Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(269,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.t (of order \(6\), degree \(2\), not 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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1485512441856.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 24x^{6} + 455x^{4} - 2904x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.3 | ||
Root | \(-3.54921 - 2.04914i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.269 |
Dual form | 1620.3.t.c.1349.3 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.17317 | + | 4.86042i | 0.234634 | + | 0.972084i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.87367 | − | 3.39116i | −0.839096 | − | 0.484452i | 0.0178610 | − | 0.999840i | \(-0.494314\pi\) |
−0.856957 | + | 0.515388i | \(0.827648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.57321 | − | 4.94975i | −0.779383 | − | 0.449977i | 0.0568285 | − | 0.998384i | \(-0.481901\pi\) |
−0.836212 | + | 0.548407i | \(0.815235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.6210 | − | 10.1735i | 1.35546 | − | 0.782577i | 0.366454 | − | 0.930436i | \(-0.380572\pi\) |
0.989008 | + | 0.147860i | \(0.0472384\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −19.1833 | −1.12843 | −0.564215 | − | 0.825628i | \(-0.690821\pi\) | ||||
−0.564215 | + | 0.825628i | \(0.690821\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.0000 | 0.631579 | 0.315789 | − | 0.948829i | \(-0.397731\pi\) | ||||
0.315789 | + | 0.948829i | \(0.397731\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79583 | + | 8.30662i | 0.208514 | + | 0.361158i | 0.951247 | − | 0.308431i | \(-0.0998038\pi\) |
−0.742732 | + | 0.669588i | \(0.766471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22.2473 | + | 11.4042i | −0.889894 | + | 0.456168i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.34847 | + | 4.24264i | 0.253395 | + | 0.146298i | 0.621318 | − | 0.783558i | \(-0.286598\pi\) |
−0.367923 | + | 0.929856i | \(0.619931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.0000 | + | 32.9090i | 0.612903 | + | 1.06158i | 0.990748 | + | 0.135711i | \(0.0433318\pi\) |
−0.377845 | + | 0.925869i | \(0.623335\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.59166 | − | 32.5269i | 0.274048 | − | 0.929340i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.78233i | 0.183306i | 0.995791 | + | 0.0916531i | \(0.0292151\pi\) | ||||
−0.995791 | + | 0.0916531i | \(0.970785\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60.0125 | − | 34.6482i | 1.46372 | − | 0.845079i | 0.464539 | − | 0.885553i | \(-0.346220\pi\) |
0.999181 | + | 0.0404739i | \(0.0128868\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 58.7367 | + | 33.9116i | 1.36597 | + | 0.788643i | 0.990411 | − | 0.138155i | \(-0.0441173\pi\) |
0.375559 | + | 0.926798i | \(0.377451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −38.3667 | + | 66.4530i | −0.816312 | + | 1.41389i | 0.0920704 | + | 0.995752i | \(0.470652\pi\) |
−0.908382 | + | 0.418141i | \(0.862682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.50000 | − | 2.59808i | −0.0306122 | − | 0.0530220i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.0000 | − | 47.4763i | 0.254545 | − | 0.863206i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −72.2599 | + | 41.7193i | −1.22474 | + | 0.707107i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35.0000 | − | 60.6218i | 0.573770 | − | 0.993800i | −0.422404 | − | 0.906408i | \(-0.638813\pi\) |
0.996174 | − | 0.0873918i | \(-0.0278532\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 70.1199 | + | 73.7102i | 1.07877 | + | 1.13400i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −93.9787 | + | 54.2586i | −1.40267 | + | 0.809830i | −0.994666 | − | 0.103151i | \(-0.967108\pi\) |
−0.408002 | + | 0.912981i | \(0.633774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 118.794i | 1.67315i | 0.547849 | + | 0.836577i | \(0.315447\pi\) | ||||
−0.547849 | + | 0.836577i | \(0.684553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.5647i | 0.185817i | 0.995675 | + | 0.0929086i | \(0.0296164\pi\) | ||||
−0.995675 | + | 0.0929086i | \(0.970384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.5708 | + | 58.1464i | 0.435985 | + | 0.755148i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0000 | + | 25.9808i | −0.189873 | + | 0.328870i | −0.945208 | − | 0.326469i | \(-0.894141\pi\) |
0.755334 | + | 0.655339i | \(0.227474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −67.1416 | + | 116.293i | −0.808935 | + | 1.40112i | 0.104666 | + | 0.994507i | \(0.466623\pi\) |
−0.913602 | + | 0.406610i | \(0.866711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.5053 | − | 93.2390i | −0.264768 | − | 1.09693i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 32.5269i | 0.365471i | 0.983162 | + | 0.182735i | \(0.0584952\pi\) | ||||
−0.983162 | + | 0.182735i | \(0.941505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −138.000 | −1.51648 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.0781 | + | 58.3250i | 0.148190 | + | 0.613948i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −82.2314 | − | 47.4763i | −0.847746 | − | 0.489446i | 0.0121436 | − | 0.999926i | \(-0.496134\pi\) |
−0.859890 | + | 0.510480i | \(0.829468\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −68.5857 | − | 39.5980i | −0.679066 | − | 0.392059i | 0.120437 | − | 0.992721i | \(-0.461570\pi\) |
−0.799503 | + | 0.600662i | \(0.794904\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.3577 | − | 44.0851i | 0.741337 | − | 0.428011i | −0.0812182 | − | 0.996696i | \(-0.525881\pi\) |
0.822555 | + | 0.568685i | \(0.192548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −57.5500 | −0.537850 | −0.268925 | − | 0.963161i | \(-0.586668\pi\) | ||||
−0.268925 | + | 0.963161i | \(0.586668\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 74.0000 | 0.678899 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 86.3250 | + | 149.519i | 0.763938 | + | 1.32318i | 0.940806 | + | 0.338945i | \(0.110070\pi\) |
−0.176869 | + | 0.984234i | \(0.556597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.7473 | + | 33.0548i | −0.302151 | + | 0.287433i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.677 | + | 65.0538i | 0.946862 | + | 0.546671i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.5000 | − | 19.9186i | −0.0950413 | − | 0.164616i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −81.5291 | − | 94.7523i | −0.652233 | − | 0.758018i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 169.558i | 1.33510i | 0.744563 | + | 0.667552i | \(0.232658\pi\) | ||||
−0.744563 | + | 0.667552i | \(0.767342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 143.295 | − | 82.7315i | 1.09386 | − | 0.631538i | 0.159256 | − | 0.987237i | \(-0.449091\pi\) |
0.934600 | + | 0.355699i | \(0.115757\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −70.4840 | − | 40.6940i | −0.529955 | − | 0.305970i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −57.5500 | + | 99.6795i | −0.420073 | + | 0.727587i | −0.995946 | − | 0.0899515i | \(-0.971329\pi\) |
0.575873 | + | 0.817539i | \(0.304662\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −31.0000 | − | 53.6936i | −0.223022 | − | 0.386285i | 0.732702 | − | 0.680549i | \(-0.238259\pi\) |
−0.955724 | + | 0.294264i | \(0.904925\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −201.425 | −1.40857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | + | 40.6940i | −0.0827586 | + | 0.280648i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 137.171 | − | 79.1960i | 0.920614 | − | 0.531517i | 0.0367828 | − | 0.999323i | \(-0.488289\pi\) |
0.883831 | + | 0.467807i | \(0.154956\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −35.0000 | + | 60.6218i | −0.231788 | + | 0.401469i | −0.958334 | − | 0.285649i | \(-0.907791\pi\) |
0.726546 | + | 0.687118i | \(0.241124\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −137.661 | + | 130.956i | −0.888136 | + | 0.844876i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −41.1157 | + | 23.7382i | −0.261883 | + | 0.151198i | −0.625193 | − | 0.780470i | \(-0.714980\pi\) |
0.363310 | + | 0.931668i | \(0.381647\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 65.0538i | − | 0.404061i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 94.9526i | − | 0.582531i | −0.956642 | − | 0.291266i | \(-0.905924\pi\) | ||
0.956642 | − | 0.291266i | \(-0.0940764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 100.712 | + | 174.439i | 0.603069 | + | 1.04455i | 0.992354 | + | 0.123428i | \(0.0393888\pi\) |
−0.389285 | + | 0.921117i | \(0.627278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 122.500 | − | 212.176i | 0.724852 | − | 1.25548i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −134.283 | + | 232.585i | −0.776204 | + | 1.34442i | 0.157911 | + | 0.987453i | \(0.449524\pi\) |
−0.934115 | + | 0.356971i | \(0.883809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 169.347 | + | 8.45987i | 0.967698 | + | 0.0483421i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 134.350i | − | 0.750560i | −0.926911 | − | 0.375280i | \(-0.877547\pi\) | ||
0.926911 | − | 0.375280i | \(-0.122453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −0.121547 | −0.0607735 | − | 0.998152i | \(-0.519357\pi\) | ||||
−0.0607735 | + | 0.998152i | \(0.519357\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32.9650 | + | 7.95683i | −0.178189 | + | 0.0430099i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 164.463 | + | 94.9526i | 0.879480 | + | 0.507768i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 169.015 | + | 97.5807i | 0.884894 | + | 0.510894i | 0.872269 | − | 0.489026i | \(-0.162648\pi\) |
0.0126252 | + | 0.999920i | \(0.495981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −234.947 | + | 135.647i | −1.21734 | + | 0.702832i | −0.964348 | − | 0.264636i | \(-0.914748\pi\) |
−0.252993 | + | 0.967468i | \(0.581415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 163.058 | 0.827707 | 0.413853 | − | 0.910344i | \(-0.364183\pi\) | ||||
0.413853 | + | 0.910344i | \(0.364183\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 294.000 | 1.47739 | 0.738693 | − | 0.674042i | \(-0.235443\pi\) | ||||
0.738693 | + | 0.674042i | \(0.235443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −28.7750 | − | 49.8397i | −0.141749 | − | 0.245516i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 238.810 | + | 251.038i | 1.16493 | + | 1.22457i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −102.879 | − | 59.3970i | −0.492242 | − | 0.284196i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.0000 | + | 36.3731i | 0.0995261 | + | 0.172384i | 0.911489 | − | 0.411325i | \(-0.134934\pi\) |
−0.811963 | + | 0.583710i | \(0.801601\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −95.9166 | + | 325.269i | −0.446124 | + | 1.51288i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 257.729i | − | 1.18769i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −338.030 | + | 195.161i | −1.52955 | + | 0.883084i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −170.336 | − | 98.3438i | −0.763841 | − | 0.441004i | 0.0668324 | − | 0.997764i | \(-0.478711\pi\) |
−0.830673 | + | 0.556761i | \(0.812044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −134.283 | + | 232.585i | −0.591556 | + | 1.02461i | 0.402467 | + | 0.915435i | \(0.368153\pi\) |
−0.994023 | + | 0.109171i | \(0.965180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 211.000 | + | 365.463i | 0.921397 | + | 1.59591i | 0.797255 | + | 0.603643i | \(0.206285\pi\) |
0.124142 | + | 0.992264i | \(0.460382\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 211.017 | 0.905651 | 0.452825 | − | 0.891599i | \(-0.350416\pi\) | ||||
0.452825 | + | 0.891599i | \(0.350416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −368.000 | − | 108.517i | −1.56596 | − | 0.461776i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 61.2372 | − | 35.3553i | 0.256223 | − | 0.147930i | −0.366388 | − | 0.930462i | \(-0.619406\pi\) |
0.622610 | + | 0.782532i | \(0.286072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −140.000 | + | 242.487i | −0.580913 | + | 1.00617i | 0.414459 | + | 0.910068i | \(0.363971\pi\) |
−0.995371 | + | 0.0961024i | \(0.969362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.8680 | − | 10.3386i | 0.0443591 | − | 0.0421984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 211.452 | − | 122.082i | 0.856081 | − | 0.494259i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 80.6102i | − | 0.321156i | −0.987023 | − | 0.160578i | \(-0.948664\pi\) | ||
0.987023 | − | 0.160578i | \(-0.0513358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 94.9526i | − | 0.375307i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.0000 | − | 39.8372i | 0.0888031 | − | 0.153811i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 33.5708 | − | 58.1464i | 0.127646 | − | 0.221089i | −0.795118 | − | 0.606454i | \(-0.792591\pi\) |
0.922764 | + | 0.385365i | \(0.125925\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 263.044i | 0.977858i | 0.872324 | + | 0.488929i | \(0.162612\pi\) | ||||
−0.872324 | + | 0.488929i | \(0.837388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 322.000 | 1.18819 | 0.594096 | − | 0.804394i | \(-0.297510\pi\) | ||||
0.594096 | + | 0.804394i | \(0.297510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 247.179 | + | 12.3480i | 0.898833 | + | 0.0449020i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.3684 | + | 16.9558i | 0.106023 | + | 0.0612124i | 0.552074 | − | 0.833795i | \(-0.313837\pi\) |
−0.446051 | + | 0.895008i | \(0.647170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 282.916 | + | 163.342i | 1.00682 | + | 0.581287i | 0.910259 | − | 0.414040i | \(-0.135883\pi\) |
0.0965601 | + | 0.995327i | \(0.469216\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 93.9787 | − | 54.2586i | 0.332080 | − | 0.191727i | −0.324684 | − | 0.945823i | \(-0.605258\pi\) |
0.656764 | + | 0.754096i | \(0.271925\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −469.991 | −1.63760 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 79.0000 | 0.273356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 100.712 | + | 174.439i | 0.343729 | + | 0.595355i | 0.985122 | − | 0.171857i | \(-0.0549767\pi\) |
−0.641393 | + | 0.767212i | \(0.721643\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −287.547 | − | 302.270i | −0.974734 | − | 1.02464i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 169.015 | + | 97.5807i | 0.565267 | + | 0.326357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −230.000 | − | 398.372i | −0.764120 | − | 1.32349i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 335.708 | + | 98.9949i | 1.10068 | + | 0.324574i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 162.776i | 0.530215i | 0.964219 | + | 0.265107i | \(0.0854074\pi\) | ||||
−0.964219 | + | 0.265107i | \(0.914593\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −154.318 | + | 89.0955i | −0.496199 | + | 0.286481i | −0.727142 | − | 0.686487i | \(-0.759152\pi\) |
0.230944 | + | 0.972967i | \(0.425819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −46.9894 | − | 27.1293i | −0.150126 | − | 0.0866751i | 0.423055 | − | 0.906104i | \(-0.360958\pi\) |
−0.573181 | + | 0.819429i | \(0.694291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 139.079 | − | 240.892i | 0.438735 | − | 0.759912i | −0.558857 | − | 0.829264i | \(-0.688760\pi\) |
0.997592 | + | 0.0693522i | \(0.0220932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.0000 | − | 72.7461i | −0.131661 | − | 0.228044i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −230.200 | −0.712693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −276.000 | + | 427.287i | −0.849231 | + | 1.31473i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 450.706 | − | 260.215i | 1.36993 | − | 0.790928i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | + | 34.6410i | −0.0604230 | + | 0.104656i | −0.894655 | − | 0.446759i | \(-0.852578\pi\) |
0.834232 | + | 0.551414i | \(0.185912\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −373.973 | − | 393.121i | −1.11634 | − | 1.17350i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 270.189 | − | 155.994i | 0.801747 | − | 0.462889i | −0.0423345 | − | 0.999103i | \(-0.513480\pi\) |
0.844082 | + | 0.536215i | \(0.180146\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 376.181i | − | 1.10317i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 352.681i | 1.02822i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −201.425 | − | 348.878i | −0.580475 | − | 1.00541i | −0.995423 | − | 0.0955674i | \(-0.969533\pi\) |
0.414948 | − | 0.909845i | \(-0.363800\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 203.000 | − | 351.606i | 0.581662 | − | 1.00747i | −0.413621 | − | 0.910449i | \(-0.635736\pi\) |
0.995283 | − | 0.0970186i | \(-0.0309306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 268.567 | − | 465.171i | 0.760812 | − | 1.31776i | −0.181621 | − | 0.983369i | \(-0.558134\pi\) |
0.942433 | − | 0.334396i | \(-0.108532\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −577.388 | + | 139.366i | −1.62645 | + | 0.392579i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 161.220i | − | 0.449082i | −0.974465 | − | 0.224541i | \(-0.927912\pi\) | ||
0.974465 | − | 0.224541i | \(-0.0720882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −217.000 | −0.601108 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −65.9299 | + | 15.9137i | −0.180630 | + | 0.0435991i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −217.326 | − | 125.473i | −0.592168 | − | 0.341889i | 0.173786 | − | 0.984783i | \(-0.444400\pi\) |
−0.765954 | + | 0.642895i | \(0.777733\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 88.1051 | − | 50.8675i | 0.236207 | − | 0.136374i | −0.377225 | − | 0.926121i | \(-0.623122\pi\) |
0.613432 | + | 0.789748i | \(0.289788\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 172.650 | 0.457957 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 538.000 | 1.41953 | 0.709763 | − | 0.704441i | \(-0.248802\pi\) | ||||
0.709763 | + | 0.704441i | \(0.248802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −134.283 | − | 232.585i | −0.350609 | − | 0.607273i | 0.635747 | − | 0.771897i | \(-0.280692\pi\) |
−0.986356 | + | 0.164625i | \(0.947359\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −243.231 | + | 231.384i | −0.631770 | + | 0.600997i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −428.661 | − | 247.487i | −1.10196 | − | 0.636214i | −0.165222 | − | 0.986256i | \(-0.552834\pi\) |
−0.936734 | + | 0.350042i | \(0.886167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −92.0000 | − | 159.349i | −0.235294 | − | 0.407541i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −143.875 | − | 42.4264i | −0.364240 | − | 0.107409i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 278.076i | − | 0.700442i | −0.936667 | − | 0.350221i | \(-0.886106\pi\) | ||
0.936667 | − | 0.350221i | \(-0.113894\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −214.330 | + | 123.744i | −0.534490 | + | 0.308588i | −0.742843 | − | 0.669466i | \(-0.766523\pi\) |
0.208353 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 669.598 | + | 386.593i | 1.66153 | + | 0.959287i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.5708 | − | 58.1464i | 0.0824836 | − | 0.142866i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 121.000 | + | 209.578i | 0.295844 | + | 0.512416i | 0.975181 | − | 0.221410i | \(-0.0710660\pi\) |
−0.679337 | + | 0.733826i | \(0.737733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 565.908 | 1.37024 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −644.000 | − | 189.905i | −1.55181 | − | 0.457603i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −684.632 | + | 395.273i | −1.63397 | + | 0.943372i | −0.651115 | + | 0.758979i | \(0.725698\pi\) |
−0.982853 | + | 0.184392i | \(0.940968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −179.000 | + | 310.037i | −0.425178 | + | 0.736430i | −0.996437 | − | 0.0843398i | \(-0.973122\pi\) |
0.571259 | + | 0.820770i | \(0.306455\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 426.778 | − | 218.771i | 1.00418 | − | 0.514754i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −411.157 | + | 237.382i | −0.962897 | + | 0.555929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1421i | 0.0328124i | 0.999865 | + | 0.0164062i | \(0.00522249\pi\) | ||||
−0.999865 | + | 0.0164062i | \(0.994778\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 257.729i | 0.595216i | 0.954688 | + | 0.297608i | \(0.0961888\pi\) | ||||
−0.954688 | + | 0.297608i | \(0.903811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 57.5500 | + | 99.6795i | 0.131693 | + | 0.228100i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 345.000 | − | 597.558i | 0.785877 | − | 1.36118i | −0.142597 | − | 0.989781i | \(-0.545545\pi\) |
0.928474 | − | 0.371398i | \(-0.121121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −201.425 | + | 348.878i | −0.454684 | + | 0.787535i | −0.998670 | − | 0.0515587i | \(-0.983581\pi\) |
0.543986 | + | 0.839094i | \(0.316914\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −158.094 | + | 38.1596i | −0.355268 | + | 0.0857520i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 80.6102i | 0.179533i | 0.995963 | + | 0.0897663i | \(0.0286120\pi\) | ||||
−0.995963 | + | 0.0897663i | \(0.971388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −686.000 | −1.52106 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −161.898 | − | 670.738i | −0.355819 | − | 1.47415i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 293.684 | + | 169.558i | 0.642633 | + | 0.371025i | 0.785628 | − | 0.618699i | \(-0.212340\pi\) |
−0.142995 | + | 0.989723i | \(0.545673\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −558.484 | − | 322.441i | −1.21146 | − | 0.699438i | −0.248384 | − | 0.968662i | \(-0.579899\pi\) |
−0.963078 | + | 0.269224i | \(0.913233\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −229.073 | + | 132.255i | −0.494758 | + | 0.285649i | −0.726546 | − | 0.687117i | \(-0.758876\pi\) |
0.231788 | + | 0.972766i | \(0.425542\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 460.400 | 0.985867 | 0.492933 | − | 0.870067i | \(-0.335925\pi\) | ||||
0.492933 | + | 0.870067i | \(0.335925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 736.000 | 1.56930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −335.708 | − | 581.464i | −0.709743 | − | 1.22931i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −266.968 | + | 136.850i | −0.562038 | + | 0.288106i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −68.5857 | − | 39.5980i | −0.143185 | − | 0.0826680i | 0.426696 | − | 0.904395i | \(-0.359677\pi\) |
−0.569881 | + | 0.821727i | \(0.693011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 69.0000 | + | 119.512i | 0.143451 | + | 0.248465i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 134.283 | − | 455.377i | 0.276873 | − | 0.938921i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 793.533i | − | 1.62943i | −0.579861 | − | 0.814715i | \(-0.696893\pi\) | ||
0.579861 | − | 0.814715i | \(-0.303107\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 488.673 | − | 282.136i | 0.995261 | − | 0.574614i | 0.0884184 | − | 0.996083i | \(-0.471819\pi\) |
0.906843 | + | 0.421469i | \(0.138485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −140.968 | − | 81.3880i | −0.285939 | − | 0.165087i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 402.850 | − | 697.756i | 0.810563 | − | 1.40394i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0000 | + | 62.3538i | 0.0721443 | + | 0.124958i | 0.899841 | − | 0.436218i | \(-0.143682\pi\) |
−0.827697 | + | 0.561176i | \(0.810349\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −230.200 | −0.457654 | −0.228827 | − | 0.973467i | \(-0.573489\pi\) | ||||
−0.228827 | + | 0.973467i | \(0.573489\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 112.000 | − | 379.810i | 0.221782 | − | 0.752100i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −426.211 | + | 246.073i | −0.837350 | + | 0.483444i | −0.856363 | − | 0.516375i | \(-0.827281\pi\) |
0.0190125 | + | 0.999819i | \(0.493948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 46.0000 | − | 79.6743i | 0.0900196 | − | 0.155918i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 303.853 | + | 319.411i | 0.590006 | + | 0.620216i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 657.851 | − | 379.810i | 1.27244 | − | 0.734643i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 69.2965i | − | 0.133007i | −0.997786 | − | 0.0665033i | \(-0.978816\pi\) | ||
0.997786 | − | 0.0665033i | \(-0.0211843\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 339.116i | − | 0.648406i | −0.945987 | − | 0.324203i | \(-0.894904\pi\) | ||
0.945987 | − | 0.324203i | \(-0.105096\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −364.483 | − | 631.303i | −0.691619 | − | 1.19792i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 218.500 | − | 378.453i | 0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 704.987 | − | 1221.07i | 1.32268 | − | 2.29095i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −67.5160 | − | 279.717i | −0.126198 | − | 0.522835i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.6985i | 0.0550992i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −590.000 | −1.09057 | −0.545287 | − | 0.838250i | \(-0.683579\pi\) | ||||
−0.545287 | + | 0.838250i | \(0.683579\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 86.8146 | + | 359.671i | 0.159293 | + | 0.659947i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −199.705 | − | 115.300i | −0.365091 | − | 0.210785i | 0.306221 | − | 0.951961i | \(-0.400935\pi\) |
−0.671312 | + | 0.741175i | \(0.734269\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 88.1816 | + | 50.9117i | 0.160039 | + | 0.0923987i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 176.210 | − | 101.735i | 0.318644 | − | 0.183969i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 690.600 | 1.23986 | 0.619928 | − | 0.784659i | \(-0.287162\pi\) | ||||
0.619928 | + | 0.784659i | \(0.287162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1380.00 | 2.46869 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.59166 | + | 16.6132i | 0.0170367 | + | 0.0295084i | 0.874418 | − | 0.485173i | \(-0.161243\pi\) |
−0.857381 | + | 0.514682i | \(0.827910\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −625.452 | + | 594.987i | −1.10699 | + | 1.05307i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −94.3054 | − | 54.4472i | −0.165739 | − | 0.0956893i | 0.414836 | − | 0.909896i | \(-0.363839\pi\) |
−0.580575 | + | 0.814207i | \(0.697172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 352.000 | + | 609.682i | 0.616462 | + | 1.06774i | 0.990126 | + | 0.140180i | \(0.0447681\pi\) |
−0.373664 | + | 0.927564i | \(0.621899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −201.425 | − | 130.108i | −0.350304 | − | 0.226274i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1125.87i | 1.95124i | 0.219462 | + | 0.975621i | \(0.429570\pi\) | ||||
−0.219462 | + | 0.975621i | \(0.570430\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 788.736 | − | 455.377i | 1.35755 | − | 0.783781i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 489.175 | − | 847.276i | 0.833347 | − | 1.44340i | −0.0620218 | − | 0.998075i | \(-0.519755\pi\) |
0.895369 | − | 0.445325i | \(-0.146912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 228.000 | + | 394.908i | 0.387097 | + | 0.670471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −184.000 | + | 623.974i | −0.309244 | + | 1.04870i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −257.196 | + | 148.492i | −0.429376 | + | 0.247901i | −0.699081 | − | 0.715043i | \(-0.746407\pi\) |
0.269705 | + | 0.962943i | \(0.413074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | + | 17.3205i | −0.0166389 | + | 0.0288195i | −0.874225 | − | 0.485521i | \(-0.838630\pi\) |
0.857586 | + | 0.514341i | \(0.171963\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 83.3212 | − | 79.2627i | 0.137721 | − | 0.131013i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.87367 | + | 3.39116i | −0.00967656 | + | 0.00558676i | −0.504830 | − | 0.863219i | \(-0.668445\pi\) |
0.495154 | + | 0.868805i | \(0.335112\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1561.29i | 2.55531i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 47.4763i | − | 0.0774491i | −0.999250 | − | 0.0387246i | \(-0.987671\pi\) | ||
0.999250 | − | 0.0387246i | \(-0.0123295\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.1833 | − | 33.2265i | −0.0310913 | − | 0.0538517i | 0.850061 | − | 0.526684i | \(-0.176565\pi\) |
−0.881152 | + | 0.472832i | \(0.843232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −89.0000 | + | 154.153i | −0.143780 | + | 0.249035i | −0.928917 | − | 0.370287i | \(-0.879259\pi\) |
0.785137 | + | 0.619322i | \(0.212593\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 110.304 | − | 191.052i | 0.177053 | − | 0.306665i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 364.888 | − | 507.426i | 0.583821 | − | 0.811882i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 130.108i | − | 0.206848i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −154.000 | −0.244057 | −0.122029 | − | 0.992527i | \(-0.538940\pi\) | ||||
−0.122029 | + | 0.992527i | \(0.538940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −824.124 | + | 198.921i | −1.29783 | + | 0.313261i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −52.8630 | − | 30.5205i | −0.0829875 | − | 0.0479128i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −699.329 | − | 403.758i | −1.09100 | − | 0.629888i | −0.157156 | − | 0.987574i | \(-0.550232\pi\) |
−0.933842 | + | 0.357686i | \(0.883566\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 881.051 | − | 508.675i | 1.37022 | − | 0.791096i | 0.379263 | − | 0.925289i | \(-0.376177\pi\) |
0.990955 | + | 0.134193i | \(0.0428441\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −805.700 | −1.24529 | −0.622643 | − | 0.782506i | \(-0.713941\pi\) | ||||
−0.622643 | + | 0.782506i | \(0.713941\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 826.000 | 1.27273 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.5708 | + | 58.1464i | 0.0514101 | + | 0.0890450i | 0.890585 | − | 0.454816i | \(-0.150295\pi\) |
−0.839175 | + | 0.543861i | \(0.816962\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 570.219 | + | 599.416i | 0.870564 | + | 0.915139i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 454.380 | + | 262.337i | 0.689500 | + | 0.398083i | 0.803425 | − | 0.595406i | \(-0.203009\pi\) |
−0.113925 | + | 0.993489i | \(0.536342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0000 | − | 64.0859i | −0.0559758 | − | 0.0969529i | 0.836680 | − | 0.547693i | \(-0.184494\pi\) |
−0.892655 | + | 0.450740i | \(0.851160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 115.100 | − | 390.323i | 0.173083 | − | 0.586952i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 81.3880i | 0.122021i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −600.125 | + | 346.482i | −0.894374 | + | 0.516367i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −599.114 | − | 345.899i | −0.890214 | − | 0.513966i | −0.0162018 | − | 0.999869i | \(-0.505157\pi\) |
−0.874013 | + | 0.485903i | \(0.838491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 139.079 | − | 240.892i | 0.205434 | − | 0.355823i | −0.744837 | − | 0.667247i | \(-0.767473\pi\) |
0.950271 | + | 0.311424i | \(0.100806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 322.000 | + | 557.720i | 0.474227 | + | 0.821385i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 422.033 | 0.617911 | 0.308955 | − | 0.951077i | \(-0.400021\pi\) | ||||
0.308955 | + | 0.951077i | \(0.400021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −552.000 | − | 162.776i | −0.805839 | − | 0.237629i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.0000 | − | 58.8897i | 0.0492041 | − | 0.0852239i | −0.840374 | − | 0.542006i | \(-0.817665\pi\) |
0.889578 | + | 0.456782i | \(0.150998\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 224.605 | − | 213.665i | 0.323173 | − | 0.307431i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1151.24 | + | 664.668i | −1.65171 | + | 0.953613i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 130.108i | − | 0.185603i | −0.995685 | − | 0.0928015i | \(-0.970418\pi\) | ||
0.995685 | − | 0.0928015i | \(-0.0295822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.3880i | 0.115772i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 268.567 | + | 465.171i | 0.379868 | + | 0.657950i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 105.000 | − | 181.865i | 0.148096 | − | 0.256510i | −0.782428 | − | 0.622741i | \(-0.786019\pi\) |
0.930524 | + | 0.366232i | \(0.119352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −182.242 | + | 315.652i | −0.255598 | + | 0.442709i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −236.306 | − | 979.009i | −0.330498 | − | 1.36924i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 121.622i | 0.169155i | 0.996417 | + | 0.0845774i | \(0.0269540\pi\) | ||||
−0.996417 | + | 0.0845774i | \(0.973046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −598.000 | −0.829404 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −211.868 | − | 10.5840i | −0.292231 | − | 0.0145987i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6210 | + | 10.1735i | 0.0242380 | + | 0.0139938i | 0.512070 | − | 0.858944i | \(-0.328879\pi\) |
−0.487832 | + | 0.872938i | \(0.662212\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1126.77 | − | 650.538i | −1.54140 | − | 0.889929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1227.60 | + | 708.753i | −1.67476 | + | 0.966922i | −0.709842 | + | 0.704361i | \(0.751233\pi\) |
−0.964916 | + | 0.262560i | \(0.915433\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1074.27 | 1.45762 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 416.000 | 0.562923 | 0.281461 | − | 0.959573i | \(-0.409181\pi\) | ||||
0.281461 | + | 0.959573i | \(0.409181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −402.850 | − | 697.756i | −0.542194 | − | 0.939107i | −0.998778 | − | 0.0494266i | \(-0.984261\pi\) |
0.456584 | − | 0.889680i | \(-0.349073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 545.851 | + | 573.800i | 0.732686 | + | 0.770202i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 338.030 | + | 195.161i | 0.451308 | + | 0.260563i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.0000 | − | 74.4782i | −0.0572570 | − | 0.0991720i | 0.835976 | − | 0.548766i | \(-0.184902\pi\) |
−0.893233 | + | 0.449594i | \(0.851569\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −335.708 | − | 98.9949i | −0.444647 | − | 0.131119i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.4763i | 0.0627164i | 0.999508 | + | 0.0313582i | \(0.00998326\pi\) | ||||
−0.999508 | + | 0.0313582i | \(0.990017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 319.658 | − | 184.555i | 0.420050 | − | 0.242516i | −0.275048 | − | 0.961430i | \(-0.588694\pi\) |
0.695099 | + | 0.718914i | \(0.255361\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −434.652 | − | 250.946i | −0.569661 | − | 0.328894i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −848.862 | + | 1470.27i | −1.10673 | + | 1.91691i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −192.000 | − | 332.554i | −0.249675 | − | 0.432450i | 0.713761 | − | 0.700390i | \(-0.246990\pi\) |
−0.963436 | + | 0.267940i | \(0.913657\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 201.425 | 0.260576 | 0.130288 | − | 0.991476i | \(-0.458410\pi\) | ||||
0.130288 | + | 0.991476i | \(0.458410\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −798.000 | − | 515.457i | −1.02968 | − | 0.665106i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 720.150 | − | 415.779i | 0.924454 | − | 0.533734i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 588.000 | − | 1018.45i | 0.752881 | − | 1.30403i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −163.613 | − | 171.991i | −0.208424 | − | 0.219096i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 411.157 | − | 237.382i | 0.522436 | − | 0.301628i | −0.215495 | − | 0.976505i | \(-0.569136\pi\) |
0.737931 | + | 0.674877i | \(0.235803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1170.97i | − | 1.48037i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1424.29i | − | 1.79608i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −249.383 | − | 431.944i | −0.312902 | − | 0.541963i | 0.666087 | − | 0.745874i | \(-0.267968\pi\) |
−0.978989 | + | 0.203911i | \(0.934635\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 736.000 | − | 1274.79i | 0.921151 | − | 1.59548i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 67.1416 | − | 116.293i | 0.0836135 | − | 0.144823i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 316.189 | − | 76.3193i | 0.392781 | − | 0.0948065i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1480.68i | − | 1.83026i | −0.403157 | − | 0.915131i | \(-0.632087\pi\) | ||
0.403157 | − | 0.915131i | \(-0.367913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −602.000 | −0.742293 | −0.371147 | − | 0.928574i | \(-0.621035\pi\) | ||||
−0.371147 | + | 0.928574i | \(0.621035\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 461.509 | − | 111.396i | 0.566269 | − | 0.136682i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 704.840 | + | 406.940i | 0.862718 | + | 0.498090i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1217.40 | + | 702.864i | 1.48282 | + | 0.856107i | 0.999810 | − | 0.0195065i | \(-0.00620952\pi\) |
0.483012 | + | 0.875614i | \(0.339543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1110.12 | + | 640.930i | −1.34887 | + | 0.778773i | −0.988090 | − | 0.153876i | \(-0.950824\pi\) |
−0.360784 | + | 0.932649i | \(0.617491\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1170.18 | −1.41497 | −0.707487 | − | 0.706727i | \(-0.750171\pi\) | ||||
−0.707487 | + | 0.706727i | \(0.750171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1074.00 | 1.29554 | 0.647768 | − | 0.761837i | \(-0.275702\pi\) | ||||
0.647768 | + | 0.761837i | \(0.275702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.7750 | + | 49.8397i | 0.0345438 | + | 0.0598316i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −729.694 | + | 694.152i | −0.873885 | + | 0.831319i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −644.216 | − | 371.938i | −0.767838 | − | 0.443311i | 0.0642650 | − | 0.997933i | \(-0.479530\pi\) |
−0.832103 | + | 0.554622i | \(0.812863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −384.500 | − | 665.974i | −0.457194 | − | 0.791883i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1174.98 | + | 346.482i | 1.39051 | + | 0.410038i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 155.994i | 0.184172i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −56.3383 | + | 32.5269i | −0.0662024 | + | 0.0382220i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −146.842 | − | 84.7791i | −0.172147 | − | 0.0993894i | 0.411451 | − | 0.911432i | \(-0.365022\pi\) |
−0.583598 | + | 0.812043i | \(0.698356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.5500 | − | 99.6795i | 0.0671528 | − | 0.116312i | −0.830494 | − | 0.557027i | \(-0.811942\pi\) |
0.897647 | + | 0.440715i | \(0.145275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −77.0000 | − | 133.368i | −0.0896391 | − | 0.155260i | 0.817719 | − | 0.575617i | \(-0.195238\pi\) |
−0.907359 | + | 0.420357i | \(0.861905\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1064.67 | −1.23369 | −0.616845 | − | 0.787085i | \(-0.711589\pi\) | ||||
−0.616845 | + | 0.787085i | \(0.711589\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1288.00 | − | 379.810i | −1.48902 | − | 0.439087i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 257.196 | − | 148.492i | 0.295968 | − | 0.170877i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1104.00 | + | 1912.18i | −1.26751 | + | 2.19539i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 157.555 | + | 833.023i | 0.180062 | + | 0.952026i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1204.10 | + | 695.189i | −1.37298 | + | 0.792690i | −0.991302 | − | 0.131606i | \(-0.957987\pi\) |
−0.381677 | + | 0.924296i | \(0.624653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 861.256i | 0.977589i | 0.872399 | + | 0.488795i | \(0.162563\pi\) | ||||
−0.872399 | + | 0.488795i | \(0.837437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1017.35i | 1.15215i | 0.817396 | + | 0.576076i | \(0.195417\pi\) | ||||
−0.817396 | + | 0.576076i | \(0.804583\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −302.137 | − | 523.317i | −0.340628 | − | 0.589986i | 0.643921 | − | 0.765092i | \(-0.277306\pi\) |
−0.984550 | + | 0.175106i | \(0.943973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 575.000 | − | 995.929i | 0.646794 | − | 1.12028i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −460.400 | + | 797.436i | −0.515565 | + | 0.892985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 652.999 | − | 157.616i | 0.729607 | − | 0.176107i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 322.441i | 0.358666i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.8098 | − | 106.929i | −0.0285191 | − | 0.118154i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −810.566 | − | 467.981i | −0.893679 | − | 0.515966i | −0.0185346 | − | 0.999828i | \(-0.505900\pi\) |
−0.875144 | + | 0.483863i | \(0.839233\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 661.362 | + | 381.838i | 0.725974 | + | 0.419141i | 0.816947 | − | 0.576712i | \(-0.195665\pi\) |
−0.0909736 | + | 0.995853i | \(0.528998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1151.24 | − | 664.668i | 1.26094 | − | 0.728005i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1122.22 | −1.22380 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.0000 | −0.0587595 | −0.0293798 | − | 0.999568i | \(-0.509353\pi\) | ||||
−0.0293798 | + | 0.999568i | \(0.509353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1208.55 | + | 2093.27i | 1.30937 | + | 2.26790i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −77.3471 | − | 150.889i | −0.0836185 | − | 0.163123i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −128.598 | − | 74.2462i | −0.138426 | − | 0.0799206i | 0.429187 | − | 0.903215i | \(-0.358800\pi\) |
−0.567614 | + | 0.823295i | \(0.692133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | − | 31.1769i | −0.0193340 | − | 0.0334876i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −268.567 | + | 910.754i | −0.287237 | + | 0.974068i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 786.750i | 0.839648i | 0.907606 | + | 0.419824i | \(0.137908\pi\) | ||||
−0.907606 | + | 0.419824i | \(0.862092\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −296.388 | + | 171.120i | −0.314972 | + | 0.181849i | −0.649149 | − | 0.760661i | \(-0.724875\pi\) |
0.334177 | + | 0.942510i | \(0.391542\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 575.620 | + | 332.334i | 0.610413 | + | 0.352422i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −201.425 | + | 348.878i | −0.212698 | + | 0.368404i | −0.952558 | − | 0.304357i | \(-0.901558\pi\) |
0.739860 | + | 0.672761i | \(0.234892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 138.000 | + | 239.023i | 0.145416 | + | 0.251868i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1074.27 | 1.12725 | 0.563623 | − | 0.826032i | \(-0.309407\pi\) | ||||
0.563623 | + | 0.826032i | \(0.309407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −276.000 | + | 935.962i | −0.289005 | + | 0.980064i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 676.059 | − | 390.323i | 0.704963 | − | 0.407010i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −241.500 | + | 418.290i | −0.251301 | + | 0.435266i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −934.932 | − | 982.803i | −0.968841 | − | 1.01845i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 346.547 | − | 200.079i | 0.358373 | − | 0.206907i | −0.309994 | − | 0.950739i | \(-0.600327\pi\) |
0.668367 | + | 0.743832i | \(0.266994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 683.065i | − | 0.703466i | −0.936100 | − | 0.351733i | \(-0.885593\pi\) | ||
0.936100 | − | 0.351733i | \(-0.114407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 420.504i | 0.432173i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 805.700 | + | 1395.51i | 0.824667 | + | 1.42837i | 0.902174 | + | 0.431373i | \(0.141971\pi\) |
−0.0775065 | + | 0.996992i | \(0.524696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 161.000 | − | 278.860i | 0.164454 | − | 0.284842i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −479.583 | + | 830.662i | −0.487877 | + | 0.845028i | −0.999903 | − | 0.0139422i | \(-0.995562\pi\) |
0.512026 | + | 0.858970i | \(0.328895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 191.295 | + | 792.531i | 0.194208 | + | 0.804600i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 650.538i | 0.657774i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1054.00 | 1.06357 | 0.531786 | − | 0.846879i | \(-0.321521\pi\) | ||||
0.531786 | + | 0.846879i | \(0.321521\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 344.912 | + | 1428.96i | 0.346645 | + | 1.43614i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1039.64 | − | 600.236i | −1.04277 | − | 0.602042i | −0.122152 | − | 0.992511i | \(-0.538979\pi\) |
−0.920616 | + | 0.390469i | \(0.872313\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))