Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8619,2,Mod(1,8619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8619, 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("8619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8619 = 3 \cdot 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8619.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: | \(68.8230615021\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 20x^{14} + 156x^{12} - 602x^{10} + 1212x^{8} - 1259x^{6} + 665x^{4} - 168x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 663) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(1.96679\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.96679 | 1.39073 | 0.695365 | − | 0.718656i | \(-0.255243\pi\) | ||||
0.695365 | + | 0.718656i | \(0.255243\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.86826 | 0.934132 | ||||||||
\(5\) | 0.562071 | 0.251366 | 0.125683 | − | 0.992070i | \(-0.459888\pi\) | ||||
0.125683 | + | 0.992070i | \(0.459888\pi\) | |||||||
\(6\) | 1.96679 | 0.802939 | ||||||||
\(7\) | −3.08512 | −1.16607 | −0.583034 | − | 0.812448i | \(-0.698134\pi\) | ||||
−0.583034 | + | 0.812448i | \(0.698134\pi\) | |||||||
\(8\) | −0.259096 | −0.0916042 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.10548 | 0.349582 | ||||||||
\(11\) | 6.04044 | 1.82126 | 0.910630 | − | 0.413222i | \(-0.135597\pi\) | ||||
0.910630 | + | 0.413222i | \(0.135597\pi\) | |||||||
\(12\) | 1.86826 | 0.539322 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −6.06779 | −1.62169 | ||||||||
\(15\) | 0.562071 | 0.145126 | ||||||||
\(16\) | −4.24612 | −1.06153 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 1.96679 | 0.463577 | ||||||||
\(19\) | −3.95727 | −0.907860 | −0.453930 | − | 0.891037i | \(-0.649978\pi\) | ||||
−0.453930 | + | 0.891037i | \(0.649978\pi\) | |||||||
\(20\) | 1.05010 | 0.234809 | ||||||||
\(21\) | −3.08512 | −0.673229 | ||||||||
\(22\) | 11.8803 | 2.53288 | ||||||||
\(23\) | −8.16527 | −1.70258 | −0.851288 | − | 0.524699i | \(-0.824178\pi\) | ||||
−0.851288 | + | 0.524699i | \(0.824178\pi\) | |||||||
\(24\) | −0.259096 | −0.0528877 | ||||||||
\(25\) | −4.68408 | −0.936815 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −5.76383 | −1.08926 | ||||||||
\(29\) | −4.22613 | −0.784773 | −0.392387 | − | 0.919800i | \(-0.628350\pi\) | ||||
−0.392387 | + | 0.919800i | \(0.628350\pi\) | |||||||
\(30\) | 1.10548 | 0.201831 | ||||||||
\(31\) | −6.39872 | −1.14924 | −0.574622 | − | 0.818419i | \(-0.694851\pi\) | ||||
−0.574622 | + | 0.818419i | \(0.694851\pi\) | |||||||
\(32\) | −7.83303 | −1.38470 | ||||||||
\(33\) | 6.04044 | 1.05151 | ||||||||
\(34\) | −1.96679 | −0.337302 | ||||||||
\(35\) | −1.73406 | −0.293110 | ||||||||
\(36\) | 1.86826 | 0.311377 | ||||||||
\(37\) | 0.741352 | 0.121878 | 0.0609388 | − | 0.998142i | \(-0.480591\pi\) | ||||
0.0609388 | + | 0.998142i | \(0.480591\pi\) | |||||||
\(38\) | −7.78312 | −1.26259 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.145630 | −0.0230262 | ||||||||
\(41\) | −8.97787 | −1.40211 | −0.701054 | − | 0.713108i | \(-0.747287\pi\) | ||||
−0.701054 | + | 0.713108i | \(0.747287\pi\) | |||||||
\(42\) | −6.06779 | −0.936281 | ||||||||
\(43\) | 8.54447 | 1.30302 | 0.651510 | − | 0.758640i | \(-0.274136\pi\) | ||||
0.651510 | + | 0.758640i | \(0.274136\pi\) | |||||||
\(44\) | 11.2851 | 1.70130 | ||||||||
\(45\) | 0.562071 | 0.0837886 | ||||||||
\(46\) | −16.0594 | −2.36782 | ||||||||
\(47\) | −5.29432 | −0.772257 | −0.386128 | − | 0.922445i | \(-0.626188\pi\) | ||||
−0.386128 | + | 0.922445i | \(0.626188\pi\) | |||||||
\(48\) | −4.24612 | −0.612874 | ||||||||
\(49\) | 2.51799 | 0.359713 | ||||||||
\(50\) | −9.21260 | −1.30286 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.35907 | 1.01085 | 0.505423 | − | 0.862872i | \(-0.331336\pi\) | ||||
0.505423 | + | 0.862872i | \(0.331336\pi\) | |||||||
\(54\) | 1.96679 | 0.267646 | ||||||||
\(55\) | 3.39516 | 0.457803 | ||||||||
\(56\) | 0.799343 | 0.106817 | ||||||||
\(57\) | −3.95727 | −0.524153 | ||||||||
\(58\) | −8.31192 | −1.09141 | ||||||||
\(59\) | 5.98304 | 0.778925 | 0.389463 | − | 0.921042i | \(-0.372661\pi\) | ||||
0.389463 | + | 0.921042i | \(0.372661\pi\) | |||||||
\(60\) | 1.05010 | 0.135567 | ||||||||
\(61\) | −4.94978 | −0.633755 | −0.316877 | − | 0.948466i | \(-0.602634\pi\) | ||||
−0.316877 | + | 0.948466i | \(0.602634\pi\) | |||||||
\(62\) | −12.5849 | −1.59829 | ||||||||
\(63\) | −3.08512 | −0.388689 | ||||||||
\(64\) | −6.91370 | −0.864212 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.8803 | 1.46236 | ||||||||
\(67\) | −7.77935 | −0.950398 | −0.475199 | − | 0.879878i | \(-0.657624\pi\) | ||||
−0.475199 | + | 0.879878i | \(0.657624\pi\) | |||||||
\(68\) | −1.86826 | −0.226560 | ||||||||
\(69\) | −8.16527 | −0.982983 | ||||||||
\(70\) | −3.41053 | −0.407636 | ||||||||
\(71\) | 9.81696 | 1.16506 | 0.582529 | − | 0.812810i | \(-0.302063\pi\) | ||||
0.582529 | + | 0.812810i | \(0.302063\pi\) | |||||||
\(72\) | −0.259096 | −0.0305347 | ||||||||
\(73\) | 8.70107 | 1.01838 | 0.509191 | − | 0.860653i | \(-0.329945\pi\) | ||||
0.509191 | + | 0.860653i | \(0.329945\pi\) | |||||||
\(74\) | 1.45808 | 0.169499 | ||||||||
\(75\) | −4.68408 | −0.540871 | ||||||||
\(76\) | −7.39323 | −0.848061 | ||||||||
\(77\) | −18.6355 | −2.12371 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.8289 | 1.89340 | 0.946702 | − | 0.322111i | \(-0.104392\pi\) | ||||
0.946702 | + | 0.322111i | \(0.104392\pi\) | |||||||
\(80\) | −2.38662 | −0.266832 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −17.6576 | −1.94996 | ||||||||
\(83\) | −4.52040 | −0.496179 | −0.248089 | − | 0.968737i | \(-0.579803\pi\) | ||||
−0.248089 | + | 0.968737i | \(0.579803\pi\) | |||||||
\(84\) | −5.76383 | −0.628885 | ||||||||
\(85\) | −0.562071 | −0.0609652 | ||||||||
\(86\) | 16.8052 | 1.81215 | ||||||||
\(87\) | −4.22613 | −0.453089 | ||||||||
\(88\) | −1.56505 | −0.166835 | ||||||||
\(89\) | −5.32147 | −0.564075 | −0.282037 | − | 0.959403i | \(-0.591010\pi\) | ||||
−0.282037 | + | 0.959403i | \(0.591010\pi\) | |||||||
\(90\) | 1.10548 | 0.116527 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.2549 | −1.59043 | ||||||||
\(93\) | −6.39872 | −0.663516 | ||||||||
\(94\) | −10.4128 | −1.07400 | ||||||||
\(95\) | −2.22427 | −0.228205 | ||||||||
\(96\) | −7.83303 | −0.799455 | ||||||||
\(97\) | −7.70576 | −0.782401 | −0.391201 | − | 0.920305i | \(-0.627940\pi\) | ||||
−0.391201 | + | 0.920305i | \(0.627940\pi\) | |||||||
\(98\) | 4.95236 | 0.500264 | ||||||||
\(99\) | 6.04044 | 0.607087 | ||||||||
\(100\) | −8.75109 | −0.875109 | ||||||||
\(101\) | −10.7781 | −1.07246 | −0.536232 | − | 0.844071i | \(-0.680153\pi\) | ||||
−0.536232 | + | 0.844071i | \(0.680153\pi\) | |||||||
\(102\) | −1.96679 | −0.194741 | ||||||||
\(103\) | −15.9795 | −1.57451 | −0.787254 | − | 0.616629i | \(-0.788498\pi\) | ||||
−0.787254 | + | 0.616629i | \(0.788498\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.73406 | −0.169227 | ||||||||
\(106\) | 14.4738 | 1.40582 | ||||||||
\(107\) | 2.30365 | 0.222703 | 0.111351 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111351 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(108\) | 1.86826 | 0.179774 | ||||||||
\(109\) | −4.13594 | −0.396151 | −0.198075 | − | 0.980187i | \(-0.563469\pi\) | ||||
−0.198075 | + | 0.980187i | \(0.563469\pi\) | |||||||
\(110\) | 6.67756 | 0.636680 | ||||||||
\(111\) | 0.741352 | 0.0703660 | ||||||||
\(112\) | 13.0998 | 1.23781 | ||||||||
\(113\) | 10.7776 | 1.01387 | 0.506936 | − | 0.861984i | \(-0.330778\pi\) | ||||
0.506936 | + | 0.861984i | \(0.330778\pi\) | |||||||
\(114\) | −7.78312 | −0.728956 | ||||||||
\(115\) | −4.58946 | −0.427969 | ||||||||
\(116\) | −7.89554 | −0.733082 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7674 | 1.08328 | ||||||||
\(119\) | 3.08512 | 0.282813 | ||||||||
\(120\) | −0.145630 | −0.0132942 | ||||||||
\(121\) | 25.4869 | 2.31699 | ||||||||
\(122\) | −9.73519 | −0.881383 | ||||||||
\(123\) | −8.97787 | −0.809508 | ||||||||
\(124\) | −11.9545 | −1.07355 | ||||||||
\(125\) | −5.44314 | −0.486849 | ||||||||
\(126\) | −6.06779 | −0.540562 | ||||||||
\(127\) | −15.1396 | −1.34343 | −0.671713 | − | 0.740812i | \(-0.734441\pi\) | ||||
−0.671713 | + | 0.740812i | \(0.734441\pi\) | |||||||
\(128\) | 2.06827 | 0.182811 | ||||||||
\(129\) | 8.54447 | 0.752298 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5864 | −1.18705 | −0.593524 | − | 0.804816i | \(-0.702264\pi\) | ||||
−0.593524 | + | 0.804816i | \(0.702264\pi\) | |||||||
\(132\) | 11.2851 | 0.982245 | ||||||||
\(133\) | 12.2087 | 1.05863 | ||||||||
\(134\) | −15.3003 | −1.32175 | ||||||||
\(135\) | 0.562071 | 0.0483754 | ||||||||
\(136\) | 0.259096 | 0.0222173 | ||||||||
\(137\) | 19.2248 | 1.64248 | 0.821241 | − | 0.570582i | \(-0.193282\pi\) | ||||
0.821241 | + | 0.570582i | \(0.193282\pi\) | |||||||
\(138\) | −16.0594 | −1.36706 | ||||||||
\(139\) | −15.8544 | −1.34475 | −0.672377 | − | 0.740208i | \(-0.734727\pi\) | ||||
−0.672377 | + | 0.740208i | \(0.734727\pi\) | |||||||
\(140\) | −3.23968 | −0.273803 | ||||||||
\(141\) | −5.29432 | −0.445863 | ||||||||
\(142\) | 19.3079 | 1.62028 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.24612 | −0.353843 | ||||||||
\(145\) | −2.37539 | −0.197265 | ||||||||
\(146\) | 17.1132 | 1.41630 | ||||||||
\(147\) | 2.51799 | 0.207680 | ||||||||
\(148\) | 1.38504 | 0.113850 | ||||||||
\(149\) | 8.07196 | 0.661281 | 0.330640 | − | 0.943757i | \(-0.392735\pi\) | ||||
0.330640 | + | 0.943757i | \(0.392735\pi\) | |||||||
\(150\) | −9.21260 | −0.752205 | ||||||||
\(151\) | 15.9640 | 1.29914 | 0.649568 | − | 0.760304i | \(-0.274950\pi\) | ||||
0.649568 | + | 0.760304i | \(0.274950\pi\) | |||||||
\(152\) | 1.02531 | 0.0831638 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −36.6521 | −2.95351 | ||||||||
\(155\) | −3.59653 | −0.288881 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2504 | −1.29692 | −0.648461 | − | 0.761247i | \(-0.724587\pi\) | ||||
−0.648461 | + | 0.761247i | \(0.724587\pi\) | |||||||
\(158\) | 33.0990 | 2.63322 | ||||||||
\(159\) | 7.35907 | 0.583612 | ||||||||
\(160\) | −4.40272 | −0.348066 | ||||||||
\(161\) | 25.1909 | 1.98532 | ||||||||
\(162\) | 1.96679 | 0.154526 | ||||||||
\(163\) | −1.25670 | −0.0984325 | −0.0492162 | − | 0.998788i | \(-0.515672\pi\) | ||||
−0.0492162 | + | 0.998788i | \(0.515672\pi\) | |||||||
\(164\) | −16.7730 | −1.30975 | ||||||||
\(165\) | 3.39516 | 0.264313 | ||||||||
\(166\) | −8.89068 | −0.690051 | ||||||||
\(167\) | 0.919963 | 0.0711889 | 0.0355944 | − | 0.999366i | \(-0.488668\pi\) | ||||
0.0355944 | + | 0.999366i | \(0.488668\pi\) | |||||||
\(168\) | 0.799343 | 0.0616706 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.10548 | −0.0847862 | ||||||||
\(171\) | −3.95727 | −0.302620 | ||||||||
\(172\) | 15.9633 | 1.21719 | ||||||||
\(173\) | 14.1127 | 1.07297 | 0.536483 | − | 0.843911i | \(-0.319752\pi\) | ||||
0.536483 | + | 0.843911i | \(0.319752\pi\) | |||||||
\(174\) | −8.31192 | −0.630125 | ||||||||
\(175\) | 14.4510 | 1.09239 | ||||||||
\(176\) | −25.6484 | −1.93332 | ||||||||
\(177\) | 5.98304 | 0.449713 | ||||||||
\(178\) | −10.4662 | −0.784476 | ||||||||
\(179\) | 5.70954 | 0.426751 | 0.213376 | − | 0.976970i | \(-0.431554\pi\) | ||||
0.213376 | + | 0.976970i | \(0.431554\pi\) | |||||||
\(180\) | 1.05010 | 0.0782697 | ||||||||
\(181\) | −19.4796 | −1.44791 | −0.723955 | − | 0.689847i | \(-0.757678\pi\) | ||||
−0.723955 | + | 0.689847i | \(0.757678\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.94978 | −0.365899 | ||||||||
\(184\) | 2.11559 | 0.155963 | ||||||||
\(185\) | 0.416693 | 0.0306358 | ||||||||
\(186\) | −12.5849 | −0.922772 | ||||||||
\(187\) | −6.04044 | −0.441721 | ||||||||
\(188\) | −9.89120 | −0.721390 | ||||||||
\(189\) | −3.08512 | −0.224410 | ||||||||
\(190\) | −4.37467 | −0.317372 | ||||||||
\(191\) | −2.55926 | −0.185181 | −0.0925907 | − | 0.995704i | \(-0.529515\pi\) | ||||
−0.0925907 | + | 0.995704i | \(0.529515\pi\) | |||||||
\(192\) | −6.91370 | −0.498953 | ||||||||
\(193\) | −12.3724 | −0.890587 | −0.445294 | − | 0.895385i | \(-0.646901\pi\) | ||||
−0.445294 | + | 0.895385i | \(0.646901\pi\) | |||||||
\(194\) | −15.1556 | −1.08811 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.70427 | 0.336019 | ||||||||
\(197\) | 10.0989 | 0.719518 | 0.359759 | − | 0.933045i | \(-0.382859\pi\) | ||||
0.359759 | + | 0.933045i | \(0.382859\pi\) | |||||||
\(198\) | 11.8803 | 0.844294 | ||||||||
\(199\) | −7.98297 | −0.565898 | −0.282949 | − | 0.959135i | \(-0.591313\pi\) | ||||
−0.282949 | + | 0.959135i | \(0.591313\pi\) | |||||||
\(200\) | 1.21362 | 0.0858162 | ||||||||
\(201\) | −7.77935 | −0.548713 | ||||||||
\(202\) | −21.1983 | −1.49151 | ||||||||
\(203\) | 13.0381 | 0.915099 | ||||||||
\(204\) | −1.86826 | −0.130805 | ||||||||
\(205\) | −5.04620 | −0.352442 | ||||||||
\(206\) | −31.4283 | −2.18972 | ||||||||
\(207\) | −8.16527 | −0.567525 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.9036 | −1.65345 | ||||||||
\(210\) | −3.41053 | −0.235349 | ||||||||
\(211\) | −13.3331 | −0.917891 | −0.458946 | − | 0.888464i | \(-0.651773\pi\) | ||||
−0.458946 | + | 0.888464i | \(0.651773\pi\) | |||||||
\(212\) | 13.7487 | 0.944264 | ||||||||
\(213\) | 9.81696 | 0.672647 | ||||||||
\(214\) | 4.53081 | 0.309719 | ||||||||
\(215\) | 4.80260 | 0.327535 | ||||||||
\(216\) | −0.259096 | −0.0176292 | ||||||||
\(217\) | 19.7408 | 1.34010 | ||||||||
\(218\) | −8.13452 | −0.550939 | ||||||||
\(219\) | 8.70107 | 0.587964 | ||||||||
\(220\) | 6.34305 | 0.427648 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.45808 | 0.0978602 | ||||||||
\(223\) | 27.3756 | 1.83321 | 0.916604 | − | 0.399796i | \(-0.130919\pi\) | ||||
0.916604 | + | 0.399796i | \(0.130919\pi\) | |||||||
\(224\) | 24.1659 | 1.61465 | ||||||||
\(225\) | −4.68408 | −0.312272 | ||||||||
\(226\) | 21.1973 | 1.41002 | ||||||||
\(227\) | 19.0770 | 1.26618 | 0.633092 | − | 0.774076i | \(-0.281785\pi\) | ||||
0.633092 | + | 0.774076i | \(0.281785\pi\) | |||||||
\(228\) | −7.39323 | −0.489628 | ||||||||
\(229\) | −17.1978 | −1.13646 | −0.568230 | − | 0.822870i | \(-0.692372\pi\) | ||||
−0.568230 | + | 0.822870i | \(0.692372\pi\) | |||||||
\(230\) | −9.02651 | −0.595190 | ||||||||
\(231\) | −18.6355 | −1.22613 | ||||||||
\(232\) | 1.09497 | 0.0718885 | ||||||||
\(233\) | 9.94963 | 0.651822 | 0.325911 | − | 0.945400i | \(-0.394329\pi\) | ||||
0.325911 | + | 0.945400i | \(0.394329\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.97579 | −0.194119 | ||||||||
\(236\) | 11.1779 | 0.727619 | ||||||||
\(237\) | 16.8289 | 1.09316 | ||||||||
\(238\) | 6.06779 | 0.393317 | ||||||||
\(239\) | −27.2630 | −1.76350 | −0.881749 | − | 0.471719i | \(-0.843634\pi\) | ||||
−0.881749 | + | 0.471719i | \(0.843634\pi\) | |||||||
\(240\) | −2.38662 | −0.154056 | ||||||||
\(241\) | 3.05756 | 0.196955 | 0.0984774 | − | 0.995139i | \(-0.468603\pi\) | ||||
0.0984774 | + | 0.995139i | \(0.468603\pi\) | |||||||
\(242\) | 50.1274 | 3.22231 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −9.24751 | −0.592011 | ||||||||
\(245\) | 1.41529 | 0.0904195 | ||||||||
\(246\) | −17.6576 | −1.12581 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.65788 | 0.105276 | ||||||||
\(249\) | −4.52040 | −0.286469 | ||||||||
\(250\) | −10.7055 | −0.677076 | ||||||||
\(251\) | 11.1255 | 0.702237 | 0.351119 | − | 0.936331i | \(-0.385801\pi\) | ||||
0.351119 | + | 0.936331i | \(0.385801\pi\) | |||||||
\(252\) | −5.76383 | −0.363087 | ||||||||
\(253\) | −49.3218 | −3.10083 | ||||||||
\(254\) | −29.7765 | −1.86834 | ||||||||
\(255\) | −0.562071 | −0.0351983 | ||||||||
\(256\) | 17.8952 | 1.11845 | ||||||||
\(257\) | 3.24747 | 0.202571 | 0.101286 | − | 0.994857i | \(-0.467704\pi\) | ||||
0.101286 | + | 0.994857i | \(0.467704\pi\) | |||||||
\(258\) | 16.8052 | 1.04624 | ||||||||
\(259\) | −2.28716 | −0.142117 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.22613 | −0.261591 | ||||||||
\(262\) | −26.7216 | −1.65086 | ||||||||
\(263\) | −30.6388 | −1.88927 | −0.944634 | − | 0.328125i | \(-0.893583\pi\) | ||||
−0.944634 | + | 0.328125i | \(0.893583\pi\) | |||||||
\(264\) | −1.56505 | −0.0963223 | ||||||||
\(265\) | 4.13632 | 0.254092 | ||||||||
\(266\) | 24.0119 | 1.47226 | ||||||||
\(267\) | −5.32147 | −0.325669 | ||||||||
\(268\) | −14.5339 | −0.887798 | ||||||||
\(269\) | 7.44447 | 0.453897 | 0.226949 | − | 0.973907i | \(-0.427125\pi\) | ||||
0.226949 | + | 0.973907i | \(0.427125\pi\) | |||||||
\(270\) | 1.10548 | 0.0672771 | ||||||||
\(271\) | −10.2116 | −0.620310 | −0.310155 | − | 0.950686i | \(-0.600381\pi\) | ||||
−0.310155 | + | 0.950686i | \(0.600381\pi\) | |||||||
\(272\) | 4.24612 | 0.257459 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 37.8111 | 2.28425 | ||||||||
\(275\) | −28.2939 | −1.70618 | ||||||||
\(276\) | −15.2549 | −0.918236 | ||||||||
\(277\) | −24.7769 | −1.48870 | −0.744350 | − | 0.667790i | \(-0.767240\pi\) | ||||
−0.744350 | + | 0.667790i | \(0.767240\pi\) | |||||||
\(278\) | −31.1823 | −1.87019 | ||||||||
\(279\) | −6.39872 | −0.383081 | ||||||||
\(280\) | 0.449287 | 0.0268501 | ||||||||
\(281\) | 18.8029 | 1.12169 | 0.560843 | − | 0.827922i | \(-0.310477\pi\) | ||||
0.560843 | + | 0.827922i | \(0.310477\pi\) | |||||||
\(282\) | −10.4128 | −0.620075 | ||||||||
\(283\) | −3.60478 | −0.214282 | −0.107141 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107141 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(284\) | 18.3407 | 1.08832 | ||||||||
\(285\) | −2.22427 | −0.131754 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.6979 | 1.63495 | ||||||||
\(288\) | −7.83303 | −0.461566 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −4.67189 | −0.274343 | ||||||||
\(291\) | −7.70576 | −0.451719 | ||||||||
\(292\) | 16.2559 | 0.951304 | ||||||||
\(293\) | 9.00209 | 0.525908 | 0.262954 | − | 0.964808i | \(-0.415303\pi\) | ||||
0.262954 | + | 0.964808i | \(0.415303\pi\) | |||||||
\(294\) | 4.95236 | 0.288827 | ||||||||
\(295\) | 3.36289 | 0.195795 | ||||||||
\(296\) | −0.192081 | −0.0111645 | ||||||||
\(297\) | 6.04044 | 0.350502 | ||||||||
\(298\) | 15.8758 | 0.919663 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −8.75109 | −0.505245 | ||||||||
\(301\) | −26.3607 | −1.51941 | ||||||||
\(302\) | 31.3979 | 1.80675 | ||||||||
\(303\) | −10.7781 | −0.619187 | ||||||||
\(304\) | 16.8030 | 0.963720 | ||||||||
\(305\) | −2.78213 | −0.159304 | ||||||||
\(306\) | −1.96679 | −0.112434 | ||||||||
\(307\) | 4.04928 | 0.231105 | 0.115552 | − | 0.993301i | \(-0.463136\pi\) | ||||
0.115552 | + | 0.993301i | \(0.463136\pi\) | |||||||
\(308\) | −34.8160 | −1.98383 | ||||||||
\(309\) | −15.9795 | −0.909042 | ||||||||
\(310\) | −7.07363 | −0.401755 | ||||||||
\(311\) | −1.39386 | −0.0790388 | −0.0395194 | − | 0.999219i | \(-0.512583\pi\) | ||||
−0.0395194 | + | 0.999219i | \(0.512583\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.24637 | −0.0704491 | −0.0352246 | − | 0.999379i | \(-0.511215\pi\) | ||||
−0.0352246 | + | 0.999379i | \(0.511215\pi\) | |||||||
\(314\) | −31.9611 | −1.80367 | ||||||||
\(315\) | −1.73406 | −0.0977032 | ||||||||
\(316\) | 31.4409 | 1.76869 | ||||||||
\(317\) | 22.7068 | 1.27534 | 0.637670 | − | 0.770310i | \(-0.279898\pi\) | ||||
0.637670 | + | 0.770310i | \(0.279898\pi\) | |||||||
\(318\) | 14.4738 | 0.811648 | ||||||||
\(319\) | −25.5277 | −1.42928 | ||||||||
\(320\) | −3.88599 | −0.217233 | ||||||||
\(321\) | 2.30365 | 0.128577 | ||||||||
\(322\) | 49.5451 | 2.76104 | ||||||||
\(323\) | 3.95727 | 0.220188 | ||||||||
\(324\) | 1.86826 | 0.103792 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.47167 | −0.136893 | ||||||||
\(327\) | −4.13594 | −0.228718 | ||||||||
\(328\) | 2.32613 | 0.128439 | ||||||||
\(329\) | 16.3336 | 0.900503 | ||||||||
\(330\) | 6.67756 | 0.367588 | ||||||||
\(331\) | 1.42852 | 0.0785187 | 0.0392593 | − | 0.999229i | \(-0.487500\pi\) | ||||
0.0392593 | + | 0.999229i | \(0.487500\pi\) | |||||||
\(332\) | −8.44531 | −0.463496 | ||||||||
\(333\) | 0.741352 | 0.0406258 | ||||||||
\(334\) | 1.80937 | 0.0990046 | ||||||||
\(335\) | −4.37255 | −0.238898 | ||||||||
\(336\) | 13.0998 | 0.714652 | ||||||||
\(337\) | −19.7837 | −1.07769 | −0.538843 | − | 0.842406i | \(-0.681138\pi\) | ||||
−0.538843 | + | 0.842406i | \(0.681138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.7776 | 0.585359 | ||||||||
\(340\) | −1.05010 | −0.0569495 | ||||||||
\(341\) | −38.6511 | −2.09307 | ||||||||
\(342\) | −7.78312 | −0.420863 | ||||||||
\(343\) | 13.8276 | 0.746618 | ||||||||
\(344\) | −2.21384 | −0.119362 | ||||||||
\(345\) | −4.58946 | −0.247088 | ||||||||
\(346\) | 27.7567 | 1.49221 | ||||||||
\(347\) | −7.16826 | −0.384812 | −0.192406 | − | 0.981315i | \(-0.561629\pi\) | ||||
−0.192406 | + | 0.981315i | \(0.561629\pi\) | |||||||
\(348\) | −7.89554 | −0.423245 | ||||||||
\(349\) | −2.72048 | −0.145624 | −0.0728120 | − | 0.997346i | \(-0.523197\pi\) | ||||
−0.0728120 | + | 0.997346i | \(0.523197\pi\) | |||||||
\(350\) | 28.4220 | 1.51922 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −47.3149 | −2.52189 | ||||||||
\(353\) | −0.700200 | −0.0372679 | −0.0186339 | − | 0.999826i | \(-0.505932\pi\) | ||||
−0.0186339 | + | 0.999826i | \(0.505932\pi\) | |||||||
\(354\) | 11.7674 | 0.625429 | ||||||||
\(355\) | 5.51783 | 0.292856 | ||||||||
\(356\) | −9.94191 | −0.526920 | ||||||||
\(357\) | 3.08512 | 0.163282 | ||||||||
\(358\) | 11.2295 | 0.593496 | ||||||||
\(359\) | 2.63317 | 0.138973 | 0.0694866 | − | 0.997583i | \(-0.477864\pi\) | ||||
0.0694866 | + | 0.997583i | \(0.477864\pi\) | |||||||
\(360\) | −0.145630 | −0.00767539 | ||||||||
\(361\) | −3.34002 | −0.175791 | ||||||||
\(362\) | −38.3124 | −2.01365 | ||||||||
\(363\) | 25.4869 | 1.33771 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.89062 | 0.255987 | ||||||||
\(366\) | −9.73519 | −0.508866 | ||||||||
\(367\) | −4.41653 | −0.230541 | −0.115271 | − | 0.993334i | \(-0.536773\pi\) | ||||
−0.115271 | + | 0.993334i | \(0.536773\pi\) | |||||||
\(368\) | 34.6707 | 1.80733 | ||||||||
\(369\) | −8.97787 | −0.467369 | ||||||||
\(370\) | 0.819547 | 0.0426062 | ||||||||
\(371\) | −22.7037 | −1.17871 | ||||||||
\(372\) | −11.9545 | −0.619812 | ||||||||
\(373\) | 13.1003 | 0.678309 | 0.339155 | − | 0.940731i | \(-0.389859\pi\) | ||||
0.339155 | + | 0.940731i | \(0.389859\pi\) | |||||||
\(374\) | −11.8803 | −0.614314 | ||||||||
\(375\) | −5.44314 | −0.281083 | ||||||||
\(376\) | 1.37174 | 0.0707420 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −6.06779 | −0.312094 | ||||||||
\(379\) | 11.1265 | 0.571530 | 0.285765 | − | 0.958300i | \(-0.407752\pi\) | ||||
0.285765 | + | 0.958300i | \(0.407752\pi\) | |||||||
\(380\) | −4.15552 | −0.213174 | ||||||||
\(381\) | −15.1396 | −0.775627 | ||||||||
\(382\) | −5.03352 | −0.257537 | ||||||||
\(383\) | −6.29283 | −0.321549 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(384\) | 2.06827 | 0.105546 | ||||||||
\(385\) | −10.4745 | −0.533829 | ||||||||
\(386\) | −24.3340 | −1.23857 | ||||||||
\(387\) | 8.54447 | 0.434340 | ||||||||
\(388\) | −14.3964 | −0.730866 | ||||||||
\(389\) | −22.4981 | −1.14070 | −0.570349 | − | 0.821403i | \(-0.693192\pi\) | ||||
−0.570349 | + | 0.821403i | \(0.693192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.16527 | 0.412935 | ||||||||
\(392\) | −0.652401 | −0.0329512 | ||||||||
\(393\) | −13.5864 | −0.685343 | ||||||||
\(394\) | 19.8625 | 1.00066 | ||||||||
\(395\) | 9.45906 | 0.475937 | ||||||||
\(396\) | 11.2851 | 0.567099 | ||||||||
\(397\) | 6.09072 | 0.305684 | 0.152842 | − | 0.988251i | \(-0.451157\pi\) | ||||
0.152842 | + | 0.988251i | \(0.451157\pi\) | |||||||
\(398\) | −15.7008 | −0.787011 | ||||||||
\(399\) | 12.2087 | 0.611198 | ||||||||
\(400\) | 19.8891 | 0.994457 | ||||||||
\(401\) | −36.0160 | −1.79855 | −0.899277 | − | 0.437380i | \(-0.855906\pi\) | ||||
−0.899277 | + | 0.437380i | \(0.855906\pi\) | |||||||
\(402\) | −15.3003 | −0.763112 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −20.1364 | −1.00182 | ||||||||
\(405\) | 0.562071 | 0.0279295 | ||||||||
\(406\) | 25.6433 | 1.27266 | ||||||||
\(407\) | 4.47809 | 0.221971 | ||||||||
\(408\) | 0.259096 | 0.0128272 | ||||||||
\(409\) | 6.24154 | 0.308624 | 0.154312 | − | 0.988022i | \(-0.450684\pi\) | ||||
0.154312 | + | 0.988022i | \(0.450684\pi\) | |||||||
\(410\) | −9.92483 | −0.490152 | ||||||||
\(411\) | 19.2248 | 0.948287 | ||||||||
\(412\) | −29.8539 | −1.47080 | ||||||||
\(413\) | −18.4584 | −0.908279 | ||||||||
\(414\) | −16.0594 | −0.789275 | ||||||||
\(415\) | −2.54079 | −0.124722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.8544 | −0.776395 | ||||||||
\(418\) | −47.0134 | −2.29950 | ||||||||
\(419\) | 25.6818 | 1.25464 | 0.627319 | − | 0.778762i | \(-0.284152\pi\) | ||||
0.627319 | + | 0.778762i | \(0.284152\pi\) | |||||||
\(420\) | −3.23968 | −0.158080 | ||||||||
\(421\) | −3.69748 | −0.180204 | −0.0901020 | − | 0.995933i | \(-0.528719\pi\) | ||||
−0.0901020 | + | 0.995933i | \(0.528719\pi\) | |||||||
\(422\) | −26.2235 | −1.27654 | ||||||||
\(423\) | −5.29432 | −0.257419 | ||||||||
\(424\) | −1.90670 | −0.0925978 | ||||||||
\(425\) | 4.68408 | 0.227211 | ||||||||
\(426\) | 19.3079 | 0.935471 | ||||||||
\(427\) | 15.2707 | 0.739001 | ||||||||
\(428\) | 4.30384 | 0.208034 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.44571 | 0.455512 | ||||||||
\(431\) | 19.3305 | 0.931117 | 0.465558 | − | 0.885017i | \(-0.345854\pi\) | ||||
0.465558 | + | 0.885017i | \(0.345854\pi\) | |||||||
\(432\) | −4.24612 | −0.204291 | ||||||||
\(433\) | −33.4638 | −1.60817 | −0.804084 | − | 0.594515i | \(-0.797344\pi\) | ||||
−0.804084 | + | 0.594515i | \(0.797344\pi\) | |||||||
\(434\) | 38.8261 | 1.86371 | ||||||||
\(435\) | −2.37539 | −0.113891 | ||||||||
\(436\) | −7.72702 | −0.370057 | ||||||||
\(437\) | 32.3122 | 1.54570 | ||||||||
\(438\) | 17.1132 | 0.817699 | ||||||||
\(439\) | 33.6697 | 1.60697 | 0.803483 | − | 0.595328i | \(-0.202978\pi\) | ||||
0.803483 | + | 0.595328i | \(0.202978\pi\) | |||||||
\(440\) | −0.879671 | −0.0419367 | ||||||||
\(441\) | 2.51799 | 0.119904 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.0256 | −1.75914 | −0.879569 | − | 0.475771i | \(-0.842169\pi\) | ||||
−0.879569 | + | 0.475771i | \(0.842169\pi\) | |||||||
\(444\) | 1.38504 | 0.0657312 | ||||||||
\(445\) | −2.99104 | −0.141789 | ||||||||
\(446\) | 53.8422 | 2.54950 | ||||||||
\(447\) | 8.07196 | 0.381790 | ||||||||
\(448\) | 21.3296 | 1.00773 | ||||||||
\(449\) | 26.7583 | 1.26280 | 0.631402 | − | 0.775456i | \(-0.282480\pi\) | ||||
0.631402 | + | 0.775456i | \(0.282480\pi\) | |||||||
\(450\) | −9.21260 | −0.434286 | ||||||||
\(451\) | −54.2303 | −2.55360 | ||||||||
\(452\) | 20.1354 | 0.947090 | ||||||||
\(453\) | 15.9640 | 0.750056 | ||||||||
\(454\) | 37.5204 | 1.76092 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.02531 | 0.0480146 | ||||||||
\(457\) | −17.9259 | −0.838537 | −0.419269 | − | 0.907862i | \(-0.637713\pi\) | ||||
−0.419269 | + | 0.907862i | \(0.637713\pi\) | |||||||
\(458\) | −33.8244 | −1.58051 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −8.57433 | −0.399780 | ||||||||
\(461\) | 21.2476 | 0.989599 | 0.494800 | − | 0.869007i | \(-0.335241\pi\) | ||||
0.494800 | + | 0.869007i | \(0.335241\pi\) | |||||||
\(462\) | −36.6521 | −1.70521 | ||||||||
\(463\) | 7.65201 | 0.355619 | 0.177809 | − | 0.984065i | \(-0.443099\pi\) | ||||
0.177809 | + | 0.984065i | \(0.443099\pi\) | |||||||
\(464\) | 17.9447 | 0.833060 | ||||||||
\(465\) | −3.59653 | −0.166785 | ||||||||
\(466\) | 19.5688 | 0.906509 | ||||||||
\(467\) | 26.0658 | 1.20618 | 0.603091 | − | 0.797672i | \(-0.293935\pi\) | ||||
0.603091 | + | 0.797672i | \(0.293935\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0002 | 1.10823 | ||||||||
\(470\) | −5.85275 | −0.269967 | ||||||||
\(471\) | −16.2504 | −0.748779 | ||||||||
\(472\) | −1.55018 | −0.0713528 | ||||||||
\(473\) | 51.6123 | 2.37314 | ||||||||
\(474\) | 33.0990 | 1.52029 | ||||||||
\(475\) | 18.5361 | 0.850497 | ||||||||
\(476\) | 5.76383 | 0.264185 | ||||||||
\(477\) | 7.35907 | 0.336949 | ||||||||
\(478\) | −53.6207 | −2.45255 | ||||||||
\(479\) | −26.2639 | −1.20003 | −0.600014 | − | 0.799989i | \(-0.704838\pi\) | ||||
−0.600014 | + | 0.799989i | \(0.704838\pi\) | |||||||
\(480\) | −4.40272 | −0.200956 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.01358 | 0.273911 | ||||||||
\(483\) | 25.1909 | 1.14622 | ||||||||
\(484\) | 47.6163 | 2.16438 | ||||||||
\(485\) | −4.33118 | −0.196669 | ||||||||
\(486\) | 1.96679 | 0.0892154 | ||||||||
\(487\) | −23.9026 | −1.08313 | −0.541564 | − | 0.840659i | \(-0.682168\pi\) | ||||
−0.541564 | + | 0.840659i | \(0.682168\pi\) | |||||||
\(488\) | 1.28247 | 0.0580546 | ||||||||
\(489\) | −1.25670 | −0.0568300 | ||||||||
\(490\) | 2.78358 | 0.125749 | ||||||||
\(491\) | 16.1493 | 0.728809 | 0.364404 | − | 0.931241i | \(-0.381273\pi\) | ||||
0.364404 | + | 0.931241i | \(0.381273\pi\) | |||||||
\(492\) | −16.7730 | −0.756187 | ||||||||
\(493\) | 4.22613 | 0.190336 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.39516 | 0.152601 | ||||||||
\(496\) | 27.1697 | 1.21996 | ||||||||
\(497\) | −30.2865 | −1.35854 | ||||||||
\(498\) | −8.89068 | −0.398401 | ||||||||
\(499\) | 14.7230 | 0.659091 | 0.329546 | − | 0.944140i | \(-0.393104\pi\) | ||||
0.329546 | + | 0.944140i | \(0.393104\pi\) | |||||||
\(500\) | −10.1692 | −0.454782 | ||||||||
\(501\) | 0.919963 | 0.0411009 | ||||||||
\(502\) | 21.8816 | 0.976623 | ||||||||
\(503\) | −31.6338 | −1.41048 | −0.705240 | − | 0.708968i | \(-0.749161\pi\) | ||||
−0.705240 | + | 0.708968i | \(0.749161\pi\) | |||||||
\(504\) | 0.799343 | 0.0356056 | ||||||||
\(505\) | −6.05808 | −0.269581 | ||||||||
\(506\) | −97.0056 | −4.31243 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.2849 | −1.25494 | ||||||||
\(509\) | 7.45932 | 0.330629 | 0.165314 | − | 0.986241i | \(-0.447136\pi\) | ||||
0.165314 | + | 0.986241i | \(0.447136\pi\) | |||||||
\(510\) | −1.10548 | −0.0489513 | ||||||||
\(511\) | −26.8439 | −1.18750 | ||||||||
\(512\) | 31.0597 | 1.37266 | ||||||||
\(513\) | −3.95727 | −0.174718 | ||||||||
\(514\) | 6.38709 | 0.281722 | ||||||||
\(515\) | −8.98162 | −0.395778 | ||||||||
\(516\) | 15.9633 | 0.702746 | ||||||||
\(517\) | −31.9800 | −1.40648 | ||||||||
\(518\) | −4.49837 | −0.197647 | ||||||||
\(519\) | 14.1127 | 0.619478 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.0678 | −0.572511 | −0.286256 | − | 0.958153i | \(-0.592411\pi\) | ||||
−0.286256 | + | 0.958153i | \(0.592411\pi\) | |||||||
\(522\) | −8.31192 | −0.363803 | ||||||||
\(523\) | 24.0924 | 1.05349 | 0.526744 | − | 0.850024i | \(-0.323413\pi\) | ||||
0.526744 | + | 0.850024i | \(0.323413\pi\) | |||||||
\(524\) | −25.3830 | −1.10886 | ||||||||
\(525\) | 14.4510 | 0.630691 | ||||||||
\(526\) | −60.2601 | −2.62746 | ||||||||
\(527\) | 6.39872 | 0.278732 | ||||||||
\(528\) | −25.6484 | −1.11620 | ||||||||
\(529\) | 43.6716 | 1.89876 | ||||||||
\(530\) | 8.13528 | 0.353374 | ||||||||
\(531\) | 5.98304 | 0.259642 | ||||||||
\(532\) | 22.8090 | 0.988896 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −10.4662 | −0.452917 | ||||||||
\(535\) | 1.29482 | 0.0559799 | ||||||||
\(536\) | 2.01560 | 0.0870605 | ||||||||
\(537\) | 5.70954 | 0.246385 | ||||||||
\(538\) | 14.6417 | 0.631249 | ||||||||
\(539\) | 15.2098 | 0.655131 | ||||||||
\(540\) | 1.05010 | 0.0451890 | ||||||||
\(541\) | −6.66483 | −0.286543 | −0.143272 | − | 0.989683i | \(-0.545762\pi\) | ||||
−0.143272 | + | 0.989683i | \(0.545762\pi\) | |||||||
\(542\) | −20.0841 | −0.862685 | ||||||||
\(543\) | −19.4796 | −0.835951 | ||||||||
\(544\) | 7.83303 | 0.335838 | ||||||||
\(545\) | −2.32469 | −0.0995788 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6141 | 1.22345 | 0.611725 | − | 0.791070i | \(-0.290476\pi\) | ||||
0.611725 | + | 0.791070i | \(0.290476\pi\) | |||||||
\(548\) | 35.9169 | 1.53430 | ||||||||
\(549\) | −4.94978 | −0.211252 | ||||||||
\(550\) | −55.6481 | −2.37284 | ||||||||
\(551\) | 16.7239 | 0.712464 | ||||||||
\(552\) | 2.11559 | 0.0900453 | ||||||||
\(553\) | −51.9194 | −2.20784 | ||||||||
\(554\) | −48.7310 | −2.07038 | ||||||||
\(555\) | 0.416693 | 0.0176876 | ||||||||
\(556\) | −29.6203 | −1.25618 | ||||||||
\(557\) | 17.2596 | 0.731311 | 0.365656 | − | 0.930750i | \(-0.380845\pi\) | ||||
0.365656 | + | 0.930750i | \(0.380845\pi\) | |||||||
\(558\) | −12.5849 | −0.532763 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.36302 | 0.311144 | ||||||||
\(561\) | −6.04044 | −0.255027 | ||||||||
\(562\) | 36.9813 | 1.55996 | ||||||||
\(563\) | −26.3297 | −1.10967 | −0.554833 | − | 0.831962i | \(-0.687218\pi\) | ||||
−0.554833 | + | 0.831962i | \(0.687218\pi\) | |||||||
\(564\) | −9.89120 | −0.416495 | ||||||||
\(565\) | 6.05778 | 0.254853 | ||||||||
\(566\) | −7.08985 | −0.298009 | ||||||||
\(567\) | −3.08512 | −0.129563 | ||||||||
\(568\) | −2.54353 | −0.106724 | ||||||||
\(569\) | −39.1628 | −1.64179 | −0.820895 | − | 0.571080i | \(-0.806525\pi\) | ||||
−0.820895 | + | 0.571080i | \(0.806525\pi\) | |||||||
\(570\) | −4.37467 | −0.183235 | ||||||||
\(571\) | −29.3757 | −1.22934 | −0.614668 | − | 0.788786i | \(-0.710710\pi\) | ||||
−0.614668 | + | 0.788786i | \(0.710710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.55926 | −0.106915 | ||||||||
\(574\) | 54.4759 | 2.27378 | ||||||||
\(575\) | 38.2467 | 1.59500 | ||||||||
\(576\) | −6.91370 | −0.288071 | ||||||||
\(577\) | −14.9551 | −0.622588 | −0.311294 | − | 0.950314i | \(-0.600762\pi\) | ||||
−0.311294 | + | 0.950314i | \(0.600762\pi\) | |||||||
\(578\) | 1.96679 | 0.0818077 | ||||||||
\(579\) | −12.3724 | −0.514181 | ||||||||
\(580\) | −4.43785 | −0.184272 | ||||||||
\(581\) | 13.9460 | 0.578578 | ||||||||
\(582\) | −15.1556 | −0.628220 | ||||||||
\(583\) | 44.4520 | 1.84101 | ||||||||
\(584\) | −2.25441 | −0.0932882 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.7052 | 0.731396 | ||||||||
\(587\) | 29.4234 | 1.21443 | 0.607217 | − | 0.794536i | \(-0.292286\pi\) | ||||
0.607217 | + | 0.794536i | \(0.292286\pi\) | |||||||
\(588\) | 4.70427 | 0.194001 | ||||||||
\(589\) | 25.3214 | 1.04335 | ||||||||
\(590\) | 6.61411 | 0.272298 | ||||||||
\(591\) | 10.0989 | 0.415414 | ||||||||
\(592\) | −3.14787 | −0.129377 | ||||||||
\(593\) | 5.44237 | 0.223491 | 0.111746 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111746 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(594\) | 11.8803 | 0.487454 | ||||||||
\(595\) | 1.73406 | 0.0710895 | ||||||||
\(596\) | 15.0806 | 0.617724 | ||||||||
\(597\) | −7.98297 | −0.326721 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.9249 | 0.936684 | 0.468342 | − | 0.883547i | \(-0.344851\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344851\pi\) | |||||||
\(600\) | 1.21362 | 0.0495460 | ||||||||
\(601\) | 10.1779 | 0.415164 | 0.207582 | − | 0.978218i | \(-0.433441\pi\) | ||||
0.207582 | + | 0.978218i | \(0.433441\pi\) | |||||||
\(602\) | −51.8461 | −2.11309 | ||||||||
\(603\) | −7.77935 | −0.316799 | ||||||||
\(604\) | 29.8251 | 1.21356 | ||||||||
\(605\) | 14.3254 | 0.582412 | ||||||||
\(606\) | −21.1983 | −0.861123 | ||||||||
\(607\) | 19.8809 | 0.806941 | 0.403470 | − | 0.914993i | \(-0.367804\pi\) | ||||
0.403470 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(608\) | 30.9974 | 1.25711 | ||||||||
\(609\) | 13.0381 | 0.528332 | ||||||||
\(610\) | −5.47187 | −0.221550 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.86826 | −0.0755201 | ||||||||
\(613\) | −9.44265 | −0.381385 | −0.190692 | − | 0.981650i | \(-0.561073\pi\) | ||||
−0.190692 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(614\) | 7.96409 | 0.321404 | ||||||||
\(615\) | −5.04620 | −0.203483 | ||||||||
\(616\) | 4.82838 | 0.194541 | ||||||||
\(617\) | −41.5469 | −1.67261 | −0.836307 | − | 0.548261i | \(-0.815290\pi\) | ||||
−0.836307 | + | 0.548261i | \(0.815290\pi\) | |||||||
\(618\) | −31.4283 | −1.26423 | ||||||||
\(619\) | 14.8723 | 0.597767 | 0.298883 | − | 0.954290i | \(-0.403386\pi\) | ||||
0.298883 | + | 0.954290i | \(0.403386\pi\) | |||||||
\(620\) | −6.71928 | −0.269853 | ||||||||
\(621\) | −8.16527 | −0.327661 | ||||||||
\(622\) | −2.74144 | −0.109922 | ||||||||
\(623\) | 16.4174 | 0.657749 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3609 | 0.814438 | ||||||||
\(626\) | −2.45135 | −0.0979758 | ||||||||
\(627\) | −23.9036 | −0.954619 | ||||||||
\(628\) | −30.3600 | −1.21150 | ||||||||
\(629\) | −0.741352 | −0.0295596 | ||||||||
\(630\) | −3.41053 | −0.135879 | ||||||||
\(631\) | −15.9012 | −0.633017 | −0.316508 | − | 0.948590i | \(-0.602511\pi\) | ||||
−0.316508 | + | 0.948590i | \(0.602511\pi\) | |||||||
\(632\) | −4.36031 | −0.173444 | ||||||||
\(633\) | −13.3331 | −0.529945 | ||||||||
\(634\) | 44.6595 | 1.77365 | ||||||||
\(635\) | −8.50955 | −0.337691 | ||||||||
\(636\) | 13.7487 | 0.545171 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −50.2076 | −1.98774 | ||||||||
\(639\) | 9.81696 | 0.388353 | ||||||||
\(640\) | 1.16252 | 0.0459524 | ||||||||
\(641\) | 9.80513 | 0.387279 | 0.193640 | − | 0.981073i | \(-0.437971\pi\) | ||||
0.193640 | + | 0.981073i | \(0.437971\pi\) | |||||||
\(642\) | 4.53081 | 0.178817 | ||||||||
\(643\) | 23.5189 | 0.927496 | 0.463748 | − | 0.885967i | \(-0.346504\pi\) | ||||
0.463748 | + | 0.885967i | \(0.346504\pi\) | |||||||
\(644\) | 47.0632 | 1.85455 | ||||||||
\(645\) | 4.80260 | 0.189102 | ||||||||
\(646\) | 7.78312 | 0.306223 | ||||||||
\(647\) | 25.9839 | 1.02153 | 0.510766 | − | 0.859720i | \(-0.329362\pi\) | ||||
0.510766 | + | 0.859720i | \(0.329362\pi\) | |||||||
\(648\) | −0.259096 | −0.0101782 | ||||||||
\(649\) | 36.1402 | 1.41863 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.7408 | 0.773704 | ||||||||
\(652\) | −2.34785 | −0.0919489 | ||||||||
\(653\) | −14.2376 | −0.557161 | −0.278581 | − | 0.960413i | \(-0.589864\pi\) | ||||
−0.278581 | + | 0.960413i | \(0.589864\pi\) | |||||||
\(654\) | −8.13452 | −0.318085 | ||||||||
\(655\) | −7.63652 | −0.298383 | ||||||||
\(656\) | 38.1211 | 1.48838 | ||||||||
\(657\) | 8.70107 | 0.339461 | ||||||||
\(658\) | 32.1249 | 1.25236 | ||||||||
\(659\) | −15.5512 | −0.605788 | −0.302894 | − | 0.953024i | \(-0.597953\pi\) | ||||
−0.302894 | + | 0.953024i | \(0.597953\pi\) | |||||||
\(660\) | 6.34305 | 0.246903 | ||||||||
\(661\) | −9.77803 | −0.380321 | −0.190161 | − | 0.981753i | \(-0.560901\pi\) | ||||
−0.190161 | + | 0.981753i | \(0.560901\pi\) | |||||||
\(662\) | 2.80960 | 0.109198 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.17122 | 0.0454520 | ||||||||
\(665\) | 6.86214 | 0.266102 | ||||||||
\(666\) | 1.45808 | 0.0564996 | ||||||||
\(667\) | 34.5075 | 1.33614 | ||||||||
\(668\) | 1.71873 | 0.0664998 | ||||||||
\(669\) | 27.3756 | 1.05840 | ||||||||
\(670\) | −8.59988 | −0.332242 | ||||||||
\(671\) | −29.8989 | −1.15423 | ||||||||
\(672\) | 24.1659 | 0.932219 | ||||||||
\(673\) | 5.28038 | 0.203544 | 0.101772 | − | 0.994808i | \(-0.467549\pi\) | ||||
0.101772 | + | 0.994808i | \(0.467549\pi\) | |||||||
\(674\) | −38.9103 | −1.49877 | ||||||||
\(675\) | −4.68408 | −0.180290 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.5267 | −1.13480 | −0.567401 | − | 0.823441i | \(-0.692051\pi\) | ||||
−0.567401 | + | 0.823441i | \(0.692051\pi\) | |||||||
\(678\) | 21.1973 | 0.814077 | ||||||||
\(679\) | 23.7732 | 0.912332 | ||||||||
\(680\) | 0.145630 | 0.00558467 | ||||||||
\(681\) | 19.0770 | 0.731032 | ||||||||
\(682\) | −76.0185 | −2.91090 | ||||||||
\(683\) | −26.6474 | −1.01963 | −0.509817 | − | 0.860283i | \(-0.670287\pi\) | ||||
−0.509817 | + | 0.860283i | \(0.670287\pi\) | |||||||
\(684\) | −7.39323 | −0.282687 | ||||||||
\(685\) | 10.8057 | 0.412864 | ||||||||
\(686\) | 27.1959 | 1.03834 | ||||||||
\(687\) | −17.1978 | −0.656135 | ||||||||
\(688\) | −36.2808 | −1.38319 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −9.02651 | −0.343633 | ||||||||
\(691\) | −3.28553 | −0.124987 | −0.0624937 | − | 0.998045i | \(-0.519905\pi\) | ||||
−0.0624937 | + | 0.998045i | \(0.519905\pi\) | |||||||
\(692\) | 26.3662 | 1.00229 | ||||||||
\(693\) | −18.6355 | −0.707904 | ||||||||
\(694\) | −14.0985 | −0.535170 | ||||||||
\(695\) | −8.91132 | −0.338026 | ||||||||
\(696\) | 1.09497 | 0.0415049 | ||||||||
\(697\) | 8.97787 | 0.340061 | ||||||||
\(698\) | −5.35061 | −0.202524 | ||||||||
\(699\) | 9.94963 | 0.376330 | ||||||||
\(700\) | 26.9982 | 1.02044 | ||||||||
\(701\) | 26.0823 | 0.985116 | 0.492558 | − | 0.870280i | \(-0.336062\pi\) | ||||
0.492558 | + | 0.870280i | \(0.336062\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.93373 | −0.110648 | ||||||||
\(704\) | −41.7617 | −1.57395 | ||||||||
\(705\) | −2.97579 | −0.112075 | ||||||||
\(706\) | −1.37715 | −0.0518296 | ||||||||
\(707\) | 33.2519 | 1.25056 | ||||||||
\(708\) | 11.1779 | 0.420091 | ||||||||
\(709\) | 32.2385 | 1.21074 | 0.605372 | − | 0.795943i | \(-0.293024\pi\) | ||||
0.605372 | + | 0.795943i | \(0.293024\pi\) | |||||||
\(710\) | 10.8524 | 0.407284 | ||||||||
\(711\) | 16.8289 | 0.631135 | ||||||||
\(712\) | 1.37877 | 0.0516716 | ||||||||
\(713\) | 52.2472 | 1.95667 | ||||||||
\(714\) | 6.06779 | 0.227081 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.6669 | 0.398642 | ||||||||
\(717\) | −27.2630 | −1.01816 | ||||||||
\(718\) | 5.17888 | 0.193274 | ||||||||
\(719\) | 15.1113 | 0.563556 | 0.281778 | − | 0.959480i | \(-0.409076\pi\) | ||||
0.281778 | + | 0.959480i | \(0.409076\pi\) | |||||||
\(720\) | −2.38662 | −0.0889441 | ||||||||
\(721\) | 49.2988 | 1.83598 | ||||||||
\(722\) | −6.56913 | −0.244478 | ||||||||
\(723\) | 3.05756 | 0.113712 | ||||||||
\(724\) | −36.3931 | −1.35254 | ||||||||
\(725\) | 19.7955 | 0.735188 | ||||||||
\(726\) | 50.1274 | 1.86040 | ||||||||
\(727\) | 12.1366 | 0.450120 | 0.225060 | − | 0.974345i | \(-0.427742\pi\) | ||||
0.225060 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.61882 | 0.356009 | ||||||||
\(731\) | −8.54447 | −0.316029 | ||||||||
\(732\) | −9.24751 | −0.341798 | ||||||||
\(733\) | −33.8030 | −1.24854 | −0.624271 | − | 0.781207i | \(-0.714604\pi\) | ||||
−0.624271 | + | 0.781207i | \(0.714604\pi\) | |||||||
\(734\) | −8.68639 | −0.320621 | ||||||||
\(735\) | 1.41529 | 0.0522037 | ||||||||
\(736\) | 63.9588 | 2.35755 | ||||||||
\(737\) | −46.9907 | −1.73092 | ||||||||
\(738\) | −17.6576 | −0.649985 | ||||||||
\(739\) | 35.2527 | 1.29679 | 0.648396 | − | 0.761303i | \(-0.275440\pi\) | ||||
0.648396 | + | 0.761303i | \(0.275440\pi\) | |||||||
\(740\) | 0.778492 | 0.0286179 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −44.6533 | −1.63928 | ||||||||
\(743\) | 23.7391 | 0.870902 | 0.435451 | − | 0.900213i | \(-0.356589\pi\) | ||||
0.435451 | + | 0.900213i | \(0.356589\pi\) | |||||||
\(744\) | 1.65788 | 0.0607809 | ||||||||
\(745\) | 4.53701 | 0.166223 | ||||||||
\(746\) | 25.7656 | 0.943346 | ||||||||
\(747\) | −4.52040 | −0.165393 | ||||||||
\(748\) | −11.2851 | −0.412625 | ||||||||
\(749\) | −7.10706 | −0.259686 | ||||||||
\(750\) | −10.7055 | −0.390910 | ||||||||
\(751\) | −44.6624 | −1.62975 | −0.814877 | − | 0.579634i | \(-0.803196\pi\) | ||||
−0.814877 | + | 0.579634i | \(0.803196\pi\) | |||||||
\(752\) | 22.4803 | 0.819773 | ||||||||
\(753\) | 11.1255 | 0.405437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.97293 | 0.326558 | ||||||||
\(756\) | −5.76383 | −0.209628 | ||||||||
\(757\) | 9.07166 | 0.329715 | 0.164858 | − | 0.986317i | \(-0.447284\pi\) | ||||
0.164858 | + | 0.986317i | \(0.447284\pi\) | |||||||
\(758\) | 21.8835 | 0.794844 | ||||||||
\(759\) | −49.3218 | −1.79027 | ||||||||
\(760\) | 0.576298 | 0.0209045 | ||||||||
\(761\) | −24.7150 | −0.895917 | −0.447959 | − | 0.894054i | \(-0.647849\pi\) | ||||
−0.447959 | + | 0.894054i | \(0.647849\pi\) | |||||||
\(762\) | −29.7765 | −1.07869 | ||||||||
\(763\) | 12.7599 | 0.461939 | ||||||||
\(764\) | −4.78137 | −0.172984 | ||||||||
\(765\) | −0.562071 | −0.0203217 | ||||||||
\(766\) | −12.3767 | −0.447188 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 17.8952 | 0.645739 | ||||||||
\(769\) | 46.3877 | 1.67278 | 0.836392 | − | 0.548132i | \(-0.184661\pi\) | ||||
0.836392 | + | 0.548132i | \(0.184661\pi\) | |||||||
\(770\) | −20.6011 | −0.742412 | ||||||||
\(771\) | 3.24747 | 0.116955 | ||||||||
\(772\) | −23.1150 | −0.831926 | ||||||||
\(773\) | 48.1734 | 1.73268 | 0.866338 | − | 0.499459i | \(-0.166468\pi\) | ||||
0.866338 | + | 0.499459i | \(0.166468\pi\) | |||||||
\(774\) | 16.8052 | 0.604050 | ||||||||
\(775\) | 29.9721 | 1.07663 | ||||||||
\(776\) | 1.99653 | 0.0716712 | ||||||||
\(777\) | −2.28716 | −0.0820515 | ||||||||
\(778\) | −44.2490 | −1.58640 | ||||||||
\(779\) | 35.5279 | 1.27292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.2987 | 2.12188 | ||||||||
\(782\) | 16.0594 | 0.574282 | ||||||||
\(783\) | −4.22613 | −0.151030 | ||||||||
\(784\) | −10.6917 | −0.381846 | ||||||||
\(785\) | −9.13388 | −0.326002 | ||||||||
\(786\) | −26.7216 | −0.953127 | ||||||||
\(787\) | 27.7635 | 0.989661 | 0.494830 | − | 0.868990i | \(-0.335230\pi\) | ||||
0.494830 | + | 0.868990i | \(0.335230\pi\) | |||||||
\(788\) | 18.8675 | 0.672125 | ||||||||
\(789\) | −30.6388 | −1.09077 | ||||||||
\(790\) | 18.6040 | 0.661900 | ||||||||
\(791\) | −33.2502 | −1.18224 | ||||||||
\(792\) | −1.56505 | −0.0556117 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.9792 | 0.425125 | ||||||||
\(795\) | 4.13632 | 0.146700 | ||||||||
\(796\) | −14.9143 | −0.528623 | ||||||||
\(797\) | 13.7497 | 0.487039 | 0.243519 | − | 0.969896i | \(-0.421698\pi\) | ||||
0.243519 | + | 0.969896i | \(0.421698\pi\) | |||||||
\(798\) | 24.0119 | 0.850011 | ||||||||
\(799\) | 5.29432 | 0.187300 | ||||||||
\(800\) | 36.6905 | 1.29721 | ||||||||
\(801\) | −5.32147 | −0.188025 | ||||||||
\(802\) | −70.8359 | −2.50130 | ||||||||
\(803\) | 52.5583 | 1.85474 | ||||||||
\(804\) | −14.5339 | −0.512570 | ||||||||
\(805\) | 14.1591 | 0.499041 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.44447 | 0.262058 | ||||||||
\(808\) | 2.79257 | 0.0982422 | ||||||||
\(809\) | 27.9241 | 0.981758 | 0.490879 | − | 0.871228i | \(-0.336676\pi\) | ||||
0.490879 | + | 0.871228i | \(0.336676\pi\) | |||||||
\(810\) | 1.10548 | 0.0388425 | ||||||||
\(811\) | −0.352736 | −0.0123862 | −0.00619312 | − | 0.999981i | \(-0.501971\pi\) | ||||
−0.00619312 | + | 0.999981i | \(0.501971\pi\) | |||||||
\(812\) | 24.3587 | 0.854823 | ||||||||
\(813\) | −10.2116 | −0.358136 | ||||||||
\(814\) | 8.80747 | 0.308701 | ||||||||
\(815\) | −0.706356 | −0.0247426 | ||||||||
\(816\) | 4.24612 | 0.148644 | ||||||||
\(817\) | −33.8128 | −1.18296 | ||||||||
\(818\) | 12.2758 | 0.429213 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.42764 | −0.329228 | ||||||||
\(821\) | −6.30618 | −0.220087 | −0.110044 | − | 0.993927i | \(-0.535099\pi\) | ||||
−0.110044 | + | 0.993927i | \(0.535099\pi\) | |||||||
\(822\) | 37.8111 | 1.31881 | ||||||||
\(823\) | −11.2909 | −0.393575 | −0.196787 | − | 0.980446i | \(-0.563051\pi\) | ||||
−0.196787 | + | 0.980446i | \(0.563051\pi\) | |||||||
\(824\) | 4.14022 | 0.144232 | ||||||||
\(825\) | −28.2939 | −0.985066 | ||||||||
\(826\) | −36.3038 | −1.26317 | ||||||||
\(827\) | 33.2092 | 1.15480 | 0.577399 | − | 0.816462i | \(-0.304068\pi\) | ||||
0.577399 | + | 0.816462i | \(0.304068\pi\) | |||||||
\(828\) | −15.2549 | −0.530144 | ||||||||
\(829\) | 11.9060 | 0.413513 | 0.206757 | − | 0.978392i | \(-0.433709\pi\) | ||||
0.206757 | + | 0.978392i | \(0.433709\pi\) | |||||||
\(830\) | −4.99720 | −0.173455 | ||||||||
\(831\) | −24.7769 | −0.859501 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.51799 | −0.0872432 | ||||||||
\(834\) | −31.1823 | −1.07976 | ||||||||
\(835\) | 0.517085 | 0.0178945 | ||||||||
\(836\) | −44.6583 | −1.54454 | ||||||||
\(837\) | −6.39872 | −0.221172 | ||||||||
\(838\) | 50.5107 | 1.74486 | ||||||||
\(839\) | 7.82667 | 0.270207 | 0.135103 | − | 0.990832i | \(-0.456863\pi\) | ||||
0.135103 | + | 0.990832i | \(0.456863\pi\) | |||||||
\(840\) | 0.449287 | 0.0155019 | ||||||||
\(841\) | −11.1398 | −0.384131 | ||||||||
\(842\) | −7.27216 | −0.250615 | ||||||||
\(843\) | 18.8029 | 0.647605 | ||||||||
\(844\) | −24.9098 | −0.857432 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −10.4128 | −0.358000 | ||||||||
\(847\) | −78.6302 | −2.70177 | ||||||||
\(848\) | −31.2475 | −1.07304 | ||||||||
\(849\) | −3.60478 | −0.123716 | ||||||||
\(850\) | 9.21260 | 0.315989 | ||||||||
\(851\) | −6.05334 | −0.207506 | ||||||||
\(852\) | 18.3407 | 0.628341 | ||||||||
\(853\) | −7.47045 | −0.255784 | −0.127892 | − | 0.991788i | \(-0.540821\pi\) | ||||
−0.127892 | + | 0.991788i | \(0.540821\pi\) | |||||||
\(854\) | 30.0343 | 1.02775 | ||||||||
\(855\) | −2.22427 | −0.0760683 | ||||||||
\(856\) | −0.596867 | −0.0204005 | ||||||||
\(857\) | −38.9743 | −1.33134 | −0.665668 | − | 0.746248i | \(-0.731853\pi\) | ||||
−0.665668 | + | 0.746248i | \(0.731853\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0228 | 0.376092 | 0.188046 | − | 0.982160i | \(-0.439785\pi\) | ||||
0.188046 | + | 0.982160i | \(0.439785\pi\) | |||||||
\(860\) | 8.97253 | 0.305961 | ||||||||
\(861\) | 27.6979 | 0.943940 | ||||||||
\(862\) | 38.0190 | 1.29493 | ||||||||
\(863\) | −29.4909 | −1.00388 | −0.501941 | − | 0.864902i | \(-0.667381\pi\) | ||||
−0.501941 | + | 0.864902i | \(0.667381\pi\) | |||||||
\(864\) | −7.83303 | −0.266485 | ||||||||
\(865\) | 7.93233 | 0.269707 | ||||||||
\(866\) | −65.8163 | −2.23653 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 36.8811 | 1.25183 | ||||||||
\(869\) | 101.654 | 3.44838 | ||||||||
\(870\) | −4.67189 | −0.158392 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.07160 | 0.0362891 | ||||||||
\(873\) | −7.70576 | −0.260800 | ||||||||
\(874\) | 63.5512 | 2.14965 | ||||||||
\(875\) | 16.7928 | 0.567699 | ||||||||
\(876\) | 16.2559 | 0.549236 | ||||||||
\(877\) | 12.0028 | 0.405305 | 0.202653 | − | 0.979251i | \(-0.435044\pi\) | ||||
0.202653 | + | 0.979251i | \(0.435044\pi\) | |||||||
\(878\) | 66.2212 | 2.23486 | ||||||||
\(879\) | 9.00209 | 0.303633 | ||||||||
\(880\) | −14.4162 | −0.485971 | ||||||||
\(881\) | −0.432480 | −0.0145706 | −0.00728530 | − | 0.999973i | \(-0.502319\pi\) | ||||
−0.00728530 | + | 0.999973i | \(0.502319\pi\) | |||||||
\(882\) | 4.95236 | 0.166755 | ||||||||
\(883\) | 40.1105 | 1.34983 | 0.674913 | − | 0.737898i | \(-0.264181\pi\) | ||||
0.674913 | + | 0.737898i | \(0.264181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.36289 | 0.113042 | ||||||||
\(886\) | −72.8216 | −2.44649 | ||||||||
\(887\) | −54.2453 | −1.82138 | −0.910690 | − | 0.413091i | \(-0.864449\pi\) | ||||
−0.910690 | + | 0.413091i | \(0.864449\pi\) | |||||||
\(888\) | −0.192081 | −0.00644582 | ||||||||
\(889\) | 46.7077 | 1.56652 | ||||||||
\(890\) | −5.88276 | −0.197190 | ||||||||
\(891\) | 6.04044 | 0.202362 | ||||||||
\(892\) | 51.1449 | 1.71246 | ||||||||
\(893\) | 20.9511 | 0.701101 | ||||||||
\(894\) | 15.8758 | 0.530968 | ||||||||
\(895\) | 3.20917 | 0.107271 | ||||||||
\(896\) | −6.38087 | −0.213170 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52.6280 | 1.75622 | ||||||||
\(899\) | 27.0418 | 0.901896 | ||||||||
\(900\) | −8.75109 | −0.291703 | ||||||||
\(901\) | −7.35907 | −0.245166 | ||||||||
\(902\) | −106.660 | −3.55138 | ||||||||
\(903\) | −26.3607 | −0.877231 | ||||||||
\(904\) | −2.79243 | −0.0928749 | ||||||||
\(905\) | −10.9489 | −0.363955 | ||||||||
\(906\) | 31.3979 | 1.04313 | ||||||||
\(907\) | 22.6243 | 0.751227 | 0.375613 | − | 0.926776i | \(-0.377432\pi\) | ||||
0.375613 | + | 0.926776i | \(0.377432\pi\) | |||||||
\(908\) | 35.6409 | 1.18278 | ||||||||
\(909\) | −10.7781 | −0.357488 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7628 | −0.455981 | −0.227990 | − | 0.973663i | \(-0.573215\pi\) | ||||
−0.227990 | + | 0.973663i | \(0.573215\pi\) | |||||||
\(912\) | 16.8030 | 0.556404 | ||||||||
\(913\) | −27.3052 | −0.903670 | ||||||||
\(914\) | −35.2565 | −1.16618 | ||||||||
\(915\) | −2.78213 | −0.0919744 | ||||||||
\(916\) | −32.1300 | −1.06160 | ||||||||
\(917\) | 41.9157 | 1.38418 | ||||||||
\(918\) | −1.96679 | −0.0649138 | ||||||||
\(919\) | −16.6604 | −0.549576 | −0.274788 | − | 0.961505i | \(-0.588608\pi\) | ||||
−0.274788 | + | 0.961505i | \(0.588608\pi\) | |||||||
\(920\) | 1.18911 | 0.0392038 | ||||||||
\(921\) | 4.04928 | 0.133428 | ||||||||
\(922\) | 41.7896 | 1.37627 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −34.8160 | −1.14536 | ||||||||
\(925\) | −3.47255 | −0.114177 | ||||||||
\(926\) | 15.0499 | 0.494570 | ||||||||
\(927\) | −15.9795 | −0.524836 | ||||||||
\(928\) | 33.1034 | 1.08667 | ||||||||
\(929\) | −19.4777 | −0.639044 | −0.319522 | − | 0.947579i | \(-0.603522\pi\) | ||||
−0.319522 | + | 0.947579i | \(0.603522\pi\) | |||||||
\(930\) | −7.07363 | −0.231953 | ||||||||
\(931\) | −9.96436 | −0.326569 | ||||||||
\(932\) | 18.5885 | 0.608888 | ||||||||
\(933\) | −1.39386 | −0.0456331 | ||||||||
\(934\) | 51.2660 | 1.67748 | ||||||||
\(935\) | −3.39516 | −0.111033 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4402 | 0.765757 | 0.382879 | − | 0.923799i | \(-0.374933\pi\) | ||||
0.382879 | + | 0.923799i | \(0.374933\pi\) | |||||||
\(938\) | 47.2035 | 1.54125 | ||||||||
\(939\) | −1.24637 | −0.0406738 | ||||||||
\(940\) | −5.55956 | −0.181333 | ||||||||
\(941\) | −6.19102 | −0.201822 | −0.100911 | − | 0.994895i | \(-0.532176\pi\) | ||||
−0.100911 | + | 0.994895i | \(0.532176\pi\) | |||||||
\(942\) | −31.9611 | −1.04135 | ||||||||
\(943\) | 73.3067 | 2.38720 | ||||||||
\(944\) | −25.4047 | −0.826852 | ||||||||
\(945\) | −1.73406 | −0.0564090 | ||||||||
\(946\) | 101.511 | 3.30040 | ||||||||
\(947\) | 39.8530 | 1.29505 | 0.647525 | − | 0.762045i | \(-0.275804\pi\) | ||||
0.647525 | + | 0.762045i | \(0.275804\pi\) | |||||||
\(948\) | 31.4409 | 1.02115 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 36.4567 | 1.18281 | ||||||||
\(951\) | 22.7068 | 0.736318 | ||||||||
\(952\) | −0.799343 | −0.0259068 | ||||||||
\(953\) | 16.5030 | 0.534586 | 0.267293 | − | 0.963615i | \(-0.413871\pi\) | ||||
0.267293 | + | 0.963615i | \(0.413871\pi\) | |||||||
\(954\) | 14.4738 | 0.468605 | ||||||||
\(955\) | −1.43849 | −0.0465483 | ||||||||
\(956\) | −50.9345 | −1.64734 | ||||||||
\(957\) | −25.5277 | −0.825193 | ||||||||
\(958\) | −51.6556 | −1.66892 | ||||||||
\(959\) | −59.3108 | −1.91524 | ||||||||
\(960\) | −3.88599 | −0.125420 | ||||||||
\(961\) | 9.94358 | 0.320761 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.30365 | 0.0742342 | ||||||||
\(964\) | 5.71234 | 0.183982 | ||||||||
\(965\) | −6.95419 | −0.223863 | ||||||||
\(966\) | 49.5451 | 1.59409 | ||||||||
\(967\) | 18.6447 | 0.599573 | 0.299786 | − | 0.954006i | \(-0.403085\pi\) | ||||
0.299786 | + | 0.954006i | \(0.403085\pi\) | |||||||
\(968\) | −6.60355 | −0.212246 | ||||||||
\(969\) | 3.95727 | 0.127126 | ||||||||
\(970\) | −8.51853 | −0.273514 | ||||||||
\(971\) | 36.1738 | 1.16087 | 0.580435 | − | 0.814306i | \(-0.302882\pi\) | ||||
0.580435 | + | 0.814306i | \(0.302882\pi\) | |||||||
\(972\) | 1.86826 | 0.0599246 | ||||||||
\(973\) | 48.9129 | 1.56807 | ||||||||
\(974\) | −47.0114 | −1.50634 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.0174 | 0.672749 | ||||||||
\(977\) | 9.18599 | 0.293886 | 0.146943 | − | 0.989145i | \(-0.453057\pi\) | ||||
0.146943 | + | 0.989145i | \(0.453057\pi\) | |||||||
\(978\) | −2.47167 | −0.0790352 | ||||||||
\(979\) | −32.1440 | −1.02733 | ||||||||
\(980\) | 2.64414 | 0.0844638 | ||||||||
\(981\) | −4.13594 | −0.132050 | ||||||||
\(982\) | 31.7623 | 1.01358 | ||||||||
\(983\) | −9.47337 | −0.302154 | −0.151077 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151077 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(984\) | 2.32613 | 0.0741543 | ||||||||
\(985\) | 5.67631 | 0.180862 | ||||||||
\(986\) | 8.31192 | 0.264705 | ||||||||
\(987\) | 16.3336 | 0.519906 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69.7679 | −2.21849 | ||||||||
\(990\) | 6.67756 | 0.212227 | ||||||||
\(991\) | −23.3313 | −0.741143 | −0.370572 | − | 0.928804i | \(-0.620838\pi\) | ||||
−0.370572 | + | 0.928804i | \(0.620838\pi\) | |||||||
\(992\) | 50.1213 | 1.59135 | ||||||||
\(993\) | 1.42852 | 0.0453328 | ||||||||
\(994\) | −59.5673 | −1.88936 | ||||||||
\(995\) | −4.48700 | −0.142247 | ||||||||
\(996\) | −8.44531 | −0.267600 | ||||||||
\(997\) | −13.2407 | −0.419337 | −0.209669 | − | 0.977772i | \(-0.567239\pi\) | ||||
−0.209669 | + | 0.977772i | \(0.567239\pi\) | |||||||
\(998\) | 28.9570 | 0.916619 | ||||||||
\(999\) | 0.741352 | 0.0234553 |
(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 | 8619.2.a.bn.1.14 | 16 | ||
13.6 | odd | 12 | 663.2.z.d.205.2 | ✓ | 16 | ||
13.11 | odd | 12 | 663.2.z.d.511.2 | yes | 16 | ||
13.12 | even | 2 | inner | 8619.2.a.bn.1.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
663.2.z.d.205.2 | ✓ | 16 | 13.6 | odd | 12 | ||
663.2.z.d.511.2 | yes | 16 | 13.11 | odd | 12 | ||
8619.2.a.bn.1.3 | 16 | 13.12 | even | 2 | inner | ||
8619.2.a.bn.1.14 | 16 | 1.1 | even | 1 | trivial |