Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.814115\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.185885 | −0.131441 | −0.0657204 | − | 0.997838i | \(-0.520935\pi\) | ||||
−0.0657204 | + | 0.997838i | \(0.520935\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.96545 | −0.982723 | ||||||||
\(5\) | −1.26288 | −0.564778 | −0.282389 | − | 0.959300i | \(-0.591127\pi\) | ||||
−0.282389 | + | 0.959300i | \(0.591127\pi\) | |||||||
\(6\) | −0.185885 | −0.0758874 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.737118 | 0.260611 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.234751 | 0.0742348 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.96545 | −0.567376 | ||||||||
\(13\) | −6.93089 | −1.92228 | −0.961142 | − | 0.276055i | \(-0.910973\pi\) | ||||
−0.961142 | + | 0.276055i | \(0.910973\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.26288 | −0.326075 | ||||||||
\(16\) | 3.79387 | 0.948468 | ||||||||
\(17\) | 5.60799 | 1.36014 | 0.680068 | − | 0.733149i | \(-0.261950\pi\) | ||||
0.680068 | + | 0.733149i | \(0.261950\pi\) | |||||||
\(18\) | −0.185885 | −0.0438136 | ||||||||
\(19\) | 5.75932 | 1.32128 | 0.660639 | − | 0.750703i | \(-0.270285\pi\) | ||||
0.660639 | + | 0.750703i | \(0.270285\pi\) | |||||||
\(20\) | 2.48213 | 0.555020 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.185885 | −0.0396309 | ||||||||
\(23\) | 4.13375 | 0.861947 | 0.430973 | − | 0.902365i | \(-0.358170\pi\) | ||||
0.430973 | + | 0.902365i | \(0.358170\pi\) | |||||||
\(24\) | 0.737118 | 0.150464 | ||||||||
\(25\) | −3.40513 | −0.681026 | ||||||||
\(26\) | 1.28835 | 0.252667 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.09131 | −1.13113 | −0.565564 | − | 0.824705i | \(-0.691341\pi\) | ||||
−0.565564 | + | 0.824705i | \(0.691341\pi\) | |||||||
\(30\) | 0.234751 | 0.0428595 | ||||||||
\(31\) | −5.30532 | −0.952864 | −0.476432 | − | 0.879211i | \(-0.658070\pi\) | ||||
−0.476432 | + | 0.879211i | \(0.658070\pi\) | |||||||
\(32\) | −2.17946 | −0.385278 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −1.04244 | −0.178777 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.96545 | −0.327574 | ||||||||
\(37\) | −3.73070 | −0.613323 | −0.306661 | − | 0.951819i | \(-0.599212\pi\) | ||||
−0.306661 | + | 0.951819i | \(0.599212\pi\) | |||||||
\(38\) | −1.07057 | −0.173670 | ||||||||
\(39\) | −6.93089 | −1.10983 | ||||||||
\(40\) | −0.930893 | −0.147187 | ||||||||
\(41\) | −11.4300 | −1.78506 | −0.892532 | − | 0.450983i | \(-0.851073\pi\) | ||||
−0.892532 | + | 0.450983i | \(0.851073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.27866 | −0.652490 | −0.326245 | − | 0.945285i | \(-0.605783\pi\) | ||||
−0.326245 | + | 0.945285i | \(0.605783\pi\) | |||||||
\(44\) | −1.96545 | −0.296302 | ||||||||
\(45\) | −1.26288 | −0.188259 | ||||||||
\(46\) | −0.768404 | −0.113295 | ||||||||
\(47\) | −13.1938 | −1.92451 | −0.962255 | − | 0.272150i | \(-0.912265\pi\) | ||||
−0.962255 | + | 0.272150i | \(0.912265\pi\) | |||||||
\(48\) | 3.79387 | 0.547599 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.632964 | 0.0895146 | ||||||||
\(51\) | 5.60799 | 0.785275 | ||||||||
\(52\) | 13.6223 | 1.88907 | ||||||||
\(53\) | −5.52310 | −0.758656 | −0.379328 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379328 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(54\) | −0.185885 | −0.0252958 | ||||||||
\(55\) | −1.26288 | −0.170287 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.75932 | 0.762841 | ||||||||
\(58\) | 1.13229 | 0.148676 | ||||||||
\(59\) | −7.86821 | −1.02435 | −0.512177 | − | 0.858880i | \(-0.671161\pi\) | ||||
−0.512177 | + | 0.858880i | \(0.671161\pi\) | |||||||
\(60\) | 2.48213 | 0.320441 | ||||||||
\(61\) | −3.77690 | −0.483583 | −0.241791 | − | 0.970328i | \(-0.577735\pi\) | ||||
−0.241791 | + | 0.970328i | \(0.577735\pi\) | |||||||
\(62\) | 0.986182 | 0.125245 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.18262 | −0.897827 | ||||||||
\(65\) | 8.75290 | 1.08566 | ||||||||
\(66\) | −0.185885 | −0.0228809 | ||||||||
\(67\) | 16.1182 | 1.96916 | 0.984579 | − | 0.174943i | \(-0.0559742\pi\) | ||||
0.984579 | + | 0.174943i | \(0.0559742\pi\) | |||||||
\(68\) | −11.0222 | −1.33664 | ||||||||
\(69\) | 4.13375 | 0.497645 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.17353 | 0.495307 | 0.247654 | − | 0.968849i | \(-0.420340\pi\) | ||||
0.247654 | + | 0.968849i | \(0.420340\pi\) | |||||||
\(72\) | 0.737118 | 0.0868702 | ||||||||
\(73\) | −5.40040 | −0.632069 | −0.316034 | − | 0.948748i | \(-0.602351\pi\) | ||||
−0.316034 | + | 0.948748i | \(0.602351\pi\) | |||||||
\(74\) | 0.693482 | 0.0806156 | ||||||||
\(75\) | −3.40513 | −0.393191 | ||||||||
\(76\) | −11.3196 | −1.29845 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.28835 | 0.145877 | ||||||||
\(79\) | 9.55912 | 1.07549 | 0.537743 | − | 0.843109i | \(-0.319277\pi\) | ||||
0.537743 | + | 0.843109i | \(0.319277\pi\) | |||||||
\(80\) | −4.79121 | −0.535674 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.12467 | 0.234630 | ||||||||
\(83\) | 6.73908 | 0.739710 | 0.369855 | − | 0.929089i | \(-0.379407\pi\) | ||||
0.369855 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.08223 | −0.768175 | ||||||||
\(86\) | 0.795340 | 0.0857638 | ||||||||
\(87\) | −6.09131 | −0.653057 | ||||||||
\(88\) | 0.737118 | 0.0785771 | ||||||||
\(89\) | 6.14867 | 0.651758 | 0.325879 | − | 0.945412i | \(-0.394340\pi\) | ||||
0.325879 | + | 0.945412i | \(0.394340\pi\) | |||||||
\(90\) | 0.234751 | 0.0247449 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.12467 | −0.847055 | ||||||||
\(93\) | −5.30532 | −0.550137 | ||||||||
\(94\) | 2.45253 | 0.252959 | ||||||||
\(95\) | −7.27334 | −0.746229 | ||||||||
\(96\) | −2.17946 | −0.222440 | ||||||||
\(97\) | −15.3249 | −1.55600 | −0.778002 | − | 0.628262i | \(-0.783767\pi\) | ||||
−0.778002 | + | 0.628262i | \(0.783767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 6.69260 | 0.669260 | ||||||||
\(101\) | −9.72803 | −0.967976 | −0.483988 | − | 0.875075i | \(-0.660812\pi\) | ||||
−0.483988 | + | 0.875075i | \(0.660812\pi\) | |||||||
\(102\) | −1.04244 | −0.103217 | ||||||||
\(103\) | −1.24444 | −0.122619 | −0.0613093 | − | 0.998119i | \(-0.519528\pi\) | ||||
−0.0613093 | + | 0.998119i | \(0.519528\pi\) | |||||||
\(104\) | −5.10889 | −0.500968 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.02666 | 0.0997184 | ||||||||
\(107\) | 2.09131 | 0.202174 | 0.101087 | − | 0.994878i | \(-0.467768\pi\) | ||||
0.101087 | + | 0.994878i | \(0.467768\pi\) | |||||||
\(108\) | −1.96545 | −0.189125 | ||||||||
\(109\) | 1.42537 | 0.136526 | 0.0682629 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682629 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(110\) | 0.234751 | 0.0223826 | ||||||||
\(111\) | −3.73070 | −0.354102 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.7731 | −1.10752 | −0.553762 | − | 0.832675i | \(-0.686808\pi\) | ||||
−0.553762 | + | 0.832675i | \(0.686808\pi\) | |||||||
\(114\) | −1.07057 | −0.100268 | ||||||||
\(115\) | −5.22044 | −0.486808 | ||||||||
\(116\) | 11.9721 | 1.11159 | ||||||||
\(117\) | −6.93089 | −0.640761 | ||||||||
\(118\) | 1.46258 | 0.134642 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.930893 | −0.0849785 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.702071 | 0.0635625 | ||||||||
\(123\) | −11.4300 | −1.03061 | ||||||||
\(124\) | 10.4273 | 0.936402 | ||||||||
\(125\) | 10.6147 | 0.949406 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.31914 | 0.205791 | 0.102895 | − | 0.994692i | \(-0.467189\pi\) | ||||
0.102895 | + | 0.994692i | \(0.467189\pi\) | |||||||
\(128\) | 5.69407 | 0.503289 | ||||||||
\(129\) | −4.27866 | −0.376715 | ||||||||
\(130\) | −1.62704 | −0.142700 | ||||||||
\(131\) | −6.61441 | −0.577904 | −0.288952 | − | 0.957344i | \(-0.593307\pi\) | ||||
−0.288952 | + | 0.957344i | \(0.593307\pi\) | |||||||
\(132\) | −1.96545 | −0.171070 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.99615 | −0.258828 | ||||||||
\(135\) | −1.26288 | −0.108692 | ||||||||
\(136\) | 4.13375 | 0.354466 | ||||||||
\(137\) | −18.3110 | −1.56442 | −0.782209 | − | 0.623016i | \(-0.785907\pi\) | ||||
−0.782209 | + | 0.623016i | \(0.785907\pi\) | |||||||
\(138\) | −0.768404 | −0.0654109 | ||||||||
\(139\) | −6.33129 | −0.537013 | −0.268506 | − | 0.963278i | \(-0.586530\pi\) | ||||
−0.268506 | + | 0.963278i | \(0.586530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.1938 | −1.11112 | ||||||||
\(142\) | −0.775799 | −0.0651036 | ||||||||
\(143\) | −6.93089 | −0.579590 | ||||||||
\(144\) | 3.79387 | 0.316156 | ||||||||
\(145\) | 7.69260 | 0.638836 | ||||||||
\(146\) | 1.00385 | 0.0830796 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.33248 | 0.602726 | ||||||||
\(149\) | −16.9069 | −1.38507 | −0.692533 | − | 0.721386i | \(-0.743505\pi\) | ||||
−0.692533 | + | 0.721386i | \(0.743505\pi\) | |||||||
\(150\) | 0.632964 | 0.0516813 | ||||||||
\(151\) | 6.48442 | 0.527695 | 0.263847 | − | 0.964564i | \(-0.415008\pi\) | ||||
0.263847 | + | 0.964564i | \(0.415008\pi\) | |||||||
\(152\) | 4.24530 | 0.344339 | ||||||||
\(153\) | 5.60799 | 0.453379 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.70000 | 0.538157 | ||||||||
\(156\) | 13.6223 | 1.09066 | ||||||||
\(157\) | −2.01285 | −0.160643 | −0.0803213 | − | 0.996769i | \(-0.525595\pi\) | ||||
−0.0803213 | + | 0.996769i | \(0.525595\pi\) | |||||||
\(158\) | −1.77690 | −0.141363 | ||||||||
\(159\) | −5.52310 | −0.438011 | ||||||||
\(160\) | 2.75240 | 0.217597 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.185885 | −0.0146045 | ||||||||
\(163\) | 8.15341 | 0.638624 | 0.319312 | − | 0.947650i | \(-0.396548\pi\) | ||||
0.319312 | + | 0.947650i | \(0.396548\pi\) | |||||||
\(164\) | 22.4650 | 1.75422 | ||||||||
\(165\) | −1.26288 | −0.0983152 | ||||||||
\(166\) | −1.25270 | −0.0972281 | ||||||||
\(167\) | −15.8258 | −1.22463 | −0.612317 | − | 0.790612i | \(-0.709762\pi\) | ||||
−0.612317 | + | 0.790612i | \(0.709762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.0373 | 2.69518 | ||||||||
\(170\) | 1.31648 | 0.100970 | ||||||||
\(171\) | 5.75932 | 0.440426 | ||||||||
\(172\) | 8.40948 | 0.641217 | ||||||||
\(173\) | 4.21778 | 0.320672 | 0.160336 | − | 0.987063i | \(-0.448742\pi\) | ||||
0.160336 | + | 0.987063i | \(0.448742\pi\) | |||||||
\(174\) | 1.13229 | 0.0858383 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.79387 | 0.285974 | ||||||||
\(177\) | −7.86821 | −0.591411 | ||||||||
\(178\) | −1.14295 | −0.0856676 | ||||||||
\(179\) | 16.2270 | 1.21286 | 0.606432 | − | 0.795135i | \(-0.292600\pi\) | ||||
0.606432 | + | 0.795135i | \(0.292600\pi\) | |||||||
\(180\) | 2.48213 | 0.185007 | ||||||||
\(181\) | −12.0684 | −0.897038 | −0.448519 | − | 0.893773i | \(-0.648048\pi\) | ||||
−0.448519 | + | 0.893773i | \(0.648048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.77690 | −0.279197 | ||||||||
\(184\) | 3.04706 | 0.224633 | ||||||||
\(185\) | 4.71143 | 0.346391 | ||||||||
\(186\) | 0.986182 | 0.0723104 | ||||||||
\(187\) | 5.60799 | 0.410097 | ||||||||
\(188\) | 25.9317 | 1.89126 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.35201 | 0.0980849 | ||||||||
\(191\) | −0.432653 | −0.0313057 | −0.0156528 | − | 0.999877i | \(-0.504983\pi\) | ||||
−0.0156528 | + | 0.999877i | \(0.504983\pi\) | |||||||
\(192\) | −7.18262 | −0.518361 | ||||||||
\(193\) | 3.42537 | 0.246564 | 0.123282 | − | 0.992372i | \(-0.460658\pi\) | ||||
0.123282 | + | 0.992372i | \(0.460658\pi\) | |||||||
\(194\) | 2.84867 | 0.204522 | ||||||||
\(195\) | 8.75290 | 0.626808 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.7522 | 1.26479 | 0.632396 | − | 0.774645i | \(-0.282072\pi\) | ||||
0.632396 | + | 0.774645i | \(0.282072\pi\) | |||||||
\(198\) | −0.185885 | −0.0132103 | ||||||||
\(199\) | 12.8840 | 0.913322 | 0.456661 | − | 0.889641i | \(-0.349045\pi\) | ||||
0.456661 | + | 0.889641i | \(0.349045\pi\) | |||||||
\(200\) | −2.50998 | −0.177483 | ||||||||
\(201\) | 16.1182 | 1.13689 | ||||||||
\(202\) | 1.80830 | 0.127231 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.0222 | −0.771708 | ||||||||
\(205\) | 14.4347 | 1.00817 | ||||||||
\(206\) | 0.231324 | 0.0161171 | ||||||||
\(207\) | 4.13375 | 0.287316 | ||||||||
\(208\) | −26.2949 | −1.82323 | ||||||||
\(209\) | 5.75932 | 0.398381 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2270 | 1.25480 | 0.627400 | − | 0.778697i | \(-0.284119\pi\) | ||||
0.627400 | + | 0.778697i | \(0.284119\pi\) | |||||||
\(212\) | 10.8554 | 0.745549 | ||||||||
\(213\) | 4.17353 | 0.285966 | ||||||||
\(214\) | −0.388744 | −0.0265740 | ||||||||
\(215\) | 5.40344 | 0.368512 | ||||||||
\(216\) | 0.737118 | 0.0501546 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.264956 | −0.0179451 | ||||||||
\(219\) | −5.40040 | −0.364925 | ||||||||
\(220\) | 2.48213 | 0.167345 | ||||||||
\(221\) | −38.8684 | −2.61457 | ||||||||
\(222\) | 0.693482 | 0.0465434 | ||||||||
\(223\) | −20.8782 | −1.39810 | −0.699052 | − | 0.715071i | \(-0.746395\pi\) | ||||
−0.699052 | + | 0.715071i | \(0.746395\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.40513 | −0.227009 | ||||||||
\(226\) | 2.18845 | 0.145574 | ||||||||
\(227\) | 1.54589 | 0.102604 | 0.0513022 | − | 0.998683i | \(-0.483663\pi\) | ||||
0.0513022 | + | 0.998683i | \(0.483663\pi\) | |||||||
\(228\) | −11.3196 | −0.749661 | ||||||||
\(229\) | 4.82397 | 0.318777 | 0.159388 | − | 0.987216i | \(-0.449048\pi\) | ||||
0.159388 | + | 0.987216i | \(0.449048\pi\) | |||||||
\(230\) | 0.970403 | 0.0639865 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.49002 | −0.294784 | ||||||||
\(233\) | −9.81085 | −0.642730 | −0.321365 | − | 0.946955i | \(-0.604142\pi\) | ||||
−0.321365 | + | 0.946955i | \(0.604142\pi\) | |||||||
\(234\) | 1.28835 | 0.0842222 | ||||||||
\(235\) | 16.6622 | 1.08692 | ||||||||
\(236\) | 15.4645 | 1.00666 | ||||||||
\(237\) | 9.55912 | 0.620932 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.3869 | −1.77151 | −0.885754 | − | 0.464155i | \(-0.846358\pi\) | ||||
−0.885754 | + | 0.464155i | \(0.846358\pi\) | |||||||
\(240\) | −4.79121 | −0.309271 | ||||||||
\(241\) | 1.15399 | 0.0743352 | 0.0371676 | − | 0.999309i | \(-0.488166\pi\) | ||||
0.0371676 | + | 0.999309i | \(0.488166\pi\) | |||||||
\(242\) | −0.185885 | −0.0119492 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.42330 | 0.475228 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.12467 | 0.135464 | ||||||||
\(247\) | −39.9172 | −2.53987 | ||||||||
\(248\) | −3.91065 | −0.248327 | ||||||||
\(249\) | 6.73908 | 0.427072 | ||||||||
\(250\) | −1.97311 | −0.124791 | ||||||||
\(251\) | −13.3869 | −0.844970 | −0.422485 | − | 0.906370i | \(-0.638842\pi\) | ||||
−0.422485 | + | 0.906370i | \(0.638842\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.13375 | 0.259887 | ||||||||
\(254\) | −0.431095 | −0.0270493 | ||||||||
\(255\) | −7.08223 | −0.443506 | ||||||||
\(256\) | 13.3068 | 0.831674 | ||||||||
\(257\) | 10.2482 | 0.639267 | 0.319634 | − | 0.947541i | \(-0.396440\pi\) | ||||
0.319634 | + | 0.947541i | \(0.396440\pi\) | |||||||
\(258\) | 0.795340 | 0.0495157 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −17.2034 | −1.06691 | ||||||||
\(261\) | −6.09131 | −0.377043 | ||||||||
\(262\) | 1.22952 | 0.0759601 | ||||||||
\(263\) | −9.59949 | −0.591930 | −0.295965 | − | 0.955199i | \(-0.595641\pi\) | ||||
−0.295965 | + | 0.955199i | \(0.595641\pi\) | |||||||
\(264\) | 0.737118 | 0.0453665 | ||||||||
\(265\) | 6.97502 | 0.428472 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.14867 | 0.376293 | ||||||||
\(268\) | −31.6796 | −1.93514 | ||||||||
\(269\) | −7.07384 | −0.431300 | −0.215650 | − | 0.976471i | \(-0.569187\pi\) | ||||
−0.215650 | + | 0.976471i | \(0.569187\pi\) | |||||||
\(270\) | 0.234751 | 0.0142865 | ||||||||
\(271\) | 14.4835 | 0.879809 | 0.439904 | − | 0.898045i | \(-0.355012\pi\) | ||||
0.439904 | + | 0.898045i | \(0.355012\pi\) | |||||||
\(272\) | 21.2760 | 1.29005 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.40376 | 0.205628 | ||||||||
\(275\) | −3.40513 | −0.205337 | ||||||||
\(276\) | −8.12467 | −0.489048 | ||||||||
\(277\) | −8.61734 | −0.517766 | −0.258883 | − | 0.965909i | \(-0.583354\pi\) | ||||
−0.258883 | + | 0.965909i | \(0.583354\pi\) | |||||||
\(278\) | 1.17689 | 0.0705854 | ||||||||
\(279\) | −5.30532 | −0.317621 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.08125 | 0.541742 | 0.270871 | − | 0.962616i | \(-0.412688\pi\) | ||||
0.270871 | + | 0.962616i | \(0.412688\pi\) | |||||||
\(282\) | 2.45253 | 0.146046 | ||||||||
\(283\) | 4.78975 | 0.284721 | 0.142360 | − | 0.989815i | \(-0.454531\pi\) | ||||
0.142360 | + | 0.989815i | \(0.454531\pi\) | |||||||
\(284\) | −8.20286 | −0.486750 | ||||||||
\(285\) | −7.27334 | −0.430835 | ||||||||
\(286\) | 1.28835 | 0.0761818 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.17946 | −0.128426 | ||||||||
\(289\) | 14.4495 | 0.849973 | ||||||||
\(290\) | −1.42994 | −0.0839691 | ||||||||
\(291\) | −15.3249 | −0.898360 | ||||||||
\(292\) | 10.6142 | 0.621148 | ||||||||
\(293\) | 13.0334 | 0.761417 | 0.380708 | − | 0.924695i | \(-0.375680\pi\) | ||||
0.380708 | + | 0.924695i | \(0.375680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.93662 | 0.578532 | ||||||||
\(296\) | −2.74996 | −0.159838 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 3.14274 | 0.182054 | ||||||||
\(299\) | −28.6506 | −1.65691 | ||||||||
\(300\) | 6.69260 | 0.386398 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.20536 | −0.0693606 | ||||||||
\(303\) | −9.72803 | −0.558861 | ||||||||
\(304\) | 21.8501 | 1.25319 | ||||||||
\(305\) | 4.76978 | 0.273117 | ||||||||
\(306\) | −1.04244 | −0.0595925 | ||||||||
\(307\) | 11.3413 | 0.647285 | 0.323642 | − | 0.946179i | \(-0.395093\pi\) | ||||
0.323642 | + | 0.946179i | \(0.395093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.24444 | −0.0707938 | ||||||||
\(310\) | −1.24543 | −0.0707357 | ||||||||
\(311\) | 9.20020 | 0.521695 | 0.260848 | − | 0.965380i | \(-0.415998\pi\) | ||||
0.260848 | + | 0.965380i | \(0.415998\pi\) | |||||||
\(312\) | −5.10889 | −0.289234 | ||||||||
\(313\) | −10.5085 | −0.593973 | −0.296987 | − | 0.954882i | \(-0.595982\pi\) | ||||
−0.296987 | + | 0.954882i | \(0.595982\pi\) | |||||||
\(314\) | 0.374159 | 0.0211150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.7879 | −1.05690 | ||||||||
\(317\) | −25.2611 | −1.41880 | −0.709402 | − | 0.704804i | \(-0.751035\pi\) | ||||
−0.709402 | + | 0.704804i | \(0.751035\pi\) | |||||||
\(318\) | 1.02666 | 0.0575725 | ||||||||
\(319\) | −6.09131 | −0.341048 | ||||||||
\(320\) | 9.07080 | 0.507073 | ||||||||
\(321\) | 2.09131 | 0.116725 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.2982 | 1.79712 | ||||||||
\(324\) | −1.96545 | −0.109191 | ||||||||
\(325\) | 23.6006 | 1.30913 | ||||||||
\(326\) | −1.51560 | −0.0839412 | ||||||||
\(327\) | 1.42537 | 0.0788232 | ||||||||
\(328\) | −8.42526 | −0.465207 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.234751 | 0.0129226 | ||||||||
\(331\) | −9.42091 | −0.517820 | −0.258910 | − | 0.965901i | \(-0.583363\pi\) | ||||
−0.258910 | + | 0.965901i | \(0.583363\pi\) | |||||||
\(332\) | −13.2453 | −0.726930 | ||||||||
\(333\) | −3.73070 | −0.204441 | ||||||||
\(334\) | 2.94178 | 0.160967 | ||||||||
\(335\) | −20.3554 | −1.11214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1636 | 0.553646 | 0.276823 | − | 0.960921i | \(-0.410718\pi\) | ||||
0.276823 | + | 0.960921i | \(0.410718\pi\) | |||||||
\(338\) | −6.51292 | −0.354256 | ||||||||
\(339\) | −11.7731 | −0.639429 | ||||||||
\(340\) | 13.9197 | 0.754904 | ||||||||
\(341\) | −5.30532 | −0.287299 | ||||||||
\(342\) | −1.07057 | −0.0578900 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.15388 | −0.170046 | ||||||||
\(345\) | −5.22044 | −0.281059 | ||||||||
\(346\) | −0.784023 | −0.0421493 | ||||||||
\(347\) | 34.0379 | 1.82725 | 0.913624 | − | 0.406560i | \(-0.133272\pi\) | ||||
0.913624 | + | 0.406560i | \(0.133272\pi\) | |||||||
\(348\) | 11.9721 | 0.641774 | ||||||||
\(349\) | 27.2845 | 1.46051 | 0.730253 | − | 0.683177i | \(-0.239402\pi\) | ||||
0.730253 | + | 0.683177i | \(0.239402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.93089 | −0.369944 | ||||||||
\(352\) | −2.17946 | −0.116166 | ||||||||
\(353\) | −19.9742 | −1.06312 | −0.531560 | − | 0.847021i | \(-0.678394\pi\) | ||||
−0.531560 | + | 0.847021i | \(0.678394\pi\) | |||||||
\(354\) | 1.46258 | 0.0777355 | ||||||||
\(355\) | −5.27068 | −0.279739 | ||||||||
\(356\) | −12.0849 | −0.640498 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.01637 | −0.159420 | ||||||||
\(359\) | −4.23888 | −0.223719 | −0.111860 | − | 0.993724i | \(-0.535681\pi\) | ||||
−0.111860 | + | 0.993724i | \(0.535681\pi\) | |||||||
\(360\) | −0.930893 | −0.0490624 | ||||||||
\(361\) | 14.1698 | 0.745777 | ||||||||
\(362\) | 2.24334 | 0.117907 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.82006 | 0.356978 | ||||||||
\(366\) | 0.702071 | 0.0366978 | ||||||||
\(367\) | −4.17337 | −0.217848 | −0.108924 | − | 0.994050i | \(-0.534741\pi\) | ||||
−0.108924 | + | 0.994050i | \(0.534741\pi\) | |||||||
\(368\) | 15.6829 | 0.817529 | ||||||||
\(369\) | −11.4300 | −0.595022 | ||||||||
\(370\) | −0.875785 | −0.0455299 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10.4273 | 0.540632 | ||||||||
\(373\) | 36.1533 | 1.87195 | 0.935973 | − | 0.352071i | \(-0.114522\pi\) | ||||
0.935973 | + | 0.352071i | \(0.114522\pi\) | |||||||
\(374\) | −1.04244 | −0.0539034 | ||||||||
\(375\) | 10.6147 | 0.548140 | ||||||||
\(376\) | −9.72537 | −0.501548 | ||||||||
\(377\) | 42.2182 | 2.17435 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.7686 | 1.32364 | 0.661821 | − | 0.749662i | \(-0.269784\pi\) | ||||
0.661821 | + | 0.749662i | \(0.269784\pi\) | |||||||
\(380\) | 14.2954 | 0.733337 | ||||||||
\(381\) | 2.31914 | 0.118813 | ||||||||
\(382\) | 0.0804239 | 0.00411484 | ||||||||
\(383\) | 6.22071 | 0.317863 | 0.158932 | − | 0.987290i | \(-0.449195\pi\) | ||||
0.158932 | + | 0.987290i | \(0.449195\pi\) | |||||||
\(384\) | 5.69407 | 0.290574 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.636726 | −0.0324085 | ||||||||
\(387\) | −4.27866 | −0.217497 | ||||||||
\(388\) | 30.1202 | 1.52912 | ||||||||
\(389\) | 21.4171 | 1.08589 | 0.542946 | − | 0.839767i | \(-0.317309\pi\) | ||||
0.542946 | + | 0.839767i | \(0.317309\pi\) | |||||||
\(390\) | −1.62704 | −0.0823881 | ||||||||
\(391\) | 23.1820 | 1.17237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.61441 | −0.333653 | ||||||||
\(394\) | −3.29987 | −0.166245 | ||||||||
\(395\) | −12.0720 | −0.607410 | ||||||||
\(396\) | −1.96545 | −0.0987674 | ||||||||
\(397\) | 1.23743 | 0.0621050 | 0.0310525 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310525 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(398\) | −2.39494 | −0.120048 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.9186 | −0.645932 | ||||||||
\(401\) | −17.4384 | −0.870831 | −0.435415 | − | 0.900230i | \(-0.643399\pi\) | ||||
−0.435415 | + | 0.900230i | \(0.643399\pi\) | |||||||
\(402\) | −2.99615 | −0.149434 | ||||||||
\(403\) | 36.7706 | 1.83168 | ||||||||
\(404\) | 19.1199 | 0.951252 | ||||||||
\(405\) | −1.26288 | −0.0627531 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.73070 | −0.184924 | ||||||||
\(408\) | 4.13375 | 0.204651 | ||||||||
\(409\) | −14.1632 | −0.700327 | −0.350163 | − | 0.936689i | \(-0.613874\pi\) | ||||
−0.350163 | + | 0.936689i | \(0.613874\pi\) | |||||||
\(410\) | −2.68320 | −0.132514 | ||||||||
\(411\) | −18.3110 | −0.903217 | ||||||||
\(412\) | 2.44588 | 0.120500 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.768404 | −0.0377650 | ||||||||
\(415\) | −8.51066 | −0.417772 | ||||||||
\(416\) | 15.1056 | 0.740614 | ||||||||
\(417\) | −6.33129 | −0.310045 | ||||||||
\(418\) | −1.07057 | −0.0523635 | ||||||||
\(419\) | 28.8378 | 1.40882 | 0.704409 | − | 0.709794i | \(-0.251212\pi\) | ||||
0.704409 | + | 0.709794i | \(0.251212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.1883 | −1.27634 | −0.638171 | − | 0.769895i | \(-0.720309\pi\) | ||||
−0.638171 | + | 0.769895i | \(0.720309\pi\) | |||||||
\(422\) | −3.38814 | −0.164932 | ||||||||
\(423\) | −13.1938 | −0.641503 | ||||||||
\(424\) | −4.07118 | −0.197714 | ||||||||
\(425\) | −19.0959 | −0.926289 | ||||||||
\(426\) | −0.775799 | −0.0375876 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.11036 | −0.198682 | ||||||||
\(429\) | −6.93089 | −0.334627 | ||||||||
\(430\) | −1.00442 | −0.0484375 | ||||||||
\(431\) | −21.4952 | −1.03539 | −0.517694 | − | 0.855566i | \(-0.673210\pi\) | ||||
−0.517694 | + | 0.855566i | \(0.673210\pi\) | |||||||
\(432\) | 3.79387 | 0.182533 | ||||||||
\(433\) | −14.9303 | −0.717505 | −0.358752 | − | 0.933433i | \(-0.616798\pi\) | ||||
−0.358752 | + | 0.933433i | \(0.616798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.69260 | 0.368832 | ||||||||
\(436\) | −2.80149 | −0.134167 | ||||||||
\(437\) | 23.8076 | 1.13887 | ||||||||
\(438\) | 1.00385 | 0.0479660 | ||||||||
\(439\) | 24.8160 | 1.18440 | 0.592201 | − | 0.805790i | \(-0.298259\pi\) | ||||
0.592201 | + | 0.805790i | \(0.298259\pi\) | |||||||
\(440\) | −0.930893 | −0.0443786 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.22506 | 0.343661 | ||||||||
\(443\) | −31.6570 | −1.50407 | −0.752035 | − | 0.659123i | \(-0.770928\pi\) | ||||
−0.752035 | + | 0.659123i | \(0.770928\pi\) | |||||||
\(444\) | 7.33248 | 0.347984 | ||||||||
\(445\) | −7.76504 | −0.368098 | ||||||||
\(446\) | 3.88094 | 0.183768 | ||||||||
\(447\) | −16.9069 | −0.799668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.3117 | −0.581027 | −0.290514 | − | 0.956871i | \(-0.593826\pi\) | ||||
−0.290514 | + | 0.956871i | \(0.593826\pi\) | |||||||
\(450\) | 0.632964 | 0.0298382 | ||||||||
\(451\) | −11.4300 | −0.538217 | ||||||||
\(452\) | 23.1395 | 1.08839 | ||||||||
\(453\) | 6.48442 | 0.304665 | ||||||||
\(454\) | −0.287359 | −0.0134864 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.24530 | 0.198804 | ||||||||
\(457\) | −9.99554 | −0.467572 | −0.233786 | − | 0.972288i | \(-0.575111\pi\) | ||||
−0.233786 | + | 0.972288i | \(0.575111\pi\) | |||||||
\(458\) | −0.896704 | −0.0419002 | ||||||||
\(459\) | 5.60799 | 0.261758 | ||||||||
\(460\) | 10.2605 | 0.478398 | ||||||||
\(461\) | −14.7163 | −0.685406 | −0.342703 | − | 0.939444i | \(-0.611342\pi\) | ||||
−0.342703 | + | 0.939444i | \(0.611342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.7650 | 1.33682 | 0.668412 | − | 0.743791i | \(-0.266974\pi\) | ||||
0.668412 | + | 0.743791i | \(0.266974\pi\) | |||||||
\(464\) | −23.1097 | −1.07284 | ||||||||
\(465\) | 6.70000 | 0.310705 | ||||||||
\(466\) | 1.82369 | 0.0844809 | ||||||||
\(467\) | 1.00462 | 0.0464883 | 0.0232442 | − | 0.999730i | \(-0.492600\pi\) | ||||
0.0232442 | + | 0.999730i | \(0.492600\pi\) | |||||||
\(468\) | 13.6223 | 0.629691 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.09725 | −0.142866 | ||||||||
\(471\) | −2.01285 | −0.0927470 | ||||||||
\(472\) | −5.79980 | −0.266958 | ||||||||
\(473\) | −4.27866 | −0.196733 | ||||||||
\(474\) | −1.77690 | −0.0816158 | ||||||||
\(475\) | −19.6112 | −0.899825 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.52310 | −0.252885 | ||||||||
\(478\) | 5.09081 | 0.232848 | ||||||||
\(479\) | 15.0159 | 0.686094 | 0.343047 | − | 0.939318i | \(-0.388541\pi\) | ||||
0.343047 | + | 0.939318i | \(0.388541\pi\) | |||||||
\(480\) | 2.75240 | 0.125629 | ||||||||
\(481\) | 25.8571 | 1.17898 | ||||||||
\(482\) | −0.214510 | −0.00977068 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.96545 | −0.0893385 | ||||||||
\(485\) | 19.3535 | 0.878797 | ||||||||
\(486\) | −0.185885 | −0.00843193 | ||||||||
\(487\) | −2.55560 | −0.115805 | −0.0579027 | − | 0.998322i | \(-0.518441\pi\) | ||||
−0.0579027 | + | 0.998322i | \(0.518441\pi\) | |||||||
\(488\) | −2.78402 | −0.126027 | ||||||||
\(489\) | 8.15341 | 0.368710 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.5637 | −1.19880 | −0.599402 | − | 0.800448i | \(-0.704595\pi\) | ||||
−0.599402 | + | 0.800448i | \(0.704595\pi\) | |||||||
\(492\) | 22.4650 | 1.01280 | ||||||||
\(493\) | −34.1600 | −1.53849 | ||||||||
\(494\) | 7.42003 | 0.333843 | ||||||||
\(495\) | −1.26288 | −0.0567623 | ||||||||
\(496\) | −20.1277 | −0.903762 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.25270 | −0.0561347 | ||||||||
\(499\) | 6.82270 | 0.305426 | 0.152713 | − | 0.988271i | \(-0.451199\pi\) | ||||
0.152713 | + | 0.988271i | \(0.451199\pi\) | |||||||
\(500\) | −20.8626 | −0.933004 | ||||||||
\(501\) | −15.8258 | −0.707043 | ||||||||
\(502\) | 2.48842 | 0.111064 | ||||||||
\(503\) | −5.42913 | −0.242073 | −0.121037 | − | 0.992648i | \(-0.538622\pi\) | ||||
−0.121037 | + | 0.992648i | \(0.538622\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2854 | 0.546691 | ||||||||
\(506\) | −0.768404 | −0.0341597 | ||||||||
\(507\) | 35.0373 | 1.55606 | ||||||||
\(508\) | −4.55815 | −0.202235 | ||||||||
\(509\) | 17.5157 | 0.776370 | 0.388185 | − | 0.921581i | \(-0.373102\pi\) | ||||
0.388185 | + | 0.921581i | \(0.373102\pi\) | |||||||
\(510\) | 1.31648 | 0.0582948 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −13.8617 | −0.612605 | ||||||||
\(513\) | 5.75932 | 0.254280 | ||||||||
\(514\) | −1.90500 | −0.0840258 | ||||||||
\(515\) | 1.57158 | 0.0692522 | ||||||||
\(516\) | 8.40948 | 0.370207 | ||||||||
\(517\) | −13.1938 | −0.580262 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.21778 | 0.185140 | ||||||||
\(520\) | 6.45192 | 0.282935 | ||||||||
\(521\) | −38.6930 | −1.69517 | −0.847586 | − | 0.530658i | \(-0.821945\pi\) | ||||
−0.847586 | + | 0.530658i | \(0.821945\pi\) | |||||||
\(522\) | 1.13229 | 0.0495588 | ||||||||
\(523\) | −1.05626 | −0.0461871 | −0.0230935 | − | 0.999733i | \(-0.507352\pi\) | ||||
−0.0230935 | + | 0.999733i | \(0.507352\pi\) | |||||||
\(524\) | 13.0003 | 0.567920 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.78440 | 0.0778037 | ||||||||
\(527\) | −29.7522 | −1.29603 | ||||||||
\(528\) | 3.79387 | 0.165107 | ||||||||
\(529\) | −5.91210 | −0.257048 | ||||||||
\(530\) | −1.29655 | −0.0563187 | ||||||||
\(531\) | −7.86821 | −0.341451 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 79.2201 | 3.43140 | ||||||||
\(534\) | −1.14295 | −0.0494602 | ||||||||
\(535\) | −2.64108 | −0.114184 | ||||||||
\(536\) | 11.8811 | 0.513183 | ||||||||
\(537\) | 16.2270 | 0.700248 | ||||||||
\(538\) | 1.31492 | 0.0566904 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.48213 | 0.106814 | ||||||||
\(541\) | −14.1120 | −0.606720 | −0.303360 | − | 0.952876i | \(-0.598109\pi\) | ||||
−0.303360 | + | 0.952876i | \(0.598109\pi\) | |||||||
\(542\) | −2.69227 | −0.115643 | ||||||||
\(543\) | −12.0684 | −0.517905 | ||||||||
\(544\) | −12.2224 | −0.524031 | ||||||||
\(545\) | −1.80007 | −0.0771067 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.08211 | −0.0890247 | −0.0445123 | − | 0.999009i | \(-0.514173\pi\) | ||||
−0.0445123 | + | 0.999009i | \(0.514173\pi\) | |||||||
\(548\) | 35.9894 | 1.53739 | ||||||||
\(549\) | −3.77690 | −0.161194 | ||||||||
\(550\) | 0.632964 | 0.0269897 | ||||||||
\(551\) | −35.0818 | −1.49453 | ||||||||
\(552\) | 3.04706 | 0.129692 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.60184 | 0.0680556 | ||||||||
\(555\) | 4.71143 | 0.199989 | ||||||||
\(556\) | 12.4438 | 0.527735 | ||||||||
\(557\) | −16.6785 | −0.706689 | −0.353345 | − | 0.935493i | \(-0.614956\pi\) | ||||
−0.353345 | + | 0.935493i | \(0.614956\pi\) | |||||||
\(558\) | 0.986182 | 0.0417484 | ||||||||
\(559\) | 29.6549 | 1.25427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.60799 | 0.236769 | ||||||||
\(562\) | −1.68807 | −0.0712070 | ||||||||
\(563\) | 35.7321 | 1.50593 | 0.752965 | − | 0.658061i | \(-0.228623\pi\) | ||||
0.752965 | + | 0.658061i | \(0.228623\pi\) | |||||||
\(564\) | 25.9317 | 1.09192 | ||||||||
\(565\) | 14.8681 | 0.625505 | ||||||||
\(566\) | −0.890344 | −0.0374239 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.07639 | 0.129082 | ||||||||
\(569\) | 37.9050 | 1.58906 | 0.794530 | − | 0.607225i | \(-0.207718\pi\) | ||||
0.794530 | + | 0.607225i | \(0.207718\pi\) | |||||||
\(570\) | 1.35201 | 0.0566294 | ||||||||
\(571\) | −37.9257 | −1.58714 | −0.793571 | − | 0.608477i | \(-0.791781\pi\) | ||||
−0.793571 | + | 0.608477i | \(0.791781\pi\) | |||||||
\(572\) | 13.6223 | 0.569577 | ||||||||
\(573\) | −0.432653 | −0.0180743 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.0760 | −0.587008 | ||||||||
\(576\) | −7.18262 | −0.299276 | ||||||||
\(577\) | −42.4001 | −1.76514 | −0.882569 | − | 0.470182i | \(-0.844188\pi\) | ||||
−0.882569 | + | 0.470182i | \(0.844188\pi\) | |||||||
\(578\) | −2.68596 | −0.111721 | ||||||||
\(579\) | 3.42537 | 0.142354 | ||||||||
\(580\) | −15.1194 | −0.627799 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.84867 | 0.118081 | ||||||||
\(583\) | −5.52310 | −0.228744 | ||||||||
\(584\) | −3.98073 | −0.164724 | ||||||||
\(585\) | 8.75290 | 0.361888 | ||||||||
\(586\) | −2.42271 | −0.100081 | ||||||||
\(587\) | 26.5924 | 1.09758 | 0.548792 | − | 0.835959i | \(-0.315088\pi\) | ||||
0.548792 | + | 0.835959i | \(0.315088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.5551 | −1.25900 | ||||||||
\(590\) | −1.84707 | −0.0760427 | ||||||||
\(591\) | 17.7522 | 0.730228 | ||||||||
\(592\) | −14.1538 | −0.581717 | ||||||||
\(593\) | 14.7749 | 0.606734 | 0.303367 | − | 0.952874i | \(-0.401889\pi\) | ||||
0.303367 | + | 0.952874i | \(0.401889\pi\) | |||||||
\(594\) | −0.185885 | −0.00762697 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 33.2296 | 1.36114 | ||||||||
\(597\) | 12.8840 | 0.527307 | ||||||||
\(598\) | 5.32573 | 0.217785 | ||||||||
\(599\) | 3.12577 | 0.127716 | 0.0638578 | − | 0.997959i | \(-0.479660\pi\) | ||||
0.0638578 | + | 0.997959i | \(0.479660\pi\) | |||||||
\(600\) | −2.50998 | −0.102470 | ||||||||
\(601\) | 19.2780 | 0.786364 | 0.393182 | − | 0.919461i | \(-0.371374\pi\) | ||||
0.393182 | + | 0.919461i | \(0.371374\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.1182 | 0.656386 | ||||||||
\(604\) | −12.7448 | −0.518578 | ||||||||
\(605\) | −1.26288 | −0.0513434 | ||||||||
\(606\) | 1.80830 | 0.0734571 | ||||||||
\(607\) | 10.5994 | 0.430216 | 0.215108 | − | 0.976590i | \(-0.430990\pi\) | ||||
0.215108 | + | 0.976590i | \(0.430990\pi\) | |||||||
\(608\) | −12.5522 | −0.509060 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.886632 | −0.0358987 | ||||||||
\(611\) | 91.4446 | 3.69945 | ||||||||
\(612\) | −11.0222 | −0.445546 | ||||||||
\(613\) | 25.1685 | 1.01655 | 0.508273 | − | 0.861196i | \(-0.330284\pi\) | ||||
0.508273 | + | 0.861196i | \(0.330284\pi\) | |||||||
\(614\) | −2.10819 | −0.0850796 | ||||||||
\(615\) | 14.4347 | 0.582064 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.5595 | −1.31080 | −0.655399 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655399 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(618\) | 0.231324 | 0.00930520 | ||||||||
\(619\) | 10.7770 | 0.433165 | 0.216582 | − | 0.976264i | \(-0.430509\pi\) | ||||
0.216582 | + | 0.976264i | \(0.430509\pi\) | |||||||
\(620\) | −13.1685 | −0.528859 | ||||||||
\(621\) | 4.13375 | 0.165882 | ||||||||
\(622\) | −1.71018 | −0.0685720 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −26.2949 | −1.05264 | ||||||||
\(625\) | 3.62056 | 0.144822 | ||||||||
\(626\) | 1.95337 | 0.0780723 | ||||||||
\(627\) | 5.75932 | 0.230005 | ||||||||
\(628\) | 3.95614 | 0.157867 | ||||||||
\(629\) | −20.9217 | −0.834203 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.2884 | −1.60386 | −0.801928 | − | 0.597420i | \(-0.796192\pi\) | ||||
−0.801928 | + | 0.597420i | \(0.796192\pi\) | |||||||
\(632\) | 7.04621 | 0.280283 | ||||||||
\(633\) | 18.2270 | 0.724459 | ||||||||
\(634\) | 4.69566 | 0.186489 | ||||||||
\(635\) | −2.92880 | −0.116226 | ||||||||
\(636\) | 10.8554 | 0.430443 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.13229 | 0.0448276 | ||||||||
\(639\) | 4.17353 | 0.165102 | ||||||||
\(640\) | −7.19093 | −0.284247 | ||||||||
\(641\) | −24.3884 | −0.963284 | −0.481642 | − | 0.876368i | \(-0.659959\pi\) | ||||
−0.481642 | + | 0.876368i | \(0.659959\pi\) | |||||||
\(642\) | −0.388744 | −0.0153425 | ||||||||
\(643\) | −23.0317 | −0.908280 | −0.454140 | − | 0.890930i | \(-0.650053\pi\) | ||||
−0.454140 | + | 0.890930i | \(0.650053\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.40344 | 0.212760 | ||||||||
\(646\) | −6.00376 | −0.236215 | ||||||||
\(647\) | −21.3671 | −0.840029 | −0.420015 | − | 0.907517i | \(-0.637975\pi\) | ||||
−0.420015 | + | 0.907517i | \(0.637975\pi\) | |||||||
\(648\) | 0.737118 | 0.0289567 | ||||||||
\(649\) | −7.86821 | −0.308854 | ||||||||
\(650\) | −4.38700 | −0.172072 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.0251 | −0.627591 | ||||||||
\(653\) | 11.4924 | 0.449733 | 0.224866 | − | 0.974390i | \(-0.427805\pi\) | ||||
0.224866 | + | 0.974390i | \(0.427805\pi\) | |||||||
\(654\) | −0.264956 | −0.0103606 | ||||||||
\(655\) | 8.35322 | 0.326387 | ||||||||
\(656\) | −43.3639 | −1.69308 | ||||||||
\(657\) | −5.40040 | −0.210690 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.40682 | −0.0937563 | −0.0468782 | − | 0.998901i | \(-0.514927\pi\) | ||||
−0.0468782 | + | 0.998901i | \(0.514927\pi\) | |||||||
\(660\) | 2.48213 | 0.0966166 | ||||||||
\(661\) | 16.5565 | 0.643972 | 0.321986 | − | 0.946744i | \(-0.395650\pi\) | ||||
0.321986 | + | 0.946744i | \(0.395650\pi\) | |||||||
\(662\) | 1.75121 | 0.0680627 | ||||||||
\(663\) | −38.8684 | −1.50952 | ||||||||
\(664\) | 4.96750 | 0.192776 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.693482 | 0.0268719 | ||||||||
\(667\) | −25.1800 | −0.974972 | ||||||||
\(668\) | 31.1047 | 1.20348 | ||||||||
\(669\) | −20.8782 | −0.807196 | ||||||||
\(670\) | 3.78378 | 0.146180 | ||||||||
\(671\) | −3.77690 | −0.145806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.2861 | 1.66856 | 0.834278 | − | 0.551344i | \(-0.185885\pi\) | ||||
0.834278 | + | 0.551344i | \(0.185885\pi\) | |||||||
\(674\) | −1.88926 | −0.0727717 | ||||||||
\(675\) | −3.40513 | −0.131064 | ||||||||
\(676\) | −68.8639 | −2.64861 | ||||||||
\(677\) | 17.3727 | 0.667689 | 0.333844 | − | 0.942628i | \(-0.391654\pi\) | ||||
0.333844 | + | 0.942628i | \(0.391654\pi\) | |||||||
\(678\) | 2.18845 | 0.0840471 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.22044 | −0.200195 | ||||||||
\(681\) | 1.54589 | 0.0592387 | ||||||||
\(682\) | 0.986182 | 0.0377629 | ||||||||
\(683\) | 12.0749 | 0.462035 | 0.231017 | − | 0.972950i | \(-0.425795\pi\) | ||||
0.231017 | + | 0.972950i | \(0.425795\pi\) | |||||||
\(684\) | −11.3196 | −0.432817 | ||||||||
\(685\) | 23.1247 | 0.883549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.82397 | 0.184046 | ||||||||
\(688\) | −16.2327 | −0.618866 | ||||||||
\(689\) | 38.2800 | 1.45835 | ||||||||
\(690\) | 0.970403 | 0.0369426 | ||||||||
\(691\) | −35.4929 | −1.35022 | −0.675108 | − | 0.737719i | \(-0.735903\pi\) | ||||
−0.675108 | + | 0.737719i | \(0.735903\pi\) | |||||||
\(692\) | −8.28982 | −0.315132 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.32714 | −0.240175 | ||||||||
\(695\) | 7.99567 | 0.303293 | ||||||||
\(696\) | −4.49002 | −0.170194 | ||||||||
\(697\) | −64.0993 | −2.42793 | ||||||||
\(698\) | −5.07179 | −0.191970 | ||||||||
\(699\) | −9.81085 | −0.371080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.81378 | −0.370661 | −0.185331 | − | 0.982676i | \(-0.559336\pi\) | ||||
−0.185331 | + | 0.982676i | \(0.559336\pi\) | |||||||
\(702\) | 1.28835 | 0.0486257 | ||||||||
\(703\) | −21.4863 | −0.810370 | ||||||||
\(704\) | −7.18262 | −0.270705 | ||||||||
\(705\) | 16.6622 | 0.627534 | ||||||||
\(706\) | 3.71291 | 0.139737 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 15.4645 | 0.581193 | ||||||||
\(709\) | 38.2551 | 1.43670 | 0.718349 | − | 0.695682i | \(-0.244898\pi\) | ||||
0.718349 | + | 0.695682i | \(0.244898\pi\) | |||||||
\(710\) | 0.979742 | 0.0367691 | ||||||||
\(711\) | 9.55912 | 0.358495 | ||||||||
\(712\) | 4.53230 | 0.169855 | ||||||||
\(713\) | −21.9309 | −0.821318 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.75290 | 0.327340 | ||||||||
\(716\) | −31.8933 | −1.19191 | ||||||||
\(717\) | −27.3869 | −1.02278 | ||||||||
\(718\) | 0.787945 | 0.0294059 | ||||||||
\(719\) | −18.5140 | −0.690456 | −0.345228 | − | 0.938519i | \(-0.612198\pi\) | ||||
−0.345228 | + | 0.938519i | \(0.612198\pi\) | |||||||
\(720\) | −4.79121 | −0.178558 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.63395 | −0.0980256 | ||||||||
\(723\) | 1.15399 | 0.0429174 | ||||||||
\(724\) | 23.7198 | 0.881540 | ||||||||
\(725\) | 20.7417 | 0.770327 | ||||||||
\(726\) | −0.185885 | −0.00689885 | ||||||||
\(727\) | −41.0658 | −1.52305 | −0.761523 | − | 0.648138i | \(-0.775548\pi\) | ||||
−0.761523 | + | 0.648138i | \(0.775548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.26775 | −0.0469215 | ||||||||
\(731\) | −23.9947 | −0.887475 | ||||||||
\(732\) | 7.42330 | 0.274373 | ||||||||
\(733\) | 10.0352 | 0.370657 | 0.185329 | − | 0.982677i | \(-0.440665\pi\) | ||||
0.185329 | + | 0.982677i | \(0.440665\pi\) | |||||||
\(734\) | 0.775769 | 0.0286342 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.00936 | −0.332089 | ||||||||
\(737\) | 16.1182 | 0.593723 | ||||||||
\(738\) | 2.12467 | 0.0782101 | ||||||||
\(739\) | 14.4054 | 0.529911 | 0.264956 | − | 0.964261i | \(-0.414643\pi\) | ||||
0.264956 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(740\) | −9.26006 | −0.340406 | ||||||||
\(741\) | −39.9172 | −1.46640 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.03505 | −0.221404 | −0.110702 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110702 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(744\) | −3.91065 | −0.143371 | ||||||||
\(745\) | 21.3514 | 0.782255 | ||||||||
\(746\) | −6.72037 | −0.246050 | ||||||||
\(747\) | 6.73908 | 0.246570 | ||||||||
\(748\) | −11.0222 | −0.403012 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.97311 | −0.0720479 | ||||||||
\(751\) | 19.1240 | 0.697844 | 0.348922 | − | 0.937152i | \(-0.386548\pi\) | ||||
0.348922 | + | 0.937152i | \(0.386548\pi\) | |||||||
\(752\) | −50.0555 | −1.82534 | ||||||||
\(753\) | −13.3869 | −0.487844 | ||||||||
\(754\) | −7.84775 | −0.285798 | ||||||||
\(755\) | −8.18906 | −0.298030 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.1103 | −1.45783 | −0.728917 | − | 0.684602i | \(-0.759976\pi\) | ||||
−0.728917 | + | 0.684602i | \(0.759976\pi\) | |||||||
\(758\) | −4.79000 | −0.173981 | ||||||||
\(759\) | 4.13375 | 0.150046 | ||||||||
\(760\) | −5.36131 | −0.194475 | ||||||||
\(761\) | 34.9471 | 1.26683 | 0.633415 | − | 0.773812i | \(-0.281653\pi\) | ||||
0.633415 | + | 0.773812i | \(0.281653\pi\) | |||||||
\(762\) | −0.431095 | −0.0156169 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.850356 | 0.0307648 | ||||||||
\(765\) | −7.08223 | −0.256058 | ||||||||
\(766\) | −1.15634 | −0.0417802 | ||||||||
\(767\) | 54.5337 | 1.96910 | ||||||||
\(768\) | 13.3068 | 0.480167 | ||||||||
\(769\) | 7.83767 | 0.282634 | 0.141317 | − | 0.989964i | \(-0.454866\pi\) | ||||
0.141317 | + | 0.989964i | \(0.454866\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.2482 | 0.369081 | ||||||||
\(772\) | −6.73238 | −0.242304 | ||||||||
\(773\) | 22.0496 | 0.793069 | 0.396535 | − | 0.918020i | \(-0.370213\pi\) | ||||
0.396535 | + | 0.918020i | \(0.370213\pi\) | |||||||
\(774\) | 0.795340 | 0.0285879 | ||||||||
\(775\) | 18.0653 | 0.648925 | ||||||||
\(776\) | −11.2962 | −0.405511 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.98113 | −0.142731 | ||||||||
\(779\) | −65.8290 | −2.35857 | ||||||||
\(780\) | −17.2034 | −0.615979 | ||||||||
\(781\) | 4.17353 | 0.149341 | ||||||||
\(782\) | −4.30920 | −0.154097 | ||||||||
\(783\) | −6.09131 | −0.217686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.54199 | 0.0907274 | ||||||||
\(786\) | 1.22952 | 0.0438556 | ||||||||
\(787\) | −32.6831 | −1.16503 | −0.582513 | − | 0.812821i | \(-0.697931\pi\) | ||||
−0.582513 | + | 0.812821i | \(0.697931\pi\) | |||||||
\(788\) | −34.8910 | −1.24294 | ||||||||
\(789\) | −9.59949 | −0.341751 | ||||||||
\(790\) | 2.24402 | 0.0798385 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.737118 | 0.0261924 | ||||||||
\(793\) | 26.1773 | 0.929583 | ||||||||
\(794\) | −0.230021 | −0.00816313 | ||||||||
\(795\) | 6.97502 | 0.247379 | ||||||||
\(796\) | −25.3228 | −0.897543 | ||||||||
\(797\) | −35.1533 | −1.24519 | −0.622597 | − | 0.782543i | \(-0.713922\pi\) | ||||
−0.622597 | + | 0.782543i | \(0.713922\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −73.9905 | −2.61760 | ||||||||
\(800\) | 7.42135 | 0.262384 | ||||||||
\(801\) | 6.14867 | 0.217253 | ||||||||
\(802\) | 3.24154 | 0.114463 | ||||||||
\(803\) | −5.40040 | −0.190576 | ||||||||
\(804\) | −31.6796 | −1.11725 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.83512 | −0.240757 | ||||||||
\(807\) | −7.07384 | −0.249011 | ||||||||
\(808\) | −7.17071 | −0.252265 | ||||||||
\(809\) | 1.69745 | 0.0596791 | 0.0298396 | − | 0.999555i | \(-0.490500\pi\) | ||||
0.0298396 | + | 0.999555i | \(0.490500\pi\) | |||||||
\(810\) | 0.234751 | 0.00824832 | ||||||||
\(811\) | 7.74549 | 0.271981 | 0.135990 | − | 0.990710i | \(-0.456578\pi\) | ||||
0.135990 | + | 0.990710i | \(0.456578\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.4835 | 0.507958 | ||||||||
\(814\) | 0.693482 | 0.0243065 | ||||||||
\(815\) | −10.2968 | −0.360681 | ||||||||
\(816\) | 21.2760 | 0.744809 | ||||||||
\(817\) | −24.6422 | −0.862121 | ||||||||
\(818\) | 2.63274 | 0.0920515 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −28.3707 | −0.990747 | ||||||||
\(821\) | −27.2852 | −0.952260 | −0.476130 | − | 0.879375i | \(-0.657961\pi\) | ||||
−0.476130 | + | 0.879375i | \(0.657961\pi\) | |||||||
\(822\) | 3.40376 | 0.118720 | ||||||||
\(823\) | 9.30028 | 0.324187 | 0.162094 | − | 0.986775i | \(-0.448175\pi\) | ||||
0.162094 | + | 0.986775i | \(0.448175\pi\) | |||||||
\(824\) | −0.917301 | −0.0319557 | ||||||||
\(825\) | −3.40513 | −0.118551 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.1262 | 1.08236 | 0.541182 | − | 0.840905i | \(-0.317977\pi\) | ||||
0.541182 | + | 0.840905i | \(0.317977\pi\) | |||||||
\(828\) | −8.12467 | −0.282352 | ||||||||
\(829\) | 14.9080 | 0.517776 | 0.258888 | − | 0.965907i | \(-0.416644\pi\) | ||||
0.258888 | + | 0.965907i | \(0.416644\pi\) | |||||||
\(830\) | 1.58201 | 0.0549123 | ||||||||
\(831\) | −8.61734 | −0.298932 | ||||||||
\(832\) | 49.7820 | 1.72588 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.17689 | 0.0407525 | ||||||||
\(835\) | 19.9861 | 0.691646 | ||||||||
\(836\) | −11.3196 | −0.391498 | ||||||||
\(837\) | −5.30532 | −0.183379 | ||||||||
\(838\) | −5.36052 | −0.185176 | ||||||||
\(839\) | 23.3541 | 0.806272 | 0.403136 | − | 0.915140i | \(-0.367920\pi\) | ||||
0.403136 | + | 0.915140i | \(0.367920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.10404 | 0.279450 | ||||||||
\(842\) | 4.86803 | 0.167763 | ||||||||
\(843\) | 9.08125 | 0.312775 | ||||||||
\(844\) | −35.8242 | −1.23312 | ||||||||
\(845\) | −44.2479 | −1.52218 | ||||||||
\(846\) | 2.45253 | 0.0843197 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −20.9540 | −0.719562 | ||||||||
\(849\) | 4.78975 | 0.164384 | ||||||||
\(850\) | 3.54965 | 0.121752 | ||||||||
\(851\) | −15.4218 | −0.528651 | ||||||||
\(852\) | −8.20286 | −0.281025 | ||||||||
\(853\) | 15.0186 | 0.514226 | 0.257113 | − | 0.966381i | \(-0.417229\pi\) | ||||
0.257113 | + | 0.966381i | \(0.417229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.27334 | −0.248743 | ||||||||
\(856\) | 1.54154 | 0.0526888 | ||||||||
\(857\) | 51.7605 | 1.76810 | 0.884052 | − | 0.467389i | \(-0.154805\pi\) | ||||
0.884052 | + | 0.467389i | \(0.154805\pi\) | |||||||
\(858\) | 1.28835 | 0.0439836 | ||||||||
\(859\) | −12.4297 | −0.424098 | −0.212049 | − | 0.977259i | \(-0.568014\pi\) | ||||
−0.212049 | + | 0.977259i | \(0.568014\pi\) | |||||||
\(860\) | −10.6202 | −0.362145 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.99565 | 0.136092 | ||||||||
\(863\) | −16.4050 | −0.558433 | −0.279217 | − | 0.960228i | \(-0.590075\pi\) | ||||
−0.279217 | + | 0.960228i | \(0.590075\pi\) | |||||||
\(864\) | −2.17946 | −0.0741468 | ||||||||
\(865\) | −5.32655 | −0.181108 | ||||||||
\(866\) | 2.77533 | 0.0943094 | ||||||||
\(867\) | 14.4495 | 0.490732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.55912 | 0.324271 | ||||||||
\(870\) | −1.42994 | −0.0484796 | ||||||||
\(871\) | −111.714 | −3.78528 | ||||||||
\(872\) | 1.05067 | 0.0355801 | ||||||||
\(873\) | −15.3249 | −0.518668 | ||||||||
\(874\) | −4.42548 | −0.149694 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6142 | 0.358620 | ||||||||
\(877\) | 24.8896 | 0.840462 | 0.420231 | − | 0.907417i | \(-0.361949\pi\) | ||||
0.420231 | + | 0.907417i | \(0.361949\pi\) | |||||||
\(878\) | −4.61293 | −0.155679 | ||||||||
\(879\) | 13.0334 | 0.439604 | ||||||||
\(880\) | −4.79121 | −0.161512 | ||||||||
\(881\) | −24.6591 | −0.830786 | −0.415393 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415393 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.8851 | −1.24128 | −0.620641 | − | 0.784095i | \(-0.713128\pi\) | ||||
−0.620641 | + | 0.784095i | \(0.713128\pi\) | |||||||
\(884\) | 76.3937 | 2.56940 | ||||||||
\(885\) | 9.93662 | 0.334016 | ||||||||
\(886\) | 5.88458 | 0.197696 | ||||||||
\(887\) | 13.0157 | 0.437023 | 0.218512 | − | 0.975834i | \(-0.429880\pi\) | ||||
0.218512 | + | 0.975834i | \(0.429880\pi\) | |||||||
\(888\) | −2.74996 | −0.0922828 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.44341 | 0.0483831 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 41.0349 | 1.37395 | ||||||||
\(893\) | −75.9872 | −2.54281 | ||||||||
\(894\) | 3.14274 | 0.105109 | ||||||||
\(895\) | −20.4928 | −0.684999 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.6506 | −0.956615 | ||||||||
\(898\) | 2.28857 | 0.0763707 | ||||||||
\(899\) | 32.3164 | 1.07781 | ||||||||
\(900\) | 6.69260 | 0.223087 | ||||||||
\(901\) | −30.9735 | −1.03188 | ||||||||
\(902\) | 2.12467 | 0.0707437 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.67820 | −0.288633 | ||||||||
\(905\) | 15.2410 | 0.506627 | ||||||||
\(906\) | −1.20536 | −0.0400454 | ||||||||
\(907\) | 26.7445 | 0.888038 | 0.444019 | − | 0.896017i | \(-0.353552\pi\) | ||||
0.444019 | + | 0.896017i | \(0.353552\pi\) | |||||||
\(908\) | −3.03837 | −0.100832 | ||||||||
\(909\) | −9.72803 | −0.322659 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.9528 | 1.29056 | 0.645282 | − | 0.763945i | \(-0.276740\pi\) | ||||
0.645282 | + | 0.763945i | \(0.276740\pi\) | |||||||
\(912\) | 21.8501 | 0.723530 | ||||||||
\(913\) | 6.73908 | 0.223031 | ||||||||
\(914\) | 1.85802 | 0.0614580 | ||||||||
\(915\) | 4.76978 | 0.157684 | ||||||||
\(916\) | −9.48125 | −0.313269 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.04244 | −0.0344057 | ||||||||
\(919\) | 40.6154 | 1.33978 | 0.669890 | − | 0.742461i | \(-0.266341\pi\) | ||||
0.669890 | + | 0.742461i | \(0.266341\pi\) | |||||||
\(920\) | −3.84808 | −0.126867 | ||||||||
\(921\) | 11.3413 | 0.373710 | ||||||||
\(922\) | 2.73554 | 0.0900903 | ||||||||
\(923\) | −28.9263 | −0.952121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.7035 | 0.417689 | ||||||||
\(926\) | −5.34700 | −0.175713 | ||||||||
\(927\) | −1.24444 | −0.0408728 | ||||||||
\(928\) | 13.2758 | 0.435799 | ||||||||
\(929\) | −24.6644 | −0.809213 | −0.404607 | − | 0.914491i | \(-0.632592\pi\) | ||||
−0.404607 | + | 0.914491i | \(0.632592\pi\) | |||||||
\(930\) | −1.24543 | −0.0408393 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.2827 | 0.631626 | ||||||||
\(933\) | 9.20020 | 0.301201 | ||||||||
\(934\) | −0.186744 | −0.00611046 | ||||||||
\(935\) | −7.08223 | −0.231614 | ||||||||
\(936\) | −5.10889 | −0.166989 | ||||||||
\(937\) | 21.9210 | 0.716127 | 0.358064 | − | 0.933697i | \(-0.383437\pi\) | ||||
0.358064 | + | 0.933697i | \(0.383437\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5085 | −0.342930 | ||||||||
\(940\) | −32.7486 | −1.06814 | ||||||||
\(941\) | −13.6736 | −0.445747 | −0.222874 | − | 0.974847i | \(-0.571544\pi\) | ||||
−0.222874 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(942\) | 0.374159 | 0.0121907 | ||||||||
\(943\) | −47.2487 | −1.53863 | ||||||||
\(944\) | −29.8510 | −0.971567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.795340 | 0.0258587 | ||||||||
\(947\) | 11.4432 | 0.371855 | 0.185927 | − | 0.982563i | \(-0.440471\pi\) | ||||
0.185927 | + | 0.982563i | \(0.440471\pi\) | |||||||
\(948\) | −18.7879 | −0.610204 | ||||||||
\(949\) | 37.4296 | 1.21502 | ||||||||
\(950\) | 3.64544 | 0.118274 | ||||||||
\(951\) | −25.2611 | −0.819147 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.02793 | −0.0332978 | −0.0166489 | − | 0.999861i | \(-0.505300\pi\) | ||||
−0.0166489 | + | 0.999861i | \(0.505300\pi\) | |||||||
\(954\) | 1.02666 | 0.0332395 | ||||||||
\(955\) | 0.546390 | 0.0176808 | ||||||||
\(956\) | 53.8274 | 1.74090 | ||||||||
\(957\) | −6.09131 | −0.196904 | ||||||||
\(958\) | −2.79123 | −0.0901807 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.07080 | 0.292759 | ||||||||
\(961\) | −2.85353 | −0.0920494 | ||||||||
\(962\) | −4.80645 | −0.154966 | ||||||||
\(963\) | 2.09131 | 0.0673915 | ||||||||
\(964\) | −2.26811 | −0.0730509 | ||||||||
\(965\) | −4.32584 | −0.139254 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.74492 | 0.0882705 | 0.0441353 | − | 0.999026i | \(-0.485947\pi\) | ||||
0.0441353 | + | 0.999026i | \(0.485947\pi\) | |||||||
\(968\) | 0.737118 | 0.0236919 | ||||||||
\(969\) | 32.2982 | 1.03757 | ||||||||
\(970\) | −3.59753 | −0.115510 | ||||||||
\(971\) | 60.3616 | 1.93709 | 0.968547 | − | 0.248829i | \(-0.0800458\pi\) | ||||
0.968547 | + | 0.248829i | \(0.0800458\pi\) | |||||||
\(972\) | −1.96545 | −0.0630417 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.475049 | 0.0152216 | ||||||||
\(975\) | 23.6006 | 0.755824 | ||||||||
\(976\) | −14.3291 | −0.458663 | ||||||||
\(977\) | 3.21291 | 0.102790 | 0.0513951 | − | 0.998678i | \(-0.483633\pi\) | ||||
0.0513951 | + | 0.998678i | \(0.483633\pi\) | |||||||
\(978\) | −1.51560 | −0.0484635 | ||||||||
\(979\) | 6.14867 | 0.196512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.42537 | 0.0455086 | ||||||||
\(982\) | 4.93781 | 0.157572 | ||||||||
\(983\) | −17.6505 | −0.562965 | −0.281482 | − | 0.959566i | \(-0.590826\pi\) | ||||
−0.281482 | + | 0.959566i | \(0.590826\pi\) | |||||||
\(984\) | −8.42526 | −0.268587 | ||||||||
\(985\) | −22.4189 | −0.714326 | ||||||||
\(986\) | 6.34984 | 0.202220 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 78.4552 | 2.49599 | ||||||||
\(989\) | −17.6869 | −0.562411 | ||||||||
\(990\) | 0.234751 | 0.00746088 | ||||||||
\(991\) | −45.7816 | −1.45430 | −0.727151 | − | 0.686478i | \(-0.759156\pi\) | ||||
−0.727151 | + | 0.686478i | \(0.759156\pi\) | |||||||
\(992\) | 11.5628 | 0.367118 | ||||||||
\(993\) | −9.42091 | −0.298964 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.2710 | −0.515824 | ||||||||
\(996\) | −13.2453 | −0.419693 | ||||||||
\(997\) | 58.4776 | 1.85200 | 0.926002 | − | 0.377519i | \(-0.123223\pi\) | ||||
0.926002 | + | 0.377519i | \(0.123223\pi\) | |||||||
\(998\) | −1.26824 | −0.0401455 | ||||||||
\(999\) | −3.73070 | −0.118034 |
(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 | 1617.2.a.v.1.3 | yes | 4 | |
3.2 | odd | 2 | 4851.2.a.by.1.2 | 4 | |||
7.6 | odd | 2 | 1617.2.a.u.1.3 | ✓ | 4 | ||
21.20 | even | 2 | 4851.2.a.bx.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.2.a.u.1.3 | ✓ | 4 | 7.6 | odd | 2 | ||
1617.2.a.v.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
4851.2.a.bx.1.2 | 4 | 21.20 | even | 2 | |||
4851.2.a.by.1.2 | 4 | 3.2 | odd | 2 |