Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1248,2,Mod(623,1248)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1248, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1248.623");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1248 = 2^{5} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1248.h (of order \(2\), degree \(1\), not 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: | \(9.96533017226\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 623.22 | ||
Character | \(\chi\) | \(=\) | 1248.623 |
Dual form | 1248.2.h.c.623.18 |
$q$-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 \(\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times\).
\(n\) | \(703\) | \(769\) | \(833\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.662918 | + | 1.60017i | 0.382736 | + | 0.923858i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.38561i | 1.06688i | 0.845839 | + | 0.533438i | \(0.179100\pi\) | ||||
−0.845839 | + | 0.533438i | \(0.820900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63829 | −0.997178 | −0.498589 | − | 0.866839i | \(-0.666148\pi\) | ||||
−0.498589 | + | 0.866839i | \(0.666148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.12108 | + | 2.12156i | −0.707026 | + | 0.707187i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.764084 | −0.230380 | −0.115190 | − | 0.993343i | \(-0.536748\pi\) | ||||
−0.115190 | + | 0.993343i | \(0.536748\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.05175 | − | 3.44874i | −0.291702 | − | 0.956509i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.81737 | + | 1.58146i | −0.985642 | + | 0.408332i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.584523i | 0.141768i | 0.997485 | + | 0.0708839i | \(0.0225820\pi\) | ||||
−0.997485 | + | 0.0708839i | \(0.977418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.28969i | 0.984122i | 0.870561 | + | 0.492061i | \(0.163756\pi\) | ||||
−0.870561 | + | 0.492061i | \(0.836244\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.74897 | − | 4.22170i | −0.381656 | − | 0.921251i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.39993 | 0.917449 | 0.458724 | − | 0.888579i | \(-0.348307\pi\) | ||||
0.458724 | + | 0.888579i | \(0.348307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.691126 | −0.138225 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.80096 | − | 1.98766i | −0.923945 | − | 0.382525i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.65308 | −1.60684 | −0.803419 | − | 0.595415i | \(-0.796988\pi\) | ||||
−0.803419 | + | 0.595415i | \(0.796988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.09996 | −1.27519 | −0.637595 | − | 0.770372i | \(-0.720071\pi\) | ||||
−0.637595 | + | 0.770372i | \(0.720071\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.506525 | − | 1.22266i | −0.0881747 | − | 0.212838i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 6.29391i | − | 1.06387i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.63475 | −1.25515 | −0.627573 | − | 0.778558i | \(-0.715951\pi\) | ||||
−0.627573 | + | 0.778558i | \(0.715951\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82135 | − | 3.96921i | 0.772034 | − | 0.635582i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.139556 | 0.0217949 | 0.0108975 | − | 0.999941i | \(-0.496531\pi\) | ||||
0.0108975 | + | 0.999941i | \(0.496531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.17544 | 0.941746 | 0.470873 | − | 0.882201i | \(-0.343939\pi\) | ||||
0.470873 | + | 0.882201i | \(0.343939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.06122 | − | 5.06006i | −0.754482 | − | 0.754309i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.889975i | − | 0.129816i | −0.997891 | − | 0.0649081i | \(-0.979325\pi\) | ||
0.997891 | − | 0.0649081i | \(-0.0206754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0394518 | −0.00563597 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.935336 | + | 0.387491i | −0.130973 | + | 0.0542596i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.803622 | 0.110386 | 0.0551930 | − | 0.998476i | \(-0.482423\pi\) | ||||
0.0551930 | + | 0.998476i | \(0.482423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.82280i | − | 0.245787i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.86423 | + | 2.84371i | −0.909189 | + | 0.376659i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.13099 | 1.18875 | 0.594377 | − | 0.804187i | \(-0.297399\pi\) | ||||
0.594377 | + | 0.804187i | \(0.297399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.47787i | − | 1.21352i | −0.794886 | − | 0.606758i | \(-0.792470\pi\) | ||
0.794886 | − | 0.606758i | \(-0.207530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.59601 | − | 5.59729i | 0.705031 | − | 0.705192i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.22735 | − | 2.50905i | 1.02048 | − | 0.311210i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.5441i | − | 1.41034i | −0.709040 | − | 0.705168i | \(-0.750872\pi\) | ||
0.709040 | − | 0.705168i | \(-0.249128\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.91679 | + | 7.04063i | 0.351141 | + | 0.847592i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.56670i | 0.304611i | 0.988333 | + | 0.152305i | \(0.0486697\pi\) | ||||
−0.988333 | + | 0.152305i | \(0.951330\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3885i | 1.56700i | 0.621391 | + | 0.783500i | \(0.286568\pi\) | ||||
−0.621391 | + | 0.783500i | \(0.713432\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.458160 | − | 1.10592i | −0.0529037 | − | 0.127700i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.01587 | 0.229730 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9069i | 1.22713i | 0.789646 | + | 0.613563i | \(0.210264\pi\) | ||||
−0.789646 | + | 0.613563i | \(0.789736\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.00205378 | − | 9.00000i | −0.000228198 | − | 1.00000i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.6776 | −1.61107 | −0.805536 | − | 0.592547i | \(-0.798123\pi\) | ||||
−0.805536 | + | 0.592547i | \(0.798123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.39444 | −0.151249 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.73629 | − | 13.8464i | −0.614995 | − | 1.48449i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.68613 | −0.602729 | −0.301364 | − | 0.953509i | \(-0.597442\pi\) | ||||
−0.301364 | + | 0.953509i | \(0.597442\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.77481 | + | 9.09877i | 0.290879 | + | 0.953810i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.70669 | − | 11.3611i | −0.488061 | − | 1.17809i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2335 | −1.04994 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.4965i | − | 1.06576i | −0.846191 | − | 0.532879i | \(-0.821110\pi\) | ||
0.846191 | − | 0.532879i | \(-0.178890\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.62068 | − | 1.62105i | 0.162885 | − | 0.162922i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4371 | 1.53605 | 0.768023 | − | 0.640422i | \(-0.221241\pi\) | ||||
0.768023 | + | 0.640422i | \(0.221241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.99712i | 0.492381i | 0.969221 | + | 0.246191i | \(0.0791789\pi\) | ||||
−0.969221 | + | 0.246191i | \(0.920821\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.0713 | − | 4.17235i | 0.982860 | − | 0.407180i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.1495i | 1.85126i | 0.378434 | + | 0.925628i | \(0.376463\pi\) | ||||
−0.378434 | + | 0.925628i | \(0.623537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.05520 | 0.675766 | 0.337883 | − | 0.941188i | \(-0.390289\pi\) | ||||
0.337883 | + | 0.941188i | \(0.390289\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.06122 | − | 12.2169i | −0.480389 | − | 1.15958i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2283i | 1.05627i | 0.849160 | + | 0.528136i | \(0.177109\pi\) | ||||
−0.849160 | + | 0.528136i | \(0.822891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.4965i | 0.978804i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.54756 | + | 5.08371i | 0.882672 | + | 0.469989i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.54214i | − | 0.141368i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4162 | −0.946925 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0925140 | + | 0.223312i | 0.00834170 | + | 0.0201354i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2793i | 0.919407i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.17432i | − | 0.281675i | −0.990033 | − | 0.140838i | \(-0.955020\pi\) | ||
0.990033 | − | 0.140838i | \(-0.0449795\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.09381 | + | 9.88174i | 0.360440 | + | 0.870039i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.42017i | 0.560933i | 0.959864 | + | 0.280467i | \(0.0904892\pi\) | ||||
−0.959864 | + | 0.280467i | \(0.909511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 11.3174i | − | 0.981345i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.74178 | − | 11.4532i | 0.408107 | − | 0.985735i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.69918 | 0.572350 | 0.286175 | − | 0.958177i | \(-0.407616\pi\) | ||||
0.286175 | + | 0.958177i | \(0.407616\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4217 | −0.883957 | −0.441979 | − | 0.897026i | \(-0.645723\pi\) | ||||
−0.441979 | + | 0.897026i | \(0.645723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.42411 | − | 0.589981i | 0.119932 | − | 0.0496854i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.803622 | + | 2.63513i | 0.0672023 | + | 0.220361i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 20.6429i | − | 1.71430i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0261533 | − | 0.0631295i | −0.00215709 | − | 0.00520683i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.48086i | 0.367086i | 0.983012 | + | 0.183543i | \(0.0587567\pi\) | ||||
−0.983012 | + | 0.183543i | \(0.941243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12597 | −0.417145 | −0.208573 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208573 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.24010 | − | 1.23982i | −0.100256 | − | 0.100233i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 16.9377i | − | 1.36047i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.23041i | 0.577050i | 0.957472 | + | 0.288525i | \(0.0931648\pi\) | ||||
−0.957472 | + | 0.288525i | \(0.906835\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.532736 | + | 1.28593i | 0.0422487 | + | 0.101981i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.6083 | −0.914860 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.7862i | − | 1.15814i | −0.815276 | − | 0.579072i | \(-0.803415\pi\) | ||
0.815276 | − | 0.579072i | \(-0.196585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.91679 | − | 1.20837i | 0.227072 | − | 0.0940715i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.3295i | 1.41838i | 0.705019 | + | 0.709189i | \(0.250938\pi\) | ||||
−0.705019 | + | 0.709189i | \(0.749062\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7877 | + | 7.25440i | −0.829820 | + | 0.558031i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.10084 | − | 9.09877i | −0.695959 | − | 0.695800i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.4371 | −1.17366 | −0.586829 | − | 0.809711i | \(-0.699624\pi\) | ||||
−0.586829 | + | 0.809711i | \(0.699624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.82339 | 0.137835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.05310 | + | 14.6111i | 0.454979 | + | 1.09824i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.31859i | 0.173300i | 0.996239 | + | 0.0866499i | \(0.0276162\pi\) | ||||
−0.996239 | + | 0.0866499i | \(0.972384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4624i | 1.52096i | 0.649364 | + | 0.760478i | \(0.275035\pi\) | ||||
−0.649364 | + | 0.760478i | \(0.724965\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.1662 | − | 6.28305i | 1.12112 | − | 0.464457i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 18.2135i | − | 1.33908i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.446625i | − | 0.0326604i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.6663 | + | 5.24401i | 0.921338 | + | 0.381446i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7061 | −1.57060 | −0.785299 | − | 0.619117i | \(-0.787491\pi\) | ||||
−0.785299 | + | 0.619117i | \(0.787491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.36245i | 0.314016i | 0.987597 | + | 0.157008i | \(0.0501849\pi\) | ||||
−0.987597 | + | 0.157008i | \(0.949815\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.46897 | + | 11.5018i | 0.678087 | + | 0.823664i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.5782i | 1.67988i | 0.542680 | + | 0.839939i | \(0.317410\pi\) | ||||
−0.542680 | + | 0.839939i | \(0.682590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.9069i | − | 0.773172i | −0.922253 | − | 0.386586i | \(-0.873654\pi\) | ||
0.922253 | − | 0.386586i | \(-0.126346\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.4725 | − | 7.65279i | 1.30295 | − | 0.539786i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.8293 | 1.60230 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.332925i | 0.0232525i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.33260 | + | 9.33473i | −0.648660 | + | 0.648808i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.27768i | − | 0.226722i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5978 | −1.34917 | −0.674584 | − | 0.738198i | \(-0.735677\pi\) | ||||
−0.674584 | + | 0.738198i | \(0.735677\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.10715 | + | 1.70151i | −0.281417 | + | 0.116586i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.7322i | 1.00473i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.7317 | 1.27159 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.4238 | + | 8.87546i | −1.44769 | + | 0.599748i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.01587 | − | 0.614770i | 0.135602 | − | 0.0413539i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.46108 | 0.432666 | 0.216333 | − | 0.976320i | \(-0.430590\pi\) | ||||
0.216333 | + | 0.976320i | \(0.430590\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.46593 | − | 1.46627i | 0.0977288 | − | 0.0977511i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9383 | 0.725998 | 0.362999 | − | 0.931789i | \(-0.381753\pi\) | ||||
0.362999 | + | 0.931789i | \(0.381753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2189 | 1.46826 | 0.734132 | − | 0.679007i | \(-0.237590\pi\) | ||||
0.734132 | + | 0.679007i | \(0.237590\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.33636 | + | 3.22573i | 0.0879259 | + | 0.212238i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.4500i | 1.07768i | 0.842409 | + | 0.538839i | \(0.181137\pi\) | ||||
−0.842409 | + | 0.538839i | \(0.818863\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.12313 | 0.138498 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.4529 | + | 7.23041i | −1.13369 | + | 0.469666i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.2054i | 1.82446i | 0.409681 | + | 0.912229i | \(0.365640\pi\) | ||||
−0.409681 | + | 0.912229i | \(0.634360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.57938i | 0.552646i | 0.961065 | + | 0.276323i | \(0.0891160\pi\) | ||||
−0.961065 | + | 0.276323i | \(0.910884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.4002 | − | 5.96955i | 0.923770 | − | 0.382947i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 0.0941165i | − | 0.00601288i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.7940 | − | 4.51166i | 0.941322 | − | 0.287070i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.73003 | − | 23.4866i | −0.616615 | − | 1.48840i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.97532i | 0.250920i | 0.992099 | + | 0.125460i | \(0.0400407\pi\) | ||||
−0.992099 | + | 0.125460i | \(0.959959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.36192 | −0.211362 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.924402 | − | 2.23134i | −0.0578883 | − | 0.139732i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.5763i | − | 0.846868i | −0.905927 | − | 0.423434i | \(-0.860825\pi\) | ||
0.905927 | − | 0.423434i | \(-0.139175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.1426 | 1.25160 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.3539 | − | 18.3581i | 1.13608 | − | 1.13633i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.86533 | 0.608322 | 0.304161 | − | 0.952621i | \(-0.401624\pi\) | ||||
0.304161 | + | 0.952621i | \(0.401624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.91713i | 0.117768i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.76944 | − | 9.09877i | −0.230686 | − | 0.556836i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4212 | −0.818305 | −0.409152 | − | 0.912466i | \(-0.634176\pi\) | ||||
−0.409152 | + | 0.912466i | \(0.634176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7867 | 0.655247 | 0.327624 | − | 0.944808i | \(-0.393752\pi\) | ||||
0.327624 | + | 0.944808i | \(0.393752\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.7201 | + | 10.4719i | −0.769855 | + | 0.633788i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.528078 | 0.0318443 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.93632i | − | 0.296594i | −0.988943 | − | 0.148297i | \(-0.952621\pi\) | ||
0.988943 | − | 0.148297i | \(-0.0473792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.0596 | − | 15.0630i | 0.901592 | − | 0.901798i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.15261 | −0.0687587 | −0.0343794 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343794 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.16258 | 0.306884 | 0.153442 | − | 0.988158i | \(-0.450964\pi\) | ||||
0.153442 | + | 0.988158i | \(0.450964\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.78399 | − | 16.3754i | −0.401849 | − | 0.969992i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.368187 | −0.0217334 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6583 | 0.979902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.7962 | − | 6.95833i | 0.984610 | − | 0.407904i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.96029i | − | 0.348204i | −0.984728 | − | 0.174102i | \(-0.944298\pi\) | ||
0.984728 | − | 0.174102i | \(-0.0557022\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.7830i | 1.26825i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.66834 | + | 1.51874i | 0.212858 | + | 0.0881262i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.62761 | − | 15.1742i | −0.267622 | − | 0.877548i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.2926 | −0.939088 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.2335 | + | 24.7019i | 0.587900 | + | 1.41909i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.6105 | 1.29467 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.30199i | 0.473820i | 0.971532 | + | 0.236910i | \(0.0761346\pi\) | ||||
−0.971532 | + | 0.236910i | \(0.923865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.99624 | + | 3.31268i | −0.454890 | + | 0.188452i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.46540 | −0.309914 | −0.154957 | − | 0.987921i | \(-0.549524\pi\) | ||||
−0.154957 | + | 0.987921i | \(0.549524\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.46660 | 0.308991 | 0.154495 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154495 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.3529 | + | 13.3499i | 0.752352 | + | 0.752181i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.11720i | − | 0.0627481i | −0.999508 | − | 0.0313741i | \(-0.990012\pi\) | ||
0.999508 | − | 0.0313741i | \(-0.00998831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.61168 | 0.370183 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.6425 | + | 12.6946i | −1.71030 | + | 0.708543i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.50742 | −0.139517 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.726889 | + | 2.38351i | 0.0403205 | + | 0.132214i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.67703 | + | 11.2895i | 0.258640 | + | 0.624312i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.34801i | 0.129450i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.5940i | − | 1.18691i | −0.804866 | − | 0.593456i | \(-0.797763\pi\) | ||
0.804866 | − | 0.593456i | \(-0.202237\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.1939 | − | 16.1976i | 0.887420 | − | 0.887623i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.5397 | 1.50465 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.6501 | −1.28830 | −0.644152 | − | 0.764898i | \(-0.722790\pi\) | ||||
−0.644152 | + | 0.764898i | \(0.722790\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.9672 | + | 7.44346i | −0.975845 | + | 0.404273i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.42496 | 0.293778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5721 | 1.00280 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.7962 | + | 6.95833i | −0.904276 | + | 0.374624i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.66848i | − | 0.357983i | −0.983851 | − | 0.178991i | \(-0.942717\pi\) | ||
0.983851 | − | 0.178991i | \(-0.0572834\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.9112 | 1.86875 | 0.934376 | − | 0.356289i | \(-0.115958\pi\) | ||||
0.934376 | + | 0.356289i | \(0.115958\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.80554 | + | 18.6478i | −0.0963725 | + | 0.995345i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.70688 | −0.250522 | −0.125261 | − | 0.992124i | \(-0.539977\pi\) | ||||
−0.125261 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.12313 | −0.324982 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.46768 | − | 1.02231i | 0.130604 | − | 0.0541065i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.1329i | − | 0.904242i | −0.891957 | − | 0.452121i | \(-0.850668\pi\) | ||
0.891957 | − | 0.452121i | \(-0.149332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.598561 | 0.0315032 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.90508 | − | 16.6676i | −0.362422 | − | 0.874824i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.9396 | −1.67180 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.48197i | − | 0.181757i | −0.995862 | − | 0.0908787i | \(-0.971032\pi\) | ||
0.995862 | − | 0.0908787i | \(-0.0289676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.296008 | + | 0.296076i | −0.0154096 | + | 0.0154131i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.12018 | −0.110074 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.5462i | 1.16740i | 0.811970 | + | 0.583699i | \(0.198395\pi\) | ||||
−0.811970 | + | 0.583699i | \(0.801605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.4486 | + | 6.81433i | −0.849401 | + | 0.351890i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.10084 | + | 29.8423i | 0.468717 | + | 1.53695i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.4044i | − | 1.25357i | −0.779193 | − | 0.626784i | \(-0.784371\pi\) | ||
0.779193 | − | 0.626784i | \(-0.215629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.07944 | − | 2.10431i | 0.260228 | − | 0.107807i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.6604i | 0.544722i | 0.962195 | + | 0.272361i | \(0.0878045\pi\) | ||||
−0.962195 | + | 0.272361i | \(0.912196\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.80908i | 0.245093i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.0986 | + | 13.1016i | −0.665839 | + | 0.665991i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.1201 | 1.47645 | 0.738224 | − | 0.674555i | \(-0.235665\pi\) | ||||
0.738224 | + | 0.674555i | \(0.235665\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.57186i | 0.130065i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.2734 | + | 4.25605i | −0.518222 | + | 0.214689i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.0197 | −1.30919 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.54151 | 0.328309 | 0.164154 | − | 0.986435i | \(-0.447510\pi\) | ||||
0.164154 | + | 0.986435i | \(0.447510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.1098 | − | 7.50253i | 0.906623 | − | 0.375596i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2966 | −1.41307 | −0.706533 | − | 0.707681i | \(-0.749742\pi\) | ||||
−0.706533 | + | 0.707681i | \(0.749742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.46735 | + | 24.4859i | 0.371975 | + | 1.21973i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.4705 | − | 0.00489951i | 1.06688 | − | 0.000243459i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.83359 | 0.289160 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 30.6927i | − | 1.51766i | −0.651290 | − | 0.758829i | \(-0.725772\pi\) | ||
0.651290 | − | 0.758829i | \(-0.274228\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.44101 | + | 10.7198i | 0.219059 | + | 0.528770i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0902 | −1.18540 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 35.0149i | − | 1.71881i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.90874 | − | 16.6765i | −0.338322 | − | 0.816651i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.78509i | − | 0.233767i | −0.993146 | − | 0.116883i | \(-0.962710\pi\) | ||
0.993146 | − | 0.116883i | \(-0.0372904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.18333 | −0.203883 | −0.101942 | − | 0.994790i | \(-0.532505\pi\) | ||||
−0.101942 | + | 0.994790i | \(0.532505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.88814 | + | 1.88771i | 0.0918044 | + | 0.0917835i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 0.403979i | − | 0.0195959i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.0053i | 1.21009i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.68391 | + | 3.03281i | −0.177861 | + | 0.146425i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.8528i | − | 0.956274i | −0.878285 | − | 0.478137i | \(-0.841312\pi\) | ||
0.878285 | − | 0.478137i | \(-0.158688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3561 | 1.17048 | 0.585240 | − | 0.810860i | \(-0.301000\pi\) | ||||
0.585240 | + | 0.810860i | \(0.301000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.0321 | − | 13.6845i | 1.58377 | − | 0.656123i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.8743i | 0.902882i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7139i | 0.797712i | 0.917014 | + | 0.398856i | \(0.130593\pi\) | ||||
−0.917014 | + | 0.398856i | \(0.869407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0836803 | − | 0.0836994i | 0.00398478 | − | 0.00398569i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4553i | 1.30444i | 0.758030 | + | 0.652219i | \(0.226162\pi\) | ||||
−0.758030 | + | 0.652219i | \(0.773838\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 13.5649i | − | 0.643037i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.17013 | + | 2.97044i | −0.339135 | + | 0.140497i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.3205 | 0.911791 | 0.455895 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455895 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.106632 | −0.00502111 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.39810 | − | 8.20241i | −0.159657 | − | 0.385383i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.7061 | + | 6.61960i | −1.01760 | + | 0.310332i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.5600i | − | 1.05531i | −0.849458 | − | 0.527656i | \(-0.823071\pi\) | ||
0.849458 | − | 0.527656i | \(-0.176929\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.16183 | − | 2.80627i | 0.0542297 | − | 0.130986i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.8735i | − | 0.832451i | −0.909261 | − | 0.416226i | \(-0.863353\pi\) | ||
0.909261 | − | 0.416226i | \(-0.136647\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69526 | 0.218207 | 0.109104 | − | 0.994030i | \(-0.465202\pi\) | ||||
0.109104 | + | 0.994030i | \(0.465202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.1032 | − | 11.2283i | 1.25688 | − | 0.520701i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 11.7976i | − | 0.545926i | −0.962025 | − | 0.272963i | \(-0.911996\pi\) | ||
0.962025 | − | 0.272963i | \(-0.0880036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.4566i | 1.40636i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5699 | + | 4.79317i | −0.533112 | + | 0.220858i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.71855 | −0.216959 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.96471i | − | 0.136030i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.70455 | + | 1.70493i | −0.0780458 | + | 0.0780636i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 33.8258i | − | 1.54554i | −0.634687 | − | 0.772770i | \(-0.718871\pi\) | ||
0.634687 | − | 0.772770i | \(-0.281129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.02982 | + | 26.3303i | 0.366128 | + | 1.20056i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.69534 | − | 18.5752i | −0.350150 | − | 0.845200i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.0406 | 1.13703 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.4952 | −0.566211 | −0.283106 | − | 0.959089i | \(-0.591365\pi\) | ||||
−0.283106 | + | 0.959089i | \(0.591365\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.6604 | − | 9.80204i | 1.06996 | − | 0.443264i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.0921i | 0.500582i | 0.968171 | + | 0.250291i | \(0.0805262\pi\) | ||||
−0.968171 | + | 0.250291i | \(0.919474\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.05793i | − | 0.227798i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.86719 | + | 3.86631i | 0.173817 | + | 0.173778i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.77168i | − | 0.303751i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.57057i | 0.383671i | 0.981427 | + | 0.191836i | \(0.0614441\pi\) | ||||
−0.981427 | + | 0.191836i | \(0.938556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.3302 | + | 12.1509i | −1.31038 | + | 0.542864i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9134 | 0.843307 | 0.421654 | − | 0.906757i | \(-0.361450\pi\) | ||||
0.421654 | + | 0.906757i | \(0.361450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.8268i | 1.63877i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.7596 | − | 12.4530i | −0.833143 | − | 0.553057i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 21.7567i | − | 0.964349i | −0.876075 | − | 0.482174i | \(-0.839847\pi\) | ||
0.876075 | − | 0.482174i | \(-0.160153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 35.3226i | − | 1.56258i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.52644 | − | 20.5946i | 0.376452 | − | 0.909275i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.9212 | −0.525310 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.680016i | 0.0299071i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.2335 | − | 24.7019i | −0.449202 | − | 1.08429i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.7964i | − | 1.56827i | −0.620591 | − | 0.784134i | \(-0.713107\pi\) | ||
0.620591 | − | 0.784134i | \(-0.286893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.4148 | −0.455406 | −0.227703 | − | 0.973731i | \(-0.573121\pi\) | ||||
−0.227703 | + | 0.973731i | \(0.573121\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.20876 | + | 2.91773i | 0.0527545 | + | 0.127340i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.15009i | − | 0.180781i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.64062 | −0.158288 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.3675 | + | 19.3720i | −0.840480 | + | 0.840672i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.146777 | − | 0.481291i | −0.00635762 | − | 0.0208470i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −45.6833 | −1.97506 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.71014 | + | 1.53704i | −0.160104 | + | 0.0663281i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0301445 | 0.00129841 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.8351 | −1.84162 | −0.920812 | − | 0.390006i | \(-0.872473\pi\) | ||||
−0.920812 | + | 0.390006i | \(0.872473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.7432 | + | 13.5649i | −1.40515 | + | 0.582125i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.8310i | 0.720959i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.86925 | 0.293708 | 0.146854 | − | 0.989158i | \(-0.453085\pi\) | ||||
0.146854 | + | 0.989158i | \(0.453085\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.1079 | + | 20.1033i | 0.858184 | + | 0.857988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 37.1190i | − | 1.58132i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 28.7756i | − | 1.22366i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.1447 | − | 12.0741i | 1.23712 | − | 0.512516i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.9362i | 1.35318i | 0.736360 | + | 0.676590i | \(0.236543\pi\) | ||||
−0.736360 | + | 0.676590i | \(0.763457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.49499 | − | 21.2975i | −0.274709 | − | 0.900788i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.714675 | − | 0.296076i | 0.0301736 | − | 0.0125003i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 6.16766i | − | 0.259936i | −0.991518 | − | 0.129968i | \(-0.958513\pi\) | ||
0.991518 | − | 0.129968i | \(-0.0414874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.7864 | −1.12691 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.00541845 | + | 23.7446i | 0.000227554 | + | 0.997178i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 0.180544i | − | 0.00756881i | −0.999993 | − | 0.00378441i | \(-0.998795\pi\) | ||
0.999993 | − | 0.00378441i | \(-0.00120462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.551781 | −0.0230913 | −0.0115457 | − | 0.999933i | \(-0.503675\pi\) | ||||
−0.0115457 | + | 0.999933i | \(0.503675\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.3894 | − | 34.7334i | −0.601125 | − | 1.45101i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.04090 | −0.126814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0177i | 1.33292i | 0.745543 | + | 0.666458i | \(0.232190\pi\) | ||||
−0.745543 | + | 0.666458i | \(0.767810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.98066 | + | 2.89195i | −0.290106 | + | 0.120185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.7236 | 1.60653 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.614035 | −0.0254307 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.1277 | + | 22.7767i | −0.501420 | + | 0.941702i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.7316 | 0.938232 | 0.469116 | − | 0.883137i | \(-0.344573\pi\) | ||||
0.469116 | + | 0.883137i | \(0.344573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 30.4566i | − | 1.25494i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.7291 | + | 15.6304i | −1.55197 | + | 0.642950i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.2588 | −0.544474 | −0.272237 | − | 0.962230i | \(-0.587763\pi\) | ||||
−0.272237 | + | 0.962230i | \(0.587763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.67894 | 0.150822 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.4529 | − | 7.23041i | 0.714301 | − | 0.295921i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6334 | −0.597906 | −0.298953 | − | 0.954268i | \(-0.596637\pi\) | ||||
−0.298953 | + | 0.954268i | \(0.596637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.6583 | 0.965044 | 0.482522 | − | 0.875884i | \(-0.339721\pi\) | ||||
0.482522 | + | 0.875884i | \(0.339721\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.4915 | + | 24.4859i | 0.997372 | + | 0.997144i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 24.8489i | − | 1.01025i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.9152i | 0.645977i | 0.946403 | + | 0.322988i | \(0.104687\pi\) | ||||
−0.946403 | + | 0.322988i | \(0.895313\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.1340 | + | 36.5307i | 0.613259 | + | 1.48030i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.06930 | + | 0.936028i | −0.124170 | + | 0.0378676i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.36313 | 0.337784 | 0.168892 | − | 0.985635i | \(-0.445981\pi\) | ||||
0.168892 | + | 0.985635i | \(0.445981\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.532736 | + | 0.220702i | −0.0214820 | + | 0.00889957i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.84880 | −0.195205 | −0.0976026 | − | 0.995225i | \(-0.531117\pi\) | ||||
−0.0976026 | + | 0.995225i | \(0.531117\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.89555i | 0.397736i | 0.980026 | + | 0.198868i | \(0.0637264\pi\) | ||||
−0.980026 | + | 0.198868i | \(0.936274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.1239 | − | 8.74556i | −0.847672 | − | 0.350947i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0016 | 0.601028 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.9780 | −1.11912 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.24484 | − | 2.17284i | 0.209459 | − | 0.0867747i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.46269i | − | 0.177939i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4569 | −0.535713 | −0.267856 | − | 0.963459i | \(-0.586315\pi\) | ||||
−0.267856 | + | 0.963459i | \(0.586315\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.9918 | − | 31.3598i | −0.516376 | − | 1.24644i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.57268 | 0.300513 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0414932 | + | 0.136059i | 0.00164402 | + | 0.00539086i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.44541 | − | 5.44416i | −0.215417 | − | 0.215368i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.939589i | 0.0371115i | 0.999828 | + | 0.0185558i | \(0.00590683\pi\) | ||||
−0.999828 | + | 0.0185558i | \(0.994093\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 42.1553i | − | 1.66244i | −0.555943 | − | 0.831221i | \(-0.687643\pi\) | ||
0.555943 | − | 0.831221i | \(-0.312357\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.5740 | + | 9.76623i | −0.928224 | + | 0.384545i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.5469 | −1.31886 | −0.659432 | − | 0.751765i | \(-0.729203\pi\) | ||||
−0.659432 | + | 0.751765i | \(0.729203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.97684 | −0.273865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.4176 | + | 29.9739i | 0.486684 | + | 1.17477i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.6194 | 0.454700 | 0.227350 | − | 0.973813i | \(-0.426994\pi\) | ||||
0.227350 | + | 0.973813i | \(0.426994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.3160 | −0.598446 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.4044 | − | 28.3980i | −1.10816 | − | 1.10791i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4797i | 0.680912i | 0.940261 | + | 0.340456i | \(0.110581\pi\) | ||||
−0.940261 | + | 0.340456i | \(0.889419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.5530 | −1.61623 | −0.808113 | − | 0.589028i | \(-0.799511\pi\) | ||||
−0.808113 | + | 0.589028i | \(0.799511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.32009 | + | 2.81819i | 0.0901050 | + | 0.109449i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.9989 | 1.04697 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.0730 | −1.47419 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.28317 | + | 10.3388i | 0.165597 | + | 0.399722i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.24189i | 0.279570i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.7494 | −0.915473 | −0.457736 | − | 0.889088i | \(-0.651340\pi\) | ||||
−0.457736 | + | 0.889088i | \(0.651340\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.31807 | + | 1.37372i | 0.127712 | + | 0.0528746i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.998225 | 0.0383649 | 0.0191824 | − | 0.999816i | \(-0.493894\pi\) | ||||
0.0191824 | + | 0.999816i | \(0.493894\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.6928i | 1.06275i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.25118 | + | 17.5031i | 0.277866 | + | 0.670719i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.6883 | 0.791615 | 0.395808 | − | 0.918333i | \(-0.370465\pi\) | ||||
0.395808 | + | 0.918333i | \(0.370465\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.9816i | 0.610626i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.7293 | + | 35.5539i | 0.561957 | + | 1.35647i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.845206 | − | 2.77149i | −0.0321998 | − | 0.105585i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.8484i | − | 1.09744i | −0.836005 | − | 0.548722i | \(-0.815115\pi\) | ||
0.836005 | − | 0.548722i | \(-0.184885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.27582 | + | 4.27680i | −0.162425 | + | 0.162462i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 24.8621i | − | 0.943073i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0815735i | 0.00308982i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.3228 | + | 10.9050i | −0.995621 | + | 0.412466i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.46047 | −0.0551611 | −0.0275805 | − | 0.999620i | \(-0.508780\pi\) | ||||
−0.0275805 | + | 0.999620i | \(0.508780\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.7507i | − | 1.23522i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.40746 | + | 3.39737i | 0.0530081 | + | 0.127952i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.7274 | −1.53171 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.9297 | −0.823586 | −0.411793 | − | 0.911277i | \(-0.635097\pi\) | ||||
−0.411793 | + | 0.911277i | \(0.635097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.1398 | − | 23.1345i | −0.867809 | − | 0.867611i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.2393 | −1.16992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.28639 | + | 1.91713i | −0.235097 | + | 0.0716965i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −45.1334 | + | 18.6979i | −1.68554 | + | 0.698286i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0016 | 0.559467 | 0.279733 | − | 0.960078i | \(-0.409754\pi\) | ||||
0.279733 | + | 0.960078i | \(0.409754\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 13.1838i | − | 0.490992i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.7285 | + | 5.68743i | −0.510567 | + | 0.211518i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.98037 | 0.222105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.4156i | 0.905526i | 0.891631 | + | 0.452763i | \(0.149562\pi\) | ||||
−0.891631 | + | 0.452763i | \(0.850438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.0984 | + | 19.0853i | 0.707349 | + | 0.706865i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.60969i | 0.133509i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6996 | −0.469071 | −0.234536 | − | 0.972108i | \(-0.575357\pi\) | ||||
−0.234536 | + | 0.972108i | \(0.575357\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.150602 | − | 0.0623915i | 0.00555505 | − | 0.00230135i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.82066i | 0.324913i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.7156i | 0.762037i | 0.924567 | + | 0.381018i | \(0.124427\pi\) | ||||
−0.924567 | + | 0.381018i | \(0.875573\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.0267 | + | 20.6821i | 0.625490 | + | 0.759776i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3626i | 1.15058i | 0.817948 | + | 0.575292i | \(0.195111\pi\) | ||||
−0.817948 | + | 0.575292i | \(0.804889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6896 | −0.391636 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.1323 | − | 31.1394i | 1.13907 | − | 1.13933i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 50.5220i | − | 1.84603i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 37.1565i | − | 1.35586i | −0.735127 | − | 0.677930i | \(-0.762877\pi\) | ||
0.735127 | − | 0.677930i | \(-0.237123\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.36118 | + | 2.63531i | −0.231814 | + | 0.0960361i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 12.2286i | − | 0.445043i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7590i | 0.391043i | 0.980699 | + | 0.195522i | \(0.0626400\pi\) | ||||
−0.980699 | + | 0.195522i | \(0.937360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.22868 | − | 5.37963i | −0.0808958 | − | 0.195268i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.7545 | 1.33235 | 0.666174 | − | 0.745796i | \(-0.267931\pi\) | ||||
0.666174 | + | 0.745796i | \(0.267931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.6136 | −0.673859 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.95772 | − | 2.95840i | 0.106937 | − | 0.106961i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.60348 | − | 31.4904i | −0.346762 | − | 1.13705i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15.7373i | − | 0.567502i | −0.958898 | − | 0.283751i | \(-0.908421\pi\) | ||
0.958898 | − | 0.283751i | \(-0.0915789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.7244 | − | 9.00000i | 0.782386 | − | 0.324127i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 11.9057i | − | 0.428220i | −0.976810 | − | 0.214110i | \(-0.931315\pi\) | ||
0.976810 | − | 0.214110i | \(-0.0686851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.90696 | 0.176263 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.3529 | + | 32.2316i | 0.479034 | + | 1.15630i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.598650i | 0.0214489i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.96117i | − | 0.0701762i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 41.5431 | + | 17.1994i | 1.48463 | + | 0.614656i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.2489 | −0.615641 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1112i | 0.574301i | 0.957885 | + | 0.287151i | \(0.0927080\pi\) | ||||
−0.957885 | + | 0.287151i | \(0.907292\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.53991 | + | 15.7862i | 0.232827 | + | 0.562003i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 29.6235i | − | 1.05329i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.6867 | + | 9.96831i | −1.16074 | + | 0.353985i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.06773 | + | 1.27090i | −0.108801 | + | 0.0450741i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.7802 | −0.523542 | −0.261771 | − | 0.965130i | \(-0.584307\pi\) | ||||
−0.261771 | + | 0.965130i | \(0.584307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.520211 | 0.0184038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0607 | − | 12.0635i | 0.426145 | − | 0.426242i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 10.2299i | − | 0.361005i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 27.6928i | − | 0.976042i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.89716 | − | 21.4762i | −0.313195 | − | 0.755997i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 18.0231i | − | 0.633657i | −0.948483 | − | 0.316829i | \(-0.897382\pi\) | ||
0.948483 | − | 0.316829i | \(-0.102618\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.5754i | 1.60037i | 0.599754 | + | 0.800185i | \(0.295265\pi\) | ||||
−0.599754 | + | 0.800185i | \(0.704735\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.15072 | + | 17.2606i | 0.250787 | + | 0.605355i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.2741 | 1.23560 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.4907i | 0.926793i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.1892 | − | 13.4123i | −0.880181 | − | 0.468663i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 43.8260i | − | 1.52954i | −0.644305 | − | 0.764769i | \(-0.722853\pi\) | ||
0.644305 | − | 0.764769i | \(-0.277147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.8348i | 1.45827i | 0.684369 | + | 0.729135i | \(0.260078\pi\) | ||||
−0.684369 | + | 0.729135i | \(0.739922\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.350073 | + | 0.845014i | 0.0121880 | + | 0.0294196i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.1625 | −1.11840 | −0.559200 | − | 0.829033i | \(-0.688892\pi\) | ||||
−0.559200 | + | 0.829033i | \(0.688892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11.0453i | − | 0.383619i | −0.981432 | − | 0.191810i | \(-0.938564\pi\) | ||
0.981432 | − | 0.191810i | \(-0.0614356\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.89894 | − | 3.27237i | 0.274011 | − | 0.113517i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 0.0230605i | − | 0.000798998i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −43.7269 | −1.51323 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.0866 | + | 14.1123i | 1.17821 | + | 0.487792i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 32.2336i | − | 1.11283i | −0.830905 | − | 0.556415i | \(-0.812177\pi\) | ||
0.830905 | − | 0.556415i | \(-0.187823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.8758 | 1.58193 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.764084 | − | 1.84436i | −0.0263164 | − | 0.0635233i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.3062 | − | 25.7351i | −0.595350 | − | 0.885315i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.4808 | 0.944253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.42237 | + | 8.26100i | 0.117456 | + | 0.283517i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.5924 | −1.15153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.1165 | 0.757256 | 0.378628 | − | 0.925549i | \(-0.376396\pi\) | ||||
0.378628 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.7061 | − | 21.7110i | 0.742333 | − | 0.742502i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.33809i | − | 0.0798678i | −0.999202 | − | 0.0399339i | \(-0.987285\pi\) | ||
0.999202 | − | 0.0399339i | \(-0.0127147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.4057 | 1.48098 | 0.740492 | − | 0.672065i | \(-0.234592\pi\) | ||||
0.740492 | + | 0.672065i | \(0.234592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.244078 | − | 0.589162i | −0.00831816 | − | 0.0200786i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.1353i | 1.43430i | 0.696917 | + | 0.717152i | \(0.254555\pi\) | ||||
−0.696917 | + | 0.717152i | \(0.745445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 36.8268i | − | 1.25215i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.0431 | + | 26.6561i | 0.375044 | + | 0.905290i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.33382i | − | 0.282705i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.8126 | + | 12.1415i | −1.34900 | + | 0.411397i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.2690 | + | 22.2639i | 0.753691 | + | 0.753519i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 27.1197i | − | 0.916813i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5223 | 1.30080 | 0.650402 | − | 0.759590i | \(-0.274600\pi\) | ||||
0.650402 | + | 0.759590i | \(0.274600\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.53747 | − | 3.95119i | 0.321691 | − | 0.133270i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.54012i | − | 0.119270i | −0.998220 | − | 0.0596348i | \(-0.981006\pi\) | ||
0.998220 | − | 0.0596348i | \(-0.0189936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1271 | 0.811942 | 0.405971 | − | 0.913886i | \(-0.366933\pi\) | ||||
0.405971 | + | 0.913886i | \(0.366933\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −34.8564 | + | 14.4403i | −1.17169 | + | 0.485406i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.9805 | 1.17453 | 0.587265 | − | 0.809394i | \(-0.300204\pi\) | ||||
0.587265 | + | 0.809394i | \(0.300204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.37475i | 0.280880i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.00156926 | + | 6.87675i | 5.25721e−5 | + | 0.230380i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.81772 | 0.127755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.53126 | −0.184890 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.2136 | − | 17.4642i | 0.708301 | − | 0.583114i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.4365 | 2.04902 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.469736i | 0.0156492i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8006 | − | 26.0709i | −0.359423 | − | 0.867584i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.8152 | −1.62267 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.1062 | 1.63054 | 0.815272 | − | 0.579078i | \(-0.196587\pi\) | ||||
0.815272 | + | 0.579078i | \(0.196587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.7432 | + | 32.7507i | −1.08602 | + | 1.08627i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.3415 | 0.972128 | 0.486064 | − | 0.873923i | \(-0.338432\pi\) | ||||
0.486064 | + | 0.873923i | \(0.338432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.2149 | 0.371159 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.9889 | + | 36.1806i | 0.495518 | + | 1.19609i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 16.9382i | − | 0.559350i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.8671i | 1.01821i | 0.860704 | + | 0.509106i | \(0.170024\pi\) | ||||
−0.860704 | + | 0.509106i | \(0.829976\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.2846 | + | 5.50354i | −0.437742 | + | 0.181348i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.85188 | − | 2.69951i | 0.291363 | − | 0.0888556i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.27657 | 0.173493 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.6017 | − | 10.5993i | −0.348206 | − | 0.348126i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.3252 | −1.84797 | −0.923985 | − | 0.382429i | \(-0.875088\pi\) | ||||
−0.923985 | + | 0.382429i | \(0.875088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.169236i | − | 0.00554648i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.62312 | − | 8.74556i | −0.118615 | − | 0.286317i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.06547 | 0.0348447 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.08988 | −0.0356047 | −0.0178024 | − | 0.999842i | \(-0.505667\pi\) | ||||
−0.0178024 | + | 0.999842i | \(0.505667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.62391 | + | 8.74748i | 0.118262 | + | 0.285463i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 11.8789i | − | 0.387240i | −0.981077 | − | 0.193620i | \(-0.937977\pi\) | ||
0.981077 | − | 0.193620i | \(-0.0620229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.614035 | 0.0199957 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.5102 | + | 30.2168i | −0.406956 | + | 0.982953i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2255 | 0.852216 | 0.426108 | − | 0.904672i | \(-0.359884\pi\) | ||||
0.426108 | + | 0.904672i | \(0.359884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.1734 | − | 14.0813i | 1.49885 | − | 0.457097i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.78771 | − | 0.740612i | 0.0579703 | − | 0.0240160i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.4039i | 0.531375i | 0.964059 | + | 0.265687i | \(0.0855989\pi\) | ||||
−0.964059 | + | 0.265687i | \(0.914401\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 51.7822i | − | 1.67563i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.38300 | + | 10.5798i | 0.141682 | + | 0.341996i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.6744 | −0.570735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.4094 | 0.626109 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.6270 | − | 40.6177i | −1.30919 | − | 1.30889i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.4071 | −0.335017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4856 | 0.755245 | 0.377622 | − | 0.925960i | \(-0.376742\pi\) | ||||
0.377622 | + | 0.925960i | \(0.376742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.66222 | − | 4.01230i | −0.0533981 | − | 0.128894i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 38.7343i | − | 1.24304i | −0.783397 | − | 0.621521i | \(-0.786515\pi\) | ||
0.783397 | − | 0.621521i | \(-0.213485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.4954 | 0.881463 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.33216 | + | 2.74322i | −0.106714 | + | 0.0878533i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.1629 | 1.95677 | 0.978387 | − | 0.206781i | \(-0.0662987\pi\) | ||||
0.978387 | + | 0.206781i | \(0.0662987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.34468 | 0.138857 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9646 | + | 14.9681i | −0.477784 | + | 0.477893i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 3.87323i | − | 0.123537i | −0.998091 | − | 0.0617684i | \(-0.980326\pi\) | ||
0.998091 | − | 0.0617684i | \(-0.0196740\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.2484 | −1.79222 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.75721 | + | 1.55654i | −0.119593 | + | 0.0495452i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.1715 | 0.864003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 20.9226i | − | 0.664627i | −0.943169 | − | 0.332313i | \(-0.892171\pi\) | ||
0.943169 | − | 0.332313i | \(-0.107829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.5540 | − | 14.3150i | 1.09654 | − | 0.454274i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.0197 | 0.824879 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 46.7104i | − | 1.47933i | −0.672974 | − | 0.739666i | \(-0.734984\pi\) | ||
0.672974 | − | 0.739666i | \(-0.265016\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.6541 | + | 15.1753i | 1.15969 | + | 0.480125i |
(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 | 1248.2.h.c.623.22 | 32 | ||
3.2 | odd | 2 | inner | 1248.2.h.c.623.20 | 32 | ||
4.3 | odd | 2 | 312.2.h.c.155.31 | yes | 32 | ||
8.3 | odd | 2 | inner | 1248.2.h.c.623.21 | 32 | ||
8.5 | even | 2 | 312.2.h.c.155.29 | yes | 32 | ||
12.11 | even | 2 | 312.2.h.c.155.2 | yes | 32 | ||
13.12 | even | 2 | inner | 1248.2.h.c.623.23 | 32 | ||
24.5 | odd | 2 | 312.2.h.c.155.4 | yes | 32 | ||
24.11 | even | 2 | inner | 1248.2.h.c.623.19 | 32 | ||
39.38 | odd | 2 | inner | 1248.2.h.c.623.17 | 32 | ||
52.51 | odd | 2 | 312.2.h.c.155.1 | ✓ | 32 | ||
104.51 | odd | 2 | inner | 1248.2.h.c.623.24 | 32 | ||
104.77 | even | 2 | 312.2.h.c.155.3 | yes | 32 | ||
156.155 | even | 2 | 312.2.h.c.155.32 | yes | 32 | ||
312.77 | odd | 2 | 312.2.h.c.155.30 | yes | 32 | ||
312.155 | even | 2 | inner | 1248.2.h.c.623.18 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.h.c.155.1 | ✓ | 32 | 52.51 | odd | 2 | ||
312.2.h.c.155.2 | yes | 32 | 12.11 | even | 2 | ||
312.2.h.c.155.3 | yes | 32 | 104.77 | even | 2 | ||
312.2.h.c.155.4 | yes | 32 | 24.5 | odd | 2 | ||
312.2.h.c.155.29 | yes | 32 | 8.5 | even | 2 | ||
312.2.h.c.155.30 | yes | 32 | 312.77 | odd | 2 | ||
312.2.h.c.155.31 | yes | 32 | 4.3 | odd | 2 | ||
312.2.h.c.155.32 | yes | 32 | 156.155 | even | 2 | ||
1248.2.h.c.623.17 | 32 | 39.38 | odd | 2 | inner | ||
1248.2.h.c.623.18 | 32 | 312.155 | even | 2 | inner | ||
1248.2.h.c.623.19 | 32 | 24.11 | even | 2 | inner | ||
1248.2.h.c.623.20 | 32 | 3.2 | odd | 2 | inner | ||
1248.2.h.c.623.21 | 32 | 8.3 | odd | 2 | inner | ||
1248.2.h.c.623.22 | 32 | 1.1 | even | 1 | trivial | ||
1248.2.h.c.623.23 | 32 | 13.12 | even | 2 | inner | ||
1248.2.h.c.623.24 | 32 | 104.51 | odd | 2 | inner |