Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5929,2,Mod(1,5929)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5929, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5929.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5929 = 7^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5929.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: | \(47.3433033584\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.11447\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5929.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11447 | −0.788047 | −0.394023 | − | 0.919100i | \(-0.628917\pi\) | ||||
−0.394023 | + | 0.919100i | \(0.628917\pi\) | |||||||
\(3\) | 2.85882 | 1.65054 | 0.825270 | − | 0.564739i | \(-0.191023\pi\) | ||||
0.825270 | + | 0.564739i | \(0.191023\pi\) | |||||||
\(4\) | −0.757964 | −0.378982 | ||||||||
\(5\) | −3.45608 | −1.54561 | −0.772803 | − | 0.634647i | \(-0.781146\pi\) | ||||
−0.772803 | + | 0.634647i | \(0.781146\pi\) | |||||||
\(6\) | −3.18606 | −1.30070 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07366 | 1.08670 | ||||||||
\(9\) | 5.17284 | 1.72428 | ||||||||
\(10\) | 3.85168 | 1.21801 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.16688 | −0.625525 | ||||||||
\(13\) | −2.05965 | −0.571245 | −0.285622 | − | 0.958342i | \(-0.592200\pi\) | ||||
−0.285622 | + | 0.958342i | \(0.592200\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.88030 | −2.55108 | ||||||||
\(16\) | −1.90956 | −0.477390 | ||||||||
\(17\) | 1.93373 | 0.468998 | 0.234499 | − | 0.972116i | \(-0.424655\pi\) | ||||
0.234499 | + | 0.972116i | \(0.424655\pi\) | |||||||
\(18\) | −5.76496 | −1.35881 | ||||||||
\(19\) | 1.62296 | 0.372333 | 0.186166 | − | 0.982518i | \(-0.440394\pi\) | ||||
0.186166 | + | 0.982518i | \(0.440394\pi\) | |||||||
\(20\) | 2.61958 | 0.585757 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.807136 | −0.168299 | −0.0841497 | − | 0.996453i | \(-0.526817\pi\) | ||||
−0.0841497 | + | 0.996453i | \(0.526817\pi\) | |||||||
\(24\) | 8.78703 | 1.79365 | ||||||||
\(25\) | 6.94447 | 1.38889 | ||||||||
\(26\) | 2.29541 | 0.450168 | ||||||||
\(27\) | 6.21176 | 1.19545 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.97368 | −1.48067 | −0.740337 | − | 0.672235i | \(-0.765334\pi\) | ||||
−0.740337 | + | 0.672235i | \(0.765334\pi\) | |||||||
\(30\) | 11.0113 | 2.01037 | ||||||||
\(31\) | −0.788420 | −0.141604 | −0.0708022 | − | 0.997490i | \(-0.522556\pi\) | ||||
−0.0708022 | + | 0.997490i | \(0.522556\pi\) | |||||||
\(32\) | −4.01918 | −0.710497 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.15508 | −0.369592 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.92083 | −0.653471 | ||||||||
\(37\) | 10.0618 | 1.65414 | 0.827072 | − | 0.562096i | \(-0.190005\pi\) | ||||
0.827072 | + | 0.562096i | \(0.190005\pi\) | |||||||
\(38\) | −1.80873 | −0.293415 | ||||||||
\(39\) | −5.88817 | −0.942862 | ||||||||
\(40\) | −10.6228 | −1.67961 | ||||||||
\(41\) | −2.12613 | −0.332046 | −0.166023 | − | 0.986122i | \(-0.553093\pi\) | ||||
−0.166023 | + | 0.986122i | \(0.553093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.08043 | −0.469761 | −0.234880 | − | 0.972024i | \(-0.575470\pi\) | ||||
−0.234880 | + | 0.972024i | \(0.575470\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.8777 | −2.66506 | ||||||||
\(46\) | 0.899526 | 0.132628 | ||||||||
\(47\) | −7.56632 | −1.10366 | −0.551831 | − | 0.833956i | \(-0.686070\pi\) | ||||
−0.551831 | + | 0.833956i | \(0.686070\pi\) | |||||||
\(48\) | −5.45909 | −0.787952 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.73938 | −1.09451 | ||||||||
\(51\) | 5.52818 | 0.774100 | ||||||||
\(52\) | 1.56114 | 0.216492 | ||||||||
\(53\) | 10.8224 | 1.48658 | 0.743289 | − | 0.668971i | \(-0.233265\pi\) | ||||
0.743289 | + | 0.668971i | \(0.233265\pi\) | |||||||
\(54\) | −6.92280 | −0.942073 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.63975 | 0.614550 | ||||||||
\(58\) | 8.88640 | 1.16684 | ||||||||
\(59\) | 3.29664 | 0.429186 | 0.214593 | − | 0.976704i | \(-0.431158\pi\) | ||||
0.214593 | + | 0.976704i | \(0.431158\pi\) | |||||||
\(60\) | 7.48891 | 0.966814 | ||||||||
\(61\) | −1.07663 | −0.137848 | −0.0689240 | − | 0.997622i | \(-0.521957\pi\) | ||||
−0.0689240 | + | 0.997622i | \(0.521957\pi\) | |||||||
\(62\) | 0.878667 | 0.111591 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.29836 | 1.03729 | ||||||||
\(65\) | 7.11832 | 0.882919 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.40314 | 0.293590 | 0.146795 | − | 0.989167i | \(-0.453104\pi\) | ||||
0.146795 | + | 0.989167i | \(0.453104\pi\) | |||||||
\(68\) | −1.46570 | −0.177742 | ||||||||
\(69\) | −2.30745 | −0.277785 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.18859 | −0.378417 | −0.189208 | − | 0.981937i | \(-0.560592\pi\) | ||||
−0.189208 | + | 0.981937i | \(0.560592\pi\) | |||||||
\(72\) | 15.8995 | 1.87378 | ||||||||
\(73\) | 1.22628 | 0.143525 | 0.0717624 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717624 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(74\) | −11.2135 | −1.30354 | ||||||||
\(75\) | 19.8530 | 2.29243 | ||||||||
\(76\) | −1.23015 | −0.141107 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.56217 | 0.743020 | ||||||||
\(79\) | 9.48182 | 1.06679 | 0.533394 | − | 0.845867i | \(-0.320916\pi\) | ||||
0.533394 | + | 0.845867i | \(0.320916\pi\) | |||||||
\(80\) | 6.59959 | 0.737857 | ||||||||
\(81\) | 2.23976 | 0.248862 | ||||||||
\(82\) | 2.36950 | 0.261668 | ||||||||
\(83\) | −16.0694 | −1.76385 | −0.881923 | − | 0.471394i | \(-0.843751\pi\) | ||||
−0.881923 | + | 0.471394i | \(0.843751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.68312 | −0.724886 | ||||||||
\(86\) | 3.43303 | 0.370193 | ||||||||
\(87\) | −22.7953 | −2.44391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.43830 | 0.470459 | 0.235230 | − | 0.971940i | \(-0.424416\pi\) | ||||
0.235230 | + | 0.971940i | \(0.424416\pi\) | |||||||
\(90\) | 19.9241 | 2.10019 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.611780 | 0.0637825 | ||||||||
\(93\) | −2.25395 | −0.233724 | ||||||||
\(94\) | 8.43241 | 0.869737 | ||||||||
\(95\) | −5.60908 | −0.575479 | ||||||||
\(96\) | −11.4901 | −1.17270 | ||||||||
\(97\) | −6.46807 | −0.656733 | −0.328366 | − | 0.944550i | \(-0.606498\pi\) | ||||
−0.328366 | + | 0.944550i | \(0.606498\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.26366 | −0.526366 | ||||||||
\(101\) | −15.4449 | −1.53682 | −0.768412 | − | 0.639955i | \(-0.778953\pi\) | ||||
−0.768412 | + | 0.639955i | \(0.778953\pi\) | |||||||
\(102\) | −6.16097 | −0.610027 | ||||||||
\(103\) | −8.90812 | −0.877743 | −0.438872 | − | 0.898550i | \(-0.644622\pi\) | ||||
−0.438872 | + | 0.898550i | \(0.644622\pi\) | |||||||
\(104\) | −6.33067 | −0.620773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0613 | −1.17149 | ||||||||
\(107\) | −3.51219 | −0.339536 | −0.169768 | − | 0.985484i | \(-0.554302\pi\) | ||||
−0.169768 | + | 0.985484i | \(0.554302\pi\) | |||||||
\(108\) | −4.70829 | −0.453055 | ||||||||
\(109\) | −3.87655 | −0.371306 | −0.185653 | − | 0.982615i | \(-0.559440\pi\) | ||||
−0.185653 | + | 0.982615i | \(0.559440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.7648 | 2.73023 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.6539 | 1.00224 | 0.501118 | − | 0.865379i | \(-0.332922\pi\) | ||||
0.501118 | + | 0.865379i | \(0.332922\pi\) | |||||||
\(114\) | −5.17084 | −0.484294 | ||||||||
\(115\) | 2.78952 | 0.260124 | ||||||||
\(116\) | 6.04376 | 0.561149 | ||||||||
\(117\) | −10.6543 | −0.984986 | ||||||||
\(118\) | −3.67399 | −0.338218 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −30.3687 | −2.77227 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.19987 | 0.108631 | ||||||||
\(123\) | −6.07823 | −0.548056 | ||||||||
\(124\) | 0.597594 | 0.0536655 | ||||||||
\(125\) | −6.72025 | −0.601078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4509 | −1.72599 | −0.862994 | − | 0.505214i | \(-0.831414\pi\) | ||||
−0.862994 | + | 0.505214i | \(0.831414\pi\) | |||||||
\(128\) | −1.20989 | −0.106941 | ||||||||
\(129\) | −8.80638 | −0.775359 | ||||||||
\(130\) | −7.93313 | −0.695782 | ||||||||
\(131\) | 5.11284 | 0.446711 | 0.223355 | − | 0.974737i | \(-0.428299\pi\) | ||||
0.223355 | + | 0.974737i | \(0.428299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.67822 | −0.231363 | ||||||||
\(135\) | −21.4683 | −1.84770 | ||||||||
\(136\) | 5.94362 | 0.509661 | ||||||||
\(137\) | 9.10052 | 0.777510 | 0.388755 | − | 0.921341i | \(-0.372905\pi\) | ||||
0.388755 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(138\) | 2.57158 | 0.218907 | ||||||||
\(139\) | −13.0166 | −1.10405 | −0.552026 | − | 0.833827i | \(-0.686145\pi\) | ||||
−0.552026 | + | 0.833827i | \(0.686145\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.6307 | −1.82164 | ||||||||
\(142\) | 3.55358 | 0.298210 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.87786 | −0.823155 | ||||||||
\(145\) | 27.5577 | 2.28854 | ||||||||
\(146\) | −1.36664 | −0.113104 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.62646 | −0.626891 | ||||||||
\(149\) | 3.14650 | 0.257771 | 0.128886 | − | 0.991659i | \(-0.458860\pi\) | ||||
0.128886 | + | 0.991659i | \(0.458860\pi\) | |||||||
\(150\) | −22.1255 | −1.80654 | ||||||||
\(151\) | −2.86696 | −0.233310 | −0.116655 | − | 0.993172i | \(-0.537217\pi\) | ||||
−0.116655 | + | 0.993172i | \(0.537217\pi\) | |||||||
\(152\) | 4.98843 | 0.404615 | ||||||||
\(153\) | 10.0029 | 0.808684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.72484 | 0.218864 | ||||||||
\(156\) | 4.46302 | 0.357328 | ||||||||
\(157\) | 21.4895 | 1.71505 | 0.857524 | − | 0.514443i | \(-0.172001\pi\) | ||||
0.857524 | + | 0.514443i | \(0.172001\pi\) | |||||||
\(158\) | −10.5672 | −0.840679 | ||||||||
\(159\) | 30.9394 | 2.45365 | ||||||||
\(160\) | 13.8906 | 1.09815 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.49614 | −0.196115 | ||||||||
\(163\) | −8.22245 | −0.644032 | −0.322016 | − | 0.946734i | \(-0.604361\pi\) | ||||
−0.322016 | + | 0.946734i | \(0.604361\pi\) | |||||||
\(164\) | 1.61153 | 0.125840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.9088 | 1.38999 | ||||||||
\(167\) | −21.7086 | −1.67986 | −0.839930 | − | 0.542695i | \(-0.817404\pi\) | ||||
−0.839930 | + | 0.542695i | \(0.817404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.75783 | −0.673679 | ||||||||
\(170\) | 7.44811 | 0.571244 | ||||||||
\(171\) | 8.39531 | 0.642006 | ||||||||
\(172\) | 2.33485 | 0.178031 | ||||||||
\(173\) | −8.04563 | −0.611698 | −0.305849 | − | 0.952080i | \(-0.598940\pi\) | ||||
−0.305849 | + | 0.952080i | \(0.598940\pi\) | |||||||
\(174\) | 25.4046 | 1.92592 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.42449 | 0.708388 | ||||||||
\(178\) | −4.94634 | −0.370744 | ||||||||
\(179\) | −3.62091 | −0.270640 | −0.135320 | − | 0.990802i | \(-0.543206\pi\) | ||||
−0.135320 | + | 0.990802i | \(0.543206\pi\) | |||||||
\(180\) | 13.5507 | 1.01001 | ||||||||
\(181\) | −15.8179 | −1.17574 | −0.587868 | − | 0.808957i | \(-0.700033\pi\) | ||||
−0.587868 | + | 0.808957i | \(0.700033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.07788 | −0.227524 | ||||||||
\(184\) | −2.48086 | −0.182891 | ||||||||
\(185\) | −34.7743 | −2.55665 | ||||||||
\(186\) | 2.51195 | 0.184185 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.73500 | 0.418268 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.25113 | 0.453504 | ||||||||
\(191\) | 0.429081 | 0.0310472 | 0.0155236 | − | 0.999880i | \(-0.495058\pi\) | ||||
0.0155236 | + | 0.999880i | \(0.495058\pi\) | |||||||
\(192\) | 23.7235 | 1.71210 | ||||||||
\(193\) | 15.1748 | 1.09231 | 0.546154 | − | 0.837685i | \(-0.316091\pi\) | ||||
0.546154 | + | 0.837685i | \(0.316091\pi\) | |||||||
\(194\) | 7.20845 | 0.517536 | ||||||||
\(195\) | 20.3500 | 1.45729 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8082 | 1.48252 | 0.741262 | − | 0.671216i | \(-0.234228\pi\) | ||||
0.741262 | + | 0.671216i | \(0.234228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.44567 | −0.598698 | −0.299349 | − | 0.954144i | \(-0.596769\pi\) | ||||
−0.299349 | + | 0.954144i | \(0.596769\pi\) | |||||||
\(200\) | 21.3449 | 1.50932 | ||||||||
\(201\) | 6.87014 | 0.484582 | ||||||||
\(202\) | 17.2128 | 1.21109 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.19016 | −0.293370 | ||||||||
\(205\) | 7.34808 | 0.513212 | ||||||||
\(206\) | 9.92781 | 0.691703 | ||||||||
\(207\) | −4.17518 | −0.290195 | ||||||||
\(208\) | 3.93303 | 0.272707 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.85927 | 0.678740 | 0.339370 | − | 0.940653i | \(-0.389786\pi\) | ||||
0.339370 | + | 0.940653i | \(0.389786\pi\) | |||||||
\(212\) | −8.20303 | −0.563386 | ||||||||
\(213\) | −9.11561 | −0.624592 | ||||||||
\(214\) | 3.91422 | 0.267570 | ||||||||
\(215\) | 10.6462 | 0.726065 | ||||||||
\(216\) | 19.0928 | 1.29910 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.32028 | 0.292606 | ||||||||
\(219\) | 3.50570 | 0.236893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.98281 | −0.267913 | ||||||||
\(222\) | −32.0574 | −2.15155 | ||||||||
\(223\) | −17.3959 | −1.16491 | −0.582457 | − | 0.812861i | \(-0.697909\pi\) | ||||
−0.582457 | + | 0.812861i | \(0.697909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 35.9227 | 2.39484 | ||||||||
\(226\) | −11.8734 | −0.789809 | ||||||||
\(227\) | −12.6315 | −0.838381 | −0.419190 | − | 0.907898i | \(-0.637686\pi\) | ||||
−0.419190 | + | 0.907898i | \(0.637686\pi\) | |||||||
\(228\) | −3.51676 | −0.232903 | ||||||||
\(229\) | −4.57341 | −0.302220 | −0.151110 | − | 0.988517i | \(-0.548285\pi\) | ||||
−0.151110 | + | 0.988517i | \(0.548285\pi\) | |||||||
\(230\) | −3.10883 | −0.204990 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −24.5084 | −1.60905 | ||||||||
\(233\) | −23.8569 | −1.56292 | −0.781458 | − | 0.623957i | \(-0.785524\pi\) | ||||
−0.781458 | + | 0.623957i | \(0.785524\pi\) | |||||||
\(234\) | 11.8738 | 0.776215 | ||||||||
\(235\) | 26.1498 | 1.70582 | ||||||||
\(236\) | −2.49873 | −0.162654 | ||||||||
\(237\) | 27.1068 | 1.76078 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.83814 | −0.571692 | −0.285846 | − | 0.958276i | \(-0.592275\pi\) | ||||
−0.285846 | + | 0.958276i | \(0.592275\pi\) | |||||||
\(240\) | 18.8670 | 1.21786 | ||||||||
\(241\) | 18.9464 | 1.22045 | 0.610224 | − | 0.792229i | \(-0.291079\pi\) | ||||
0.610224 | + | 0.792229i | \(0.291079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.2322 | −0.784696 | ||||||||
\(244\) | 0.816045 | 0.0522419 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.77398 | 0.431893 | ||||||||
\(247\) | −3.34273 | −0.212693 | ||||||||
\(248\) | −2.42333 | −0.153882 | ||||||||
\(249\) | −45.9395 | −2.91130 | ||||||||
\(250\) | 7.48950 | 0.473678 | ||||||||
\(251\) | 2.86691 | 0.180958 | 0.0904790 | − | 0.995898i | \(-0.471160\pi\) | ||||
0.0904790 | + | 0.995898i | \(0.471160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.6774 | 1.36016 | ||||||||
\(255\) | −19.1058 | −1.19645 | ||||||||
\(256\) | −15.2483 | −0.953021 | ||||||||
\(257\) | −22.4159 | −1.39826 | −0.699132 | − | 0.714993i | \(-0.746430\pi\) | ||||
−0.699132 | + | 0.714993i | \(0.746430\pi\) | |||||||
\(258\) | 9.81442 | 0.611019 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.39543 | −0.334611 | ||||||||
\(261\) | −41.2466 | −2.55310 | ||||||||
\(262\) | −5.69808 | −0.352029 | ||||||||
\(263\) | −0.990706 | −0.0610895 | −0.0305448 | − | 0.999533i | \(-0.509724\pi\) | ||||
−0.0305448 | + | 0.999533i | \(0.509724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.4032 | −2.29766 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.6883 | 0.776511 | ||||||||
\(268\) | −1.82149 | −0.111265 | ||||||||
\(269\) | 7.19036 | 0.438404 | 0.219202 | − | 0.975679i | \(-0.429655\pi\) | ||||
0.219202 | + | 0.975679i | \(0.429655\pi\) | |||||||
\(270\) | 23.9257 | 1.45607 | ||||||||
\(271\) | −27.1643 | −1.65011 | −0.825056 | − | 0.565050i | \(-0.808857\pi\) | ||||
−0.825056 | + | 0.565050i | \(0.808857\pi\) | |||||||
\(272\) | −3.69257 | −0.223895 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1422 | −0.612714 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.74897 | 0.105275 | ||||||||
\(277\) | −20.9856 | −1.26090 | −0.630451 | − | 0.776229i | \(-0.717130\pi\) | ||||
−0.630451 | + | 0.776229i | \(0.717130\pi\) | |||||||
\(278\) | 14.5065 | 0.870045 | ||||||||
\(279\) | −4.07837 | −0.244166 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.1580 | 1.67977 | 0.839883 | − | 0.542768i | \(-0.182624\pi\) | ||||
0.839883 | + | 0.542768i | \(0.182624\pi\) | |||||||
\(282\) | 24.1067 | 1.43553 | ||||||||
\(283\) | −26.1917 | −1.55694 | −0.778469 | − | 0.627684i | \(-0.784003\pi\) | ||||
−0.778469 | + | 0.627684i | \(0.784003\pi\) | |||||||
\(284\) | 2.41684 | 0.143413 | ||||||||
\(285\) | −16.0353 | −0.949851 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −20.7906 | −1.22510 | ||||||||
\(289\) | −13.2607 | −0.780041 | ||||||||
\(290\) | −30.7121 | −1.80348 | ||||||||
\(291\) | −18.4910 | −1.08396 | ||||||||
\(292\) | −0.929473 | −0.0543933 | ||||||||
\(293\) | −4.46385 | −0.260781 | −0.130391 | − | 0.991463i | \(-0.541623\pi\) | ||||
−0.130391 | + | 0.991463i | \(0.541623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3934 | −0.663351 | ||||||||
\(296\) | 30.9264 | 1.79756 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.50667 | −0.203136 | ||||||||
\(299\) | 1.66242 | 0.0961402 | ||||||||
\(300\) | −15.0479 | −0.868788 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.19513 | 0.183859 | ||||||||
\(303\) | −44.1542 | −2.53659 | ||||||||
\(304\) | −3.09914 | −0.177748 | ||||||||
\(305\) | 3.72091 | 0.213059 | ||||||||
\(306\) | −11.1479 | −0.637281 | ||||||||
\(307\) | 12.8841 | 0.735334 | 0.367667 | − | 0.929957i | \(-0.380157\pi\) | ||||
0.367667 | + | 0.929957i | \(0.380157\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.4667 | −1.44875 | ||||||||
\(310\) | −3.03674 | −0.172475 | ||||||||
\(311\) | −26.8199 | −1.52081 | −0.760407 | − | 0.649447i | \(-0.775001\pi\) | ||||
−0.760407 | + | 0.649447i | \(0.775001\pi\) | |||||||
\(312\) | −18.0982 | −1.02461 | ||||||||
\(313\) | −3.58869 | −0.202845 | −0.101422 | − | 0.994843i | \(-0.532339\pi\) | ||||
−0.101422 | + | 0.994843i | \(0.532339\pi\) | |||||||
\(314\) | −23.9493 | −1.35154 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.18688 | −0.404294 | ||||||||
\(317\) | −16.9181 | −0.950213 | −0.475106 | − | 0.879928i | \(-0.657590\pi\) | ||||
−0.475106 | + | 0.879928i | \(0.657590\pi\) | |||||||
\(318\) | −34.4809 | −1.93359 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −28.6798 | −1.60325 | ||||||||
\(321\) | −10.0407 | −0.560418 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.13836 | 0.174623 | ||||||||
\(324\) | −1.69766 | −0.0943144 | ||||||||
\(325\) | −14.3032 | −0.793399 | ||||||||
\(326\) | 9.16365 | 0.507528 | ||||||||
\(327\) | −11.0823 | −0.612855 | ||||||||
\(328\) | −6.53501 | −0.360836 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23826 | −0.0680610 | −0.0340305 | − | 0.999421i | \(-0.510834\pi\) | ||||
−0.0340305 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(332\) | 12.1800 | 0.668466 | ||||||||
\(333\) | 52.0479 | 2.85221 | ||||||||
\(334\) | 24.1935 | 1.32381 | ||||||||
\(335\) | −8.30544 | −0.453774 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4806 | 1.11565 | 0.557824 | − | 0.829959i | \(-0.311636\pi\) | ||||
0.557824 | + | 0.829959i | \(0.311636\pi\) | |||||||
\(338\) | 9.76031 | 0.530891 | ||||||||
\(339\) | 30.4576 | 1.65423 | ||||||||
\(340\) | 5.06556 | 0.274719 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.35630 | −0.505931 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −9.46818 | −0.510490 | ||||||||
\(345\) | 7.97474 | 0.429346 | ||||||||
\(346\) | 8.96659 | 0.482047 | ||||||||
\(347\) | −27.2699 | −1.46392 | −0.731961 | − | 0.681346i | \(-0.761395\pi\) | ||||
−0.731961 | + | 0.681346i | \(0.761395\pi\) | |||||||
\(348\) | 17.2780 | 0.926199 | ||||||||
\(349\) | 7.98434 | 0.427392 | 0.213696 | − | 0.976900i | \(-0.431450\pi\) | ||||
0.213696 | + | 0.976900i | \(0.431450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.7941 | −0.682897 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.93472 | −0.315873 | −0.157937 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157937 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(354\) | −10.5033 | −0.558243 | ||||||||
\(355\) | 11.0200 | 0.584883 | ||||||||
\(356\) | −3.36407 | −0.178296 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.03538 | 0.213277 | ||||||||
\(359\) | −28.4203 | −1.49996 | −0.749982 | − | 0.661458i | \(-0.769938\pi\) | ||||
−0.749982 | + | 0.661458i | \(0.769938\pi\) | |||||||
\(360\) | −54.9501 | −2.89612 | ||||||||
\(361\) | −16.3660 | −0.861368 | ||||||||
\(362\) | 17.6285 | 0.926535 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.23810 | −0.221832 | ||||||||
\(366\) | 3.43020 | 0.179299 | ||||||||
\(367\) | 30.4014 | 1.58694 | 0.793471 | − | 0.608608i | \(-0.208272\pi\) | ||||
0.793471 | + | 0.608608i | \(0.208272\pi\) | |||||||
\(368\) | 1.54128 | 0.0803445 | ||||||||
\(369\) | −10.9982 | −0.572541 | ||||||||
\(370\) | 38.7547 | 2.01476 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.70841 | 0.0885771 | ||||||||
\(373\) | −14.4226 | −0.746772 | −0.373386 | − | 0.927676i | \(-0.621803\pi\) | ||||
−0.373386 | + | 0.927676i | \(0.621803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.2120 | −0.992103 | ||||||||
\(376\) | −23.2563 | −1.19935 | ||||||||
\(377\) | 16.4230 | 0.845828 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4072 | −1.15098 | −0.575490 | − | 0.817809i | \(-0.695189\pi\) | ||||
−0.575490 | + | 0.817809i | \(0.695189\pi\) | |||||||
\(380\) | 4.25148 | 0.218096 | ||||||||
\(381\) | −55.6066 | −2.84881 | ||||||||
\(382\) | −0.478196 | −0.0244667 | ||||||||
\(383\) | −33.6785 | −1.72089 | −0.860446 | − | 0.509541i | \(-0.829815\pi\) | ||||
−0.860446 | + | 0.509541i | \(0.829815\pi\) | |||||||
\(384\) | −3.45887 | −0.176510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.9118 | −0.860790 | ||||||||
\(387\) | −15.9346 | −0.809999 | ||||||||
\(388\) | 4.90256 | 0.248890 | ||||||||
\(389\) | 2.42783 | 0.123096 | 0.0615479 | − | 0.998104i | \(-0.480396\pi\) | ||||
0.0615479 | + | 0.998104i | \(0.480396\pi\) | |||||||
\(390\) | −22.6794 | −1.14841 | ||||||||
\(391\) | −1.56078 | −0.0789321 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.6167 | 0.737313 | ||||||||
\(394\) | −23.1900 | −1.16830 | ||||||||
\(395\) | −32.7699 | −1.64883 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.89696 | 0.295960 | 0.147980 | − | 0.988990i | \(-0.452723\pi\) | ||||
0.147980 | + | 0.988990i | \(0.452723\pi\) | |||||||
\(398\) | 9.41242 | 0.471802 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.2609 | −0.663045 | ||||||||
\(401\) | 11.2396 | 0.561278 | 0.280639 | − | 0.959813i | \(-0.409454\pi\) | ||||
0.280639 | + | 0.959813i | \(0.409454\pi\) | |||||||
\(402\) | −7.65654 | −0.381873 | ||||||||
\(403\) | 1.62387 | 0.0808908 | ||||||||
\(404\) | 11.7067 | 0.582429 | ||||||||
\(405\) | −7.74079 | −0.384643 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 16.9917 | 0.841216 | ||||||||
\(409\) | 29.3344 | 1.45049 | 0.725246 | − | 0.688490i | \(-0.241726\pi\) | ||||
0.725246 | + | 0.688490i | \(0.241726\pi\) | |||||||
\(410\) | −8.18919 | −0.404435 | ||||||||
\(411\) | 26.0167 | 1.28331 | ||||||||
\(412\) | 6.75204 | 0.332649 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.65310 | 0.228688 | ||||||||
\(415\) | 55.5371 | 2.72621 | ||||||||
\(416\) | 8.27811 | 0.405868 | ||||||||
\(417\) | −37.2120 | −1.82228 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.2858 | 0.991027 | 0.495514 | − | 0.868600i | \(-0.334980\pi\) | ||||
0.495514 | + | 0.868600i | \(0.334980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.06003 | −0.149137 | −0.0745683 | − | 0.997216i | \(-0.523758\pi\) | ||||
−0.0745683 | + | 0.997216i | \(0.523758\pi\) | |||||||
\(422\) | −10.9878 | −0.534879 | ||||||||
\(423\) | −39.1394 | −1.90302 | ||||||||
\(424\) | 33.2645 | 1.61547 | ||||||||
\(425\) | 13.4287 | 0.651389 | ||||||||
\(426\) | 10.1590 | 0.492207 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.66211 | 0.128678 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.8648 | −0.572173 | ||||||||
\(431\) | −7.54197 | −0.363284 | −0.181642 | − | 0.983365i | \(-0.558141\pi\) | ||||
−0.181642 | + | 0.983365i | \(0.558141\pi\) | |||||||
\(432\) | −11.8617 | −0.570698 | ||||||||
\(433\) | 32.1616 | 1.54559 | 0.772794 | − | 0.634657i | \(-0.218859\pi\) | ||||
0.772794 | + | 0.634657i | \(0.218859\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 78.7823 | 3.77732 | ||||||||
\(436\) | 2.93828 | 0.140718 | ||||||||
\(437\) | −1.30995 | −0.0626633 | ||||||||
\(438\) | −3.90698 | −0.186683 | ||||||||
\(439\) | −4.66725 | −0.222756 | −0.111378 | − | 0.993778i | \(-0.535526\pi\) | ||||
−0.111378 | + | 0.993778i | \(0.535526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.43871 | 0.211128 | ||||||||
\(443\) | 17.2772 | 0.820862 | 0.410431 | − | 0.911892i | \(-0.365378\pi\) | ||||
0.410431 | + | 0.911892i | \(0.365378\pi\) | |||||||
\(444\) | −21.8027 | −1.03471 | ||||||||
\(445\) | −15.3391 | −0.727144 | ||||||||
\(446\) | 19.3871 | 0.918007 | ||||||||
\(447\) | 8.99527 | 0.425461 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.7401 | −0.790013 | −0.395007 | − | 0.918678i | \(-0.629258\pi\) | ||||
−0.395007 | + | 0.918678i | \(0.629258\pi\) | |||||||
\(450\) | −40.0346 | −1.88725 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −8.07529 | −0.379829 | ||||||||
\(453\) | −8.19612 | −0.385088 | ||||||||
\(454\) | 14.0774 | 0.660683 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.2610 | 0.667833 | ||||||||
\(457\) | 21.6974 | 1.01496 | 0.507481 | − | 0.861663i | \(-0.330577\pi\) | ||||
0.507481 | + | 0.861663i | \(0.330577\pi\) | |||||||
\(458\) | 5.09692 | 0.238163 | ||||||||
\(459\) | 12.0119 | 0.560665 | ||||||||
\(460\) | −2.11436 | −0.0985825 | ||||||||
\(461\) | −6.07778 | −0.283070 | −0.141535 | − | 0.989933i | \(-0.545204\pi\) | ||||
−0.141535 | + | 0.989933i | \(0.545204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.14719 | −0.239210 | −0.119605 | − | 0.992822i | \(-0.538163\pi\) | ||||
−0.119605 | + | 0.992822i | \(0.538163\pi\) | |||||||
\(464\) | 15.2262 | 0.706860 | ||||||||
\(465\) | 7.78982 | 0.361244 | ||||||||
\(466\) | 26.5877 | 1.23165 | ||||||||
\(467\) | 3.91927 | 0.181362 | 0.0906812 | − | 0.995880i | \(-0.471096\pi\) | ||||
0.0906812 | + | 0.995880i | \(0.471096\pi\) | |||||||
\(468\) | 8.07555 | 0.373292 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −29.1431 | −1.34427 | ||||||||
\(471\) | 61.4346 | 2.83076 | ||||||||
\(472\) | 10.1327 | 0.466397 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −30.2096 | −1.38757 | ||||||||
\(475\) | 11.2706 | 0.517131 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 55.9828 | 2.56328 | ||||||||
\(478\) | 9.84982 | 0.450520 | ||||||||
\(479\) | −15.1129 | −0.690527 | −0.345263 | − | 0.938506i | \(-0.612210\pi\) | ||||
−0.345263 | + | 0.938506i | \(0.612210\pi\) | |||||||
\(480\) | 39.7106 | 1.81253 | ||||||||
\(481\) | −20.7237 | −0.944922 | ||||||||
\(482\) | −21.1152 | −0.961770 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.3541 | 1.01505 | ||||||||
\(486\) | 13.6324 | 0.618377 | ||||||||
\(487\) | 25.0768 | 1.13634 | 0.568169 | − | 0.822912i | \(-0.307652\pi\) | ||||
0.568169 | + | 0.822912i | \(0.307652\pi\) | |||||||
\(488\) | −3.30919 | −0.149800 | ||||||||
\(489\) | −23.5065 | −1.06300 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.2208 | −1.67975 | −0.839875 | − | 0.542780i | \(-0.817372\pi\) | ||||
−0.839875 | + | 0.542780i | \(0.817372\pi\) | |||||||
\(492\) | 4.60708 | 0.207703 | ||||||||
\(493\) | −15.4189 | −0.694434 | ||||||||
\(494\) | 3.72536 | 0.167612 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50554 | 0.0676006 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 51.1980 | 2.29424 | ||||||||
\(499\) | −31.8134 | −1.42416 | −0.712081 | − | 0.702098i | \(-0.752247\pi\) | ||||
−0.712081 | + | 0.702098i | \(0.752247\pi\) | |||||||
\(500\) | 5.09371 | 0.227798 | ||||||||
\(501\) | −62.0609 | −2.77267 | ||||||||
\(502\) | −3.19508 | −0.142603 | ||||||||
\(503\) | −19.2058 | −0.856346 | −0.428173 | − | 0.903697i | \(-0.640843\pi\) | ||||
−0.428173 | + | 0.903697i | \(0.640843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.3788 | 2.37532 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.0370 | −1.11193 | ||||||||
\(508\) | 14.7431 | 0.654119 | ||||||||
\(509\) | −2.51549 | −0.111497 | −0.0557485 | − | 0.998445i | \(-0.517754\pi\) | ||||
−0.0557485 | + | 0.998445i | \(0.517754\pi\) | |||||||
\(510\) | 21.2928 | 0.942861 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.4135 | 0.857966 | ||||||||
\(513\) | 10.0814 | 0.445106 | ||||||||
\(514\) | 24.9817 | 1.10190 | ||||||||
\(515\) | 30.7872 | 1.35664 | ||||||||
\(516\) | 6.67492 | 0.293847 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.0010 | −1.00963 | ||||||||
\(520\) | 21.8793 | 0.959470 | ||||||||
\(521\) | −14.8968 | −0.652639 | −0.326320 | − | 0.945260i | \(-0.605809\pi\) | ||||
−0.326320 | + | 0.945260i | \(0.605809\pi\) | |||||||
\(522\) | 45.9679 | 2.01196 | ||||||||
\(523\) | −9.90502 | −0.433116 | −0.216558 | − | 0.976270i | \(-0.569483\pi\) | ||||
−0.216558 | + | 0.976270i | \(0.569483\pi\) | |||||||
\(524\) | −3.87535 | −0.169295 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.10411 | 0.0481414 | ||||||||
\(527\) | −1.52459 | −0.0664122 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3485 | −0.971675 | ||||||||
\(530\) | 41.6846 | 1.81066 | ||||||||
\(531\) | 17.0530 | 0.740036 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.37910 | 0.189680 | ||||||||
\(534\) | −14.1407 | −0.611927 | ||||||||
\(535\) | 12.1384 | 0.524789 | ||||||||
\(536\) | 7.38643 | 0.319045 | ||||||||
\(537\) | −10.3515 | −0.446701 | ||||||||
\(538\) | −8.01342 | −0.345483 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16.2722 | 0.700245 | ||||||||
\(541\) | 22.0084 | 0.946214 | 0.473107 | − | 0.881005i | \(-0.343132\pi\) | ||||
0.473107 | + | 0.881005i | \(0.343132\pi\) | |||||||
\(542\) | 30.2737 | 1.30037 | ||||||||
\(543\) | −45.2205 | −1.94060 | ||||||||
\(544\) | −7.77199 | −0.333222 | ||||||||
\(545\) | 13.3977 | 0.573892 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.8643 | 0.464523 | 0.232261 | − | 0.972653i | \(-0.425388\pi\) | ||||
0.232261 | + | 0.972653i | \(0.425388\pi\) | |||||||
\(548\) | −6.89787 | −0.294662 | ||||||||
\(549\) | −5.56922 | −0.237689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.9410 | −0.551303 | ||||||||
\(552\) | −7.09233 | −0.301869 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.3878 | 0.993650 | ||||||||
\(555\) | −99.4133 | −4.21986 | ||||||||
\(556\) | 9.86610 | 0.418416 | ||||||||
\(557\) | −33.6126 | −1.42421 | −0.712106 | − | 0.702072i | \(-0.752258\pi\) | ||||
−0.712106 | + | 0.702072i | \(0.752258\pi\) | |||||||
\(558\) | 4.54521 | 0.192414 | ||||||||
\(559\) | 6.34461 | 0.268348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.3811 | −1.32373 | ||||||||
\(563\) | −2.05348 | −0.0865440 | −0.0432720 | − | 0.999063i | \(-0.513778\pi\) | ||||
−0.0432720 | + | 0.999063i | \(0.513778\pi\) | |||||||
\(564\) | 16.3953 | 0.690367 | ||||||||
\(565\) | −36.8208 | −1.54906 | ||||||||
\(566\) | 29.1898 | 1.22694 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.80065 | −0.411226 | ||||||||
\(569\) | −3.27416 | −0.137260 | −0.0686300 | − | 0.997642i | \(-0.521863\pi\) | ||||
−0.0686300 | + | 0.997642i | \(0.521863\pi\) | |||||||
\(570\) | 17.8708 | 0.748527 | ||||||||
\(571\) | 43.8897 | 1.83673 | 0.918363 | − | 0.395738i | \(-0.129511\pi\) | ||||
0.918363 | + | 0.395738i | \(0.129511\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.22666 | 0.0512446 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.60513 | −0.233750 | ||||||||
\(576\) | 42.9261 | 1.78859 | ||||||||
\(577\) | 43.8904 | 1.82718 | 0.913591 | − | 0.406635i | \(-0.133298\pi\) | ||||
0.913591 | + | 0.406635i | \(0.133298\pi\) | |||||||
\(578\) | 14.7786 | 0.614709 | ||||||||
\(579\) | 43.3821 | 1.80290 | ||||||||
\(580\) | −20.8877 | −0.867315 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.6076 | 0.854214 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.76915 | 0.155969 | ||||||||
\(585\) | 36.8219 | 1.52240 | ||||||||
\(586\) | 4.97481 | 0.205508 | ||||||||
\(587\) | −2.79166 | −0.115224 | −0.0576121 | − | 0.998339i | \(-0.518349\pi\) | ||||
−0.0576121 | + | 0.998339i | \(0.518349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.27957 | −0.0527239 | ||||||||
\(590\) | 12.6976 | 0.522752 | ||||||||
\(591\) | 59.4869 | 2.44696 | ||||||||
\(592\) | −19.2136 | −0.789673 | ||||||||
\(593\) | 23.2526 | 0.954871 | 0.477435 | − | 0.878667i | \(-0.341566\pi\) | ||||
0.477435 | + | 0.878667i | \(0.341566\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.38493 | −0.0976907 | ||||||||
\(597\) | −24.1446 | −0.988175 | ||||||||
\(598\) | −1.85271 | −0.0757630 | ||||||||
\(599\) | 10.4595 | 0.427362 | 0.213681 | − | 0.976904i | \(-0.431455\pi\) | ||||
0.213681 | + | 0.976904i | \(0.431455\pi\) | |||||||
\(600\) | 61.0213 | 2.49118 | ||||||||
\(601\) | 22.3096 | 0.910029 | 0.455015 | − | 0.890484i | \(-0.349634\pi\) | ||||
0.455015 | + | 0.890484i | \(0.349634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4311 | 0.506232 | ||||||||
\(604\) | 2.17306 | 0.0884204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 49.2083 | 1.99895 | ||||||||
\(607\) | 18.9884 | 0.770716 | 0.385358 | − | 0.922767i | \(-0.374078\pi\) | ||||
0.385358 | + | 0.922767i | \(0.374078\pi\) | |||||||
\(608\) | −6.52296 | −0.264541 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.14683 | −0.167900 | ||||||||
\(611\) | 15.5840 | 0.630461 | ||||||||
\(612\) | −7.58182 | −0.306477 | ||||||||
\(613\) | −20.1617 | −0.814323 | −0.407161 | − | 0.913356i | \(-0.633481\pi\) | ||||
−0.407161 | + | 0.913356i | \(0.633481\pi\) | |||||||
\(614\) | −14.3589 | −0.579478 | ||||||||
\(615\) | 21.0068 | 0.847077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.03919 | 0.283387 | 0.141694 | − | 0.989911i | \(-0.454745\pi\) | ||||
0.141694 | + | 0.989911i | \(0.454745\pi\) | |||||||
\(618\) | 28.3818 | 1.14168 | ||||||||
\(619\) | 31.0831 | 1.24933 | 0.624667 | − | 0.780891i | \(-0.285235\pi\) | ||||
0.624667 | + | 0.780891i | \(0.285235\pi\) | |||||||
\(620\) | −2.06533 | −0.0829457 | ||||||||
\(621\) | −5.01373 | −0.201194 | ||||||||
\(622\) | 29.8898 | 1.19847 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.2438 | 0.450113 | ||||||||
\(625\) | −11.4966 | −0.459866 | ||||||||
\(626\) | 3.99947 | 0.159851 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.2883 | −0.649973 | ||||||||
\(629\) | 19.4567 | 0.775791 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9720 | 0.874690 | 0.437345 | − | 0.899294i | \(-0.355919\pi\) | ||||
0.437345 | + | 0.899294i | \(0.355919\pi\) | |||||||
\(632\) | 29.1439 | 1.15928 | ||||||||
\(633\) | 28.1859 | 1.12029 | ||||||||
\(634\) | 18.8546 | 0.748812 | ||||||||
\(635\) | 67.2238 | 2.66770 | ||||||||
\(636\) | −23.4510 | −0.929891 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.4941 | −0.652496 | ||||||||
\(640\) | 4.18149 | 0.165288 | ||||||||
\(641\) | −13.2909 | −0.524961 | −0.262480 | − | 0.964937i | \(-0.584540\pi\) | ||||
−0.262480 | + | 0.964937i | \(0.584540\pi\) | |||||||
\(642\) | 11.1900 | 0.441636 | ||||||||
\(643\) | −14.6904 | −0.579333 | −0.289666 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289666 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 30.4355 | 1.19840 | ||||||||
\(646\) | −3.49760 | −0.137611 | ||||||||
\(647\) | 6.14523 | 0.241594 | 0.120797 | − | 0.992677i | \(-0.461455\pi\) | ||||
0.120797 | + | 0.992677i | \(0.461455\pi\) | |||||||
\(648\) | 6.88426 | 0.270439 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 15.9404 | 0.625236 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.23232 | 0.244077 | ||||||||
\(653\) | −40.6691 | −1.59151 | −0.795753 | − | 0.605622i | \(-0.792924\pi\) | ||||
−0.795753 | + | 0.605622i | \(0.792924\pi\) | |||||||
\(654\) | 12.3509 | 0.482959 | ||||||||
\(655\) | −17.6704 | −0.690438 | ||||||||
\(656\) | 4.05998 | 0.158516 | ||||||||
\(657\) | 6.34333 | 0.247477 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.0090 | −0.701531 | −0.350765 | − | 0.936463i | \(-0.614079\pi\) | ||||
−0.350765 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.1420 | 0.666745 | 0.333373 | − | 0.942795i | \(-0.391813\pi\) | ||||
0.333373 | + | 0.942795i | \(0.391813\pi\) | |||||||
\(662\) | 1.38000 | 0.0536353 | ||||||||
\(663\) | −11.3861 | −0.442201 | ||||||||
\(664\) | −49.3919 | −1.91678 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −58.0057 | −2.24767 | ||||||||
\(667\) | 6.43584 | 0.249197 | ||||||||
\(668\) | 16.4543 | 0.636637 | ||||||||
\(669\) | −49.7317 | −1.92274 | ||||||||
\(670\) | 9.25613 | 0.357596 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.1926 | 0.894008 | 0.447004 | − | 0.894532i | \(-0.352491\pi\) | ||||
0.447004 | + | 0.894532i | \(0.352491\pi\) | |||||||
\(674\) | −22.8249 | −0.879183 | ||||||||
\(675\) | 43.1374 | 1.66036 | ||||||||
\(676\) | 6.63812 | 0.255312 | ||||||||
\(677\) | −27.5705 | −1.05962 | −0.529811 | − | 0.848116i | \(-0.677737\pi\) | ||||
−0.529811 | + | 0.848116i | \(0.677737\pi\) | |||||||
\(678\) | −33.9440 | −1.30361 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −20.5416 | −0.787735 | ||||||||
\(681\) | −36.1111 | −1.38378 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.9351 | 0.839322 | 0.419661 | − | 0.907681i | \(-0.362149\pi\) | ||||
0.419661 | + | 0.907681i | \(0.362149\pi\) | |||||||
\(684\) | −6.36335 | −0.243309 | ||||||||
\(685\) | −31.4521 | −1.20172 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.0746 | −0.498826 | ||||||||
\(688\) | 5.88227 | 0.224259 | ||||||||
\(689\) | −22.2905 | −0.849200 | ||||||||
\(690\) | −8.88758 | −0.338344 | ||||||||
\(691\) | 25.6666 | 0.976404 | 0.488202 | − | 0.872731i | \(-0.337653\pi\) | ||||
0.488202 | + | 0.872731i | \(0.337653\pi\) | |||||||
\(692\) | 6.09830 | 0.231823 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.3913 | 1.15364 | ||||||||
\(695\) | 44.9863 | 1.70643 | ||||||||
\(696\) | −70.0650 | −2.65581 | ||||||||
\(697\) | −4.11137 | −0.155729 | ||||||||
\(698\) | −8.89828 | −0.336805 | ||||||||
\(699\) | −68.2025 | −2.57966 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.4135 | 0.695467 | 0.347733 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347733 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(702\) | 14.2586 | 0.538154 | ||||||||
\(703\) | 16.3298 | 0.615892 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 74.7575 | 2.81553 | ||||||||
\(706\) | 6.61404 | 0.248923 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.14342 | −0.268466 | ||||||||
\(709\) | 23.6621 | 0.888647 | 0.444323 | − | 0.895866i | \(-0.353444\pi\) | ||||
0.444323 | + | 0.895866i | \(0.353444\pi\) | |||||||
\(710\) | −12.2815 | −0.460915 | ||||||||
\(711\) | 49.0480 | 1.83944 | ||||||||
\(712\) | 13.6418 | 0.511249 | ||||||||
\(713\) | 0.636362 | 0.0238319 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.74452 | 0.102568 | ||||||||
\(717\) | −25.2666 | −0.943600 | ||||||||
\(718\) | 31.6734 | 1.18204 | ||||||||
\(719\) | −11.1222 | −0.414790 | −0.207395 | − | 0.978257i | \(-0.566498\pi\) | ||||
−0.207395 | + | 0.978257i | \(0.566498\pi\) | |||||||
\(720\) | 34.1387 | 1.27227 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.2394 | 0.678799 | ||||||||
\(723\) | 54.1644 | 2.01440 | ||||||||
\(724\) | 11.9894 | 0.445583 | ||||||||
\(725\) | −55.3730 | −2.05650 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.4803 | −1.57551 | −0.787753 | − | 0.615991i | \(-0.788756\pi\) | ||||
−0.787753 | + | 0.615991i | \(0.788756\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.6889 | −1.54403 | ||||||||
\(730\) | 4.72323 | 0.174814 | ||||||||
\(731\) | −5.95671 | −0.220317 | ||||||||
\(732\) | 2.33292 | 0.0862274 | ||||||||
\(733\) | 22.1884 | 0.819548 | 0.409774 | − | 0.912187i | \(-0.365607\pi\) | ||||
0.409774 | + | 0.912187i | \(0.365607\pi\) | |||||||
\(734\) | −33.8814 | −1.25058 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.24402 | 0.119576 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 12.2571 | 0.451189 | ||||||||
\(739\) | −29.4481 | −1.08327 | −0.541633 | − | 0.840615i | \(-0.682194\pi\) | ||||
−0.541633 | + | 0.840615i | \(0.682194\pi\) | |||||||
\(740\) | 26.3576 | 0.968926 | ||||||||
\(741\) | −9.55627 | −0.351058 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.9059 | −0.620217 | −0.310109 | − | 0.950701i | \(-0.600365\pi\) | ||||
−0.310109 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(744\) | −6.92787 | −0.253988 | ||||||||
\(745\) | −10.8745 | −0.398412 | ||||||||
\(746\) | 16.0735 | 0.588491 | ||||||||
\(747\) | −83.1244 | −3.04136 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 21.4111 | 0.781823 | ||||||||
\(751\) | −1.55147 | −0.0566138 | −0.0283069 | − | 0.999599i | \(-0.509012\pi\) | ||||
−0.0283069 | + | 0.999599i | \(0.509012\pi\) | |||||||
\(752\) | 14.4484 | 0.526877 | ||||||||
\(753\) | 8.19598 | 0.298678 | ||||||||
\(754\) | −18.3029 | −0.666552 | ||||||||
\(755\) | 9.90845 | 0.360605 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5467 | 0.456016 | 0.228008 | − | 0.973659i | \(-0.426779\pi\) | ||||
0.228008 | + | 0.973659i | \(0.426779\pi\) | |||||||
\(758\) | 24.9721 | 0.907027 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.2404 | −0.625375 | ||||||||
\(761\) | −9.03436 | −0.327495 | −0.163748 | − | 0.986502i | \(-0.552358\pi\) | ||||
−0.163748 | + | 0.986502i | \(0.552358\pi\) | |||||||
\(762\) | 61.9717 | 2.24500 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.325228 | −0.0117663 | ||||||||
\(765\) | −34.5707 | −1.24991 | ||||||||
\(766\) | 37.5336 | 1.35614 | ||||||||
\(767\) | −6.78993 | −0.245170 | ||||||||
\(768\) | −43.5922 | −1.57300 | ||||||||
\(769\) | −16.1383 | −0.581963 | −0.290981 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −64.0829 | −2.30789 | ||||||||
\(772\) | −11.5020 | −0.413965 | ||||||||
\(773\) | 18.4134 | 0.662285 | 0.331143 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331143 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(774\) | 17.7585 | 0.638317 | ||||||||
\(775\) | −5.47516 | −0.196674 | ||||||||
\(776\) | −19.8806 | −0.713673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.70573 | −0.0970053 | ||||||||
\(779\) | −3.45063 | −0.123632 | ||||||||
\(780\) | −15.4246 | −0.552288 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.73944 | 0.0622022 | ||||||||
\(783\) | −49.5306 | −1.77008 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −74.2694 | −2.65079 | ||||||||
\(786\) | −16.2898 | −0.581037 | ||||||||
\(787\) | 46.9870 | 1.67491 | 0.837453 | − | 0.546509i | \(-0.184043\pi\) | ||||
0.837453 | + | 0.546509i | \(0.184043\pi\) | |||||||
\(788\) | −15.7719 | −0.561850 | ||||||||
\(789\) | −2.83225 | −0.100831 | ||||||||
\(790\) | 36.5210 | 1.29936 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.21748 | 0.0787450 | ||||||||
\(794\) | −6.57197 | −0.233230 | ||||||||
\(795\) | −106.929 | −3.79238 | ||||||||
\(796\) | 6.40152 | 0.226896 | ||||||||
\(797\) | 3.12454 | 0.110677 | 0.0553385 | − | 0.998468i | \(-0.482376\pi\) | ||||
0.0553385 | + | 0.998468i | \(0.482376\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.6312 | −0.517615 | ||||||||
\(800\) | −27.9111 | −0.986805 | ||||||||
\(801\) | 22.9586 | 0.811203 | ||||||||
\(802\) | −12.5261 | −0.442314 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −5.20732 | −0.183648 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.80975 | −0.0637457 | ||||||||
\(807\) | 20.5559 | 0.723604 | ||||||||
\(808\) | −47.4724 | −1.67007 | ||||||||
\(809\) | 32.7257 | 1.15057 | 0.575286 | − | 0.817952i | \(-0.304891\pi\) | ||||
0.575286 | + | 0.817952i | \(0.304891\pi\) | |||||||
\(810\) | 8.62685 | 0.303117 | ||||||||
\(811\) | 32.6613 | 1.14689 | 0.573447 | − | 0.819243i | \(-0.305606\pi\) | ||||
0.573447 | + | 0.819243i | \(0.305606\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −77.6578 | −2.72358 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.4174 | 0.995419 | ||||||||
\(816\) | −10.5564 | −0.369548 | ||||||||
\(817\) | −4.99941 | −0.174907 | ||||||||
\(818\) | −32.6922 | −1.14306 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.56958 | −0.194498 | ||||||||
\(821\) | 7.43142 | 0.259358 | 0.129679 | − | 0.991556i | \(-0.458605\pi\) | ||||
0.129679 | + | 0.991556i | \(0.458605\pi\) | |||||||
\(822\) | −28.9948 | −1.01131 | ||||||||
\(823\) | 6.55866 | 0.228621 | 0.114310 | − | 0.993445i | \(-0.463534\pi\) | ||||
0.114310 | + | 0.993445i | \(0.463534\pi\) | |||||||
\(824\) | −27.3805 | −0.953846 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.8538 | −0.829479 | −0.414739 | − | 0.909940i | \(-0.636127\pi\) | ||||
−0.414739 | + | 0.909940i | \(0.636127\pi\) | |||||||
\(828\) | 3.16464 | 0.109979 | ||||||||
\(829\) | 26.1431 | 0.907989 | 0.453994 | − | 0.891005i | \(-0.349999\pi\) | ||||
0.453994 | + | 0.891005i | \(0.349999\pi\) | |||||||
\(830\) | −61.8942 | −2.14838 | ||||||||
\(831\) | −59.9940 | −2.08117 | ||||||||
\(832\) | −17.0917 | −0.592549 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 41.4716 | 1.43604 | ||||||||
\(835\) | 75.0265 | 2.59640 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.89747 | −0.169281 | ||||||||
\(838\) | −22.6079 | −0.780976 | ||||||||
\(839\) | −34.2890 | −1.18379 | −0.591893 | − | 0.806016i | \(-0.701619\pi\) | ||||
−0.591893 | + | 0.806016i | \(0.701619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.5795 | 1.19240 | ||||||||
\(842\) | 3.41030 | 0.117527 | ||||||||
\(843\) | 80.4986 | 2.77252 | ||||||||
\(844\) | −7.47297 | −0.257230 | ||||||||
\(845\) | 30.2677 | 1.04124 | ||||||||
\(846\) | 43.6195 | 1.49967 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.6661 | −0.709678 | ||||||||
\(849\) | −74.8774 | −2.56979 | ||||||||
\(850\) | −14.9659 | −0.513325 | ||||||||
\(851\) | −8.12121 | −0.278392 | ||||||||
\(852\) | 6.90931 | 0.236709 | ||||||||
\(853\) | 21.3842 | 0.732181 | 0.366090 | − | 0.930579i | \(-0.380696\pi\) | ||||
0.366090 | + | 0.930579i | \(0.380696\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.0149 | −0.992287 | ||||||||
\(856\) | −10.7953 | −0.368975 | ||||||||
\(857\) | 42.8697 | 1.46440 | 0.732200 | − | 0.681090i | \(-0.238494\pi\) | ||||
0.732200 | + | 0.681090i | \(0.238494\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.3915 | 1.03695 | 0.518473 | − | 0.855094i | \(-0.326501\pi\) | ||||
0.518473 | + | 0.855094i | \(0.326501\pi\) | |||||||
\(860\) | −8.06944 | −0.275165 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.40527 | 0.286285 | ||||||||
\(863\) | 11.8184 | 0.402304 | 0.201152 | − | 0.979560i | \(-0.435532\pi\) | ||||
0.201152 | + | 0.979560i | \(0.435532\pi\) | |||||||
\(864\) | −24.9661 | −0.849365 | ||||||||
\(865\) | 27.8063 | 0.945444 | ||||||||
\(866\) | −35.8430 | −1.21800 | ||||||||
\(867\) | −37.9099 | −1.28749 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −87.8003 | −2.97671 | ||||||||
\(871\) | −4.94963 | −0.167712 | ||||||||
\(872\) | −11.9152 | −0.403499 | ||||||||
\(873\) | −33.4583 | −1.13239 | ||||||||
\(874\) | 1.45989 | 0.0493816 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.65719 | −0.0897783 | ||||||||
\(877\) | 9.20488 | 0.310827 | 0.155413 | − | 0.987850i | \(-0.450329\pi\) | ||||
0.155413 | + | 0.987850i | \(0.450329\pi\) | |||||||
\(878\) | 5.20149 | 0.175542 | ||||||||
\(879\) | −12.7613 | −0.430429 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.9030 | 1.41175 | 0.705874 | − | 0.708338i | \(-0.250555\pi\) | ||||
0.705874 | + | 0.708338i | \(0.250555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.0478 | −0.540053 | −0.270026 | − | 0.962853i | \(-0.587032\pi\) | ||||
−0.270026 | + | 0.962853i | \(0.587032\pi\) | |||||||
\(884\) | 3.01883 | 0.101534 | ||||||||
\(885\) | −32.5718 | −1.09489 | ||||||||
\(886\) | −19.2548 | −0.646878 | ||||||||
\(887\) | −33.8483 | −1.13652 | −0.568258 | − | 0.822850i | \(-0.692382\pi\) | ||||
−0.568258 | + | 0.822850i | \(0.692382\pi\) | |||||||
\(888\) | 88.4131 | 2.96695 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 17.0949 | 0.573024 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.1855 | 0.441482 | ||||||||
\(893\) | −12.2798 | −0.410929 | ||||||||
\(894\) | −10.0249 | −0.335284 | ||||||||
\(895\) | 12.5141 | 0.418302 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.75255 | 0.158683 | ||||||||
\(898\) | 18.6563 | 0.622568 | ||||||||
\(899\) | 6.28660 | 0.209670 | ||||||||
\(900\) | −27.2281 | −0.907603 | ||||||||
\(901\) | 20.9277 | 0.697202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.7465 | 1.08913 | ||||||||
\(905\) | 54.6679 | 1.81722 | ||||||||
\(906\) | 9.13431 | 0.303467 | ||||||||
\(907\) | −44.1013 | −1.46436 | −0.732181 | − | 0.681111i | \(-0.761497\pi\) | ||||
−0.732181 | + | 0.681111i | \(0.761497\pi\) | |||||||
\(908\) | 9.57421 | 0.317731 | ||||||||
\(909\) | −79.8940 | −2.64992 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.5756 | 1.64251 | 0.821257 | − | 0.570558i | \(-0.193273\pi\) | ||||
0.821257 | + | 0.570558i | \(0.193273\pi\) | |||||||
\(912\) | −8.85988 | −0.293380 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.1810 | −0.799837 | ||||||||
\(915\) | 10.6374 | 0.351662 | ||||||||
\(916\) | 3.46648 | 0.114536 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.3868 | −0.441831 | ||||||||
\(919\) | 40.7926 | 1.34563 | 0.672813 | − | 0.739813i | \(-0.265086\pi\) | ||||
0.672813 | + | 0.739813i | \(0.265086\pi\) | |||||||
\(920\) | 8.57404 | 0.282678 | ||||||||
\(921\) | 36.8333 | 1.21370 | ||||||||
\(922\) | 6.77348 | 0.223073 | ||||||||
\(923\) | 6.56740 | 0.216169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.8737 | 2.29743 | ||||||||
\(926\) | 5.73637 | 0.188509 | ||||||||
\(927\) | −46.0803 | −1.51348 | ||||||||
\(928\) | 32.0476 | 1.05201 | ||||||||
\(929\) | −41.3929 | −1.35806 | −0.679029 | − | 0.734112i | \(-0.737599\pi\) | ||||
−0.679029 | + | 0.734112i | \(0.737599\pi\) | |||||||
\(930\) | −8.68150 | −0.284677 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18.0827 | 0.592318 | ||||||||
\(933\) | −76.6731 | −2.51016 | ||||||||
\(934\) | −4.36790 | −0.142922 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −32.7476 | −1.07039 | ||||||||
\(937\) | 1.59644 | 0.0521534 | 0.0260767 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260767 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.2594 | −0.334803 | ||||||||
\(940\) | −19.8206 | −0.646477 | ||||||||
\(941\) | 7.10787 | 0.231710 | 0.115855 | − | 0.993266i | \(-0.463039\pi\) | ||||
0.115855 | + | 0.993266i | \(0.463039\pi\) | |||||||
\(942\) | −68.4668 | −2.23077 | ||||||||
\(943\) | 1.71608 | 0.0558832 | ||||||||
\(944\) | −6.29513 | −0.204889 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.45986 | −0.0799347 | −0.0399674 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399674 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(948\) | −20.5460 | −0.667303 | ||||||||
\(949\) | −2.52570 | −0.0819878 | ||||||||
\(950\) | −12.5607 | −0.407523 | ||||||||
\(951\) | −48.3656 | −1.56836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.6000 | 0.926446 | 0.463223 | − | 0.886242i | \(-0.346693\pi\) | ||||
0.463223 | + | 0.886242i | \(0.346693\pi\) | |||||||
\(954\) | −62.3910 | −2.01998 | ||||||||
\(955\) | −1.48294 | −0.0479867 | ||||||||
\(956\) | 6.69900 | 0.216661 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.8428 | 0.544168 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −81.9903 | −2.64622 | ||||||||
\(961\) | −30.3784 | −0.979948 | ||||||||
\(962\) | 23.0959 | 0.744643 | ||||||||
\(963\) | −18.1680 | −0.585456 | ||||||||
\(964\) | −14.3607 | −0.462528 | ||||||||
\(965\) | −52.4454 | −1.68828 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.213338 | 0.00686047 | 0.00343024 | − | 0.999994i | \(-0.498908\pi\) | ||||
0.00343024 | + | 0.999994i | \(0.498908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.97201 | 0.288223 | ||||||||
\(970\) | −24.9129 | −0.799907 | ||||||||
\(971\) | 0.828199 | 0.0265782 | 0.0132891 | − | 0.999912i | \(-0.495770\pi\) | ||||
0.0132891 | + | 0.999912i | \(0.495770\pi\) | |||||||
\(972\) | 9.27157 | 0.297386 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27.9473 | −0.895488 | ||||||||
\(975\) | −40.8903 | −1.30954 | ||||||||
\(976\) | 2.05589 | 0.0658073 | ||||||||
\(977\) | 9.75714 | 0.312159 | 0.156079 | − | 0.987745i | \(-0.450114\pi\) | ||||
0.156079 | + | 0.987745i | \(0.450114\pi\) | |||||||
\(978\) | 26.1972 | 0.837694 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.0528 | −0.640236 | ||||||||
\(982\) | 41.4813 | 1.32372 | ||||||||
\(983\) | −45.1198 | −1.43910 | −0.719548 | − | 0.694442i | \(-0.755651\pi\) | ||||
−0.719548 | + | 0.694442i | \(0.755651\pi\) | |||||||
\(984\) | −18.6824 | −0.595573 | ||||||||
\(985\) | −71.9148 | −2.29140 | ||||||||
\(986\) | 17.1839 | 0.547246 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.53367 | 0.0806069 | ||||||||
\(989\) | 2.48632 | 0.0790604 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.5405 | 1.70077 | 0.850384 | − | 0.526162i | \(-0.176369\pi\) | ||||
0.850384 | + | 0.526162i | \(0.176369\pi\) | |||||||
\(992\) | 3.16880 | 0.100609 | ||||||||
\(993\) | −3.53997 | −0.112337 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.1889 | 0.925351 | ||||||||
\(996\) | 34.8205 | 1.10333 | ||||||||
\(997\) | −31.1607 | −0.986869 | −0.493435 | − | 0.869783i | \(-0.664259\pi\) | ||||
−0.493435 | + | 0.869783i | \(0.664259\pi\) | |||||||
\(998\) | 35.4549 | 1.12231 | ||||||||
\(999\) | 62.5013 | 1.97745 |
(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 | 5929.2.a.bs.1.3 | 8 | ||
7.6 | odd | 2 | 847.2.a.o.1.3 | 8 | |||
11.2 | odd | 10 | 539.2.f.e.246.2 | 16 | |||
11.6 | odd | 10 | 539.2.f.e.344.2 | 16 | |||
11.10 | odd | 2 | 5929.2.a.bt.1.6 | 8 | |||
21.20 | even | 2 | 7623.2.a.cw.1.6 | 8 | |||
77.2 | odd | 30 | 539.2.q.f.312.2 | 32 | |||
77.6 | even | 10 | 77.2.f.b.36.2 | yes | 16 | ||
77.13 | even | 10 | 77.2.f.b.15.2 | ✓ | 16 | ||
77.17 | even | 30 | 539.2.q.g.520.2 | 32 | |||
77.20 | odd | 10 | 847.2.f.x.323.3 | 16 | |||
77.24 | even | 30 | 539.2.q.g.422.3 | 32 | |||
77.27 | odd | 10 | 847.2.f.x.729.3 | 16 | |||
77.39 | odd | 30 | 539.2.q.f.520.2 | 32 | |||
77.41 | even | 10 | 847.2.f.w.372.3 | 16 | |||
77.46 | odd | 30 | 539.2.q.f.422.3 | 32 | |||
77.48 | odd | 10 | 847.2.f.v.148.2 | 16 | |||
77.61 | even | 30 | 539.2.q.g.410.3 | 32 | |||
77.62 | even | 10 | 847.2.f.w.148.3 | 16 | |||
77.68 | even | 30 | 539.2.q.g.312.2 | 32 | |||
77.69 | odd | 10 | 847.2.f.v.372.2 | 16 | |||
77.72 | odd | 30 | 539.2.q.f.410.3 | 32 | |||
77.76 | even | 2 | 847.2.a.p.1.6 | 8 | |||
231.83 | odd | 10 | 693.2.m.i.190.3 | 16 | |||
231.167 | odd | 10 | 693.2.m.i.631.3 | 16 | |||
231.230 | odd | 2 | 7623.2.a.ct.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.2 | ✓ | 16 | 77.13 | even | 10 | ||
77.2.f.b.36.2 | yes | 16 | 77.6 | even | 10 | ||
539.2.f.e.246.2 | 16 | 11.2 | odd | 10 | |||
539.2.f.e.344.2 | 16 | 11.6 | odd | 10 | |||
539.2.q.f.312.2 | 32 | 77.2 | odd | 30 | |||
539.2.q.f.410.3 | 32 | 77.72 | odd | 30 | |||
539.2.q.f.422.3 | 32 | 77.46 | odd | 30 | |||
539.2.q.f.520.2 | 32 | 77.39 | odd | 30 | |||
539.2.q.g.312.2 | 32 | 77.68 | even | 30 | |||
539.2.q.g.410.3 | 32 | 77.61 | even | 30 | |||
539.2.q.g.422.3 | 32 | 77.24 | even | 30 | |||
539.2.q.g.520.2 | 32 | 77.17 | even | 30 | |||
693.2.m.i.190.3 | 16 | 231.83 | odd | 10 | |||
693.2.m.i.631.3 | 16 | 231.167 | odd | 10 | |||
847.2.a.o.1.3 | 8 | 7.6 | odd | 2 | |||
847.2.a.p.1.6 | 8 | 77.76 | even | 2 | |||
847.2.f.v.148.2 | 16 | 77.48 | odd | 10 | |||
847.2.f.v.372.2 | 16 | 77.69 | odd | 10 | |||
847.2.f.w.148.3 | 16 | 77.62 | even | 10 | |||
847.2.f.w.372.3 | 16 | 77.41 | even | 10 | |||
847.2.f.x.323.3 | 16 | 77.20 | odd | 10 | |||
847.2.f.x.729.3 | 16 | 77.27 | odd | 10 | |||
5929.2.a.bs.1.3 | 8 | 1.1 | even | 1 | trivial | ||
5929.2.a.bt.1.6 | 8 | 11.10 | odd | 2 | |||
7623.2.a.ct.1.3 | 8 | 231.230 | odd | 2 | |||
7623.2.a.cw.1.6 | 8 | 21.20 | even | 2 |