Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.35944 | −1.66838 | −0.834189 | − | 0.551478i | \(-0.814064\pi\) | ||||
−0.834189 | + | 0.551478i | \(0.814064\pi\) | |||||||
\(3\) | 3.36081 | 1.94037 | 0.970184 | − | 0.242372i | \(-0.0779253\pi\) | ||||
0.970184 | + | 0.242372i | \(0.0779253\pi\) | |||||||
\(4\) | 3.56697 | 1.78349 | ||||||||
\(5\) | −2.07702 | −0.928872 | −0.464436 | − | 0.885607i | \(-0.653743\pi\) | ||||
−0.464436 | + | 0.885607i | \(0.653743\pi\) | |||||||
\(6\) | −7.92965 | −3.23727 | ||||||||
\(7\) | −0.337523 | −0.127572 | −0.0637858 | − | 0.997964i | \(-0.520317\pi\) | ||||
−0.0637858 | + | 0.997964i | \(0.520317\pi\) | |||||||
\(8\) | −3.69718 | −1.30715 | ||||||||
\(9\) | 8.29507 | 2.76502 | ||||||||
\(10\) | 4.90061 | 1.54971 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 11.9879 | 3.46062 | ||||||||
\(13\) | −4.41805 | −1.22535 | −0.612673 | − | 0.790337i | \(-0.709906\pi\) | ||||
−0.612673 | + | 0.790337i | \(0.709906\pi\) | |||||||
\(14\) | 0.796366 | 0.212838 | ||||||||
\(15\) | −6.98048 | −1.80235 | ||||||||
\(16\) | 1.58935 | 0.397337 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −19.5718 | −4.61311 | ||||||||
\(19\) | −3.97263 | −0.911384 | −0.455692 | − | 0.890137i | \(-0.650608\pi\) | ||||
−0.455692 | + | 0.890137i | \(0.650608\pi\) | |||||||
\(20\) | −7.40868 | −1.65663 | ||||||||
\(21\) | −1.13435 | −0.247536 | ||||||||
\(22\) | −2.35944 | −0.503035 | ||||||||
\(23\) | −1.36597 | −0.284825 | −0.142412 | − | 0.989807i | \(-0.545486\pi\) | ||||
−0.142412 | + | 0.989807i | \(0.545486\pi\) | |||||||
\(24\) | −12.4255 | −2.53635 | ||||||||
\(25\) | −0.685985 | −0.137197 | ||||||||
\(26\) | 10.4241 | 2.04434 | ||||||||
\(27\) | 17.7958 | 3.42479 | ||||||||
\(28\) | −1.20393 | −0.227522 | ||||||||
\(29\) | −3.07221 | −0.570495 | −0.285248 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285248 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(30\) | 16.4700 | 3.00701 | ||||||||
\(31\) | 10.8484 | 1.94843 | 0.974214 | − | 0.225624i | \(-0.0724422\pi\) | ||||
0.974214 | + | 0.225624i | \(0.0724422\pi\) | |||||||
\(32\) | 3.64439 | 0.644243 | ||||||||
\(33\) | 3.36081 | 0.585043 | ||||||||
\(34\) | 2.35944 | 0.404641 | ||||||||
\(35\) | 0.701042 | 0.118498 | ||||||||
\(36\) | 29.5883 | 4.93138 | ||||||||
\(37\) | 8.29228 | 1.36324 | 0.681621 | − | 0.731706i | \(-0.261275\pi\) | ||||
0.681621 | + | 0.731706i | \(0.261275\pi\) | |||||||
\(38\) | 9.37320 | 1.52053 | ||||||||
\(39\) | −14.8482 | −2.37762 | ||||||||
\(40\) | 7.67912 | 1.21418 | ||||||||
\(41\) | 7.25830 | 1.13356 | 0.566778 | − | 0.823871i | \(-0.308190\pi\) | ||||
0.566778 | + | 0.823871i | \(0.308190\pi\) | |||||||
\(42\) | 2.67644 | 0.412983 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 3.56697 | 0.537741 | ||||||||
\(45\) | −17.2290 | −2.56835 | ||||||||
\(46\) | 3.22293 | 0.475195 | ||||||||
\(47\) | −1.36584 | −0.199229 | −0.0996143 | − | 0.995026i | \(-0.531761\pi\) | ||||
−0.0996143 | + | 0.995026i | \(0.531761\pi\) | |||||||
\(48\) | 5.34150 | 0.770979 | ||||||||
\(49\) | −6.88608 | −0.983725 | ||||||||
\(50\) | 1.61854 | 0.228897 | ||||||||
\(51\) | −3.36081 | −0.470608 | ||||||||
\(52\) | −15.7590 | −2.18539 | ||||||||
\(53\) | 5.56854 | 0.764898 | 0.382449 | − | 0.923977i | \(-0.375081\pi\) | ||||
0.382449 | + | 0.923977i | \(0.375081\pi\) | |||||||
\(54\) | −41.9881 | −5.71385 | ||||||||
\(55\) | −2.07702 | −0.280065 | ||||||||
\(56\) | 1.24788 | 0.166755 | ||||||||
\(57\) | −13.3513 | −1.76842 | ||||||||
\(58\) | 7.24871 | 0.951802 | ||||||||
\(59\) | −6.38624 | −0.831418 | −0.415709 | − | 0.909498i | \(-0.636467\pi\) | ||||
−0.415709 | + | 0.909498i | \(0.636467\pi\) | |||||||
\(60\) | −24.8992 | −3.21447 | ||||||||
\(61\) | −4.07858 | −0.522208 | −0.261104 | − | 0.965311i | \(-0.584087\pi\) | ||||
−0.261104 | + | 0.965311i | \(0.584087\pi\) | |||||||
\(62\) | −25.5962 | −3.25072 | ||||||||
\(63\) | −2.79978 | −0.352739 | ||||||||
\(64\) | −11.7774 | −1.47218 | ||||||||
\(65\) | 9.17637 | 1.13819 | ||||||||
\(66\) | −7.92965 | −0.976072 | ||||||||
\(67\) | 8.90319 | 1.08770 | 0.543849 | − | 0.839183i | \(-0.316966\pi\) | ||||
0.543849 | + | 0.839183i | \(0.316966\pi\) | |||||||
\(68\) | −3.56697 | −0.432559 | ||||||||
\(69\) | −4.59078 | −0.552664 | ||||||||
\(70\) | −1.65407 | −0.197699 | ||||||||
\(71\) | 2.21407 | 0.262762 | 0.131381 | − | 0.991332i | \(-0.458059\pi\) | ||||
0.131381 | + | 0.991332i | \(0.458059\pi\) | |||||||
\(72\) | −30.6684 | −3.61430 | ||||||||
\(73\) | −8.86341 | −1.03738 | −0.518692 | − | 0.854961i | \(-0.673581\pi\) | ||||
−0.518692 | + | 0.854961i | \(0.673581\pi\) | |||||||
\(74\) | −19.5652 | −2.27440 | ||||||||
\(75\) | −2.30547 | −0.266213 | ||||||||
\(76\) | −14.1703 | −1.62544 | ||||||||
\(77\) | −0.337523 | −0.0384643 | ||||||||
\(78\) | 35.0336 | 3.96677 | ||||||||
\(79\) | 12.6005 | 1.41767 | 0.708835 | − | 0.705374i | \(-0.249221\pi\) | ||||
0.708835 | + | 0.705374i | \(0.249221\pi\) | |||||||
\(80\) | −3.30111 | −0.369075 | ||||||||
\(81\) | 34.9230 | 3.88033 | ||||||||
\(82\) | −17.1255 | −1.89120 | ||||||||
\(83\) | −2.84870 | −0.312686 | −0.156343 | − | 0.987703i | \(-0.549971\pi\) | ||||
−0.156343 | + | 0.987703i | \(0.549971\pi\) | |||||||
\(84\) | −4.04620 | −0.441477 | ||||||||
\(85\) | 2.07702 | 0.225285 | ||||||||
\(86\) | 2.35944 | 0.254425 | ||||||||
\(87\) | −10.3251 | −1.10697 | ||||||||
\(88\) | −3.69718 | −0.394121 | ||||||||
\(89\) | −2.02201 | −0.214332 | −0.107166 | − | 0.994241i | \(-0.534178\pi\) | ||||
−0.107166 | + | 0.994241i | \(0.534178\pi\) | |||||||
\(90\) | 40.6509 | 4.28498 | ||||||||
\(91\) | 1.49119 | 0.156319 | ||||||||
\(92\) | −4.87238 | −0.507981 | ||||||||
\(93\) | 36.4594 | 3.78067 | ||||||||
\(94\) | 3.22263 | 0.332389 | ||||||||
\(95\) | 8.25124 | 0.846559 | ||||||||
\(96\) | 12.2481 | 1.25007 | ||||||||
\(97\) | −4.54717 | −0.461695 | −0.230848 | − | 0.972990i | \(-0.574150\pi\) | ||||
−0.230848 | + | 0.972990i | \(0.574150\pi\) | |||||||
\(98\) | 16.2473 | 1.64123 | ||||||||
\(99\) | 8.29507 | 0.833686 | ||||||||
\(100\) | −2.44689 | −0.244689 | ||||||||
\(101\) | 9.41960 | 0.937285 | 0.468642 | − | 0.883388i | \(-0.344743\pi\) | ||||
0.468642 | + | 0.883388i | \(0.344743\pi\) | |||||||
\(102\) | 7.92965 | 0.785152 | ||||||||
\(103\) | −6.17442 | −0.608384 | −0.304192 | − | 0.952611i | \(-0.598386\pi\) | ||||
−0.304192 | + | 0.952611i | \(0.598386\pi\) | |||||||
\(104\) | 16.3343 | 1.60171 | ||||||||
\(105\) | 2.35607 | 0.229929 | ||||||||
\(106\) | −13.1386 | −1.27614 | ||||||||
\(107\) | 9.65230 | 0.933123 | 0.466561 | − | 0.884489i | \(-0.345493\pi\) | ||||
0.466561 | + | 0.884489i | \(0.345493\pi\) | |||||||
\(108\) | 63.4770 | 6.10807 | ||||||||
\(109\) | −2.50036 | −0.239491 | −0.119745 | − | 0.992805i | \(-0.538208\pi\) | ||||
−0.119745 | + | 0.992805i | \(0.538208\pi\) | |||||||
\(110\) | 4.90061 | 0.467255 | ||||||||
\(111\) | 27.8688 | 2.64519 | ||||||||
\(112\) | −0.536441 | −0.0506889 | ||||||||
\(113\) | −6.96650 | −0.655353 | −0.327677 | − | 0.944790i | \(-0.606266\pi\) | ||||
−0.327677 | + | 0.944790i | \(0.606266\pi\) | |||||||
\(114\) | 31.5016 | 2.95039 | ||||||||
\(115\) | 2.83715 | 0.264566 | ||||||||
\(116\) | −10.9585 | −1.01747 | ||||||||
\(117\) | −36.6480 | −3.38811 | ||||||||
\(118\) | 15.0680 | 1.38712 | ||||||||
\(119\) | 0.337523 | 0.0309407 | ||||||||
\(120\) | 25.8081 | 2.35595 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.62317 | 0.871241 | ||||||||
\(123\) | 24.3938 | 2.19951 | ||||||||
\(124\) | 38.6959 | 3.47500 | ||||||||
\(125\) | 11.8099 | 1.05631 | ||||||||
\(126\) | 6.60591 | 0.588502 | ||||||||
\(127\) | 2.95295 | 0.262032 | 0.131016 | − | 0.991380i | \(-0.458176\pi\) | ||||
0.131016 | + | 0.991380i | \(0.458176\pi\) | |||||||
\(128\) | 20.4994 | 1.81191 | ||||||||
\(129\) | −3.36081 | −0.295903 | ||||||||
\(130\) | −21.6511 | −1.89893 | ||||||||
\(131\) | 12.9188 | 1.12872 | 0.564360 | − | 0.825529i | \(-0.309123\pi\) | ||||
0.564360 | + | 0.825529i | \(0.309123\pi\) | |||||||
\(132\) | 11.9879 | 1.04342 | ||||||||
\(133\) | 1.34085 | 0.116267 | ||||||||
\(134\) | −21.0066 | −1.81469 | ||||||||
\(135\) | −36.9622 | −3.18120 | ||||||||
\(136\) | 3.69718 | 0.317031 | ||||||||
\(137\) | 17.3914 | 1.48585 | 0.742925 | − | 0.669375i | \(-0.233438\pi\) | ||||
0.742925 | + | 0.669375i | \(0.233438\pi\) | |||||||
\(138\) | 10.8317 | 0.922053 | ||||||||
\(139\) | −16.9105 | −1.43433 | −0.717165 | − | 0.696904i | \(-0.754561\pi\) | ||||
−0.717165 | + | 0.696904i | \(0.754561\pi\) | |||||||
\(140\) | 2.50060 | 0.211339 | ||||||||
\(141\) | −4.59034 | −0.386577 | ||||||||
\(142\) | −5.22397 | −0.438386 | ||||||||
\(143\) | −4.41805 | −0.369456 | ||||||||
\(144\) | 13.1837 | 1.09865 | ||||||||
\(145\) | 6.38105 | 0.529917 | ||||||||
\(146\) | 20.9127 | 1.73075 | ||||||||
\(147\) | −23.1428 | −1.90879 | ||||||||
\(148\) | 29.5783 | 2.43132 | ||||||||
\(149\) | 21.5320 | 1.76397 | 0.881984 | − | 0.471280i | \(-0.156208\pi\) | ||||
0.881984 | + | 0.471280i | \(0.156208\pi\) | |||||||
\(150\) | 5.43962 | 0.444143 | ||||||||
\(151\) | 2.06410 | 0.167974 | 0.0839872 | − | 0.996467i | \(-0.473235\pi\) | ||||
0.0839872 | + | 0.996467i | \(0.473235\pi\) | |||||||
\(152\) | 14.6875 | 1.19132 | ||||||||
\(153\) | −8.29507 | −0.670617 | ||||||||
\(154\) | 0.796366 | 0.0641730 | ||||||||
\(155\) | −22.5323 | −1.80984 | ||||||||
\(156\) | −52.9632 | −4.24045 | ||||||||
\(157\) | 13.4726 | 1.07523 | 0.537616 | − | 0.843190i | \(-0.319325\pi\) | ||||
0.537616 | + | 0.843190i | \(0.319325\pi\) | |||||||
\(158\) | −29.7302 | −2.36521 | ||||||||
\(159\) | 18.7148 | 1.48418 | ||||||||
\(160\) | −7.56948 | −0.598420 | ||||||||
\(161\) | 0.461046 | 0.0363356 | ||||||||
\(162\) | −82.3989 | −6.47387 | ||||||||
\(163\) | 6.11928 | 0.479299 | 0.239650 | − | 0.970859i | \(-0.422967\pi\) | ||||
0.239650 | + | 0.970859i | \(0.422967\pi\) | |||||||
\(164\) | 25.8902 | 2.02168 | ||||||||
\(165\) | −6.98048 | −0.543430 | ||||||||
\(166\) | 6.72136 | 0.521678 | ||||||||
\(167\) | 13.4644 | 1.04191 | 0.520953 | − | 0.853585i | \(-0.325577\pi\) | ||||
0.520953 | + | 0.853585i | \(0.325577\pi\) | |||||||
\(168\) | 4.19390 | 0.323567 | ||||||||
\(169\) | 6.51914 | 0.501472 | ||||||||
\(170\) | −4.90061 | −0.375860 | ||||||||
\(171\) | −32.9533 | −2.52000 | ||||||||
\(172\) | −3.56697 | −0.271979 | ||||||||
\(173\) | 17.8587 | 1.35777 | 0.678886 | − | 0.734243i | \(-0.262463\pi\) | ||||
0.678886 | + | 0.734243i | \(0.262463\pi\) | |||||||
\(174\) | 24.3616 | 1.84685 | ||||||||
\(175\) | 0.231536 | 0.0175025 | ||||||||
\(176\) | 1.58935 | 0.119802 | ||||||||
\(177\) | −21.4630 | −1.61326 | ||||||||
\(178\) | 4.77081 | 0.357587 | ||||||||
\(179\) | 13.4325 | 1.00399 | 0.501994 | − | 0.864871i | \(-0.332600\pi\) | ||||
0.501994 | + | 0.864871i | \(0.332600\pi\) | |||||||
\(180\) | −61.4555 | −4.58062 | ||||||||
\(181\) | −10.8415 | −0.805842 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(182\) | −3.51838 | −0.260800 | ||||||||
\(183\) | −13.7073 | −1.01328 | ||||||||
\(184\) | 5.05024 | 0.372309 | ||||||||
\(185\) | −17.2232 | −1.26628 | ||||||||
\(186\) | −86.0240 | −6.30758 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −4.87192 | −0.355321 | ||||||||
\(189\) | −6.00647 | −0.436907 | ||||||||
\(190\) | −19.4683 | −1.41238 | ||||||||
\(191\) | 0.770083 | 0.0557212 | 0.0278606 | − | 0.999612i | \(-0.491131\pi\) | ||||
0.0278606 | + | 0.999612i | \(0.491131\pi\) | |||||||
\(192\) | −39.5817 | −2.85657 | ||||||||
\(193\) | 1.00907 | 0.0726342 | 0.0363171 | − | 0.999340i | \(-0.488437\pi\) | ||||
0.0363171 | + | 0.999340i | \(0.488437\pi\) | |||||||
\(194\) | 10.7288 | 0.770282 | ||||||||
\(195\) | 30.8401 | 2.20850 | ||||||||
\(196\) | −24.5625 | −1.75446 | ||||||||
\(197\) | −3.76355 | −0.268141 | −0.134071 | − | 0.990972i | \(-0.542805\pi\) | ||||
−0.134071 | + | 0.990972i | \(0.542805\pi\) | |||||||
\(198\) | −19.5718 | −1.39090 | ||||||||
\(199\) | 8.12239 | 0.575781 | 0.287891 | − | 0.957663i | \(-0.407046\pi\) | ||||
0.287891 | + | 0.957663i | \(0.407046\pi\) | |||||||
\(200\) | 2.53621 | 0.179337 | ||||||||
\(201\) | 29.9220 | 2.11053 | ||||||||
\(202\) | −22.2250 | −1.56375 | ||||||||
\(203\) | 1.03694 | 0.0727790 | ||||||||
\(204\) | −11.9879 | −0.839323 | ||||||||
\(205\) | −15.0756 | −1.05293 | ||||||||
\(206\) | 14.5682 | 1.01501 | ||||||||
\(207\) | −11.3308 | −0.787547 | ||||||||
\(208\) | −7.02181 | −0.486875 | ||||||||
\(209\) | −3.97263 | −0.274793 | ||||||||
\(210\) | −5.55902 | −0.383609 | ||||||||
\(211\) | −12.3384 | −0.849407 | −0.424704 | − | 0.905332i | \(-0.639622\pi\) | ||||
−0.424704 | + | 0.905332i | \(0.639622\pi\) | |||||||
\(212\) | 19.8628 | 1.36418 | ||||||||
\(213\) | 7.44108 | 0.509854 | ||||||||
\(214\) | −22.7740 | −1.55680 | ||||||||
\(215\) | 2.07702 | 0.141652 | ||||||||
\(216\) | −65.7941 | −4.47672 | ||||||||
\(217\) | −3.66158 | −0.248564 | ||||||||
\(218\) | 5.89945 | 0.399561 | ||||||||
\(219\) | −29.7883 | −2.01291 | ||||||||
\(220\) | −7.40868 | −0.499493 | ||||||||
\(221\) | 4.41805 | 0.297190 | ||||||||
\(222\) | −65.7548 | −4.41318 | ||||||||
\(223\) | 14.1723 | 0.949044 | 0.474522 | − | 0.880244i | \(-0.342621\pi\) | ||||
0.474522 | + | 0.880244i | \(0.342621\pi\) | |||||||
\(224\) | −1.23007 | −0.0821872 | ||||||||
\(225\) | −5.69030 | −0.379353 | ||||||||
\(226\) | 16.4371 | 1.09338 | ||||||||
\(227\) | 10.7318 | 0.712297 | 0.356149 | − | 0.934429i | \(-0.384090\pi\) | ||||
0.356149 | + | 0.934429i | \(0.384090\pi\) | |||||||
\(228\) | −47.6236 | −3.15395 | ||||||||
\(229\) | 16.9360 | 1.11916 | 0.559580 | − | 0.828776i | \(-0.310962\pi\) | ||||
0.559580 | + | 0.828776i | \(0.310962\pi\) | |||||||
\(230\) | −6.69410 | −0.441396 | ||||||||
\(231\) | −1.13435 | −0.0746349 | ||||||||
\(232\) | 11.3585 | 0.745724 | ||||||||
\(233\) | −9.96306 | −0.652702 | −0.326351 | − | 0.945249i | \(-0.605819\pi\) | ||||
−0.326351 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(234\) | 86.4689 | 5.65265 | ||||||||
\(235\) | 2.83688 | 0.185058 | ||||||||
\(236\) | −22.7795 | −1.48282 | ||||||||
\(237\) | 42.3480 | 2.75080 | ||||||||
\(238\) | −0.796366 | −0.0516207 | ||||||||
\(239\) | −1.81570 | −0.117448 | −0.0587240 | − | 0.998274i | \(-0.518703\pi\) | ||||
−0.0587240 | + | 0.998274i | \(0.518703\pi\) | |||||||
\(240\) | −11.0944 | −0.716141 | ||||||||
\(241\) | −3.91834 | −0.252402 | −0.126201 | − | 0.992005i | \(-0.540279\pi\) | ||||
−0.126201 | + | 0.992005i | \(0.540279\pi\) | |||||||
\(242\) | −2.35944 | −0.151671 | ||||||||
\(243\) | 63.9825 | 4.10448 | ||||||||
\(244\) | −14.5482 | −0.931351 | ||||||||
\(245\) | 14.3025 | 0.913755 | ||||||||
\(246\) | −57.5558 | −3.66962 | ||||||||
\(247\) | 17.5513 | 1.11676 | ||||||||
\(248\) | −40.1085 | −2.54689 | ||||||||
\(249\) | −9.57397 | −0.606725 | ||||||||
\(250\) | −27.8648 | −1.76233 | ||||||||
\(251\) | −20.5519 | −1.29722 | −0.648611 | − | 0.761120i | \(-0.724650\pi\) | ||||
−0.648611 | + | 0.761120i | \(0.724650\pi\) | |||||||
\(252\) | −9.98672 | −0.629105 | ||||||||
\(253\) | −1.36597 | −0.0858779 | ||||||||
\(254\) | −6.96732 | −0.437169 | ||||||||
\(255\) | 6.98048 | 0.437135 | ||||||||
\(256\) | −24.8123 | −1.55077 | ||||||||
\(257\) | −20.4704 | −1.27691 | −0.638453 | − | 0.769660i | \(-0.720426\pi\) | ||||
−0.638453 | + | 0.769660i | \(0.720426\pi\) | |||||||
\(258\) | 7.92965 | 0.493678 | ||||||||
\(259\) | −2.79883 | −0.173911 | ||||||||
\(260\) | 32.7319 | 2.02994 | ||||||||
\(261\) | −25.4842 | −1.57743 | ||||||||
\(262\) | −30.4812 | −1.88313 | ||||||||
\(263\) | 12.9079 | 0.795938 | 0.397969 | − | 0.917399i | \(-0.369715\pi\) | ||||
0.397969 | + | 0.917399i | \(0.369715\pi\) | |||||||
\(264\) | −12.4255 | −0.764739 | ||||||||
\(265\) | −11.5660 | −0.710492 | ||||||||
\(266\) | −3.16367 | −0.193977 | ||||||||
\(267\) | −6.79559 | −0.415883 | ||||||||
\(268\) | 31.7574 | 1.93989 | ||||||||
\(269\) | 22.5383 | 1.37419 | 0.687093 | − | 0.726570i | \(-0.258887\pi\) | ||||
0.687093 | + | 0.726570i | \(0.258887\pi\) | |||||||
\(270\) | 87.2101 | 5.30744 | ||||||||
\(271\) | 9.55883 | 0.580658 | 0.290329 | − | 0.956927i | \(-0.406235\pi\) | ||||
0.290329 | + | 0.956927i | \(0.406235\pi\) | |||||||
\(272\) | −1.58935 | −0.0963683 | ||||||||
\(273\) | 5.01162 | 0.303317 | ||||||||
\(274\) | −41.0341 | −2.47896 | ||||||||
\(275\) | −0.685985 | −0.0413665 | ||||||||
\(276\) | −16.3752 | −0.985669 | ||||||||
\(277\) | 30.9053 | 1.85692 | 0.928459 | − | 0.371434i | \(-0.121134\pi\) | ||||
0.928459 | + | 0.371434i | \(0.121134\pi\) | |||||||
\(278\) | 39.8994 | 2.39300 | ||||||||
\(279\) | 89.9882 | 5.38745 | ||||||||
\(280\) | −2.59188 | −0.154894 | ||||||||
\(281\) | −4.37637 | −0.261073 | −0.130536 | − | 0.991444i | \(-0.541670\pi\) | ||||
−0.130536 | + | 0.991444i | \(0.541670\pi\) | |||||||
\(282\) | 10.8307 | 0.644956 | ||||||||
\(283\) | −2.52979 | −0.150380 | −0.0751902 | − | 0.997169i | \(-0.523956\pi\) | ||||
−0.0751902 | + | 0.997169i | \(0.523956\pi\) | |||||||
\(284\) | 7.89753 | 0.468632 | ||||||||
\(285\) | 27.7309 | 1.64264 | ||||||||
\(286\) | 10.4241 | 0.616392 | ||||||||
\(287\) | −2.44984 | −0.144610 | ||||||||
\(288\) | 30.2305 | 1.78135 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −15.0557 | −0.884102 | ||||||||
\(291\) | −15.2822 | −0.895858 | ||||||||
\(292\) | −31.6156 | −1.85016 | ||||||||
\(293\) | −13.9521 | −0.815090 | −0.407545 | − | 0.913185i | \(-0.633615\pi\) | ||||
−0.407545 | + | 0.913185i | \(0.633615\pi\) | |||||||
\(294\) | 54.6042 | 3.18458 | ||||||||
\(295\) | 13.2644 | 0.772281 | ||||||||
\(296\) | −30.6581 | −1.78196 | ||||||||
\(297\) | 17.7958 | 1.03261 | ||||||||
\(298\) | −50.8034 | −2.94296 | ||||||||
\(299\) | 6.03492 | 0.349009 | ||||||||
\(300\) | −8.22354 | −0.474786 | ||||||||
\(301\) | 0.337523 | 0.0194545 | ||||||||
\(302\) | −4.87014 | −0.280245 | ||||||||
\(303\) | 31.6575 | 1.81868 | ||||||||
\(304\) | −6.31389 | −0.362126 | ||||||||
\(305\) | 8.47129 | 0.485065 | ||||||||
\(306\) | 19.5718 | 1.11884 | ||||||||
\(307\) | −27.4919 | −1.56904 | −0.784522 | − | 0.620101i | \(-0.787092\pi\) | ||||
−0.784522 | + | 0.620101i | \(0.787092\pi\) | |||||||
\(308\) | −1.20393 | −0.0686005 | ||||||||
\(309\) | −20.7511 | −1.18049 | ||||||||
\(310\) | 53.1638 | 3.01950 | ||||||||
\(311\) | −6.52604 | −0.370058 | −0.185029 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185029 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(312\) | 54.8966 | 3.10791 | ||||||||
\(313\) | 12.7582 | 0.721139 | 0.360569 | − | 0.932732i | \(-0.382582\pi\) | ||||
0.360569 | + | 0.932732i | \(0.382582\pi\) | |||||||
\(314\) | −31.7879 | −1.79389 | ||||||||
\(315\) | 5.81519 | 0.327649 | ||||||||
\(316\) | 44.9457 | 2.52840 | ||||||||
\(317\) | 25.2961 | 1.42077 | 0.710385 | − | 0.703814i | \(-0.248521\pi\) | ||||
0.710385 | + | 0.703814i | \(0.248521\pi\) | |||||||
\(318\) | −44.1566 | −2.47618 | ||||||||
\(319\) | −3.07221 | −0.172011 | ||||||||
\(320\) | 24.4620 | 1.36747 | ||||||||
\(321\) | 32.4396 | 1.81060 | ||||||||
\(322\) | −1.08781 | −0.0606214 | ||||||||
\(323\) | 3.97263 | 0.221043 | ||||||||
\(324\) | 124.569 | 6.92052 | ||||||||
\(325\) | 3.03071 | 0.168114 | ||||||||
\(326\) | −14.4381 | −0.799652 | ||||||||
\(327\) | −8.40323 | −0.464700 | ||||||||
\(328\) | −26.8353 | −1.48173 | ||||||||
\(329\) | 0.461003 | 0.0254159 | ||||||||
\(330\) | 16.4700 | 0.906646 | ||||||||
\(331\) | 25.9915 | 1.42862 | 0.714312 | − | 0.699827i | \(-0.246740\pi\) | ||||
0.714312 | + | 0.699827i | \(0.246740\pi\) | |||||||
\(332\) | −10.1612 | −0.557671 | ||||||||
\(333\) | 68.7850 | 3.76940 | ||||||||
\(334\) | −31.7685 | −1.73829 | ||||||||
\(335\) | −18.4921 | −1.01033 | ||||||||
\(336\) | −1.80288 | −0.0983550 | ||||||||
\(337\) | −11.3756 | −0.619671 | −0.309835 | − | 0.950790i | \(-0.600274\pi\) | ||||
−0.309835 | + | 0.950790i | \(0.600274\pi\) | |||||||
\(338\) | −15.3815 | −0.836645 | ||||||||
\(339\) | −23.4131 | −1.27163 | ||||||||
\(340\) | 7.40868 | 0.401792 | ||||||||
\(341\) | 10.8484 | 0.587473 | ||||||||
\(342\) | 77.7514 | 4.20431 | ||||||||
\(343\) | 4.68687 | 0.253067 | ||||||||
\(344\) | 3.69718 | 0.199339 | ||||||||
\(345\) | 9.53514 | 0.513354 | ||||||||
\(346\) | −42.1366 | −2.26528 | ||||||||
\(347\) | 17.1926 | 0.922945 | 0.461472 | − | 0.887155i | \(-0.347321\pi\) | ||||
0.461472 | + | 0.887155i | \(0.347321\pi\) | |||||||
\(348\) | −36.8295 | −1.97427 | ||||||||
\(349\) | 4.40790 | 0.235949 | 0.117975 | − | 0.993017i | \(-0.462360\pi\) | ||||
0.117975 | + | 0.993017i | \(0.462360\pi\) | |||||||
\(350\) | −0.546295 | −0.0292007 | ||||||||
\(351\) | −78.6225 | −4.19656 | ||||||||
\(352\) | 3.64439 | 0.194247 | ||||||||
\(353\) | −12.6940 | −0.675636 | −0.337818 | − | 0.941211i | \(-0.609689\pi\) | ||||
−0.337818 | + | 0.941211i | \(0.609689\pi\) | |||||||
\(354\) | 50.6407 | 2.69152 | ||||||||
\(355\) | −4.59867 | −0.244072 | ||||||||
\(356\) | −7.21244 | −0.382259 | ||||||||
\(357\) | 1.13435 | 0.0600363 | ||||||||
\(358\) | −31.6931 | −1.67503 | ||||||||
\(359\) | 35.6820 | 1.88323 | 0.941613 | − | 0.336697i | \(-0.109310\pi\) | ||||
0.941613 | + | 0.336697i | \(0.109310\pi\) | |||||||
\(360\) | 63.6989 | 3.35723 | ||||||||
\(361\) | −3.21820 | −0.169379 | ||||||||
\(362\) | 25.5799 | 1.34445 | ||||||||
\(363\) | 3.36081 | 0.176397 | ||||||||
\(364\) | 5.31904 | 0.278793 | ||||||||
\(365\) | 18.4095 | 0.963597 | ||||||||
\(366\) | 32.3417 | 1.69053 | ||||||||
\(367\) | −36.2408 | −1.89175 | −0.945877 | − | 0.324524i | \(-0.894796\pi\) | ||||
−0.945877 | + | 0.324524i | \(0.894796\pi\) | |||||||
\(368\) | −2.17100 | −0.113171 | ||||||||
\(369\) | 60.2081 | 3.13431 | ||||||||
\(370\) | 40.6372 | 2.11263 | ||||||||
\(371\) | −1.87951 | −0.0975792 | ||||||||
\(372\) | 130.050 | 6.74277 | ||||||||
\(373\) | −21.2432 | −1.09993 | −0.549967 | − | 0.835187i | \(-0.685360\pi\) | ||||
−0.549967 | + | 0.835187i | \(0.685360\pi\) | |||||||
\(374\) | 2.35944 | 0.122004 | ||||||||
\(375\) | 39.6909 | 2.04963 | ||||||||
\(376\) | 5.04977 | 0.260422 | ||||||||
\(377\) | 13.5732 | 0.699054 | ||||||||
\(378\) | 14.1719 | 0.728926 | ||||||||
\(379\) | −4.01803 | −0.206393 | −0.103196 | − | 0.994661i | \(-0.532907\pi\) | ||||
−0.103196 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(380\) | 29.4319 | 1.50983 | ||||||||
\(381\) | 9.92432 | 0.508438 | ||||||||
\(382\) | −1.81697 | −0.0929641 | ||||||||
\(383\) | −17.3698 | −0.887556 | −0.443778 | − | 0.896137i | \(-0.646362\pi\) | ||||
−0.443778 | + | 0.896137i | \(0.646362\pi\) | |||||||
\(384\) | 68.8946 | 3.51576 | ||||||||
\(385\) | 0.701042 | 0.0357284 | ||||||||
\(386\) | −2.38083 | −0.121181 | ||||||||
\(387\) | −8.29507 | −0.421662 | ||||||||
\(388\) | −16.2196 | −0.823427 | ||||||||
\(389\) | 12.7440 | 0.646147 | 0.323074 | − | 0.946374i | \(-0.395284\pi\) | ||||
0.323074 | + | 0.946374i | \(0.395284\pi\) | |||||||
\(390\) | −72.7654 | −3.68462 | ||||||||
\(391\) | 1.36597 | 0.0690801 | ||||||||
\(392\) | 25.4591 | 1.28588 | ||||||||
\(393\) | 43.4177 | 2.19013 | ||||||||
\(394\) | 8.87987 | 0.447361 | ||||||||
\(395\) | −26.1716 | −1.31683 | ||||||||
\(396\) | 29.5883 | 1.48687 | ||||||||
\(397\) | −30.0644 | −1.50889 | −0.754445 | − | 0.656363i | \(-0.772094\pi\) | ||||
−0.754445 | + | 0.656363i | \(0.772094\pi\) | |||||||
\(398\) | −19.1643 | −0.960621 | ||||||||
\(399\) | 4.50636 | 0.225600 | ||||||||
\(400\) | −1.09027 | −0.0545134 | ||||||||
\(401\) | 14.6341 | 0.730794 | 0.365397 | − | 0.930852i | \(-0.380933\pi\) | ||||
0.365397 | + | 0.930852i | \(0.380933\pi\) | |||||||
\(402\) | −70.5992 | −3.52117 | ||||||||
\(403\) | −47.9287 | −2.38750 | ||||||||
\(404\) | 33.5994 | 1.67163 | ||||||||
\(405\) | −72.5358 | −3.60433 | ||||||||
\(406\) | −2.44661 | −0.121423 | ||||||||
\(407\) | 8.29228 | 0.411033 | ||||||||
\(408\) | 12.4255 | 0.615156 | ||||||||
\(409\) | −5.37086 | −0.265572 | −0.132786 | − | 0.991145i | \(-0.542392\pi\) | ||||
−0.132786 | + | 0.991145i | \(0.542392\pi\) | |||||||
\(410\) | 35.5701 | 1.75668 | ||||||||
\(411\) | 58.4494 | 2.88309 | ||||||||
\(412\) | −22.0240 | −1.08504 | ||||||||
\(413\) | 2.15550 | 0.106065 | ||||||||
\(414\) | 26.7345 | 1.31393 | ||||||||
\(415\) | 5.91682 | 0.290445 | ||||||||
\(416\) | −16.1011 | −0.789421 | ||||||||
\(417\) | −56.8330 | −2.78313 | ||||||||
\(418\) | 9.37320 | 0.458458 | ||||||||
\(419\) | −20.6886 | −1.01070 | −0.505352 | − | 0.862914i | \(-0.668637\pi\) | ||||
−0.505352 | + | 0.862914i | \(0.668637\pi\) | |||||||
\(420\) | 8.40404 | 0.410075 | ||||||||
\(421\) | 30.3001 | 1.47674 | 0.738369 | − | 0.674397i | \(-0.235596\pi\) | ||||
0.738369 | + | 0.674397i | \(0.235596\pi\) | |||||||
\(422\) | 29.1116 | 1.41713 | ||||||||
\(423\) | −11.3298 | −0.550872 | ||||||||
\(424\) | −20.5879 | −0.999837 | ||||||||
\(425\) | 0.685985 | 0.0332752 | ||||||||
\(426\) | −17.5568 | −0.850630 | ||||||||
\(427\) | 1.37661 | 0.0666190 | ||||||||
\(428\) | 34.4295 | 1.66421 | ||||||||
\(429\) | −14.8482 | −0.716879 | ||||||||
\(430\) | −4.90061 | −0.236329 | ||||||||
\(431\) | 19.5301 | 0.940734 | 0.470367 | − | 0.882471i | \(-0.344122\pi\) | ||||
0.470367 | + | 0.882471i | \(0.344122\pi\) | |||||||
\(432\) | 28.2836 | 1.36080 | ||||||||
\(433\) | 16.0481 | 0.771224 | 0.385612 | − | 0.922661i | \(-0.373990\pi\) | ||||
0.385612 | + | 0.922661i | \(0.373990\pi\) | |||||||
\(434\) | 8.63929 | 0.414699 | ||||||||
\(435\) | 21.4455 | 1.02823 | ||||||||
\(436\) | −8.91870 | −0.427128 | ||||||||
\(437\) | 5.42650 | 0.259585 | ||||||||
\(438\) | 70.2838 | 3.35829 | ||||||||
\(439\) | −2.35071 | −0.112193 | −0.0560966 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560966 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(440\) | 7.67912 | 0.366088 | ||||||||
\(441\) | −57.1205 | −2.72002 | ||||||||
\(442\) | −10.4241 | −0.495825 | ||||||||
\(443\) | −0.379417 | −0.0180266 | −0.00901331 | − | 0.999959i | \(-0.502869\pi\) | ||||
−0.00901331 | + | 0.999959i | \(0.502869\pi\) | |||||||
\(444\) | 99.4072 | 4.71766 | ||||||||
\(445\) | 4.19975 | 0.199087 | ||||||||
\(446\) | −33.4386 | −1.58336 | ||||||||
\(447\) | 72.3649 | 3.42274 | ||||||||
\(448\) | 3.97515 | 0.187808 | ||||||||
\(449\) | −17.1371 | −0.808750 | −0.404375 | − | 0.914593i | \(-0.632511\pi\) | ||||
−0.404375 | + | 0.914593i | \(0.632511\pi\) | |||||||
\(450\) | 13.4259 | 0.632905 | ||||||||
\(451\) | 7.25830 | 0.341780 | ||||||||
\(452\) | −24.8493 | −1.16881 | ||||||||
\(453\) | 6.93707 | 0.325932 | ||||||||
\(454\) | −25.3212 | −1.18838 | ||||||||
\(455\) | −3.09724 | −0.145201 | ||||||||
\(456\) | 49.3621 | 2.31159 | ||||||||
\(457\) | −26.6400 | −1.24617 | −0.623084 | − | 0.782155i | \(-0.714121\pi\) | ||||
−0.623084 | + | 0.782155i | \(0.714121\pi\) | |||||||
\(458\) | −39.9594 | −1.86718 | ||||||||
\(459\) | −17.7958 | −0.830635 | ||||||||
\(460\) | 10.1200 | 0.471849 | ||||||||
\(461\) | −16.2355 | −0.756162 | −0.378081 | − | 0.925773i | \(-0.623416\pi\) | ||||
−0.378081 | + | 0.925773i | \(0.623416\pi\) | |||||||
\(462\) | 2.67644 | 0.124519 | ||||||||
\(463\) | −11.0304 | −0.512628 | −0.256314 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256314 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(464\) | −4.88281 | −0.226679 | ||||||||
\(465\) | −75.7270 | −3.51176 | ||||||||
\(466\) | 23.5073 | 1.08895 | ||||||||
\(467\) | −29.4707 | −1.36374 | −0.681870 | − | 0.731473i | \(-0.738833\pi\) | ||||
−0.681870 | + | 0.731473i | \(0.738833\pi\) | |||||||
\(468\) | −130.722 | −6.04265 | ||||||||
\(469\) | −3.00503 | −0.138759 | ||||||||
\(470\) | −6.69347 | −0.308747 | ||||||||
\(471\) | 45.2790 | 2.08635 | ||||||||
\(472\) | 23.6111 | 1.08679 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −99.9178 | −4.58938 | ||||||||
\(475\) | 2.72517 | 0.125039 | ||||||||
\(476\) | 1.20393 | 0.0551823 | ||||||||
\(477\) | 46.1914 | 2.11496 | ||||||||
\(478\) | 4.28404 | 0.195948 | ||||||||
\(479\) | 4.34472 | 0.198515 | 0.0992576 | − | 0.995062i | \(-0.468353\pi\) | ||||
0.0992576 | + | 0.995062i | \(0.468353\pi\) | |||||||
\(480\) | −25.4396 | −1.16115 | ||||||||
\(481\) | −36.6357 | −1.67044 | ||||||||
\(482\) | 9.24510 | 0.421103 | ||||||||
\(483\) | 1.54949 | 0.0705043 | ||||||||
\(484\) | 3.56697 | 0.162135 | ||||||||
\(485\) | 9.44456 | 0.428856 | ||||||||
\(486\) | −150.963 | −6.84782 | ||||||||
\(487\) | 13.3720 | 0.605944 | 0.302972 | − | 0.952999i | \(-0.402021\pi\) | ||||
0.302972 | + | 0.952999i | \(0.402021\pi\) | |||||||
\(488\) | 15.0792 | 0.682605 | ||||||||
\(489\) | 20.5658 | 0.930016 | ||||||||
\(490\) | −33.7460 | −1.52449 | ||||||||
\(491\) | 25.4078 | 1.14664 | 0.573319 | − | 0.819333i | \(-0.305656\pi\) | ||||
0.573319 | + | 0.819333i | \(0.305656\pi\) | |||||||
\(492\) | 87.0120 | 3.92280 | ||||||||
\(493\) | 3.07221 | 0.138365 | ||||||||
\(494\) | −41.4112 | −1.86318 | ||||||||
\(495\) | −17.2290 | −0.774388 | ||||||||
\(496\) | 17.2419 | 0.774182 | ||||||||
\(497\) | −0.747299 | −0.0335210 | ||||||||
\(498\) | 22.5892 | 1.01225 | ||||||||
\(499\) | 7.54504 | 0.337762 | 0.168881 | − | 0.985636i | \(-0.445985\pi\) | ||||
0.168881 | + | 0.985636i | \(0.445985\pi\) | |||||||
\(500\) | 42.1256 | 1.88391 | ||||||||
\(501\) | 45.2514 | 2.02168 | ||||||||
\(502\) | 48.4909 | 2.16426 | ||||||||
\(503\) | −17.2015 | −0.766975 | −0.383488 | − | 0.923546i | \(-0.625277\pi\) | ||||
−0.383488 | + | 0.923546i | \(0.625277\pi\) | |||||||
\(504\) | 10.3513 | 0.461083 | ||||||||
\(505\) | −19.5647 | −0.870618 | ||||||||
\(506\) | 3.22293 | 0.143277 | ||||||||
\(507\) | 21.9096 | 0.973040 | ||||||||
\(508\) | 10.5331 | 0.467330 | ||||||||
\(509\) | 39.4081 | 1.74674 | 0.873368 | − | 0.487062i | \(-0.161931\pi\) | ||||
0.873368 | + | 0.487062i | \(0.161931\pi\) | |||||||
\(510\) | −16.4700 | −0.729306 | ||||||||
\(511\) | 2.99160 | 0.132341 | ||||||||
\(512\) | 17.5444 | 0.775361 | ||||||||
\(513\) | −70.6960 | −3.12130 | ||||||||
\(514\) | 48.2987 | 2.13036 | ||||||||
\(515\) | 12.8244 | 0.565111 | ||||||||
\(516\) | −11.9879 | −0.527739 | ||||||||
\(517\) | −1.36584 | −0.0600697 | ||||||||
\(518\) | 6.60369 | 0.290149 | ||||||||
\(519\) | 60.0198 | 2.63458 | ||||||||
\(520\) | −33.9267 | −1.48779 | ||||||||
\(521\) | −12.2266 | −0.535656 | −0.267828 | − | 0.963467i | \(-0.586306\pi\) | ||||
−0.267828 | + | 0.963467i | \(0.586306\pi\) | |||||||
\(522\) | 60.1286 | 2.63176 | ||||||||
\(523\) | −23.0443 | −1.00766 | −0.503828 | − | 0.863804i | \(-0.668075\pi\) | ||||
−0.503828 | + | 0.863804i | \(0.668075\pi\) | |||||||
\(524\) | 46.0810 | 2.01306 | ||||||||
\(525\) | 0.778148 | 0.0339612 | ||||||||
\(526\) | −30.4556 | −1.32793 | ||||||||
\(527\) | −10.8484 | −0.472563 | ||||||||
\(528\) | 5.34150 | 0.232459 | ||||||||
\(529\) | −21.1341 | −0.918875 | ||||||||
\(530\) | 27.2892 | 1.18537 | ||||||||
\(531\) | −52.9743 | −2.29889 | ||||||||
\(532\) | 4.78279 | 0.207360 | ||||||||
\(533\) | −32.0675 | −1.38900 | ||||||||
\(534\) | 16.0338 | 0.693850 | ||||||||
\(535\) | −20.0480 | −0.866751 | ||||||||
\(536\) | −32.9167 | −1.42179 | ||||||||
\(537\) | 45.1440 | 1.94811 | ||||||||
\(538\) | −53.1779 | −2.29266 | ||||||||
\(539\) | −6.88608 | −0.296604 | ||||||||
\(540\) | −131.843 | −5.67362 | ||||||||
\(541\) | −2.70828 | −0.116438 | −0.0582189 | − | 0.998304i | \(-0.518542\pi\) | ||||
−0.0582189 | + | 0.998304i | \(0.518542\pi\) | |||||||
\(542\) | −22.5535 | −0.968757 | ||||||||
\(543\) | −36.4363 | −1.56363 | ||||||||
\(544\) | −3.64439 | −0.156252 | ||||||||
\(545\) | 5.19329 | 0.222456 | ||||||||
\(546\) | −11.8246 | −0.506047 | ||||||||
\(547\) | 5.03151 | 0.215132 | 0.107566 | − | 0.994198i | \(-0.465694\pi\) | ||||
0.107566 | + | 0.994198i | \(0.465694\pi\) | |||||||
\(548\) | 62.0347 | 2.64999 | ||||||||
\(549\) | −33.8321 | −1.44392 | ||||||||
\(550\) | 1.61854 | 0.0690149 | ||||||||
\(551\) | 12.2048 | 0.519941 | ||||||||
\(552\) | 16.9729 | 0.722416 | ||||||||
\(553\) | −4.25297 | −0.180855 | ||||||||
\(554\) | −72.9193 | −3.09804 | ||||||||
\(555\) | −57.8841 | −2.45704 | ||||||||
\(556\) | −60.3193 | −2.55811 | ||||||||
\(557\) | 0.182720 | 0.00774211 | 0.00387106 | − | 0.999993i | \(-0.498768\pi\) | ||||
0.00387106 | + | 0.999993i | \(0.498768\pi\) | |||||||
\(558\) | −212.322 | −8.98831 | ||||||||
\(559\) | 4.41805 | 0.186863 | ||||||||
\(560\) | 1.11420 | 0.0470835 | ||||||||
\(561\) | −3.36081 | −0.141894 | ||||||||
\(562\) | 10.3258 | 0.435568 | ||||||||
\(563\) | −0.876473 | −0.0369389 | −0.0184695 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184695 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(564\) | −16.3736 | −0.689454 | ||||||||
\(565\) | 14.4696 | 0.608739 | ||||||||
\(566\) | 5.96890 | 0.250891 | ||||||||
\(567\) | −11.7873 | −0.495021 | ||||||||
\(568\) | −8.18582 | −0.343469 | ||||||||
\(569\) | 24.0649 | 1.00885 | 0.504426 | − | 0.863455i | \(-0.331704\pi\) | ||||
0.504426 | + | 0.863455i | \(0.331704\pi\) | |||||||
\(570\) | −65.4294 | −2.74054 | ||||||||
\(571\) | 2.91979 | 0.122189 | 0.0610947 | − | 0.998132i | \(-0.480541\pi\) | ||||
0.0610947 | + | 0.998132i | \(0.480541\pi\) | |||||||
\(572\) | −15.7590 | −0.658919 | ||||||||
\(573\) | 2.58811 | 0.108120 | ||||||||
\(574\) | 5.78026 | 0.241264 | ||||||||
\(575\) | 0.937036 | 0.0390771 | ||||||||
\(576\) | −97.6946 | −4.07061 | ||||||||
\(577\) | 33.2108 | 1.38258 | 0.691291 | − | 0.722576i | \(-0.257042\pi\) | ||||
0.691291 | + | 0.722576i | \(0.257042\pi\) | |||||||
\(578\) | −2.35944 | −0.0981399 | ||||||||
\(579\) | 3.39128 | 0.140937 | ||||||||
\(580\) | 22.7610 | 0.945100 | ||||||||
\(581\) | 0.961503 | 0.0398899 | ||||||||
\(582\) | 36.0575 | 1.49463 | ||||||||
\(583\) | 5.56854 | 0.230625 | ||||||||
\(584\) | 32.7697 | 1.35602 | ||||||||
\(585\) | 76.1187 | 3.14712 | ||||||||
\(586\) | 32.9192 | 1.35988 | ||||||||
\(587\) | 11.3106 | 0.466838 | 0.233419 | − | 0.972376i | \(-0.425009\pi\) | ||||
0.233419 | + | 0.972376i | \(0.425009\pi\) | |||||||
\(588\) | −82.5498 | −3.40430 | ||||||||
\(589\) | −43.0967 | −1.77577 | ||||||||
\(590\) | −31.2965 | −1.28846 | ||||||||
\(591\) | −12.6486 | −0.520293 | ||||||||
\(592\) | 13.1793 | 0.541666 | ||||||||
\(593\) | 22.2422 | 0.913376 | 0.456688 | − | 0.889627i | \(-0.349036\pi\) | ||||
0.456688 | + | 0.889627i | \(0.349036\pi\) | |||||||
\(594\) | −41.9881 | −1.72279 | ||||||||
\(595\) | −0.701042 | −0.0287399 | ||||||||
\(596\) | 76.8039 | 3.14601 | ||||||||
\(597\) | 27.2979 | 1.11723 | ||||||||
\(598\) | −14.2391 | −0.582279 | ||||||||
\(599\) | 43.8440 | 1.79142 | 0.895709 | − | 0.444640i | \(-0.146669\pi\) | ||||
0.895709 | + | 0.444640i | \(0.146669\pi\) | |||||||
\(600\) | 8.52374 | 0.347980 | ||||||||
\(601\) | −39.7992 | −1.62344 | −0.811722 | − | 0.584043i | \(-0.801470\pi\) | ||||
−0.811722 | + | 0.584043i | \(0.801470\pi\) | |||||||
\(602\) | −0.796366 | −0.0324575 | ||||||||
\(603\) | 73.8526 | 3.00751 | ||||||||
\(604\) | 7.36260 | 0.299580 | ||||||||
\(605\) | −2.07702 | −0.0844429 | ||||||||
\(606\) | −74.6941 | −3.03424 | ||||||||
\(607\) | −1.22924 | −0.0498934 | −0.0249467 | − | 0.999689i | \(-0.507942\pi\) | ||||
−0.0249467 | + | 0.999689i | \(0.507942\pi\) | |||||||
\(608\) | −14.4778 | −0.587153 | ||||||||
\(609\) | 3.48497 | 0.141218 | ||||||||
\(610\) | −19.9875 | −0.809271 | ||||||||
\(611\) | 6.03436 | 0.244124 | ||||||||
\(612\) | −29.5883 | −1.19604 | ||||||||
\(613\) | −30.0021 | −1.21177 | −0.605887 | − | 0.795551i | \(-0.707181\pi\) | ||||
−0.605887 | + | 0.795551i | \(0.707181\pi\) | |||||||
\(614\) | 64.8655 | 2.61776 | ||||||||
\(615\) | −50.6664 | −2.04307 | ||||||||
\(616\) | 1.24788 | 0.0502787 | ||||||||
\(617\) | 37.2819 | 1.50091 | 0.750456 | − | 0.660920i | \(-0.229834\pi\) | ||||
0.750456 | + | 0.660920i | \(0.229834\pi\) | |||||||
\(618\) | 48.9610 | 1.96950 | ||||||||
\(619\) | 20.8779 | 0.839153 | 0.419577 | − | 0.907720i | \(-0.362179\pi\) | ||||
0.419577 | + | 0.907720i | \(0.362179\pi\) | |||||||
\(620\) | −80.3722 | −3.22783 | ||||||||
\(621\) | −24.3085 | −0.975466 | ||||||||
\(622\) | 15.3978 | 0.617397 | ||||||||
\(623\) | 0.682473 | 0.0273427 | ||||||||
\(624\) | −23.5990 | −0.944716 | ||||||||
\(625\) | −21.0995 | −0.843980 | ||||||||
\(626\) | −30.1024 | −1.20313 | ||||||||
\(627\) | −13.3513 | −0.533199 | ||||||||
\(628\) | 48.0565 | 1.91766 | ||||||||
\(629\) | −8.29228 | −0.330635 | ||||||||
\(630\) | −13.7206 | −0.546643 | ||||||||
\(631\) | 41.5113 | 1.65254 | 0.826270 | − | 0.563275i | \(-0.190459\pi\) | ||||
0.826270 | + | 0.563275i | \(0.190459\pi\) | |||||||
\(632\) | −46.5865 | −1.85311 | ||||||||
\(633\) | −41.4669 | −1.64816 | ||||||||
\(634\) | −59.6847 | −2.37038 | ||||||||
\(635\) | −6.13334 | −0.243394 | ||||||||
\(636\) | 66.7553 | 2.64702 | ||||||||
\(637\) | 30.4230 | 1.20540 | ||||||||
\(638\) | 7.24871 | 0.286979 | ||||||||
\(639\) | 18.3659 | 0.726543 | ||||||||
\(640\) | −42.5777 | −1.68303 | ||||||||
\(641\) | 24.9781 | 0.986574 | 0.493287 | − | 0.869867i | \(-0.335795\pi\) | ||||
0.493287 | + | 0.869867i | \(0.335795\pi\) | |||||||
\(642\) | −76.5393 | −3.02077 | ||||||||
\(643\) | −44.5545 | −1.75706 | −0.878528 | − | 0.477691i | \(-0.841474\pi\) | ||||
−0.878528 | + | 0.477691i | \(0.841474\pi\) | |||||||
\(644\) | 1.64454 | 0.0648040 | ||||||||
\(645\) | 6.98048 | 0.274856 | ||||||||
\(646\) | −9.37320 | −0.368784 | ||||||||
\(647\) | −22.1384 | −0.870352 | −0.435176 | − | 0.900345i | \(-0.643314\pi\) | ||||
−0.435176 | + | 0.900345i | \(0.643314\pi\) | |||||||
\(648\) | −129.117 | −5.07218 | ||||||||
\(649\) | −6.38624 | −0.250682 | ||||||||
\(650\) | −7.15080 | −0.280477 | ||||||||
\(651\) | −12.3059 | −0.482306 | ||||||||
\(652\) | 21.8273 | 0.854823 | ||||||||
\(653\) | −31.4314 | −1.23001 | −0.615004 | − | 0.788524i | \(-0.710846\pi\) | ||||
−0.615004 | + | 0.788524i | \(0.710846\pi\) | |||||||
\(654\) | 19.8269 | 0.775295 | ||||||||
\(655\) | −26.8326 | −1.04844 | ||||||||
\(656\) | 11.5360 | 0.450403 | ||||||||
\(657\) | −73.5227 | −2.86839 | ||||||||
\(658\) | −1.08771 | −0.0424034 | ||||||||
\(659\) | 1.53993 | 0.0599872 | 0.0299936 | − | 0.999550i | \(-0.490451\pi\) | ||||
0.0299936 | + | 0.999550i | \(0.490451\pi\) | |||||||
\(660\) | −24.8992 | −0.969199 | ||||||||
\(661\) | −3.03722 | −0.118134 | −0.0590670 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590670 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(662\) | −61.3256 | −2.38349 | ||||||||
\(663\) | 14.8482 | 0.576658 | ||||||||
\(664\) | 10.5322 | 0.408728 | ||||||||
\(665\) | −2.78498 | −0.107997 | ||||||||
\(666\) | −162.294 | −6.28878 | ||||||||
\(667\) | 4.19655 | 0.162491 | ||||||||
\(668\) | 48.0271 | 1.85823 | ||||||||
\(669\) | 47.6303 | 1.84149 | ||||||||
\(670\) | 43.6311 | 1.68562 | ||||||||
\(671\) | −4.07858 | −0.157452 | ||||||||
\(672\) | −4.13402 | −0.159473 | ||||||||
\(673\) | −33.5405 | −1.29289 | −0.646445 | − | 0.762960i | \(-0.723745\pi\) | ||||
−0.646445 | + | 0.762960i | \(0.723745\pi\) | |||||||
\(674\) | 26.8402 | 1.03385 | ||||||||
\(675\) | −12.2076 | −0.469872 | ||||||||
\(676\) | 23.2536 | 0.894368 | ||||||||
\(677\) | −1.78472 | −0.0685922 | −0.0342961 | − | 0.999412i | \(-0.510919\pi\) | ||||
−0.0342961 | + | 0.999412i | \(0.510919\pi\) | |||||||
\(678\) | 55.2419 | 2.12155 | ||||||||
\(679\) | 1.53477 | 0.0588992 | ||||||||
\(680\) | −7.67912 | −0.294481 | ||||||||
\(681\) | 36.0677 | 1.38212 | ||||||||
\(682\) | −25.5962 | −0.980128 | ||||||||
\(683\) | 4.28474 | 0.163951 | 0.0819756 | − | 0.996634i | \(-0.473877\pi\) | ||||
0.0819756 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(684\) | −117.543 | −4.49438 | ||||||||
\(685\) | −36.1224 | −1.38016 | ||||||||
\(686\) | −11.0584 | −0.422212 | ||||||||
\(687\) | 56.9186 | 2.17158 | ||||||||
\(688\) | −1.58935 | −0.0605933 | ||||||||
\(689\) | −24.6021 | −0.937264 | ||||||||
\(690\) | −22.4976 | −0.856469 | ||||||||
\(691\) | 48.2437 | 1.83528 | 0.917639 | − | 0.397415i | \(-0.130093\pi\) | ||||
0.917639 | + | 0.397415i | \(0.130093\pi\) | |||||||
\(692\) | 63.7015 | 2.42157 | ||||||||
\(693\) | −2.79978 | −0.106355 | ||||||||
\(694\) | −40.5649 | −1.53982 | ||||||||
\(695\) | 35.1234 | 1.33231 | ||||||||
\(696\) | 38.1739 | 1.44698 | ||||||||
\(697\) | −7.25830 | −0.274928 | ||||||||
\(698\) | −10.4002 | −0.393653 | ||||||||
\(699\) | −33.4840 | −1.26648 | ||||||||
\(700\) | 0.825881 | 0.0312154 | ||||||||
\(701\) | 31.9011 | 1.20489 | 0.602444 | − | 0.798161i | \(-0.294194\pi\) | ||||
0.602444 | + | 0.798161i | \(0.294194\pi\) | |||||||
\(702\) | 185.505 | 7.00144 | ||||||||
\(703\) | −32.9422 | −1.24244 | ||||||||
\(704\) | −11.7774 | −0.443878 | ||||||||
\(705\) | 9.53424 | 0.359080 | ||||||||
\(706\) | 29.9509 | 1.12722 | ||||||||
\(707\) | −3.17933 | −0.119571 | ||||||||
\(708\) | −76.5578 | −2.87722 | ||||||||
\(709\) | −13.9798 | −0.525021 | −0.262511 | − | 0.964929i | \(-0.584551\pi\) | ||||
−0.262511 | + | 0.964929i | \(0.584551\pi\) | |||||||
\(710\) | 10.8503 | 0.407205 | ||||||||
\(711\) | 104.522 | 3.91989 | ||||||||
\(712\) | 7.47572 | 0.280165 | ||||||||
\(713\) | −14.8186 | −0.554961 | ||||||||
\(714\) | −2.67644 | −0.100163 | ||||||||
\(715\) | 9.17637 | 0.343177 | ||||||||
\(716\) | 47.9132 | 1.79060 | ||||||||
\(717\) | −6.10224 | −0.227892 | ||||||||
\(718\) | −84.1898 | −3.14193 | ||||||||
\(719\) | −11.9355 | −0.445119 | −0.222560 | − | 0.974919i | \(-0.571441\pi\) | ||||
−0.222560 | + | 0.974919i | \(0.571441\pi\) | |||||||
\(720\) | −27.3829 | −1.02050 | ||||||||
\(721\) | 2.08401 | 0.0776125 | ||||||||
\(722\) | 7.59316 | 0.282588 | ||||||||
\(723\) | −13.1688 | −0.489753 | ||||||||
\(724\) | −38.6713 | −1.43721 | ||||||||
\(725\) | 2.10749 | 0.0782703 | ||||||||
\(726\) | −7.92965 | −0.294297 | ||||||||
\(727\) | −27.7919 | −1.03074 | −0.515372 | − | 0.856967i | \(-0.672346\pi\) | ||||
−0.515372 | + | 0.856967i | \(0.672346\pi\) | |||||||
\(728\) | −5.51321 | −0.204333 | ||||||||
\(729\) | 110.264 | 4.08386 | ||||||||
\(730\) | −43.4362 | −1.60764 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −48.8937 | −1.80716 | ||||||||
\(733\) | 40.5665 | 1.49836 | 0.749179 | − | 0.662368i | \(-0.230448\pi\) | ||||
0.749179 | + | 0.662368i | \(0.230448\pi\) | |||||||
\(734\) | 85.5081 | 3.15616 | ||||||||
\(735\) | 48.0681 | 1.77302 | ||||||||
\(736\) | −4.97813 | −0.183496 | ||||||||
\(737\) | 8.90319 | 0.327953 | ||||||||
\(738\) | −142.058 | −5.22921 | ||||||||
\(739\) | 15.8992 | 0.584861 | 0.292430 | − | 0.956287i | \(-0.405536\pi\) | ||||
0.292430 | + | 0.956287i | \(0.405536\pi\) | |||||||
\(740\) | −61.4348 | −2.25839 | ||||||||
\(741\) | 58.9866 | 2.16693 | ||||||||
\(742\) | 4.43459 | 0.162799 | ||||||||
\(743\) | 40.0958 | 1.47097 | 0.735486 | − | 0.677540i | \(-0.236954\pi\) | ||||
0.735486 | + | 0.677540i | \(0.236954\pi\) | |||||||
\(744\) | −134.797 | −4.94190 | ||||||||
\(745\) | −44.7223 | −1.63850 | ||||||||
\(746\) | 50.1222 | 1.83510 | ||||||||
\(747\) | −23.6302 | −0.864584 | ||||||||
\(748\) | −3.56697 | −0.130421 | ||||||||
\(749\) | −3.25787 | −0.119040 | ||||||||
\(750\) | −93.6484 | −3.41956 | ||||||||
\(751\) | −5.93359 | −0.216520 | −0.108260 | − | 0.994123i | \(-0.534528\pi\) | ||||
−0.108260 | + | 0.994123i | \(0.534528\pi\) | |||||||
\(752\) | −2.17080 | −0.0791608 | ||||||||
\(753\) | −69.0710 | −2.51709 | ||||||||
\(754\) | −32.0251 | −1.16629 | ||||||||
\(755\) | −4.28719 | −0.156027 | ||||||||
\(756\) | −21.4249 | −0.779217 | ||||||||
\(757\) | 51.6664 | 1.87785 | 0.938924 | − | 0.344125i | \(-0.111824\pi\) | ||||
0.938924 | + | 0.344125i | \(0.111824\pi\) | |||||||
\(758\) | 9.48032 | 0.344341 | ||||||||
\(759\) | −4.59078 | −0.166635 | ||||||||
\(760\) | −30.5063 | −1.10658 | ||||||||
\(761\) | 2.99731 | 0.108652 | 0.0543262 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543262 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(762\) | −23.4159 | −0.848267 | ||||||||
\(763\) | 0.843927 | 0.0305522 | ||||||||
\(764\) | 2.74686 | 0.0993780 | ||||||||
\(765\) | 17.2290 | 0.622917 | ||||||||
\(766\) | 40.9831 | 1.48078 | ||||||||
\(767\) | 28.2147 | 1.01877 | ||||||||
\(768\) | −83.3895 | −3.00906 | ||||||||
\(769\) | 10.3755 | 0.374150 | 0.187075 | − | 0.982346i | \(-0.440099\pi\) | ||||
0.187075 | + | 0.982346i | \(0.440099\pi\) | |||||||
\(770\) | −1.65407 | −0.0596085 | ||||||||
\(771\) | −68.7971 | −2.47767 | ||||||||
\(772\) | 3.59931 | 0.129542 | ||||||||
\(773\) | 14.3298 | 0.515408 | 0.257704 | − | 0.966224i | \(-0.417034\pi\) | ||||
0.257704 | + | 0.966224i | \(0.417034\pi\) | |||||||
\(774\) | 19.5718 | 0.703492 | ||||||||
\(775\) | −7.44184 | −0.267319 | ||||||||
\(776\) | 16.8117 | 0.603505 | ||||||||
\(777\) | −9.40636 | −0.337451 | ||||||||
\(778\) | −30.0688 | −1.07802 | ||||||||
\(779\) | −28.8345 | −1.03310 | ||||||||
\(780\) | 110.006 | 3.93884 | ||||||||
\(781\) | 2.21407 | 0.0792257 | ||||||||
\(782\) | −3.22293 | −0.115252 | ||||||||
\(783\) | −54.6723 | −1.95383 | ||||||||
\(784\) | −10.9444 | −0.390870 | ||||||||
\(785\) | −27.9829 | −0.998753 | ||||||||
\(786\) | −102.442 | −3.65397 | ||||||||
\(787\) | 1.35046 | 0.0481386 | 0.0240693 | − | 0.999710i | \(-0.492338\pi\) | ||||
0.0240693 | + | 0.999710i | \(0.492338\pi\) | |||||||
\(788\) | −13.4245 | −0.478227 | ||||||||
\(789\) | 43.3812 | 1.54441 | ||||||||
\(790\) | 61.7503 | 2.19698 | ||||||||
\(791\) | 2.35135 | 0.0836045 | ||||||||
\(792\) | −30.6684 | −1.08975 | ||||||||
\(793\) | 18.0193 | 0.639886 | ||||||||
\(794\) | 70.9353 | 2.51740 | ||||||||
\(795\) | −38.8711 | −1.37861 | ||||||||
\(796\) | 28.9723 | 1.02690 | ||||||||
\(797\) | −17.0552 | −0.604125 | −0.302063 | − | 0.953288i | \(-0.597675\pi\) | ||||
−0.302063 | + | 0.953288i | \(0.597675\pi\) | |||||||
\(798\) | −10.6325 | −0.376386 | ||||||||
\(799\) | 1.36584 | 0.0483200 | ||||||||
\(800\) | −2.50000 | −0.0883883 | ||||||||
\(801\) | −16.7727 | −0.592634 | ||||||||
\(802\) | −34.5284 | −1.21924 | ||||||||
\(803\) | −8.86341 | −0.312783 | ||||||||
\(804\) | 106.731 | 3.76411 | ||||||||
\(805\) | −0.957603 | −0.0337511 | ||||||||
\(806\) | 113.085 | 3.98325 | ||||||||
\(807\) | 75.7471 | 2.66642 | ||||||||
\(808\) | −34.8260 | −1.22517 | ||||||||
\(809\) | 20.0216 | 0.703921 | 0.351960 | − | 0.936015i | \(-0.385515\pi\) | ||||
0.351960 | + | 0.936015i | \(0.385515\pi\) | |||||||
\(810\) | 171.144 | 6.01339 | ||||||||
\(811\) | 45.0362 | 1.58144 | 0.790718 | − | 0.612180i | \(-0.209707\pi\) | ||||
0.790718 | + | 0.612180i | \(0.209707\pi\) | |||||||
\(812\) | 3.69874 | 0.129800 | ||||||||
\(813\) | 32.1255 | 1.12669 | ||||||||
\(814\) | −19.5652 | −0.685758 | ||||||||
\(815\) | −12.7099 | −0.445207 | ||||||||
\(816\) | −5.34150 | −0.186990 | ||||||||
\(817\) | 3.97263 | 0.138985 | ||||||||
\(818\) | 12.6722 | 0.443074 | ||||||||
\(819\) | 12.3695 | 0.432227 | ||||||||
\(820\) | −53.7744 | −1.87788 | ||||||||
\(821\) | −30.3782 | −1.06021 | −0.530104 | − | 0.847933i | \(-0.677847\pi\) | ||||
−0.530104 | + | 0.847933i | \(0.677847\pi\) | |||||||
\(822\) | −137.908 | −4.81009 | ||||||||
\(823\) | −52.8826 | −1.84337 | −0.921686 | − | 0.387936i | \(-0.873188\pi\) | ||||
−0.921686 | + | 0.387936i | \(0.873188\pi\) | |||||||
\(824\) | 22.8280 | 0.795250 | ||||||||
\(825\) | −2.30547 | −0.0802661 | ||||||||
\(826\) | −5.08579 | −0.176957 | ||||||||
\(827\) | −12.6229 | −0.438942 | −0.219471 | − | 0.975619i | \(-0.570433\pi\) | ||||
−0.219471 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(828\) | −40.4168 | −1.40458 | ||||||||
\(829\) | −25.8805 | −0.898865 | −0.449433 | − | 0.893314i | \(-0.648374\pi\) | ||||
−0.449433 | + | 0.893314i | \(0.648374\pi\) | |||||||
\(830\) | −13.9604 | −0.484572 | ||||||||
\(831\) | 103.867 | 3.60310 | ||||||||
\(832\) | 52.0332 | 1.80393 | ||||||||
\(833\) | 6.88608 | 0.238588 | ||||||||
\(834\) | 134.094 | 4.64331 | ||||||||
\(835\) | −27.9658 | −0.967798 | ||||||||
\(836\) | −14.1703 | −0.490089 | ||||||||
\(837\) | 193.055 | 6.67297 | ||||||||
\(838\) | 48.8135 | 1.68623 | ||||||||
\(839\) | −26.1294 | −0.902085 | −0.451043 | − | 0.892502i | \(-0.648948\pi\) | ||||
−0.451043 | + | 0.892502i | \(0.648948\pi\) | |||||||
\(840\) | −8.71083 | −0.300552 | ||||||||
\(841\) | −19.5615 | −0.674535 | ||||||||
\(842\) | −71.4914 | −2.46376 | ||||||||
\(843\) | −14.7082 | −0.506576 | ||||||||
\(844\) | −44.0106 | −1.51491 | ||||||||
\(845\) | −13.5404 | −0.465803 | ||||||||
\(846\) | 26.7319 | 0.919063 | ||||||||
\(847\) | −0.337523 | −0.0115974 | ||||||||
\(848\) | 8.85034 | 0.303922 | ||||||||
\(849\) | −8.50215 | −0.291793 | ||||||||
\(850\) | −1.61854 | −0.0555156 | ||||||||
\(851\) | −11.3270 | −0.388285 | ||||||||
\(852\) | 26.5421 | 0.909318 | ||||||||
\(853\) | 26.0421 | 0.891666 | 0.445833 | − | 0.895116i | \(-0.352908\pi\) | ||||
0.445833 | + | 0.895116i | \(0.352908\pi\) | |||||||
\(854\) | −3.24804 | −0.111146 | ||||||||
\(855\) | 68.4446 | 2.34076 | ||||||||
\(856\) | −35.6863 | −1.21973 | ||||||||
\(857\) | 46.5265 | 1.58931 | 0.794657 | − | 0.607059i | \(-0.207651\pi\) | ||||
0.794657 | + | 0.607059i | \(0.207651\pi\) | |||||||
\(858\) | 35.0336 | 1.19603 | ||||||||
\(859\) | −27.4136 | −0.935340 | −0.467670 | − | 0.883903i | \(-0.654906\pi\) | ||||
−0.467670 | + | 0.883903i | \(0.654906\pi\) | |||||||
\(860\) | 7.40868 | 0.252634 | ||||||||
\(861\) | −8.23346 | −0.280596 | ||||||||
\(862\) | −46.0803 | −1.56950 | ||||||||
\(863\) | 28.5879 | 0.973143 | 0.486571 | − | 0.873641i | \(-0.338247\pi\) | ||||
0.486571 | + | 0.873641i | \(0.338247\pi\) | |||||||
\(864\) | 64.8547 | 2.20640 | ||||||||
\(865\) | −37.0929 | −1.26120 | ||||||||
\(866\) | −37.8647 | −1.28669 | ||||||||
\(867\) | 3.36081 | 0.114139 | ||||||||
\(868\) | −13.0608 | −0.443311 | ||||||||
\(869\) | 12.6005 | 0.427444 | ||||||||
\(870\) | −50.5995 | −1.71548 | ||||||||
\(871\) | −39.3347 | −1.33281 | ||||||||
\(872\) | 9.24427 | 0.313050 | ||||||||
\(873\) | −37.7191 | −1.27660 | ||||||||
\(874\) | −12.8035 | −0.433085 | ||||||||
\(875\) | −3.98611 | −0.134755 | ||||||||
\(876\) | −106.254 | −3.58999 | ||||||||
\(877\) | −21.0458 | −0.710667 | −0.355334 | − | 0.934740i | \(-0.615633\pi\) | ||||
−0.355334 | + | 0.934740i | \(0.615633\pi\) | |||||||
\(878\) | 5.54636 | 0.187181 | ||||||||
\(879\) | −46.8904 | −1.58157 | ||||||||
\(880\) | −3.30111 | −0.111280 | ||||||||
\(881\) | 50.2925 | 1.69440 | 0.847199 | − | 0.531275i | \(-0.178287\pi\) | ||||
0.847199 | + | 0.531275i | \(0.178287\pi\) | |||||||
\(882\) | 134.773 | 4.53803 | ||||||||
\(883\) | −8.48445 | −0.285525 | −0.142762 | − | 0.989757i | \(-0.545598\pi\) | ||||
−0.142762 | + | 0.989757i | \(0.545598\pi\) | |||||||
\(884\) | 15.7590 | 0.530034 | ||||||||
\(885\) | 44.5790 | 1.49851 | ||||||||
\(886\) | 0.895212 | 0.0300752 | ||||||||
\(887\) | −43.9041 | −1.47416 | −0.737078 | − | 0.675807i | \(-0.763795\pi\) | ||||
−0.737078 | + | 0.675807i | \(0.763795\pi\) | |||||||
\(888\) | −103.036 | −3.45766 | ||||||||
\(889\) | −0.996688 | −0.0334279 | ||||||||
\(890\) | −9.90907 | −0.332153 | ||||||||
\(891\) | 34.9230 | 1.16996 | ||||||||
\(892\) | 50.5520 | 1.69261 | ||||||||
\(893\) | 5.42599 | 0.181574 | ||||||||
\(894\) | −170.741 | −5.71043 | ||||||||
\(895\) | −27.8995 | −0.932577 | ||||||||
\(896\) | −6.91901 | −0.231148 | ||||||||
\(897\) | 20.2823 | 0.677205 | ||||||||
\(898\) | 40.4341 | 1.34930 | ||||||||
\(899\) | −33.3286 | −1.11157 | ||||||||
\(900\) | −20.2971 | −0.676571 | ||||||||
\(901\) | −5.56854 | −0.185515 | ||||||||
\(902\) | −17.1255 | −0.570218 | ||||||||
\(903\) | 1.13435 | 0.0377489 | ||||||||
\(904\) | 25.7564 | 0.856646 | ||||||||
\(905\) | 22.5180 | 0.748524 | ||||||||
\(906\) | −16.3676 | −0.543778 | ||||||||
\(907\) | 13.1570 | 0.436870 | 0.218435 | − | 0.975852i | \(-0.429905\pi\) | ||||
0.218435 | + | 0.975852i | \(0.429905\pi\) | |||||||
\(908\) | 38.2802 | 1.27037 | ||||||||
\(909\) | 78.1362 | 2.59162 | ||||||||
\(910\) | 7.30775 | 0.242250 | ||||||||
\(911\) | −51.9515 | −1.72123 | −0.860616 | − | 0.509255i | \(-0.829921\pi\) | ||||
−0.860616 | + | 0.509255i | \(0.829921\pi\) | |||||||
\(912\) | −21.2198 | −0.702658 | ||||||||
\(913\) | −2.84870 | −0.0942784 | ||||||||
\(914\) | 62.8556 | 2.07908 | ||||||||
\(915\) | 28.4704 | 0.941203 | ||||||||
\(916\) | 60.4101 | 1.99601 | ||||||||
\(917\) | −4.36039 | −0.143993 | ||||||||
\(918\) | 41.9881 | 1.38581 | ||||||||
\(919\) | 37.0574 | 1.22241 | 0.611206 | − | 0.791472i | \(-0.290685\pi\) | ||||
0.611206 | + | 0.791472i | \(0.290685\pi\) | |||||||
\(920\) | −10.4895 | −0.345827 | ||||||||
\(921\) | −92.3951 | −3.04452 | ||||||||
\(922\) | 38.3067 | 1.26156 | ||||||||
\(923\) | −9.78187 | −0.321974 | ||||||||
\(924\) | −4.04620 | −0.133110 | ||||||||
\(925\) | −5.68838 | −0.187033 | ||||||||
\(926\) | 26.0257 | 0.855258 | ||||||||
\(927\) | −51.2173 | −1.68220 | ||||||||
\(928\) | −11.1963 | −0.367538 | ||||||||
\(929\) | 41.6931 | 1.36791 | 0.683953 | − | 0.729526i | \(-0.260259\pi\) | ||||
0.683953 | + | 0.729526i | \(0.260259\pi\) | |||||||
\(930\) | 178.674 | 5.85894 | ||||||||
\(931\) | 27.3559 | 0.896552 | ||||||||
\(932\) | −35.5380 | −1.16408 | ||||||||
\(933\) | −21.9328 | −0.718048 | ||||||||
\(934\) | 69.5344 | 2.27524 | ||||||||
\(935\) | 2.07702 | 0.0679258 | ||||||||
\(936\) | 135.494 | 4.42877 | ||||||||
\(937\) | 38.0417 | 1.24277 | 0.621384 | − | 0.783506i | \(-0.286571\pi\) | ||||
0.621384 | + | 0.783506i | \(0.286571\pi\) | |||||||
\(938\) | 7.09020 | 0.231503 | ||||||||
\(939\) | 42.8781 | 1.39927 | ||||||||
\(940\) | 10.1191 | 0.330048 | ||||||||
\(941\) | −48.6921 | −1.58732 | −0.793658 | − | 0.608364i | \(-0.791826\pi\) | ||||
−0.793658 | + | 0.608364i | \(0.791826\pi\) | |||||||
\(942\) | −106.833 | −3.48081 | ||||||||
\(943\) | −9.91463 | −0.322865 | ||||||||
\(944\) | −10.1500 | −0.330353 | ||||||||
\(945\) | 12.4756 | 0.405830 | ||||||||
\(946\) | 2.35944 | 0.0767121 | ||||||||
\(947\) | −6.18677 | −0.201043 | −0.100522 | − | 0.994935i | \(-0.532051\pi\) | ||||
−0.100522 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(948\) | 151.054 | 4.90602 | ||||||||
\(949\) | 39.1590 | 1.27115 | ||||||||
\(950\) | −6.42988 | −0.208613 | ||||||||
\(951\) | 85.0154 | 2.75681 | ||||||||
\(952\) | −1.24788 | −0.0404441 | ||||||||
\(953\) | −27.0302 | −0.875594 | −0.437797 | − | 0.899074i | \(-0.644241\pi\) | ||||
−0.437797 | + | 0.899074i | \(0.644241\pi\) | |||||||
\(954\) | −108.986 | −3.52855 | ||||||||
\(955\) | −1.59948 | −0.0517579 | ||||||||
\(956\) | −6.47656 | −0.209467 | ||||||||
\(957\) | −10.3251 | −0.333764 | ||||||||
\(958\) | −10.2511 | −0.331198 | ||||||||
\(959\) | −5.87000 | −0.189552 | ||||||||
\(960\) | 82.2121 | 2.65338 | ||||||||
\(961\) | 86.6876 | 2.79637 | ||||||||
\(962\) | 86.4398 | 2.78693 | ||||||||
\(963\) | 80.0665 | 2.58011 | ||||||||
\(964\) | −13.9766 | −0.450156 | ||||||||
\(965\) | −2.09585 | −0.0674678 | ||||||||
\(966\) | −3.65594 | −0.117628 | ||||||||
\(967\) | 35.3552 | 1.13695 | 0.568473 | − | 0.822702i | \(-0.307534\pi\) | ||||
0.568473 | + | 0.822702i | \(0.307534\pi\) | |||||||
\(968\) | −3.69718 | −0.118832 | ||||||||
\(969\) | 13.3513 | 0.428905 | ||||||||
\(970\) | −22.2839 | −0.715493 | ||||||||
\(971\) | 46.4813 | 1.49165 | 0.745827 | − | 0.666139i | \(-0.232054\pi\) | ||||
0.745827 | + | 0.666139i | \(0.232054\pi\) | |||||||
\(972\) | 228.224 | 7.32028 | ||||||||
\(973\) | 5.70768 | 0.182980 | ||||||||
\(974\) | −31.5505 | −1.01094 | ||||||||
\(975\) | 10.1857 | 0.326202 | ||||||||
\(976\) | −6.48227 | −0.207492 | ||||||||
\(977\) | −5.89654 | −0.188647 | −0.0943235 | − | 0.995542i | \(-0.530069\pi\) | ||||
−0.0943235 | + | 0.995542i | \(0.530069\pi\) | |||||||
\(978\) | −48.5238 | −1.55162 | ||||||||
\(979\) | −2.02201 | −0.0646236 | ||||||||
\(980\) | 51.0167 | 1.62967 | ||||||||
\(981\) | −20.7406 | −0.662197 | ||||||||
\(982\) | −59.9482 | −1.91302 | ||||||||
\(983\) | 6.13640 | 0.195721 | 0.0978604 | − | 0.995200i | \(-0.468800\pi\) | ||||
0.0978604 | + | 0.995200i | \(0.468800\pi\) | |||||||
\(984\) | −90.1883 | −2.87510 | ||||||||
\(985\) | 7.81696 | 0.249069 | ||||||||
\(986\) | −7.24871 | −0.230846 | ||||||||
\(987\) | 1.54935 | 0.0493162 | ||||||||
\(988\) | 62.6049 | 1.99173 | ||||||||
\(989\) | 1.36597 | 0.0434354 | ||||||||
\(990\) | 40.6509 | 1.29197 | ||||||||
\(991\) | 18.5991 | 0.590819 | 0.295409 | − | 0.955371i | \(-0.404544\pi\) | ||||
0.295409 | + | 0.955371i | \(0.404544\pi\) | |||||||
\(992\) | 39.5358 | 1.25526 | ||||||||
\(993\) | 87.3527 | 2.77206 | ||||||||
\(994\) | 1.76321 | 0.0559256 | ||||||||
\(995\) | −16.8704 | −0.534827 | ||||||||
\(996\) | −34.1501 | −1.08209 | ||||||||
\(997\) | 2.40123 | 0.0760476 | 0.0380238 | − | 0.999277i | \(-0.487894\pi\) | ||||
0.0380238 | + | 0.999277i | \(0.487894\pi\) | |||||||
\(998\) | −17.8021 | −0.563515 | ||||||||
\(999\) | 147.567 | 4.66882 |
(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 | 8041.2.a.i.1.8 | ✓ | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.i.1.8 | ✓ | 78 | 1.1 | even | 1 | trivial |