Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7168,2,Mod(1,7168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7168, 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("7168.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7168.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: | \(57.2367681689\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.9433055232.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 6x^{6} + 32x^{5} + 9x^{4} - 76x^{3} - 4x^{2} + 48x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1792) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.02908\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7168.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.42180 | −1.97558 | −0.987788 | − | 0.155801i | \(-0.950204\pi\) | ||||
−0.987788 | + | 0.155801i | \(0.950204\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.59402 | −1.60730 | −0.803648 | − | 0.595105i | \(-0.797110\pi\) | ||||
−0.803648 | + | 0.595105i | \(0.797110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.70871 | 2.90290 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.08150 | 0.326086 | 0.163043 | − | 0.986619i | \(-0.447869\pi\) | ||||
0.163043 | + | 0.986619i | \(0.447869\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.79014 | −0.496496 | −0.248248 | − | 0.968696i | \(-0.579855\pi\) | ||||
−0.248248 | + | 0.968696i | \(0.579855\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.2980 | 3.17534 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.65390 | −1.37127 | −0.685636 | − | 0.727945i | \(-0.740476\pi\) | ||||
−0.685636 | + | 0.727945i | \(0.740476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0630276 | −0.0144595 | −0.00722977 | − | 0.999974i | \(-0.502301\pi\) | ||||
−0.00722977 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.42180 | 0.746698 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.46467 | −0.305404 | −0.152702 | − | 0.988272i | \(-0.548797\pi\) | ||||
−0.152702 | + | 0.988272i | \(0.548797\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.91700 | 1.58340 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19.5341 | −3.75933 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.04356 | −0.936565 | −0.468282 | − | 0.883579i | \(-0.655127\pi\) | ||||
−0.468282 | + | 0.883579i | \(0.655127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.75455 | 0.853943 | 0.426971 | − | 0.904265i | \(-0.359581\pi\) | ||||
0.426971 | + | 0.904265i | \(0.359581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.70069 | −0.644208 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.59402 | 0.607501 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.19951 | −1.18359 | −0.591796 | − | 0.806088i | \(-0.701581\pi\) | ||||
−0.591796 | + | 0.806088i | \(0.701581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.12551 | 0.980867 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.50243 | −1.17168 | −0.585841 | − | 0.810426i | \(-0.699236\pi\) | ||||
−0.585841 | + | 0.810426i | \(0.699236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.56166 | 0.695647 | 0.347824 | − | 0.937560i | \(-0.386921\pi\) | ||||
0.347824 | + | 0.937560i | \(0.386921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −31.2993 | −4.66583 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.52393 | 0.222287 | 0.111144 | − | 0.993804i | \(-0.464549\pi\) | ||||
0.111144 | + | 0.993804i | \(0.464549\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.3465 | 2.70905 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.59185 | −0.905460 | −0.452730 | − | 0.891648i | \(-0.649550\pi\) | ||||
−0.452730 | + | 0.891648i | \(0.649550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.88695 | −0.524117 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.215668 | 0.0285659 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.62071 | 0.992132 | 0.496066 | − | 0.868285i | \(-0.334777\pi\) | ||||
0.496066 | + | 0.868285i | \(0.334777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.62680 | 1.23258 | 0.616292 | − | 0.787517i | \(-0.288634\pi\) | ||||
0.616292 | + | 0.787517i | \(0.288634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.70871 | −1.09719 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.43381 | 0.798016 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.97006 | 0.851529 | 0.425764 | − | 0.904834i | \(-0.360005\pi\) | ||||
0.425764 | + | 0.904834i | \(0.360005\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.01180 | 0.603349 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.19187 | 0.734839 | 0.367420 | − | 0.930055i | \(-0.380241\pi\) | ||||
0.367420 | + | 0.930055i | \(0.380241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.59924 | 1.00647 | 0.503233 | − | 0.864151i | \(-0.332144\pi\) | ||||
0.503233 | + | 0.864151i | \(0.332144\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −27.0904 | −3.12813 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.08150 | −0.123249 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.84435 | −0.882558 | −0.441279 | − | 0.897370i | \(-0.645475\pi\) | ||||
−0.441279 | + | 0.897370i | \(0.645475\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 40.7155 | 4.52395 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5197 | 1.15469 | 0.577345 | − | 0.816500i | \(-0.304089\pi\) | ||||
0.577345 | + | 0.816500i | \(0.304089\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.3202 | 2.20404 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.2580 | 1.85026 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.32780 | 0.988745 | 0.494373 | − | 0.869250i | \(-0.335398\pi\) | ||||
0.494373 | + | 0.869250i | \(0.335398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.79014 | 0.187658 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.2691 | −1.68703 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.226523 | 0.0232407 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.485578 | 0.0493030 | 0.0246515 | − | 0.999696i | \(-0.492152\pi\) | ||||
0.0246515 | + | 0.999696i | \(0.492152\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.41852 | 0.946597 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.44571 | −0.641372 | −0.320686 | − | 0.947186i | \(-0.603913\pi\) | ||||
−0.320686 | + | 0.947186i | \(0.603913\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.26862 | −0.420599 | −0.210300 | − | 0.977637i | \(-0.567444\pi\) | ||||
−0.210300 | + | 0.977637i | \(0.567444\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.2980 | −1.20016 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.55775 | 0.247267 | 0.123633 | − | 0.992328i | \(-0.460545\pi\) | ||||
0.123633 | + | 0.992328i | \(0.460545\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5780 | 1.49210 | 0.746050 | − | 0.665890i | \(-0.231948\pi\) | ||||
0.746050 | + | 0.665890i | \(0.231948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.6353 | 2.33828 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6345 | 1.09449 | 0.547243 | − | 0.836974i | \(-0.315677\pi\) | ||||
0.547243 | + | 0.836974i | \(0.315677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.26404 | 0.490875 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.5898 | −1.44128 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.65390 | 0.518292 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.83035 | −0.893668 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.6718 | 2.31475 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4838 | −0.937695 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7630 | 1.04380 | 0.521899 | − | 0.853007i | \(-0.325224\pi\) | ||||
0.521899 | + | 0.853007i | \(0.325224\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.6091 | −1.37430 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.6871 | −1.37059 | −0.685294 | − | 0.728267i | \(-0.740326\pi\) | ||||
−0.685294 | + | 0.728267i | \(0.740326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0630276 | 0.00546519 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 70.2059 | 6.04236 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.47159 | −0.638341 | −0.319170 | − | 0.947697i | \(-0.603404\pi\) | ||||
−0.319170 | + | 0.947697i | \(0.603404\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.352269 | 0.0298790 | 0.0149395 | − | 0.999888i | \(-0.495244\pi\) | ||||
0.0149395 | + | 0.999888i | \(0.495244\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.21457 | −0.439146 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.93605 | −0.161901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.1267 | 1.50534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.42180 | −0.282225 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.26539 | −0.513281 | −0.256640 | − | 0.966507i | \(-0.582616\pi\) | ||||
−0.256640 | + | 0.966507i | \(0.582616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4475 | 1.01297 | 0.506483 | − | 0.862250i | \(-0.330945\pi\) | ||||
0.506483 | + | 0.862250i | \(0.330945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −49.2382 | −3.98067 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.0880 | −1.37254 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.24808 | −0.418842 | −0.209421 | − | 0.977826i | \(-0.567158\pi\) | ||||
−0.209421 | + | 0.977826i | \(0.567158\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.5560 | 1.78881 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.46467 | 0.115432 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.72263 | 0.604883 | 0.302442 | − | 0.953168i | \(-0.402198\pi\) | ||||
0.302442 | + | 0.953168i | \(0.402198\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.3004 | 1.03543 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.39368 | −0.649523 | −0.324761 | − | 0.945796i | \(-0.605284\pi\) | ||||
−0.324761 | + | 0.945796i | \(0.605284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.79539 | −0.753491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.548890 | −0.0419746 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.5546 | −0.878482 | −0.439241 | − | 0.898369i | \(-0.644753\pi\) | ||||
−0.439241 | + | 0.898369i | \(0.644753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.91700 | −0.598469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.0765 | −1.96003 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.4675 | 1.45507 | 0.727536 | − | 0.686070i | \(-0.240666\pi\) | ||||
0.727536 | + | 0.686070i | \(0.240666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4791 | 0.853233 | 0.426617 | − | 0.904433i | \(-0.359705\pi\) | ||||
0.426617 | + | 0.904433i | \(0.359705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −32.9410 | −2.43507 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.8752 | 1.90238 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.11472 | −0.447153 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.5341 | 1.42089 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.5900 | 1.20041 | 0.600206 | − | 0.799846i | \(-0.295085\pi\) | ||||
0.600206 | + | 0.799846i | \(0.295085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.32261 | −0.0952033 | −0.0476016 | − | 0.998866i | \(-0.515158\pi\) | ||||
−0.0476016 | + | 0.998866i | \(0.515158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.0152 | −1.57654 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.3452 | 1.16454 | 0.582272 | − | 0.812994i | \(-0.302164\pi\) | ||||
0.582272 | + | 0.812994i | \(0.302164\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.1422 | −1.85317 | −0.926587 | − | 0.376081i | \(-0.877272\pi\) | ||||
−0.926587 | + | 0.376081i | \(0.877272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.8502 | −1.68226 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.04356 | 0.353988 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.9639 | 1.88324 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7554 | −0.886559 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0681647 | −0.00471505 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7253 | 1.70216 | 0.851081 | − | 0.525034i | \(-0.175947\pi\) | ||||
0.851081 | + | 0.525034i | \(0.175947\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.1873 | −1.45173 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.3947 | −1.11811 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.75455 | −0.322760 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.4249 | −1.98835 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1213 | 0.680831 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.70637 | 0.649987 | 0.324993 | − | 0.945716i | \(-0.394638\pi\) | ||||
0.324993 | + | 0.945716i | \(0.394638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 68.9469 | 4.59646 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.7536 | 1.57658 | 0.788292 | − | 0.615301i | \(-0.210966\pi\) | ||||
0.788292 | + | 0.615301i | \(0.210966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6093 | −1.22974 | −0.614868 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614868 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.70069 | 0.243488 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.7832 | −0.706431 | −0.353216 | − | 0.935542i | \(-0.614912\pi\) | ||||
−0.353216 | + | 0.935542i | \(0.614912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.47702 | −0.357282 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.8418 | 1.74356 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.08310 | 0.134745 | 0.0673724 | − | 0.997728i | \(-0.478538\pi\) | ||||
0.0673724 | + | 0.997728i | \(0.478538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8817 | 1.02303 | 0.511516 | − | 0.859274i | \(-0.329084\pi\) | ||||
0.511516 | + | 0.859274i | \(0.329084\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −80.7182 | −5.17808 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.59402 | −0.229614 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.112828 | 0.00717911 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35.9964 | −2.28118 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.2151 | −1.52844 | −0.764220 | − | 0.644955i | \(-0.776876\pi\) | ||||
−0.764220 | + | 0.644955i | \(0.776876\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.58404 | −0.0995880 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −69.5318 | −4.35425 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.3998 | −1.02299 | −0.511497 | − | 0.859285i | \(-0.670909\pi\) | ||||
−0.511497 | + | 0.859285i | \(0.670909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.19951 | 0.447356 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −43.9229 | −2.71876 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.4978 | −1.51060 | −0.755300 | − | 0.655379i | \(-0.772509\pi\) | ||||
−0.755300 | + | 0.655379i | \(0.772509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.6912 | 1.45534 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.9179 | −1.95334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.48885 | −0.0907768 | −0.0453884 | − | 0.998969i | \(-0.514453\pi\) | ||||
−0.0453884 | + | 0.998969i | \(0.514453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.0458 | 1.70366 | 0.851829 | − | 0.523820i | \(-0.175493\pi\) | ||||
0.851829 | + | 0.523820i | \(0.175493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.12551 | −0.370733 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.56227 | 0.516324 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.08702 | −0.305650 | −0.152825 | − | 0.988253i | \(-0.548837\pi\) | ||||
−0.152825 | + | 0.988253i | \(0.548837\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 41.4060 | 2.47891 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.33236 | 0.139137 | 0.0695683 | − | 0.997577i | \(-0.477838\pi\) | ||||
0.0695683 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.35544 | −0.377791 | −0.188896 | − | 0.981997i | \(-0.560491\pi\) | ||||
−0.188896 | + | 0.981997i | \(0.560491\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.775116 | −0.0459139 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.50243 | 0.442854 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9666 | 0.880386 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.66155 | −0.0974019 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.45568 | 0.0850415 | 0.0425207 | − | 0.999096i | \(-0.486461\pi\) | ||||
0.0425207 | + | 0.999096i | \(0.486461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.3890 | −1.59465 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.1262 | −1.22587 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.62196 | 0.151632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.56166 | −0.262930 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.0559 | 1.26708 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.5989 | −1.98113 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.44089 | 0.424674 | 0.212337 | − | 0.977196i | \(-0.431893\pi\) | ||||
0.212337 | + | 0.977196i | \(0.431893\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.6064 | 0.830926 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.74660 | 0.495974 | 0.247987 | − | 0.968763i | \(-0.420231\pi\) | ||||
0.247987 | + | 0.968763i | \(0.420231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.77036 | −0.495730 | −0.247865 | − | 0.968795i | \(-0.579729\pi\) | ||||
−0.247865 | + | 0.968795i | \(0.579729\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 31.2993 | 1.76352 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.5025 | −1.20770 | −0.603851 | − | 0.797097i | \(-0.706368\pi\) | ||||
−0.603851 | + | 0.797097i | \(0.706368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.45463 | −0.305401 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.75210 | −0.488495 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.356352 | 0.0198279 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1726 | −0.786152 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −53.3047 | −2.94776 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.52393 | −0.0840167 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.96891 | 0.383046 | 0.191523 | − | 0.981488i | \(-0.438657\pi\) | ||||
0.191523 | + | 0.981488i | \(0.438657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −62.6985 | −3.43586 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.0506 | −1.36866 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5793 | 0.685237 | 0.342619 | − | 0.939475i | \(-0.388686\pi\) | ||||
0.342619 | + | 0.939475i | \(0.388686\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.8111 | −2.16224 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.14207 | 0.278459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.0125 | −0.969761 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.78717 | 0.256989 | 0.128494 | − | 0.991710i | \(-0.458986\pi\) | ||||
0.128494 | + | 0.991710i | \(0.458986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.1475 | 1.88140 | 0.940702 | − | 0.339233i | \(-0.110168\pi\) | ||||
0.940702 | + | 0.339233i | \(0.110168\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.9688 | 1.86650 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.70479 | 0.463309 | 0.231655 | − | 0.972798i | \(-0.425586\pi\) | ||||
0.231655 | + | 0.972798i | \(0.425586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.2537 | −1.18110 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.3465 | −1.02393 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.04735 | 0.213611 | 0.106805 | − | 0.994280i | \(-0.465938\pi\) | ||||
0.106805 | + | 0.994280i | \(0.465938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9960 | −0.999791 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33.6375 | 1.76551 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.9059 | −1.61769 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.6904 | −1.65423 | −0.827113 | − | 0.562036i | \(-0.810018\pi\) | ||||
−0.827113 | + | 0.562036i | \(0.810018\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −65.3365 | −3.40128 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.59185 | 0.342232 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.4087 | −1.10850 | −0.554251 | − | 0.832349i | \(-0.686995\pi\) | ||||
−0.554251 | + | 0.832349i | \(0.686995\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 35.8733 | 1.85249 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.02869 | 0.465001 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5360 | 1.00350 | 0.501749 | − | 0.865014i | \(-0.332690\pi\) | ||||
0.501749 | + | 0.865014i | \(0.332690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.2507 | −2.06210 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3513 | −0.886610 | −0.443305 | − | 0.896371i | \(-0.646194\pi\) | ||||
−0.443305 | + | 0.896371i | \(0.646194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.88695 | 0.198097 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 39.7262 | 2.01940 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.2975 | 1.28263 | 0.641316 | − | 0.767277i | \(-0.278389\pi\) | ||||
0.641316 | + | 0.767277i | \(0.278389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.28108 | 0.418792 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 53.6781 | 2.70770 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.1928 | 1.41853 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.15919 | 0.309121 | 0.154560 | − | 0.987983i | \(-0.450604\pi\) | ||||
0.154560 | + | 0.987983i | \(0.450604\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.215668 | −0.0107969 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.6318 | −0.880492 | −0.440246 | − | 0.897877i | \(-0.645109\pi\) | ||||
−0.440246 | + | 0.897877i | \(0.645109\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.51133 | −0.423979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −146.333 | −7.27132 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.78631 | −0.385953 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7264 | 1.22264 | 0.611320 | − | 0.791383i | \(-0.290639\pi\) | ||||
0.611320 | + | 0.791383i | \(0.290639\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.5663 | 1.26109 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.62071 | −0.374991 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.8081 | −1.85593 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.20539 | −0.0590283 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.36688 | 0.115630 | 0.0578149 | − | 0.998327i | \(-0.481587\pi\) | ||||
0.0578149 | + | 0.998327i | \(0.481587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.4952 | −1.53498 | −0.767492 | − | 0.641059i | \(-0.778495\pi\) | ||||
−0.767492 | + | 0.641059i | \(0.778495\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.2714 | 0.645279 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.7619 | −2.17127 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.62680 | −0.465873 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.62477 | 0.319847 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.0028 | −1.10800 | −0.554002 | − | 0.832515i | \(-0.686900\pi\) | ||||
−0.554002 | + | 0.832515i | \(0.686900\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.31078 | 0.0629921 | 0.0314960 | − | 0.999504i | \(-0.489973\pi\) | ||||
0.0314960 | + | 0.999504i | \(0.489973\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −62.0258 | −2.97391 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0923145 | 0.00441600 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.2799 | −1.73155 | −0.865773 | − | 0.500437i | \(-0.833173\pi\) | ||||
−0.865773 | + | 0.500437i | \(0.833173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.70871 | 0.414701 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5410 | 0.643352 | 0.321676 | − | 0.946850i | \(-0.395754\pi\) | ||||
0.321676 | + | 0.946850i | \(0.395754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.5243 | −1.58921 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.4389 | 1.01403 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.60363 | −0.170066 | −0.0850329 | − | 0.996378i | \(-0.527100\pi\) | ||||
−0.0850329 | + | 0.996378i | \(0.527100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.11391 | −0.382069 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.5929 | −2.00119 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.43381 | −0.301622 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.35277 | −0.297170 | −0.148585 | − | 0.988900i | \(-0.547472\pi\) | ||||
−0.148585 | + | 0.988900i | \(0.547472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 110.444 | 5.15507 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.88792 | 0.274228 | 0.137114 | − | 0.990555i | \(-0.456217\pi\) | ||||
0.137114 | + | 0.990555i | \(0.456217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7205 | −0.591171 | −0.295585 | − | 0.955316i | \(-0.595515\pi\) | ||||
−0.295585 | + | 0.955316i | \(0.595515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 58.4716 | 2.71156 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.7910 | 1.00836 | 0.504182 | − | 0.863597i | \(-0.331794\pi\) | ||||
0.504182 | + | 0.863597i | \(0.331794\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.97006 | −0.321848 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.9579 | 0.827455 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.93346 | 0.226841 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.498990 | −0.0228952 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −57.4065 | −2.62846 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.3235 | 1.20275 | 0.601375 | − | 0.798967i | \(-0.294620\pi\) | ||||
0.601375 | + | 0.798967i | \(0.294620\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8882 | 0.587649 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.01180 | −0.228045 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.74518 | −0.0792445 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.62575 | −0.209613 | −0.104806 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104806 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −26.4253 | −1.19499 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.87808 | −0.175015 | −0.0875076 | − | 0.996164i | \(-0.527890\pi\) | ||||
−0.0875076 | + | 0.996164i | \(0.527890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.5157 | 1.28428 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −33.8504 | −1.52146 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.19187 | −0.277743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.994539 | 0.0445217 | 0.0222608 | − | 0.999752i | \(-0.492914\pi\) | ||||
0.0222608 | + | 0.999752i | \(0.492914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.7215 | 1.28318 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.3204 | −1.03980 | −0.519902 | − | 0.854226i | \(-0.674032\pi\) | ||||
−0.519902 | + | 0.854226i | \(0.674032\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.1660 | 1.03087 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.5179 | 1.48858 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.79254 | 0.301074 | 0.150537 | − | 0.988604i | \(-0.451900\pi\) | ||||
0.150537 | + | 0.988604i | \(0.451900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.59924 | −0.380408 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.23119 | 0.0543582 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.3415 | 0.676027 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.64813 | 0.0724848 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.5376 | 1.73551 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.2330 | 1.45596 | 0.727982 | − | 0.685596i | \(-0.240458\pi\) | ||||
0.727982 | + | 0.685596i | \(0.240458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.8901 | −1.26328 | −0.631638 | − | 0.775264i | \(-0.717617\pi\) | ||||
−0.631638 | + | 0.775264i | \(0.717617\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.0904 | 1.18232 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.8818 | −1.17099 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8548 | −0.906728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 66.3666 | 2.88006 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4304 | 0.581736 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.19260 | −0.397431 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −66.6140 | −2.87461 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.08150 | 0.0465837 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.95435 | 0.213004 | 0.106502 | − | 0.994312i | \(-0.466035\pi\) | ||||
0.106502 | + | 0.994312i | \(0.466035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.2791 | −1.68563 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.9876 | −2.39824 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.0796 | −1.32887 | −0.664434 | − | 0.747347i | \(-0.731328\pi\) | ||||
−0.664434 | + | 0.747347i | \(0.731328\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 83.8370 | 3.57808 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.317883 | 0.0135423 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.84435 | 0.333576 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −88.5398 | −3.75830 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.01930 | −0.255046 | −0.127523 | − | 0.991836i | \(-0.540703\pi\) | ||||
−0.127523 | + | 0.991836i | \(0.540703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.16603 | −0.345386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9233 | 0.883384 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.6945 | −0.535008 | −0.267504 | − | 0.963557i | \(-0.586199\pi\) | ||||
−0.267504 | + | 0.963557i | \(0.586199\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.8148 | −1.75916 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −40.7155 | −1.70989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.3968 | 0.519701 | 0.259851 | − | 0.965649i | \(-0.416327\pi\) | ||||
0.259851 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.41186 | 0.310177 | 0.155088 | − | 0.987901i | \(-0.450434\pi\) | ||||
0.155088 | + | 0.987901i | \(0.450434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −56.7677 | −2.37151 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.5958 | −0.483577 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.5232 | 1.81189 | 0.905947 | − | 0.423390i | \(-0.139160\pi\) | ||||
0.905947 | + | 0.423390i | \(0.139160\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.52569 | 0.188081 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5197 | −0.436432 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.12912 | −0.295258 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 56.0302 | 2.31657 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.74658 | 0.154638 | 0.0773190 | − | 0.997006i | \(-0.475364\pi\) | ||||
0.0773190 | + | 0.997006i | \(0.475364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.299668 | −0.0123476 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −55.9299 | −2.30065 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.12318 | −0.210384 | −0.105192 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105192 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.3202 | −0.833048 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 89.4535 | 3.66109 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.6945 | −1.62187 | −0.810936 | − | 0.585135i | \(-0.801041\pi\) | ||||
−0.810936 | + | 0.585135i | \(0.801041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6274 | −0.800620 | −0.400310 | − | 0.916380i | \(-0.631097\pi\) | ||||
−0.400310 | + | 0.916380i | \(0.631097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 60.7003 | 2.47191 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 35.3305 | 1.43639 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.7837 | −1.04653 | −0.523264 | − | 0.852170i | \(-0.675286\pi\) | ||||
−0.523264 | + | 0.852170i | \(0.675286\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.2580 | −0.699331 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.72804 | −0.110365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.78639 | 0.233710 | 0.116855 | − | 0.993149i | \(-0.462719\pi\) | ||||
0.116855 | + | 0.993149i | \(0.462719\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −92.2651 | −3.72049 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.4658 | −0.421337 | −0.210668 | − | 0.977558i | \(-0.567564\pi\) | ||||
−0.210668 | + | 0.977558i | \(0.567564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.4411 | −1.22353 | −0.611765 | − | 0.791040i | \(-0.709540\pi\) | ||||
−0.611765 | + | 0.791040i | \(0.709540\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.6109 | 1.14812 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.32780 | −0.373711 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.90615 | −0.0762459 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.233246 | 0.00931495 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.7053 | 1.62303 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.948167 | 0.0377459 | 0.0188730 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188730 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −84.6052 | −3.36275 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.2765 | −1.67769 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.79014 | −0.0709280 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 53.9232 | 2.13317 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.1984 | 0.481808 | 0.240904 | − | 0.970549i | \(-0.422556\pi\) | ||||
0.240904 | + | 0.970549i | \(0.422556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 50.4676 | 1.99025 | 0.995124 | − | 0.0986311i | \(-0.0314464\pi\) | ||||
0.995124 | + | 0.0986311i | \(0.0314464\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 56.0995 | 2.20891 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.4906 | 1.15939 | 0.579697 | − | 0.814832i | \(-0.303171\pi\) | ||||
0.579697 | + | 0.814832i | \(0.303171\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.24183 | 0.323520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.2691 | 0.637637 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.6924 | −1.70982 | −0.854908 | − | 0.518779i | \(-0.826387\pi\) | ||||
−0.854908 | + | 0.518779i | \(0.826387\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.3798 | 2.20294 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 74.8883 | 2.92167 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8415 | −0.695006 | −0.347503 | − | 0.937679i | \(-0.612970\pi\) | ||||
−0.347503 | + | 0.937679i | \(0.612970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.0216 | 1.12881 | 0.564405 | − | 0.825498i | \(-0.309106\pi\) | ||||
0.564405 | + | 0.825498i | \(0.309106\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −34.6330 | −1.34503 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.226523 | −0.00878418 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.38713 | 0.286031 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.2133 | −1.28410 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4114 | 0.401929 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4620 | 0.750205 | 0.375103 | − | 0.926983i | \(-0.377607\pi\) | ||||
0.375103 | + | 0.926983i | \(0.377607\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −154.651 | −5.95253 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.21145 | −0.200292 | −0.100146 | − | 0.994973i | \(-0.531931\pi\) | ||||
−0.100146 | + | 0.994973i | \(0.531931\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.485578 | −0.0186348 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −81.2802 | −3.11466 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.15851 | −0.0443292 | −0.0221646 | − | 0.999754i | \(-0.507056\pi\) | ||||
−0.0221646 | + | 0.999754i | \(0.507056\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.8531 | 1.02600 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 63.6772 | 2.42944 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.8003 | 0.449558 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.8345 | −0.488247 | −0.244123 | − | 0.969744i | \(-0.578500\pi\) | ||||
−0.244123 | + | 0.969744i | \(0.578500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.41852 | −0.357780 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.26606 | −0.0480244 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.4180 | 1.60670 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.8980 | 1.39561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.9498 | −1.20673 | −0.603364 | − | 0.797466i | \(-0.706173\pi\) | ||||
−0.603364 | + | 0.797466i | \(0.706173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.453768 | 0.0171142 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.7413 | 0.705837 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.44571 | 0.242416 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.2624 | 0.723415 | 0.361708 | − | 0.932292i | \(-0.382194\pi\) | ||||
0.361708 | + | 0.932292i | \(0.382194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −68.3142 | −2.56198 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.96383 | −0.260798 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.95820 | 0.260222 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.12796 | −0.266199 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.9785 | −0.968836 | −0.484418 | − | 0.874837i | \(-0.660969\pi\) | ||||
−0.484418 | + | 0.874837i | \(0.660969\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.26862 | 0.158972 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.3441 | −2.02108 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.9298 | −1.48296 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.5763 | 1.02275 | 0.511375 | − | 0.859358i | \(-0.329136\pi\) | ||||
0.511375 | + | 0.859358i | \(0.329136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 154.055 | 5.70574 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.7912 | −0.953922 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.7081 | 1.57746 | 0.788730 | − | 0.614740i | \(-0.210739\pi\) | ||||
0.788730 | + | 0.614740i | \(0.210739\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.2980 | 0.453619 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.53816 | 0.277672 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.6817 | −1.90114 | −0.950571 | − | 0.310508i | \(-0.899501\pi\) | ||||
−0.950571 | + | 0.310508i | \(0.899501\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.386077 | −0.0141829 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.1375 | 1.58256 | 0.791281 | − | 0.611452i | \(-0.209414\pi\) | ||||
0.791281 | + | 0.611452i | \(0.209414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.5180 | 0.824994 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 91.6133 | 3.35196 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.55775 | −0.0934581 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.04305 | 0.329986 | 0.164993 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164993 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 82.8591 | 3.01955 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.7367 | −1.62813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.51946 | 0.0552258 | 0.0276129 | − | 0.999619i | \(-0.491209\pi\) | ||||
0.0276129 | + | 0.999619i | \(0.491209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.42028 | 0.196744 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.1138 | 1.23662 | 0.618312 | − | 0.785932i | \(-0.287817\pi\) | ||||
0.618312 | + | 0.785932i | \(0.287817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.5780 | −0.563961 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 176.963 | 6.39811 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.6422 | −0.492590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −54.2612 | −1.95671 | −0.978354 | − | 0.206939i | \(-0.933650\pi\) | ||||
−0.978354 | + | 0.206939i | \(0.933650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.1169 | 2.02100 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.3141 | 1.30613 | 0.653063 | − | 0.757303i | \(-0.273484\pi\) | ||||
0.653063 | + | 0.757303i | \(0.273484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.6418 | 1.35213 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.6353 | −0.883786 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.472860 | 0.0169420 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.69653 | 0.239621 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 98.5212 | 3.52086 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.8617 | 0.673203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.1195 | 0.824120 | 0.412060 | − | 0.911157i | \(-0.364809\pi\) | ||||
0.412060 | + | 0.911157i | \(0.364809\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 83.8266 | 2.98431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.6345 | −0.413677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.2333 | −0.611974 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −81.0667 | −2.87514 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.1734 | 1.49386 | 0.746929 | − | 0.664904i | \(-0.231528\pi\) | ||||
0.746929 | + | 0.664904i | \(0.231528\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.61612 | −0.304816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 81.2332 | 2.87023 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.30012 | 0.328194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.26404 | −0.185533 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.09455 | 0.179337 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.6378 | 1.18264 | 0.591320 | − | 0.806437i | \(-0.298607\pi\) | ||||
0.591320 | + | 0.806437i | \(0.298607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5082 | −1.00106 | −0.500528 | − | 0.865720i | \(-0.666861\pi\) | ||||
−0.500528 | + | 0.865720i | \(0.666861\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −95.9670 | −3.36571 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.7553 | −0.972226 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.287511 | −0.0100587 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.5898 | 0.544753 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −55.8856 | −1.95042 | −0.975210 | − | 0.221282i | \(-0.928976\pi\) | ||||
−0.975210 | + | 0.221282i | \(0.928976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.35542 | 0.326109 | 0.163055 | − | 0.986617i | \(-0.447865\pi\) | ||||
0.163055 | + | 0.986617i | \(0.447865\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.2984 | −1.02004 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.6961 | −1.58901 | −0.794504 | − | 0.607259i | \(-0.792269\pi\) | ||||
−0.794504 | + | 0.607259i | \(0.792269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.18848 | 0.249666 | 0.124833 | − | 0.992178i | \(-0.460160\pi\) | ||||
0.124833 | + | 0.992178i | \(0.460160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4068 | 0.603834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.65390 | −0.195896 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.1671 | 1.04397 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −92.8758 | −3.21026 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.28514 | 0.0443681 | 0.0221841 | − | 0.999754i | \(-0.492938\pi\) | ||||
0.0221841 | + | 0.999754i | \(0.492938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.56255 | −0.122846 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.98085 | −0.274875 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.2048 | 1.21108 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.83035 | 0.337775 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.7470 | 0.746356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.5449 | 0.361474 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5876 | −0.465232 | −0.232616 | − | 0.972569i | \(-0.574729\pi\) | ||||
−0.232616 | + | 0.972569i | \(0.574729\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.97272 | 0.0674657 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.7439 | −1.22099 | −0.610494 | − | 0.792021i | \(-0.709029\pi\) | ||||
−0.610494 | + | 0.792021i | \(0.709029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.4359 | 1.20906 | 0.604529 | − | 0.796583i | \(-0.293361\pi\) | ||||
0.604529 | + | 0.796583i | \(0.293361\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.6718 | −0.874893 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5689 | 0.632092 | 0.316046 | − | 0.948744i | \(-0.397645\pi\) | ||||
0.316046 | + | 0.948744i | \(0.397645\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.5276 | 1.41198 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −51.2126 | −1.73927 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.48370 | −0.287790 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4774 | −0.422781 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.22876 | 0.143122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.4838 | 0.354415 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −56.4896 | −1.90752 | −0.953759 | − | 0.300572i | \(-0.902823\pi\) | ||||
−0.953759 | + | 0.300572i | \(0.902823\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.98103 | −0.168006 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.1798 | −1.38738 | −0.693691 | − | 0.720273i | \(-0.744017\pi\) | ||||
−0.693691 | + | 0.720273i | \(0.744017\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.1836 | 1.28498 | 0.642490 | − | 0.766294i | \(-0.277901\pi\) | ||||
0.642490 | + | 0.766294i | \(0.277901\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 93.7197 | 3.15035 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.5720 | 1.59731 | 0.798656 | − | 0.601788i | \(-0.205545\pi\) | ||||
0.798656 | + | 0.601788i | \(0.205545\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.7630 | −0.394519 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 44.0341 | 1.47520 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0960494 | −0.00321417 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.9667 | −2.33873 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.97183 | −0.299561 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.9798 | −0.799773 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.2696 | 1.24163 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.6091 | 0.519438 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.2561 | −1.37140 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.0681 | −1.09801 | −0.549004 | − | 0.835820i | \(-0.684993\pi\) | ||||
−0.549004 | + | 0.835820i | \(0.684993\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56.1338 | −1.86184 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.5816 | −1.21200 | −0.606002 | − | 0.795463i | \(-0.707228\pi\) | ||||
−0.606002 | + | 0.795463i | \(0.707228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3771 | 0.376528 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 118.391 | 3.91387 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.6871 | 0.518033 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.2676 | 0.536618 | 0.268309 | − | 0.963333i | \(-0.413535\pi\) | ||||
0.268309 | + | 0.963333i | \(0.413535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.4612 | −0.838976 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.0843 | −0.364845 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −56.9985 | −1.87410 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.1742 | −1.22096 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.1820 | 0.366871 | 0.183435 | − | 0.983032i | \(-0.441278\pi\) | ||||
0.183435 | + | 0.983032i | \(0.441278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0630276 | −0.00206565 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.9291 | −0.979835 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.9764 | 0.718706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.5933 | 1.22812 | 0.614059 | − | 0.789260i | \(-0.289536\pi\) | ||||
0.614059 | + | 0.789260i | \(0.289536\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 30.0104 | 0.979352 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.9354 | −0.649876 | −0.324938 | − | 0.945735i | \(-0.605344\pi\) | ||||
−0.324938 | + | 0.945735i | \(0.605344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.9886 | 0.357837 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −70.2059 | −2.28380 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.2482 | 0.365518 | 0.182759 | − | 0.983158i | \(-0.441497\pi\) | ||||
0.182759 | + | 0.983158i | \(0.441497\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3939 | −0.499706 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73.5774 | 2.38591 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.7695 | −0.964329 | −0.482164 | − | 0.876081i | \(-0.660149\pi\) | ||||
−0.482164 | + | 0.876081i | \(0.660149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59.6249 | −1.92942 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.6647 | 0.603343 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.47159 | 0.241270 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.39424 | −0.270782 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.2747 | 0.717792 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.75348 | 0.153020 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.3211 | −1.77901 | −0.889504 | − | 0.456927i | \(-0.848950\pi\) | ||||
−0.889504 | + | 0.456927i | \(0.848950\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.21936 | −0.0391716 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.9746 | 0.384284 | 0.192142 | − | 0.981367i | \(-0.438457\pi\) | ||||
0.192142 | + | 0.981367i | \(0.438457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.352269 | −0.0112932 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 48.4956 | 1.55310 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.7381 | −1.27133 | −0.635667 | − | 0.771963i | \(-0.719275\pi\) | ||||
−0.635667 | + | 0.771963i | \(0.719275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0881 | 0.322416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 135.664 | 4.33142 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.03380 | −0.160553 | −0.0802766 | − | 0.996773i | \(-0.525580\pi\) | ||||
−0.0802766 | + | 0.996773i | \(0.525580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58.7449 | −1.87177 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.21457 | 0.165982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.68132 | −0.212454 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.5560 | −0.907110 | −0.453555 | − | 0.891228i | \(-0.649844\pi\) | ||||
−0.453555 | + | 0.891228i | \(0.649844\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.8462 | −0.756737 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 93.9558 | 2.97860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.4015 | −0.836144 | −0.418072 | − | 0.908414i | \(-0.637294\pi\) | ||||
−0.418072 | + | 0.908414i | \(0.637294\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 140.636 | 4.44952 |
(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 | 7168.2.a.ba.1.1 | 8 | ||
4.3 | odd | 2 | 7168.2.a.bb.1.8 | 8 | |||
8.3 | odd | 2 | 7168.2.a.bf.1.1 | 8 | |||
8.5 | even | 2 | 7168.2.a.be.1.8 | 8 | |||
32.3 | odd | 8 | 1792.2.m.h.1345.8 | yes | 16 | ||
32.5 | even | 8 | 1792.2.m.g.449.8 | yes | 16 | ||
32.11 | odd | 8 | 1792.2.m.h.449.8 | yes | 16 | ||
32.13 | even | 8 | 1792.2.m.g.1345.8 | yes | 16 | ||
32.19 | odd | 8 | 1792.2.m.e.1345.1 | yes | 16 | ||
32.21 | even | 8 | 1792.2.m.f.449.1 | yes | 16 | ||
32.27 | odd | 8 | 1792.2.m.e.449.1 | ✓ | 16 | ||
32.29 | even | 8 | 1792.2.m.f.1345.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.1 | ✓ | 16 | 32.27 | odd | 8 | ||
1792.2.m.e.1345.1 | yes | 16 | 32.19 | odd | 8 | ||
1792.2.m.f.449.1 | yes | 16 | 32.21 | even | 8 | ||
1792.2.m.f.1345.1 | yes | 16 | 32.29 | even | 8 | ||
1792.2.m.g.449.8 | yes | 16 | 32.5 | even | 8 | ||
1792.2.m.g.1345.8 | yes | 16 | 32.13 | even | 8 | ||
1792.2.m.h.449.8 | yes | 16 | 32.11 | odd | 8 | ||
1792.2.m.h.1345.8 | yes | 16 | 32.3 | odd | 8 | ||
7168.2.a.ba.1.1 | 8 | 1.1 | even | 1 | trivial | ||
7168.2.a.bb.1.8 | 8 | 4.3 | odd | 2 | |||
7168.2.a.be.1.8 | 8 | 8.5 | even | 2 | |||
7168.2.a.bf.1.1 | 8 | 8.3 | odd | 2 |