Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(57,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.n (of order \(5\), degree \(4\), minimal) |
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: | no |
Analytic conductor: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 12 x^{14} - 19 x^{13} + 49 x^{12} - 91 x^{11} + 269 x^{10} - 367 x^{9} + 1058 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 57.4 | ||
Root | \(-1.67741 - 1.21871i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.57 |
Dual form | 1148.2.n.c.141.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.07339 | 1.19707 | 0.598537 | − | 0.801095i | \(-0.295749\pi\) | ||||
0.598537 | + | 0.801095i | \(0.295749\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.15094 | − | 1.56275i | −0.961931 | − | 0.698884i | −0.00833287 | − | 0.999965i | \(-0.502652\pi\) |
−0.953598 | + | 0.301081i | \(0.902652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.29895 | 0.432984 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.978799 | − | 0.711139i | 0.295119 | − | 0.214417i | −0.430366 | − | 0.902654i | \(-0.641615\pi\) |
0.725485 | + | 0.688238i | \(0.241615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50683 | − | 4.63753i | 0.417918 | − | 1.28622i | −0.491696 | − | 0.870767i | \(-0.663623\pi\) |
0.909615 | − | 0.415453i | \(-0.136377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.45975 | − | 3.24020i | −1.15150 | − | 0.836615i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.06409 | + | 2.95273i | −0.985686 | + | 0.716142i | −0.958972 | − | 0.283501i | \(-0.908504\pi\) |
−0.0267135 | + | 0.999643i | \(0.508504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500524 | − | 1.54045i | −0.114828 | − | 0.353404i | 0.877083 | − | 0.480339i | \(-0.159486\pi\) |
−0.991911 | + | 0.126934i | \(0.959486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.640713 | − | 1.97191i | −0.139815 | − | 0.430307i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.09860 | − | 3.38115i | 0.229074 | − | 0.705018i | −0.768778 | − | 0.639516i | \(-0.779135\pi\) |
0.997852 | − | 0.0655024i | \(-0.0208650\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.639280 | + | 1.96750i | 0.127856 | + | 0.393500i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.52694 | −0.678759 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0761582 | − | 0.0553321i | −0.0141422 | − | 0.0102749i | 0.580692 | − | 0.814124i | \(-0.302782\pi\) |
−0.594834 | + | 0.803849i | \(0.702782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.98750 | + | 2.17055i | −0.536571 | + | 0.389842i | −0.822810 | − | 0.568316i | \(-0.807595\pi\) |
0.286239 | + | 0.958158i | \(0.407595\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.02943 | − | 1.47447i | 0.353279 | − | 0.256672i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.821587 | + | 2.52859i | −0.138874 | + | 0.427409i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.15009 | − | 4.46830i | −1.01107 | − | 0.734584i | −0.0466355 | − | 0.998912i | \(-0.514850\pi\) |
−0.964433 | + | 0.264328i | \(0.914850\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.12424 | − | 9.61542i | 0.500279 | − | 1.53970i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.39630 | + | 3.44672i | 0.842761 | + | 0.538288i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.06649 | − | 9.43767i | 0.467635 | − | 1.43923i | −0.388004 | − | 0.921658i | \(-0.626835\pi\) |
0.855639 | − | 0.517574i | \(-0.173165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.79398 | − | 2.02994i | −0.416501 | − | 0.302606i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.59676 | − | 7.99201i | 0.378777 | − | 1.16575i | −0.562118 | − | 0.827057i | \(-0.690013\pi\) |
0.940895 | − | 0.338698i | \(-0.109987\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.42644 | + | 6.12217i | −1.17994 | + | 0.857275i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.13499 | + | 3.00425i | 0.567984 | + | 0.412665i | 0.834372 | − | 0.551201i | \(-0.185830\pi\) |
−0.266388 | + | 0.963866i | \(0.585830\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.21668 | −0.433737 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.03778 | − | 3.19396i | −0.137458 | − | 0.423051i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.23821 | + | 6.88850i | −0.291390 | + | 0.896806i | 0.693020 | + | 0.720918i | \(0.256280\pi\) |
−0.984410 | + | 0.175888i | \(0.943720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09856 | − | 6.45870i | −0.268693 | − | 0.826952i | −0.990820 | − | 0.135191i | \(-0.956835\pi\) |
0.722127 | − | 0.691761i | \(-0.243165\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.401399 | − | 1.23538i | −0.0505715 | − | 0.155643i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4884 | + | 7.62028i | −1.30093 | + | 0.945179i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8851 | − | 8.63501i | −1.45199 | − | 1.05493i | −0.985361 | − | 0.170482i | \(-0.945467\pi\) |
−0.466631 | − | 0.884452i | \(-0.654533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.27783 | − | 7.01044i | 0.274219 | − | 0.843958i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.09080 | − | 6.60486i | 1.07888 | − | 0.783852i | 0.101393 | − | 0.994846i | \(-0.467670\pi\) |
0.977487 | + | 0.210994i | \(0.0676702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.58657 | 0.536817 | 0.268408 | − | 0.963305i | \(-0.413502\pi\) | ||||
0.268408 | + | 0.963305i | \(0.413502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.32548 | + | 4.07940i | 0.153053 | + | 0.471049i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.978799 | − | 0.711139i | −0.111544 | − | 0.0810418i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0411 | 1.35473 | 0.677366 | − | 0.735646i | \(-0.263121\pi\) | ||||
0.677366 | + | 0.735646i | \(0.263121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2096 | −1.24551 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.731917 | 0.0803383 | 0.0401692 | − | 0.999193i | \(-0.487210\pi\) | ||||
0.0401692 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3560 | 1.44866 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.157906 | − | 0.114725i | −0.0169293 | − | 0.0122998i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.78534 | + | 8.57239i | 0.295245 | + | 0.908672i | 0.983139 | + | 0.182860i | \(0.0585355\pi\) |
−0.687894 | + | 0.725811i | \(0.741464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.87619 | −0.511164 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.19426 | + | 4.50040i | −0.642315 | + | 0.466669i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.33075 | + | 4.09562i | −0.136532 | + | 0.420202i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.31745 | + | 4.58989i | 0.641440 | + | 0.466033i | 0.860344 | − | 0.509713i | \(-0.170248\pi\) |
−0.218905 | + | 0.975746i | \(0.570248\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.27141 | − | 0.923737i | 0.127782 | − | 0.0928390i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.30459 | + | 10.1705i | 0.328819 | + | 1.01200i | 0.969687 | + | 0.244350i | \(0.0785746\pi\) |
−0.640868 | + | 0.767651i | \(0.721425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.56977 | + | 14.0643i | 0.450273 | + | 1.38580i | 0.876596 | + | 0.481226i | \(0.159809\pi\) |
−0.426323 | + | 0.904571i | \(0.640191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.70347 | + | 5.24275i | −0.166242 | + | 0.511640i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.65554 | + | 11.2506i | 0.353394 | + | 1.08764i | 0.956935 | + | 0.290303i | \(0.0937562\pi\) |
−0.603541 | + | 0.797332i | \(0.706244\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.10817 | −0.297709 | −0.148854 | − | 0.988859i | \(-0.547559\pi\) | ||||
−0.148854 | + | 0.988859i | \(0.547559\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.7515 | − | 9.26454i | −1.21032 | − | 0.879351i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4891 | − | 11.2535i | 1.45710 | − | 1.05864i | 0.472988 | − | 0.881069i | \(-0.343175\pi\) |
0.984108 | − | 0.177573i | \(-0.0568246\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.64693 | + | 5.55582i | −0.713079 | + | 0.518083i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.95730 | − | 6.02394i | 0.180952 | − | 0.556913i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.06409 | + | 2.95273i | 0.372554 | + | 0.270676i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.94686 | + | 9.06950i | −0.267896 | + | 0.824500i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.1887 | + | 7.14641i | 1.00885 | + | 0.644370i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.40827 | + | 7.41191i | −0.215403 | + | 0.662941i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.86734 | + | 4.98942i | 0.609378 | + | 0.442739i | 0.849195 | − | 0.528079i | \(-0.177087\pi\) |
−0.239817 | + | 0.970818i | \(0.577087\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.35803 | − | 19.5680i | 0.559793 | − | 1.72287i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.52880 | − | 4.74345i | 0.570424 | − | 0.414437i | −0.264835 | − | 0.964294i | \(-0.585318\pi\) |
0.835259 | + | 0.549856i | \(0.185318\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.31039 | + | 0.952052i | −0.113625 | + | 0.0825534i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.58624 | + | 5.51173i | 0.652920 | + | 0.474374i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.46554 | 0.125209 | 0.0626047 | − | 0.998038i | \(-0.480059\pi\) | ||||
0.0626047 | + | 0.998038i | \(0.480059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0229614 | + | 0.0706680i | 0.00194756 | + | 0.00599398i | 0.952026 | − | 0.306018i | \(-0.0989969\pi\) |
−0.950078 | + | 0.312012i | \(0.898997\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.38411 | − | 16.5706i | 0.453423 | − | 1.39549i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.82305 | − | 5.61077i | −0.152451 | − | 0.469196i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0773415 | + | 0.238033i | 0.00642286 | + | 0.0197675i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.67741 | + | 1.21871i | −0.138350 | + | 0.100517i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3796 | − | 7.54121i | −0.850329 | − | 0.617800i | 0.0749079 | − | 0.997190i | \(-0.476134\pi\) |
−0.925237 | + | 0.379390i | \(0.876134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.951876 | − | 2.92957i | 0.0774626 | − | 0.238405i | −0.904825 | − | 0.425783i | \(-0.859999\pi\) |
0.982288 | + | 0.187378i | \(0.0599988\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.27906 | + | 3.83546i | −0.426787 | + | 0.310079i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.81798 | 0.788599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.13354 | − | 12.7217i | −0.329893 | − | 1.01531i | −0.969183 | − | 0.246340i | \(-0.920772\pi\) |
0.639291 | − | 0.768965i | \(-0.279228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.57345 | + | 6.22898i | 0.679919 | + | 0.493990i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.55515 | −0.280185 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6568 | −1.38299 | −0.691493 | − | 0.722383i | \(-0.743047\pi\) | ||||
−0.691493 | + | 0.722383i | \(0.743047\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.66943 | −0.519214 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3511 | −1.18791 | −0.593954 | − | 0.804499i | \(-0.702434\pi\) | ||||
−0.593954 | + | 0.804499i | \(0.702434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.71895 | − | 6.33469i | −0.670689 | − | 0.487284i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.650157 | − | 2.00098i | −0.0497187 | − | 0.153019i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5820 | 0.804532 | 0.402266 | − | 0.915523i | \(-0.368223\pi\) | ||||
0.402266 | + | 0.915523i | \(0.368223\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.67366 | − | 1.21598i | 0.126517 | − | 0.0919197i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.64068 | + | 14.2826i | −0.348815 | + | 1.07354i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.81579 | + | 5.67850i | 0.584179 | + | 0.424431i | 0.840228 | − | 0.542233i | \(-0.182421\pi\) |
−0.256049 | + | 0.966664i | \(0.582421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.65356 | − | 5.56064i | 0.568885 | − | 0.413319i | −0.265815 | − | 0.964024i | \(-0.585641\pi\) |
0.834700 | + | 0.550705i | \(0.185641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.35113 | − | 13.3914i | −0.321645 | − | 0.989922i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.24565 | + | 19.2221i | 0.459189 | + | 1.41324i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.87812 | + | 5.78026i | −0.137342 | + | 0.422695i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.08988 | + | 3.35432i | 0.0792773 | + | 0.243991i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.63899 | 0.408023 | 0.204012 | − | 0.978968i | \(-0.434602\pi\) | ||||
0.204012 | + | 0.978968i | \(0.434602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8235 | − | 10.0434i | −0.995040 | − | 0.722939i | −0.0340213 | − | 0.999421i | \(-0.510831\pi\) |
−0.961019 | + | 0.276482i | \(0.910831\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.7466 | + | 15.7998i | −1.55731 | + | 1.13145i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7292 | − | 9.97483i | 0.978164 | − | 0.710677i | 0.0208662 | − | 0.999782i | \(-0.493358\pi\) |
0.957297 | + | 0.289105i | \(0.0933576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.69075 | + | 20.5920i | −0.474294 | + | 1.45973i | 0.372613 | + | 0.927987i | \(0.378462\pi\) |
−0.846907 | + | 0.531741i | \(0.821538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.6424 | − | 17.9038i | −1.73814 | − | 1.26283i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0290898 | + | 0.0895293i | −0.00204171 | + | 0.00628372i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.22077 | − | 15.8468i | −0.434477 | − | 1.10679i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.42703 | − | 4.39195i | 0.0991856 | − | 0.305262i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.58539 | − | 1.15185i | −0.109664 | − | 0.0796753i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.24595 | + | 9.99001i | −0.223461 | + | 0.687741i | 0.774984 | + | 0.631981i | \(0.217758\pi\) |
−0.998444 | + | 0.0557596i | \(0.982242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.8488 | − | 13.6945i | 1.29150 | − | 0.938328i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.3446 | + | 15.5077i | −1.45569 | + | 1.05762i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.98750 | + | 2.17055i | 0.202805 | + | 0.147346i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.50975 | 0.642609 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.56952 | + | 23.2966i | 0.509181 | + | 1.56710i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.446264 | − | 1.37346i | 0.0298840 | − | 0.0919736i | −0.935002 | − | 0.354642i | \(-0.884603\pi\) |
0.964886 | + | 0.262669i | \(0.0846026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.830395 | + | 2.55569i | 0.0553597 | + | 0.170380i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.23275 | + | 3.79402i | 0.0818205 | + | 0.251818i | 0.983596 | − | 0.180388i | \(-0.0577354\pi\) |
−0.901775 | + | 0.432206i | \(0.857735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.5219 | − | 17.0896i | 1.55437 | − | 1.12932i | 0.613927 | − | 0.789363i | \(-0.289589\pi\) |
0.940442 | − | 0.339953i | \(-0.110411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.02943 | − | 1.47447i | −0.133527 | − | 0.0970130i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.22215 | − | 3.76140i | 0.0800658 | − | 0.246417i | −0.903009 | − | 0.429622i | \(-0.858647\pi\) |
0.983075 | + | 0.183204i | \(0.0586470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0750 | + | 13.1323i | −1.17908 | + | 0.856655i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.9660 | 1.62171 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.21338 | + | 9.88975i | 0.207856 | + | 0.639715i | 0.999584 | + | 0.0288412i | \(0.00918170\pi\) |
−0.791728 | + | 0.610874i | \(0.790818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.94915 | − | 2.86923i | −0.254387 | − | 0.184823i | 0.453282 | − | 0.891367i | \(-0.350253\pi\) |
−0.707669 | + | 0.706544i | \(0.750253\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.6610 | −0.812206 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.65871 | 0.169859 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.89810 | −0.502544 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.51755 | 0.0961709 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.24518 | + | 2.35776i | 0.204834 | + | 0.148821i | 0.685473 | − | 0.728098i | \(-0.259595\pi\) |
−0.480639 | + | 0.876918i | \(0.659595\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.32916 | − | 4.09072i | −0.0835633 | − | 0.257181i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.6922 | 1.73416 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.49050 | + | 6.16871i | −0.529623 | + | 0.384794i | −0.820217 | − | 0.572053i | \(-0.806147\pi\) |
0.290594 | + | 0.956847i | \(0.406147\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.34913 | + | 7.22986i | −0.145968 | + | 0.449242i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0989259 | − | 0.0718739i | −0.00612336 | − | 0.00444888i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8568 | − | 9.34098i | 0.792782 | − | 0.575990i | −0.116006 | − | 0.993249i | \(-0.537009\pi\) |
0.908788 | + | 0.417259i | \(0.137009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.19924 | − | 12.9239i | −0.257957 | − | 0.793910i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.77510 | + | 17.7739i | 0.353430 | + | 1.08775i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.96442 | − | 27.5896i | 0.546570 | − | 1.68217i | −0.170657 | − | 0.985330i | \(-0.554589\pi\) |
0.717227 | − | 0.696839i | \(-0.245411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.72735 | + | 20.7047i | 0.408658 | + | 1.25772i | 0.917802 | + | 0.397038i | \(0.129962\pi\) |
−0.509145 | + | 0.860681i | \(0.670038\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.1103 | −0.611900 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.02489 | + | 1.47117i | 0.122106 | + | 0.0887150i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2547 | − | 13.2628i | 1.09682 | − | 0.796887i | 0.116283 | − | 0.993216i | \(-0.462902\pi\) |
0.980538 | + | 0.196329i | \(0.0629022\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.88063 | + | 2.81944i | −0.232327 | + | 0.168795i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.889222 | + | 2.73674i | −0.0530465 | + | 0.163260i | −0.974070 | − | 0.226246i | \(-0.927355\pi\) |
0.921024 | + | 0.389507i | \(0.127355\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.51035 | − | 6.18313i | −0.505888 | − | 0.367549i | 0.305374 | − | 0.952233i | \(-0.401219\pi\) |
−0.811261 | + | 0.584684i | \(0.801219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.75916 | + | 8.49183i | −0.163439 | + | 0.503013i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.61048 | − | 6.19729i | 0.0950636 | − | 0.365814i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.54488 | − | 7.83234i | 0.149699 | − | 0.460726i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.0985 | + | 9.51665i | 0.767850 | + | 0.557876i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.503378 | + | 1.54924i | −0.0294077 | + | 0.0905075i | −0.964683 | − | 0.263413i | \(-0.915152\pi\) |
0.935275 | + | 0.353921i | \(0.115152\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5793 | − | 11.3190i | 0.907060 | − | 0.659018i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.45216 | + | 2.50814i | −0.200315 | + | 0.145537i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.0248 | − | 10.1896i | −0.811074 | − | 0.589280i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.92336 | −0.571973 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.85171 | + | 21.0874i | 0.393621 | + | 1.21144i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.57946 | + | 17.1718i | −0.319479 | + | 0.983256i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.48514 | + | 16.8815i | 0.313053 | + | 0.963479i | 0.976548 | + | 0.215298i | \(0.0690723\pi\) |
−0.663495 | + | 0.748181i | \(0.730928\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.47492 | + | 29.1608i | 0.539010 | + | 1.65890i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.2421 | + | 10.3475i | −0.807596 | + | 0.586753i | −0.913133 | − | 0.407663i | \(-0.866344\pi\) |
0.105537 | + | 0.994415i | \(0.466344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.982709 | − | 0.713980i | −0.0555460 | − | 0.0403565i | 0.559666 | − | 0.828718i | \(-0.310930\pi\) |
−0.615212 | + | 0.788362i | \(0.710930\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.06720 | + | 3.28452i | −0.0601301 | + | 0.185061i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6587 | + | 11.3767i | −0.879480 | + | 0.638980i | −0.933114 | − | 0.359581i | \(-0.882920\pi\) |
0.0536337 | + | 0.998561i | \(0.482920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.113892 | −0.00637675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.57936 | + | 23.3269i | 0.423039 | + | 1.30198i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.58271 | + | 4.78262i | 0.366272 | + | 0.266112i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0876 | 0.559561 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.44446 | −0.356379 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.40330 | −0.463289 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.5799 | 1.18614 | 0.593068 | − | 0.805152i | \(-0.297917\pi\) | ||||
0.593068 | + | 0.805152i | \(0.297917\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.98868 | − | 5.80412i | −0.437777 | − | 0.318064i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0697 | + | 37.1468i | 0.659440 | + | 2.02955i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0314 | −0.600919 | −0.300460 | − | 0.953795i | \(-0.597140\pi\) | ||||
−0.300460 | + | 0.953795i | \(0.597140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 32.1151 | − | 23.3330i | 1.74425 | − | 1.26727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.38060 | + | 4.24906i | −0.0747639 | + | 0.230100i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.8551 | + | 11.5194i | −0.853608 | + | 0.620183i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.66258 | + | 20.5053i | 0.357666 | + | 1.10078i | 0.954447 | + | 0.298379i | \(0.0964460\pi\) |
−0.596781 | + | 0.802404i | \(0.703554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.63119 | − | 20.4087i | −0.354960 | − | 1.09245i | −0.956033 | − | 0.293259i | \(-0.905260\pi\) |
0.601073 | − | 0.799194i | \(-0.294740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.31448 | + | 16.3563i | −0.283666 | + | 0.873033i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.41981 | + | 13.6028i | 0.235243 | + | 0.724003i | 0.997089 | + | 0.0762448i | \(0.0242931\pi\) |
−0.761846 | + | 0.647758i | \(0.775707\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.8756 | −1.58563 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.42644 | + | 6.12217i | 0.445975 | + | 0.324020i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.14169 | − | 4.46220i | 0.324146 | − | 0.235506i | −0.413797 | − | 0.910369i | \(-0.635798\pi\) |
0.737942 | + | 0.674864i | \(0.235798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2489 | − | 9.62585i | 0.697308 | − | 0.506624i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.10999 | + | 18.8046i | −0.320691 | + | 0.986987i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.86544 | − | 7.16767i | −0.516381 | − | 0.375173i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.81715 | − | 24.0587i | 0.408052 | − | 1.25586i | −0.510268 | − | 0.860016i | \(-0.670454\pi\) |
0.918320 | − | 0.395839i | \(-0.129546\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.00955 | + | 4.47713i | 0.364902 | + | 0.233070i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.57943 | − | 4.86097i | 0.0819997 | − | 0.252369i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8946 | − | 9.36846i | −0.667656 | − | 0.485081i | 0.201584 | − | 0.979471i | \(-0.435391\pi\) |
−0.869240 | + | 0.494391i | \(0.835391\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.99330 | + | 15.3678i | −0.257853 | + | 0.793589i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.371362 | + | 0.269810i | −0.0191261 | + | 0.0138959i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8391 | − | 13.6874i | 0.967702 | − | 0.703077i | 0.0127753 | − | 0.999918i | \(-0.495933\pi\) |
0.954927 | + | 0.296842i | \(0.0959334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.2387 | + | 10.3450i | 0.729470 | + | 0.529991i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.33830 | −0.0683840 | −0.0341920 | − | 0.999415i | \(-0.510886\pi\) | ||||
−0.0341920 | + | 0.999415i | \(0.510886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.994008 | + | 3.05924i | 0.0506593 | + | 0.155913i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.98322 | − | 12.2591i | 0.202479 | − | 0.623165i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.61729 | + | 4.97750i | 0.0819997 | + | 0.252369i | 0.983648 | − | 0.180101i | \(-0.0576423\pi\) |
−0.901649 | + | 0.432470i | \(0.857642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.51881 | + | 16.9851i | 0.279098 | + | 0.858976i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5368 | − | 9.83503i | 0.682839 | − | 0.496112i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −25.8998 | − | 18.8173i | −1.30316 | − | 0.946801i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.48930 | + | 13.8167i | −0.225312 | + | 0.693438i | 0.772948 | + | 0.634469i | \(0.218781\pi\) |
−0.998260 | + | 0.0589687i | \(0.981219\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.71695 | + | 1.97398i | −0.136017 | + | 0.0988225i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8150 | 1.48889 | 0.744445 | − | 0.667684i | \(-0.232714\pi\) | ||||
0.744445 | + | 0.667684i | \(0.232714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.56434 | + | 17.1253i | 0.277179 | + | 0.853071i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.1112 | + | 17.5178i | 1.19809 | + | 0.870466i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.19729 | −0.455893 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.26735 | −0.211007 | −0.105503 | − | 0.994419i | \(-0.533645\pi\) | ||||
−0.105503 | + | 0.994419i | \(0.533645\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.03864 | 0.149885 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.24299 | 0.356404 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.57431 | − | 1.14380i | −0.0772800 | − | 0.0561472i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0476080 | + | 0.146522i | 0.00233137 | + | 0.00717523i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.9188 | −1.70590 | −0.852948 | − | 0.521996i | \(-0.825187\pi\) | ||||
−0.852948 | + | 0.521996i | \(0.825187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0506 | − | 10.9349i | 0.733519 | − | 0.532933i | −0.157156 | − | 0.987574i | \(-0.550232\pi\) |
0.890675 | + | 0.454641i | \(0.150232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.37307 | − | 10.3813i | 0.164004 | − | 0.504754i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.40759 | − | 6.10848i | −0.407828 | − | 0.296305i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.49410 | + | 3.99170i | −0.265878 | + | 0.193172i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.77990 | − | 11.6333i | −0.182495 | − | 0.561663i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.68988 | − | 23.6670i | −0.370408 | − | 1.14000i | −0.946525 | − | 0.322632i | \(-0.895432\pi\) |
0.576116 | − | 0.817368i | \(-0.304568\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.13466 | − | 18.8805i | 0.294813 | − | 0.907341i | −0.688471 | − | 0.725264i | \(-0.741718\pi\) |
0.983284 | − | 0.182078i | \(-0.0582822\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.160359 | + | 0.493535i | 0.00768864 | + | 0.0236632i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.75837 | −0.275460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7789 | + | 12.1906i | 0.800813 | + | 0.581825i | 0.911153 | − | 0.412069i | \(-0.135194\pi\) |
−0.110339 | + | 0.993894i | \(0.535194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.05088 | + | 0.763506i | −0.0500417 | + | 0.0363574i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.16941 | + | 5.20888i | −0.340629 | + | 0.247482i | −0.744927 | − | 0.667146i | \(-0.767516\pi\) |
0.404298 | + | 0.914627i | \(0.367516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.40541 | − | 22.7915i | 0.351050 | − | 1.08042i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.5209 | − | 15.6359i | −1.01791 | − | 0.739552i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.79030 | − | 17.8207i | 0.273261 | − | 0.841011i | −0.716413 | − | 0.697676i | \(-0.754217\pi\) |
0.989674 | − | 0.143335i | \(-0.0457826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.73300 | − | 0.463872i | 0.364133 | − | 0.0218429i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.97361 | − | 6.07415i | 0.0927284 | − | 0.285389i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4884 | + | 7.62028i | 0.491704 | + | 0.357244i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.13428 | − | 9.64632i | 0.146615 | − | 0.451236i | −0.850600 | − | 0.525814i | \(-0.823761\pi\) |
0.997215 | + | 0.0745779i | \(0.0237610\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.3338 | − | 10.4141i | 0.669043 | − | 0.486088i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.3889 | + | 14.0869i | −0.903031 | + | 0.656091i | −0.939243 | − | 0.343254i | \(-0.888471\pi\) |
0.0362116 | + | 0.999344i | \(0.488471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7106 | − | 11.4144i | −0.730134 | − | 0.530473i | 0.159472 | − | 0.987202i | \(-0.449021\pi\) |
−0.889606 | + | 0.456729i | \(0.849021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.3565 | 0.944011 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.92767 | + | 24.3989i | 0.366849 | + | 1.12904i | 0.948815 | + | 0.315831i | \(0.102283\pi\) |
−0.581967 | + | 0.813213i | \(0.697717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.53969 | + | 13.9717i | −0.209624 | + | 0.645155i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.57046 | − | 26.3772i | −0.394906 | − | 1.21540i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.71002 | − | 11.4183i | −0.170587 | − | 0.525013i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.71087 | − | 1.96956i | 0.124383 | − | 0.0903697i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.37116 | + | 3.90237i | 0.245928 | + | 0.178677i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.97174 | − | 6.06840i | 0.0900912 | − | 0.277272i | −0.895852 | − | 0.444352i | \(-0.853434\pi\) |
0.985943 | + | 0.167080i | \(0.0534339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.9890 | + | 21.7883i | −1.36738 | + | 0.993460i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.37122 | −0.335402 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.41561 | − | 19.7452i | −0.291318 | − | 0.896584i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.98602 | − | 2.16947i | −0.135310 | − | 0.0983082i | 0.518072 | − | 0.855337i | \(-0.326650\pi\) |
−0.653381 | + | 0.757029i | \(0.726650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.6094 | −1.65554 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.6915 | −1.29483 | −0.647414 | − | 0.762139i | \(-0.724149\pi\) | ||||
−0.647414 | + | 0.762139i | \(0.724149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.472894 | 0.0212981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.17831 | −0.187801 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.09080 | − | 6.60486i | −0.407778 | − | 0.296268i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.22333 | − | 19.1534i | −0.278594 | − | 0.857426i | −0.988246 | − | 0.152873i | \(-0.951148\pi\) |
0.709651 | − | 0.704553i | \(-0.248852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.8289 | −1.42201 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.3187 | + | 19.1216i | −1.17349 | + | 0.852592i | −0.991423 | − | 0.130694i | \(-0.958279\pi\) |
−0.182069 | + | 0.983286i | \(0.558279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.78596 | − | 27.0404i | 0.390970 | − | 1.20328i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.0778 | − | 13.1343i | −0.802864 | − | 0.583315i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.45107 | + | 3.96044i | −0.241615 | + | 0.175543i | −0.702002 | − | 0.712175i | \(-0.747710\pi\) |
0.460388 | + | 0.887718i | \(0.347710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.41733 | − | 4.36208i | −0.0626988 | − | 0.192967i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.76531 | + | 5.43308i | 0.0779405 | + | 0.239876i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.1497 | − | 37.3930i | 0.535380 | − | 1.64773i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.14172 | − | 9.66923i | −0.138173 | − | 0.425252i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.9406 | 0.963083 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.7191 | − | 12.8737i | −0.776288 | − | 0.564006i | 0.127575 | − | 0.991829i | \(-0.459281\pi\) |
−0.903863 | + | 0.427823i | \(0.859281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.39094 | − | 3.91675i | 0.235729 | − | 0.171267i | −0.463649 | − | 0.886019i | \(-0.653460\pi\) |
0.699379 | + | 0.714751i | \(0.253460\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.47015 | − | 2.52121i | 0.151450 | − | 0.110035i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.73242 | − | 17.6426i | 0.249708 | − | 0.768523i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.38216 | + | 6.09000i | 0.364442 | + | 0.264782i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.90733 | + | 8.94784i | −0.126167 | + | 0.388303i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.1156 | − | 19.8319i | 1.04456 | − | 0.859016i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.71903 | − | 29.9121i | 0.420190 | − | 1.29321i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.2052 | + | 11.7738i | 0.699305 | + | 0.508075i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.373868 | + | 1.15065i | −0.0161036 | + | 0.0495619i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9991 | + | 15.9833i | −0.945815 | + | 0.687175i | −0.949813 | − | 0.312817i | \(-0.898727\pi\) |
0.00399866 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8688 | − | 11.5294i | 0.680997 | − | 0.494773i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.68551 | + | 4.85730i | 0.286376 | + | 0.208064i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3516 | 0.613631 | 0.306815 | − | 0.951769i | \(-0.400737\pi\) | ||||
0.306815 | + | 0.951769i | \(0.400737\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.72593 | − | 8.38955i | −0.116340 | − | 0.358057i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0471176 | + | 0.145013i | −0.00200728 | + | 0.00617777i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.72091 | − | 11.4518i | −0.158229 | − | 0.486980i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.9497 | + | 39.8550i | 0.549683 | + | 1.69175i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.4051 | − | 20.6375i | 1.20356 | − | 0.874438i | 0.208931 | − | 0.977930i | \(-0.433002\pi\) |
0.994630 | + | 0.103492i | \(0.0330017\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.1468 | − | 28.4418i | −1.65574 | − | 1.20296i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.89408 | + | 11.9847i | −0.164408 | + | 0.505996i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.1906 | + | 11.0366i | −0.640209 | + | 0.465139i | −0.859922 | − | 0.510426i | \(-0.829488\pi\) |
0.219713 | + | 0.975565i | \(0.429488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.9027 | −2.14149 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.46395 | + | 10.6609i | 0.145472 | + | 0.447718i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5881 | + | 11.3254i | 0.653487 | + | 0.474786i | 0.864457 | − | 0.502706i | \(-0.167662\pi\) |
−0.210970 | + | 0.977492i | \(0.567662\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.94797 | 0.248915 | 0.124457 | − | 0.992225i | \(-0.460281\pi\) | ||||
0.124457 | + | 0.992225i | \(0.460281\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.6918 | 0.488434 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.35473 | 0.306713 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.08366 | 0.336527 | 0.168264 | − | 0.985742i | \(-0.446184\pi\) | ||||
0.168264 | + | 0.985742i | \(0.446184\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.6616 | − | 20.8239i | −1.19114 | − | 0.865411i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.226175 | − | 0.696094i | −0.00938331 | − | 0.0288789i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.18376 | 0.256105 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.6240 | + | 9.89838i | −0.563281 | + | 0.409248i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.38098 | − | 22.7163i | 0.304646 | − | 0.937603i | −0.675163 | − | 0.737668i | \(-0.735927\pi\) |
0.979809 | − | 0.199935i | \(-0.0640731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.83894 | + | 3.51570i | 0.199385 | + | 0.144862i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.4660 | − | 20.6817i | 1.17093 | − | 0.850733i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.34823 | − | 13.3825i | −0.178561 | − | 0.549553i | 0.821218 | − | 0.570615i | \(-0.193295\pi\) |
−0.999778 | + | 0.0210623i | \(0.993295\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.12723 | − | 12.7023i | −0.169200 | − | 0.520744i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8725 | + | 42.6953i | −0.567765 | + | 1.74740i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.23566 | − | 13.0360i | −0.173064 | − | 0.532637i | 0.826476 | − | 0.562973i | \(-0.190342\pi\) |
−0.999540 | + | 0.0303357i | \(0.990342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.2318 | −0.539737 | −0.269868 | − | 0.962897i | \(-0.586980\pi\) | ||||
−0.269868 | + | 0.962897i | \(0.586980\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.4382 | − | 11.2165i | −0.628690 | − | 0.456770i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.5119 | − | 14.9028i | 0.833927 | − | 0.605884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.4413 | + | 9.76566i | −0.545565 | + | 0.396376i | −0.826148 | − | 0.563454i | \(-0.809472\pi\) |
0.280583 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0603146 | + | 0.185629i | −0.00244407 | + | 0.00752208i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.1503 | − | 24.0851i | −1.34112 | − | 0.974380i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0874 | − | 37.2011i | 0.488204 | − | 1.50254i | −0.339082 | − | 0.940757i | \(-0.610117\pi\) |
0.827286 | − | 0.561781i | \(-0.189883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.8981 | − | 32.8566i | −0.520101 | − | 1.32491i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.64479 | + | 5.06214i | −0.0662167 | + | 0.203794i | −0.978690 | − | 0.205341i | \(-0.934170\pi\) |
0.912474 | + | 0.409135i | \(0.134170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0651 | − | 10.9454i | −0.605516 | − | 0.439933i | 0.242316 | − | 0.970197i | \(-0.422093\pi\) |
−0.847833 | + | 0.530264i | \(0.822093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.87470 | + | 11.9251i | −0.155486 | + | 0.478537i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.29211 | − | 5.29803i | 0.292152 | − | 0.212261i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.1313 | − | 18.2590i | 1.00525 | − | 0.730359i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.28713 | − | 2.38824i | −0.131275 | − | 0.0953771i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.1882 | 1.52266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.26378 | − | 28.5110i | −0.368785 | − | 1.13500i | −0.947577 | − | 0.319528i | \(-0.896476\pi\) |
0.578792 | − | 0.815475i | \(-0.303524\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.73013 | + | 20.7132i | −0.267499 | + | 0.823276i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.97405 | − | 21.4639i | −0.276757 | − | 0.851769i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50683 | + | 4.63753i | 0.0597026 | + | 0.183746i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.8085 | − | 8.57940i | 0.467138 | − | 0.339396i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.33459 | − | 0.969637i | −0.0527132 | − | 0.0382984i | 0.561117 | − | 0.827737i | \(-0.310372\pi\) |
−0.613830 | + | 0.789438i | \(0.710372\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.51070 | − | 20.0379i | 0.256757 | − | 0.790216i | −0.736722 | − | 0.676196i | \(-0.763627\pi\) |
0.993478 | − | 0.114020i | \(-0.0363728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −44.2557 | + | 32.1536i | −1.74257 | + | 1.26605i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.04163 | −0.237521 | −0.118760 | − | 0.992923i | \(-0.537892\pi\) | ||||
−0.118760 | + | 0.992923i | \(0.537892\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.70792 | + | 8.33413i | 0.106295 | + | 0.327143i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.19426 | + | 4.50040i | 0.242772 | + | 0.176384i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.9878 | 0.938715 | 0.469358 | − | 0.883008i | \(-0.344485\pi\) | ||||
0.469358 | + | 0.883008i | \(0.344485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.4559 | −0.838352 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.95773 | 0.232433 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.0486 | 0.625164 | 0.312582 | − | 0.949891i | \(-0.398806\pi\) | ||||
0.312582 | + | 0.949891i | \(0.398806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1098 | − | 8.07171i | −0.432119 | − | 0.313953i | 0.350376 | − | 0.936609i | \(-0.386054\pi\) |
−0.782496 | + | 0.622656i | \(0.786054\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.6946 | + | 48.3029i | 0.609527 | + | 1.87593i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.30639 | 0.166995 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.270754 | + | 0.196714i | −0.0104836 | + | 0.00761680i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.925279 | − | 2.84772i | 0.0357734 | − | 0.110099i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.64710 | − | 4.82940i | −0.256608 | − | 0.186437i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.581325 | − | 0.422358i | 0.0224084 | − | 0.0162807i | −0.576525 | − | 0.817080i | \(-0.695592\pi\) |
0.598933 | + | 0.800799i | \(0.295592\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.25470 | − | 6.93925i | −0.0867835 | − | 0.267092i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.18645 | − | 6.72920i | −0.0840321 | − | 0.258624i | 0.900208 | − | 0.435459i | \(-0.143414\pi\) |
−0.984240 | + | 0.176835i | \(0.943414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.41305 | − | 7.42660i | 0.0926044 | − | 0.285007i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.55597 | + | 7.86648i | 0.0979452 | + | 0.301444i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.5554 | 0.863060 | 0.431530 | − | 0.902099i | \(-0.357974\pi\) | ||||
0.431530 | + | 0.902099i | \(0.357974\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.15229 | − | 2.29027i | −0.120443 | − | 0.0875069i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 48.7701 | − | 35.4335i | 1.86069 | − | 1.35187i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.1630 | − | 14.6493i | 0.768149 | − | 0.558093i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.97175 | + | 9.14611i | −0.113051 | + | 0.347934i | −0.991535 | − | 0.129836i | \(-0.958555\pi\) |
0.878485 | + | 0.477770i | \(0.158555\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.27141 | − | 0.923737i | −0.0482970 | − | 0.0350899i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0610478 | − | 0.187886i | 0.00231568 | − | 0.00712692i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.1083 | + | 1.92605i | −1.21619 | + | 0.0729544i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.53400 | − | 7.79885i | 0.0958447 | − | 0.294980i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.6367 | − | 22.2589i | −1.15713 | − | 0.840707i | −0.167720 | − | 0.985835i | \(-0.553641\pi\) |
−0.989413 | + | 0.145128i | \(0.953641\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.80494 | + | 11.7104i | −0.143506 | + | 0.441667i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37.4766 | + | 27.2283i | −1.41145 | + | 1.02548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.65153 | − | 6.28571i | 0.325374 | − | 0.236398i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.9208 | + | 26.8245i | 1.38659 | + | 1.00742i | 0.996230 | + | 0.0867537i | \(0.0276493\pi\) |
0.390360 | + | 0.920662i | \(0.372351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.6409 | 0.586578 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.05687 | + | 12.4858i | 0.151931 | + | 0.467595i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.84697 | + | 14.9174i | −0.181266 | + | 0.557880i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.66259 | + | 20.5053i | 0.248819 | + | 0.765786i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.75246 | − | 5.39350i | −0.0653556 | − | 0.201144i | 0.913046 | − | 0.407856i | \(-0.133724\pi\) |
−0.978402 | + | 0.206712i | \(0.933724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.9638 | − | 8.69222i | 0.445556 | − | 0.323715i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.18813 | − | 5.94903i | −0.304520 | − | 0.221247i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0601797 | − | 0.185214i | 0.00223502 | − | 0.00687868i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.0384 | + | 31.2693i | −1.59621 | + | 1.15971i | −0.701885 | + | 0.712290i | \(0.747658\pi\) |
−0.894323 | + | 0.447422i | \(0.852342\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.37744 | 0.273238 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4044 | + | 47.4100i | 0.569754 | + | 1.75352i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.9549 | − | 21.0370i | −1.06948 | − | 0.777019i | −0.0936573 | − | 0.995604i | \(-0.529856\pi\) |
−0.975818 | + | 0.218585i | \(0.929856\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.51255 | 0.203334 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.7738 | −0.654706 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.2076 | 1.69977 | 0.849887 | − | 0.526965i | \(-0.176670\pi\) | ||||
0.849887 | + | 0.526965i | \(0.176670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.3759 | −0.601582 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.3000 | − | 14.0223i | −0.708048 | − | 0.514427i | 0.174495 | − | 0.984658i | \(-0.444171\pi\) |
−0.882543 | + | 0.470231i | \(0.844171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5409 | + | 32.4414i | 0.386187 | + | 1.18856i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.950726 | 0.0347852 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.57032 | − | 6.95325i | 0.349692 | − | 0.254066i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.92443 | − | 12.0782i | 0.143205 | − | 0.440739i | −0.853571 | − | 0.520976i | \(-0.825568\pi\) |
0.996776 | + | 0.0802378i | \(0.0255680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.72854 | + | 4.88857i | 0.245202 | + | 0.178149i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.62563 | + | 4.81380i | −0.241131 | + | 0.175192i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.58652 | − | 4.88280i | −0.0576630 | − | 0.177468i | 0.918076 | − | 0.396403i | \(-0.129742\pi\) |
−0.975739 | + | 0.218935i | \(0.929742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.75586 | − | 8.48167i | −0.100031 | − | 0.307865i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.73711 | + | 11.5017i | −0.135470 | + | 0.416935i | −0.995663 | − | 0.0930348i | \(-0.970343\pi\) |
0.860193 | + | 0.509969i | \(0.170343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.960478 | + | 2.95605i | 0.0347716 | + | 0.107016i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.3488 | 0.627248 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.5730 | + | 20.7595i | 1.03171 | + | 0.749583i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.0231 | − | 23.9927i | 1.19084 | − | 0.865199i | 0.197491 | − | 0.980305i | \(-0.436721\pi\) |
0.993353 | + | 0.115106i | \(0.0367207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.6041 | + | 12.7902i | −0.633997 | + | 0.460626i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.47035 | + | 26.0691i | −0.304657 | + | 0.937639i | 0.675147 | + | 0.737683i | \(0.264080\pi\) |
−0.979805 | + | 0.199956i | \(0.935920\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.18041 | − | 4.49033i | −0.222007 | − | 0.161297i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.87066 | + | 14.9903i | −0.174734 | + | 0.537775i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.60854 | − | 10.0379i | 0.0934606 | − | 0.359646i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.20110 | − | 12.9297i | 0.150327 | − | 0.462659i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.268605 | + | 0.195153i | 0.00959916 | + | 0.00697420i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.9899 | + | 33.8235i | −0.392247 | + | 1.20721i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5673 | − | 13.4900i | 0.661854 | − | 0.480865i | −0.205435 | − | 0.978671i | \(-0.565861\pi\) |
0.867289 | + | 0.497806i | \(0.165861\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 26.6571 | − | 19.3675i | 0.949018 | − | 0.689502i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.4891 | − | 11.2535i | −0.550730 | − | 0.400129i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.1146 | −1.17593 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.70667 | − | 26.7964i | −0.308794 | − | 0.950369i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.9129 | + | 48.9750i | −0.563666 | + | 1.73478i | 0.108218 | + | 0.994127i | \(0.465486\pi\) |
−0.671883 | + | 0.740657i | \(0.734514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.0448 | + | 40.1478i | 0.461492 | + | 1.42033i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.61802 | + | 11.1351i | 0.127837 | + | 0.393441i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.48933 | − | 3.26169i | 0.158425 | − | 0.115102i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.64693 | + | 5.55582i | 0.269519 | + | 0.195817i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.5867 | − | 57.2041i | 0.654284 | − | 2.01368i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.3619 | + | 31.5043i | −1.52452 | + | 1.10763i | −0.565336 | + | 0.824861i | \(0.691253\pi\) |
−0.959188 | + | 0.282770i | \(0.908747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.9584 | 1.50847 | 0.754237 | − | 0.656603i | \(-0.228007\pi\) | ||||
0.754237 | + | 0.656603i | \(0.228007\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.9484 | + | 42.9289i | 0.489193 | + | 1.50558i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.9788 | + | 27.5932i | 1.33034 | + | 0.966547i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0731 | −0.562328 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.33394 | −0.221326 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.5436 | −1.58948 | −0.794742 | − | 0.606947i | \(-0.792394\pi\) | ||||
−0.794742 | + | 0.606947i | \(0.792394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4586 | 0.852572 | 0.426286 | − | 0.904588i | \(-0.359822\pi\) | ||||
0.426286 | + | 0.904588i | \(0.359822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.19840 | + | 3.05032i | 0.146170 | + | 0.106198i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.2768 | − | 43.9394i | −0.496453 | − | 1.52792i | −0.814681 | − | 0.579910i | \(-0.803088\pi\) |
0.318228 | − | 0.948014i | \(-0.396912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.2775 | −1.29470 | −0.647350 | − | 0.762193i | \(-0.724123\pi\) | ||||
−0.647350 | + | 0.762193i | \(0.724123\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.8492 | − | 27.4991i | 1.31297 | − | 0.953932i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.55234 | − | 4.77762i | 0.0537855 | − | 0.165535i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.0195 | + | 23.9900i | 1.14269 | + | 0.830210i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.5367 | − | 7.65538i | 0.364203 | − | 0.264609i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.05830 | + | 12.4902i | 0.140108 | + | 0.431208i | 0.996350 | − | 0.0853677i | \(-0.0272065\pi\) |
−0.856242 | + | 0.516576i | \(0.827206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.95875 | − | 27.5722i | −0.308923 | − | 0.950766i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.84371 | + | 5.67434i | −0.0635006 | + | 0.195435i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.85443 | + | 27.2511i | 0.304602 | + | 0.937467i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.53623 | 0.327669 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6453 | − | 12.8201i | −0.605585 | − | 0.439983i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.8645 | + | 15.8855i | −0.749505 | + | 0.544547i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.5065 | − | 30.1563i | 1.42116 | − | 1.03253i | 0.429578 | − | 0.903030i | \(-0.358662\pi\) |
0.991579 | − | 0.129501i | \(-0.0413376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.72858 | + | 5.32002i | −0.0591162 | + | 0.181941i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.8664 | + | 12.2542i | 0.576146 | + | 0.418594i | 0.837333 | − | 0.546694i | \(-0.184114\pi\) |
−0.261187 | + | 0.965288i | \(0.584114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.54122 | + | 7.82109i | −0.0867055 | + | 0.266852i | −0.985003 | − | 0.172535i | \(-0.944804\pi\) |
0.898298 | + | 0.439387i | \(0.144804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.33916 | − | 12.8494i | 0.113798 | − | 0.437906i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.5387 | + | 35.5124i | −0.392781 | + | 1.20886i | 0.537894 | + | 0.843012i | \(0.319220\pi\) |
−0.930676 | + | 0.365845i | \(0.880780\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.7612 | − | 16.5370i | −0.773904 | − | 0.562274i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.27654 | − | 16.2395i | 0.179201 | − | 0.551523i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.7858 | − | 8.56292i | 0.399807 | − | 0.290477i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.9538 | + | 42.1059i | −1.96369 | + | 1.42671i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.20607 | + | 5.96206i | 0.277733 | + | 0.201785i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.79334 | 0.263463 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.19770 | − | 6.76381i | −0.0742109 | − | 0.228398i | 0.907070 | − | 0.420980i | \(-0.138314\pi\) |
−0.981281 | + | 0.192582i | \(0.938314\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.04370 | + | 3.21218i | −0.0352031 | + | 0.108344i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6898 | + | 39.0552i | 0.427531 | + | 1.31580i | 0.900550 | + | 0.434753i | \(0.143164\pi\) |
−0.473019 | + | 0.881052i | \(0.656836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.5915 | + | 44.9080i | 0.491043 | + | 1.51127i | 0.823034 | + | 0.567992i | \(0.192280\pi\) |
−0.331991 | + | 0.943282i | \(0.607720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.3019 | − | 23.4687i | 1.08582 | − | 0.788893i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.131343 | − | 0.0954264i | −0.00441007 | − | 0.00320411i | 0.585578 | − | 0.810616i | \(-0.300868\pi\) |
−0.589988 | + | 0.807412i | \(0.700868\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.62309 | − | 8.07305i | 0.0879757 | − | 0.270761i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.9719 | + | 7.97157i | −0.367573 | + | 0.267058i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6111 | −0.455477 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.93723 | − | 24.4283i | −0.265312 | − | 0.816547i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.0789 | − | 21.1270i | −0.970915 | − | 0.705411i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.347624 | 0.0115939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.6757 | −0.855381 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.5750 | −0.684693 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.1523 | −0.836090 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.3995 | − | 12.6415i | −0.577742 | − | 0.419754i | 0.260167 | − | 0.965564i | \(-0.416222\pi\) |
−0.837909 | + | 0.545809i | \(0.816222\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.29251 | + | 13.2110i | 0.142374 | + | 0.438181i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.7756 | 1.08590 | 0.542952 | − | 0.839764i | \(-0.317307\pi\) | ||||
0.542952 | + | 0.839764i | \(0.317307\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.716400 | − | 0.520495i | 0.0237094 | − | 0.0172259i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.5684 | + | 35.6039i | −0.382440 | + | 1.17703i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.52880 | − | 4.74345i | −0.215600 | − | 0.156643i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.95450 | − | 5.77928i | 0.262395 | − | 0.190641i | −0.448807 | − | 0.893629i | \(-0.648151\pi\) |
0.711202 | + | 0.702988i | \(0.248151\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.3728 | + | 35.0020i | 0.374748 | + | 1.15335i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.9320 | − | 52.1112i | −0.557323 | − | 1.71526i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.85976 | − | 14.9568i | 0.159788 | − | 0.491777i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.93592 | + | 18.2689i | 0.194961 | + | 0.600029i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.0832 | −0.330818 | −0.165409 | − | 0.986225i | \(-0.552894\pi\) | ||||
−0.165409 | + | 0.986225i | \(0.552894\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.31039 | + | 0.952052i | 0.0429462 | + | 0.0312023i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.5295 | + | 21.4544i | −0.966752 | + | 0.702386i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.0728 | − | 9.49798i | 0.427528 | − | 0.310617i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.64873 | − | 29.6957i | 0.315210 | − | 0.970117i | −0.660458 | − | 0.750863i | \(-0.729638\pi\) |
0.975668 | − | 0.219254i | \(-0.0703624\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.03754 | − | 1.48036i | −0.0664926 | − | 0.0483097i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.76564 | − | 23.9002i | 0.253153 | − | 0.779123i | −0.741036 | − | 0.671466i | \(-0.765665\pi\) |
0.994188 | − | 0.107658i | \(-0.0343350\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.5823 | − | 14.4591i | 0.572557 | − | 0.470854i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.89769 | − | 8.91816i | 0.0942617 | − | 0.290108i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.4945 | + | 30.8741i | 1.38089 | + | 1.00327i | 0.996797 | + | 0.0799757i | \(0.0254843\pi\) |
0.384089 | + | 0.923296i | \(0.374516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.91115 | − | 21.2703i | 0.224346 | − | 0.690464i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.4666 | + | 23.5884i | −1.05280 | + | 0.764906i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.00782 | + | 6.54457i | −0.291792 | + | 0.211999i | −0.724044 | − | 0.689753i | \(-0.757719\pi\) |
0.432252 | + | 0.901753i | \(0.357719\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1292 | − | 8.81235i | −0.392490 | − | 0.285161i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.236144 | −0.00763344 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.452876 | − | 1.39381i | −0.0146241 | − | 0.0450085i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.36563 | + | 16.5137i | −0.173085 | + | 0.532701i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.74837 | + | 14.6140i | 0.153014 | + | 0.470929i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0383 | + | 43.2055i | 0.451910 | + | 1.39084i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0628 | + | 16.0295i | −0.709491 | + | 0.515475i | −0.883009 | − | 0.469355i | \(-0.844486\pi\) |
0.173518 | + | 0.984831i | \(0.444486\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.6485 | + | 9.91625i | 0.438454 | + | 0.318556i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3335 | − | 44.1138i | 0.459982 | − | 1.41568i | −0.405202 | − | 0.914227i | \(-0.632799\pi\) |
0.865185 | − | 0.501453i | \(-0.167201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.0601138 | − | 0.0436752i | 0.00192716 | − | 0.00140016i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.9156 | 0.669836 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.94350 | − | 24.4476i | −0.254135 | − | 0.782147i | −0.993999 | − | 0.109391i | \(-0.965110\pi\) |
0.739864 | − | 0.672757i | \(-0.234890\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.82245 | + | 6.40988i | 0.281967 | + | 0.204861i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.03737 | −0.128903 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.6330 | −0.977039 | −0.488520 | − | 0.872553i | \(-0.662463\pi\) | ||||
−0.488520 | + | 0.872553i | \(0.662463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.1189 | −1.43761 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.4233 | −0.554591 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.5413 | − | 20.7365i | −0.907561 | − | 0.659382i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.34713 | + | 10.3014i | 0.106325 | + | 0.327235i | 0.990039 | − | 0.140792i | \(-0.0449649\pi\) |
−0.883714 | + | 0.468027i | \(0.844965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.7435 | 1.41989 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.5716 | − | 33.8363i | 1.47642 | − | 1.07268i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0727 | + | 31.0007i | −0.319007 | + | 0.981803i | 0.655066 | + | 0.755571i | \(0.272641\pi\) |
−0.974074 | + | 0.226232i | \(0.927359\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.6910 | + | 15.7594i | 0.686272 | + | 0.498606i |
(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 | 1148.2.n.c.57.4 | ✓ | 16 | |
41.18 | even | 5 | inner | 1148.2.n.c.141.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.n.c.57.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1148.2.n.c.141.4 | yes | 16 | 41.18 | even | 5 | inner |