Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25270 | −1.59290 | −0.796451 | − | 0.604704i | \(-0.793292\pi\) | ||||
−0.796451 | + | 0.604704i | \(0.793292\pi\) | |||||||
\(3\) | 2.53862 | 1.46568 | 0.732838 | − | 0.680404i | \(-0.238196\pi\) | ||||
0.732838 | + | 0.680404i | \(0.238196\pi\) | |||||||
\(4\) | 3.07467 | 1.53733 | ||||||||
\(5\) | −2.69802 | −1.20659 | −0.603296 | − | 0.797517i | \(-0.706146\pi\) | ||||
−0.603296 | + | 0.797517i | \(0.706146\pi\) | |||||||
\(6\) | −5.71876 | −2.33468 | ||||||||
\(7\) | −2.07248 | −0.783323 | −0.391661 | − | 0.920109i | \(-0.628099\pi\) | ||||
−0.391661 | + | 0.920109i | \(0.628099\pi\) | |||||||
\(8\) | −2.42091 | −0.855920 | ||||||||
\(9\) | 3.44461 | 1.14820 | ||||||||
\(10\) | 6.07784 | 1.92198 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 7.80543 | 2.25323 | ||||||||
\(13\) | 1.22220 | 0.338979 | 0.169489 | − | 0.985532i | \(-0.445788\pi\) | ||||
0.169489 | + | 0.985532i | \(0.445788\pi\) | |||||||
\(14\) | 4.66867 | 1.24776 | ||||||||
\(15\) | −6.84926 | −1.76847 | ||||||||
\(16\) | −0.695751 | −0.173938 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −7.75968 | −1.82897 | ||||||||
\(19\) | 2.33904 | 0.536612 | 0.268306 | − | 0.963334i | \(-0.413536\pi\) | ||||
0.268306 | + | 0.963334i | \(0.413536\pi\) | |||||||
\(20\) | −8.29553 | −1.85494 | ||||||||
\(21\) | −5.26124 | −1.14810 | ||||||||
\(22\) | −2.25270 | −0.480278 | ||||||||
\(23\) | 3.99896 | 0.833840 | 0.416920 | − | 0.908943i | \(-0.363109\pi\) | ||||
0.416920 | + | 0.908943i | \(0.363109\pi\) | |||||||
\(24\) | −6.14578 | −1.25450 | ||||||||
\(25\) | 2.27933 | 0.455865 | ||||||||
\(26\) | −2.75326 | −0.539960 | ||||||||
\(27\) | 1.12870 | 0.217218 | ||||||||
\(28\) | −6.37218 | −1.20423 | ||||||||
\(29\) | −3.37911 | −0.627485 | −0.313743 | − | 0.949508i | \(-0.601583\pi\) | ||||
−0.313743 | + | 0.949508i | \(0.601583\pi\) | |||||||
\(30\) | 15.4294 | 2.81700 | ||||||||
\(31\) | 5.27548 | 0.947504 | 0.473752 | − | 0.880658i | \(-0.342899\pi\) | ||||
0.473752 | + | 0.880658i | \(0.342899\pi\) | |||||||
\(32\) | 6.40914 | 1.13299 | ||||||||
\(33\) | 2.53862 | 0.441918 | ||||||||
\(34\) | −2.25270 | −0.386335 | ||||||||
\(35\) | 5.59159 | 0.945151 | ||||||||
\(36\) | 10.5910 | 1.76517 | ||||||||
\(37\) | −3.32932 | −0.547337 | −0.273669 | − | 0.961824i | \(-0.588237\pi\) | ||||
−0.273669 | + | 0.961824i | \(0.588237\pi\) | |||||||
\(38\) | −5.26916 | −0.854770 | ||||||||
\(39\) | 3.10272 | 0.496833 | ||||||||
\(40\) | 6.53167 | 1.03275 | ||||||||
\(41\) | −9.84032 | −1.53680 | −0.768400 | − | 0.639970i | \(-0.778947\pi\) | ||||
−0.768400 | + | 0.639970i | \(0.778947\pi\) | |||||||
\(42\) | 11.8520 | 1.82880 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 3.07467 | 0.463524 | ||||||||
\(45\) | −9.29364 | −1.38541 | ||||||||
\(46\) | −9.00846 | −1.32823 | ||||||||
\(47\) | 9.90673 | 1.44504 | 0.722522 | − | 0.691348i | \(-0.242983\pi\) | ||||
0.722522 | + | 0.691348i | \(0.242983\pi\) | |||||||
\(48\) | −1.76625 | −0.254936 | ||||||||
\(49\) | −2.70484 | −0.386406 | ||||||||
\(50\) | −5.13465 | −0.726149 | ||||||||
\(51\) | 2.53862 | 0.355478 | ||||||||
\(52\) | 3.75788 | 0.521124 | ||||||||
\(53\) | 1.52330 | 0.209242 | 0.104621 | − | 0.994512i | \(-0.466637\pi\) | ||||
0.104621 | + | 0.994512i | \(0.466637\pi\) | |||||||
\(54\) | −2.54262 | −0.346007 | ||||||||
\(55\) | −2.69802 | −0.363801 | ||||||||
\(56\) | 5.01728 | 0.670462 | ||||||||
\(57\) | 5.93794 | 0.786499 | ||||||||
\(58\) | 7.61213 | 0.999522 | ||||||||
\(59\) | 5.02001 | 0.653550 | 0.326775 | − | 0.945102i | \(-0.394038\pi\) | ||||
0.326775 | + | 0.945102i | \(0.394038\pi\) | |||||||
\(60\) | −21.0592 | −2.71873 | ||||||||
\(61\) | −5.30301 | −0.678981 | −0.339490 | − | 0.940610i | \(-0.610255\pi\) | ||||
−0.339490 | + | 0.940610i | \(0.610255\pi\) | |||||||
\(62\) | −11.8841 | −1.50928 | ||||||||
\(63\) | −7.13888 | −0.899414 | ||||||||
\(64\) | −13.0464 | −1.63080 | ||||||||
\(65\) | −3.29754 | −0.409009 | ||||||||
\(66\) | −5.71876 | −0.703931 | ||||||||
\(67\) | −3.52986 | −0.431241 | −0.215621 | − | 0.976477i | \(-0.569177\pi\) | ||||
−0.215621 | + | 0.976477i | \(0.569177\pi\) | |||||||
\(68\) | 3.07467 | 0.372858 | ||||||||
\(69\) | 10.1519 | 1.22214 | ||||||||
\(70\) | −12.5962 | −1.50553 | ||||||||
\(71\) | −10.1166 | −1.20062 | −0.600311 | − | 0.799767i | \(-0.704956\pi\) | ||||
−0.600311 | + | 0.799767i | \(0.704956\pi\) | |||||||
\(72\) | −8.33909 | −0.982771 | ||||||||
\(73\) | −5.09905 | −0.596799 | −0.298399 | − | 0.954441i | \(-0.596453\pi\) | ||||
−0.298399 | + | 0.954441i | \(0.596453\pi\) | |||||||
\(74\) | 7.49997 | 0.871854 | ||||||||
\(75\) | 5.78635 | 0.668151 | ||||||||
\(76\) | 7.19176 | 0.824952 | ||||||||
\(77\) | −2.07248 | −0.236181 | ||||||||
\(78\) | −6.98950 | −0.791405 | ||||||||
\(79\) | 6.37136 | 0.716834 | 0.358417 | − | 0.933562i | \(-0.383317\pi\) | ||||
0.358417 | + | 0.933562i | \(0.383317\pi\) | |||||||
\(80\) | 1.87715 | 0.209872 | ||||||||
\(81\) | −7.46849 | −0.829832 | ||||||||
\(82\) | 22.1673 | 2.44797 | ||||||||
\(83\) | 17.9066 | 1.96550 | 0.982752 | − | 0.184928i | \(-0.0592051\pi\) | ||||
0.982752 | + | 0.184928i | \(0.0592051\pi\) | |||||||
\(84\) | −16.1766 | −1.76501 | ||||||||
\(85\) | −2.69802 | −0.292642 | ||||||||
\(86\) | −2.25270 | −0.242915 | ||||||||
\(87\) | −8.57829 | −0.919689 | ||||||||
\(88\) | −2.42091 | −0.258070 | ||||||||
\(89\) | 12.4966 | 1.32464 | 0.662318 | − | 0.749223i | \(-0.269573\pi\) | ||||
0.662318 | + | 0.749223i | \(0.269573\pi\) | |||||||
\(90\) | 20.9358 | 2.20683 | ||||||||
\(91\) | −2.53299 | −0.265530 | ||||||||
\(92\) | 12.2955 | 1.28189 | ||||||||
\(93\) | 13.3925 | 1.38873 | ||||||||
\(94\) | −22.3169 | −2.30181 | ||||||||
\(95\) | −6.31078 | −0.647472 | ||||||||
\(96\) | 16.2704 | 1.66059 | ||||||||
\(97\) | 8.54706 | 0.867822 | 0.433911 | − | 0.900956i | \(-0.357133\pi\) | ||||
0.433911 | + | 0.900956i | \(0.357133\pi\) | |||||||
\(98\) | 6.09320 | 0.615506 | ||||||||
\(99\) | 3.44461 | 0.346196 | ||||||||
\(100\) | 7.00817 | 0.700817 | ||||||||
\(101\) | 2.27426 | 0.226298 | 0.113149 | − | 0.993578i | \(-0.463906\pi\) | ||||
0.113149 | + | 0.993578i | \(0.463906\pi\) | |||||||
\(102\) | −5.71876 | −0.566242 | ||||||||
\(103\) | 14.8724 | 1.46542 | 0.732712 | − | 0.680538i | \(-0.238254\pi\) | ||||
0.732712 | + | 0.680538i | \(0.238254\pi\) | |||||||
\(104\) | −2.95885 | −0.290139 | ||||||||
\(105\) | 14.1949 | 1.38528 | ||||||||
\(106\) | −3.43155 | −0.333301 | ||||||||
\(107\) | −0.832362 | −0.0804675 | −0.0402338 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402338 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(108\) | 3.47037 | 0.333937 | ||||||||
\(109\) | 2.08727 | 0.199924 | 0.0999622 | − | 0.994991i | \(-0.468128\pi\) | ||||
0.0999622 | + | 0.994991i | \(0.468128\pi\) | |||||||
\(110\) | 6.07784 | 0.579500 | ||||||||
\(111\) | −8.45190 | −0.802219 | ||||||||
\(112\) | 1.44193 | 0.136249 | ||||||||
\(113\) | 0.757367 | 0.0712471 | 0.0356235 | − | 0.999365i | \(-0.488658\pi\) | ||||
0.0356235 | + | 0.999365i | \(0.488658\pi\) | |||||||
\(114\) | −13.3764 | −1.25281 | ||||||||
\(115\) | −10.7893 | −1.00611 | ||||||||
\(116\) | −10.3896 | −0.964654 | ||||||||
\(117\) | 4.21002 | 0.389216 | ||||||||
\(118\) | −11.3086 | −1.04104 | ||||||||
\(119\) | −2.07248 | −0.189984 | ||||||||
\(120\) | 16.5814 | 1.51367 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.9461 | 1.08155 | ||||||||
\(123\) | −24.9809 | −2.25245 | ||||||||
\(124\) | 16.2203 | 1.45663 | ||||||||
\(125\) | 7.34044 | 0.656549 | ||||||||
\(126\) | 16.0818 | 1.43268 | ||||||||
\(127\) | −12.2963 | −1.09112 | −0.545560 | − | 0.838072i | \(-0.683683\pi\) | ||||
−0.545560 | + | 0.838072i | \(0.683683\pi\) | |||||||
\(128\) | 16.5713 | 1.46471 | ||||||||
\(129\) | 2.53862 | 0.223513 | ||||||||
\(130\) | 7.42837 | 0.651511 | ||||||||
\(131\) | −12.8405 | −1.12188 | −0.560939 | − | 0.827857i | \(-0.689560\pi\) | ||||
−0.560939 | + | 0.827857i | \(0.689560\pi\) | |||||||
\(132\) | 7.80543 | 0.679375 | ||||||||
\(133\) | −4.84760 | −0.420340 | ||||||||
\(134\) | 7.95173 | 0.686925 | ||||||||
\(135\) | −3.04525 | −0.262094 | ||||||||
\(136\) | −2.42091 | −0.207591 | ||||||||
\(137\) | −4.39364 | −0.375374 | −0.187687 | − | 0.982229i | \(-0.560099\pi\) | ||||
−0.187687 | + | 0.982229i | \(0.560099\pi\) | |||||||
\(138\) | −22.8691 | −1.94675 | ||||||||
\(139\) | −19.4582 | −1.65042 | −0.825211 | − | 0.564824i | \(-0.808944\pi\) | ||||
−0.825211 | + | 0.564824i | \(0.808944\pi\) | |||||||
\(140\) | 17.1923 | 1.45301 | ||||||||
\(141\) | 25.1495 | 2.11797 | ||||||||
\(142\) | 22.7897 | 1.91247 | ||||||||
\(143\) | 1.22220 | 0.102206 | ||||||||
\(144\) | −2.39659 | −0.199716 | ||||||||
\(145\) | 9.11692 | 0.757119 | ||||||||
\(146\) | 11.4866 | 0.950642 | ||||||||
\(147\) | −6.86657 | −0.566345 | ||||||||
\(148\) | −10.2366 | −0.841440 | ||||||||
\(149\) | 10.4419 | 0.855433 | 0.427717 | − | 0.903913i | \(-0.359318\pi\) | ||||
0.427717 | + | 0.903913i | \(0.359318\pi\) | |||||||
\(150\) | −13.0349 | −1.06430 | ||||||||
\(151\) | −0.944962 | −0.0768999 | −0.0384500 | − | 0.999261i | \(-0.512242\pi\) | ||||
−0.0384500 | + | 0.999261i | \(0.512242\pi\) | |||||||
\(152\) | −5.66260 | −0.459297 | ||||||||
\(153\) | 3.44461 | 0.278480 | ||||||||
\(154\) | 4.66867 | 0.376212 | ||||||||
\(155\) | −14.2334 | −1.14325 | ||||||||
\(156\) | 9.53983 | 0.763798 | ||||||||
\(157\) | 8.54009 | 0.681573 | 0.340787 | − | 0.940141i | \(-0.389307\pi\) | ||||
0.340787 | + | 0.940141i | \(0.389307\pi\) | |||||||
\(158\) | −14.3528 | −1.14185 | ||||||||
\(159\) | 3.86709 | 0.306680 | ||||||||
\(160\) | −17.2920 | −1.36705 | ||||||||
\(161\) | −8.28775 | −0.653166 | ||||||||
\(162\) | 16.8243 | 1.32184 | ||||||||
\(163\) | −6.94489 | −0.543966 | −0.271983 | − | 0.962302i | \(-0.587679\pi\) | ||||
−0.271983 | + | 0.962302i | \(0.587679\pi\) | |||||||
\(164\) | −30.2557 | −2.36258 | ||||||||
\(165\) | −6.84926 | −0.533215 | ||||||||
\(166\) | −40.3382 | −3.13085 | ||||||||
\(167\) | −13.2286 | −1.02366 | −0.511831 | − | 0.859086i | \(-0.671033\pi\) | ||||
−0.511831 | + | 0.859086i | \(0.671033\pi\) | |||||||
\(168\) | 12.7370 | 0.982679 | ||||||||
\(169\) | −11.5062 | −0.885093 | ||||||||
\(170\) | 6.07784 | 0.466149 | ||||||||
\(171\) | 8.05707 | 0.616140 | ||||||||
\(172\) | 3.07467 | 0.234441 | ||||||||
\(173\) | 7.15541 | 0.544016 | 0.272008 | − | 0.962295i | \(-0.412312\pi\) | ||||
0.272008 | + | 0.962295i | \(0.412312\pi\) | |||||||
\(174\) | 19.3243 | 1.46497 | ||||||||
\(175\) | −4.72385 | −0.357090 | ||||||||
\(176\) | −0.695751 | −0.0524442 | ||||||||
\(177\) | 12.7439 | 0.957892 | ||||||||
\(178\) | −28.1511 | −2.11001 | ||||||||
\(179\) | 12.1309 | 0.906708 | 0.453354 | − | 0.891331i | \(-0.350227\pi\) | ||||
0.453354 | + | 0.891331i | \(0.350227\pi\) | |||||||
\(180\) | −28.5749 | −2.12984 | ||||||||
\(181\) | 0.219538 | 0.0163181 | 0.00815905 | − | 0.999967i | \(-0.497403\pi\) | ||||
0.00815905 | + | 0.999967i | \(0.497403\pi\) | |||||||
\(182\) | 5.70608 | 0.422963 | ||||||||
\(183\) | −13.4623 | −0.995165 | ||||||||
\(184\) | −9.68111 | −0.713701 | ||||||||
\(185\) | 8.98259 | 0.660413 | ||||||||
\(186\) | −30.1692 | −2.21211 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 30.4599 | 2.22152 | ||||||||
\(189\) | −2.33920 | −0.170152 | ||||||||
\(190\) | 14.2163 | 1.03136 | ||||||||
\(191\) | −7.23933 | −0.523820 | −0.261910 | − | 0.965092i | \(-0.584352\pi\) | ||||
−0.261910 | + | 0.965092i | \(0.584352\pi\) | |||||||
\(192\) | −33.1198 | −2.39022 | ||||||||
\(193\) | 12.1202 | 0.872430 | 0.436215 | − | 0.899842i | \(-0.356319\pi\) | ||||
0.436215 | + | 0.899842i | \(0.356319\pi\) | |||||||
\(194\) | −19.2540 | −1.38235 | ||||||||
\(195\) | −8.37121 | −0.599474 | ||||||||
\(196\) | −8.31649 | −0.594035 | ||||||||
\(197\) | −5.79951 | −0.413198 | −0.206599 | − | 0.978426i | \(-0.566240\pi\) | ||||
−0.206599 | + | 0.978426i | \(0.566240\pi\) | |||||||
\(198\) | −7.75968 | −0.551457 | ||||||||
\(199\) | 11.2251 | 0.795727 | 0.397864 | − | 0.917445i | \(-0.369752\pi\) | ||||
0.397864 | + | 0.917445i | \(0.369752\pi\) | |||||||
\(200\) | −5.51804 | −0.390184 | ||||||||
\(201\) | −8.96099 | −0.632059 | ||||||||
\(202\) | −5.12324 | −0.360470 | ||||||||
\(203\) | 7.00313 | 0.491523 | ||||||||
\(204\) | 7.80543 | 0.546489 | ||||||||
\(205\) | 26.5494 | 1.85429 | ||||||||
\(206\) | −33.5032 | −2.33428 | ||||||||
\(207\) | 13.7749 | 0.957419 | ||||||||
\(208\) | −0.850350 | −0.0589612 | ||||||||
\(209\) | 2.33904 | 0.161795 | ||||||||
\(210\) | −31.9770 | −2.20662 | ||||||||
\(211\) | −16.3880 | −1.12820 | −0.564098 | − | 0.825708i | \(-0.690776\pi\) | ||||
−0.564098 | + | 0.825708i | \(0.690776\pi\) | |||||||
\(212\) | 4.68365 | 0.321674 | ||||||||
\(213\) | −25.6823 | −1.75972 | ||||||||
\(214\) | 1.87506 | 0.128177 | ||||||||
\(215\) | −2.69802 | −0.184004 | ||||||||
\(216\) | −2.73248 | −0.185921 | ||||||||
\(217\) | −10.9333 | −0.742201 | ||||||||
\(218\) | −4.70200 | −0.318460 | ||||||||
\(219\) | −12.9446 | −0.874713 | ||||||||
\(220\) | −8.29553 | −0.559284 | ||||||||
\(221\) | 1.22220 | 0.0822144 | ||||||||
\(222\) | 19.0396 | 1.27785 | ||||||||
\(223\) | −5.50360 | −0.368548 | −0.184274 | − | 0.982875i | \(-0.558993\pi\) | ||||
−0.184274 | + | 0.982875i | \(0.558993\pi\) | |||||||
\(224\) | −13.2828 | −0.887493 | ||||||||
\(225\) | 7.85139 | 0.523426 | ||||||||
\(226\) | −1.70612 | −0.113490 | ||||||||
\(227\) | −12.6639 | −0.840534 | −0.420267 | − | 0.907401i | \(-0.638064\pi\) | ||||
−0.420267 | + | 0.907401i | \(0.638064\pi\) | |||||||
\(228\) | 18.2572 | 1.20911 | ||||||||
\(229\) | 4.79412 | 0.316804 | 0.158402 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158402 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(230\) | 24.3050 | 1.60263 | ||||||||
\(231\) | −5.26124 | −0.346164 | ||||||||
\(232\) | 8.18052 | 0.537077 | ||||||||
\(233\) | 3.27279 | 0.214408 | 0.107204 | − | 0.994237i | \(-0.465810\pi\) | ||||
0.107204 | + | 0.994237i | \(0.465810\pi\) | |||||||
\(234\) | −9.48392 | −0.619983 | ||||||||
\(235\) | −26.7286 | −1.74358 | ||||||||
\(236\) | 15.4349 | 1.00472 | ||||||||
\(237\) | 16.1745 | 1.05065 | ||||||||
\(238\) | 4.66867 | 0.302625 | ||||||||
\(239\) | 25.8317 | 1.67091 | 0.835457 | − | 0.549556i | \(-0.185203\pi\) | ||||
0.835457 | + | 0.549556i | \(0.185203\pi\) | |||||||
\(240\) | 4.76538 | 0.307604 | ||||||||
\(241\) | −8.71206 | −0.561193 | −0.280597 | − | 0.959826i | \(-0.590532\pi\) | ||||
−0.280597 | + | 0.959826i | \(0.590532\pi\) | |||||||
\(242\) | −2.25270 | −0.144809 | ||||||||
\(243\) | −22.3458 | −1.43348 | ||||||||
\(244\) | −16.3050 | −1.04382 | ||||||||
\(245\) | 7.29772 | 0.466234 | ||||||||
\(246\) | 56.2745 | 3.58793 | ||||||||
\(247\) | 2.85878 | 0.181900 | ||||||||
\(248\) | −12.7714 | −0.810988 | ||||||||
\(249\) | 45.4581 | 2.88079 | ||||||||
\(250\) | −16.5358 | −1.04582 | ||||||||
\(251\) | 14.4717 | 0.913443 | 0.456721 | − | 0.889610i | \(-0.349024\pi\) | ||||
0.456721 | + | 0.889610i | \(0.349024\pi\) | |||||||
\(252\) | −21.9497 | −1.38270 | ||||||||
\(253\) | 3.99896 | 0.251412 | ||||||||
\(254\) | 27.6999 | 1.73805 | ||||||||
\(255\) | −6.84926 | −0.428918 | ||||||||
\(256\) | −11.2375 | −0.702345 | ||||||||
\(257\) | 28.1495 | 1.75592 | 0.877960 | − | 0.478734i | \(-0.158904\pi\) | ||||
0.877960 | + | 0.478734i | \(0.158904\pi\) | |||||||
\(258\) | −5.71876 | −0.356035 | ||||||||
\(259\) | 6.89994 | 0.428742 | ||||||||
\(260\) | −10.1388 | −0.628784 | ||||||||
\(261\) | −11.6397 | −0.720481 | ||||||||
\(262\) | 28.9258 | 1.78704 | ||||||||
\(263\) | 0.766205 | 0.0472462 | 0.0236231 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236231 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(264\) | −6.14578 | −0.378246 | ||||||||
\(265\) | −4.10990 | −0.252469 | ||||||||
\(266\) | 10.9202 | 0.669561 | ||||||||
\(267\) | 31.7241 | 1.94149 | ||||||||
\(268\) | −10.8532 | −0.662962 | ||||||||
\(269\) | 13.9161 | 0.848477 | 0.424238 | − | 0.905551i | \(-0.360542\pi\) | ||||
0.424238 | + | 0.905551i | \(0.360542\pi\) | |||||||
\(270\) | 6.86005 | 0.417489 | ||||||||
\(271\) | 26.2183 | 1.59265 | 0.796325 | − | 0.604869i | \(-0.206774\pi\) | ||||
0.796325 | + | 0.604869i | \(0.206774\pi\) | |||||||
\(272\) | −0.695751 | −0.0421861 | ||||||||
\(273\) | −6.43031 | −0.389180 | ||||||||
\(274\) | 9.89755 | 0.597933 | ||||||||
\(275\) | 2.27933 | 0.137449 | ||||||||
\(276\) | 31.2136 | 1.87884 | ||||||||
\(277\) | −15.5451 | −0.934015 | −0.467008 | − | 0.884253i | \(-0.654668\pi\) | ||||
−0.467008 | + | 0.884253i | \(0.654668\pi\) | |||||||
\(278\) | 43.8335 | 2.62896 | ||||||||
\(279\) | 18.1720 | 1.08793 | ||||||||
\(280\) | −13.5367 | −0.808974 | ||||||||
\(281\) | 21.4381 | 1.27889 | 0.639446 | − | 0.768836i | \(-0.279164\pi\) | ||||
0.639446 | + | 0.768836i | \(0.279164\pi\) | |||||||
\(282\) | −56.6542 | −3.37371 | ||||||||
\(283\) | −6.83917 | −0.406547 | −0.203273 | − | 0.979122i | \(-0.565158\pi\) | ||||
−0.203273 | + | 0.979122i | \(0.565158\pi\) | |||||||
\(284\) | −31.1052 | −1.84576 | ||||||||
\(285\) | −16.0207 | −0.948984 | ||||||||
\(286\) | −2.75326 | −0.162804 | ||||||||
\(287\) | 20.3938 | 1.20381 | ||||||||
\(288\) | 22.0770 | 1.30090 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −20.5377 | −1.20602 | ||||||||
\(291\) | 21.6978 | 1.27195 | ||||||||
\(292\) | −15.6779 | −0.917479 | ||||||||
\(293\) | 24.3396 | 1.42193 | 0.710966 | − | 0.703226i | \(-0.248258\pi\) | ||||
0.710966 | + | 0.703226i | \(0.248258\pi\) | |||||||
\(294\) | 15.4683 | 0.902132 | ||||||||
\(295\) | −13.5441 | −0.788569 | ||||||||
\(296\) | 8.05998 | 0.468477 | ||||||||
\(297\) | 1.12870 | 0.0654937 | ||||||||
\(298\) | −23.5225 | −1.36262 | ||||||||
\(299\) | 4.88755 | 0.282654 | ||||||||
\(300\) | 17.7911 | 1.02717 | ||||||||
\(301\) | −2.07248 | −0.119456 | ||||||||
\(302\) | 2.12872 | 0.122494 | ||||||||
\(303\) | 5.77350 | 0.331679 | ||||||||
\(304\) | −1.62739 | −0.0933370 | ||||||||
\(305\) | 14.3076 | 0.819253 | ||||||||
\(306\) | −7.75968 | −0.443592 | ||||||||
\(307\) | −4.88601 | −0.278859 | −0.139430 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139430 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(308\) | −6.37218 | −0.363089 | ||||||||
\(309\) | 37.7555 | 2.14784 | ||||||||
\(310\) | 32.0635 | 1.82109 | ||||||||
\(311\) | 8.28068 | 0.469554 | 0.234777 | − | 0.972049i | \(-0.424564\pi\) | ||||
0.234777 | + | 0.972049i | \(0.424564\pi\) | |||||||
\(312\) | −7.51140 | −0.425249 | ||||||||
\(313\) | 18.0872 | 1.02235 | 0.511174 | − | 0.859477i | \(-0.329211\pi\) | ||||
0.511174 | + | 0.859477i | \(0.329211\pi\) | |||||||
\(314\) | −19.2383 | −1.08568 | ||||||||
\(315\) | 19.2608 | 1.08523 | ||||||||
\(316\) | 19.5898 | 1.10201 | ||||||||
\(317\) | 6.61130 | 0.371327 | 0.185664 | − | 0.982613i | \(-0.440556\pi\) | ||||
0.185664 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(318\) | −8.71141 | −0.488511 | ||||||||
\(319\) | −3.37911 | −0.189194 | ||||||||
\(320\) | 35.1994 | 1.96771 | ||||||||
\(321\) | −2.11306 | −0.117939 | ||||||||
\(322\) | 18.6698 | 1.04043 | ||||||||
\(323\) | 2.33904 | 0.130148 | ||||||||
\(324\) | −22.9631 | −1.27573 | ||||||||
\(325\) | 2.78580 | 0.154529 | ||||||||
\(326\) | 15.6448 | 0.866483 | ||||||||
\(327\) | 5.29880 | 0.293024 | ||||||||
\(328\) | 23.8225 | 1.31538 | ||||||||
\(329\) | −20.5315 | −1.13194 | ||||||||
\(330\) | 15.4294 | 0.849358 | ||||||||
\(331\) | −29.5351 | −1.62340 | −0.811698 | − | 0.584077i | \(-0.801457\pi\) | ||||
−0.811698 | + | 0.584077i | \(0.801457\pi\) | |||||||
\(332\) | 55.0568 | 3.02164 | ||||||||
\(333\) | −11.4682 | −0.628455 | ||||||||
\(334\) | 29.8002 | 1.63059 | ||||||||
\(335\) | 9.52365 | 0.520332 | ||||||||
\(336\) | 3.66051 | 0.199697 | ||||||||
\(337\) | −28.3966 | −1.54686 | −0.773431 | − | 0.633880i | \(-0.781461\pi\) | ||||
−0.773431 | + | 0.633880i | \(0.781461\pi\) | |||||||
\(338\) | 25.9201 | 1.40987 | ||||||||
\(339\) | 1.92267 | 0.104425 | ||||||||
\(340\) | −8.29553 | −0.449888 | ||||||||
\(341\) | 5.27548 | 0.285683 | ||||||||
\(342\) | −18.1502 | −0.981450 | ||||||||
\(343\) | 20.1131 | 1.08600 | ||||||||
\(344\) | −2.42091 | −0.130527 | ||||||||
\(345\) | −27.3899 | −1.47462 | ||||||||
\(346\) | −16.1190 | −0.866564 | ||||||||
\(347\) | −9.40481 | −0.504877 | −0.252438 | − | 0.967613i | \(-0.581232\pi\) | ||||
−0.252438 | + | 0.967613i | \(0.581232\pi\) | |||||||
\(348\) | −26.3754 | −1.41387 | ||||||||
\(349\) | 34.5889 | 1.85150 | 0.925750 | − | 0.378136i | \(-0.123435\pi\) | ||||
0.925750 | + | 0.378136i | \(0.123435\pi\) | |||||||
\(350\) | 10.6414 | 0.568809 | ||||||||
\(351\) | 1.37950 | 0.0736323 | ||||||||
\(352\) | 6.40914 | 0.341608 | ||||||||
\(353\) | 1.60975 | 0.0856783 | 0.0428391 | − | 0.999082i | \(-0.486360\pi\) | ||||
0.0428391 | + | 0.999082i | \(0.486360\pi\) | |||||||
\(354\) | −28.7083 | −1.52583 | ||||||||
\(355\) | 27.2949 | 1.44866 | ||||||||
\(356\) | 38.4229 | 2.03641 | ||||||||
\(357\) | −5.26124 | −0.278454 | ||||||||
\(358\) | −27.3274 | −1.44430 | ||||||||
\(359\) | −31.1633 | −1.64474 | −0.822368 | − | 0.568956i | \(-0.807347\pi\) | ||||
−0.822368 | + | 0.568956i | \(0.807347\pi\) | |||||||
\(360\) | 22.4990 | 1.18580 | ||||||||
\(361\) | −13.5289 | −0.712048 | ||||||||
\(362\) | −0.494553 | −0.0259931 | ||||||||
\(363\) | 2.53862 | 0.133243 | ||||||||
\(364\) | −7.78811 | −0.408208 | ||||||||
\(365\) | 13.7574 | 0.720093 | ||||||||
\(366\) | 30.3267 | 1.58520 | ||||||||
\(367\) | 28.1321 | 1.46848 | 0.734242 | − | 0.678888i | \(-0.237538\pi\) | ||||
0.734242 | + | 0.678888i | \(0.237538\pi\) | |||||||
\(368\) | −2.78228 | −0.145036 | ||||||||
\(369\) | −33.8961 | −1.76456 | ||||||||
\(370\) | −20.2351 | −1.05197 | ||||||||
\(371\) | −3.15701 | −0.163904 | ||||||||
\(372\) | 41.1774 | 2.13495 | ||||||||
\(373\) | 10.0689 | 0.521347 | 0.260674 | − | 0.965427i | \(-0.416055\pi\) | ||||
0.260674 | + | 0.965427i | \(0.416055\pi\) | |||||||
\(374\) | −2.25270 | −0.116484 | ||||||||
\(375\) | 18.6346 | 0.962287 | ||||||||
\(376\) | −23.9833 | −1.23684 | ||||||||
\(377\) | −4.12997 | −0.212704 | ||||||||
\(378\) | 5.26952 | 0.271035 | ||||||||
\(379\) | 15.4194 | 0.792040 | 0.396020 | − | 0.918242i | \(-0.370391\pi\) | ||||
0.396020 | + | 0.918242i | \(0.370391\pi\) | |||||||
\(380\) | −19.4035 | −0.995381 | ||||||||
\(381\) | −31.2157 | −1.59923 | ||||||||
\(382\) | 16.3081 | 0.834393 | ||||||||
\(383\) | 15.6070 | 0.797483 | 0.398741 | − | 0.917063i | \(-0.369447\pi\) | ||||
0.398741 | + | 0.917063i | \(0.369447\pi\) | |||||||
\(384\) | 42.0684 | 2.14679 | ||||||||
\(385\) | 5.59159 | 0.284974 | ||||||||
\(386\) | −27.3032 | −1.38970 | ||||||||
\(387\) | 3.44461 | 0.175099 | ||||||||
\(388\) | 26.2794 | 1.33413 | ||||||||
\(389\) | 31.2811 | 1.58601 | 0.793006 | − | 0.609214i | \(-0.208515\pi\) | ||||
0.793006 | + | 0.609214i | \(0.208515\pi\) | |||||||
\(390\) | 18.8578 | 0.954904 | ||||||||
\(391\) | 3.99896 | 0.202236 | ||||||||
\(392\) | 6.54817 | 0.330733 | ||||||||
\(393\) | −32.5971 | −1.64431 | ||||||||
\(394\) | 13.0646 | 0.658183 | ||||||||
\(395\) | −17.1901 | −0.864926 | ||||||||
\(396\) | 10.5910 | 0.532220 | ||||||||
\(397\) | 23.5654 | 1.18271 | 0.591357 | − | 0.806410i | \(-0.298592\pi\) | ||||
0.591357 | + | 0.806410i | \(0.298592\pi\) | |||||||
\(398\) | −25.2868 | −1.26751 | ||||||||
\(399\) | −12.3062 | −0.616082 | ||||||||
\(400\) | −1.58584 | −0.0792922 | ||||||||
\(401\) | 2.46060 | 0.122877 | 0.0614383 | − | 0.998111i | \(-0.480431\pi\) | ||||
0.0614383 | + | 0.998111i | \(0.480431\pi\) | |||||||
\(402\) | 20.1864 | 1.00681 | ||||||||
\(403\) | 6.44772 | 0.321184 | ||||||||
\(404\) | 6.99261 | 0.347895 | ||||||||
\(405\) | 20.1502 | 1.00127 | ||||||||
\(406\) | −15.7760 | −0.782948 | ||||||||
\(407\) | −3.32932 | −0.165028 | ||||||||
\(408\) | −6.14578 | −0.304261 | ||||||||
\(409\) | 18.0781 | 0.893907 | 0.446953 | − | 0.894557i | \(-0.352509\pi\) | ||||
0.446953 | + | 0.894557i | \(0.352509\pi\) | |||||||
\(410\) | −59.8079 | −2.95370 | ||||||||
\(411\) | −11.1538 | −0.550176 | ||||||||
\(412\) | 45.7278 | 2.25285 | ||||||||
\(413\) | −10.4039 | −0.511940 | ||||||||
\(414\) | −31.0306 | −1.52507 | ||||||||
\(415\) | −48.3124 | −2.37156 | ||||||||
\(416\) | 7.83328 | 0.384058 | ||||||||
\(417\) | −49.3970 | −2.41898 | ||||||||
\(418\) | −5.26916 | −0.257723 | ||||||||
\(419\) | 9.24303 | 0.451552 | 0.225776 | − | 0.974179i | \(-0.427508\pi\) | ||||
0.225776 | + | 0.974179i | \(0.427508\pi\) | |||||||
\(420\) | 43.6447 | 2.12965 | ||||||||
\(421\) | 30.9745 | 1.50960 | 0.754802 | − | 0.655953i | \(-0.227733\pi\) | ||||
0.754802 | + | 0.655953i | \(0.227733\pi\) | |||||||
\(422\) | 36.9173 | 1.79710 | ||||||||
\(423\) | 34.1248 | 1.65921 | ||||||||
\(424\) | −3.68778 | −0.179094 | ||||||||
\(425\) | 2.27933 | 0.110564 | ||||||||
\(426\) | 57.8545 | 2.80306 | ||||||||
\(427\) | 10.9904 | 0.531861 | ||||||||
\(428\) | −2.55924 | −0.123705 | ||||||||
\(429\) | 3.10272 | 0.149801 | ||||||||
\(430\) | 6.07784 | 0.293100 | ||||||||
\(431\) | 4.28745 | 0.206519 | 0.103260 | − | 0.994654i | \(-0.467073\pi\) | ||||
0.103260 | + | 0.994654i | \(0.467073\pi\) | |||||||
\(432\) | −0.785293 | −0.0377824 | ||||||||
\(433\) | −12.2719 | −0.589748 | −0.294874 | − | 0.955536i | \(-0.595278\pi\) | ||||
−0.294874 | + | 0.955536i | \(0.595278\pi\) | |||||||
\(434\) | 24.6295 | 1.18225 | ||||||||
\(435\) | 23.1444 | 1.10969 | ||||||||
\(436\) | 6.41767 | 0.307351 | ||||||||
\(437\) | 9.35371 | 0.447449 | ||||||||
\(438\) | 29.1603 | 1.39333 | ||||||||
\(439\) | 11.3644 | 0.542392 | 0.271196 | − | 0.962524i | \(-0.412581\pi\) | ||||
0.271196 | + | 0.962524i | \(0.412581\pi\) | |||||||
\(440\) | 6.53167 | 0.311385 | ||||||||
\(441\) | −9.31712 | −0.443672 | ||||||||
\(442\) | −2.75326 | −0.130959 | ||||||||
\(443\) | 36.1347 | 1.71681 | 0.858407 | − | 0.512970i | \(-0.171455\pi\) | ||||
0.858407 | + | 0.512970i | \(0.171455\pi\) | |||||||
\(444\) | −25.9868 | −1.23328 | ||||||||
\(445\) | −33.7161 | −1.59830 | ||||||||
\(446\) | 12.3980 | 0.587061 | ||||||||
\(447\) | 26.5080 | 1.25379 | ||||||||
\(448\) | 27.0383 | 1.27744 | ||||||||
\(449\) | −12.1611 | −0.573916 | −0.286958 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286958 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(450\) | −17.6869 | −0.833766 | ||||||||
\(451\) | −9.84032 | −0.463363 | ||||||||
\(452\) | 2.32865 | 0.109531 | ||||||||
\(453\) | −2.39890 | −0.112710 | ||||||||
\(454\) | 28.5280 | 1.33889 | ||||||||
\(455\) | 6.83407 | 0.320386 | ||||||||
\(456\) | −14.3752 | −0.673180 | ||||||||
\(457\) | 13.2266 | 0.618713 | 0.309357 | − | 0.950946i | \(-0.399886\pi\) | ||||
0.309357 | + | 0.950946i | \(0.399886\pi\) | |||||||
\(458\) | −10.7997 | −0.504638 | ||||||||
\(459\) | 1.12870 | 0.0526831 | ||||||||
\(460\) | −33.1735 | −1.54672 | ||||||||
\(461\) | 18.3851 | 0.856282 | 0.428141 | − | 0.903712i | \(-0.359169\pi\) | ||||
0.428141 | + | 0.903712i | \(0.359169\pi\) | |||||||
\(462\) | 11.8520 | 0.551405 | ||||||||
\(463\) | −22.0656 | −1.02547 | −0.512737 | − | 0.858546i | \(-0.671368\pi\) | ||||
−0.512737 | + | 0.858546i | \(0.671368\pi\) | |||||||
\(464\) | 2.35102 | 0.109143 | ||||||||
\(465\) | −36.1331 | −1.67563 | ||||||||
\(466\) | −7.37263 | −0.341530 | ||||||||
\(467\) | 9.77489 | 0.452328 | 0.226164 | − | 0.974089i | \(-0.427381\pi\) | ||||
0.226164 | + | 0.974089i | \(0.427381\pi\) | |||||||
\(468\) | 12.9444 | 0.598356 | ||||||||
\(469\) | 7.31556 | 0.337801 | ||||||||
\(470\) | 60.2115 | 2.77735 | ||||||||
\(471\) | 21.6801 | 0.998965 | ||||||||
\(472\) | −12.1530 | −0.559387 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | −36.4363 | −1.67357 | ||||||||
\(475\) | 5.33143 | 0.244623 | ||||||||
\(476\) | −6.37218 | −0.292068 | ||||||||
\(477\) | 5.24718 | 0.240252 | ||||||||
\(478\) | −58.1911 | −2.66160 | ||||||||
\(479\) | 33.3551 | 1.52403 | 0.762017 | − | 0.647557i | \(-0.224209\pi\) | ||||
0.762017 | + | 0.647557i | \(0.224209\pi\) | |||||||
\(480\) | −43.8979 | −2.00365 | ||||||||
\(481\) | −4.06911 | −0.185536 | ||||||||
\(482\) | 19.6257 | 0.893925 | ||||||||
\(483\) | −21.0395 | −0.957329 | ||||||||
\(484\) | 3.07467 | 0.139758 | ||||||||
\(485\) | −23.0601 | −1.04711 | ||||||||
\(486\) | 50.3384 | 2.28340 | ||||||||
\(487\) | 28.2469 | 1.27999 | 0.639994 | − | 0.768380i | \(-0.278937\pi\) | ||||
0.639994 | + | 0.768380i | \(0.278937\pi\) | |||||||
\(488\) | 12.8381 | 0.581153 | ||||||||
\(489\) | −17.6305 | −0.797277 | ||||||||
\(490\) | −16.4396 | −0.742665 | ||||||||
\(491\) | 22.0923 | 0.997014 | 0.498507 | − | 0.866886i | \(-0.333882\pi\) | ||||
0.498507 | + | 0.866886i | \(0.333882\pi\) | |||||||
\(492\) | −76.8079 | −3.46277 | ||||||||
\(493\) | −3.37911 | −0.152188 | ||||||||
\(494\) | −6.43999 | −0.289749 | ||||||||
\(495\) | −9.29364 | −0.417718 | ||||||||
\(496\) | −3.67042 | −0.164807 | ||||||||
\(497\) | 20.9664 | 0.940474 | ||||||||
\(498\) | −102.404 | −4.58881 | ||||||||
\(499\) | 29.3635 | 1.31449 | 0.657245 | − | 0.753677i | \(-0.271722\pi\) | ||||
0.657245 | + | 0.753677i | \(0.271722\pi\) | |||||||
\(500\) | 22.5694 | 1.00933 | ||||||||
\(501\) | −33.5825 | −1.50036 | ||||||||
\(502\) | −32.6003 | −1.45502 | ||||||||
\(503\) | −11.5657 | −0.515691 | −0.257846 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257846 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(504\) | 17.2826 | 0.769827 | ||||||||
\(505\) | −6.13602 | −0.273049 | ||||||||
\(506\) | −9.00846 | −0.400475 | ||||||||
\(507\) | −29.2100 | −1.29726 | ||||||||
\(508\) | −37.8070 | −1.67742 | ||||||||
\(509\) | 16.0722 | 0.712386 | 0.356193 | − | 0.934412i | \(-0.384075\pi\) | ||||
0.356193 | + | 0.934412i | \(0.384075\pi\) | |||||||
\(510\) | 15.4294 | 0.683223 | ||||||||
\(511\) | 10.5677 | 0.467486 | ||||||||
\(512\) | −7.82786 | −0.345946 | ||||||||
\(513\) | 2.64007 | 0.116562 | ||||||||
\(514\) | −63.4125 | −2.79701 | ||||||||
\(515\) | −40.1262 | −1.76817 | ||||||||
\(516\) | 7.80543 | 0.343615 | ||||||||
\(517\) | 9.90673 | 0.435697 | ||||||||
\(518\) | −15.5435 | −0.682943 | ||||||||
\(519\) | 18.1649 | 0.797351 | ||||||||
\(520\) | 7.98303 | 0.350079 | ||||||||
\(521\) | 26.8079 | 1.17447 | 0.587237 | − | 0.809415i | \(-0.300216\pi\) | ||||
0.587237 | + | 0.809415i | \(0.300216\pi\) | |||||||
\(522\) | 26.2208 | 1.14765 | ||||||||
\(523\) | 1.14213 | 0.0499420 | 0.0249710 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249710 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(524\) | −39.4802 | −1.72470 | ||||||||
\(525\) | −11.9921 | −0.523377 | ||||||||
\(526\) | −1.72603 | −0.0752586 | ||||||||
\(527\) | 5.27548 | 0.229803 | ||||||||
\(528\) | −1.76625 | −0.0768661 | ||||||||
\(529\) | −7.00833 | −0.304710 | ||||||||
\(530\) | 9.25839 | 0.402159 | ||||||||
\(531\) | 17.2920 | 0.750408 | ||||||||
\(532\) | −14.9048 | −0.646204 | ||||||||
\(533\) | −12.0269 | −0.520942 | ||||||||
\(534\) | −71.4650 | −3.09259 | ||||||||
\(535\) | 2.24573 | 0.0970915 | ||||||||
\(536\) | 8.54547 | 0.369108 | ||||||||
\(537\) | 30.7959 | 1.32894 | ||||||||
\(538\) | −31.3487 | −1.35154 | ||||||||
\(539\) | −2.70484 | −0.116506 | ||||||||
\(540\) | −9.36315 | −0.402926 | ||||||||
\(541\) | 7.97118 | 0.342708 | 0.171354 | − | 0.985210i | \(-0.445186\pi\) | ||||
0.171354 | + | 0.985210i | \(0.445186\pi\) | |||||||
\(542\) | −59.0621 | −2.53693 | ||||||||
\(543\) | 0.557323 | 0.0239170 | ||||||||
\(544\) | 6.40914 | 0.274789 | ||||||||
\(545\) | −5.63151 | −0.241227 | ||||||||
\(546\) | 14.4856 | 0.619926 | ||||||||
\(547\) | −28.4476 | −1.21633 | −0.608165 | − | 0.793811i | \(-0.708094\pi\) | ||||
−0.608165 | + | 0.793811i | \(0.708094\pi\) | |||||||
\(548\) | −13.5090 | −0.577075 | ||||||||
\(549\) | −18.2668 | −0.779608 | ||||||||
\(550\) | −5.13465 | −0.218942 | ||||||||
\(551\) | −7.90387 | −0.336716 | ||||||||
\(552\) | −24.5767 | −1.04605 | ||||||||
\(553\) | −13.2045 | −0.561512 | ||||||||
\(554\) | 35.0185 | 1.48779 | ||||||||
\(555\) | 22.8034 | 0.967951 | ||||||||
\(556\) | −59.8275 | −2.53725 | ||||||||
\(557\) | −38.2834 | −1.62212 | −0.811059 | − | 0.584964i | \(-0.801109\pi\) | ||||
−0.811059 | + | 0.584964i | \(0.801109\pi\) | |||||||
\(558\) | −40.9360 | −1.73296 | ||||||||
\(559\) | 1.22220 | 0.0516938 | ||||||||
\(560\) | −3.89035 | −0.164397 | ||||||||
\(561\) | 2.53862 | 0.107181 | ||||||||
\(562\) | −48.2937 | −2.03715 | ||||||||
\(563\) | −43.6484 | −1.83956 | −0.919781 | − | 0.392432i | \(-0.871634\pi\) | ||||
−0.919781 | + | 0.392432i | \(0.871634\pi\) | |||||||
\(564\) | 77.3262 | 3.25602 | ||||||||
\(565\) | −2.04339 | −0.0859662 | ||||||||
\(566\) | 15.4066 | 0.647589 | ||||||||
\(567\) | 15.4783 | 0.650026 | ||||||||
\(568\) | 24.4914 | 1.02764 | ||||||||
\(569\) | −28.2975 | −1.18629 | −0.593147 | − | 0.805094i | \(-0.702115\pi\) | ||||
−0.593147 | + | 0.805094i | \(0.702115\pi\) | |||||||
\(570\) | 36.0898 | 1.51164 | ||||||||
\(571\) | −15.1814 | −0.635320 | −0.317660 | − | 0.948205i | \(-0.602897\pi\) | ||||
−0.317660 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(572\) | 3.75788 | 0.157125 | ||||||||
\(573\) | −18.3779 | −0.767749 | ||||||||
\(574\) | −45.9412 | −1.91755 | ||||||||
\(575\) | 9.11493 | 0.380119 | ||||||||
\(576\) | −44.9397 | −1.87249 | ||||||||
\(577\) | 40.3111 | 1.67817 | 0.839087 | − | 0.543997i | \(-0.183090\pi\) | ||||
0.839087 | + | 0.543997i | \(0.183090\pi\) | |||||||
\(578\) | −2.25270 | −0.0937001 | ||||||||
\(579\) | 30.7686 | 1.27870 | ||||||||
\(580\) | 28.0315 | 1.16394 | ||||||||
\(581\) | −37.1110 | −1.53962 | ||||||||
\(582\) | −48.8786 | −2.02608 | ||||||||
\(583\) | 1.52330 | 0.0630887 | ||||||||
\(584\) | 12.3443 | 0.510812 | ||||||||
\(585\) | −11.3587 | −0.469626 | ||||||||
\(586\) | −54.8298 | −2.26500 | ||||||||
\(587\) | 23.6597 | 0.976539 | 0.488269 | − | 0.872693i | \(-0.337628\pi\) | ||||
0.488269 | + | 0.872693i | \(0.337628\pi\) | |||||||
\(588\) | −21.1124 | −0.870662 | ||||||||
\(589\) | 12.3395 | 0.508442 | ||||||||
\(590\) | 30.5108 | 1.25611 | ||||||||
\(591\) | −14.7228 | −0.605614 | ||||||||
\(592\) | 2.31638 | 0.0952026 | ||||||||
\(593\) | −3.34731 | −0.137458 | −0.0687288 | − | 0.997635i | \(-0.521894\pi\) | ||||
−0.0687288 | + | 0.997635i | \(0.521894\pi\) | |||||||
\(594\) | −2.54262 | −0.104325 | ||||||||
\(595\) | 5.59159 | 0.229233 | ||||||||
\(596\) | 32.1054 | 1.31509 | ||||||||
\(597\) | 28.4963 | 1.16628 | ||||||||
\(598\) | −11.0102 | −0.450240 | ||||||||
\(599\) | 19.1550 | 0.782652 | 0.391326 | − | 0.920252i | \(-0.372017\pi\) | ||||
0.391326 | + | 0.920252i | \(0.372017\pi\) | |||||||
\(600\) | −14.0082 | −0.571884 | ||||||||
\(601\) | 8.23332 | 0.335844 | 0.167922 | − | 0.985800i | \(-0.446294\pi\) | ||||
0.167922 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(602\) | 4.66867 | 0.190281 | ||||||||
\(603\) | −12.1590 | −0.495153 | ||||||||
\(604\) | −2.90544 | −0.118221 | ||||||||
\(605\) | −2.69802 | −0.109690 | ||||||||
\(606\) | −13.0060 | −0.528332 | ||||||||
\(607\) | −21.7263 | −0.881845 | −0.440923 | − | 0.897545i | \(-0.645349\pi\) | ||||
−0.440923 | + | 0.897545i | \(0.645349\pi\) | |||||||
\(608\) | 14.9912 | 0.607974 | ||||||||
\(609\) | 17.7783 | 0.720413 | ||||||||
\(610\) | −32.2309 | −1.30499 | ||||||||
\(611\) | 12.1081 | 0.489839 | ||||||||
\(612\) | 10.5910 | 0.428117 | ||||||||
\(613\) | 29.0227 | 1.17222 | 0.586108 | − | 0.810233i | \(-0.300659\pi\) | ||||
0.586108 | + | 0.810233i | \(0.300659\pi\) | |||||||
\(614\) | 11.0067 | 0.444196 | ||||||||
\(615\) | 67.3990 | 2.71779 | ||||||||
\(616\) | 5.01728 | 0.202152 | ||||||||
\(617\) | −32.0365 | −1.28974 | −0.644871 | − | 0.764291i | \(-0.723089\pi\) | ||||
−0.644871 | + | 0.764291i | \(0.723089\pi\) | |||||||
\(618\) | −85.0520 | −3.42129 | ||||||||
\(619\) | −20.3053 | −0.816138 | −0.408069 | − | 0.912951i | \(-0.633798\pi\) | ||||
−0.408069 | + | 0.912951i | \(0.633798\pi\) | |||||||
\(620\) | −43.7629 | −1.75756 | ||||||||
\(621\) | 4.51362 | 0.181125 | ||||||||
\(622\) | −18.6539 | −0.747954 | ||||||||
\(623\) | −25.8989 | −1.03762 | ||||||||
\(624\) | −2.15872 | −0.0864179 | ||||||||
\(625\) | −31.2013 | −1.24805 | ||||||||
\(626\) | −40.7451 | −1.62850 | ||||||||
\(627\) | 5.93794 | 0.237138 | ||||||||
\(628\) | 26.2579 | 1.04781 | ||||||||
\(629\) | −3.32932 | −0.132749 | ||||||||
\(630\) | −43.3890 | −1.72866 | ||||||||
\(631\) | 1.88309 | 0.0749647 | 0.0374823 | − | 0.999297i | \(-0.488066\pi\) | ||||
0.0374823 | + | 0.999297i | \(0.488066\pi\) | |||||||
\(632\) | −15.4245 | −0.613553 | ||||||||
\(633\) | −41.6029 | −1.65357 | ||||||||
\(634\) | −14.8933 | −0.591488 | ||||||||
\(635\) | 33.1757 | 1.31654 | ||||||||
\(636\) | 11.8900 | 0.471470 | ||||||||
\(637\) | −3.30587 | −0.130983 | ||||||||
\(638\) | 7.61213 | 0.301367 | ||||||||
\(639\) | −34.8478 | −1.37856 | ||||||||
\(640\) | −44.7098 | −1.76731 | ||||||||
\(641\) | 27.3336 | 1.07961 | 0.539807 | − | 0.841789i | \(-0.318497\pi\) | ||||
0.539807 | + | 0.841789i | \(0.318497\pi\) | |||||||
\(642\) | 4.76008 | 0.187866 | ||||||||
\(643\) | −31.0099 | −1.22291 | −0.611455 | − | 0.791279i | \(-0.709416\pi\) | ||||
−0.611455 | + | 0.791279i | \(0.709416\pi\) | |||||||
\(644\) | −25.4821 | −1.00413 | ||||||||
\(645\) | −6.84926 | −0.269690 | ||||||||
\(646\) | −5.26916 | −0.207312 | ||||||||
\(647\) | 8.92462 | 0.350863 | 0.175431 | − | 0.984492i | \(-0.443868\pi\) | ||||
0.175431 | + | 0.984492i | \(0.443868\pi\) | |||||||
\(648\) | 18.0805 | 0.710270 | ||||||||
\(649\) | 5.02001 | 0.197053 | ||||||||
\(650\) | −6.27559 | −0.246149 | ||||||||
\(651\) | −27.7556 | −1.08783 | ||||||||
\(652\) | −21.3532 | −0.836257 | ||||||||
\(653\) | −3.73419 | −0.146130 | −0.0730651 | − | 0.997327i | \(-0.523278\pi\) | ||||
−0.0730651 | + | 0.997327i | \(0.523278\pi\) | |||||||
\(654\) | −11.9366 | −0.466759 | ||||||||
\(655\) | 34.6439 | 1.35365 | ||||||||
\(656\) | 6.84641 | 0.267307 | ||||||||
\(657\) | −17.5642 | −0.685247 | ||||||||
\(658\) | 46.2513 | 1.80306 | ||||||||
\(659\) | −2.38540 | −0.0929221 | −0.0464610 | − | 0.998920i | \(-0.514794\pi\) | ||||
−0.0464610 | + | 0.998920i | \(0.514794\pi\) | |||||||
\(660\) | −21.0592 | −0.819729 | ||||||||
\(661\) | −14.0868 | −0.547912 | −0.273956 | − | 0.961742i | \(-0.588332\pi\) | ||||
−0.273956 | + | 0.961742i | \(0.588332\pi\) | |||||||
\(662\) | 66.5338 | 2.58591 | ||||||||
\(663\) | 3.10272 | 0.120500 | ||||||||
\(664\) | −43.3502 | −1.68232 | ||||||||
\(665\) | 13.0789 | 0.507179 | ||||||||
\(666\) | 25.8345 | 1.00107 | ||||||||
\(667\) | −13.5129 | −0.523223 | ||||||||
\(668\) | −40.6736 | −1.57371 | ||||||||
\(669\) | −13.9716 | −0.540172 | ||||||||
\(670\) | −21.4539 | −0.828838 | ||||||||
\(671\) | −5.30301 | −0.204720 | ||||||||
\(672\) | −33.7200 | −1.30078 | ||||||||
\(673\) | −1.19080 | −0.0459022 | −0.0229511 | − | 0.999737i | \(-0.507306\pi\) | ||||
−0.0229511 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(674\) | 63.9691 | 2.46400 | ||||||||
\(675\) | 2.57267 | 0.0990222 | ||||||||
\(676\) | −35.3778 | −1.36068 | ||||||||
\(677\) | −6.80576 | −0.261567 | −0.130783 | − | 0.991411i | \(-0.541749\pi\) | ||||
−0.130783 | + | 0.991411i | \(0.541749\pi\) | |||||||
\(678\) | −4.33120 | −0.166339 | ||||||||
\(679\) | −17.7136 | −0.679785 | ||||||||
\(680\) | 6.53167 | 0.250478 | ||||||||
\(681\) | −32.1489 | −1.23195 | ||||||||
\(682\) | −11.8841 | −0.455065 | ||||||||
\(683\) | 46.2536 | 1.76985 | 0.884923 | − | 0.465737i | \(-0.154211\pi\) | ||||
0.884923 | + | 0.465737i | \(0.154211\pi\) | |||||||
\(684\) | 24.7728 | 0.947213 | ||||||||
\(685\) | 11.8541 | 0.452923 | ||||||||
\(686\) | −45.3087 | −1.72990 | ||||||||
\(687\) | 12.1705 | 0.464332 | ||||||||
\(688\) | −0.695751 | −0.0265252 | ||||||||
\(689\) | 1.86179 | 0.0709285 | ||||||||
\(690\) | 61.7014 | 2.34893 | ||||||||
\(691\) | −13.4198 | −0.510515 | −0.255258 | − | 0.966873i | \(-0.582160\pi\) | ||||
−0.255258 | + | 0.966873i | \(0.582160\pi\) | |||||||
\(692\) | 22.0005 | 0.836334 | ||||||||
\(693\) | −7.13888 | −0.271183 | ||||||||
\(694\) | 21.1862 | 0.804219 | ||||||||
\(695\) | 52.4987 | 1.99139 | ||||||||
\(696\) | 20.7673 | 0.787181 | ||||||||
\(697\) | −9.84032 | −0.372729 | ||||||||
\(698\) | −77.9185 | −2.94926 | ||||||||
\(699\) | 8.30839 | 0.314252 | ||||||||
\(700\) | −14.5243 | −0.548966 | ||||||||
\(701\) | −15.8949 | −0.600343 | −0.300171 | − | 0.953885i | \(-0.597044\pi\) | ||||
−0.300171 | + | 0.953885i | \(0.597044\pi\) | |||||||
\(702\) | −3.10761 | −0.117289 | ||||||||
\(703\) | −7.78741 | −0.293708 | ||||||||
\(704\) | −13.0464 | −0.491704 | ||||||||
\(705\) | −67.8538 | −2.55552 | ||||||||
\(706\) | −3.62629 | −0.136477 | ||||||||
\(707\) | −4.71336 | −0.177264 | ||||||||
\(708\) | 39.1833 | 1.47260 | ||||||||
\(709\) | 23.6411 | 0.887862 | 0.443931 | − | 0.896061i | \(-0.353584\pi\) | ||||
0.443931 | + | 0.896061i | \(0.353584\pi\) | |||||||
\(710\) | −61.4872 | −2.30757 | ||||||||
\(711\) | 21.9468 | 0.823071 | ||||||||
\(712\) | −30.2531 | −1.13378 | ||||||||
\(713\) | 21.0964 | 0.790067 | ||||||||
\(714\) | 11.8520 | 0.443550 | ||||||||
\(715\) | −3.29754 | −0.123321 | ||||||||
\(716\) | 37.2986 | 1.39391 | ||||||||
\(717\) | 65.5769 | 2.44902 | ||||||||
\(718\) | 70.2016 | 2.61990 | ||||||||
\(719\) | −26.2428 | −0.978692 | −0.489346 | − | 0.872090i | \(-0.662764\pi\) | ||||
−0.489346 | + | 0.872090i | \(0.662764\pi\) | |||||||
\(720\) | 6.46605 | 0.240976 | ||||||||
\(721\) | −30.8228 | −1.14790 | ||||||||
\(722\) | 30.4766 | 1.13422 | ||||||||
\(723\) | −22.1166 | −0.822527 | ||||||||
\(724\) | 0.675005 | 0.0250864 | ||||||||
\(725\) | −7.70210 | −0.286049 | ||||||||
\(726\) | −5.71876 | −0.212243 | ||||||||
\(727\) | 16.9405 | 0.628289 | 0.314144 | − | 0.949375i | \(-0.398282\pi\) | ||||
0.314144 | + | 0.949375i | \(0.398282\pi\) | |||||||
\(728\) | 6.13214 | 0.227272 | ||||||||
\(729\) | −34.3221 | −1.27119 | ||||||||
\(730\) | −30.9912 | −1.14704 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −41.3922 | −1.52990 | ||||||||
\(733\) | −46.6879 | −1.72446 | −0.862228 | − | 0.506521i | \(-0.830931\pi\) | ||||
−0.862228 | + | 0.506521i | \(0.830931\pi\) | |||||||
\(734\) | −63.3732 | −2.33915 | ||||||||
\(735\) | 18.5262 | 0.683348 | ||||||||
\(736\) | 25.6299 | 0.944729 | ||||||||
\(737\) | −3.52986 | −0.130024 | ||||||||
\(738\) | 76.3578 | 2.81077 | ||||||||
\(739\) | 44.8070 | 1.64825 | 0.824126 | − | 0.566406i | \(-0.191667\pi\) | ||||
0.824126 | + | 0.566406i | \(0.191667\pi\) | |||||||
\(740\) | 27.6185 | 1.01528 | ||||||||
\(741\) | 7.25737 | 0.266606 | ||||||||
\(742\) | 7.11180 | 0.261082 | ||||||||
\(743\) | 8.45192 | 0.310071 | 0.155035 | − | 0.987909i | \(-0.450451\pi\) | ||||
0.155035 | + | 0.987909i | \(0.450451\pi\) | |||||||
\(744\) | −32.4219 | −1.18864 | ||||||||
\(745\) | −28.1725 | −1.03216 | ||||||||
\(746\) | −22.6822 | −0.830455 | ||||||||
\(747\) | 61.6812 | 2.25680 | ||||||||
\(748\) | 3.07467 | 0.112421 | ||||||||
\(749\) | 1.72505 | 0.0630320 | ||||||||
\(750\) | −41.9782 | −1.53283 | ||||||||
\(751\) | −38.5382 | −1.40628 | −0.703140 | − | 0.711052i | \(-0.748219\pi\) | ||||
−0.703140 | + | 0.711052i | \(0.748219\pi\) | |||||||
\(752\) | −6.89261 | −0.251348 | ||||||||
\(753\) | 36.7381 | 1.33881 | ||||||||
\(754\) | 9.30359 | 0.338817 | ||||||||
\(755\) | 2.54953 | 0.0927869 | ||||||||
\(756\) | −7.19227 | −0.261580 | ||||||||
\(757\) | 0.975598 | 0.0354587 | 0.0177294 | − | 0.999843i | \(-0.494356\pi\) | ||||
0.0177294 | + | 0.999843i | \(0.494356\pi\) | |||||||
\(758\) | −34.7353 | −1.26164 | ||||||||
\(759\) | 10.1519 | 0.368489 | ||||||||
\(760\) | 15.2778 | 0.554184 | ||||||||
\(761\) | 24.0879 | 0.873187 | 0.436593 | − | 0.899659i | \(-0.356185\pi\) | ||||
0.436593 | + | 0.899659i | \(0.356185\pi\) | |||||||
\(762\) | 70.3196 | 2.54741 | ||||||||
\(763\) | −4.32582 | −0.156605 | ||||||||
\(764\) | −22.2585 | −0.805286 | ||||||||
\(765\) | −9.29364 | −0.336012 | ||||||||
\(766\) | −35.1580 | −1.27031 | ||||||||
\(767\) | 6.13548 | 0.221540 | ||||||||
\(768\) | −28.5278 | −1.02941 | ||||||||
\(769\) | 15.0132 | 0.541391 | 0.270696 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270696 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(770\) | −12.5962 | −0.453935 | ||||||||
\(771\) | 71.4611 | 2.57361 | ||||||||
\(772\) | 37.2656 | 1.34122 | ||||||||
\(773\) | −10.0063 | −0.359903 | −0.179952 | − | 0.983675i | \(-0.557594\pi\) | ||||
−0.179952 | + | 0.983675i | \(0.557594\pi\) | |||||||
\(774\) | −7.75968 | −0.278916 | ||||||||
\(775\) | 12.0245 | 0.431934 | ||||||||
\(776\) | −20.6916 | −0.742786 | ||||||||
\(777\) | 17.5164 | 0.628396 | ||||||||
\(778\) | −70.4669 | −2.52636 | ||||||||
\(779\) | −23.0169 | −0.824665 | ||||||||
\(780\) | −25.7387 | −0.921593 | ||||||||
\(781\) | −10.1166 | −0.362001 | ||||||||
\(782\) | −9.00846 | −0.322142 | ||||||||
\(783\) | −3.81400 | −0.136301 | ||||||||
\(784\) | 1.88189 | 0.0672105 | ||||||||
\(785\) | −23.0413 | −0.822381 | ||||||||
\(786\) | 73.4317 | 2.61922 | ||||||||
\(787\) | −20.6709 | −0.736839 | −0.368420 | − | 0.929660i | \(-0.620101\pi\) | ||||
−0.368420 | + | 0.929660i | \(0.620101\pi\) | |||||||
\(788\) | −17.8316 | −0.635223 | ||||||||
\(789\) | 1.94511 | 0.0692476 | ||||||||
\(790\) | 38.7241 | 1.37774 | ||||||||
\(791\) | −1.56963 | −0.0558095 | ||||||||
\(792\) | −8.33909 | −0.296317 | ||||||||
\(793\) | −6.48136 | −0.230160 | ||||||||
\(794\) | −53.0859 | −1.88395 | ||||||||
\(795\) | −10.4335 | −0.370038 | ||||||||
\(796\) | 34.5135 | 1.22330 | ||||||||
\(797\) | −8.22826 | −0.291460 | −0.145730 | − | 0.989324i | \(-0.546553\pi\) | ||||
−0.145730 | + | 0.989324i | \(0.546553\pi\) | |||||||
\(798\) | 27.7223 | 0.981358 | ||||||||
\(799\) | 9.90673 | 0.350475 | ||||||||
\(800\) | 14.6085 | 0.516489 | ||||||||
\(801\) | 43.0459 | 1.52095 | ||||||||
\(802\) | −5.54300 | −0.195730 | ||||||||
\(803\) | −5.09905 | −0.179942 | ||||||||
\(804\) | −27.5521 | −0.971687 | ||||||||
\(805\) | 22.3605 | 0.788105 | ||||||||
\(806\) | −14.5248 | −0.511614 | ||||||||
\(807\) | 35.3276 | 1.24359 | ||||||||
\(808\) | −5.50578 | −0.193693 | ||||||||
\(809\) | 50.7744 | 1.78513 | 0.892567 | − | 0.450915i | \(-0.148902\pi\) | ||||
0.892567 | + | 0.450915i | \(0.148902\pi\) | |||||||
\(810\) | −45.3923 | −1.59492 | ||||||||
\(811\) | −5.39691 | −0.189511 | −0.0947556 | − | 0.995501i | \(-0.530207\pi\) | ||||
−0.0947556 | + | 0.995501i | \(0.530207\pi\) | |||||||
\(812\) | 21.5323 | 0.755636 | ||||||||
\(813\) | 66.5585 | 2.33431 | ||||||||
\(814\) | 7.49997 | 0.262874 | ||||||||
\(815\) | 18.7375 | 0.656345 | ||||||||
\(816\) | −1.76625 | −0.0618311 | ||||||||
\(817\) | 2.33904 | 0.0818326 | ||||||||
\(818\) | −40.7247 | −1.42391 | ||||||||
\(819\) | −8.72517 | −0.304882 | ||||||||
\(820\) | 81.6306 | 2.85067 | ||||||||
\(821\) | 4.24978 | 0.148318 | 0.0741591 | − | 0.997246i | \(-0.476373\pi\) | ||||
0.0741591 | + | 0.997246i | \(0.476373\pi\) | |||||||
\(822\) | 25.1262 | 0.876376 | ||||||||
\(823\) | 12.1155 | 0.422319 | 0.211160 | − | 0.977452i | \(-0.432276\pi\) | ||||
0.211160 | + | 0.977452i | \(0.432276\pi\) | |||||||
\(824\) | −36.0048 | −1.25429 | ||||||||
\(825\) | 5.78635 | 0.201455 | ||||||||
\(826\) | 23.4368 | 0.815471 | ||||||||
\(827\) | 19.0989 | 0.664135 | 0.332068 | − | 0.943256i | \(-0.392254\pi\) | ||||
0.332068 | + | 0.943256i | \(0.392254\pi\) | |||||||
\(828\) | 42.3531 | 1.47187 | ||||||||
\(829\) | 27.1789 | 0.943963 | 0.471981 | − | 0.881609i | \(-0.343539\pi\) | ||||
0.471981 | + | 0.881609i | \(0.343539\pi\) | |||||||
\(830\) | 108.833 | 3.77767 | ||||||||
\(831\) | −39.4632 | −1.36896 | ||||||||
\(832\) | −15.9453 | −0.552805 | ||||||||
\(833\) | −2.70484 | −0.0937171 | ||||||||
\(834\) | 111.277 | 3.85320 | ||||||||
\(835\) | 35.6911 | 1.23514 | ||||||||
\(836\) | 7.19176 | 0.248732 | ||||||||
\(837\) | 5.95442 | 0.205815 | ||||||||
\(838\) | −20.8218 | −0.719277 | ||||||||
\(839\) | 26.7474 | 0.923424 | 0.461712 | − | 0.887030i | \(-0.347235\pi\) | ||||
0.461712 | + | 0.887030i | \(0.347235\pi\) | |||||||
\(840\) | −34.3647 | −1.18569 | ||||||||
\(841\) | −17.5816 | −0.606262 | ||||||||
\(842\) | −69.7763 | −2.40465 | ||||||||
\(843\) | 54.4234 | 1.87444 | ||||||||
\(844\) | −50.3876 | −1.73441 | ||||||||
\(845\) | 31.0440 | 1.06795 | ||||||||
\(846\) | −76.8731 | −2.64295 | ||||||||
\(847\) | −2.07248 | −0.0712111 | ||||||||
\(848\) | −1.05984 | −0.0363950 | ||||||||
\(849\) | −17.3621 | −0.595865 | ||||||||
\(850\) | −5.13465 | −0.176117 | ||||||||
\(851\) | −13.3138 | −0.456392 | ||||||||
\(852\) | −78.9645 | −2.70528 | ||||||||
\(853\) | 25.5588 | 0.875118 | 0.437559 | − | 0.899190i | \(-0.355843\pi\) | ||||
0.437559 | + | 0.899190i | \(0.355843\pi\) | |||||||
\(854\) | −24.7580 | −0.847202 | ||||||||
\(855\) | −21.7382 | −0.743430 | ||||||||
\(856\) | 2.01507 | 0.0688738 | ||||||||
\(857\) | 22.8162 | 0.779386 | 0.389693 | − | 0.920945i | \(-0.372581\pi\) | ||||
0.389693 | + | 0.920945i | \(0.372581\pi\) | |||||||
\(858\) | −6.98950 | −0.238618 | ||||||||
\(859\) | −38.4709 | −1.31261 | −0.656304 | − | 0.754496i | \(-0.727881\pi\) | ||||
−0.656304 | + | 0.754496i | \(0.727881\pi\) | |||||||
\(860\) | −8.29553 | −0.282875 | ||||||||
\(861\) | 51.7723 | 1.76439 | ||||||||
\(862\) | −9.65834 | −0.328964 | ||||||||
\(863\) | −32.5189 | −1.10696 | −0.553478 | − | 0.832864i | \(-0.686700\pi\) | ||||
−0.553478 | + | 0.832864i | \(0.686700\pi\) | |||||||
\(864\) | 7.23398 | 0.246105 | ||||||||
\(865\) | −19.3055 | −0.656406 | ||||||||
\(866\) | 27.6449 | 0.939411 | ||||||||
\(867\) | 2.53862 | 0.0862162 | ||||||||
\(868\) | −33.6163 | −1.14101 | ||||||||
\(869\) | 6.37136 | 0.216134 | ||||||||
\(870\) | −52.1375 | −1.76763 | ||||||||
\(871\) | −4.31421 | −0.146182 | ||||||||
\(872\) | −5.05309 | −0.171119 | ||||||||
\(873\) | 29.4413 | 0.996436 | ||||||||
\(874\) | −21.0711 | −0.712742 | ||||||||
\(875\) | −15.2129 | −0.514289 | ||||||||
\(876\) | −39.8003 | −1.34473 | ||||||||
\(877\) | 0.292773 | 0.00988623 | 0.00494312 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494312 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(878\) | −25.6006 | −0.863978 | ||||||||
\(879\) | 61.7890 | 2.08409 | ||||||||
\(880\) | 1.87715 | 0.0632788 | ||||||||
\(881\) | 46.2265 | 1.55741 | 0.778706 | − | 0.627389i | \(-0.215876\pi\) | ||||
0.778706 | + | 0.627389i | \(0.215876\pi\) | |||||||
\(882\) | 20.9887 | 0.706726 | ||||||||
\(883\) | 1.37310 | 0.0462085 | 0.0231043 | − | 0.999733i | \(-0.492645\pi\) | ||||
0.0231043 | + | 0.999733i | \(0.492645\pi\) | |||||||
\(884\) | 3.75788 | 0.126391 | ||||||||
\(885\) | −34.3834 | −1.15579 | ||||||||
\(886\) | −81.4008 | −2.73471 | ||||||||
\(887\) | 16.0227 | 0.537990 | 0.268995 | − | 0.963142i | \(-0.413308\pi\) | ||||
0.268995 | + | 0.963142i | \(0.413308\pi\) | |||||||
\(888\) | 20.4613 | 0.686635 | ||||||||
\(889\) | 25.4838 | 0.854699 | ||||||||
\(890\) | 75.9523 | 2.54593 | ||||||||
\(891\) | −7.46849 | −0.250204 | ||||||||
\(892\) | −16.9217 | −0.566582 | ||||||||
\(893\) | 23.1722 | 0.775428 | ||||||||
\(894\) | −59.7147 | −1.99716 | ||||||||
\(895\) | −32.7295 | −1.09403 | ||||||||
\(896\) | −34.3437 | −1.14734 | ||||||||
\(897\) | 12.4076 | 0.414279 | ||||||||
\(898\) | 27.3953 | 0.914192 | ||||||||
\(899\) | −17.8264 | −0.594545 | ||||||||
\(900\) | 24.1404 | 0.804681 | ||||||||
\(901\) | 1.52330 | 0.0507486 | ||||||||
\(902\) | 22.1673 | 0.738091 | ||||||||
\(903\) | −5.26124 | −0.175083 | ||||||||
\(904\) | −1.83352 | −0.0609818 | ||||||||
\(905\) | −0.592317 | −0.0196893 | ||||||||
\(906\) | 5.40401 | 0.179536 | ||||||||
\(907\) | 9.61190 | 0.319158 | 0.159579 | − | 0.987185i | \(-0.448986\pi\) | ||||
0.159579 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(908\) | −38.9374 | −1.29218 | ||||||||
\(909\) | 7.83395 | 0.259836 | ||||||||
\(910\) | −15.3951 | −0.510343 | ||||||||
\(911\) | 29.8926 | 0.990385 | 0.495193 | − | 0.868783i | \(-0.335097\pi\) | ||||
0.495193 | + | 0.868783i | \(0.335097\pi\) | |||||||
\(912\) | −4.13132 | −0.136802 | ||||||||
\(913\) | 17.9066 | 0.592622 | ||||||||
\(914\) | −29.7956 | −0.985549 | ||||||||
\(915\) | 36.3217 | 1.20076 | ||||||||
\(916\) | 14.7403 | 0.487034 | ||||||||
\(917\) | 26.6116 | 0.878792 | ||||||||
\(918\) | −2.54262 | −0.0839190 | ||||||||
\(919\) | −28.3193 | −0.934166 | −0.467083 | − | 0.884213i | \(-0.654695\pi\) | ||||
−0.467083 | + | 0.884213i | \(0.654695\pi\) | |||||||
\(920\) | 26.1199 | 0.861146 | ||||||||
\(921\) | −12.4037 | −0.408717 | ||||||||
\(922\) | −41.4163 | −1.36397 | ||||||||
\(923\) | −12.3646 | −0.406985 | ||||||||
\(924\) | −16.1766 | −0.532170 | ||||||||
\(925\) | −7.58861 | −0.249512 | ||||||||
\(926\) | 49.7071 | 1.63348 | ||||||||
\(927\) | 51.2297 | 1.68261 | ||||||||
\(928\) | −21.6572 | −0.710932 | ||||||||
\(929\) | −4.37703 | −0.143606 | −0.0718029 | − | 0.997419i | \(-0.522875\pi\) | ||||
−0.0718029 | + | 0.997419i | \(0.522875\pi\) | |||||||
\(930\) | 81.3972 | 2.66912 | ||||||||
\(931\) | −6.32672 | −0.207350 | ||||||||
\(932\) | 10.0628 | 0.329616 | ||||||||
\(933\) | 21.0215 | 0.688214 | ||||||||
\(934\) | −22.0199 | −0.720514 | ||||||||
\(935\) | −2.69802 | −0.0882348 | ||||||||
\(936\) | −10.1921 | −0.333138 | ||||||||
\(937\) | −17.3124 | −0.565570 | −0.282785 | − | 0.959183i | \(-0.591258\pi\) | ||||
−0.282785 | + | 0.959183i | \(0.591258\pi\) | |||||||
\(938\) | −16.4798 | −0.538084 | ||||||||
\(939\) | 45.9166 | 1.49843 | ||||||||
\(940\) | −82.1815 | −2.68047 | ||||||||
\(941\) | 35.1224 | 1.14496 | 0.572479 | − | 0.819920i | \(-0.305982\pi\) | ||||
0.572479 | + | 0.819920i | \(0.305982\pi\) | |||||||
\(942\) | −48.8387 | −1.59125 | ||||||||
\(943\) | −39.3510 | −1.28145 | ||||||||
\(944\) | −3.49268 | −0.113677 | ||||||||
\(945\) | 6.31122 | 0.205304 | ||||||||
\(946\) | −2.25270 | −0.0732417 | ||||||||
\(947\) | 41.0402 | 1.33363 | 0.666813 | − | 0.745225i | \(-0.267658\pi\) | ||||
0.666813 | + | 0.745225i | \(0.267658\pi\) | |||||||
\(948\) | 49.7312 | 1.61519 | ||||||||
\(949\) | −6.23209 | −0.202302 | ||||||||
\(950\) | −12.0101 | −0.389660 | ||||||||
\(951\) | 16.7836 | 0.544245 | ||||||||
\(952\) | 5.01728 | 0.162611 | ||||||||
\(953\) | 34.0470 | 1.10289 | 0.551445 | − | 0.834211i | \(-0.314077\pi\) | ||||
0.551445 | + | 0.834211i | \(0.314077\pi\) | |||||||
\(954\) | −11.8203 | −0.382698 | ||||||||
\(955\) | 19.5319 | 0.632037 | ||||||||
\(956\) | 79.4239 | 2.56875 | ||||||||
\(957\) | −8.57829 | −0.277297 | ||||||||
\(958\) | −75.1392 | −2.42764 | ||||||||
\(959\) | 9.10571 | 0.294039 | ||||||||
\(960\) | 89.3581 | 2.88402 | ||||||||
\(961\) | −3.16933 | −0.102236 | ||||||||
\(962\) | 9.16650 | 0.295540 | ||||||||
\(963\) | −2.86716 | −0.0923931 | ||||||||
\(964\) | −26.7867 | −0.862741 | ||||||||
\(965\) | −32.7005 | −1.05267 | ||||||||
\(966\) | 47.3957 | 1.52493 | ||||||||
\(967\) | 16.8578 | 0.542110 | 0.271055 | − | 0.962564i | \(-0.412628\pi\) | ||||
0.271055 | + | 0.962564i | \(0.412628\pi\) | |||||||
\(968\) | −2.42091 | −0.0778109 | ||||||||
\(969\) | 5.93794 | 0.190754 | ||||||||
\(970\) | 51.9477 | 1.66794 | ||||||||
\(971\) | 24.9096 | 0.799387 | 0.399694 | − | 0.916649i | \(-0.369117\pi\) | ||||
0.399694 | + | 0.916649i | \(0.369117\pi\) | |||||||
\(972\) | −68.7059 | −2.20374 | ||||||||
\(973\) | 40.3267 | 1.29281 | ||||||||
\(974\) | −63.6318 | −2.03889 | ||||||||
\(975\) | 7.07211 | 0.226489 | ||||||||
\(976\) | 3.68957 | 0.118100 | ||||||||
\(977\) | −38.2055 | −1.22230 | −0.611150 | − | 0.791515i | \(-0.709293\pi\) | ||||
−0.611150 | + | 0.791515i | \(0.709293\pi\) | |||||||
\(978\) | 39.7162 | 1.26998 | ||||||||
\(979\) | 12.4966 | 0.399393 | ||||||||
\(980\) | 22.4381 | 0.716758 | ||||||||
\(981\) | 7.18984 | 0.229554 | ||||||||
\(982\) | −49.7675 | −1.58814 | ||||||||
\(983\) | −20.6473 | −0.658547 | −0.329273 | − | 0.944235i | \(-0.606804\pi\) | ||||
−0.329273 | + | 0.944235i | \(0.606804\pi\) | |||||||
\(984\) | 60.4764 | 1.92792 | ||||||||
\(985\) | 15.6472 | 0.498561 | ||||||||
\(986\) | 7.61213 | 0.242420 | ||||||||
\(987\) | −52.1217 | −1.65905 | ||||||||
\(988\) | 8.78981 | 0.279641 | ||||||||
\(989\) | 3.99896 | 0.127159 | ||||||||
\(990\) | 20.9358 | 0.665383 | ||||||||
\(991\) | −10.5298 | −0.334490 | −0.167245 | − | 0.985915i | \(-0.553487\pi\) | ||||
−0.167245 | + | 0.985915i | \(0.553487\pi\) | |||||||
\(992\) | 33.8113 | 1.07351 | ||||||||
\(993\) | −74.9785 | −2.37937 | ||||||||
\(994\) | −47.2312 | −1.49808 | ||||||||
\(995\) | −30.2856 | −0.960118 | ||||||||
\(996\) | 139.769 | 4.42874 | ||||||||
\(997\) | −19.6324 | −0.621766 | −0.310883 | − | 0.950448i | \(-0.600625\pi\) | ||||
−0.310883 | + | 0.950448i | \(0.600625\pi\) | |||||||
\(998\) | −66.1472 | −2.09385 | ||||||||
\(999\) | −3.75780 | −0.118892 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8041.2.a.j.1.12 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.12 | ✓ | 82 | 1.1 | even | 1 | trivial |