||||
\(207\) | −2698.19 | + | 3942.85i | −0.905976 | + | 1.32390i | ||||
\(208\) | −964.434 | + | 964.434i | −0.321498 | + | 0.321498i | ||||
\(209\) | 1321.23 | + | 2288.44i | 0.437279 | + | 0.757389i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −676.141 | + | 1171.11i | −0.220604 | + | 0.382098i | −0.954992 | − | 0.296633i | \(-0.904136\pi\) |
0.734387 | + | 0.678731i | \(0.237470\pi\) | |||||||
\(212\) | 755.809 | + | 2820.72i | 0.244855 | + | 0.913810i | ||||
\(213\) | −5061.99 | + | 1873.25i | −1.62836 | + | 0.602596i | ||||
\(214\) | −4942.67 | + | 2853.65i | −1.57885 | + | 0.911550i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −396.544 | − | 1389.98i | −0.124914 | − | 0.437852i | ||||
\(217\) | −472.006 | − | 472.006i | −0.147658 | − | 0.147658i | ||||
\(218\) | −1168.86 | + | 4362.26i | −0.363144 | + | 1.35527i | ||||
\(219\) | 2264.76 | + | 1041.31i | 0.698804 | + | 0.321301i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −809.296 | − | 467.247i | −0.246331 | − | 0.142219i | ||||
\(222\) | 3405.18 | − | 4102.67i | 1.02946 | − | 1.24033i | ||||
\(223\) | −98.8770 | − | 26.4940i | −0.0296919 | − | 0.00795592i | 0.243943 | − | 0.969790i | \(-0.421559\pi\) |
−0.273634 | + | 0.961834i | \(0.588226\pi\) | |||||||
\(224\) | −3771.70 | −1.12503 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5031.00 | 1.48078 | ||||||||
\(227\) | 1402.92 | + | 375.911i | 0.410198 | + | 0.109912i | 0.458016 | − | 0.888944i | \(-0.348560\pi\) |
−0.0478183 | + | 0.998856i | \(0.515227\pi\) | |||||||
\(228\) | 2864.49 | + | 489.245i | 0.832042 | + | 0.142110i | ||||
\(229\) | 4802.27 | + | 2772.59i | 1.38578 | + | 0.800079i | 0.992836 | − | 0.119485i | \(-0.0381243\pi\) |
0.392941 | + | 0.919564i | \(0.371458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3146.71 | − | 2228.62i | 0.896270 | − | 0.634773i | ||||
\(232\) | −586.658 | + | 2189.44i | −0.166017 | + | 0.619585i | ||||
\(233\) | −870.893 | − | 870.893i | −0.244867 | − | 0.244867i | 0.573993 | − | 0.818860i | \(-0.305394\pi\) |
−0.818860 | + | 0.573993i | \(0.805394\pi\) | |||||||
\(234\) | −2635.62 | − | 3073.37i | −0.736306 | − | 0.858601i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1160.11 | + | 669.790i | −0.319986 | + | 0.184744i | ||||
\(237\) | 1374.37 | + | 1140.71i | 0.376687 | + | 0.312647i | ||||
\(238\) | −448.153 | − | 1672.53i | −0.122057 | − | 0.455521i | ||||
\(239\) | −45.9510 | + | 79.5895i | −0.0124365 | + | 0.0215406i | −0.872177 | − | 0.489191i | \(-0.837292\pi\) |
0.859740 | + | 0.510732i | \(0.170625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −979.248 | − | 1696.11i | −0.261738 | − | 0.453344i | 0.704966 | − | 0.709241i | \(-0.250962\pi\) |
−0.966704 | + | 0.255898i | \(0.917629\pi\) | |||||||
\(242\) | −3289.62 | + | 3289.62i | −0.873821 | + | 0.873821i | ||||
\(243\) | −3711.45 | + | 757.670i | −0.979792 | + | 0.200019i | ||||
\(244\) | − | 696.348i | − | 0.182701i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −452.847 | + | 984.905i | −0.117368 | + | 0.255265i | ||||
\(247\) | 1815.40 | − | 486.435i | 0.467656 | − | 0.125308i | ||||
\(248\) | 439.958 | − | 117.886i | 0.112651 | − | 0.0301847i | ||||
\(249\) | −4509.49 | + | 418.937i | −1.14770 | + | 0.106623i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1167.85i | 0.293681i | 0.989160 | + | 0.146840i | \(0.0469104\pi\) | ||||
−0.989160 | + | 0.146840i | \(0.953090\pi\) | |||||||
\(252\) | 324.204 | − | 4228.10i | 0.0810435 | − | 1.05692i | ||||
\(253\) | 6149.55 | − | 6149.55i | 1.52814 | − | 1.52814i | ||||
\(254\) | 8.43606 | + | 14.6117i | 0.00208396 | + | 0.00360952i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −336.610 | + | 583.026i | −0.0821802 | + | 0.142340i | ||||
\(257\) | 6.78155 | + | 25.3091i | 0.00164600 | + | 0.00614295i | 0.966744 | − | 0.255746i | \(-0.0823212\pi\) |
−0.965098 | + | 0.261889i | \(0.915654\pi\) | |||||||
\(258\) | 1339.47 | − | 7842.49i | 0.323224 | − | 1.89245i | ||||
\(259\) | 3127.77 | − | 1805.82i | 0.750387 | − | 0.433236i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5603.43 | + | 1971.61i | 1.32890 | + | 0.467584i | ||||
\(262\) | 1595.27 | + | 1595.27i | 0.376169 | + | 0.376169i | ||||
\(263\) | 154.510 | − | 576.639i | 0.0362262 | − | 0.135198i | −0.945444 | − | 0.325783i | \(-0.894372\pi\) |
0.981671 | + | 0.190585i | \(0.0610386\pi\) | |||||||
\(264\) | 243.385 | + | 2619.83i | 0.0567399 | + | 0.610755i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3015.87 | + | 1741.21i | 0.695168 | + | 0.401356i | ||||
\(267\) | 415.344 | + | 1122.36i | 0.0952009 | + | 0.257257i | ||||
\(268\) | 725.638 | + | 194.434i | 0.165393 | + | 0.0443170i | ||||
\(269\) | 6123.85 | 1.38802 | 0.694011 | − | 0.719965i | \(-0.255842\pi\) | ||||
0.694011 | + | 0.719965i | \(0.255842\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −122.463 | −0.0274505 | −0.0137253 | − | 0.999906i | \(-0.504369\pi\) | ||||
−0.0137253 | + | 0.999906i | \(0.504369\pi\) | |||||||
\(272\) | −1007.53 | − | 269.968i | −0.224598 | − | 0.0601809i | ||||
\(273\) | −951.830 | − | 2572.08i | −0.211016 | − | 0.570218i | ||||
\(274\) | 6925.58 | + | 3998.49i | 1.52697 | + | 0.881596i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −884.701 | − | 9523.04i | −0.192945 | − | 2.07688i | ||||
\(277\) | −401.012 | + | 1496.60i | −0.0869836 | + | 0.324627i | −0.995682 | − | 0.0928250i | \(-0.970410\pi\) |
0.908699 | + | 0.417452i | \(0.137077\pi\) | |||||||
\(278\) | 7272.76 | + | 7272.76i | 1.56903 | + | 1.56903i | ||||
\(279\) | −219.886 | − | 1173.23i | −0.0471836 | − | 0.251753i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2397.24 | + | 1384.04i | −0.508922 | + | 0.293826i | −0.732390 | − | 0.680885i | \(-0.761595\pi\) |
0.223468 | + | 0.974711i | \(0.428262\pi\) | |||||||
\(282\) | 1990.20 | − | 11652.5i | 0.420265 | − | 2.46062i | ||||
\(283\) | 1593.68 | + | 5947.68i | 0.334750 | + | 1.24930i | 0.904140 | + | 0.427236i | \(0.140513\pi\) |
−0.569391 | + | 0.822067i | \(0.692821\pi\) | |||||||
\(284\) | 5402.37 | − | 9357.18i | 1.12877 | − | 1.95509i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3684.91 | + | 6382.46i | 0.761866 | + | 1.31959i | ||||
\(287\) | −519.232 | + | 519.232i | −0.106792 | + | 0.106792i | ||||
\(288\) | −5566.03 | − | 3808.97i | −1.13882 | − | 0.779325i | ||||
\(289\) | 4198.33i | 0.854535i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2962.52 | + | 275.222i | −0.596791 | + | 0.0554426i | ||||
\(292\) | −4819.85 | + | 1291.47i | −0.965960 | + | 0.258828i | ||||
\(293\) | 6825.62 | − | 1828.92i | 1.36094 | − | 0.364664i | 0.496781 | − | 0.867876i | \(-0.334515\pi\) |
0.864163 | + | 0.503212i | \(0.167848\pi\) | |||||||
\(294\) | −1071.02 | + | 2329.38i | −0.212459 | + | 0.462081i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2464.39i | 0.483918i | ||||||||
\(297\) | 6894.35 | − | 111.053i | 1.34697 | − | 0.0216968i | ||||
\(298\) | −6592.65 | + | 6592.65i | −1.28155 | + | 1.28155i | ||||
\(299\) | −3092.77 | − | 5356.84i | −0.598193 | − | 1.03610i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2694.67 | − | 4667.30i | 0.516007 | − | 0.893750i | ||||
\(302\) | 2922.31 | + | 10906.2i | 0.556821 | + | 2.07809i | ||||
\(303\) | 565.391 | + | 469.269i | 0.107197 | + | 0.0889730i | ||||
\(304\) | 1816.76 | − | 1048.91i | 0.342758 | − | 0.197892i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1027.70 | − | 2920.79i | 0.191993 | − | 0.545655i | ||||
\(307\) | −496.221 | − | 496.221i | −0.0922502 | − | 0.0922502i | 0.659476 | − | 0.751726i | \(-0.270778\pi\) |
−0.751726 | + | 0.659476i | \(0.770778\pi\) | |||||||
\(308\) | −1997.81 | + | 7455.93i | −0.369597 | + | 1.37935i | ||||
\(309\) | 508.037 | − | 359.811i | 0.0935314 | − | 0.0662426i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2763.77 | + | 1595.66i | 0.503920 | + | 0.290938i | 0.730331 | − | 0.683094i | \(-0.239366\pi\) |
−0.226411 | + | 0.974032i | \(0.572699\pi\) | |||||||
\(312\) | 1844.66 | + | 315.061i | 0.334722 | + | 0.0571692i | ||||
\(313\) | −4214.66 | − | 1129.32i | −0.761108 | − | 0.203938i | −0.142669 | − | 0.989771i | \(-0.545568\pi\) |
−0.618440 | + | 0.785832i | \(0.712235\pi\) | |||||||
\(314\) | −12428.4 | −2.23367 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3575.42 | −0.636496 | ||||||||
\(317\) | 3888.50 | + | 1041.92i | 0.688959 | + | 0.184606i | 0.586280 | − | 0.810109i | \(-0.300592\pi\) |
0.102679 | + | 0.994715i | \(0.467259\pi\) | |||||||
\(318\) | −3996.64 | + | 4815.28i | −0.704781 | + | 0.849143i | ||||
\(319\) | −9364.18 | − | 5406.41i | −1.64355 | − | 0.948906i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6281.15 | − | 2888.00i | −1.09215 | − | 0.502156i | ||||
\(322\) | 2966.39 | − | 11070.7i | 0.513386 | − | 1.91598i | ||||
\(323\) | 1016.35 | + | 1016.35i | 0.175081 | + | 0.175081i | ||||
\(324\) | 4748.31 | − | 5912.13i | 0.814182 | − | 1.01374i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5764.75 | + | 3328.28i | −0.979386 | + | 0.565449i | ||||
\(327\) | −5130.39 | + | 1898.56i | −0.867618 | + | 0.321073i | ||||
\(328\) | −129.681 | − | 483.977i | −0.0218306 | − | 0.0814731i | ||||
\(329\) | 4003.77 | − | 6934.73i | 0.670926 | − | 1.16208i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −324.017 | − | 561.214i | −0.0538054 | − | 0.0931937i | 0.837868 | − | 0.545873i | \(-0.183802\pi\) |
−0.891674 | + | 0.452679i | \(0.850468\pi\) | |||||||
\(332\) | 6410.65 | − | 6410.65i | 1.05973 | − | 1.05973i | ||||
\(333\) | 6439.41 | + | 493.765i | 1.05969 | + | 0.0812558i | ||||
\(334\) | 14920.4i | 2.44433i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1769.28 | − | 2498.14i | −0.287268 | − | 0.405609i | ||||
\(337\) | −10867.4 | + | 2911.92i | −1.75664 | + | 0.470689i | −0.986022 | − | 0.166614i | \(-0.946717\pi\) |
−0.770614 | + | 0.637303i | \(0.780050\pi\) | |||||||
\(338\) | −4040.23 | + | 1082.58i | −0.650177 | + | 0.174214i | ||||
\(339\) | 3522.16 | + | 4973.12i | 0.564299 | + | 0.796764i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2172.79i | 0.345054i | ||||||||
\(342\) | 2692.20 | + | 5615.23i | 0.425666 | + | 0.887828i | ||||
\(343\) | −4890.10 | + | 4890.10i | −0.769798 | + | 0.769798i | ||||
\(344\) | 1838.70 | + | 3184.72i | 0.288186 | + | 0.499152i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1898.13 | − | 3287.66i | 0.294926 | − | 0.510826i | ||||
\(347\) | −2545.25 | − | 9499.02i | −0.393765 | − | 1.46955i | −0.823874 | − | 0.566774i | \(-0.808191\pi\) |
0.430109 | − | 0.902777i | \(-0.358475\pi\) | |||||||
\(348\) | −11152.0 | + | 4126.94i | −1.71785 | + | 0.635710i | ||||
\(349\) | −8795.71 | + | 5078.20i | −1.34906 | + | 0.778883i | −0.988117 | − | 0.153703i | \(-0.950880\pi\) |
−0.360947 | + | 0.932586i | \(0.617547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1192.85 | − | 4756.94i | 0.181394 | − | 0.723381i | ||||
\(352\) | 8681.16 | + | 8681.16i | 1.31451 | + | 1.31451i | ||||
\(353\) | −1129.50 | + | 4215.36i | −0.170304 | + | 0.635584i | 0.827000 | + | 0.562202i | \(0.190046\pi\) |
−0.997304 | + | 0.0733816i | \(0.976621\pi\) | |||||||
\(354\) | −2608.13 | − | 1199.19i | −0.391584 | − | 0.180045i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2074.71 | − | 1197.83i | −0.308875 | − | 0.178329i | ||||
\(357\) | 1339.54 | − | 1613.92i | 0.198589 | − | 0.239266i | ||||
\(358\) | 8075.54 | + | 2163.84i | 1.19219 | + | 0.319448i | ||||
\(359\) | 5672.13 | 0.833881 | 0.416941 | − | 0.908934i | \(-0.363102\pi\) | ||||
0.416941 | + | 0.908934i | \(0.363102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3968.27 | 0.578549 | ||||||||
\(362\) | −6593.12 | − | 1766.62i | −0.957256 | − | 0.256496i | ||||
\(363\) | −5554.81 | − | 948.742i | −0.803174 | − | 0.137179i | ||||
\(364\) | 4754.54 | + | 2745.04i | 0.684631 | + | 0.395272i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1217.74 | − | 862.451i | 0.173913 | − | 0.123172i | ||||
\(367\) | −1093.81 | + | 4082.14i | −0.155576 | + | 0.580616i | 0.843480 | + | 0.537161i | \(0.180503\pi\) |
−0.999055 | + | 0.0434549i | \(0.986164\pi\) | |||||||
\(368\) | −4882.05 | − | 4882.05i | −0.691562 | − | 0.691562i | ||||
\(369\) | −1290.61 | + | 241.886i | −0.182077 | + | 0.0341249i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3671.04 | + | 2119.48i | −0.513723 | + | 0.296598i | ||||
\(372\) | 1838.66 | + | 1526.07i | 0.256264 | + | 0.212697i | ||||
\(373\) | −59.8461 | − | 223.349i | −0.00830755 | − | 0.0310042i | 0.961648 | − | 0.274288i | \(-0.0884421\pi\) |
−0.969955 | + | 0.243284i | \(0.921775\pi\) | |||||||
\(374\) | −2818.10 | + | 4881.09i | −0.389627 | + | 0.674853i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2731.96 | + | 4731.89i | 0.374707 | + | 0.649012i | ||||
\(377\) | −5438.07 | + | 5438.07i | −0.742904 | + | 0.742904i | ||||
\(378\) | 7795.43 | − | 4669.69i | 1.06072 | − | 0.635404i | ||||
\(379\) | − | 7586.66i | − | 1.02823i | −0.857720 | − | 0.514117i | \(-0.828120\pi\) | ||
0.857720 | − | 0.514117i | \(-0.171880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.53759 | + | 18.5685i | −0.00114802 | + | 0.00249684i | ||||
\(382\) | 8256.40 | − | 2212.30i | 1.10585 | − | 0.296311i | ||||
\(383\) | 4331.56 | − | 1160.64i | 0.577891 | − | 0.154846i | 0.0419781 | − | 0.999119i | \(-0.486634\pi\) |
0.535913 | + | 0.844273i | \(0.319967\pi\) | |||||||
\(384\) | 6515.58 | − | 605.305i | 0.865877 | − | 0.0804410i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 10554.6i | − | 1.39175i | ||||||
\(387\) | 8690.03 | − | 4166.40i | 1.14144 | − | 0.547261i | ||||
\(388\) | 4211.50 | − | 4211.50i | 0.551047 | − | 0.551047i | ||||
\(389\) | 1695.52 | + | 2936.72i | 0.220993 | + | 0.382771i | 0.955110 | − | 0.296252i | \(-0.0957370\pi\) |
−0.734117 | + | 0.679023i | \(0.762404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2365.25 | − | 4096.73i | 0.305923 | − | 0.529874i | ||||
\(392\) | −306.706 | − | 1144.64i | −0.0395179 | − | 0.147483i | ||||
\(393\) | −460.084 | + | 2693.76i | −0.0590539 | + | 0.345756i | ||||
\(394\) | −2611.81 | + | 1507.93i | −0.333962 | + | 0.192813i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10477.8 | + | 8985.41i | −1.32962 | + | 1.14024i | ||||
\(397\) | 1130.27 | + | 1130.27i | 0.142889 | + | 0.142889i | 0.774933 | − | 0.632044i | \(-0.217784\pi\) |
−0.632044 | + | 0.774933i | \(0.717784\pi\) | |||||||
\(398\) | 1409.73 | − | 5261.19i | 0.177546 | − | 0.662612i | ||||
\(399\) | 390.202 | + | 4200.18i | 0.0489587 | + | 0.526998i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6469.25 | + | 3735.03i | 0.805634 | + | 0.465133i | 0.845437 | − | 0.534075i | \(-0.179340\pi\) |
−0.0398035 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(402\) | 558.710 | + | 1509.77i | 0.0693183 | + | 0.187315i | ||||
\(403\) | 1492.73 | + | 399.977i | 0.184512 | + | 0.0494399i | ||||
\(404\) | −1470.86 | −0.181134 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14249.9 | −1.74190 | ||||||||
\(407\) | −11355.4 | − | 3042.68i | −1.38297 | − | 0.370565i | ||||
\(408\) | 496.698 | + | 1342.20i | 0.0602702 | + | 0.162865i | ||||
\(409\) | −8609.85 | − | 4970.90i | −1.04090 | − | 0.600966i | −0.120815 | − | 0.992675i | \(-0.538551\pi\) |
−0.920089 | + | 0.391709i | \(0.871884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 896.052 | + | 9645.22i | 0.107540 | + | 1.15758i | ||||
\(412\) | −322.547 | + | 1203.76i | −0.0385697 | + | 0.143944i | ||||
\(413\) | −1374.98 | − | 1374.98i | −0.163822 | − | 0.163822i | ||||
\(414\) | 15557.7 | − | 13341.7i | 1.84691 | − | 1.58384i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7562.12 | − | 4365.99i | 0.891258 | − | 0.514568i | ||||
\(417\) | −2097.50 | + | 12280.7i | −0.246319 | + | 1.44218i | ||||
\(418\) | −2933.82 | − | 10949.2i | −0.343296 | − | 1.28120i | ||||
\(419\) | −1659.67 | + | 2874.63i | −0.193508 | + | 0.335167i | −0.946411 | − | 0.322966i | \(-0.895320\pi\) |
0.752902 | + | 0.658133i | \(0.228653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5046.60 | + | 8740.97i | 0.584219 | + | 1.01190i | 0.994972 | + | 0.100150i | \(0.0319324\pi\) |
−0.410753 | + | 0.911747i | \(0.634734\pi\) | |||||||
\(422\) | 4101.87 | − | 4101.87i | 0.473165 | − | 0.473165i | ||||
\(423\) | 12911.7 | − | 6190.48i | 1.48414 | − | 0.711564i | ||||
\(424\) | − | 2892.44i | − | 0.331295i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 23054.4 | − | 2141.78i | 2.62204 | − | 0.243591i | ||||
\(427\) | 976.367 | − | 261.617i | 0.110655 | − | 0.0296499i | ||||
\(428\) | 13367.5 | − | 3581.82i | 1.50968 | − | 0.404518i | ||||
\(429\) | −3729.26 | + | 8110.83i | −0.419698 | + | 0.912808i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4785.97i | 0.534877i | 0.963575 | + | 0.267439i | \(0.0861773\pi\) | ||||
−0.963575 | + | 0.267439i | \(0.913823\pi\) | |||||||
\(432\) | −88.1636 | − | 5473.34i | −0.00981892 | − | 0.609575i | ||||
\(433\) | 5732.64 | − | 5732.64i | 0.636243 | − | 0.636243i | −0.313384 | − | 0.949627i | \(-0.601463\pi\) |
0.949627 | + | 0.313384i | \(0.101463\pi\) | |||||||
\(434\) | 1431.73 | + | 2479.84i | 0.158353 | + | 0.274276i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5475.37 | − | 9483.62i | 0.601428 | − | 1.04170i | ||||
\(437\) | 2462.38 | + | 9189.71i | 0.269546 | + | 1.00596i | ||||
\(438\) | −8228.02 | − | 6829.18i | −0.897602 | − | 0.745002i | ||||
\(439\) | 14876.1 | − | 8588.72i | 1.61731 | − | 0.933753i | 0.629694 | − | 0.776843i | \(-0.283180\pi\) |
0.987613 | − | 0.156910i | \(-0.0501531\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3052.39 | + | 572.079i | −0.329596 | + | 0.0617729i | ||||
\(442\) | 2834.60 | + | 2834.60i | 0.305041 | + | 0.305041i | ||||
\(443\) | −1800.67 | + | 6720.19i | −0.193121 | + | 0.720736i | 0.799625 | + | 0.600500i | \(0.205032\pi\) |
−0.992745 | + | 0.120236i | \(0.961635\pi\) | |||||||
\(444\) | −10550.3 | + | 7472.15i | −1.12769 | + | 0.798677i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 380.287 | + | 219.559i | 0.0403747 | + | 0.0233103i | ||||
\(447\) | −11132.3 | − | 1901.35i | −1.17794 | − | 0.201188i | ||||
\(448\) | 11075.8 | + | 2967.75i | 1.16804 | + | 0.312975i | ||||
\(449\) | −3397.64 | −0.357115 | −0.178558 | − | 0.983929i | \(-0.557143\pi\) | ||||
−0.178558 | + | 0.983929i | \(0.557143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2390.19 | 0.249555 | ||||||||
\(452\) | −11783.5 | − | 3157.38i | −1.22621 | − | 0.328563i | ||||
\(453\) | −8734.86 | + | 10524.0i | −0.905959 | + | 1.09153i | ||||
\(454\) | −5395.71 | − | 3115.21i | −0.557782 | − | 0.322036i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2615.14 | − | 1202.41i | −0.268564 | − | 0.123482i | ||||
\(457\) | 2243.74 | − | 8373.74i | 0.229666 | − | 0.857127i | −0.750815 | − | 0.660513i | \(-0.770339\pi\) |
0.980481 | − | 0.196614i | \(-0.0629945\pi\) | |||||||
\(458\) | −16820.2 | − | 16820.2i | −1.71606 | − | 1.71606i | ||||
\(459\) | 3606.68 | − | 1028.94i | 0.366765 | − | 0.104634i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7004.05 | − | 4043.79i | 0.707617 | − | 0.408543i | −0.102561 | − | 0.994727i | \(-0.532704\pi\) |
0.810178 | + | 0.586184i | \(0.199370\pi\) | |||||||
\(462\) | −15512.9 | + | 5740.75i | −1.56218 | + | 0.578103i | ||||
\(463\) | −1952.78 | − | 7287.87i | −0.196012 | − | 0.731525i | −0.992003 | − | 0.126217i | \(-0.959716\pi\) |
0.795991 | − | 0.605308i | \(-0.206950\pi\) | |||||||
\(464\) | −4292.09 | + | 7434.12i | −0.429430 | + | 0.743794i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2641.67 | + | 4575.51i | 0.262603 | + | 0.454842i | ||||
\(467\) | 9156.39 | − | 9156.39i | 0.907296 | − | 0.907296i | −0.0887572 | − | 0.996053i | \(-0.528290\pi\) |
0.996053 | + | 0.0887572i | \(0.0282895\pi\) | |||||||
\(468\) | 4244.28 | + | 8852.46i | 0.419214 | + | 0.874370i | ||||
\(469\) | 1090.48i | 0.107364i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8700.99 | − | 12285.4i | −0.851211 | − | 1.20187i | ||||
\(472\) | 1281.62 | − | 343.410i | 0.124982 | − | 0.0334888i | ||||
\(473\) | −16944.7 | + | 4540.33i | −1.64719 | + | 0.441362i | ||||
\(474\) | −4428.27 | − | 6252.51i | −0.429108 | − | 0.605881i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4198.62i | 0.404293i | ||||||||
\(477\) | −7557.90 | − | 579.529i | −0.725477 | − | 0.0556286i | ||||
\(478\) | 278.766 | − | 278.766i | 0.0266746 | − | 0.0266746i | ||||
\(479\) | 383.279 | + | 663.859i | 0.0365605 | + | 0.0633246i | 0.883727 | − | 0.468003i | \(-0.155027\pi\) |
−0.847166 | + | 0.531328i | \(0.821693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4180.71 | + | 7241.20i | −0.396307 | + | 0.686425i | ||||
\(482\) | 2174.44 | + | 8115.13i | 0.205484 | + | 0.766876i | ||||
\(483\) | 13020.1 | − | 4818.25i | 1.22657 | − | 0.453909i | ||||
\(484\) | 9769.39 | − | 5640.36i | 0.917486 | − | 0.529711i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 16219.8 | + | 981.234i | 1.51388 | + | 0.0915837i | ||||
\(487\) | −3894.85 | − | 3894.85i | −0.362408 | − | 0.362408i | 0.502291 | − | 0.864699i | \(-0.332491\pi\) |
−0.864699 | + | 0.502291i | \(0.832491\pi\) | |||||||
\(488\) | −178.513 | + | 666.221i | −0.0165593 | + | 0.0618000i | ||||
\(489\) | −7325.84 | − | 3368.33i | −0.677476 | − | 0.311495i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12685.9 | − | 7324.19i | −1.16600 | − | 0.673190i | −0.213265 | − | 0.976994i | \(-0.568410\pi\) |
−0.952734 | + | 0.303805i | \(0.901743\pi\) | |||||||
\(492\) | 1678.76 | − | 2022.62i | 0.153830 | − | 0.185339i | ||||
\(493\) | −5681.09 | − | 1522.24i | −0.518993 | − | 0.139064i | ||||
\(494\) | −8062.27 | −0.734289 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1724.96 | 0.156155 | ||||||||
\(497\) | 15149.6 | + | 4059.32i | 1.36731 | + | 0.366369i | ||||
\(498\) | 19150.4 | + | 3270.83i | 1.72320 | + | 0.294316i | ||||
\(499\) | −11810.8 | − | 6818.95i | −1.05956 | − | 0.611739i | −0.134252 | − | 0.990947i | \(-0.542863\pi\) |
−0.925311 | + | 0.379208i | \(0.876197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14748.7 | + | 10445.6i | −1.31522 | + | 0.931488i | ||||
\(502\) | 1296.62 | − | 4839.04i | 0.115281 | − | 0.430233i | ||||
\(503\) | 12517.9 | + | 12517.9i | 1.10964 | + | 1.10964i | 0.993198 | + | 0.116438i | \(0.0371477\pi\) |
0.116438 | + | 0.993198i | \(0.462852\pi\) | |||||||
\(504\) | −1394.08 | + | 3962.05i | −0.123209 | + | 0.350166i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −32308.6 | + | 18653.4i | −2.83852 | + | 1.63882i | ||||
\(507\) | −3898.66 | − | 3235.85i | −0.341510 | − | 0.283450i | ||||
\(508\) | −10.5887 | − | 39.5175i | −0.000924798 | − | 0.00345139i | ||||
\(509\) | −3526.64 | + | 6108.32i | −0.307103 | + | 0.531918i | −0.977727 | − | 0.209879i | \(-0.932693\pi\) |
0.670624 | + | 0.741797i | \(0.266026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3621.62 | − | 6272.83i | −0.313524 | − | 0.543040i | ||||
\(512\) | 9165.88 | − | 9165.88i | 0.791169 | − | 0.791169i | ||||
\(513\) | −3665.85 | + | 6592.41i | −0.315499 | + | 0.567372i | ||||
\(514\) | − | 112.399i | − | 0.00964534i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8059.11 | + | 17527.9i | −0.687563 | + | 1.49539i | ||||
\(517\) | −25176.6 | + | 6746.06i | −2.14172 | + | 0.573871i | ||||
\(518\) | −14965.0 | + | 4009.86i | −1.26935 | + | 0.340122i | ||||
\(519\) | 4578.71 | − | 425.368i | 0.387251 | − | 0.0359760i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17522.3i | − | 1.47344i | −0.676196 | − | 0.736722i | \(-0.736373\pi\) | ||
0.676196 | − | 0.736722i | \(-0.263627\pi\) | |||||||
\(522\) | −21029.1 | − | 14390.7i | −1.76326 | − | 1.20664i | ||||
\(523\) | 5784.54 | − | 5784.54i | 0.483633 | − | 0.483633i | −0.422657 | − | 0.906290i | \(-0.638902\pi\) |
0.906290 | + | 0.422657i | \(0.138902\pi\) | |||||||
\(524\) | −2735.25 | − | 4737.58i | −0.228034 | − | 0.394966i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1280.44 | + | 2217.79i | −0.106140 | + | 0.183841i | ||||
\(527\) | 305.889 | + | 1141.59i | 0.0252841 | + | 0.0943615i | ||||
\(528\) | −1677.58 | + | 9822.13i | −0.138272 | + | 0.809570i | ||||
\(529\) | 16579.9 | − | 9572.40i | 1.36269 | − | 0.786751i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −640.539 | − | 3417.67i | −0.0523484 | − | 0.279311i | ||||
\(532\) | −5970.95 | − | 5970.95i | −0.486604 | − | 0.486604i | ||||
\(533\) | 439.995 | − | 1642.09i | 0.0357567 | − | 0.133446i | ||||
\(534\) | −474.884 | − | 5111.71i | −0.0384836 | − | 0.414243i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −644.399 | − | 372.044i | −0.0519287 | − | 0.0299811i | ||||
\(537\) | 3514.68 | + | 9497.53i | 0.282439 | + | 0.763219i | ||||
\(538\) | −25374.5 | − | 6799.08i | −2.03341 | − | 0.544850i | ||||
\(539\) | 5652.97 | 0.451745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10105.8 | 0.803113 | 0.401557 | − | 0.915834i | \(-0.368469\pi\) | ||||
0.401557 | + | 0.915834i | \(0.368469\pi\) | |||||||
\(542\) | 507.432 | + | 135.966i | 0.0402141 | + | 0.0107753i | ||||
\(543\) | −2869.49 | − | 7754.07i | −0.226780 | − | 0.612816i | ||||
\(544\) | 5783.25 | + | 3338.96i | 0.455799 | + | 0.263156i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1088.28 | + | 11714.3i | 0.0853002 | + | 0.918182i | ||||
\(547\) | −170.158 | + | 635.040i | −0.0133006 | + | 0.0496386i | −0.972257 | − | 0.233914i | \(-0.924846\pi\) |
0.958957 | + | 0.283553i | \(0.0915132\pi\) | |||||||
\(548\) | −13711.6 | − | 13711.6i | −1.06885 | − | 1.06885i | ||||
\(549\) | 1705.06 | + | 599.937i | 0.132550 | + | 0.0466388i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10244.0 | − | 5914.38i | 0.792032 | − | 0.457280i | ||||
\(552\) | −1594.87 | + | 9337.82i | −0.122975 | + | 0.720007i | ||||
\(553\) | −1343.28 | − | 5013.18i | −0.103295 | − | 0.385501i | ||||
\(554\) | 3323.23 | − | 5756.00i | 0.254856 | − | 0.441424i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12469.8 | − | 21598.4i | −0.951148 | − | 1.64744i | ||||
\(557\) | −6427.65 | + | 6427.65i | −0.488956 | + | 0.488956i | −0.907977 | − | 0.419021i | \(-0.862373\pi\) |
0.419021 | + | 0.907977i | \(0.362373\pi\) | |||||||
\(558\) | −391.479 | + | 5105.46i | −0.0297001 | + | 0.387332i | ||||
\(559\) | 12477.0i | 0.944046i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6797.86 | + | 631.529i | −0.511597 | + | 0.0475280i | ||||
\(562\) | 11469.7 | − | 3073.31i | 0.860892 | − | 0.230675i | ||||
\(563\) | 3623.57 | − | 970.932i | 0.271253 | − | 0.0726819i | −0.120629 | − | 0.992698i | \(-0.538491\pi\) |
0.391881 | + | 0.920016i | \(0.371824\pi\) | |||||||
\(564\) | −11974.3 | + | 26043.1i | −0.893988 | + | 1.94435i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 26413.9i | − | 1.96159i | ||||||
\(567\) | 10073.5 | + | 4436.54i | 0.746114 | + | 0.328602i | ||||
\(568\) | −7567.41 | + | 7567.41i | −0.559017 | + | 0.559017i | ||||
\(569\) | 4162.66 | + | 7209.93i | 0.306692 | + | 0.531206i | 0.977637 | − | 0.210302i | \(-0.0674446\pi\) |
−0.670945 | + | 0.741507i | \(0.734111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13072.8 | + | 22642.7i | −0.958107 | + | 1.65949i | −0.231013 | + | 0.972951i | \(0.574204\pi\) |
−0.727093 | + | 0.686539i | \(0.759129\pi\) | |||||||
\(572\) | −4625.19 | − | 17261.5i | −0.338093 | − | 1.26178i | ||||
\(573\) | 7967.09 | + | 6612.62i | 0.580855 | + | 0.482105i | ||||
\(574\) | 2727.95 | − | 1574.98i | 0.198367 | − | 0.114527i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 13347.8 | + | 15564.8i | 0.965556 | + | 1.12593i | ||||
\(577\) | 17789.3 | + | 17789.3i | 1.28349 | + | 1.28349i | 0.938665 | + | 0.344829i | \(0.112063\pi\) |
0.344829 | + | 0.938665i | \(0.387937\pi\) | |||||||
\(578\) | 4661.25 | − | 17396.0i | 0.335437 | − | 1.25187i | ||||
\(579\) | 10433.2 | − | 7389.17i | 0.748855 | − | 0.530369i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11397.0 | + | 6580.06i | 0.813816 | + | 0.469857i | ||||
\(582\) | 12580.9 | + | 2148.78i | 0.896043 | + | 0.153041i | ||||
\(583\) | 13327.8 | + | 3571.17i | 0.946794 | + | 0.253693i | ||||
\(584\) | 4942.39 | 0.350202 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30312.9 | −2.13688 | ||||||||
\(587\) | 6380.84 | + | 1709.74i | 0.448664 | + | 0.120219i | 0.476074 | − | 0.879405i | \(-0.342059\pi\) |
−0.0274104 | + | 0.999624i | \(0.508726\pi\) | |||||||
\(588\) | 3970.40 | − | 4783.66i | 0.278463 | − | 0.335501i | ||||
\(589\) | −2058.49 | − | 1188.47i | −0.144005 | − | 0.0831411i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3319.08 | − | 1526.07i | −0.231013 | − | 0.106217i | ||||
\(592\) | −2415.55 | + | 9014.94i | −0.167700 | + | 0.625865i | ||||
\(593\) | 1466.22 | + | 1466.22i | 0.101535 | + | 0.101535i | 0.756050 | − | 0.654514i | \(-0.227127\pi\) |
−0.654514 | + | 0.756050i | \(0.727127\pi\) | |||||||
\(594\) | −28690.4 | − | 7194.38i | −1.98179 | − | 0.496951i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19578.6 | − | 11303.7i | 1.34559 | − | 0.776877i | ||||
\(597\) | 6187.61 | − | 2289.80i | 0.424191 | − | 0.156977i | ||||
\(598\) | 6867.58 | + | 25630.2i | 0.469626 | + | 1.75267i | ||||
\(599\) | 8093.94 | − | 14019.1i | 0.552102 | − | 0.956269i | −0.446020 | − | 0.895023i | \(-0.647159\pi\) |
0.998123 | − | 0.0612464i | \(-0.0195075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4667.92 | − | 8085.07i | −0.316819 | − | 0.548747i | 0.663003 | − | 0.748617i | \(-0.269282\pi\) |
−0.979823 | + | 0.199869i | \(0.935948\pi\) | |||||||
\(602\) | −16347.4 | + | 16347.4i | −1.10676 | + | 1.10676i | ||||
\(603\) | −1101.26 | + | 1609.26i | −0.0743726 | + | 0.108680i | ||||
\(604\) | − | 27378.3i | − | 1.84438i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1821.71 | − | 2572.18i | −0.122116 | − | 0.172422i | ||||
\(607\) | 4851.38 | − | 1299.92i | 0.324401 | − | 0.0869230i | −0.0929433 | − | 0.995671i | \(-0.529628\pi\) |
0.417344 | + | 0.908748i | \(0.362961\pi\) | |||||||
\(608\) | −12972.9 | + | 3476.07i | −0.865329 | + | 0.231864i | ||||
\(609\) | −9976.27 | − | 14086.0i | −0.663807 | − | 0.937265i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18538.5i | 1.22747i | ||||||||
\(612\) | −4240.10 | + | 6196.05i | −0.280059 | + | 0.409249i | ||||
\(613\) | −17030.5 | + | 17030.5i | −1.12212 | + | 1.12212i | −0.130693 | + | 0.991423i | \(0.541720\pi\) |
−0.991423 | + | 0.130693i | \(0.958280\pi\) | |||||||
\(614\) | 1505.18 | + | 2607.05i | 0.0989320 | + | 0.171355i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3822.75 | − | 6621.19i | 0.250037 | − | 0.433077i | ||||
\(617\) | −1676.06 | − | 6255.15i | −0.109361 | − | 0.408141i | 0.889442 | − | 0.457047i | \(-0.151093\pi\) |
−0.998803 | + | 0.0489065i | \(0.984426\pi\) | |||||||
\(618\) | −2504.56 | + | 926.844i | −0.163023 | + | 0.0603287i | ||||
\(619\) | −10407.7 | + | 6008.87i | −0.675799 | + | 0.390173i | −0.798270 | − | 0.602300i | \(-0.794251\pi\) |
0.122472 | + | 0.992472i | \(0.460918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24080.1 | + | 6038.29i | 1.55604 | + | 0.390191i | ||||
\(622\) | −9680.22 | − | 9680.22i | −0.624022 | − | 0.624022i | ||||
\(623\) | 900.049 | − | 3359.03i | 0.0578807 | − | 0.216014i | ||||
\(624\) | 6439.10 | + | 2960.62i | 0.413093 | + | 0.189935i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16209.9 | + | 9358.77i | 1.03495 | + | 0.597526i | ||||
\(627\) | 8769.27 | − | 10565.5i | 0.558550 | − | 0.672959i | ||||
\(628\) | 29109.4 | + | 7799.85i | 1.84967 | + | 0.495618i | ||||
\(629\) | −6394.53 | −0.405352 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1233.51 | 0.0778212 | 0.0389106 | − | 0.999243i | \(-0.487611\pi\) | ||||
0.0389106 | + | 0.999243i | \(0.487611\pi\) | |||||||
\(632\) | 3420.72 | + | 916.580i | 0.215299 | + | 0.0576892i | ||||
\(633\) | 6926.37 | + | 1183.00i | 0.434910 | + | 0.0742812i | ||||
\(634\) | −14955.4 | − | 8634.51i | −0.936838 | − | 0.540884i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 12382.8 | − | 8770.01i | 0.772031 | − | 0.546782i | ||||
\(637\) | 1040.62 | − | 3883.66i | 0.0647268 | − | 0.241564i | ||||
\(638\) | 32798.5 | + | 32798.5i | 2.03527 | + | 2.03527i | ||||
\(639\) | 18257.3 | + | 21289.8i | 1.13028 | + | 1.31801i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22917.1 | − | 13231.2i | 1.41212 | − | 0.815291i | 0.416536 | − | 0.909119i | \(-0.363244\pi\) |
0.995588 | + | 0.0938285i | \(0.0299105\pi\) | |||||||
\(642\) | 22819.9 | + | 18940.3i | 1.40285 | + | 1.16435i | ||||
\(643\) | −6178.54 | − | 23058.6i | −0.378939 | − | 1.41422i | −0.847503 | − | 0.530791i | \(-0.821895\pi\) |
0.468564 | − | 0.883430i | \(-0.344772\pi\) | |||||||
\(644\) | −13895.6 | + | 24067.9i | −0.850255 | + | 1.47269i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3082.88 | − | 5339.70i | −0.187762 | − | 0.325213i | ||||
\(647\) | 11613.4 | − | 11613.4i | 0.705670 | − | 0.705670i | −0.259951 | − | 0.965622i | \(-0.583706\pi\) |
0.965622 | + | 0.259951i | \(0.0837065\pi\) | |||||||
\(648\) | −6058.49 | + | 4439.09i | −0.367284 | + | 0.269111i | ||||
\(649\) | 6329.46i | 0.382825i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1448.96 | + | 3151.38i | −0.0872340 | + | 0.189727i | ||||
\(652\) | 15590.8 | − | 4177.55i | 0.936479 | − | 0.250929i | ||||
\(653\) | 18351.3 | − | 4917.23i | 1.09976 | − | 0.294680i | 0.337094 | − | 0.941471i | \(-0.390556\pi\) |
0.762667 | + | 0.646791i | \(0.223889\pi\) | |||||||
\(654\) | 23365.9 | − | 2170.72i | 1.39706 | − | 0.129789i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1897.54i | − | 0.112937i | ||||||
\(657\) | 990.260 | − | 12914.4i | 0.0588032 | − | 0.766879i | ||||
\(658\) | −24289.2 | + | 24289.2i | −1.43904 | + | 1.43904i | ||||
\(659\) | 10618.4 | + | 18391.6i | 0.627670 | + | 1.08716i | 0.988018 | + | 0.154338i | \(0.0493246\pi\) |
−0.360348 | + | 0.932818i | \(0.617342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7686.03 | − | 13312.6i | 0.452272 | − | 0.783359i | −0.546254 | − | 0.837619i | \(-0.683947\pi\) |
0.998527 | + | 0.0542605i | \(0.0172801\pi\) | |||||||
\(662\) | 719.488 | + | 2685.16i | 0.0422412 | + | 0.157646i | ||||
\(663\) | −817.511 | + | 4786.46i | −0.0478876 | + | 0.280378i | ||||
\(664\) | −7776.70 | + | 4489.88i | −0.454510 | + | 0.262411i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26133.9 | − | 9195.38i | −1.52052 | − | 0.535006i | ||||
\(667\) | −27528.0 | − | 27528.0i | −1.59803 | − | 1.59803i | ||||
\(668\) | 9363.79 | − | 34946.1i | 0.542359 | − | 2.02411i | ||||
\(669\) | 49.2027 | + | 529.624i | 0.00284347 | + | 0.0306075i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2849.41 | − | 1645.11i | −0.163935 | − | 0.0946479i | ||||
\(672\) | 6801.80 | + | 18380.2i | 0.390454 | + | 1.05510i | ||||
\(673\) | −29592.1 | − | 7929.17i | −1.69493 | − | 0.454156i | −0.723278 | − | 0.690557i | \(-0.757365\pi\) |
−0.971656 | + | 0.236401i | \(0.924032\pi\) | |||||||
\(674\) | 48262.8 | 2.75818 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10142.4 | 0.577057 | ||||||||
\(677\) | 30707.2 | + | 8227.98i | 1.74324 | + | 0.467100i | 0.983163 | − | 0.182731i | \(-0.0584936\pi\) |
0.760079 | + | 0.649831i | \(0.225160\pi\) | |||||||
\(678\) | −9072.79 | − | 24516.9i | −0.513921 | − | 1.38874i | ||||
\(679\) | 7487.30 | + | 4322.79i | 0.423175 | + | 0.244320i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −698.112 | − | 7514.57i | −0.0392830 | − | 0.422847i | ||||
\(682\) | 2412.37 | − | 9003.09i | 0.135446 | − | 0.505493i | ||||
\(683\) | −10544.6 | − | 10544.6i | −0.590742 | − | 0.590742i | 0.347090 | − | 0.937832i | \(-0.387170\pi\) |
−0.937832 | + | 0.347090i | \(0.887170\pi\) | |||||||
\(684\) | −2781.59 | − | 14841.5i | −0.155492 | − | 0.829646i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25691.7 | − | 14833.1i | 1.42990 | − | 0.825555i | ||||
\(687\) | 4851.02 | − | 28402.3i | 0.269400 | − | 1.57732i | ||||
\(688\) | 3604.51 | + | 13452.2i | 0.199739 | + | 0.745438i | ||||
\(689\) | 4906.87 | − | 8498.95i | 0.271316 | − | 0.469933i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1725.29 | + | 2988.28i | 0.0949825 | + | 0.164515i | 0.909601 | − | 0.415482i | \(-0.136387\pi\) |
−0.814619 | + | 0.579997i | \(0.803054\pi\) | |||||||
\(692\) | −6509.06 | + | 6509.06i | −0.357568 | + | 0.357568i | ||||
\(693\) | −16535.2 | − | 11315.4i | −0.906377 | − | 0.620256i | ||||
\(694\) | 42185.6i | 2.30741i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11727.5 | − | 1089.50i | 0.638691 | − | 0.0593351i | ||||
\(697\) | 1255.81 | − | 336.493i | 0.0682457 | − | 0.0182864i | ||||
\(698\) | 42083.6 | − | 11276.3i | 2.28208 | − | 0.611481i | ||||
\(699\) | −2673.46 | + | 5814.56i | −0.144663 | + | 0.314631i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33118.2i | 1.78439i | 0.451650 | + | 0.892195i | \(0.350835\pi\) | ||||
−0.451650 | + | 0.892195i | \(0.649165\pi\) | |||||||
\(702\) | −10224.1 | + | 18386.3i | −0.549691 | + | 0.988526i | ||||
\(703\) | 9093.79 | − | 9093.79i | 0.487879 | − | 0.487879i | ||||
\(704\) | −18661.9 | − | 32323.4i | −0.999074 | − | 1.73045i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9360.31 | − | 16212.5i | 0.498980 | − | 0.864259i | ||||
\(707\) | −552.601 | − | 2062.33i | −0.0293956 | − | 0.109706i | ||||
\(708\) | 5356.12 | + | 4445.53i | 0.284315 | + | 0.235979i | ||||
\(709\) | −24955.0 | + | 14407.8i | −1.32187 | + | 0.763181i | −0.984027 | − | 0.178021i | \(-0.943030\pi\) |
−0.337842 | + | 0.941203i | \(0.609697\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3080.39 | − | 8754.66i | 0.162481 | − | 0.461780i | ||||
\(712\) | 1677.88 | + | 1677.88i | 0.0883161 | + | 0.0883161i | ||||
\(713\) | −2024.72 | + | 7556.35i | −0.106348 | + | 0.396897i | ||||
\(714\) | −7342.35 | + | 5200.13i | −0.384846 | + | 0.272563i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17556.4 | − | 10136.2i | −0.916358 | − | 0.529060i | ||||
\(717\) | 470.720 | + | 80.3973i | 0.0245180 | + | 0.00418758i | ||||
\(718\) | −23502.8 | − | 6297.55i | −1.22161 | − | 0.327329i | ||||
\(719\) | 11652.8 | 0.604418 | 0.302209 | − | 0.953242i | \(-0.402276\pi\) | ||||
0.302209 | + | 0.953242i | \(0.402276\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1809.00 | −0.0934407 | ||||||||
\(722\) | −16442.7 | − | 4405.82i | −0.847555 | − | 0.227102i | ||||
\(723\) | −6499.47 | + | 7830.76i | −0.334326 | + | 0.402807i | ||||
\(724\) | 14333.6 | + | 8275.48i | 0.735777 | + | 0.424801i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 21963.3 | + | 10098.5i | 1.12278 | + | 0.516238i | ||||
\(727\) | −3260.88 | + | 12169.8i | −0.166354 | + | 0.620841i | 0.831510 | + | 0.555510i | \(0.187477\pi\) |
−0.997864 | + | 0.0653308i | \(0.979190\pi\) | |||||||
\(728\) | −3845.13 | − | 3845.13i | −0.195755 | − | 0.195755i | ||||
\(729\) | 10385.4 | + | 16720.2i | 0.527633 | + | 0.849472i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8263.62 | + | 4771.00i | −0.418113 | + | 0.241398i | ||||
\(732\) | −3393.43 | + | 1255.78i | −0.171345 | + | 0.0634084i | ||||
\(733\) | 7029.55 | + | 26234.6i | 0.354219 | + | 1.32196i | 0.881465 | + | 0.472250i | \(0.156558\pi\) |
−0.527246 | + | 0.849713i | \(0.676775\pi\) | |||||||
\(734\) | 9064.49 | − | 15700.2i | 0.455826 | − | 0.789514i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22101.0 | + | 38280.1i | 1.10687 | + | 1.91715i | ||||
\(737\) | 2509.92 | − | 2509.92i | 0.125446 | − | 0.125446i | ||||
\(738\) | 5616.27 | + | 430.648i | 0.280132 | + | 0.0214802i | ||||
\(739\) | − | 18361.9i | − | 0.914008i | −0.889465 | − | 0.457004i | \(-0.848923\pi\) | ||
0.889465 | − | 0.457004i | \(-0.151077\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5644.33 | − | 7969.53i | −0.279824 | − | 0.395098i | ||||
\(742\) | 17564.3 | − | 4706.35i | 0.869013 | − | 0.232851i | ||||
\(743\) | −13531.1 | + | 3625.64i | −0.668112 | + | 0.179020i | −0.576904 | − | 0.816812i | \(-0.695739\pi\) |
−0.0912077 | + | 0.995832i | \(0.529073\pi\) | |||||||
\(744\) | −1367.89 | − | 1931.40i | −0.0674051 | − | 0.0951728i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 991.903i | 0.0486811i | ||||||||
\(747\) | 10173.9 | + | 21220.0i | 0.498316 | + | 1.03936i | ||||
\(748\) | 9663.78 | − | 9663.78i | 0.472384 | − | 0.472384i | ||||
\(749\) | 10044.3 | + | 17397.3i | 0.490002 | + | 0.848708i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12757.5 | + | 22096.6i | −0.619876 | + | 1.07366i | 0.369632 | + | 0.929178i | \(0.379484\pi\) |
−0.989508 | + | 0.144478i | \(0.953850\pi\) | |||||||
\(752\) | 5355.62 | + | 19987.5i | 0.259707 | + | 0.969239i | ||||
\(753\) | 5691.12 | − | 2106.07i | 0.275426 | − | 0.101925i | ||||
\(754\) | 28570.6 | − | 16495.3i | 1.37995 | − | 0.796713i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −21188.9 | + | 6044.95i | −1.01936 | + | 0.290810i | ||||
\(757\) | 14733.2 | + | 14733.2i | 0.707382 | + | 0.707382i | 0.965984 | − | 0.258602i | \(-0.0832617\pi\) |
−0.258602 | + | 0.965984i | \(0.583262\pi\) | |||||||
\(758\) | −8423.18 | + | 31435.7i | −0.403620 | + | 1.50633i | ||||
\(759\) | −41057.8 | − | 18877.9i | −1.96351 | − | 0.902797i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1768.38 | + | 1020.97i | 0.0842361 | + | 0.0486337i | 0.541526 | − | 0.840684i | \(-0.317847\pi\) |
−0.457290 | + | 0.889317i | \(0.651180\pi\) | |||||||
\(762\) | 55.9919 | − | 67.4608i | 0.00266191 | − | 0.00320715i | ||||
\(763\) | 15354.3 | + | 4114.18i | 0.728523 | + | 0.195207i | ||||
\(764\) | −20726.4 | −0.981484 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19236.7 | −0.907375 | ||||||||
\(767\) | 4348.41 | + | 1165.15i | 0.204709 | + | 0.0548517i | ||||
\(768\) | 3448.22 | + | 588.944i | 0.162014 | + | 0.0276715i | ||||
\(769\) | 7810.71 | + | 4509.51i | 0.366270 | + | 0.211466i | 0.671828 | − | 0.740708i | \(-0.265510\pi\) |
−0.305558 | + | 0.952174i | \(0.598843\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 111.106 | − | 78.6896i | 0.00518986 | − | 0.00367566i | ||||
\(772\) | −6623.89 | + | 24720.7i | −0.308807 | + | 1.15248i | ||||
\(773\) | −12401.6 | − | 12401.6i | −0.577042 | − | 0.577042i | 0.357045 | − | 0.934087i | \(-0.383784\pi\) |
−0.934087 | + | 0.357045i | \(0.883784\pi\) | |||||||
\(774\) | −40633.4 | + | 7615.51i | −1.88700 | + | 0.353661i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5108.93 | + | 2949.64i | −0.236340 | + | 0.136451i | ||||
\(777\) | −14440.6 | − | 11985.6i | −0.666737 | − | 0.553386i | ||||
\(778\) | −3764.94 | − | 14050.9i | −0.173496 | − | 0.647494i | ||||
\(779\) | −1307.38 | + | 2264.45i | −0.0601306 | + | 0.104149i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25526.0 | − | 44212.3i | −1.16952 | − | 2.02566i | ||||
\(782\) | −14349.0 | + | 14349.0i | −0.656162 | + | 0.656162i | ||||
\(783\) | −497.120 | − | 30862.0i | −0.0226892 | − | 1.40858i | ||||
\(784\) | − | 4487.83i | − | 0.204438i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4897.16 | − | 10650.9i | 0.222234 | − | 0.483341i | ||||
\(787\) | −32028.5 | + | 8582.02i | −1.45069 | + | 0.388712i | −0.896264 | − | 0.443521i | \(-0.853729\pi\) |
−0.554427 | + | 0.832232i | \(0.687063\pi\) | |||||||
\(788\) | 7063.67 | − | 1892.70i | 0.319331 | − | 0.0855645i | ||||
\(789\) | −3088.70 | + | 286.944i | −0.139367 | + | 0.0129474i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 17708.1i | − | 0.795991i | ||||||
\(792\) | 12328.0 | − | 5910.60i | 0.553100 | − | 0.265182i | ||||
\(793\) | −1654.74 | + | 1654.74i | −0.0741004 | + | 0.0741004i | ||||
\(794\) | −3428.45 | − | 5938.26i | −0.153238 | − | 0.265417i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6603.69 | + | 11437.9i | −0.294047 | + | 0.509305i | ||||
\(797\) | 2230.32 | + | 8323.68i | 0.0991243 | + | 0.369937i | 0.997612 | − | 0.0690608i | \(-0.0220003\pi\) |
−0.898488 | + | 0.438998i | \(0.855334\pi\) | |||||||
\(798\) | 3046.48 | − | 17836.9i | 0.135143 | − | 0.791253i | ||||
\(799\) | −12278.2 | + | 7088.80i | −0.543642 | + | 0.313872i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4720.45 | − | 4048.09i | 0.208226 | − | 0.178567i | ||||
\(802\) | −22658.9 | − | 22658.9i | −0.997646 | − | 0.997646i | ||||
\(803\) | −6102.17 | + | 22773.6i | −0.268170 | + | 1.00083i | ||||
\(804\) | −361.088 | − | 3886.80i | −0.0158390 | − | 0.170494i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5741.14 | − | 3314.65i | −0.250897 | − | 0.144856i | ||||
\(807\) | −11043.6 | − | 29842.6i | −0.481727 | − | 1.30175i | ||||
\(808\) | 1407.23 | + | 377.065i | 0.0612699 | + | 0.0164172i | ||||
\(809\) | −23450.0 | −1.01911 | −0.509554 | − | 0.860439i | \(-0.670190\pi\) | ||||
−0.509554 | + | 0.860439i | \(0.670190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12488.0 | 0.540705 | 0.270352 | − | 0.962761i | \(-0.412860\pi\) | ||||
0.270352 | + | 0.962761i | \(0.412860\pi\) | |||||||
\(812\) | 33375.9 | + | 8943.05i | 1.44244 | + | 0.386502i | ||||
\(813\) | 220.847 | + | 596.783i | 0.00952699 | + | 0.0257443i | ||||
\(814\) | 43673.7 | + | 25215.0i | 1.88054 | + | 1.08573i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 501.364 | + | 5396.75i | 0.0215089 | + | 0.231524i | ||||
\(817\) | 4966.92 | − | 18536.8i | 0.212693 | − | 0.793783i | ||||
\(818\) | 30156.4 | + | 30156.4i | 1.28899 | + | 1.28899i | ||||
\(819\) | −10817.7 | + | 9276.87i | −0.461539 | + | 0.395800i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7534.17 | + | 4349.85i | −0.320273 | + | 0.184910i | −0.651514 | − | 0.758636i | \(-0.725866\pi\) |
0.331241 | + | 0.943546i | \(0.392533\pi\) | |||||||
\(822\) | 6995.88 | − | 40960.3i | 0.296848 | − | 1.73802i | ||||
\(823\) | 7812.50 | + | 29156.6i | 0.330895 | + | 1.23492i | 0.908251 | + | 0.418425i | \(0.137418\pi\) |
−0.577356 | + | 0.816492i | \(0.695916\pi\) | |||||||
\(824\) | 617.183 | − | 1068.99i | 0.0260930 | − | 0.0451943i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4170.72 | + | 7223.89i | 0.175687 | + | 0.304299i | ||||
\(827\) | −26730.4 | + | 26730.4i | −1.12395 | + | 1.12395i | −0.132810 | + | 0.991141i | \(0.542400\pi\) |
−0.991141 | + | 0.132810i | \(0.957600\pi\) | |||||||
\(828\) | −44812.0 | + | 21484.9i | −1.88083 | + | 0.901755i | ||||
\(829\) | − | 39741.7i | − | 1.66500i | −0.554025 | − | 0.832500i | \(-0.686909\pi\) | ||
0.554025 | − | 0.832500i | \(-0.313091\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8016.35 | − | 744.728i | 0.334638 | − | 0.0310883i | ||||
\(832\) | −25641.9 | + | 6870.73i | −1.06848 | + | 0.286298i | ||||
\(833\) | 2970.09 | − | 795.833i | 0.123538 | − | 0.0331020i | ||||
\(834\) | 22325.9 | − | 48557.0i | 0.926957 | − | 2.01605i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27486.1i | 1.13711i | ||||||||
\(837\) | −5320.80 | + | 3187.31i | −0.219730 | + | 0.131624i | ||||
\(838\) | 10068.5 | − | 10068.5i | 0.415049 | − | 0.415049i | ||||
\(839\) | −14713.2 | − | 25484.1i | −0.605431 | − | 1.04864i | −0.991983 | − | 0.126370i | \(-0.959667\pi\) |
0.386552 | − | 0.922268i | \(-0.373666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12006.9 | + | 20796.6i | −0.492309 | + | 0.852704i | ||||
\(842\) | −11206.1 | − | 41821.7i | −0.458655 | − | 1.71172i | ||||
\(843\) | 11067.8 | + | 9186.19i | 0.452190 | + | 0.375314i | ||||
\(844\) | −12181.6 | + | 7033.04i | −0.496810 | + | 0.286833i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −60373.5 | + | 11315.2i | −2.45353 | + | 0.459840i | ||||
\(847\) | 11578.8 | + | 11578.8i | 0.469721 | + | 0.469721i | ||||
\(848\) | 2835.11 | − | 10580.8i | 0.114809 | − | 0.428473i | ||||
\(849\) | 26110.1 | − | 18492.2i | 1.05547 | − | 0.747526i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36655.6 | − | 21163.1i | −1.47654 | − | 0.852482i | ||||
\(852\) | −55341.7 | − | 9452.17i | −2.22532 | − | 0.380077i | ||||
\(853\) | −18129.3 | − | 4857.73i | −0.727709 | − | 0.194989i | −0.124100 | − | 0.992270i | \(-0.539604\pi\) |
−0.603609 | + | 0.797281i | \(0.706271\pi\) | |||||||
\(854\) | −4336.09 | −0.173745 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13707.4 | −0.547324 | ||||||||
\(857\) | −15665.5 | − | 4197.56i | −0.624415 | − | 0.167312i | −0.0672811 | − | 0.997734i | \(-0.521432\pi\) |
−0.557134 | + | 0.830422i | \(0.688099\pi\) | |||||||
\(858\) | 24457.5 | − | 29467.2i | 0.973155 | − | 1.17249i | ||||
\(859\) | −601.750 | − | 347.420i | −0.0239016 | − | 0.0137996i | 0.488002 | − | 0.872843i | \(-0.337726\pi\) |
−0.511903 | + | 0.859043i | \(0.671059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3466.68 | + | 1593.94i | 0.137217 | + | 0.0630908i | ||||
\(862\) | 5313.68 | − | 19830.9i | 0.209959 | − | 0.783578i | ||||
\(863\) | −15470.7 | − | 15470.7i | −0.610228 | − | 0.610228i | 0.332777 | − | 0.943006i | \(-0.392014\pi\) |
−0.943006 | + | 0.332777i | \(0.892014\pi\) | |||||||
\(864\) | −8524.11 | + | 33993.2i | −0.335644 | + | 1.33851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30118.3 | + | 17388.8i | −1.18182 | + | 0.682327i | ||||
\(867\) | 20459.2 | − | 7571.18i | 0.801420 | − | 0.296575i | ||||
\(868\) | −1797.07 | − | 6706.75i | −0.0702724 | − | 0.262260i | ||||
\(869\) | −8446.85 | + | 14630.4i | −0.329735 | + | 0.571118i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1262.31 | − | 2186.38i | −0.0491063 | − | 0.0850547i | ||||
\(872\) | −7669.67 | + | 7669.67i | −0.297853 | + | 0.297853i | ||||
\(873\) | 6683.75 | + | 13940.6i | 0.259119 | + | 0.540454i | ||||
\(874\) | − | 40812.0i | − | 1.57950i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14985.6 | + | 21158.9i | 0.577986 | + | 0.816090i | ||||
\(877\) | 18848.8 | − | 5050.52i | 0.725746 | − | 0.194463i | 0.123012 | − | 0.992405i | \(-0.460745\pi\) |
0.602734 | + | 0.797942i | \(0.294078\pi\) | |||||||
\(878\) | −71175.7 | + | 19071.5i | −2.73584 | + | 0.733065i | ||||
\(879\) | −21221.8 | − | 29964.2i | −0.814327 | − | 1.14979i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22685.6i | 0.867533i | 0.901025 | + | 0.433766i | \(0.142816\pi\) | ||||
−0.901025 | + | 0.433766i | \(0.857184\pi\) | |||||||
\(882\) | 13282.9 | + | 1018.51i | 0.507096 | + | 0.0388834i | ||||
\(883\) | 6561.23 | − | 6561.23i | 0.250060 | − | 0.250060i | −0.570935 | − | 0.820995i | \(-0.693419\pi\) |
0.820995 | + | 0.570935i | \(0.193419\pi\) | |||||||
\(884\) | −4860.18 | − | 8418.08i | −0.184916 | − | 0.320284i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14922.3 | − | 25846.3i | 0.565831 | − | 0.980048i | ||||
\(887\) | −3384.46 | − | 12631.0i | −0.128116 | − | 0.478137i | 0.871815 | − | 0.489835i | \(-0.162943\pi\) |
−0.999932 | + | 0.0116982i | \(0.996276\pi\) | |||||||
\(888\) | 12009.4 | − | 4444.22i | 0.453839 | − | 0.167949i | ||||
\(889\) | 51.4304 | − | 29.6933i | 0.00194029 | − | 0.00112023i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12974.3 | − | 33397.1i | −0.487829 | − | 1.25572i | ||||
\(892\) | −752.908 | − | 752.908i | −0.0282615 | − | 0.0282615i | ||||
\(893\) | 7379.90 | − | 27542.2i | 0.276550 | − | 1.03210i | ||||
\(894\) | 44016.2 | + | 20238.1i | 1.64667 | + | 0.757118i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16467.1 | − | 9507.27i | −0.613980 | − | 0.354482i | ||||
\(897\) | −20527.4 | + | 24732.0i | −0.764091 | + | 0.920601i | ||||
\(898\) | 14078.3 | + | 3772.27i | 0.523162 | + | 0.140181i | ||||
\(899\) | 9726.35 | 0.360836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7505.21 | 0.277508 | ||||||||
\(902\) | −9903.87 | − | 2653.73i | −0.365591 | − | 0.0979597i | ||||
\(903\) | −27604.1 | − | 4714.68i | −1.01728 | − | 0.173748i | ||||
\(904\) | 10464.3 | + | 6041.54i | 0.384996 | + | 0.222277i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 47877.8 | − | 33908.9i | 1.75567 | − | 1.24343i | ||||
\(907\) | −3282.57 | + | 12250.7i | −0.120172 | + | 0.448488i | −0.999622 | − | 0.0275041i | \(-0.991244\pi\) |
0.879450 | + | 0.475992i | \(0.157911\pi\) | |||||||
\(908\) | 10682.7 | + | 10682.7i | 0.390436 | + | 0.390436i | ||||
\(909\) | 1267.22 | − | 3601.52i | 0.0462387 | − | 0.131413i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19788.0 | + | 11424.6i | −0.719655 | + | 0.415493i | −0.814626 | − | 0.579987i | \(-0.803058\pi\) |
0.0949706 | + | 0.995480i | \(0.469724\pi\) | |||||||
\(912\) | −8387.82 | − | 6961.82i | −0.304549 | − | 0.252773i | ||||
\(913\) | −11086.9 | − | 41377.0i | −0.401888 | − | 1.49987i | ||||
\(914\) | −18594.1 | + | 32205.9i | −0.672908 | + | 1.16551i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28839.8 | + | 49951.9i | 1.04028 | + | 1.80181i | ||||
\(917\) | 5615.06 | − | 5615.06i | 0.202209 | − | 0.202209i | ||||
\(918\) | −16086.9 | + | 259.124i | −0.578372 | + | 0.00931631i | ||||
\(919\) | 34032.1i | 1.22156i | 0.791800 | + | 0.610780i | \(0.209144\pi\) | ||||
−0.791800 | + | 0.610780i | \(0.790856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1523.30 | + | 3313.04i | −0.0544998 | + | 0.118533i | ||||
\(922\) | −33511.3 | + | 8979.34i | −1.19700 | + | 0.320736i | ||||
\(923\) | −35073.3 | + | 9397.87i | −1.25076 | + | 0.335140i | ||||
\(924\) | 39936.8 | − | 3710.18i | 1.42189 | − | 0.132095i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32365.8i | 1.14860i | ||||||||
\(927\) | −2669.61 | − | 1826.88i | −0.0945861 | − | 0.0647276i | ||||
\(928\) | 38860.6 | − | 38860.6i | 1.37463 | − | 1.37463i | ||||
\(929\) | −10629.2 | − | 18410.4i | −0.375386 | − | 0.650188i | 0.614998 | − | 0.788528i | \(-0.289157\pi\) |
−0.990385 | + | 0.138340i | \(0.955823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3092.05 | + | 5355.60i | −0.108849 | + | 0.188531i | ||||
\(932\) | −3315.75 | − | 12374.5i | −0.116535 | − | 0.434916i | ||||
\(933\) | 2791.82 | − | 16345.9i | 0.0979638 | − | 0.573570i | ||||
\(934\) | −48106.0 | + | 27774.0i | −1.68531 | + | 0.973012i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1791.27 | − | 9557.51i | −0.0625528 | − | 0.333757i | ||||
\(937\) | 376.587 | + | 376.587i | 0.0131297 | + | 0.0131297i | 0.713641 | − | 0.700511i | \(-0.247045\pi\) |
−0.700511 | + | 0.713641i | \(0.747045\pi\) | |||||||
\(938\) | 1210.72 | − | 4518.48i | 0.0421445 | − | 0.157285i | ||||
\(939\) | 2097.28 | + | 22575.4i | 0.0728883 | + | 0.784579i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24030.3 | + | 13873.9i | 0.832481 | + | 0.480633i | 0.854701 | − | 0.519120i | \(-0.173740\pi\) |
−0.0222206 | + | 0.999753i | \(0.507074\pi\) | |||||||
\(942\) | 22413.0 | + | 60565.6i | 0.775219 | + | 2.09483i | ||||
\(943\) | 8312.38 | + | 2227.30i | 0.287050 | + | 0.0769149i | ||||
\(944\) | 5024.89 | 0.173248 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 75252.4 | 2.58633 | ||||||||
\(947\) | −12152.6 | − | 3256.28i | −0.417008 | − | 0.111737i | 0.0442131 | − | 0.999022i | \(-0.485922\pi\) |
−0.461221 | + | 0.887285i | \(0.652589\pi\) | |||||||
\(948\) | 6447.82 | + | 17423.6i | 0.220903 | + | 0.596933i | ||||
\(949\) | 14522.4 | + | 8384.52i | 0.496752 | + | 0.286800i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1934.97 | − | 20828.3i | −0.0659788 | − | 0.710204i | ||||
\(952\) | 1076.34 | − | 4016.97i | 0.0366434 | − | 0.136755i | ||||
\(953\) | 1723.37 | + | 1723.37i | 0.0585787 | + | 0.0585787i | 0.735789 | − | 0.677211i | \(-0.236811\pi\) |
−0.677211 | + | 0.735789i | \(0.736811\pi\) | |||||||
\(954\) | 30673.1 | + | 10792.6i | 1.04096 | + | 0.366271i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −827.868 | + | 477.970i | −0.0280075 | + | 0.0161701i | ||||
\(957\) | −9459.24 | + | 55383.1i | −0.319513 | + | 1.87072i | ||||
\(958\) | −851.080 | − | 3176.28i | −0.0287027 | − | 0.107120i | ||||
\(959\) | 14073.9 | − | 24376.7i | 0.473900 | − | 0.820819i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13918.3 | + | 24107.1i | 0.467197 | + | 0.809209i | ||||
\(962\) | 25362.6 | − | 25362.6i | 0.850025 | − | 0.850025i | ||||
\(963\) | −2746.42 | + | 35817.3i | −0.0919025 | + | 1.19854i | ||||
\(964\) | − | 20371.7i | − | 0.680632i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −59299.0 | + | 5508.95i | −1.97507 | + | 0.183486i | ||||
\(967\) | 30387.5 | − | 8142.30i | 1.01054 | − | 0.270774i | 0.284687 | − | 0.958621i | \(-0.408110\pi\) |
0.725856 | + | 0.687846i | \(0.241444\pi\) | |||||||
\(968\) | −10792.7 | + | 2891.88i | −0.358357 | + | 0.0960214i | ||||
\(969\) | 3119.98 | − | 6785.69i | 0.103435 | − | 0.224962i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 51764.9i | − | 1.71083i | −0.517943 | − | 0.855415i | \(-0.673302\pi\) | ||
0.517943 | − | 0.855415i | \(-0.326698\pi\) | |||||||
\(972\) | −37373.9 | − | 12477.5i | −1.23330 | − | 0.411746i | ||||
\(973\) | 25598.7 | − | 25598.7i | 0.843430 | − | 0.843430i | ||||
\(974\) | 11814.2 | + | 20462.8i | 0.388657 | + | 0.673174i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1306.03 | + | 2262.12i | −0.0428331 | + | 0.0741891i | ||||
\(977\) | −9722.09 | − | 36283.3i | −0.318359 | − | 1.18813i | −0.920821 | − | 0.389985i | \(-0.872480\pi\) |
0.602462 | − | 0.798148i | \(-0.294187\pi\) | |||||||
\(978\) | 26615.3 | + | 22090.5i | 0.870208 | + | 0.722265i | ||||
\(979\) | −9802.93 | + | 5659.73i | −0.320024 | + | 0.184766i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18504.0 | + | 21577.4i | 0.602231 | + | 0.702258i | ||||
\(982\) | 44432.8 | + | 44432.8i | 1.44390 | + | 1.44390i | ||||
\(983\) | 13195.0 | − | 49244.5i | 0.428134 | − | 1.59782i | −0.328849 | − | 0.944382i | \(-0.606661\pi\) |
0.756983 | − | 0.653435i | \(-0.226673\pi\) | |||||||
\(984\) | −2124.64 | + | 1504.75i | −0.0688324 | + | 0.0487498i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21849.8 | + | 12615.0i | 0.705720 | + | 0.407448i | ||||
\(987\) | −41014.4 | − | 7005.12i | −1.32270 | − | 0.225912i | ||||
\(988\) | 18883.3 | + | 5059.76i | 0.608054 | + | 0.162928i | ||||
\(989\) | −63159.8 | −2.03070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61805.9 | 1.98116 | 0.990580 | − | 0.136936i | \(-0.0437255\pi\) | ||||
0.990580 | + | 0.136936i | \(0.0437255\pi\) | |||||||
\(992\) | −10667.1 | − | 2858.24i | −0.341413 | − | 0.0914812i | ||||
\(993\) | −2150.57 | + | 2591.07i | −0.0687273 | + | 0.0828048i | ||||
\(994\) | −58266.3 | − | 33640.1i | −1.85925 | − | 1.07344i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −42801.0 | − | 19679.4i | −1.36165 | − | 0.626070i | ||||
\(997\) | −3006.06 | + | 11218.8i | −0.0954892 | + | 0.356371i | −0.997093 | − | 0.0761919i | \(-0.975724\pi\) |
0.901604 | + | 0.432562i | \(0.142390\pi\) | |||||||
\(998\) | 41367.7 | + | 41367.7i | 1.31210 | + | 1.31210i | ||||
\(999\) | −9206.49 | − | 32270.8i | −0.291572 | − | 1.02203i |
(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 | 225.4.p.b.32.3 | 64 | ||
5.2 | odd | 4 | 45.4.l.a.23.14 | yes | 64 | ||
5.3 | odd | 4 | inner | 225.4.p.b.68.3 | 64 | ||
5.4 | even | 2 | 45.4.l.a.32.14 | yes | 64 | ||
9.2 | odd | 6 | inner | 225.4.p.b.182.3 | 64 | ||
15.2 | even | 4 | 135.4.m.a.98.3 | 64 | |||
15.14 | odd | 2 | 135.4.m.a.17.3 | 64 | |||
45.2 | even | 12 | 45.4.l.a.38.14 | yes | 64 | ||
45.7 | odd | 12 | 135.4.m.a.8.3 | 64 | |||
45.29 | odd | 6 | 45.4.l.a.2.14 | ✓ | 64 | ||
45.34 | even | 6 | 135.4.m.a.62.3 | 64 | |||
45.38 | even | 12 | inner | 225.4.p.b.218.3 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.l.a.2.14 | ✓ | 64 | 45.29 | odd | 6 | ||
45.4.l.a.23.14 | yes | 64 | 5.2 | odd | 4 | ||
45.4.l.a.32.14 | yes | 64 | 5.4 | even | 2 | ||
45.4.l.a.38.14 | yes | 64 | 45.2 | even | 12 | ||
135.4.m.a.8.3 | 64 | 45.7 | odd | 12 | |||
135.4.m.a.17.3 | 64 | 15.14 | odd | 2 | |||
135.4.m.a.62.3 | 64 | 45.34 | even | 6 | |||
135.4.m.a.98.3 | 64 | 15.2 | even | 4 | |||
225.4.p.b.32.3 | 64 | 1.1 | even | 1 | trivial | ||
225.4.p.b.68.3 | 64 | 5.3 | odd | 4 | inner | ||
225.4.p.b.182.3 | 64 | 9.2 | odd | 6 | inner | ||
225.4.p.b.218.3 | 64 | 45.38 | even | 12 | inner |