Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, 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("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.732051 | −0.327383 | −0.163692 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163692 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.732051 | 0.231495 | ||||||||
\(11\) | 5.19615 | 1.56670 | 0.783349 | − | 0.621582i | \(-0.213510\pi\) | ||||
0.783349 | + | 0.621582i | \(0.213510\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −0.732051 | −0.189015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.26795 | −0.550058 | −0.275029 | − | 0.961436i | \(-0.588688\pi\) | ||||
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.464102 | −0.106472 | −0.0532361 | − | 0.998582i | \(-0.516954\pi\) | ||||
−0.0532361 | + | 0.998582i | \(0.516954\pi\) | |||||||
\(20\) | −0.732051 | −0.163692 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −5.19615 | −1.10782 | ||||||||
\(23\) | −7.46410 | −1.55637 | −0.778186 | − | 0.628033i | \(-0.783860\pi\) | ||||
−0.778186 | + | 0.628033i | \(0.783860\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −3.53590 | −0.656600 | −0.328300 | − | 0.944574i | \(-0.606476\pi\) | ||||
−0.328300 | + | 0.944574i | \(0.606476\pi\) | |||||||
\(30\) | 0.732051 | 0.133654 | ||||||||
\(31\) | 3.26795 | 0.586941 | 0.293471 | − | 0.955968i | \(-0.405190\pi\) | ||||
0.293471 | + | 0.955968i | \(0.405190\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.19615 | 0.904534 | ||||||||
\(34\) | 2.26795 | 0.388950 | ||||||||
\(35\) | 0.732051 | 0.123739 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.73205 | 1.10674 | 0.553371 | − | 0.832935i | \(-0.313341\pi\) | ||||
0.553371 | + | 0.832935i | \(0.313341\pi\) | |||||||
\(38\) | 0.464102 | 0.0752872 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.732051 | 0.115747 | ||||||||
\(41\) | 8.46410 | 1.32187 | 0.660935 | − | 0.750443i | \(-0.270160\pi\) | ||||
0.660935 | + | 0.750443i | \(0.270160\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −8.73205 | −1.33163 | −0.665813 | − | 0.746119i | \(-0.731915\pi\) | ||||
−0.665813 | + | 0.746119i | \(0.731915\pi\) | |||||||
\(44\) | 5.19615 | 0.783349 | ||||||||
\(45\) | −0.732051 | −0.109128 | ||||||||
\(46\) | 7.46410 | 1.10052 | ||||||||
\(47\) | 3.92820 | 0.572987 | 0.286494 | − | 0.958082i | \(-0.407510\pi\) | ||||
0.286494 | + | 0.958082i | \(0.407510\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.46410 | 0.631319 | ||||||||
\(51\) | −2.26795 | −0.317576 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.92820 | −1.36374 | −0.681872 | − | 0.731472i | \(-0.738834\pi\) | ||||
−0.681872 | + | 0.731472i | \(0.738834\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.80385 | −0.512911 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −0.464102 | −0.0614718 | ||||||||
\(58\) | 3.53590 | 0.464286 | ||||||||
\(59\) | −8.92820 | −1.16235 | −0.581177 | − | 0.813778i | \(-0.697407\pi\) | ||||
−0.581177 | + | 0.813778i | \(0.697407\pi\) | |||||||
\(60\) | −0.732051 | −0.0945074 | ||||||||
\(61\) | 3.73205 | 0.477840 | 0.238920 | − | 0.971039i | \(-0.423207\pi\) | ||||
0.238920 | + | 0.971039i | \(0.423207\pi\) | |||||||
\(62\) | −3.26795 | −0.415030 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.19615 | −0.639602 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | −2.26795 | −0.275029 | ||||||||
\(69\) | −7.46410 | −0.898572 | ||||||||
\(70\) | −0.732051 | −0.0874968 | ||||||||
\(71\) | 7.26795 | 0.862547 | 0.431273 | − | 0.902221i | \(-0.358064\pi\) | ||||
0.431273 | + | 0.902221i | \(0.358064\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.46410 | −0.171360 | −0.0856801 | − | 0.996323i | \(-0.527306\pi\) | ||||
−0.0856801 | + | 0.996323i | \(0.527306\pi\) | |||||||
\(74\) | −6.73205 | −0.782585 | ||||||||
\(75\) | −4.46410 | −0.515470 | ||||||||
\(76\) | −0.464102 | −0.0532361 | ||||||||
\(77\) | −5.19615 | −0.592157 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.00000 | 1.01258 | 0.506290 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506290 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(80\) | −0.732051 | −0.0818458 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.46410 | −0.934704 | ||||||||
\(83\) | −9.26795 | −1.01729 | −0.508645 | − | 0.860976i | \(-0.669853\pi\) | ||||
−0.508645 | + | 0.860976i | \(0.669853\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 1.66025 | 0.180080 | ||||||||
\(86\) | 8.73205 | 0.941601 | ||||||||
\(87\) | −3.53590 | −0.379088 | ||||||||
\(88\) | −5.19615 | −0.553912 | ||||||||
\(89\) | −16.8564 | −1.78678 | −0.893388 | − | 0.449286i | \(-0.851678\pi\) | ||||
−0.893388 | + | 0.449286i | \(0.851678\pi\) | |||||||
\(90\) | 0.732051 | 0.0771649 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.46410 | −0.778186 | ||||||||
\(93\) | 3.26795 | 0.338871 | ||||||||
\(94\) | −3.92820 | −0.405163 | ||||||||
\(95\) | 0.339746 | 0.0348572 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.1962 | −1.44140 | −0.720700 | − | 0.693247i | \(-0.756180\pi\) | ||||
−0.720700 | + | 0.693247i | \(0.756180\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 5.19615 | 0.522233 | ||||||||
\(100\) | −4.46410 | −0.446410 | ||||||||
\(101\) | 4.92820 | 0.490375 | 0.245187 | − | 0.969476i | \(-0.421151\pi\) | ||||
0.245187 | + | 0.969476i | \(0.421151\pi\) | |||||||
\(102\) | 2.26795 | 0.224560 | ||||||||
\(103\) | −16.1962 | −1.59585 | −0.797927 | − | 0.602754i | \(-0.794070\pi\) | ||||
−0.797927 | + | 0.602754i | \(0.794070\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.732051 | 0.0714408 | ||||||||
\(106\) | 9.92820 | 0.964312 | ||||||||
\(107\) | −6.07180 | −0.586983 | −0.293491 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293491 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −11.2679 | −1.07927 | −0.539637 | − | 0.841898i | \(-0.681438\pi\) | ||||
−0.539637 | + | 0.841898i | \(0.681438\pi\) | |||||||
\(110\) | 3.80385 | 0.362683 | ||||||||
\(111\) | 6.73205 | 0.638978 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 7.66025 | 0.720616 | 0.360308 | − | 0.932833i | \(-0.382672\pi\) | ||||
0.360308 | + | 0.932833i | \(0.382672\pi\) | |||||||
\(114\) | 0.464102 | 0.0434671 | ||||||||
\(115\) | 5.46410 | 0.509530 | ||||||||
\(116\) | −3.53590 | −0.328300 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.92820 | 0.821908 | ||||||||
\(119\) | 2.26795 | 0.207903 | ||||||||
\(120\) | 0.732051 | 0.0668268 | ||||||||
\(121\) | 16.0000 | 1.45455 | ||||||||
\(122\) | −3.73205 | −0.337884 | ||||||||
\(123\) | 8.46410 | 0.763182 | ||||||||
\(124\) | 3.26795 | 0.293471 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 14.3923 | 1.27711 | 0.638555 | − | 0.769576i | \(-0.279532\pi\) | ||||
0.638555 | + | 0.769576i | \(0.279532\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.73205 | −0.768814 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9282 | −1.30428 | −0.652142 | − | 0.758097i | \(-0.726129\pi\) | ||||
−0.652142 | + | 0.758097i | \(0.726129\pi\) | |||||||
\(132\) | 5.19615 | 0.452267 | ||||||||
\(133\) | 0.464102 | 0.0402427 | ||||||||
\(134\) | 10.0000 | 0.863868 | ||||||||
\(135\) | −0.732051 | −0.0630049 | ||||||||
\(136\) | 2.26795 | 0.194475 | ||||||||
\(137\) | 19.4641 | 1.66293 | 0.831465 | − | 0.555577i | \(-0.187503\pi\) | ||||
0.831465 | + | 0.555577i | \(0.187503\pi\) | |||||||
\(138\) | 7.46410 | 0.635387 | ||||||||
\(139\) | 17.0526 | 1.44638 | 0.723190 | − | 0.690650i | \(-0.242675\pi\) | ||||
0.723190 | + | 0.690650i | \(0.242675\pi\) | |||||||
\(140\) | 0.732051 | 0.0618696 | ||||||||
\(141\) | 3.92820 | 0.330814 | ||||||||
\(142\) | −7.26795 | −0.609913 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.58846 | 0.214960 | ||||||||
\(146\) | 1.46410 | 0.121170 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 6.73205 | 0.553371 | ||||||||
\(149\) | −8.00000 | −0.655386 | −0.327693 | − | 0.944784i | \(-0.606271\pi\) | ||||
−0.327693 | + | 0.944784i | \(0.606271\pi\) | |||||||
\(150\) | 4.46410 | 0.364492 | ||||||||
\(151\) | −1.19615 | −0.0973415 | −0.0486708 | − | 0.998815i | \(-0.515499\pi\) | ||||
−0.0486708 | + | 0.998815i | \(0.515499\pi\) | |||||||
\(152\) | 0.464102 | 0.0376436 | ||||||||
\(153\) | −2.26795 | −0.183353 | ||||||||
\(154\) | 5.19615 | 0.418718 | ||||||||
\(155\) | −2.39230 | −0.192155 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4641 | −0.914935 | −0.457467 | − | 0.889226i | \(-0.651243\pi\) | ||||
−0.457467 | + | 0.889226i | \(0.651243\pi\) | |||||||
\(158\) | −9.00000 | −0.716002 | ||||||||
\(159\) | −9.92820 | −0.787358 | ||||||||
\(160\) | 0.732051 | 0.0578737 | ||||||||
\(161\) | 7.46410 | 0.588254 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 7.12436 | 0.558023 | 0.279011 | − | 0.960288i | \(-0.409993\pi\) | ||||
0.279011 | + | 0.960288i | \(0.409993\pi\) | |||||||
\(164\) | 8.46410 | 0.660935 | ||||||||
\(165\) | −3.80385 | −0.296129 | ||||||||
\(166\) | 9.26795 | 0.719332 | ||||||||
\(167\) | −5.07180 | −0.392467 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.66025 | −0.127336 | ||||||||
\(171\) | −0.464102 | −0.0354907 | ||||||||
\(172\) | −8.73205 | −0.665813 | ||||||||
\(173\) | 2.19615 | 0.166970 | 0.0834852 | − | 0.996509i | \(-0.473395\pi\) | ||||
0.0834852 | + | 0.996509i | \(0.473395\pi\) | |||||||
\(174\) | 3.53590 | 0.268056 | ||||||||
\(175\) | 4.46410 | 0.337454 | ||||||||
\(176\) | 5.19615 | 0.391675 | ||||||||
\(177\) | −8.92820 | −0.671085 | ||||||||
\(178\) | 16.8564 | 1.26344 | ||||||||
\(179\) | −3.46410 | −0.258919 | −0.129460 | − | 0.991585i | \(-0.541324\pi\) | ||||
−0.129460 | + | 0.991585i | \(0.541324\pi\) | |||||||
\(180\) | −0.732051 | −0.0545638 | ||||||||
\(181\) | −14.2679 | −1.06053 | −0.530264 | − | 0.847832i | \(-0.677907\pi\) | ||||
−0.530264 | + | 0.847832i | \(0.677907\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.73205 | 0.275881 | ||||||||
\(184\) | 7.46410 | 0.550261 | ||||||||
\(185\) | −4.92820 | −0.362329 | ||||||||
\(186\) | −3.26795 | −0.239618 | ||||||||
\(187\) | −11.7846 | −0.861776 | ||||||||
\(188\) | 3.92820 | 0.286494 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.339746 | −0.0246478 | ||||||||
\(191\) | −8.19615 | −0.593053 | −0.296526 | − | 0.955025i | \(-0.595828\pi\) | ||||
−0.296526 | + | 0.955025i | \(0.595828\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 7.58846 | 0.546229 | 0.273115 | − | 0.961982i | \(-0.411946\pi\) | ||||
0.273115 | + | 0.961982i | \(0.411946\pi\) | |||||||
\(194\) | 14.1962 | 1.01922 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −0.267949 | −0.0190906 | −0.00954529 | − | 0.999954i | \(-0.503038\pi\) | ||||
−0.00954529 | + | 0.999954i | \(0.503038\pi\) | |||||||
\(198\) | −5.19615 | −0.369274 | ||||||||
\(199\) | 24.5885 | 1.74303 | 0.871515 | − | 0.490369i | \(-0.163138\pi\) | ||||
0.871515 | + | 0.490369i | \(0.163138\pi\) | |||||||
\(200\) | 4.46410 | 0.315660 | ||||||||
\(201\) | −10.0000 | −0.705346 | ||||||||
\(202\) | −4.92820 | −0.346747 | ||||||||
\(203\) | 3.53590 | 0.248171 | ||||||||
\(204\) | −2.26795 | −0.158788 | ||||||||
\(205\) | −6.19615 | −0.432758 | ||||||||
\(206\) | 16.1962 | 1.12844 | ||||||||
\(207\) | −7.46410 | −0.518791 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.41154 | −0.166810 | ||||||||
\(210\) | −0.732051 | −0.0505163 | ||||||||
\(211\) | 24.9282 | 1.71613 | 0.858064 | − | 0.513543i | \(-0.171667\pi\) | ||||
0.858064 | + | 0.513543i | \(0.171667\pi\) | |||||||
\(212\) | −9.92820 | −0.681872 | ||||||||
\(213\) | 7.26795 | 0.497992 | ||||||||
\(214\) | 6.07180 | 0.415059 | ||||||||
\(215\) | 6.39230 | 0.435952 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.26795 | −0.221843 | ||||||||
\(218\) | 11.2679 | 0.763162 | ||||||||
\(219\) | −1.46410 | −0.0989348 | ||||||||
\(220\) | −3.80385 | −0.256455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.73205 | −0.451826 | ||||||||
\(223\) | 5.46410 | 0.365903 | 0.182952 | − | 0.983122i | \(-0.441435\pi\) | ||||
0.182952 | + | 0.983122i | \(0.441435\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −4.46410 | −0.297607 | ||||||||
\(226\) | −7.66025 | −0.509553 | ||||||||
\(227\) | −13.3205 | −0.884113 | −0.442057 | − | 0.896987i | \(-0.645751\pi\) | ||||
−0.442057 | + | 0.896987i | \(0.645751\pi\) | |||||||
\(228\) | −0.464102 | −0.0307359 | ||||||||
\(229\) | 17.3923 | 1.14932 | 0.574658 | − | 0.818394i | \(-0.305135\pi\) | ||||
0.574658 | + | 0.818394i | \(0.305135\pi\) | |||||||
\(230\) | −5.46410 | −0.360292 | ||||||||
\(231\) | −5.19615 | −0.341882 | ||||||||
\(232\) | 3.53590 | 0.232143 | ||||||||
\(233\) | −18.5885 | −1.21777 | −0.608885 | − | 0.793258i | \(-0.708383\pi\) | ||||
−0.608885 | + | 0.793258i | \(0.708383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.87564 | −0.187586 | ||||||||
\(236\) | −8.92820 | −0.581177 | ||||||||
\(237\) | 9.00000 | 0.584613 | ||||||||
\(238\) | −2.26795 | −0.147009 | ||||||||
\(239\) | −26.5885 | −1.71986 | −0.859932 | − | 0.510408i | \(-0.829494\pi\) | ||||
−0.859932 | + | 0.510408i | \(0.829494\pi\) | |||||||
\(240\) | −0.732051 | −0.0472537 | ||||||||
\(241\) | −10.9282 | −0.703947 | −0.351974 | − | 0.936010i | \(-0.614489\pi\) | ||||
−0.351974 | + | 0.936010i | \(0.614489\pi\) | |||||||
\(242\) | −16.0000 | −1.02852 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.73205 | 0.238920 | ||||||||
\(245\) | −0.732051 | −0.0467690 | ||||||||
\(246\) | −8.46410 | −0.539651 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.26795 | −0.207515 | ||||||||
\(249\) | −9.26795 | −0.587332 | ||||||||
\(250\) | −6.92820 | −0.438178 | ||||||||
\(251\) | 17.5167 | 1.10564 | 0.552821 | − | 0.833300i | \(-0.313551\pi\) | ||||
0.552821 | + | 0.833300i | \(0.313551\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −38.7846 | −2.43837 | ||||||||
\(254\) | −14.3923 | −0.903054 | ||||||||
\(255\) | 1.66025 | 0.103969 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.0526 | −1.56274 | −0.781368 | − | 0.624071i | \(-0.785478\pi\) | ||||
−0.781368 | + | 0.624071i | \(0.785478\pi\) | |||||||
\(258\) | 8.73205 | 0.543634 | ||||||||
\(259\) | −6.73205 | −0.418309 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.53590 | −0.218867 | ||||||||
\(262\) | 14.9282 | 0.922267 | ||||||||
\(263\) | 3.12436 | 0.192656 | 0.0963280 | − | 0.995350i | \(-0.469290\pi\) | ||||
0.0963280 | + | 0.995350i | \(0.469290\pi\) | |||||||
\(264\) | −5.19615 | −0.319801 | ||||||||
\(265\) | 7.26795 | 0.446467 | ||||||||
\(266\) | −0.464102 | −0.0284559 | ||||||||
\(267\) | −16.8564 | −1.03160 | ||||||||
\(268\) | −10.0000 | −0.610847 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0.732051 | 0.0445512 | ||||||||
\(271\) | 7.66025 | 0.465327 | 0.232664 | − | 0.972557i | \(-0.425256\pi\) | ||||
0.232664 | + | 0.972557i | \(0.425256\pi\) | |||||||
\(272\) | −2.26795 | −0.137515 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.4641 | −1.17587 | ||||||||
\(275\) | −23.1962 | −1.39878 | ||||||||
\(276\) | −7.46410 | −0.449286 | ||||||||
\(277\) | −14.3923 | −0.864750 | −0.432375 | − | 0.901694i | \(-0.642324\pi\) | ||||
−0.432375 | + | 0.901694i | \(0.642324\pi\) | |||||||
\(278\) | −17.0526 | −1.02274 | ||||||||
\(279\) | 3.26795 | 0.195647 | ||||||||
\(280\) | −0.732051 | −0.0437484 | ||||||||
\(281\) | 12.7321 | 0.759530 | 0.379765 | − | 0.925083i | \(-0.376005\pi\) | ||||
0.379765 | + | 0.925083i | \(0.376005\pi\) | |||||||
\(282\) | −3.92820 | −0.233921 | ||||||||
\(283\) | −17.8564 | −1.06145 | −0.530727 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530727 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(284\) | 7.26795 | 0.431273 | ||||||||
\(285\) | 0.339746 | 0.0201248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.46410 | −0.499620 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | −2.58846 | −0.151999 | ||||||||
\(291\) | −14.1962 | −0.832193 | ||||||||
\(292\) | −1.46410 | −0.0856801 | ||||||||
\(293\) | −1.07180 | −0.0626150 | −0.0313075 | − | 0.999510i | \(-0.509967\pi\) | ||||
−0.0313075 | + | 0.999510i | \(0.509967\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 6.53590 | 0.380535 | ||||||||
\(296\) | −6.73205 | −0.391293 | ||||||||
\(297\) | 5.19615 | 0.301511 | ||||||||
\(298\) | 8.00000 | 0.463428 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.46410 | −0.257735 | ||||||||
\(301\) | 8.73205 | 0.503307 | ||||||||
\(302\) | 1.19615 | 0.0688308 | ||||||||
\(303\) | 4.92820 | 0.283118 | ||||||||
\(304\) | −0.464102 | −0.0266181 | ||||||||
\(305\) | −2.73205 | −0.156437 | ||||||||
\(306\) | 2.26795 | 0.129650 | ||||||||
\(307\) | −5.00000 | −0.285365 | −0.142683 | − | 0.989769i | \(-0.545573\pi\) | ||||
−0.142683 | + | 0.989769i | \(0.545573\pi\) | |||||||
\(308\) | −5.19615 | −0.296078 | ||||||||
\(309\) | −16.1962 | −0.921367 | ||||||||
\(310\) | 2.39230 | 0.135874 | ||||||||
\(311\) | −14.8038 | −0.839449 | −0.419725 | − | 0.907652i | \(-0.637873\pi\) | ||||
−0.419725 | + | 0.907652i | \(0.637873\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.87564 | 0.388634 | 0.194317 | − | 0.980939i | \(-0.437751\pi\) | ||||
0.194317 | + | 0.980939i | \(0.437751\pi\) | |||||||
\(314\) | 11.4641 | 0.646957 | ||||||||
\(315\) | 0.732051 | 0.0412464 | ||||||||
\(316\) | 9.00000 | 0.506290 | ||||||||
\(317\) | −14.7846 | −0.830386 | −0.415193 | − | 0.909733i | \(-0.636286\pi\) | ||||
−0.415193 | + | 0.909733i | \(0.636286\pi\) | |||||||
\(318\) | 9.92820 | 0.556746 | ||||||||
\(319\) | −18.3731 | −1.02869 | ||||||||
\(320\) | −0.732051 | −0.0409229 | ||||||||
\(321\) | −6.07180 | −0.338895 | ||||||||
\(322\) | −7.46410 | −0.415958 | ||||||||
\(323\) | 1.05256 | 0.0585659 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.12436 | −0.394582 | ||||||||
\(327\) | −11.2679 | −0.623119 | ||||||||
\(328\) | −8.46410 | −0.467352 | ||||||||
\(329\) | −3.92820 | −0.216569 | ||||||||
\(330\) | 3.80385 | 0.209395 | ||||||||
\(331\) | 6.78461 | 0.372916 | 0.186458 | − | 0.982463i | \(-0.440299\pi\) | ||||
0.186458 | + | 0.982463i | \(0.440299\pi\) | |||||||
\(332\) | −9.26795 | −0.508645 | ||||||||
\(333\) | 6.73205 | 0.368914 | ||||||||
\(334\) | 5.07180 | 0.277516 | ||||||||
\(335\) | 7.32051 | 0.399962 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 11.0000 | 0.599208 | 0.299604 | − | 0.954064i | \(-0.403145\pi\) | ||||
0.299604 | + | 0.954064i | \(0.403145\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.66025 | 0.416048 | ||||||||
\(340\) | 1.66025 | 0.0900399 | ||||||||
\(341\) | 16.9808 | 0.919560 | ||||||||
\(342\) | 0.464102 | 0.0250957 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.73205 | 0.470801 | ||||||||
\(345\) | 5.46410 | 0.294177 | ||||||||
\(346\) | −2.19615 | −0.118066 | ||||||||
\(347\) | −6.46410 | −0.347011 | −0.173506 | − | 0.984833i | \(-0.555509\pi\) | ||||
−0.173506 | + | 0.984833i | \(0.555509\pi\) | |||||||
\(348\) | −3.53590 | −0.189544 | ||||||||
\(349\) | 6.14359 | 0.328859 | 0.164430 | − | 0.986389i | \(-0.447422\pi\) | ||||
0.164430 | + | 0.986389i | \(0.447422\pi\) | |||||||
\(350\) | −4.46410 | −0.238616 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.19615 | −0.276956 | ||||||||
\(353\) | −31.3205 | −1.66702 | −0.833511 | − | 0.552503i | \(-0.813673\pi\) | ||||
−0.833511 | + | 0.552503i | \(0.813673\pi\) | |||||||
\(354\) | 8.92820 | 0.474529 | ||||||||
\(355\) | −5.32051 | −0.282383 | ||||||||
\(356\) | −16.8564 | −0.893388 | ||||||||
\(357\) | 2.26795 | 0.120033 | ||||||||
\(358\) | 3.46410 | 0.183083 | ||||||||
\(359\) | −34.4449 | −1.81793 | −0.908965 | − | 0.416872i | \(-0.863126\pi\) | ||||
−0.908965 | + | 0.416872i | \(0.863126\pi\) | |||||||
\(360\) | 0.732051 | 0.0385825 | ||||||||
\(361\) | −18.7846 | −0.988664 | ||||||||
\(362\) | 14.2679 | 0.749907 | ||||||||
\(363\) | 16.0000 | 0.839782 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.07180 | 0.0561004 | ||||||||
\(366\) | −3.73205 | −0.195077 | ||||||||
\(367\) | 13.3205 | 0.695325 | 0.347662 | − | 0.937620i | \(-0.386976\pi\) | ||||
0.347662 | + | 0.937620i | \(0.386976\pi\) | |||||||
\(368\) | −7.46410 | −0.389093 | ||||||||
\(369\) | 8.46410 | 0.440624 | ||||||||
\(370\) | 4.92820 | 0.256205 | ||||||||
\(371\) | 9.92820 | 0.515447 | ||||||||
\(372\) | 3.26795 | 0.169435 | ||||||||
\(373\) | −15.1244 | −0.783109 | −0.391555 | − | 0.920155i | \(-0.628063\pi\) | ||||
−0.391555 | + | 0.920155i | \(0.628063\pi\) | |||||||
\(374\) | 11.7846 | 0.609368 | ||||||||
\(375\) | 6.92820 | 0.357771 | ||||||||
\(376\) | −3.92820 | −0.202582 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 36.0526 | 1.85190 | 0.925948 | − | 0.377652i | \(-0.123268\pi\) | ||||
0.925948 | + | 0.377652i | \(0.123268\pi\) | |||||||
\(380\) | 0.339746 | 0.0174286 | ||||||||
\(381\) | 14.3923 | 0.737340 | ||||||||
\(382\) | 8.19615 | 0.419352 | ||||||||
\(383\) | 31.0000 | 1.58403 | 0.792013 | − | 0.610504i | \(-0.209033\pi\) | ||||
0.792013 | + | 0.610504i | \(0.209033\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 3.80385 | 0.193862 | ||||||||
\(386\) | −7.58846 | −0.386242 | ||||||||
\(387\) | −8.73205 | −0.443875 | ||||||||
\(388\) | −14.1962 | −0.720700 | ||||||||
\(389\) | −21.4641 | −1.08827 | −0.544137 | − | 0.838997i | \(-0.683143\pi\) | ||||
−0.544137 | + | 0.838997i | \(0.683143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.9282 | 0.856096 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −14.9282 | −0.753028 | ||||||||
\(394\) | 0.267949 | 0.0134991 | ||||||||
\(395\) | −6.58846 | −0.331501 | ||||||||
\(396\) | 5.19615 | 0.261116 | ||||||||
\(397\) | 21.3923 | 1.07365 | 0.536825 | − | 0.843694i | \(-0.319624\pi\) | ||||
0.536825 | + | 0.843694i | \(0.319624\pi\) | |||||||
\(398\) | −24.5885 | −1.23251 | ||||||||
\(399\) | 0.464102 | 0.0232341 | ||||||||
\(400\) | −4.46410 | −0.223205 | ||||||||
\(401\) | −11.0718 | −0.552899 | −0.276450 | − | 0.961028i | \(-0.589158\pi\) | ||||
−0.276450 | + | 0.961028i | \(0.589158\pi\) | |||||||
\(402\) | 10.0000 | 0.498755 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.92820 | 0.245187 | ||||||||
\(405\) | −0.732051 | −0.0363759 | ||||||||
\(406\) | −3.53590 | −0.175484 | ||||||||
\(407\) | 34.9808 | 1.73393 | ||||||||
\(408\) | 2.26795 | 0.112280 | ||||||||
\(409\) | −16.5885 | −0.820246 | −0.410123 | − | 0.912030i | \(-0.634514\pi\) | ||||
−0.410123 | + | 0.912030i | \(0.634514\pi\) | |||||||
\(410\) | 6.19615 | 0.306006 | ||||||||
\(411\) | 19.4641 | 0.960093 | ||||||||
\(412\) | −16.1962 | −0.797927 | ||||||||
\(413\) | 8.92820 | 0.439328 | ||||||||
\(414\) | 7.46410 | 0.366841 | ||||||||
\(415\) | 6.78461 | 0.333043 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.0526 | 0.835067 | ||||||||
\(418\) | 2.41154 | 0.117952 | ||||||||
\(419\) | −14.5885 | −0.712693 | −0.356346 | − | 0.934354i | \(-0.615978\pi\) | ||||
−0.356346 | + | 0.934354i | \(0.615978\pi\) | |||||||
\(420\) | 0.732051 | 0.0357204 | ||||||||
\(421\) | −25.3205 | −1.23405 | −0.617023 | − | 0.786945i | \(-0.711661\pi\) | ||||
−0.617023 | + | 0.786945i | \(0.711661\pi\) | |||||||
\(422\) | −24.9282 | −1.21349 | ||||||||
\(423\) | 3.92820 | 0.190996 | ||||||||
\(424\) | 9.92820 | 0.482156 | ||||||||
\(425\) | 10.1244 | 0.491103 | ||||||||
\(426\) | −7.26795 | −0.352133 | ||||||||
\(427\) | −3.73205 | −0.180607 | ||||||||
\(428\) | −6.07180 | −0.293491 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.39230 | −0.308264 | ||||||||
\(431\) | −13.1244 | −0.632178 | −0.316089 | − | 0.948730i | \(-0.602370\pi\) | ||||
−0.316089 | + | 0.948730i | \(0.602370\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 12.1436 | 0.583584 | 0.291792 | − | 0.956482i | \(-0.405749\pi\) | ||||
0.291792 | + | 0.956482i | \(0.405749\pi\) | |||||||
\(434\) | 3.26795 | 0.156867 | ||||||||
\(435\) | 2.58846 | 0.124107 | ||||||||
\(436\) | −11.2679 | −0.539637 | ||||||||
\(437\) | 3.46410 | 0.165710 | ||||||||
\(438\) | 1.46410 | 0.0699575 | ||||||||
\(439\) | 23.3205 | 1.11303 | 0.556514 | − | 0.830839i | \(-0.312139\pi\) | ||||
0.556514 | + | 0.830839i | \(0.312139\pi\) | |||||||
\(440\) | 3.80385 | 0.181341 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.0000 | −1.18779 | −0.593893 | − | 0.804544i | \(-0.702410\pi\) | ||||
−0.593893 | + | 0.804544i | \(0.702410\pi\) | |||||||
\(444\) | 6.73205 | 0.319489 | ||||||||
\(445\) | 12.3397 | 0.584960 | ||||||||
\(446\) | −5.46410 | −0.258733 | ||||||||
\(447\) | −8.00000 | −0.378387 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −28.9808 | −1.36769 | −0.683843 | − | 0.729629i | \(-0.739693\pi\) | ||||
−0.683843 | + | 0.729629i | \(0.739693\pi\) | |||||||
\(450\) | 4.46410 | 0.210440 | ||||||||
\(451\) | 43.9808 | 2.07097 | ||||||||
\(452\) | 7.66025 | 0.360308 | ||||||||
\(453\) | −1.19615 | −0.0562001 | ||||||||
\(454\) | 13.3205 | 0.625162 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.464102 | 0.0217335 | ||||||||
\(457\) | 29.7128 | 1.38991 | 0.694953 | − | 0.719055i | \(-0.255425\pi\) | ||||
0.694953 | + | 0.719055i | \(0.255425\pi\) | |||||||
\(458\) | −17.3923 | −0.812689 | ||||||||
\(459\) | −2.26795 | −0.105859 | ||||||||
\(460\) | 5.46410 | 0.254765 | ||||||||
\(461\) | 6.92820 | 0.322679 | 0.161339 | − | 0.986899i | \(-0.448419\pi\) | ||||
0.161339 | + | 0.986899i | \(0.448419\pi\) | |||||||
\(462\) | 5.19615 | 0.241747 | ||||||||
\(463\) | 15.3397 | 0.712898 | 0.356449 | − | 0.934315i | \(-0.383987\pi\) | ||||
0.356449 | + | 0.934315i | \(0.383987\pi\) | |||||||
\(464\) | −3.53590 | −0.164150 | ||||||||
\(465\) | −2.39230 | −0.110940 | ||||||||
\(466\) | 18.5885 | 0.861094 | ||||||||
\(467\) | −18.9282 | −0.875893 | −0.437946 | − | 0.899001i | \(-0.644294\pi\) | ||||
−0.437946 | + | 0.899001i | \(0.644294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | 0.461757 | ||||||||
\(470\) | 2.87564 | 0.132644 | ||||||||
\(471\) | −11.4641 | −0.528238 | ||||||||
\(472\) | 8.92820 | 0.410954 | ||||||||
\(473\) | −45.3731 | −2.08626 | ||||||||
\(474\) | −9.00000 | −0.413384 | ||||||||
\(475\) | 2.07180 | 0.0950606 | ||||||||
\(476\) | 2.26795 | 0.103951 | ||||||||
\(477\) | −9.92820 | −0.454581 | ||||||||
\(478\) | 26.5885 | 1.21613 | ||||||||
\(479\) | 4.85641 | 0.221895 | 0.110947 | − | 0.993826i | \(-0.464611\pi\) | ||||
0.110947 | + | 0.993826i | \(0.464611\pi\) | |||||||
\(480\) | 0.732051 | 0.0334134 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.9282 | 0.497766 | ||||||||
\(483\) | 7.46410 | 0.339628 | ||||||||
\(484\) | 16.0000 | 0.727273 | ||||||||
\(485\) | 10.3923 | 0.471890 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −29.4449 | −1.33427 | −0.667137 | − | 0.744935i | \(-0.732480\pi\) | ||||
−0.667137 | + | 0.744935i | \(0.732480\pi\) | |||||||
\(488\) | −3.73205 | −0.168942 | ||||||||
\(489\) | 7.12436 | 0.322174 | ||||||||
\(490\) | 0.732051 | 0.0330707 | ||||||||
\(491\) | −6.39230 | −0.288481 | −0.144240 | − | 0.989543i | \(-0.546074\pi\) | ||||
−0.144240 | + | 0.989543i | \(0.546074\pi\) | |||||||
\(492\) | 8.46410 | 0.381591 | ||||||||
\(493\) | 8.01924 | 0.361168 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.80385 | −0.170970 | ||||||||
\(496\) | 3.26795 | 0.146735 | ||||||||
\(497\) | −7.26795 | −0.326012 | ||||||||
\(498\) | 9.26795 | 0.415307 | ||||||||
\(499\) | −20.5885 | −0.921666 | −0.460833 | − | 0.887487i | \(-0.652449\pi\) | ||||
−0.460833 | + | 0.887487i | \(0.652449\pi\) | |||||||
\(500\) | 6.92820 | 0.309839 | ||||||||
\(501\) | −5.07180 | −0.226591 | ||||||||
\(502\) | −17.5167 | −0.781807 | ||||||||
\(503\) | −30.9282 | −1.37902 | −0.689510 | − | 0.724276i | \(-0.742174\pi\) | ||||
−0.689510 | + | 0.724276i | \(0.742174\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −3.60770 | −0.160540 | ||||||||
\(506\) | 38.7846 | 1.72419 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.3923 | 0.638555 | ||||||||
\(509\) | 29.6603 | 1.31467 | 0.657334 | − | 0.753600i | \(-0.271684\pi\) | ||||
0.657334 | + | 0.753600i | \(0.271684\pi\) | |||||||
\(510\) | −1.66025 | −0.0735173 | ||||||||
\(511\) | 1.46410 | 0.0647680 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.464102 | −0.0204906 | ||||||||
\(514\) | 25.0526 | 1.10502 | ||||||||
\(515\) | 11.8564 | 0.522456 | ||||||||
\(516\) | −8.73205 | −0.384407 | ||||||||
\(517\) | 20.4115 | 0.897699 | ||||||||
\(518\) | 6.73205 | 0.295789 | ||||||||
\(519\) | 2.19615 | 0.0964004 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.5885 | −0.945807 | −0.472904 | − | 0.881114i | \(-0.656794\pi\) | ||||
−0.472904 | + | 0.881114i | \(0.656794\pi\) | |||||||
\(522\) | 3.53590 | 0.154762 | ||||||||
\(523\) | −25.1962 | −1.10175 | −0.550875 | − | 0.834587i | \(-0.685706\pi\) | ||||
−0.550875 | + | 0.834587i | \(0.685706\pi\) | |||||||
\(524\) | −14.9282 | −0.652142 | ||||||||
\(525\) | 4.46410 | 0.194829 | ||||||||
\(526\) | −3.12436 | −0.136228 | ||||||||
\(527\) | −7.41154 | −0.322852 | ||||||||
\(528\) | 5.19615 | 0.226134 | ||||||||
\(529\) | 32.7128 | 1.42230 | ||||||||
\(530\) | −7.26795 | −0.315700 | ||||||||
\(531\) | −8.92820 | −0.387451 | ||||||||
\(532\) | 0.464102 | 0.0201214 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 16.8564 | 0.729448 | ||||||||
\(535\) | 4.44486 | 0.192168 | ||||||||
\(536\) | 10.0000 | 0.431934 | ||||||||
\(537\) | −3.46410 | −0.149487 | ||||||||
\(538\) | 4.00000 | 0.172452 | ||||||||
\(539\) | 5.19615 | 0.223814 | ||||||||
\(540\) | −0.732051 | −0.0315025 | ||||||||
\(541\) | 8.05256 | 0.346207 | 0.173103 | − | 0.984904i | \(-0.444621\pi\) | ||||
0.173103 | + | 0.984904i | \(0.444621\pi\) | |||||||
\(542\) | −7.66025 | −0.329036 | ||||||||
\(543\) | −14.2679 | −0.612296 | ||||||||
\(544\) | 2.26795 | 0.0972375 | ||||||||
\(545\) | 8.24871 | 0.353336 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.19615 | −0.179415 | −0.0897073 | − | 0.995968i | \(-0.528593\pi\) | ||||
−0.0897073 | + | 0.995968i | \(0.528593\pi\) | |||||||
\(548\) | 19.4641 | 0.831465 | ||||||||
\(549\) | 3.73205 | 0.159280 | ||||||||
\(550\) | 23.1962 | 0.989087 | ||||||||
\(551\) | 1.64102 | 0.0699096 | ||||||||
\(552\) | 7.46410 | 0.317693 | ||||||||
\(553\) | −9.00000 | −0.382719 | ||||||||
\(554\) | 14.3923 | 0.611470 | ||||||||
\(555\) | −4.92820 | −0.209191 | ||||||||
\(556\) | 17.0526 | 0.723190 | ||||||||
\(557\) | 19.7321 | 0.836074 | 0.418037 | − | 0.908430i | \(-0.362718\pi\) | ||||
0.418037 | + | 0.908430i | \(0.362718\pi\) | |||||||
\(558\) | −3.26795 | −0.138343 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.732051 | 0.0309348 | ||||||||
\(561\) | −11.7846 | −0.497547 | ||||||||
\(562\) | −12.7321 | −0.537069 | ||||||||
\(563\) | −13.6603 | −0.575711 | −0.287856 | − | 0.957674i | \(-0.592942\pi\) | ||||
−0.287856 | + | 0.957674i | \(0.592942\pi\) | |||||||
\(564\) | 3.92820 | 0.165407 | ||||||||
\(565\) | −5.60770 | −0.235918 | ||||||||
\(566\) | 17.8564 | 0.750561 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −7.26795 | −0.304956 | ||||||||
\(569\) | 1.66025 | 0.0696015 | 0.0348007 | − | 0.999394i | \(-0.488920\pi\) | ||||
0.0348007 | + | 0.999394i | \(0.488920\pi\) | |||||||
\(570\) | −0.339746 | −0.0142304 | ||||||||
\(571\) | −39.5167 | −1.65372 | −0.826860 | − | 0.562407i | \(-0.809875\pi\) | ||||
−0.826860 | + | 0.562407i | \(0.809875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.19615 | −0.342399 | ||||||||
\(574\) | 8.46410 | 0.353285 | ||||||||
\(575\) | 33.3205 | 1.38956 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 28.5885 | 1.19015 | 0.595077 | − | 0.803669i | \(-0.297122\pi\) | ||||
0.595077 | + | 0.803669i | \(0.297122\pi\) | |||||||
\(578\) | 11.8564 | 0.493161 | ||||||||
\(579\) | 7.58846 | 0.315366 | ||||||||
\(580\) | 2.58846 | 0.107480 | ||||||||
\(581\) | 9.26795 | 0.384499 | ||||||||
\(582\) | 14.1962 | 0.588449 | ||||||||
\(583\) | −51.5885 | −2.13658 | ||||||||
\(584\) | 1.46410 | 0.0605850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.07180 | 0.0442755 | ||||||||
\(587\) | 5.12436 | 0.211505 | 0.105752 | − | 0.994392i | \(-0.466275\pi\) | ||||
0.105752 | + | 0.994392i | \(0.466275\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −1.51666 | −0.0624929 | ||||||||
\(590\) | −6.53590 | −0.269079 | ||||||||
\(591\) | −0.267949 | −0.0110220 | ||||||||
\(592\) | 6.73205 | 0.276686 | ||||||||
\(593\) | −37.0000 | −1.51941 | −0.759704 | − | 0.650269i | \(-0.774656\pi\) | ||||
−0.759704 | + | 0.650269i | \(0.774656\pi\) | |||||||
\(594\) | −5.19615 | −0.213201 | ||||||||
\(595\) | −1.66025 | −0.0680638 | ||||||||
\(596\) | −8.00000 | −0.327693 | ||||||||
\(597\) | 24.5885 | 1.00634 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.5692 | −1.94363 | −0.971813 | − | 0.235754i | \(-0.924244\pi\) | ||||
−0.971813 | + | 0.235754i | \(0.924244\pi\) | |||||||
\(600\) | 4.46410 | 0.182246 | ||||||||
\(601\) | −48.3013 | −1.97025 | −0.985125 | − | 0.171840i | \(-0.945029\pi\) | ||||
−0.985125 | + | 0.171840i | \(0.945029\pi\) | |||||||
\(602\) | −8.73205 | −0.355892 | ||||||||
\(603\) | −10.0000 | −0.407231 | ||||||||
\(604\) | −1.19615 | −0.0486708 | ||||||||
\(605\) | −11.7128 | −0.476194 | ||||||||
\(606\) | −4.92820 | −0.200195 | ||||||||
\(607\) | −25.6603 | −1.04152 | −0.520759 | − | 0.853704i | \(-0.674351\pi\) | ||||
−0.520759 | + | 0.853704i | \(0.674351\pi\) | |||||||
\(608\) | 0.464102 | 0.0188218 | ||||||||
\(609\) | 3.53590 | 0.143282 | ||||||||
\(610\) | 2.73205 | 0.110618 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.26795 | −0.0916764 | ||||||||
\(613\) | 47.7128 | 1.92710 | 0.963551 | − | 0.267524i | \(-0.0862055\pi\) | ||||
0.963551 | + | 0.267524i | \(0.0862055\pi\) | |||||||
\(614\) | 5.00000 | 0.201784 | ||||||||
\(615\) | −6.19615 | −0.249853 | ||||||||
\(616\) | 5.19615 | 0.209359 | ||||||||
\(617\) | 13.8038 | 0.555722 | 0.277861 | − | 0.960621i | \(-0.410375\pi\) | ||||
0.277861 | + | 0.960621i | \(0.410375\pi\) | |||||||
\(618\) | 16.1962 | 0.651505 | ||||||||
\(619\) | 11.3923 | 0.457895 | 0.228948 | − | 0.973439i | \(-0.426472\pi\) | ||||
0.228948 | + | 0.973439i | \(0.426472\pi\) | |||||||
\(620\) | −2.39230 | −0.0960773 | ||||||||
\(621\) | −7.46410 | −0.299524 | ||||||||
\(622\) | 14.8038 | 0.593580 | ||||||||
\(623\) | 16.8564 | 0.675338 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | −6.87564 | −0.274806 | ||||||||
\(627\) | −2.41154 | −0.0963077 | ||||||||
\(628\) | −11.4641 | −0.457467 | ||||||||
\(629\) | −15.2679 | −0.608773 | ||||||||
\(630\) | −0.732051 | −0.0291656 | ||||||||
\(631\) | −1.87564 | −0.0746682 | −0.0373341 | − | 0.999303i | \(-0.511887\pi\) | ||||
−0.0373341 | + | 0.999303i | \(0.511887\pi\) | |||||||
\(632\) | −9.00000 | −0.358001 | ||||||||
\(633\) | 24.9282 | 0.990807 | ||||||||
\(634\) | 14.7846 | 0.587172 | ||||||||
\(635\) | −10.5359 | −0.418104 | ||||||||
\(636\) | −9.92820 | −0.393679 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.3731 | 0.727397 | ||||||||
\(639\) | 7.26795 | 0.287516 | ||||||||
\(640\) | 0.732051 | 0.0289368 | ||||||||
\(641\) | −17.3205 | −0.684119 | −0.342059 | − | 0.939678i | \(-0.611124\pi\) | ||||
−0.342059 | + | 0.939678i | \(0.611124\pi\) | |||||||
\(642\) | 6.07180 | 0.239635 | ||||||||
\(643\) | 2.32051 | 0.0915119 | 0.0457560 | − | 0.998953i | \(-0.485430\pi\) | ||||
0.0457560 | + | 0.998953i | \(0.485430\pi\) | |||||||
\(644\) | 7.46410 | 0.294127 | ||||||||
\(645\) | 6.39230 | 0.251697 | ||||||||
\(646\) | −1.05256 | −0.0414124 | ||||||||
\(647\) | −23.7321 | −0.933003 | −0.466502 | − | 0.884520i | \(-0.654486\pi\) | ||||
−0.466502 | + | 0.884520i | \(0.654486\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −46.3923 | −1.82106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.26795 | −0.128081 | ||||||||
\(652\) | 7.12436 | 0.279011 | ||||||||
\(653\) | −14.7128 | −0.575757 | −0.287878 | − | 0.957667i | \(-0.592950\pi\) | ||||
−0.287878 | + | 0.957667i | \(0.592950\pi\) | |||||||
\(654\) | 11.2679 | 0.440612 | ||||||||
\(655\) | 10.9282 | 0.427000 | ||||||||
\(656\) | 8.46410 | 0.330468 | ||||||||
\(657\) | −1.46410 | −0.0571200 | ||||||||
\(658\) | 3.92820 | 0.153137 | ||||||||
\(659\) | −13.2487 | −0.516097 | −0.258048 | − | 0.966132i | \(-0.583079\pi\) | ||||
−0.258048 | + | 0.966132i | \(0.583079\pi\) | |||||||
\(660\) | −3.80385 | −0.148065 | ||||||||
\(661\) | 22.5359 | 0.876545 | 0.438272 | − | 0.898842i | \(-0.355591\pi\) | ||||
0.438272 | + | 0.898842i | \(0.355591\pi\) | |||||||
\(662\) | −6.78461 | −0.263691 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.26795 | 0.359666 | ||||||||
\(665\) | −0.339746 | −0.0131748 | ||||||||
\(666\) | −6.73205 | −0.260862 | ||||||||
\(667\) | 26.3923 | 1.02191 | ||||||||
\(668\) | −5.07180 | −0.196234 | ||||||||
\(669\) | 5.46410 | 0.211254 | ||||||||
\(670\) | −7.32051 | −0.282816 | ||||||||
\(671\) | 19.3923 | 0.748632 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −43.6410 | −1.68224 | −0.841119 | − | 0.540850i | \(-0.818102\pi\) | ||||
−0.841119 | + | 0.540850i | \(0.818102\pi\) | |||||||
\(674\) | −11.0000 | −0.423704 | ||||||||
\(675\) | −4.46410 | −0.171823 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.2679 | 1.66292 | 0.831461 | − | 0.555583i | \(-0.187505\pi\) | ||||
0.831461 | + | 0.555583i | \(0.187505\pi\) | |||||||
\(678\) | −7.66025 | −0.294190 | ||||||||
\(679\) | 14.1962 | 0.544798 | ||||||||
\(680\) | −1.66025 | −0.0636678 | ||||||||
\(681\) | −13.3205 | −0.510443 | ||||||||
\(682\) | −16.9808 | −0.650227 | ||||||||
\(683\) | 17.3205 | 0.662751 | 0.331375 | − | 0.943499i | \(-0.392487\pi\) | ||||
0.331375 | + | 0.943499i | \(0.392487\pi\) | |||||||
\(684\) | −0.464102 | −0.0177454 | ||||||||
\(685\) | −14.2487 | −0.544415 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 17.3923 | 0.663558 | ||||||||
\(688\) | −8.73205 | −0.332906 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.46410 | −0.208015 | ||||||||
\(691\) | −37.0718 | −1.41028 | −0.705139 | − | 0.709069i | \(-0.749115\pi\) | ||||
−0.705139 | + | 0.709069i | \(0.749115\pi\) | |||||||
\(692\) | 2.19615 | 0.0834852 | ||||||||
\(693\) | −5.19615 | −0.197386 | ||||||||
\(694\) | 6.46410 | 0.245374 | ||||||||
\(695\) | −12.4833 | −0.473520 | ||||||||
\(696\) | 3.53590 | 0.134028 | ||||||||
\(697\) | −19.1962 | −0.727106 | ||||||||
\(698\) | −6.14359 | −0.232538 | ||||||||
\(699\) | −18.5885 | −0.703080 | ||||||||
\(700\) | 4.46410 | 0.168727 | ||||||||
\(701\) | 25.7846 | 0.973871 | 0.486936 | − | 0.873438i | \(-0.338115\pi\) | ||||
0.486936 | + | 0.873438i | \(0.338115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.12436 | −0.117837 | ||||||||
\(704\) | 5.19615 | 0.195837 | ||||||||
\(705\) | −2.87564 | −0.108303 | ||||||||
\(706\) | 31.3205 | 1.17876 | ||||||||
\(707\) | −4.92820 | −0.185344 | ||||||||
\(708\) | −8.92820 | −0.335542 | ||||||||
\(709\) | −51.3731 | −1.92936 | −0.964678 | − | 0.263432i | \(-0.915146\pi\) | ||||
−0.964678 | + | 0.263432i | \(0.915146\pi\) | |||||||
\(710\) | 5.32051 | 0.199675 | ||||||||
\(711\) | 9.00000 | 0.337526 | ||||||||
\(712\) | 16.8564 | 0.631721 | ||||||||
\(713\) | −24.3923 | −0.913499 | ||||||||
\(714\) | −2.26795 | −0.0848759 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.46410 | −0.129460 | ||||||||
\(717\) | −26.5885 | −0.992964 | ||||||||
\(718\) | 34.4449 | 1.28547 | ||||||||
\(719\) | 39.4449 | 1.47105 | 0.735523 | − | 0.677500i | \(-0.236937\pi\) | ||||
0.735523 | + | 0.677500i | \(0.236937\pi\) | |||||||
\(720\) | −0.732051 | −0.0272819 | ||||||||
\(721\) | 16.1962 | 0.603176 | ||||||||
\(722\) | 18.7846 | 0.699091 | ||||||||
\(723\) | −10.9282 | −0.406424 | ||||||||
\(724\) | −14.2679 | −0.530264 | ||||||||
\(725\) | 15.7846 | 0.586226 | ||||||||
\(726\) | −16.0000 | −0.593816 | ||||||||
\(727\) | −3.60770 | −0.133802 | −0.0669010 | − | 0.997760i | \(-0.521311\pi\) | ||||
−0.0669010 | + | 0.997760i | \(0.521311\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.07180 | −0.0396690 | ||||||||
\(731\) | 19.8038 | 0.732472 | ||||||||
\(732\) | 3.73205 | 0.137941 | ||||||||
\(733\) | 25.7846 | 0.952376 | 0.476188 | − | 0.879343i | \(-0.342018\pi\) | ||||
0.476188 | + | 0.879343i | \(0.342018\pi\) | |||||||
\(734\) | −13.3205 | −0.491669 | ||||||||
\(735\) | −0.732051 | −0.0270021 | ||||||||
\(736\) | 7.46410 | 0.275130 | ||||||||
\(737\) | −51.9615 | −1.91403 | ||||||||
\(738\) | −8.46410 | −0.311568 | ||||||||
\(739\) | −39.1769 | −1.44115 | −0.720573 | − | 0.693379i | \(-0.756121\pi\) | ||||
−0.720573 | + | 0.693379i | \(0.756121\pi\) | |||||||
\(740\) | −4.92820 | −0.181164 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.92820 | −0.364476 | ||||||||
\(743\) | −14.0526 | −0.515538 | −0.257769 | − | 0.966207i | \(-0.582987\pi\) | ||||
−0.257769 | + | 0.966207i | \(0.582987\pi\) | |||||||
\(744\) | −3.26795 | −0.119809 | ||||||||
\(745\) | 5.85641 | 0.214562 | ||||||||
\(746\) | 15.1244 | 0.553742 | ||||||||
\(747\) | −9.26795 | −0.339097 | ||||||||
\(748\) | −11.7846 | −0.430888 | ||||||||
\(749\) | 6.07180 | 0.221859 | ||||||||
\(750\) | −6.92820 | −0.252982 | ||||||||
\(751\) | 5.14359 | 0.187692 | 0.0938462 | − | 0.995587i | \(-0.470084\pi\) | ||||
0.0938462 | + | 0.995587i | \(0.470084\pi\) | |||||||
\(752\) | 3.92820 | 0.143247 | ||||||||
\(753\) | 17.5167 | 0.638343 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.875644 | 0.0318680 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 16.1962 | 0.588659 | 0.294330 | − | 0.955704i | \(-0.404904\pi\) | ||||
0.294330 | + | 0.955704i | \(0.404904\pi\) | |||||||
\(758\) | −36.0526 | −1.30949 | ||||||||
\(759\) | −38.7846 | −1.40779 | ||||||||
\(760\) | −0.339746 | −0.0123239 | ||||||||
\(761\) | 18.2487 | 0.661515 | 0.330758 | − | 0.943716i | \(-0.392696\pi\) | ||||
0.330758 | + | 0.943716i | \(0.392696\pi\) | |||||||
\(762\) | −14.3923 | −0.521378 | ||||||||
\(763\) | 11.2679 | 0.407927 | ||||||||
\(764\) | −8.19615 | −0.296526 | ||||||||
\(765\) | 1.66025 | 0.0600266 | ||||||||
\(766\) | −31.0000 | −1.12008 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 43.2679 | 1.56028 | 0.780141 | − | 0.625604i | \(-0.215147\pi\) | ||||
0.780141 | + | 0.625604i | \(0.215147\pi\) | |||||||
\(770\) | −3.80385 | −0.137081 | ||||||||
\(771\) | −25.0526 | −0.902246 | ||||||||
\(772\) | 7.58846 | 0.273115 | ||||||||
\(773\) | 19.1769 | 0.689746 | 0.344873 | − | 0.938649i | \(-0.387922\pi\) | ||||
0.344873 | + | 0.938649i | \(0.387922\pi\) | |||||||
\(774\) | 8.73205 | 0.313867 | ||||||||
\(775\) | −14.5885 | −0.524033 | ||||||||
\(776\) | 14.1962 | 0.509612 | ||||||||
\(777\) | −6.73205 | −0.241511 | ||||||||
\(778\) | 21.4641 | 0.769525 | ||||||||
\(779\) | −3.92820 | −0.140742 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.7654 | 1.35135 | ||||||||
\(782\) | −16.9282 | −0.605351 | ||||||||
\(783\) | −3.53590 | −0.126363 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 8.39230 | 0.299534 | ||||||||
\(786\) | 14.9282 | 0.532471 | ||||||||
\(787\) | −8.85641 | −0.315697 | −0.157848 | − | 0.987463i | \(-0.550456\pi\) | ||||
−0.157848 | + | 0.987463i | \(0.550456\pi\) | |||||||
\(788\) | −0.267949 | −0.00954529 | ||||||||
\(789\) | 3.12436 | 0.111230 | ||||||||
\(790\) | 6.58846 | 0.234407 | ||||||||
\(791\) | −7.66025 | −0.272367 | ||||||||
\(792\) | −5.19615 | −0.184637 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.3923 | −0.759184 | ||||||||
\(795\) | 7.26795 | 0.257768 | ||||||||
\(796\) | 24.5885 | 0.871515 | ||||||||
\(797\) | 35.3731 | 1.25298 | 0.626489 | − | 0.779430i | \(-0.284491\pi\) | ||||
0.626489 | + | 0.779430i | \(0.284491\pi\) | |||||||
\(798\) | −0.464102 | −0.0164290 | ||||||||
\(799\) | −8.90897 | −0.315177 | ||||||||
\(800\) | 4.46410 | 0.157830 | ||||||||
\(801\) | −16.8564 | −0.595592 | ||||||||
\(802\) | 11.0718 | 0.390959 | ||||||||
\(803\) | −7.60770 | −0.268470 | ||||||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | −5.46410 | −0.192584 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.00000 | −0.140807 | ||||||||
\(808\) | −4.92820 | −0.173374 | ||||||||
\(809\) | −9.26795 | −0.325844 | −0.162922 | − | 0.986639i | \(-0.552092\pi\) | ||||
−0.162922 | + | 0.986639i | \(0.552092\pi\) | |||||||
\(810\) | 0.732051 | 0.0257216 | ||||||||
\(811\) | 22.1051 | 0.776216 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(812\) | 3.53590 | 0.124086 | ||||||||
\(813\) | 7.66025 | 0.268657 | ||||||||
\(814\) | −34.9808 | −1.22608 | ||||||||
\(815\) | −5.21539 | −0.182687 | ||||||||
\(816\) | −2.26795 | −0.0793941 | ||||||||
\(817\) | 4.05256 | 0.141781 | ||||||||
\(818\) | 16.5885 | 0.580002 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.19615 | −0.216379 | ||||||||
\(821\) | 18.8038 | 0.656259 | 0.328129 | − | 0.944633i | \(-0.393582\pi\) | ||||
0.328129 | + | 0.944633i | \(0.393582\pi\) | |||||||
\(822\) | −19.4641 | −0.678889 | ||||||||
\(823\) | 21.7128 | 0.756861 | 0.378431 | − | 0.925630i | \(-0.376464\pi\) | ||||
0.378431 | + | 0.925630i | \(0.376464\pi\) | |||||||
\(824\) | 16.1962 | 0.564220 | ||||||||
\(825\) | −23.1962 | −0.807586 | ||||||||
\(826\) | −8.92820 | −0.310652 | ||||||||
\(827\) | −4.39230 | −0.152735 | −0.0763677 | − | 0.997080i | \(-0.524332\pi\) | ||||
−0.0763677 | + | 0.997080i | \(0.524332\pi\) | |||||||
\(828\) | −7.46410 | −0.259395 | ||||||||
\(829\) | 1.48334 | 0.0515185 | 0.0257593 | − | 0.999668i | \(-0.491800\pi\) | ||||
0.0257593 | + | 0.999668i | \(0.491800\pi\) | |||||||
\(830\) | −6.78461 | −0.235497 | ||||||||
\(831\) | −14.3923 | −0.499264 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.26795 | −0.0785798 | ||||||||
\(834\) | −17.0526 | −0.590482 | ||||||||
\(835\) | 3.71281 | 0.128487 | ||||||||
\(836\) | −2.41154 | −0.0834049 | ||||||||
\(837\) | 3.26795 | 0.112957 | ||||||||
\(838\) | 14.5885 | 0.503950 | ||||||||
\(839\) | 37.3205 | 1.28845 | 0.644224 | − | 0.764837i | \(-0.277181\pi\) | ||||
0.644224 | + | 0.764837i | \(0.277181\pi\) | |||||||
\(840\) | −0.732051 | −0.0252582 | ||||||||
\(841\) | −16.4974 | −0.568877 | ||||||||
\(842\) | 25.3205 | 0.872602 | ||||||||
\(843\) | 12.7321 | 0.438515 | ||||||||
\(844\) | 24.9282 | 0.858064 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.92820 | −0.135054 | ||||||||
\(847\) | −16.0000 | −0.549767 | ||||||||
\(848\) | −9.92820 | −0.340936 | ||||||||
\(849\) | −17.8564 | −0.612830 | ||||||||
\(850\) | −10.1244 | −0.347263 | ||||||||
\(851\) | −50.2487 | −1.72250 | ||||||||
\(852\) | 7.26795 | 0.248996 | ||||||||
\(853\) | −25.2487 | −0.864499 | −0.432250 | − | 0.901754i | \(-0.642280\pi\) | ||||
−0.432250 | + | 0.901754i | \(0.642280\pi\) | |||||||
\(854\) | 3.73205 | 0.127708 | ||||||||
\(855\) | 0.339746 | 0.0116191 | ||||||||
\(856\) | 6.07180 | 0.207530 | ||||||||
\(857\) | 19.4641 | 0.664881 | 0.332441 | − | 0.943124i | \(-0.392128\pi\) | ||||
0.332441 | + | 0.943124i | \(0.392128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8038 | 0.573340 | 0.286670 | − | 0.958029i | \(-0.407452\pi\) | ||||
0.286670 | + | 0.958029i | \(0.407452\pi\) | |||||||
\(860\) | 6.39230 | 0.217976 | ||||||||
\(861\) | −8.46410 | −0.288456 | ||||||||
\(862\) | 13.1244 | 0.447017 | ||||||||
\(863\) | 15.8564 | 0.539758 | 0.269879 | − | 0.962894i | \(-0.413016\pi\) | ||||
0.269879 | + | 0.962894i | \(0.413016\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −1.60770 | −0.0546633 | ||||||||
\(866\) | −12.1436 | −0.412656 | ||||||||
\(867\) | −11.8564 | −0.402665 | ||||||||
\(868\) | −3.26795 | −0.110921 | ||||||||
\(869\) | 46.7654 | 1.58641 | ||||||||
\(870\) | −2.58846 | −0.0877569 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 11.2679 | 0.381581 | ||||||||
\(873\) | −14.1962 | −0.480467 | ||||||||
\(874\) | −3.46410 | −0.117175 | ||||||||
\(875\) | −6.92820 | −0.234216 | ||||||||
\(876\) | −1.46410 | −0.0494674 | ||||||||
\(877\) | −50.5885 | −1.70825 | −0.854125 | − | 0.520067i | \(-0.825907\pi\) | ||||
−0.854125 | + | 0.520067i | \(0.825907\pi\) | |||||||
\(878\) | −23.3205 | −0.787029 | ||||||||
\(879\) | −1.07180 | −0.0361508 | ||||||||
\(880\) | −3.80385 | −0.128228 | ||||||||
\(881\) | −39.7128 | −1.33796 | −0.668979 | − | 0.743281i | \(-0.733269\pi\) | ||||
−0.668979 | + | 0.743281i | \(0.733269\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 25.5167 | 0.858704 | 0.429352 | − | 0.903137i | \(-0.358742\pi\) | ||||
0.429352 | + | 0.903137i | \(0.358742\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.53590 | 0.219702 | ||||||||
\(886\) | 25.0000 | 0.839891 | ||||||||
\(887\) | −20.6603 | −0.693703 | −0.346852 | − | 0.937920i | \(-0.612749\pi\) | ||||
−0.346852 | + | 0.937920i | \(0.612749\pi\) | |||||||
\(888\) | −6.73205 | −0.225913 | ||||||||
\(889\) | −14.3923 | −0.482702 | ||||||||
\(890\) | −12.3397 | −0.413629 | ||||||||
\(891\) | 5.19615 | 0.174078 | ||||||||
\(892\) | 5.46410 | 0.182952 | ||||||||
\(893\) | −1.82309 | −0.0610072 | ||||||||
\(894\) | 8.00000 | 0.267560 | ||||||||
\(895\) | 2.53590 | 0.0847657 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 28.9808 | 0.967101 | ||||||||
\(899\) | −11.5551 | −0.385385 | ||||||||
\(900\) | −4.46410 | −0.148803 | ||||||||
\(901\) | 22.5167 | 0.750139 | ||||||||
\(902\) | −43.9808 | −1.46440 | ||||||||
\(903\) | 8.73205 | 0.290584 | ||||||||
\(904\) | −7.66025 | −0.254776 | ||||||||
\(905\) | 10.4449 | 0.347199 | ||||||||
\(906\) | 1.19615 | 0.0397395 | ||||||||
\(907\) | 30.3923 | 1.00916 | 0.504580 | − | 0.863365i | \(-0.331647\pi\) | ||||
0.504580 | + | 0.863365i | \(0.331647\pi\) | |||||||
\(908\) | −13.3205 | −0.442057 | ||||||||
\(909\) | 4.92820 | 0.163458 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.1244 | 1.29625 | 0.648124 | − | 0.761535i | \(-0.275554\pi\) | ||||
0.648124 | + | 0.761535i | \(0.275554\pi\) | |||||||
\(912\) | −0.464102 | −0.0153679 | ||||||||
\(913\) | −48.1577 | −1.59379 | ||||||||
\(914\) | −29.7128 | −0.982812 | ||||||||
\(915\) | −2.73205 | −0.0903188 | ||||||||
\(916\) | 17.3923 | 0.574658 | ||||||||
\(917\) | 14.9282 | 0.492973 | ||||||||
\(918\) | 2.26795 | 0.0748535 | ||||||||
\(919\) | −12.7128 | −0.419357 | −0.209679 | − | 0.977770i | \(-0.567242\pi\) | ||||
−0.209679 | + | 0.977770i | \(0.567242\pi\) | |||||||
\(920\) | −5.46410 | −0.180146 | ||||||||
\(921\) | −5.00000 | −0.164756 | ||||||||
\(922\) | −6.92820 | −0.228168 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −5.19615 | −0.170941 | ||||||||
\(925\) | −30.0526 | −0.988122 | ||||||||
\(926\) | −15.3397 | −0.504095 | ||||||||
\(927\) | −16.1962 | −0.531951 | ||||||||
\(928\) | 3.53590 | 0.116072 | ||||||||
\(929\) | 3.92820 | 0.128880 | 0.0644401 | − | 0.997922i | \(-0.479474\pi\) | ||||
0.0644401 | + | 0.997922i | \(0.479474\pi\) | |||||||
\(930\) | 2.39230 | 0.0784468 | ||||||||
\(931\) | −0.464102 | −0.0152103 | ||||||||
\(932\) | −18.5885 | −0.608885 | ||||||||
\(933\) | −14.8038 | −0.484656 | ||||||||
\(934\) | 18.9282 | 0.619350 | ||||||||
\(935\) | 8.62693 | 0.282131 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.7128 | 1.42804 | 0.714018 | − | 0.700128i | \(-0.246874\pi\) | ||||
0.714018 | + | 0.700128i | \(0.246874\pi\) | |||||||
\(938\) | −10.0000 | −0.326512 | ||||||||
\(939\) | 6.87564 | 0.224378 | ||||||||
\(940\) | −2.87564 | −0.0937932 | ||||||||
\(941\) | 27.3205 | 0.890623 | 0.445312 | − | 0.895376i | \(-0.353093\pi\) | ||||
0.445312 | + | 0.895376i | \(0.353093\pi\) | |||||||
\(942\) | 11.4641 | 0.373521 | ||||||||
\(943\) | −63.1769 | −2.05732 | ||||||||
\(944\) | −8.92820 | −0.290588 | ||||||||
\(945\) | 0.732051 | 0.0238136 | ||||||||
\(946\) | 45.3731 | 1.47521 | ||||||||
\(947\) | −42.9090 | −1.39435 | −0.697177 | − | 0.716899i | \(-0.745561\pi\) | ||||
−0.697177 | + | 0.716899i | \(0.745561\pi\) | |||||||
\(948\) | 9.00000 | 0.292306 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.07180 | −0.0672180 | ||||||||
\(951\) | −14.7846 | −0.479424 | ||||||||
\(952\) | −2.26795 | −0.0735047 | ||||||||
\(953\) | −0.339746 | −0.0110055 | −0.00550273 | − | 0.999985i | \(-0.501752\pi\) | ||||
−0.00550273 | + | 0.999985i | \(0.501752\pi\) | |||||||
\(954\) | 9.92820 | 0.321437 | ||||||||
\(955\) | 6.00000 | 0.194155 | ||||||||
\(956\) | −26.5885 | −0.859932 | ||||||||
\(957\) | −18.3731 | −0.593917 | ||||||||
\(958\) | −4.85641 | −0.156903 | ||||||||
\(959\) | −19.4641 | −0.628529 | ||||||||
\(960\) | −0.732051 | −0.0236268 | ||||||||
\(961\) | −20.3205 | −0.655500 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.07180 | −0.195661 | ||||||||
\(964\) | −10.9282 | −0.351974 | ||||||||
\(965\) | −5.55514 | −0.178826 | ||||||||
\(966\) | −7.46410 | −0.240154 | ||||||||
\(967\) | 12.7846 | 0.411125 | 0.205563 | − | 0.978644i | \(-0.434098\pi\) | ||||
0.205563 | + | 0.978644i | \(0.434098\pi\) | |||||||
\(968\) | −16.0000 | −0.514259 | ||||||||
\(969\) | 1.05256 | 0.0338131 | ||||||||
\(970\) | −10.3923 | −0.333677 | ||||||||
\(971\) | 38.1051 | 1.22285 | 0.611426 | − | 0.791302i | \(-0.290596\pi\) | ||||
0.611426 | + | 0.791302i | \(0.290596\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −17.0526 | −0.546680 | ||||||||
\(974\) | 29.4449 | 0.943474 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.73205 | 0.119460 | ||||||||
\(977\) | 40.3923 | 1.29226 | 0.646132 | − | 0.763226i | \(-0.276385\pi\) | ||||
0.646132 | + | 0.763226i | \(0.276385\pi\) | |||||||
\(978\) | −7.12436 | −0.227812 | ||||||||
\(979\) | −87.5885 | −2.79934 | ||||||||
\(980\) | −0.732051 | −0.0233845 | ||||||||
\(981\) | −11.2679 | −0.359758 | ||||||||
\(982\) | 6.39230 | 0.203987 | ||||||||
\(983\) | 18.0000 | 0.574111 | 0.287055 | − | 0.957914i | \(-0.407324\pi\) | ||||
0.287055 | + | 0.957914i | \(0.407324\pi\) | |||||||
\(984\) | −8.46410 | −0.269826 | ||||||||
\(985\) | 0.196152 | 0.00624994 | ||||||||
\(986\) | −8.01924 | −0.255385 | ||||||||
\(987\) | −3.92820 | −0.125036 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 65.1769 | 2.07251 | ||||||||
\(990\) | 3.80385 | 0.120894 | ||||||||
\(991\) | 37.2487 | 1.18324 | 0.591622 | − | 0.806215i | \(-0.298488\pi\) | ||||
0.591622 | + | 0.806215i | \(0.298488\pi\) | |||||||
\(992\) | −3.26795 | −0.103757 | ||||||||
\(993\) | 6.78461 | 0.215303 | ||||||||
\(994\) | 7.26795 | 0.230525 | ||||||||
\(995\) | −18.0000 | −0.570638 | ||||||||
\(996\) | −9.26795 | −0.293666 | ||||||||
\(997\) | 56.9090 | 1.80233 | 0.901163 | − | 0.433481i | \(-0.142715\pi\) | ||||
0.901163 | + | 0.433481i | \(0.142715\pi\) | |||||||
\(998\) | 20.5885 | 0.651716 | ||||||||
\(999\) | 6.73205 | 0.212993 |
(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 | 7098.2.a.bo.1.1 | 2 | ||
13.6 | odd | 12 | 546.2.s.b.127.2 | yes | 4 | ||
13.11 | odd | 12 | 546.2.s.b.43.2 | ✓ | 4 | ||
13.12 | even | 2 | 7098.2.a.by.1.2 | 2 | |||
39.11 | even | 12 | 1638.2.bj.a.1135.1 | 4 | |||
39.32 | even | 12 | 1638.2.bj.a.127.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.b.43.2 | ✓ | 4 | 13.11 | odd | 12 | ||
546.2.s.b.127.2 | yes | 4 | 13.6 | odd | 12 | ||
1638.2.bj.a.127.1 | 4 | 39.32 | even | 12 | |||
1638.2.bj.a.1135.1 | 4 | 39.11 | even | 12 | |||
7098.2.a.bo.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7098.2.a.by.1.2 | 2 | 13.12 | even | 2 |