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: | \(1\) |
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 | \(-0.327301\pi\) | ||||
0.516322 | + | 0.856394i | \(0.327301\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0.919131 | 0.237319 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.31694 | −0.319404 | −0.159702 | − | 0.987165i | \(-0.551053\pi\) | ||||
−0.159702 | + | 0.987165i | \(0.551053\pi\) | |||||||
\(18\) | 2.15520 | 0.507985 | ||||||||
\(19\) | −2.70741 | −0.621123 | −0.310561 | − | 0.950553i | \(-0.600517\pi\) | ||||
−0.310561 | + | 0.950553i | \(0.600517\pi\) | |||||||
\(20\) | −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 | \(-0.588315\pi\) | ||||
−0.273902 | + | 0.961757i | \(0.588315\pi\) | |||||||
\(30\) | −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 | \(-0.418465\pi\) | ||||
0.253359 | + | 0.967372i | \(0.418465\pi\) | |||||||
\(42\) | −0.919131 | −0.141825 | ||||||||
\(43\) | 6.48064 | 0.988289 | 0.494145 | − | 0.869380i | \(-0.335481\pi\) | ||||
0.494145 | + | 0.869380i | \(0.335481\pi\) | |||||||
\(44\) | 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 | \(-0.470481\pi\) | ||||
0.0926030 | + | 0.995703i | \(0.470481\pi\) | |||||||
\(62\) | −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 | \(-0.524813\pi\) | ||||
−0.0778736 | + | 0.996963i | \(0.524813\pi\) | |||||||
\(74\) | 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 | \(-0.643063\pi\) | ||||
−0.434467 | + | 0.900688i | \(0.643063\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 2.11048 | 0.234498 | ||||||||
\(82\) | −3.24458 | −0.358304 | ||||||||
\(83\) | 0.285256 | 0.0313109 | 0.0156555 | − | 0.999877i | \(-0.495017\pi\) | ||||
0.0156555 | + | 0.999877i | \(0.495017\pi\) | |||||||
\(84\) | 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 | \(-0.747486\pi\) | ||||
−0.701499 | + | 0.712670i | \(0.747486\pi\) | |||||||
\(102\) | −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 | \(-0.0921544\pi\) | ||||
0.958383 | + | 0.285484i | \(0.0921544\pi\) | |||||||
\(108\) | 4.73830 | 0.455943 | ||||||||
\(109\) | −0.995533 | −0.0953548 | −0.0476774 | − | 0.998863i | \(-0.515182\pi\) | ||||
−0.0476774 | + | 0.998863i | \(0.515182\pi\) | |||||||
\(110\) | 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 | \(-0.406847\pi\) | ||||
0.288490 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −5.95656 | −0.524446 | ||||||||
\(130\) | 3.72325 | 0.326551 | ||||||||
\(131\) | −21.7622 | −1.90137 | −0.950684 | − | 0.310160i | \(-0.899617\pi\) | ||||
−0.950684 | + | 0.310160i | \(0.899617\pi\) | |||||||
\(132\) | 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 | \(-0.517122\pi\) | ||||
−0.0537645 | + | 0.998554i | \(0.517122\pi\) | |||||||
\(140\) | 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 | \(-0.422910\pi\) | ||||
0.239826 | + | 0.970816i | \(0.422910\pi\) | |||||||
\(150\) | 0.919131 | 0.0750467 | ||||||||
\(151\) | 10.2243 | 0.832039 | 0.416020 | − | 0.909356i | \(-0.363425\pi\) | ||||
0.416020 | + | 0.909356i | \(0.363425\pi\) | |||||||
\(152\) | 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 | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | −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 | \(-0.657261\pi\) | ||||
−0.474194 | + | 0.880420i | \(0.657261\pi\) | |||||||
\(174\) | −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 | \(-0.755235\pi\) | ||||
−0.718640 | + | 0.695382i | \(0.755235\pi\) | |||||||
\(194\) | −14.7984 | −1.06246 | ||||||||
\(195\) | 3.42216 | 0.245066 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −21.1717 | −1.50842 | −0.754212 | − | 0.656631i | \(-0.771981\pi\) | ||||
−0.754212 | + | 0.656631i | \(0.771981\pi\) | |||||||
\(198\) | 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 | \(-0.680318\pi\) | ||||
−0.536671 | + | 0.843792i | \(0.680318\pi\) | |||||||
\(212\) | 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 | \(-0.512649\pi\) | ||||
−0.0397291 | + | 0.999210i | \(0.512649\pi\) | |||||||
\(228\) | 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 | \(-0.433496\pi\) | ||||
0.207411 | + | 0.978254i | \(0.433496\pi\) | |||||||
\(234\) | 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 | \(-0.376577\pi\) | ||||
0.378101 | + | 0.925764i | \(0.376577\pi\) | |||||||
\(240\) | 0.919131 | 0.0593296 | ||||||||
\(241\) | −10.3945 | −0.669566 | −0.334783 | − | 0.942295i | \(-0.608663\pi\) | ||||
−0.334783 | + | 0.942295i | \(0.608663\pi\) | |||||||
\(242\) | 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 | \(-0.786130\pi\) | ||||
−0.782645 | + | 0.622469i | \(0.786130\pi\) | |||||||
\(264\) | 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 | \(-0.601560\pi\) | ||||
−0.313673 | + | 0.949531i | \(0.601560\pi\) | |||||||
\(272\) | −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 | \(-0.260326\pi\) | ||||
0.683799 | + | 0.729670i | \(0.260326\pi\) | |||||||
\(278\) | 1.26775 | 0.0760345 | ||||||||
\(279\) | −16.6127 | −0.994577 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 3.07890 | 0.183672 | 0.0918359 | − | 0.995774i | \(-0.470726\pi\) | ||||
0.0918359 | + | 0.995774i | \(0.470726\pi\) | |||||||
\(282\) | −8.61308 | −0.512901 | ||||||||
\(283\) | 10.9791 | 0.652642 | 0.326321 | − | 0.945259i | \(-0.394191\pi\) | ||||
0.326321 | + | 0.945259i | \(0.394191\pi\) | |||||||
\(284\) | 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 | \(-0.575568\pi\) | ||||
−0.235180 | + | 0.971952i | \(0.575568\pi\) | |||||||
\(294\) | 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 | \(-0.211373\pi\) | ||||
0.787503 | + | 0.616311i | \(0.211373\pi\) | |||||||
\(308\) | 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 | \(-0.691378\pi\) | ||||
−0.565658 | + | 0.824640i | \(0.691378\pi\) | |||||||
\(338\) | −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 | \(-0.639036\pi\) | ||||
−0.423036 | + | 0.906113i | \(0.639036\pi\) | |||||||
\(348\) | 2.71145 | 0.145349 | ||||||||
\(349\) | −23.2953 | −1.24697 | −0.623484 | − | 0.781836i | \(-0.714283\pi\) | ||||
−0.623484 | + | 0.781836i | \(0.714283\pi\) | |||||||
\(350\) | 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 | \(-0.821073\pi\) | ||||
−0.846130 | + | 0.532977i | \(0.821073\pi\) | |||||||
\(360\) | −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 | \(-0.348248\pi\) | ||||
0.458889 | + | 0.888494i | \(0.348248\pi\) | |||||||
\(374\) | 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 | \(-0.726267\pi\) | ||||
−0.652470 | + | 0.757815i | \(0.726267\pi\) | |||||||
\(410\) | 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 | \(-0.789213\pi\) | ||||
−0.788638 | + | 0.614858i | \(0.789213\pi\) | |||||||
\(432\) | 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 | \(-0.529588\pi\) | ||||
−0.0928184 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(440\) | 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 | \(-0.508620\pi\) | ||||
−0.0270774 | + | 0.999633i | \(0.508620\pi\) | |||||||
\(458\) | −14.8613 | −0.694424 | ||||||||
\(459\) | −6.24005 | −0.291260 | ||||||||
\(460\) | 2.00000 | 0.0932505 | ||||||||
\(461\) | −10.3088 | −0.480129 | −0.240065 | − | 0.970757i | \(-0.577169\pi\) | ||||
−0.240065 | + | 0.970757i | \(0.577169\pi\) | |||||||
\(462\) | 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 | \(-0.469518\pi\) | ||||
0.0956146 | + | 0.995418i | \(0.469518\pi\) | |||||||
\(480\) | −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 | \(-0.321342\pi\) | ||||
0.532261 | + | 0.846580i | \(0.321342\pi\) | |||||||
\(492\) | −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 | \(-0.418331\pi\) | ||||
0.253766 | + | 0.967266i | \(0.418331\pi\) | |||||||
\(504\) | −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 | \(-0.721495\pi\) | ||||
−0.641035 | + | 0.767512i | \(0.721495\pi\) | |||||||
\(524\) | −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 | \(-0.482567\pi\) | ||||
0.0547392 | + | 0.998501i | \(0.482567\pi\) | |||||||
\(542\) | 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 | \(-0.258920\pi\) | ||||
0.687016 | + | 0.726642i | \(0.258920\pi\) | |||||||
\(548\) | −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 | \(-0.459562\pi\) | ||||
0.126699 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(558\) | 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 | \(-0.512096\pi\) | ||||
−0.0379903 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(564\) | 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 | \(-0.717650\pi\) | ||||
−0.631718 | + | 0.775198i | \(0.717650\pi\) | |||||||
\(570\) | 2.48847 | 0.104230 | ||||||||
\(571\) | −30.3322 | −1.26936 | −0.634681 | − | 0.772774i | \(-0.718869\pi\) | ||||
−0.634681 | + | 0.772774i | \(0.718869\pi\) | |||||||
\(572\) | 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 | \(-0.483099\pi\) | ||||
0.0530702 | + | 0.998591i | \(0.483099\pi\) | |||||||
\(594\) | 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 | \(-0.506979\pi\) | ||||
−0.0219227 | + | 0.999760i | \(0.506979\pi\) | |||||||
\(602\) | 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 | \(-0.582812\pi\) | ||||
−0.257236 | + | 0.966349i | \(0.582812\pi\) | |||||||
\(608\) | 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 | \(-0.359934\pi\) | ||||
0.425968 | + | 0.904738i | \(0.359934\pi\) | |||||||
\(614\) | −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 | \(-0.340090\pi\) | ||||
0.481506 | + | 0.876443i | \(0.340090\pi\) | |||||||
\(660\) | 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 | \(-0.819768\pi\) | ||||
−0.843937 | + | 0.536442i | \(0.819768\pi\) | |||||||
\(674\) | 20.7682 | 0.799962 | ||||||||
\(675\) | 4.73830 | 0.182377 | ||||||||
\(676\) | 0.862611 | 0.0331773 | ||||||||
\(677\) | 20.9199 | 0.804018 | 0.402009 | − | 0.915636i | \(-0.368312\pi\) | ||||
0.402009 | + | 0.915636i | \(0.368312\pi\) | |||||||
\(678\) | 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 | \(-0.723593\pi\) | ||||
−0.646081 | + | 0.763269i | \(0.723593\pi\) | |||||||
\(702\) | −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 | \(-0.755407\pi\) | ||||
−0.719015 | + | 0.694995i | \(0.755407\pi\) | |||||||
\(734\) | 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 | \(-0.681569\pi\) | ||||
−0.539981 | + | 0.841677i | \(0.681569\pi\) | |||||||
\(740\) | 8.04870 | 0.295876 | ||||||||
\(741\) | 9.26519 | 0.340365 | ||||||||
\(742\) | 13.2848 | 0.487699 | ||||||||
\(743\) | −27.1351 | −0.995491 | −0.497746 | − | 0.867323i | \(-0.665839\pi\) | ||||
−0.497746 | + | 0.867323i | \(0.665839\pi\) | |||||||
\(744\) | 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 | \(-0.515177\pi\) | ||||
−0.0476614 | + | 0.998864i | \(0.515177\pi\) | |||||||
\(762\) | 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 | \(-0.688980\pi\) | ||||
−0.559431 | + | 0.828877i | \(0.688980\pi\) | |||||||
\(770\) | 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 | \(-0.534972\pi\) | ||||
−0.109647 | + | 0.993971i | \(0.534972\pi\) | |||||||
\(788\) | −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 | \(-0.555102\pi\) | ||||
−0.172246 | + | 0.985054i | \(0.555102\pi\) | |||||||
\(810\) | 2.11048 | 0.0741546 | ||||||||
\(811\) | −20.9999 | −0.737406 | −0.368703 | − | 0.929547i | \(-0.620198\pi\) | ||||
−0.368703 | + | 0.929547i | \(0.620198\pi\) | |||||||
\(812\) | 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 | \(-0.817559\pi\) | ||||
−0.840194 | + | 0.542286i | \(0.817559\pi\) | |||||||
\(822\) | −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 | \(-0.778110\pi\) | ||||
−0.766714 | + | 0.641988i | \(0.778110\pi\) | |||||||
\(828\) | 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 | \(-0.547350\pi\) | ||||
−0.148205 | + | 0.988957i | \(0.547350\pi\) | |||||||
\(854\) | 1.44651 | 0.0494984 | ||||||||
\(855\) | −5.83501 | −0.199553 | ||||||||
\(856\) | −19.8272 | −0.677679 | ||||||||
\(857\) | −46.7535 | −1.59707 | −0.798534 | − | 0.601950i | \(-0.794391\pi\) | ||||
−0.798534 | + | 0.601950i | \(0.794391\pi\) | |||||||
\(858\) | 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 | \(-0.284643\pi\) | ||||
0.626117 | + | 0.779729i | \(0.284643\pi\) | |||||||
\(878\) | 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 | \(-0.376676\pi\) | ||||
0.377813 | + | 0.925882i | \(0.376676\pi\) | |||||||
\(888\) | −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 | \(-0.398772\pi\) | ||||
0.312683 | + | 0.949858i | \(0.398772\pi\) | |||||||
\(920\) | −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 | \(-0.320507\pi\) | ||||
0.534482 | + | 0.845180i | \(0.320507\pi\) | |||||||
\(938\) | −6.70741 | −0.219005 | ||||||||
\(939\) | −28.4152 | −0.927295 | ||||||||
\(940\) | 9.37090 | 0.305645 | ||||||||
\(941\) | −14.5193 | −0.473314 | −0.236657 | − | 0.971593i | \(-0.576052\pi\) | ||||
−0.236657 | + | 0.971593i | \(0.576052\pi\) | |||||||
\(942\) | 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 | \(-0.341227\pi\) | ||||
0.478373 | + | 0.878157i | \(0.341227\pi\) | |||||||
\(954\) | 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 | \(-0.298815\pi\) | ||||
0.590794 | + | 0.806823i | \(0.298815\pi\) | |||||||
\(968\) | 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 | \(-0.229460\pi\) | ||||
0.751232 | + | 0.660038i | \(0.229460\pi\) | |||||||
\(998\) | −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.cq.1.2 | 4 | ||
11.3 | even | 5 | 770.2.n.e.141.2 | yes | 8 | ||
11.4 | even | 5 | 770.2.n.e.71.2 | ✓ | 8 | ||
11.10 | odd | 2 | 8470.2.a.ct.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.e.71.2 | ✓ | 8 | 11.4 | even | 5 | ||
770.2.n.e.141.2 | yes | 8 | 11.3 | even | 5 | ||
8470.2.a.cq.1.2 | 4 | 1.1 | even | 1 | trivial | ||
8470.2.a.ct.1.2 | 4 | 11.10 | odd | 2 |