Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.48718\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.919131 | −0.530660 | −0.265330 | − | 0.964158i | \(-0.585481\pi\) | ||||
−0.265330 | + | 0.964158i | \(0.585481\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.919131 | −0.375234 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.15520 | −0.718400 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.919131 | −0.265330 | ||||||||
\(13\) | −3.72325 | −1.03264 | −0.516322 | − | 0.856394i | \(-0.672699\pi\) | ||||
−0.516322 | + | 0.856394i | \(0.672699\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.919131 | 0.237319 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.31694 | 0.319404 | 0.159702 | − | 0.987165i | \(-0.448947\pi\) | ||||
0.159702 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(18\) | −2.15520 | −0.507985 | ||||||||
\(19\) | 2.70741 | 0.621123 | 0.310561 | − | 0.950553i | \(-0.399483\pi\) | ||||
0.310561 | + | 0.950553i | \(0.399483\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.919131 | −0.200571 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | −0.919131 | −0.187617 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.72325 | −0.730190 | ||||||||
\(27\) | 4.73830 | 0.911887 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 2.95002 | 0.547805 | 0.273902 | − | 0.961757i | \(-0.411685\pi\) | ||||
0.273902 | + | 0.961757i | \(0.411685\pi\) | |||||||
\(30\) | 0.919131 | 0.167810 | ||||||||
\(31\) | 7.70820 | 1.38443 | 0.692217 | − | 0.721689i | \(-0.256634\pi\) | ||||
0.692217 | + | 0.721689i | \(0.256634\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.31694 | 0.225853 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.15520 | −0.359200 | ||||||||
\(37\) | −8.04870 | −1.32320 | −0.661599 | − | 0.749858i | \(-0.730122\pi\) | ||||
−0.661599 | + | 0.749858i | \(0.730122\pi\) | |||||||
\(38\) | 2.70741 | 0.439200 | ||||||||
\(39\) | 3.42216 | 0.547984 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.24458 | −0.506718 | −0.253359 | − | 0.967372i | \(-0.581535\pi\) | ||||
−0.253359 | + | 0.967372i | \(0.581535\pi\) | |||||||
\(42\) | −0.919131 | −0.141825 | ||||||||
\(43\) | −6.48064 | −0.988289 | −0.494145 | − | 0.869380i | \(-0.664519\pi\) | ||||
−0.494145 | + | 0.869380i | \(0.664519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.15520 | 0.321278 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | −9.37090 | −1.36689 | −0.683443 | − | 0.730004i | \(-0.739518\pi\) | ||||
−0.683443 | + | 0.730004i | \(0.739518\pi\) | |||||||
\(48\) | −0.919131 | −0.132665 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.21044 | −0.169495 | ||||||||
\(52\) | −3.72325 | −0.516322 | ||||||||
\(53\) | 13.2848 | 1.82480 | 0.912402 | − | 0.409296i | \(-0.134226\pi\) | ||||
0.912402 | + | 0.409296i | \(0.134226\pi\) | |||||||
\(54\) | 4.73830 | 0.644801 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −2.48847 | −0.329605 | ||||||||
\(58\) | 2.95002 | 0.387357 | ||||||||
\(59\) | −2.83905 | −0.369613 | −0.184807 | − | 0.982775i | \(-0.559166\pi\) | ||||
−0.184807 | + | 0.982775i | \(0.559166\pi\) | |||||||
\(60\) | 0.919131 | 0.118659 | ||||||||
\(61\) | −1.44651 | −0.185206 | −0.0926030 | − | 0.995703i | \(-0.529519\pi\) | ||||
−0.0926030 | + | 0.995703i | \(0.529519\pi\) | |||||||
\(62\) | 7.70820 | 0.978943 | ||||||||
\(63\) | −2.15520 | −0.271530 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.72325 | 0.461813 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.70741 | −0.819441 | −0.409720 | − | 0.912211i | \(-0.634374\pi\) | ||||
−0.409720 | + | 0.912211i | \(0.634374\pi\) | |||||||
\(68\) | 1.31694 | 0.159702 | ||||||||
\(69\) | 1.83826 | 0.221301 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | 8.03365 | 0.953419 | 0.476709 | − | 0.879061i | \(-0.341829\pi\) | ||||
0.476709 | + | 0.879061i | \(0.341829\pi\) | |||||||
\(72\) | −2.15520 | −0.253993 | ||||||||
\(73\) | 1.33071 | 0.155747 | 0.0778736 | − | 0.996963i | \(-0.475187\pi\) | ||||
0.0778736 | + | 0.996963i | \(0.475187\pi\) | |||||||
\(74\) | −8.04870 | −0.935642 | ||||||||
\(75\) | −0.919131 | −0.106132 | ||||||||
\(76\) | 2.70741 | 0.310561 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.42216 | 0.387483 | ||||||||
\(79\) | 7.72325 | 0.868934 | 0.434467 | − | 0.900688i | \(-0.356937\pi\) | ||||
0.434467 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 2.11048 | 0.234498 | ||||||||
\(82\) | −3.24458 | −0.358304 | ||||||||
\(83\) | −0.285256 | −0.0313109 | −0.0156555 | − | 0.999877i | \(-0.504983\pi\) | ||||
−0.0156555 | + | 0.999877i | \(0.504983\pi\) | |||||||
\(84\) | −0.919131 | −0.100285 | ||||||||
\(85\) | −1.31694 | −0.142842 | ||||||||
\(86\) | −6.48064 | −0.698826 | ||||||||
\(87\) | −2.71145 | −0.290698 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.14015 | −0.862854 | −0.431427 | − | 0.902148i | \(-0.641990\pi\) | ||||
−0.431427 | + | 0.902148i | \(0.641990\pi\) | |||||||
\(90\) | 2.15520 | 0.227178 | ||||||||
\(91\) | −3.72325 | −0.390303 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | −7.08485 | −0.734664 | ||||||||
\(94\) | −9.37090 | −0.966534 | ||||||||
\(95\) | −2.70741 | −0.277775 | ||||||||
\(96\) | −0.919131 | −0.0938084 | ||||||||
\(97\) | 14.7984 | 1.50255 | 0.751274 | − | 0.659991i | \(-0.229440\pi\) | ||||
0.751274 | + | 0.659991i | \(0.229440\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 14.1000 | 1.40300 | 0.701499 | − | 0.712670i | \(-0.252514\pi\) | ||||
0.701499 | + | 0.712670i | \(0.252514\pi\) | |||||||
\(102\) | −1.21044 | −0.119851 | ||||||||
\(103\) | 11.7627 | 1.15901 | 0.579504 | − | 0.814969i | \(-0.303246\pi\) | ||||
0.579504 | + | 0.814969i | \(0.303246\pi\) | |||||||
\(104\) | −3.72325 | −0.365095 | ||||||||
\(105\) | 0.919131 | 0.0896980 | ||||||||
\(106\) | 13.2848 | 1.29033 | ||||||||
\(107\) | −19.8272 | −1.91677 | −0.958383 | − | 0.285484i | \(-0.907846\pi\) | ||||
−0.958383 | + | 0.285484i | \(0.907846\pi\) | |||||||
\(108\) | 4.73830 | 0.455943 | ||||||||
\(109\) | 0.995533 | 0.0953548 | 0.0476774 | − | 0.998863i | \(-0.484818\pi\) | ||||
0.0476774 | + | 0.998863i | \(0.484818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.39781 | 0.702169 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 11.0691 | 1.04129 | 0.520645 | − | 0.853773i | \(-0.325691\pi\) | ||||
0.520645 | + | 0.853773i | \(0.325691\pi\) | |||||||
\(114\) | −2.48847 | −0.233066 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 2.95002 | 0.273902 | ||||||||
\(117\) | 8.02435 | 0.741851 | ||||||||
\(118\) | −2.83905 | −0.261356 | ||||||||
\(119\) | 1.31694 | 0.120723 | ||||||||
\(120\) | 0.919131 | 0.0839048 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.44651 | −0.130960 | ||||||||
\(123\) | 2.98219 | 0.268895 | ||||||||
\(124\) | 7.70820 | 0.692217 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.15520 | −0.192000 | ||||||||
\(127\) | −6.50223 | −0.576980 | −0.288490 | − | 0.957483i | \(-0.593153\pi\) | ||||
−0.288490 | + | 0.957483i | \(0.593153\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.95656 | 0.524446 | ||||||||
\(130\) | 3.72325 | 0.326551 | ||||||||
\(131\) | 21.7622 | 1.90137 | 0.950684 | − | 0.310160i | \(-0.100383\pi\) | ||||
0.950684 | + | 0.310160i | \(0.100383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.70741 | 0.234762 | ||||||||
\(134\) | −6.70741 | −0.579432 | ||||||||
\(135\) | −4.73830 | −0.407808 | ||||||||
\(136\) | 1.31694 | 0.112926 | ||||||||
\(137\) | −2.90408 | −0.248112 | −0.124056 | − | 0.992275i | \(-0.539590\pi\) | ||||
−0.124056 | + | 0.992275i | \(0.539590\pi\) | |||||||
\(138\) | 1.83826 | 0.156483 | ||||||||
\(139\) | 1.26775 | 0.107529 | 0.0537645 | − | 0.998554i | \(-0.482878\pi\) | ||||
0.0537645 | + | 0.998554i | \(0.482878\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 8.61308 | 0.725352 | ||||||||
\(142\) | 8.03365 | 0.674169 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.15520 | −0.179600 | ||||||||
\(145\) | −2.95002 | −0.244986 | ||||||||
\(146\) | 1.33071 | 0.110130 | ||||||||
\(147\) | −0.919131 | −0.0758086 | ||||||||
\(148\) | −8.04870 | −0.661599 | ||||||||
\(149\) | −5.85489 | −0.479652 | −0.239826 | − | 0.970816i | \(-0.577090\pi\) | ||||
−0.239826 | + | 0.970816i | \(0.577090\pi\) | |||||||
\(150\) | −0.919131 | −0.0750467 | ||||||||
\(151\) | −10.2243 | −0.832039 | −0.416020 | − | 0.909356i | \(-0.636575\pi\) | ||||
−0.416020 | + | 0.909356i | \(0.636575\pi\) | |||||||
\(152\) | 2.70741 | 0.219600 | ||||||||
\(153\) | −2.83826 | −0.229460 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.70820 | −0.619138 | ||||||||
\(156\) | 3.42216 | 0.273992 | ||||||||
\(157\) | 1.18004 | 0.0941772 | 0.0470886 | − | 0.998891i | \(-0.485006\pi\) | ||||
0.0470886 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(158\) | 7.72325 | 0.614429 | ||||||||
\(159\) | −12.2104 | −0.968351 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 2.11048 | 0.165815 | ||||||||
\(163\) | 13.5818 | 1.06381 | 0.531905 | − | 0.846804i | \(-0.321476\pi\) | ||||
0.531905 | + | 0.846804i | \(0.321476\pi\) | |||||||
\(164\) | −3.24458 | −0.253359 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.285256 | −0.0221402 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | −0.919131 | −0.0709125 | ||||||||
\(169\) | 0.862611 | 0.0663547 | ||||||||
\(170\) | −1.31694 | −0.101004 | ||||||||
\(171\) | −5.83501 | −0.446214 | ||||||||
\(172\) | −6.48064 | −0.494145 | ||||||||
\(173\) | 12.4741 | 0.948389 | 0.474194 | − | 0.880420i | \(-0.342739\pi\) | ||||
0.474194 | + | 0.880420i | \(0.342739\pi\) | |||||||
\(174\) | −2.71145 | −0.205555 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.60946 | 0.196139 | ||||||||
\(178\) | −8.14015 | −0.610130 | ||||||||
\(179\) | 12.2295 | 0.914078 | 0.457039 | − | 0.889447i | \(-0.348910\pi\) | ||||
0.457039 | + | 0.889447i | \(0.348910\pi\) | |||||||
\(180\) | 2.15520 | 0.160639 | ||||||||
\(181\) | 20.9718 | 1.55882 | 0.779411 | − | 0.626513i | \(-0.215518\pi\) | ||||
0.779411 | + | 0.626513i | \(0.215518\pi\) | |||||||
\(182\) | −3.72325 | −0.275986 | ||||||||
\(183\) | 1.32953 | 0.0982815 | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | 8.04870 | 0.591752 | ||||||||
\(186\) | −7.08485 | −0.519486 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.37090 | −0.683443 | ||||||||
\(189\) | 4.73830 | 0.344661 | ||||||||
\(190\) | −2.70741 | −0.196416 | ||||||||
\(191\) | 6.74632 | 0.488147 | 0.244073 | − | 0.969757i | \(-0.421516\pi\) | ||||
0.244073 | + | 0.969757i | \(0.421516\pi\) | |||||||
\(192\) | −0.919131 | −0.0663325 | ||||||||
\(193\) | 19.9673 | 1.43728 | 0.718640 | − | 0.695382i | \(-0.244765\pi\) | ||||
0.718640 | + | 0.695382i | \(0.244765\pi\) | |||||||
\(194\) | 14.7984 | 1.06246 | ||||||||
\(195\) | −3.42216 | −0.245066 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.1717 | 1.50842 | 0.754212 | − | 0.656631i | \(-0.228019\pi\) | ||||
0.754212 | + | 0.656631i | \(0.228019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.27872 | 0.586863 | 0.293431 | − | 0.955980i | \(-0.405203\pi\) | ||||
0.293431 | + | 0.955980i | \(0.405203\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 6.16499 | 0.434845 | ||||||||
\(202\) | 14.1000 | 0.992070 | ||||||||
\(203\) | 2.95002 | 0.207051 | ||||||||
\(204\) | −1.21044 | −0.0847476 | ||||||||
\(205\) | 3.24458 | 0.226611 | ||||||||
\(206\) | 11.7627 | 0.819543 | ||||||||
\(207\) | 4.31040 | 0.299593 | ||||||||
\(208\) | −3.72325 | −0.258161 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.919131 | 0.0634260 | ||||||||
\(211\) | 15.5912 | 1.07334 | 0.536671 | − | 0.843792i | \(-0.319682\pi\) | ||||
0.536671 | + | 0.843792i | \(0.319682\pi\) | |||||||
\(212\) | 13.2848 | 0.912402 | ||||||||
\(213\) | −7.38397 | −0.505942 | ||||||||
\(214\) | −19.8272 | −1.35536 | ||||||||
\(215\) | 6.48064 | 0.441976 | ||||||||
\(216\) | 4.73830 | 0.322401 | ||||||||
\(217\) | 7.70820 | 0.523267 | ||||||||
\(218\) | 0.995533 | 0.0674260 | ||||||||
\(219\) | −1.22309 | −0.0826489 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.90329 | −0.329831 | ||||||||
\(222\) | 7.39781 | 0.496508 | ||||||||
\(223\) | −16.6313 | −1.11372 | −0.556858 | − | 0.830608i | \(-0.687993\pi\) | ||||
−0.556858 | + | 0.830608i | \(0.687993\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −2.15520 | −0.143680 | ||||||||
\(226\) | 11.0691 | 0.736304 | ||||||||
\(227\) | 1.19716 | 0.0794582 | 0.0397291 | − | 0.999210i | \(-0.487351\pi\) | ||||
0.0397291 | + | 0.999210i | \(0.487351\pi\) | |||||||
\(228\) | −2.48847 | −0.164803 | ||||||||
\(229\) | 14.8613 | 0.982064 | 0.491032 | − | 0.871141i | \(-0.336620\pi\) | ||||
0.491032 | + | 0.871141i | \(0.336620\pi\) | |||||||
\(230\) | 2.00000 | 0.131876 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.95002 | 0.193678 | ||||||||
\(233\) | −6.33199 | −0.414822 | −0.207411 | − | 0.978254i | \(-0.566504\pi\) | ||||
−0.207411 | + | 0.978254i | \(0.566504\pi\) | |||||||
\(234\) | 8.02435 | 0.524568 | ||||||||
\(235\) | 9.37090 | 0.611290 | ||||||||
\(236\) | −2.83905 | −0.184807 | ||||||||
\(237\) | −7.09868 | −0.461109 | ||||||||
\(238\) | 1.31694 | 0.0853644 | ||||||||
\(239\) | −11.6906 | −0.756202 | −0.378101 | − | 0.925764i | \(-0.623423\pi\) | ||||
−0.378101 | + | 0.925764i | \(0.623423\pi\) | |||||||
\(240\) | 0.919131 | 0.0593296 | ||||||||
\(241\) | 10.3945 | 0.669566 | 0.334783 | − | 0.942295i | \(-0.391337\pi\) | ||||
0.334783 | + | 0.942295i | \(0.391337\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1547 | −1.03633 | ||||||||
\(244\) | −1.44651 | −0.0926030 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 2.98219 | 0.190138 | ||||||||
\(247\) | −10.0804 | −0.641399 | ||||||||
\(248\) | 7.70820 | 0.489471 | ||||||||
\(249\) | 0.262188 | 0.0166155 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −22.3395 | −1.41006 | −0.705029 | − | 0.709179i | \(-0.749066\pi\) | ||||
−0.705029 | + | 0.709179i | \(0.749066\pi\) | |||||||
\(252\) | −2.15520 | −0.135765 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.50223 | −0.407986 | ||||||||
\(255\) | 1.21044 | 0.0758005 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.28201 | −0.329482 | −0.164741 | − | 0.986337i | \(-0.552679\pi\) | ||||
−0.164741 | + | 0.986337i | \(0.552679\pi\) | |||||||
\(258\) | 5.95656 | 0.370839 | ||||||||
\(259\) | −8.04870 | −0.500122 | ||||||||
\(260\) | 3.72325 | 0.230906 | ||||||||
\(261\) | −6.35788 | −0.393543 | ||||||||
\(262\) | 21.7622 | 1.34447 | ||||||||
\(263\) | 25.3847 | 1.56529 | 0.782645 | − | 0.622469i | \(-0.213870\pi\) | ||||
0.782645 | + | 0.622469i | \(0.213870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.2848 | −0.816077 | ||||||||
\(266\) | 2.70741 | 0.166002 | ||||||||
\(267\) | 7.48186 | 0.457883 | ||||||||
\(268\) | −6.70741 | −0.409720 | ||||||||
\(269\) | −15.3782 | −0.937627 | −0.468814 | − | 0.883297i | \(-0.655318\pi\) | ||||
−0.468814 | + | 0.883297i | \(0.655318\pi\) | |||||||
\(270\) | −4.73830 | −0.288364 | ||||||||
\(271\) | 10.3274 | 0.627346 | 0.313673 | − | 0.949531i | \(-0.398440\pi\) | ||||
0.313673 | + | 0.949531i | \(0.398440\pi\) | |||||||
\(272\) | 1.31694 | 0.0798510 | ||||||||
\(273\) | 3.42216 | 0.207118 | ||||||||
\(274\) | −2.90408 | −0.175442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.83826 | 0.110650 | ||||||||
\(277\) | −22.7614 | −1.36760 | −0.683799 | − | 0.729670i | \(-0.739674\pi\) | ||||
−0.683799 | + | 0.729670i | \(0.739674\pi\) | |||||||
\(278\) | 1.26775 | 0.0760345 | ||||||||
\(279\) | −16.6127 | −0.994577 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −3.07890 | −0.183672 | −0.0918359 | − | 0.995774i | \(-0.529274\pi\) | ||||
−0.0918359 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(282\) | 8.61308 | 0.512901 | ||||||||
\(283\) | −10.9791 | −0.652642 | −0.326321 | − | 0.945259i | \(-0.605809\pi\) | ||||
−0.326321 | + | 0.945259i | \(0.605809\pi\) | |||||||
\(284\) | 8.03365 | 0.476709 | ||||||||
\(285\) | 2.48847 | 0.147404 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.24458 | −0.191521 | ||||||||
\(288\) | −2.15520 | −0.126996 | ||||||||
\(289\) | −15.2657 | −0.897981 | ||||||||
\(290\) | −2.95002 | −0.173231 | ||||||||
\(291\) | −13.6016 | −0.797342 | ||||||||
\(292\) | 1.33071 | 0.0778736 | ||||||||
\(293\) | 8.05126 | 0.470360 | 0.235180 | − | 0.971952i | \(-0.424432\pi\) | ||||
0.235180 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(294\) | −0.919131 | −0.0536048 | ||||||||
\(295\) | 2.83905 | 0.165296 | ||||||||
\(296\) | −8.04870 | −0.467821 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.85489 | −0.339165 | ||||||||
\(299\) | 7.44651 | 0.430643 | ||||||||
\(300\) | −0.919131 | −0.0530660 | ||||||||
\(301\) | −6.48064 | −0.373538 | ||||||||
\(302\) | −10.2243 | −0.588341 | ||||||||
\(303\) | −12.9597 | −0.744516 | ||||||||
\(304\) | 2.70741 | 0.155281 | ||||||||
\(305\) | 1.44651 | 0.0828267 | ||||||||
\(306\) | −2.83826 | −0.162253 | ||||||||
\(307\) | −27.5963 | −1.57501 | −0.787503 | − | 0.616311i | \(-0.788627\pi\) | ||||
−0.787503 | + | 0.616311i | \(0.788627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.8114 | −0.615040 | ||||||||
\(310\) | −7.70820 | −0.437797 | ||||||||
\(311\) | 29.7870 | 1.68907 | 0.844533 | − | 0.535504i | \(-0.179878\pi\) | ||||
0.844533 | + | 0.535504i | \(0.179878\pi\) | |||||||
\(312\) | 3.42216 | 0.193741 | ||||||||
\(313\) | 30.9153 | 1.74744 | 0.873718 | − | 0.486433i | \(-0.161702\pi\) | ||||
0.873718 | + | 0.486433i | \(0.161702\pi\) | |||||||
\(314\) | 1.18004 | 0.0665934 | ||||||||
\(315\) | 2.15520 | 0.121432 | ||||||||
\(316\) | 7.72325 | 0.434467 | ||||||||
\(317\) | −2.32189 | −0.130411 | −0.0652053 | − | 0.997872i | \(-0.520770\pi\) | ||||
−0.0652053 | + | 0.997872i | \(0.520770\pi\) | |||||||
\(318\) | −12.2104 | −0.684727 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 18.2238 | 1.01715 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | 3.56549 | 0.198389 | ||||||||
\(324\) | 2.11048 | 0.117249 | ||||||||
\(325\) | −3.72325 | −0.206529 | ||||||||
\(326\) | 13.5818 | 0.752228 | ||||||||
\(327\) | −0.915025 | −0.0506010 | ||||||||
\(328\) | −3.24458 | −0.179152 | ||||||||
\(329\) | −9.37090 | −0.516634 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.95686 | −0.547279 | −0.273639 | − | 0.961832i | \(-0.588227\pi\) | ||||
−0.273639 | + | 0.961832i | \(0.588227\pi\) | |||||||
\(332\) | −0.285256 | −0.0156555 | ||||||||
\(333\) | 17.3465 | 0.950585 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 6.70741 | 0.366465 | ||||||||
\(336\) | −0.919131 | −0.0501427 | ||||||||
\(337\) | 20.7682 | 1.13132 | 0.565658 | − | 0.824640i | \(-0.308622\pi\) | ||||
0.565658 | + | 0.824640i | \(0.308622\pi\) | |||||||
\(338\) | 0.862611 | 0.0469198 | ||||||||
\(339\) | −10.1739 | −0.552572 | ||||||||
\(340\) | −1.31694 | −0.0714210 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −5.83501 | −0.315521 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.48064 | −0.349413 | ||||||||
\(345\) | −1.83826 | −0.0989687 | ||||||||
\(346\) | 12.4741 | 0.670612 | ||||||||
\(347\) | 15.7606 | 0.846072 | 0.423036 | − | 0.906113i | \(-0.360964\pi\) | ||||
0.423036 | + | 0.906113i | \(0.360964\pi\) | |||||||
\(348\) | −2.71145 | −0.145349 | ||||||||
\(349\) | 23.2953 | 1.24697 | 0.623484 | − | 0.781836i | \(-0.285717\pi\) | ||||
0.623484 | + | 0.781836i | \(0.285717\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −17.6419 | −0.941655 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.1303 | 1.44400 | 0.721999 | − | 0.691894i | \(-0.243224\pi\) | ||||
0.721999 | + | 0.691894i | \(0.243224\pi\) | |||||||
\(354\) | 2.60946 | 0.138691 | ||||||||
\(355\) | −8.03365 | −0.426382 | ||||||||
\(356\) | −8.14015 | −0.431427 | ||||||||
\(357\) | −1.21044 | −0.0640631 | ||||||||
\(358\) | 12.2295 | 0.646351 | ||||||||
\(359\) | 32.0637 | 1.69226 | 0.846130 | − | 0.532977i | \(-0.178927\pi\) | ||||
0.846130 | + | 0.532977i | \(0.178927\pi\) | |||||||
\(360\) | 2.15520 | 0.113589 | ||||||||
\(361\) | −11.6699 | −0.614206 | ||||||||
\(362\) | 20.9718 | 1.10225 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.72325 | −0.195151 | ||||||||
\(365\) | −1.33071 | −0.0696523 | ||||||||
\(366\) | 1.32953 | 0.0694955 | ||||||||
\(367\) | −11.6037 | −0.605709 | −0.302854 | − | 0.953037i | \(-0.597940\pi\) | ||||
−0.302854 | + | 0.953037i | \(0.597940\pi\) | |||||||
\(368\) | −2.00000 | −0.104257 | ||||||||
\(369\) | 6.99271 | 0.364026 | ||||||||
\(370\) | 8.04870 | 0.418432 | ||||||||
\(371\) | 13.2848 | 0.689711 | ||||||||
\(372\) | −7.08485 | −0.367332 | ||||||||
\(373\) | −17.7252 | −0.917777 | −0.458889 | − | 0.888494i | \(-0.651752\pi\) | ||||
−0.458889 | + | 0.888494i | \(0.651752\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.919131 | 0.0474637 | ||||||||
\(376\) | −9.37090 | −0.483267 | ||||||||
\(377\) | −10.9837 | −0.565688 | ||||||||
\(378\) | 4.73830 | 0.243712 | ||||||||
\(379\) | −12.0540 | −0.619174 | −0.309587 | − | 0.950871i | \(-0.600191\pi\) | ||||
−0.309587 | + | 0.950871i | \(0.600191\pi\) | |||||||
\(380\) | −2.70741 | −0.138887 | ||||||||
\(381\) | 5.97640 | 0.306180 | ||||||||
\(382\) | 6.74632 | 0.345172 | ||||||||
\(383\) | 6.75538 | 0.345184 | 0.172592 | − | 0.984993i | \(-0.444786\pi\) | ||||
0.172592 | + | 0.984993i | \(0.444786\pi\) | |||||||
\(384\) | −0.919131 | −0.0469042 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.9673 | 1.01631 | ||||||||
\(387\) | 13.9671 | 0.709986 | ||||||||
\(388\) | 14.7984 | 0.751274 | ||||||||
\(389\) | −24.1441 | −1.22416 | −0.612078 | − | 0.790797i | \(-0.709666\pi\) | ||||
−0.612078 | + | 0.790797i | \(0.709666\pi\) | |||||||
\(390\) | −3.42216 | −0.173288 | ||||||||
\(391\) | −2.63387 | −0.133201 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −20.0023 | −1.00898 | ||||||||
\(394\) | 21.1717 | 1.06662 | ||||||||
\(395\) | −7.72325 | −0.388599 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.5163 | 0.527798 | 0.263899 | − | 0.964550i | \(-0.414991\pi\) | ||||
0.263899 | + | 0.964550i | \(0.414991\pi\) | |||||||
\(398\) | 8.27872 | 0.414975 | ||||||||
\(399\) | −2.48847 | −0.124579 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −37.1997 | −1.85766 | −0.928831 | − | 0.370503i | \(-0.879185\pi\) | ||||
−0.928831 | + | 0.370503i | \(0.879185\pi\) | |||||||
\(402\) | 6.16499 | 0.307482 | ||||||||
\(403\) | −28.6996 | −1.42963 | ||||||||
\(404\) | 14.1000 | 0.701499 | ||||||||
\(405\) | −2.11048 | −0.104870 | ||||||||
\(406\) | 2.95002 | 0.146407 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.21044 | −0.0599256 | ||||||||
\(409\) | 26.3908 | 1.30494 | 0.652470 | − | 0.757815i | \(-0.273733\pi\) | ||||
0.652470 | + | 0.757815i | \(0.273733\pi\) | |||||||
\(410\) | 3.24458 | 0.160238 | ||||||||
\(411\) | 2.66923 | 0.131663 | ||||||||
\(412\) | 11.7627 | 0.579504 | ||||||||
\(413\) | −2.83905 | −0.139701 | ||||||||
\(414\) | 4.31040 | 0.211844 | ||||||||
\(415\) | 0.285256 | 0.0140027 | ||||||||
\(416\) | −3.72325 | −0.182547 | ||||||||
\(417\) | −1.16523 | −0.0570614 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0447 | 0.637273 | 0.318637 | − | 0.947877i | \(-0.396775\pi\) | ||||
0.318637 | + | 0.947877i | \(0.396775\pi\) | |||||||
\(420\) | 0.919131 | 0.0448490 | ||||||||
\(421\) | −13.4510 | −0.655563 | −0.327782 | − | 0.944753i | \(-0.606301\pi\) | ||||
−0.327782 | + | 0.944753i | \(0.606301\pi\) | |||||||
\(422\) | 15.5912 | 0.758967 | ||||||||
\(423\) | 20.1961 | 0.981970 | ||||||||
\(424\) | 13.2848 | 0.645165 | ||||||||
\(425\) | 1.31694 | 0.0638808 | ||||||||
\(426\) | −7.38397 | −0.357755 | ||||||||
\(427\) | −1.44651 | −0.0700013 | ||||||||
\(428\) | −19.8272 | −0.958383 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.48064 | 0.312524 | ||||||||
\(431\) | 32.7451 | 1.57728 | 0.788638 | − | 0.614858i | \(-0.210787\pi\) | ||||
0.788638 | + | 0.614858i | \(0.210787\pi\) | |||||||
\(432\) | 4.73830 | 0.227972 | ||||||||
\(433\) | 9.00434 | 0.432721 | 0.216361 | − | 0.976314i | \(-0.430581\pi\) | ||||
0.216361 | + | 0.976314i | \(0.430581\pi\) | |||||||
\(434\) | 7.70820 | 0.370006 | ||||||||
\(435\) | 2.71145 | 0.130004 | ||||||||
\(436\) | 0.995533 | 0.0476774 | ||||||||
\(437\) | −5.41482 | −0.259026 | ||||||||
\(438\) | −1.22309 | −0.0584416 | ||||||||
\(439\) | 3.88952 | 0.185637 | 0.0928184 | − | 0.995683i | \(-0.470412\pi\) | ||||
0.0928184 | + | 0.995683i | \(0.470412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.15520 | −0.102629 | ||||||||
\(442\) | −4.90329 | −0.233226 | ||||||||
\(443\) | 5.63377 | 0.267669 | 0.133834 | − | 0.991004i | \(-0.457271\pi\) | ||||
0.133834 | + | 0.991004i | \(0.457271\pi\) | |||||||
\(444\) | 7.39781 | 0.351084 | ||||||||
\(445\) | 8.14015 | 0.385880 | ||||||||
\(446\) | −16.6313 | −0.787515 | ||||||||
\(447\) | 5.38141 | 0.254532 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −5.62855 | −0.265628 | −0.132814 | − | 0.991141i | \(-0.542401\pi\) | ||||
−0.132814 | + | 0.991141i | \(0.542401\pi\) | |||||||
\(450\) | −2.15520 | −0.101597 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 11.0691 | 0.520645 | ||||||||
\(453\) | 9.39744 | 0.441530 | ||||||||
\(454\) | 1.19716 | 0.0561855 | ||||||||
\(455\) | 3.72325 | 0.174549 | ||||||||
\(456\) | −2.48847 | −0.116533 | ||||||||
\(457\) | 1.15770 | 0.0541548 | 0.0270774 | − | 0.999633i | \(-0.491380\pi\) | ||||
0.0270774 | + | 0.999633i | \(0.491380\pi\) | |||||||
\(458\) | 14.8613 | 0.694424 | ||||||||
\(459\) | 6.24005 | 0.291260 | ||||||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | 10.3088 | 0.480129 | 0.240065 | − | 0.970757i | \(-0.422831\pi\) | ||||
0.240065 | + | 0.970757i | \(0.422831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4740 | −1.36977 | −0.684887 | − | 0.728649i | \(-0.740149\pi\) | ||||
−0.684887 | + | 0.728649i | \(0.740149\pi\) | |||||||
\(464\) | 2.95002 | 0.136951 | ||||||||
\(465\) | 7.08485 | 0.328552 | ||||||||
\(466\) | −6.33199 | −0.293324 | ||||||||
\(467\) | 20.5977 | 0.953146 | 0.476573 | − | 0.879135i | \(-0.341879\pi\) | ||||
0.476573 | + | 0.879135i | \(0.341879\pi\) | |||||||
\(468\) | 8.02435 | 0.370926 | ||||||||
\(469\) | −6.70741 | −0.309720 | ||||||||
\(470\) | 9.37090 | 0.432247 | ||||||||
\(471\) | −1.08461 | −0.0499761 | ||||||||
\(472\) | −2.83905 | −0.130678 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −7.09868 | −0.326053 | ||||||||
\(475\) | 2.70741 | 0.124225 | ||||||||
\(476\) | 1.31694 | 0.0603617 | ||||||||
\(477\) | −28.6313 | −1.31094 | ||||||||
\(478\) | −11.6906 | −0.534715 | ||||||||
\(479\) | −4.18526 | −0.191229 | −0.0956146 | − | 0.995418i | \(-0.530482\pi\) | ||||
−0.0956146 | + | 0.995418i | \(0.530482\pi\) | |||||||
\(480\) | 0.919131 | 0.0419524 | ||||||||
\(481\) | 29.9673 | 1.36639 | ||||||||
\(482\) | 10.3945 | 0.473454 | ||||||||
\(483\) | 1.83826 | 0.0836438 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.7984 | −0.671960 | ||||||||
\(486\) | −16.1547 | −0.732792 | ||||||||
\(487\) | −8.06730 | −0.365564 | −0.182782 | − | 0.983153i | \(-0.558510\pi\) | ||||
−0.182782 | + | 0.983153i | \(0.558510\pi\) | |||||||
\(488\) | −1.44651 | −0.0654802 | ||||||||
\(489\) | −12.4835 | −0.564522 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −23.5882 | −1.06452 | −0.532261 | − | 0.846580i | \(-0.678658\pi\) | ||||
−0.532261 | + | 0.846580i | \(0.678658\pi\) | |||||||
\(492\) | 2.98219 | 0.134448 | ||||||||
\(493\) | 3.88499 | 0.174971 | ||||||||
\(494\) | −10.0804 | −0.453538 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.70820 | 0.346109 | ||||||||
\(497\) | 8.03365 | 0.360358 | ||||||||
\(498\) | 0.262188 | 0.0117489 | ||||||||
\(499\) | 7.22181 | 0.323293 | 0.161646 | − | 0.986849i | \(-0.448320\pi\) | ||||
0.161646 | + | 0.986849i | \(0.448320\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −11.0296 | −0.492765 | ||||||||
\(502\) | −22.3395 | −0.997061 | ||||||||
\(503\) | −11.3828 | −0.507532 | −0.253766 | − | 0.967266i | \(-0.581669\pi\) | ||||
−0.253766 | + | 0.967266i | \(0.581669\pi\) | |||||||
\(504\) | −2.15520 | −0.0960002 | ||||||||
\(505\) | −14.1000 | −0.627440 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.792852 | −0.0352118 | ||||||||
\(508\) | −6.50223 | −0.288490 | ||||||||
\(509\) | 12.1422 | 0.538192 | 0.269096 | − | 0.963113i | \(-0.413275\pi\) | ||||
0.269096 | + | 0.963113i | \(0.413275\pi\) | |||||||
\(510\) | 1.21044 | 0.0535991 | ||||||||
\(511\) | 1.33071 | 0.0588669 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 12.8285 | 0.566394 | ||||||||
\(514\) | −5.28201 | −0.232979 | ||||||||
\(515\) | −11.7627 | −0.518324 | ||||||||
\(516\) | 5.95656 | 0.262223 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −8.04870 | −0.353640 | ||||||||
\(519\) | −11.4653 | −0.503272 | ||||||||
\(520\) | 3.72325 | 0.163275 | ||||||||
\(521\) | 12.1565 | 0.532585 | 0.266293 | − | 0.963892i | \(-0.414201\pi\) | ||||
0.266293 | + | 0.963892i | \(0.414201\pi\) | |||||||
\(522\) | −6.35788 | −0.278277 | ||||||||
\(523\) | 29.3199 | 1.28207 | 0.641035 | − | 0.767512i | \(-0.278505\pi\) | ||||
0.641035 | + | 0.767512i | \(0.278505\pi\) | |||||||
\(524\) | 21.7622 | 0.950684 | ||||||||
\(525\) | −0.919131 | −0.0401142 | ||||||||
\(526\) | 25.3847 | 1.10683 | ||||||||
\(527\) | 10.1512 | 0.442194 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | −13.2848 | −0.577053 | ||||||||
\(531\) | 6.11872 | 0.265530 | ||||||||
\(532\) | 2.70741 | 0.117381 | ||||||||
\(533\) | 12.0804 | 0.523259 | ||||||||
\(534\) | 7.48186 | 0.323772 | ||||||||
\(535\) | 19.8272 | 0.857204 | ||||||||
\(536\) | −6.70741 | −0.289716 | ||||||||
\(537\) | −11.2405 | −0.485065 | ||||||||
\(538\) | −15.3782 | −0.663002 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.73830 | −0.203904 | ||||||||
\(541\) | −2.54640 | −0.109478 | −0.0547392 | − | 0.998501i | \(-0.517433\pi\) | ||||
−0.0547392 | + | 0.998501i | \(0.517433\pi\) | |||||||
\(542\) | 10.3274 | 0.443600 | ||||||||
\(543\) | −19.2758 | −0.827205 | ||||||||
\(544\) | 1.31694 | 0.0564632 | ||||||||
\(545\) | −0.995533 | −0.0426439 | ||||||||
\(546\) | 3.42216 | 0.146455 | ||||||||
\(547\) | −32.1359 | −1.37403 | −0.687016 | − | 0.726642i | \(-0.741080\pi\) | ||||
−0.687016 | + | 0.726642i | \(0.741080\pi\) | |||||||
\(548\) | −2.90408 | −0.124056 | ||||||||
\(549\) | 3.11751 | 0.133052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.98692 | 0.340254 | ||||||||
\(552\) | 1.83826 | 0.0782416 | ||||||||
\(553\) | 7.72325 | 0.328426 | ||||||||
\(554\) | −22.7614 | −0.967038 | ||||||||
\(555\) | −7.39781 | −0.314019 | ||||||||
\(556\) | 1.26775 | 0.0537645 | ||||||||
\(557\) | −5.98042 | −0.253399 | −0.126699 | − | 0.991941i | \(-0.540438\pi\) | ||||
−0.126699 | + | 0.991941i | \(0.540438\pi\) | |||||||
\(558\) | −16.6127 | −0.703272 | ||||||||
\(559\) | 24.1291 | 1.02055 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.07890 | −0.129876 | ||||||||
\(563\) | 1.80284 | 0.0759807 | 0.0379903 | − | 0.999278i | \(-0.487904\pi\) | ||||
0.0379903 | + | 0.999278i | \(0.487904\pi\) | |||||||
\(564\) | 8.61308 | 0.362676 | ||||||||
\(565\) | −11.0691 | −0.465679 | ||||||||
\(566\) | −10.9791 | −0.461488 | ||||||||
\(567\) | 2.11048 | 0.0886317 | ||||||||
\(568\) | 8.03365 | 0.337084 | ||||||||
\(569\) | 30.1377 | 1.26344 | 0.631718 | − | 0.775198i | \(-0.282350\pi\) | ||||
0.631718 | + | 0.775198i | \(0.282350\pi\) | |||||||
\(570\) | 2.48847 | 0.104230 | ||||||||
\(571\) | 30.3322 | 1.26936 | 0.634681 | − | 0.772774i | \(-0.281131\pi\) | ||||
0.634681 | + | 0.772774i | \(0.281131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.20075 | −0.259040 | ||||||||
\(574\) | −3.24458 | −0.135426 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | −2.15520 | −0.0897999 | ||||||||
\(577\) | −15.7849 | −0.657135 | −0.328568 | − | 0.944480i | \(-0.606566\pi\) | ||||
−0.328568 | + | 0.944480i | \(0.606566\pi\) | |||||||
\(578\) | −15.2657 | −0.634968 | ||||||||
\(579\) | −18.3526 | −0.762708 | ||||||||
\(580\) | −2.95002 | −0.122493 | ||||||||
\(581\) | −0.285256 | −0.0118344 | ||||||||
\(582\) | −13.6016 | −0.563806 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.33071 | 0.0550650 | ||||||||
\(585\) | −8.02435 | −0.331766 | ||||||||
\(586\) | 8.05126 | 0.332595 | ||||||||
\(587\) | 25.9219 | 1.06991 | 0.534956 | − | 0.844880i | \(-0.320328\pi\) | ||||
0.534956 | + | 0.844880i | \(0.320328\pi\) | |||||||
\(588\) | −0.919131 | −0.0379043 | ||||||||
\(589\) | 20.8693 | 0.859904 | ||||||||
\(590\) | 2.83905 | 0.116882 | ||||||||
\(591\) | −19.4596 | −0.800460 | ||||||||
\(592\) | −8.04870 | −0.330799 | ||||||||
\(593\) | −2.58469 | −0.106140 | −0.0530702 | − | 0.998591i | \(-0.516901\pi\) | ||||
−0.0530702 | + | 0.998591i | \(0.516901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.31694 | −0.0539892 | ||||||||
\(596\) | −5.85489 | −0.239826 | ||||||||
\(597\) | −7.60922 | −0.311425 | ||||||||
\(598\) | 7.44651 | 0.304510 | ||||||||
\(599\) | 8.01529 | 0.327496 | 0.163748 | − | 0.986502i | \(-0.447642\pi\) | ||||
0.163748 | + | 0.986502i | \(0.447642\pi\) | |||||||
\(600\) | −0.919131 | −0.0375234 | ||||||||
\(601\) | 1.07488 | 0.0438454 | 0.0219227 | − | 0.999760i | \(-0.493021\pi\) | ||||
0.0219227 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(602\) | −6.48064 | −0.264131 | ||||||||
\(603\) | 14.4558 | 0.588686 | ||||||||
\(604\) | −10.2243 | −0.416020 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.9597 | −0.526452 | ||||||||
\(607\) | 12.6752 | 0.514472 | 0.257236 | − | 0.966349i | \(-0.417188\pi\) | ||||
0.257236 | + | 0.966349i | \(0.417188\pi\) | |||||||
\(608\) | 2.70741 | 0.109800 | ||||||||
\(609\) | −2.71145 | −0.109874 | ||||||||
\(610\) | 1.44651 | 0.0585673 | ||||||||
\(611\) | 34.8902 | 1.41151 | ||||||||
\(612\) | −2.83826 | −0.114730 | ||||||||
\(613\) | −21.0929 | −0.851935 | −0.425968 | − | 0.904738i | \(-0.640066\pi\) | ||||
−0.425968 | + | 0.904738i | \(0.640066\pi\) | |||||||
\(614\) | −27.5963 | −1.11370 | ||||||||
\(615\) | −2.98219 | −0.120254 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.4070 | −0.620263 | −0.310131 | − | 0.950694i | \(-0.600373\pi\) | ||||
−0.310131 | + | 0.950694i | \(0.600373\pi\) | |||||||
\(618\) | −10.8114 | −0.434899 | ||||||||
\(619\) | 18.6431 | 0.749328 | 0.374664 | − | 0.927161i | \(-0.377758\pi\) | ||||
0.374664 | + | 0.927161i | \(0.377758\pi\) | |||||||
\(620\) | −7.70820 | −0.309569 | ||||||||
\(621\) | −9.47660 | −0.380283 | ||||||||
\(622\) | 29.7870 | 1.19435 | ||||||||
\(623\) | −8.14015 | −0.326128 | ||||||||
\(624\) | 3.42216 | 0.136996 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 30.9153 | 1.23562 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.18004 | 0.0470886 | ||||||||
\(629\) | −10.5996 | −0.422635 | ||||||||
\(630\) | 2.15520 | 0.0858652 | ||||||||
\(631\) | 27.4709 | 1.09360 | 0.546799 | − | 0.837264i | \(-0.315846\pi\) | ||||
0.546799 | + | 0.837264i | \(0.315846\pi\) | |||||||
\(632\) | 7.72325 | 0.307214 | ||||||||
\(633\) | −14.3303 | −0.569580 | ||||||||
\(634\) | −2.32189 | −0.0922142 | ||||||||
\(635\) | 6.50223 | 0.258033 | ||||||||
\(636\) | −12.2104 | −0.484175 | ||||||||
\(637\) | −3.72325 | −0.147521 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.3141 | −0.684936 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −32.4224 | −1.28061 | −0.640304 | − | 0.768121i | \(-0.721192\pi\) | ||||
−0.640304 | + | 0.768121i | \(0.721192\pi\) | |||||||
\(642\) | 18.2238 | 0.719235 | ||||||||
\(643\) | 1.62945 | 0.0642591 | 0.0321296 | − | 0.999484i | \(-0.489771\pi\) | ||||
0.0321296 | + | 0.999484i | \(0.489771\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | −5.95656 | −0.234539 | ||||||||
\(646\) | 3.56549 | 0.140282 | ||||||||
\(647\) | 36.2914 | 1.42676 | 0.713382 | − | 0.700775i | \(-0.247163\pi\) | ||||
0.713382 | + | 0.700775i | \(0.247163\pi\) | |||||||
\(648\) | 2.11048 | 0.0829074 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.72325 | −0.146038 | ||||||||
\(651\) | −7.08485 | −0.277677 | ||||||||
\(652\) | 13.5818 | 0.531905 | ||||||||
\(653\) | −32.1275 | −1.25725 | −0.628623 | − | 0.777710i | \(-0.716381\pi\) | ||||
−0.628623 | + | 0.777710i | \(0.716381\pi\) | |||||||
\(654\) | −0.915025 | −0.0357803 | ||||||||
\(655\) | −21.7622 | −0.850318 | ||||||||
\(656\) | −3.24458 | −0.126679 | ||||||||
\(657\) | −2.86793 | −0.111889 | ||||||||
\(658\) | −9.37090 | −0.365316 | ||||||||
\(659\) | −24.7215 | −0.963012 | −0.481506 | − | 0.876443i | \(-0.659910\pi\) | ||||
−0.481506 | + | 0.876443i | \(0.659910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.3370 | −0.946598 | −0.473299 | − | 0.880902i | \(-0.656937\pi\) | ||||
−0.473299 | + | 0.880902i | \(0.656937\pi\) | |||||||
\(662\) | −9.95686 | −0.386984 | ||||||||
\(663\) | 4.50676 | 0.175028 | ||||||||
\(664\) | −0.285256 | −0.0110701 | ||||||||
\(665\) | −2.70741 | −0.104989 | ||||||||
\(666\) | 17.3465 | 0.672165 | ||||||||
\(667\) | −5.90004 | −0.228450 | ||||||||
\(668\) | 12.0000 | 0.464294 | ||||||||
\(669\) | 15.2864 | 0.591004 | ||||||||
\(670\) | 6.70741 | 0.259130 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.919131 | −0.0354562 | ||||||||
\(673\) | 43.7873 | 1.68787 | 0.843937 | − | 0.536442i | \(-0.180232\pi\) | ||||
0.843937 | + | 0.536442i | \(0.180232\pi\) | |||||||
\(674\) | 20.7682 | 0.799962 | ||||||||
\(675\) | 4.73830 | 0.182377 | ||||||||
\(676\) | 0.862611 | 0.0331773 | ||||||||
\(677\) | −20.9199 | −0.804018 | −0.402009 | − | 0.915636i | \(-0.631688\pi\) | ||||
−0.402009 | + | 0.915636i | \(0.631688\pi\) | |||||||
\(678\) | −10.1739 | −0.390727 | ||||||||
\(679\) | 14.7984 | 0.567909 | ||||||||
\(680\) | −1.31694 | −0.0505022 | ||||||||
\(681\) | −1.10035 | −0.0421653 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.79955 | −0.260178 | −0.130089 | − | 0.991502i | \(-0.541526\pi\) | ||||
−0.130089 | + | 0.991502i | \(0.541526\pi\) | |||||||
\(684\) | −5.83501 | −0.223107 | ||||||||
\(685\) | 2.90408 | 0.110959 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −13.6595 | −0.521143 | ||||||||
\(688\) | −6.48064 | −0.247072 | ||||||||
\(689\) | −49.4625 | −1.88437 | ||||||||
\(690\) | −1.83826 | −0.0699814 | ||||||||
\(691\) | 33.0127 | 1.25586 | 0.627931 | − | 0.778269i | \(-0.283902\pi\) | ||||
0.627931 | + | 0.778269i | \(0.283902\pi\) | |||||||
\(692\) | 12.4741 | 0.474194 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.7606 | 0.598263 | ||||||||
\(695\) | −1.26775 | −0.0480885 | ||||||||
\(696\) | −2.71145 | −0.102777 | ||||||||
\(697\) | −4.27290 | −0.161848 | ||||||||
\(698\) | 23.2953 | 0.881740 | ||||||||
\(699\) | 5.81992 | 0.220130 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 34.2118 | 1.29216 | 0.646081 | − | 0.763269i | \(-0.276407\pi\) | ||||
0.646081 | + | 0.763269i | \(0.276407\pi\) | |||||||
\(702\) | −17.6419 | −0.665850 | ||||||||
\(703\) | −21.7911 | −0.821869 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.61308 | −0.324387 | ||||||||
\(706\) | 27.1303 | 1.02106 | ||||||||
\(707\) | 14.1000 | 0.530284 | ||||||||
\(708\) | 2.60946 | 0.0980695 | ||||||||
\(709\) | −10.7815 | −0.404909 | −0.202455 | − | 0.979292i | \(-0.564892\pi\) | ||||
−0.202455 | + | 0.979292i | \(0.564892\pi\) | |||||||
\(710\) | −8.03365 | −0.301498 | ||||||||
\(711\) | −16.6451 | −0.624242 | ||||||||
\(712\) | −8.14015 | −0.305065 | ||||||||
\(713\) | −15.4164 | −0.577349 | ||||||||
\(714\) | −1.21044 | −0.0452995 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.2295 | 0.457039 | ||||||||
\(717\) | 10.7452 | 0.401286 | ||||||||
\(718\) | 32.0637 | 1.19661 | ||||||||
\(719\) | −48.7392 | −1.81767 | −0.908833 | − | 0.417160i | \(-0.863026\pi\) | ||||
−0.908833 | + | 0.417160i | \(0.863026\pi\) | |||||||
\(720\) | 2.15520 | 0.0803195 | ||||||||
\(721\) | 11.7627 | 0.438064 | ||||||||
\(722\) | −11.6699 | −0.434309 | ||||||||
\(723\) | −9.55386 | −0.355312 | ||||||||
\(724\) | 20.9718 | 0.779411 | ||||||||
\(725\) | 2.95002 | 0.109561 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9416 | 0.442891 | 0.221446 | − | 0.975173i | \(-0.428922\pi\) | ||||
0.221446 | + | 0.975173i | \(0.428922\pi\) | |||||||
\(728\) | −3.72325 | −0.137993 | ||||||||
\(729\) | 8.51686 | 0.315439 | ||||||||
\(730\) | −1.33071 | −0.0492516 | ||||||||
\(731\) | −8.53460 | −0.315664 | ||||||||
\(732\) | 1.32953 | 0.0491408 | ||||||||
\(733\) | 38.9332 | 1.43803 | 0.719015 | − | 0.694995i | \(-0.244593\pi\) | ||||
0.719015 | + | 0.694995i | \(0.244593\pi\) | |||||||
\(734\) | −11.6037 | −0.428301 | ||||||||
\(735\) | 0.919131 | 0.0339026 | ||||||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 6.99271 | 0.257405 | ||||||||
\(739\) | 29.3583 | 1.07996 | 0.539981 | − | 0.841677i | \(-0.318431\pi\) | ||||
0.539981 | + | 0.841677i | \(0.318431\pi\) | |||||||
\(740\) | 8.04870 | 0.295876 | ||||||||
\(741\) | 9.26519 | 0.340365 | ||||||||
\(742\) | 13.2848 | 0.487699 | ||||||||
\(743\) | 27.1351 | 0.995491 | 0.497746 | − | 0.867323i | \(-0.334161\pi\) | ||||
0.497746 | + | 0.867323i | \(0.334161\pi\) | |||||||
\(744\) | −7.08485 | −0.259743 | ||||||||
\(745\) | 5.85489 | 0.214507 | ||||||||
\(746\) | −17.7252 | −0.648966 | ||||||||
\(747\) | 0.614784 | 0.0224938 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.8272 | −0.724470 | ||||||||
\(750\) | 0.919131 | 0.0335619 | ||||||||
\(751\) | −36.8507 | −1.34470 | −0.672350 | − | 0.740233i | \(-0.734715\pi\) | ||||
−0.672350 | + | 0.740233i | \(0.734715\pi\) | |||||||
\(752\) | −9.37090 | −0.341721 | ||||||||
\(753\) | 20.5329 | 0.748262 | ||||||||
\(754\) | −10.9837 | −0.400002 | ||||||||
\(755\) | 10.2243 | 0.372099 | ||||||||
\(756\) | 4.73830 | 0.172330 | ||||||||
\(757\) | 1.04667 | 0.0380417 | 0.0190209 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190209 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(758\) | −12.0540 | −0.437822 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.70741 | −0.0982082 | ||||||||
\(761\) | 2.62959 | 0.0953227 | 0.0476614 | − | 0.998864i | \(-0.484823\pi\) | ||||
0.0476614 | + | 0.998864i | \(0.484823\pi\) | |||||||
\(762\) | 5.97640 | 0.216502 | ||||||||
\(763\) | 0.995533 | 0.0360407 | ||||||||
\(764\) | 6.74632 | 0.244073 | ||||||||
\(765\) | 2.83826 | 0.102618 | ||||||||
\(766\) | 6.75538 | 0.244082 | ||||||||
\(767\) | 10.5705 | 0.381679 | ||||||||
\(768\) | −0.919131 | −0.0331663 | ||||||||
\(769\) | 31.0270 | 1.11886 | 0.559431 | − | 0.828877i | \(-0.311020\pi\) | ||||
0.559431 | + | 0.828877i | \(0.311020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.85485 | 0.174843 | ||||||||
\(772\) | 19.9673 | 0.718640 | ||||||||
\(773\) | −8.84786 | −0.318236 | −0.159118 | − | 0.987260i | \(-0.550865\pi\) | ||||
−0.159118 | + | 0.987260i | \(0.550865\pi\) | |||||||
\(774\) | 13.9671 | 0.502036 | ||||||||
\(775\) | 7.70820 | 0.276887 | ||||||||
\(776\) | 14.7984 | 0.531231 | ||||||||
\(777\) | 7.39781 | 0.265395 | ||||||||
\(778\) | −24.1441 | −0.865609 | ||||||||
\(779\) | −8.78441 | −0.314734 | ||||||||
\(780\) | −3.42216 | −0.122533 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.63387 | −0.0941872 | ||||||||
\(783\) | 13.9781 | 0.499536 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −1.18004 | −0.0421173 | ||||||||
\(786\) | −20.0023 | −0.713457 | ||||||||
\(787\) | 6.15195 | 0.219293 | 0.109647 | − | 0.993971i | \(-0.465028\pi\) | ||||
0.109647 | + | 0.993971i | \(0.465028\pi\) | |||||||
\(788\) | 21.1717 | 0.754212 | ||||||||
\(789\) | −23.3319 | −0.830637 | ||||||||
\(790\) | −7.72325 | −0.274781 | ||||||||
\(791\) | 11.0691 | 0.393571 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.38571 | 0.191252 | ||||||||
\(794\) | 10.5163 | 0.373210 | ||||||||
\(795\) | 12.2104 | 0.433060 | ||||||||
\(796\) | 8.27872 | 0.293431 | ||||||||
\(797\) | −47.3736 | −1.67806 | −0.839030 | − | 0.544085i | \(-0.816877\pi\) | ||||
−0.839030 | + | 0.544085i | \(0.816877\pi\) | |||||||
\(798\) | −2.48847 | −0.0880907 | ||||||||
\(799\) | −12.3409 | −0.436589 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 17.5436 | 0.619874 | ||||||||
\(802\) | −37.1997 | −1.31357 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.16499 | 0.217422 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | −28.6996 | −1.01090 | ||||||||
\(807\) | 14.1346 | 0.497562 | ||||||||
\(808\) | 14.1000 | 0.496035 | ||||||||
\(809\) | 9.79837 | 0.344492 | 0.172246 | − | 0.985054i | \(-0.444898\pi\) | ||||
0.172246 | + | 0.985054i | \(0.444898\pi\) | |||||||
\(810\) | −2.11048 | −0.0741546 | ||||||||
\(811\) | 20.9999 | 0.737406 | 0.368703 | − | 0.929547i | \(-0.379802\pi\) | ||||
0.368703 | + | 0.929547i | \(0.379802\pi\) | |||||||
\(812\) | 2.95002 | 0.103525 | ||||||||
\(813\) | −9.49224 | −0.332908 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5818 | −0.475750 | ||||||||
\(816\) | −1.21044 | −0.0423738 | ||||||||
\(817\) | −17.5458 | −0.613849 | ||||||||
\(818\) | 26.3908 | 0.922732 | ||||||||
\(819\) | 8.02435 | 0.280393 | ||||||||
\(820\) | 3.24458 | 0.113306 | ||||||||
\(821\) | 48.1483 | 1.68039 | 0.840194 | − | 0.542286i | \(-0.182441\pi\) | ||||
0.840194 | + | 0.542286i | \(0.182441\pi\) | |||||||
\(822\) | 2.66923 | 0.0931001 | ||||||||
\(823\) | −35.5348 | −1.23867 | −0.619333 | − | 0.785128i | \(-0.712597\pi\) | ||||
−0.619333 | + | 0.785128i | \(0.712597\pi\) | |||||||
\(824\) | 11.7627 | 0.409771 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.83905 | −0.0987833 | ||||||||
\(827\) | 44.0977 | 1.53343 | 0.766714 | − | 0.641988i | \(-0.221890\pi\) | ||||
0.766714 | + | 0.641988i | \(0.221890\pi\) | |||||||
\(828\) | 4.31040 | 0.149797 | ||||||||
\(829\) | −6.77860 | −0.235430 | −0.117715 | − | 0.993047i | \(-0.537557\pi\) | ||||
−0.117715 | + | 0.993047i | \(0.537557\pi\) | |||||||
\(830\) | 0.285256 | 0.00990139 | ||||||||
\(831\) | 20.9207 | 0.725730 | ||||||||
\(832\) | −3.72325 | −0.129081 | ||||||||
\(833\) | 1.31694 | 0.0456292 | ||||||||
\(834\) | −1.16523 | −0.0403485 | ||||||||
\(835\) | −12.0000 | −0.415277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.5238 | 1.26245 | ||||||||
\(838\) | 13.0447 | 0.450620 | ||||||||
\(839\) | −53.6528 | −1.85230 | −0.926150 | − | 0.377155i | \(-0.876902\pi\) | ||||
−0.926150 | + | 0.377155i | \(0.876902\pi\) | |||||||
\(840\) | 0.919131 | 0.0317130 | ||||||||
\(841\) | −20.2974 | −0.699910 | ||||||||
\(842\) | −13.4510 | −0.463553 | ||||||||
\(843\) | 2.82991 | 0.0974673 | ||||||||
\(844\) | 15.5912 | 0.536671 | ||||||||
\(845\) | −0.862611 | −0.0296747 | ||||||||
\(846\) | 20.1961 | 0.694358 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 13.2848 | 0.456201 | ||||||||
\(849\) | 10.0913 | 0.346331 | ||||||||
\(850\) | 1.31694 | 0.0451706 | ||||||||
\(851\) | 16.0974 | 0.551812 | ||||||||
\(852\) | −7.38397 | −0.252971 | ||||||||
\(853\) | 8.65701 | 0.296410 | 0.148205 | − | 0.988957i | \(-0.452650\pi\) | ||||
0.148205 | + | 0.988957i | \(0.452650\pi\) | |||||||
\(854\) | −1.44651 | −0.0494984 | ||||||||
\(855\) | 5.83501 | 0.199553 | ||||||||
\(856\) | −19.8272 | −0.677679 | ||||||||
\(857\) | 46.7535 | 1.59707 | 0.798534 | − | 0.601950i | \(-0.205609\pi\) | ||||
0.798534 | + | 0.601950i | \(0.205609\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.5377 | −1.21253 | −0.606265 | − | 0.795263i | \(-0.707333\pi\) | ||||
−0.606265 | + | 0.795263i | \(0.707333\pi\) | |||||||
\(860\) | 6.48064 | 0.220988 | ||||||||
\(861\) | 2.98219 | 0.101633 | ||||||||
\(862\) | 32.7451 | 1.11530 | ||||||||
\(863\) | 40.0753 | 1.36418 | 0.682089 | − | 0.731269i | \(-0.261072\pi\) | ||||
0.682089 | + | 0.731269i | \(0.261072\pi\) | |||||||
\(864\) | 4.73830 | 0.161200 | ||||||||
\(865\) | −12.4741 | −0.424132 | ||||||||
\(866\) | 9.00434 | 0.305980 | ||||||||
\(867\) | 14.0312 | 0.476523 | ||||||||
\(868\) | 7.70820 | 0.261633 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.71145 | 0.0919269 | ||||||||
\(871\) | 24.9734 | 0.846191 | ||||||||
\(872\) | 0.995533 | 0.0337130 | ||||||||
\(873\) | −31.8934 | −1.07943 | ||||||||
\(874\) | −5.41482 | −0.183159 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −1.22309 | −0.0413244 | ||||||||
\(877\) | −37.0839 | −1.25223 | −0.626117 | − | 0.779729i | \(-0.715357\pi\) | ||||
−0.626117 | + | 0.779729i | \(0.715357\pi\) | |||||||
\(878\) | 3.88952 | 0.131265 | ||||||||
\(879\) | −7.40016 | −0.249601 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.7764 | −0.834737 | −0.417369 | − | 0.908737i | \(-0.637048\pi\) | ||||
−0.417369 | + | 0.908737i | \(0.637048\pi\) | |||||||
\(882\) | −2.15520 | −0.0725693 | ||||||||
\(883\) | −5.49721 | −0.184996 | −0.0924980 | − | 0.995713i | \(-0.529485\pi\) | ||||
−0.0924980 | + | 0.995713i | \(0.529485\pi\) | |||||||
\(884\) | −4.90329 | −0.164915 | ||||||||
\(885\) | −2.60946 | −0.0877161 | ||||||||
\(886\) | 5.63377 | 0.189270 | ||||||||
\(887\) | −22.5044 | −0.755625 | −0.377813 | − | 0.925882i | \(-0.623324\pi\) | ||||
−0.377813 | + | 0.925882i | \(0.623324\pi\) | |||||||
\(888\) | 7.39781 | 0.248254 | ||||||||
\(889\) | −6.50223 | −0.218078 | ||||||||
\(890\) | 8.14015 | 0.272858 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.6313 | −0.556858 | ||||||||
\(893\) | −25.3709 | −0.849004 | ||||||||
\(894\) | 5.38141 | 0.179981 | ||||||||
\(895\) | −12.2295 | −0.408788 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −6.84431 | −0.228525 | ||||||||
\(898\) | −5.62855 | −0.187827 | ||||||||
\(899\) | 22.7394 | 0.758400 | ||||||||
\(900\) | −2.15520 | −0.0718400 | ||||||||
\(901\) | 17.4952 | 0.582850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.95656 | 0.198222 | ||||||||
\(904\) | 11.0691 | 0.368152 | ||||||||
\(905\) | −20.9718 | −0.697126 | ||||||||
\(906\) | 9.39744 | 0.312209 | ||||||||
\(907\) | −10.0800 | −0.334702 | −0.167351 | − | 0.985897i | \(-0.553521\pi\) | ||||
−0.167351 | + | 0.985897i | \(0.553521\pi\) | |||||||
\(908\) | 1.19716 | 0.0397291 | ||||||||
\(909\) | −30.3882 | −1.00791 | ||||||||
\(910\) | 3.72325 | 0.123425 | ||||||||
\(911\) | 16.3242 | 0.540846 | 0.270423 | − | 0.962742i | \(-0.412836\pi\) | ||||
0.270423 | + | 0.962742i | \(0.412836\pi\) | |||||||
\(912\) | −2.48847 | −0.0824013 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.15770 | 0.0382932 | ||||||||
\(915\) | −1.32953 | −0.0439528 | ||||||||
\(916\) | 14.8613 | 0.491032 | ||||||||
\(917\) | 21.7622 | 0.718650 | ||||||||
\(918\) | 6.24005 | 0.205952 | ||||||||
\(919\) | −18.9580 | −0.625366 | −0.312683 | − | 0.949858i | \(-0.601228\pi\) | ||||
−0.312683 | + | 0.949858i | \(0.601228\pi\) | |||||||
\(920\) | 2.00000 | 0.0659380 | ||||||||
\(921\) | 25.3646 | 0.835793 | ||||||||
\(922\) | 10.3088 | 0.339503 | ||||||||
\(923\) | −29.9113 | −0.984543 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.04870 | −0.264640 | ||||||||
\(926\) | −29.4740 | −0.968577 | ||||||||
\(927\) | −25.3509 | −0.832631 | ||||||||
\(928\) | 2.95002 | 0.0968392 | ||||||||
\(929\) | −15.5873 | −0.511404 | −0.255702 | − | 0.966756i | \(-0.582307\pi\) | ||||
−0.255702 | + | 0.966756i | \(0.582307\pi\) | |||||||
\(930\) | 7.08485 | 0.232321 | ||||||||
\(931\) | 2.70741 | 0.0887319 | ||||||||
\(932\) | −6.33199 | −0.207411 | ||||||||
\(933\) | −27.3781 | −0.896320 | ||||||||
\(934\) | 20.5977 | 0.673976 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.02435 | 0.262284 | ||||||||
\(937\) | −32.7215 | −1.06896 | −0.534482 | − | 0.845180i | \(-0.679493\pi\) | ||||
−0.534482 | + | 0.845180i | \(0.679493\pi\) | |||||||
\(938\) | −6.70741 | −0.219005 | ||||||||
\(939\) | −28.4152 | −0.927295 | ||||||||
\(940\) | 9.37090 | 0.305645 | ||||||||
\(941\) | 14.5193 | 0.473314 | 0.236657 | − | 0.971593i | \(-0.423948\pi\) | ||||
0.236657 | + | 0.971593i | \(0.423948\pi\) | |||||||
\(942\) | −1.08461 | −0.0353385 | ||||||||
\(943\) | 6.48915 | 0.211316 | ||||||||
\(944\) | −2.83905 | −0.0924033 | ||||||||
\(945\) | −4.73830 | −0.154137 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.5854 | 0.538954 | 0.269477 | − | 0.963007i | \(-0.413149\pi\) | ||||
0.269477 | + | 0.963007i | \(0.413149\pi\) | |||||||
\(948\) | −7.09868 | −0.230554 | ||||||||
\(949\) | −4.95455 | −0.160832 | ||||||||
\(950\) | 2.70741 | 0.0878401 | ||||||||
\(951\) | 2.13412 | 0.0692037 | ||||||||
\(952\) | 1.31694 | 0.0426822 | ||||||||
\(953\) | −29.5354 | −0.956745 | −0.478373 | − | 0.878157i | \(-0.658773\pi\) | ||||
−0.478373 | + | 0.878157i | \(0.658773\pi\) | |||||||
\(954\) | −28.6313 | −0.926973 | ||||||||
\(955\) | −6.74632 | −0.218306 | ||||||||
\(956\) | −11.6906 | −0.378101 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.18526 | −0.135220 | ||||||||
\(959\) | −2.90408 | −0.0937777 | ||||||||
\(960\) | 0.919131 | 0.0296648 | ||||||||
\(961\) | 28.4164 | 0.916658 | ||||||||
\(962\) | 29.9673 | 0.966186 | ||||||||
\(963\) | 42.7315 | 1.37700 | ||||||||
\(964\) | 10.3945 | 0.334783 | ||||||||
\(965\) | −19.9673 | −0.642771 | ||||||||
\(966\) | 1.83826 | 0.0591451 | ||||||||
\(967\) | −36.7434 | −1.18159 | −0.590794 | − | 0.806823i | \(-0.701185\pi\) | ||||
−0.590794 | + | 0.806823i | \(0.701185\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.27715 | −0.105277 | ||||||||
\(970\) | −14.7984 | −0.475147 | ||||||||
\(971\) | −22.2877 | −0.715245 | −0.357622 | − | 0.933866i | \(-0.616412\pi\) | ||||
−0.357622 | + | 0.933866i | \(0.616412\pi\) | |||||||
\(972\) | −16.1547 | −0.518163 | ||||||||
\(973\) | 1.26775 | 0.0406422 | ||||||||
\(974\) | −8.06730 | −0.258493 | ||||||||
\(975\) | 3.42216 | 0.109597 | ||||||||
\(976\) | −1.44651 | −0.0463015 | ||||||||
\(977\) | −40.5549 | −1.29747 | −0.648733 | − | 0.761016i | \(-0.724701\pi\) | ||||
−0.648733 | + | 0.761016i | \(0.724701\pi\) | |||||||
\(978\) | −12.4835 | −0.399177 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −2.14557 | −0.0685028 | ||||||||
\(982\) | −23.5882 | −0.752731 | ||||||||
\(983\) | −39.8706 | −1.27167 | −0.635837 | − | 0.771824i | \(-0.719345\pi\) | ||||
−0.635837 | + | 0.771824i | \(0.719345\pi\) | |||||||
\(984\) | 2.98219 | 0.0950688 | ||||||||
\(985\) | −21.1717 | −0.674587 | ||||||||
\(986\) | 3.88499 | 0.123723 | ||||||||
\(987\) | 8.61308 | 0.274157 | ||||||||
\(988\) | −10.0804 | −0.320700 | ||||||||
\(989\) | 12.9613 | 0.412145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.5410 | 1.12900 | 0.564498 | − | 0.825435i | \(-0.309070\pi\) | ||||
0.564498 | + | 0.825435i | \(0.309070\pi\) | |||||||
\(992\) | 7.70820 | 0.244736 | ||||||||
\(993\) | 9.15166 | 0.290419 | ||||||||
\(994\) | 8.03365 | 0.254812 | ||||||||
\(995\) | −8.27872 | −0.262453 | ||||||||
\(996\) | 0.262188 | 0.00830774 | ||||||||
\(997\) | −47.4408 | −1.50246 | −0.751232 | − | 0.660038i | \(-0.770540\pi\) | ||||
−0.751232 | + | 0.660038i | \(0.770540\pi\) | |||||||
\(998\) | 7.22181 | 0.228602 | ||||||||
\(999\) | −38.1372 | −1.20661 |
(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 | 8470.2.a.ct.1.2 | 4 | ||
11.7 | odd | 10 | 770.2.n.e.71.2 | ✓ | 8 | ||
11.8 | odd | 10 | 770.2.n.e.141.2 | yes | 8 | ||
11.10 | odd | 2 | 8470.2.a.cq.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.71.2 | ✓ | 8 | 11.7 | odd | 10 | ||
770.2.n.e.141.2 | yes | 8 | 11.8 | odd | 10 | ||
8470.2.a.cq.1.2 | 4 | 11.10 | odd | 2 | |||
8470.2.a.ct.1.2 | 4 | 1.1 | even | 1 | trivial |