Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73131 | −1.93133 | −0.965663 | − | 0.259799i | \(-0.916344\pi\) | ||||
−0.965663 | + | 0.259799i | \(0.916344\pi\) | |||||||
\(3\) | −2.15430 | −1.24379 | −0.621894 | − | 0.783101i | \(-0.713637\pi\) | ||||
−0.621894 | + | 0.783101i | \(0.713637\pi\) | |||||||
\(4\) | 5.46003 | 2.73002 | ||||||||
\(5\) | −2.36711 | −1.05860 | −0.529301 | − | 0.848434i | \(-0.677546\pi\) | ||||
−0.529301 | + | 0.848434i | \(0.677546\pi\) | |||||||
\(6\) | 5.88407 | 2.40216 | ||||||||
\(7\) | −3.03890 | −1.14860 | −0.574298 | − | 0.818646i | \(-0.694725\pi\) | ||||
−0.574298 | + | 0.818646i | \(0.694725\pi\) | |||||||
\(8\) | −9.45041 | −3.34123 | ||||||||
\(9\) | 1.64103 | 0.547010 | ||||||||
\(10\) | 6.46530 | 2.04451 | ||||||||
\(11\) | −1.23686 | −0.372927 | −0.186464 | − | 0.982462i | \(-0.559703\pi\) | ||||
−0.186464 | + | 0.982462i | \(0.559703\pi\) | |||||||
\(12\) | −11.7626 | −3.39556 | ||||||||
\(13\) | 0.935944 | 0.259584 | 0.129792 | − | 0.991541i | \(-0.458569\pi\) | ||||
0.129792 | + | 0.991541i | \(0.458569\pi\) | |||||||
\(14\) | 8.30017 | 2.21831 | ||||||||
\(15\) | 5.09947 | 1.31668 | ||||||||
\(16\) | 14.8919 | 3.72298 | ||||||||
\(17\) | 3.71828 | 0.901815 | 0.450908 | − | 0.892571i | \(-0.351100\pi\) | ||||
0.450908 | + | 0.892571i | \(0.351100\pi\) | |||||||
\(18\) | −4.48215 | −1.05645 | ||||||||
\(19\) | 6.12994 | 1.40631 | 0.703153 | − | 0.711039i | \(-0.251775\pi\) | ||||
0.703153 | + | 0.711039i | \(0.251775\pi\) | |||||||
\(20\) | −12.9245 | −2.89000 | ||||||||
\(21\) | 6.54672 | 1.42861 | ||||||||
\(22\) | 3.37824 | 0.720244 | ||||||||
\(23\) | −3.46566 | −0.722640 | −0.361320 | − | 0.932442i | \(-0.617674\pi\) | ||||
−0.361320 | + | 0.932442i | \(0.617674\pi\) | |||||||
\(24\) | 20.3591 | 4.15578 | ||||||||
\(25\) | 0.603200 | 0.120640 | ||||||||
\(26\) | −2.55635 | −0.501341 | ||||||||
\(27\) | 2.92764 | 0.563424 | ||||||||
\(28\) | −16.5925 | −3.13569 | ||||||||
\(29\) | −5.46018 | −1.01393 | −0.506965 | − | 0.861967i | \(-0.669233\pi\) | ||||
−0.506965 | + | 0.861967i | \(0.669233\pi\) | |||||||
\(30\) | −13.9282 | −2.54293 | ||||||||
\(31\) | 4.47779 | 0.804236 | 0.402118 | − | 0.915588i | \(-0.368274\pi\) | ||||
0.402118 | + | 0.915588i | \(0.368274\pi\) | |||||||
\(32\) | −21.7735 | −3.84905 | ||||||||
\(33\) | 2.66457 | 0.463843 | ||||||||
\(34\) | −10.1558 | −1.74170 | ||||||||
\(35\) | 7.19341 | 1.21591 | ||||||||
\(36\) | 8.96007 | 1.49335 | ||||||||
\(37\) | −1.25753 | −0.206736 | −0.103368 | − | 0.994643i | \(-0.532962\pi\) | ||||
−0.103368 | + | 0.994643i | \(0.532962\pi\) | |||||||
\(38\) | −16.7427 | −2.71603 | ||||||||
\(39\) | −2.01631 | −0.322868 | ||||||||
\(40\) | 22.3701 | 3.53703 | ||||||||
\(41\) | −5.00276 | −0.781300 | −0.390650 | − | 0.920539i | \(-0.627750\pi\) | ||||
−0.390650 | + | 0.920539i | \(0.627750\pi\) | |||||||
\(42\) | −17.8811 | −2.75911 | ||||||||
\(43\) | −8.04498 | −1.22685 | −0.613424 | − | 0.789754i | \(-0.710208\pi\) | ||||
−0.613424 | + | 0.789754i | \(0.710208\pi\) | |||||||
\(44\) | −6.75330 | −1.01810 | ||||||||
\(45\) | −3.88449 | −0.579066 | ||||||||
\(46\) | 9.46578 | 1.39565 | ||||||||
\(47\) | −11.1410 | −1.62509 | −0.812544 | − | 0.582900i | \(-0.801918\pi\) | ||||
−0.812544 | + | 0.582900i | \(0.801918\pi\) | |||||||
\(48\) | −32.0817 | −4.63060 | ||||||||
\(49\) | 2.23492 | 0.319274 | ||||||||
\(50\) | −1.64752 | −0.232995 | ||||||||
\(51\) | −8.01031 | −1.12167 | ||||||||
\(52\) | 5.11029 | 0.708669 | ||||||||
\(53\) | 1.52281 | 0.209174 | 0.104587 | − | 0.994516i | \(-0.466648\pi\) | ||||
0.104587 | + | 0.994516i | \(0.466648\pi\) | |||||||
\(54\) | −7.99628 | −1.08816 | ||||||||
\(55\) | 2.92778 | 0.394782 | ||||||||
\(56\) | 28.7189 | 3.83772 | ||||||||
\(57\) | −13.2058 | −1.74915 | ||||||||
\(58\) | 14.9134 | 1.95823 | ||||||||
\(59\) | −2.78143 | −0.362111 | −0.181056 | − | 0.983473i | \(-0.557951\pi\) | ||||
−0.181056 | + | 0.983473i | \(0.557951\pi\) | |||||||
\(60\) | 27.8433 | 3.59455 | ||||||||
\(61\) | −10.6917 | −1.36893 | −0.684466 | − | 0.729044i | \(-0.739965\pi\) | ||||
−0.684466 | + | 0.729044i | \(0.739965\pi\) | |||||||
\(62\) | −12.2302 | −1.55324 | ||||||||
\(63\) | −4.98692 | −0.628293 | ||||||||
\(64\) | 29.6864 | 3.71080 | ||||||||
\(65\) | −2.21548 | −0.274797 | ||||||||
\(66\) | −7.27777 | −0.895831 | ||||||||
\(67\) | −5.50665 | −0.672745 | −0.336372 | − | 0.941729i | \(-0.609200\pi\) | ||||
−0.336372 | + | 0.941729i | \(0.609200\pi\) | |||||||
\(68\) | 20.3019 | 2.46197 | ||||||||
\(69\) | 7.46609 | 0.898811 | ||||||||
\(70\) | −19.6474 | −2.34831 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −15.5084 | −1.82768 | ||||||||
\(73\) | −7.75902 | −0.908124 | −0.454062 | − | 0.890970i | \(-0.650026\pi\) | ||||
−0.454062 | + | 0.890970i | \(0.650026\pi\) | |||||||
\(74\) | 3.43469 | 0.399274 | ||||||||
\(75\) | −1.29948 | −0.150051 | ||||||||
\(76\) | 33.4697 | 3.83924 | ||||||||
\(77\) | 3.75869 | 0.428343 | ||||||||
\(78\) | 5.50716 | 0.623563 | ||||||||
\(79\) | 12.1551 | 1.36755 | 0.683776 | − | 0.729692i | \(-0.260336\pi\) | ||||
0.683776 | + | 0.729692i | \(0.260336\pi\) | |||||||
\(80\) | −35.2508 | −3.94115 | ||||||||
\(81\) | −11.2301 | −1.24779 | ||||||||
\(82\) | 13.6641 | 1.50894 | ||||||||
\(83\) | −1.58835 | −0.174344 | −0.0871719 | − | 0.996193i | \(-0.527783\pi\) | ||||
−0.0871719 | + | 0.996193i | \(0.527783\pi\) | |||||||
\(84\) | 35.7453 | 3.90013 | ||||||||
\(85\) | −8.80157 | −0.954664 | ||||||||
\(86\) | 21.9733 | 2.36944 | ||||||||
\(87\) | 11.7629 | 1.26111 | ||||||||
\(88\) | 11.6888 | 1.24603 | ||||||||
\(89\) | 16.4018 | 1.73859 | 0.869293 | − | 0.494296i | \(-0.164574\pi\) | ||||
0.869293 | + | 0.494296i | \(0.164574\pi\) | |||||||
\(90\) | 10.6097 | 1.11836 | ||||||||
\(91\) | −2.84424 | −0.298157 | ||||||||
\(92\) | −18.9226 | −1.97282 | ||||||||
\(93\) | −9.64653 | −1.00030 | ||||||||
\(94\) | 30.4296 | 3.13857 | ||||||||
\(95\) | −14.5102 | −1.48872 | ||||||||
\(96\) | 46.9068 | 4.78741 | ||||||||
\(97\) | 8.08872 | 0.821285 | 0.410643 | − | 0.911796i | \(-0.365304\pi\) | ||||
0.410643 | + | 0.911796i | \(0.365304\pi\) | |||||||
\(98\) | −6.10424 | −0.616622 | ||||||||
\(99\) | −2.02972 | −0.203995 | ||||||||
\(100\) | 3.29349 | 0.329349 | ||||||||
\(101\) | 7.11014 | 0.707486 | 0.353743 | − | 0.935343i | \(-0.384909\pi\) | ||||
0.353743 | + | 0.935343i | \(0.384909\pi\) | |||||||
\(102\) | 21.8786 | 2.16630 | ||||||||
\(103\) | 19.9876 | 1.96943 | 0.984716 | − | 0.174166i | \(-0.0557230\pi\) | ||||
0.984716 | + | 0.174166i | \(0.0557230\pi\) | |||||||
\(104\) | −8.84506 | −0.867329 | ||||||||
\(105\) | −15.4968 | −1.51233 | ||||||||
\(106\) | −4.15926 | −0.403983 | ||||||||
\(107\) | −14.9027 | −1.44070 | −0.720351 | − | 0.693610i | \(-0.756019\pi\) | ||||
−0.720351 | + | 0.693610i | \(0.756019\pi\) | |||||||
\(108\) | 15.9850 | 1.53816 | ||||||||
\(109\) | 15.8787 | 1.52090 | 0.760450 | − | 0.649396i | \(-0.224978\pi\) | ||||
0.760450 | + | 0.649396i | \(0.224978\pi\) | |||||||
\(110\) | −7.99667 | −0.762452 | ||||||||
\(111\) | 2.70909 | 0.257136 | ||||||||
\(112\) | −45.2550 | −4.27620 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 36.0690 | 3.37817 | ||||||||
\(115\) | 8.20359 | 0.764989 | ||||||||
\(116\) | −29.8128 | −2.76805 | ||||||||
\(117\) | 1.53591 | 0.141995 | ||||||||
\(118\) | 7.59694 | 0.699355 | ||||||||
\(119\) | −11.2995 | −1.03582 | ||||||||
\(120\) | −48.1921 | −4.39932 | ||||||||
\(121\) | −9.47018 | −0.860925 | ||||||||
\(122\) | 29.2023 | 2.64385 | ||||||||
\(123\) | 10.7775 | 0.971772 | ||||||||
\(124\) | 24.4489 | 2.19558 | ||||||||
\(125\) | 10.4077 | 0.930893 | ||||||||
\(126\) | 13.6208 | 1.21344 | ||||||||
\(127\) | 19.1330 | 1.69778 | 0.848889 | − | 0.528571i | \(-0.177272\pi\) | ||||
0.848889 | + | 0.528571i | \(0.177272\pi\) | |||||||
\(128\) | −37.5355 | −3.31770 | ||||||||
\(129\) | 17.3313 | 1.52594 | ||||||||
\(130\) | 6.05116 | 0.530721 | ||||||||
\(131\) | 0.763075 | 0.0666702 | 0.0333351 | − | 0.999444i | \(-0.489387\pi\) | ||||
0.0333351 | + | 0.999444i | \(0.489387\pi\) | |||||||
\(132\) | 14.5487 | 1.26630 | ||||||||
\(133\) | −18.6283 | −1.61528 | ||||||||
\(134\) | 15.0404 | 1.29929 | ||||||||
\(135\) | −6.93004 | −0.596443 | ||||||||
\(136\) | −35.1393 | −3.01317 | ||||||||
\(137\) | 2.64401 | 0.225893 | 0.112946 | − | 0.993601i | \(-0.463971\pi\) | ||||
0.112946 | + | 0.993601i | \(0.463971\pi\) | |||||||
\(138\) | −20.3922 | −1.73590 | ||||||||
\(139\) | 12.7257 | 1.07938 | 0.539690 | − | 0.841864i | \(-0.318541\pi\) | ||||
0.539690 | + | 0.841864i | \(0.318541\pi\) | |||||||
\(140\) | 39.2762 | 3.31945 | ||||||||
\(141\) | 24.0012 | 2.02127 | ||||||||
\(142\) | 2.73131 | 0.229206 | ||||||||
\(143\) | −1.15763 | −0.0968060 | ||||||||
\(144\) | 24.4380 | 2.03650 | ||||||||
\(145\) | 12.9248 | 1.07335 | ||||||||
\(146\) | 21.1923 | 1.75388 | ||||||||
\(147\) | −4.81469 | −0.397109 | ||||||||
\(148\) | −6.86613 | −0.564392 | ||||||||
\(149\) | 9.38599 | 0.768930 | 0.384465 | − | 0.923140i | \(-0.374386\pi\) | ||||
0.384465 | + | 0.923140i | \(0.374386\pi\) | |||||||
\(150\) | 3.54927 | 0.289796 | ||||||||
\(151\) | −19.1757 | −1.56050 | −0.780249 | − | 0.625469i | \(-0.784908\pi\) | ||||
−0.780249 | + | 0.625469i | \(0.784908\pi\) | |||||||
\(152\) | −57.9305 | −4.69878 | ||||||||
\(153\) | 6.10180 | 0.493302 | ||||||||
\(154\) | −10.2661 | −0.827270 | ||||||||
\(155\) | −10.5994 | −0.851366 | ||||||||
\(156\) | −11.0091 | −0.881435 | ||||||||
\(157\) | −12.4573 | −0.994201 | −0.497101 | − | 0.867693i | \(-0.665602\pi\) | ||||
−0.497101 | + | 0.867693i | \(0.665602\pi\) | |||||||
\(158\) | −33.1992 | −2.64119 | ||||||||
\(159\) | −3.28060 | −0.260168 | ||||||||
\(160\) | 51.5403 | 4.07462 | ||||||||
\(161\) | 10.5318 | 0.830022 | ||||||||
\(162\) | 30.6729 | 2.40989 | ||||||||
\(163\) | 5.12401 | 0.401343 | 0.200672 | − | 0.979659i | \(-0.435688\pi\) | ||||
0.200672 | + | 0.979659i | \(0.435688\pi\) | |||||||
\(164\) | −27.3152 | −2.13296 | ||||||||
\(165\) | −6.30733 | −0.491025 | ||||||||
\(166\) | 4.33826 | 0.336714 | ||||||||
\(167\) | 7.07034 | 0.547119 | 0.273560 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273560 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(168\) | −61.8692 | −4.77331 | ||||||||
\(169\) | −12.1240 | −0.932616 | ||||||||
\(170\) | 24.0398 | 1.84377 | ||||||||
\(171\) | 10.0594 | 0.769262 | ||||||||
\(172\) | −43.9259 | −3.34932 | ||||||||
\(173\) | 17.0444 | 1.29586 | 0.647930 | − | 0.761700i | \(-0.275635\pi\) | ||||
0.647930 | + | 0.761700i | \(0.275635\pi\) | |||||||
\(174\) | −32.1281 | −2.43562 | ||||||||
\(175\) | −1.83306 | −0.138567 | ||||||||
\(176\) | −18.4192 | −1.38840 | ||||||||
\(177\) | 5.99205 | 0.450390 | ||||||||
\(178\) | −44.7983 | −3.35778 | ||||||||
\(179\) | 12.4273 | 0.928863 | 0.464432 | − | 0.885609i | \(-0.346259\pi\) | ||||
0.464432 | + | 0.885609i | \(0.346259\pi\) | |||||||
\(180\) | −21.2095 | −1.58086 | ||||||||
\(181\) | 24.8628 | 1.84803 | 0.924017 | − | 0.382351i | \(-0.124885\pi\) | ||||
0.924017 | + | 0.382351i | \(0.124885\pi\) | |||||||
\(182\) | 7.76849 | 0.575839 | ||||||||
\(183\) | 23.0332 | 1.70266 | ||||||||
\(184\) | 32.7519 | 2.41450 | ||||||||
\(185\) | 2.97670 | 0.218851 | ||||||||
\(186\) | 26.3476 | 1.93190 | ||||||||
\(187\) | −4.59899 | −0.336312 | ||||||||
\(188\) | −60.8305 | −4.43652 | ||||||||
\(189\) | −8.89680 | −0.647147 | ||||||||
\(190\) | 39.6319 | 2.87520 | ||||||||
\(191\) | 7.44465 | 0.538676 | 0.269338 | − | 0.963046i | \(-0.413195\pi\) | ||||
0.269338 | + | 0.963046i | \(0.413195\pi\) | |||||||
\(192\) | −63.9535 | −4.61545 | ||||||||
\(193\) | −16.3689 | −1.17826 | −0.589128 | − | 0.808040i | \(-0.700529\pi\) | ||||
−0.589128 | + | 0.808040i | \(0.700529\pi\) | |||||||
\(194\) | −22.0928 | −1.58617 | ||||||||
\(195\) | 4.77282 | 0.341789 | ||||||||
\(196\) | 12.2027 | 0.871623 | ||||||||
\(197\) | −12.0292 | −0.857044 | −0.428522 | − | 0.903531i | \(-0.640966\pi\) | ||||
−0.428522 | + | 0.903531i | \(0.640966\pi\) | |||||||
\(198\) | 5.54379 | 0.393980 | ||||||||
\(199\) | −8.12373 | −0.575876 | −0.287938 | − | 0.957649i | \(-0.592970\pi\) | ||||
−0.287938 | + | 0.957649i | \(0.592970\pi\) | |||||||
\(200\) | −5.70049 | −0.403085 | ||||||||
\(201\) | 11.8630 | 0.836752 | ||||||||
\(202\) | −19.4200 | −1.36638 | ||||||||
\(203\) | 16.5929 | 1.16460 | ||||||||
\(204\) | −43.7366 | −3.06217 | ||||||||
\(205\) | 11.8421 | 0.827086 | ||||||||
\(206\) | −54.5921 | −3.80361 | ||||||||
\(207\) | −5.68725 | −0.395291 | ||||||||
\(208\) | 13.9380 | 0.966426 | ||||||||
\(209\) | −7.58188 | −0.524450 | ||||||||
\(210\) | 42.3265 | 2.92080 | ||||||||
\(211\) | 25.7925 | 1.77563 | 0.887813 | − | 0.460204i | \(-0.152224\pi\) | ||||
0.887813 | + | 0.460204i | \(0.152224\pi\) | |||||||
\(212\) | 8.31459 | 0.571049 | ||||||||
\(213\) | 2.15430 | 0.147611 | ||||||||
\(214\) | 40.7039 | 2.78246 | ||||||||
\(215\) | 19.0433 | 1.29875 | ||||||||
\(216\) | −27.6674 | −1.88253 | ||||||||
\(217\) | −13.6076 | −0.923742 | ||||||||
\(218\) | −43.3695 | −2.93735 | ||||||||
\(219\) | 16.7153 | 1.12951 | ||||||||
\(220\) | 15.9858 | 1.07776 | ||||||||
\(221\) | 3.48010 | 0.234097 | ||||||||
\(222\) | −7.39936 | −0.496613 | ||||||||
\(223\) | 1.06724 | 0.0714674 | 0.0357337 | − | 0.999361i | \(-0.488623\pi\) | ||||
0.0357337 | + | 0.999361i | \(0.488623\pi\) | |||||||
\(224\) | 66.1676 | 4.42101 | ||||||||
\(225\) | 0.989868 | 0.0659912 | ||||||||
\(226\) | 2.73131 | 0.181684 | ||||||||
\(227\) | −23.0156 | −1.52760 | −0.763798 | − | 0.645455i | \(-0.776668\pi\) | ||||
−0.763798 | + | 0.645455i | \(0.776668\pi\) | |||||||
\(228\) | −72.1039 | −4.77520 | ||||||||
\(229\) | 2.63761 | 0.174298 | 0.0871492 | − | 0.996195i | \(-0.472224\pi\) | ||||
0.0871492 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(230\) | −22.4065 | −1.47744 | ||||||||
\(231\) | −8.09737 | −0.532768 | ||||||||
\(232\) | 51.6010 | 3.38777 | ||||||||
\(233\) | 16.4544 | 1.07796 | 0.538981 | − | 0.842318i | \(-0.318810\pi\) | ||||
0.538981 | + | 0.842318i | \(0.318810\pi\) | |||||||
\(234\) | −4.19504 | −0.274239 | ||||||||
\(235\) | 26.3721 | 1.72032 | ||||||||
\(236\) | −15.1867 | −0.988570 | ||||||||
\(237\) | −26.1857 | −1.70095 | ||||||||
\(238\) | 30.8624 | 2.00051 | ||||||||
\(239\) | −22.5202 | −1.45671 | −0.728356 | − | 0.685199i | \(-0.759715\pi\) | ||||
−0.728356 | + | 0.685199i | \(0.759715\pi\) | |||||||
\(240\) | 75.9409 | 4.90196 | ||||||||
\(241\) | 5.06501 | 0.326266 | 0.163133 | − | 0.986604i | \(-0.447840\pi\) | ||||
0.163133 | + | 0.986604i | \(0.447840\pi\) | |||||||
\(242\) | 25.8660 | 1.66273 | ||||||||
\(243\) | 15.4102 | 0.988563 | ||||||||
\(244\) | −58.3771 | −3.73721 | ||||||||
\(245\) | −5.29029 | −0.337984 | ||||||||
\(246\) | −29.4366 | −1.87681 | ||||||||
\(247\) | 5.73728 | 0.365055 | ||||||||
\(248\) | −42.3170 | −2.68713 | ||||||||
\(249\) | 3.42178 | 0.216847 | ||||||||
\(250\) | −28.4266 | −1.79786 | ||||||||
\(251\) | 0.702492 | 0.0443409 | 0.0221704 | − | 0.999754i | \(-0.492942\pi\) | ||||
0.0221704 | + | 0.999754i | \(0.492942\pi\) | |||||||
\(252\) | −27.2288 | −1.71525 | ||||||||
\(253\) | 4.28654 | 0.269492 | ||||||||
\(254\) | −52.2581 | −3.27896 | ||||||||
\(255\) | 18.9613 | 1.18740 | ||||||||
\(256\) | 43.1483 | 2.69677 | ||||||||
\(257\) | −8.68978 | −0.542054 | −0.271027 | − | 0.962572i | \(-0.587363\pi\) | ||||
−0.271027 | + | 0.962572i | \(0.587363\pi\) | |||||||
\(258\) | −47.3372 | −2.94709 | ||||||||
\(259\) | 3.82149 | 0.237456 | ||||||||
\(260\) | −12.0966 | −0.750199 | ||||||||
\(261\) | −8.96031 | −0.554629 | ||||||||
\(262\) | −2.08419 | −0.128762 | ||||||||
\(263\) | −17.5100 | −1.07972 | −0.539858 | − | 0.841756i | \(-0.681522\pi\) | ||||
−0.539858 | + | 0.841756i | \(0.681522\pi\) | |||||||
\(264\) | −25.1813 | −1.54980 | ||||||||
\(265\) | −3.60466 | −0.221432 | ||||||||
\(266\) | 50.8795 | 3.11963 | ||||||||
\(267\) | −35.3345 | −2.16243 | ||||||||
\(268\) | −30.0665 | −1.83660 | ||||||||
\(269\) | −17.9562 | −1.09481 | −0.547406 | − | 0.836867i | \(-0.684385\pi\) | ||||
−0.547406 | + | 0.836867i | \(0.684385\pi\) | |||||||
\(270\) | 18.9281 | 1.15192 | ||||||||
\(271\) | −1.01763 | −0.0618164 | −0.0309082 | − | 0.999522i | \(-0.509840\pi\) | ||||
−0.0309082 | + | 0.999522i | \(0.509840\pi\) | |||||||
\(272\) | 55.3723 | 3.35744 | ||||||||
\(273\) | 6.12736 | 0.370845 | ||||||||
\(274\) | −7.22159 | −0.436272 | ||||||||
\(275\) | −0.746073 | −0.0449899 | ||||||||
\(276\) | 40.7651 | 2.45377 | ||||||||
\(277\) | 27.5483 | 1.65521 | 0.827607 | − | 0.561307i | \(-0.189701\pi\) | ||||
0.827607 | + | 0.561307i | \(0.189701\pi\) | |||||||
\(278\) | −34.7578 | −2.08464 | ||||||||
\(279\) | 7.34819 | 0.439924 | ||||||||
\(280\) | −67.9807 | −4.06262 | ||||||||
\(281\) | 14.4506 | 0.862048 | 0.431024 | − | 0.902341i | \(-0.358153\pi\) | ||||
0.431024 | + | 0.902341i | \(0.358153\pi\) | |||||||
\(282\) | −65.5546 | −3.90372 | ||||||||
\(283\) | 13.2348 | 0.786730 | 0.393365 | − | 0.919382i | \(-0.371311\pi\) | ||||
0.393365 | + | 0.919382i | \(0.371311\pi\) | |||||||
\(284\) | −5.46003 | −0.323993 | ||||||||
\(285\) | 31.2595 | 1.85165 | ||||||||
\(286\) | 3.16185 | 0.186964 | ||||||||
\(287\) | 15.2029 | 0.897398 | ||||||||
\(288\) | −35.7310 | −2.10547 | ||||||||
\(289\) | −3.17439 | −0.186729 | ||||||||
\(290\) | −35.3017 | −2.07299 | ||||||||
\(291\) | −17.4256 | −1.02151 | ||||||||
\(292\) | −42.3645 | −2.47920 | ||||||||
\(293\) | 14.9887 | 0.875648 | 0.437824 | − | 0.899061i | \(-0.355749\pi\) | ||||
0.437824 | + | 0.899061i | \(0.355749\pi\) | |||||||
\(294\) | 13.1504 | 0.766947 | ||||||||
\(295\) | 6.58395 | 0.383332 | ||||||||
\(296\) | 11.8841 | 0.690751 | ||||||||
\(297\) | −3.62108 | −0.210116 | ||||||||
\(298\) | −25.6360 | −1.48505 | ||||||||
\(299\) | −3.24366 | −0.187586 | ||||||||
\(300\) | −7.09518 | −0.409640 | ||||||||
\(301\) | 24.4479 | 1.40915 | ||||||||
\(302\) | 52.3748 | 3.01383 | ||||||||
\(303\) | −15.3174 | −0.879962 | ||||||||
\(304\) | 91.2865 | 5.23564 | ||||||||
\(305\) | 25.3084 | 1.44916 | ||||||||
\(306\) | −16.6659 | −0.952726 | ||||||||
\(307\) | 21.4218 | 1.22260 | 0.611302 | − | 0.791397i | \(-0.290646\pi\) | ||||
0.611302 | + | 0.791397i | \(0.290646\pi\) | |||||||
\(308\) | 20.5226 | 1.16938 | ||||||||
\(309\) | −43.0593 | −2.44956 | ||||||||
\(310\) | 28.9503 | 1.64426 | ||||||||
\(311\) | 20.8186 | 1.18051 | 0.590257 | − | 0.807215i | \(-0.299026\pi\) | ||||
0.590257 | + | 0.807215i | \(0.299026\pi\) | |||||||
\(312\) | 19.0550 | 1.07877 | ||||||||
\(313\) | 2.42545 | 0.137094 | 0.0685472 | − | 0.997648i | \(-0.478164\pi\) | ||||
0.0685472 | + | 0.997648i | \(0.478164\pi\) | |||||||
\(314\) | 34.0247 | 1.92013 | ||||||||
\(315\) | 11.8046 | 0.665113 | ||||||||
\(316\) | 66.3671 | 3.73344 | ||||||||
\(317\) | −12.9570 | −0.727736 | −0.363868 | − | 0.931451i | \(-0.618544\pi\) | ||||
−0.363868 | + | 0.931451i | \(0.618544\pi\) | |||||||
\(318\) | 8.96031 | 0.502469 | ||||||||
\(319\) | 6.75348 | 0.378122 | ||||||||
\(320\) | −70.2709 | −3.92826 | ||||||||
\(321\) | 32.1050 | 1.79193 | ||||||||
\(322\) | −28.7656 | −1.60304 | ||||||||
\(323\) | 22.7928 | 1.26823 | ||||||||
\(324\) | −61.3168 | −3.40649 | ||||||||
\(325\) | 0.564561 | 0.0313162 | ||||||||
\(326\) | −13.9952 | −0.775124 | ||||||||
\(327\) | −34.2075 | −1.89168 | ||||||||
\(328\) | 47.2782 | 2.61050 | ||||||||
\(329\) | 33.8565 | 1.86657 | ||||||||
\(330\) | 17.2273 | 0.948329 | ||||||||
\(331\) | −12.0179 | −0.660562 | −0.330281 | − | 0.943883i | \(-0.607144\pi\) | ||||
−0.330281 | + | 0.943883i | \(0.607144\pi\) | |||||||
\(332\) | −8.67243 | −0.475961 | ||||||||
\(333\) | −2.06363 | −0.113086 | ||||||||
\(334\) | −19.3113 | −1.05666 | ||||||||
\(335\) | 13.0348 | 0.712169 | ||||||||
\(336\) | 97.4931 | 5.31869 | ||||||||
\(337\) | −15.0255 | −0.818492 | −0.409246 | − | 0.912424i | \(-0.634208\pi\) | ||||
−0.409246 | + | 0.912424i | \(0.634208\pi\) | |||||||
\(338\) | 33.1144 | 1.80118 | ||||||||
\(339\) | 2.15430 | 0.117006 | ||||||||
\(340\) | −48.0569 | −2.60625 | ||||||||
\(341\) | −5.53840 | −0.299921 | ||||||||
\(342\) | −27.4753 | −1.48570 | ||||||||
\(343\) | 14.4806 | 0.781880 | ||||||||
\(344\) | 76.0284 | 4.09918 | ||||||||
\(345\) | −17.6730 | −0.951484 | ||||||||
\(346\) | −46.5534 | −2.50273 | ||||||||
\(347\) | −25.1866 | −1.35209 | −0.676043 | − | 0.736862i | \(-0.736307\pi\) | ||||
−0.676043 | + | 0.736862i | \(0.736307\pi\) | |||||||
\(348\) | 64.2258 | 3.44286 | ||||||||
\(349\) | −24.6754 | −1.32084 | −0.660422 | − | 0.750894i | \(-0.729623\pi\) | ||||
−0.660422 | + | 0.750894i | \(0.729623\pi\) | |||||||
\(350\) | 5.00666 | 0.267617 | ||||||||
\(351\) | 2.74011 | 0.146256 | ||||||||
\(352\) | 26.9308 | 1.43542 | ||||||||
\(353\) | 26.1979 | 1.39438 | 0.697188 | − | 0.716889i | \(-0.254434\pi\) | ||||
0.697188 | + | 0.716889i | \(0.254434\pi\) | |||||||
\(354\) | −16.3661 | −0.869850 | ||||||||
\(355\) | 2.36711 | 0.125633 | ||||||||
\(356\) | 89.5544 | 4.74637 | ||||||||
\(357\) | 24.3425 | 1.28834 | ||||||||
\(358\) | −33.9429 | −1.79394 | ||||||||
\(359\) | 17.8907 | 0.944236 | 0.472118 | − | 0.881535i | \(-0.343490\pi\) | ||||
0.472118 | + | 0.881535i | \(0.343490\pi\) | |||||||
\(360\) | 36.7101 | 1.93479 | ||||||||
\(361\) | 18.5762 | 0.977694 | ||||||||
\(362\) | −67.9078 | −3.56916 | ||||||||
\(363\) | 20.4016 | 1.07081 | ||||||||
\(364\) | −15.5297 | −0.813975 | ||||||||
\(365\) | 18.3664 | 0.961343 | ||||||||
\(366\) | −62.9107 | −3.28840 | ||||||||
\(367\) | 20.3121 | 1.06028 | 0.530142 | − | 0.847909i | \(-0.322138\pi\) | ||||
0.530142 | + | 0.847909i | \(0.322138\pi\) | |||||||
\(368\) | −51.6103 | −2.69037 | ||||||||
\(369\) | −8.20967 | −0.427379 | ||||||||
\(370\) | −8.13027 | −0.422673 | ||||||||
\(371\) | −4.62767 | −0.240257 | ||||||||
\(372\) | −52.6704 | −2.73083 | ||||||||
\(373\) | −22.9192 | −1.18671 | −0.593356 | − | 0.804940i | \(-0.702197\pi\) | ||||
−0.593356 | + | 0.804940i | \(0.702197\pi\) | |||||||
\(374\) | 12.5613 | 0.649527 | ||||||||
\(375\) | −22.4214 | −1.15783 | ||||||||
\(376\) | 105.287 | 5.42979 | ||||||||
\(377\) | −5.11042 | −0.263200 | ||||||||
\(378\) | 24.2999 | 1.24985 | ||||||||
\(379\) | 4.09003 | 0.210091 | 0.105045 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105045 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(380\) | −79.2264 | −4.06423 | ||||||||
\(381\) | −41.2183 | −2.11168 | ||||||||
\(382\) | −20.3336 | −1.04036 | ||||||||
\(383\) | 9.79989 | 0.500751 | 0.250376 | − | 0.968149i | \(-0.419446\pi\) | ||||
0.250376 | + | 0.968149i | \(0.419446\pi\) | |||||||
\(384\) | 80.8629 | 4.12652 | ||||||||
\(385\) | −8.89724 | −0.453445 | ||||||||
\(386\) | 44.7084 | 2.27560 | ||||||||
\(387\) | −13.2020 | −0.671098 | ||||||||
\(388\) | 44.1647 | 2.24212 | ||||||||
\(389\) | −31.9861 | −1.62176 | −0.810881 | − | 0.585211i | \(-0.801012\pi\) | ||||
−0.810881 | + | 0.585211i | \(0.801012\pi\) | |||||||
\(390\) | −13.0360 | −0.660105 | ||||||||
\(391\) | −12.8863 | −0.651688 | ||||||||
\(392\) | −21.1209 | −1.06677 | ||||||||
\(393\) | −1.64390 | −0.0829236 | ||||||||
\(394\) | 32.8554 | 1.65523 | ||||||||
\(395\) | −28.7724 | −1.44770 | ||||||||
\(396\) | −11.0824 | −0.556909 | ||||||||
\(397\) | 2.08595 | 0.104691 | 0.0523453 | − | 0.998629i | \(-0.483330\pi\) | ||||
0.0523453 | + | 0.998629i | \(0.483330\pi\) | |||||||
\(398\) | 22.1884 | 1.11220 | ||||||||
\(399\) | 40.1310 | 2.00906 | ||||||||
\(400\) | 8.98279 | 0.449140 | ||||||||
\(401\) | −4.66681 | −0.233049 | −0.116525 | − | 0.993188i | \(-0.537175\pi\) | ||||
−0.116525 | + | 0.993188i | \(0.537175\pi\) | |||||||
\(402\) | −32.4015 | −1.61604 | ||||||||
\(403\) | 4.19096 | 0.208767 | ||||||||
\(404\) | 38.8216 | 1.93145 | ||||||||
\(405\) | 26.5829 | 1.32091 | ||||||||
\(406\) | −45.3204 | −2.24921 | ||||||||
\(407\) | 1.55538 | 0.0770974 | ||||||||
\(408\) | 75.7007 | 3.74774 | ||||||||
\(409\) | 33.5809 | 1.66047 | 0.830234 | − | 0.557414i | \(-0.188207\pi\) | ||||
0.830234 | + | 0.557414i | \(0.188207\pi\) | |||||||
\(410\) | −32.3443 | −1.59737 | ||||||||
\(411\) | −5.69600 | −0.280963 | ||||||||
\(412\) | 109.133 | 5.37658 | ||||||||
\(413\) | 8.45249 | 0.415920 | ||||||||
\(414\) | 15.5336 | 0.763435 | ||||||||
\(415\) | 3.75979 | 0.184561 | ||||||||
\(416\) | −20.3788 | −0.999153 | ||||||||
\(417\) | −27.4151 | −1.34252 | ||||||||
\(418\) | 20.7084 | 1.01288 | ||||||||
\(419\) | 37.4391 | 1.82902 | 0.914509 | − | 0.404565i | \(-0.132577\pi\) | ||||
0.914509 | + | 0.404565i | \(0.132577\pi\) | |||||||
\(420\) | −84.6130 | −4.12869 | ||||||||
\(421\) | 16.7445 | 0.816075 | 0.408038 | − | 0.912965i | \(-0.366213\pi\) | ||||
0.408038 | + | 0.912965i | \(0.366213\pi\) | |||||||
\(422\) | −70.4471 | −3.42931 | ||||||||
\(423\) | −18.2828 | −0.888939 | ||||||||
\(424\) | −14.3912 | −0.698898 | ||||||||
\(425\) | 2.24287 | 0.108795 | ||||||||
\(426\) | −5.88407 | −0.285084 | ||||||||
\(427\) | 32.4910 | 1.57235 | ||||||||
\(428\) | −81.3694 | −3.93314 | ||||||||
\(429\) | 2.49389 | 0.120406 | ||||||||
\(430\) | −52.0132 | −2.50830 | ||||||||
\(431\) | −18.3487 | −0.883825 | −0.441912 | − | 0.897058i | \(-0.645700\pi\) | ||||
−0.441912 | + | 0.897058i | \(0.645700\pi\) | |||||||
\(432\) | 43.5981 | 2.09762 | ||||||||
\(433\) | 3.11096 | 0.149503 | 0.0747516 | − | 0.997202i | \(-0.476184\pi\) | ||||
0.0747516 | + | 0.997202i | \(0.476184\pi\) | |||||||
\(434\) | 37.1664 | 1.78405 | ||||||||
\(435\) | −27.8440 | −1.33502 | ||||||||
\(436\) | 86.6981 | 4.15209 | ||||||||
\(437\) | −21.2443 | −1.01625 | ||||||||
\(438\) | −45.6546 | −2.18146 | ||||||||
\(439\) | −9.54411 | −0.455515 | −0.227758 | − | 0.973718i | \(-0.573139\pi\) | ||||
−0.227758 | + | 0.973718i | \(0.573139\pi\) | |||||||
\(440\) | −27.6687 | −1.31906 | ||||||||
\(441\) | 3.66756 | 0.174646 | ||||||||
\(442\) | −9.50523 | −0.452117 | ||||||||
\(443\) | 31.0567 | 1.47555 | 0.737773 | − | 0.675048i | \(-0.235877\pi\) | ||||
0.737773 | + | 0.675048i | \(0.235877\pi\) | |||||||
\(444\) | 14.7917 | 0.701985 | ||||||||
\(445\) | −38.8248 | −1.84047 | ||||||||
\(446\) | −2.91495 | −0.138027 | ||||||||
\(447\) | −20.2203 | −0.956386 | ||||||||
\(448\) | −90.2139 | −4.26221 | ||||||||
\(449\) | −23.3840 | −1.10356 | −0.551781 | − | 0.833989i | \(-0.686051\pi\) | ||||
−0.551781 | + | 0.833989i | \(0.686051\pi\) | |||||||
\(450\) | −2.70363 | −0.127450 | ||||||||
\(451\) | 6.18772 | 0.291368 | ||||||||
\(452\) | −5.46003 | −0.256818 | ||||||||
\(453\) | 41.3104 | 1.94093 | ||||||||
\(454\) | 62.8626 | 2.95029 | ||||||||
\(455\) | 6.73262 | 0.315630 | ||||||||
\(456\) | 124.800 | 5.84429 | ||||||||
\(457\) | −3.43198 | −0.160541 | −0.0802705 | − | 0.996773i | \(-0.525578\pi\) | ||||
−0.0802705 | + | 0.996773i | \(0.525578\pi\) | |||||||
\(458\) | −7.20413 | −0.336627 | ||||||||
\(459\) | 10.8858 | 0.508105 | ||||||||
\(460\) | 44.7919 | 2.08843 | ||||||||
\(461\) | 5.27951 | 0.245891 | 0.122946 | − | 0.992413i | \(-0.460766\pi\) | ||||
0.122946 | + | 0.992413i | \(0.460766\pi\) | |||||||
\(462\) | 22.1164 | 1.02895 | ||||||||
\(463\) | −22.0355 | −1.02408 | −0.512039 | − | 0.858962i | \(-0.671110\pi\) | ||||
−0.512039 | + | 0.858962i | \(0.671110\pi\) | |||||||
\(464\) | −81.3125 | −3.77484 | ||||||||
\(465\) | 22.8344 | 1.05892 | ||||||||
\(466\) | −44.9419 | −2.08189 | ||||||||
\(467\) | 0.867223 | 0.0401303 | 0.0200651 | − | 0.999799i | \(-0.493613\pi\) | ||||
0.0200651 | + | 0.999799i | \(0.493613\pi\) | |||||||
\(468\) | 8.38613 | 0.387649 | ||||||||
\(469\) | 16.7342 | 0.772712 | ||||||||
\(470\) | −72.0302 | −3.32250 | ||||||||
\(471\) | 26.8368 | 1.23658 | ||||||||
\(472\) | 26.2857 | 1.20990 | ||||||||
\(473\) | 9.95052 | 0.457525 | ||||||||
\(474\) | 71.5213 | 3.28508 | ||||||||
\(475\) | 3.69758 | 0.169657 | ||||||||
\(476\) | −61.6956 | −2.82781 | ||||||||
\(477\) | 2.49897 | 0.114420 | ||||||||
\(478\) | 61.5096 | 2.81338 | ||||||||
\(479\) | 16.1246 | 0.736751 | 0.368376 | − | 0.929677i | \(-0.379914\pi\) | ||||
0.368376 | + | 0.929677i | \(0.379914\pi\) | |||||||
\(480\) | −111.034 | −5.06796 | ||||||||
\(481\) | −1.17697 | −0.0536654 | ||||||||
\(482\) | −13.8341 | −0.630125 | ||||||||
\(483\) | −22.6887 | −1.03237 | ||||||||
\(484\) | −51.7075 | −2.35034 | ||||||||
\(485\) | −19.1469 | −0.869415 | ||||||||
\(486\) | −42.0899 | −1.90924 | ||||||||
\(487\) | −0.454083 | −0.0205765 | −0.0102882 | − | 0.999947i | \(-0.503275\pi\) | ||||
−0.0102882 | + | 0.999947i | \(0.503275\pi\) | |||||||
\(488\) | 101.041 | 4.57391 | ||||||||
\(489\) | −11.0387 | −0.499186 | ||||||||
\(490\) | 14.4494 | 0.652757 | ||||||||
\(491\) | 25.4965 | 1.15064 | 0.575320 | − | 0.817928i | \(-0.304877\pi\) | ||||
0.575320 | + | 0.817928i | \(0.304877\pi\) | |||||||
\(492\) | 58.8454 | 2.65295 | ||||||||
\(493\) | −20.3025 | −0.914378 | ||||||||
\(494\) | −15.6703 | −0.705039 | ||||||||
\(495\) | 4.80457 | 0.215949 | ||||||||
\(496\) | 66.6829 | 2.99415 | ||||||||
\(497\) | 3.03890 | 0.136313 | ||||||||
\(498\) | −9.34594 | −0.418802 | ||||||||
\(499\) | 22.7943 | 1.02041 | 0.510206 | − | 0.860052i | \(-0.329569\pi\) | ||||
0.510206 | + | 0.860052i | \(0.329569\pi\) | |||||||
\(500\) | 56.8264 | 2.54135 | ||||||||
\(501\) | −15.2317 | −0.680500 | ||||||||
\(502\) | −1.91872 | −0.0856367 | ||||||||
\(503\) | 11.6202 | 0.518119 | 0.259060 | − | 0.965861i | \(-0.416587\pi\) | ||||
0.259060 | + | 0.965861i | \(0.416587\pi\) | |||||||
\(504\) | 47.1285 | 2.09927 | ||||||||
\(505\) | −16.8305 | −0.748946 | ||||||||
\(506\) | −11.7078 | −0.520477 | ||||||||
\(507\) | 26.1188 | 1.15998 | ||||||||
\(508\) | 104.467 | 4.63496 | ||||||||
\(509\) | −17.7606 | −0.787224 | −0.393612 | − | 0.919277i | \(-0.628775\pi\) | ||||
−0.393612 | + | 0.919277i | \(0.628775\pi\) | |||||||
\(510\) | −51.7890 | −2.29326 | ||||||||
\(511\) | 23.5789 | 1.04307 | ||||||||
\(512\) | −42.7801 | −1.89063 | ||||||||
\(513\) | 17.9463 | 0.792346 | ||||||||
\(514\) | 23.7345 | 1.04688 | ||||||||
\(515\) | −47.3127 | −2.08485 | ||||||||
\(516\) | 94.6297 | 4.16584 | ||||||||
\(517\) | 13.7799 | 0.606040 | ||||||||
\(518\) | −10.4377 | −0.458605 | ||||||||
\(519\) | −36.7188 | −1.61178 | ||||||||
\(520\) | 20.9372 | 0.918157 | ||||||||
\(521\) | 19.5249 | 0.855401 | 0.427700 | − | 0.903921i | \(-0.359324\pi\) | ||||
0.427700 | + | 0.903921i | \(0.359324\pi\) | |||||||
\(522\) | 24.4734 | 1.07117 | ||||||||
\(523\) | −39.6157 | −1.73228 | −0.866138 | − | 0.499806i | \(-0.833405\pi\) | ||||
−0.866138 | + | 0.499806i | \(0.833405\pi\) | |||||||
\(524\) | 4.16642 | 0.182011 | ||||||||
\(525\) | 3.94898 | 0.172347 | ||||||||
\(526\) | 47.8253 | 2.08528 | ||||||||
\(527\) | 16.6497 | 0.725272 | ||||||||
\(528\) | 39.6806 | 1.72688 | ||||||||
\(529\) | −10.9892 | −0.477791 | ||||||||
\(530\) | 9.84542 | 0.427658 | ||||||||
\(531\) | −4.56441 | −0.198078 | ||||||||
\(532\) | −101.711 | −4.40973 | ||||||||
\(533\) | −4.68230 | −0.202813 | ||||||||
\(534\) | 96.5093 | 4.17636 | ||||||||
\(535\) | 35.2764 | 1.52513 | ||||||||
\(536\) | 52.0401 | 2.24779 | ||||||||
\(537\) | −26.7723 | −1.15531 | ||||||||
\(538\) | 49.0440 | 2.11444 | ||||||||
\(539\) | −2.76428 | −0.119066 | ||||||||
\(540\) | −37.8382 | −1.62830 | ||||||||
\(541\) | −14.9299 | −0.641887 | −0.320943 | − | 0.947098i | \(-0.604000\pi\) | ||||
−0.320943 | + | 0.947098i | \(0.604000\pi\) | |||||||
\(542\) | 2.77945 | 0.119388 | ||||||||
\(543\) | −53.5620 | −2.29856 | ||||||||
\(544\) | −80.9601 | −3.47114 | ||||||||
\(545\) | −37.5865 | −1.61003 | ||||||||
\(546\) | −16.7357 | −0.716222 | ||||||||
\(547\) | 27.1105 | 1.15916 | 0.579581 | − | 0.814915i | \(-0.303216\pi\) | ||||
0.579581 | + | 0.814915i | \(0.303216\pi\) | |||||||
\(548\) | 14.4364 | 0.616691 | ||||||||
\(549\) | −17.5454 | −0.748819 | ||||||||
\(550\) | 2.03775 | 0.0868902 | ||||||||
\(551\) | −33.4706 | −1.42590 | ||||||||
\(552\) | −70.5576 | −3.00313 | ||||||||
\(553\) | −36.9381 | −1.57077 | ||||||||
\(554\) | −75.2428 | −3.19676 | ||||||||
\(555\) | −6.41271 | −0.272205 | ||||||||
\(556\) | 69.4828 | 2.94673 | ||||||||
\(557\) | −21.9844 | −0.931507 | −0.465753 | − | 0.884915i | \(-0.654217\pi\) | ||||
−0.465753 | + | 0.884915i | \(0.654217\pi\) | |||||||
\(558\) | −20.0702 | −0.849637 | ||||||||
\(559\) | −7.52965 | −0.318470 | ||||||||
\(560\) | 107.124 | 4.52680 | ||||||||
\(561\) | 9.90763 | 0.418300 | ||||||||
\(562\) | −39.4689 | −1.66489 | ||||||||
\(563\) | 13.6587 | 0.575646 | 0.287823 | − | 0.957684i | \(-0.407069\pi\) | ||||
0.287823 | + | 0.957684i | \(0.407069\pi\) | |||||||
\(564\) | 131.047 | 5.51809 | ||||||||
\(565\) | 2.36711 | 0.0995850 | ||||||||
\(566\) | −36.1484 | −1.51943 | ||||||||
\(567\) | 34.1272 | 1.43321 | ||||||||
\(568\) | 9.45041 | 0.396531 | ||||||||
\(569\) | 0.482899 | 0.0202442 | 0.0101221 | − | 0.999949i | \(-0.496778\pi\) | ||||
0.0101221 | + | 0.999949i | \(0.496778\pi\) | |||||||
\(570\) | −85.3792 | −3.57614 | ||||||||
\(571\) | −21.6107 | −0.904382 | −0.452191 | − | 0.891921i | \(-0.649357\pi\) | ||||
−0.452191 | + | 0.891921i | \(0.649357\pi\) | |||||||
\(572\) | −6.32071 | −0.264282 | ||||||||
\(573\) | −16.0380 | −0.669999 | ||||||||
\(574\) | −41.5238 | −1.73317 | ||||||||
\(575\) | −2.09048 | −0.0871792 | ||||||||
\(576\) | 48.7162 | 2.02984 | ||||||||
\(577\) | −22.6379 | −0.942429 | −0.471215 | − | 0.882019i | \(-0.656184\pi\) | ||||
−0.471215 | + | 0.882019i | \(0.656184\pi\) | |||||||
\(578\) | 8.67023 | 0.360634 | ||||||||
\(579\) | 35.2635 | 1.46550 | ||||||||
\(580\) | 70.5701 | 2.93026 | ||||||||
\(581\) | 4.82683 | 0.200251 | ||||||||
\(582\) | 47.5946 | 1.97286 | ||||||||
\(583\) | −1.88350 | −0.0780067 | ||||||||
\(584\) | 73.3259 | 3.03425 | ||||||||
\(585\) | −3.63567 | −0.150316 | ||||||||
\(586\) | −40.9387 | −1.69116 | ||||||||
\(587\) | −19.7275 | −0.814239 | −0.407120 | − | 0.913375i | \(-0.633467\pi\) | ||||
−0.407120 | + | 0.913375i | \(0.633467\pi\) | |||||||
\(588\) | −26.2884 | −1.08411 | ||||||||
\(589\) | 27.4486 | 1.13100 | ||||||||
\(590\) | −17.9828 | −0.740339 | ||||||||
\(591\) | 25.9145 | 1.06598 | ||||||||
\(592\) | −18.7269 | −0.769673 | ||||||||
\(593\) | −7.00780 | −0.287776 | −0.143888 | − | 0.989594i | \(-0.545960\pi\) | ||||
−0.143888 | + | 0.989594i | \(0.545960\pi\) | |||||||
\(594\) | 9.89028 | 0.405803 | ||||||||
\(595\) | 26.7471 | 1.09652 | ||||||||
\(596\) | 51.2478 | 2.09919 | ||||||||
\(597\) | 17.5010 | 0.716268 | ||||||||
\(598\) | 8.85944 | 0.362289 | ||||||||
\(599\) | 4.92010 | 0.201030 | 0.100515 | − | 0.994936i | \(-0.467951\pi\) | ||||
0.100515 | + | 0.994936i | \(0.467951\pi\) | |||||||
\(600\) | 12.2806 | 0.501353 | ||||||||
\(601\) | −25.5714 | −1.04308 | −0.521539 | − | 0.853227i | \(-0.674642\pi\) | ||||
−0.521539 | + | 0.853227i | \(0.674642\pi\) | |||||||
\(602\) | −66.7747 | −2.72153 | ||||||||
\(603\) | −9.03657 | −0.367998 | ||||||||
\(604\) | −104.700 | −4.26019 | ||||||||
\(605\) | 22.4169 | 0.911378 | ||||||||
\(606\) | 41.8366 | 1.69949 | ||||||||
\(607\) | 36.0934 | 1.46499 | 0.732494 | − | 0.680774i | \(-0.238356\pi\) | ||||
0.732494 | + | 0.680774i | \(0.238356\pi\) | |||||||
\(608\) | −133.470 | −5.41294 | ||||||||
\(609\) | −35.7463 | −1.44851 | ||||||||
\(610\) | −69.1251 | −2.79879 | ||||||||
\(611\) | −10.4274 | −0.421847 | ||||||||
\(612\) | 33.3161 | 1.34672 | ||||||||
\(613\) | −24.1949 | −0.977225 | −0.488612 | − | 0.872501i | \(-0.662497\pi\) | ||||
−0.488612 | + | 0.872501i | \(0.662497\pi\) | |||||||
\(614\) | −58.5094 | −2.36125 | ||||||||
\(615\) | −25.5114 | −1.02872 | ||||||||
\(616\) | −35.5212 | −1.43119 | ||||||||
\(617\) | −28.8112 | −1.15990 | −0.579948 | − | 0.814654i | \(-0.696927\pi\) | ||||
−0.579948 | + | 0.814654i | \(0.696927\pi\) | |||||||
\(618\) | 117.608 | 4.73089 | ||||||||
\(619\) | −16.4666 | −0.661850 | −0.330925 | − | 0.943657i | \(-0.607361\pi\) | ||||
−0.330925 | + | 0.943657i | \(0.607361\pi\) | |||||||
\(620\) | −57.8732 | −2.32424 | ||||||||
\(621\) | −10.1462 | −0.407153 | ||||||||
\(622\) | −56.8620 | −2.27996 | ||||||||
\(623\) | −49.8434 | −1.99693 | ||||||||
\(624\) | −30.0267 | −1.20203 | ||||||||
\(625\) | −27.6521 | −1.10609 | ||||||||
\(626\) | −6.62464 | −0.264774 | ||||||||
\(627\) | 16.3337 | 0.652304 | ||||||||
\(628\) | −68.0173 | −2.71419 | ||||||||
\(629\) | −4.67583 | −0.186438 | ||||||||
\(630\) | −32.2419 | −1.28455 | ||||||||
\(631\) | −20.6199 | −0.820865 | −0.410433 | − | 0.911891i | \(-0.634622\pi\) | ||||
−0.410433 | + | 0.911891i | \(0.634622\pi\) | |||||||
\(632\) | −114.870 | −4.56930 | ||||||||
\(633\) | −55.5648 | −2.20850 | ||||||||
\(634\) | 35.3895 | 1.40549 | ||||||||
\(635\) | −45.2899 | −1.79727 | ||||||||
\(636\) | −17.9122 | −0.710264 | ||||||||
\(637\) | 2.09176 | 0.0828784 | ||||||||
\(638\) | −18.4458 | −0.730277 | ||||||||
\(639\) | −1.64103 | −0.0649181 | ||||||||
\(640\) | 88.8506 | 3.51213 | ||||||||
\(641\) | −25.7511 | −1.01711 | −0.508553 | − | 0.861031i | \(-0.669819\pi\) | ||||
−0.508553 | + | 0.861031i | \(0.669819\pi\) | |||||||
\(642\) | −87.6887 | −3.46080 | ||||||||
\(643\) | 13.8453 | 0.546006 | 0.273003 | − | 0.962013i | \(-0.411983\pi\) | ||||
0.273003 | + | 0.962013i | \(0.411983\pi\) | |||||||
\(644\) | 57.5040 | 2.26597 | ||||||||
\(645\) | −41.0252 | −1.61536 | ||||||||
\(646\) | −62.2542 | −2.44936 | ||||||||
\(647\) | −28.6234 | −1.12530 | −0.562651 | − | 0.826695i | \(-0.690218\pi\) | ||||
−0.562651 | + | 0.826695i | \(0.690218\pi\) | |||||||
\(648\) | 106.129 | 4.16915 | ||||||||
\(649\) | 3.44024 | 0.135041 | ||||||||
\(650\) | −1.54199 | −0.0604818 | ||||||||
\(651\) | 29.3149 | 1.14894 | ||||||||
\(652\) | 27.9773 | 1.09567 | ||||||||
\(653\) | 20.6703 | 0.808892 | 0.404446 | − | 0.914562i | \(-0.367464\pi\) | ||||
0.404446 | + | 0.914562i | \(0.367464\pi\) | |||||||
\(654\) | 93.4312 | 3.65345 | ||||||||
\(655\) | −1.80628 | −0.0705773 | ||||||||
\(656\) | −74.5007 | −2.90876 | ||||||||
\(657\) | −12.7328 | −0.496753 | ||||||||
\(658\) | −92.4725 | −3.60495 | ||||||||
\(659\) | −50.1946 | −1.95530 | −0.977652 | − | 0.210230i | \(-0.932579\pi\) | ||||
−0.977652 | + | 0.210230i | \(0.932579\pi\) | |||||||
\(660\) | −34.4383 | −1.34051 | ||||||||
\(661\) | 41.6228 | 1.61894 | 0.809469 | − | 0.587163i | \(-0.199755\pi\) | ||||
0.809469 | + | 0.587163i | \(0.199755\pi\) | |||||||
\(662\) | 32.8245 | 1.27576 | ||||||||
\(663\) | −7.49720 | −0.291167 | ||||||||
\(664\) | 15.0105 | 0.582522 | ||||||||
\(665\) | 44.0952 | 1.70994 | ||||||||
\(666\) | 5.63642 | 0.218407 | ||||||||
\(667\) | 18.9231 | 0.732707 | ||||||||
\(668\) | 38.6043 | 1.49364 | ||||||||
\(669\) | −2.29915 | −0.0888903 | ||||||||
\(670\) | −35.6021 | −1.37543 | ||||||||
\(671\) | 13.2241 | 0.510512 | ||||||||
\(672\) | −142.545 | −5.49880 | ||||||||
\(673\) | 31.1387 | 1.20031 | 0.600155 | − | 0.799884i | \(-0.295106\pi\) | ||||
0.600155 | + | 0.799884i | \(0.295106\pi\) | |||||||
\(674\) | 41.0393 | 1.58077 | ||||||||
\(675\) | 1.76595 | 0.0679715 | ||||||||
\(676\) | −66.1975 | −2.54606 | ||||||||
\(677\) | −3.84088 | −0.147617 | −0.0738085 | − | 0.997272i | \(-0.523515\pi\) | ||||
−0.0738085 | + | 0.997272i | \(0.523515\pi\) | |||||||
\(678\) | −5.88407 | −0.225976 | ||||||||
\(679\) | −24.5808 | −0.943325 | ||||||||
\(680\) | 83.1785 | 3.18975 | ||||||||
\(681\) | 49.5825 | 1.90001 | ||||||||
\(682\) | 15.1271 | 0.579246 | ||||||||
\(683\) | 40.8975 | 1.56490 | 0.782450 | − | 0.622714i | \(-0.213970\pi\) | ||||
0.782450 | + | 0.622714i | \(0.213970\pi\) | |||||||
\(684\) | 54.9247 | 2.10010 | ||||||||
\(685\) | −6.25865 | −0.239131 | ||||||||
\(686\) | −39.5510 | −1.51006 | ||||||||
\(687\) | −5.68222 | −0.216790 | ||||||||
\(688\) | −119.805 | −4.56753 | ||||||||
\(689\) | 1.42526 | 0.0542983 | ||||||||
\(690\) | 48.2705 | 1.83763 | ||||||||
\(691\) | 18.0490 | 0.686615 | 0.343307 | − | 0.939223i | \(-0.388453\pi\) | ||||
0.343307 | + | 0.939223i | \(0.388453\pi\) | |||||||
\(692\) | 93.0629 | 3.53772 | ||||||||
\(693\) | 6.16813 | 0.234308 | ||||||||
\(694\) | 68.7922 | 2.61132 | ||||||||
\(695\) | −30.1231 | −1.14264 | ||||||||
\(696\) | −111.164 | −4.21367 | ||||||||
\(697\) | −18.6017 | −0.704588 | ||||||||
\(698\) | 67.3961 | 2.55098 | ||||||||
\(699\) | −35.4477 | −1.34076 | ||||||||
\(700\) | −10.0086 | −0.378289 | ||||||||
\(701\) | 3.32529 | 0.125595 | 0.0627973 | − | 0.998026i | \(-0.479998\pi\) | ||||
0.0627973 | + | 0.998026i | \(0.479998\pi\) | |||||||
\(702\) | −7.48407 | −0.282468 | ||||||||
\(703\) | −7.70856 | −0.290734 | ||||||||
\(704\) | −36.7179 | −1.38386 | ||||||||
\(705\) | −56.8134 | −2.13972 | ||||||||
\(706\) | −71.5546 | −2.69299 | ||||||||
\(707\) | −21.6070 | −0.812616 | ||||||||
\(708\) | 32.7168 | 1.22957 | ||||||||
\(709\) | −40.5549 | −1.52307 | −0.761535 | − | 0.648123i | \(-0.775554\pi\) | ||||
−0.761535 | + | 0.648123i | \(0.775554\pi\) | |||||||
\(710\) | −6.46530 | −0.242638 | ||||||||
\(711\) | 19.9468 | 0.748064 | ||||||||
\(712\) | −155.004 | −5.80901 | ||||||||
\(713\) | −15.5185 | −0.581173 | ||||||||
\(714\) | −66.4869 | −2.48821 | ||||||||
\(715\) | 2.74024 | 0.102479 | ||||||||
\(716\) | 67.8537 | 2.53581 | ||||||||
\(717\) | 48.5154 | 1.81184 | ||||||||
\(718\) | −48.8650 | −1.82363 | ||||||||
\(719\) | 40.5804 | 1.51339 | 0.756696 | − | 0.653767i | \(-0.226812\pi\) | ||||
0.756696 | + | 0.653767i | \(0.226812\pi\) | |||||||
\(720\) | −57.8475 | −2.15585 | ||||||||
\(721\) | −60.7402 | −2.26208 | ||||||||
\(722\) | −50.7372 | −1.88824 | ||||||||
\(723\) | −10.9116 | −0.405805 | ||||||||
\(724\) | 135.752 | 5.04517 | ||||||||
\(725\) | −3.29358 | −0.122320 | ||||||||
\(726\) | −55.7231 | −2.06808 | ||||||||
\(727\) | 25.0655 | 0.929629 | 0.464814 | − | 0.885408i | \(-0.346121\pi\) | ||||
0.464814 | + | 0.885408i | \(0.346121\pi\) | |||||||
\(728\) | 26.8793 | 0.996211 | ||||||||
\(729\) | 0.492142 | 0.0182275 | ||||||||
\(730\) | −50.1644 | −1.85667 | ||||||||
\(731\) | −29.9135 | −1.10639 | ||||||||
\(732\) | 125.762 | 4.64830 | ||||||||
\(733\) | −2.20054 | −0.0812789 | −0.0406395 | − | 0.999174i | \(-0.512940\pi\) | ||||
−0.0406395 | + | 0.999174i | \(0.512940\pi\) | |||||||
\(734\) | −55.4787 | −2.04775 | ||||||||
\(735\) | 11.3969 | 0.420381 | ||||||||
\(736\) | 75.4597 | 2.78148 | ||||||||
\(737\) | 6.81096 | 0.250885 | ||||||||
\(738\) | 22.4231 | 0.825407 | ||||||||
\(739\) | −2.52192 | −0.0927702 | −0.0463851 | − | 0.998924i | \(-0.514770\pi\) | ||||
−0.0463851 | + | 0.998924i | \(0.514770\pi\) | |||||||
\(740\) | 16.2529 | 0.597467 | ||||||||
\(741\) | −12.3599 | −0.454051 | ||||||||
\(742\) | 12.6396 | 0.464014 | ||||||||
\(743\) | −8.75925 | −0.321346 | −0.160673 | − | 0.987008i | \(-0.551366\pi\) | ||||
−0.160673 | + | 0.987008i | \(0.551366\pi\) | |||||||
\(744\) | 91.1637 | 3.34222 | ||||||||
\(745\) | −22.2176 | −0.813992 | ||||||||
\(746\) | 62.5994 | 2.29193 | ||||||||
\(747\) | −2.60652 | −0.0953677 | ||||||||
\(748\) | −25.1107 | −0.918137 | ||||||||
\(749\) | 45.2879 | 1.65478 | ||||||||
\(750\) | 61.2396 | 2.23615 | ||||||||
\(751\) | 2.34396 | 0.0855324 | 0.0427662 | − | 0.999085i | \(-0.486383\pi\) | ||||
0.0427662 | + | 0.999085i | \(0.486383\pi\) | |||||||
\(752\) | −165.911 | −6.05017 | ||||||||
\(753\) | −1.51338 | −0.0551507 | ||||||||
\(754\) | 13.9581 | 0.508325 | ||||||||
\(755\) | 45.3910 | 1.65195 | ||||||||
\(756\) | −48.5768 | −1.76672 | ||||||||
\(757\) | −28.3654 | −1.03096 | −0.515478 | − | 0.856903i | \(-0.672386\pi\) | ||||
−0.515478 | + | 0.856903i | \(0.672386\pi\) | |||||||
\(758\) | −11.1711 | −0.405754 | ||||||||
\(759\) | −9.23450 | −0.335191 | ||||||||
\(760\) | 137.128 | 4.97414 | ||||||||
\(761\) | −36.4088 | −1.31982 | −0.659909 | − | 0.751346i | \(-0.729405\pi\) | ||||
−0.659909 | + | 0.751346i | \(0.729405\pi\) | |||||||
\(762\) | 112.580 | 4.07834 | ||||||||
\(763\) | −48.2537 | −1.74690 | ||||||||
\(764\) | 40.6481 | 1.47060 | ||||||||
\(765\) | −14.4436 | −0.522211 | ||||||||
\(766\) | −26.7665 | −0.967113 | ||||||||
\(767\) | −2.60326 | −0.0939984 | ||||||||
\(768\) | −92.9545 | −3.35421 | ||||||||
\(769\) | 20.1093 | 0.725159 | 0.362579 | − | 0.931953i | \(-0.381896\pi\) | ||||
0.362579 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(770\) | 24.3011 | 0.875750 | ||||||||
\(771\) | 18.7204 | 0.674200 | ||||||||
\(772\) | −89.3745 | −3.21666 | ||||||||
\(773\) | −16.5548 | −0.595435 | −0.297717 | − | 0.954654i | \(-0.596225\pi\) | ||||
−0.297717 | + | 0.954654i | \(0.596225\pi\) | |||||||
\(774\) | 36.0588 | 1.29611 | ||||||||
\(775\) | 2.70100 | 0.0970229 | ||||||||
\(776\) | −76.4418 | −2.74410 | ||||||||
\(777\) | −8.23266 | −0.295345 | ||||||||
\(778\) | 87.3639 | 3.13215 | ||||||||
\(779\) | −30.6666 | −1.09875 | ||||||||
\(780\) | 26.0598 | 0.933089 | ||||||||
\(781\) | 1.23686 | 0.0442583 | ||||||||
\(782\) | 35.1964 | 1.25862 | ||||||||
\(783\) | −15.9854 | −0.571273 | ||||||||
\(784\) | 33.2822 | 1.18865 | ||||||||
\(785\) | 29.4878 | 1.05246 | ||||||||
\(786\) | 4.48999 | 0.160152 | ||||||||
\(787\) | −13.9026 | −0.495574 | −0.247787 | − | 0.968815i | \(-0.579703\pi\) | ||||
−0.247787 | + | 0.968815i | \(0.579703\pi\) | |||||||
\(788\) | −65.6798 | −2.33974 | ||||||||
\(789\) | 37.7220 | 1.34294 | ||||||||
\(790\) | 78.5862 | 2.79597 | ||||||||
\(791\) | 3.03890 | 0.108051 | ||||||||
\(792\) | 19.1817 | 0.681593 | ||||||||
\(793\) | −10.0068 | −0.355353 | ||||||||
\(794\) | −5.69736 | −0.202192 | ||||||||
\(795\) | 7.76553 | 0.275415 | ||||||||
\(796\) | −44.3558 | −1.57215 | ||||||||
\(797\) | −21.7510 | −0.770460 | −0.385230 | − | 0.922820i | \(-0.625878\pi\) | ||||
−0.385230 | + | 0.922820i | \(0.625878\pi\) | |||||||
\(798\) | −109.610 | −3.88015 | ||||||||
\(799\) | −41.4255 | −1.46553 | ||||||||
\(800\) | −13.1338 | −0.464349 | ||||||||
\(801\) | 26.9158 | 0.951024 | ||||||||
\(802\) | 12.7465 | 0.450094 | ||||||||
\(803\) | 9.59682 | 0.338664 | ||||||||
\(804\) | 64.7724 | 2.28435 | ||||||||
\(805\) | −24.9299 | −0.878663 | ||||||||
\(806\) | −11.4468 | −0.403197 | ||||||||
\(807\) | 38.6832 | 1.36171 | ||||||||
\(808\) | −67.1938 | −2.36387 | ||||||||
\(809\) | 22.9969 | 0.808529 | 0.404264 | − | 0.914642i | \(-0.367528\pi\) | ||||
0.404264 | + | 0.914642i | \(0.367528\pi\) | |||||||
\(810\) | −72.6060 | −2.55111 | ||||||||
\(811\) | −1.16332 | −0.0408496 | −0.0204248 | − | 0.999791i | \(-0.506502\pi\) | ||||
−0.0204248 | + | 0.999791i | \(0.506502\pi\) | |||||||
\(812\) | 90.5981 | 3.17937 | ||||||||
\(813\) | 2.19228 | 0.0768866 | ||||||||
\(814\) | −4.24823 | −0.148900 | ||||||||
\(815\) | −12.1291 | −0.424863 | ||||||||
\(816\) | −119.289 | −4.17594 | ||||||||
\(817\) | −49.3153 | −1.72532 | ||||||||
\(818\) | −91.7197 | −3.20691 | ||||||||
\(819\) | −4.66748 | −0.163095 | ||||||||
\(820\) | 64.6581 | 2.25796 | ||||||||
\(821\) | 48.8168 | 1.70372 | 0.851859 | − | 0.523771i | \(-0.175475\pi\) | ||||
0.851859 | + | 0.523771i | \(0.175475\pi\) | |||||||
\(822\) | 15.5575 | 0.542631 | ||||||||
\(823\) | 13.0705 | 0.455609 | 0.227805 | − | 0.973707i | \(-0.426845\pi\) | ||||
0.227805 | + | 0.973707i | \(0.426845\pi\) | |||||||
\(824\) | −188.891 | −6.58032 | ||||||||
\(825\) | 1.60727 | 0.0559579 | ||||||||
\(826\) | −23.0863 | −0.803277 | ||||||||
\(827\) | 46.6586 | 1.62248 | 0.811240 | − | 0.584713i | \(-0.198793\pi\) | ||||
0.811240 | + | 0.584713i | \(0.198793\pi\) | |||||||
\(828\) | −31.0526 | −1.07915 | ||||||||
\(829\) | 29.9062 | 1.03869 | 0.519343 | − | 0.854566i | \(-0.326177\pi\) | ||||
0.519343 | + | 0.854566i | \(0.326177\pi\) | |||||||
\(830\) | −10.2691 | −0.356447 | ||||||||
\(831\) | −59.3474 | −2.05874 | ||||||||
\(832\) | 27.7848 | 0.963264 | ||||||||
\(833\) | 8.31005 | 0.287926 | ||||||||
\(834\) | 74.8789 | 2.59285 | ||||||||
\(835\) | −16.7362 | −0.579182 | ||||||||
\(836\) | −41.3973 | −1.43176 | ||||||||
\(837\) | 13.1094 | 0.453126 | ||||||||
\(838\) | −102.258 | −3.53243 | ||||||||
\(839\) | 18.2890 | 0.631405 | 0.315702 | − | 0.948858i | \(-0.397760\pi\) | ||||
0.315702 | + | 0.948858i | \(0.397760\pi\) | |||||||
\(840\) | 146.451 | 5.05304 | ||||||||
\(841\) | 0.813577 | 0.0280544 | ||||||||
\(842\) | −45.7343 | −1.57611 | ||||||||
\(843\) | −31.1309 | −1.07220 | ||||||||
\(844\) | 140.828 | 4.84749 | ||||||||
\(845\) | 28.6988 | 0.987270 | ||||||||
\(846\) | 49.9358 | 1.71683 | ||||||||
\(847\) | 28.7789 | 0.988856 | ||||||||
\(848\) | 22.6775 | 0.778750 | ||||||||
\(849\) | −28.5119 | −0.978526 | ||||||||
\(850\) | −6.12595 | −0.210118 | ||||||||
\(851\) | 4.35815 | 0.149396 | ||||||||
\(852\) | 11.7626 | 0.402979 | ||||||||
\(853\) | 19.7229 | 0.675298 | 0.337649 | − | 0.941272i | \(-0.390368\pi\) | ||||
0.337649 | + | 0.941272i | \(0.390368\pi\) | |||||||
\(854\) | −88.7430 | −3.03672 | ||||||||
\(855\) | −23.8117 | −0.814343 | ||||||||
\(856\) | 140.837 | 4.81371 | ||||||||
\(857\) | 10.0471 | 0.343203 | 0.171602 | − | 0.985166i | \(-0.445106\pi\) | ||||
0.171602 | + | 0.985166i | \(0.445106\pi\) | |||||||
\(858\) | −6.81158 | −0.232544 | ||||||||
\(859\) | 20.1108 | 0.686173 | 0.343086 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343086 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(860\) | 103.977 | 3.54560 | ||||||||
\(861\) | −32.7517 | −1.11617 | ||||||||
\(862\) | 50.1159 | 1.70695 | ||||||||
\(863\) | −6.02748 | −0.205178 | −0.102589 | − | 0.994724i | \(-0.532713\pi\) | ||||
−0.102589 | + | 0.994724i | \(0.532713\pi\) | |||||||
\(864\) | −63.7450 | −2.16865 | ||||||||
\(865\) | −40.3459 | −1.37180 | ||||||||
\(866\) | −8.49699 | −0.288739 | ||||||||
\(867\) | 6.83860 | 0.232251 | ||||||||
\(868\) | −74.2978 | −2.52183 | ||||||||
\(869\) | −15.0341 | −0.509998 | ||||||||
\(870\) | 76.0506 | 2.57836 | ||||||||
\(871\) | −5.15392 | −0.174634 | ||||||||
\(872\) | −150.060 | −5.08167 | ||||||||
\(873\) | 13.2738 | 0.449251 | ||||||||
\(874\) | 58.0247 | 1.96271 | ||||||||
\(875\) | −31.6280 | −1.06922 | ||||||||
\(876\) | 91.2661 | 3.08359 | ||||||||
\(877\) | 34.2354 | 1.15605 | 0.578023 | − | 0.816020i | \(-0.303824\pi\) | ||||
0.578023 | + | 0.816020i | \(0.303824\pi\) | |||||||
\(878\) | 26.0679 | 0.879748 | ||||||||
\(879\) | −32.2902 | −1.08912 | ||||||||
\(880\) | 43.6002 | 1.46976 | ||||||||
\(881\) | 15.1195 | 0.509389 | 0.254695 | − | 0.967022i | \(-0.418025\pi\) | ||||
0.254695 | + | 0.967022i | \(0.418025\pi\) | |||||||
\(882\) | −10.0172 | −0.337298 | ||||||||
\(883\) | 31.2169 | 1.05053 | 0.525265 | − | 0.850938i | \(-0.323966\pi\) | ||||
0.525265 | + | 0.850938i | \(0.323966\pi\) | |||||||
\(884\) | 19.0015 | 0.639089 | ||||||||
\(885\) | −14.1838 | −0.476784 | ||||||||
\(886\) | −84.8253 | −2.84976 | ||||||||
\(887\) | 4.70125 | 0.157852 | 0.0789262 | − | 0.996880i | \(-0.474851\pi\) | ||||
0.0789262 | + | 0.996880i | \(0.474851\pi\) | |||||||
\(888\) | −25.6020 | −0.859148 | ||||||||
\(889\) | −58.1433 | −1.95006 | ||||||||
\(890\) | 106.042 | 3.55455 | ||||||||
\(891\) | 13.8901 | 0.465335 | ||||||||
\(892\) | 5.82714 | 0.195107 | ||||||||
\(893\) | −68.2939 | −2.28537 | ||||||||
\(894\) | 55.2278 | 1.84709 | ||||||||
\(895\) | −29.4169 | −0.983297 | ||||||||
\(896\) | 114.067 | 3.81070 | ||||||||
\(897\) | 6.98784 | 0.233317 | ||||||||
\(898\) | 63.8690 | 2.13134 | ||||||||
\(899\) | −24.4496 | −0.815439 | ||||||||
\(900\) | 5.40471 | 0.180157 | ||||||||
\(901\) | 5.66223 | 0.188636 | ||||||||
\(902\) | −16.9005 | −0.562727 | ||||||||
\(903\) | −52.6682 | −1.75269 | ||||||||
\(904\) | 9.45041 | 0.314316 | ||||||||
\(905\) | −58.8528 | −1.95633 | ||||||||
\(906\) | −112.831 | −3.74857 | ||||||||
\(907\) | −22.0554 | −0.732339 | −0.366170 | − | 0.930548i | \(-0.619331\pi\) | ||||
−0.366170 | + | 0.930548i | \(0.619331\pi\) | |||||||
\(908\) | −125.666 | −4.17036 | ||||||||
\(909\) | 11.6679 | 0.387001 | ||||||||
\(910\) | −18.3889 | −0.609585 | ||||||||
\(911\) | 35.0388 | 1.16089 | 0.580444 | − | 0.814300i | \(-0.302879\pi\) | ||||
0.580444 | + | 0.814300i | \(0.302879\pi\) | |||||||
\(912\) | −196.659 | −6.51203 | ||||||||
\(913\) | 1.96456 | 0.0650175 | ||||||||
\(914\) | 9.37378 | 0.310057 | ||||||||
\(915\) | −54.5221 | −1.80244 | ||||||||
\(916\) | 14.4015 | 0.475837 | ||||||||
\(917\) | −2.31891 | −0.0765772 | ||||||||
\(918\) | −29.7324 | −0.981316 | ||||||||
\(919\) | 29.6631 | 0.978495 | 0.489247 | − | 0.872145i | \(-0.337272\pi\) | ||||
0.489247 | + | 0.872145i | \(0.337272\pi\) | |||||||
\(920\) | −77.5273 | −2.55600 | ||||||||
\(921\) | −46.1490 | −1.52066 | ||||||||
\(922\) | −14.4200 | −0.474896 | ||||||||
\(923\) | −0.935944 | −0.0308070 | ||||||||
\(924\) | −44.2119 | −1.45447 | ||||||||
\(925\) | −0.758539 | −0.0249406 | ||||||||
\(926\) | 60.1857 | 1.97783 | ||||||||
\(927\) | 32.8002 | 1.07730 | ||||||||
\(928\) | 118.887 | 3.90267 | ||||||||
\(929\) | 3.28682 | 0.107837 | 0.0539185 | − | 0.998545i | \(-0.482829\pi\) | ||||
0.0539185 | + | 0.998545i | \(0.482829\pi\) | |||||||
\(930\) | −62.3677 | −2.04512 | ||||||||
\(931\) | 13.6999 | 0.448996 | ||||||||
\(932\) | 89.8414 | 2.94285 | ||||||||
\(933\) | −44.8496 | −1.46831 | ||||||||
\(934\) | −2.36865 | −0.0775046 | ||||||||
\(935\) | 10.8863 | 0.356020 | ||||||||
\(936\) | −14.5150 | −0.474437 | ||||||||
\(937\) | −0.832310 | −0.0271904 | −0.0135952 | − | 0.999908i | \(-0.504328\pi\) | ||||
−0.0135952 | + | 0.999908i | \(0.504328\pi\) | |||||||
\(938\) | −45.7061 | −1.49236 | ||||||||
\(939\) | −5.22515 | −0.170516 | ||||||||
\(940\) | 143.992 | 4.69651 | ||||||||
\(941\) | 4.22292 | 0.137663 | 0.0688316 | − | 0.997628i | \(-0.478073\pi\) | ||||
0.0688316 | + | 0.997628i | \(0.478073\pi\) | |||||||
\(942\) | −73.2996 | −2.38823 | ||||||||
\(943\) | 17.3379 | 0.564599 | ||||||||
\(944\) | −41.4208 | −1.34813 | ||||||||
\(945\) | 21.0597 | 0.685072 | ||||||||
\(946\) | −27.1779 | −0.883630 | ||||||||
\(947\) | −0.415723 | −0.0135092 | −0.00675459 | − | 0.999977i | \(-0.502150\pi\) | ||||
−0.00675459 | + | 0.999977i | \(0.502150\pi\) | |||||||
\(948\) | −142.975 | −4.64361 | ||||||||
\(949\) | −7.26201 | −0.235735 | ||||||||
\(950\) | −10.0992 | −0.327662 | ||||||||
\(951\) | 27.9133 | 0.905149 | ||||||||
\(952\) | 106.785 | 3.46092 | ||||||||
\(953\) | −20.1205 | −0.651768 | −0.325884 | − | 0.945410i | \(-0.605662\pi\) | ||||
−0.325884 | + | 0.945410i | \(0.605662\pi\) | |||||||
\(954\) | −6.82547 | −0.220983 | ||||||||
\(955\) | −17.6223 | −0.570244 | ||||||||
\(956\) | −122.961 | −3.97685 | ||||||||
\(957\) | −14.5491 | −0.470304 | ||||||||
\(958\) | −44.0412 | −1.42291 | ||||||||
\(959\) | −8.03488 | −0.259460 | ||||||||
\(960\) | 151.385 | 4.88592 | ||||||||
\(961\) | −10.9494 | −0.353205 | ||||||||
\(962\) | 3.21467 | 0.103645 | ||||||||
\(963\) | −24.4558 | −0.788078 | ||||||||
\(964\) | 27.6551 | 0.890711 | ||||||||
\(965\) | 38.7469 | 1.24731 | ||||||||
\(966\) | 61.9698 | 1.99385 | ||||||||
\(967\) | −14.3615 | −0.461835 | −0.230918 | − | 0.972973i | \(-0.574173\pi\) | ||||
−0.230918 | + | 0.972973i | \(0.574173\pi\) | |||||||
\(968\) | 89.4971 | 2.87655 | ||||||||
\(969\) | −49.1027 | −1.57741 | ||||||||
\(970\) | 52.2960 | 1.67912 | ||||||||
\(971\) | −6.37382 | −0.204545 | −0.102273 | − | 0.994756i | \(-0.532611\pi\) | ||||
−0.102273 | + | 0.994756i | \(0.532611\pi\) | |||||||
\(972\) | 84.1400 | 2.69879 | ||||||||
\(973\) | −38.6722 | −1.23977 | ||||||||
\(974\) | 1.24024 | 0.0397398 | ||||||||
\(975\) | −1.21624 | −0.0389507 | ||||||||
\(976\) | −159.220 | −5.09651 | ||||||||
\(977\) | 1.79537 | 0.0574389 | 0.0287194 | − | 0.999588i | \(-0.490857\pi\) | ||||
0.0287194 | + | 0.999588i | \(0.490857\pi\) | |||||||
\(978\) | 30.1500 | 0.964091 | ||||||||
\(979\) | −20.2867 | −0.648367 | ||||||||
\(980\) | −28.8852 | −0.922703 | ||||||||
\(981\) | 26.0574 | 0.831947 | ||||||||
\(982\) | −69.6387 | −2.22226 | ||||||||
\(983\) | −27.1107 | −0.864697 | −0.432348 | − | 0.901707i | \(-0.642315\pi\) | ||||
−0.432348 | + | 0.901707i | \(0.642315\pi\) | |||||||
\(984\) | −101.852 | −3.24691 | ||||||||
\(985\) | 28.4744 | 0.907269 | ||||||||
\(986\) | 55.4523 | 1.76596 | ||||||||
\(987\) | −72.9373 | −2.32162 | ||||||||
\(988\) | 31.3258 | 0.996605 | ||||||||
\(989\) | 27.8812 | 0.886570 | ||||||||
\(990\) | −13.1228 | −0.417069 | ||||||||
\(991\) | 18.1880 | 0.577762 | 0.288881 | − | 0.957365i | \(-0.406717\pi\) | ||||
0.288881 | + | 0.957365i | \(0.406717\pi\) | |||||||
\(992\) | −97.4974 | −3.09555 | ||||||||
\(993\) | 25.8902 | 0.821600 | ||||||||
\(994\) | −8.30017 | −0.263265 | ||||||||
\(995\) | 19.2297 | 0.609624 | ||||||||
\(996\) | 18.6831 | 0.591995 | ||||||||
\(997\) | 49.2180 | 1.55875 | 0.779375 | − | 0.626558i | \(-0.215537\pi\) | ||||
0.779375 | + | 0.626558i | \(0.215537\pi\) | |||||||
\(998\) | −62.2582 | −1.97075 | ||||||||
\(999\) | −3.68158 | −0.116480 |
(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 | 8023.2.a.c.1.6 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.6 | ✓ | 158 | 1.1 | even | 1 | trivial |