Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1848,2,Mod(881,1848)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1848, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1848.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1848.v (of order \(2\), degree \(1\), 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: | \(14.7563542935\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.9 | ||
Character | \(\chi\) | \(=\) | 1848.881 |
Dual form | 1848.2.v.e.881.10 |
$q$-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 \(\left(\mathbb{Z}/1848\mathbb{Z}\right)^\times\).
\(n\) | \(463\) | \(617\) | \(673\) | \(925\) | \(1585\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.12980 | − | 1.31284i | −0.652289 | − | 0.757970i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.68437 | −0.753273 | −0.376636 | − | 0.926361i | \(-0.622919\pi\) | ||||
−0.376636 | + | 0.926361i | \(0.622919\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.40047 | + | 1.11255i | −0.907291 | + | 0.420504i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.447111 | + | 2.96649i | −0.149037 | + | 0.988832i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.48628i | − | 1.24427i | −0.782910 | − | 0.622134i | \(-0.786266\pi\) | ||
0.782910 | − | 0.622134i | \(-0.213734\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.90300 | + | 2.21131i | 0.491352 | + | 0.570958i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.63878 | −1.12507 | −0.562535 | − | 0.826774i | \(-0.690174\pi\) | ||||
−0.562535 | + | 0.826774i | \(0.690174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.439499i | 0.100828i | 0.998728 | + | 0.0504140i | \(0.0160541\pi\) | ||||
−0.998728 | + | 0.0504140i | \(0.983946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.17264 | + | 1.89448i | 0.910545 | + | 0.413409i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.90671i | 0.814605i | 0.913293 | + | 0.407303i | \(0.133531\pi\) | ||||
−0.913293 | + | 0.407303i | \(0.866469\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.16290 | −0.432580 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.39969 | − | 2.76456i | 0.846720 | − | 0.532039i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.885307i | 0.164397i | 0.996616 | + | 0.0821987i | \(0.0261942\pi\) | ||||
−0.996616 | + | 0.0821987i | \(0.973806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.28536i | 0.230858i | 0.993316 | + | 0.115429i | \(0.0368243\pi\) | ||||
−0.993316 | + | 0.115429i | \(0.963176\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.31284 | − | 1.12980i | 0.228537 | − | 0.196673i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.04327 | − | 1.87394i | 0.683437 | − | 0.316754i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.462685 | −0.0760649 | −0.0380324 | − | 0.999277i | \(-0.512109\pi\) | ||||
−0.0380324 | + | 0.999277i | \(0.512109\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.88977 | + | 5.06859i | −0.943118 | + | 0.811623i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.71558 | −0.424103 | −0.212051 | − | 0.977259i | \(-0.568014\pi\) | ||||
−0.212051 | + | 0.977259i | \(0.568014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.77465 | 1.03312 | 0.516562 | − | 0.856250i | \(-0.327211\pi\) | ||||
0.516562 | + | 0.856250i | \(0.327211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.753100 | − | 4.99667i | 0.112265 | − | 0.744860i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4640 | 1.67219 | 0.836096 | − | 0.548584i | \(-0.184833\pi\) | ||||
0.836096 | + | 0.548584i | \(0.184833\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.52447 | − | 5.34127i | 0.646353 | − | 0.763038i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.24089 | + | 6.08999i | 0.733871 | + | 0.852769i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.17336i | 1.12270i | 0.827580 | + | 0.561348i | \(0.189717\pi\) | ||||
−0.827580 | + | 0.561348i | \(0.810283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.68437i | − | 0.227120i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.576993 | − | 0.496546i | 0.0764246 | − | 0.0657691i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.54560 | 0.721975 | 0.360988 | − | 0.932571i | \(-0.382440\pi\) | ||||
0.360988 | + | 0.932571i | \(0.382440\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.1658i | − | 1.30160i | −0.759250 | − | 0.650800i | \(-0.774434\pi\) | ||
0.759250 | − | 0.650800i | \(-0.225566\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.22709 | − | 7.61840i | −0.280587 | − | 0.959828i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.55654i | 0.937274i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.56513 | 0.557719 | 0.278860 | − | 0.960332i | \(-0.410044\pi\) | ||||
0.278860 | + | 0.960332i | \(0.410044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.12890 | − | 4.41380i | 0.617446 | − | 0.531359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.24037i | 0.265883i | 0.991124 | + | 0.132941i | \(0.0424422\pi\) | ||||
−0.991124 | + | 0.132941i | \(0.957558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.389877i | 0.0456317i | 0.999740 | + | 0.0228158i | \(0.00726314\pi\) | ||||
−0.999740 | + | 0.0228158i | \(0.992737\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.44364 | + | 2.83955i | 0.282168 | + | 0.327883i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.11255 | − | 2.40047i | −0.126787 | − | 0.273558i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.2758 | 1.38114 | 0.690568 | − | 0.723268i | \(-0.257361\pi\) | ||||
0.690568 | + | 0.723268i | \(0.257361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.60018 | − | 2.65270i | −0.955576 | − | 0.294745i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.78586 | 0.305788 | 0.152894 | − | 0.988243i | \(-0.451141\pi\) | ||||
0.152894 | + | 0.988243i | \(0.451141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.81342 | 0.847484 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.16227 | − | 1.00022i | 0.124608 | − | 0.107235i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.78140 | 0.188828 | 0.0944142 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944142 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.99120 | + | 10.7692i | 0.523220 | + | 1.12891i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.68748 | − | 1.45220i | 0.174983 | − | 0.150586i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.740279i | − | 0.0759510i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.4243i | − | 1.56610i | −0.621957 | − | 0.783052i | \(-0.713662\pi\) | ||
0.621957 | − | 0.783052i | \(-0.286338\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.96649 | − | 0.447111i | −0.298144 | − | 0.0449363i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.71466 | −0.568630 | −0.284315 | − | 0.958731i | \(-0.591766\pi\) | ||||
−0.284315 | + | 0.958731i | \(0.591766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.93058i | − | 0.485825i | −0.970048 | − | 0.242912i | \(-0.921897\pi\) | ||
0.970048 | − | 0.242912i | \(-0.0781028\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.02827 | − | 3.19100i | −0.685889 | − | 0.311410i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 20.3066i | − | 1.96312i | −0.191161 | − | 0.981559i | \(-0.561225\pi\) | ||
0.191161 | − | 0.981559i | \(-0.438775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9381 | 1.43081 | 0.715405 | − | 0.698710i | \(-0.246242\pi\) | ||||
0.715405 | + | 0.698710i | \(0.246242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.522740 | + | 0.607432i | 0.0496163 | + | 0.0576549i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.7484i | − | 1.01113i | −0.862789 | − | 0.505563i | \(-0.831285\pi\) | ||
0.862789 | − | 0.505563i | \(-0.168715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.58034i | − | 0.613620i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.3085 | + | 2.00586i | 1.23037 | + | 0.185442i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.1352 | − | 5.16087i | 1.02077 | − | 0.473096i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.06806 | + | 3.56513i | 0.276638 | + | 0.321457i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0650 | 1.07912 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7931 | −1.49014 | −0.745072 | − | 0.666984i | \(-0.767585\pi\) | ||||
−0.745072 | + | 0.666984i | \(0.767585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.65399 | − | 8.89405i | −0.673896 | − | 0.783078i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8878 | −1.21338 | −0.606692 | − | 0.794937i | \(-0.707504\pi\) | ||||
−0.606692 | + | 0.794937i | \(0.707504\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.488964 | − | 1.05500i | −0.0423986 | − | 0.0914804i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.41069 | + | 4.65653i | −0.637811 | + | 0.400770i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.60846i | − | 0.650035i | −0.945708 | − | 0.325017i | \(-0.894630\pi\) | ||
0.945708 | − | 0.325017i | \(-0.105370\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4781i | 1.39765i | 0.715292 | + | 0.698825i | \(0.246294\pi\) | ||||
−0.715292 | + | 0.698825i | \(0.753706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9520 | − | 15.0504i | −1.09075 | − | 1.26747i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.48628 | 0.375161 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.49118i | − | 0.123836i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.1240 | + | 0.0946350i | −0.999970 | + | 0.00780537i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9231i | 1.14062i | 0.821428 | + | 0.570312i | \(0.193178\pi\) | ||||
−0.821428 | + | 0.570312i | \(0.806822\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4496 | −0.931759 | −0.465879 | − | 0.884848i | \(-0.654262\pi\) | ||||
−0.465879 | + | 0.884848i | \(0.654262\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.07405 | − | 13.7609i | 0.167677 | − | 1.11250i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.16502i | − | 0.173899i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.9900i | 1.43576i | 0.696167 | + | 0.717879i | \(0.254887\pi\) | ||||
−0.696167 | + | 0.717879i | \(0.745113\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.7303 | − | 9.23425i | 0.850971 | − | 0.732323i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.34640 | − | 9.37793i | −0.342545 | − | 0.739084i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1943 | 1.11178 | 0.555892 | − | 0.831255i | \(-0.312377\pi\) | ||||
0.555892 | + | 0.831255i | \(0.312377\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.21131 | + | 1.90300i | −0.172150 | + | 0.148148i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6473 | 1.28820 | 0.644102 | − | 0.764940i | \(-0.277231\pi\) | ||||
0.644102 | + | 0.764940i | \(0.277231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.12666 | −0.548205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.30377 | − | 0.196505i | −0.0997019 | − | 0.0150271i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.05227 | −0.232060 | −0.116030 | − | 0.993246i | \(-0.537017\pi\) | ||||
−0.116030 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.19197 | − | 2.40633i | 0.392476 | − | 0.181902i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.26541 | − | 7.28050i | −0.470937 | − | 0.547236i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.3581i | 0.923691i | 0.886960 | + | 0.461845i | \(0.152813\pi\) | ||||
−0.886960 | + | 0.461845i | \(0.847187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.319529i | − | 0.0237504i | −0.999929 | − | 0.0118752i | \(-0.996220\pi\) | ||
0.999929 | − | 0.0118752i | \(-0.00378008\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3461 | + | 11.4853i | −0.986573 | + | 0.849019i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.779332 | 0.0572976 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.63878i | − | 0.339221i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.48559 | + | 11.5311i | −0.544497 | + | 0.838763i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.1850i | 1.53290i | 0.642306 | + | 0.766448i | \(0.277978\pi\) | ||||
−0.642306 | + | 0.766448i | \(0.722022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.8293 | 1.93122 | 0.965608 | − | 0.260001i | \(-0.0837229\pi\) | ||||
0.965608 | + | 0.260001i | \(0.0837229\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.92055 | − | 8.53737i | 0.710425 | − | 0.611374i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.76470i | − | 0.339471i | −0.985490 | − | 0.169735i | \(-0.945709\pi\) | ||
0.985490 | − | 0.169735i | \(-0.0542913\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5564i | 1.52809i | 0.645161 | + | 0.764047i | \(0.276790\pi\) | ||||
−0.645161 | + | 0.764047i | \(0.723210\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.15768 | − | 5.99329i | −0.363794 | − | 0.422734i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.984946 | − | 2.12515i | −0.0691297 | − | 0.149156i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.57404 | 0.319465 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.5892 | − | 1.74673i | −0.805508 | − | 0.121406i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.439499 | −0.0304008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.7602 | 1.91109 | 0.955544 | − | 0.294848i | \(-0.0952689\pi\) | ||||
0.955544 | + | 0.294848i | \(0.0952689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.94125 | − | 2.53116i | 0.201531 | − | 0.173432i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.4110 | −0.778225 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.43003 | − | 3.08547i | −0.0970766 | − | 0.209455i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.511847 | − | 0.440483i | 0.0345874 | − | 0.0297651i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8109i | 1.39989i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.67499i | 0.179131i | 0.995981 | + | 0.0895654i | \(0.0285478\pi\) | ||||
−0.995981 | + | 0.0895654i | \(0.971452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.967056 | − | 6.41624i | 0.0644704 | − | 0.427749i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.82767 | 0.519541 | 0.259770 | − | 0.965670i | \(-0.416353\pi\) | ||||
0.259770 | + | 0.965670i | \(0.416353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0327i | 1.05947i | 0.848164 | + | 0.529734i | \(0.177708\pi\) | ||||
−0.848164 | + | 0.529734i | \(0.822292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.89448 | + | 4.17264i | −0.124648 | + | 0.274540i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.975484i | − | 0.0639061i | −0.999489 | − | 0.0319530i | \(-0.989827\pi\) | ||
0.999489 | − | 0.0319530i | \(-0.0101727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.3095 | −1.25962 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8692 | − | 16.1162i | −0.900900 | − | 1.04686i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.78695i | − | 0.115588i | −0.998329 | − | 0.0577942i | \(-0.981593\pi\) | ||
0.998329 | − | 0.0577942i | \(-0.0184067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3850i | 0.733374i | 0.930344 | + | 0.366687i | \(0.119508\pi\) | ||||
−0.930344 | + | 0.366687i | \(0.880492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.23389 | + | 14.2877i | 0.399904 | + | 0.916557i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.62088 | + | 8.99667i | −0.486880 | + | 0.574776i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.97171 | 0.125457 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.14746 | − | 3.65740i | −0.199462 | − | 0.231778i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.42838 | 0.468875 | 0.234438 | − | 0.972131i | \(-0.424675\pi\) | ||||
0.234438 | + | 0.972131i | \(0.424675\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.90671 | −0.245613 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.82759 | − | 10.2578i | −0.552805 | − | 0.642368i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.40337 | −0.0875397 | −0.0437699 | − | 0.999042i | \(-0.513937\pi\) | ||||
−0.0437699 | + | 0.999042i | \(0.513937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.11066 | − | 0.514759i | 0.0690130 | − | 0.0319856i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.62626 | − | 0.395830i | −0.162561 | − | 0.0245013i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.486075i | − | 0.0299726i | −0.999888 | − | 0.0149863i | \(-0.995230\pi\) | ||
0.999888 | − | 0.0149863i | \(-0.00477047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 13.7669i | − | 0.845697i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.01263 | − | 2.33870i | −0.123171 | − | 0.143126i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.5487 | −1.25288 | −0.626439 | − | 0.779471i | \(-0.715488\pi\) | ||||
−0.626439 | + | 0.779471i | \(0.715488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.54878i | 0.580047i | 0.957019 | + | 0.290024i | \(0.0936632\pi\) | ||||
−0.957019 | + | 0.290024i | \(0.906337\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.49915 | − | 18.7196i | 0.514392 | − | 1.13296i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 2.16290i | − | 0.130428i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.8813 | 1.43489 | 0.717444 | − | 0.696616i | \(-0.245312\pi\) | ||||
0.717444 | + | 0.696616i | \(0.245312\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.81302 | − | 0.574699i | −0.228280 | − | 0.0344063i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 20.1241i | − | 1.20051i | −0.799810 | − | 0.600253i | \(-0.795067\pi\) | ||
0.799810 | − | 0.600253i | \(-0.204933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.50788i | 0.386853i | 0.981115 | + | 0.193427i | \(0.0619601\pi\) | ||||
−0.981115 | + | 0.193427i | \(0.938040\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.971869 | + | 0.836366i | −0.0575686 | + | 0.0495420i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.51866 | − | 3.02122i | 0.384785 | − | 0.178337i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.51830 | 0.265782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.2497 | + | 17.4264i | −1.18706 | + | 1.02155i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.9406 | 0.814417 | 0.407209 | − | 0.913335i | \(-0.366502\pi\) | ||||
0.407209 | + | 0.913335i | \(0.366502\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.34083 | −0.543844 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.76456 | + | 4.39969i | 0.160416 | + | 0.255296i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.5266 | 1.01359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.2623 | + | 7.53713i | −0.937345 | + | 0.434433i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.45641 | + | 7.50245i | 0.370911 | + | 0.431004i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.1230i | 0.980459i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0330843i | 0.00188822i | 1.00000 | 0.000944111i | \(0.000300520\pi\) | |||||
−1.00000 | 0.000944111i | \(0.999699\pi\) | ||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.47308 | + | 5.57057i | −0.368241 | + | 0.316898i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.78417 | −0.214581 | −0.107290 | − | 0.994228i | \(-0.534217\pi\) | ||||
−0.107290 | + | 0.994228i | \(0.534217\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.4717i | − | 0.591898i | −0.955204 | − | 0.295949i | \(-0.904364\pi\) | ||
0.955204 | − | 0.295949i | \(-0.0956358\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.75125 | + | 12.8322i | 0.211359 | + | 0.723013i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.28784i | − | 0.184663i | −0.995728 | − | 0.0923316i | \(-0.970568\pi\) | ||
0.995728 | − | 0.0923316i | \(-0.0294320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.885307 | −0.0495677 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.6594 | + | 22.9424i | −1.48798 | + | 1.28052i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.03874i | − | 0.113439i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.70337i | 0.538246i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.8770 | − | 19.6114i | −0.933303 | − | 1.08451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.5189 | + | 12.7542i | −1.51716 | + | 0.703163i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4468 | −1.34372 | −0.671860 | − | 0.740678i | \(-0.734504\pi\) | ||||
−0.671860 | + | 0.740678i | \(0.734504\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.206871 | − | 1.37255i | 0.0113365 | − | 0.0752154i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.68936 | −0.420115 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.5672 | 1.44721 | 0.723605 | − | 0.690214i | \(-0.242484\pi\) | ||||
0.723605 | + | 0.690214i | \(0.242484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.1110 | + | 12.1436i | −0.766404 | + | 0.659547i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.28536 | −0.0696063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.91843 | + | 17.8552i | −0.265570 | + | 0.964092i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.63895 | + | 7.43446i | −0.465106 | + | 0.400258i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.8583i | − | 1.11973i | −0.828583 | − | 0.559866i | \(-0.810853\pi\) | ||
0.828583 | − | 0.559866i | \(-0.189147\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.40855i | − | 0.128927i | −0.997920 | − | 0.0644634i | \(-0.979466\pi\) | ||
0.997920 | − | 0.0644634i | \(-0.0205336\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.4026 | − | 19.7382i | −0.661999 | − | 1.05355i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.15710 | −0.487383 | −0.243692 | − | 0.969853i | \(-0.578358\pi\) | ||||
−0.243692 | + | 0.969853i | \(0.578358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.77360i | − | 0.200282i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.3560 | − | 8.78807i | −1.02443 | − | 0.465114i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0224i | 1.26785i | 0.773393 | + | 0.633927i | \(0.218558\pi\) | ||||
−0.773393 | + | 0.633927i | \(0.781442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8068 | 0.989834 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.12980 | + | 1.31284i | 0.0592990 | + | 0.0689064i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.656697i | − | 0.0343731i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.130678i | 0.00682135i | 0.999994 | + | 0.00341067i | \(0.00108565\pi\) | ||||
−0.999994 | + | 0.00341067i | \(0.998914\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.21417 | − | 8.05576i | 0.0632070 | − | 0.419366i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.09325 | − | 19.6199i | −0.472098 | − | 1.01861i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.03624 | 0.312544 | 0.156272 | − | 0.987714i | \(-0.450052\pi\) | ||||
0.156272 | + | 0.987714i | \(0.450052\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.6310 | − | 15.8394i | −0.703901 | − | 0.817943i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.97173 | 0.204555 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.85601 | 0.198070 | 0.0990349 | − | 0.995084i | \(-0.468424\pi\) | ||||
0.0990349 | + | 0.995084i | \(0.468424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.9728 | + | 22.0467i | 0.972006 | + | 1.12948i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.3546 | −1.39776 | −0.698879 | − | 0.715240i | \(-0.746317\pi\) | ||||
−0.698879 | + | 0.715240i | \(0.746317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.87394 | + | 4.04327i | 0.0955049 | + | 0.206064i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.02902 | + | 20.0970i | −0.153974 | + | 1.02159i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.62052i | − | 0.335674i | −0.985815 | − | 0.167837i | \(-0.946322\pi\) | ||
0.985815 | − | 0.167837i | \(-0.0536782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.1224i | − | 0.916488i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.6904 | + | 18.2325i | 0.791478 | + | 0.919709i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.6770 | −1.04037 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3381i | 1.37206i | 0.727574 | + | 0.686029i | \(0.240648\pi\) | ||||
−0.727574 | + | 0.686029i | \(0.759352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.832622 | + | 1.83387i | −0.0416832 | + | 0.0918085i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.0945i | − | 0.504096i | −0.967715 | − | 0.252048i | \(-0.918896\pi\) | ||
0.967715 | − | 0.252048i | \(-0.0811041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.76649 | 0.287249 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.4859 | + | 4.46813i | 0.719809 | + | 0.222023i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.462685i | − | 0.0229344i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6161i | 1.36553i | 0.730639 | + | 0.682764i | \(0.239222\pi\) | ||||
−0.730639 | + | 0.682764i | \(0.760778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.98871 | + | 8.59603i | −0.492707 | + | 0.424011i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3120 | + | 6.16974i | −0.655042 | + | 0.303593i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.69242 | −0.230342 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.6331 | − | 18.6169i | 1.05938 | − | 0.911673i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.3531 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888888\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4509 | −0.558080 | −0.279040 | − | 0.960279i | \(-0.590016\pi\) | ||||
−0.279040 | + | 0.960279i | \(0.590016\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.12566 | + | 34.0078i | −0.249218 | + | 1.65352i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.0332 | 0.486683 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3100 | + | 24.4027i | 0.547327 | + | 1.18093i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.06859 | − | 5.88977i | −0.244714 | − | 0.284361i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 32.9444i | − | 1.58688i | −0.608651 | − | 0.793438i | \(-0.708289\pi\) | ||
0.608651 | − | 0.793438i | \(-0.291711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.8943i | − | 1.24440i | −0.782859 | − | 0.622200i | \(-0.786239\pi\) | ||
0.782859 | − | 0.622200i | \(-0.213761\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.95769 | + | 1.68474i | −0.0938640 | + | 0.0807769i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.71700 | −0.0821351 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.583243i | 0.0278367i | 0.999903 | + | 0.0139183i | \(0.00443049\pi\) | ||||
−0.999903 | + | 0.0139183i | \(0.995570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.8219 | + | 15.8100i | 0.658186 | + | 0.752856i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2184i | 1.05563i | 0.849359 | + | 0.527815i | \(0.176989\pi\) | ||||
−0.849359 | + | 0.527815i | \(0.823011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00054 | −0.142239 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.2788 | − | 15.7303i | 0.864559 | − | 0.744018i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 0.319547i | − | 0.0150803i | −0.999972 | − | 0.00754017i | \(-0.997600\pi\) | ||
0.999972 | − | 0.00754017i | \(-0.00240013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.71558i | − | 0.127872i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.9358 | + | 15.0316i | 0.607776 | + | 0.706245i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.40702 | − | 18.1392i | −0.394127 | − | 0.850380i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.6727 | −1.62192 | −0.810960 | − | 0.585101i | \(-0.801055\pi\) | ||||
−0.810960 | + | 0.585101i | \(0.801055\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.4092 | + | 12.8242i | −0.952619 | + | 0.598581i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.89425 | 0.367672 | 0.183836 | − | 0.982957i | \(-0.441148\pi\) | ||||
0.183836 | + | 0.982957i | \(0.441148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.76395 | −0.267873 | −0.133937 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133937 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.84234 | + | 2.44604i | −0.131810 | + | 0.113432i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.5418 | −1.73723 | −0.868613 | − | 0.495490i | \(-0.834988\pi\) | ||||
−0.868613 | + | 0.495490i | \(0.834988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.9584 | + | 5.07892i | −0.506014 | + | 0.234523i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.6180 | − | 20.3251i | 1.08826 | − | 0.936530i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.77465i | 0.311499i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.950593i | − | 0.0436162i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.2462 | − | 3.65440i | −1.11016 | − | 0.167323i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5673 | −0.848362 | −0.424181 | − | 0.905577i | \(-0.639438\pi\) | ||||
−0.424181 | + | 0.905577i | \(0.639438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.07573i | 0.0946451i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.40118 | + | 16.3013i | −0.336765 | + | 0.741735i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.9803i | 1.17970i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.718171 | −0.0325434 | −0.0162717 | − | 0.999868i | \(-0.505180\pi\) | ||||
−0.0162717 | + | 0.999868i | \(0.505180\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0367 | − | 18.6349i | −0.725204 | − | 0.842698i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.0980i | − | 0.861881i | −0.902380 | − | 0.430940i | \(-0.858182\pi\) | ||
0.902380 | − | 0.430940i | \(-0.141818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.10675i | − | 0.184959i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.99667 | + | 0.753100i | 0.224584 | + | 0.0338493i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.49252 | − | 5.37793i | −0.111805 | − | 0.241233i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.97171 | 0.267331 | 0.133665 | − | 0.991027i | \(-0.457325\pi\) | ||||
0.133665 | + | 0.991027i | \(0.457325\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.8081 | − | 21.8552i | −0.840282 | − | 0.976420i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.82442 | 0.170523 | 0.0852613 | − | 0.996359i | \(-0.472828\pi\) | ||||
0.0852613 | + | 0.996359i | \(0.472828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.62559 | 0.428333 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.05169 | + | 9.35619i | 0.357588 | + | 0.415523i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.1349 | 1.06976 | 0.534881 | − | 0.844927i | \(-0.320356\pi\) | ||||
0.534881 | + | 0.844927i | \(0.320356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.433757 | − | 0.935887i | −0.0191883 | − | 0.0414012i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.21502 | + | 1.93366i | 0.0536444 | + | 0.0853731i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.30492i | 0.365959i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4640i | 0.504185i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.44845 | + | 4.00715i | 0.151370 | + | 0.175894i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.7449 | −1.21552 | −0.607762 | − | 0.794119i | \(-0.707933\pi\) | ||||
−0.607762 | + | 0.794119i | \(0.707933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 32.2482i | − | 1.41012i | −0.709149 | − | 0.705059i | \(-0.750921\pi\) | ||
0.709149 | − | 0.705059i | \(-0.249079\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.02501 | − | 4.09757i | −0.393884 | − | 0.178833i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.96251i | − | 0.259731i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.73761 | 0.336418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.47950 | + | 16.4510i | −0.107601 | + | 0.713912i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1829i | 0.527698i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.2039i | 1.47876i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.2243 | − | 13.9622i | 0.700130 | − | 0.602514i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.34127 | + | 4.52447i | 0.230065 | + | 0.194883i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.8203 | −1.41105 | −0.705527 | − | 0.708683i | \(-0.749290\pi\) | ||||
−0.705527 | + | 0.708683i | \(0.749290\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.419491 | + | 0.361003i | −0.0180021 | + | 0.0154921i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −25.1613 | −1.07779 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.3011 | 1.03904 | 0.519520 | − | 0.854458i | \(-0.326111\pi\) | ||||
0.519520 | + | 0.854458i | \(0.326111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.1568 | + | 4.54524i | 1.28706 | + | 0.193986i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.389092 | −0.0165759 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.4676 | + | 13.6574i | −1.25309 | + | 0.580773i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.880488 | − | 1.02314i | −0.0373746 | − | 0.0434299i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 27.4493i | − | 1.16307i | −0.813523 | − | 0.581533i | \(-0.802453\pi\) | ||
0.813523 | − | 0.581533i | \(-0.197547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 30.3930i | − | 1.28548i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.08999 | + | 5.24089i | −0.257120 | + | 0.221271i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.83605 | 0.245960 | 0.122980 | − | 0.992409i | \(-0.460755\pi\) | ||||
0.122980 | + | 0.992409i | \(0.460755\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.1043i | 0.761654i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.5957 | − | 3.20039i | 0.990927 | − | 0.134404i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.62414i | − | 0.235776i | −0.993027 | − | 0.117888i | \(-0.962388\pi\) | ||
0.993027 | − | 0.117888i | \(-0.0376124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.3368 | 1.10216 | 0.551081 | − | 0.834452i | \(-0.314216\pi\) | ||||
0.551081 | + | 0.834452i | \(0.314216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.8126 | − | 23.9348i | 1.16189 | − | 0.999892i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.44983i | − | 0.352382i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.69194i | − | 0.403481i | −0.979439 | − | 0.201740i | \(-0.935340\pi\) | ||
0.979439 | − | 0.201740i | \(-0.0646597\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.3117 | − | 35.2227i | −1.25971 | − | 1.46380i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.68737 | + | 3.09940i | −0.277439 | + | 0.128585i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.17336 | −0.338506 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.4164 | − | 3.37861i | −0.926806 | − | 0.139688i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.4357 | 1.21494 | 0.607470 | − | 0.794342i | \(-0.292184\pi\) | ||||
0.607470 | + | 0.794342i | \(0.292184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.564916 | −0.0232769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.25530 | + | 5.38315i | −0.257308 | + | 0.221433i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.5449 | −0.884743 | −0.442372 | − | 0.896832i | \(-0.645863\pi\) | ||||
−0.442372 | + | 0.896832i | \(0.645863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.7559 | + | 8.69281i | −0.768915 | + | 0.356370i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.3002 | − | 24.3544i | 1.15825 | − | 0.996759i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.91553i | − | 0.364279i | −0.983273 | − | 0.182139i | \(-0.941698\pi\) | ||
0.983273 | − | 0.182139i | \(-0.0583022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6715i | 0.435300i | 0.976027 | + | 0.217650i | \(0.0698391\pi\) | ||||
−0.976027 | + | 0.217650i | \(0.930161\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.04112 | + | 13.5424i | −0.0831208 | + | 0.551490i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.68437 | 0.0684793 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.2957i | − | 1.55438i | −0.629268 | − | 0.777188i | \(-0.716645\pi\) | ||
0.629268 | − | 0.777188i | \(-0.283355\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.67719 | + | 3.69407i | −0.0679634 | + | 0.149691i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 51.4305i | − | 2.08066i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2896 | −0.577153 | −0.288577 | − | 0.957457i | \(-0.593182\pi\) | ||||
−0.288577 | + | 0.957457i | \(0.593182\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.16775 | − | 6.00500i | −0.208384 | − | 0.242145i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.9821i | 1.69014i | 0.534658 | + | 0.845069i | \(0.320440\pi\) | ||||
−0.534658 | + | 0.845069i | \(0.679560\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 29.0832i | − | 1.16895i | −0.811411 | − | 0.584476i | \(-0.801300\pi\) | ||
0.811411 | − | 0.584476i | \(-0.198700\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8003 | + | 17.1883i | 0.433402 | + | 0.689743i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.27620 | + | 1.98190i | −0.171322 | + | 0.0794031i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.50735 | −0.380294 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.496546 | + | 0.576993i | 0.0198301 | + | 0.0230429i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.14629 | 0.0855783 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.0921 | 1.67566 | 0.837831 | − | 0.545930i | \(-0.183823\pi\) | ||||
0.837831 | + | 0.545930i | \(0.183823\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.3634 | − | 36.4447i | −1.24658 | − | 1.44855i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.2857 | 1.12249 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9624 | − | 20.2980i | −0.949425 | − | 0.804237i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.64604 | − | 1.00169i | −0.262913 | − | 0.0396263i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.70860i | 0.146481i | 0.997314 | + | 0.0732404i | \(0.0233340\pi\) | ||||
−0.997314 | + | 0.0732404i | \(0.976666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.2231i | − | 1.03414i | −0.855943 | − | 0.517069i | \(-0.827023\pi\) | ||
0.855943 | − | 0.517069i | \(-0.172977\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.8921 | + | 14.9809i | 0.507628 | + | 0.589871i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.9863 | −1.57202 | −0.786012 | − | 0.618212i | \(-0.787858\pi\) | ||||
−0.786012 | + | 0.618212i | \(0.787858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.54560i | 0.217684i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.43509 | + | 5.36336i | −0.0954387 | + | 0.210207i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 17.3435i | − | 0.678704i | −0.940659 | − | 0.339352i | \(-0.889792\pi\) | ||
0.940659 | − | 0.339352i | \(-0.110208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.3922 | 0.914009 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.15657 | − | 0.174318i | −0.0451220 | − | 0.00680080i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.108834i | − | 0.00423958i | −0.999998 | − | 0.00211979i | \(-0.999325\pi\) | ||
0.999998 | − | 0.00211979i | \(-0.000674751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.1145i | 1.21021i | 0.796144 | + | 0.605107i | \(0.206870\pi\) | ||||
−0.796144 | + | 0.605107i | \(0.793130\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.3214 | − | 23.5121i | 1.06107 | − | 0.913133i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.823596 | + | 1.77701i | 0.0319377 | + | 0.0689097i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.45864 | −0.133919 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.51185 | − | 3.02220i | 0.135776 | − | 0.116845i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1658 | 0.392447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.4056 | −0.593841 | −0.296920 | − | 0.954902i | \(-0.595960\pi\) | ||||
−0.296920 | + | 0.954902i | \(0.595960\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.51608 | + | 5.97946i | −0.366274 | + | 0.230150i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.9871 | 1.53683 | 0.768414 | − | 0.639953i | \(-0.221046\pi\) | ||||
0.768414 | + | 0.639953i | \(0.221046\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.1603 | + | 37.0256i | 0.658552 | + | 1.42091i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.84369 | − | 10.2765i | −0.338891 | − | 0.393796i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.3682i | − | 0.779369i | −0.920948 | − | 0.389684i | \(-0.872584\pi\) | ||
0.920948 | − | 0.389684i | \(-0.127416\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.8155i | 0.489653i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.0484 | − | 18.1137i | 0.803045 | − | 0.691080i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.6679 | 1.39694 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.2967i | 1.22863i | 0.789062 | + | 0.614313i | \(0.210567\pi\) | ||||
−0.789062 | + | 0.614313i | \(0.789433\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.61840 | − | 2.22709i | 0.289399 | − | 0.0846003i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 27.7551i | − | 1.05281i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5970 | 0.477145 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.28066 | + | 1.10210i | −0.0484389 | + | 0.0416853i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.51685i | 0.283908i | 0.989873 | + | 0.141954i | \(0.0453385\pi\) | ||||
−0.989873 | + | 0.141954i | \(0.954662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.203349i | − | 0.00766947i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.8159 | + | 25.3504i | 0.821634 | + | 0.954751i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7178 | − | 6.35783i | 0.515913 | − | 0.239111i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.2608 | 1.09891 | 0.549456 | − | 0.835523i | \(-0.314835\pi\) | ||||
0.549456 | + | 0.835523i | \(0.314835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.48864 | + | 36.4161i | −0.205840 | + | 1.36571i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.02154 | −0.188058 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.55654 | −0.282599 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.34599 | + | 2.01890i | −0.0876126 | + | 0.0753971i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0916 | −0.674702 | −0.337351 | − | 0.941379i | \(-0.609531\pi\) | ||||
−0.337351 | + | 0.941379i | \(0.609531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.48551 | + | 11.8357i | 0.204291 | + | 0.440785i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.9467 | − | 12.8628i | 0.555875 | − | 0.478372i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.91483i | − | 0.0711150i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7259i | 1.02830i | 0.857701 | + | 0.514149i | \(0.171892\pi\) | ||||
−0.857701 | + | 0.514149i | \(0.828108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.7145 | − | 24.3263i | 0.433869 | − | 0.900976i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.4261 | −1.16234 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5678i | 0.611946i | 0.952040 | + | 0.305973i | \(0.0989817\pi\) | ||||
−0.952040 | + | 0.305973i | \(0.901018\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.4213 | − | 0.159400i | 0.753250 | − | 0.00587957i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.56513i | 0.168159i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.7944 | 0.544220 | 0.272110 | − | 0.962266i | \(-0.412278\pi\) | ||||
0.272110 | + | 0.962266i | \(0.412278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.22764 | − | 2.58855i | −0.0818344 | − | 0.0950928i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.5654i | 1.74500i | 0.488610 | + | 0.872502i | \(0.337504\pi\) | ||||
−0.488610 | + | 0.872502i | \(0.662496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 23.4516i | − | 0.859202i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.24559 | + | 8.26424i | −0.0455737 | + | 0.302373i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.5921 | + | 48.7454i | 0.825498 | + | 1.78112i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.0295 | 1.31474 | 0.657368 | − | 0.753570i | \(-0.271670\pi\) | ||||
0.657368 | + | 0.753570i | \(0.271670\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.39257 | − | 9.75229i | −0.305842 | − | 0.355393i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.2854 | 0.701868 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.0938 | −1.16647 | −0.583234 | − | 0.812304i | \(-0.698213\pi\) | ||||
−0.583234 | + | 0.812304i | \(0.698213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.41380 | + | 5.12890i | 0.160211 | + | 0.186167i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.8725 | −0.647879 | −0.323940 | − | 0.946078i | \(-0.605007\pi\) | ||||
−0.323940 | + | 0.946078i | \(0.605007\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.8584 | + | 16.6194i | −1.29816 | + | 0.601661i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.49346 | + | 23.1785i | −0.126306 | + | 0.838019i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 24.8791i | − | 0.898331i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 40.9792i | − | 1.47775i | −0.673843 | − | 0.738875i | \(-0.735358\pi\) | ||
0.673843 | − | 0.738875i | \(-0.264642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.58552 | + | 1.84240i | 0.0571012 | + | 0.0663525i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.96160 | 0.214424 | 0.107212 | − | 0.994236i | \(-0.465808\pi\) | ||||
0.107212 | + | 0.994236i | \(0.465808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.78011i | − | 0.0998645i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.93062 | − | 0.876546i | −0.0692605 | − | 0.0314459i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.19350i | − | 0.0427614i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.24037 | −0.0801666 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.44748 | + | 3.89507i | 0.0874658 | + | 0.139199i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 30.3018i | − | 1.08152i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.9974i | − | 1.06929i | −0.845077 | − | 0.534645i | \(-0.820445\pi\) | ||
0.845077 | − | 0.534645i | \(-0.179555\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.638139 | + | 0.549166i | −0.0227184 | + | 0.0195508i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9581 | + | 25.8012i | 0.425182 | + | 0.917386i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.6066 | −1.61954 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.0738 | + | 15.5539i | −0.641013 | + | 0.551639i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.6607 | 1.58196 | 0.790982 | − | 0.611839i | \(-0.209570\pi\) | ||||
0.790982 | + | 0.611839i | \(0.209570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.1788 | −1.88133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.796485 | + | 5.28453i | −0.0281424 | + | 0.186720i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.389877 | −0.0137585 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.32095 | + | 15.7959i | 0.258029 | + | 0.556732i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2159 | + | 26.9772i | 0.817239 | + | 0.949643i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.0773i | − | 0.494933i | −0.968896 | − | 0.247467i | \(-0.920402\pi\) | ||
0.968896 | − | 0.247467i | \(-0.0795980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 44.2560i | − | 1.55404i | −0.629477 | − | 0.777019i | \(-0.716731\pi\) | ||
0.629477 | − | 0.777019i | \(-0.283269\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.5360 | − | 10.7882i | 0.439658 | − | 0.378359i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.9084 | −0.837476 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.97745i | 0.104168i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −34.1782 | + | 9.99136i | −1.19428 | + | 0.349126i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1.90237i | − | 0.0663932i | −0.999449 | − | 0.0331966i | \(-0.989431\pi\) | ||
0.999449 | − | 0.0331966i | \(-0.0105687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.1076 | 1.11920 | 0.559600 | − | 0.828763i | \(-0.310955\pi\) | ||||
0.559600 | + | 0.828763i | \(0.310955\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.83955 | + | 2.44364i | −0.0988604 | + | 0.0850767i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.9825i | 0.451446i | 0.974192 | + | 0.225723i | \(0.0724744\pi\) | ||||
−0.974192 | + | 0.225723i | \(0.927526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.6568i | − | 0.856365i | −0.903692 | − | 0.428183i | \(-0.859154\pi\) | ||
0.903692 | − | 0.428183i | \(-0.140846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.9811 | − | 31.3524i | −0.935963 | − | 1.08760i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.9880 | + | 24.7770i | −0.727193 | + | 0.858471i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.0401 | −0.970369 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.55345 | + | 5.65519i | 0.122825 | + | 0.195472i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6311 | 0.539647 | 0.269823 | − | 0.962910i | \(-0.413035\pi\) | ||||
0.269823 | + | 0.962910i | \(0.413035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.2162 | 0.972974 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.4198 | + | 22.7362i | −0.909947 | + | 0.783077i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0039 | 0.412948 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.40047 | − | 1.11255i | 0.0824810 | − | 0.0382276i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.54382 | − | 7.35259i | 0.293223 | − | 0.252340i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.80757i | − | 0.0619629i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.39059i | − | 0.218810i | −0.993997 | − | 0.109405i | \(-0.965106\pi\) | ||
0.993997 | − | 0.109405i | \(-0.0348945\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.19603 | + | 0.330987i | 0.0751028 | + | 0.0113195i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.92927 | 0.202540 | 0.101270 | − | 0.994859i | \(-0.467709\pi\) | ||||
0.101270 | + | 0.994859i | \(0.467709\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.3899i | 1.03689i | 0.855111 | + | 0.518445i | \(0.173489\pi\) | ||||
−0.855111 | + | 0.518445i | \(0.826511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.3312 | − | 5.14461i | −0.386165 | − | 0.175328i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 19.6054i | − | 0.667375i | −0.942684 | − | 0.333688i | \(-0.891707\pi\) | ||
0.942684 | − | 0.333688i | \(-0.108293\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.14115 | 0.174804 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.10477 | − | 5.93182i | −0.173367 | − | 0.201455i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2758i | 0.416428i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.4804i | − | 0.693953i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45.7562 | + | 6.89638i | 1.54861 | + | 0.233407i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.9615 | + | 13.4229i | −0.979079 | + | 0.453775i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.709577 | −0.0239607 | −0.0119804 | − | 0.999928i | \(-0.503814\pi\) | ||||
−0.0119804 | + | 0.999928i | \(0.503814\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.7500 | − | 18.3018i | −0.531236 | − | 0.617304i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.3383 | 1.22427 | 0.612134 | − | 0.790754i | \(-0.290311\pi\) | ||||
0.612134 | + | 0.790754i | \(0.290311\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.56741 | 0.321969 | 0.160985 | − | 0.986957i | \(-0.448533\pi\) | ||||
0.160985 | + | 0.986957i | \(0.448533\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.5533 | + | 12.2630i | 0.354744 | + | 0.412218i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.1585 | 1.18051 | 0.590253 | − | 0.807218i | \(-0.299028\pi\) | ||||
0.590253 | + | 0.807218i | \(0.299028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.3112 | − | 18.6831i | 1.35199 | − | 0.626611i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.65270 | − | 8.60018i | 0.0888689 | − | 0.288117i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.03840i | 0.168604i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 20.8157i | − | 0.695791i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.8015 | − | 23.0096i | −0.661153 | − | 0.768269i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.13794 | −0.0379524 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 37.9144i | − | 1.26311i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.2682 | + | 12.8344i | 0.940707 | + | 0.427103i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.538205i | 0.0178905i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.4473 | 1.07739 | 0.538697 | − | 0.842499i | \(-0.318917\pi\) | ||||
0.538697 | + | 0.842499i | \(0.318917\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.55509 | − | 16.9525i | 0.0847468 | − | 0.562279i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.2924i | 1.30181i | 0.759157 | + | 0.650907i | \(0.225611\pi\) | ||||
−0.759157 | + | 0.650907i | \(0.774389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.78586i | 0.0921986i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.4798 | − | 19.3455i | 0.743159 | − | 0.639543i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.3372 | − | 15.4509i | 1.10089 | − | 0.510232i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.9754 | −0.362046 | −0.181023 | − | 0.983479i | \(-0.557941\pi\) | ||||
−0.181023 | + | 0.983479i | \(0.557941\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.0434345 | − | 0.0373786i | 0.00143122 | − | 0.00123167i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0509 | 0.330830 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00074 | 0.0329042 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6266 | + | 2.20452i | 0.480399 | + | 0.0724059i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.33274 | −0.109344 | −0.0546718 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546718 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.34748 | + | 1.98850i | 0.0769356 | + | 0.0651705i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.27535 | + | 4.96802i | 0.139969 | + | 0.162646i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.81342i | 0.255526i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.7480i | − | 0.743145i | −0.928404 | − | 0.371572i | \(-0.878819\pi\) | ||
0.928404 | − | 0.371572i | \(-0.121181\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.7477 | + | 11.8310i | −0.448641 | + | 0.386089i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.0624 | −0.784412 | −0.392206 | − | 0.919877i | \(-0.628288\pi\) | ||||
−0.392206 | + | 0.919877i | \(0.628288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10.6090i | − | 0.345476i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.6085 | − | 19.4226i | 0.410155 | − | 0.631817i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 18.7369i | − | 0.608867i | −0.952534 | − | 0.304433i | \(-0.901533\pi\) | ||
0.952534 | − | 0.304433i | \(-0.0984671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.74910 | 0.0567781 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.31641 | + | 3.71459i | −0.139969 | + | 0.120454i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.3763i | 0.595267i | 0.954680 | + | 0.297633i | \(0.0961973\pi\) | ||||
−0.954680 | + | 0.297633i | \(0.903803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 35.6834i | − | 1.15469i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.00022 | + | 1.16227i | 0.0323325 | + | 0.0375708i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.46478 | + | 18.2639i | 0.273342 | + | 0.589770i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3478 | 0.946705 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 60.2396 | + | 9.07932i | 1.94119 | + | 0.292577i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45.1905 | −1.45473 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.42754 | 0.0780645 | 0.0390323 | − | 0.999238i | \(-0.487572\pi\) | ||||
0.0390323 | + | 0.999238i | \(0.487572\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.67655 | + | 2.30337i | −0.0859830 | + | 0.0739948i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.9178 | −0.350368 | −0.175184 | − | 0.984536i | \(-0.556052\pi\) | ||||
−0.175184 | + | 0.984536i | \(0.556052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3326 | − | 39.5550i | −0.587717 | − | 1.26808i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.7390 | − | 10.9629i | 0.407974 | − | 0.351092i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.2872i | 1.76879i | 0.466736 | + | 0.884397i | \(0.345430\pi\) | ||||
−0.466736 | + | 0.884397i | \(0.654570\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.78140i | 0.0569339i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.67899 | + | 44.3138i | −0.213244 | + | 1.41483i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.3288 | 0.680283 | 0.340142 | − | 0.940374i | \(-0.389525\pi\) | ||||
0.340142 | + | 0.940374i | \(0.389525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.02551i | 0.255714i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 47.8350 | + | 21.7182i | 1.52261 | + | 0.691299i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.4666i | 0.841589i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.1534 | −0.862555 | −0.431278 | − | 0.902219i | \(-0.641937\pi\) | ||||
−0.431278 | + | 0.902219i | \(0.641937\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.6200 | + | 32.0948i | 0.876494 | + | 1.01850i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 36.3089i | − | 1.15107i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.4497i | 0.932681i | 0.884605 | + | 0.466341i | \(0.154428\pi\) | ||||
−0.884605 | + | 0.466341i | \(0.845572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.03567 | + | 1.27912i | −0.0644056 | + | 0.0404695i |
(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 | 1848.2.v.e.881.9 | ✓ | 32 | |
3.2 | odd | 2 | inner | 1848.2.v.e.881.23 | yes | 32 | |
7.6 | odd | 2 | inner | 1848.2.v.e.881.24 | yes | 32 | |
21.20 | even | 2 | inner | 1848.2.v.e.881.10 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1848.2.v.e.881.9 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1848.2.v.e.881.10 | yes | 32 | 21.20 | even | 2 | inner | |
1848.2.v.e.881.23 | yes | 32 | 3.2 | odd | 2 | inner | |
1848.2.v.e.881.24 | yes | 32 | 7.6 | odd | 2 | inner |