Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 82 x^{9} + 334 x^{8} - 684 x^{7} - 1561 x^{6} + 1551 x^{5} + 3573 x^{4} + \cdots - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.815716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.815716 | 0.364799 | 0.182400 | − | 0.983224i | \(-0.441614\pi\) | ||||
0.182400 | + | 0.983224i | \(0.441614\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.13057 | −1.56121 | −0.780604 | − | 0.625026i | \(-0.785089\pi\) | ||||
−0.780604 | + | 0.625026i | \(0.785089\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.815716 | 0.257952 | ||||||||
\(11\) | 5.38614 | 1.62398 | 0.811991 | − | 0.583671i | \(-0.198384\pi\) | ||||
0.811991 | + | 0.583671i | \(0.198384\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.53585 | 1.53537 | 0.767684 | − | 0.640829i | \(-0.221409\pi\) | ||||
0.767684 | + | 0.640829i | \(0.221409\pi\) | |||||||
\(14\) | −4.13057 | −1.10394 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.97728 | −0.479561 | −0.239781 | − | 0.970827i | \(-0.577076\pi\) | ||||
−0.239781 | + | 0.970827i | \(0.577076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.77630 | −1.78401 | −0.892003 | − | 0.452030i | \(-0.850700\pi\) | ||||
−0.892003 | + | 0.452030i | \(0.850700\pi\) | |||||||
\(20\) | 0.815716 | 0.182400 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.38614 | 1.14833 | ||||||||
\(23\) | −4.49804 | −0.937906 | −0.468953 | − | 0.883223i | \(-0.655369\pi\) | ||||
−0.468953 | + | 0.883223i | \(0.655369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.33461 | −0.866922 | ||||||||
\(26\) | 5.53585 | 1.08567 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.13057 | −0.780604 | ||||||||
\(29\) | −4.21302 | −0.782339 | −0.391169 | − | 0.920319i | \(-0.627929\pi\) | ||||
−0.391169 | + | 0.920319i | \(0.627929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.64708 | −1.19385 | −0.596925 | − | 0.802297i | \(-0.703611\pi\) | ||||
−0.596925 | + | 0.802297i | \(0.703611\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.97728 | −0.339101 | ||||||||
\(35\) | −3.36937 | −0.569528 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.33356 | −0.219236 | −0.109618 | − | 0.993974i | \(-0.534963\pi\) | ||||
−0.109618 | + | 0.993974i | \(0.534963\pi\) | |||||||
\(38\) | −7.77630 | −1.26148 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.815716 | 0.128976 | ||||||||
\(41\) | 4.44186 | 0.693702 | 0.346851 | − | 0.937920i | \(-0.387251\pi\) | ||||
0.346851 | + | 0.937920i | \(0.387251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7772 | −1.64350 | −0.821752 | − | 0.569846i | \(-0.807003\pi\) | ||||
−0.821752 | + | 0.569846i | \(0.807003\pi\) | |||||||
\(44\) | 5.38614 | 0.811991 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.49804 | −0.663200 | ||||||||
\(47\) | 3.59563 | 0.524477 | 0.262238 | − | 0.965003i | \(-0.415539\pi\) | ||||
0.262238 | + | 0.965003i | \(0.415539\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.0616 | 1.43737 | ||||||||
\(50\) | −4.33461 | −0.613006 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.53585 | 0.767684 | ||||||||
\(53\) | −6.44635 | −0.885475 | −0.442737 | − | 0.896651i | \(-0.645993\pi\) | ||||
−0.442737 | + | 0.896651i | \(0.645993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.39356 | 0.592427 | ||||||||
\(56\) | −4.13057 | −0.551971 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.21302 | −0.553197 | ||||||||
\(59\) | 5.75290 | 0.748964 | 0.374482 | − | 0.927234i | \(-0.377821\pi\) | ||||
0.374482 | + | 0.927234i | \(0.377821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.55640 | −0.711424 | −0.355712 | − | 0.934596i | \(-0.615762\pi\) | ||||
−0.355712 | + | 0.934596i | \(0.615762\pi\) | |||||||
\(62\) | −6.64708 | −0.844180 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.51568 | 0.560101 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.76096 | 1.19249 | 0.596246 | − | 0.802802i | \(-0.296658\pi\) | ||||
0.596246 | + | 0.802802i | \(0.296658\pi\) | |||||||
\(68\) | −1.97728 | −0.239781 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.36937 | −0.402717 | ||||||||
\(71\) | −1.83453 | −0.217719 | −0.108859 | − | 0.994057i | \(-0.534720\pi\) | ||||
−0.108859 | + | 0.994057i | \(0.534720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.66077 | −0.428461 | −0.214231 | − | 0.976783i | \(-0.568724\pi\) | ||||
−0.214231 | + | 0.976783i | \(0.568724\pi\) | |||||||
\(74\) | −1.33356 | −0.155024 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.77630 | −0.892003 | ||||||||
\(77\) | −22.2478 | −2.53537 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.21104 | −1.03632 | −0.518161 | − | 0.855283i | \(-0.673383\pi\) | ||||
−0.518161 | + | 0.855283i | \(0.673383\pi\) | |||||||
\(80\) | 0.815716 | 0.0911998 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.44186 | 0.490521 | ||||||||
\(83\) | −1.93224 | −0.212091 | −0.106046 | − | 0.994361i | \(-0.533819\pi\) | ||||
−0.106046 | + | 0.994361i | \(0.533819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.61290 | −0.174944 | ||||||||
\(86\) | −10.7772 | −1.16213 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.38614 | 0.574164 | ||||||||
\(89\) | 14.0973 | 1.49431 | 0.747156 | − | 0.664649i | \(-0.231419\pi\) | ||||
0.747156 | + | 0.664649i | \(0.231419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.8662 | −2.39703 | ||||||||
\(92\) | −4.49804 | −0.468953 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.59563 | 0.370861 | ||||||||
\(95\) | −6.34325 | −0.650804 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.98324 | −0.912110 | −0.456055 | − | 0.889952i | \(-0.650738\pi\) | ||||
−0.456055 | + | 0.889952i | \(0.650738\pi\) | |||||||
\(98\) | 10.0616 | 1.01638 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.33461 | −0.433461 | ||||||||
\(101\) | 1.31930 | 0.131275 | 0.0656377 | − | 0.997844i | \(-0.479092\pi\) | ||||
0.0656377 | + | 0.997844i | \(0.479092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.52663 | −0.347489 | −0.173745 | − | 0.984791i | \(-0.555587\pi\) | ||||
−0.173745 | + | 0.984791i | \(0.555587\pi\) | |||||||
\(104\) | 5.53585 | 0.542835 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.44635 | −0.626125 | ||||||||
\(107\) | −0.332526 | −0.0321465 | −0.0160732 | − | 0.999871i | \(-0.505116\pi\) | ||||
−0.0160732 | + | 0.999871i | \(0.505116\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.79744 | −0.363729 | −0.181864 | − | 0.983324i | \(-0.558213\pi\) | ||||
−0.181864 | + | 0.983324i | \(0.558213\pi\) | |||||||
\(110\) | 4.39356 | 0.418909 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.13057 | −0.390302 | ||||||||
\(113\) | 0.758572 | 0.0713604 | 0.0356802 | − | 0.999363i | \(-0.488640\pi\) | ||||
0.0356802 | + | 0.999363i | \(0.488640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.66912 | −0.342147 | ||||||||
\(116\) | −4.21302 | −0.391169 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.75290 | 0.529598 | ||||||||
\(119\) | 8.16730 | 0.748695 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.0105 | 1.63731 | ||||||||
\(122\) | −5.55640 | −0.503053 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.64708 | −0.596925 | ||||||||
\(125\) | −7.61439 | −0.681051 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5200 | 1.02223 | 0.511117 | − | 0.859511i | \(-0.329232\pi\) | ||||
0.511117 | + | 0.859511i | \(0.329232\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.51568 | 0.396051 | ||||||||
\(131\) | 0.430517 | 0.0376145 | 0.0188072 | − | 0.999823i | \(-0.494013\pi\) | ||||
0.0188072 | + | 0.999823i | \(0.494013\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 32.1205 | 2.78520 | ||||||||
\(134\) | 9.76096 | 0.843219 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.97728 | −0.169551 | ||||||||
\(137\) | 18.9496 | 1.61897 | 0.809487 | − | 0.587138i | \(-0.199745\pi\) | ||||
0.809487 | + | 0.587138i | \(0.199745\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9711 | −0.930561 | −0.465280 | − | 0.885163i | \(-0.654046\pi\) | ||||
−0.465280 | + | 0.885163i | \(0.654046\pi\) | |||||||
\(140\) | −3.36937 | −0.284764 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.83453 | −0.153950 | ||||||||
\(143\) | 29.8168 | 2.49341 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.43663 | −0.285396 | ||||||||
\(146\) | −3.66077 | −0.302968 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.33356 | −0.109618 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.47150 | −0.526643 | −0.263322 | − | 0.964708i | \(-0.584818\pi\) | ||||
−0.263322 | + | 0.964708i | \(0.584818\pi\) | |||||||
\(152\) | −7.77630 | −0.630741 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.2478 | −1.79278 | ||||||||
\(155\) | −5.42213 | −0.435516 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0774 | 0.963883 | 0.481941 | − | 0.876203i | \(-0.339932\pi\) | ||||
0.481941 | + | 0.876203i | \(0.339932\pi\) | |||||||
\(158\) | −9.21104 | −0.732791 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.815716 | 0.0644880 | ||||||||
\(161\) | 18.5795 | 1.46427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.69644 | −0.446179 | −0.223090 | − | 0.974798i | \(-0.571614\pi\) | ||||
−0.223090 | + | 0.974798i | \(0.571614\pi\) | |||||||
\(164\) | 4.44186 | 0.346851 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.93224 | −0.149971 | ||||||||
\(167\) | −17.9694 | −1.39051 | −0.695255 | − | 0.718763i | \(-0.744709\pi\) | ||||
−0.695255 | + | 0.718763i | \(0.744709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.6456 | 1.35735 | ||||||||
\(170\) | −1.61290 | −0.123704 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.7772 | −0.821752 | ||||||||
\(173\) | −20.4869 | −1.55759 | −0.778796 | − | 0.627278i | \(-0.784169\pi\) | ||||
−0.778796 | + | 0.627278i | \(0.784169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.9044 | 1.35345 | ||||||||
\(176\) | 5.38614 | 0.405995 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.0973 | 1.05664 | ||||||||
\(179\) | −14.2118 | −1.06224 | −0.531120 | − | 0.847296i | \(-0.678229\pi\) | ||||
−0.531120 | + | 0.847296i | \(0.678229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.73904 | 0.203592 | 0.101796 | − | 0.994805i | \(-0.467541\pi\) | ||||
0.101796 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(182\) | −22.8662 | −1.69496 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.49804 | −0.331600 | ||||||||
\(185\) | −1.08781 | −0.0799772 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6499 | −0.778799 | ||||||||
\(188\) | 3.59563 | 0.262238 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.34325 | −0.460188 | ||||||||
\(191\) | 9.80574 | 0.709518 | 0.354759 | − | 0.934958i | \(-0.384563\pi\) | ||||
0.354759 | + | 0.934958i | \(0.384563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.34693 | −0.0969545 | −0.0484772 | − | 0.998824i | \(-0.515437\pi\) | ||||
−0.0484772 | + | 0.998824i | \(0.515437\pi\) | |||||||
\(194\) | −8.98324 | −0.644959 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0616 | 0.718686 | ||||||||
\(197\) | −22.1831 | −1.58048 | −0.790239 | − | 0.612798i | \(-0.790044\pi\) | ||||
−0.790239 | + | 0.612798i | \(0.790044\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.9250 | −1.76689 | −0.883444 | − | 0.468538i | \(-0.844781\pi\) | ||||
−0.883444 | + | 0.468538i | \(0.844781\pi\) | |||||||
\(200\) | −4.33461 | −0.306503 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.31930 | 0.0928257 | ||||||||
\(203\) | 17.4022 | 1.22139 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.62329 | 0.253062 | ||||||||
\(206\) | −3.52663 | −0.245712 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.53585 | 0.383842 | ||||||||
\(209\) | −41.8842 | −2.89719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.38099 | 0.370442 | 0.185221 | − | 0.982697i | \(-0.440700\pi\) | ||||
0.185221 | + | 0.982697i | \(0.440700\pi\) | |||||||
\(212\) | −6.44635 | −0.442737 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.332526 | −0.0227310 | ||||||||
\(215\) | −8.79111 | −0.599549 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.4562 | 1.86385 | ||||||||
\(218\) | −3.79744 | −0.257195 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.39356 | 0.296213 | ||||||||
\(221\) | −10.9459 | −0.736303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5623 | 0.841237 | 0.420618 | − | 0.907238i | \(-0.361813\pi\) | ||||
0.420618 | + | 0.907238i | \(0.361813\pi\) | |||||||
\(224\) | −4.13057 | −0.275985 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.758572 | 0.0504594 | ||||||||
\(227\) | −3.13674 | −0.208193 | −0.104096 | − | 0.994567i | \(-0.533195\pi\) | ||||
−0.104096 | + | 0.994567i | \(0.533195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.77927 | 0.249741 | 0.124870 | − | 0.992173i | \(-0.460148\pi\) | ||||
0.124870 | + | 0.992173i | \(0.460148\pi\) | |||||||
\(230\) | −3.66912 | −0.241935 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.21302 | −0.276598 | ||||||||
\(233\) | 1.22631 | 0.0803383 | 0.0401691 | − | 0.999193i | \(-0.487210\pi\) | ||||
0.0401691 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.93301 | 0.191329 | ||||||||
\(236\) | 5.75290 | 0.374482 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.16730 | 0.529407 | ||||||||
\(239\) | −9.21295 | −0.595936 | −0.297968 | − | 0.954576i | \(-0.596309\pi\) | ||||
−0.297968 | + | 0.954576i | \(0.596309\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.6802 | −1.33213 | −0.666064 | − | 0.745895i | \(-0.732022\pi\) | ||||
−0.666064 | + | 0.745895i | \(0.732022\pi\) | |||||||
\(242\) | 18.0105 | 1.15776 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.55640 | −0.355712 | ||||||||
\(245\) | 8.20741 | 0.524352 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −43.0484 | −2.73910 | ||||||||
\(248\) | −6.64708 | −0.422090 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.61439 | −0.481576 | ||||||||
\(251\) | 1.30517 | 0.0823814 | 0.0411907 | − | 0.999151i | \(-0.486885\pi\) | ||||
0.0411907 | + | 0.999151i | \(0.486885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.2271 | −1.52314 | ||||||||
\(254\) | 11.5200 | 0.722829 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.03800 | 0.376640 | 0.188320 | − | 0.982108i | \(-0.439696\pi\) | ||||
0.188320 | + | 0.982108i | \(0.439696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.50837 | 0.342274 | ||||||||
\(260\) | 4.51568 | 0.280050 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.430517 | 0.0265974 | ||||||||
\(263\) | −31.5018 | −1.94249 | −0.971243 | − | 0.238091i | \(-0.923478\pi\) | ||||
−0.971243 | + | 0.238091i | \(0.923478\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.25839 | −0.323020 | ||||||||
\(266\) | 32.1205 | 1.96944 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.76096 | 0.596246 | ||||||||
\(269\) | −25.9304 | −1.58100 | −0.790501 | − | 0.612460i | \(-0.790180\pi\) | ||||
−0.790501 | + | 0.612460i | \(0.790180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.66121 | 0.161657 | 0.0808285 | − | 0.996728i | \(-0.474243\pi\) | ||||
0.0808285 | + | 0.996728i | \(0.474243\pi\) | |||||||
\(272\) | −1.97728 | −0.119890 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.9496 | 1.14479 | ||||||||
\(275\) | −23.3468 | −1.40786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.3539 | 1.88387 | 0.941936 | − | 0.335792i | \(-0.109004\pi\) | ||||
0.941936 | + | 0.335792i | \(0.109004\pi\) | |||||||
\(278\) | −10.9711 | −0.658006 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.36937 | −0.201358 | ||||||||
\(281\) | −25.4005 | −1.51526 | −0.757632 | − | 0.652682i | \(-0.773644\pi\) | ||||
−0.757632 | + | 0.652682i | \(0.773644\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6996 | −1.28991 | −0.644954 | − | 0.764221i | \(-0.723124\pi\) | ||||
−0.644954 | + | 0.764221i | \(0.723124\pi\) | |||||||
\(284\) | −1.83453 | −0.108859 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29.8168 | 1.76311 | ||||||||
\(287\) | −18.3474 | −1.08301 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0904 | −0.770021 | ||||||||
\(290\) | −3.43663 | −0.201806 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.66077 | −0.214231 | ||||||||
\(293\) | 31.8104 | 1.85839 | 0.929193 | − | 0.369594i | \(-0.120503\pi\) | ||||
0.929193 | + | 0.369594i | \(0.120503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.69273 | 0.273221 | ||||||||
\(296\) | −1.33356 | −0.0775118 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −24.9005 | −1.44003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 44.5159 | 2.56585 | ||||||||
\(302\) | −6.47150 | −0.372393 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.77630 | −0.446001 | ||||||||
\(305\) | −4.53244 | −0.259527 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.8509 | −1.36124 | −0.680622 | − | 0.732635i | \(-0.738290\pi\) | ||||
−0.680622 | + | 0.732635i | \(0.738290\pi\) | |||||||
\(308\) | −22.2478 | −1.26769 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.42213 | −0.307956 | ||||||||
\(311\) | −26.7058 | −1.51435 | −0.757173 | − | 0.653215i | \(-0.773420\pi\) | ||||
−0.757173 | + | 0.653215i | \(0.773420\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6816 | 1.11247 | 0.556235 | − | 0.831025i | \(-0.312245\pi\) | ||||
0.556235 | + | 0.831025i | \(0.312245\pi\) | |||||||
\(314\) | 12.0774 | 0.681568 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.21104 | −0.518161 | ||||||||
\(317\) | 9.46320 | 0.531507 | 0.265753 | − | 0.964041i | \(-0.414379\pi\) | ||||
0.265753 | + | 0.964041i | \(0.414379\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.6919 | −1.27050 | ||||||||
\(320\) | 0.815716 | 0.0455999 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 18.5795 | 1.03539 | ||||||||
\(323\) | 15.3759 | 0.855540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.9957 | −1.33104 | ||||||||
\(326\) | −5.69644 | −0.315496 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.44186 | 0.245261 | ||||||||
\(329\) | −14.8520 | −0.818818 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3797 | 0.570518 | 0.285259 | − | 0.958450i | \(-0.407920\pi\) | ||||
0.285259 | + | 0.958450i | \(0.407920\pi\) | |||||||
\(332\) | −1.93224 | −0.106046 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.9694 | −0.983240 | ||||||||
\(335\) | 7.96217 | 0.435020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.3299 | 1.76112 | 0.880561 | − | 0.473934i | \(-0.157166\pi\) | ||||
0.880561 | + | 0.473934i | \(0.157166\pi\) | |||||||
\(338\) | 17.6456 | 0.959795 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.61290 | −0.0874718 | ||||||||
\(341\) | −35.8021 | −1.93879 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6462 | −0.682830 | ||||||||
\(344\) | −10.7772 | −0.581066 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.4869 | −1.10138 | ||||||||
\(347\) | 21.3366 | 1.14541 | 0.572704 | − | 0.819763i | \(-0.305895\pi\) | ||||
0.572704 | + | 0.819763i | \(0.305895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.35420 | −0.286604 | −0.143302 | − | 0.989679i | \(-0.545772\pi\) | ||||
−0.143302 | + | 0.989679i | \(0.545772\pi\) | |||||||
\(350\) | 17.9044 | 0.957031 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.38614 | 0.287082 | ||||||||
\(353\) | −2.67919 | −0.142599 | −0.0712995 | − | 0.997455i | \(-0.522715\pi\) | ||||
−0.0712995 | + | 0.997455i | \(0.522715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.49646 | −0.0794236 | ||||||||
\(356\) | 14.0973 | 0.747156 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.2118 | −0.751118 | ||||||||
\(359\) | −35.7281 | −1.88566 | −0.942830 | − | 0.333275i | \(-0.891846\pi\) | ||||
−0.942830 | + | 0.333275i | \(0.891846\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.4708 | 2.18268 | ||||||||
\(362\) | 2.73904 | 0.143961 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.8662 | −1.19851 | ||||||||
\(365\) | −2.98615 | −0.156302 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.5484 | 1.43801 | 0.719007 | − | 0.695003i | \(-0.244597\pi\) | ||||
0.719007 | + | 0.695003i | \(0.244597\pi\) | |||||||
\(368\) | −4.49804 | −0.234477 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.08781 | −0.0565524 | ||||||||
\(371\) | 26.6271 | 1.38241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2867 | −0.739740 | −0.369870 | − | 0.929084i | \(-0.620598\pi\) | ||||
−0.369870 | + | 0.929084i | \(0.620598\pi\) | |||||||
\(374\) | −10.6499 | −0.550694 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.59563 | 0.185431 | ||||||||
\(377\) | −23.3227 | −1.20118 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.7017 | 1.62841 | 0.814203 | − | 0.580581i | \(-0.197174\pi\) | ||||
0.814203 | + | 0.580581i | \(0.197174\pi\) | |||||||
\(380\) | −6.34325 | −0.325402 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.80574 | 0.501705 | ||||||||
\(383\) | −1.71332 | −0.0875468 | −0.0437734 | − | 0.999041i | \(-0.513938\pi\) | ||||
−0.0437734 | + | 0.999041i | \(0.513938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.1479 | −0.924902 | ||||||||
\(386\) | −1.34693 | −0.0685572 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.98324 | −0.456055 | ||||||||
\(389\) | 31.3579 | 1.58991 | 0.794953 | − | 0.606671i | \(-0.207495\pi\) | ||||
0.794953 | + | 0.606671i | \(0.207495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.89389 | 0.449784 | ||||||||
\(392\) | 10.0616 | 0.508188 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.1831 | −1.11757 | ||||||||
\(395\) | −7.51359 | −0.378050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.58737 | −0.180045 | −0.0900226 | − | 0.995940i | \(-0.528694\pi\) | ||||
−0.0900226 | + | 0.995940i | \(0.528694\pi\) | |||||||
\(398\) | −24.9250 | −1.24938 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.33461 | −0.216730 | ||||||||
\(401\) | −11.6963 | −0.584087 | −0.292044 | − | 0.956405i | \(-0.594335\pi\) | ||||
−0.292044 | + | 0.956405i | \(0.594335\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.7972 | −1.83300 | ||||||||
\(404\) | 1.31930 | 0.0656377 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.4022 | 0.863656 | ||||||||
\(407\) | −7.18275 | −0.356036 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7319 | −1.12402 | −0.562010 | − | 0.827131i | \(-0.689972\pi\) | ||||
−0.562010 | + | 0.827131i | \(0.689972\pi\) | |||||||
\(410\) | 3.62329 | 0.178942 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.52663 | −0.173745 | ||||||||
\(413\) | −23.7628 | −1.16929 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.57616 | −0.0773707 | ||||||||
\(416\) | 5.53585 | 0.271417 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −41.8842 | −2.04862 | ||||||||
\(419\) | 12.6330 | 0.617161 | 0.308580 | − | 0.951198i | \(-0.400146\pi\) | ||||
0.308580 | + | 0.951198i | \(0.400146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.516091 | 0.0251528 | 0.0125764 | − | 0.999921i | \(-0.495997\pi\) | ||||
0.0125764 | + | 0.999921i | \(0.495997\pi\) | |||||||
\(422\) | 5.38099 | 0.261942 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.44635 | −0.313063 | ||||||||
\(425\) | 8.57074 | 0.415742 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.9511 | 1.11068 | ||||||||
\(428\) | −0.332526 | −0.0160732 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.79111 | −0.423945 | ||||||||
\(431\) | −28.7458 | −1.38464 | −0.692319 | − | 0.721592i | \(-0.743411\pi\) | ||||
−0.692319 | + | 0.721592i | \(0.743411\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.6484 | −0.896186 | −0.448093 | − | 0.893987i | \(-0.647897\pi\) | ||||
−0.448093 | + | 0.893987i | \(0.647897\pi\) | |||||||
\(434\) | 27.4562 | 1.31794 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.79744 | −0.181864 | ||||||||
\(437\) | 34.9781 | 1.67323 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6890 | 0.557885 | 0.278942 | − | 0.960308i | \(-0.410016\pi\) | ||||
0.278942 | + | 0.960308i | \(0.410016\pi\) | |||||||
\(440\) | 4.39356 | 0.209455 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.9459 | −0.520645 | ||||||||
\(443\) | 19.7049 | 0.936207 | 0.468104 | − | 0.883674i | \(-0.344937\pi\) | ||||
0.468104 | + | 0.883674i | \(0.344937\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.4994 | 0.545124 | ||||||||
\(446\) | 12.5623 | 0.594844 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.13057 | −0.195151 | ||||||||
\(449\) | −3.01542 | −0.142306 | −0.0711532 | − | 0.997465i | \(-0.522668\pi\) | ||||
−0.0711532 | + | 0.997465i | \(0.522668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.9245 | 1.12656 | ||||||||
\(452\) | 0.758572 | 0.0356802 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.13674 | −0.147214 | ||||||||
\(455\) | −18.6523 | −0.874434 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.4588 | 0.629576 | 0.314788 | − | 0.949162i | \(-0.398067\pi\) | ||||
0.314788 | + | 0.949162i | \(0.398067\pi\) | |||||||
\(458\) | 3.77927 | 0.176593 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.66912 | −0.171074 | ||||||||
\(461\) | −36.1944 | −1.68574 | −0.842870 | − | 0.538117i | \(-0.819136\pi\) | ||||
−0.842870 | + | 0.538117i | \(0.819136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.1225 | −1.35344 | −0.676719 | − | 0.736241i | \(-0.736599\pi\) | ||||
−0.676719 | + | 0.736241i | \(0.736599\pi\) | |||||||
\(464\) | −4.21302 | −0.195585 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.22631 | 0.0568077 | ||||||||
\(467\) | 34.6912 | 1.60532 | 0.802658 | − | 0.596440i | \(-0.203419\pi\) | ||||
0.802658 | + | 0.596440i | \(0.203419\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.3183 | −1.86173 | ||||||||
\(470\) | 2.93301 | 0.135290 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.75290 | 0.264799 | ||||||||
\(473\) | −58.0473 | −2.66902 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 33.7072 | 1.54659 | ||||||||
\(476\) | 8.16730 | 0.374348 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.21295 | −0.421391 | ||||||||
\(479\) | 38.0159 | 1.73699 | 0.868494 | − | 0.495699i | \(-0.165088\pi\) | ||||
0.868494 | + | 0.495699i | \(0.165088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.38240 | −0.336608 | ||||||||
\(482\) | −20.6802 | −0.941957 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0105 | 0.818657 | ||||||||
\(485\) | −7.32777 | −0.332737 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5858 | 0.751575 | 0.375787 | − | 0.926706i | \(-0.377372\pi\) | ||||
0.375787 | + | 0.926706i | \(0.377372\pi\) | |||||||
\(488\) | −5.55640 | −0.251526 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.20741 | 0.370773 | ||||||||
\(491\) | −32.0610 | −1.44689 | −0.723446 | − | 0.690381i | \(-0.757443\pi\) | ||||
−0.723446 | + | 0.690381i | \(0.757443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.33033 | 0.375179 | ||||||||
\(494\) | −43.0484 | −1.93684 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.64708 | −0.298463 | ||||||||
\(497\) | 7.57766 | 0.339905 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.4267 | −1.58592 | −0.792959 | − | 0.609275i | \(-0.791460\pi\) | ||||
−0.792959 | + | 0.609275i | \(0.791460\pi\) | |||||||
\(500\) | −7.61439 | −0.340526 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.30517 | 0.0582524 | ||||||||
\(503\) | 0.256073 | 0.0114177 | 0.00570886 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570886 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.07617 | 0.0478892 | ||||||||
\(506\) | −24.2271 | −1.07702 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.5200 | 0.511117 | ||||||||
\(509\) | −3.41418 | −0.151331 | −0.0756655 | − | 0.997133i | \(-0.524108\pi\) | ||||
−0.0756655 | + | 0.997133i | \(0.524108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1211 | 0.668917 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.03800 | 0.266325 | ||||||||
\(515\) | −2.87673 | −0.126764 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.3666 | 0.851740 | ||||||||
\(518\) | 5.50837 | 0.242024 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.51568 | 0.198026 | ||||||||
\(521\) | 17.3318 | 0.759321 | 0.379661 | − | 0.925126i | \(-0.376041\pi\) | ||||
0.379661 | + | 0.925126i | \(0.376041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.1909 | 1.14525 | 0.572623 | − | 0.819819i | \(-0.305926\pi\) | ||||
0.572623 | + | 0.819819i | \(0.305926\pi\) | |||||||
\(524\) | 0.430517 | 0.0188072 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.5018 | −1.37354 | ||||||||
\(527\) | 13.1432 | 0.572525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.76763 | −0.120332 | ||||||||
\(530\) | −5.25839 | −0.228410 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 32.1205 | 1.39260 | ||||||||
\(533\) | 24.5895 | 1.06509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.271247 | −0.0117270 | ||||||||
\(536\) | 9.76096 | 0.421609 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.9304 | −1.11794 | ||||||||
\(539\) | 54.1932 | 2.33427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.7760 | 1.45214 | 0.726071 | − | 0.687620i | \(-0.241344\pi\) | ||||
0.726071 | + | 0.687620i | \(0.241344\pi\) | |||||||
\(542\) | 2.66121 | 0.114309 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.97728 | −0.0847753 | ||||||||
\(545\) | −3.09763 | −0.132688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9610 | 1.28104 | 0.640521 | − | 0.767941i | \(-0.278719\pi\) | ||||
0.640521 | + | 0.767941i | \(0.278719\pi\) | |||||||
\(548\) | 18.9496 | 0.809487 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.3468 | −0.995510 | ||||||||
\(551\) | 32.7617 | 1.39570 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.0468 | 1.61792 | ||||||||
\(554\) | 31.3539 | 1.33210 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.9711 | −0.465280 | ||||||||
\(557\) | 42.0778 | 1.78289 | 0.891446 | − | 0.453126i | \(-0.149691\pi\) | ||||
0.891446 | + | 0.453126i | \(0.149691\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −59.6608 | −2.52338 | ||||||||
\(560\) | −3.36937 | −0.142382 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.4005 | −1.07145 | ||||||||
\(563\) | −3.18789 | −0.134354 | −0.0671768 | − | 0.997741i | \(-0.521399\pi\) | ||||
−0.0671768 | + | 0.997741i | \(0.521399\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.618779 | 0.0260322 | ||||||||
\(566\) | −21.6996 | −0.912103 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.83453 | −0.0769752 | ||||||||
\(569\) | 13.5411 | 0.567674 | 0.283837 | − | 0.958872i | \(-0.408392\pi\) | ||||
0.283837 | + | 0.958872i | \(0.408392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.7747 | −1.66452 | −0.832259 | − | 0.554387i | \(-0.812953\pi\) | ||||
−0.832259 | + | 0.554387i | \(0.812953\pi\) | |||||||
\(572\) | 29.8168 | 1.24670 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.3474 | −0.765806 | ||||||||
\(575\) | 19.4972 | 0.813091 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.9722 | −1.41428 | −0.707140 | − | 0.707073i | \(-0.750015\pi\) | ||||
−0.707140 | + | 0.707073i | \(0.750015\pi\) | |||||||
\(578\) | −13.0904 | −0.544487 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.43663 | −0.142698 | ||||||||
\(581\) | 7.98127 | 0.331119 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.7209 | −1.43799 | ||||||||
\(584\) | −3.66077 | −0.151484 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.8104 | 1.31408 | ||||||||
\(587\) | −9.05854 | −0.373886 | −0.186943 | − | 0.982371i | \(-0.559858\pi\) | ||||
−0.186943 | + | 0.982371i | \(0.559858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.6897 | 2.12984 | ||||||||
\(590\) | 4.69273 | 0.193197 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.33356 | −0.0548091 | ||||||||
\(593\) | 13.8029 | 0.566818 | 0.283409 | − | 0.958999i | \(-0.408535\pi\) | ||||
0.283409 | + | 0.958999i | \(0.408535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.66219 | 0.273123 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.9005 | −1.01826 | ||||||||
\(599\) | 28.9207 | 1.18167 | 0.590834 | − | 0.806793i | \(-0.298799\pi\) | ||||
0.590834 | + | 0.806793i | \(0.298799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.3839 | −1.03543 | −0.517716 | − | 0.855553i | \(-0.673217\pi\) | ||||
−0.517716 | + | 0.855553i | \(0.673217\pi\) | |||||||
\(602\) | 44.5159 | 1.81433 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.47150 | −0.263322 | ||||||||
\(605\) | 14.6914 | 0.597291 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.3343 | 1.27182 | 0.635909 | − | 0.771764i | \(-0.280625\pi\) | ||||
0.635909 | + | 0.771764i | \(0.280625\pi\) | |||||||
\(608\) | −7.77630 | −0.315371 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.53244 | −0.183513 | ||||||||
\(611\) | 19.9049 | 0.805265 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.743160 | −0.0300160 | −0.0150080 | − | 0.999887i | \(-0.504777\pi\) | ||||
−0.0150080 | + | 0.999887i | \(0.504777\pi\) | |||||||
\(614\) | −23.8509 | −0.962545 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.2478 | −0.896390 | ||||||||
\(617\) | −32.4336 | −1.30573 | −0.652863 | − | 0.757476i | \(-0.726432\pi\) | ||||
−0.652863 | + | 0.757476i | \(0.726432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.74612 | 0.110376 | 0.0551879 | − | 0.998476i | \(-0.482424\pi\) | ||||
0.0551879 | + | 0.998476i | \(0.482424\pi\) | |||||||
\(620\) | −5.42213 | −0.217758 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.7058 | −1.07080 | ||||||||
\(623\) | −58.2299 | −2.33293 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.4619 | 0.618475 | ||||||||
\(626\) | 19.6816 | 0.786636 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.0774 | 0.481941 | ||||||||
\(629\) | 2.63683 | 0.105137 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.8303 | 1.50600 | 0.752999 | − | 0.658021i | \(-0.228606\pi\) | ||||
0.752999 | + | 0.658021i | \(0.228606\pi\) | |||||||
\(632\) | −9.21104 | −0.366395 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.46320 | 0.375832 | ||||||||
\(635\) | 9.39704 | 0.372910 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 55.6995 | 2.20690 | ||||||||
\(638\) | −22.6919 | −0.898381 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.815716 | 0.0322440 | ||||||||
\(641\) | −20.1362 | −0.795331 | −0.397665 | − | 0.917531i | \(-0.630179\pi\) | ||||
−0.397665 | + | 0.917531i | \(0.630179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.4318 | −0.963496 | −0.481748 | − | 0.876310i | \(-0.659998\pi\) | ||||
−0.481748 | + | 0.876310i | \(0.659998\pi\) | |||||||
\(644\) | 18.5795 | 0.732134 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.3759 | 0.604958 | ||||||||
\(647\) | −8.54734 | −0.336031 | −0.168015 | − | 0.985784i | \(-0.553736\pi\) | ||||
−0.168015 | + | 0.985784i | \(0.553736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.9859 | 1.21630 | ||||||||
\(650\) | −23.9957 | −0.941190 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.69644 | −0.223090 | ||||||||
\(653\) | 2.59605 | 0.101591 | 0.0507957 | − | 0.998709i | \(-0.483824\pi\) | ||||
0.0507957 | + | 0.998709i | \(0.483824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.351180 | 0.0137217 | ||||||||
\(656\) | 4.44186 | 0.173425 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.8520 | −0.578992 | ||||||||
\(659\) | 7.82570 | 0.304846 | 0.152423 | − | 0.988315i | \(-0.451292\pi\) | ||||
0.152423 | + | 0.988315i | \(0.451292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3756 | 0.870312 | 0.435156 | − | 0.900355i | \(-0.356693\pi\) | ||||
0.435156 | + | 0.900355i | \(0.356693\pi\) | |||||||
\(662\) | 10.3797 | 0.403417 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.93224 | −0.0749856 | ||||||||
\(665\) | 26.2012 | 1.01604 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.9503 | 0.733760 | ||||||||
\(668\) | −17.9694 | −0.695255 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.96217 | 0.307605 | ||||||||
\(671\) | −29.9275 | −1.15534 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.4435 | 0.903681 | 0.451841 | − | 0.892099i | \(-0.350768\pi\) | ||||
0.451841 | + | 0.892099i | \(0.350768\pi\) | |||||||
\(674\) | 32.3299 | 1.24530 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.6456 | 0.678677 | ||||||||
\(677\) | 20.3237 | 0.781102 | 0.390551 | − | 0.920581i | \(-0.372285\pi\) | ||||
0.390551 | + | 0.920581i | \(0.372285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.1059 | 1.42399 | ||||||||
\(680\) | −1.61290 | −0.0618519 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −35.8021 | −1.37093 | ||||||||
\(683\) | −42.7978 | −1.63761 | −0.818806 | − | 0.574070i | \(-0.805364\pi\) | ||||
−0.818806 | + | 0.574070i | \(0.805364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4575 | 0.590600 | ||||||||
\(686\) | −12.6462 | −0.482833 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.7772 | −0.410876 | ||||||||
\(689\) | −35.6860 | −1.35953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.9261 | 1.36669 | 0.683346 | − | 0.730094i | \(-0.260524\pi\) | ||||
0.683346 | + | 0.730094i | \(0.260524\pi\) | |||||||
\(692\) | −20.4869 | −0.778796 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.3366 | 0.809925 | ||||||||
\(695\) | −8.94934 | −0.339468 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.78281 | −0.332673 | ||||||||
\(698\) | −5.35420 | −0.202659 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.9044 | 0.676723 | ||||||||
\(701\) | 41.3499 | 1.56176 | 0.780882 | − | 0.624679i | \(-0.214770\pi\) | ||||
0.780882 | + | 0.624679i | \(0.214770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3702 | 0.391119 | ||||||||
\(704\) | 5.38614 | 0.202998 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.67919 | −0.100833 | ||||||||
\(707\) | −5.44947 | −0.204948 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8015 | −0.743662 | −0.371831 | − | 0.928300i | \(-0.621270\pi\) | ||||
−0.371831 | + | 0.928300i | \(0.621270\pi\) | |||||||
\(710\) | −1.49646 | −0.0561610 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0973 | 0.528319 | ||||||||
\(713\) | 29.8988 | 1.11972 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.3221 | 0.909593 | ||||||||
\(716\) | −14.2118 | −0.531120 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −35.7281 | −1.33336 | ||||||||
\(719\) | 33.4253 | 1.24655 | 0.623276 | − | 0.782002i | \(-0.285801\pi\) | ||||
0.623276 | + | 0.782002i | \(0.285801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5670 | 0.542503 | ||||||||
\(722\) | 41.4708 | 1.54338 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.73904 | 0.101796 | ||||||||
\(725\) | 18.2618 | 0.678226 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.38165 | 0.347946 | 0.173973 | − | 0.984750i | \(-0.444339\pi\) | ||||
0.173973 | + | 0.984750i | \(0.444339\pi\) | |||||||
\(728\) | −22.8662 | −0.847478 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.98615 | −0.110522 | ||||||||
\(731\) | 21.3095 | 0.788161 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.4962 | 1.01560 | 0.507799 | − | 0.861476i | \(-0.330459\pi\) | ||||
0.507799 | + | 0.861476i | \(0.330459\pi\) | |||||||
\(734\) | 27.5484 | 1.01683 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.49804 | −0.165800 | ||||||||
\(737\) | 52.5739 | 1.93658 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.6651 | 0.613035 | 0.306517 | − | 0.951865i | \(-0.400836\pi\) | ||||
0.306517 | + | 0.951865i | \(0.400836\pi\) | |||||||
\(740\) | −1.08781 | −0.0399886 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.6271 | 0.977512 | ||||||||
\(743\) | −8.50144 | −0.311888 | −0.155944 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155944 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.815716 | 0.0298855 | ||||||||
\(746\) | −14.2867 | −0.523075 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.6499 | −0.389399 | ||||||||
\(749\) | 1.37352 | 0.0501874 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.87802 | 0.214492 | 0.107246 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107246 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(752\) | 3.59563 | 0.131119 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.3227 | −0.849361 | ||||||||
\(755\) | −5.27891 | −0.192119 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8609 | 0.794548 | 0.397274 | − | 0.917700i | \(-0.369956\pi\) | ||||
0.397274 | + | 0.917700i | \(0.369956\pi\) | |||||||
\(758\) | 31.7017 | 1.15146 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.34325 | −0.230094 | ||||||||
\(761\) | 1.67436 | 0.0606955 | 0.0303477 | − | 0.999539i | \(-0.490339\pi\) | ||||
0.0303477 | + | 0.999539i | \(0.490339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.6856 | 0.567856 | ||||||||
\(764\) | 9.80574 | 0.354759 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.71332 | −0.0619049 | ||||||||
\(767\) | 31.8472 | 1.14994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.908246 | 0.0327522 | 0.0163761 | − | 0.999866i | \(-0.494787\pi\) | ||||
0.0163761 | + | 0.999866i | \(0.494787\pi\) | |||||||
\(770\) | −18.1479 | −0.654004 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.34693 | −0.0484772 | ||||||||
\(773\) | −24.9132 | −0.896066 | −0.448033 | − | 0.894017i | \(-0.647875\pi\) | ||||
−0.448033 | + | 0.894017i | \(0.647875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.8125 | 1.03498 | ||||||||
\(776\) | −8.98324 | −0.322480 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.3579 | 1.12423 | ||||||||
\(779\) | −34.5412 | −1.23757 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.88104 | −0.353571 | ||||||||
\(782\) | 8.89389 | 0.318045 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.0616 | 0.359343 | ||||||||
\(785\) | 9.85174 | 0.351624 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.2675 | 0.365996 | 0.182998 | − | 0.983113i | \(-0.441420\pi\) | ||||
0.182998 | + | 0.983113i | \(0.441420\pi\) | |||||||
\(788\) | −22.1831 | −0.790239 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.51359 | −0.267321 | ||||||||
\(791\) | −3.13333 | −0.111409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7594 | −1.09230 | ||||||||
\(794\) | −3.58737 | −0.127311 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.9250 | −0.883444 | ||||||||
\(797\) | −9.46275 | −0.335188 | −0.167594 | − | 0.985856i | \(-0.553600\pi\) | ||||
−0.167594 | + | 0.985856i | \(0.553600\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.10958 | −0.251519 | ||||||||
\(800\) | −4.33461 | −0.153252 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.6963 | −0.413012 | ||||||||
\(803\) | −19.7174 | −0.695813 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.1556 | 0.534163 | ||||||||
\(806\) | −36.7972 | −1.29613 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.31930 | 0.0464129 | ||||||||
\(809\) | −45.0849 | −1.58510 | −0.792550 | − | 0.609807i | \(-0.791247\pi\) | ||||
−0.792550 | + | 0.609807i | \(0.791247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8789 | 0.592697 | 0.296349 | − | 0.955080i | \(-0.404231\pi\) | ||||
0.296349 | + | 0.955080i | \(0.404231\pi\) | |||||||
\(812\) | 17.4022 | 0.610697 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.18275 | −0.251755 | ||||||||
\(815\) | −4.64667 | −0.162766 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 83.8065 | 2.93202 | ||||||||
\(818\) | −22.7319 | −0.794802 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.62329 | 0.126531 | ||||||||
\(821\) | 28.2057 | 0.984385 | 0.492192 | − | 0.870486i | \(-0.336196\pi\) | ||||
0.492192 | + | 0.870486i | \(0.336196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.4450 | −1.51440 | −0.757199 | − | 0.653185i | \(-0.773433\pi\) | ||||
−0.757199 | + | 0.653185i | \(0.773433\pi\) | |||||||
\(824\) | −3.52663 | −0.122856 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.7628 | −0.826812 | ||||||||
\(827\) | −4.21075 | −0.146422 | −0.0732111 | − | 0.997316i | \(-0.523325\pi\) | ||||
−0.0732111 | + | 0.997316i | \(0.523325\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.6071 | 1.65346 | 0.826732 | − | 0.562596i | \(-0.190197\pi\) | ||||
0.826732 | + | 0.562596i | \(0.190197\pi\) | |||||||
\(830\) | −1.57616 | −0.0547094 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.53585 | 0.191921 | ||||||||
\(833\) | −19.8946 | −0.689308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6579 | −0.507257 | ||||||||
\(836\) | −41.8842 | −1.44860 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.6330 | 0.436399 | ||||||||
\(839\) | −18.6965 | −0.645475 | −0.322738 | − | 0.946488i | \(-0.604603\pi\) | ||||
−0.322738 | + | 0.946488i | \(0.604603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2504 | −0.387946 | ||||||||
\(842\) | 0.516091 | 0.0177857 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.38099 | 0.185221 | ||||||||
\(845\) | 14.3938 | 0.495162 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −74.3935 | −2.55619 | ||||||||
\(848\) | −6.44635 | −0.221369 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.57074 | 0.293974 | ||||||||
\(851\) | 5.99842 | 0.205623 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.3731 | 0.423647 | 0.211824 | − | 0.977308i | \(-0.432060\pi\) | ||||
0.211824 | + | 0.977308i | \(0.432060\pi\) | |||||||
\(854\) | 22.9511 | 0.785370 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.332526 | −0.0113655 | ||||||||
\(857\) | −32.1567 | −1.09845 | −0.549227 | − | 0.835673i | \(-0.685078\pi\) | ||||
−0.549227 | + | 0.835673i | \(0.685078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2702 | −0.384534 | −0.192267 | − | 0.981343i | \(-0.561584\pi\) | ||||
−0.192267 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(860\) | −8.79111 | −0.299774 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.7458 | −0.979087 | ||||||||
\(863\) | −3.08277 | −0.104939 | −0.0524693 | − | 0.998623i | \(-0.516709\pi\) | ||||
−0.0524693 | + | 0.998623i | \(0.516709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.7115 | −0.568208 | ||||||||
\(866\) | −18.6484 | −0.633699 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 27.4562 | 0.931925 | ||||||||
\(869\) | −49.6119 | −1.68297 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.0352 | 1.83091 | ||||||||
\(872\) | −3.79744 | −0.128597 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34.9781 | 1.18315 | ||||||||
\(875\) | 31.4518 | 1.06326 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −50.6336 | −1.70977 | −0.854887 | − | 0.518814i | \(-0.826374\pi\) | ||||
−0.854887 | + | 0.518814i | \(0.826374\pi\) | |||||||
\(878\) | 11.6890 | 0.394484 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.39356 | 0.148107 | ||||||||
\(881\) | 51.6908 | 1.74151 | 0.870753 | − | 0.491720i | \(-0.163632\pi\) | ||||
0.870753 | + | 0.491720i | \(0.163632\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.7164 | −1.16830 | −0.584149 | − | 0.811646i | \(-0.698572\pi\) | ||||
−0.584149 | + | 0.811646i | \(0.698572\pi\) | |||||||
\(884\) | −10.9459 | −0.368152 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.7049 | 0.661999 | ||||||||
\(887\) | 14.0754 | 0.472604 | 0.236302 | − | 0.971680i | \(-0.424065\pi\) | ||||
0.236302 | + | 0.971680i | \(0.424065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.5841 | −1.59592 | ||||||||
\(890\) | 11.4994 | 0.385461 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.5623 | 0.420618 | ||||||||
\(893\) | −27.9607 | −0.935669 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.5928 | −0.387505 | ||||||||
\(896\) | −4.13057 | −0.137993 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.01542 | −0.100626 | ||||||||
\(899\) | 28.0043 | 0.933996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.7463 | 0.424639 | ||||||||
\(902\) | 23.9245 | 0.796597 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.758572 | 0.0252297 | ||||||||
\(905\) | 2.23428 | 0.0742700 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.6751 | 1.01855 | 0.509275 | − | 0.860604i | \(-0.329914\pi\) | ||||
0.509275 | + | 0.860604i | \(0.329914\pi\) | |||||||
\(908\) | −3.13674 | −0.104096 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.6523 | −0.618318 | ||||||||
\(911\) | −12.8968 | −0.427290 | −0.213645 | − | 0.976911i | \(-0.568534\pi\) | ||||
−0.213645 | + | 0.976911i | \(0.568534\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.4073 | −0.344432 | ||||||||
\(914\) | 13.4588 | 0.445178 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.77927 | 0.124870 | ||||||||
\(917\) | −1.77828 | −0.0587240 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0395 | 0.529094 | 0.264547 | − | 0.964373i | \(-0.414778\pi\) | ||||
0.264547 | + | 0.964373i | \(0.414778\pi\) | |||||||
\(920\) | −3.66912 | −0.120967 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.1944 | −1.19200 | ||||||||
\(923\) | −10.1557 | −0.334279 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.78047 | 0.190061 | ||||||||
\(926\) | −29.1225 | −0.957026 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.21302 | −0.138299 | ||||||||
\(929\) | 31.8120 | 1.04372 | 0.521858 | − | 0.853032i | \(-0.325239\pi\) | ||||
0.521858 | + | 0.853032i | \(0.325239\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78.2421 | −2.56428 | ||||||||
\(932\) | 1.22631 | 0.0401691 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.6912 | 1.13513 | ||||||||
\(935\) | −8.68730 | −0.284105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0768 | −0.623213 | −0.311606 | − | 0.950211i | \(-0.600867\pi\) | ||||
−0.311606 | + | 0.950211i | \(0.600867\pi\) | |||||||
\(938\) | −40.3183 | −1.31644 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.93301 | 0.0956643 | ||||||||
\(941\) | −29.3725 | −0.957517 | −0.478758 | − | 0.877947i | \(-0.658913\pi\) | ||||
−0.478758 | + | 0.877947i | \(0.658913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.9797 | −0.650627 | ||||||||
\(944\) | 5.75290 | 0.187241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −58.0473 | −1.88728 | ||||||||
\(947\) | −13.3442 | −0.433629 | −0.216815 | − | 0.976213i | \(-0.569567\pi\) | ||||
−0.216815 | + | 0.976213i | \(0.569567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.2655 | −0.657846 | ||||||||
\(950\) | 33.7072 | 1.09361 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.16730 | 0.264704 | ||||||||
\(953\) | 13.8031 | 0.447127 | 0.223563 | − | 0.974689i | \(-0.428231\pi\) | ||||
0.223563 | + | 0.974689i | \(0.428231\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.99869 | 0.258832 | ||||||||
\(956\) | −9.21295 | −0.297968 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 38.0159 | 1.22824 | ||||||||
\(959\) | −78.2726 | −2.52756 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1837 | 0.425280 | ||||||||
\(962\) | −7.38240 | −0.238018 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.6802 | −0.666064 | ||||||||
\(965\) | −1.09872 | −0.0353689 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.7669 | 1.69687 | 0.848434 | − | 0.529301i | \(-0.177546\pi\) | ||||
0.848434 | + | 0.529301i | \(0.177546\pi\) | |||||||
\(968\) | 18.0105 | 0.578878 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.32777 | −0.235281 | ||||||||
\(971\) | 7.77643 | 0.249557 | 0.124779 | − | 0.992185i | \(-0.460178\pi\) | ||||
0.124779 | + | 0.992185i | \(0.460178\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.3171 | 1.45280 | ||||||||
\(974\) | 16.5858 | 0.531444 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.55640 | −0.177856 | ||||||||
\(977\) | 3.56867 | 0.114172 | 0.0570859 | − | 0.998369i | \(-0.481819\pi\) | ||||
0.0570859 | + | 0.998369i | \(0.481819\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.9300 | 2.42673 | ||||||||
\(980\) | 8.20741 | 0.262176 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −32.0610 | −1.02311 | ||||||||
\(983\) | −37.1515 | −1.18495 | −0.592475 | − | 0.805589i | \(-0.701849\pi\) | ||||
−0.592475 | + | 0.805589i | \(0.701849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0951 | −0.576557 | ||||||||
\(986\) | 8.33033 | 0.265292 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43.0484 | −1.36955 | ||||||||
\(989\) | 48.4762 | 1.54145 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5462 | 0.684437 | 0.342218 | − | 0.939620i | \(-0.388822\pi\) | ||||
0.342218 | + | 0.939620i | \(0.388822\pi\) | |||||||
\(992\) | −6.64708 | −0.211045 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.57766 | 0.240349 | ||||||||
\(995\) | −20.3317 | −0.644559 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.42721 | 0.235222 | 0.117611 | − | 0.993060i | \(-0.462476\pi\) | ||||
0.117611 | + | 0.993060i | \(0.462476\pi\) | |||||||
\(998\) | −35.4267 | −1.12141 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.n.1.8 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.k.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.k.1.5 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.n.1.8 | yes | 12 | 1.1 | even | 1 | trivial |