Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, 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("6033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6033 = 3 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6033.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: | \(48.1737475394\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42144 | −1.71221 | −0.856107 | − | 0.516798i | \(-0.827124\pi\) | ||||
−0.856107 | + | 0.516798i | \(0.827124\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.86336 | 1.93168 | ||||||||
\(5\) | 1.61348 | 0.721571 | 0.360785 | − | 0.932649i | \(-0.382509\pi\) | ||||
0.360785 | + | 0.932649i | \(0.382509\pi\) | |||||||
\(6\) | 2.42144 | 0.988548 | ||||||||
\(7\) | −0.957963 | −0.362076 | −0.181038 | − | 0.983476i | \(-0.557946\pi\) | ||||
−0.181038 | + | 0.983476i | \(0.557946\pi\) | |||||||
\(8\) | −4.51200 | −1.59523 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.90694 | −1.23548 | ||||||||
\(11\) | 4.96714 | 1.49765 | 0.748824 | − | 0.662769i | \(-0.230619\pi\) | ||||
0.748824 | + | 0.662769i | \(0.230619\pi\) | |||||||
\(12\) | −3.86336 | −1.11526 | ||||||||
\(13\) | 6.60137 | 1.83089 | 0.915445 | − | 0.402443i | \(-0.131839\pi\) | ||||
0.915445 | + | 0.402443i | \(0.131839\pi\) | |||||||
\(14\) | 2.31965 | 0.619952 | ||||||||
\(15\) | −1.61348 | −0.416599 | ||||||||
\(16\) | 3.19882 | 0.799704 | ||||||||
\(17\) | −2.48372 | −0.602390 | −0.301195 | − | 0.953563i | \(-0.597385\pi\) | ||||
−0.301195 | + | 0.953563i | \(0.597385\pi\) | |||||||
\(18\) | −2.42144 | −0.570738 | ||||||||
\(19\) | −1.70780 | −0.391797 | −0.195898 | − | 0.980624i | \(-0.562762\pi\) | ||||
−0.195898 | + | 0.980624i | \(0.562762\pi\) | |||||||
\(20\) | 6.23345 | 1.39384 | ||||||||
\(21\) | 0.957963 | 0.209045 | ||||||||
\(22\) | −12.0276 | −2.56430 | ||||||||
\(23\) | 0.0237908 | 0.00496072 | 0.00248036 | − | 0.999997i | \(-0.499210\pi\) | ||||
0.00248036 | + | 0.999997i | \(0.499210\pi\) | |||||||
\(24\) | 4.51200 | 0.921009 | ||||||||
\(25\) | −2.39668 | −0.479336 | ||||||||
\(26\) | −15.9848 | −3.13488 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.70096 | −0.699415 | ||||||||
\(29\) | −5.14557 | −0.955508 | −0.477754 | − | 0.878494i | \(-0.658549\pi\) | ||||
−0.477754 | + | 0.878494i | \(0.658549\pi\) | |||||||
\(30\) | 3.90694 | 0.713307 | ||||||||
\(31\) | −2.01254 | −0.361463 | −0.180731 | − | 0.983532i | \(-0.557846\pi\) | ||||
−0.180731 | + | 0.983532i | \(0.557846\pi\) | |||||||
\(32\) | 1.27827 | 0.225969 | ||||||||
\(33\) | −4.96714 | −0.864668 | ||||||||
\(34\) | 6.01417 | 1.03142 | ||||||||
\(35\) | −1.54566 | −0.261263 | ||||||||
\(36\) | 3.86336 | 0.643893 | ||||||||
\(37\) | 0.922557 | 0.151667 | 0.0758337 | − | 0.997120i | \(-0.475838\pi\) | ||||
0.0758337 | + | 0.997120i | \(0.475838\pi\) | |||||||
\(38\) | 4.13534 | 0.670840 | ||||||||
\(39\) | −6.60137 | −1.05706 | ||||||||
\(40\) | −7.28003 | −1.15107 | ||||||||
\(41\) | 9.18372 | 1.43426 | 0.717128 | − | 0.696941i | \(-0.245456\pi\) | ||||
0.717128 | + | 0.696941i | \(0.245456\pi\) | |||||||
\(42\) | −2.31965 | −0.357929 | ||||||||
\(43\) | 7.22362 | 1.10159 | 0.550796 | − | 0.834640i | \(-0.314324\pi\) | ||||
0.550796 | + | 0.834640i | \(0.314324\pi\) | |||||||
\(44\) | 19.1898 | 2.89298 | ||||||||
\(45\) | 1.61348 | 0.240524 | ||||||||
\(46\) | −0.0576079 | −0.00849382 | ||||||||
\(47\) | 1.75920 | 0.256606 | 0.128303 | − | 0.991735i | \(-0.459047\pi\) | ||||
0.128303 | + | 0.991735i | \(0.459047\pi\) | |||||||
\(48\) | −3.19882 | −0.461710 | ||||||||
\(49\) | −6.08231 | −0.868901 | ||||||||
\(50\) | 5.80341 | 0.820726 | ||||||||
\(51\) | 2.48372 | 0.347790 | ||||||||
\(52\) | 25.5034 | 3.53669 | ||||||||
\(53\) | 3.75167 | 0.515331 | 0.257666 | − | 0.966234i | \(-0.417047\pi\) | ||||
0.257666 | + | 0.966234i | \(0.417047\pi\) | |||||||
\(54\) | 2.42144 | 0.329516 | ||||||||
\(55\) | 8.01438 | 1.08066 | ||||||||
\(56\) | 4.32233 | 0.577596 | ||||||||
\(57\) | 1.70780 | 0.226204 | ||||||||
\(58\) | 12.4597 | 1.63603 | ||||||||
\(59\) | 4.70218 | 0.612172 | 0.306086 | − | 0.952004i | \(-0.400980\pi\) | ||||
0.306086 | + | 0.952004i | \(0.400980\pi\) | |||||||
\(60\) | −6.23345 | −0.804735 | ||||||||
\(61\) | −10.3653 | −1.32714 | −0.663570 | − | 0.748114i | \(-0.730960\pi\) | ||||
−0.663570 | + | 0.748114i | \(0.730960\pi\) | |||||||
\(62\) | 4.87324 | 0.618902 | ||||||||
\(63\) | −0.957963 | −0.120692 | ||||||||
\(64\) | −9.49289 | −1.18661 | ||||||||
\(65\) | 10.6512 | 1.32112 | ||||||||
\(66\) | 12.0276 | 1.48050 | ||||||||
\(67\) | 13.8015 | 1.68612 | 0.843058 | − | 0.537822i | \(-0.180753\pi\) | ||||
0.843058 | + | 0.537822i | \(0.180753\pi\) | |||||||
\(68\) | −9.59549 | −1.16362 | ||||||||
\(69\) | −0.0237908 | −0.00286407 | ||||||||
\(70\) | 3.74271 | 0.447339 | ||||||||
\(71\) | 5.39446 | 0.640205 | 0.320102 | − | 0.947383i | \(-0.396283\pi\) | ||||
0.320102 | + | 0.947383i | \(0.396283\pi\) | |||||||
\(72\) | −4.51200 | −0.531745 | ||||||||
\(73\) | 4.67594 | 0.547277 | 0.273639 | − | 0.961833i | \(-0.411773\pi\) | ||||
0.273639 | + | 0.961833i | \(0.411773\pi\) | |||||||
\(74\) | −2.23391 | −0.259687 | ||||||||
\(75\) | 2.39668 | 0.276745 | ||||||||
\(76\) | −6.59785 | −0.756825 | ||||||||
\(77\) | −4.75834 | −0.542263 | ||||||||
\(78\) | 15.9848 | 1.80992 | ||||||||
\(79\) | 1.17576 | 0.132283 | 0.0661417 | − | 0.997810i | \(-0.478931\pi\) | ||||
0.0661417 | + | 0.997810i | \(0.478931\pi\) | |||||||
\(80\) | 5.16123 | 0.577043 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −22.2378 | −2.45575 | ||||||||
\(83\) | −17.1010 | −1.87708 | −0.938538 | − | 0.345175i | \(-0.887820\pi\) | ||||
−0.938538 | + | 0.345175i | \(0.887820\pi\) | |||||||
\(84\) | 3.70096 | 0.403807 | ||||||||
\(85\) | −4.00743 | −0.434667 | ||||||||
\(86\) | −17.4915 | −1.88616 | ||||||||
\(87\) | 5.14557 | 0.551663 | ||||||||
\(88\) | −22.4117 | −2.38910 | ||||||||
\(89\) | 4.29441 | 0.455207 | 0.227603 | − | 0.973754i | \(-0.426911\pi\) | ||||
0.227603 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(90\) | −3.90694 | −0.411828 | ||||||||
\(91\) | −6.32387 | −0.662922 | ||||||||
\(92\) | 0.0919123 | 0.00958252 | ||||||||
\(93\) | 2.01254 | 0.208691 | ||||||||
\(94\) | −4.25979 | −0.439364 | ||||||||
\(95\) | −2.75551 | −0.282709 | ||||||||
\(96\) | −1.27827 | −0.130463 | ||||||||
\(97\) | −4.58146 | −0.465177 | −0.232588 | − | 0.972575i | \(-0.574719\pi\) | ||||
−0.232588 | + | 0.972575i | \(0.574719\pi\) | |||||||
\(98\) | 14.7279 | 1.48774 | ||||||||
\(99\) | 4.96714 | 0.499216 | ||||||||
\(100\) | −9.25923 | −0.925923 | ||||||||
\(101\) | 5.82248 | 0.579359 | 0.289679 | − | 0.957124i | \(-0.406451\pi\) | ||||
0.289679 | + | 0.957124i | \(0.406451\pi\) | |||||||
\(102\) | −6.01417 | −0.595491 | ||||||||
\(103\) | 2.68653 | 0.264711 | 0.132356 | − | 0.991202i | \(-0.457746\pi\) | ||||
0.132356 | + | 0.991202i | \(0.457746\pi\) | |||||||
\(104\) | −29.7854 | −2.92070 | ||||||||
\(105\) | 1.54566 | 0.150841 | ||||||||
\(106\) | −9.08443 | −0.882358 | ||||||||
\(107\) | 10.6391 | 1.02852 | 0.514259 | − | 0.857635i | \(-0.328067\pi\) | ||||
0.514259 | + | 0.857635i | \(0.328067\pi\) | |||||||
\(108\) | −3.86336 | −0.371752 | ||||||||
\(109\) | 1.51029 | 0.144660 | 0.0723299 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723299 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(110\) | −19.4063 | −1.85032 | ||||||||
\(111\) | −0.922557 | −0.0875652 | ||||||||
\(112\) | −3.06435 | −0.289554 | ||||||||
\(113\) | 12.7433 | 1.19879 | 0.599395 | − | 0.800454i | \(-0.295408\pi\) | ||||
0.599395 | + | 0.800454i | \(0.295408\pi\) | |||||||
\(114\) | −4.13534 | −0.387310 | ||||||||
\(115\) | 0.0383860 | 0.00357951 | ||||||||
\(116\) | −19.8792 | −1.84573 | ||||||||
\(117\) | 6.60137 | 0.610297 | ||||||||
\(118\) | −11.3860 | −1.04817 | ||||||||
\(119\) | 2.37931 | 0.218111 | ||||||||
\(120\) | 7.28003 | 0.664573 | ||||||||
\(121\) | 13.6725 | 1.24295 | ||||||||
\(122\) | 25.0989 | 2.27235 | ||||||||
\(123\) | −9.18372 | −0.828068 | ||||||||
\(124\) | −7.77516 | −0.698230 | ||||||||
\(125\) | −11.9344 | −1.06745 | ||||||||
\(126\) | 2.31965 | 0.206651 | ||||||||
\(127\) | −2.81709 | −0.249976 | −0.124988 | − | 0.992158i | \(-0.539889\pi\) | ||||
−0.124988 | + | 0.992158i | \(0.539889\pi\) | |||||||
\(128\) | 20.4299 | 1.80576 | ||||||||
\(129\) | −7.22362 | −0.636004 | ||||||||
\(130\) | −25.7912 | −2.26203 | ||||||||
\(131\) | 21.5539 | 1.88317 | 0.941587 | − | 0.336770i | \(-0.109335\pi\) | ||||
0.941587 | + | 0.336770i | \(0.109335\pi\) | |||||||
\(132\) | −19.1898 | −1.67026 | ||||||||
\(133\) | 1.63601 | 0.141860 | ||||||||
\(134\) | −33.4194 | −2.88699 | ||||||||
\(135\) | −1.61348 | −0.138866 | ||||||||
\(136\) | 11.2065 | 0.960953 | ||||||||
\(137\) | 8.68182 | 0.741738 | 0.370869 | − | 0.928685i | \(-0.379060\pi\) | ||||
0.370869 | + | 0.928685i | \(0.379060\pi\) | |||||||
\(138\) | 0.0576079 | 0.00490391 | ||||||||
\(139\) | −18.7505 | −1.59039 | −0.795197 | − | 0.606351i | \(-0.792633\pi\) | ||||
−0.795197 | + | 0.606351i | \(0.792633\pi\) | |||||||
\(140\) | −5.97142 | −0.504677 | ||||||||
\(141\) | −1.75920 | −0.148151 | ||||||||
\(142\) | −13.0623 | −1.09617 | ||||||||
\(143\) | 32.7899 | 2.74203 | ||||||||
\(144\) | 3.19882 | 0.266568 | ||||||||
\(145\) | −8.30227 | −0.689466 | ||||||||
\(146\) | −11.3225 | −0.937056 | ||||||||
\(147\) | 6.08231 | 0.501660 | ||||||||
\(148\) | 3.56417 | 0.292973 | ||||||||
\(149\) | 18.2742 | 1.49708 | 0.748539 | − | 0.663091i | \(-0.230756\pi\) | ||||
0.748539 | + | 0.663091i | \(0.230756\pi\) | |||||||
\(150\) | −5.80341 | −0.473846 | ||||||||
\(151\) | −2.19947 | −0.178990 | −0.0894952 | − | 0.995987i | \(-0.528525\pi\) | ||||
−0.0894952 | + | 0.995987i | \(0.528525\pi\) | |||||||
\(152\) | 7.70561 | 0.625008 | ||||||||
\(153\) | −2.48372 | −0.200797 | ||||||||
\(154\) | 11.5220 | 0.928470 | ||||||||
\(155\) | −3.24719 | −0.260821 | ||||||||
\(156\) | −25.5034 | −2.04191 | ||||||||
\(157\) | 9.57699 | 0.764327 | 0.382164 | − | 0.924095i | \(-0.375179\pi\) | ||||
0.382164 | + | 0.924095i | \(0.375179\pi\) | |||||||
\(158\) | −2.84703 | −0.226497 | ||||||||
\(159\) | −3.75167 | −0.297527 | ||||||||
\(160\) | 2.06247 | 0.163052 | ||||||||
\(161\) | −0.0227907 | −0.00179616 | ||||||||
\(162\) | −2.42144 | −0.190246 | ||||||||
\(163\) | −3.83487 | −0.300370 | −0.150185 | − | 0.988658i | \(-0.547987\pi\) | ||||
−0.150185 | + | 0.988658i | \(0.547987\pi\) | |||||||
\(164\) | 35.4800 | 2.77052 | ||||||||
\(165\) | −8.01438 | −0.623919 | ||||||||
\(166\) | 41.4090 | 3.21396 | ||||||||
\(167\) | −4.05802 | −0.314019 | −0.157009 | − | 0.987597i | \(-0.550185\pi\) | ||||
−0.157009 | + | 0.987597i | \(0.550185\pi\) | |||||||
\(168\) | −4.32233 | −0.333475 | ||||||||
\(169\) | 30.5781 | 2.35216 | ||||||||
\(170\) | 9.70374 | 0.744243 | ||||||||
\(171\) | −1.70780 | −0.130599 | ||||||||
\(172\) | 27.9074 | 2.12792 | ||||||||
\(173\) | −3.16297 | −0.240476 | −0.120238 | − | 0.992745i | \(-0.538366\pi\) | ||||
−0.120238 | + | 0.992745i | \(0.538366\pi\) | |||||||
\(174\) | −12.4597 | −0.944565 | ||||||||
\(175\) | 2.29593 | 0.173556 | ||||||||
\(176\) | 15.8890 | 1.19768 | ||||||||
\(177\) | −4.70218 | −0.353438 | ||||||||
\(178\) | −10.3986 | −0.779411 | ||||||||
\(179\) | −10.4284 | −0.779458 | −0.389729 | − | 0.920930i | \(-0.627431\pi\) | ||||
−0.389729 | + | 0.920930i | \(0.627431\pi\) | |||||||
\(180\) | 6.23345 | 0.464614 | ||||||||
\(181\) | −19.5701 | −1.45463 | −0.727317 | − | 0.686302i | \(-0.759233\pi\) | ||||
−0.727317 | + | 0.686302i | \(0.759233\pi\) | |||||||
\(182\) | 15.3129 | 1.13506 | ||||||||
\(183\) | 10.3653 | 0.766225 | ||||||||
\(184\) | −0.107344 | −0.00791351 | ||||||||
\(185\) | 1.48853 | 0.109439 | ||||||||
\(186\) | −4.87324 | −0.357323 | ||||||||
\(187\) | −12.3370 | −0.902168 | ||||||||
\(188\) | 6.79641 | 0.495679 | ||||||||
\(189\) | 0.957963 | 0.0696816 | ||||||||
\(190\) | 6.67228 | 0.484058 | ||||||||
\(191\) | 15.8707 | 1.14836 | 0.574181 | − | 0.818729i | \(-0.305321\pi\) | ||||
0.574181 | + | 0.818729i | \(0.305321\pi\) | |||||||
\(192\) | 9.49289 | 0.685090 | ||||||||
\(193\) | −24.2289 | −1.74403 | −0.872017 | − | 0.489476i | \(-0.837188\pi\) | ||||
−0.872017 | + | 0.489476i | \(0.837188\pi\) | |||||||
\(194\) | 11.0937 | 0.796482 | ||||||||
\(195\) | −10.6512 | −0.762747 | ||||||||
\(196\) | −23.4981 | −1.67844 | ||||||||
\(197\) | 6.89095 | 0.490960 | 0.245480 | − | 0.969402i | \(-0.421054\pi\) | ||||
0.245480 | + | 0.969402i | \(0.421054\pi\) | |||||||
\(198\) | −12.0276 | −0.854765 | ||||||||
\(199\) | −20.4711 | −1.45116 | −0.725580 | − | 0.688138i | \(-0.758428\pi\) | ||||
−0.725580 | + | 0.688138i | \(0.758428\pi\) | |||||||
\(200\) | 10.8138 | 0.764653 | ||||||||
\(201\) | −13.8015 | −0.973480 | ||||||||
\(202\) | −14.0988 | −0.991986 | ||||||||
\(203\) | 4.92927 | 0.345967 | ||||||||
\(204\) | 9.59549 | 0.671819 | ||||||||
\(205\) | 14.8178 | 1.03492 | ||||||||
\(206\) | −6.50526 | −0.453243 | ||||||||
\(207\) | 0.0237908 | 0.00165357 | ||||||||
\(208\) | 21.1166 | 1.46417 | ||||||||
\(209\) | −8.48289 | −0.586774 | ||||||||
\(210\) | −3.74271 | −0.258271 | ||||||||
\(211\) | 9.26658 | 0.637937 | 0.318969 | − | 0.947765i | \(-0.396664\pi\) | ||||
0.318969 | + | 0.947765i | \(0.396664\pi\) | |||||||
\(212\) | 14.4940 | 0.995455 | ||||||||
\(213\) | −5.39446 | −0.369622 | ||||||||
\(214\) | −25.7618 | −1.76104 | ||||||||
\(215\) | 11.6552 | 0.794876 | ||||||||
\(216\) | 4.51200 | 0.307003 | ||||||||
\(217\) | 1.92794 | 0.130877 | ||||||||
\(218\) | −3.65708 | −0.247689 | ||||||||
\(219\) | −4.67594 | −0.315971 | ||||||||
\(220\) | 30.9624 | 2.08749 | ||||||||
\(221\) | −16.3959 | −1.10291 | ||||||||
\(222\) | 2.23391 | 0.149930 | ||||||||
\(223\) | 26.5273 | 1.77640 | 0.888199 | − | 0.459458i | \(-0.151956\pi\) | ||||
0.888199 | + | 0.459458i | \(0.151956\pi\) | |||||||
\(224\) | −1.22454 | −0.0818178 | ||||||||
\(225\) | −2.39668 | −0.159779 | ||||||||
\(226\) | −30.8571 | −2.05258 | ||||||||
\(227\) | 6.40963 | 0.425422 | 0.212711 | − | 0.977115i | \(-0.431771\pi\) | ||||
0.212711 | + | 0.977115i | \(0.431771\pi\) | |||||||
\(228\) | 6.59785 | 0.436953 | ||||||||
\(229\) | 20.9395 | 1.38372 | 0.691859 | − | 0.722032i | \(-0.256792\pi\) | ||||
0.691859 | + | 0.722032i | \(0.256792\pi\) | |||||||
\(230\) | −0.0929492 | −0.00612889 | ||||||||
\(231\) | 4.75834 | 0.313075 | ||||||||
\(232\) | 23.2168 | 1.52426 | ||||||||
\(233\) | −13.5153 | −0.885416 | −0.442708 | − | 0.896666i | \(-0.645982\pi\) | ||||
−0.442708 | + | 0.896666i | \(0.645982\pi\) | |||||||
\(234\) | −15.9848 | −1.04496 | ||||||||
\(235\) | 2.83843 | 0.185159 | ||||||||
\(236\) | 18.1662 | 1.18252 | ||||||||
\(237\) | −1.17576 | −0.0763738 | ||||||||
\(238\) | −5.76135 | −0.373453 | ||||||||
\(239\) | −7.51812 | −0.486306 | −0.243153 | − | 0.969988i | \(-0.578182\pi\) | ||||
−0.243153 | + | 0.969988i | \(0.578182\pi\) | |||||||
\(240\) | −5.16123 | −0.333156 | ||||||||
\(241\) | −13.4155 | −0.864169 | −0.432084 | − | 0.901833i | \(-0.642222\pi\) | ||||
−0.432084 | + | 0.901833i | \(0.642222\pi\) | |||||||
\(242\) | −33.1070 | −2.12820 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −40.0449 | −2.56361 | ||||||||
\(245\) | −9.81368 | −0.626973 | ||||||||
\(246\) | 22.2378 | 1.41783 | ||||||||
\(247\) | −11.2738 | −0.717337 | ||||||||
\(248\) | 9.08059 | 0.576618 | ||||||||
\(249\) | 17.1010 | 1.08373 | ||||||||
\(250\) | 28.8984 | 1.82770 | ||||||||
\(251\) | −24.0858 | −1.52028 | −0.760141 | − | 0.649759i | \(-0.774870\pi\) | ||||
−0.760141 | + | 0.649759i | \(0.774870\pi\) | |||||||
\(252\) | −3.70096 | −0.233138 | ||||||||
\(253\) | 0.118172 | 0.00742941 | ||||||||
\(254\) | 6.82140 | 0.428012 | ||||||||
\(255\) | 4.00743 | 0.250955 | ||||||||
\(256\) | −30.4839 | −1.90525 | ||||||||
\(257\) | −15.0582 | −0.939307 | −0.469654 | − | 0.882851i | \(-0.655621\pi\) | ||||
−0.469654 | + | 0.882851i | \(0.655621\pi\) | |||||||
\(258\) | 17.4915 | 1.08898 | ||||||||
\(259\) | −0.883776 | −0.0549151 | ||||||||
\(260\) | 41.1493 | 2.55197 | ||||||||
\(261\) | −5.14557 | −0.318503 | ||||||||
\(262\) | −52.1914 | −3.22440 | ||||||||
\(263\) | 27.2371 | 1.67951 | 0.839754 | − | 0.542967i | \(-0.182699\pi\) | ||||
0.839754 | + | 0.542967i | \(0.182699\pi\) | |||||||
\(264\) | 22.4117 | 1.37935 | ||||||||
\(265\) | 6.05325 | 0.371848 | ||||||||
\(266\) | −3.96150 | −0.242895 | ||||||||
\(267\) | −4.29441 | −0.262814 | ||||||||
\(268\) | 53.3200 | 3.25704 | ||||||||
\(269\) | −9.03426 | −0.550829 | −0.275414 | − | 0.961326i | \(-0.588815\pi\) | ||||
−0.275414 | + | 0.961326i | \(0.588815\pi\) | |||||||
\(270\) | 3.90694 | 0.237769 | ||||||||
\(271\) | −10.6330 | −0.645908 | −0.322954 | − | 0.946415i | \(-0.604676\pi\) | ||||
−0.322954 | + | 0.946415i | \(0.604676\pi\) | |||||||
\(272\) | −7.94496 | −0.481734 | ||||||||
\(273\) | 6.32387 | 0.382738 | ||||||||
\(274\) | −21.0225 | −1.27001 | ||||||||
\(275\) | −11.9046 | −0.717877 | ||||||||
\(276\) | −0.0919123 | −0.00553247 | ||||||||
\(277\) | −16.4006 | −0.985417 | −0.492708 | − | 0.870195i | \(-0.663993\pi\) | ||||
−0.492708 | + | 0.870195i | \(0.663993\pi\) | |||||||
\(278\) | 45.4031 | 2.72310 | ||||||||
\(279\) | −2.01254 | −0.120488 | ||||||||
\(280\) | 6.97400 | 0.416776 | ||||||||
\(281\) | 9.43465 | 0.562824 | 0.281412 | − | 0.959587i | \(-0.409197\pi\) | ||||
0.281412 | + | 0.959587i | \(0.409197\pi\) | |||||||
\(282\) | 4.25979 | 0.253667 | ||||||||
\(283\) | 28.4391 | 1.69053 | 0.845266 | − | 0.534346i | \(-0.179442\pi\) | ||||
0.845266 | + | 0.534346i | \(0.179442\pi\) | |||||||
\(284\) | 20.8407 | 1.23667 | ||||||||
\(285\) | 2.75551 | 0.163222 | ||||||||
\(286\) | −79.3987 | −4.69494 | ||||||||
\(287\) | −8.79767 | −0.519310 | ||||||||
\(288\) | 1.27827 | 0.0753228 | ||||||||
\(289\) | −10.8311 | −0.637126 | ||||||||
\(290\) | 20.1034 | 1.18051 | ||||||||
\(291\) | 4.58146 | 0.268570 | ||||||||
\(292\) | 18.0648 | 1.05716 | ||||||||
\(293\) | 19.9400 | 1.16491 | 0.582454 | − | 0.812863i | \(-0.302092\pi\) | ||||
0.582454 | + | 0.812863i | \(0.302092\pi\) | |||||||
\(294\) | −14.7279 | −0.858950 | ||||||||
\(295\) | 7.58688 | 0.441725 | ||||||||
\(296\) | −4.16258 | −0.241945 | ||||||||
\(297\) | −4.96714 | −0.288223 | ||||||||
\(298\) | −44.2497 | −2.56332 | ||||||||
\(299\) | 0.157052 | 0.00908253 | ||||||||
\(300\) | 9.25923 | 0.534582 | ||||||||
\(301\) | −6.91996 | −0.398860 | ||||||||
\(302\) | 5.32588 | 0.306470 | ||||||||
\(303\) | −5.82248 | −0.334493 | ||||||||
\(304\) | −5.46295 | −0.313322 | ||||||||
\(305\) | −16.7242 | −0.957626 | ||||||||
\(306\) | 6.01417 | 0.343807 | ||||||||
\(307\) | −5.84888 | −0.333813 | −0.166907 | − | 0.985973i | \(-0.553378\pi\) | ||||
−0.166907 | + | 0.985973i | \(0.553378\pi\) | |||||||
\(308\) | −18.3832 | −1.04748 | ||||||||
\(309\) | −2.68653 | −0.152831 | ||||||||
\(310\) | 7.86288 | 0.446581 | ||||||||
\(311\) | −30.6160 | −1.73607 | −0.868037 | − | 0.496499i | \(-0.834618\pi\) | ||||
−0.868037 | + | 0.496499i | \(0.834618\pi\) | |||||||
\(312\) | 29.7854 | 1.68627 | ||||||||
\(313\) | 7.93216 | 0.448352 | 0.224176 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224176 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(314\) | −23.1901 | −1.30869 | ||||||||
\(315\) | −1.54566 | −0.0870878 | ||||||||
\(316\) | 4.54238 | 0.255529 | ||||||||
\(317\) | 10.7324 | 0.602794 | 0.301397 | − | 0.953499i | \(-0.402547\pi\) | ||||
0.301397 | + | 0.953499i | \(0.402547\pi\) | |||||||
\(318\) | 9.08443 | 0.509430 | ||||||||
\(319\) | −25.5587 | −1.43101 | ||||||||
\(320\) | −15.3166 | −0.856224 | ||||||||
\(321\) | −10.6391 | −0.593815 | ||||||||
\(322\) | 0.0551862 | 0.00307541 | ||||||||
\(323\) | 4.24170 | 0.236014 | ||||||||
\(324\) | 3.86336 | 0.214631 | ||||||||
\(325\) | −15.8214 | −0.877612 | ||||||||
\(326\) | 9.28589 | 0.514298 | ||||||||
\(327\) | −1.51029 | −0.0835194 | ||||||||
\(328\) | −41.4370 | −2.28797 | ||||||||
\(329\) | −1.68525 | −0.0929107 | ||||||||
\(330\) | 19.4063 | 1.06828 | ||||||||
\(331\) | 32.9905 | 1.81332 | 0.906661 | − | 0.421860i | \(-0.138623\pi\) | ||||
0.906661 | + | 0.421860i | \(0.138623\pi\) | |||||||
\(332\) | −66.0672 | −3.62591 | ||||||||
\(333\) | 0.922557 | 0.0505558 | ||||||||
\(334\) | 9.82624 | 0.537668 | ||||||||
\(335\) | 22.2684 | 1.21665 | ||||||||
\(336\) | 3.06435 | 0.167174 | ||||||||
\(337\) | −31.1729 | −1.69810 | −0.849048 | − | 0.528316i | \(-0.822824\pi\) | ||||
−0.849048 | + | 0.528316i | \(0.822824\pi\) | |||||||
\(338\) | −74.0429 | −4.02740 | ||||||||
\(339\) | −12.7433 | −0.692121 | ||||||||
\(340\) | −15.4821 | −0.839637 | ||||||||
\(341\) | −9.99656 | −0.541344 | ||||||||
\(342\) | 4.13534 | 0.223613 | ||||||||
\(343\) | 12.5324 | 0.676684 | ||||||||
\(344\) | −32.5930 | −1.75730 | ||||||||
\(345\) | −0.0383860 | −0.00206663 | ||||||||
\(346\) | 7.65893 | 0.411746 | ||||||||
\(347\) | 26.2290 | 1.40805 | 0.704023 | − | 0.710177i | \(-0.251385\pi\) | ||||
0.704023 | + | 0.710177i | \(0.251385\pi\) | |||||||
\(348\) | 19.8792 | 1.06564 | ||||||||
\(349\) | −12.8802 | −0.689461 | −0.344731 | − | 0.938702i | \(-0.612030\pi\) | ||||
−0.344731 | + | 0.938702i | \(0.612030\pi\) | |||||||
\(350\) | −5.55945 | −0.297165 | ||||||||
\(351\) | −6.60137 | −0.352355 | ||||||||
\(352\) | 6.34935 | 0.338421 | ||||||||
\(353\) | 10.3508 | 0.550916 | 0.275458 | − | 0.961313i | \(-0.411170\pi\) | ||||
0.275458 | + | 0.961313i | \(0.411170\pi\) | |||||||
\(354\) | 11.3860 | 0.605161 | ||||||||
\(355\) | 8.70386 | 0.461953 | ||||||||
\(356\) | 16.5908 | 0.879313 | ||||||||
\(357\) | −2.37931 | −0.125926 | ||||||||
\(358\) | 25.2518 | 1.33460 | ||||||||
\(359\) | 14.9176 | 0.787323 | 0.393661 | − | 0.919256i | \(-0.371208\pi\) | ||||
0.393661 | + | 0.919256i | \(0.371208\pi\) | |||||||
\(360\) | −7.28003 | −0.383691 | ||||||||
\(361\) | −16.0834 | −0.846495 | ||||||||
\(362\) | 47.3878 | 2.49065 | ||||||||
\(363\) | −13.6725 | −0.717618 | ||||||||
\(364\) | −24.4314 | −1.28055 | ||||||||
\(365\) | 7.54454 | 0.394899 | ||||||||
\(366\) | −25.0989 | −1.31194 | ||||||||
\(367\) | −29.6456 | −1.54749 | −0.773745 | − | 0.633498i | \(-0.781619\pi\) | ||||
−0.773745 | + | 0.633498i | \(0.781619\pi\) | |||||||
\(368\) | 0.0761023 | 0.00396711 | ||||||||
\(369\) | 9.18372 | 0.478085 | ||||||||
\(370\) | −3.60438 | −0.187383 | ||||||||
\(371\) | −3.59396 | −0.186589 | ||||||||
\(372\) | 7.77516 | 0.403123 | ||||||||
\(373\) | 31.4667 | 1.62928 | 0.814642 | − | 0.579964i | \(-0.196933\pi\) | ||||
0.814642 | + | 0.579964i | \(0.196933\pi\) | |||||||
\(374\) | 29.8732 | 1.54471 | ||||||||
\(375\) | 11.9344 | 0.616290 | ||||||||
\(376\) | −7.93751 | −0.409346 | ||||||||
\(377\) | −33.9678 | −1.74943 | ||||||||
\(378\) | −2.31965 | −0.119310 | ||||||||
\(379\) | −15.2183 | −0.781713 | −0.390857 | − | 0.920452i | \(-0.627821\pi\) | ||||
−0.390857 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(380\) | −10.6455 | −0.546103 | ||||||||
\(381\) | 2.81709 | 0.144324 | ||||||||
\(382\) | −38.4298 | −1.96624 | ||||||||
\(383\) | 31.9739 | 1.63379 | 0.816896 | − | 0.576785i | \(-0.195693\pi\) | ||||
0.816896 | + | 0.576785i | \(0.195693\pi\) | |||||||
\(384\) | −20.4299 | −1.04256 | ||||||||
\(385\) | −7.67748 | −0.391281 | ||||||||
\(386\) | 58.6687 | 2.98616 | ||||||||
\(387\) | 7.22362 | 0.367197 | ||||||||
\(388\) | −17.6998 | −0.898572 | ||||||||
\(389\) | 4.30499 | 0.218271 | 0.109136 | − | 0.994027i | \(-0.465192\pi\) | ||||
0.109136 | + | 0.994027i | \(0.465192\pi\) | |||||||
\(390\) | 25.7912 | 1.30599 | ||||||||
\(391\) | −0.0590895 | −0.00298829 | ||||||||
\(392\) | 27.4434 | 1.38610 | ||||||||
\(393\) | −21.5539 | −1.08725 | ||||||||
\(394\) | −16.6860 | −0.840628 | ||||||||
\(395\) | 1.89707 | 0.0954518 | ||||||||
\(396\) | 19.1898 | 0.964325 | ||||||||
\(397\) | −2.29107 | −0.114986 | −0.0574928 | − | 0.998346i | \(-0.518311\pi\) | ||||
−0.0574928 | + | 0.998346i | \(0.518311\pi\) | |||||||
\(398\) | 49.5695 | 2.48470 | ||||||||
\(399\) | −1.63601 | −0.0819030 | ||||||||
\(400\) | −7.66654 | −0.383327 | ||||||||
\(401\) | −28.3611 | −1.41629 | −0.708143 | − | 0.706069i | \(-0.750467\pi\) | ||||
−0.708143 | + | 0.706069i | \(0.750467\pi\) | |||||||
\(402\) | 33.4194 | 1.66681 | ||||||||
\(403\) | −13.2855 | −0.661799 | ||||||||
\(404\) | 22.4943 | 1.11913 | ||||||||
\(405\) | 1.61348 | 0.0801745 | ||||||||
\(406\) | −11.9359 | −0.592369 | ||||||||
\(407\) | 4.58247 | 0.227144 | ||||||||
\(408\) | −11.2065 | −0.554806 | ||||||||
\(409\) | 0.444555 | 0.0219818 | 0.0109909 | − | 0.999940i | \(-0.496501\pi\) | ||||
0.0109909 | + | 0.999940i | \(0.496501\pi\) | |||||||
\(410\) | −35.8803 | −1.77200 | ||||||||
\(411\) | −8.68182 | −0.428243 | ||||||||
\(412\) | 10.3790 | 0.511337 | ||||||||
\(413\) | −4.50452 | −0.221653 | ||||||||
\(414\) | −0.0576079 | −0.00283127 | ||||||||
\(415\) | −27.5921 | −1.35444 | ||||||||
\(416\) | 8.43834 | 0.413724 | ||||||||
\(417\) | 18.7505 | 0.918215 | ||||||||
\(418\) | 20.5408 | 1.00468 | ||||||||
\(419\) | −23.3583 | −1.14113 | −0.570565 | − | 0.821253i | \(-0.693276\pi\) | ||||
−0.570565 | + | 0.821253i | \(0.693276\pi\) | |||||||
\(420\) | 5.97142 | 0.291375 | ||||||||
\(421\) | 5.22449 | 0.254626 | 0.127313 | − | 0.991863i | \(-0.459365\pi\) | ||||
0.127313 | + | 0.991863i | \(0.459365\pi\) | |||||||
\(422\) | −22.4384 | −1.09229 | ||||||||
\(423\) | 1.75920 | 0.0855352 | ||||||||
\(424\) | −16.9275 | −0.822074 | ||||||||
\(425\) | 5.95268 | 0.288747 | ||||||||
\(426\) | 13.0623 | 0.632873 | ||||||||
\(427\) | 9.92958 | 0.480526 | ||||||||
\(428\) | 41.1025 | 1.98677 | ||||||||
\(429\) | −32.7899 | −1.58311 | ||||||||
\(430\) | −28.2223 | −1.36100 | ||||||||
\(431\) | 31.6031 | 1.52227 | 0.761135 | − | 0.648593i | \(-0.224642\pi\) | ||||
0.761135 | + | 0.648593i | \(0.224642\pi\) | |||||||
\(432\) | −3.19882 | −0.153903 | ||||||||
\(433\) | −20.1063 | −0.966248 | −0.483124 | − | 0.875552i | \(-0.660498\pi\) | ||||
−0.483124 | + | 0.875552i | \(0.660498\pi\) | |||||||
\(434\) | −4.66839 | −0.224090 | ||||||||
\(435\) | 8.30227 | 0.398064 | ||||||||
\(436\) | 5.83480 | 0.279436 | ||||||||
\(437\) | −0.0406299 | −0.00194359 | ||||||||
\(438\) | 11.3225 | 0.541010 | ||||||||
\(439\) | −19.4198 | −0.926858 | −0.463429 | − | 0.886134i | \(-0.653381\pi\) | ||||
−0.463429 | + | 0.886134i | \(0.653381\pi\) | |||||||
\(440\) | −36.1609 | −1.72390 | ||||||||
\(441\) | −6.08231 | −0.289634 | ||||||||
\(442\) | 39.7017 | 1.88842 | ||||||||
\(443\) | 25.4266 | 1.20806 | 0.604028 | − | 0.796963i | \(-0.293561\pi\) | ||||
0.604028 | + | 0.796963i | \(0.293561\pi\) | |||||||
\(444\) | −3.56417 | −0.169148 | ||||||||
\(445\) | 6.92895 | 0.328464 | ||||||||
\(446\) | −64.2342 | −3.04158 | ||||||||
\(447\) | −18.2742 | −0.864338 | ||||||||
\(448\) | 9.09384 | 0.429644 | ||||||||
\(449\) | −18.2866 | −0.862997 | −0.431499 | − | 0.902114i | \(-0.642015\pi\) | ||||
−0.431499 | + | 0.902114i | \(0.642015\pi\) | |||||||
\(450\) | 5.80341 | 0.273575 | ||||||||
\(451\) | 45.6168 | 2.14801 | ||||||||
\(452\) | 49.2320 | 2.31568 | ||||||||
\(453\) | 2.19947 | 0.103340 | ||||||||
\(454\) | −15.5205 | −0.728414 | ||||||||
\(455\) | −10.2034 | −0.478345 | ||||||||
\(456\) | −7.70561 | −0.360848 | ||||||||
\(457\) | −22.6083 | −1.05757 | −0.528785 | − | 0.848756i | \(-0.677352\pi\) | ||||
−0.528785 | + | 0.848756i | \(0.677352\pi\) | |||||||
\(458\) | −50.7036 | −2.36922 | ||||||||
\(459\) | 2.48372 | 0.115930 | ||||||||
\(460\) | 0.148299 | 0.00691446 | ||||||||
\(461\) | −9.11367 | −0.424466 | −0.212233 | − | 0.977219i | \(-0.568074\pi\) | ||||
−0.212233 | + | 0.977219i | \(0.568074\pi\) | |||||||
\(462\) | −11.5220 | −0.536052 | ||||||||
\(463\) | 13.9641 | 0.648966 | 0.324483 | − | 0.945891i | \(-0.394810\pi\) | ||||
0.324483 | + | 0.945891i | \(0.394810\pi\) | |||||||
\(464\) | −16.4597 | −0.764124 | ||||||||
\(465\) | 3.24719 | 0.150585 | ||||||||
\(466\) | 32.7264 | 1.51602 | ||||||||
\(467\) | 25.2799 | 1.16981 | 0.584907 | − | 0.811100i | \(-0.301131\pi\) | ||||
0.584907 | + | 0.811100i | \(0.301131\pi\) | |||||||
\(468\) | 25.5034 | 1.17890 | ||||||||
\(469\) | −13.2213 | −0.610503 | ||||||||
\(470\) | −6.87309 | −0.317032 | ||||||||
\(471\) | −9.57699 | −0.441285 | ||||||||
\(472\) | −21.2163 | −0.976558 | ||||||||
\(473\) | 35.8807 | 1.64980 | ||||||||
\(474\) | 2.84703 | 0.130768 | ||||||||
\(475\) | 4.09306 | 0.187802 | ||||||||
\(476\) | 9.19213 | 0.421320 | ||||||||
\(477\) | 3.75167 | 0.171777 | ||||||||
\(478\) | 18.2046 | 0.832661 | ||||||||
\(479\) | 13.6265 | 0.622613 | 0.311306 | − | 0.950310i | \(-0.399233\pi\) | ||||
0.311306 | + | 0.950310i | \(0.399233\pi\) | |||||||
\(480\) | −2.06247 | −0.0941382 | ||||||||
\(481\) | 6.09014 | 0.277686 | ||||||||
\(482\) | 32.4848 | 1.47964 | ||||||||
\(483\) | 0.0227907 | 0.00103701 | ||||||||
\(484\) | 52.8216 | 2.40098 | ||||||||
\(485\) | −7.39209 | −0.335658 | ||||||||
\(486\) | 2.42144 | 0.109839 | ||||||||
\(487\) | 25.6166 | 1.16080 | 0.580400 | − | 0.814332i | \(-0.302896\pi\) | ||||
0.580400 | + | 0.814332i | \(0.302896\pi\) | |||||||
\(488\) | 46.7683 | 2.11710 | ||||||||
\(489\) | 3.83487 | 0.173419 | ||||||||
\(490\) | 23.7632 | 1.07351 | ||||||||
\(491\) | 26.8885 | 1.21346 | 0.606730 | − | 0.794908i | \(-0.292481\pi\) | ||||
0.606730 | + | 0.794908i | \(0.292481\pi\) | |||||||
\(492\) | −35.4800 | −1.59956 | ||||||||
\(493\) | 12.7801 | 0.575588 | ||||||||
\(494\) | 27.2989 | 1.22823 | ||||||||
\(495\) | 8.01438 | 0.360220 | ||||||||
\(496\) | −6.43775 | −0.289064 | ||||||||
\(497\) | −5.16769 | −0.231803 | ||||||||
\(498\) | −41.4090 | −1.85558 | ||||||||
\(499\) | 7.47479 | 0.334618 | 0.167309 | − | 0.985905i | \(-0.446492\pi\) | ||||
0.167309 | + | 0.985905i | \(0.446492\pi\) | |||||||
\(500\) | −46.1069 | −2.06196 | ||||||||
\(501\) | 4.05802 | 0.181299 | ||||||||
\(502\) | 58.3222 | 2.60305 | ||||||||
\(503\) | −32.1006 | −1.43130 | −0.715648 | − | 0.698461i | \(-0.753869\pi\) | ||||
−0.715648 | + | 0.698461i | \(0.753869\pi\) | |||||||
\(504\) | 4.32233 | 0.192532 | ||||||||
\(505\) | 9.39446 | 0.418048 | ||||||||
\(506\) | −0.286146 | −0.0127207 | ||||||||
\(507\) | −30.5781 | −1.35802 | ||||||||
\(508\) | −10.8834 | −0.482873 | ||||||||
\(509\) | 26.0521 | 1.15474 | 0.577369 | − | 0.816483i | \(-0.304079\pi\) | ||||
0.577369 | + | 0.816483i | \(0.304079\pi\) | |||||||
\(510\) | −9.70374 | −0.429689 | ||||||||
\(511\) | −4.47938 | −0.198156 | ||||||||
\(512\) | 32.9551 | 1.45642 | ||||||||
\(513\) | 1.70780 | 0.0754013 | ||||||||
\(514\) | 36.4626 | 1.60830 | ||||||||
\(515\) | 4.33466 | 0.191008 | ||||||||
\(516\) | −27.9074 | −1.22856 | ||||||||
\(517\) | 8.73818 | 0.384305 | ||||||||
\(518\) | 2.14001 | 0.0940265 | ||||||||
\(519\) | 3.16297 | 0.138839 | ||||||||
\(520\) | −48.0582 | −2.10749 | ||||||||
\(521\) | 7.77855 | 0.340784 | 0.170392 | − | 0.985376i | \(-0.445497\pi\) | ||||
0.170392 | + | 0.985376i | \(0.445497\pi\) | |||||||
\(522\) | 12.4597 | 0.545345 | ||||||||
\(523\) | 25.0355 | 1.09472 | 0.547362 | − | 0.836896i | \(-0.315632\pi\) | ||||
0.547362 | + | 0.836896i | \(0.315632\pi\) | |||||||
\(524\) | 83.2705 | 3.63769 | ||||||||
\(525\) | −2.29593 | −0.100203 | ||||||||
\(526\) | −65.9528 | −2.87568 | ||||||||
\(527\) | 4.99858 | 0.217742 | ||||||||
\(528\) | −15.8890 | −0.691479 | ||||||||
\(529\) | −22.9994 | −0.999975 | ||||||||
\(530\) | −14.6576 | −0.636683 | ||||||||
\(531\) | 4.70218 | 0.204057 | ||||||||
\(532\) | 6.32050 | 0.274028 | ||||||||
\(533\) | 60.6251 | 2.62597 | ||||||||
\(534\) | 10.3986 | 0.449993 | ||||||||
\(535\) | 17.1659 | 0.742148 | ||||||||
\(536\) | −62.2722 | −2.68975 | ||||||||
\(537\) | 10.4284 | 0.450020 | ||||||||
\(538\) | 21.8759 | 0.943137 | ||||||||
\(539\) | −30.2116 | −1.30131 | ||||||||
\(540\) | −6.23345 | −0.268245 | ||||||||
\(541\) | 22.0380 | 0.947488 | 0.473744 | − | 0.880663i | \(-0.342902\pi\) | ||||
0.473744 | + | 0.880663i | \(0.342902\pi\) | |||||||
\(542\) | 25.7471 | 1.10593 | ||||||||
\(543\) | 19.5701 | 0.839833 | ||||||||
\(544\) | −3.17486 | −0.136121 | ||||||||
\(545\) | 2.43683 | 0.104382 | ||||||||
\(546\) | −15.3129 | −0.655330 | ||||||||
\(547\) | −25.8946 | −1.10717 | −0.553586 | − | 0.832792i | \(-0.686741\pi\) | ||||
−0.553586 | + | 0.832792i | \(0.686741\pi\) | |||||||
\(548\) | 33.5410 | 1.43280 | ||||||||
\(549\) | −10.3653 | −0.442380 | ||||||||
\(550\) | 28.8263 | 1.22916 | ||||||||
\(551\) | 8.78761 | 0.374365 | ||||||||
\(552\) | 0.107344 | 0.00456887 | ||||||||
\(553\) | −1.12634 | −0.0478966 | ||||||||
\(554\) | 39.7130 | 1.68724 | ||||||||
\(555\) | −1.48853 | −0.0631845 | ||||||||
\(556\) | −72.4398 | −3.07213 | ||||||||
\(557\) | 28.1511 | 1.19280 | 0.596400 | − | 0.802687i | \(-0.296597\pi\) | ||||
0.596400 | + | 0.802687i | \(0.296597\pi\) | |||||||
\(558\) | 4.87324 | 0.206301 | ||||||||
\(559\) | 47.6858 | 2.01689 | ||||||||
\(560\) | −4.94427 | −0.208934 | ||||||||
\(561\) | 12.3370 | 0.520867 | ||||||||
\(562\) | −22.8454 | −0.963676 | ||||||||
\(563\) | 17.4970 | 0.737409 | 0.368705 | − | 0.929547i | \(-0.379801\pi\) | ||||
0.368705 | + | 0.929547i | \(0.379801\pi\) | |||||||
\(564\) | −6.79641 | −0.286181 | ||||||||
\(565\) | 20.5611 | 0.865011 | ||||||||
\(566\) | −68.8636 | −2.89455 | ||||||||
\(567\) | −0.957963 | −0.0402307 | ||||||||
\(568\) | −24.3398 | −1.02128 | ||||||||
\(569\) | −39.9250 | −1.67374 | −0.836872 | − | 0.547398i | \(-0.815618\pi\) | ||||
−0.836872 | + | 0.547398i | \(0.815618\pi\) | |||||||
\(570\) | −6.67228 | −0.279471 | ||||||||
\(571\) | 19.5354 | 0.817532 | 0.408766 | − | 0.912639i | \(-0.365959\pi\) | ||||
0.408766 | + | 0.912639i | \(0.365959\pi\) | |||||||
\(572\) | 126.679 | 5.29672 | ||||||||
\(573\) | −15.8707 | −0.663007 | ||||||||
\(574\) | 21.3030 | 0.889170 | ||||||||
\(575\) | −0.0570189 | −0.00237785 | ||||||||
\(576\) | −9.49289 | −0.395537 | ||||||||
\(577\) | −1.78291 | −0.0742236 | −0.0371118 | − | 0.999311i | \(-0.511816\pi\) | ||||
−0.0371118 | + | 0.999311i | \(0.511816\pi\) | |||||||
\(578\) | 26.2269 | 1.09090 | ||||||||
\(579\) | 24.2289 | 1.00692 | ||||||||
\(580\) | −32.0747 | −1.33183 | ||||||||
\(581\) | 16.3821 | 0.679645 | ||||||||
\(582\) | −11.0937 | −0.459849 | ||||||||
\(583\) | 18.6351 | 0.771785 | ||||||||
\(584\) | −21.0979 | −0.873036 | ||||||||
\(585\) | 10.6512 | 0.440372 | ||||||||
\(586\) | −48.2835 | −1.99457 | ||||||||
\(587\) | 36.9682 | 1.52584 | 0.762920 | − | 0.646493i | \(-0.223765\pi\) | ||||
0.762920 | + | 0.646493i | \(0.223765\pi\) | |||||||
\(588\) | 23.4981 | 0.969046 | ||||||||
\(589\) | 3.43702 | 0.141620 | ||||||||
\(590\) | −18.3712 | −0.756329 | ||||||||
\(591\) | −6.89095 | −0.283456 | ||||||||
\(592\) | 2.95109 | 0.121289 | ||||||||
\(593\) | −28.6103 | −1.17489 | −0.587443 | − | 0.809266i | \(-0.699865\pi\) | ||||
−0.587443 | + | 0.809266i | \(0.699865\pi\) | |||||||
\(594\) | 12.0276 | 0.493499 | ||||||||
\(595\) | 3.83897 | 0.157382 | ||||||||
\(596\) | 70.5996 | 2.89187 | ||||||||
\(597\) | 20.4711 | 0.837827 | ||||||||
\(598\) | −0.380291 | −0.0155512 | ||||||||
\(599\) | −47.7663 | −1.95168 | −0.975840 | − | 0.218488i | \(-0.929888\pi\) | ||||
−0.975840 | + | 0.218488i | \(0.929888\pi\) | |||||||
\(600\) | −10.8138 | −0.441473 | ||||||||
\(601\) | −3.36864 | −0.137410 | −0.0687049 | − | 0.997637i | \(-0.521887\pi\) | ||||
−0.0687049 | + | 0.997637i | \(0.521887\pi\) | |||||||
\(602\) | 16.7563 | 0.682934 | ||||||||
\(603\) | 13.8015 | 0.562039 | ||||||||
\(604\) | −8.49734 | −0.345752 | ||||||||
\(605\) | 22.0602 | 0.896876 | ||||||||
\(606\) | 14.0988 | 0.572723 | ||||||||
\(607\) | 13.7141 | 0.556640 | 0.278320 | − | 0.960488i | \(-0.410222\pi\) | ||||
0.278320 | + | 0.960488i | \(0.410222\pi\) | |||||||
\(608\) | −2.18303 | −0.0885337 | ||||||||
\(609\) | −4.92927 | −0.199744 | ||||||||
\(610\) | 40.4966 | 1.63966 | ||||||||
\(611\) | 11.6131 | 0.469817 | ||||||||
\(612\) | −9.59549 | −0.387875 | ||||||||
\(613\) | 30.1698 | 1.21854 | 0.609272 | − | 0.792961i | \(-0.291462\pi\) | ||||
0.609272 | + | 0.792961i | \(0.291462\pi\) | |||||||
\(614\) | 14.1627 | 0.571560 | ||||||||
\(615\) | −14.8178 | −0.597510 | ||||||||
\(616\) | 21.4696 | 0.865036 | ||||||||
\(617\) | 29.8768 | 1.20279 | 0.601397 | − | 0.798951i | \(-0.294611\pi\) | ||||
0.601397 | + | 0.798951i | \(0.294611\pi\) | |||||||
\(618\) | 6.50526 | 0.261680 | ||||||||
\(619\) | 31.8033 | 1.27828 | 0.639141 | − | 0.769090i | \(-0.279290\pi\) | ||||
0.639141 | + | 0.769090i | \(0.279290\pi\) | |||||||
\(620\) | −12.5451 | −0.503822 | ||||||||
\(621\) | −0.0237908 | −0.000954691 0 | ||||||||
\(622\) | 74.1347 | 2.97253 | ||||||||
\(623\) | −4.11389 | −0.164819 | ||||||||
\(624\) | −21.1166 | −0.845340 | ||||||||
\(625\) | −7.27252 | −0.290901 | ||||||||
\(626\) | −19.2072 | −0.767675 | ||||||||
\(627\) | 8.48289 | 0.338774 | ||||||||
\(628\) | 36.9994 | 1.47643 | ||||||||
\(629\) | −2.29137 | −0.0913629 | ||||||||
\(630\) | 3.74271 | 0.149113 | ||||||||
\(631\) | 30.3041 | 1.20639 | 0.603193 | − | 0.797595i | \(-0.293895\pi\) | ||||
0.603193 | + | 0.797595i | \(0.293895\pi\) | |||||||
\(632\) | −5.30503 | −0.211023 | ||||||||
\(633\) | −9.26658 | −0.368313 | ||||||||
\(634\) | −25.9879 | −1.03211 | ||||||||
\(635\) | −4.54531 | −0.180375 | ||||||||
\(636\) | −14.4940 | −0.574726 | ||||||||
\(637\) | −40.1515 | −1.59086 | ||||||||
\(638\) | 61.8889 | 2.45020 | ||||||||
\(639\) | 5.39446 | 0.213402 | ||||||||
\(640\) | 32.9632 | 1.30299 | ||||||||
\(641\) | −38.4368 | −1.51816 | −0.759081 | − | 0.650996i | \(-0.774351\pi\) | ||||
−0.759081 | + | 0.650996i | \(0.774351\pi\) | |||||||
\(642\) | 25.7618 | 1.01674 | ||||||||
\(643\) | 22.5934 | 0.890997 | 0.445498 | − | 0.895283i | \(-0.353026\pi\) | ||||
0.445498 | + | 0.895283i | \(0.353026\pi\) | |||||||
\(644\) | −0.0880486 | −0.00346960 | ||||||||
\(645\) | −11.6552 | −0.458922 | ||||||||
\(646\) | −10.2710 | −0.404107 | ||||||||
\(647\) | 0.440884 | 0.0173329 | 0.00866647 | − | 0.999962i | \(-0.497241\pi\) | ||||
0.00866647 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(648\) | −4.51200 | −0.177248 | ||||||||
\(649\) | 23.3564 | 0.916819 | ||||||||
\(650\) | 38.3104 | 1.50266 | ||||||||
\(651\) | −1.92794 | −0.0755619 | ||||||||
\(652\) | −14.8155 | −0.580219 | ||||||||
\(653\) | −41.6110 | −1.62836 | −0.814182 | − | 0.580609i | \(-0.802814\pi\) | ||||
−0.814182 | + | 0.580609i | \(0.802814\pi\) | |||||||
\(654\) | 3.65708 | 0.143003 | ||||||||
\(655\) | 34.7768 | 1.35884 | ||||||||
\(656\) | 29.3771 | 1.14698 | ||||||||
\(657\) | 4.67594 | 0.182426 | ||||||||
\(658\) | 4.08072 | 0.159083 | ||||||||
\(659\) | 13.9094 | 0.541833 | 0.270916 | − | 0.962603i | \(-0.412673\pi\) | ||||
0.270916 | + | 0.962603i | \(0.412673\pi\) | |||||||
\(660\) | −30.9624 | −1.20521 | ||||||||
\(661\) | 37.0319 | 1.44037 | 0.720186 | − | 0.693781i | \(-0.244056\pi\) | ||||
0.720186 | + | 0.693781i | \(0.244056\pi\) | |||||||
\(662\) | −79.8844 | −3.10480 | ||||||||
\(663\) | 16.3959 | 0.636765 | ||||||||
\(664\) | 77.1597 | 2.99438 | ||||||||
\(665\) | 2.63967 | 0.102362 | ||||||||
\(666\) | −2.23391 | −0.0865624 | ||||||||
\(667\) | −0.122417 | −0.00474001 | ||||||||
\(668\) | −15.6776 | −0.606584 | ||||||||
\(669\) | −26.5273 | −1.02560 | ||||||||
\(670\) | −53.9215 | −2.08317 | ||||||||
\(671\) | −51.4859 | −1.98759 | ||||||||
\(672\) | 1.22454 | 0.0472375 | ||||||||
\(673\) | −2.45981 | −0.0948186 | −0.0474093 | − | 0.998876i | \(-0.515097\pi\) | ||||
−0.0474093 | + | 0.998876i | \(0.515097\pi\) | |||||||
\(674\) | 75.4832 | 2.90750 | ||||||||
\(675\) | 2.39668 | 0.0922483 | ||||||||
\(676\) | 118.134 | 4.54361 | ||||||||
\(677\) | −24.9543 | −0.959074 | −0.479537 | − | 0.877522i | \(-0.659195\pi\) | ||||
−0.479537 | + | 0.877522i | \(0.659195\pi\) | |||||||
\(678\) | 30.8571 | 1.18506 | ||||||||
\(679\) | 4.38887 | 0.168429 | ||||||||
\(680\) | 18.0815 | 0.693395 | ||||||||
\(681\) | −6.40963 | −0.245617 | ||||||||
\(682\) | 24.2061 | 0.926898 | ||||||||
\(683\) | −1.52721 | −0.0584370 | −0.0292185 | − | 0.999573i | \(-0.509302\pi\) | ||||
−0.0292185 | + | 0.999573i | \(0.509302\pi\) | |||||||
\(684\) | −6.59785 | −0.252275 | ||||||||
\(685\) | 14.0080 | 0.535216 | ||||||||
\(686\) | −30.3463 | −1.15863 | ||||||||
\(687\) | −20.9395 | −0.798890 | ||||||||
\(688\) | 23.1070 | 0.880948 | ||||||||
\(689\) | 24.7661 | 0.943515 | ||||||||
\(690\) | 0.0929492 | 0.00353851 | ||||||||
\(691\) | −14.0182 | −0.533277 | −0.266638 | − | 0.963797i | \(-0.585913\pi\) | ||||
−0.266638 | + | 0.963797i | \(0.585913\pi\) | |||||||
\(692\) | −12.2197 | −0.464522 | ||||||||
\(693\) | −4.75834 | −0.180754 | ||||||||
\(694\) | −63.5118 | −2.41088 | ||||||||
\(695\) | −30.2535 | −1.14758 | ||||||||
\(696\) | −23.2168 | −0.880031 | ||||||||
\(697\) | −22.8098 | −0.863982 | ||||||||
\(698\) | 31.1886 | 1.18051 | ||||||||
\(699\) | 13.5153 | 0.511195 | ||||||||
\(700\) | 8.87001 | 0.335255 | ||||||||
\(701\) | 5.05638 | 0.190977 | 0.0954884 | − | 0.995431i | \(-0.469559\pi\) | ||||
0.0954884 | + | 0.995431i | \(0.469559\pi\) | |||||||
\(702\) | 15.9848 | 0.603307 | ||||||||
\(703\) | −1.57554 | −0.0594228 | ||||||||
\(704\) | −47.1525 | −1.77713 | ||||||||
\(705\) | −2.83843 | −0.106902 | ||||||||
\(706\) | −25.0637 | −0.943287 | ||||||||
\(707\) | −5.57772 | −0.209772 | ||||||||
\(708\) | −18.1662 | −0.682728 | ||||||||
\(709\) | 34.9209 | 1.31148 | 0.655740 | − | 0.754987i | \(-0.272357\pi\) | ||||
0.655740 | + | 0.754987i | \(0.272357\pi\) | |||||||
\(710\) | −21.0758 | −0.790962 | ||||||||
\(711\) | 1.17576 | 0.0440945 | ||||||||
\(712\) | −19.3764 | −0.726161 | ||||||||
\(713\) | −0.0478799 | −0.00179312 | ||||||||
\(714\) | 5.76135 | 0.215613 | ||||||||
\(715\) | 52.9059 | 1.97857 | ||||||||
\(716\) | −40.2888 | −1.50566 | ||||||||
\(717\) | 7.51812 | 0.280769 | ||||||||
\(718\) | −36.1221 | −1.34807 | ||||||||
\(719\) | −41.5889 | −1.55100 | −0.775501 | − | 0.631346i | \(-0.782503\pi\) | ||||
−0.775501 | + | 0.631346i | \(0.782503\pi\) | |||||||
\(720\) | 5.16123 | 0.192348 | ||||||||
\(721\) | −2.57359 | −0.0958457 | ||||||||
\(722\) | 38.9450 | 1.44938 | ||||||||
\(723\) | 13.4155 | 0.498928 | ||||||||
\(724\) | −75.6063 | −2.80989 | ||||||||
\(725\) | 12.3323 | 0.458009 | ||||||||
\(726\) | 33.1070 | 1.22872 | ||||||||
\(727\) | −15.3774 | −0.570318 | −0.285159 | − | 0.958480i | \(-0.592046\pi\) | ||||
−0.285159 | + | 0.958480i | \(0.592046\pi\) | |||||||
\(728\) | 28.5333 | 1.05752 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.2686 | −0.676152 | ||||||||
\(731\) | −17.9414 | −0.663588 | ||||||||
\(732\) | 40.0449 | 1.48010 | ||||||||
\(733\) | 21.1324 | 0.780542 | 0.390271 | − | 0.920700i | \(-0.372381\pi\) | ||||
0.390271 | + | 0.920700i | \(0.372381\pi\) | |||||||
\(734\) | 71.7850 | 2.64963 | ||||||||
\(735\) | 9.81368 | 0.361983 | ||||||||
\(736\) | 0.0304111 | 0.00112097 | ||||||||
\(737\) | 68.5537 | 2.52521 | ||||||||
\(738\) | −22.2378 | −0.818585 | ||||||||
\(739\) | −32.0807 | −1.18011 | −0.590054 | − | 0.807364i | \(-0.700893\pi\) | ||||
−0.590054 | + | 0.807364i | \(0.700893\pi\) | |||||||
\(740\) | 5.75072 | 0.211400 | ||||||||
\(741\) | 11.2738 | 0.414155 | ||||||||
\(742\) | 8.70255 | 0.319481 | ||||||||
\(743\) | 15.5713 | 0.571254 | 0.285627 | − | 0.958341i | \(-0.407798\pi\) | ||||
0.285627 | + | 0.958341i | \(0.407798\pi\) | |||||||
\(744\) | −9.08059 | −0.332911 | ||||||||
\(745\) | 29.4850 | 1.08025 | ||||||||
\(746\) | −76.1947 | −2.78968 | ||||||||
\(747\) | −17.1010 | −0.625692 | ||||||||
\(748\) | −47.6621 | −1.74270 | ||||||||
\(749\) | −10.1918 | −0.372402 | ||||||||
\(750\) | −28.8984 | −1.05522 | ||||||||
\(751\) | 13.9185 | 0.507893 | 0.253947 | − | 0.967218i | \(-0.418271\pi\) | ||||
0.253947 | + | 0.967218i | \(0.418271\pi\) | |||||||
\(752\) | 5.62736 | 0.205209 | ||||||||
\(753\) | 24.0858 | 0.877735 | ||||||||
\(754\) | 82.2509 | 2.99540 | ||||||||
\(755\) | −3.54880 | −0.129154 | ||||||||
\(756\) | 3.70096 | 0.134602 | ||||||||
\(757\) | 25.5963 | 0.930312 | 0.465156 | − | 0.885229i | \(-0.345998\pi\) | ||||
0.465156 | + | 0.885229i | \(0.345998\pi\) | |||||||
\(758\) | 36.8502 | 1.33846 | ||||||||
\(759\) | −0.118172 | −0.00428937 | ||||||||
\(760\) | 12.4329 | 0.450987 | ||||||||
\(761\) | 30.8106 | 1.11688 | 0.558442 | − | 0.829543i | \(-0.311399\pi\) | ||||
0.558442 | + | 0.829543i | \(0.311399\pi\) | |||||||
\(762\) | −6.82140 | −0.247113 | ||||||||
\(763\) | −1.44681 | −0.0523779 | ||||||||
\(764\) | 61.3141 | 2.21827 | ||||||||
\(765\) | −4.00743 | −0.144889 | ||||||||
\(766\) | −77.4229 | −2.79740 | ||||||||
\(767\) | 31.0408 | 1.12082 | ||||||||
\(768\) | 30.4839 | 1.09999 | ||||||||
\(769\) | 13.5562 | 0.488847 | 0.244424 | − | 0.969669i | \(-0.421401\pi\) | ||||
0.244424 | + | 0.969669i | \(0.421401\pi\) | |||||||
\(770\) | 18.5905 | 0.669957 | ||||||||
\(771\) | 15.0582 | 0.542309 | ||||||||
\(772\) | −93.6049 | −3.36891 | ||||||||
\(773\) | 3.90499 | 0.140453 | 0.0702263 | − | 0.997531i | \(-0.477628\pi\) | ||||
0.0702263 | + | 0.997531i | \(0.477628\pi\) | |||||||
\(774\) | −17.4915 | −0.628721 | ||||||||
\(775\) | 4.82342 | 0.173262 | ||||||||
\(776\) | 20.6716 | 0.742066 | ||||||||
\(777\) | 0.883776 | 0.0317053 | ||||||||
\(778\) | −10.4243 | −0.373728 | ||||||||
\(779\) | −15.6840 | −0.561937 | ||||||||
\(780\) | −41.1493 | −1.47338 | ||||||||
\(781\) | 26.7950 | 0.958801 | ||||||||
\(782\) | 0.143082 | 0.00511659 | ||||||||
\(783\) | 5.14557 | 0.183888 | ||||||||
\(784\) | −19.4562 | −0.694864 | ||||||||
\(785\) | 15.4523 | 0.551516 | ||||||||
\(786\) | 52.1914 | 1.86161 | ||||||||
\(787\) | −2.72751 | −0.0972254 | −0.0486127 | − | 0.998818i | \(-0.515480\pi\) | ||||
−0.0486127 | + | 0.998818i | \(0.515480\pi\) | |||||||
\(788\) | 26.6222 | 0.948376 | ||||||||
\(789\) | −27.2371 | −0.969665 | ||||||||
\(790\) | −4.59363 | −0.163434 | ||||||||
\(791\) | −12.2076 | −0.434053 | ||||||||
\(792\) | −22.4117 | −0.796367 | ||||||||
\(793\) | −68.4252 | −2.42985 | ||||||||
\(794\) | 5.54769 | 0.196880 | ||||||||
\(795\) | −6.05325 | −0.214686 | ||||||||
\(796\) | −79.0873 | −2.80317 | ||||||||
\(797\) | −42.3180 | −1.49898 | −0.749491 | − | 0.662015i | \(-0.769702\pi\) | ||||
−0.749491 | + | 0.662015i | \(0.769702\pi\) | |||||||
\(798\) | 3.96150 | 0.140236 | ||||||||
\(799\) | −4.36935 | −0.154577 | ||||||||
\(800\) | −3.06361 | −0.108315 | ||||||||
\(801\) | 4.29441 | 0.151736 | ||||||||
\(802\) | 68.6746 | 2.42499 | ||||||||
\(803\) | 23.2260 | 0.819629 | ||||||||
\(804\) | −53.3200 | −1.88045 | ||||||||
\(805\) | −0.0367723 | −0.00129605 | ||||||||
\(806\) | 32.1701 | 1.13314 | ||||||||
\(807\) | 9.03426 | 0.318021 | ||||||||
\(808\) | −26.2711 | −0.924213 | ||||||||
\(809\) | 23.9958 | 0.843647 | 0.421824 | − | 0.906678i | \(-0.361390\pi\) | ||||
0.421824 | + | 0.906678i | \(0.361390\pi\) | |||||||
\(810\) | −3.90694 | −0.137276 | ||||||||
\(811\) | 9.77499 | 0.343246 | 0.171623 | − | 0.985163i | \(-0.445099\pi\) | ||||
0.171623 | + | 0.985163i | \(0.445099\pi\) | |||||||
\(812\) | 19.0435 | 0.668296 | ||||||||
\(813\) | 10.6330 | 0.372915 | ||||||||
\(814\) | −11.0962 | −0.388920 | ||||||||
\(815\) | −6.18749 | −0.216738 | ||||||||
\(816\) | 7.94496 | 0.278129 | ||||||||
\(817\) | −12.3365 | −0.431600 | ||||||||
\(818\) | −1.07646 | −0.0376376 | ||||||||
\(819\) | −6.32387 | −0.220974 | ||||||||
\(820\) | 57.2463 | 1.99913 | ||||||||
\(821\) | −13.4645 | −0.469916 | −0.234958 | − | 0.972006i | \(-0.575495\pi\) | ||||
−0.234958 | + | 0.972006i | \(0.575495\pi\) | |||||||
\(822\) | 21.0225 | 0.733243 | ||||||||
\(823\) | 28.0814 | 0.978857 | 0.489429 | − | 0.872043i | \(-0.337205\pi\) | ||||
0.489429 | + | 0.872043i | \(0.337205\pi\) | |||||||
\(824\) | −12.1216 | −0.422277 | ||||||||
\(825\) | 11.9046 | 0.414466 | ||||||||
\(826\) | 10.9074 | 0.379517 | ||||||||
\(827\) | 12.2920 | 0.427435 | 0.213717 | − | 0.976896i | \(-0.431443\pi\) | ||||
0.213717 | + | 0.976896i | \(0.431443\pi\) | |||||||
\(828\) | 0.0919123 | 0.00319417 | ||||||||
\(829\) | −1.64799 | −0.0572370 | −0.0286185 | − | 0.999590i | \(-0.509111\pi\) | ||||
−0.0286185 | + | 0.999590i | \(0.509111\pi\) | |||||||
\(830\) | 66.8126 | 2.31910 | ||||||||
\(831\) | 16.4006 | 0.568931 | ||||||||
\(832\) | −62.6661 | −2.17255 | ||||||||
\(833\) | 15.1067 | 0.523417 | ||||||||
\(834\) | −45.4031 | −1.57218 | ||||||||
\(835\) | −6.54754 | −0.226587 | ||||||||
\(836\) | −32.7724 | −1.13346 | ||||||||
\(837\) | 2.01254 | 0.0695636 | ||||||||
\(838\) | 56.5607 | 1.95386 | ||||||||
\(839\) | 14.6464 | 0.505650 | 0.252825 | − | 0.967512i | \(-0.418640\pi\) | ||||
0.252825 | + | 0.967512i | \(0.418640\pi\) | |||||||
\(840\) | −6.97400 | −0.240626 | ||||||||
\(841\) | −2.52313 | −0.0870046 | ||||||||
\(842\) | −12.6508 | −0.435974 | ||||||||
\(843\) | −9.43465 | −0.324947 | ||||||||
\(844\) | 35.8001 | 1.23229 | ||||||||
\(845\) | 49.3371 | 1.69725 | ||||||||
\(846\) | −4.25979 | −0.146455 | ||||||||
\(847\) | −13.0977 | −0.450043 | ||||||||
\(848\) | 12.0009 | 0.412113 | ||||||||
\(849\) | −28.4391 | −0.976029 | ||||||||
\(850\) | −14.4140 | −0.494397 | ||||||||
\(851\) | 0.0219483 | 0.000752379 0 | ||||||||
\(852\) | −20.8407 | −0.713992 | ||||||||
\(853\) | 4.53653 | 0.155328 | 0.0776639 | − | 0.996980i | \(-0.475254\pi\) | ||||
0.0776639 | + | 0.996980i | \(0.475254\pi\) | |||||||
\(854\) | −24.0439 | −0.822764 | ||||||||
\(855\) | −2.75551 | −0.0942363 | ||||||||
\(856\) | −48.0035 | −1.64073 | ||||||||
\(857\) | 41.1667 | 1.40623 | 0.703114 | − | 0.711077i | \(-0.251792\pi\) | ||||
0.703114 | + | 0.711077i | \(0.251792\pi\) | |||||||
\(858\) | 79.3987 | 2.71063 | ||||||||
\(859\) | 50.1858 | 1.71232 | 0.856158 | − | 0.516714i | \(-0.172845\pi\) | ||||
0.856158 | + | 0.516714i | \(0.172845\pi\) | |||||||
\(860\) | 45.0281 | 1.53545 | ||||||||
\(861\) | 8.79767 | 0.299824 | ||||||||
\(862\) | −76.5250 | −2.60645 | ||||||||
\(863\) | −3.71230 | −0.126368 | −0.0631841 | − | 0.998002i | \(-0.520126\pi\) | ||||
−0.0631841 | + | 0.998002i | \(0.520126\pi\) | |||||||
\(864\) | −1.27827 | −0.0434877 | ||||||||
\(865\) | −5.10339 | −0.173520 | ||||||||
\(866\) | 48.6862 | 1.65442 | ||||||||
\(867\) | 10.8311 | 0.367845 | ||||||||
\(868\) | 7.44832 | 0.252813 | ||||||||
\(869\) | 5.84016 | 0.198114 | ||||||||
\(870\) | −20.1034 | −0.681570 | ||||||||
\(871\) | 91.1085 | 3.08709 | ||||||||
\(872\) | −6.81445 | −0.230766 | ||||||||
\(873\) | −4.58146 | −0.155059 | ||||||||
\(874\) | 0.0983828 | 0.00332785 | ||||||||
\(875\) | 11.4327 | 0.386496 | ||||||||
\(876\) | −18.0648 | −0.610354 | ||||||||
\(877\) | −49.0483 | −1.65624 | −0.828122 | − | 0.560548i | \(-0.810591\pi\) | ||||
−0.828122 | + | 0.560548i | \(0.810591\pi\) | |||||||
\(878\) | 47.0239 | 1.58698 | ||||||||
\(879\) | −19.9400 | −0.672560 | ||||||||
\(880\) | 25.6365 | 0.864208 | ||||||||
\(881\) | 43.0972 | 1.45198 | 0.725991 | − | 0.687705i | \(-0.241382\pi\) | ||||
0.725991 | + | 0.687705i | \(0.241382\pi\) | |||||||
\(882\) | 14.7279 | 0.495915 | ||||||||
\(883\) | 36.4929 | 1.22808 | 0.614042 | − | 0.789274i | \(-0.289543\pi\) | ||||
0.614042 | + | 0.789274i | \(0.289543\pi\) | |||||||
\(884\) | −63.3433 | −2.13047 | ||||||||
\(885\) | −7.58688 | −0.255030 | ||||||||
\(886\) | −61.5690 | −2.06845 | ||||||||
\(887\) | −9.98684 | −0.335325 | −0.167663 | − | 0.985844i | \(-0.553622\pi\) | ||||
−0.167663 | + | 0.985844i | \(0.553622\pi\) | |||||||
\(888\) | 4.16258 | 0.139687 | ||||||||
\(889\) | 2.69866 | 0.0905103 | ||||||||
\(890\) | −16.7780 | −0.562400 | ||||||||
\(891\) | 4.96714 | 0.166405 | ||||||||
\(892\) | 102.484 | 3.43143 | ||||||||
\(893\) | −3.00436 | −0.100537 | ||||||||
\(894\) | 44.2497 | 1.47993 | ||||||||
\(895\) | −16.8261 | −0.562434 | ||||||||
\(896\) | −19.5711 | −0.653824 | ||||||||
\(897\) | −0.157052 | −0.00524380 | ||||||||
\(898\) | 44.2798 | 1.47764 | ||||||||
\(899\) | 10.3557 | 0.345381 | ||||||||
\(900\) | −9.25923 | −0.308641 | ||||||||
\(901\) | −9.31808 | −0.310430 | ||||||||
\(902\) | −110.458 | −3.67786 | ||||||||
\(903\) | 6.91996 | 0.230282 | ||||||||
\(904\) | −57.4978 | −1.91235 | ||||||||
\(905\) | −31.5760 | −1.04962 | ||||||||
\(906\) | −5.32588 | −0.176940 | ||||||||
\(907\) | −48.0432 | −1.59525 | −0.797624 | − | 0.603155i | \(-0.793910\pi\) | ||||
−0.797624 | + | 0.603155i | \(0.793910\pi\) | |||||||
\(908\) | 24.7627 | 0.821779 | ||||||||
\(909\) | 5.82248 | 0.193120 | ||||||||
\(910\) | 24.7070 | 0.819029 | ||||||||
\(911\) | −46.6180 | −1.54452 | −0.772261 | − | 0.635305i | \(-0.780874\pi\) | ||||
−0.772261 | + | 0.635305i | \(0.780874\pi\) | |||||||
\(912\) | 5.46295 | 0.180896 | ||||||||
\(913\) | −84.9429 | −2.81120 | ||||||||
\(914\) | 54.7445 | 1.81079 | ||||||||
\(915\) | 16.7242 | 0.552885 | ||||||||
\(916\) | 80.8966 | 2.67290 | ||||||||
\(917\) | −20.6479 | −0.681852 | ||||||||
\(918\) | −6.01417 | −0.198497 | ||||||||
\(919\) | 42.2503 | 1.39371 | 0.696855 | − | 0.717212i | \(-0.254582\pi\) | ||||
0.696855 | + | 0.717212i | \(0.254582\pi\) | |||||||
\(920\) | −0.173198 | −0.00571015 | ||||||||
\(921\) | 5.84888 | 0.192727 | ||||||||
\(922\) | 22.0682 | 0.726777 | ||||||||
\(923\) | 35.6108 | 1.17214 | ||||||||
\(924\) | 18.3832 | 0.604761 | ||||||||
\(925\) | −2.21107 | −0.0726997 | ||||||||
\(926\) | −33.8132 | −1.11117 | ||||||||
\(927\) | 2.68653 | 0.0882371 | ||||||||
\(928\) | −6.57743 | −0.215915 | ||||||||
\(929\) | 6.96846 | 0.228628 | 0.114314 | − | 0.993445i | \(-0.463533\pi\) | ||||
0.114314 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(930\) | −7.86288 | −0.257834 | ||||||||
\(931\) | 10.3874 | 0.340433 | ||||||||
\(932\) | −52.2144 | −1.71034 | ||||||||
\(933\) | 30.6160 | 1.00232 | ||||||||
\(934\) | −61.2137 | −2.00297 | ||||||||
\(935\) | −19.9055 | −0.650978 | ||||||||
\(936\) | −29.7854 | −0.973566 | ||||||||
\(937\) | −12.7551 | −0.416690 | −0.208345 | − | 0.978055i | \(-0.566808\pi\) | ||||
−0.208345 | + | 0.978055i | \(0.566808\pi\) | |||||||
\(938\) | 32.0145 | 1.04531 | ||||||||
\(939\) | −7.93216 | −0.258856 | ||||||||
\(940\) | 10.9659 | 0.357668 | ||||||||
\(941\) | 31.5941 | 1.02994 | 0.514969 | − | 0.857209i | \(-0.327803\pi\) | ||||
0.514969 | + | 0.857209i | \(0.327803\pi\) | |||||||
\(942\) | 23.1901 | 0.755574 | ||||||||
\(943\) | 0.218488 | 0.00711494 | ||||||||
\(944\) | 15.0414 | 0.489557 | ||||||||
\(945\) | 1.54566 | 0.0502802 | ||||||||
\(946\) | −86.8829 | −2.82481 | ||||||||
\(947\) | 25.1084 | 0.815915 | 0.407957 | − | 0.913001i | \(-0.366241\pi\) | ||||
0.407957 | + | 0.913001i | \(0.366241\pi\) | |||||||
\(948\) | −4.54238 | −0.147530 | ||||||||
\(949\) | 30.8676 | 1.00200 | ||||||||
\(950\) | −9.91108 | −0.321558 | ||||||||
\(951\) | −10.7324 | −0.348023 | ||||||||
\(952\) | −10.7355 | −0.347938 | ||||||||
\(953\) | 14.4020 | 0.466526 | 0.233263 | − | 0.972414i | \(-0.425060\pi\) | ||||
0.233263 | + | 0.972414i | \(0.425060\pi\) | |||||||
\(954\) | −9.08443 | −0.294119 | ||||||||
\(955\) | 25.6070 | 0.828624 | ||||||||
\(956\) | −29.0452 | −0.939388 | ||||||||
\(957\) | 25.5587 | 0.826197 | ||||||||
\(958\) | −32.9958 | −1.06605 | ||||||||
\(959\) | −8.31687 | −0.268566 | ||||||||
\(960\) | 15.3166 | 0.494341 | ||||||||
\(961\) | −26.9497 | −0.869345 | ||||||||
\(962\) | −14.7469 | −0.475459 | ||||||||
\(963\) | 10.6391 | 0.342839 | ||||||||
\(964\) | −51.8289 | −1.66930 | ||||||||
\(965\) | −39.0928 | −1.25844 | ||||||||
\(966\) | −0.0551862 | −0.00177559 | ||||||||
\(967\) | −7.70633 | −0.247819 | −0.123909 | − | 0.992294i | \(-0.539543\pi\) | ||||
−0.123909 | + | 0.992294i | \(0.539543\pi\) | |||||||
\(968\) | −61.6902 | −1.98280 | ||||||||
\(969\) | −4.24170 | −0.136263 | ||||||||
\(970\) | 17.8995 | 0.574718 | ||||||||
\(971\) | −19.5480 | −0.627326 | −0.313663 | − | 0.949534i | \(-0.601556\pi\) | ||||
−0.313663 | + | 0.949534i | \(0.601556\pi\) | |||||||
\(972\) | −3.86336 | −0.123917 | ||||||||
\(973\) | 17.9623 | 0.575844 | ||||||||
\(974\) | −62.0290 | −1.98754 | ||||||||
\(975\) | 15.8214 | 0.506689 | ||||||||
\(976\) | −33.1567 | −1.06132 | ||||||||
\(977\) | 15.7430 | 0.503664 | 0.251832 | − | 0.967771i | \(-0.418967\pi\) | ||||
0.251832 | + | 0.967771i | \(0.418967\pi\) | |||||||
\(978\) | −9.28589 | −0.296930 | ||||||||
\(979\) | 21.3309 | 0.681739 | ||||||||
\(980\) | −37.9138 | −1.21111 | ||||||||
\(981\) | 1.51029 | 0.0482199 | ||||||||
\(982\) | −65.1087 | −2.07770 | ||||||||
\(983\) | −48.6284 | −1.55100 | −0.775502 | − | 0.631345i | \(-0.782503\pi\) | ||||
−0.775502 | + | 0.631345i | \(0.782503\pi\) | |||||||
\(984\) | 41.4370 | 1.32096 | ||||||||
\(985\) | 11.1184 | 0.354262 | ||||||||
\(986\) | −30.9463 | −0.985531 | ||||||||
\(987\) | 1.68525 | 0.0536420 | ||||||||
\(988\) | −43.5548 | −1.38566 | ||||||||
\(989\) | 0.171856 | 0.00546469 | ||||||||
\(990\) | −19.4063 | −0.616773 | ||||||||
\(991\) | −41.7164 | −1.32516 | −0.662582 | − | 0.748989i | \(-0.730539\pi\) | ||||
−0.662582 | + | 0.748989i | \(0.730539\pi\) | |||||||
\(992\) | −2.57257 | −0.0816792 | ||||||||
\(993\) | −32.9905 | −1.04692 | ||||||||
\(994\) | 12.5132 | 0.396896 | ||||||||
\(995\) | −33.0298 | −1.04711 | ||||||||
\(996\) | 66.0672 | 2.09342 | ||||||||
\(997\) | −47.0553 | −1.49026 | −0.745128 | − | 0.666922i | \(-0.767611\pi\) | ||||
−0.745128 | + | 0.666922i | \(0.767611\pi\) | |||||||
\(998\) | −18.0997 | −0.572937 | ||||||||
\(999\) | −0.922557 | −0.0291884 |
(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 | 6033.2.a.c.1.7 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6033.2.a.c.1.7 | ✓ | 82 | 1.1 | even | 1 | trivial |