Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1791,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.f (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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 448) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1791 |
Dual form | 1792.2.f.j.1791.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | + | 1.00000i | −0.925820 | + | 0.377964i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000i | 0.516398i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.89898i | − | 1.18818i | −0.804400 | − | 0.594089i | \(-0.797513\pi\) | ||
0.804400 | − | 0.594089i | \(-0.202487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24264 | −0.973329 | −0.486664 | − | 0.873589i | \(-0.661786\pi\) | ||||
−0.486664 | + | 0.873589i | \(0.661786\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.46410 | − | 1.41421i | 0.755929 | − | 0.308607i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.89898 | 0.879883 | 0.439941 | − | 0.898027i | \(-0.354999\pi\) | ||||
0.439941 | + | 0.898027i | \(0.354999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.89898i | − | 0.852803i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | + | 3.46410i | 0.239046 | + | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92820 | 1.13899 | 0.569495 | − | 0.821995i | \(-0.307139\pi\) | ||||
0.569495 | + | 0.821995i | \(0.307139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.00000i | − | 0.960769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.79796i | − | 1.53018i | −0.643921 | − | 0.765092i | \(-0.722693\pi\) | ||
0.643921 | − | 0.765092i | \(-0.277307\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421i | 0.210819i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.89898 | −0.714590 | −0.357295 | − | 0.933992i | \(-0.616301\pi\) | ||||
−0.357295 | + | 0.933992i | \(0.616301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.92820i | 0.970143i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.8564 | −1.90332 | −0.951662 | − | 0.307148i | \(-0.900625\pi\) | ||||
−0.951662 | + | 0.307148i | \(0.900625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.89898 | 0.660578 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.07107 | −0.920575 | −0.460287 | − | 0.887770i | \(-0.652254\pi\) | ||||
−0.460287 | + | 0.887770i | \(0.652254\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.24264i | − | 0.543214i | −0.962408 | − | 0.271607i | \(-0.912445\pi\) | ||
0.962408 | − | 0.271607i | \(-0.0875552\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.44949 | − | 1.00000i | 0.308607 | − | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.3923i | − | 1.26962i | −0.772667 | − | 0.634811i | \(-0.781078\pi\) | ||
0.772667 | − | 0.634811i | \(-0.218922\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.89898i | − | 0.573382i | −0.958023 | − | 0.286691i | \(-0.907445\pi\) | ||
0.958023 | − | 0.286691i | \(-0.0925553\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.24264 | −0.489898 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.46410 | − | 8.48528i | −0.394771 | − | 0.966988i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.0000i | − | 1.57512i | −0.616236 | − | 0.787562i | \(-0.711343\pi\) | ||
0.616236 | − | 0.787562i | \(-0.288657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.89949 | 1.08661 | 0.543305 | − | 0.839535i | \(-0.317173\pi\) | ||||
0.543305 | + | 0.839535i | \(0.317173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.92820 | −0.751469 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14.6969i | − | 1.55787i | −0.627103 | − | 0.778936i | \(-0.715760\pi\) | ||
0.627103 | − | 0.778936i | \(-0.284240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.24264 | − | 10.3923i | −0.444750 | − | 1.08941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000i | 0.615587i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.46410i | − | 0.348155i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.3848i | 1.82935i | 0.404186 | + | 0.914677i | \(0.367555\pi\) | ||||
−0.404186 | + | 0.914677i | \(0.632445\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | − | 4.89898i | −0.195180 | − | 0.478091i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 17.3205i | − | 1.67444i | −0.546869 | − | 0.837218i | \(-0.684180\pi\) | ||
0.546869 | − | 0.837218i | \(-0.315820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8564 | 1.32720 | 0.663602 | − | 0.748086i | \(-0.269027\pi\) | ||||
0.663602 | + | 0.748086i | \(0.269027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.79796 | −0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 4.24264i | − | 0.392232i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.89898 | + | 12.0000i | 0.449089 | + | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.8564i | 1.24939i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 4.89898i | − | 0.431331i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5563 | 1.35916 | 0.679582 | − | 0.733599i | \(-0.262161\pi\) | ||||
0.679582 | + | 0.733599i | \(0.262161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3923 | − | 4.24264i | 0.901127 | − | 0.367884i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.00000i | − | 0.688530i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.0000 | 1.53784 | 0.768922 | − | 0.639343i | \(-0.220793\pi\) | ||||
0.768922 | + | 0.639343i | \(0.220793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24264 | 0.359856 | 0.179928 | − | 0.983680i | \(-0.442414\pi\) | ||||
0.179928 | + | 0.983680i | \(0.442414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820 | 0.583460 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.6969 | −1.22902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.07107 | + | 6.92820i | −0.583212 | + | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.92820 | 0.567581 | 0.283790 | − | 0.958886i | \(-0.408408\pi\) | ||||
0.283790 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.00000i | − | 0.651031i | −0.945537 | − | 0.325515i | \(-0.894462\pi\) | ||
0.945537 | − | 0.325515i | \(-0.105538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.89898i | 0.396059i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 6.92820i | − | 0.556487i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.2132i | 1.69300i | 0.532390 | + | 0.846499i | \(0.321294\pi\) | ||||
−0.532390 | + | 0.846499i | \(0.678706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.5959 | 1.55406 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.92820 | −0.539360 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.79796 | −0.758189 | −0.379094 | − | 0.925358i | \(-0.623764\pi\) | ||||
−0.379094 | + | 0.925358i | \(0.623764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.24264 | 0.324443 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.07107i | − | 0.537603i | −0.963196 | − | 0.268802i | \(-0.913372\pi\) | ||
0.963196 | − | 0.268802i | \(-0.0866276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.34847 | + | 3.00000i | −0.555492 | + | 0.226779i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0000 | 0.751646 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.3205i | − | 1.29460i | −0.762237 | − | 0.647298i | \(-0.775899\pi\) | ||
0.762237 | − | 0.647298i | \(-0.224101\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.24264i | 0.315353i | 0.987491 | + | 0.157676i | \(0.0504003\pi\) | ||||
−0.987491 | + | 0.157676i | \(0.949600\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.79796i | − | 0.720360i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9706 | 1.24101 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.8564 | + | 5.65685i | −1.00791 | + | 0.411476i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 18.0000i | − | 1.30243i | −0.758891 | − | 0.651217i | \(-0.774259\pi\) | ||
0.758891 | − | 0.651217i | \(-0.225741\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.48528 | −0.607644 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.92820 | 0.493614 | 0.246807 | − | 0.969065i | \(-0.420619\pi\) | ||||
0.246807 | + | 0.969065i | \(0.420619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.79796 | −0.694559 | −0.347279 | − | 0.937762i | \(-0.612894\pi\) | ||||
−0.347279 | + | 0.937762i | \(0.612894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.6969i | 1.03664i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.8564 | −0.967773 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 14.6969i | − | 1.01661i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.3923i | − | 0.715436i | −0.933830 | − | 0.357718i | \(-0.883555\pi\) | ||
0.933830 | − | 0.357718i | \(-0.116445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.48528i | − | 0.581402i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.89898 | 0.334108 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0000 | + | 4.89898i | −0.814613 | + | 0.332564i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.92820i | 0.468165i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.7846 | 1.39812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.3939 | 1.96836 | 0.984180 | − | 0.177173i | \(-0.0566951\pi\) | ||||
0.984180 | + | 0.177173i | \(0.0566951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.89949 | −0.657053 | −0.328526 | − | 0.944495i | \(-0.606552\pi\) | ||||
−0.328526 | + | 0.944495i | \(0.606552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.2132i | − | 1.40181i | −0.713256 | − | 0.700904i | \(-0.752780\pi\) | ||
0.713256 | − | 0.700904i | \(-0.247220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.89898 | + | 12.0000i | 0.322329 | + | 0.789542i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.92820i | 0.451946i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.7990i | 1.28608i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6969i | 0.946713i | 0.880871 | + | 0.473357i | \(0.156958\pi\) | ||||
−0.880871 | + | 0.473357i | \(0.843042\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.92820 | − | 7.07107i | −0.442627 | − | 0.451754i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.0000i | − | 1.14531i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.0000 | −0.887214 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5563 | −0.981908 | −0.490954 | − | 0.871185i | \(-0.663352\pi\) | ||||
−0.490954 | + | 0.871185i | \(0.663352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.79796 | 0.613572 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.9706 | + | 6.92820i | −1.05450 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.0000i | − | 1.10993i | −0.831875 | − | 0.554964i | \(-0.812732\pi\) | ||
0.831875 | − | 0.554964i | \(-0.187268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.5959i | 1.20377i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.7846i | 1.27200i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.89949i | 0.603583i | 0.953374 | + | 0.301791i | \(0.0975846\pi\) | ||||
−0.953374 | + | 0.301791i | \(0.902415\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5959 | −1.19037 | −0.595184 | − | 0.803590i | \(-0.702921\pi\) | ||||
−0.595184 | + | 0.803590i | \(0.702921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.00000 | + | 14.6969i | 0.363137 | + | 0.889499i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3923i | 0.626680i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.8564 | 0.832551 | 0.416275 | − | 0.909239i | \(-0.363335\pi\) | ||||
0.416275 | + | 0.909239i | \(0.363335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.89898 | −0.293294 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7279 | 0.756596 | 0.378298 | − | 0.925684i | \(-0.376509\pi\) | ||||
0.378298 | + | 0.925684i | \(0.376509\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 8.48528i | − | 0.502625i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.79796 | + | 24.0000i | 0.578355 | + | 1.41668i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.92820i | 0.406138i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.07107i | 0.413096i | 0.978436 | + | 0.206548i | \(0.0662230\pi\) | ||||
−0.978436 | + | 0.206548i | \(0.933777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000i | 0.582223i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.5959i | 1.13707i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.46410 | − | 8.48528i | −0.199667 | − | 0.489083i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 26.0000i | − | 1.49366i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | −0.343559 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.24264 | 0.242140 | 0.121070 | − | 0.992644i | \(-0.461367\pi\) | ||||
0.121070 | + | 0.992644i | \(0.461367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.4949 | 1.38898 | 0.694489 | − | 0.719503i | \(-0.255630\pi\) | ||||
0.694489 | + | 0.719503i | \(0.255630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5959i | 1.10763i | 0.832641 | + | 0.553813i | \(0.186828\pi\) | ||||
−0.832641 | + | 0.553813i | \(0.813172\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.41421 | − | 3.46410i | −0.0796819 | − | 0.195180i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.92820 | −0.389127 | −0.194563 | − | 0.980890i | \(-0.562329\pi\) | ||||
−0.194563 | + | 0.980890i | \(0.562329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.4949i | 1.36717i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.7846i | 1.15649i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7279i | 0.706018i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.5959 | −1.08366 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | − | 4.89898i | 0.661581 | − | 0.270089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.46410i | − | 0.190404i | −0.995458 | − | 0.0952021i | \(-0.969650\pi\) | ||
0.995458 | − | 0.0952021i | \(-0.0303497\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.92820 | −0.379663 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.6969 | −0.802980 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0000 | −0.871576 | −0.435788 | − | 0.900049i | \(-0.643530\pi\) | ||||
−0.435788 | + | 0.900049i | \(0.643530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | + | 17.0000i | −0.396780 | + | 0.917914i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.46410i | 0.185963i | 0.995668 | + | 0.0929814i | \(0.0296397\pi\) | ||||
−0.995668 | + | 0.0929814i | \(0.970360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.24264i | − | 0.227103i | −0.993532 | − | 0.113552i | \(-0.963777\pi\) | ||
0.993532 | − | 0.113552i | \(-0.0362227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0000i | 1.28103i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.79796i | 0.521493i | 0.965407 | + | 0.260746i | \(0.0839686\pi\) | ||||
−0.965407 | + | 0.260746i | \(0.916031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.48528 | 0.450352 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.92820 | − | 16.9706i | −0.366679 | − | 0.898177i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41421 | 0.0742270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.92820 | −0.362639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.79796 | −0.511449 | −0.255725 | − | 0.966750i | \(-0.582314\pi\) | ||||
−0.255725 | + | 0.966750i | \(0.582314\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.79796i | 0.510061i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 33.9411 | − | 13.8564i | 1.76214 | − | 0.719389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8564 | −0.717458 | −0.358729 | − | 0.933442i | \(-0.616790\pi\) | ||||
−0.358729 | + | 0.933442i | \(0.616790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.0000i | 0.826236i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.46410i | − | 0.177939i | −0.996034 | − | 0.0889695i | \(-0.971643\pi\) | ||
0.996034 | − | 0.0889695i | \(-0.0283574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 22.6274i | − | 1.15924i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.89898 | −0.250326 | −0.125163 | − | 0.992136i | \(-0.539945\pi\) | ||||
−0.125163 | + | 0.992136i | \(0.539945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | + | 4.89898i | −0.611577 | + | 0.249675i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3.46410i | − | 0.176090i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.92820 | −0.351274 | −0.175637 | − | 0.984455i | \(-0.556198\pi\) | ||||
−0.175637 | + | 0.984455i | \(0.556198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.0000 | −1.10975 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.7990 | −0.996195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.24264i | − | 0.212932i | −0.994316 | − | 0.106466i | \(-0.966046\pi\) | ||
0.994316 | − | 0.106466i | \(-0.0339535\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.6969 | + | 6.00000i | −0.735767 | + | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | −0.599251 | −0.299626 | − | 0.954057i | \(-0.596862\pi\) | ||||
−0.299626 | + | 0.954057i | \(0.596862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.7846i | 1.03536i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.07107i | 0.351364i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000i | 1.18964i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.5959i | 0.968956i | 0.874804 | + | 0.484478i | \(0.160990\pi\) | ||||
−0.874804 | + | 0.484478i | \(0.839010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.4558 | −1.25564 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.3205 | − | 7.07107i | 0.852286 | − | 0.347945i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14.0000i | − | 0.687233i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.00000 | −0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.07107 | −0.345444 | −0.172722 | − | 0.984971i | \(-0.555256\pi\) | ||||
−0.172722 | + | 0.984971i | \(0.555256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7846 | −1.01298 | −0.506490 | − | 0.862246i | \(-0.669057\pi\) | ||||
−0.506490 | + | 0.862246i | \(0.669057\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.89898 | 0.238197 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 14.6969i | − | 0.712906i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.24264 | + | 10.3923i | 0.205316 | + | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.7846 | 1.00349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 24.0000i | − | 1.15604i | −0.816023 | − | 0.578020i | \(-0.803826\pi\) | ||
0.816023 | − | 0.578020i | \(-0.196174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2929i | 1.64801i | 0.566583 | + | 0.824005i | \(0.308265\pi\) | ||||
−0.566583 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.4949 | 1.16908 | 0.584539 | − | 0.811366i | \(-0.301275\pi\) | ||||
0.584539 | + | 0.811366i | \(0.301275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | + | 4.89898i | −0.238095 | + | 0.233285i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3923i | 0.493753i | 0.969047 | + | 0.246877i | \(0.0794043\pi\) | ||||
−0.969047 | + | 0.246877i | \(0.920596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.7846 | −0.985285 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.79796 | −0.463428 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.9411 | 1.59823 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3137i | 0.531564i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.6969 | + | 6.00000i | −0.689003 | + | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.0000 | −0.748448 | −0.374224 | − | 0.927338i | \(-0.622091\pi\) | ||||
−0.374224 | + | 0.927338i | \(0.622091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 27.7128i | − | 1.29352i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15.5563i | − | 0.724531i | −0.932075 | − | 0.362266i | \(-0.882003\pi\) | ||
0.932075 | − | 0.362266i | \(-0.117997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000i | 0.650635i | 0.945605 | + | 0.325318i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325318i | \(0.894529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.79796i | 0.454369i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.8701 | −1.24340 | −0.621699 | − | 0.783256i | \(-0.713557\pi\) | ||||
−0.621699 | + | 0.783256i | \(0.713557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3923 | + | 25.4558i | 0.479872 | + | 1.17544i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 30.0000i | − | 1.38233i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | −0.551761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.7279 | −0.583997 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.8564 | 0.634441 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.2929 | 1.56688 | 0.783440 | − | 0.621467i | \(-0.213463\pi\) | ||||
0.783440 | + | 0.621467i | \(0.213463\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.3939i | 1.34025i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.92820 | −0.314594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0000i | 0.725029i | 0.931978 | + | 0.362515i | \(0.118082\pi\) | ||||
−0.931978 | + | 0.362515i | \(0.881918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4.89898i | − | 0.221540i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 38.1051i | − | 1.71966i | −0.510581 | − | 0.859830i | \(-0.670569\pi\) | ||
0.510581 | − | 0.859830i | \(-0.329431\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.89898 | −0.220193 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | − | 14.6969i | −0.269137 | − | 0.659248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.2487i | − | 1.08552i | −0.839887 | − | 0.542761i | \(-0.817379\pi\) | ||
0.839887 | − | 0.542761i | \(-0.182621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8564 | 0.619059 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4949 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.0000 | 1.15698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.07107 | 0.314037 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.0416i | 1.06563i | 0.846233 | + | 0.532813i | \(0.178865\pi\) | ||||
−0.846233 | + | 0.532813i | \(0.821135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.89898 | + | 12.0000i | 0.216718 | + | 0.530849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0000 | −1.05963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.9706i | − | 0.746364i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.0000i | 0.438951i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.79796i | − | 0.429256i | −0.976696 | − | 0.214628i | \(-0.931146\pi\) | ||
0.976696 | − | 0.214628i | \(-0.0688540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.7279 | −0.556553 | −0.278277 | − | 0.960501i | \(-0.589763\pi\) | ||||
−0.278277 | + | 0.960501i | \(0.589763\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.3923 | − | 4.24264i | 0.453557 | − | 0.185164i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.0000i | − | 1.04546i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.07107 | 0.306858 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.5692 | 1.80056 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.4949 | −1.05901 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.4949i | 1.05703i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.9706 | + | 17.3205i | 0.730974 | + | 0.746047i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.6410 | 1.48933 | 0.744667 | − | 0.667436i | \(-0.232608\pi\) | ||||
0.744667 | + | 0.667436i | \(0.232608\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.00000i | − | 0.257485i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 19.5959i | − | 0.839397i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 24.2487i | − | 1.03680i | −0.855138 | − | 0.518400i | \(-0.826528\pi\) | ||
0.855138 | − | 0.518400i | \(-0.173472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.24264i | 0.181071i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0000 | + | 34.2929i | 0.595341 | + | 1.45828i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8564i | 0.588172i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.7128 | −1.17423 | −0.587115 | − | 0.809504i | \(-0.699736\pi\) | ||||
−0.587115 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6969 | −0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.5563 | −0.655622 | −0.327811 | − | 0.944743i | \(-0.606311\pi\) | ||||
−0.327811 | + | 0.944743i | \(0.606311\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.2474 | − | 5.00000i | 0.514344 | − | 0.209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.1051i | − | 1.59465i | −0.603550 | − | 0.797325i | \(-0.706248\pi\) | ||
0.603550 | − | 0.797325i | \(-0.293752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.4558i | 1.06343i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.65685 | 0.235091 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.2487 | + | 9.89949i | −1.00601 | + | 0.410700i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 48.0000i | − | 1.98796i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.5269 | 1.34253 | 0.671265 | − | 0.741218i | \(-0.265751\pi\) | ||||
0.671265 | + | 0.741218i | \(0.265751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.7846 | −0.856415 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.79796 | −0.403034 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 9.79796i | − | 0.402354i | −0.979555 | − | 0.201177i | \(-0.935523\pi\) | ||
0.979555 | − | 0.201177i | \(-0.0644766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.9706 | − | 6.92820i | 0.695725 | − | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.8564 | 0.567105 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 30.0000i | − | 1.22577i | −0.790173 | − | 0.612883i | \(-0.790010\pi\) | ||
0.790173 | − | 0.612883i | \(-0.209990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 4.89898i | − | 0.199834i | −0.994996 | − | 0.0999168i | \(-0.968142\pi\) | ||
0.994996 | − | 0.0999168i | \(-0.0318577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.3923i | 0.423207i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.41421i | 0.0574960i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.3939 | 1.19306 | 0.596530 | − | 0.802591i | \(-0.296546\pi\) | ||||
0.596530 | + | 0.802591i | \(0.296546\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 20.7846i | − | 0.840855i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.7846 | 0.839482 | 0.419741 | − | 0.907644i | \(-0.362121\pi\) | ||||
0.419741 | + | 0.907644i | \(0.362121\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.5959 | 0.790184 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0000 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.7279 | 0.511578 | 0.255789 | − | 0.966733i | \(-0.417665\pi\) | ||||
0.255789 | + | 0.966733i | \(0.417665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.6969 | + | 36.0000i | 0.588820 | + | 1.44231i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.7846i | 0.830057i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 33.9411i | − | 1.35332i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0000i | 1.35352i | 0.736204 | + | 0.676759i | \(0.236616\pi\) | ||||
−0.736204 | + | 0.676759i | \(0.763384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.6969i | 0.584151i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.6274 | 0.897942 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.7846 | + | 21.2132i | 0.823516 | + | 0.840498i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 6.00000i | − | 0.237356i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0000 | 0.473972 | 0.236986 | − | 0.971513i | \(-0.423841\pi\) | ||||
0.236986 | + | 0.971513i | \(0.423841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.1838 | −1.50582 | −0.752910 | − | 0.658123i | \(-0.771351\pi\) | ||||
−0.752910 | + | 0.658123i | \(0.771351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.92820 | −0.272798 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.3939 | −1.15559 | −0.577796 | − | 0.816181i | \(-0.696087\pi\) | ||||
−0.577796 | + | 0.816181i | \(0.696087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.4949i | − | 0.961509i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.9706 | − | 6.92820i | 0.665129 | − | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.92820 | 0.271122 | 0.135561 | − | 0.990769i | \(-0.456716\pi\) | ||||
0.135561 | + | 0.990769i | \(0.456716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 22.0000i | − | 0.859611i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.89898i | 0.191127i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2487i | 0.944596i | 0.881439 | + | 0.472298i | \(0.156575\pi\) | ||||
−0.881439 | + | 0.472298i | \(0.843425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 21.2132i | − | 0.825098i | −0.910935 | − | 0.412549i | \(-0.864639\pi\) | ||
0.910935 | − | 0.412549i | \(-0.135361\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.3939 | −1.14156 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.00000 | − | 14.6969i | −0.232670 | − | 0.569923i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −41.5692 | −1.60716 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6969 | 0.567369 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.9706 | 0.653197 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 41.0122i | − | 1.57623i | −0.615530 | − | 0.788113i | \(-0.711058\pi\) | ||
0.615530 | − | 0.788113i | \(-0.288942\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.89898 | + | 12.0000i | 0.188006 | + | 0.460518i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.0000 | 0.536481 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3923i | 0.397650i | 0.980035 | + | 0.198825i | \(0.0637126\pi\) | ||||
−0.980035 | + | 0.198825i | \(0.936287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 25.4558i | − | 0.972618i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.0000i | 1.14457i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 58.7878i | − | 2.23964i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.7279 | −0.484193 | −0.242096 | − | 0.970252i | \(-0.577835\pi\) | ||||
−0.242096 | + | 0.970252i | \(0.577835\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.46410 | + | 8.48528i | 0.131590 | + | 0.322329i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.00000i | − | 0.227593i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.0000 | −1.81813 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.48528 | 0.320943 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.6410 | −1.30837 | −0.654187 | − | 0.756333i | \(-0.726989\pi\) | ||||
−0.654187 | + | 0.756333i | \(0.726989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.3939 | −1.10861 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 9.79796i | − | 0.369012i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.3848 | − | 45.0333i | −0.691431 | − | 1.69365i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.7128 | −1.04078 | −0.520388 | − | 0.853930i | \(-0.674213\pi\) | ||||
−0.520388 | + | 0.853930i | \(0.674213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000i | 0.525041i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.7846i | 0.777300i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.89898 | 0.182701 | 0.0913506 | − | 0.995819i | \(-0.470882\pi\) | ||||
0.0913506 | + | 0.995819i | \(0.470882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 20.7846i | − | 0.772988i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5959 | −0.726772 | −0.363386 | − | 0.931639i | \(-0.618379\pi\) | ||||
−0.363386 | + | 0.931639i | \(0.618379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.9706 | 0.627679 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7279i | 0.470117i | 0.971981 | + | 0.235058i | \(0.0755281\pi\) | ||||
−0.971981 | + | 0.235058i | \(0.924472\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.79796 | + | 10.0000i | 0.361403 | + | 0.368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.0000 | 1.32608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.1769i | 1.14686i | 0.819254 | + | 0.573431i | \(0.194388\pi\) | ||||
−0.819254 | + | 0.573431i | \(0.805612\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.4558i | 0.935144i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.79796i | − | 0.358969i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.89949 | −0.362204 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3205 | + | 42.4264i | 0.632878 | + | 1.55023i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 8.00000i | − | 0.291924i | −0.989290 | − | 0.145962i | \(-0.953372\pi\) | ||
0.989290 | − | 0.145962i | \(-0.0466277\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.0000 | 0.801725 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.3137 | −0.411748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.6410 | −1.25905 | −0.629525 | − | 0.776981i | \(-0.716750\pi\) | ||||
−0.629525 | + | 0.776981i | \(0.716750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.5959i | − | 0.710351i | −0.934800 | − | 0.355176i | \(-0.884421\pi\) | ||
0.934800 | − | 0.355176i | \(-0.115579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.9411 | + | 13.8564i | −1.22875 | + | 0.501636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.92820 | 0.250490 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 30.0000i | − | 1.08324i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 24.4949i | − | 0.883309i | −0.897185 | − | 0.441654i | \(-0.854392\pi\) | ||
0.897185 | − | 0.441654i | \(-0.145608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 35.3553i | − | 1.27164i | −0.771836 | − | 0.635822i | \(-0.780661\pi\) | ||
0.771836 | − | 0.635822i | \(-0.219339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.6969 | 0.527930 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.0000 | − | 9.79796i | 0.860995 | − | 0.351500i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41.5692i | 1.48937i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.7846 | −0.743732 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0000 | 1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2132 | −0.756169 | −0.378085 | − | 0.925771i | \(-0.623417\pi\) | ||||
−0.378085 | + | 0.925771i | \(0.623417\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.4558i | 0.906252i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 27.7128i | − | 0.982872i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.5563i | 0.551034i | 0.961296 | + | 0.275517i | \(0.0888491\pi\) | ||||
−0.961296 | + | 0.275517i | \(0.911151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000i | 0.849059i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.6969i | 0.519291i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9706 | 0.598878 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 14.0000i | − | 0.492823i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.0000 | 1.68759 | 0.843795 | − | 0.536666i | \(-0.180316\pi\) | ||||
0.843795 | + | 0.536666i | \(0.180316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.1543 | −1.93673 | −0.968365 | − | 0.249537i | \(-0.919722\pi\) | ||||
−0.968365 | + | 0.249537i | \(0.919722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.7128 | 0.971931 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.89898 | 0.171604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.6969i | − | 0.514181i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.24264 | + | 10.3923i | 0.148250 | + | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0000i | 0.766872i | 0.923567 | + | 0.383436i | \(0.125259\pi\) | ||||
−0.923567 | + | 0.383436i | \(0.874741\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14.6969i | − | 0.511682i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 10.3923i | − | 0.361376i | −0.983540 | − | 0.180688i | \(-0.942168\pi\) | ||
0.983540 | − | 0.180688i | \(-0.0578324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 55.1543i | − | 1.91559i | −0.287454 | − | 0.957795i | \(-0.592809\pi\) | ||
0.287454 | − | 0.957795i | \(-0.407191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.5959 | −0.679775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.0000 | − | 24.4949i | −0.831551 | − | 0.848698i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.8564i | 0.479521i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.7128 | 0.957895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.9898 | −1.69132 | −0.845658 | − | 0.533726i | \(-0.820792\pi\) | ||||
−0.845658 | + | 0.533726i | \(0.820792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.48528 | −0.292249 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.07107i | 0.243252i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.44949 | − | 1.00000i | 0.0841655 | − | 0.0343604i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.0000 | −0.617758 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4.24264i | − | 0.145265i | −0.997359 | − | 0.0726326i | \(-0.976860\pi\) | ||
0.997359 | − | 0.0726326i | \(-0.0231401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.00000i | − | 0.205196i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 39.1918i | − | 1.33877i | −0.742917 | − | 0.669384i | \(-0.766558\pi\) | ||
0.742917 | − | 0.669384i | \(-0.233442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.6985 | 1.01330 | 0.506650 | − | 0.862152i | \(-0.330884\pi\) | ||||
0.506650 | + | 0.862152i | \(0.330884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8564 | − | 33.9411i | −0.472225 | − | 1.15671i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | −0.340010 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.89949 | 0.336204 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.4974 | 1.64516 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.0908 | 1.49396 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.89898i | 0.165805i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137 | + | 27.7128i | 0.382473 | + | 0.936864i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.92820 | −0.233949 | −0.116974 | − | 0.993135i | \(-0.537320\pi\) | ||||
−0.116974 | + | 0.993135i | \(0.537320\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 10.0000i | − | 0.337292i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.3939i | − | 0.990305i | −0.868806 | − | 0.495152i | \(-0.835112\pi\) | ||
0.868806 | − | 0.495152i | \(-0.164888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.2487i | 0.816034i | 0.912974 | + | 0.408017i | \(0.133780\pi\) | ||||
−0.912974 | + | 0.408017i | \(0.866220\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 14.1421i | − | 0.475383i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5959 | 0.657967 | 0.328983 | − | 0.944336i | \(-0.393294\pi\) | ||||
0.328983 | + | 0.944336i | \(0.393294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0000 | − | 39.1918i | −0.536623 | − | 1.31445i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 17.3205i | − | 0.580259i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.7846 | 0.695530 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.4949 | −0.818774 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.8823i | 2.26149i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.89898 | + | 12.0000i | 0.163028 | + | 0.399335i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | 0.199447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.3205i | − | 0.575118i | −0.957763 | − | 0.287559i | \(-0.907156\pi\) | ||
0.957763 | − | 0.287559i | \(-0.0928437\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 18.3848i | − | 0.609785i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.2929i | 1.13493i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.48528 | 0.280515 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.1051 | + | 15.5563i | −1.25834 | + | 0.513716i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.0000i | − | 1.12156i | −0.827966 | − | 0.560778i | \(-0.810502\pi\) | ||
0.827966 | − | 0.560778i | \(-0.189498\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | −0.197707 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.4558 | −0.837889 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.7846 | 0.683394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 53.8888i | − | 1.76803i | −0.467455 | − | 0.884017i | \(-0.654829\pi\) | ||
0.467455 | − | 0.884017i | \(-0.345171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.2132 | + | 20.7846i | −0.695235 | + | 0.681188i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.6410 | −1.13410 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 24.0000i | − | 0.784884i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.89898i | − | 0.160043i | −0.996793 | − | 0.0800213i | \(-0.974501\pi\) | ||
0.996793 | − | 0.0800213i | \(-0.0254988\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 27.7128i | − | 0.904373i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.41421i | − | 0.0461020i | −0.999734 | − | 0.0230510i | \(-0.992662\pi\) | ||
0.999734 | − | 0.0230510i | \(-0.00733802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | + | 19.5959i | 0.260240 | + | 0.637455i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2487i | 0.787977i | 0.919115 | + | 0.393989i | \(0.128905\pi\) | ||||
−0.919115 | + | 0.393989i | \(0.871095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.7846 | 0.674697 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.79796 | 0.317721 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.4558 | −0.823732 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.0908 | + | 18.0000i | −1.42377 | + | 0.581250i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.00000 | −0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.3205i | 0.558146i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.65685i | 0.182101i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 29.3939i | − | 0.944267i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.07107 | −0.226921 | −0.113461 | − | 0.993542i | \(-0.536194\pi\) | ||||
−0.113461 | + | 0.993542i | \(0.536194\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3923 | + | 4.24264i | −0.333162 | + | 0.136013i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 18.0000i | − | 0.576461i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.0000 | 0.959785 | 0.479893 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479893 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.9117 | 1.62714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.8564 | −0.442401 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.79796 | 0.312506 | 0.156253 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156253 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.79796i | − | 0.312189i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.9706 | + | 6.92820i | −0.540179 | + | 0.220527i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000i | 0.0635321i | 0.999495 | + | 0.0317660i | \(0.0101131\pi\) | ||||
−0.999495 | + | 0.0317660i | \(0.989887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.89898i | 0.155464i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.8564i | 0.439278i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.24264i | 0.134366i | 0.997741 | + | 0.0671829i | \(0.0214011\pi\) | ||||
−0.997741 | + | 0.0671829i | \(0.978599\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.1918 | 1.23997 |
(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 | 1792.2.f.j.1791.1 | 8 | ||
4.3 | odd | 2 | inner | 1792.2.f.j.1791.6 | 8 | ||
7.6 | odd | 2 | inner | 1792.2.f.j.1791.8 | 8 | ||
8.3 | odd | 2 | inner | 1792.2.f.j.1791.4 | 8 | ||
8.5 | even | 2 | inner | 1792.2.f.j.1791.7 | 8 | ||
16.3 | odd | 4 | 448.2.e.b.223.5 | yes | 8 | ||
16.5 | even | 4 | 448.2.e.b.223.8 | yes | 8 | ||
16.11 | odd | 4 | 448.2.e.b.223.3 | yes | 8 | ||
16.13 | even | 4 | 448.2.e.b.223.2 | yes | 8 | ||
28.27 | even | 2 | inner | 1792.2.f.j.1791.3 | 8 | ||
48.5 | odd | 4 | 4032.2.p.f.1567.3 | 8 | |||
48.11 | even | 4 | 4032.2.p.f.1567.2 | 8 | |||
48.29 | odd | 4 | 4032.2.p.f.1567.7 | 8 | |||
48.35 | even | 4 | 4032.2.p.f.1567.6 | 8 | |||
56.13 | odd | 2 | inner | 1792.2.f.j.1791.2 | 8 | ||
56.27 | even | 2 | inner | 1792.2.f.j.1791.5 | 8 | ||
112.13 | odd | 4 | 448.2.e.b.223.7 | yes | 8 | ||
112.27 | even | 4 | 448.2.e.b.223.6 | yes | 8 | ||
112.69 | odd | 4 | 448.2.e.b.223.1 | ✓ | 8 | ||
112.83 | even | 4 | 448.2.e.b.223.4 | yes | 8 | ||
336.83 | odd | 4 | 4032.2.p.f.1567.4 | 8 | |||
336.125 | even | 4 | 4032.2.p.f.1567.1 | 8 | |||
336.251 | odd | 4 | 4032.2.p.f.1567.8 | 8 | |||
336.293 | even | 4 | 4032.2.p.f.1567.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
448.2.e.b.223.1 | ✓ | 8 | 112.69 | odd | 4 | ||
448.2.e.b.223.2 | yes | 8 | 16.13 | even | 4 | ||
448.2.e.b.223.3 | yes | 8 | 16.11 | odd | 4 | ||
448.2.e.b.223.4 | yes | 8 | 112.83 | even | 4 | ||
448.2.e.b.223.5 | yes | 8 | 16.3 | odd | 4 | ||
448.2.e.b.223.6 | yes | 8 | 112.27 | even | 4 | ||
448.2.e.b.223.7 | yes | 8 | 112.13 | odd | 4 | ||
448.2.e.b.223.8 | yes | 8 | 16.5 | even | 4 | ||
1792.2.f.j.1791.1 | 8 | 1.1 | even | 1 | trivial | ||
1792.2.f.j.1791.2 | 8 | 56.13 | odd | 2 | inner | ||
1792.2.f.j.1791.3 | 8 | 28.27 | even | 2 | inner | ||
1792.2.f.j.1791.4 | 8 | 8.3 | odd | 2 | inner | ||
1792.2.f.j.1791.5 | 8 | 56.27 | even | 2 | inner | ||
1792.2.f.j.1791.6 | 8 | 4.3 | odd | 2 | inner | ||
1792.2.f.j.1791.7 | 8 | 8.5 | even | 2 | inner | ||
1792.2.f.j.1791.8 | 8 | 7.6 | odd | 2 | inner | ||
4032.2.p.f.1567.1 | 8 | 336.125 | even | 4 | |||
4032.2.p.f.1567.2 | 8 | 48.11 | even | 4 | |||
4032.2.p.f.1567.3 | 8 | 48.5 | odd | 4 | |||
4032.2.p.f.1567.4 | 8 | 336.83 | odd | 4 | |||
4032.2.p.f.1567.5 | 8 | 336.293 | even | 4 | |||
4032.2.p.f.1567.6 | 8 | 48.35 | even | 4 | |||
4032.2.p.f.1567.7 | 8 | 48.29 | odd | 4 | |||
4032.2.p.f.1567.8 | 8 | 336.251 | odd | 4 |