Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50194 | −1.76914 | −0.884569 | − | 0.466409i | \(-0.845547\pi\) | ||||
−0.884569 | + | 0.466409i | \(0.845547\pi\) | |||||||
\(3\) | −1.32701 | −0.766152 | −0.383076 | − | 0.923717i | \(-0.625135\pi\) | ||||
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(4\) | 4.25970 | 2.12985 | ||||||||
\(5\) | 0.884945 | 0.395760 | 0.197880 | − | 0.980226i | \(-0.436594\pi\) | ||||
0.197880 | + | 0.980226i | \(0.436594\pi\) | |||||||
\(6\) | 3.32011 | 1.35543 | ||||||||
\(7\) | 3.50232 | 1.32375 | 0.661876 | − | 0.749613i | \(-0.269760\pi\) | ||||
0.661876 | + | 0.749613i | \(0.269760\pi\) | |||||||
\(8\) | −5.65363 | −1.99886 | ||||||||
\(9\) | −1.23903 | −0.413011 | ||||||||
\(10\) | −2.21408 | −0.700153 | ||||||||
\(11\) | −4.48523 | −1.35235 | −0.676174 | − | 0.736742i | \(-0.736363\pi\) | ||||
−0.676174 | + | 0.736742i | \(0.736363\pi\) | |||||||
\(12\) | −5.65268 | −1.63179 | ||||||||
\(13\) | 5.37759 | 1.49148 | 0.745738 | − | 0.666240i | \(-0.232097\pi\) | ||||
0.745738 | + | 0.666240i | \(0.232097\pi\) | |||||||
\(14\) | −8.76259 | −2.34190 | ||||||||
\(15\) | −1.17434 | −0.303212 | ||||||||
\(16\) | 5.62563 | 1.40641 | ||||||||
\(17\) | −1.17262 | −0.284402 | −0.142201 | − | 0.989838i | \(-0.545418\pi\) | ||||
−0.142201 | + | 0.989838i | \(0.545418\pi\) | |||||||
\(18\) | 3.09999 | 0.730674 | ||||||||
\(19\) | −4.42541 | −1.01526 | −0.507630 | − | 0.861575i | \(-0.669478\pi\) | ||||
−0.507630 | + | 0.861575i | \(0.669478\pi\) | |||||||
\(20\) | 3.76960 | 0.842908 | ||||||||
\(21\) | −4.64763 | −1.01420 | ||||||||
\(22\) | 11.2218 | 2.39249 | ||||||||
\(23\) | 4.56091 | 0.951015 | 0.475507 | − | 0.879712i | \(-0.342264\pi\) | ||||
0.475507 | + | 0.879712i | \(0.342264\pi\) | |||||||
\(24\) | 7.50244 | 1.53143 | ||||||||
\(25\) | −4.21687 | −0.843374 | ||||||||
\(26\) | −13.4544 | −2.63863 | ||||||||
\(27\) | 5.62526 | 1.08258 | ||||||||
\(28\) | 14.9188 | 2.81939 | ||||||||
\(29\) | −3.23052 | −0.599893 | −0.299947 | − | 0.953956i | \(-0.596969\pi\) | ||||
−0.299947 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(30\) | 2.93811 | 0.536424 | ||||||||
\(31\) | 4.33076 | 0.777828 | 0.388914 | − | 0.921274i | \(-0.372850\pi\) | ||||
0.388914 | + | 0.921274i | \(0.372850\pi\) | |||||||
\(32\) | −2.76773 | −0.489270 | ||||||||
\(33\) | 5.95196 | 1.03610 | ||||||||
\(34\) | 2.93382 | 0.503147 | ||||||||
\(35\) | 3.09936 | 0.523888 | ||||||||
\(36\) | −5.27791 | −0.879651 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 11.0721 | 1.79613 | ||||||||
\(39\) | −7.13614 | −1.14270 | ||||||||
\(40\) | −5.00315 | −0.791067 | ||||||||
\(41\) | 7.45389 | 1.16410 | 0.582051 | − | 0.813153i | \(-0.302251\pi\) | ||||
0.582051 | + | 0.813153i | \(0.302251\pi\) | |||||||
\(42\) | 11.6281 | 1.79425 | ||||||||
\(43\) | −1.49518 | −0.228012 | −0.114006 | − | 0.993480i | \(-0.536368\pi\) | ||||
−0.114006 | + | 0.993480i | \(0.536368\pi\) | |||||||
\(44\) | −19.1057 | −2.88030 | ||||||||
\(45\) | −1.09648 | −0.163453 | ||||||||
\(46\) | −11.4111 | −1.68248 | ||||||||
\(47\) | −6.64711 | −0.969581 | −0.484790 | − | 0.874630i | \(-0.661104\pi\) | ||||
−0.484790 | + | 0.874630i | \(0.661104\pi\) | |||||||
\(48\) | −7.46529 | −1.07752 | ||||||||
\(49\) | 5.26625 | 0.752321 | ||||||||
\(50\) | 10.5504 | 1.49205 | ||||||||
\(51\) | 1.55608 | 0.217895 | ||||||||
\(52\) | 22.9069 | 3.17662 | ||||||||
\(53\) | −4.00673 | −0.550367 | −0.275184 | − | 0.961392i | \(-0.588739\pi\) | ||||
−0.275184 | + | 0.961392i | \(0.588739\pi\) | |||||||
\(54\) | −14.0740 | −1.91524 | ||||||||
\(55\) | −3.96918 | −0.535205 | ||||||||
\(56\) | −19.8008 | −2.64599 | ||||||||
\(57\) | 5.87258 | 0.777843 | ||||||||
\(58\) | 8.08257 | 1.06129 | ||||||||
\(59\) | −12.1204 | −1.57794 | −0.788971 | − | 0.614430i | \(-0.789386\pi\) | ||||
−0.788971 | + | 0.614430i | \(0.789386\pi\) | |||||||
\(60\) | −5.00231 | −0.645796 | ||||||||
\(61\) | −7.69862 | −0.985708 | −0.492854 | − | 0.870112i | \(-0.664046\pi\) | ||||
−0.492854 | + | 0.870112i | \(0.664046\pi\) | |||||||
\(62\) | −10.8353 | −1.37608 | ||||||||
\(63\) | −4.33949 | −0.546725 | ||||||||
\(64\) | −4.32657 | −0.540821 | ||||||||
\(65\) | 4.75888 | 0.590266 | ||||||||
\(66\) | −14.8915 | −1.83301 | ||||||||
\(67\) | 10.7112 | 1.30858 | 0.654290 | − | 0.756244i | \(-0.272967\pi\) | ||||
0.654290 | + | 0.756244i | \(0.272967\pi\) | |||||||
\(68\) | −4.99501 | −0.605734 | ||||||||
\(69\) | −6.05239 | −0.728622 | ||||||||
\(70\) | −7.75442 | −0.926830 | ||||||||
\(71\) | −2.74529 | −0.325806 | −0.162903 | − | 0.986642i | \(-0.552086\pi\) | ||||
−0.162903 | + | 0.986642i | \(0.552086\pi\) | |||||||
\(72\) | 7.00503 | 0.825551 | ||||||||
\(73\) | −1.71574 | −0.200812 | −0.100406 | − | 0.994947i | \(-0.532014\pi\) | ||||
−0.100406 | + | 0.994947i | \(0.532014\pi\) | |||||||
\(74\) | −2.50194 | −0.290844 | ||||||||
\(75\) | 5.59585 | 0.646153 | ||||||||
\(76\) | −18.8509 | −2.16235 | ||||||||
\(77\) | −15.7087 | −1.79017 | ||||||||
\(78\) | 17.8542 | 2.02159 | ||||||||
\(79\) | 1.00469 | 0.113037 | 0.0565185 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565185 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(80\) | 4.97837 | 0.556599 | ||||||||
\(81\) | −3.74770 | −0.416411 | ||||||||
\(82\) | −18.6492 | −2.05946 | ||||||||
\(83\) | −1.43104 | −0.157077 | −0.0785384 | − | 0.996911i | \(-0.525025\pi\) | ||||
−0.0785384 | + | 0.996911i | \(0.525025\pi\) | |||||||
\(84\) | −19.7975 | −2.16008 | ||||||||
\(85\) | −1.03771 | −0.112555 | ||||||||
\(86\) | 3.74084 | 0.403385 | ||||||||
\(87\) | 4.28695 | 0.459609 | ||||||||
\(88\) | 25.3578 | 2.70315 | ||||||||
\(89\) | −3.22123 | −0.341450 | −0.170725 | − | 0.985319i | \(-0.554611\pi\) | ||||
−0.170725 | + | 0.985319i | \(0.554611\pi\) | |||||||
\(90\) | 2.74332 | 0.289171 | ||||||||
\(91\) | 18.8341 | 1.97435 | ||||||||
\(92\) | 19.4281 | 2.02552 | ||||||||
\(93\) | −5.74698 | −0.595934 | ||||||||
\(94\) | 16.6307 | 1.71532 | ||||||||
\(95\) | −3.91625 | −0.401799 | ||||||||
\(96\) | 3.67282 | 0.374855 | ||||||||
\(97\) | 2.13007 | 0.216276 | 0.108138 | − | 0.994136i | \(-0.465511\pi\) | ||||
0.108138 | + | 0.994136i | \(0.465511\pi\) | |||||||
\(98\) | −13.1758 | −1.33096 | ||||||||
\(99\) | 5.55735 | 0.558535 | ||||||||
\(100\) | −17.9626 | −1.79626 | ||||||||
\(101\) | 3.08886 | 0.307353 | 0.153677 | − | 0.988121i | \(-0.450889\pi\) | ||||
0.153677 | + | 0.988121i | \(0.450889\pi\) | |||||||
\(102\) | −3.89323 | −0.385487 | ||||||||
\(103\) | −11.5266 | −1.13575 | −0.567875 | − | 0.823115i | \(-0.692234\pi\) | ||||
−0.567875 | + | 0.823115i | \(0.692234\pi\) | |||||||
\(104\) | −30.4029 | −2.98125 | ||||||||
\(105\) | −4.11290 | −0.401378 | ||||||||
\(106\) | 10.0246 | 0.973676 | ||||||||
\(107\) | 0.543476 | 0.0525399 | 0.0262699 | − | 0.999655i | \(-0.491637\pi\) | ||||
0.0262699 | + | 0.999655i | \(0.491637\pi\) | |||||||
\(108\) | 23.9619 | 2.30573 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 9.93066 | 0.946851 | ||||||||
\(111\) | −1.32701 | −0.125955 | ||||||||
\(112\) | 19.7028 | 1.86174 | ||||||||
\(113\) | −12.0434 | −1.13295 | −0.566475 | − | 0.824079i | \(-0.691693\pi\) | ||||
−0.566475 | + | 0.824079i | \(0.691693\pi\) | |||||||
\(114\) | −14.6928 | −1.37611 | ||||||||
\(115\) | 4.03615 | 0.376373 | ||||||||
\(116\) | −13.7611 | −1.27768 | ||||||||
\(117\) | −6.66302 | −0.615996 | ||||||||
\(118\) | 30.3245 | 2.79160 | ||||||||
\(119\) | −4.10689 | −0.376478 | ||||||||
\(120\) | 6.63925 | 0.606078 | ||||||||
\(121\) | 9.11730 | 0.828845 | ||||||||
\(122\) | 19.2615 | 1.74385 | ||||||||
\(123\) | −9.89141 | −0.891879 | ||||||||
\(124\) | 18.4477 | 1.65666 | ||||||||
\(125\) | −8.15643 | −0.729533 | ||||||||
\(126\) | 10.8571 | 0.967231 | ||||||||
\(127\) | −3.51331 | −0.311756 | −0.155878 | − | 0.987776i | \(-0.549821\pi\) | ||||
−0.155878 | + | 0.987776i | \(0.549821\pi\) | |||||||
\(128\) | 16.3603 | 1.44606 | ||||||||
\(129\) | 1.98412 | 0.174692 | ||||||||
\(130\) | −11.9064 | −1.04426 | ||||||||
\(131\) | −17.9215 | −1.56581 | −0.782904 | − | 0.622142i | \(-0.786263\pi\) | ||||
−0.782904 | + | 0.622142i | \(0.786263\pi\) | |||||||
\(132\) | 25.3536 | 2.20675 | ||||||||
\(133\) | −15.4992 | −1.34395 | ||||||||
\(134\) | −26.7987 | −2.31506 | ||||||||
\(135\) | 4.97805 | 0.428442 | ||||||||
\(136\) | 6.62956 | 0.568480 | ||||||||
\(137\) | 3.11898 | 0.266473 | 0.133236 | − | 0.991084i | \(-0.457463\pi\) | ||||
0.133236 | + | 0.991084i | \(0.457463\pi\) | |||||||
\(138\) | 15.1427 | 1.28903 | ||||||||
\(139\) | 11.9092 | 1.01013 | 0.505064 | − | 0.863082i | \(-0.331469\pi\) | ||||
0.505064 | + | 0.863082i | \(0.331469\pi\) | |||||||
\(140\) | 13.2023 | 1.11580 | ||||||||
\(141\) | 8.82081 | 0.742846 | ||||||||
\(142\) | 6.86855 | 0.576396 | ||||||||
\(143\) | −24.1197 | −2.01699 | ||||||||
\(144\) | −6.97034 | −0.580862 | ||||||||
\(145\) | −2.85884 | −0.237413 | ||||||||
\(146\) | 4.29267 | 0.355264 | ||||||||
\(147\) | −6.98839 | −0.576392 | ||||||||
\(148\) | 4.25970 | 0.350145 | ||||||||
\(149\) | −18.7177 | −1.53341 | −0.766705 | − | 0.642000i | \(-0.778105\pi\) | ||||
−0.766705 | + | 0.642000i | \(0.778105\pi\) | |||||||
\(150\) | −14.0005 | −1.14313 | ||||||||
\(151\) | −4.02808 | −0.327801 | −0.163900 | − | 0.986477i | \(-0.552408\pi\) | ||||
−0.163900 | + | 0.986477i | \(0.552408\pi\) | |||||||
\(152\) | 25.0196 | 2.02936 | ||||||||
\(153\) | 1.45292 | 0.117461 | ||||||||
\(154\) | 39.3022 | 3.16707 | ||||||||
\(155\) | 3.83249 | 0.307833 | ||||||||
\(156\) | −30.3978 | −2.43377 | ||||||||
\(157\) | 23.6495 | 1.88743 | 0.943717 | − | 0.330754i | \(-0.107303\pi\) | ||||
0.943717 | + | 0.330754i | \(0.107303\pi\) | |||||||
\(158\) | −2.51368 | −0.199978 | ||||||||
\(159\) | 5.31699 | 0.421665 | ||||||||
\(160\) | −2.44929 | −0.193633 | ||||||||
\(161\) | 15.9738 | 1.25891 | ||||||||
\(162\) | 9.37651 | 0.736688 | ||||||||
\(163\) | 6.03174 | 0.472442 | 0.236221 | − | 0.971699i | \(-0.424091\pi\) | ||||
0.236221 | + | 0.971699i | \(0.424091\pi\) | |||||||
\(164\) | 31.7513 | 2.47936 | ||||||||
\(165\) | 5.26716 | 0.410048 | ||||||||
\(166\) | 3.58037 | 0.277891 | ||||||||
\(167\) | −20.1750 | −1.56119 | −0.780593 | − | 0.625040i | \(-0.785083\pi\) | ||||
−0.780593 | + | 0.625040i | \(0.785083\pi\) | |||||||
\(168\) | 26.2760 | 2.02723 | ||||||||
\(169\) | 15.9185 | 1.22450 | ||||||||
\(170\) | 2.59627 | 0.199125 | ||||||||
\(171\) | 5.48323 | 0.419313 | ||||||||
\(172\) | −6.36900 | −0.485631 | ||||||||
\(173\) | 25.8441 | 1.96489 | 0.982446 | − | 0.186546i | \(-0.0597293\pi\) | ||||
0.982446 | + | 0.186546i | \(0.0597293\pi\) | |||||||
\(174\) | −10.7257 | −0.813112 | ||||||||
\(175\) | −14.7688 | −1.11642 | ||||||||
\(176\) | −25.2322 | −1.90195 | ||||||||
\(177\) | 16.0839 | 1.20894 | ||||||||
\(178\) | 8.05932 | 0.604072 | ||||||||
\(179\) | 23.1020 | 1.72672 | 0.863360 | − | 0.504588i | \(-0.168355\pi\) | ||||
0.863360 | + | 0.504588i | \(0.168355\pi\) | |||||||
\(180\) | −4.67066 | −0.348130 | ||||||||
\(181\) | 24.1166 | 1.79257 | 0.896285 | − | 0.443478i | \(-0.146256\pi\) | ||||
0.896285 | + | 0.443478i | \(0.146256\pi\) | |||||||
\(182\) | −47.1216 | −3.49289 | ||||||||
\(183\) | 10.2162 | 0.755202 | ||||||||
\(184\) | −25.7857 | −1.90094 | ||||||||
\(185\) | 0.884945 | 0.0650625 | ||||||||
\(186\) | 14.3786 | 1.05429 | ||||||||
\(187\) | 5.25947 | 0.384611 | ||||||||
\(188\) | −28.3147 | −2.06506 | ||||||||
\(189\) | 19.7015 | 1.43307 | ||||||||
\(190\) | 9.79821 | 0.710837 | ||||||||
\(191\) | −5.42464 | −0.392513 | −0.196257 | − | 0.980553i | \(-0.562879\pi\) | ||||
−0.196257 | + | 0.980553i | \(0.562879\pi\) | |||||||
\(192\) | 5.74142 | 0.414351 | ||||||||
\(193\) | −4.26746 | −0.307179 | −0.153589 | − | 0.988135i | \(-0.549083\pi\) | ||||
−0.153589 | + | 0.988135i | \(0.549083\pi\) | |||||||
\(194\) | −5.32930 | −0.382621 | ||||||||
\(195\) | −6.31510 | −0.452233 | ||||||||
\(196\) | 22.4326 | 1.60233 | ||||||||
\(197\) | 3.27902 | 0.233620 | 0.116810 | − | 0.993154i | \(-0.462733\pi\) | ||||
0.116810 | + | 0.993154i | \(0.462733\pi\) | |||||||
\(198\) | −13.9042 | −0.988125 | ||||||||
\(199\) | 1.00345 | 0.0711324 | 0.0355662 | − | 0.999367i | \(-0.488677\pi\) | ||||
0.0355662 | + | 0.999367i | \(0.488677\pi\) | |||||||
\(200\) | 23.8406 | 1.68579 | ||||||||
\(201\) | −14.2139 | −1.00257 | ||||||||
\(202\) | −7.72814 | −0.543750 | ||||||||
\(203\) | −11.3143 | −0.794110 | ||||||||
\(204\) | 6.62845 | 0.464084 | ||||||||
\(205\) | 6.59628 | 0.460704 | ||||||||
\(206\) | 28.8388 | 2.00930 | ||||||||
\(207\) | −5.65112 | −0.392780 | ||||||||
\(208\) | 30.2523 | 2.09762 | ||||||||
\(209\) | 19.8490 | 1.37298 | ||||||||
\(210\) | 10.2902 | 0.710093 | ||||||||
\(211\) | −7.73143 | −0.532254 | −0.266127 | − | 0.963938i | \(-0.585744\pi\) | ||||
−0.266127 | + | 0.963938i | \(0.585744\pi\) | |||||||
\(212\) | −17.0675 | −1.17220 | ||||||||
\(213\) | 3.64304 | 0.249617 | ||||||||
\(214\) | −1.35974 | −0.0929502 | ||||||||
\(215\) | −1.32315 | −0.0902380 | ||||||||
\(216\) | −31.8031 | −2.16393 | ||||||||
\(217\) | 15.1677 | 1.02965 | ||||||||
\(218\) | −2.50194 | −0.169453 | ||||||||
\(219\) | 2.27681 | 0.153852 | ||||||||
\(220\) | −16.9075 | −1.13991 | ||||||||
\(221\) | −6.30587 | −0.424179 | ||||||||
\(222\) | 3.32011 | 0.222831 | ||||||||
\(223\) | −23.6653 | −1.58475 | −0.792373 | − | 0.610036i | \(-0.791155\pi\) | ||||
−0.792373 | + | 0.610036i | \(0.791155\pi\) | |||||||
\(224\) | −9.69348 | −0.647673 | ||||||||
\(225\) | 5.22484 | 0.348323 | ||||||||
\(226\) | 30.1319 | 2.00435 | ||||||||
\(227\) | 14.8729 | 0.987149 | 0.493574 | − | 0.869704i | \(-0.335690\pi\) | ||||
0.493574 | + | 0.869704i | \(0.335690\pi\) | |||||||
\(228\) | 25.0154 | 1.65669 | ||||||||
\(229\) | −19.5755 | −1.29359 | −0.646794 | − | 0.762665i | \(-0.723890\pi\) | ||||
−0.646794 | + | 0.762665i | \(0.723890\pi\) | |||||||
\(230\) | −10.0982 | −0.665856 | ||||||||
\(231\) | 20.8457 | 1.37155 | ||||||||
\(232\) | 18.2642 | 1.19910 | ||||||||
\(233\) | −5.69124 | −0.372846 | −0.186423 | − | 0.982470i | \(-0.559689\pi\) | ||||
−0.186423 | + | 0.982470i | \(0.559689\pi\) | |||||||
\(234\) | 16.6705 | 1.08978 | ||||||||
\(235\) | −5.88233 | −0.383721 | ||||||||
\(236\) | −51.6293 | −3.36078 | ||||||||
\(237\) | −1.33324 | −0.0866035 | ||||||||
\(238\) | 10.2752 | 0.666042 | ||||||||
\(239\) | 6.60256 | 0.427084 | 0.213542 | − | 0.976934i | \(-0.431500\pi\) | ||||
0.213542 | + | 0.976934i | \(0.431500\pi\) | |||||||
\(240\) | −6.60637 | −0.426440 | ||||||||
\(241\) | 0.513070 | 0.0330497 | 0.0165249 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165249 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(242\) | −22.8109 | −1.46634 | ||||||||
\(243\) | −11.9025 | −0.763547 | ||||||||
\(244\) | −32.7938 | −2.09941 | ||||||||
\(245\) | 4.66034 | 0.297738 | ||||||||
\(246\) | 24.7477 | 1.57786 | ||||||||
\(247\) | −23.7981 | −1.51423 | ||||||||
\(248\) | −24.4845 | −1.55477 | ||||||||
\(249\) | 1.89901 | 0.120345 | ||||||||
\(250\) | 20.4069 | 1.29064 | ||||||||
\(251\) | 10.6401 | 0.671594 | 0.335797 | − | 0.941934i | \(-0.390994\pi\) | ||||
0.335797 | + | 0.941934i | \(0.390994\pi\) | |||||||
\(252\) | −18.4849 | −1.16444 | ||||||||
\(253\) | −20.4567 | −1.28610 | ||||||||
\(254\) | 8.79009 | 0.551539 | ||||||||
\(255\) | 1.37705 | 0.0862342 | ||||||||
\(256\) | −32.2793 | −2.01745 | ||||||||
\(257\) | −21.9428 | −1.36876 | −0.684379 | − | 0.729127i | \(-0.739926\pi\) | ||||
−0.684379 | + | 0.729127i | \(0.739926\pi\) | |||||||
\(258\) | −4.96414 | −0.309054 | ||||||||
\(259\) | 3.50232 | 0.217624 | ||||||||
\(260\) | 20.2714 | 1.25718 | ||||||||
\(261\) | 4.00273 | 0.247763 | ||||||||
\(262\) | 44.8385 | 2.77013 | ||||||||
\(263\) | −15.1740 | −0.935668 | −0.467834 | − | 0.883816i | \(-0.654966\pi\) | ||||
−0.467834 | + | 0.883816i | \(0.654966\pi\) | |||||||
\(264\) | −33.6502 | −2.07103 | ||||||||
\(265\) | −3.54574 | −0.217813 | ||||||||
\(266\) | 38.7781 | 2.37764 | ||||||||
\(267\) | 4.27462 | 0.261602 | ||||||||
\(268\) | 45.6264 | 2.78708 | ||||||||
\(269\) | 0.441830 | 0.0269388 | 0.0134694 | − | 0.999909i | \(-0.495712\pi\) | ||||
0.0134694 | + | 0.999909i | \(0.495712\pi\) | |||||||
\(270\) | −12.4548 | −0.757973 | ||||||||
\(271\) | −16.5646 | −1.00623 | −0.503113 | − | 0.864221i | \(-0.667812\pi\) | ||||
−0.503113 | + | 0.864221i | \(0.667812\pi\) | |||||||
\(272\) | −6.59673 | −0.399985 | ||||||||
\(273\) | −24.9931 | −1.51265 | ||||||||
\(274\) | −7.80350 | −0.471427 | ||||||||
\(275\) | 18.9136 | 1.14054 | ||||||||
\(276\) | −25.7813 | −1.55185 | ||||||||
\(277\) | 18.7002 | 1.12358 | 0.561792 | − | 0.827279i | \(-0.310112\pi\) | ||||
0.561792 | + | 0.827279i | \(0.310112\pi\) | |||||||
\(278\) | −29.7962 | −1.78706 | ||||||||
\(279\) | −5.36596 | −0.321251 | ||||||||
\(280\) | −17.5226 | −1.04718 | ||||||||
\(281\) | 7.59191 | 0.452896 | 0.226448 | − | 0.974023i | \(-0.427289\pi\) | ||||
0.226448 | + | 0.974023i | \(0.427289\pi\) | |||||||
\(282\) | −22.0691 | −1.31420 | ||||||||
\(283\) | −10.4888 | −0.623496 | −0.311748 | − | 0.950165i | \(-0.600914\pi\) | ||||
−0.311748 | + | 0.950165i | \(0.600914\pi\) | |||||||
\(284\) | −11.6941 | −0.693917 | ||||||||
\(285\) | 5.19692 | 0.307839 | ||||||||
\(286\) | 60.3461 | 3.56834 | ||||||||
\(287\) | 26.1059 | 1.54098 | ||||||||
\(288\) | 3.42931 | 0.202074 | ||||||||
\(289\) | −15.6250 | −0.919115 | ||||||||
\(290\) | 7.15263 | 0.420017 | ||||||||
\(291\) | −2.82663 | −0.165700 | ||||||||
\(292\) | −7.30853 | −0.427699 | ||||||||
\(293\) | −8.13804 | −0.475429 | −0.237715 | − | 0.971335i | \(-0.576398\pi\) | ||||
−0.237715 | + | 0.971335i | \(0.576398\pi\) | |||||||
\(294\) | 17.4845 | 1.01972 | ||||||||
\(295\) | −10.7259 | −0.624486 | ||||||||
\(296\) | −5.65363 | −0.328610 | ||||||||
\(297\) | −25.2306 | −1.46403 | ||||||||
\(298\) | 46.8304 | 2.71281 | ||||||||
\(299\) | 24.5267 | 1.41842 | ||||||||
\(300\) | 23.8366 | 1.37621 | ||||||||
\(301\) | −5.23658 | −0.301832 | ||||||||
\(302\) | 10.0780 | 0.579925 | ||||||||
\(303\) | −4.09896 | −0.235479 | ||||||||
\(304\) | −24.8957 | −1.42787 | ||||||||
\(305\) | −6.81286 | −0.390103 | ||||||||
\(306\) | −3.63511 | −0.207805 | ||||||||
\(307\) | 3.43091 | 0.195812 | 0.0979061 | − | 0.995196i | \(-0.468786\pi\) | ||||
0.0979061 | + | 0.995196i | \(0.468786\pi\) | |||||||
\(308\) | −66.9144 | −3.81280 | ||||||||
\(309\) | 15.2960 | 0.870157 | ||||||||
\(310\) | −9.58865 | −0.544599 | ||||||||
\(311\) | 23.0456 | 1.30679 | 0.653397 | − | 0.757015i | \(-0.273343\pi\) | ||||
0.653397 | + | 0.757015i | \(0.273343\pi\) | |||||||
\(312\) | 40.3451 | 2.28409 | ||||||||
\(313\) | −15.0625 | −0.851381 | −0.425690 | − | 0.904869i | \(-0.639969\pi\) | ||||
−0.425690 | + | 0.904869i | \(0.639969\pi\) | |||||||
\(314\) | −59.1696 | −3.33913 | ||||||||
\(315\) | −3.84021 | −0.216372 | ||||||||
\(316\) | 4.27969 | 0.240752 | ||||||||
\(317\) | −2.32553 | −0.130615 | −0.0653074 | − | 0.997865i | \(-0.520803\pi\) | ||||
−0.0653074 | + | 0.997865i | \(0.520803\pi\) | |||||||
\(318\) | −13.3028 | −0.745984 | ||||||||
\(319\) | 14.4896 | 0.811264 | ||||||||
\(320\) | −3.82878 | −0.214035 | ||||||||
\(321\) | −0.721201 | −0.0402535 | ||||||||
\(322\) | −39.9654 | −2.22718 | ||||||||
\(323\) | 5.18933 | 0.288742 | ||||||||
\(324\) | −15.9641 | −0.886892 | ||||||||
\(325\) | −22.6766 | −1.25787 | ||||||||
\(326\) | −15.0910 | −0.835815 | ||||||||
\(327\) | −1.32701 | −0.0733841 | ||||||||
\(328\) | −42.1415 | −2.32687 | ||||||||
\(329\) | −23.2803 | −1.28349 | ||||||||
\(330\) | −13.1781 | −0.725432 | ||||||||
\(331\) | −4.58489 | −0.252008 | −0.126004 | − | 0.992030i | \(-0.540215\pi\) | ||||
−0.126004 | + | 0.992030i | \(0.540215\pi\) | |||||||
\(332\) | −6.09579 | −0.334550 | ||||||||
\(333\) | −1.23903 | −0.0678986 | ||||||||
\(334\) | 50.4765 | 2.76195 | ||||||||
\(335\) | 9.47882 | 0.517883 | ||||||||
\(336\) | −26.1458 | −1.42637 | ||||||||
\(337\) | −27.8529 | −1.51724 | −0.758622 | − | 0.651531i | \(-0.774127\pi\) | ||||
−0.758622 | + | 0.651531i | \(0.774127\pi\) | |||||||
\(338\) | −39.8271 | −2.16631 | ||||||||
\(339\) | 15.9818 | 0.868012 | ||||||||
\(340\) | −4.42031 | −0.239725 | ||||||||
\(341\) | −19.4245 | −1.05189 | ||||||||
\(342\) | −13.7187 | −0.741823 | ||||||||
\(343\) | −6.07215 | −0.327865 | ||||||||
\(344\) | 8.45316 | 0.455764 | ||||||||
\(345\) | −5.35603 | −0.288359 | ||||||||
\(346\) | −64.6604 | −3.47617 | ||||||||
\(347\) | −22.8303 | −1.22560 | −0.612798 | − | 0.790239i | \(-0.709956\pi\) | ||||
−0.612798 | + | 0.790239i | \(0.709956\pi\) | |||||||
\(348\) | 18.2611 | 0.978898 | ||||||||
\(349\) | 9.52748 | 0.509994 | 0.254997 | − | 0.966942i | \(-0.417925\pi\) | ||||
0.254997 | + | 0.966942i | \(0.417925\pi\) | |||||||
\(350\) | 36.9507 | 1.97510 | ||||||||
\(351\) | 30.2503 | 1.61464 | ||||||||
\(352\) | 12.4139 | 0.661663 | ||||||||
\(353\) | 27.6987 | 1.47425 | 0.737127 | − | 0.675754i | \(-0.236182\pi\) | ||||
0.737127 | + | 0.675754i | \(0.236182\pi\) | |||||||
\(354\) | −40.2410 | −2.13879 | ||||||||
\(355\) | −2.42943 | −0.128941 | ||||||||
\(356\) | −13.7215 | −0.727236 | ||||||||
\(357\) | 5.44990 | 0.288440 | ||||||||
\(358\) | −57.7997 | −3.05481 | ||||||||
\(359\) | −25.1704 | −1.32844 | −0.664222 | − | 0.747536i | \(-0.731237\pi\) | ||||
−0.664222 | + | 0.747536i | \(0.731237\pi\) | |||||||
\(360\) | 6.19907 | 0.326720 | ||||||||
\(361\) | 0.584268 | 0.0307509 | ||||||||
\(362\) | −60.3382 | −3.17130 | ||||||||
\(363\) | −12.0988 | −0.635021 | ||||||||
\(364\) | 80.2274 | 4.20506 | ||||||||
\(365\) | −1.51833 | −0.0794733 | ||||||||
\(366\) | −25.5603 | −1.33606 | ||||||||
\(367\) | −32.2517 | −1.68352 | −0.841762 | − | 0.539849i | \(-0.818481\pi\) | ||||
−0.841762 | + | 0.539849i | \(0.818481\pi\) | |||||||
\(368\) | 25.6580 | 1.33751 | ||||||||
\(369\) | −9.23561 | −0.480787 | ||||||||
\(370\) | −2.21408 | −0.115105 | ||||||||
\(371\) | −14.0329 | −0.728550 | ||||||||
\(372\) | −24.4804 | −1.26925 | ||||||||
\(373\) | −7.45951 | −0.386239 | −0.193120 | − | 0.981175i | \(-0.561861\pi\) | ||||
−0.193120 | + | 0.981175i | \(0.561861\pi\) | |||||||
\(374\) | −13.1589 | −0.680429 | ||||||||
\(375\) | 10.8237 | 0.558933 | ||||||||
\(376\) | 37.5803 | 1.93805 | ||||||||
\(377\) | −17.3724 | −0.894726 | ||||||||
\(378\) | −49.2918 | −2.53530 | ||||||||
\(379\) | −14.3885 | −0.739085 | −0.369543 | − | 0.929214i | \(-0.620486\pi\) | ||||
−0.369543 | + | 0.929214i | \(0.620486\pi\) | |||||||
\(380\) | −16.6820 | −0.855770 | ||||||||
\(381\) | 4.66221 | 0.238852 | ||||||||
\(382\) | 13.5721 | 0.694410 | ||||||||
\(383\) | 32.1230 | 1.64141 | 0.820704 | − | 0.571353i | \(-0.193581\pi\) | ||||
0.820704 | + | 0.571353i | \(0.193581\pi\) | |||||||
\(384\) | −21.7103 | −1.10790 | ||||||||
\(385\) | −13.9014 | −0.708479 | ||||||||
\(386\) | 10.6769 | 0.543442 | ||||||||
\(387\) | 1.85257 | 0.0941716 | ||||||||
\(388\) | 9.07344 | 0.460634 | ||||||||
\(389\) | 33.8430 | 1.71591 | 0.857954 | − | 0.513727i | \(-0.171736\pi\) | ||||
0.857954 | + | 0.513727i | \(0.171736\pi\) | |||||||
\(390\) | 15.8000 | 0.800063 | ||||||||
\(391\) | −5.34821 | −0.270471 | ||||||||
\(392\) | −29.7734 | −1.50378 | ||||||||
\(393\) | 23.7821 | 1.19965 | ||||||||
\(394\) | −8.20390 | −0.413307 | ||||||||
\(395\) | 0.889100 | 0.0447355 | ||||||||
\(396\) | 23.6726 | 1.18959 | ||||||||
\(397\) | 31.5540 | 1.58365 | 0.791824 | − | 0.610750i | \(-0.209132\pi\) | ||||
0.791824 | + | 0.610750i | \(0.209132\pi\) | |||||||
\(398\) | −2.51056 | −0.125843 | ||||||||
\(399\) | 20.5677 | 1.02967 | ||||||||
\(400\) | −23.7226 | −1.18613 | ||||||||
\(401\) | −39.7735 | −1.98619 | −0.993097 | − | 0.117298i | \(-0.962577\pi\) | ||||
−0.993097 | + | 0.117298i | \(0.962577\pi\) | |||||||
\(402\) | 35.5623 | 1.77369 | ||||||||
\(403\) | 23.2891 | 1.16011 | ||||||||
\(404\) | 13.1576 | 0.654616 | ||||||||
\(405\) | −3.31651 | −0.164799 | ||||||||
\(406\) | 28.3078 | 1.40489 | ||||||||
\(407\) | −4.48523 | −0.222325 | ||||||||
\(408\) | −8.79752 | −0.435542 | ||||||||
\(409\) | 13.2685 | 0.656085 | 0.328042 | − | 0.944663i | \(-0.393611\pi\) | ||||
0.328042 | + | 0.944663i | \(0.393611\pi\) | |||||||
\(410\) | −16.5035 | −0.815049 | ||||||||
\(411\) | −4.13893 | −0.204159 | ||||||||
\(412\) | −49.0998 | −2.41897 | ||||||||
\(413\) | −42.4495 | −2.08881 | ||||||||
\(414\) | 14.1387 | 0.694881 | ||||||||
\(415\) | −1.26639 | −0.0621647 | ||||||||
\(416\) | −14.8837 | −0.729734 | ||||||||
\(417\) | −15.8037 | −0.773912 | ||||||||
\(418\) | −49.6610 | −2.42900 | ||||||||
\(419\) | −21.6152 | −1.05597 | −0.527986 | − | 0.849253i | \(-0.677052\pi\) | ||||
−0.527986 | + | 0.849253i | \(0.677052\pi\) | |||||||
\(420\) | −17.5197 | −0.854874 | ||||||||
\(421\) | 22.3574 | 1.08964 | 0.544818 | − | 0.838555i | \(-0.316599\pi\) | ||||
0.544818 | + | 0.838555i | \(0.316599\pi\) | |||||||
\(422\) | 19.3436 | 0.941631 | ||||||||
\(423\) | 8.23599 | 0.400448 | ||||||||
\(424\) | 22.6526 | 1.10011 | ||||||||
\(425\) | 4.94479 | 0.239858 | ||||||||
\(426\) | −9.11466 | −0.441607 | ||||||||
\(427\) | −26.9630 | −1.30483 | ||||||||
\(428\) | 2.31505 | 0.111902 | ||||||||
\(429\) | 32.0072 | 1.54532 | ||||||||
\(430\) | 3.31044 | 0.159643 | ||||||||
\(431\) | −6.13660 | −0.295590 | −0.147795 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147795 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(432\) | 31.6456 | 1.52255 | ||||||||
\(433\) | −33.9002 | −1.62914 | −0.814571 | − | 0.580064i | \(-0.803027\pi\) | ||||
−0.814571 | + | 0.580064i | \(0.803027\pi\) | |||||||
\(434\) | −37.9487 | −1.82160 | ||||||||
\(435\) | 3.79372 | 0.181895 | ||||||||
\(436\) | 4.25970 | 0.204003 | ||||||||
\(437\) | −20.1839 | −0.965526 | ||||||||
\(438\) | −5.69644 | −0.272186 | ||||||||
\(439\) | −12.3584 | −0.589833 | −0.294916 | − | 0.955523i | \(-0.595292\pi\) | ||||
−0.294916 | + | 0.955523i | \(0.595292\pi\) | |||||||
\(440\) | 22.4403 | 1.06980 | ||||||||
\(441\) | −6.52506 | −0.310717 | ||||||||
\(442\) | 15.7769 | 0.750431 | ||||||||
\(443\) | −32.8474 | −1.56063 | −0.780314 | − | 0.625388i | \(-0.784941\pi\) | ||||
−0.780314 | + | 0.625388i | \(0.784941\pi\) | |||||||
\(444\) | −5.65268 | −0.268264 | ||||||||
\(445\) | −2.85061 | −0.135132 | ||||||||
\(446\) | 59.2092 | 2.80364 | ||||||||
\(447\) | 24.8386 | 1.17483 | ||||||||
\(448\) | −15.1530 | −0.715913 | ||||||||
\(449\) | 0.917788 | 0.0433131 | 0.0216566 | − | 0.999765i | \(-0.493106\pi\) | ||||
0.0216566 | + | 0.999765i | \(0.493106\pi\) | |||||||
\(450\) | −13.0722 | −0.616231 | ||||||||
\(451\) | −33.4324 | −1.57427 | ||||||||
\(452\) | −51.3014 | −2.41301 | ||||||||
\(453\) | 5.34532 | 0.251145 | ||||||||
\(454\) | −37.2111 | −1.74640 | ||||||||
\(455\) | 16.6671 | 0.781366 | ||||||||
\(456\) | −33.2014 | −1.55480 | ||||||||
\(457\) | −0.783520 | −0.0366515 | −0.0183258 | − | 0.999832i | \(-0.505834\pi\) | ||||
−0.0183258 | + | 0.999832i | \(0.505834\pi\) | |||||||
\(458\) | 48.9768 | 2.28853 | ||||||||
\(459\) | −6.59629 | −0.307889 | ||||||||
\(460\) | 17.1928 | 0.801618 | ||||||||
\(461\) | −20.2801 | −0.944538 | −0.472269 | − | 0.881454i | \(-0.656565\pi\) | ||||
−0.472269 | + | 0.881454i | \(0.656565\pi\) | |||||||
\(462\) | −52.1546 | −2.42645 | ||||||||
\(463\) | 17.8543 | 0.829759 | 0.414880 | − | 0.909876i | \(-0.363824\pi\) | ||||
0.414880 | + | 0.909876i | \(0.363824\pi\) | |||||||
\(464\) | −18.1737 | −0.843694 | ||||||||
\(465\) | −5.08576 | −0.235847 | ||||||||
\(466\) | 14.2391 | 0.659616 | ||||||||
\(467\) | −31.8193 | −1.47242 | −0.736210 | − | 0.676753i | \(-0.763386\pi\) | ||||
−0.736210 | + | 0.676753i | \(0.763386\pi\) | |||||||
\(468\) | −28.3824 | −1.31198 | ||||||||
\(469\) | 37.5140 | 1.73224 | ||||||||
\(470\) | 14.7172 | 0.678855 | ||||||||
\(471\) | −31.3832 | −1.44606 | ||||||||
\(472\) | 68.5242 | 3.15408 | ||||||||
\(473\) | 6.70621 | 0.308352 | ||||||||
\(474\) | 3.33569 | 0.153214 | ||||||||
\(475\) | 18.6614 | 0.856243 | ||||||||
\(476\) | −17.4941 | −0.801842 | ||||||||
\(477\) | 4.96448 | 0.227308 | ||||||||
\(478\) | −16.5192 | −0.755571 | ||||||||
\(479\) | −29.8291 | −1.36293 | −0.681464 | − | 0.731852i | \(-0.738656\pi\) | ||||
−0.681464 | + | 0.731852i | \(0.738656\pi\) | |||||||
\(480\) | 3.25024 | 0.148353 | ||||||||
\(481\) | 5.37759 | 0.245197 | ||||||||
\(482\) | −1.28367 | −0.0584695 | ||||||||
\(483\) | −21.1974 | −0.964515 | ||||||||
\(484\) | 38.8369 | 1.76531 | ||||||||
\(485\) | 1.88499 | 0.0855931 | ||||||||
\(486\) | 29.7794 | 1.35082 | ||||||||
\(487\) | −8.76289 | −0.397084 | −0.198542 | − | 0.980092i | \(-0.563621\pi\) | ||||
−0.198542 | + | 0.980092i | \(0.563621\pi\) | |||||||
\(488\) | 43.5251 | 1.97029 | ||||||||
\(489\) | −8.00420 | −0.361963 | ||||||||
\(490\) | −11.6599 | −0.526740 | ||||||||
\(491\) | 10.5491 | 0.476076 | 0.238038 | − | 0.971256i | \(-0.423496\pi\) | ||||
0.238038 | + | 0.971256i | \(0.423496\pi\) | |||||||
\(492\) | −42.1344 | −1.89957 | ||||||||
\(493\) | 3.78818 | 0.170611 | ||||||||
\(494\) | 59.5413 | 2.67889 | ||||||||
\(495\) | 4.91795 | 0.221046 | ||||||||
\(496\) | 24.3633 | 1.09394 | ||||||||
\(497\) | −9.61488 | −0.431286 | ||||||||
\(498\) | −4.75120 | −0.212906 | ||||||||
\(499\) | 4.48063 | 0.200580 | 0.100290 | − | 0.994958i | \(-0.468023\pi\) | ||||
0.100290 | + | 0.994958i | \(0.468023\pi\) | |||||||
\(500\) | −34.7439 | −1.55380 | ||||||||
\(501\) | 26.7725 | 1.19610 | ||||||||
\(502\) | −26.6208 | −1.18814 | ||||||||
\(503\) | 11.3964 | 0.508141 | 0.254071 | − | 0.967186i | \(-0.418230\pi\) | ||||
0.254071 | + | 0.967186i | \(0.418230\pi\) | |||||||
\(504\) | 24.5339 | 1.09283 | ||||||||
\(505\) | 2.73347 | 0.121638 | ||||||||
\(506\) | 51.1815 | 2.27529 | ||||||||
\(507\) | −21.1241 | −0.938153 | ||||||||
\(508\) | −14.9656 | −0.663993 | ||||||||
\(509\) | −15.3577 | −0.680717 | −0.340358 | − | 0.940296i | \(-0.610548\pi\) | ||||
−0.340358 | + | 0.940296i | \(0.610548\pi\) | |||||||
\(510\) | −3.44529 | −0.152560 | ||||||||
\(511\) | −6.00906 | −0.265825 | ||||||||
\(512\) | 48.0402 | 2.12310 | ||||||||
\(513\) | −24.8941 | −1.09910 | ||||||||
\(514\) | 54.8997 | 2.42152 | ||||||||
\(515\) | −10.2004 | −0.449484 | ||||||||
\(516\) | 8.45175 | 0.372067 | ||||||||
\(517\) | 29.8138 | 1.31121 | ||||||||
\(518\) | −8.76259 | −0.385006 | ||||||||
\(519\) | −34.2955 | −1.50541 | ||||||||
\(520\) | −26.9049 | −1.17986 | ||||||||
\(521\) | 40.8593 | 1.79008 | 0.895039 | − | 0.445988i | \(-0.147148\pi\) | ||||
0.895039 | + | 0.445988i | \(0.147148\pi\) | |||||||
\(522\) | −10.0146 | −0.438326 | ||||||||
\(523\) | 8.08457 | 0.353513 | 0.176757 | − | 0.984255i | \(-0.443439\pi\) | ||||
0.176757 | + | 0.984255i | \(0.443439\pi\) | |||||||
\(524\) | −76.3402 | −3.33494 | ||||||||
\(525\) | 19.5985 | 0.855347 | ||||||||
\(526\) | 37.9644 | 1.65533 | ||||||||
\(527\) | −5.07834 | −0.221216 | ||||||||
\(528\) | 33.4835 | 1.45718 | ||||||||
\(529\) | −2.19813 | −0.0955708 | ||||||||
\(530\) | 8.87123 | 0.385342 | ||||||||
\(531\) | 15.0176 | 0.651708 | ||||||||
\(532\) | −66.0219 | −2.86241 | ||||||||
\(533\) | 40.0840 | 1.73623 | ||||||||
\(534\) | −10.6948 | −0.462811 | ||||||||
\(535\) | 0.480947 | 0.0207932 | ||||||||
\(536\) | −60.5571 | −2.61567 | ||||||||
\(537\) | −30.6566 | −1.32293 | ||||||||
\(538\) | −1.10543 | −0.0476585 | ||||||||
\(539\) | −23.6203 | −1.01740 | ||||||||
\(540\) | 21.2050 | 0.912517 | ||||||||
\(541\) | −17.6935 | −0.760704 | −0.380352 | − | 0.924842i | \(-0.624197\pi\) | ||||
−0.380352 | + | 0.924842i | \(0.624197\pi\) | |||||||
\(542\) | 41.4435 | 1.78015 | ||||||||
\(543\) | −32.0030 | −1.37338 | ||||||||
\(544\) | 3.24550 | 0.139149 | ||||||||
\(545\) | 0.884945 | 0.0379069 | ||||||||
\(546\) | 62.5311 | 2.67608 | ||||||||
\(547\) | 0.740083 | 0.0316437 | 0.0158218 | − | 0.999875i | \(-0.494964\pi\) | ||||
0.0158218 | + | 0.999875i | \(0.494964\pi\) | |||||||
\(548\) | 13.2859 | 0.567547 | ||||||||
\(549\) | 9.53885 | 0.407108 | ||||||||
\(550\) | −47.3208 | −2.01776 | ||||||||
\(551\) | 14.2964 | 0.609047 | ||||||||
\(552\) | 34.2179 | 1.45641 | ||||||||
\(553\) | 3.51876 | 0.149633 | ||||||||
\(554\) | −46.7867 | −1.98778 | ||||||||
\(555\) | −1.17434 | −0.0498477 | ||||||||
\(556\) | 50.7298 | 2.15142 | ||||||||
\(557\) | −22.8839 | −0.969620 | −0.484810 | − | 0.874619i | \(-0.661111\pi\) | ||||
−0.484810 | + | 0.874619i | \(0.661111\pi\) | |||||||
\(558\) | 13.4253 | 0.568338 | ||||||||
\(559\) | −8.04044 | −0.340075 | ||||||||
\(560\) | 17.4359 | 0.736800 | ||||||||
\(561\) | −6.97940 | −0.294670 | ||||||||
\(562\) | −18.9945 | −0.801235 | ||||||||
\(563\) | 7.02549 | 0.296089 | 0.148045 | − | 0.988981i | \(-0.452702\pi\) | ||||
0.148045 | + | 0.988981i | \(0.452702\pi\) | |||||||
\(564\) | 37.5740 | 1.58215 | ||||||||
\(565\) | −10.6578 | −0.448376 | ||||||||
\(566\) | 26.2424 | 1.10305 | ||||||||
\(567\) | −13.1256 | −0.551225 | ||||||||
\(568\) | 15.5208 | 0.651240 | ||||||||
\(569\) | 24.2155 | 1.01517 | 0.507584 | − | 0.861602i | \(-0.330539\pi\) | ||||
0.507584 | + | 0.861602i | \(0.330539\pi\) | |||||||
\(570\) | −13.0024 | −0.544609 | ||||||||
\(571\) | 11.8109 | 0.494272 | 0.247136 | − | 0.968981i | \(-0.420511\pi\) | ||||
0.247136 | + | 0.968981i | \(0.420511\pi\) | |||||||
\(572\) | −102.743 | −4.29589 | ||||||||
\(573\) | 7.19858 | 0.300725 | ||||||||
\(574\) | −65.3154 | −2.72621 | ||||||||
\(575\) | −19.2328 | −0.802061 | ||||||||
\(576\) | 5.36076 | 0.223365 | ||||||||
\(577\) | 10.0171 | 0.417016 | 0.208508 | − | 0.978021i | \(-0.433139\pi\) | ||||
0.208508 | + | 0.978021i | \(0.433139\pi\) | |||||||
\(578\) | 39.0927 | 1.62604 | ||||||||
\(579\) | 5.66298 | 0.235346 | ||||||||
\(580\) | −12.1778 | −0.505655 | ||||||||
\(581\) | −5.01196 | −0.207931 | ||||||||
\(582\) | 7.07205 | 0.293146 | ||||||||
\(583\) | 17.9711 | 0.744288 | ||||||||
\(584\) | 9.70014 | 0.401395 | ||||||||
\(585\) | −5.89641 | −0.243786 | ||||||||
\(586\) | 20.3609 | 0.841100 | ||||||||
\(587\) | 40.5417 | 1.67334 | 0.836668 | − | 0.547711i | \(-0.184501\pi\) | ||||
0.836668 | + | 0.547711i | \(0.184501\pi\) | |||||||
\(588\) | −29.7684 | −1.22763 | ||||||||
\(589\) | −19.1654 | −0.789697 | ||||||||
\(590\) | 26.8355 | 1.10480 | ||||||||
\(591\) | −4.35130 | −0.178989 | ||||||||
\(592\) | 5.62563 | 0.231212 | ||||||||
\(593\) | 38.0633 | 1.56307 | 0.781535 | − | 0.623861i | \(-0.214437\pi\) | ||||
0.781535 | + | 0.623861i | \(0.214437\pi\) | |||||||
\(594\) | 63.1254 | 2.59006 | ||||||||
\(595\) | −3.63438 | −0.148995 | ||||||||
\(596\) | −79.7316 | −3.26593 | ||||||||
\(597\) | −1.33159 | −0.0544982 | ||||||||
\(598\) | −61.3643 | −2.50937 | ||||||||
\(599\) | −27.4896 | −1.12320 | −0.561598 | − | 0.827410i | \(-0.689813\pi\) | ||||
−0.561598 | + | 0.827410i | \(0.689813\pi\) | |||||||
\(600\) | −31.6368 | −1.29157 | ||||||||
\(601\) | 23.2242 | 0.947335 | 0.473667 | − | 0.880704i | \(-0.342930\pi\) | ||||
0.473667 | + | 0.880704i | \(0.342930\pi\) | |||||||
\(602\) | 13.1016 | 0.533982 | ||||||||
\(603\) | −13.2715 | −0.540458 | ||||||||
\(604\) | −17.1584 | −0.698166 | ||||||||
\(605\) | 8.06831 | 0.328023 | ||||||||
\(606\) | 10.2554 | 0.416595 | ||||||||
\(607\) | −17.0012 | −0.690057 | −0.345028 | − | 0.938592i | \(-0.612131\pi\) | ||||
−0.345028 | + | 0.938592i | \(0.612131\pi\) | |||||||
\(608\) | 12.2483 | 0.496736 | ||||||||
\(609\) | 15.0143 | 0.608409 | ||||||||
\(610\) | 17.0454 | 0.690146 | ||||||||
\(611\) | −35.7454 | −1.44611 | ||||||||
\(612\) | 6.18898 | 0.250175 | ||||||||
\(613\) | −42.2179 | −1.70516 | −0.852582 | − | 0.522594i | \(-0.824964\pi\) | ||||
−0.852582 | + | 0.522594i | \(0.824964\pi\) | |||||||
\(614\) | −8.58392 | −0.346419 | ||||||||
\(615\) | −8.75336 | −0.352970 | ||||||||
\(616\) | 88.8112 | 3.57831 | ||||||||
\(617\) | −21.1010 | −0.849496 | −0.424748 | − | 0.905312i | \(-0.639637\pi\) | ||||
−0.424748 | + | 0.905312i | \(0.639637\pi\) | |||||||
\(618\) | −38.2696 | −1.53943 | ||||||||
\(619\) | −32.5241 | −1.30726 | −0.653628 | − | 0.756816i | \(-0.726754\pi\) | ||||
−0.653628 | + | 0.756816i | \(0.726754\pi\) | |||||||
\(620\) | 16.3252 | 0.655637 | ||||||||
\(621\) | 25.6563 | 1.02955 | ||||||||
\(622\) | −57.6586 | −2.31190 | ||||||||
\(623\) | −11.2818 | −0.451995 | ||||||||
\(624\) | −40.1453 | −1.60710 | ||||||||
\(625\) | 13.8664 | 0.554655 | ||||||||
\(626\) | 37.6854 | 1.50621 | ||||||||
\(627\) | −26.3399 | −1.05191 | ||||||||
\(628\) | 100.740 | 4.01995 | ||||||||
\(629\) | −1.17262 | −0.0467554 | ||||||||
\(630\) | 9.60798 | 0.382791 | ||||||||
\(631\) | −43.3737 | −1.72668 | −0.863340 | − | 0.504623i | \(-0.831631\pi\) | ||||
−0.863340 | + | 0.504623i | \(0.831631\pi\) | |||||||
\(632\) | −5.68017 | −0.225945 | ||||||||
\(633\) | 10.2597 | 0.407787 | ||||||||
\(634\) | 5.81834 | 0.231076 | ||||||||
\(635\) | −3.10909 | −0.123380 | ||||||||
\(636\) | 22.6488 | 0.898083 | ||||||||
\(637\) | 28.3197 | 1.12207 | ||||||||
\(638\) | −36.2522 | −1.43524 | ||||||||
\(639\) | 3.40151 | 0.134561 | ||||||||
\(640\) | 14.4779 | 0.572291 | ||||||||
\(641\) | 7.80477 | 0.308270 | 0.154135 | − | 0.988050i | \(-0.450741\pi\) | ||||
0.154135 | + | 0.988050i | \(0.450741\pi\) | |||||||
\(642\) | 1.80440 | 0.0712140 | ||||||||
\(643\) | −10.8545 | −0.428059 | −0.214030 | − | 0.976827i | \(-0.568659\pi\) | ||||
−0.214030 | + | 0.976827i | \(0.568659\pi\) | |||||||
\(644\) | 68.0434 | 2.68128 | ||||||||
\(645\) | 1.75584 | 0.0691360 | ||||||||
\(646\) | −12.9834 | −0.510824 | ||||||||
\(647\) | 9.68352 | 0.380699 | 0.190349 | − | 0.981716i | \(-0.439038\pi\) | ||||
0.190349 | + | 0.981716i | \(0.439038\pi\) | |||||||
\(648\) | 21.1881 | 0.832346 | ||||||||
\(649\) | 54.3628 | 2.13393 | ||||||||
\(650\) | 56.7355 | 2.22535 | ||||||||
\(651\) | −20.1278 | −0.788869 | ||||||||
\(652\) | 25.6934 | 1.00623 | ||||||||
\(653\) | −22.8846 | −0.895545 | −0.447773 | − | 0.894147i | \(-0.647783\pi\) | ||||
−0.447773 | + | 0.894147i | \(0.647783\pi\) | |||||||
\(654\) | 3.32011 | 0.129827 | ||||||||
\(655\) | −15.8595 | −0.619684 | ||||||||
\(656\) | 41.9328 | 1.63720 | ||||||||
\(657\) | 2.12586 | 0.0829376 | ||||||||
\(658\) | 58.2459 | 2.27066 | ||||||||
\(659\) | −18.3564 | −0.715065 | −0.357533 | − | 0.933901i | \(-0.616382\pi\) | ||||
−0.357533 | + | 0.933901i | \(0.616382\pi\) | |||||||
\(660\) | 22.4365 | 0.873341 | ||||||||
\(661\) | −31.1275 | −1.21072 | −0.605360 | − | 0.795952i | \(-0.706971\pi\) | ||||
−0.605360 | + | 0.795952i | \(0.706971\pi\) | |||||||
\(662\) | 11.4711 | 0.445838 | ||||||||
\(663\) | 8.36798 | 0.324986 | ||||||||
\(664\) | 8.09056 | 0.313974 | ||||||||
\(665\) | −13.7160 | −0.531882 | ||||||||
\(666\) | 3.09999 | 0.120122 | ||||||||
\(667\) | −14.7341 | −0.570507 | ||||||||
\(668\) | −85.9392 | −3.32509 | ||||||||
\(669\) | 31.4042 | 1.21416 | ||||||||
\(670\) | −23.7154 | −0.916207 | ||||||||
\(671\) | 34.5301 | 1.33302 | ||||||||
\(672\) | 12.8634 | 0.496216 | ||||||||
\(673\) | −33.9278 | −1.30782 | −0.653910 | − | 0.756573i | \(-0.726872\pi\) | ||||
−0.653910 | + | 0.756573i | \(0.726872\pi\) | |||||||
\(674\) | 69.6863 | 2.68421 | ||||||||
\(675\) | −23.7210 | −0.913021 | ||||||||
\(676\) | 67.8080 | 2.60800 | ||||||||
\(677\) | −26.8990 | −1.03381 | −0.516906 | − | 0.856042i | \(-0.672916\pi\) | ||||
−0.516906 | + | 0.856042i | \(0.672916\pi\) | |||||||
\(678\) | −39.9855 | −1.53563 | ||||||||
\(679\) | 7.46018 | 0.286295 | ||||||||
\(680\) | 5.86680 | 0.224981 | ||||||||
\(681\) | −19.7365 | −0.756306 | ||||||||
\(682\) | 48.5988 | 1.86094 | ||||||||
\(683\) | −9.41892 | −0.360405 | −0.180202 | − | 0.983630i | \(-0.557675\pi\) | ||||
−0.180202 | + | 0.983630i | \(0.557675\pi\) | |||||||
\(684\) | 23.3569 | 0.893074 | ||||||||
\(685\) | 2.76013 | 0.105459 | ||||||||
\(686\) | 15.1921 | 0.580039 | ||||||||
\(687\) | 25.9770 | 0.991084 | ||||||||
\(688\) | −8.41130 | −0.320678 | ||||||||
\(689\) | −21.5466 | −0.820859 | ||||||||
\(690\) | 13.4005 | 0.510147 | ||||||||
\(691\) | 27.8333 | 1.05883 | 0.529415 | − | 0.848363i | \(-0.322412\pi\) | ||||
0.529415 | + | 0.848363i | \(0.322412\pi\) | |||||||
\(692\) | 110.088 | 4.18492 | ||||||||
\(693\) | 19.4636 | 0.739362 | ||||||||
\(694\) | 57.1201 | 2.16825 | ||||||||
\(695\) | 10.5390 | 0.399768 | ||||||||
\(696\) | −24.2368 | −0.918694 | ||||||||
\(697\) | −8.74058 | −0.331073 | ||||||||
\(698\) | −23.8372 | −0.902250 | ||||||||
\(699\) | 7.55236 | 0.285657 | ||||||||
\(700\) | −62.9108 | −2.37780 | ||||||||
\(701\) | 28.0050 | 1.05773 | 0.528866 | − | 0.848705i | \(-0.322617\pi\) | ||||
0.528866 | + | 0.848705i | \(0.322617\pi\) | |||||||
\(702\) | −75.6845 | −2.85653 | ||||||||
\(703\) | −4.42541 | −0.166908 | ||||||||
\(704\) | 19.4057 | 0.731378 | ||||||||
\(705\) | 7.80593 | 0.293989 | ||||||||
\(706\) | −69.3005 | −2.60816 | ||||||||
\(707\) | 10.8182 | 0.406860 | ||||||||
\(708\) | 68.5127 | 2.57487 | ||||||||
\(709\) | −20.9124 | −0.785381 | −0.392690 | − | 0.919671i | \(-0.628456\pi\) | ||||
−0.392690 | + | 0.919671i | \(0.628456\pi\) | |||||||
\(710\) | 6.07829 | 0.228114 | ||||||||
\(711\) | −1.24485 | −0.0466855 | ||||||||
\(712\) | 18.2116 | 0.682510 | ||||||||
\(713\) | 19.7522 | 0.739726 | ||||||||
\(714\) | −13.6353 | −0.510289 | ||||||||
\(715\) | −21.3447 | −0.798245 | ||||||||
\(716\) | 98.4073 | 3.67765 | ||||||||
\(717\) | −8.76169 | −0.327211 | ||||||||
\(718\) | 62.9748 | 2.35020 | ||||||||
\(719\) | 34.2369 | 1.27682 | 0.638411 | − | 0.769696i | \(-0.279592\pi\) | ||||
0.638411 | + | 0.769696i | \(0.279592\pi\) | |||||||
\(720\) | −6.16837 | −0.229882 | ||||||||
\(721\) | −40.3698 | −1.50345 | ||||||||
\(722\) | −1.46180 | −0.0544026 | ||||||||
\(723\) | −0.680851 | −0.0253211 | ||||||||
\(724\) | 102.729 | 3.81790 | ||||||||
\(725\) | 13.6227 | 0.505934 | ||||||||
\(726\) | 30.2704 | 1.12344 | ||||||||
\(727\) | 19.5323 | 0.724411 | 0.362206 | − | 0.932098i | \(-0.382024\pi\) | ||||
0.362206 | + | 0.932098i | \(0.382024\pi\) | |||||||
\(728\) | −106.481 | −3.94644 | ||||||||
\(729\) | 27.0379 | 1.00140 | ||||||||
\(730\) | 3.79878 | 0.140599 | ||||||||
\(731\) | 1.75327 | 0.0648472 | ||||||||
\(732\) | 43.5178 | 1.60847 | ||||||||
\(733\) | 27.5561 | 1.01781 | 0.508903 | − | 0.860824i | \(-0.330051\pi\) | ||||
0.508903 | + | 0.860824i | \(0.330051\pi\) | |||||||
\(734\) | 80.6917 | 2.97839 | ||||||||
\(735\) | −6.18434 | −0.228113 | ||||||||
\(736\) | −12.6234 | −0.465303 | ||||||||
\(737\) | −48.0422 | −1.76966 | ||||||||
\(738\) | 23.1069 | 0.850578 | ||||||||
\(739\) | −40.1398 | −1.47657 | −0.738284 | − | 0.674490i | \(-0.764364\pi\) | ||||
−0.738284 | + | 0.674490i | \(0.764364\pi\) | |||||||
\(740\) | 3.76960 | 0.138573 | ||||||||
\(741\) | 31.5804 | 1.16013 | ||||||||
\(742\) | 35.1094 | 1.28891 | ||||||||
\(743\) | −19.5049 | −0.715564 | −0.357782 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357782 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(744\) | 32.4913 | 1.19119 | ||||||||
\(745\) | −16.5641 | −0.606862 | ||||||||
\(746\) | 18.6632 | 0.683310 | ||||||||
\(747\) | 1.77310 | 0.0648745 | ||||||||
\(748\) | 22.4038 | 0.819163 | ||||||||
\(749\) | 1.90343 | 0.0695498 | ||||||||
\(750\) | −27.0802 | −0.988830 | ||||||||
\(751\) | −23.6160 | −0.861759 | −0.430879 | − | 0.902410i | \(-0.641797\pi\) | ||||
−0.430879 | + | 0.902410i | \(0.641797\pi\) | |||||||
\(752\) | −37.3942 | −1.36363 | ||||||||
\(753\) | −14.1195 | −0.514543 | ||||||||
\(754\) | 43.4648 | 1.58289 | ||||||||
\(755\) | −3.56463 | −0.129730 | ||||||||
\(756\) | 83.9222 | 3.05222 | ||||||||
\(757\) | −26.2217 | −0.953043 | −0.476521 | − | 0.879163i | \(-0.658103\pi\) | ||||
−0.476521 | + | 0.879163i | \(0.658103\pi\) | |||||||
\(758\) | 35.9990 | 1.30754 | ||||||||
\(759\) | 27.1464 | 0.985350 | ||||||||
\(760\) | 22.1410 | 0.803138 | ||||||||
\(761\) | −35.4323 | −1.28442 | −0.642210 | − | 0.766529i | \(-0.721982\pi\) | ||||
−0.642210 | + | 0.766529i | \(0.721982\pi\) | |||||||
\(762\) | −11.6646 | −0.422563 | ||||||||
\(763\) | 3.50232 | 0.126793 | ||||||||
\(764\) | −23.1073 | −0.835994 | ||||||||
\(765\) | 1.28575 | 0.0464864 | ||||||||
\(766\) | −80.3698 | −2.90388 | ||||||||
\(767\) | −65.1786 | −2.35346 | ||||||||
\(768\) | 42.8350 | 1.54568 | ||||||||
\(769\) | 26.6840 | 0.962248 | 0.481124 | − | 0.876652i | \(-0.340229\pi\) | ||||
0.481124 | + | 0.876652i | \(0.340229\pi\) | |||||||
\(770\) | 34.7803 | 1.25340 | ||||||||
\(771\) | 29.1185 | 1.04868 | ||||||||
\(772\) | −18.1781 | −0.654244 | ||||||||
\(773\) | −26.0098 | −0.935508 | −0.467754 | − | 0.883859i | \(-0.654937\pi\) | ||||
−0.467754 | + | 0.883859i | \(0.654937\pi\) | |||||||
\(774\) | −4.63502 | −0.166602 | ||||||||
\(775\) | −18.2623 | −0.656000 | ||||||||
\(776\) | −12.0426 | −0.432304 | ||||||||
\(777\) | −4.64763 | −0.166733 | ||||||||
\(778\) | −84.6731 | −3.03568 | ||||||||
\(779\) | −32.9865 | −1.18186 | ||||||||
\(780\) | −26.9004 | −0.963189 | ||||||||
\(781\) | 12.3133 | 0.440603 | ||||||||
\(782\) | 13.3809 | 0.478500 | ||||||||
\(783\) | −18.1725 | −0.649433 | ||||||||
\(784\) | 29.6260 | 1.05807 | ||||||||
\(785\) | 20.9285 | 0.746970 | ||||||||
\(786\) | −59.5013 | −2.12234 | ||||||||
\(787\) | −16.0989 | −0.573865 | −0.286932 | − | 0.957951i | \(-0.592636\pi\) | ||||
−0.286932 | + | 0.957951i | \(0.592636\pi\) | |||||||
\(788\) | 13.9676 | 0.497576 | ||||||||
\(789\) | 20.1361 | 0.716864 | ||||||||
\(790\) | −2.22447 | −0.0791432 | ||||||||
\(791\) | −42.1799 | −1.49975 | ||||||||
\(792\) | −31.4192 | −1.11643 | ||||||||
\(793\) | −41.4001 | −1.47016 | ||||||||
\(794\) | −78.9461 | −2.80169 | ||||||||
\(795\) | 4.70525 | 0.166878 | ||||||||
\(796\) | 4.27438 | 0.151501 | ||||||||
\(797\) | 7.50731 | 0.265922 | 0.132961 | − | 0.991121i | \(-0.457551\pi\) | ||||
0.132961 | + | 0.991121i | \(0.457551\pi\) | |||||||
\(798\) | −51.4591 | −1.82163 | ||||||||
\(799\) | 7.79454 | 0.275751 | ||||||||
\(800\) | 11.6712 | 0.412638 | ||||||||
\(801\) | 3.99121 | 0.141023 | ||||||||
\(802\) | 99.5108 | 3.51385 | ||||||||
\(803\) | 7.69548 | 0.271568 | ||||||||
\(804\) | −60.5469 | −2.13533 | ||||||||
\(805\) | 14.1359 | 0.498225 | ||||||||
\(806\) | −58.2678 | −2.05240 | ||||||||
\(807\) | −0.586314 | −0.0206392 | ||||||||
\(808\) | −17.4633 | −0.614356 | ||||||||
\(809\) | −5.93362 | −0.208615 | −0.104308 | − | 0.994545i | \(-0.533263\pi\) | ||||
−0.104308 | + | 0.994545i | \(0.533263\pi\) | |||||||
\(810\) | 8.29770 | 0.291551 | ||||||||
\(811\) | −34.4794 | −1.21074 | −0.605368 | − | 0.795946i | \(-0.706974\pi\) | ||||
−0.605368 | + | 0.795946i | \(0.706974\pi\) | |||||||
\(812\) | −48.1956 | −1.69133 | ||||||||
\(813\) | 21.9814 | 0.770921 | ||||||||
\(814\) | 11.2218 | 0.393323 | ||||||||
\(815\) | 5.33776 | 0.186974 | ||||||||
\(816\) | 8.75395 | 0.306450 | ||||||||
\(817\) | 6.61677 | 0.231491 | ||||||||
\(818\) | −33.1970 | −1.16070 | ||||||||
\(819\) | −23.3360 | −0.815427 | ||||||||
\(820\) | 28.0982 | 0.981231 | ||||||||
\(821\) | 53.0957 | 1.85305 | 0.926526 | − | 0.376230i | \(-0.122780\pi\) | ||||
0.926526 | + | 0.376230i | \(0.122780\pi\) | |||||||
\(822\) | 10.3554 | 0.361185 | ||||||||
\(823\) | 6.01333 | 0.209611 | 0.104806 | − | 0.994493i | \(-0.466578\pi\) | ||||
0.104806 | + | 0.994493i | \(0.466578\pi\) | |||||||
\(824\) | 65.1671 | 2.27020 | ||||||||
\(825\) | −25.0987 | −0.873824 | ||||||||
\(826\) | 106.206 | 3.69538 | ||||||||
\(827\) | −16.6818 | −0.580083 | −0.290042 | − | 0.957014i | \(-0.593669\pi\) | ||||
−0.290042 | + | 0.957014i | \(0.593669\pi\) | |||||||
\(828\) | −24.0720 | −0.836561 | ||||||||
\(829\) | 15.8589 | 0.550803 | 0.275401 | − | 0.961329i | \(-0.411189\pi\) | ||||
0.275401 | + | 0.961329i | \(0.411189\pi\) | |||||||
\(830\) | 3.16843 | 0.109978 | ||||||||
\(831\) | −24.8154 | −0.860836 | ||||||||
\(832\) | −23.2665 | −0.806622 | ||||||||
\(833\) | −6.17531 | −0.213962 | ||||||||
\(834\) | 39.5400 | 1.36916 | ||||||||
\(835\) | −17.8537 | −0.617854 | ||||||||
\(836\) | 84.5507 | 2.92425 | ||||||||
\(837\) | 24.3616 | 0.842062 | ||||||||
\(838\) | 54.0799 | 1.86816 | ||||||||
\(839\) | 43.5188 | 1.50243 | 0.751217 | − | 0.660055i | \(-0.229467\pi\) | ||||
0.751217 | + | 0.660055i | \(0.229467\pi\) | |||||||
\(840\) | 23.2528 | 0.802297 | ||||||||
\(841\) | −18.5637 | −0.640128 | ||||||||
\(842\) | −55.9369 | −1.92771 | ||||||||
\(843\) | −10.0746 | −0.346987 | ||||||||
\(844\) | −32.9336 | −1.13362 | ||||||||
\(845\) | 14.0870 | 0.484608 | ||||||||
\(846\) | −20.6059 | −0.708447 | ||||||||
\(847\) | 31.9317 | 1.09719 | ||||||||
\(848\) | −22.5404 | −0.774041 | ||||||||
\(849\) | 13.9188 | 0.477693 | ||||||||
\(850\) | −12.3716 | −0.424341 | ||||||||
\(851\) | 4.56091 | 0.156346 | ||||||||
\(852\) | 15.5182 | 0.531646 | ||||||||
\(853\) | 45.8385 | 1.56948 | 0.784741 | − | 0.619824i | \(-0.212796\pi\) | ||||
0.784741 | + | 0.619824i | \(0.212796\pi\) | |||||||
\(854\) | 67.4599 | 2.30843 | ||||||||
\(855\) | 4.85236 | 0.165947 | ||||||||
\(856\) | −3.07261 | −0.105020 | ||||||||
\(857\) | 11.1379 | 0.380463 | 0.190232 | − | 0.981739i | \(-0.439076\pi\) | ||||
0.190232 | + | 0.981739i | \(0.439076\pi\) | |||||||
\(858\) | −80.0802 | −2.73389 | ||||||||
\(859\) | −28.7456 | −0.980786 | −0.490393 | − | 0.871501i | \(-0.663147\pi\) | ||||
−0.490393 | + | 0.871501i | \(0.663147\pi\) | |||||||
\(860\) | −5.63621 | −0.192193 | ||||||||
\(861\) | −34.6429 | −1.18063 | ||||||||
\(862\) | 15.3534 | 0.522939 | ||||||||
\(863\) | −37.8318 | −1.28781 | −0.643905 | − | 0.765106i | \(-0.722687\pi\) | ||||
−0.643905 | + | 0.765106i | \(0.722687\pi\) | |||||||
\(864\) | −15.5692 | −0.529675 | ||||||||
\(865\) | 22.8706 | 0.777625 | ||||||||
\(866\) | 84.8163 | 2.88218 | ||||||||
\(867\) | 20.7345 | 0.704182 | ||||||||
\(868\) | 64.6099 | 2.19300 | ||||||||
\(869\) | −4.50629 | −0.152865 | ||||||||
\(870\) | −9.49165 | −0.321797 | ||||||||
\(871\) | 57.6004 | 1.95172 | ||||||||
\(872\) | −5.65363 | −0.191456 | ||||||||
\(873\) | −2.63922 | −0.0893242 | ||||||||
\(874\) | 50.4989 | 1.70815 | ||||||||
\(875\) | −28.5664 | −0.965721 | ||||||||
\(876\) | 9.69852 | 0.327683 | ||||||||
\(877\) | 23.6325 | 0.798014 | 0.399007 | − | 0.916948i | \(-0.369355\pi\) | ||||
0.399007 | + | 0.916948i | \(0.369355\pi\) | |||||||
\(878\) | 30.9199 | 1.04350 | ||||||||
\(879\) | 10.7993 | 0.364251 | ||||||||
\(880\) | −22.3292 | −0.752716 | ||||||||
\(881\) | −49.4645 | −1.66650 | −0.833250 | − | 0.552896i | \(-0.813523\pi\) | ||||
−0.833250 | + | 0.552896i | \(0.813523\pi\) | |||||||
\(882\) | 16.3253 | 0.549701 | ||||||||
\(883\) | 26.5051 | 0.891968 | 0.445984 | − | 0.895041i | \(-0.352854\pi\) | ||||
0.445984 | + | 0.895041i | \(0.352854\pi\) | |||||||
\(884\) | −26.8611 | −0.903437 | ||||||||
\(885\) | 14.2334 | 0.478451 | ||||||||
\(886\) | 82.1823 | 2.76097 | ||||||||
\(887\) | −13.5636 | −0.455420 | −0.227710 | − | 0.973729i | \(-0.573124\pi\) | ||||
−0.227710 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(888\) | 7.50244 | 0.251765 | ||||||||
\(889\) | −12.3047 | −0.412688 | ||||||||
\(890\) | 7.13206 | 0.239067 | ||||||||
\(891\) | 16.8093 | 0.563132 | ||||||||
\(892\) | −100.807 | −3.37527 | ||||||||
\(893\) | 29.4162 | 0.984376 | ||||||||
\(894\) | −62.1446 | −2.07843 | ||||||||
\(895\) | 20.4440 | 0.683366 | ||||||||
\(896\) | 57.2989 | 1.91422 | ||||||||
\(897\) | −32.5473 | −1.08672 | ||||||||
\(898\) | −2.29625 | −0.0766269 | ||||||||
\(899\) | −13.9906 | −0.466613 | ||||||||
\(900\) | 22.2563 | 0.741875 | ||||||||
\(901\) | 4.69838 | 0.156526 | ||||||||
\(902\) | 83.6458 | 2.78510 | ||||||||
\(903\) | 6.94902 | 0.231249 | ||||||||
\(904\) | 68.0890 | 2.26461 | ||||||||
\(905\) | 21.3418 | 0.709427 | ||||||||
\(906\) | −13.3737 | −0.444311 | ||||||||
\(907\) | −24.0455 | −0.798419 | −0.399210 | − | 0.916860i | \(-0.630715\pi\) | ||||
−0.399210 | + | 0.916860i | \(0.630715\pi\) | |||||||
\(908\) | 63.3540 | 2.10248 | ||||||||
\(909\) | −3.82720 | −0.126940 | ||||||||
\(910\) | −41.7001 | −1.38234 | ||||||||
\(911\) | 26.3707 | 0.873700 | 0.436850 | − | 0.899534i | \(-0.356094\pi\) | ||||
0.436850 | + | 0.899534i | \(0.356094\pi\) | |||||||
\(912\) | 33.0370 | 1.09396 | ||||||||
\(913\) | 6.41854 | 0.212423 | ||||||||
\(914\) | 1.96032 | 0.0648416 | ||||||||
\(915\) | 9.04076 | 0.298878 | ||||||||
\(916\) | −83.3858 | −2.75515 | ||||||||
\(917\) | −62.7668 | −2.07274 | ||||||||
\(918\) | 16.5035 | 0.544697 | ||||||||
\(919\) | 13.9155 | 0.459031 | 0.229516 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229516 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(920\) | −22.8189 | −0.752317 | ||||||||
\(921\) | −4.55286 | −0.150022 | ||||||||
\(922\) | 50.7396 | 1.67102 | ||||||||
\(923\) | −14.7630 | −0.485932 | ||||||||
\(924\) | 88.7963 | 2.92118 | ||||||||
\(925\) | −4.21687 | −0.138650 | ||||||||
\(926\) | −44.6703 | −1.46796 | ||||||||
\(927\) | 14.2818 | 0.469077 | ||||||||
\(928\) | 8.94121 | 0.293510 | ||||||||
\(929\) | 2.10560 | 0.0690825 | 0.0345412 | − | 0.999403i | \(-0.489003\pi\) | ||||
0.0345412 | + | 0.999403i | \(0.489003\pi\) | |||||||
\(930\) | 12.7243 | 0.417245 | ||||||||
\(931\) | −23.3053 | −0.763801 | ||||||||
\(932\) | −24.2430 | −0.794105 | ||||||||
\(933\) | −30.5818 | −1.00120 | ||||||||
\(934\) | 79.6099 | 2.60491 | ||||||||
\(935\) | 4.65435 | 0.152213 | ||||||||
\(936\) | 37.6702 | 1.23129 | ||||||||
\(937\) | −14.4051 | −0.470594 | −0.235297 | − | 0.971923i | \(-0.575606\pi\) | ||||
−0.235297 | + | 0.971923i | \(0.575606\pi\) | |||||||
\(938\) | −93.8578 | −3.06457 | ||||||||
\(939\) | 19.9881 | 0.652287 | ||||||||
\(940\) | −25.0569 | −0.817267 | ||||||||
\(941\) | −30.3757 | −0.990220 | −0.495110 | − | 0.868830i | \(-0.664872\pi\) | ||||
−0.495110 | + | 0.868830i | \(0.664872\pi\) | |||||||
\(942\) | 78.5188 | 2.55828 | ||||||||
\(943\) | 33.9965 | 1.10708 | ||||||||
\(944\) | −68.1849 | −2.21923 | ||||||||
\(945\) | 17.4347 | 0.567151 | ||||||||
\(946\) | −16.7785 | −0.545517 | ||||||||
\(947\) | 40.7034 | 1.32268 | 0.661342 | − | 0.750085i | \(-0.269987\pi\) | ||||
0.661342 | + | 0.750085i | \(0.269987\pi\) | |||||||
\(948\) | −5.67922 | −0.184452 | ||||||||
\(949\) | −9.22654 | −0.299506 | ||||||||
\(950\) | −46.6897 | −1.51481 | ||||||||
\(951\) | 3.08601 | 0.100071 | ||||||||
\(952\) | 23.2188 | 0.752527 | ||||||||
\(953\) | 25.6023 | 0.829338 | 0.414669 | − | 0.909972i | \(-0.363897\pi\) | ||||
0.414669 | + | 0.909972i | \(0.363897\pi\) | |||||||
\(954\) | −12.4208 | −0.402139 | ||||||||
\(955\) | −4.80051 | −0.155341 | ||||||||
\(956\) | 28.1249 | 0.909625 | ||||||||
\(957\) | −19.2280 | −0.621552 | ||||||||
\(958\) | 74.6307 | 2.41121 | ||||||||
\(959\) | 10.9237 | 0.352744 | ||||||||
\(960\) | 5.08084 | 0.163983 | ||||||||
\(961\) | −12.2445 | −0.394984 | ||||||||
\(962\) | −13.4544 | −0.433787 | ||||||||
\(963\) | −0.673386 | −0.0216995 | ||||||||
\(964\) | 2.18552 | 0.0703909 | ||||||||
\(965\) | −3.77647 | −0.121569 | ||||||||
\(966\) | 53.0346 | 1.70636 | ||||||||
\(967\) | −8.39277 | −0.269893 | −0.134947 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134947 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(968\) | −51.5458 | −1.65674 | ||||||||
\(969\) | −6.88631 | −0.221220 | ||||||||
\(970\) | −4.71614 | −0.151426 | ||||||||
\(971\) | −30.5381 | −0.980015 | −0.490007 | − | 0.871718i | \(-0.663006\pi\) | ||||
−0.490007 | + | 0.871718i | \(0.663006\pi\) | |||||||
\(972\) | −50.7012 | −1.62624 | ||||||||
\(973\) | 41.7100 | 1.33716 | ||||||||
\(974\) | 21.9242 | 0.702497 | ||||||||
\(975\) | 30.0922 | 0.963721 | ||||||||
\(976\) | −43.3096 | −1.38631 | ||||||||
\(977\) | 22.5658 | 0.721945 | 0.360973 | − | 0.932576i | \(-0.382445\pi\) | ||||
0.360973 | + | 0.932576i | \(0.382445\pi\) | |||||||
\(978\) | 20.0260 | 0.640362 | ||||||||
\(979\) | 14.4480 | 0.461759 | ||||||||
\(980\) | 19.8517 | 0.634138 | ||||||||
\(981\) | −1.23903 | −0.0395593 | ||||||||
\(982\) | −26.3933 | −0.842245 | ||||||||
\(983\) | −42.5095 | −1.35584 | −0.677921 | − | 0.735135i | \(-0.737119\pi\) | ||||
−0.677921 | + | 0.735135i | \(0.737119\pi\) | |||||||
\(984\) | 55.9223 | 1.78274 | ||||||||
\(985\) | 2.90175 | 0.0924575 | ||||||||
\(986\) | −9.47779 | −0.301834 | ||||||||
\(987\) | 30.8933 | 0.983345 | ||||||||
\(988\) | −101.373 | −3.22509 | ||||||||
\(989\) | −6.81936 | −0.216843 | ||||||||
\(990\) | −12.3044 | −0.391060 | ||||||||
\(991\) | 45.8357 | 1.45602 | 0.728009 | − | 0.685568i | \(-0.240446\pi\) | ||||
0.728009 | + | 0.685568i | \(0.240446\pi\) | |||||||
\(992\) | −11.9864 | −0.380568 | ||||||||
\(993\) | 6.08421 | 0.193077 | ||||||||
\(994\) | 24.0558 | 0.763005 | ||||||||
\(995\) | 0.887995 | 0.0281513 | ||||||||
\(996\) | 8.08920 | 0.256316 | ||||||||
\(997\) | 27.0201 | 0.855735 | 0.427867 | − | 0.903842i | \(-0.359265\pi\) | ||||
0.427867 | + | 0.903842i | \(0.359265\pi\) | |||||||
\(998\) | −11.2103 | −0.354854 | ||||||||
\(999\) | 5.62526 | 0.177975 |
(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 | 4033.2.a.c.1.8 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.c.1.8 | ✓ | 77 | 1.1 | even | 1 | trivial |