Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-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 | ||||||||
\(3\) | −3.36322 | −1.94176 | −0.970878 | − | 0.239575i | \(-0.922992\pi\) | ||||
−0.970878 | + | 0.239575i | \(0.922992\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.90848 | 1.74792 | 0.873962 | − | 0.485994i | \(-0.161542\pi\) | ||||
0.873962 | + | 0.485994i | \(0.161542\pi\) | |||||||
\(6\) | −3.36322 | −1.37303 | ||||||||
\(7\) | −1.71915 | −0.649776 | −0.324888 | − | 0.945753i | \(-0.605327\pi\) | ||||
−0.324888 | + | 0.945753i | \(0.605327\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.31124 | 2.77041 | ||||||||
\(10\) | 3.90848 | 1.23597 | ||||||||
\(11\) | −1.66701 | −0.502623 | −0.251312 | − | 0.967906i | \(-0.580862\pi\) | ||||
−0.251312 | + | 0.967906i | \(0.580862\pi\) | |||||||
\(12\) | −3.36322 | −0.970878 | ||||||||
\(13\) | −0.631638 | −0.175185 | −0.0875924 | − | 0.996156i | \(-0.527917\pi\) | ||||
−0.0875924 | + | 0.996156i | \(0.527917\pi\) | |||||||
\(14\) | −1.71915 | −0.459461 | ||||||||
\(15\) | −13.1451 | −3.39404 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.65196 | 0.643194 | 0.321597 | − | 0.946877i | \(-0.395780\pi\) | ||||
0.321597 | + | 0.946877i | \(0.395780\pi\) | |||||||
\(18\) | 8.31124 | 1.95898 | ||||||||
\(19\) | −3.22088 | −0.738922 | −0.369461 | − | 0.929246i | \(-0.620458\pi\) | ||||
−0.369461 | + | 0.929246i | \(0.620458\pi\) | |||||||
\(20\) | 3.90848 | 0.873962 | ||||||||
\(21\) | 5.78186 | 1.26171 | ||||||||
\(22\) | −1.66701 | −0.355408 | ||||||||
\(23\) | 2.00580 | 0.418237 | 0.209119 | − | 0.977890i | \(-0.432940\pi\) | ||||
0.209119 | + | 0.977890i | \(0.432940\pi\) | |||||||
\(24\) | −3.36322 | −0.686514 | ||||||||
\(25\) | 10.2762 | 2.05524 | ||||||||
\(26\) | −0.631638 | −0.123874 | ||||||||
\(27\) | −17.8629 | −3.43771 | ||||||||
\(28\) | −1.71915 | −0.324888 | ||||||||
\(29\) | −6.75737 | −1.25481 | −0.627406 | − | 0.778692i | \(-0.715883\pi\) | ||||
−0.627406 | + | 0.778692i | \(0.715883\pi\) | |||||||
\(30\) | −13.1451 | −2.39995 | ||||||||
\(31\) | −4.06395 | −0.729908 | −0.364954 | − | 0.931026i | \(-0.618915\pi\) | ||||
−0.364954 | + | 0.931026i | \(0.618915\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.60653 | 0.975971 | ||||||||
\(34\) | 2.65196 | 0.454807 | ||||||||
\(35\) | −6.71924 | −1.13576 | ||||||||
\(36\) | 8.31124 | 1.38521 | ||||||||
\(37\) | −2.95478 | −0.485762 | −0.242881 | − | 0.970056i | \(-0.578093\pi\) | ||||
−0.242881 | + | 0.970056i | \(0.578093\pi\) | |||||||
\(38\) | −3.22088 | −0.522497 | ||||||||
\(39\) | 2.12434 | 0.340166 | ||||||||
\(40\) | 3.90848 | 0.617984 | ||||||||
\(41\) | 2.41376 | 0.376966 | 0.188483 | − | 0.982076i | \(-0.439643\pi\) | ||||
0.188483 | + | 0.982076i | \(0.439643\pi\) | |||||||
\(42\) | 5.78186 | 0.892161 | ||||||||
\(43\) | 3.91405 | 0.596887 | 0.298443 | − | 0.954427i | \(-0.403533\pi\) | ||||
0.298443 | + | 0.954427i | \(0.403533\pi\) | |||||||
\(44\) | −1.66701 | −0.251312 | ||||||||
\(45\) | 32.4843 | 4.84247 | ||||||||
\(46\) | 2.00580 | 0.295739 | ||||||||
\(47\) | −7.79943 | −1.13766 | −0.568832 | − | 0.822454i | \(-0.692605\pi\) | ||||
−0.568832 | + | 0.822454i | \(0.692605\pi\) | |||||||
\(48\) | −3.36322 | −0.485439 | ||||||||
\(49\) | −4.04454 | −0.577791 | ||||||||
\(50\) | 10.2762 | 1.45327 | ||||||||
\(51\) | −8.91911 | −1.24893 | ||||||||
\(52\) | −0.631638 | −0.0875924 | ||||||||
\(53\) | −10.4966 | −1.44182 | −0.720911 | − | 0.693028i | \(-0.756276\pi\) | ||||
−0.720911 | + | 0.693028i | \(0.756276\pi\) | |||||||
\(54\) | −17.8629 | −2.43083 | ||||||||
\(55\) | −6.51548 | −0.878547 | ||||||||
\(56\) | −1.71915 | −0.229730 | ||||||||
\(57\) | 10.8325 | 1.43481 | ||||||||
\(58\) | −6.75737 | −0.887286 | ||||||||
\(59\) | −6.59901 | −0.859117 | −0.429559 | − | 0.903039i | \(-0.641331\pi\) | ||||
−0.429559 | + | 0.903039i | \(0.641331\pi\) | |||||||
\(60\) | −13.1451 | −1.69702 | ||||||||
\(61\) | 6.19818 | 0.793595 | 0.396798 | − | 0.917906i | \(-0.370122\pi\) | ||||
0.396798 | + | 0.917906i | \(0.370122\pi\) | |||||||
\(62\) | −4.06395 | −0.516123 | ||||||||
\(63\) | −14.2882 | −1.80015 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.46874 | −0.306210 | ||||||||
\(66\) | 5.60653 | 0.690116 | ||||||||
\(67\) | −2.95815 | −0.361395 | −0.180698 | − | 0.983539i | \(-0.557836\pi\) | ||||
−0.180698 | + | 0.983539i | \(0.557836\pi\) | |||||||
\(68\) | 2.65196 | 0.321597 | ||||||||
\(69\) | −6.74593 | −0.812115 | ||||||||
\(70\) | −6.71924 | −0.803103 | ||||||||
\(71\) | 11.4309 | 1.35660 | 0.678302 | − | 0.734784i | \(-0.262716\pi\) | ||||
0.678302 | + | 0.734784i | \(0.262716\pi\) | |||||||
\(72\) | 8.31124 | 0.979490 | ||||||||
\(73\) | −7.30030 | −0.854435 | −0.427218 | − | 0.904149i | \(-0.640506\pi\) | ||||
−0.427218 | + | 0.904149i | \(0.640506\pi\) | |||||||
\(74\) | −2.95478 | −0.343486 | ||||||||
\(75\) | −34.5611 | −3.99077 | ||||||||
\(76\) | −3.22088 | −0.369461 | ||||||||
\(77\) | 2.86584 | 0.326592 | ||||||||
\(78\) | 2.12434 | 0.240534 | ||||||||
\(79\) | −17.2392 | −1.93957 | −0.969783 | − | 0.243968i | \(-0.921551\pi\) | ||||
−0.969783 | + | 0.243968i | \(0.921551\pi\) | |||||||
\(80\) | 3.90848 | 0.436981 | ||||||||
\(81\) | 35.1431 | 3.90478 | ||||||||
\(82\) | 2.41376 | 0.266555 | ||||||||
\(83\) | 13.7900 | 1.51365 | 0.756823 | − | 0.653619i | \(-0.226750\pi\) | ||||
0.756823 | + | 0.653619i | \(0.226750\pi\) | |||||||
\(84\) | 5.78186 | 0.630853 | ||||||||
\(85\) | 10.3651 | 1.12425 | ||||||||
\(86\) | 3.91405 | 0.422063 | ||||||||
\(87\) | 22.7265 | 2.43654 | ||||||||
\(88\) | −1.66701 | −0.177704 | ||||||||
\(89\) | 0.657803 | 0.0697269 | 0.0348635 | − | 0.999392i | \(-0.488900\pi\) | ||||
0.0348635 | + | 0.999392i | \(0.488900\pi\) | |||||||
\(90\) | 32.4843 | 3.42415 | ||||||||
\(91\) | 1.08588 | 0.113831 | ||||||||
\(92\) | 2.00580 | 0.209119 | ||||||||
\(93\) | 13.6680 | 1.41730 | ||||||||
\(94\) | −7.79943 | −0.804450 | ||||||||
\(95\) | −12.5888 | −1.29158 | ||||||||
\(96\) | −3.36322 | −0.343257 | ||||||||
\(97\) | −1.90755 | −0.193682 | −0.0968410 | − | 0.995300i | \(-0.530874\pi\) | ||||
−0.0968410 | + | 0.995300i | \(0.530874\pi\) | |||||||
\(98\) | −4.04454 | −0.408560 | ||||||||
\(99\) | −13.8549 | −1.39247 | ||||||||
\(100\) | 10.2762 | 1.02762 | ||||||||
\(101\) | −15.8143 | −1.57358 | −0.786789 | − | 0.617221i | \(-0.788258\pi\) | ||||
−0.786789 | + | 0.617221i | \(0.788258\pi\) | |||||||
\(102\) | −8.91911 | −0.883124 | ||||||||
\(103\) | 0.266726 | 0.0262813 | 0.0131406 | − | 0.999914i | \(-0.495817\pi\) | ||||
0.0131406 | + | 0.999914i | \(0.495817\pi\) | |||||||
\(104\) | −0.631638 | −0.0619372 | ||||||||
\(105\) | 22.5983 | 2.20537 | ||||||||
\(106\) | −10.4966 | −1.01952 | ||||||||
\(107\) | 0.701684 | 0.0678343 | 0.0339172 | − | 0.999425i | \(-0.489202\pi\) | ||||
0.0339172 | + | 0.999425i | \(0.489202\pi\) | |||||||
\(108\) | −17.8629 | −1.71886 | ||||||||
\(109\) | −8.15785 | −0.781381 | −0.390690 | − | 0.920522i | \(-0.627764\pi\) | ||||
−0.390690 | + | 0.920522i | \(0.627764\pi\) | |||||||
\(110\) | −6.51548 | −0.621226 | ||||||||
\(111\) | 9.93756 | 0.943232 | ||||||||
\(112\) | −1.71915 | −0.162444 | ||||||||
\(113\) | −14.5249 | −1.36638 | −0.683192 | − | 0.730239i | \(-0.739409\pi\) | ||||
−0.683192 | + | 0.730239i | \(0.739409\pi\) | |||||||
\(114\) | 10.8325 | 1.01456 | ||||||||
\(115\) | 7.83961 | 0.731047 | ||||||||
\(116\) | −6.75737 | −0.627406 | ||||||||
\(117\) | −5.24970 | −0.485335 | ||||||||
\(118\) | −6.59901 | −0.607488 | ||||||||
\(119\) | −4.55910 | −0.417932 | ||||||||
\(120\) | −13.1451 | −1.19997 | ||||||||
\(121\) | −8.22107 | −0.747370 | ||||||||
\(122\) | 6.19818 | 0.561156 | ||||||||
\(123\) | −8.11800 | −0.731975 | ||||||||
\(124\) | −4.06395 | −0.364954 | ||||||||
\(125\) | 20.6219 | 1.84448 | ||||||||
\(126\) | −14.2882 | −1.27290 | ||||||||
\(127\) | −10.1089 | −0.897016 | −0.448508 | − | 0.893779i | \(-0.648044\pi\) | ||||
−0.448508 | + | 0.893779i | \(0.648044\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −13.1638 | −1.15901 | ||||||||
\(130\) | −2.46874 | −0.216523 | ||||||||
\(131\) | 6.27545 | 0.548289 | 0.274144 | − | 0.961689i | \(-0.411605\pi\) | ||||
0.274144 | + | 0.961689i | \(0.411605\pi\) | |||||||
\(132\) | 5.60653 | 0.487986 | ||||||||
\(133\) | 5.53717 | 0.480133 | ||||||||
\(134\) | −2.95815 | −0.255545 | ||||||||
\(135\) | −69.8167 | −6.00886 | ||||||||
\(136\) | 2.65196 | 0.227403 | ||||||||
\(137\) | 8.02851 | 0.685922 | 0.342961 | − | 0.939350i | \(-0.388570\pi\) | ||||
0.342961 | + | 0.939350i | \(0.388570\pi\) | |||||||
\(138\) | −6.74593 | −0.574252 | ||||||||
\(139\) | 19.1640 | 1.62547 | 0.812735 | − | 0.582633i | \(-0.197977\pi\) | ||||
0.812735 | + | 0.582633i | \(0.197977\pi\) | |||||||
\(140\) | −6.71924 | −0.567879 | ||||||||
\(141\) | 26.2312 | 2.20907 | ||||||||
\(142\) | 11.4309 | 0.959263 | ||||||||
\(143\) | 1.05295 | 0.0880519 | ||||||||
\(144\) | 8.31124 | 0.692604 | ||||||||
\(145\) | −26.4110 | −2.19332 | ||||||||
\(146\) | −7.30030 | −0.604177 | ||||||||
\(147\) | 13.6027 | 1.12193 | ||||||||
\(148\) | −2.95478 | −0.242881 | ||||||||
\(149\) | 19.4108 | 1.59019 | 0.795097 | − | 0.606482i | \(-0.207420\pi\) | ||||
0.795097 | + | 0.606482i | \(0.207420\pi\) | |||||||
\(150\) | −34.5611 | −2.82190 | ||||||||
\(151\) | −16.5830 | −1.34951 | −0.674753 | − | 0.738044i | \(-0.735750\pi\) | ||||
−0.674753 | + | 0.738044i | \(0.735750\pi\) | |||||||
\(152\) | −3.22088 | −0.261248 | ||||||||
\(153\) | 22.0411 | 1.78191 | ||||||||
\(154\) | 2.86584 | 0.230936 | ||||||||
\(155\) | −15.8839 | −1.27582 | ||||||||
\(156\) | 2.12434 | 0.170083 | ||||||||
\(157\) | 5.27524 | 0.421010 | 0.210505 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210505 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(158\) | −17.2392 | −1.37148 | ||||||||
\(159\) | 35.3025 | 2.79967 | ||||||||
\(160\) | 3.90848 | 0.308992 | ||||||||
\(161\) | −3.44826 | −0.271761 | ||||||||
\(162\) | 35.1431 | 2.76110 | ||||||||
\(163\) | 14.3426 | 1.12340 | 0.561700 | − | 0.827341i | \(-0.310147\pi\) | ||||
0.561700 | + | 0.827341i | \(0.310147\pi\) | |||||||
\(164\) | 2.41376 | 0.188483 | ||||||||
\(165\) | 21.9130 | 1.70592 | ||||||||
\(166\) | 13.7900 | 1.07031 | ||||||||
\(167\) | −9.09146 | −0.703518 | −0.351759 | − | 0.936091i | \(-0.614416\pi\) | ||||
−0.351759 | + | 0.936091i | \(0.614416\pi\) | |||||||
\(168\) | 5.78186 | 0.446080 | ||||||||
\(169\) | −12.6010 | −0.969310 | ||||||||
\(170\) | 10.3651 | 0.794968 | ||||||||
\(171\) | −26.7696 | −2.04712 | ||||||||
\(172\) | 3.91405 | 0.298443 | ||||||||
\(173\) | 8.30753 | 0.631610 | 0.315805 | − | 0.948824i | \(-0.397725\pi\) | ||||
0.315805 | + | 0.948824i | \(0.397725\pi\) | |||||||
\(174\) | 22.7265 | 1.72289 | ||||||||
\(175\) | −17.6663 | −1.33544 | ||||||||
\(176\) | −1.66701 | −0.125656 | ||||||||
\(177\) | 22.1939 | 1.66820 | ||||||||
\(178\) | 0.657803 | 0.0493044 | ||||||||
\(179\) | −17.8449 | −1.33379 | −0.666894 | − | 0.745153i | \(-0.732377\pi\) | ||||
−0.666894 | + | 0.745153i | \(0.732377\pi\) | |||||||
\(180\) | 32.4843 | 2.42124 | ||||||||
\(181\) | 6.30891 | 0.468938 | 0.234469 | − | 0.972124i | \(-0.424665\pi\) | ||||
0.234469 | + | 0.972124i | \(0.424665\pi\) | |||||||
\(182\) | 1.08588 | 0.0804906 | ||||||||
\(183\) | −20.8458 | −1.54097 | ||||||||
\(184\) | 2.00580 | 0.147869 | ||||||||
\(185\) | −11.5487 | −0.849076 | ||||||||
\(186\) | 13.6680 | 1.00218 | ||||||||
\(187\) | −4.42084 | −0.323284 | ||||||||
\(188\) | −7.79943 | −0.568832 | ||||||||
\(189\) | 30.7089 | 2.23374 | ||||||||
\(190\) | −12.5888 | −0.913284 | ||||||||
\(191\) | 10.6681 | 0.771919 | 0.385960 | − | 0.922516i | \(-0.373870\pi\) | ||||
0.385960 | + | 0.922516i | \(0.373870\pi\) | |||||||
\(192\) | −3.36322 | −0.242719 | ||||||||
\(193\) | 21.7456 | 1.56528 | 0.782641 | − | 0.622473i | \(-0.213872\pi\) | ||||
0.782641 | + | 0.622473i | \(0.213872\pi\) | |||||||
\(194\) | −1.90755 | −0.136954 | ||||||||
\(195\) | 8.30292 | 0.594585 | ||||||||
\(196\) | −4.04454 | −0.288896 | ||||||||
\(197\) | 14.0173 | 0.998691 | 0.499346 | − | 0.866403i | \(-0.333574\pi\) | ||||
0.499346 | + | 0.866403i | \(0.333574\pi\) | |||||||
\(198\) | −13.8549 | −0.984628 | ||||||||
\(199\) | −25.7549 | −1.82572 | −0.912859 | − | 0.408274i | \(-0.866131\pi\) | ||||
−0.912859 | + | 0.408274i | \(0.866131\pi\) | |||||||
\(200\) | 10.2762 | 0.726637 | ||||||||
\(201\) | 9.94891 | 0.701742 | ||||||||
\(202\) | −15.8143 | −1.11269 | ||||||||
\(203\) | 11.6169 | 0.815347 | ||||||||
\(204\) | −8.91911 | −0.624463 | ||||||||
\(205\) | 9.43412 | 0.658907 | ||||||||
\(206\) | 0.266726 | 0.0185837 | ||||||||
\(207\) | 16.6707 | 1.15869 | ||||||||
\(208\) | −0.631638 | −0.0437962 | ||||||||
\(209\) | 5.36925 | 0.371399 | ||||||||
\(210\) | 22.5983 | 1.55943 | ||||||||
\(211\) | 20.2343 | 1.39299 | 0.696495 | − | 0.717562i | \(-0.254742\pi\) | ||||
0.696495 | + | 0.717562i | \(0.254742\pi\) | |||||||
\(212\) | −10.4966 | −0.720911 | ||||||||
\(213\) | −38.4448 | −2.63419 | ||||||||
\(214\) | 0.701684 | 0.0479661 | ||||||||
\(215\) | 15.2980 | 1.04331 | ||||||||
\(216\) | −17.8629 | −1.21542 | ||||||||
\(217\) | 6.98653 | 0.474276 | ||||||||
\(218\) | −8.15785 | −0.552519 | ||||||||
\(219\) | 24.5525 | 1.65910 | ||||||||
\(220\) | −6.51548 | −0.439273 | ||||||||
\(221\) | −1.67508 | −0.112678 | ||||||||
\(222\) | 9.93756 | 0.666966 | ||||||||
\(223\) | 3.49374 | 0.233958 | 0.116979 | − | 0.993134i | \(-0.462679\pi\) | ||||
0.116979 | + | 0.993134i | \(0.462679\pi\) | |||||||
\(224\) | −1.71915 | −0.114865 | ||||||||
\(225\) | 85.4080 | 5.69386 | ||||||||
\(226\) | −14.5249 | −0.966179 | ||||||||
\(227\) | 5.78724 | 0.384113 | 0.192056 | − | 0.981384i | \(-0.438484\pi\) | ||||
0.192056 | + | 0.981384i | \(0.438484\pi\) | |||||||
\(228\) | 10.8325 | 0.717403 | ||||||||
\(229\) | 7.87808 | 0.520598 | 0.260299 | − | 0.965528i | \(-0.416179\pi\) | ||||
0.260299 | + | 0.965528i | \(0.416179\pi\) | |||||||
\(230\) | 7.83961 | 0.516929 | ||||||||
\(231\) | −9.63843 | −0.634162 | ||||||||
\(232\) | −6.75737 | −0.443643 | ||||||||
\(233\) | −17.0866 | −1.11938 | −0.559692 | − | 0.828701i | \(-0.689080\pi\) | ||||
−0.559692 | + | 0.828701i | \(0.689080\pi\) | |||||||
\(234\) | −5.24970 | −0.343183 | ||||||||
\(235\) | −30.4839 | −1.98855 | ||||||||
\(236\) | −6.59901 | −0.429559 | ||||||||
\(237\) | 57.9794 | 3.76616 | ||||||||
\(238\) | −4.55910 | −0.295522 | ||||||||
\(239\) | 6.15898 | 0.398391 | 0.199196 | − | 0.979960i | \(-0.436167\pi\) | ||||
0.199196 | + | 0.979960i | \(0.436167\pi\) | |||||||
\(240\) | −13.1451 | −0.848510 | ||||||||
\(241\) | 1.72196 | 0.110921 | 0.0554607 | − | 0.998461i | \(-0.482337\pi\) | ||||
0.0554607 | + | 0.998461i | \(0.482337\pi\) | |||||||
\(242\) | −8.22107 | −0.528470 | ||||||||
\(243\) | −64.6052 | −4.14442 | ||||||||
\(244\) | 6.19818 | 0.396798 | ||||||||
\(245\) | −15.8080 | −1.00994 | ||||||||
\(246\) | −8.11800 | −0.517585 | ||||||||
\(247\) | 2.03443 | 0.129448 | ||||||||
\(248\) | −4.06395 | −0.258061 | ||||||||
\(249\) | −46.3787 | −2.93913 | ||||||||
\(250\) | 20.6219 | 1.30424 | ||||||||
\(251\) | −7.50315 | −0.473594 | −0.236797 | − | 0.971559i | \(-0.576098\pi\) | ||||
−0.236797 | + | 0.971559i | \(0.576098\pi\) | |||||||
\(252\) | −14.2882 | −0.900074 | ||||||||
\(253\) | −3.34369 | −0.210216 | ||||||||
\(254\) | −10.1089 | −0.634286 | ||||||||
\(255\) | −34.8601 | −2.18303 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.17366 | 0.385102 | 0.192551 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192551 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(258\) | −13.1638 | −0.819542 | ||||||||
\(259\) | 5.07969 | 0.315637 | ||||||||
\(260\) | −2.46874 | −0.153105 | ||||||||
\(261\) | −56.1622 | −3.47635 | ||||||||
\(262\) | 6.27545 | 0.387699 | ||||||||
\(263\) | −13.7257 | −0.846362 | −0.423181 | − | 0.906045i | \(-0.639087\pi\) | ||||
−0.423181 | + | 0.906045i | \(0.639087\pi\) | |||||||
\(264\) | 5.60653 | 0.345058 | ||||||||
\(265\) | −41.0258 | −2.52020 | ||||||||
\(266\) | 5.53717 | 0.339506 | ||||||||
\(267\) | −2.21233 | −0.135393 | ||||||||
\(268\) | −2.95815 | −0.180698 | ||||||||
\(269\) | −1.70806 | −0.104142 | −0.0520711 | − | 0.998643i | \(-0.516582\pi\) | ||||
−0.0520711 | + | 0.998643i | \(0.516582\pi\) | |||||||
\(270\) | −69.8167 | −4.24891 | ||||||||
\(271\) | 13.4289 | 0.815748 | 0.407874 | − | 0.913038i | \(-0.366270\pi\) | ||||
0.407874 | + | 0.913038i | \(0.366270\pi\) | |||||||
\(272\) | 2.65196 | 0.160798 | ||||||||
\(273\) | −3.65204 | −0.221032 | ||||||||
\(274\) | 8.02851 | 0.485020 | ||||||||
\(275\) | −17.1305 | −1.03301 | ||||||||
\(276\) | −6.74593 | −0.406057 | ||||||||
\(277\) | −24.5829 | −1.47705 | −0.738523 | − | 0.674228i | \(-0.764476\pi\) | ||||
−0.738523 | + | 0.674228i | \(0.764476\pi\) | |||||||
\(278\) | 19.1640 | 1.14938 | ||||||||
\(279\) | −33.7765 | −2.02215 | ||||||||
\(280\) | −6.71924 | −0.401551 | ||||||||
\(281\) | −29.0664 | −1.73396 | −0.866978 | − | 0.498347i | \(-0.833941\pi\) | ||||
−0.866978 | + | 0.498347i | \(0.833941\pi\) | |||||||
\(282\) | 26.2312 | 1.56205 | ||||||||
\(283\) | 11.1403 | 0.662222 | 0.331111 | − | 0.943592i | \(-0.392576\pi\) | ||||
0.331111 | + | 0.943592i | \(0.392576\pi\) | |||||||
\(284\) | 11.4309 | 0.678302 | ||||||||
\(285\) | 42.3387 | 2.50793 | ||||||||
\(286\) | 1.05295 | 0.0622621 | ||||||||
\(287\) | −4.14960 | −0.244943 | ||||||||
\(288\) | 8.31124 | 0.489745 | ||||||||
\(289\) | −9.96713 | −0.586302 | ||||||||
\(290\) | −26.4110 | −1.55091 | ||||||||
\(291\) | 6.41549 | 0.376083 | ||||||||
\(292\) | −7.30030 | −0.427218 | ||||||||
\(293\) | −17.0762 | −0.997602 | −0.498801 | − | 0.866717i | \(-0.666226\pi\) | ||||
−0.498801 | + | 0.866717i | \(0.666226\pi\) | |||||||
\(294\) | 13.6027 | 0.793324 | ||||||||
\(295\) | −25.7921 | −1.50167 | ||||||||
\(296\) | −2.95478 | −0.171743 | ||||||||
\(297\) | 29.7776 | 1.72787 | ||||||||
\(298\) | 19.4108 | 1.12444 | ||||||||
\(299\) | −1.26694 | −0.0732689 | ||||||||
\(300\) | −34.5611 | −1.99539 | ||||||||
\(301\) | −6.72882 | −0.387843 | ||||||||
\(302\) | −16.5830 | −0.954245 | ||||||||
\(303\) | 53.1869 | 3.05551 | ||||||||
\(304\) | −3.22088 | −0.184730 | ||||||||
\(305\) | 24.2254 | 1.38714 | ||||||||
\(306\) | 22.0411 | 1.26000 | ||||||||
\(307\) | 13.5648 | 0.774187 | 0.387093 | − | 0.922041i | \(-0.373479\pi\) | ||||
0.387093 | + | 0.922041i | \(0.373479\pi\) | |||||||
\(308\) | 2.86584 | 0.163296 | ||||||||
\(309\) | −0.897058 | −0.0510318 | ||||||||
\(310\) | −15.8839 | −0.902143 | ||||||||
\(311\) | −8.01758 | −0.454635 | −0.227318 | − | 0.973821i | \(-0.572996\pi\) | ||||
−0.227318 | + | 0.973821i | \(0.572996\pi\) | |||||||
\(312\) | 2.12434 | 0.120267 | ||||||||
\(313\) | −4.93652 | −0.279029 | −0.139514 | − | 0.990220i | \(-0.544554\pi\) | ||||
−0.139514 | + | 0.990220i | \(0.544554\pi\) | |||||||
\(314\) | 5.27524 | 0.297699 | ||||||||
\(315\) | −55.8452 | −3.14652 | ||||||||
\(316\) | −17.2392 | −0.969783 | ||||||||
\(317\) | −8.73521 | −0.490618 | −0.245309 | − | 0.969445i | \(-0.578889\pi\) | ||||
−0.245309 | + | 0.969445i | \(0.578889\pi\) | |||||||
\(318\) | 35.3025 | 1.97966 | ||||||||
\(319\) | 11.2646 | 0.630698 | ||||||||
\(320\) | 3.90848 | 0.218491 | ||||||||
\(321\) | −2.35992 | −0.131718 | ||||||||
\(322\) | −3.44826 | −0.192164 | ||||||||
\(323\) | −8.54165 | −0.475270 | ||||||||
\(324\) | 35.1431 | 1.95239 | ||||||||
\(325\) | −6.49083 | −0.360047 | ||||||||
\(326\) | 14.3426 | 0.794364 | ||||||||
\(327\) | 27.4366 | 1.51725 | ||||||||
\(328\) | 2.41376 | 0.133277 | ||||||||
\(329\) | 13.4084 | 0.739227 | ||||||||
\(330\) | 21.9130 | 1.20627 | ||||||||
\(331\) | −12.5613 | −0.690433 | −0.345216 | − | 0.938523i | \(-0.612194\pi\) | ||||
−0.345216 | + | 0.938523i | \(0.612194\pi\) | |||||||
\(332\) | 13.7900 | 0.756823 | ||||||||
\(333\) | −24.5579 | −1.34576 | ||||||||
\(334\) | −9.09146 | −0.497463 | ||||||||
\(335\) | −11.5619 | −0.631692 | ||||||||
\(336\) | 5.78186 | 0.315426 | ||||||||
\(337\) | −9.26971 | −0.504953 | −0.252477 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252477 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(338\) | −12.6010 | −0.685406 | ||||||||
\(339\) | 48.8503 | 2.65318 | ||||||||
\(340\) | 10.3651 | 0.562127 | ||||||||
\(341\) | 6.77466 | 0.366868 | ||||||||
\(342\) | −26.7696 | −1.44753 | ||||||||
\(343\) | 18.9872 | 1.02521 | ||||||||
\(344\) | 3.91405 | 0.211031 | ||||||||
\(345\) | −26.3663 | −1.41952 | ||||||||
\(346\) | 8.30753 | 0.446616 | ||||||||
\(347\) | −20.3167 | −1.09066 | −0.545330 | − | 0.838222i | \(-0.683596\pi\) | ||||
−0.545330 | + | 0.838222i | \(0.683596\pi\) | |||||||
\(348\) | 22.7265 | 1.21827 | ||||||||
\(349\) | −5.58689 | −0.299060 | −0.149530 | − | 0.988757i | \(-0.547776\pi\) | ||||
−0.149530 | + | 0.988757i | \(0.547776\pi\) | |||||||
\(350\) | −17.6663 | −0.944302 | ||||||||
\(351\) | 11.2829 | 0.602235 | ||||||||
\(352\) | −1.66701 | −0.0888520 | ||||||||
\(353\) | 24.3701 | 1.29709 | 0.648546 | − | 0.761176i | \(-0.275377\pi\) | ||||
0.648546 | + | 0.761176i | \(0.275377\pi\) | |||||||
\(354\) | 22.1939 | 1.17959 | ||||||||
\(355\) | 44.6776 | 2.37124 | ||||||||
\(356\) | 0.657803 | 0.0348635 | ||||||||
\(357\) | 15.3332 | 0.811522 | ||||||||
\(358\) | −17.8449 | −0.943131 | ||||||||
\(359\) | −6.81820 | −0.359851 | −0.179925 | − | 0.983680i | \(-0.557586\pi\) | ||||
−0.179925 | + | 0.983680i | \(0.557586\pi\) | |||||||
\(360\) | 32.4843 | 1.71207 | ||||||||
\(361\) | −8.62590 | −0.453995 | ||||||||
\(362\) | 6.30891 | 0.331589 | ||||||||
\(363\) | 27.6493 | 1.45121 | ||||||||
\(364\) | 1.08588 | 0.0569154 | ||||||||
\(365\) | −28.5331 | −1.49349 | ||||||||
\(366\) | −20.8458 | −1.08963 | ||||||||
\(367\) | −4.85785 | −0.253578 | −0.126789 | − | 0.991930i | \(-0.540467\pi\) | ||||
−0.126789 | + | 0.991930i | \(0.540467\pi\) | |||||||
\(368\) | 2.00580 | 0.104559 | ||||||||
\(369\) | 20.0613 | 1.04435 | ||||||||
\(370\) | −11.5487 | −0.600387 | ||||||||
\(371\) | 18.0452 | 0.936861 | ||||||||
\(372\) | 13.6680 | 0.708651 | ||||||||
\(373\) | 4.02390 | 0.208350 | 0.104175 | − | 0.994559i | \(-0.466780\pi\) | ||||
0.104175 | + | 0.994559i | \(0.466780\pi\) | |||||||
\(374\) | −4.42084 | −0.228596 | ||||||||
\(375\) | −69.3559 | −3.58152 | ||||||||
\(376\) | −7.79943 | −0.402225 | ||||||||
\(377\) | 4.26821 | 0.219824 | ||||||||
\(378\) | 30.7089 | 1.57949 | ||||||||
\(379\) | −7.91538 | −0.406586 | −0.203293 | − | 0.979118i | \(-0.565164\pi\) | ||||
−0.203293 | + | 0.979118i | \(0.565164\pi\) | |||||||
\(380\) | −12.5888 | −0.645789 | ||||||||
\(381\) | 33.9983 | 1.74178 | ||||||||
\(382\) | 10.6681 | 0.545829 | ||||||||
\(383\) | 5.04462 | 0.257768 | 0.128884 | − | 0.991660i | \(-0.458861\pi\) | ||||
0.128884 | + | 0.991660i | \(0.458861\pi\) | |||||||
\(384\) | −3.36322 | −0.171629 | ||||||||
\(385\) | 11.2011 | 0.570859 | ||||||||
\(386\) | 21.7456 | 1.10682 | ||||||||
\(387\) | 32.5306 | 1.65362 | ||||||||
\(388\) | −1.90755 | −0.0968410 | ||||||||
\(389\) | 4.90941 | 0.248917 | 0.124459 | − | 0.992225i | \(-0.460281\pi\) | ||||
0.124459 | + | 0.992225i | \(0.460281\pi\) | |||||||
\(390\) | 8.30292 | 0.420435 | ||||||||
\(391\) | 5.31928 | 0.269008 | ||||||||
\(392\) | −4.04454 | −0.204280 | ||||||||
\(393\) | −21.1057 | −1.06464 | ||||||||
\(394\) | 14.0173 | 0.706181 | ||||||||
\(395\) | −67.3792 | −3.39022 | ||||||||
\(396\) | −13.8549 | −0.696237 | ||||||||
\(397\) | 7.90142 | 0.396561 | 0.198280 | − | 0.980145i | \(-0.436464\pi\) | ||||
0.198280 | + | 0.980145i | \(0.436464\pi\) | |||||||
\(398\) | −25.7549 | −1.29098 | ||||||||
\(399\) | −18.6227 | −0.932302 | ||||||||
\(400\) | 10.2762 | 0.513810 | ||||||||
\(401\) | −36.5778 | −1.82661 | −0.913304 | − | 0.407279i | \(-0.866478\pi\) | ||||
−0.913304 | + | 0.407279i | \(0.866478\pi\) | |||||||
\(402\) | 9.94891 | 0.496206 | ||||||||
\(403\) | 2.56695 | 0.127869 | ||||||||
\(404\) | −15.8143 | −0.786789 | ||||||||
\(405\) | 137.356 | 6.82527 | ||||||||
\(406\) | 11.6169 | 0.576537 | ||||||||
\(407\) | 4.92565 | 0.244155 | ||||||||
\(408\) | −8.91911 | −0.441562 | ||||||||
\(409\) | 23.6810 | 1.17095 | 0.585474 | − | 0.810691i | \(-0.300908\pi\) | ||||
0.585474 | + | 0.810691i | \(0.300908\pi\) | |||||||
\(410\) | 9.43412 | 0.465918 | ||||||||
\(411\) | −27.0017 | −1.33189 | ||||||||
\(412\) | 0.266726 | 0.0131406 | ||||||||
\(413\) | 11.3447 | 0.558234 | ||||||||
\(414\) | 16.6707 | 0.819318 | ||||||||
\(415\) | 53.8978 | 2.64574 | ||||||||
\(416\) | −0.631638 | −0.0309686 | ||||||||
\(417\) | −64.4528 | −3.15627 | ||||||||
\(418\) | 5.36925 | 0.262619 | ||||||||
\(419\) | −6.30101 | −0.307824 | −0.153912 | − | 0.988085i | \(-0.549187\pi\) | ||||
−0.153912 | + | 0.988085i | \(0.549187\pi\) | |||||||
\(420\) | 22.5983 | 1.10268 | ||||||||
\(421\) | 40.7075 | 1.98396 | 0.991981 | − | 0.126390i | \(-0.0403389\pi\) | ||||
0.991981 | + | 0.126390i | \(0.0403389\pi\) | |||||||
\(422\) | 20.2343 | 0.984993 | ||||||||
\(423\) | −64.8230 | −3.15180 | ||||||||
\(424\) | −10.4966 | −0.509761 | ||||||||
\(425\) | 27.2520 | 1.32192 | ||||||||
\(426\) | −38.4448 | −1.86265 | ||||||||
\(427\) | −10.6556 | −0.515659 | ||||||||
\(428\) | 0.701684 | 0.0339172 | ||||||||
\(429\) | −3.54130 | −0.170975 | ||||||||
\(430\) | 15.2980 | 0.737733 | ||||||||
\(431\) | −32.1445 | −1.54834 | −0.774172 | − | 0.632975i | \(-0.781834\pi\) | ||||
−0.774172 | + | 0.632975i | \(0.781834\pi\) | |||||||
\(432\) | −17.8629 | −0.859428 | ||||||||
\(433\) | −27.3389 | −1.31382 | −0.656912 | − | 0.753967i | \(-0.728138\pi\) | ||||
−0.656912 | + | 0.753967i | \(0.728138\pi\) | |||||||
\(434\) | 6.98653 | 0.335364 | ||||||||
\(435\) | 88.8261 | 4.25889 | ||||||||
\(436\) | −8.15785 | −0.390690 | ||||||||
\(437\) | −6.46044 | −0.309045 | ||||||||
\(438\) | 24.5525 | 1.17316 | ||||||||
\(439\) | −7.46270 | −0.356175 | −0.178088 | − | 0.984015i | \(-0.556991\pi\) | ||||
−0.178088 | + | 0.984015i | \(0.556991\pi\) | |||||||
\(440\) | −6.51548 | −0.310613 | ||||||||
\(441\) | −33.6152 | −1.60072 | ||||||||
\(442\) | −1.67508 | −0.0796753 | ||||||||
\(443\) | 25.9025 | 1.23066 | 0.615332 | − | 0.788268i | \(-0.289022\pi\) | ||||
0.615332 | + | 0.788268i | \(0.289022\pi\) | |||||||
\(444\) | 9.93756 | 0.471616 | ||||||||
\(445\) | 2.57101 | 0.121877 | ||||||||
\(446\) | 3.49374 | 0.165433 | ||||||||
\(447\) | −65.2828 | −3.08777 | ||||||||
\(448\) | −1.71915 | −0.0812220 | ||||||||
\(449\) | 5.51032 | 0.260048 | 0.130024 | − | 0.991511i | \(-0.458495\pi\) | ||||
0.130024 | + | 0.991511i | \(0.458495\pi\) | |||||||
\(450\) | 85.4080 | 4.02617 | ||||||||
\(451\) | −4.02376 | −0.189472 | ||||||||
\(452\) | −14.5249 | −0.683192 | ||||||||
\(453\) | 55.7723 | 2.62041 | ||||||||
\(454\) | 5.78724 | 0.271609 | ||||||||
\(455\) | 4.24413 | 0.198968 | ||||||||
\(456\) | 10.8325 | 0.507280 | ||||||||
\(457\) | −15.4448 | −0.722478 | −0.361239 | − | 0.932473i | \(-0.617646\pi\) | ||||
−0.361239 | + | 0.932473i | \(0.617646\pi\) | |||||||
\(458\) | 7.87808 | 0.368118 | ||||||||
\(459\) | −47.3716 | −2.21112 | ||||||||
\(460\) | 7.83961 | 0.365524 | ||||||||
\(461\) | −37.5298 | −1.74794 | −0.873969 | − | 0.485982i | \(-0.838462\pi\) | ||||
−0.873969 | + | 0.485982i | \(0.838462\pi\) | |||||||
\(462\) | −9.63843 | −0.448421 | ||||||||
\(463\) | −28.0159 | −1.30201 | −0.651004 | − | 0.759074i | \(-0.725652\pi\) | ||||
−0.651004 | + | 0.759074i | \(0.725652\pi\) | |||||||
\(464\) | −6.75737 | −0.313703 | ||||||||
\(465\) | 53.4209 | 2.47734 | ||||||||
\(466\) | −17.0866 | −0.791523 | ||||||||
\(467\) | −18.2634 | −0.845131 | −0.422565 | − | 0.906332i | \(-0.638870\pi\) | ||||
−0.422565 | + | 0.906332i | \(0.638870\pi\) | |||||||
\(468\) | −5.24970 | −0.242667 | ||||||||
\(469\) | 5.08549 | 0.234826 | ||||||||
\(470\) | −30.4839 | −1.40612 | ||||||||
\(471\) | −17.7418 | −0.817499 | ||||||||
\(472\) | −6.59901 | −0.303744 | ||||||||
\(473\) | −6.52476 | −0.300009 | ||||||||
\(474\) | 57.9794 | 2.66308 | ||||||||
\(475\) | −33.0984 | −1.51866 | ||||||||
\(476\) | −4.55910 | −0.208966 | ||||||||
\(477\) | −87.2400 | −3.99445 | ||||||||
\(478\) | 6.15898 | 0.281705 | ||||||||
\(479\) | −26.7325 | −1.22144 | −0.610721 | − | 0.791846i | \(-0.709120\pi\) | ||||
−0.610721 | + | 0.791846i | \(0.709120\pi\) | |||||||
\(480\) | −13.1451 | −0.599987 | ||||||||
\(481\) | 1.86635 | 0.0850982 | ||||||||
\(482\) | 1.72196 | 0.0784333 | ||||||||
\(483\) | 11.5972 | 0.527693 | ||||||||
\(484\) | −8.22107 | −0.373685 | ||||||||
\(485\) | −7.45560 | −0.338541 | ||||||||
\(486\) | −64.6052 | −2.93055 | ||||||||
\(487\) | 30.5225 | 1.38311 | 0.691553 | − | 0.722326i | \(-0.256927\pi\) | ||||
0.691553 | + | 0.722326i | \(0.256927\pi\) | |||||||
\(488\) | 6.19818 | 0.280578 | ||||||||
\(489\) | −48.2374 | −2.18137 | ||||||||
\(490\) | −15.8080 | −0.714132 | ||||||||
\(491\) | −27.7964 | −1.25443 | −0.627216 | − | 0.778845i | \(-0.715806\pi\) | ||||
−0.627216 | + | 0.778845i | \(0.715806\pi\) | |||||||
\(492\) | −8.11800 | −0.365988 | ||||||||
\(493\) | −17.9203 | −0.807088 | ||||||||
\(494\) | 2.03443 | 0.0915335 | ||||||||
\(495\) | −54.1517 | −2.43394 | ||||||||
\(496\) | −4.06395 | −0.182477 | ||||||||
\(497\) | −19.6514 | −0.881488 | ||||||||
\(498\) | −46.3787 | −2.07828 | ||||||||
\(499\) | −28.3537 | −1.26929 | −0.634644 | − | 0.772805i | \(-0.718853\pi\) | ||||
−0.634644 | + | 0.772805i | \(0.718853\pi\) | |||||||
\(500\) | 20.6219 | 0.922238 | ||||||||
\(501\) | 30.5766 | 1.36606 | ||||||||
\(502\) | −7.50315 | −0.334882 | ||||||||
\(503\) | −26.6814 | −1.18967 | −0.594833 | − | 0.803850i | \(-0.702782\pi\) | ||||
−0.594833 | + | 0.803850i | \(0.702782\pi\) | |||||||
\(504\) | −14.2882 | −0.636449 | ||||||||
\(505\) | −61.8097 | −2.75050 | ||||||||
\(506\) | −3.34369 | −0.148645 | ||||||||
\(507\) | 42.3800 | 1.88216 | ||||||||
\(508\) | −10.1089 | −0.448508 | ||||||||
\(509\) | −26.2488 | −1.16346 | −0.581728 | − | 0.813383i | \(-0.697623\pi\) | ||||
−0.581728 | + | 0.813383i | \(0.697623\pi\) | |||||||
\(510\) | −34.8601 | −1.54363 | ||||||||
\(511\) | 12.5503 | 0.555192 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 57.5343 | 2.54020 | ||||||||
\(514\) | 6.17366 | 0.272309 | ||||||||
\(515\) | 1.04249 | 0.0459377 | ||||||||
\(516\) | −13.1638 | −0.579504 | ||||||||
\(517\) | 13.0017 | 0.571816 | ||||||||
\(518\) | 5.07969 | 0.223189 | ||||||||
\(519\) | −27.9401 | −1.22643 | ||||||||
\(520\) | −2.46874 | −0.108262 | ||||||||
\(521\) | 4.04006 | 0.176998 | 0.0884991 | − | 0.996076i | \(-0.471793\pi\) | ||||
0.0884991 | + | 0.996076i | \(0.471793\pi\) | |||||||
\(522\) | −56.1622 | −2.45815 | ||||||||
\(523\) | 20.9331 | 0.915342 | 0.457671 | − | 0.889122i | \(-0.348684\pi\) | ||||
0.457671 | + | 0.889122i | \(0.348684\pi\) | |||||||
\(524\) | 6.27545 | 0.274144 | ||||||||
\(525\) | 59.4155 | 2.59311 | ||||||||
\(526\) | −13.7257 | −0.598468 | ||||||||
\(527\) | −10.7774 | −0.469472 | ||||||||
\(528\) | 5.60653 | 0.243993 | ||||||||
\(529\) | −18.9768 | −0.825077 | ||||||||
\(530\) | −41.0258 | −1.78205 | ||||||||
\(531\) | −54.8460 | −2.38011 | ||||||||
\(532\) | 5.53717 | 0.240067 | ||||||||
\(533\) | −1.52462 | −0.0660387 | ||||||||
\(534\) | −2.21233 | −0.0957371 | ||||||||
\(535\) | 2.74251 | 0.118569 | ||||||||
\(536\) | −2.95815 | −0.127773 | ||||||||
\(537\) | 60.0162 | 2.58989 | ||||||||
\(538\) | −1.70806 | −0.0736397 | ||||||||
\(539\) | 6.74230 | 0.290411 | ||||||||
\(540\) | −69.8167 | −3.00443 | ||||||||
\(541\) | 4.38341 | 0.188458 | 0.0942289 | − | 0.995551i | \(-0.469961\pi\) | ||||
0.0942289 | + | 0.995551i | \(0.469961\pi\) | |||||||
\(542\) | 13.4289 | 0.576821 | ||||||||
\(543\) | −21.2182 | −0.910562 | ||||||||
\(544\) | 2.65196 | 0.113702 | ||||||||
\(545\) | −31.8848 | −1.36579 | ||||||||
\(546\) | −3.65204 | −0.156293 | ||||||||
\(547\) | 0.715201 | 0.0305798 | 0.0152899 | − | 0.999883i | \(-0.495133\pi\) | ||||
0.0152899 | + | 0.999883i | \(0.495133\pi\) | |||||||
\(548\) | 8.02851 | 0.342961 | ||||||||
\(549\) | 51.5145 | 2.19859 | ||||||||
\(550\) | −17.1305 | −0.730449 | ||||||||
\(551\) | 21.7647 | 0.927208 | ||||||||
\(552\) | −6.74593 | −0.287126 | ||||||||
\(553\) | 29.6368 | 1.26028 | ||||||||
\(554\) | −24.5829 | −1.04443 | ||||||||
\(555\) | 38.8407 | 1.64870 | ||||||||
\(556\) | 19.1640 | 0.812735 | ||||||||
\(557\) | 27.7402 | 1.17539 | 0.587694 | − | 0.809083i | \(-0.300036\pi\) | ||||
0.587694 | + | 0.809083i | \(0.300036\pi\) | |||||||
\(558\) | −33.7765 | −1.42987 | ||||||||
\(559\) | −2.47226 | −0.104565 | ||||||||
\(560\) | −6.71924 | −0.283940 | ||||||||
\(561\) | 14.8683 | 0.627739 | ||||||||
\(562\) | −29.0664 | −1.22609 | ||||||||
\(563\) | 32.3622 | 1.36391 | 0.681953 | − | 0.731396i | \(-0.261131\pi\) | ||||
0.681953 | + | 0.731396i | \(0.261131\pi\) | |||||||
\(564\) | 26.2312 | 1.10453 | ||||||||
\(565\) | −56.7701 | −2.38834 | ||||||||
\(566\) | 11.1403 | 0.468262 | ||||||||
\(567\) | −60.4160 | −2.53723 | ||||||||
\(568\) | 11.4309 | 0.479632 | ||||||||
\(569\) | −16.0787 | −0.674055 | −0.337028 | − | 0.941495i | \(-0.609422\pi\) | ||||
−0.337028 | + | 0.941495i | \(0.609422\pi\) | |||||||
\(570\) | 42.3387 | 1.77337 | ||||||||
\(571\) | 30.1474 | 1.26163 | 0.630814 | − | 0.775934i | \(-0.282721\pi\) | ||||
0.630814 | + | 0.775934i | \(0.282721\pi\) | |||||||
\(572\) | 1.05295 | 0.0440260 | ||||||||
\(573\) | −35.8793 | −1.49888 | ||||||||
\(574\) | −4.14960 | −0.173201 | ||||||||
\(575\) | 20.6120 | 0.859578 | ||||||||
\(576\) | 8.31124 | 0.346302 | ||||||||
\(577\) | −39.7986 | −1.65684 | −0.828419 | − | 0.560110i | \(-0.810759\pi\) | ||||
−0.828419 | + | 0.560110i | \(0.810759\pi\) | |||||||
\(578\) | −9.96713 | −0.414578 | ||||||||
\(579\) | −73.1352 | −3.03940 | ||||||||
\(580\) | −26.4110 | −1.09666 | ||||||||
\(581\) | −23.7070 | −0.983531 | ||||||||
\(582\) | 6.41549 | 0.265931 | ||||||||
\(583\) | 17.4980 | 0.724693 | ||||||||
\(584\) | −7.30030 | −0.302089 | ||||||||
\(585\) | −20.5183 | −0.848328 | ||||||||
\(586\) | −17.0762 | −0.705411 | ||||||||
\(587\) | −16.7439 | −0.691095 | −0.345548 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345548 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(588\) | 13.6027 | 0.560965 | ||||||||
\(589\) | 13.0895 | 0.539344 | ||||||||
\(590\) | −25.7921 | −1.06184 | ||||||||
\(591\) | −47.1433 | −1.93921 | ||||||||
\(592\) | −2.95478 | −0.121441 | ||||||||
\(593\) | 3.03276 | 0.124541 | 0.0622703 | − | 0.998059i | \(-0.480166\pi\) | ||||
0.0622703 | + | 0.998059i | \(0.480166\pi\) | |||||||
\(594\) | 29.7776 | 1.22179 | ||||||||
\(595\) | −17.8191 | −0.730513 | ||||||||
\(596\) | 19.4108 | 0.795097 | ||||||||
\(597\) | 86.6195 | 3.54510 | ||||||||
\(598\) | −1.26694 | −0.0518089 | ||||||||
\(599\) | −8.84889 | −0.361556 | −0.180778 | − | 0.983524i | \(-0.557862\pi\) | ||||
−0.180778 | + | 0.983524i | \(0.557862\pi\) | |||||||
\(600\) | −34.5611 | −1.41095 | ||||||||
\(601\) | −46.1425 | −1.88219 | −0.941095 | − | 0.338141i | \(-0.890202\pi\) | ||||
−0.941095 | + | 0.338141i | \(0.890202\pi\) | |||||||
\(602\) | −6.72882 | −0.274246 | ||||||||
\(603\) | −24.5859 | −1.00122 | ||||||||
\(604\) | −16.5830 | −0.674753 | ||||||||
\(605\) | −32.1319 | −1.30635 | ||||||||
\(606\) | 53.1869 | 2.16057 | ||||||||
\(607\) | 21.6279 | 0.877850 | 0.438925 | − | 0.898524i | \(-0.355359\pi\) | ||||
0.438925 | + | 0.898524i | \(0.355359\pi\) | |||||||
\(608\) | −3.22088 | −0.130624 | ||||||||
\(609\) | −39.0702 | −1.58320 | ||||||||
\(610\) | 24.2254 | 0.980859 | ||||||||
\(611\) | 4.92642 | 0.199301 | ||||||||
\(612\) | 22.0411 | 0.890957 | ||||||||
\(613\) | −0.159695 | −0.00645002 | −0.00322501 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322501 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(614\) | 13.5648 | 0.547433 | ||||||||
\(615\) | −31.7290 | −1.27944 | ||||||||
\(616\) | 2.86584 | 0.115468 | ||||||||
\(617\) | 28.1834 | 1.13462 | 0.567311 | − | 0.823504i | \(-0.307984\pi\) | ||||
0.567311 | + | 0.823504i | \(0.307984\pi\) | |||||||
\(618\) | −0.897058 | −0.0360849 | ||||||||
\(619\) | −1.85877 | −0.0747103 | −0.0373551 | − | 0.999302i | \(-0.511893\pi\) | ||||
−0.0373551 | + | 0.999302i | \(0.511893\pi\) | |||||||
\(620\) | −15.8839 | −0.637911 | ||||||||
\(621\) | −35.8293 | −1.43778 | ||||||||
\(622\) | −8.01758 | −0.321476 | ||||||||
\(623\) | −1.13086 | −0.0453069 | ||||||||
\(624\) | 2.12434 | 0.0850415 | ||||||||
\(625\) | 29.2192 | 1.16877 | ||||||||
\(626\) | −4.93652 | −0.197303 | ||||||||
\(627\) | −18.0580 | −0.721166 | ||||||||
\(628\) | 5.27524 | 0.210505 | ||||||||
\(629\) | −7.83594 | −0.312439 | ||||||||
\(630\) | −55.8452 | −2.22493 | ||||||||
\(631\) | 4.29589 | 0.171017 | 0.0855083 | − | 0.996337i | \(-0.472749\pi\) | ||||
0.0855083 | + | 0.996337i | \(0.472749\pi\) | |||||||
\(632\) | −17.2392 | −0.685740 | ||||||||
\(633\) | −68.0525 | −2.70485 | ||||||||
\(634\) | −8.73521 | −0.346920 | ||||||||
\(635\) | −39.5102 | −1.56792 | ||||||||
\(636\) | 35.3025 | 1.39983 | ||||||||
\(637\) | 2.55468 | 0.101220 | ||||||||
\(638\) | 11.2646 | 0.445971 | ||||||||
\(639\) | 95.0054 | 3.75835 | ||||||||
\(640\) | 3.90848 | 0.154496 | ||||||||
\(641\) | −48.7776 | −1.92660 | −0.963300 | − | 0.268427i | \(-0.913496\pi\) | ||||
−0.963300 | + | 0.268427i | \(0.913496\pi\) | |||||||
\(642\) | −2.35992 | −0.0931385 | ||||||||
\(643\) | 31.3870 | 1.23778 | 0.618891 | − | 0.785477i | \(-0.287582\pi\) | ||||
0.618891 | + | 0.785477i | \(0.287582\pi\) | |||||||
\(644\) | −3.44826 | −0.135880 | ||||||||
\(645\) | −51.4504 | −2.02586 | ||||||||
\(646\) | −8.54165 | −0.336067 | ||||||||
\(647\) | −41.4036 | −1.62774 | −0.813872 | − | 0.581044i | \(-0.802644\pi\) | ||||
−0.813872 | + | 0.581044i | \(0.802644\pi\) | |||||||
\(648\) | 35.1431 | 1.38055 | ||||||||
\(649\) | 11.0006 | 0.431812 | ||||||||
\(650\) | −6.49083 | −0.254591 | ||||||||
\(651\) | −23.4972 | −0.920929 | ||||||||
\(652\) | 14.3426 | 0.561700 | ||||||||
\(653\) | 36.0006 | 1.40881 | 0.704407 | − | 0.709796i | \(-0.251213\pi\) | ||||
0.704407 | + | 0.709796i | \(0.251213\pi\) | |||||||
\(654\) | 27.4366 | 1.07286 | ||||||||
\(655\) | 24.5275 | 0.958368 | ||||||||
\(656\) | 2.41376 | 0.0942414 | ||||||||
\(657\) | −60.6746 | −2.36714 | ||||||||
\(658\) | 13.4084 | 0.522712 | ||||||||
\(659\) | −7.06885 | −0.275363 | −0.137682 | − | 0.990477i | \(-0.543965\pi\) | ||||
−0.137682 | + | 0.990477i | \(0.543965\pi\) | |||||||
\(660\) | 21.9130 | 0.852962 | ||||||||
\(661\) | 7.26222 | 0.282468 | 0.141234 | − | 0.989976i | \(-0.454893\pi\) | ||||
0.141234 | + | 0.989976i | \(0.454893\pi\) | |||||||
\(662\) | −12.5613 | −0.488210 | ||||||||
\(663\) | 5.63365 | 0.218793 | ||||||||
\(664\) | 13.7900 | 0.535155 | ||||||||
\(665\) | 21.6419 | 0.839237 | ||||||||
\(666\) | −24.5579 | −0.951598 | ||||||||
\(667\) | −13.5539 | −0.524810 | ||||||||
\(668\) | −9.09146 | −0.351759 | ||||||||
\(669\) | −11.7502 | −0.454289 | ||||||||
\(670\) | −11.5619 | −0.446674 | ||||||||
\(671\) | −10.3324 | −0.398879 | ||||||||
\(672\) | 5.78186 | 0.223040 | ||||||||
\(673\) | 9.74807 | 0.375760 | 0.187880 | − | 0.982192i | \(-0.439838\pi\) | ||||
0.187880 | + | 0.982192i | \(0.439838\pi\) | |||||||
\(674\) | −9.26971 | −0.357056 | ||||||||
\(675\) | −183.562 | −7.06532 | ||||||||
\(676\) | −12.6010 | −0.484655 | ||||||||
\(677\) | −12.6333 | −0.485538 | −0.242769 | − | 0.970084i | \(-0.578056\pi\) | ||||
−0.242769 | + | 0.970084i | \(0.578056\pi\) | |||||||
\(678\) | 48.8503 | 1.87608 | ||||||||
\(679\) | 3.27935 | 0.125850 | ||||||||
\(680\) | 10.3651 | 0.397484 | ||||||||
\(681\) | −19.4638 | −0.745853 | ||||||||
\(682\) | 6.77466 | 0.259415 | ||||||||
\(683\) | 10.6884 | 0.408980 | 0.204490 | − | 0.978869i | \(-0.434446\pi\) | ||||
0.204490 | + | 0.978869i | \(0.434446\pi\) | |||||||
\(684\) | −26.7696 | −1.02356 | ||||||||
\(685\) | 31.3793 | 1.19894 | ||||||||
\(686\) | 18.9872 | 0.724933 | ||||||||
\(687\) | −26.4957 | −1.01087 | ||||||||
\(688\) | 3.91405 | 0.149222 | ||||||||
\(689\) | 6.63007 | 0.252585 | ||||||||
\(690\) | −26.3663 | −1.00375 | ||||||||
\(691\) | 15.5769 | 0.592574 | 0.296287 | − | 0.955099i | \(-0.404252\pi\) | ||||
0.296287 | + | 0.955099i | \(0.404252\pi\) | |||||||
\(692\) | 8.30753 | 0.315805 | ||||||||
\(693\) | 23.8187 | 0.904796 | ||||||||
\(694\) | −20.3167 | −0.771213 | ||||||||
\(695\) | 74.9021 | 2.84120 | ||||||||
\(696\) | 22.7265 | 0.861447 | ||||||||
\(697\) | 6.40118 | 0.242462 | ||||||||
\(698\) | −5.58689 | −0.211467 | ||||||||
\(699\) | 57.4661 | 2.17357 | ||||||||
\(700\) | −17.6663 | −0.667722 | ||||||||
\(701\) | 12.2139 | 0.461313 | 0.230656 | − | 0.973035i | \(-0.425913\pi\) | ||||
0.230656 | + | 0.973035i | \(0.425913\pi\) | |||||||
\(702\) | 11.2829 | 0.425845 | ||||||||
\(703\) | 9.51700 | 0.358940 | ||||||||
\(704\) | −1.66701 | −0.0628279 | ||||||||
\(705\) | 102.524 | 3.86128 | ||||||||
\(706\) | 24.3701 | 0.917182 | ||||||||
\(707\) | 27.1870 | 1.02247 | ||||||||
\(708\) | 22.1939 | 0.834098 | ||||||||
\(709\) | 3.03355 | 0.113927 | 0.0569636 | − | 0.998376i | \(-0.481858\pi\) | ||||
0.0569636 | + | 0.998376i | \(0.481858\pi\) | |||||||
\(710\) | 44.6776 | 1.67672 | ||||||||
\(711\) | −143.280 | −5.37340 | ||||||||
\(712\) | 0.657803 | 0.0246522 | ||||||||
\(713\) | −8.15146 | −0.305275 | ||||||||
\(714\) | 15.3332 | 0.573832 | ||||||||
\(715\) | 4.11542 | 0.153908 | ||||||||
\(716\) | −17.8449 | −0.666894 | ||||||||
\(717\) | −20.7140 | −0.773578 | ||||||||
\(718\) | −6.81820 | −0.254453 | ||||||||
\(719\) | 52.2647 | 1.94914 | 0.974572 | − | 0.224075i | \(-0.0719360\pi\) | ||||
0.974572 | + | 0.224075i | \(0.0719360\pi\) | |||||||
\(720\) | 32.4843 | 1.21062 | ||||||||
\(721\) | −0.458540 | −0.0170769 | ||||||||
\(722\) | −8.62590 | −0.321023 | ||||||||
\(723\) | −5.79134 | −0.215382 | ||||||||
\(724\) | 6.30891 | 0.234469 | ||||||||
\(725\) | −69.4401 | −2.57894 | ||||||||
\(726\) | 27.6493 | 1.02616 | ||||||||
\(727\) | −18.4591 | −0.684610 | −0.342305 | − | 0.939589i | \(-0.611208\pi\) | ||||
−0.342305 | + | 0.939589i | \(0.611208\pi\) | |||||||
\(728\) | 1.08588 | 0.0402453 | ||||||||
\(729\) | 111.852 | 4.14267 | ||||||||
\(730\) | −28.5331 | −1.05606 | ||||||||
\(731\) | 10.3799 | 0.383914 | ||||||||
\(732\) | −20.8458 | −0.770484 | ||||||||
\(733\) | −0.903406 | −0.0333681 | −0.0166840 | − | 0.999861i | \(-0.505311\pi\) | ||||
−0.0166840 | + | 0.999861i | \(0.505311\pi\) | |||||||
\(734\) | −4.85785 | −0.179307 | ||||||||
\(735\) | 53.1657 | 1.96105 | ||||||||
\(736\) | 2.00580 | 0.0739346 | ||||||||
\(737\) | 4.93127 | 0.181646 | ||||||||
\(738\) | 20.0613 | 0.738468 | ||||||||
\(739\) | −10.4273 | −0.383573 | −0.191787 | − | 0.981437i | \(-0.561428\pi\) | ||||
−0.191787 | + | 0.981437i | \(0.561428\pi\) | |||||||
\(740\) | −11.5487 | −0.424538 | ||||||||
\(741\) | −6.84224 | −0.251356 | ||||||||
\(742\) | 18.0452 | 0.662461 | ||||||||
\(743\) | 12.8836 | 0.472654 | 0.236327 | − | 0.971674i | \(-0.424056\pi\) | ||||
0.236327 | + | 0.971674i | \(0.424056\pi\) | |||||||
\(744\) | 13.6680 | 0.501092 | ||||||||
\(745\) | 75.8667 | 2.77954 | ||||||||
\(746\) | 4.02390 | 0.147325 | ||||||||
\(747\) | 114.612 | 4.19343 | ||||||||
\(748\) | −4.42084 | −0.161642 | ||||||||
\(749\) | −1.20630 | −0.0440771 | ||||||||
\(750\) | −69.3559 | −2.53252 | ||||||||
\(751\) | −23.7808 | −0.867773 | −0.433886 | − | 0.900968i | \(-0.642858\pi\) | ||||
−0.433886 | + | 0.900968i | \(0.642858\pi\) | |||||||
\(752\) | −7.79943 | −0.284416 | ||||||||
\(753\) | 25.2347 | 0.919605 | ||||||||
\(754\) | 4.26821 | 0.155439 | ||||||||
\(755\) | −64.8143 | −2.35883 | ||||||||
\(756\) | 30.7089 | 1.11687 | ||||||||
\(757\) | −8.15142 | −0.296268 | −0.148134 | − | 0.988967i | \(-0.547327\pi\) | ||||
−0.148134 | + | 0.988967i | \(0.547327\pi\) | |||||||
\(758\) | −7.91538 | −0.287500 | ||||||||
\(759\) | 11.2456 | 0.408188 | ||||||||
\(760\) | −12.5888 | −0.456642 | ||||||||
\(761\) | −31.4531 | −1.14017 | −0.570087 | − | 0.821585i | \(-0.693090\pi\) | ||||
−0.570087 | + | 0.821585i | \(0.693090\pi\) | |||||||
\(762\) | 33.9983 | 1.23163 | ||||||||
\(763\) | 14.0245 | 0.507722 | ||||||||
\(764\) | 10.6681 | 0.385960 | ||||||||
\(765\) | 86.1470 | 3.11465 | ||||||||
\(766\) | 5.04462 | 0.182269 | ||||||||
\(767\) | 4.16818 | 0.150504 | ||||||||
\(768\) | −3.36322 | −0.121360 | ||||||||
\(769\) | 17.6032 | 0.634787 | 0.317394 | − | 0.948294i | \(-0.397192\pi\) | ||||
0.317394 | + | 0.948294i | \(0.397192\pi\) | |||||||
\(770\) | 11.2011 | 0.403658 | ||||||||
\(771\) | −20.7634 | −0.747775 | ||||||||
\(772\) | 21.7456 | 0.782641 | ||||||||
\(773\) | −0.721276 | −0.0259425 | −0.0129712 | − | 0.999916i | \(-0.504129\pi\) | ||||
−0.0129712 | + | 0.999916i | \(0.504129\pi\) | |||||||
\(774\) | 32.5306 | 1.16929 | ||||||||
\(775\) | −41.7620 | −1.50013 | ||||||||
\(776\) | −1.90755 | −0.0684769 | ||||||||
\(777\) | −17.0841 | −0.612889 | ||||||||
\(778\) | 4.90941 | 0.176011 | ||||||||
\(779\) | −7.77444 | −0.278548 | ||||||||
\(780\) | 8.30292 | 0.297292 | ||||||||
\(781\) | −19.0555 | −0.681860 | ||||||||
\(782\) | 5.31928 | 0.190217 | ||||||||
\(783\) | 120.706 | 4.31369 | ||||||||
\(784\) | −4.04454 | −0.144448 | ||||||||
\(785\) | 20.6182 | 0.735894 | ||||||||
\(786\) | −21.1057 | −0.752816 | ||||||||
\(787\) | −2.58409 | −0.0921128 | −0.0460564 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460564 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(788\) | 14.0173 | 0.499346 | ||||||||
\(789\) | 46.1625 | 1.64343 | ||||||||
\(790\) | −67.3792 | −2.39724 | ||||||||
\(791\) | 24.9703 | 0.887843 | ||||||||
\(792\) | −13.8549 | −0.492314 | ||||||||
\(793\) | −3.91500 | −0.139026 | ||||||||
\(794\) | 7.90142 | 0.280411 | ||||||||
\(795\) | 137.979 | 4.89360 | ||||||||
\(796\) | −25.7549 | −0.912859 | ||||||||
\(797\) | −10.7106 | −0.379390 | −0.189695 | − | 0.981843i | \(-0.560750\pi\) | ||||
−0.189695 | + | 0.981843i | \(0.560750\pi\) | |||||||
\(798\) | −18.6227 | −0.659237 | ||||||||
\(799\) | −20.6838 | −0.731739 | ||||||||
\(800\) | 10.2762 | 0.363318 | ||||||||
\(801\) | 5.46716 | 0.193173 | ||||||||
\(802\) | −36.5778 | −1.29161 | ||||||||
\(803\) | 12.1697 | 0.429459 | ||||||||
\(804\) | 9.94891 | 0.350871 | ||||||||
\(805\) | −13.4774 | −0.475017 | ||||||||
\(806\) | 2.56695 | 0.0904168 | ||||||||
\(807\) | 5.74458 | 0.202219 | ||||||||
\(808\) | −15.8143 | −0.556344 | ||||||||
\(809\) | 25.2088 | 0.886295 | 0.443148 | − | 0.896449i | \(-0.353862\pi\) | ||||
0.443148 | + | 0.896449i | \(0.353862\pi\) | |||||||
\(810\) | 137.356 | 4.82619 | ||||||||
\(811\) | −10.3146 | −0.362194 | −0.181097 | − | 0.983465i | \(-0.557965\pi\) | ||||
−0.181097 | + | 0.983465i | \(0.557965\pi\) | |||||||
\(812\) | 11.6169 | 0.407673 | ||||||||
\(813\) | −45.1643 | −1.58398 | ||||||||
\(814\) | 4.92565 | 0.172644 | ||||||||
\(815\) | 56.0578 | 1.96362 | ||||||||
\(816\) | −8.91911 | −0.312231 | ||||||||
\(817\) | −12.6067 | −0.441052 | ||||||||
\(818\) | 23.6810 | 0.827986 | ||||||||
\(819\) | 9.02499 | 0.315359 | ||||||||
\(820\) | 9.43412 | 0.329454 | ||||||||
\(821\) | 18.5346 | 0.646861 | 0.323430 | − | 0.946252i | \(-0.395164\pi\) | ||||
0.323430 | + | 0.946252i | \(0.395164\pi\) | |||||||
\(822\) | −27.0017 | −0.941791 | ||||||||
\(823\) | 38.3771 | 1.33774 | 0.668871 | − | 0.743378i | \(-0.266778\pi\) | ||||
0.668871 | + | 0.743378i | \(0.266778\pi\) | |||||||
\(824\) | 0.266726 | 0.00929184 | ||||||||
\(825\) | 57.6138 | 2.00585 | ||||||||
\(826\) | 11.3447 | 0.394731 | ||||||||
\(827\) | −50.5317 | −1.75716 | −0.878580 | − | 0.477595i | \(-0.841509\pi\) | ||||
−0.878580 | + | 0.477595i | \(0.841509\pi\) | |||||||
\(828\) | 16.6707 | 0.579346 | ||||||||
\(829\) | 43.9252 | 1.52558 | 0.762792 | − | 0.646644i | \(-0.223828\pi\) | ||||
0.762792 | + | 0.646644i | \(0.223828\pi\) | |||||||
\(830\) | 53.8978 | 1.87082 | ||||||||
\(831\) | 82.6778 | 2.86806 | ||||||||
\(832\) | −0.631638 | −0.0218981 | ||||||||
\(833\) | −10.7259 | −0.371632 | ||||||||
\(834\) | −64.4528 | −2.23182 | ||||||||
\(835\) | −35.5338 | −1.22970 | ||||||||
\(836\) | 5.36925 | 0.185700 | ||||||||
\(837\) | 72.5939 | 2.50921 | ||||||||
\(838\) | −6.30101 | −0.217665 | ||||||||
\(839\) | 44.7174 | 1.54382 | 0.771908 | − | 0.635735i | \(-0.219303\pi\) | ||||
0.771908 | + | 0.635735i | \(0.219303\pi\) | |||||||
\(840\) | 22.5983 | 0.779715 | ||||||||
\(841\) | 16.6621 | 0.574554 | ||||||||
\(842\) | 40.7075 | 1.40287 | ||||||||
\(843\) | 97.7566 | 3.36692 | ||||||||
\(844\) | 20.2343 | 0.696495 | ||||||||
\(845\) | −49.2509 | −1.69428 | ||||||||
\(846\) | −64.8230 | −2.22866 | ||||||||
\(847\) | 14.1332 | 0.485623 | ||||||||
\(848\) | −10.4966 | −0.360456 | ||||||||
\(849\) | −37.4673 | −1.28587 | ||||||||
\(850\) | 27.2520 | 0.934736 | ||||||||
\(851\) | −5.92668 | −0.203164 | ||||||||
\(852\) | −38.4448 | −1.31710 | ||||||||
\(853\) | −7.21418 | −0.247009 | −0.123504 | − | 0.992344i | \(-0.539413\pi\) | ||||
−0.123504 | + | 0.992344i | \(0.539413\pi\) | |||||||
\(854\) | −10.6556 | −0.364626 | ||||||||
\(855\) | −104.628 | −3.57821 | ||||||||
\(856\) | 0.701684 | 0.0239831 | ||||||||
\(857\) | −1.41440 | −0.0483149 | −0.0241574 | − | 0.999708i | \(-0.507690\pi\) | ||||
−0.0241574 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(858\) | −3.54130 | −0.120898 | ||||||||
\(859\) | −8.15761 | −0.278334 | −0.139167 | − | 0.990269i | \(-0.544443\pi\) | ||||
−0.139167 | + | 0.990269i | \(0.544443\pi\) | |||||||
\(860\) | 15.2980 | 0.521656 | ||||||||
\(861\) | 13.9560 | 0.475620 | ||||||||
\(862\) | −32.1445 | −1.09484 | ||||||||
\(863\) | 53.0919 | 1.80727 | 0.903635 | − | 0.428303i | \(-0.140888\pi\) | ||||
0.903635 | + | 0.428303i | \(0.140888\pi\) | |||||||
\(864\) | −17.8629 | −0.607708 | ||||||||
\(865\) | 32.4698 | 1.10401 | ||||||||
\(866\) | −27.3389 | −0.929014 | ||||||||
\(867\) | 33.5216 | 1.13845 | ||||||||
\(868\) | 6.98653 | 0.237138 | ||||||||
\(869\) | 28.7380 | 0.974871 | ||||||||
\(870\) | 88.8261 | 3.01149 | ||||||||
\(871\) | 1.86848 | 0.0633110 | ||||||||
\(872\) | −8.15785 | −0.276260 | ||||||||
\(873\) | −15.8541 | −0.536579 | ||||||||
\(874\) | −6.46044 | −0.218528 | ||||||||
\(875\) | −35.4520 | −1.19850 | ||||||||
\(876\) | 24.5525 | 0.829552 | ||||||||
\(877\) | −22.1155 | −0.746789 | −0.373394 | − | 0.927673i | \(-0.621806\pi\) | ||||
−0.373394 | + | 0.927673i | \(0.621806\pi\) | |||||||
\(878\) | −7.46270 | −0.251854 | ||||||||
\(879\) | 57.4310 | 1.93710 | ||||||||
\(880\) | −6.51548 | −0.219637 | ||||||||
\(881\) | −28.8797 | −0.972981 | −0.486490 | − | 0.873686i | \(-0.661723\pi\) | ||||
−0.486490 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(882\) | −33.6152 | −1.13188 | ||||||||
\(883\) | 30.2326 | 1.01741 | 0.508704 | − | 0.860942i | \(-0.330125\pi\) | ||||
0.508704 | + | 0.860942i | \(0.330125\pi\) | |||||||
\(884\) | −1.67508 | −0.0563389 | ||||||||
\(885\) | 86.7444 | 2.91588 | ||||||||
\(886\) | 25.9025 | 0.870211 | ||||||||
\(887\) | 14.7967 | 0.496824 | 0.248412 | − | 0.968655i | \(-0.420091\pi\) | ||||
0.248412 | + | 0.968655i | \(0.420091\pi\) | |||||||
\(888\) | 9.93756 | 0.333483 | ||||||||
\(889\) | 17.3786 | 0.582859 | ||||||||
\(890\) | 2.57101 | 0.0861803 | ||||||||
\(891\) | −58.5839 | −1.96263 | ||||||||
\(892\) | 3.49374 | 0.116979 | ||||||||
\(893\) | 25.1211 | 0.840645 | ||||||||
\(894\) | −65.2828 | −2.18338 | ||||||||
\(895\) | −69.7463 | −2.33136 | ||||||||
\(896\) | −1.71915 | −0.0574326 | ||||||||
\(897\) | 4.26099 | 0.142270 | ||||||||
\(898\) | 5.51032 | 0.183882 | ||||||||
\(899\) | 27.4616 | 0.915897 | ||||||||
\(900\) | 85.4080 | 2.84693 | ||||||||
\(901\) | −27.8366 | −0.927371 | ||||||||
\(902\) | −4.02376 | −0.133977 | ||||||||
\(903\) | 22.6305 | 0.753095 | ||||||||
\(904\) | −14.5249 | −0.483090 | ||||||||
\(905\) | 24.6582 | 0.819667 | ||||||||
\(906\) | 55.7723 | 1.85291 | ||||||||
\(907\) | −23.3848 | −0.776480 | −0.388240 | − | 0.921558i | \(-0.626917\pi\) | ||||
−0.388240 | + | 0.921558i | \(0.626917\pi\) | |||||||
\(908\) | 5.78724 | 0.192056 | ||||||||
\(909\) | −131.436 | −4.35947 | ||||||||
\(910\) | 4.24413 | 0.140691 | ||||||||
\(911\) | −1.29699 | −0.0429712 | −0.0214856 | − | 0.999769i | \(-0.506840\pi\) | ||||
−0.0214856 | + | 0.999769i | \(0.506840\pi\) | |||||||
\(912\) | 10.8325 | 0.358701 | ||||||||
\(913\) | −22.9881 | −0.760794 | ||||||||
\(914\) | −15.4448 | −0.510869 | ||||||||
\(915\) | −81.4754 | −2.69349 | ||||||||
\(916\) | 7.87808 | 0.260299 | ||||||||
\(917\) | −10.7884 | −0.356265 | ||||||||
\(918\) | −47.3716 | −1.56350 | ||||||||
\(919\) | 4.20700 | 0.138776 | 0.0693880 | − | 0.997590i | \(-0.477895\pi\) | ||||
0.0693880 | + | 0.997590i | \(0.477895\pi\) | |||||||
\(920\) | 7.83961 | 0.258464 | ||||||||
\(921\) | −45.6216 | −1.50328 | ||||||||
\(922\) | −37.5298 | −1.23598 | ||||||||
\(923\) | −7.22022 | −0.237656 | ||||||||
\(924\) | −9.63843 | −0.317081 | ||||||||
\(925\) | −30.3639 | −0.998358 | ||||||||
\(926\) | −28.0159 | −0.920659 | ||||||||
\(927\) | 2.21682 | 0.0728100 | ||||||||
\(928\) | −6.75737 | −0.221822 | ||||||||
\(929\) | 12.1176 | 0.397564 | 0.198782 | − | 0.980044i | \(-0.436301\pi\) | ||||
0.198782 | + | 0.980044i | \(0.436301\pi\) | |||||||
\(930\) | 53.4209 | 1.75174 | ||||||||
\(931\) | 13.0270 | 0.426943 | ||||||||
\(932\) | −17.0866 | −0.559692 | ||||||||
\(933\) | 26.9649 | 0.882790 | ||||||||
\(934\) | −18.2634 | −0.597598 | ||||||||
\(935\) | −17.2788 | −0.565076 | ||||||||
\(936\) | −5.24970 | −0.171592 | ||||||||
\(937\) | 18.2879 | 0.597439 | 0.298719 | − | 0.954341i | \(-0.403441\pi\) | ||||
0.298719 | + | 0.954341i | \(0.403441\pi\) | |||||||
\(938\) | 5.08549 | 0.166047 | ||||||||
\(939\) | 16.6026 | 0.541806 | ||||||||
\(940\) | −30.4839 | −0.994275 | ||||||||
\(941\) | 0.0297097 | 0.000968509 0 | 0.000484254 | − | 1.00000i | \(-0.499846\pi\) | ||||
0.000484254 | 1.00000i | \(0.499846\pi\) | ||||||||
\(942\) | −17.7418 | −0.578059 | ||||||||
\(943\) | 4.84151 | 0.157661 | ||||||||
\(944\) | −6.59901 | −0.214779 | ||||||||
\(945\) | 120.025 | 3.90441 | ||||||||
\(946\) | −6.52476 | −0.212138 | ||||||||
\(947\) | −7.28252 | −0.236650 | −0.118325 | − | 0.992975i | \(-0.537752\pi\) | ||||
−0.118325 | + | 0.992975i | \(0.537752\pi\) | |||||||
\(948\) | 57.9794 | 1.88308 | ||||||||
\(949\) | 4.61115 | 0.149684 | ||||||||
\(950\) | −33.0984 | −1.07385 | ||||||||
\(951\) | 29.3784 | 0.952661 | ||||||||
\(952\) | −4.55910 | −0.147761 | ||||||||
\(953\) | −39.5165 | −1.28007 | −0.640033 | − | 0.768348i | \(-0.721079\pi\) | ||||
−0.640033 | + | 0.768348i | \(0.721079\pi\) | |||||||
\(954\) | −87.2400 | −2.82450 | ||||||||
\(955\) | 41.6962 | 1.34926 | ||||||||
\(956\) | 6.15898 | 0.199196 | ||||||||
\(957\) | −37.8854 | −1.22466 | ||||||||
\(958\) | −26.7325 | −0.863689 | ||||||||
\(959\) | −13.8022 | −0.445696 | ||||||||
\(960\) | −13.1451 | −0.424255 | ||||||||
\(961\) | −14.4843 | −0.467235 | ||||||||
\(962\) | 1.86635 | 0.0601735 | ||||||||
\(963\) | 5.83186 | 0.187929 | ||||||||
\(964\) | 1.72196 | 0.0554607 | ||||||||
\(965\) | 84.9922 | 2.73599 | ||||||||
\(966\) | 11.5972 | 0.373135 | ||||||||
\(967\) | 0.783289 | 0.0251889 | 0.0125944 | − | 0.999921i | \(-0.495991\pi\) | ||||
0.0125944 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(968\) | −8.22107 | −0.264235 | ||||||||
\(969\) | 28.7274 | 0.922858 | ||||||||
\(970\) | −7.45560 | −0.239385 | ||||||||
\(971\) | −35.8632 | −1.15091 | −0.575453 | − | 0.817835i | \(-0.695174\pi\) | ||||
−0.575453 | + | 0.817835i | \(0.695174\pi\) | |||||||
\(972\) | −64.6052 | −2.07221 | ||||||||
\(973\) | −32.9457 | −1.05619 | ||||||||
\(974\) | 30.5225 | 0.978004 | ||||||||
\(975\) | 21.8301 | 0.699123 | ||||||||
\(976\) | 6.19818 | 0.198399 | ||||||||
\(977\) | 45.6513 | 1.46051 | 0.730257 | − | 0.683172i | \(-0.239400\pi\) | ||||
0.730257 | + | 0.683172i | \(0.239400\pi\) | |||||||
\(978\) | −48.2374 | −1.54246 | ||||||||
\(979\) | −1.09656 | −0.0350464 | ||||||||
\(980\) | −15.8080 | −0.504968 | ||||||||
\(981\) | −67.8019 | −2.16475 | ||||||||
\(982\) | −27.7964 | −0.887018 | ||||||||
\(983\) | −19.2422 | −0.613730 | −0.306865 | − | 0.951753i | \(-0.599280\pi\) | ||||
−0.306865 | + | 0.951753i | \(0.599280\pi\) | |||||||
\(984\) | −8.11800 | −0.258792 | ||||||||
\(985\) | 54.7863 | 1.74564 | ||||||||
\(986\) | −17.9203 | −0.570697 | ||||||||
\(987\) | −45.0952 | −1.43540 | ||||||||
\(988\) | 2.03443 | 0.0647239 | ||||||||
\(989\) | 7.85078 | 0.249640 | ||||||||
\(990\) | −54.1517 | −1.72106 | ||||||||
\(991\) | 41.4527 | 1.31679 | 0.658395 | − | 0.752673i | \(-0.271236\pi\) | ||||
0.658395 | + | 0.752673i | \(0.271236\pi\) | |||||||
\(992\) | −4.06395 | −0.129031 | ||||||||
\(993\) | 42.2465 | 1.34065 | ||||||||
\(994\) | −19.6514 | −0.623306 | ||||||||
\(995\) | −100.663 | −3.19122 | ||||||||
\(996\) | −46.3787 | −1.46957 | ||||||||
\(997\) | 55.6727 | 1.76317 | 0.881586 | − | 0.472023i | \(-0.156476\pi\) | ||||
0.881586 | + | 0.472023i | \(0.156476\pi\) | |||||||
\(998\) | −28.3537 | −0.897522 | ||||||||
\(999\) | 52.7808 | 1.66991 |
(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 | 8006.2.a.a.1.1 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.a.1.1 | ✓ | 69 | 1.1 | even | 1 | trivial |