Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), 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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 18x^{8} + 103x^{6} + 239x^{4} + 197x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.1 | ||
Root | \(0.144312i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.v.4049.10 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.08344i | − 1.78022i | −0.455742 | − | 0.890112i | \(-0.650626\pi\) | ||||
0.455742 | − | 0.890112i | \(-0.349374\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.555022i | − 0.209779i | −0.994484 | − | 0.104889i | \(-0.966551\pi\) | ||||
0.994484 | − | 0.104889i | \(-0.0334488\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.50759 | −2.16920 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.65190 | 1.40260 | 0.701301 | − | 0.712866i | \(-0.252603\pi\) | ||||
0.701301 | + | 0.712866i | \(0.252603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.02256i | − 1.39301i | −0.717553 | − | 0.696504i | \(-0.754738\pi\) | ||||
0.717553 | − | 0.696504i | \(-0.245262\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.32867i | 0.322251i | 0.986934 | + | 0.161125i | \(0.0515123\pi\) | ||||
−0.986934 | + | 0.161125i | \(0.948488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.196402 | 0.0450577 | 0.0225288 | − | 0.999746i | \(-0.492828\pi\) | ||||
0.0225288 | + | 0.999746i | \(0.492828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71138 | −0.373453 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.8154i | 2.08143i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.812298 | 0.150840 | 0.0754200 | − | 0.997152i | \(-0.475970\pi\) | ||||
0.0754200 | + | 0.997152i | \(0.475970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.11145 | −0.379227 | −0.189613 | − | 0.981859i | \(-0.560723\pi\) | ||||
−0.189613 | + | 0.981859i | \(0.560723\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 14.3439i | − 2.49694i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.64564i | − 0.928138i | −0.885799 | − | 0.464069i | \(-0.846389\pi\) | ||||
0.885799 | − | 0.464069i | \(-0.153611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.4868 | −2.47987 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89714 | −0.764804 | −0.382402 | − | 0.923996i | \(-0.624903\pi\) | ||||
−0.382402 | + | 0.923996i | \(0.624903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.66507i | − 0.253920i | −0.991908 | − | 0.126960i | \(-0.959478\pi\) | ||||
0.991908 | − | 0.126960i | \(-0.0405220\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 9.89310i | − 1.44306i | −0.692385 | − | 0.721528i | \(-0.743440\pi\) | ||||
0.692385 | − | 0.721528i | \(-0.256560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.69195 | 0.955993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.09688 | 0.573678 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.23261i | − 0.306673i | −0.988174 | − | 0.153336i | \(-0.950998\pi\) | ||||
0.988174 | − | 0.153336i | \(-0.0490018\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 0.605593i | − 0.0802127i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.43488 | −0.316994 | −0.158497 | − | 0.987359i | \(-0.550665\pi\) | ||||
−0.158497 | + | 0.987359i | \(0.550665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71138 | −0.731267 | −0.365633 | − | 0.930759i | \(-0.619148\pi\) | ||||
−0.365633 | + | 0.930759i | \(0.619148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.61185i | 0.455051i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.91830i | 0.845205i | 0.906315 | + | 0.422602i | \(0.138883\pi\) | ||||
−0.906315 | + | 0.422602i | \(0.861117\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.08344 | −0.371202 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0120411 | 0.00142902 | 0.000714510 | − | 1.00000i | \(-0.499773\pi\) | ||||
0.000714510 | 1.00000i | \(0.499773\pi\) | ||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.2989i | − 1.79061i | −0.445458 | − | 0.895303i | \(-0.646959\pi\) | ||||
0.445458 | − | 0.895303i | \(-0.353041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.58191i | − 0.294236i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6351 | −1.19654 | −0.598272 | − | 0.801293i | \(-0.704146\pi\) | ||||
−0.598272 | + | 0.801293i | \(0.704146\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 13.8260 | 1.53622 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.64020i | 0.619092i | 0.950884 | + | 0.309546i | \(0.100177\pi\) | ||||
−0.950884 | + | 0.309546i | \(0.899823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.50467i | − 0.268529i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.06693 | −0.961093 | −0.480547 | − | 0.876969i | \(-0.659562\pi\) | ||||
−0.480547 | + | 0.876969i | \(0.659562\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.78763 | −0.292223 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.51051i | 0.675108i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 14.0720i | − 1.42880i | −0.699739 | − | 0.714398i | \(-0.746701\pi\) | ||||
0.699739 | − | 0.714398i | \(-0.253299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30.2727 | −3.04252 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.53015 | 0.749278 | 0.374639 | − | 0.927171i | \(-0.377767\pi\) | ||||
0.374639 | + | 0.927171i | \(0.377767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4476i | 1.42357i | 0.702399 | + | 0.711784i | \(0.252112\pi\) | ||||
−0.702399 | + | 0.711784i | \(0.747888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.35862i | 0.228016i | 0.993480 | + | 0.114008i | \(0.0363690\pi\) | ||||
−0.993480 | + | 0.114008i | \(0.963631\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3578 | 0.992101 | 0.496050 | − | 0.868294i | \(-0.334783\pi\) | ||||
0.496050 | + | 0.868294i | \(0.334783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.4080 | −1.65229 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.2723i | 1.81298i | 0.422226 | + | 0.906491i | \(0.361249\pi\) | ||||
−0.422226 | + | 0.906491i | \(0.638751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 32.6848i | 3.02171i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.737442 | 0.0676012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6402 | 0.967291 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.1000i | 1.36152i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 18.4934i | − 1.64102i | −0.571632 | − | 0.820510i | \(-0.693689\pi\) | ||||
0.571632 | − | 0.820510i | \(-0.306311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.13413 | −0.452035 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7727 | −1.29070 | −0.645351 | − | 0.763887i | \(-0.723289\pi\) | ||||
−0.645351 | + | 0.763887i | \(0.723289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.109007i | − 0.00945213i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6173i | 0.992533i | 0.868170 | + | 0.496266i | \(0.165296\pi\) | ||||
−0.868170 | + | 0.496266i | \(0.834704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1389 | −0.944787 | −0.472393 | − | 0.881388i | \(-0.656610\pi\) | ||||
−0.472393 | + | 0.881388i | \(0.656610\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.5047 | −2.56896 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 23.3645i | − 1.95384i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 20.6342i | − 1.70188i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4796 | 1.02237 | 0.511184 | − | 0.859472i | \(-0.329207\pi\) | ||||
0.511184 | + | 0.859472i | \(0.329207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.32673 | 0.107968 | 0.0539840 | − | 0.998542i | \(-0.482808\pi\) | ||||
0.0539840 | + | 0.998542i | \(0.482808\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 8.64646i | − 0.699025i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.1754i | 1.84960i | 0.380458 | + | 0.924798i | \(0.375766\pi\) | ||||
−0.380458 | + | 0.924798i | \(0.624234\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.88412 | −0.545946 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.555022 | −0.0437418 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 25.0682i | − 1.96349i | −0.190196 | − | 0.981746i | \(-0.560912\pi\) | ||||
0.190196 | − | 0.981746i | \(-0.439088\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 4.39603i | − 0.340175i | −0.985429 | − | 0.170087i | \(-0.945595\pi\) | ||||
0.985429 | − | 0.170087i | \(-0.0544050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2261 | −0.940473 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.27810 | −0.0977389 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 19.4211i | − 1.47656i | −0.674493 | − | 0.738281i | \(-0.735638\pi\) | ||||
0.674493 | − | 0.738281i | \(-0.264362\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.50779i | 0.564320i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.4169 | −0.778592 | −0.389296 | − | 0.921113i | \(-0.627282\pi\) | ||||
−0.389296 | + | 0.921113i | \(0.627282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.13693 | −0.679143 | −0.339571 | − | 0.940580i | \(-0.610282\pi\) | ||||
−0.339571 | + | 0.940580i | \(0.610282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.6107i | 1.30182i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.18086i | 0.451989i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.00280 | 0.436640 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.49819 | −0.108405 | −0.0542026 | − | 0.998530i | \(-0.517262\pi\) | ||||
−0.0542026 | + | 0.998530i | \(0.517262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 14.4113i | − 1.03735i | −0.854972 | − | 0.518675i | \(-0.826425\pi\) | ||||
0.854972 | − | 0.518675i | \(-0.173575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.4686i | 1.74331i | 0.490116 | + | 0.871657i | \(0.336954\pi\) | ||||
−0.490116 | + | 0.871657i | \(0.663046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.61185 | 0.114261 | 0.0571307 | − | 0.998367i | \(-0.481805\pi\) | ||||
0.0571307 | + | 0.998367i | \(0.481805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3321 | 1.50465 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.450843i | − 0.0316430i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.50759i | 0.452309i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.913642 | 0.0631979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.25081 | 0.430324 | 0.215162 | − | 0.976578i | \(-0.430972\pi\) | ||||
0.215162 | + | 0.976578i | \(0.430972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 0.0371281i | − 0.00254398i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.17190i | 0.0795536i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −47.1733 | −3.18768 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.67334 | 0.448898 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 21.2953i | − 1.42604i | −0.701144 | − | 0.713019i | \(-0.747327\pi\) | ||||
0.701144 | − | 0.713019i | \(-0.252673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5174i | 0.698061i | 0.937111 | + | 0.349031i | \(0.113489\pi\) | ||||
−0.937111 | + | 0.349031i | \(0.886511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.0063 | 1.58638 | 0.793190 | − | 0.608975i | \(-0.208419\pi\) | ||||
0.793190 | + | 0.608975i | \(0.208419\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.96115 | −0.523805 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3112i | 0.741021i | 0.928828 | + | 0.370510i | \(0.120817\pi\) | ||||
−0.928828 | + | 0.370510i | \(0.879183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 32.7927i | 2.13012i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.5592 | 1.65329 | 0.826644 | − | 0.562726i | \(-0.190247\pi\) | ||||
0.826644 | + | 0.562726i | \(0.190247\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1617 | −1.04106 | −0.520532 | − | 0.853842i | \(-0.674266\pi\) | ||||
−0.520532 | + | 0.853842i | \(0.674266\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 10.1852i | − 0.653380i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.986440i | − 0.0627657i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.3912 | 1.10212 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.3497 | −0.842627 | −0.421313 | − | 0.906915i | \(-0.638431\pi\) | ||||
−0.421313 | + | 0.906915i | \(0.638431\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.65190i | − 0.292463i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1834i | 0.635222i | 0.948221 | + | 0.317611i | \(0.102881\pi\) | ||||
−0.948221 | + | 0.317611i | \(0.897119\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.13345 | −0.194703 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.28610 | −0.327201 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3073i | 1.43719i | 0.695430 | + | 0.718594i | \(0.255214\pi\) | ||||
−0.695430 | + | 0.718594i | \(0.744786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.9573i | 1.71096i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.80817 | −0.598015 | −0.299007 | − | 0.954251i | \(-0.596656\pi\) | ||||
−0.299007 | + | 0.954251i | \(0.596656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.08332 | −0.369535 | −0.184768 | − | 0.982782i | \(-0.559153\pi\) | ||||
−0.184768 | + | 0.982782i | \(0.559153\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.59549i | 0.520223i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.0445722i | 0.00267809i | 0.999999 | + | 0.00133904i | \(0.000426231\pi\) | ||||
−0.999999 | + | 0.00133904i | \(0.999574\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.7404 | 0.822617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.9996 | 1.67032 | 0.835158 | − | 0.550010i | \(-0.185376\pi\) | ||||
0.835158 | + | 0.550010i | \(0.185376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1798i | 0.724013i | 0.932176 | + | 0.362006i | \(0.117908\pi\) | ||||
−0.932176 | + | 0.362006i | \(0.882092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.71802i | 0.160440i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.2346 | 0.896155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −43.3902 | −2.54358 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2.71056i | − 0.158352i | −0.996861 | − | 0.0791762i | \(-0.974771\pi\) | ||||
0.996861 | − | 0.0791762i | \(-0.0252290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 50.3124i | 2.91942i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.02256 | −0.290462 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.924148 | −0.0532670 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 23.2188i | − 1.33388i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.1631i | 1.83564i | 0.396994 | + | 0.917821i | \(0.370053\pi\) | ||||
−0.396994 | + | 0.917821i | \(0.629947\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 44.5484 | 2.53427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.07951 | −0.231328 | −0.115664 | − | 0.993288i | \(-0.536900\pi\) | ||||
−0.115664 | + | 0.993288i | \(0.536900\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7806i | 0.778925i | 0.921042 | + | 0.389462i | \(0.127339\pi\) | ||||
−0.921042 | + | 0.389462i | \(0.872661\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 10.4630i | − 0.587658i | −0.955858 | − | 0.293829i | \(-0.905070\pi\) | ||||
0.955858 | − | 0.293829i | \(-0.0949297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.77873 | 0.211568 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.27266 | 0.405920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.260954i | 0.0145199i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 31.9377i | − 1.76616i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.49088 | −0.302722 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.6451 | −0.695038 | −0.347519 | − | 0.937673i | \(-0.612976\pi\) | ||||
−0.347519 | + | 0.937673i | \(0.612976\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.7395i | 2.01331i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 24.5733i | − 1.33859i | −0.742997 | − | 0.669295i | \(-0.766596\pi\) | ||||
0.742997 | − | 0.669295i | \(-0.233404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 59.4248 | 3.22751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.82224 | −0.531904 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 7.59933i | − 0.410325i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.50569i | 0.188195i | 0.995563 | + | 0.0940977i | \(0.0299966\pi\) | ||||
−0.995563 | + | 0.0940977i | \(0.970003\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.1085 | 0.969327 | 0.484664 | − | 0.874701i | \(-0.338942\pi\) | ||||
0.484664 | + | 0.874701i | \(0.338942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54.3212 | 2.89945 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 20.1915i | − 1.07469i | −0.843364 | − | 0.537343i | \(-0.819428\pi\) | ||||
0.843364 | − | 0.537343i | \(-0.180572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.27386i | − 0.120345i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.43409 | 0.497912 | 0.248956 | − | 0.968515i | \(-0.419912\pi\) | ||||
0.248956 | + | 0.968515i | \(0.419912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9614 | −0.997970 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 32.8084i | − 1.72199i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.3412i | 1.58380i | 0.610652 | + | 0.791899i | \(0.290908\pi\) | ||||
−0.610652 | + | 0.791899i | \(0.709092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 31.8686 | 1.65901 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.23915 | −0.0643333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7893i | 0.765758i | 0.923798 | + | 0.382879i | \(0.125067\pi\) | ||||
−0.923798 | + | 0.382879i | \(0.874933\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 4.07982i | − 0.210121i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2405 | 0.577385 | 0.288693 | − | 0.957422i | \(-0.406779\pi\) | ||||
0.288693 | + | 0.957422i | \(0.406779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −57.0231 | −2.92138 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 30.4602i | − 1.55644i | −0.627991 | − | 0.778221i | \(-0.716122\pi\) | ||||
0.627991 | − | 0.778221i | \(-0.283878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.8356i | 0.550803i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.94011 | −0.0983673 | −0.0491836 | − | 0.998790i | \(-0.515662\pi\) | ||||
−0.0491836 | + | 0.998790i | \(0.515662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.32867 | 0.0671939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 45.5509i | 2.29774i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 18.3206i | − 0.919487i | −0.888052 | − | 0.459743i | \(-0.847941\pi\) | ||||
0.888052 | − | 0.459743i | \(-0.152059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.336117 | −0.0168269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.32199 | −0.0660170 | −0.0330085 | − | 0.999455i | \(-0.510509\pi\) | ||||
−0.0330085 | + | 0.999455i | \(0.510509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6049i | 0.528266i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 26.2630i | − 1.30181i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9963 | −1.08765 | −0.543823 | − | 0.839200i | \(-0.683024\pi\) | ||||
−0.543823 | + | 0.839200i | \(0.683024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.8212 | 1.76693 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.35141i | 0.0664985i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.3460i | 1.68193i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.3194 | −1.38349 | −0.691746 | − | 0.722141i | \(-0.743158\pi\) | ||||
−0.691746 | + | 0.722141i | \(0.743158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7650 | 0.719602 | 0.359801 | − | 0.933029i | \(-0.382845\pi\) | ||||
0.359801 | + | 0.933029i | \(0.382845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 64.3802i | 3.13027i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.16994i | 0.153404i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −72.0429 | −3.47826 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0514 | −1.30302 | −0.651510 | − | 0.758640i | \(-0.725864\pi\) | ||||
−0.651510 | + | 0.758640i | \(0.725864\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.2700i | 1.83914i | 0.392926 | + | 0.919570i | \(0.371463\pi\) | ||||
−0.392926 | + | 0.919570i | \(0.628537\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 0.196402i | − 0.00939517i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.39959 | 0.114526 | 0.0572630 | − | 0.998359i | \(-0.481763\pi\) | ||||
0.0572630 | + | 0.998359i | \(0.481763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −43.5485 | −2.07374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10.6542i | − 0.506198i | −0.967440 | − | 0.253099i | \(-0.918550\pi\) | ||||
0.967440 | − | 0.253099i | \(-0.0814499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 38.4800i | − 1.82004i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9533 | 1.36639 | 0.683195 | − | 0.730236i | \(-0.260590\pi\) | ||||
0.683195 | + | 0.730236i | \(0.260590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.7810 | −1.07272 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.09090i | − 0.192207i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 38.5855i | − 1.80496i | −0.430736 | − | 0.902478i | \(-0.641746\pi\) | ||||
0.430736 | − | 0.902478i | \(-0.358254\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.3702 | −0.670743 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.07659 | −0.376164 | −0.188082 | − | 0.982153i | \(-0.560227\pi\) | ||||
−0.188082 | + | 0.982153i | \(0.560227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.07771i | − 0.282455i | −0.989977 | − | 0.141228i | \(-0.954895\pi\) | ||||
0.989977 | − | 0.141228i | \(-0.0451050\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 10.2961i | − 0.476446i | −0.971210 | − | 0.238223i | \(-0.923435\pi\) | ||||
0.971210 | − | 0.238223i | \(-0.0765649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.83981 | 0.177306 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 71.4598 | 3.29270 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.74572i | − 0.356149i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5289i | 0.665233i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.9760 | 1.55240 | 0.776201 | − | 0.630486i | \(-0.217144\pi\) | ||||
0.776201 | + | 0.630486i | \(0.217144\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.3556 | −1.29290 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.71138i | 0.0778703i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4951i | 0.747464i | 0.927537 | + | 0.373732i | \(0.121922\pi\) | ||||
−0.927537 | + | 0.373732i | \(0.878078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −77.2962 | −3.49546 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.4876 | 1.24050 | 0.620249 | − | 0.784405i | \(-0.287032\pi\) | ||||
0.620249 | + | 0.784405i | \(0.287032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.07928i | 0.0486082i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 0.00668310i | 0 0.000299778i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.2961 | −0.819045 | −0.409523 | − | 0.912300i | \(-0.634305\pi\) | ||||
−0.409523 | + | 0.912300i | \(0.634305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5549 | −0.605587 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.97389i | 0.0880115i | 0.999031 | + | 0.0440058i | \(0.0140120\pi\) | ||||
−0.999031 | + | 0.0440058i | \(0.985988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.6986i | 1.67425i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.3441 | 1.69957 | 0.849787 | − | 0.527126i | \(-0.176731\pi\) | ||||
0.849787 | + | 0.527126i | \(0.176731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.49125 | −0.375631 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.12417i | 0.0937844i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 46.0217i | − 2.02403i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −59.8839 | −2.62861 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.1814 | −1.01560 | −0.507799 | − | 0.861476i | \(-0.669541\pi\) | ||||
−0.507799 | + | 0.861476i | \(0.669541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.5123i | 1.90266i | 0.308172 | + | 0.951331i | \(0.400283\pi\) | ||||
−0.308172 | + | 0.951331i | \(0.599717\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.80542i | − 0.122206i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.8452 | 0.687622 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5962i | 1.06538i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.1197i | 1.38607i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.1303 | 1.34088 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6112 | 0.800158 | 0.400079 | − | 0.916481i | \(-0.368983\pi\) | ||||
0.400079 | + | 0.916481i | \(0.368983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.1732i | 1.20903i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.78956i | 0.290300i | 0.989410 | + | 0.145150i | \(0.0463665\pi\) | ||||
−0.989410 | + | 0.145150i | \(0.953633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.1673 | 1.58626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.159537 | 0.00679649 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.90272i | 0.251009i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 24.9869i | − 1.05873i | −0.848395 | − | 0.529364i | \(-0.822430\pi\) | ||||
0.848395 | − | 0.529364i | \(-0.177570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.36290 | −0.353713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.0583 | 0.804642 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 44.7551i | − 1.88620i | −0.332508 | − | 0.943100i | \(-0.607895\pi\) | ||||
0.332508 | − | 0.943100i | \(-0.392105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 7.67371i | − 0.322265i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.4895 | 1.15242 | 0.576211 | − | 0.817301i | \(-0.304531\pi\) | ||||
0.576211 | + | 0.817301i | \(0.304531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.40495 | −0.0587952 | −0.0293976 | − | 0.999568i | \(-0.509359\pi\) | ||||
−0.0293976 | + | 0.999568i | \(0.509359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.61957i | 0.192985i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.1987i | 0.799253i | 0.916678 | + | 0.399627i | \(0.130860\pi\) | ||||
−0.916678 | + | 0.399627i | \(0.869140\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −44.4364 | −1.84671 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.13043 | 0.129872 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 10.3859i | − 0.430139i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.8565i | 0.943390i | 0.881762 | + | 0.471695i | \(0.156358\pi\) | ||||
−0.881762 | + | 0.471695i | \(0.843642\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.414692 | −0.0170871 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 75.4473 | 3.10349 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 26.5387i | − 1.08981i | −0.838497 | − | 0.544906i | \(-0.816565\pi\) | ||||
0.838497 | − | 0.544906i | \(-0.183435\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.97005i | − 0.203411i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.82768 | 0.360689 | 0.180345 | − | 0.983603i | \(-0.442279\pi\) | ||||
0.180345 | + | 0.983603i | \(0.442279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3072 | −1.23626 | −0.618129 | − | 0.786077i | \(-0.712109\pi\) | ||||
−0.618129 | + | 0.786077i | \(0.712109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 45.0215i | − 1.83342i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 38.0102i | − 1.54278i | −0.636360 | − | 0.771392i | \(-0.719561\pi\) | ||||
0.636360 | − | 0.771392i | \(-0.280439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.39015 | −0.0563316 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.6887 | −2.01019 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 31.7417i | − 1.28204i | −0.767526 | − | 0.641018i | \(-0.778512\pi\) | ||||
0.767526 | − | 0.641018i | \(-0.221488\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 46.6699i | − 1.87886i | −0.342741 | − | 0.939430i | \(-0.611355\pi\) | ||||
0.342741 | − | 0.939430i | \(-0.388645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.2223 | −0.933383 | −0.466692 | − | 0.884420i | \(-0.654554\pi\) | ||||
−0.466692 | + | 0.884420i | \(0.654554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8154 | 0.434009 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.03235i | 0.201617i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.81716i | − 0.112506i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.50121 | 0.299093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.0906 | −0.521129 | −0.260565 | − | 0.965456i | \(-0.583909\pi\) | ||||
−0.260565 | + | 0.965456i | \(0.583909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 19.2740i | − 0.766072i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 33.6107i | − 1.33171i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.0783588 | −0.00309983 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8746 | 0.903494 | 0.451747 | − | 0.892146i | \(-0.350801\pi\) | ||||
0.451747 | + | 0.892146i | \(0.350801\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 30.6333i | − 1.20806i | −0.796962 | − | 0.604030i | \(-0.793561\pi\) | ||||
0.796962 | − | 0.604030i | \(-0.206439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.74454i | 0.343783i | 0.985116 | + | 0.171892i | \(0.0549879\pi\) | ||||
−0.985116 | + | 0.171892i | \(0.945012\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.3268 | −0.444616 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.61348 | 0.141623 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 24.7443i | − 0.968320i | −0.874979 | − | 0.484160i | \(-0.839125\pi\) | ||||
0.874979 | − | 0.484160i | \(-0.160875\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 99.5593i | 3.88418i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.30726 | −0.323605 | −0.161803 | − | 0.986823i | \(-0.551731\pi\) | ||||
−0.161803 | + | 0.986823i | \(0.551731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.1755 | −0.551364 | −0.275682 | − | 0.961249i | \(-0.588904\pi\) | ||||
−0.275682 | + | 0.961249i | \(0.588904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 20.5768i | − 0.799138i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.812298i | − 0.0314523i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −65.6627 | −2.53867 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.5688 | −1.02568 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.30229i | 0.281482i | 0.990046 | + | 0.140741i | \(0.0449486\pi\) | ||||
−0.990046 | + | 0.140741i | \(0.955051\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 39.7090i | − 1.52614i | −0.646315 | − | 0.763071i | \(-0.723691\pi\) | ||||
0.646315 | − | 0.763071i | \(-0.276309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.81027 | −0.299731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 32.4296 | 1.24271 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 38.5993i | − 1.47696i | −0.674274 | − | 0.738481i | \(-0.735543\pi\) | ||||
0.674274 | − | 0.738481i | \(-0.264457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 74.0219i | − 2.82411i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.2134 | −0.427198 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4163 | −0.814713 | −0.407357 | − | 0.913269i | \(-0.633549\pi\) | ||||
−0.407357 | + | 0.913269i | \(0.633549\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.8020i | 0.638255i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 6.50669i | − 0.246459i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.8773 | 1.31918 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.40147 | −0.204011 | −0.102005 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102005 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1.10881i | − 0.0418197i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 4.17940i | − 0.157182i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.3161 | 0.575208 | 0.287604 | − | 0.957749i | \(-0.407141\pi\) | ||||
0.287604 | + | 0.957749i | \(0.407141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 69.2090 | 2.59554 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.11145i | 0.0790742i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 78.8102i | − 2.94322i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.6505 | −0.434491 | −0.217245 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217245 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.01875 | 0.298634 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.8334i | 1.85333i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.8188i | 1.06883i | 0.845223 | + | 0.534415i | \(0.179468\pi\) | ||||
−0.845223 | + | 0.534415i | \(0.820532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.0725 | 0.373056 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.21233 | 0.0818259 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.2304i | 0.931906i | 0.884810 | + | 0.465953i | \(0.154288\pi\) | ||||
−0.884810 | + | 0.465953i | \(0.845712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.1833i | 1.18549i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.22800 | 0.0451728 | 0.0225864 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225864 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.04163 | −0.111737 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 35.1117i | − 1.28812i | −0.764974 | − | 0.644061i | \(-0.777248\pi\) | ||||
0.764974 | − | 0.644061i | \(-0.222752\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 36.7041i | − 1.34293i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.30909 | 0.0478329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.7367 | 1.15809 | 0.579044 | − | 0.815296i | \(-0.303426\pi\) | ||||
0.579044 | + | 0.815296i | \(0.303426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 41.1630i | 1.50006i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.22287i | − 0.117137i | −0.998283 | − | 0.0585685i | \(-0.981346\pi\) | ||||
0.998283 | − | 0.0585685i | \(-0.0186536\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.3439 | −0.520649 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.60077 | −0.348027 | −0.174014 | − | 0.984743i | \(-0.555674\pi\) | ||||
−0.174014 | + | 0.984743i | \(0.555674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.74882i | − 0.208121i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2293i | 0.441575i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9778 | −0.540113 | −0.270056 | − | 0.962844i | \(-0.587042\pi\) | ||||
−0.270056 | + | 0.962844i | \(0.587042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.3998 | 1.13084 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 28.7430i | − 1.03381i | −0.856042 | − | 0.516906i | \(-0.827084\pi\) | ||||
0.856042 | − | 0.516906i | \(-0.172916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.66181i | 0.346616i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.961806 | −0.0344603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0560142 | 0.00200435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.78536i | 0.313963i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.1965i | − 1.21897i | −0.792797 | − | 0.609486i | \(-0.791376\pi\) | ||||
0.792797 | − | 0.609486i | \(-0.208624\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 71.8666 | 2.55852 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.6965 | 0.380324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6857i | 1.01866i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 0.303391i | − 0.0107467i | −0.999986 | − | 0.00537334i | \(-0.998290\pi\) | ||||
0.999986 | − | 0.00537334i | \(-0.00171039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1447 | 0.465026 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 59.0039 | 2.08480 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 71.1692i | − 2.51151i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.2429i | 1.06460i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1865 | 0.463611 | 0.231806 | − | 0.972762i | \(-0.425537\pi\) | ||||
0.231806 | + | 0.972762i | \(0.425537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.7284 | 0.517185 | 0.258593 | − | 0.965986i | \(-0.416741\pi\) | ||||
0.258593 | + | 0.965986i | \(0.416741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.7575i | 0.657856i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 0.327022i | − 0.0114410i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.1408 | 0.633890 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.6177 | 1.27797 | 0.638984 | − | 0.769220i | \(-0.279355\pi\) | ||||
0.638984 | + | 0.769220i | \(0.279355\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 0.420867i | − 0.0146705i | −0.999973 | − | 0.00733525i | \(-0.997665\pi\) | ||||
0.999973 | − | 0.00733525i | \(-0.00233490\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.1118i | 1.22096i | 0.792032 | + | 0.610479i | \(0.209023\pi\) | ||||
−0.792032 | + | 0.610479i | \(0.790977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.6234 | 1.23725 | 0.618626 | − | 0.785685i | \(-0.287689\pi\) | ||||
0.618626 | + | 0.785685i | \(0.287689\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.137436 | 0.00476759 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.89141i | 0.308069i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 22.8362i | − 0.789335i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.9998 | 0.690469 | 0.345235 | − | 0.938516i | \(-0.387799\pi\) | ||||
0.345235 | + | 0.938516i | \(0.387799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3402 | −0.977247 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 86.3350i | − 2.97354i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 5.90554i | − 0.202917i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.5556 | 1.28890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.64564 | −0.193530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 42.4994i | − 1.45515i | −0.686026 | − | 0.727577i | \(-0.740647\pi\) | ||||
0.686026 | − | 0.727577i | \(-0.259353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 18.0100i | − 0.615208i | −0.951514 | − | 0.307604i | \(-0.900473\pi\) | ||||
0.951514 | − | 0.307604i | \(-0.0995273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.3869 | −0.763832 | −0.381916 | − | 0.924197i | \(-0.624736\pi\) | ||||
−0.381916 | + | 0.924197i | \(0.624736\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.38084 | 0.285618 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 18.7613i | − 0.638642i | −0.947647 | − | 0.319321i | \(-0.896545\pi\) | ||||
0.947647 | − | 0.319321i | \(-0.103455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 46.9750i | − 1.59536i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.4735 | −1.67827 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.7476 | 1.17738 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 91.5749i | 3.09934i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 31.6345i | − 1.06822i | −0.845415 | − | 0.534111i | \(-0.820647\pi\) | ||||
0.845415 | − | 0.534111i | \(-0.179353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.35783 | −0.281903 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.6850 | 1.33702 | 0.668512 | − | 0.743702i | \(-0.266932\pi\) | ||||
0.668512 | + | 0.743702i | \(0.266932\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3778i | 0.349242i | 0.984636 | + | 0.174621i | \(0.0558701\pi\) | ||||
−0.984636 | + | 0.174621i | \(0.944130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0199i | 0.806508i | 0.915088 | + | 0.403254i | \(0.132121\pi\) | ||||
−0.915088 | + | 0.403254i | \(0.867879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2642 | −0.344251 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 64.3170 | 2.15470 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.94302i | − 0.0650207i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4868i | 0.517088i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.71512 | −0.0572025 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.96641 | 0.0988254 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.84955i | 0.0948271i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 18.5181i | − 0.614885i | −0.951567 | − | 0.307442i | \(-0.900527\pi\) | ||||
0.951567 | − | 0.307442i | \(-0.0994731\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −49.0032 | −1.62533 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.34956 | −0.110976 | −0.0554879 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554879 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2376i | 0.868339i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.19920i | 0.270761i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.9754 | 1.08776 | 0.543878 | − | 0.839164i | \(-0.316955\pi\) | ||||
0.543878 | + | 0.839164i | \(0.316955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 99.1728 | 3.26785 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.0604774i | − 0.00199064i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 94.0193i | − 3.08800i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.5008 | 1.19755 | 0.598777 | − | 0.800916i | \(-0.295654\pi\) | ||||
0.598777 | + | 0.800916i | \(0.295654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.31431 | 0.0430748 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.5789i | 0.411816i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 12.4598i | − 0.407043i | −0.979071 | − | 0.203521i | \(-0.934761\pi\) | ||||
0.979071 | − | 0.203521i | \(-0.0652386\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.4916 | 1.38666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.2938 | −1.47653 | −0.738267 | − | 0.674508i | \(-0.764356\pi\) | ||||
−0.738267 | + | 0.674508i | \(0.764356\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.89714i | 0.159473i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 41.4016i | − 1.34537i | −0.739929 | − | 0.672685i | \(-0.765141\pi\) | ||||
0.739929 | − | 0.672685i | \(-0.234859\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.8399 | −2.49433 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.2619 | −1.04616 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 15.3738i | − 0.498006i | −0.968503 | − | 0.249003i | \(-0.919897\pi\) | ||||
0.968503 | − | 0.249003i | \(-0.0801029\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 11.6515i | − 0.376639i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.44785 | 0.208212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.5418 | −0.856187 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 15.3489i | − 0.494612i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 53.4925i | − 1.72020i | −0.510124 | − | 0.860101i | \(-0.670400\pi\) | ||||
0.510124 | − | 0.860101i | \(-0.329600\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.804635 | 0.0258486 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.8881 | 0.638241 | 0.319120 | − | 0.947714i | \(-0.396613\pi\) | ||||
0.319120 | + | 0.947714i | \(0.396613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.18231i | 0.198196i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.8758i | 0.475919i | 0.971275 | + | 0.237960i | \(0.0764786\pi\) | ||||
−0.971275 | + | 0.237960i | \(0.923521\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.1785 | −1.34803 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −67.4045 | −2.15206 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.16403i | − 0.0371269i | −0.999828 | − | 0.0185634i | \(-0.994091\pi\) | ||||
0.999828 | − | 0.0185634i | \(-0.00590926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.9308i | 0.538913i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.66507 | −0.0529460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.8693 | −1.52062 | −0.760310 | − | 0.649561i | \(-0.774953\pi\) | ||||
−0.760310 | + | 0.649561i | \(0.774953\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 38.9904i | 1.23732i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4353i | 0.362159i | 0.983468 | + | 0.181079i | \(0.0579591\pi\) | ||||
−0.983468 | + | 0.181079i | \(0.942041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 61.0601 | 1.93186 |
(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 | 4600.2.e.v.4049.1 | 10 | ||
5.2 | odd | 4 | 4600.2.a.bc.1.1 | ✓ | 5 | ||
5.3 | odd | 4 | 4600.2.a.bg.1.5 | yes | 5 | ||
5.4 | even | 2 | inner | 4600.2.e.v.4049.10 | 10 | ||
20.3 | even | 4 | 9200.2.a.cs.1.1 | 5 | |||
20.7 | even | 4 | 9200.2.a.cw.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.1 | ✓ | 5 | 5.2 | odd | 4 | ||
4600.2.a.bg.1.5 | yes | 5 | 5.3 | odd | 4 | ||
4600.2.e.v.4049.1 | 10 | 1.1 | even | 1 | trivial | ||
4600.2.e.v.4049.10 | 10 | 5.4 | even | 2 | inner | ||
9200.2.a.cs.1.1 | 5 | 20.3 | even | 4 | |||
9200.2.a.cw.1.5 | 5 | 20.7 | even | 4 |