Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.89723 | −1.67271 | −0.836357 | − | 0.548185i | \(-0.815319\pi\) | ||||
−0.836357 | + | 0.548185i | \(0.815319\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.96349 | −0.878101 | −0.439051 | − | 0.898462i | \(-0.644685\pi\) | ||||
−0.439051 | + | 0.898462i | \(0.644685\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82850 | −1.06907 | −0.534537 | − | 0.845145i | \(-0.679514\pi\) | ||||
−0.534537 | + | 0.845145i | \(0.679514\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.39392 | 1.79797 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.91397 | 1.78313 | 0.891564 | − | 0.452895i | \(-0.149609\pi\) | ||||
0.891564 | + | 0.452895i | \(0.149609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.24542 | −1.45482 | −0.727409 | − | 0.686204i | \(-0.759276\pi\) | ||||
−0.727409 | + | 0.686204i | \(0.759276\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.68869 | 1.46881 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.885173 | −0.214686 | −0.107343 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107343 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.74515 | 1.54744 | 0.773722 | − | 0.633526i | \(-0.218393\pi\) | ||||
0.773722 | + | 0.633526i | \(0.218393\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.19481 | 1.78825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.73298 | −1.19541 | −0.597704 | − | 0.801717i | \(-0.703920\pi\) | ||||
−0.597704 | + | 0.801717i | \(0.703920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.14469 | −0.228938 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.93574 | −1.33478 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.96134 | −1.84977 | −0.924887 | − | 0.380242i | \(-0.875841\pi\) | ||||
−0.924887 | + | 0.380242i | \(0.875841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.549277 | −0.0986530 | −0.0493265 | − | 0.998783i | \(-0.515707\pi\) | ||||
−0.0493265 | + | 0.998783i | \(0.515707\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.1341 | −2.98266 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.55375 | 0.938754 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.03248 | 0.991733 | 0.495867 | − | 0.868399i | \(-0.334851\pi\) | ||||
0.495867 | + | 0.868399i | \(0.334851\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.1972 | 2.43350 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.81883 | 0.440228 | 0.220114 | − | 0.975474i | \(-0.429357\pi\) | ||||
0.220114 | + | 0.975474i | \(0.429357\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4268 | −1.74257 | −0.871286 | − | 0.490775i | \(-0.836714\pi\) | ||||
−0.871286 | + | 0.490775i | \(0.836714\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.5909 | −1.57880 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.25534 | 1.20416 | 0.602082 | − | 0.798434i | \(-0.294338\pi\) | ||||
0.602082 | + | 0.798434i | \(0.294338\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00042 | 0.142918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.56455 | 0.359108 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.66698 | −0.641059 | −0.320529 | − | 0.947239i | \(-0.603861\pi\) | ||||
−0.320529 | + | 0.947239i | \(0.603861\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.6120 | −1.56577 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19.5422 | −2.58843 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.78874 | 0.232874 | 0.116437 | − | 0.993198i | \(-0.462853\pi\) | ||||
0.116437 | + | 0.993198i | \(0.462853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.68018 | −0.983346 | −0.491673 | − | 0.870780i | \(-0.663614\pi\) | ||||
−0.491673 | + | 0.870780i | \(0.663614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.2567 | −1.92217 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.2994 | 1.27748 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.96915 | 0.362739 | 0.181370 | − | 0.983415i | \(-0.441947\pi\) | ||||
0.181370 | + | 0.983415i | \(0.441947\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.6097 | 1.99958 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7082 | 1.86422 | 0.932109 | − | 0.362178i | \(-0.117967\pi\) | ||||
0.932109 | + | 0.362178i | \(0.117967\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8478 | 1.26964 | 0.634818 | − | 0.772662i | \(-0.281075\pi\) | ||||
0.634818 | + | 0.772662i | \(0.281075\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.31643 | 0.382949 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.7277 | −1.90629 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.2472 | 1.82796 | 0.913979 | − | 0.405761i | \(-0.132994\pi\) | ||||
0.913979 | + | 0.405761i | \(0.132994\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.91265 | 0.434739 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.57081 | 1.05053 | 0.525266 | − | 0.850938i | \(-0.323966\pi\) | ||||
0.525266 | + | 0.850938i | \(0.323966\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73803 | 0.188516 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.8603 | 3.09414 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.66435 | 0.812419 | 0.406209 | − | 0.913780i | \(-0.366850\pi\) | ||||
0.406209 | + | 0.913780i | \(0.366850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.8367 | 1.55531 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.59138 | 0.165018 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.2441 | −1.35881 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.26689 | −0.230167 | −0.115084 | − | 0.993356i | \(-0.536714\pi\) | ||||
−0.115084 | + | 0.993356i | \(0.536714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.8995 | 3.20602 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.21332 | 0.319737 | 0.159868 | − | 0.987138i | \(-0.448893\pi\) | ||||
0.159868 | + | 0.987138i | \(0.448893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8095 | 1.26216 | 0.631078 | − | 0.775720i | \(-0.282613\pi\) | ||||
0.631078 | + | 0.775720i | \(0.282613\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.0905 | −1.57027 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.94467 | −0.478019 | −0.239009 | − | 0.971017i | \(-0.576823\pi\) | ||||
−0.239009 | + | 0.971017i | \(0.576823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2598 | 1.65318 | 0.826592 | − | 0.562801i | \(-0.190276\pi\) | ||||
0.826592 | + | 0.562801i | \(0.190276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.4775 | −1.65889 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.43103 | 0.604980 | 0.302490 | − | 0.953153i | \(-0.402182\pi\) | ||||
0.302490 | + | 0.953153i | \(0.402182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.2567 | 1.04969 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.2934 | −2.61573 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.50371 | 0.229515 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.9750 | 2.17955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.16680 | −0.736376 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0651 | 1.07913 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7812 | −1.48909 | −0.744545 | − | 0.667572i | \(-0.767334\pi\) | ||||
−0.744545 | + | 0.667572i | \(0.767334\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 33.1061 | 2.91483 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2727 | −0.897532 | −0.448766 | − | 0.893649i | \(-0.648136\pi\) | ||||
−0.448766 | + | 0.893649i | \(0.648136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.0787 | −1.65433 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.6183 | 1.17208 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.5903 | −1.07566 | −0.537830 | − | 0.843053i | \(-0.680756\pi\) | ||||
−0.537830 | + | 0.843053i | \(0.680756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2390 | −0.868458 | −0.434229 | − | 0.900803i | \(-0.642979\pi\) | ||||
−0.434229 | + | 0.900803i | \(0.642979\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.9176 | −2.01422 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.0213 | −2.59413 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.5590 | 1.62429 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.89845 | −0.239060 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.9960 | −0.982752 | −0.491376 | − | 0.870948i | \(-0.663506\pi\) | ||||
−0.491376 | + | 0.870948i | \(0.663506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.2519 | −1.56670 | −0.783350 | − | 0.621580i | \(-0.786491\pi\) | ||||
−0.783350 | + | 0.621580i | \(0.786491\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.77455 | −0.386000 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.07850 | 0.0866273 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.60624 | 0.607044 | 0.303522 | − | 0.952824i | \(-0.401837\pi\) | ||||
0.303522 | + | 0.952824i | \(0.401837\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.5213 | 1.07231 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.2157 | 1.27798 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.9299 | 1.24772 | 0.623861 | − | 0.781535i | \(-0.285563\pi\) | ||||
0.623861 | + | 0.781535i | \(0.285563\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 33.6427 | 2.61908 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.36948 | −0.105973 | −0.0529867 | − | 0.998595i | \(-0.516874\pi\) | ||||
−0.0529867 | + | 0.998595i | \(0.516874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.5145 | 1.11650 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 36.3828 | 2.78226 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3098 | 0.783837 | 0.391918 | − | 0.920000i | \(-0.371812\pi\) | ||||
0.391918 | + | 0.920000i | \(0.371812\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.23776 | 0.244752 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.18239 | −0.389533 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.59185 | −0.268468 | −0.134234 | − | 0.990950i | \(-0.542857\pi\) | ||||
−0.134234 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4691 | −0.926821 | −0.463410 | − | 0.886144i | \(-0.653374\pi\) | ||||
−0.463410 | + | 0.886144i | \(0.653374\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 22.2512 | 1.64486 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.8447 | −0.870842 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.23488 | −0.382812 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.6178 | 1.42698 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.7753 | −1.43089 | −0.715445 | − | 0.698669i | \(-0.753776\pi\) | ||||
−0.715445 | + | 0.698669i | \(0.753776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.12365 | 0.584753 | 0.292376 | − | 0.956303i | \(-0.405554\pi\) | ||||
0.292376 | + | 0.956303i | \(0.405554\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29.8396 | −2.13686 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.6046 | −1.25427 | −0.627137 | − | 0.778909i | \(-0.715774\pi\) | ||||
−0.627137 | + | 0.778909i | \(0.715774\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7180 | 0.830665 | 0.415332 | − | 0.909670i | \(-0.363665\pi\) | ||||
0.415332 | + | 0.909670i | \(0.363665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.60229 | −0.606759 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.1757 | 1.97754 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.53476 | −0.386565 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30.9232 | −2.14931 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 39.8906 | 2.75929 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0254 | 1.03439 | 0.517194 | − | 0.855868i | \(-0.326976\pi\) | ||||
0.517194 | + | 0.855868i | \(0.326976\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −45.5102 | −3.11831 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.4365 | 1.53015 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.55363 | 0.105467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.4285 | −2.12374 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.64311 | 0.312329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.49435 | 0.300964 | 0.150482 | − | 0.988613i | \(-0.451917\pi\) | ||||
0.150482 | + | 0.988613i | \(0.451917\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.17438 | −0.411625 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.92460 | 0.525974 | 0.262987 | − | 0.964799i | \(-0.415292\pi\) | ||||
0.262987 | + | 0.964799i | \(0.415292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.8508 | 1.77435 | 0.887174 | − | 0.461434i | \(-0.152665\pi\) | ||||
0.887174 | + | 0.461434i | \(0.152665\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 48.4639 | 3.18869 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1047 | 1.05505 | 0.527527 | − | 0.849538i | \(-0.323119\pi\) | ||||
0.527527 | + | 0.849538i | \(0.323119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.2093 | −1.05738 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −47.0720 | −3.05765 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.556383 | 0.0359894 | 0.0179947 | − | 0.999838i | \(-0.494272\pi\) | ||||
0.0179947 | + | 0.999838i | \(0.494272\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.7226 | −1.52811 | −0.764055 | − | 0.645151i | \(-0.776794\pi\) | ||||
−0.764055 | + | 0.645151i | \(0.776794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.47140 | 0.607590 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.96433 | −0.125496 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.3812 | −2.25125 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.7288 | −1.75724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.95962 | −0.628646 | −0.314323 | − | 0.949316i | \(-0.601777\pi\) | ||||
−0.314323 | + | 0.949316i | \(0.601777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.9046 | −2.13157 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.03547 | −0.315333 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.5503 | 1.34427 | 0.672136 | − | 0.740428i | \(-0.265377\pi\) | ||||
0.672136 | + | 0.740428i | \(0.265377\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.0629 | −1.06024 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −53.7307 | −3.32585 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.8835 | 1.16440 | 0.582202 | − | 0.813044i | \(-0.302191\pi\) | ||||
0.582202 | + | 0.813044i | \(0.302191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.16359 | 0.562915 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.2053 | −1.35895 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.0557 | −1.16185 | −0.580925 | − | 0.813957i | \(-0.697309\pi\) | ||||
−0.580925 | + | 0.813957i | \(0.697309\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.9458 | 1.51535 | 0.757673 | − | 0.652634i | \(-0.226336\pi\) | ||||
0.757673 | + | 0.652634i | \(0.226336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.9853 | −2.60159 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.76967 | −0.408226 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2851 | −1.21881 | −0.609406 | − | 0.792858i | \(-0.708592\pi\) | ||||
−0.609406 | + | 0.792858i | \(0.708592\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.96276 | −0.177376 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5942 | −0.989927 | −0.494963 | − | 0.868914i | \(-0.664819\pi\) | ||||
−0.494963 | + | 0.868914i | \(0.664819\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.44632 | −0.0859745 | −0.0429873 | − | 0.999076i | \(-0.513687\pi\) | ||||
−0.0429873 | + | 0.999076i | \(0.513687\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38.3710 | 2.27290 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.97308 | −0.470636 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2165 | −0.953910 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.56768 | 0.385004 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.8511 | −1.62708 | −0.813538 | − | 0.581512i | \(-0.802461\pi\) | ||||
−0.813538 | + | 0.581512i | \(0.802461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.51218 | −0.204487 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −41.0178 | −2.38009 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.0719 | 1.73910 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.3208 | 1.86294 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.30970 | −0.534829 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.0800 | 0.863477 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.60883 | −0.320113 | −0.160057 | − | 0.987108i | \(-0.551168\pi\) | ||||
−0.160057 | + | 0.987108i | \(0.551168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.1120 | −2.11123 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.62958 | 0.205814 | 0.102907 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102907 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3094 | 1.76971 | 0.884856 | − | 0.465865i | \(-0.154257\pi\) | ||||
0.884856 | + | 0.465865i | \(0.154257\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.9565 | 1.68786 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.0319 | −1.68676 | −0.843379 | − | 0.537320i | \(-0.819437\pi\) | ||||
−0.843379 | + | 0.537320i | \(0.819437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −58.9110 | −3.29838 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.3258 | 0.799589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.97062 | −0.332214 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00439 | 0.333064 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −50.0054 | −2.76531 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.3502 | −1.28734 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.3224 | −1.50178 | −0.750888 | − | 0.660429i | \(-0.770374\pi\) | ||||
−0.750888 | + | 0.660429i | \(0.770374\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.5387 | 1.78311 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.82990 | −0.318522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0173 | −0.763573 | −0.381787 | − | 0.924251i | \(-0.624691\pi\) | ||||
−0.381787 | + | 0.924251i | \(0.624691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.6321 | −1.01196 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.24840 | −0.175911 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9698 | 0.916284 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −32.6131 | −1.75583 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.56304 | 0.191274 | 0.0956371 | − | 0.995416i | \(-0.469511\pi\) | ||||
0.0956371 | + | 0.995416i | \(0.469511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.10170 | −0.219559 | −0.109779 | − | 0.993956i | \(-0.535014\pi\) | ||||
−0.109779 | + | 0.993956i | \(0.535014\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.3809 | 1.94187 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.81928 | 0.0968303 | 0.0484152 | − | 0.998827i | \(-0.484583\pi\) | ||||
0.0484152 | + | 0.998827i | \(0.484583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.8429 | −1.63697 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.25382 | −0.383913 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.6082 | 0.929326 | 0.464663 | − | 0.885488i | \(-0.346175\pi\) | ||||
0.464663 | + | 0.885488i | \(0.346175\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4970 | 1.39458 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −69.4610 | −3.64576 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.2995 | −1.11487 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.0930 | −1.46644 | −0.733220 | − | 0.679991i | \(-0.761984\pi\) | ||||
−0.733220 | + | 0.679991i | \(0.761984\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.2046 | 0.791519 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.2006 | 0.685339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.09615 | −0.212091 | −0.106045 | − | 0.994361i | \(-0.533819\pi\) | ||||
−0.106045 | + | 0.994361i | \(0.533819\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.9552 | −1.80508 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 52.2514 | 2.69109 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.3145 | −1.45442 | −0.727209 | − | 0.686416i | \(-0.759183\pi\) | ||||
−0.727209 | + | 0.686416i | \(0.759183\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.6189 | 2.49082 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.05496 | 0.207199 | 0.103599 | − | 0.994619i | \(-0.466964\pi\) | ||||
0.103599 | + | 0.994619i | \(0.466964\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.8447 | 1.67392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −61.6354 | −3.13310 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4208 | −0.731164 | −0.365582 | − | 0.930779i | \(-0.619130\pi\) | ||||
−0.365582 | + | 0.930779i | \(0.619130\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.07467 | 0.256637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.7624 | 1.50131 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.9014 | −1.60513 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.8229 | −1.04507 | −0.522535 | − | 0.852618i | \(-0.675014\pi\) | ||||
−0.522535 | + | 0.852618i | \(0.675014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 55.2752 | 2.76722 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.08829 | 0.403910 | 0.201955 | − | 0.979395i | \(-0.435271\pi\) | ||||
0.201955 | + | 0.979395i | \(0.435271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.88119 | 0.143522 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.68246 | −0.381745 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.6759 | 1.76839 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1393 | 1.53974 | 0.769871 | − | 0.638200i | \(-0.220321\pi\) | ||||
0.769871 | + | 0.638200i | \(0.220321\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.4769 | 1.79927 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.05946 | −0.248960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.7922 | −0.922474 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.6646 | 1.45268 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.9688 | −1.12210 | −0.561050 | − | 0.827782i | \(-0.689602\pi\) | ||||
−0.561050 | + | 0.827782i | \(0.689602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.36313 | −0.358857 | −0.179428 | − | 0.983771i | \(-0.557425\pi\) | ||||
−0.179428 | + | 0.983771i | \(0.557425\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44.5287 | 2.16506 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.01325 | 0.0491498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.7234 | 1.05127 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 89.8756 | 4.33924 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.47834 | 0.119378 | 0.0596888 | − | 0.998217i | \(-0.480989\pi\) | ||||
0.0596888 | + | 0.998217i | \(0.480989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3130 | 0.495610 | 0.247805 | − | 0.968810i | \(-0.420291\pi\) | ||||
0.247805 | + | 0.968810i | \(0.420291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −56.6669 | −2.71697 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −38.6698 | −1.84983 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.99261 | 0.476921 | 0.238461 | − | 0.971152i | \(-0.423357\pi\) | ||||
0.238461 | + | 0.971152i | \(0.423357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.39621 | 0.256962 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.6060 | 0.788973 | 0.394487 | − | 0.918902i | \(-0.370922\pi\) | ||||
0.394487 | + | 0.918902i | \(0.370922\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0489 | −0.713386 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 34.7552 | 1.64386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.9995 | −0.849448 | −0.424724 | − | 0.905323i | \(-0.639629\pi\) | ||||
−0.424724 | + | 0.905323i | \(0.639629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.6705 | 0.784983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 55.7772 | 2.62064 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.1318 | −1.36572 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.86419 | 0.180759 | 0.0903797 | − | 0.995907i | \(-0.471192\pi\) | ||||
0.0903797 | + | 0.995907i | \(0.471192\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.13933 | 0.286559 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.89511 | −0.460861 | −0.230431 | − | 0.973089i | \(-0.574013\pi\) | ||||
−0.230431 | + | 0.973089i | \(0.574013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.13438 | 0.238615 | 0.119307 | − | 0.992857i | \(-0.461933\pi\) | ||||
0.119307 | + | 0.992857i | \(0.461933\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.12466 | −0.144903 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.6977 | 1.65189 | 0.825947 | − | 0.563748i | \(-0.190641\pi\) | ||||
0.825947 | + | 0.563748i | \(0.190641\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.39824 | −0.387795 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.0370 | −1.01541 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −67.5778 | −3.10723 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.72112 | −0.354269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.1733 | −1.15261 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4946 | 0.479511 | 0.239756 | − | 0.970833i | \(-0.422933\pi\) | ||||
0.239756 | + | 0.970833i | \(0.422933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.6429 | −1.44279 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −46.9807 | −2.13769 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.45102 | 0.202110 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.77888 | −0.216552 | −0.108276 | − | 0.994121i | \(-0.534533\pi\) | ||||
−0.108276 | + | 0.994121i | \(0.534533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.1524 | −2.08708 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1654 | −0.819792 | −0.409896 | − | 0.912132i | \(-0.634435\pi\) | ||||
−0.409896 | + | 0.912132i | \(0.634435\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.81750 | 0.397120 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −62.6345 | −2.81521 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −44.4306 | −1.99299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.2912 | 0.774060 | 0.387030 | − | 0.922067i | \(-0.373501\pi\) | ||||
0.387030 | + | 0.922067i | \(0.373501\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.96769 | 0.177263 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.30933 | −0.280761 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −42.0517 | −1.86758 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.1695 | 1.24859 | 0.624295 | − | 0.781188i | \(-0.285386\pi\) | ||||
0.624295 | + | 0.781188i | \(0.285386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.6829 | −1.35733 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.7826 | −2.06550 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.1513 | −1.10830 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.8218 | 2.14718 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.8697 | −1.31114 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.9674 | 1.31290 | 0.656448 | − | 0.754371i | \(-0.272058\pi\) | ||||
0.656448 | + | 0.754371i | \(0.272058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.3252 | −1.50093 | −0.750467 | − | 0.660907i | \(-0.770172\pi\) | ||||
−0.750467 | + | 0.660907i | \(0.770172\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.38053 | −0.409400 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.486205 | 0.0211794 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.86701 | 0.429001 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.64834 | 0.418702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.7860 | −0.640452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.70882 | 0.419749 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.4064 | 0.449070 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.91647 | 0.254840 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.1364 | 0.865732 | 0.432866 | − | 0.901458i | \(-0.357502\pi\) | ||||
0.432866 | + | 0.901458i | \(0.357502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.1258 | 1.55031 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.8894 | −1.45166 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.2845 | −0.653518 | −0.326759 | − | 0.945108i | \(-0.605957\pi\) | ||||
−0.326759 | + | 0.945108i | \(0.605957\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.4263 | −1.76803 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −67.1907 | −2.86242 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.9554 | −1.95422 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.3169 | 1.45667 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8257 | −0.543443 | −0.271721 | − | 0.962376i | \(-0.587593\pi\) | ||||
−0.271721 | + | 0.962376i | \(0.587593\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 59.9385 | 2.53513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.1666 | 0.640336 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.61580 | 0.194533 | 0.0972664 | − | 0.995258i | \(-0.468990\pi\) | ||||
0.0972664 | + | 0.995258i | \(0.468990\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.6273 | −0.531234 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.0669 | −0.464768 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.53204 | 0.189993 | 0.0949965 | − | 0.995478i | \(-0.469716\pi\) | ||||
0.0949965 | + | 0.995478i | \(0.469716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.28024 | 0.0535763 | 0.0267882 | − | 0.999641i | \(-0.491472\pi\) | ||||
0.0267882 | + | 0.999641i | \(0.491472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 57.2935 | 2.39347 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.56249 | 0.273675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.4646 | −0.518909 | −0.259455 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259455 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.5360 | −0.978125 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.0710 | −1.12310 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.6004 | −1.14309 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 55.5540 | 2.29687 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.2510 | −0.959670 | −0.479835 | − | 0.877359i | \(-0.659303\pi\) | ||||
−0.479835 | + | 0.877359i | \(0.659303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.70495 | −0.152660 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 51.0045 | 2.09804 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.5175 | 0.760421 | 0.380210 | − | 0.924900i | \(-0.375852\pi\) | ||||
0.380210 | + | 0.924900i | \(0.375852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.91602 | −0.201537 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −33.9496 | −1.38946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.6620 | 1.70227 | 0.851133 | − | 0.524951i | \(-0.175916\pi\) | ||||
0.851133 | + | 0.524951i | \(0.175916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.47016 | −0.223132 | −0.111566 | − | 0.993757i | \(-0.535587\pi\) | ||||
−0.111566 | + | 0.993757i | \(0.535587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.0154 | 0.652196 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −47.0748 | −1.91386 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.25588 | −0.213330 | −0.106665 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106665 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −81.6313 | −3.30787 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.3027 | −1.75184 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.8948 | 1.32861 | 0.664303 | − | 0.747463i | \(-0.268728\pi\) | ||||
0.664303 | + | 0.747463i | \(0.268728\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0355 | 0.646612 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.66495 | −0.268321 | −0.134160 | − | 0.990960i | \(-0.542834\pi\) | ||||
−0.134160 | + | 0.990960i | \(0.542834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.5637 | −1.38923 | −0.694617 | − | 0.719380i | \(-0.744426\pi\) | ||||
−0.694617 | + | 0.719380i | \(0.744426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.7625 | 1.59561 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.6786 | −0.868535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.9662 | −0.718649 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −115.572 | −4.61550 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.33978 | −0.212911 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.68292 | −0.226233 | −0.113117 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113117 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −43.5319 | −1.73024 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.9498 | 1.30757 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.24765 | −0.207919 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 84.7288 | 3.35182 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3525 | −0.961865 | −0.480932 | − | 0.876758i | \(-0.659702\pi\) | ||||
−0.480932 | + | 0.876758i | \(0.659702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.4231 | −0.568790 | −0.284395 | − | 0.958707i | \(-0.591793\pi\) | ||||
−0.284395 | + | 0.958707i | \(0.591793\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −65.0036 | −2.55951 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.0850 | −1.61522 | −0.807608 | − | 0.589719i | \(-0.799238\pi\) | ||||
−0.807608 | + | 0.589719i | \(0.799238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.5786 | 0.415245 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.50122 | −0.176417 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.6034 | −1.27587 | −0.637935 | − | 0.770090i | \(-0.720211\pi\) | ||||
−0.637935 | + | 0.770090i | \(0.720211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.1704 | 0.788124 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 58.5121 | 2.28277 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.2682 | 1.02326 | 0.511631 | − | 0.859205i | \(-0.329041\pi\) | ||||
0.511631 | + | 0.859205i | \(0.329041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.7102 | −0.844430 | −0.422215 | − | 0.906496i | \(-0.638747\pi\) | ||||
−0.422215 | + | 0.906496i | \(0.638747\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.4521 | −0.522437 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 37.4608 | 1.45267 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.1081 | 2.21123 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.0211 | −0.503426 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.4203 | −1.75343 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.6069 | −0.601600 | −0.300800 | − | 0.953687i | \(-0.597254\pi\) | ||||
−0.300800 | + | 0.953687i | \(0.597254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.93929 | 0.305583 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.6421 | 0.716474 | 0.358237 | − | 0.933631i | \(-0.383378\pi\) | ||||
0.358237 | + | 0.933631i | \(0.383378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.41189 | 0.246066 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.9594 | −0.879805 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.2022 | 0.466903 | 0.233451 | − | 0.972368i | \(-0.424998\pi\) | ||||
0.233451 | + | 0.972368i | \(0.424998\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.7209 | 0.944538 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −77.7928 | −2.96798 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.4803 | 0.932625 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.6452 | −0.899506 | −0.449753 | − | 0.893153i | \(-0.648488\pi\) | ||||
−0.449753 | + | 0.893153i | \(0.648488\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −90.2278 | −3.42747 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.1042 | 0.762594 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.49515 | −0.0945107 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −46.6590 | −1.76480 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0573 | 0.719785 | 0.359893 | − | 0.932994i | \(-0.382813\pi\) | ||||
0.359893 | + | 0.932994i | \(0.382813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.6900 | 1.53465 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.9620 | 1.76869 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.08887 | −0.341822 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.1610 | 0.832274 | 0.416137 | − | 0.909302i | \(-0.363384\pi\) | ||||
0.416137 | + | 0.909302i | \(0.363384\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 87.6364 | 3.28662 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.14899 | 0.117931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 60.9101 | 2.27791 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.61197 | −0.0602000 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.65057 | 0.136143 | 0.0680716 | − | 0.997680i | \(-0.478315\pi\) | ||||
0.0680716 | + | 0.997680i | \(0.478315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.2316 | −1.34934 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 68.7299 | 2.55609 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.4027 | 0.423484 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.6398 | −0.542960 | −0.271480 | − | 0.962444i | \(-0.587513\pi\) | ||||
−0.271480 | + | 0.962444i | \(0.587513\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.1787 | −1.45106 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1147 | 0.374106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.7076 | −1.68825 | −0.844125 | − | 0.536146i | \(-0.819880\pi\) | ||||
−0.844125 | + | 0.536146i | \(0.819880\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.69110 | 0.209919 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.5594 | 0.646810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.6620 | 1.01756 | 0.508781 | − | 0.860896i | \(-0.330096\pi\) | ||||
0.508781 | + | 0.860896i | \(0.330096\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 102.507 | 3.76570 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.1666 | −0.556410 | −0.278205 | − | 0.960522i | \(-0.589739\pi\) | ||||
−0.278205 | + | 0.960522i | \(0.589739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.5541 | 0.862956 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 51.6242 | 1.88883 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.9860 | 0.511037 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.3066 | −1.06941 | −0.534707 | − | 0.845038i | \(-0.679578\pi\) | ||||
−0.534707 | + | 0.845038i | \(0.679578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.8553 | 1.05155 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.8011 | 1.37572 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.8165 | 0.756589 | 0.378295 | − | 0.925685i | \(-0.376511\pi\) | ||||
0.378295 | + | 0.925685i | \(0.376511\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 98.2294 | 3.56550 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3601 | −1.13680 | −0.568401 | − | 0.822752i | \(-0.692438\pi\) | ||||
−0.568401 | + | 0.822752i | \(0.692438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −48.8192 | −1.76738 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.37481 | 0.338947 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.38271 | −0.338790 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.137445 | 0.00495640 | 0.00247820 | − | 0.999997i | \(-0.499211\pi\) | ||||
0.00247820 | + | 0.999997i | \(0.499211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −62.4361 | −2.24858 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.1120 | −1.08305 | −0.541526 | − | 0.840684i | \(-0.682153\pi\) | ||||
−0.541526 | + | 0.840684i | \(0.682153\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.628752 | 0.0225855 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 49.4350 | 1.77347 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.0135 | 0.681228 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 92.8977 | 3.32414 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 69.0893 | 2.46905 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.9348 | −0.533046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.4682 | 1.05043 | 0.525214 | − | 0.850970i | \(-0.323985\pi\) | ||||
0.525214 | + | 0.850970i | \(0.323985\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.7097 | −1.94772 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.1902 | −0.646768 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.2858 | 1.43059 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.5490 | −0.941596 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.9883 | 1.02682 | 0.513408 | − | 0.858144i | \(-0.328383\pi\) | ||||
0.513408 | + | 0.858144i | \(0.328383\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.30740 | −0.258517 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.3409 | 1.46071 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 64.1534 | 2.26392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.8395 | −1.12219 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 55.2088 | 1.94344 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.8567 | −1.29581 | −0.647907 | − | 0.761720i | \(-0.724355\pi\) | ||||
−0.647907 | + | 0.761720i | \(0.724355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4827 | 1.21085 | 0.605425 | − | 0.795902i | \(-0.293003\pi\) | ||||
0.605425 | + | 0.795902i | \(0.293003\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −72.2735 | −2.53474 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −31.2782 | −1.09563 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −77.0755 | −2.69653 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 80.0280 | 2.79640 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0859 | 0.631204 | 0.315602 | − | 0.948892i | \(-0.397794\pi\) | ||||
0.315602 | + | 0.948892i | \(0.397794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.44917 | −0.224804 | −0.112402 | − | 0.993663i | \(-0.535854\pi\) | ||||
−0.112402 | + | 0.993663i | \(0.535854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.6133 | 0.682846 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.33358 | 0.0811466 | 0.0405733 | − | 0.999177i | \(-0.487082\pi\) | ||||
0.0405733 | + | 0.999177i | \(0.487082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.4949 | −0.954938 | −0.477469 | − | 0.878649i | \(-0.658446\pi\) | ||||
−0.477469 | + | 0.878649i | \(0.658446\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.7705 | 2.03872 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.885547 | −0.0306824 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.68896 | 0.0930553 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.80964 | 0.131680 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.0866 | −1.34942 | −0.674710 | − | 0.738083i | \(-0.735731\pi\) | ||||
−0.674710 | + | 0.738083i | \(0.735731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 70.2282 | 2.42166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 48.0772 | 1.65587 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.4991 | −0.980398 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −67.8133 | −2.33009 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.19030 | 0.143811 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.5840 | −1.18553 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.4262 | 0.356988 | 0.178494 | − | 0.983941i | \(-0.442878\pi\) | ||||
0.178494 | + | 0.983941i | \(0.442878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −71.4375 | −2.44311 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.8938 | −1.05531 | −0.527656 | − | 0.849458i | \(-0.676929\pi\) | ||||
−0.527656 | + | 0.849458i | \(0.676929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.6266 | −1.52264 | −0.761320 | − | 0.648377i | \(-0.775448\pi\) | ||||
−0.761320 | + | 0.648377i | \(0.775448\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.0998 | 0.787240 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.60527 | −0.0886844 | −0.0443422 | − | 0.999016i | \(-0.514119\pi\) | ||||
−0.0443422 | + | 0.999016i | \(0.514119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.2432 | −0.688288 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.9828 | 1.59562 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 96.0857 | 3.25948 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.5744 | −0.527720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.2274 | −0.413835 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.1261 | −1.15367 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.1095 | −1.21933 | −0.609666 | − | 0.792658i | \(-0.708697\pi\) | ||||
−0.609666 | + | 0.792658i | \(0.708697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 80.6908 | 2.72163 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.9625 | −0.908390 | −0.454195 | − | 0.890902i | \(-0.650073\pi\) | ||||
−0.454195 | + | 0.890902i | \(0.650073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6289 | 0.391345 | 0.195672 | − | 0.980669i | \(-0.437311\pi\) | ||||
0.195672 | + | 0.980669i | \(0.437311\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1756 | 0.342049 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3652 | 0.549491 | 0.274746 | − | 0.961517i | \(-0.411406\pi\) | ||||
0.274746 | + | 0.961517i | \(0.411406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.4657 | 1.59195 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.1393 | 0.775195 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.6835 | 1.86338 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.05258 | 0.235742 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −87.1251 | −2.90902 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.47153 | 0.182486 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.13108 | 0.137626 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −93.6406 | −3.11616 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.4830 | 0.813843 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.36503 | 0.310961 | 0.155480 | − | 0.987839i | \(-0.450307\pi\) | ||||
0.155480 | + | 0.987839i | \(0.450307\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3324 | 0.574879 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0428 | −1.59173 | −0.795864 | − | 0.605475i | \(-0.792983\pi\) | ||||
−0.795864 | + | 0.605475i | \(0.792983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.6014 | 1.87323 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43.6901 | −1.44435 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.0564 | 0.959527 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.6245 | 1.10917 | 0.554585 | − | 0.832127i | \(-0.312877\pi\) | ||||
0.554585 | + | 0.832127i | \(0.312877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.2501 | 0.535458 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −82.3961 | −2.71210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.90533 | −0.227046 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 69.0934 | 2.26932 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.4329 | −0.867235 | −0.433618 | − | 0.901097i | \(-0.642763\pi\) | ||||
−0.433618 | + | 0.901097i | \(0.642763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.74801 | 0.221157 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.5157 | −0.344269 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.2787 | 0.336148 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.70987 | 0.186533 | 0.0932666 | − | 0.995641i | \(-0.470269\pi\) | ||||
0.0932666 | + | 0.995641i | \(0.470269\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −90.7104 | −2.96022 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.9969 | 1.10827 | 0.554134 | − | 0.832427i | \(-0.313049\pi\) | ||||
0.554134 | + | 0.832427i | \(0.313049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.1603 | −0.526252 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38.5194 | −1.25303 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.1654 | −1.53267 | −0.766334 | − | 0.642442i | \(-0.777921\pi\) | ||||
−0.766334 | + | 0.642442i | \(0.777921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −56.9012 | −1.84709 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 87.0091 | 2.82146 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.07255 | 0.164316 | 0.0821581 | − | 0.996619i | \(-0.473819\pi\) | ||||
0.0821581 | + | 0.996619i | \(0.473819\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.8287 | 1.25647 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 170.679 | 5.51726 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.6116 | 1.14996 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6983 | −0.990268 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.6712 | −0.859466 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.9507 | −0.513472 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.30261 | 0.202678 | 0.101339 | − | 0.994852i | \(-0.467687\pi\) | ||||
0.101339 | + | 0.994852i | \(0.467687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.2982 | 0.555700 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.764960 | 0.0245487 | 0.0122744 | − | 0.999925i | \(-0.496093\pi\) | ||||
0.0122744 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.9609 | 0.928445 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.3961 | −0.557121 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.2135 | −1.83042 | −0.915211 | − | 0.402974i | \(-0.867976\pi\) | ||||
−0.915211 | + | 0.402974i | \(0.867976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.3267 | 1.44865 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 93.0978 | 2.97238 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.2431 | −0.677548 | −0.338774 | − | 0.940868i | \(-0.610012\pi\) | ||||
−0.338774 | + | 0.940868i | \(0.610012\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.5665 | 1.10138 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 67.6509 | 2.15335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 65.5096 | 2.08309 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.70053 | −0.0540193 | −0.0270096 | − | 0.999635i | \(-0.508598\pi\) | ||||
−0.0270096 | + | 0.999635i | \(0.508598\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 79.1593 | 2.51204 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.0082 | −0.729408 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.3205 | −1.02360 | −0.511800 | − | 0.859104i | \(-0.671021\pi\) | ||||
−0.511800 | + | 0.859104i | \(0.671021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −41.8397 | −1.32375 |
(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 | 8048.2.a.v.1.2 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.27 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.27 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.2 | 28 | 1.1 | even | 1 | trivial |