Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(571,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.571");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 53x^{10} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 571.15 | ||
Root | \(-1.09266 - 0.897823i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 572.571 |
Dual form | 572.2.b.b.571.16 |
$q$-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 \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09266 | − | 0.897823i | 0.772630 | − | 0.634856i | ||||
\(3\) | − | 3.43055i | − | 1.98063i | −0.138841 | − | 0.990315i | \(-0.544338\pi\) | ||
0.138841 | − | 0.990315i | \(-0.455662\pi\) | |||||||
\(4\) | 0.387829 | − | 1.96204i | 0.193915 | − | 0.981018i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | −3.08003 | − | 3.74844i | −1.25742 | − | 1.53029i | ||||
\(7\) | 0.803843i | 0.303824i | 0.988394 | + | 0.151912i | \(0.0485431\pi\) | ||||
−0.988394 | + | 0.151912i | \(0.951457\pi\) | |||||||
\(8\) | −1.33779 | − | 2.49205i | −0.472982 | − | 0.881072i | ||||
\(9\) | −8.76868 | −2.92289 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31662i | 1.00000i | ||||||||
\(12\) | −6.73087 | − | 1.33047i | −1.94303 | − | 0.384073i | ||||
\(13\) | 3.60555 | 1.00000 | ||||||||
\(14\) | 0.721709 | + | 0.878331i | 0.192885 | + | 0.234744i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.69918 | − | 1.52187i | −0.924794 | − | 0.380467i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −9.58122 | + | 7.87272i | −2.25832 | + | 1.85562i | ||||
\(19\) | − | 5.18645i | − | 1.18985i | −0.803780 | − | 0.594926i | \(-0.797181\pi\) | ||
0.803780 | − | 0.594926i | \(-0.202819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.75763 | 0.601763 | ||||||||
\(22\) | 2.97774 | + | 3.62396i | 0.634856 | + | 0.772630i | ||||
\(23\) | − | 6.19820i | − | 1.29241i | −0.763162 | − | 0.646207i | \(-0.776354\pi\) | ||
0.763162 | − | 0.646207i | \(-0.223646\pi\) | |||||||
\(24\) | −8.54910 | + | 4.58937i | −1.74508 | + | 0.936801i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 3.93966 | − | 3.23715i | 0.772630 | − | 0.634856i | ||||
\(27\) | 19.7897i | 3.80854i | ||||||||
\(28\) | 1.57717 | + | 0.311754i | 0.298057 | + | 0.0589159i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | −5.40833 | + | 1.65831i | −0.956066 | + | 0.293151i | ||||
\(33\) | 11.3779 | 1.98063 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.40075 | + | 17.2045i | −0.566792 | + | 2.86741i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −4.65651 | − | 5.66704i | −0.755385 | − | 0.919316i | ||||
\(39\) | − | 12.3690i | − | 1.98063i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3391 | 1.61469 | 0.807347 | − | 0.590076i | \(-0.200902\pi\) | ||||
0.807347 | + | 0.590076i | \(0.200902\pi\) | |||||||
\(42\) | 3.01316 | − | 2.47586i | 0.464940 | − | 0.382033i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 6.50734 | + | 1.28628i | 0.981018 | + | 0.193915i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.56488 | − | 6.77255i | −0.820497 | − | 0.998558i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −5.22085 | + | 12.6902i | −0.753565 | + | 1.83167i | ||||
\(49\) | 6.35384 | 0.907691 | ||||||||
\(50\) | 5.46332 | − | 4.48911i | 0.772630 | − | 0.634856i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.39834 | − | 7.07422i | 0.193915 | − | 0.981018i | ||||
\(53\) | −14.3158 | −1.96642 | −0.983210 | − | 0.182479i | \(-0.941588\pi\) | ||||
−0.983210 | + | 0.182479i | \(0.941588\pi\) | |||||||
\(54\) | 17.7677 | + | 21.6235i | 2.41788 | + | 2.94259i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00322 | − | 1.07538i | 0.267691 | − | 0.143703i | ||||
\(57\) | −17.7924 | −2.35666 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 7.04865i | − | 0.888046i | ||||||
\(64\) | −4.42061 | + | 6.66770i | −0.552577 | + | 0.833462i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.4322 | − | 10.2153i | 1.53029 | − | 1.25742i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −21.2632 | −2.55979 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 11.7307 | + | 21.8520i | 1.38247 | + | 2.57528i | ||||
\(73\) | −6.10477 | −0.714510 | −0.357255 | − | 0.934007i | \(-0.616287\pi\) | ||||
−0.357255 | + | 0.934007i | \(0.616287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 17.1528i | − | 1.98063i | ||||||
\(76\) | −10.1760 | − | 2.01145i | −1.16727 | − | 0.230730i | ||||
\(77\) | −2.66605 | −0.303824 | ||||||||
\(78\) | −11.1052 | − | 13.5152i | −1.25742 | − | 1.53029i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 41.5837 | 4.62041 | ||||||||
\(82\) | 11.2972 | − | 9.28267i | 1.24756 | − | 1.02510i | ||||
\(83\) | 17.5249i | 1.92360i | 0.273747 | + | 0.961802i | \(0.411737\pi\) | ||||
−0.273747 | + | 0.961802i | \(0.588263\pi\) | |||||||
\(84\) | 1.06949 | − | 5.41056i | 0.116691 | − | 0.590341i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.26519 | − | 4.43696i | 0.881072 | − | 0.472982i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.89830i | 0.303824i | ||||||||
\(92\) | −12.1611 | − | 2.40384i | −1.26788 | − | 0.250618i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.68893 | + | 18.5535i | 0.580623 | + | 1.89361i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 6.94261 | − | 5.70462i | 0.701309 | − | 0.576253i | ||||
\(99\) | − | 29.0824i | − | 2.92289i | ||||||
\(100\) | 1.93915 | − | 9.81018i | 0.193915 | − | 0.981018i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.7980i | − | 1.26102i | −0.776179 | − | 0.630512i | \(-0.782845\pi\) | ||
0.776179 | − | 0.630512i | \(-0.217155\pi\) | |||||||
\(104\) | −4.82349 | − | 8.98521i | −0.472982 | − | 0.881072i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.6423 | + | 12.8530i | −1.51932 | + | 1.24839i | ||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 38.8282 | + | 7.67504i | 3.73625 | + | 0.738531i | ||||
\(109\) | 20.1192 | 1.92707 | 0.963533 | − | 0.267589i | \(-0.0862270\pi\) | ||||
0.963533 | + | 0.267589i | \(0.0862270\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.22335 | − | 2.97356i | 0.115595 | − | 0.280975i | ||||
\(113\) | 11.4300 | 1.07524 | 0.537622 | − | 0.843186i | \(-0.319323\pi\) | ||||
0.537622 | + | 0.843186i | \(0.319323\pi\) | |||||||
\(114\) | −19.4411 | + | 15.9744i | −1.82082 | + | 1.49614i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −31.6159 | −2.92289 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 35.4688i | − | 3.19811i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.32843 | − | 7.70180i | −0.563782 | − | 0.686131i | ||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 1.15616 | + | 11.2545i | 0.102191 | + | 0.994765i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 4.41266 | − | 22.3238i | 0.384073 | − | 1.94303i | ||||
\(133\) | 4.16909 | 0.361506 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | −23.2336 | + | 19.0906i | −1.97777 | + | 1.62510i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.9583i | 1.00000i | ||||||||
\(144\) | 32.4369 | + | 13.3448i | 2.70307 | + | 1.11207i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −6.67047 | + | 5.48100i | −0.552052 | + | 0.453611i | ||||
\(147\) | − | 21.7972i | − | 1.79780i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.0414 | 1.72378 | 0.861891 | − | 0.507093i | \(-0.169280\pi\) | ||||
0.861891 | + | 0.507093i | \(0.169280\pi\) | |||||||
\(150\) | −15.4001 | − | 18.7422i | −1.25742 | − | 1.53029i | ||||
\(151\) | 19.8997i | 1.61942i | 0.586831 | + | 0.809709i | \(0.300375\pi\) | ||||
−0.586831 | + | 0.809709i | \(0.699625\pi\) | |||||||
\(152\) | −12.9249 | + | 6.93840i | −1.04835 | + | 0.562778i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.91309 | + | 2.39364i | −0.234744 | + | 0.192885i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −24.2685 | − | 4.79707i | −1.94303 | − | 0.384073i | ||||
\(157\) | 14.2034 | 1.13356 | 0.566778 | − | 0.823871i | \(-0.308190\pi\) | ||||
0.566778 | + | 0.823871i | \(0.308190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 49.1109i | 3.89475i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.98238 | 0.392667 | ||||||||
\(162\) | 45.4370 | − | 37.3348i | 3.56987 | − | 2.93330i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 4.00980 | − | 20.2857i | 0.313113 | − | 1.58405i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.7342 | + | 19.1488i | 1.22121 | + | 1.48623i | ||||
\(167\) | 22.7419i | 1.75982i | 0.475138 | + | 0.879911i | \(0.342398\pi\) | ||||
−0.475138 | + | 0.879911i | \(0.657602\pi\) | |||||||
\(168\) | −3.68914 | − | 6.87214i | −0.284623 | − | 0.530197i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 45.4783i | 3.47781i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.01922i | 0.303824i | ||||||||
\(176\) | 5.04747 | − | 12.2688i | 0.380467 | − | 0.924794i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 23.9165i | − | 1.78760i | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||
0.448461 | − | 0.893802i | \(-0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4681 | −0.778087 | −0.389044 | − | 0.921219i | \(-0.627194\pi\) | ||||
−0.389044 | + | 0.921219i | \(0.627194\pi\) | |||||||
\(182\) | 2.60216 | + | 3.16687i | 0.192885 | + | 0.234744i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.4462 | + | 8.29191i | −1.13871 | + | 0.611288i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.9079 | −1.15713 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.97779i | − | 0.360181i | −0.983650 | − | 0.180090i | \(-0.942361\pi\) | ||
0.983650 | − | 0.180090i | \(-0.0576390\pi\) | |||||||
\(192\) | 22.8739 | + | 15.1651i | 1.65078 | + | 1.09445i | ||||
\(193\) | −10.0969 | −0.726792 | −0.363396 | − | 0.931635i | \(-0.618383\pi\) | ||||
−0.363396 | + | 0.931635i | \(0.618383\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.46420 | − | 12.4665i | 0.176014 | − | 0.890461i | ||||
\(197\) | −25.3922 | −1.80912 | −0.904561 | − | 0.426344i | \(-0.859801\pi\) | ||||
−0.904561 | + | 0.426344i | \(0.859801\pi\) | |||||||
\(198\) | −26.1109 | − | 31.7773i | −1.85562 | − | 2.25832i | ||||
\(199\) | − | 1.88331i | − | 0.133504i | −0.997770 | − | 0.0667521i | \(-0.978736\pi\) | ||
0.997770 | − | 0.0667521i | \(-0.0212636\pi\) | |||||||
\(200\) | −6.68897 | − | 12.4602i | −0.472982 | − | 0.881072i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.4903 | − | 13.9839i | −0.800569 | − | 0.974305i | ||||
\(207\) | 54.3500i | 3.77759i | ||||||||
\(208\) | −13.3376 | − | 5.48718i | −0.924794 | − | 0.380467i | ||||
\(209\) | 17.2015 | 1.18985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | −5.55206 | + | 28.0880i | −0.381317 | + | 1.92909i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 49.3170 | − | 26.4746i | 3.35560 | − | 1.80137i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 21.9835 | − | 18.0634i | 1.48891 | − | 1.22341i | ||||
\(219\) | 20.9427i | 1.41518i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | −1.33302 | − | 4.34745i | −0.0890664 | − | 0.290476i | ||||
\(225\) | −43.8434 | −2.92289 | ||||||||
\(226\) | 12.4892 | − | 10.2621i | 0.830766 | − | 0.682626i | ||||
\(227\) | 29.9245i | 1.98616i | 0.117445 | + | 0.993079i | \(0.462530\pi\) | ||||
−0.117445 | + | 0.993079i | \(0.537470\pi\) | |||||||
\(228\) | −6.90040 | + | 34.9093i | −0.456990 | + | 2.31192i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.14601i | 0.601763i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | −34.5456 | + | 28.3855i | −2.25832 | + | 1.85562i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.37676i | 0.541847i | 0.962601 | + | 0.270924i | \(0.0873291\pi\) | ||||
−0.962601 | + | 0.270924i | \(0.912671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.8234 | 0.697199 | 0.348600 | − | 0.937272i | \(-0.386657\pi\) | ||||
0.348600 | + | 0.937272i | \(0.386657\pi\) | |||||||
\(242\) | −12.0193 | + | 9.87605i | −0.772630 | + | 0.634856i | ||||
\(243\) | − | 83.2858i | − | 5.34278i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −31.8447 | − | 38.7555i | −2.03034 | − | 2.47096i | ||||
\(247\) | − | 18.7000i | − | 1.18985i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 60.1199 | 3.80995 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0979i | 1.01609i | 0.861330 | + | 0.508045i | \(0.169632\pi\) | ||||
−0.861330 | + | 0.508045i | \(0.830368\pi\) | |||||||
\(252\) | −13.8297 | − | 2.73367i | −0.871189 | − | 0.172205i | ||||
\(253\) | 20.5571 | 1.29241 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.3678 | + | 11.2593i | 0.710489 | + | 0.703708i | ||||
\(257\) | −11.9739 | −0.746914 | −0.373457 | − | 0.927647i | \(-0.621828\pi\) | ||||
−0.373457 | + | 0.927647i | \(0.621828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | −15.2212 | − | 28.3542i | −0.936801 | − | 1.74508i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.55542 | − | 3.74310i | 0.279310 | − | 0.229504i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.9460 | −1.94778 | −0.973892 | − | 0.227012i | \(-0.927104\pi\) | ||||
−0.973892 | + | 0.227012i | \(0.927104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 26.7342i | − | 1.62399i | −0.583667 | − | 0.811993i | \(-0.698383\pi\) | ||
0.583667 | − | 0.811993i | \(-0.301617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.94276 | 0.601763 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.5831i | 1.00000i | ||||||||
\(276\) | −8.24650 | + | 41.7192i | −0.496381 | + | 2.51120i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.831696 | 0.0496148 | 0.0248074 | − | 0.999692i | \(-0.492103\pi\) | ||||
0.0248074 | + | 0.999692i | \(0.492103\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.7364 | + | 13.0664i | 0.634856 | + | 0.772630i | ||||
\(287\) | 8.31101i | 0.490583i | ||||||||
\(288\) | 47.4239 | − | 14.5412i | 2.79448 | − | 0.856849i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.36761 | + | 11.9778i | −0.138554 | + | 0.700947i | ||||
\(293\) | −21.6333 | −1.26383 | −0.631916 | − | 0.775037i | \(-0.717731\pi\) | ||||
−0.631916 | + | 0.775037i | \(0.717731\pi\) | |||||||
\(294\) | −19.5700 | − | 23.8170i | −1.14134 | − | 1.38903i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −65.6352 | −3.80854 | ||||||||
\(298\) | 22.9912 | − | 18.8915i | 1.33185 | − | 1.09435i | ||||
\(299\) | − | 22.3479i | − | 1.29241i | ||||||
\(300\) | −33.6543 | − | 6.65234i | −1.94303 | − | 0.384073i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.8664 | + | 21.7437i | 1.02810 | + | 1.25121i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.89310 | + | 19.1856i | −0.452700 | + | 1.10037i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 19.8997i | − | 1.13574i | −0.823119 | − | 0.567869i | \(-0.807768\pi\) | ||
0.823119 | − | 0.567869i | \(-0.192232\pi\) | |||||||
\(308\) | −1.03397 | + | 5.23088i | −0.0589159 | + | 0.298057i | ||||
\(309\) | −43.9042 | −2.49762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.5611i | 1.44944i | 0.689045 | + | 0.724719i | \(0.258030\pi\) | ||||
−0.689045 | + | 0.724719i | \(0.741970\pi\) | |||||||
\(312\) | −30.8242 | + | 16.5472i | −1.74508 | + | 0.936801i | ||||
\(313\) | 23.5113 | 1.32894 | 0.664469 | − | 0.747316i | \(-0.268658\pi\) | ||||
0.664469 | + | 0.747316i | \(0.268658\pi\) | |||||||
\(314\) | 15.5196 | − | 12.7521i | 0.875819 | − | 0.719645i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | 44.0929 | + | 53.6617i | 2.47261 | + | 3.00920i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.44407 | − | 4.47329i | 0.303386 | − | 0.249287i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 16.1274 | − | 81.5888i | 0.895965 | − | 4.53271i | ||||
\(325\) | 18.0278 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 69.0198i | − | 3.81680i | ||||||
\(328\) | −13.8316 | − | 25.7655i | −0.763721 | − | 1.42266i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 34.3844 | + | 6.79665i | 1.88709 | + | 0.373015i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.4182 | + | 24.8493i | 1.11723 | + | 1.35969i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.2009 | − | 4.19675i | −0.556507 | − | 0.228951i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 14.2046 | − | 11.6717i | 0.772630 | − | 0.634856i | ||||
\(339\) | − | 39.2112i | − | 2.12966i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 40.8314 | + | 49.6925i | 2.20791 | + | 2.68706i | ||||
\(343\) | 10.7344i | 0.579603i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.2836 | −1.13929 | −0.569643 | − | 0.821892i | \(-0.692919\pi\) | ||||
−0.569643 | + | 0.821892i | \(0.692919\pi\) | |||||||
\(350\) | 3.60854 | + | 4.39165i | 0.192885 | + | 0.234744i | ||||
\(351\) | 71.3530i | 3.80854i | ||||||||
\(352\) | −5.50000 | − | 17.9374i | −0.293151 | − | 0.956066i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.4728 | − | 26.1327i | −1.13487 | − | 1.38116i | ||||
\(359\) | 37.4612i | 1.97713i | 0.150798 | + | 0.988565i | \(0.451816\pi\) | ||||
−0.150798 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.89923 | −0.415749 | ||||||||
\(362\) | −11.4381 | + | 9.39849i | −0.601173 | + | 0.493974i | ||||
\(363\) | 37.7361i | 1.98063i | ||||||||
\(364\) | 5.68657 | + | 1.12404i | 0.298057 | + | 0.0589159i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.4666i | 1.17275i | 0.810041 | + | 0.586374i | \(0.199445\pi\) | ||||
−0.810041 | + | 0.586374i | \(0.800555\pi\) | |||||||
\(368\) | −9.43285 | + | 22.9282i | −0.491721 | + | 1.19522i | ||||
\(369\) | −90.6602 | −4.71958 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.5076i | − | 0.597446i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −17.3819 | + | 14.2824i | −0.894031 | + | 0.734609i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.46918 | − | 5.43906i | −0.228663 | − | 0.278286i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 38.6091 | − | 3.96628i | 1.97026 | − | 0.202403i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0325 | + | 9.06524i | −0.561541 | + | 0.461409i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.54426 | −0.433211 | −0.216606 | − | 0.976259i | \(-0.569499\pi\) | ||||
−0.216606 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −8.50012 | − | 15.8341i | −0.429321 | − | 0.799741i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −27.7452 | + | 22.7977i | −1.39778 | + | 1.14853i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −57.0608 | − | 11.2790i | −2.86741 | − | 0.566792i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −1.69088 | − | 2.05782i | −0.0847559 | − | 0.103149i | ||||
\(399\) | − | 14.3023i | − | 0.716009i | ||||||
\(400\) | −18.4959 | − | 7.60935i | −0.924794 | − | 0.380467i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.21110 | −0.356566 | −0.178283 | − | 0.983979i | \(-0.557054\pi\) | ||||
−0.178283 | + | 0.983979i | \(0.557054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −25.1101 | − | 4.96344i | −1.23709 | − | 0.244531i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 48.7967 | + | 59.3863i | 2.39823 | + | 2.91868i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.5000 | + | 5.97913i | −0.956066 | + | 0.293151i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.7955 | − | 15.4439i | 0.919316 | − | 0.755385i | ||||
\(419\) | 40.8907i | 1.99764i | 0.0485577 | + | 0.998820i | \(0.484538\pi\) | ||||
−0.0485577 | + | 0.998820i | \(0.515462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.1515 | + | 35.6755i | 0.930080 | + | 1.73256i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.0234 | 1.98063 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.6382i | − | 1.57213i | −0.618146 | − | 0.786063i | \(-0.712116\pi\) | ||
0.618146 | − | 0.786063i | \(-0.287884\pi\) | |||||||
\(432\) | 30.1174 | − | 73.2058i | 1.44903 | − | 3.52212i | ||||
\(433\) | 19.1253 | 0.919105 | 0.459552 | − | 0.888151i | \(-0.348010\pi\) | ||||
0.459552 | + | 0.888151i | \(0.348010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.80280 | − | 39.4745i | 0.373686 | − | 1.89049i | ||||
\(437\) | −32.1466 | −1.53778 | ||||||||
\(438\) | 18.8029 | + | 22.8834i | 0.898435 | + | 1.09341i | ||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −55.7148 | −2.65308 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 3.70150i | − | 0.175864i | −0.996126 | − | 0.0879318i | \(-0.971974\pi\) | ||
0.996126 | − | 0.0879318i | \(-0.0280258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 72.1837i | − | 3.41417i | ||||||
\(448\) | −5.35978 | − | 3.55348i | −0.253226 | − | 0.167886i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −47.9061 | + | 39.3636i | −2.25832 | + | 1.85562i | ||||
\(451\) | 34.2909i | 1.61469i | ||||||||
\(452\) | 4.43289 | − | 22.4261i | 0.208506 | − | 1.05483i | ||||
\(453\) | 68.2671 | 3.20747 | ||||||||
\(454\) | 26.8669 | + | 32.6974i | 1.26093 | + | 1.53457i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 23.8025 | + | 44.3394i | 1.11466 | + | 2.07638i | ||||
\(457\) | 21.9240 | 1.02556 | 0.512781 | − | 0.858520i | \(-0.328615\pi\) | ||||
0.512781 | + | 0.858520i | \(0.328615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −42.8749 | −1.99688 | −0.998441 | − | 0.0558223i | \(-0.982222\pi\) | ||||
−0.998441 | + | 0.0558223i | \(0.982222\pi\) | |||||||
\(462\) | 8.21149 | + | 9.99352i | 0.382033 | + | 0.464940i | ||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 23.9165i | − | 1.10672i | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||
0.832941 | − | 0.553362i | \(-0.186655\pi\) | |||||||
\(468\) | −12.2616 | + | 62.0316i | −0.566792 | + | 2.86741i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 48.7255i | − | 2.24515i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25.9322i | − | 1.18985i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 125.530 | 5.74763 | ||||||||
\(478\) | 7.52084 | + | 9.15298i | 0.343995 | + | 0.418648i | ||||
\(479\) | − | 6.63325i | − | 0.303081i | −0.988451 | − | 0.151540i | \(-0.951577\pi\) | ||
0.988451 | − | 0.151540i | \(-0.0484234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.8264 | − | 9.71753i | 0.538677 | − | 0.442621i | ||||
\(483\) | − | 17.0923i | − | 0.777727i | ||||||
\(484\) | −4.26612 | + | 21.5824i | −0.193915 | + | 0.981018i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −74.7758 | − | 91.0034i | −3.39190 | − | 4.12800i | ||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −69.5911 | − | 13.7558i | −3.13741 | − | 0.620161i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −16.7893 | − | 20.4328i | −0.755385 | − | 0.919316i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 65.6909 | − | 53.9770i | 2.94368 | − | 2.41877i | ||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 78.0173 | 3.48556 | ||||||||
\(502\) | 14.4531 | + | 17.5896i | 0.645071 | + | 0.785062i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −17.5656 | + | 9.42964i | −0.782433 | + | 0.420029i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.4620 | − | 18.4566i | 0.998558 | − | 0.820497i | ||||
\(507\) | − | 44.5972i | − | 1.98063i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.90728i | − | 0.217085i | ||||||
\(512\) | 22.5301 | + | 2.09638i | 0.995699 | + | 0.0926477i | ||||
\(513\) | 102.638 | 4.53160 | ||||||||
\(514\) | −13.0835 | + | 10.7505i | −0.577088 | + | 0.474183i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.6381 | −0.991795 | −0.495897 | − | 0.868381i | \(-0.665161\pi\) | ||||
−0.495897 | + | 0.868381i | \(0.665161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.7881 | 0.601763 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −42.0887 | − | 17.3156i | −1.83167 | − | 0.753565i | ||||
\(529\) | −15.4177 | −0.670333 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.61689 | − | 8.17991i | 0.0701013 | − | 0.354644i | ||||
\(533\) | 37.2781 | 1.61469 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −82.0468 | −3.54058 | ||||||||
\(538\) | −34.9063 | + | 28.6819i | −1.50492 | + | 1.23656i | ||||
\(539\) | 21.0733i | 0.907691i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.4775 | 1.78326 | 0.891628 | − | 0.452770i | \(-0.149564\pi\) | ||||
0.891628 | + | 0.452770i | \(0.149564\pi\) | |||||||
\(542\) | −24.0026 | − | 29.2115i | −1.03100 | − | 1.25474i | ||||
\(543\) | 35.9113i | 1.54110i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.8641 | − | 8.92684i | 0.464940 | − | 0.382033i | ||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.8887 | + | 18.1198i | 0.634856 | + | 0.772630i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 28.4458 | + | 52.9890i | 1.21073 | + | 2.25536i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.3149 | −0.860771 | −0.430385 | − | 0.902645i | \(-0.641622\pi\) | ||||
−0.430385 | + | 0.902645i | \(0.641622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.908764 | − | 0.746716i | 0.0383339 | − | 0.0314983i | ||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 33.4268i | 1.40379i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 23.4625 | + | 4.63776i | 0.981018 | + | 0.193915i | ||||
\(573\) | −17.0766 | −0.713384 | ||||||||
\(574\) | 7.46181 | + | 9.08114i | 0.311450 | + | 0.379040i | ||||
\(575\) | − | 30.9910i | − | 1.29241i | ||||||
\(576\) | 38.7629 | − | 58.4669i | 1.61512 | − | 2.43612i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 18.5753 | − | 15.2630i | 0.772630 | − | 0.634856i | ||||
\(579\) | 34.6380i | 1.43951i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.0872 | −0.584437 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 47.4800i | − | 1.96642i | ||||||
\(584\) | 8.16693 | + | 15.2134i | 0.337950 | + | 0.629535i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.6379 | + | 19.4229i | −0.976474 | + | 0.802351i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −42.7668 | − | 8.45357i | −1.76367 | − | 0.348619i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 87.1094i | 3.58320i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0656 | −0.454410 | −0.227205 | − | 0.973847i | \(-0.572959\pi\) | ||||
−0.227205 | + | 0.973847i | \(0.572959\pi\) | |||||||
\(594\) | −71.7172 | + | 58.9287i | −2.94259 | + | 2.41788i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.16048 | − | 41.2841i | 0.334266 | − | 1.69106i | ||||
\(597\) | −6.46078 | −0.264422 | ||||||||
\(598\) | −20.0645 | − | 24.4188i | −0.820497 | − | 0.998558i | ||||
\(599\) | 36.1888i | 1.47863i | 0.673357 | + | 0.739317i | \(0.264852\pi\) | ||||
−0.673357 | + | 0.739317i | \(0.735148\pi\) | |||||||
\(600\) | −42.7455 | + | 22.9469i | −1.74508 | + | 0.936801i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 39.0440 | + | 7.71770i | 1.58868 | + | 0.314029i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 8.60075 | + | 28.0500i | 0.348806 | + | 1.13758i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.3287 | −1.30574 | −0.652872 | − | 0.757468i | \(-0.726436\pi\) | ||||
−0.652872 | + | 0.757468i | \(0.726436\pi\) | |||||||
\(614\) | −17.8664 | − | 21.7437i | −0.721031 | − | 0.877506i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.56662 | + | 6.64392i | 0.143703 | + | 0.267691i | ||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | −47.9725 | + | 39.4182i | −1.92974 | + | 1.58563i | ||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 122.661 | 4.92221 | ||||||||
\(622\) | 22.9493 | + | 27.9297i | 0.920184 | + | 1.11988i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −18.8241 | + | 45.7552i | −0.753565 | + | 1.83167i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 25.6900 | − | 21.1090i | 1.02678 | − | 0.843685i | ||||
\(627\) | − | 59.0106i | − | 2.35666i | ||||||
\(628\) | 5.50849 | − | 27.8676i | 0.219813 | − | 1.11204i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 96.3574 | + | 19.0466i | 3.82082 | + | 0.755248i | ||||
\(637\) | 22.9091 | 0.907691 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.5860 | 1.84004 | 0.920019 | − | 0.391875i | \(-0.128173\pi\) | ||||
0.920019 | + | 0.391875i | \(0.128173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 1.93231 | − | 9.77561i | 0.0761438 | − | 0.385213i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 46.1444i | − | 1.81412i | −0.420997 | − | 0.907062i | \(-0.638320\pi\) | ||
0.420997 | − | 0.907062i | \(-0.361680\pi\) | |||||||
\(648\) | −55.6304 | − | 103.629i | −2.18537 | − | 4.07092i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 19.6983 | − | 16.1857i | 0.772630 | − | 0.634856i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | −61.9675 | − | 75.4155i | −2.42312 | − | 2.94898i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −38.2461 | − | 15.7348i | −1.49326 | − | 0.614339i | ||||
\(657\) | 53.5308 | 2.08844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 43.6728 | − | 23.4447i | 1.69483 | − | 0.909829i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 44.6205 | + | 8.81998i | 1.72642 | + | 0.341255i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −14.9141 | + | 4.57300i | −0.575325 | + | 0.176407i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 98.9487i | 3.80854i | ||||||||
\(676\) | 5.04178 | − | 25.5065i | 0.193915 | − | 0.981018i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | −35.2047 | − | 42.8447i | −1.35203 | − | 1.64544i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 102.658 | 3.93384 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 89.2301 | + | 17.6378i | 3.41180 | + | 0.674398i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.63758 | + | 11.7291i | 0.367965 | + | 0.447819i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −51.6162 | −1.96642 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.3777 | 0.888046 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −23.2558 | + | 19.1089i | −0.880247 | + | 0.723283i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.88585 | + | 1.55877i | 0.298057 | + | 0.0589159i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 64.0623 | + | 77.9648i | 2.41788 | + | 2.94259i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −22.1142 | − | 14.6615i | −0.833462 | − | 0.552577i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −46.9251 | − | 9.27552i | −1.75367 | − | 0.346643i | ||||
\(717\) | 28.7369 | 1.07320 | ||||||||
\(718\) | 33.6336 | + | 40.9326i | 1.25519 | + | 1.52759i | ||||
\(719\) | 23.9165i | 0.891936i | 0.895049 | + | 0.445968i | \(0.147140\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2876 | 0.383130 | ||||||||
\(722\) | −8.63120 | + | 7.09210i | −0.321220 | + | 0.263941i | ||||
\(723\) | − | 37.1304i | − | 1.38089i | ||||||
\(724\) | −4.05983 | + | 20.5388i | −0.150882 | + | 0.763318i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 33.8803 | + | 41.2328i | 1.25742 | + | 1.53029i | ||||
\(727\) | 7.00140i | 0.259668i | 0.991536 | + | 0.129834i | \(0.0414444\pi\) | ||||
−0.991536 | + | 0.129834i | \(0.958556\pi\) | |||||||
\(728\) | 7.22270 | − | 3.87733i | 0.267691 | − | 0.143703i | ||||
\(729\) | −160.965 | −5.96167 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.2040 | −1.55884 | −0.779420 | − | 0.626502i | \(-0.784486\pi\) | ||||
−0.779420 | + | 0.626502i | \(0.784486\pi\) | |||||||
\(734\) | 20.1710 | + | 24.5485i | 0.744526 | + | 0.906100i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.2785 | + | 33.5219i | 0.378872 | + | 1.23563i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −99.0611 | + | 81.3968i | −3.64649 | + | 2.99626i | ||||
\(739\) | 54.1823i | 1.99313i | 0.0828332 | + | 0.996563i | \(0.473603\pi\) | ||||
−0.0828332 | + | 0.996563i | \(0.526397\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −64.1513 | −2.35666 | ||||||||
\(742\) | −10.3318 | − | 12.5740i | −0.379292 | − | 0.461605i | ||||
\(743\) | − | 33.1662i | − | 1.21675i | −0.793649 | − | 0.608376i | \(-0.791821\pi\) | ||
0.793649 | − | 0.608376i | \(-0.208179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 153.670i | − | 5.62249i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 43.0499i | − | 1.57091i | −0.618916 | − | 0.785457i | \(-0.712428\pi\) | ||
0.618916 | − | 0.785457i | \(-0.287572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 55.2247 | 2.01250 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.16953 | + | 31.2118i | −0.224384 | + | 1.13516i | ||||
\(757\) | −55.0208 | −1.99976 | −0.999882 | − | 0.0153878i | \(-0.995102\pi\) | ||||
−0.999882 | + | 0.0153878i | \(0.995102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 70.5222i | − | 2.55979i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.4220 | −1.90030 | −0.950148 | − | 0.311800i | \(-0.899068\pi\) | ||||
−0.950148 | + | 0.311800i | \(0.899068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.1727i | 0.585489i | ||||||||
\(764\) | −9.76662 | − | 1.93053i | −0.353344 | − | 0.0698443i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 38.6257 | − | 38.9979i | 1.39379 | − | 1.40722i | ||||
\(769\) | −51.9376 | −1.87292 | −0.936459 | − | 0.350776i | \(-0.885918\pi\) | ||||
−0.936459 | + | 0.350776i | \(0.885918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.0772i | 1.47936i | ||||||||
\(772\) | −3.91588 | + | 19.8105i | −0.140936 | + | 0.712996i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.33600 | + | 7.67123i | −0.334712 | + | 0.275027i | ||||
\(779\) | − | 53.6231i | − | 1.92125i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.5040 | − | 9.66971i | −0.839427 | − | 0.345347i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 55.7900i | − | 1.98870i | −0.106165 | − | 0.994349i | \(-0.533857\pi\) | ||
0.106165 | − | 0.994349i | \(-0.466143\pi\) | |||||||
\(788\) | −9.84785 | + | 49.8205i | −0.350815 | + | 1.77478i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.18793i | 0.326685i | ||||||||
\(792\) | −72.4748 | + | 38.9063i | −2.57528 | + | 1.38247i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.69512 | − | 0.730401i | −0.130970 | − | 0.0258884i | ||||
\(797\) | 30.0000 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321693\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321693\pi\) | |||||||
\(798\) | −12.8409 | − | 15.6276i | −0.454563 | − | 0.553210i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −27.0416 | + | 8.29156i | −0.956066 | + | 0.293151i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 20.2472i | − | 0.714510i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 109.592i | 3.85784i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.9669i | 1.78969i | 0.446377 | + | 0.894845i | \(0.352714\pi\) | ||||
−0.446377 | + | 0.894845i | \(0.647286\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −91.7130 | −3.21652 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −7.87931 | + | 6.47429i | −0.275494 | + | 0.226368i | ||||
\(819\) | − | 25.4143i | − | 0.888046i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.6333 | −0.755008 | −0.377504 | − | 0.926008i | \(-0.623217\pi\) | ||||
−0.377504 | + | 0.926008i | \(0.623217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.9872i | 1.74244i | 0.490890 | + | 0.871222i | \(0.336672\pi\) | ||||
−0.490890 | + | 0.871222i | \(0.663328\pi\) | |||||||
\(824\) | −31.8932 | + | 17.1211i | −1.11105 | + | 0.596441i | ||||
\(825\) | 56.8893 | 1.98063 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.1710i | − | 0.458000i | −0.973426 | − | 0.229000i | \(-0.926454\pi\) | ||
0.973426 | − | 0.229000i | \(-0.0735456\pi\) | |||||||
\(828\) | 106.637 | + | 21.0785i | 3.70588 | + | 0.732529i | ||||
\(829\) | −48.8155 | −1.69543 | −0.847716 | − | 0.530450i | \(-0.822023\pi\) | ||||
−0.847716 | + | 0.530450i | \(0.822023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.9387 | + | 24.0407i | −0.552577 | + | 0.833462i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.67124 | − | 33.7500i | 0.230730 | − | 1.16727i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.7126 | + | 44.6798i | 1.26822 | + | 1.54344i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 2.85318i | − | 0.0982686i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.84228i | − | 0.303824i | ||||||
\(848\) | 52.9565 | + | 21.7867i | 1.81853 | + | 0.748159i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.29993 | −0.147227 | −0.0736134 | − | 0.997287i | \(-0.523453\pi\) | ||||
−0.0736134 | + | 0.997287i | \(0.523453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 44.8248 | − | 36.8318i | 1.53029 | − | 1.25742i | ||||
\(859\) | 27.1083i | 0.924925i | 0.886639 | + | 0.462462i | \(0.153034\pi\) | ||||
−0.886639 | + | 0.462462i | \(0.846966\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 28.5113 | 0.971664 | ||||||||
\(862\) | −29.3033 | − | 35.6626i | −0.998074 | − | 1.21467i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −32.8176 | − | 107.029i | −1.11648 | − | 3.64122i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.8976 | − | 17.1712i | 0.710128 | − | 0.583499i | ||||
\(867\) | − | 58.3194i | − | 1.98063i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −26.9153 | − | 50.1379i | −0.911467 | − | 1.69788i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −35.1255 | + | 28.8620i | −1.18814 | + | 0.976270i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 41.0904 | + | 8.12220i | 1.38832 | + | 0.274424i | ||||
\(877\) | −35.9384 | −1.21355 | −0.606777 | − | 0.794872i | \(-0.707538\pi\) | ||||
−0.606777 | + | 0.794872i | \(0.707538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 74.2142i | 2.50318i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.65851 | 0.190640 | 0.0953201 | − | 0.995447i | \(-0.469613\pi\) | ||||
0.0953201 | + | 0.995447i | \(0.469613\pi\) | |||||||
\(882\) | −60.8775 | + | 50.0220i | −2.04985 | + | 1.68433i | ||||
\(883\) | − | 14.0583i | − | 0.473098i | −0.971620 | − | 0.236549i | \(-0.923984\pi\) | ||
0.971620 | − | 0.236549i | \(-0.0760164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.32329 | − | 4.04450i | −0.111648 | − | 0.135877i | ||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 137.918i | 4.62041i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −64.8082 | − | 78.8726i | −2.16751 | − | 2.63789i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.04684 | + | 0.929374i | −0.302234 | + | 0.0310482i | ||||
\(897\) | −76.6657 | −2.55979 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −17.0037 | + | 86.0224i | −0.566792 | + | 2.86741i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 30.7871 | + | 37.4684i | 1.02510 | + | 1.24756i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.2910 | − | 28.4841i | −0.508571 | − | 0.947368i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 74.5930 | − | 61.2917i | 2.47819 | − | 2.03628i | ||||
\(907\) | − | 59.8869i | − | 1.98851i | −0.107032 | − | 0.994256i | \(-0.534135\pi\) | ||
0.107032 | − | 0.994256i | \(-0.465865\pi\) | |||||||
\(908\) | 58.7130 | + | 11.6056i | 1.94846 | + | 0.385145i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 50.7904i | − | 1.68276i | −0.540444 | − | 0.841380i | \(-0.681744\pi\) | ||
0.540444 | − | 0.841380i | \(-0.318256\pi\) | |||||||
\(912\) | 65.8171 | + | 27.0777i | 2.17942 | + | 0.896631i | ||||
\(913\) | −58.1234 | −1.92360 | ||||||||
\(914\) | 23.9556 | − | 19.6839i | 0.792380 | − | 0.651084i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −68.2671 | −2.24948 | ||||||||
\(922\) | −46.8478 | + | 38.4940i | −1.54285 | + | 1.26773i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 17.9448 | + | 3.54709i | 0.590341 | + | 0.116691i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 112.222i | 3.68584i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 32.9538i | − | 1.08002i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 87.6887 | 2.87080 | ||||||||
\(934\) | −21.4728 | − | 26.1327i | −0.702611 | − | 0.855089i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 42.2956 | + | 78.7884i | 1.38247 | + | 2.57528i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 80.6567i | − | 2.63213i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0556 | 0.881988 | 0.440994 | − | 0.897510i | \(-0.354626\pi\) | ||||
0.440994 | + | 0.897510i | \(0.354626\pi\) | |||||||
\(942\) | −43.7469 | − | 53.2406i | −1.42535 | − | 1.73467i | ||||
\(943\) | − | 64.0837i | − | 2.08685i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0111 | −0.714510 | ||||||||
\(950\) | −23.2825 | − | 28.3352i | −0.755385 | − | 0.919316i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 137.162 | − | 112.704i | 4.44080 | − | 3.64892i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.4355 | + | 3.24875i | 0.531562 | + | 0.105072i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.95548 | − | 7.24791i | −0.192413 | − | 0.234169i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.19765 | − | 21.2360i | 0.135197 | − | 0.683965i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −15.3459 | − | 18.6762i | −0.493745 | − | 0.600895i | ||||
\(967\) | 57.8529i | 1.86042i | 0.367024 | + | 0.930211i | \(0.380377\pi\) | ||||
−0.367024 | + | 0.930211i | \(0.619623\pi\) | |||||||
\(968\) | 14.7157 | + | 27.4125i | 0.472982 | + | 0.881072i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.9194i | 0.671335i | 0.941981 | + | 0.335667i | \(0.108962\pi\) | ||||
−0.941981 | + | 0.335667i | \(0.891038\pi\) | |||||||
\(972\) | −163.410 | − | 32.3006i | −5.24137 | − | 1.03604i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 61.8451i | − | 1.98063i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −176.418 | −5.63261 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | −88.3899 | + | 47.4499i | −2.81777 | + | 1.51265i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.6901 | − | 7.25240i | −1.16727 | − | 0.230730i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 59.8666i | − | 1.90173i | −0.309613 | − | 0.950863i | \(-0.600199\pi\) | ||
0.309613 | − | 0.950863i | \(-0.399801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 23.3163 | − | 117.958i | 0.738804 | − | 3.73763i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 572.2.b.b.571.15 | yes | 20 | |
4.3 | odd | 2 | inner | 572.2.b.b.571.16 | yes | 20 | |
11.10 | odd | 2 | inner | 572.2.b.b.571.6 | yes | 20 | |
13.12 | even | 2 | inner | 572.2.b.b.571.6 | yes | 20 | |
44.43 | even | 2 | inner | 572.2.b.b.571.5 | ✓ | 20 | |
52.51 | odd | 2 | inner | 572.2.b.b.571.5 | ✓ | 20 | |
143.142 | odd | 2 | CM | 572.2.b.b.571.15 | yes | 20 | |
572.571 | even | 2 | inner | 572.2.b.b.571.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.b.b.571.5 | ✓ | 20 | 44.43 | even | 2 | inner | |
572.2.b.b.571.5 | ✓ | 20 | 52.51 | odd | 2 | inner | |
572.2.b.b.571.6 | yes | 20 | 11.10 | odd | 2 | inner | |
572.2.b.b.571.6 | yes | 20 | 13.12 | even | 2 | inner | |
572.2.b.b.571.15 | yes | 20 | 1.1 | even | 1 | trivial | |
572.2.b.b.571.15 | yes | 20 | 143.142 | odd | 2 | CM | |
572.2.b.b.571.16 | yes | 20 | 4.3 | odd | 2 | inner | |
572.2.b.b.571.16 | yes | 20 | 572.571 | even | 2 | inner |