Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
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: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 21 x^{12} + 20 x^{11} + 167 x^{10} - 148 x^{9} - 627 x^{8} + 497 x^{7} + 1123 x^{6} - 745 x^{5} - 802 x^{4} + 386 x^{3} + 74 x^{2} - 15 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.69494\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.69494 | −1.19851 | −0.599253 | − | 0.800560i | \(-0.704536\pi\) | ||||
−0.599253 | + | 0.800560i | \(0.704536\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.872835 | 0.436418 | ||||||||
\(5\) | −1.13650 | −0.508256 | −0.254128 | − | 0.967171i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967171i | \(0.581789\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.14659 | 1.56726 | 0.783632 | − | 0.621225i | \(-0.213365\pi\) | ||||
0.783632 | + | 0.621225i | \(0.213365\pi\) | |||||||
\(8\) | 1.91048 | 0.675457 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.92630 | 0.609149 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.80864 | 0.778977 | 0.389488 | − | 0.921031i | \(-0.372652\pi\) | ||||
0.389488 | + | 0.921031i | \(0.372652\pi\) | |||||||
\(14\) | −7.02824 | −1.87838 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.98383 | −1.24596 | ||||||||
\(17\) | 0.763911 | 0.185276 | 0.0926379 | − | 0.995700i | \(-0.470470\pi\) | ||||
0.0926379 | + | 0.995700i | \(0.470470\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.34950 | 0.768428 | 0.384214 | − | 0.923244i | \(-0.374473\pi\) | ||||
0.384214 | + | 0.923244i | \(0.374473\pi\) | |||||||
\(20\) | −0.991974 | −0.221812 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.69494 | −0.361363 | ||||||||
\(23\) | −3.86313 | −0.805518 | −0.402759 | − | 0.915306i | \(-0.631949\pi\) | ||||
−0.402759 | + | 0.915306i | \(0.631949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.70838 | −0.741675 | ||||||||
\(26\) | −4.76049 | −0.933609 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.61929 | 0.683982 | ||||||||
\(29\) | −2.17513 | −0.403911 | −0.201955 | − | 0.979395i | \(-0.564730\pi\) | ||||
−0.201955 | + | 0.979395i | \(0.564730\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.15568 | 1.10559 | 0.552796 | − | 0.833317i | \(-0.313561\pi\) | ||||
0.552796 | + | 0.833317i | \(0.313561\pi\) | |||||||
\(32\) | 4.62635 | 0.817831 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.29479 | −0.222054 | ||||||||
\(35\) | −4.71258 | −0.796572 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.38312 | 0.556181 | 0.278091 | − | 0.960555i | \(-0.410298\pi\) | ||||
0.278091 | + | 0.960555i | \(0.410298\pi\) | |||||||
\(38\) | −5.67721 | −0.920965 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.17125 | −0.343305 | ||||||||
\(41\) | −1.67214 | −0.261144 | −0.130572 | − | 0.991439i | \(-0.541681\pi\) | ||||
−0.130572 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.23257 | 0.797959 | 0.398980 | − | 0.916960i | \(-0.369364\pi\) | ||||
0.398980 | + | 0.916960i | \(0.369364\pi\) | |||||||
\(44\) | 0.872835 | 0.131585 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.54779 | 0.965419 | ||||||||
\(47\) | 12.4466 | 1.81553 | 0.907764 | − | 0.419481i | \(-0.137788\pi\) | ||||
0.907764 | + | 0.419481i | \(0.137788\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.1942 | 1.45632 | ||||||||
\(50\) | 6.28549 | 0.888903 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.45148 | 0.339959 | ||||||||
\(53\) | −4.85562 | −0.666971 | −0.333485 | − | 0.942755i | \(-0.608225\pi\) | ||||
−0.333485 | + | 0.942755i | \(0.608225\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.13650 | −0.153245 | ||||||||
\(56\) | 7.92198 | 1.05862 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.68672 | 0.484090 | ||||||||
\(59\) | 11.2371 | 1.46295 | 0.731473 | − | 0.681871i | \(-0.238833\pi\) | ||||
0.731473 | + | 0.681871i | \(0.238833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −10.4335 | −1.32506 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.12626 | 0.265782 | ||||||||
\(65\) | −3.19201 | −0.395920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.11299 | 0.380313 | 0.190156 | − | 0.981754i | \(-0.439101\pi\) | ||||
0.190156 | + | 0.981754i | \(0.439101\pi\) | |||||||
\(68\) | 0.666769 | 0.0808576 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.98757 | 0.954697 | ||||||||
\(71\) | 0.313422 | 0.0371964 | 0.0185982 | − | 0.999827i | \(-0.494080\pi\) | ||||
0.0185982 | + | 0.999827i | \(0.494080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.11415 | 0.481525 | 0.240762 | − | 0.970584i | \(-0.422603\pi\) | ||||
0.240762 | + | 0.970584i | \(0.422603\pi\) | |||||||
\(74\) | −5.73420 | −0.666587 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.92356 | 0.335355 | ||||||||
\(77\) | 4.14659 | 0.472548 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.122521 | 0.0137846 | 0.00689232 | − | 0.999976i | \(-0.497806\pi\) | ||||
0.00689232 | + | 0.999976i | \(0.497806\pi\) | |||||||
\(80\) | 5.66410 | 0.633266 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.83418 | 0.312983 | ||||||||
\(83\) | 2.98302 | 0.327430 | 0.163715 | − | 0.986508i | \(-0.447652\pi\) | ||||
0.163715 | + | 0.986508i | \(0.447652\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.868182 | −0.0941676 | ||||||||
\(86\) | −8.86891 | −0.956359 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.91048 | 0.203658 | ||||||||
\(89\) | −12.3890 | −1.31323 | −0.656617 | − | 0.754224i | \(-0.728013\pi\) | ||||
−0.656617 | + | 0.754224i | \(0.728013\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.6463 | 1.22086 | ||||||||
\(92\) | −3.37187 | −0.351542 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.0963 | −2.17592 | ||||||||
\(95\) | −3.80669 | −0.390558 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.287224 | 0.0291632 | 0.0145816 | − | 0.999894i | \(-0.495358\pi\) | ||||
0.0145816 | + | 0.999894i | \(0.495358\pi\) | |||||||
\(98\) | −17.2786 | −1.74540 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.23680 | −0.323680 | ||||||||
\(101\) | −8.25985 | −0.821886 | −0.410943 | − | 0.911661i | \(-0.634800\pi\) | ||||
−0.410943 | + | 0.911661i | \(0.634800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1319 | 1.09686 | 0.548428 | − | 0.836198i | \(-0.315226\pi\) | ||||
0.548428 | + | 0.836198i | \(0.315226\pi\) | |||||||
\(104\) | 5.36586 | 0.526165 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.23000 | 0.799368 | ||||||||
\(107\) | −20.5662 | −1.98821 | −0.994104 | − | 0.108435i | \(-0.965416\pi\) | ||||
−0.994104 | + | 0.108435i | \(0.965416\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.42639 | −0.232406 | −0.116203 | − | 0.993225i | \(-0.537072\pi\) | ||||
−0.116203 | + | 0.993225i | \(0.537072\pi\) | |||||||
\(110\) | 1.92630 | 0.183665 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −20.6659 | −1.95274 | ||||||||
\(113\) | 0.194417 | 0.0182892 | 0.00914462 | − | 0.999958i | \(-0.497089\pi\) | ||||
0.00914462 | + | 0.999958i | \(0.497089\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.39043 | 0.409410 | ||||||||
\(116\) | −1.89853 | −0.176274 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.0462 | −1.75335 | ||||||||
\(119\) | 3.16763 | 0.290376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.69494 | −0.153453 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.37289 | 0.482500 | ||||||||
\(125\) | 9.89704 | 0.885218 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.09170 | −0.0968730 | −0.0484365 | − | 0.998826i | \(-0.515424\pi\) | ||||
−0.0484365 | + | 0.998826i | \(0.515424\pi\) | |||||||
\(128\) | −12.8566 | −1.13637 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.41028 | 0.474513 | ||||||||
\(131\) | 8.56374 | 0.748217 | 0.374109 | − | 0.927385i | \(-0.377949\pi\) | ||||
0.374109 | + | 0.927385i | \(0.377949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8890 | 1.20433 | ||||||||
\(134\) | −5.27635 | −0.455807 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.45944 | 0.125146 | ||||||||
\(137\) | 15.2173 | 1.30010 | 0.650049 | − | 0.759892i | \(-0.274748\pi\) | ||||
0.650049 | + | 0.759892i | \(0.274748\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.34342 | −0.622861 | −0.311430 | − | 0.950269i | \(-0.600808\pi\) | ||||
−0.311430 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(140\) | −4.11331 | −0.347638 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.531233 | −0.0445801 | ||||||||
\(143\) | 2.80864 | 0.234870 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.47202 | 0.205290 | ||||||||
\(146\) | −6.97325 | −0.577111 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.95291 | 0.242727 | ||||||||
\(149\) | −8.97409 | −0.735186 | −0.367593 | − | 0.929987i | \(-0.619818\pi\) | ||||
−0.367593 | + | 0.929987i | \(0.619818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.70128 | 0.463963 | 0.231982 | − | 0.972720i | \(-0.425479\pi\) | ||||
0.231982 | + | 0.972720i | \(0.425479\pi\) | |||||||
\(152\) | 6.39915 | 0.519040 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.02824 | −0.566352 | ||||||||
\(155\) | −6.99590 | −0.561924 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.592821 | −0.0473123 | −0.0236561 | − | 0.999720i | \(-0.507531\pi\) | ||||
−0.0236561 | + | 0.999720i | \(0.507531\pi\) | |||||||
\(158\) | −0.207665 | −0.0165210 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.25783 | −0.415668 | ||||||||
\(161\) | −16.0188 | −1.26246 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0035 | −1.56680 | −0.783398 | − | 0.621521i | \(-0.786515\pi\) | ||||
−0.783398 | + | 0.621521i | \(0.786515\pi\) | |||||||
\(164\) | −1.45950 | −0.113968 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.05606 | −0.392426 | ||||||||
\(167\) | −1.97988 | −0.153208 | −0.0766038 | − | 0.997062i | \(-0.524408\pi\) | ||||
−0.0766038 | + | 0.997062i | \(0.524408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.11154 | −0.393195 | ||||||||
\(170\) | 1.47152 | 0.112860 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.56717 | 0.348244 | ||||||||
\(173\) | 5.75321 | 0.437408 | 0.218704 | − | 0.975791i | \(-0.429817\pi\) | ||||
0.218704 | + | 0.975791i | \(0.429817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.3771 | −1.16240 | ||||||||
\(176\) | −4.98383 | −0.375670 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 20.9987 | 1.57392 | ||||||||
\(179\) | 21.2013 | 1.58466 | 0.792329 | − | 0.610095i | \(-0.208869\pi\) | ||||
0.792329 | + | 0.610095i | \(0.208869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2793 | −1.35869 | −0.679345 | − | 0.733819i | \(-0.737736\pi\) | ||||
−0.679345 | + | 0.733819i | \(0.737736\pi\) | |||||||
\(182\) | −19.7398 | −1.46321 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.38044 | −0.544093 | ||||||||
\(185\) | −3.84490 | −0.282683 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.763911 | 0.0558627 | ||||||||
\(188\) | 10.8639 | 0.792328 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.45213 | 0.468087 | ||||||||
\(191\) | 6.81813 | 0.493342 | 0.246671 | − | 0.969099i | \(-0.420663\pi\) | ||||
0.246671 | + | 0.969099i | \(0.420663\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.6061 | −1.84317 | −0.921583 | − | 0.388181i | \(-0.873104\pi\) | ||||
−0.921583 | + | 0.388181i | \(0.873104\pi\) | |||||||
\(194\) | −0.486828 | −0.0349522 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.89787 | 0.635562 | ||||||||
\(197\) | 4.60372 | 0.328002 | 0.164001 | − | 0.986460i | \(-0.447560\pi\) | ||||
0.164001 | + | 0.986460i | \(0.447560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.2809 | −0.728796 | −0.364398 | − | 0.931243i | \(-0.618725\pi\) | ||||
−0.364398 | + | 0.931243i | \(0.618725\pi\) | |||||||
\(200\) | −7.08478 | −0.500970 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.0000 | 0.985035 | ||||||||
\(203\) | −9.01936 | −0.633035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.90038 | 0.132728 | ||||||||
\(206\) | −18.8679 | −1.31459 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.9978 | −0.970572 | ||||||||
\(209\) | 3.34950 | 0.231690 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.2901 | 1.32798 | 0.663991 | − | 0.747740i | \(-0.268861\pi\) | ||||
0.663991 | + | 0.747740i | \(0.268861\pi\) | |||||||
\(212\) | −4.23816 | −0.291078 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 34.8585 | 2.38288 | ||||||||
\(215\) | −5.94680 | −0.405568 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.5251 | 1.73275 | ||||||||
\(218\) | 4.11259 | 0.278540 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.991974 | −0.0668789 | ||||||||
\(221\) | 2.14555 | 0.144325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7966 | 1.45961 | 0.729803 | − | 0.683657i | \(-0.239612\pi\) | ||||
0.729803 | + | 0.683657i | \(0.239612\pi\) | |||||||
\(224\) | 19.1836 | 1.28176 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.329526 | −0.0219198 | ||||||||
\(227\) | 19.0029 | 1.26127 | 0.630633 | − | 0.776081i | \(-0.282795\pi\) | ||||
0.630633 | + | 0.776081i | \(0.282795\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.4656 | −1.88106 | −0.940529 | − | 0.339713i | \(-0.889670\pi\) | ||||
−0.940529 | + | 0.339713i | \(0.889670\pi\) | |||||||
\(230\) | −7.44153 | −0.490680 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.15554 | −0.272824 | ||||||||
\(233\) | 7.38981 | 0.484123 | 0.242061 | − | 0.970261i | \(-0.422176\pi\) | ||||
0.242061 | + | 0.970261i | \(0.422176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.1456 | −0.922754 | ||||||||
\(236\) | 9.80813 | 0.638455 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.36895 | −0.348017 | ||||||||
\(239\) | −10.8094 | −0.699205 | −0.349602 | − | 0.936898i | \(-0.613683\pi\) | ||||
−0.349602 | + | 0.936898i | \(0.613683\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.6577 | −1.71718 | −0.858588 | − | 0.512666i | \(-0.828658\pi\) | ||||
−0.858588 | + | 0.512666i | \(0.828658\pi\) | |||||||
\(242\) | −1.69494 | −0.108955 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.872835 | 0.0558775 | ||||||||
\(245\) | −11.5857 | −0.740182 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.40754 | 0.598587 | ||||||||
\(248\) | 11.7603 | 0.746780 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.7749 | −1.06094 | ||||||||
\(251\) | −12.8841 | −0.813236 | −0.406618 | − | 0.913598i | \(-0.633292\pi\) | ||||
−0.406618 | + | 0.913598i | \(0.633292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.86313 | −0.242873 | ||||||||
\(254\) | 1.85038 | 0.116103 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.5387 | 1.09617 | ||||||||
\(257\) | 26.0777 | 1.62668 | 0.813341 | − | 0.581788i | \(-0.197647\pi\) | ||||
0.813341 | + | 0.581788i | \(0.197647\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.0284 | 0.871683 | ||||||||
\(260\) | −2.78610 | −0.172786 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.5151 | −0.896743 | ||||||||
\(263\) | 21.6443 | 1.33464 | 0.667322 | − | 0.744769i | \(-0.267441\pi\) | ||||
0.667322 | + | 0.744769i | \(0.267441\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.51839 | 0.338992 | ||||||||
\(266\) | −23.5411 | −1.44340 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.71713 | 0.165975 | ||||||||
\(269\) | 1.70348 | 0.103863 | 0.0519315 | − | 0.998651i | \(-0.483462\pi\) | ||||
0.0519315 | + | 0.998651i | \(0.483462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.2091 | 1.28836 | 0.644180 | − | 0.764874i | \(-0.277199\pi\) | ||||
0.644180 | + | 0.764874i | \(0.277199\pi\) | |||||||
\(272\) | −3.80720 | −0.230846 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.7924 | −1.55818 | ||||||||
\(275\) | −3.70838 | −0.223624 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.64693 | −0.279207 | −0.139603 | − | 0.990207i | \(-0.544583\pi\) | ||||
−0.139603 | + | 0.990207i | \(0.544583\pi\) | |||||||
\(278\) | 12.4467 | 0.746503 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.00330 | −0.538050 | ||||||||
\(281\) | 3.70914 | 0.221269 | 0.110634 | − | 0.993861i | \(-0.464712\pi\) | ||||
0.110634 | + | 0.993861i | \(0.464712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.52229 | 0.0904910 | 0.0452455 | − | 0.998976i | \(-0.485593\pi\) | ||||
0.0452455 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(284\) | 0.273566 | 0.0162331 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.76049 | −0.281494 | ||||||||
\(287\) | −6.93367 | −0.409281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4164 | −0.965673 | ||||||||
\(290\) | −4.18994 | −0.246042 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.59098 | 0.210146 | ||||||||
\(293\) | 25.9504 | 1.51604 | 0.758018 | − | 0.652234i | \(-0.226168\pi\) | ||||
0.758018 | + | 0.652234i | \(0.226168\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.7709 | −0.743551 | ||||||||
\(296\) | 6.46339 | 0.375677 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2106 | 0.881125 | ||||||||
\(299\) | −10.8501 | −0.627480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.6973 | 1.25061 | ||||||||
\(302\) | −9.66335 | −0.556063 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.6933 | −0.957428 | ||||||||
\(305\) | −1.13650 | −0.0650756 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7503 | 0.727700 | 0.363850 | − | 0.931458i | \(-0.381462\pi\) | ||||
0.363850 | + | 0.931458i | \(0.381462\pi\) | |||||||
\(308\) | 3.61929 | 0.206228 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.8577 | 0.673470 | ||||||||
\(311\) | −2.42241 | −0.137362 | −0.0686812 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686812 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.39019 | 0.0785779 | 0.0392890 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392890 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(314\) | 1.00480 | 0.0567040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.106940 | 0.00601586 | ||||||||
\(317\) | −4.56623 | −0.256465 | −0.128233 | − | 0.991744i | \(-0.540930\pi\) | ||||
−0.128233 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.17513 | −0.121784 | ||||||||
\(320\) | −2.41648 | −0.135085 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 27.1510 | 1.51307 | ||||||||
\(323\) | 2.55872 | 0.142371 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4155 | −0.577748 | ||||||||
\(326\) | 33.9048 | 1.87781 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.19459 | −0.176391 | ||||||||
\(329\) | 51.6111 | 2.84541 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.68359 | 0.477293 | 0.238647 | − | 0.971106i | \(-0.423296\pi\) | ||||
0.238647 | + | 0.971106i | \(0.423296\pi\) | |||||||
\(332\) | 2.60369 | 0.142896 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.35579 | 0.183620 | ||||||||
\(335\) | −3.53790 | −0.193296 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.3769 | −1.05553 | −0.527764 | − | 0.849391i | \(-0.676969\pi\) | ||||
−0.527764 | + | 0.849391i | \(0.676969\pi\) | |||||||
\(338\) | 8.66377 | 0.471247 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.757780 | −0.0410964 | ||||||||
\(341\) | 6.15568 | 0.333349 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2451 | 0.715168 | ||||||||
\(344\) | 9.99673 | 0.538987 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.75137 | −0.524237 | ||||||||
\(347\) | −12.5548 | −0.673978 | −0.336989 | − | 0.941509i | \(-0.609409\pi\) | ||||
−0.336989 | + | 0.941509i | \(0.609409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.5352 | 1.25981 | 0.629907 | − | 0.776671i | \(-0.283093\pi\) | ||||
0.629907 | + | 0.776671i | \(0.283093\pi\) | |||||||
\(350\) | 26.0634 | 1.39315 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.62635 | 0.246585 | ||||||||
\(353\) | 29.5091 | 1.57061 | 0.785306 | − | 0.619108i | \(-0.212506\pi\) | ||||
0.785306 | + | 0.619108i | \(0.212506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.356203 | −0.0189053 | ||||||||
\(356\) | −10.8136 | −0.573118 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −35.9350 | −1.89922 | ||||||||
\(359\) | 5.82428 | 0.307394 | 0.153697 | − | 0.988118i | \(-0.450882\pi\) | ||||
0.153697 | + | 0.988118i | \(0.450882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.78086 | −0.409519 | ||||||||
\(362\) | 30.9824 | 1.62840 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.1653 | 0.532806 | ||||||||
\(365\) | −4.67572 | −0.244738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.4023 | 1.69139 | 0.845693 | − | 0.533670i | \(-0.179188\pi\) | ||||
0.845693 | + | 0.533670i | \(0.179188\pi\) | |||||||
\(368\) | 19.2532 | 1.00364 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.51689 | 0.338797 | ||||||||
\(371\) | −20.1343 | −1.04532 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.55651 | 0.235927 | 0.117964 | − | 0.993018i | \(-0.462363\pi\) | ||||
0.117964 | + | 0.993018i | \(0.462363\pi\) | |||||||
\(374\) | −1.29479 | −0.0669518 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.7791 | 1.22631 | ||||||||
\(377\) | −6.10915 | −0.314637 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0481 | −1.33800 | −0.669001 | − | 0.743262i | \(-0.733278\pi\) | ||||
−0.669001 | + | 0.743262i | \(0.733278\pi\) | |||||||
\(380\) | −3.32261 | −0.170447 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.5563 | −0.591274 | ||||||||
\(383\) | −9.19798 | −0.469995 | −0.234997 | − | 0.971996i | \(-0.575508\pi\) | ||||
−0.234997 | + | 0.971996i | \(0.575508\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.71258 | −0.240176 | ||||||||
\(386\) | 43.4009 | 2.20905 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.250699 | 0.0127273 | ||||||||
\(389\) | −4.77997 | −0.242354 | −0.121177 | − | 0.992631i | \(-0.538667\pi\) | ||||
−0.121177 | + | 0.992631i | \(0.538667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.95109 | −0.149243 | ||||||||
\(392\) | 19.4759 | 0.983679 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.80306 | −0.393112 | ||||||||
\(395\) | −0.139244 | −0.00700613 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.984062 | −0.0493886 | −0.0246943 | − | 0.999695i | \(-0.507861\pi\) | ||||
−0.0246943 | + | 0.999695i | \(0.507861\pi\) | |||||||
\(398\) | 17.4256 | 0.873466 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.4819 | 0.924096 | ||||||||
\(401\) | −18.2690 | −0.912312 | −0.456156 | − | 0.889900i | \(-0.650774\pi\) | ||||
−0.456156 | + | 0.889900i | \(0.650774\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2891 | 0.861231 | ||||||||
\(404\) | −7.20949 | −0.358685 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.2873 | 0.758696 | ||||||||
\(407\) | 3.38312 | 0.167695 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.2832 | 1.44796 | 0.723981 | − | 0.689820i | \(-0.242310\pi\) | ||||
0.723981 | + | 0.689820i | \(0.242310\pi\) | |||||||
\(410\) | −3.22103 | −0.159075 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.71630 | 0.478688 | ||||||||
\(413\) | 46.5956 | 2.29282 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.39020 | −0.166418 | ||||||||
\(416\) | 12.9938 | 0.637071 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.67721 | −0.277681 | ||||||||
\(419\) | 30.2004 | 1.47539 | 0.737694 | − | 0.675135i | \(-0.235915\pi\) | ||||
0.737694 | + | 0.675135i | \(0.235915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.3462 | 1.28404 | 0.642018 | − | 0.766689i | \(-0.278097\pi\) | ||||
0.642018 | + | 0.766689i | \(0.278097\pi\) | |||||||
\(422\) | −32.6956 | −1.59160 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.27657 | −0.450510 | ||||||||
\(425\) | −2.83287 | −0.137414 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.14659 | 0.200668 | ||||||||
\(428\) | −17.9509 | −0.867689 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0795 | 0.486076 | ||||||||
\(431\) | −27.7478 | −1.33656 | −0.668282 | − | 0.743908i | \(-0.732970\pi\) | ||||
−0.668282 | + | 0.743908i | \(0.732970\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.30026 | −0.350828 | −0.175414 | − | 0.984495i | \(-0.556126\pi\) | ||||
−0.175414 | + | 0.984495i | \(0.556126\pi\) | |||||||
\(434\) | −43.2636 | −2.07672 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.11784 | −0.101426 | ||||||||
\(437\) | −12.9395 | −0.618982 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.66481 | 0.0794573 | 0.0397286 | − | 0.999211i | \(-0.487351\pi\) | ||||
0.0397286 | + | 0.999211i | \(0.487351\pi\) | |||||||
\(440\) | −2.17125 | −0.103510 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.63659 | −0.172975 | ||||||||
\(443\) | 2.28757 | 0.108686 | 0.0543428 | − | 0.998522i | \(-0.482694\pi\) | ||||
0.0543428 | + | 0.998522i | \(0.482694\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0801 | 0.667460 | ||||||||
\(446\) | −36.9440 | −1.74935 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.81671 | 0.416551 | ||||||||
\(449\) | 10.2005 | 0.481390 | 0.240695 | − | 0.970601i | \(-0.422625\pi\) | ||||
0.240695 | + | 0.970601i | \(0.422625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.67214 | −0.0787378 | ||||||||
\(452\) | 0.169694 | 0.00798174 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −32.2088 | −1.51163 | ||||||||
\(455\) | −13.2360 | −0.620511 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.8187 | −1.53520 | −0.767598 | − | 0.640932i | \(-0.778548\pi\) | ||||
−0.767598 | + | 0.640932i | \(0.778548\pi\) | |||||||
\(458\) | 48.2476 | 2.25446 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.83212 | 0.178674 | ||||||||
\(461\) | −17.3153 | −0.806455 | −0.403228 | − | 0.915100i | \(-0.632112\pi\) | ||||
−0.403228 | + | 0.915100i | \(0.632112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.6210 | −1.33013 | −0.665066 | − | 0.746785i | \(-0.731597\pi\) | ||||
−0.665066 | + | 0.746785i | \(0.731597\pi\) | |||||||
\(464\) | 10.8405 | 0.503256 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.5253 | −0.580224 | ||||||||
\(467\) | 16.1513 | 0.747393 | 0.373696 | − | 0.927551i | \(-0.378090\pi\) | ||||
0.373696 | + | 0.927551i | \(0.378090\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9083 | 0.596050 | ||||||||
\(470\) | 23.9759 | 1.10593 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.4683 | 0.988157 | ||||||||
\(473\) | 5.23257 | 0.240594 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.4212 | −0.569924 | ||||||||
\(476\) | 2.76482 | 0.126725 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.3214 | 0.838001 | ||||||||
\(479\) | −15.7906 | −0.721493 | −0.360747 | − | 0.932664i | \(-0.617478\pi\) | ||||
−0.360747 | + | 0.932664i | \(0.617478\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.50197 | 0.433252 | ||||||||
\(482\) | 45.1834 | 2.05805 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.872835 | 0.0396743 | ||||||||
\(485\) | −0.326429 | −0.0148224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.39301 | −0.335009 | −0.167505 | − | 0.985871i | \(-0.553571\pi\) | ||||
−0.167505 | + | 0.985871i | \(0.553571\pi\) | |||||||
\(488\) | 1.91048 | 0.0864834 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19.6371 | 0.887113 | ||||||||
\(491\) | 23.8693 | 1.07721 | 0.538604 | − | 0.842559i | \(-0.318952\pi\) | ||||
0.538604 | + | 0.842559i | \(0.318952\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.66160 | −0.0748349 | ||||||||
\(494\) | −15.9452 | −0.717411 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.6788 | −1.37752 | ||||||||
\(497\) | 1.29963 | 0.0582965 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.5180 | 1.14234 | 0.571172 | − | 0.820830i | \(-0.306489\pi\) | ||||
0.571172 | + | 0.820830i | \(0.306489\pi\) | |||||||
\(500\) | 8.63848 | 0.386325 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.8378 | 0.974669 | ||||||||
\(503\) | 0.804971 | 0.0358919 | 0.0179459 | − | 0.999839i | \(-0.494287\pi\) | ||||
0.0179459 | + | 0.999839i | \(0.494287\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.38729 | 0.417729 | ||||||||
\(506\) | 6.54779 | 0.291085 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.952877 | −0.0422771 | ||||||||
\(509\) | −33.1176 | −1.46791 | −0.733955 | − | 0.679198i | \(-0.762328\pi\) | ||||
−0.733955 | + | 0.679198i | \(0.762328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.0597 | 0.754677 | ||||||||
\(512\) | −4.01391 | −0.177391 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −44.2002 | −1.94959 | ||||||||
\(515\) | −12.6513 | −0.557485 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4466 | 0.547402 | ||||||||
\(518\) | −23.7774 | −1.04472 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.09827 | −0.267427 | ||||||||
\(521\) | −9.15916 | −0.401270 | −0.200635 | − | 0.979666i | \(-0.564301\pi\) | ||||
−0.200635 | + | 0.979666i | \(0.564301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3574 | 0.933893 | 0.466947 | − | 0.884285i | \(-0.345354\pi\) | ||||
0.466947 | + | 0.884285i | \(0.345354\pi\) | |||||||
\(524\) | 7.47473 | 0.326535 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −36.6858 | −1.59958 | ||||||||
\(527\) | 4.70239 | 0.204839 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.07623 | −0.351141 | ||||||||
\(530\) | −9.35337 | −0.406284 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.1228 | 0.525590 | ||||||||
\(533\) | −4.69643 | −0.203425 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3734 | 1.01052 | ||||||||
\(536\) | 5.94732 | 0.256885 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.88731 | −0.124481 | ||||||||
\(539\) | 10.1942 | 0.439096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.7604 | −1.06453 | −0.532266 | − | 0.846577i | \(-0.678659\pi\) | ||||
−0.532266 | + | 0.846577i | \(0.678659\pi\) | |||||||
\(542\) | −35.9482 | −1.54411 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.53412 | 0.151524 | ||||||||
\(545\) | 2.75758 | 0.118122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.04043 | 0.0872427 | 0.0436213 | − | 0.999048i | \(-0.486110\pi\) | ||||
0.0436213 | + | 0.999048i | \(0.486110\pi\) | |||||||
\(548\) | 13.2822 | 0.567386 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.28549 | 0.268014 | ||||||||
\(551\) | −7.28558 | −0.310376 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.508042 | 0.0216042 | ||||||||
\(554\) | 7.87628 | 0.334631 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.40960 | −0.271827 | ||||||||
\(557\) | 6.92621 | 0.293473 | 0.146737 | − | 0.989176i | \(-0.453123\pi\) | ||||
0.146737 | + | 0.989176i | \(0.453123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6964 | 0.621592 | ||||||||
\(560\) | 23.4867 | 0.992495 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.28679 | −0.265192 | ||||||||
\(563\) | −24.0659 | −1.01426 | −0.507128 | − | 0.861871i | \(-0.669293\pi\) | ||||
−0.507128 | + | 0.861871i | \(0.669293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.220954 | −0.00929562 | ||||||||
\(566\) | −2.58020 | −0.108454 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.598787 | 0.0251245 | ||||||||
\(569\) | 10.8199 | 0.453594 | 0.226797 | − | 0.973942i | \(-0.427175\pi\) | ||||
0.226797 | + | 0.973942i | \(0.427175\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.3189 | 0.975867 | 0.487933 | − | 0.872881i | \(-0.337751\pi\) | ||||
0.487933 | + | 0.872881i | \(0.337751\pi\) | |||||||
\(572\) | 2.45148 | 0.102502 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.7522 | 0.490526 | ||||||||
\(575\) | 14.3259 | 0.597433 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.0741 | 0.794066 | 0.397033 | − | 0.917804i | \(-0.370040\pi\) | ||||
0.397033 | + | 0.917804i | \(0.370040\pi\) | |||||||
\(578\) | 27.8249 | 1.15737 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.15767 | 0.0895923 | ||||||||
\(581\) | 12.3694 | 0.513168 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.85562 | −0.201099 | ||||||||
\(584\) | 7.86001 | 0.325249 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.9844 | −1.81698 | ||||||||
\(587\) | 19.9932 | 0.825206 | 0.412603 | − | 0.910911i | \(-0.364620\pi\) | ||||
0.412603 | + | 0.910911i | \(0.364620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.6184 | 0.849568 | ||||||||
\(590\) | 21.6460 | 0.891151 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.8609 | −0.692978 | ||||||||
\(593\) | −20.8462 | −0.856052 | −0.428026 | − | 0.903766i | \(-0.640791\pi\) | ||||
−0.428026 | + | 0.903766i | \(0.640791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.60000 | −0.147585 | ||||||||
\(596\) | −7.83290 | −0.320848 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.3904 | 0.752039 | ||||||||
\(599\) | 35.7082 | 1.45900 | 0.729498 | − | 0.683983i | \(-0.239754\pi\) | ||||
0.729498 | + | 0.683983i | \(0.239754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.3646 | −1.03464 | −0.517322 | − | 0.855791i | \(-0.673071\pi\) | ||||
−0.517322 | + | 0.855791i | \(0.673071\pi\) | |||||||
\(602\) | −36.7758 | −1.49887 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.97628 | 0.202482 | ||||||||
\(605\) | −1.13650 | −0.0462051 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.9208 | 1.29562 | 0.647812 | − | 0.761800i | \(-0.275684\pi\) | ||||
0.647812 | + | 0.761800i | \(0.275684\pi\) | |||||||
\(608\) | 15.4959 | 0.628444 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.92630 | 0.0779935 | ||||||||
\(611\) | 34.9581 | 1.41425 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.6456 | 0.510751 | 0.255376 | − | 0.966842i | \(-0.417801\pi\) | ||||
0.255376 | + | 0.966842i | \(0.417801\pi\) | |||||||
\(614\) | −21.6111 | −0.872153 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.92198 | 0.319186 | ||||||||
\(617\) | 11.8467 | 0.476930 | 0.238465 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238465 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.81776 | 0.233835 | 0.116918 | − | 0.993142i | \(-0.462699\pi\) | ||||
0.116918 | + | 0.993142i | \(0.462699\pi\) | |||||||
\(620\) | −6.10627 | −0.245234 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.10585 | 0.164630 | ||||||||
\(623\) | −51.3722 | −2.05818 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.29394 | 0.291758 | ||||||||
\(626\) | −2.35629 | −0.0941762 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.517435 | −0.0206479 | ||||||||
\(629\) | 2.58440 | 0.103047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.1087 | 1.11899 | 0.559495 | − | 0.828834i | \(-0.310995\pi\) | ||||
0.559495 | + | 0.828834i | \(0.310995\pi\) | |||||||
\(632\) | 0.234073 | 0.00931093 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.73951 | 0.307375 | ||||||||
\(635\) | 1.24072 | 0.0492363 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.6319 | 1.13444 | ||||||||
\(638\) | 3.68672 | 0.145959 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.6115 | 0.577568 | ||||||||
\(641\) | 17.8256 | 0.704069 | 0.352034 | − | 0.935987i | \(-0.385490\pi\) | ||||
0.352034 | + | 0.935987i | \(0.385490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.3216 | −0.840842 | −0.420421 | − | 0.907329i | \(-0.638118\pi\) | ||||
−0.420421 | + | 0.907329i | \(0.638118\pi\) | |||||||
\(644\) | −13.9818 | −0.550960 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.33689 | −0.170633 | ||||||||
\(647\) | 37.4930 | 1.47400 | 0.737000 | − | 0.675893i | \(-0.236242\pi\) | ||||
0.737000 | + | 0.675893i | \(0.236242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2371 | 0.441095 | ||||||||
\(650\) | 17.6537 | 0.692435 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.4598 | −0.683777 | ||||||||
\(653\) | −26.0148 | −1.01804 | −0.509018 | − | 0.860756i | \(-0.669991\pi\) | ||||
−0.509018 | + | 0.860756i | \(0.669991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.73266 | −0.380286 | ||||||||
\(656\) | 8.33364 | 0.325374 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −87.4779 | −3.41024 | ||||||||
\(659\) | 1.69718 | 0.0661127 | 0.0330564 | − | 0.999453i | \(-0.489476\pi\) | ||||
0.0330564 | + | 0.999453i | \(0.489476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7729 | 1.11914 | 0.559569 | − | 0.828784i | \(-0.310967\pi\) | ||||
0.559569 | + | 0.828784i | \(0.310967\pi\) | |||||||
\(662\) | −14.7182 | −0.572039 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.69901 | 0.221165 | ||||||||
\(665\) | −15.7848 | −0.612108 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.40280 | 0.325358 | ||||||||
\(668\) | −1.72811 | −0.0668625 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.99655 | 0.231667 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.1045 | −1.19899 | −0.599496 | − | 0.800378i | \(-0.704632\pi\) | ||||
−0.599496 | + | 0.800378i | \(0.704632\pi\) | |||||||
\(674\) | 32.8428 | 1.26506 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.46153 | −0.171597 | ||||||||
\(677\) | −24.6673 | −0.948043 | −0.474021 | − | 0.880513i | \(-0.657198\pi\) | ||||
−0.474021 | + | 0.880513i | \(0.657198\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.19100 | 0.0457064 | ||||||||
\(680\) | −1.65865 | −0.0636062 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.4335 | −0.399520 | ||||||||
\(683\) | −42.6506 | −1.63198 | −0.815990 | − | 0.578066i | \(-0.803807\pi\) | ||||
−0.815990 | + | 0.578066i | \(0.803807\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.2944 | −0.660783 | ||||||||
\(686\) | −22.4497 | −0.857133 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.0782 | −0.994223 | ||||||||
\(689\) | −13.6377 | −0.519555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0177 | −0.495218 | −0.247609 | − | 0.968860i | \(-0.579645\pi\) | ||||
−0.247609 | + | 0.968860i | \(0.579645\pi\) | |||||||
\(692\) | 5.02160 | 0.190893 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.2797 | 0.807767 | ||||||||
\(695\) | 8.34577 | 0.316573 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.27736 | −0.0483836 | ||||||||
\(698\) | −39.8909 | −1.50989 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.4217 | −0.507292 | ||||||||
\(701\) | −28.0409 | −1.05909 | −0.529545 | − | 0.848282i | \(-0.677638\pi\) | ||||
−0.529545 | + | 0.848282i | \(0.677638\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3318 | 0.427385 | ||||||||
\(704\) | 2.12626 | 0.0801363 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −50.0163 | −1.88239 | ||||||||
\(707\) | −34.2502 | −1.28811 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.5510 | −0.959587 | −0.479794 | − | 0.877381i | \(-0.659288\pi\) | ||||
−0.479794 | + | 0.877381i | \(0.659288\pi\) | |||||||
\(710\) | 0.603744 | 0.0226581 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.6690 | −0.887033 | ||||||||
\(713\) | −23.7802 | −0.890575 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.19201 | −0.119374 | ||||||||
\(716\) | 18.5052 | 0.691572 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.87182 | −0.368413 | ||||||||
\(719\) | −29.5599 | −1.10240 | −0.551200 | − | 0.834373i | \(-0.685830\pi\) | ||||
−0.551200 | + | 0.834373i | \(0.685830\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.1594 | 1.71906 | ||||||||
\(722\) | 13.1881 | 0.490811 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.9548 | −0.592956 | ||||||||
\(725\) | 8.06619 | 0.299571 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.5039 | 1.72473 | 0.862367 | − | 0.506285i | \(-0.168981\pi\) | ||||
0.862367 | + | 0.506285i | \(0.168981\pi\) | |||||||
\(728\) | 22.2500 | 0.824640 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.92508 | 0.293320 | ||||||||
\(731\) | 3.99722 | 0.147843 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.3793 | 1.12209 | 0.561043 | − | 0.827787i | \(-0.310400\pi\) | ||||
0.561043 | + | 0.827787i | \(0.310400\pi\) | |||||||
\(734\) | −54.9201 | −2.02714 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.8722 | −0.658777 | ||||||||
\(737\) | 3.11299 | 0.114669 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5413 | 0.902765 | 0.451382 | − | 0.892331i | \(-0.350931\pi\) | ||||
0.451382 | + | 0.892331i | \(0.350931\pi\) | |||||||
\(740\) | −3.35597 | −0.123368 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 34.1264 | 1.25282 | ||||||||
\(743\) | 24.7861 | 0.909313 | 0.454657 | − | 0.890667i | \(-0.349762\pi\) | ||||
0.454657 | + | 0.890667i | \(0.349762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.1990 | 0.373663 | ||||||||
\(746\) | −7.72304 | −0.282760 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.666769 | 0.0243795 | ||||||||
\(749\) | −85.2795 | −3.11605 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7265 | 0.865793 | 0.432897 | − | 0.901444i | \(-0.357491\pi\) | ||||
0.432897 | + | 0.901444i | \(0.357491\pi\) | |||||||
\(752\) | −62.0319 | −2.26207 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.3547 | 0.377095 | ||||||||
\(755\) | −6.47948 | −0.235812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6491 | −0.459739 | −0.229869 | − | 0.973222i | \(-0.573830\pi\) | ||||
−0.229869 | + | 0.973222i | \(0.573830\pi\) | |||||||
\(758\) | 44.1501 | 1.60360 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.27261 | −0.263805 | ||||||||
\(761\) | 14.7959 | 0.536352 | 0.268176 | − | 0.963370i | \(-0.413579\pi\) | ||||
0.268176 | + | 0.963370i | \(0.413579\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0612 | −0.364241 | ||||||||
\(764\) | 5.95110 | 0.215303 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.5901 | 0.563292 | ||||||||
\(767\) | 31.5610 | 1.13960 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.1700 | 0.907652 | 0.453826 | − | 0.891090i | \(-0.350059\pi\) | ||||
0.453826 | + | 0.891090i | \(0.350059\pi\) | |||||||
\(770\) | 7.98757 | 0.287852 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.3499 | −0.804390 | ||||||||
\(773\) | 23.2571 | 0.836500 | 0.418250 | − | 0.908332i | \(-0.362644\pi\) | ||||
0.418250 | + | 0.908332i | \(0.362644\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.8276 | −0.819991 | ||||||||
\(776\) | 0.548736 | 0.0196985 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.10178 | 0.290463 | ||||||||
\(779\) | −5.60082 | −0.200670 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.313422 | 0.0112151 | ||||||||
\(782\) | 5.00193 | 0.178869 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −50.8062 | −1.81451 | ||||||||
\(785\) | 0.673739 | 0.0240468 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.9096 | 1.24439 | 0.622196 | − | 0.782862i | \(-0.286241\pi\) | ||||
0.622196 | + | 0.782862i | \(0.286241\pi\) | |||||||
\(788\) | 4.01829 | 0.143146 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.236011 | 0.00839689 | ||||||||
\(791\) | 0.806168 | 0.0286641 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.80864 | 0.0997378 | ||||||||
\(794\) | 1.66793 | 0.0591926 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.97355 | −0.318059 | ||||||||
\(797\) | −24.0098 | −0.850472 | −0.425236 | − | 0.905082i | \(-0.639809\pi\) | ||||
−0.425236 | + | 0.905082i | \(0.639809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.50812 | 0.336373 | ||||||||
\(800\) | −17.1562 | −0.606565 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.9650 | 1.09341 | ||||||||
\(803\) | 4.11415 | 0.145185 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.2053 | 0.641653 | ||||||||
\(806\) | −29.3040 | −1.03219 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.7803 | −0.555149 | ||||||||
\(809\) | 50.4476 | 1.77364 | 0.886822 | − | 0.462112i | \(-0.152908\pi\) | ||||
0.886822 | + | 0.462112i | \(0.152908\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.5727 | −1.10867 | −0.554334 | − | 0.832295i | \(-0.687027\pi\) | ||||
−0.554334 | + | 0.832295i | \(0.687027\pi\) | |||||||
\(812\) | −7.87241 | −0.276268 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.73420 | −0.200984 | ||||||||
\(815\) | 22.7339 | 0.796334 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.5265 | 0.613174 | ||||||||
\(818\) | −49.6334 | −1.73539 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.65872 | 0.0579249 | ||||||||
\(821\) | −5.36610 | −0.187278 | −0.0936390 | − | 0.995606i | \(-0.529850\pi\) | ||||
−0.0936390 | + | 0.995606i | \(0.529850\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.2346 | −1.19334 | −0.596671 | − | 0.802486i | \(-0.703510\pi\) | ||||
−0.596671 | + | 0.802486i | \(0.703510\pi\) | |||||||
\(824\) | 21.2672 | 0.740880 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −78.9770 | −2.74796 | ||||||||
\(827\) | −27.0655 | −0.941159 | −0.470579 | − | 0.882358i | \(-0.655955\pi\) | ||||
−0.470579 | + | 0.882358i | \(0.655955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.45949 | −0.293810 | −0.146905 | − | 0.989151i | \(-0.546931\pi\) | ||||
−0.146905 | + | 0.989151i | \(0.546931\pi\) | |||||||
\(830\) | 5.74619 | 0.199453 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.97189 | 0.207038 | ||||||||
\(833\) | 7.78748 | 0.269820 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.25013 | 0.0778688 | ||||||||
\(836\) | 2.92356 | 0.101113 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −51.1881 | −1.76826 | ||||||||
\(839\) | 41.7580 | 1.44165 | 0.720824 | − | 0.693119i | \(-0.243764\pi\) | ||||
0.720824 | + | 0.693119i | \(0.243764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2688 | −0.836856 | ||||||||
\(842\) | −44.6554 | −1.53893 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.8370 | 0.579555 | ||||||||
\(845\) | 5.80924 | 0.199844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.14659 | 0.142479 | ||||||||
\(848\) | 24.1996 | 0.831017 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.80156 | 0.164692 | ||||||||
\(851\) | −13.0694 | −0.448014 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.48751 | 0.222128 | 0.111064 | − | 0.993813i | \(-0.464574\pi\) | ||||
0.111064 | + | 0.993813i | \(0.464574\pi\) | |||||||
\(854\) | −7.02824 | −0.240501 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −39.2913 | −1.34295 | ||||||||
\(857\) | 53.2173 | 1.81787 | 0.908933 | − | 0.416941i | \(-0.136898\pi\) | ||||
0.908933 | + | 0.416941i | \(0.136898\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.5457 | 1.86107 | 0.930537 | − | 0.366198i | \(-0.119341\pi\) | ||||
0.930537 | + | 0.366198i | \(0.119341\pi\) | |||||||
\(860\) | −5.19057 | −0.176997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 47.0310 | 1.60188 | ||||||||
\(863\) | −9.97813 | −0.339660 | −0.169830 | − | 0.985473i | \(-0.554322\pi\) | ||||
−0.169830 | + | 0.985473i | \(0.554322\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.53850 | −0.222316 | ||||||||
\(866\) | 12.3735 | 0.420469 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.2792 | 0.756205 | ||||||||
\(869\) | 0.122521 | 0.00415622 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.74328 | 0.296255 | ||||||||
\(872\) | −4.63557 | −0.156980 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.9318 | 0.741854 | ||||||||
\(875\) | 41.0390 | 1.38737 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.1582 | 0.613159 | 0.306580 | − | 0.951845i | \(-0.400815\pi\) | ||||
0.306580 | + | 0.951845i | \(0.400815\pi\) | |||||||
\(878\) | −2.82177 | −0.0952300 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.66410 | 0.190937 | ||||||||
\(881\) | 26.6452 | 0.897700 | 0.448850 | − | 0.893607i | \(-0.351834\pi\) | ||||
0.448850 | + | 0.893607i | \(0.351834\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.9254 | −0.367668 | −0.183834 | − | 0.982957i | \(-0.558851\pi\) | ||||
−0.183834 | + | 0.982957i | \(0.558851\pi\) | |||||||
\(884\) | 1.87271 | 0.0629862 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.87730 | −0.130260 | ||||||||
\(887\) | 34.3580 | 1.15363 | 0.576814 | − | 0.816875i | \(-0.304296\pi\) | ||||
0.576814 | + | 0.816875i | \(0.304296\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.52685 | −0.151826 | ||||||||
\(890\) | −23.8649 | −0.799955 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.0248 | 0.636998 | ||||||||
\(893\) | 41.6900 | 1.39510 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0952 | −0.805412 | ||||||||
\(896\) | −53.3110 | −1.78099 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2892 | −0.576949 | ||||||||
\(899\) | −13.3894 | −0.446561 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.70926 | −0.123573 | ||||||||
\(902\) | 2.83418 | 0.0943678 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.371430 | 0.0123536 | ||||||||
\(905\) | 20.7743 | 0.690563 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.294342 | −0.00977345 | −0.00488673 | − | 0.999988i | \(-0.501555\pi\) | ||||
−0.00488673 | + | 0.999988i | \(0.501555\pi\) | |||||||
\(908\) | 16.5864 | 0.550438 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.4342 | 0.743687 | ||||||||
\(911\) | 5.06741 | 0.167891 | 0.0839454 | − | 0.996470i | \(-0.473248\pi\) | ||||
0.0839454 | + | 0.996470i | \(0.473248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.98302 | 0.0987237 | ||||||||
\(914\) | 55.6259 | 1.83994 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.8458 | −0.820927 | ||||||||
\(917\) | 35.5103 | 1.17265 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.35956 | −0.0448476 | −0.0224238 | − | 0.999749i | \(-0.507138\pi\) | ||||
−0.0224238 | + | 0.999749i | \(0.507138\pi\) | |||||||
\(920\) | 8.38784 | 0.276539 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.3485 | 0.966542 | ||||||||
\(923\) | 0.880290 | 0.0289751 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.5459 | −0.412506 | ||||||||
\(926\) | 48.5110 | 1.59417 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.0629 | −0.330331 | ||||||||
\(929\) | −28.0140 | −0.919111 | −0.459555 | − | 0.888149i | \(-0.651991\pi\) | ||||
−0.459555 | + | 0.888149i | \(0.651991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.1455 | 1.11907 | ||||||||
\(932\) | 6.45009 | 0.211280 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.3755 | −0.895755 | ||||||||
\(935\) | −0.868182 | −0.0283926 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.1476 | −0.984879 | −0.492439 | − | 0.870347i | \(-0.663895\pi\) | ||||
−0.492439 | + | 0.870347i | \(0.663895\pi\) | |||||||
\(938\) | −21.8789 | −0.714370 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.3467 | −0.402706 | ||||||||
\(941\) | 38.8303 | 1.26583 | 0.632916 | − | 0.774221i | \(-0.281858\pi\) | ||||
0.632916 | + | 0.774221i | \(0.281858\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.45968 | 0.210356 | ||||||||
\(944\) | −56.0038 | −1.82277 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.86891 | −0.288353 | ||||||||
\(947\) | −8.12694 | −0.264090 | −0.132045 | − | 0.991244i | \(-0.542154\pi\) | ||||
−0.132045 | + | 0.991244i | \(0.542154\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.5552 | 0.375097 | ||||||||
\(950\) | 21.0532 | 0.683057 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.05169 | 0.196136 | ||||||||
\(953\) | 15.8810 | 0.514436 | 0.257218 | − | 0.966353i | \(-0.417194\pi\) | ||||
0.257218 | + | 0.966353i | \(0.417194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.74877 | −0.250744 | ||||||||
\(956\) | −9.43486 | −0.305145 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.7643 | 0.864714 | ||||||||
\(959\) | 63.0997 | 2.03760 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.89236 | 0.222334 | ||||||||
\(962\) | −16.1053 | −0.519256 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.2678 | −0.749406 | ||||||||
\(965\) | 29.1012 | 0.936801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.2586 | −0.394209 | −0.197104 | − | 0.980383i | \(-0.563154\pi\) | ||||
−0.197104 | + | 0.980383i | \(0.563154\pi\) | |||||||
\(968\) | 1.91048 | 0.0614052 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.553278 | 0.0177647 | ||||||||
\(971\) | 31.0824 | 0.997482 | 0.498741 | − | 0.866751i | \(-0.333796\pi\) | ||||
0.498741 | + | 0.866751i | \(0.333796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.4502 | −0.976187 | ||||||||
\(974\) | 12.5307 | 0.401511 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.98383 | −0.159528 | ||||||||
\(977\) | 33.1624 | 1.06096 | 0.530480 | − | 0.847697i | \(-0.322012\pi\) | ||||
0.530480 | + | 0.847697i | \(0.322012\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.3890 | −0.395955 | ||||||||
\(980\) | −10.1124 | −0.323029 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40.4572 | −1.29104 | ||||||||
\(983\) | 15.8218 | 0.504638 | 0.252319 | − | 0.967644i | \(-0.418807\pi\) | ||||
0.252319 | + | 0.967644i | \(0.418807\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.23212 | −0.166709 | ||||||||
\(986\) | 2.81633 | 0.0896901 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.21123 | 0.261234 | ||||||||
\(989\) | −20.2141 | −0.642771 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.275528 | −0.00875245 | −0.00437623 | − | 0.999990i | \(-0.501393\pi\) | ||||
−0.00437623 | + | 0.999990i | \(0.501393\pi\) | |||||||
\(992\) | 28.4783 | 0.904187 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.20281 | −0.0698687 | ||||||||
\(995\) | 11.6842 | 0.370415 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.5754 | 1.44339 | 0.721694 | − | 0.692212i | \(-0.243364\pi\) | ||||
0.721694 | + | 0.692212i | \(0.243364\pi\) | |||||||
\(998\) | −43.2516 | −1.36911 | ||||||||
\(999\) | 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 | 6039.2.a.j.1.4 | 14 | ||
3.2 | odd | 2 | 2013.2.a.h.1.11 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.h.1.11 | ✓ | 14 | 3.2 | odd | 2 | ||
6039.2.a.j.1.4 | 14 | 1.1 | even | 1 | trivial |