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 | 623.21 | ||
Character | \(\chi\) | \(=\) | 1248.623 |
Dual form | 1248.2.h.c.623.17 |
$q$-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 | \(-0.820900\pi\) | ||
0.845839 | − | 0.533438i | \(-0.179100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63829 | 0.997178 | 0.498589 | − | 0.866839i | \(-0.333852\pi\) | ||||
0.498589 | + | 0.866839i | \(0.333852\pi\) | |||||||
\(8\) | 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 | \(-0.651693\pi\) | ||||
−0.458724 | + | 0.888579i | \(0.651693\pi\) | |||||||
\(24\) | 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 | \(-0.203012\pi\) | ||||
0.803419 | + | 0.595415i | \(0.203012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.09996 | 1.27519 | 0.637595 | − | 0.770372i | \(-0.279929\pi\) | ||||
0.637595 | + | 0.770372i | \(0.279929\pi\) | |||||||
\(32\) | 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 | \(-0.284049\pi\) | ||||
0.627573 | + | 0.778558i | \(0.284049\pi\) | |||||||
\(38\) | 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 | \(0.0206754\pi\) | ||||
−0.997891 | + | 0.0649081i | \(0.979325\pi\) | |||||||
\(48\) | 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 | \(-0.517577\pi\) | ||||
−0.0551930 | + | 0.998476i | \(0.517577\pi\) | |||||||
\(54\) | 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 | \(0.207530\pi\) | ||||
−0.794886 | + | 0.606758i | \(0.792470\pi\) | |||||||
\(62\) | 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 | \(-0.951330\pi\) | ||
0.988333 | − | 0.152305i | \(-0.0486697\pi\) | |||||||
\(72\) | 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 | \(-0.789736\pi\) | ||
0.789646 | − | 0.613563i | \(-0.210264\pi\) | |||||||
\(80\) | 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 | \(-0.778759\pi\) | ||||
−0.768023 | + | 0.640422i | \(0.778759\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.99712i | − | 0.492381i | −0.969221 | − | 0.246191i | \(-0.920821\pi\) | ||
0.969221 | − | 0.246191i | \(-0.0791789\pi\) | |||||||
\(104\) | 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 | \(-0.609711\pi\) | ||||
−0.337883 | + | 0.941188i | \(0.609711\pi\) | |||||||
\(110\) | 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 | \(0.0449795\pi\) | ||||
−0.990033 | + | 0.140838i | \(0.955020\pi\) | |||||||
\(128\) | 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 | \(-0.941243\pi\) | ||
0.983012 | − | 0.183543i | \(-0.0587567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.12597 | 0.417145 | 0.208573 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208573 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(152\) | 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 | \(-0.906835\pi\) | ||
0.957472 | − | 0.288525i | \(-0.0931648\pi\) | |||||||
\(158\) | 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 | \(-0.749062\pi\) | ||
0.705019 | − | 0.709189i | \(-0.250938\pi\) | |||||||
\(168\) | 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 | \(-0.300376\pi\) | ||||
0.586829 | + | 0.809711i | \(0.300376\pi\) | |||||||
\(174\) | 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 | \(-0.724965\pi\) | ||
0.649364 | − | 0.760478i | \(-0.275035\pi\) | |||||||
\(182\) | 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 | \(-0.212509\pi\) | ||||
0.785299 | + | 0.619117i | \(0.212509\pi\) | |||||||
\(192\) | 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 | \(-0.682590\pi\) | ||
0.542680 | − | 0.839939i | \(-0.317410\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.9069i | 0.773172i | 0.922253 | + | 0.386586i | \(0.126346\pi\) | ||||
−0.922253 | + | 0.386586i | \(0.873654\pi\) | |||||||
\(200\) | 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 | \(-0.569410\pi\) | ||||
−0.216333 | + | 0.976320i | \(0.569410\pi\) | |||||||
\(224\) | 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 | \(-0.762410\pi\) | ||||
−0.734132 | + | 0.679007i | \(0.762410\pi\) | |||||||
\(230\) | 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 | \(-0.634360\pi\) | ||
0.409681 | − | 0.912229i | \(-0.365640\pi\) | |||||||
\(240\) | 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 | \(-0.598376\pi\) | ||||
−0.304161 | + | 0.952621i | \(0.598376\pi\) | |||||||
\(264\) | 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 | \(-0.365824\pi\) | ||||
0.409152 | + | 0.912466i | \(0.365824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7867 | −0.655247 | −0.327624 | − | 0.944808i | \(-0.606248\pi\) | ||||
−0.327624 | + | 0.944808i | \(0.606248\pi\) | |||||||
\(272\) | 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 | \(0.0473792\pi\) | ||||
−0.988943 | + | 0.148297i | \(0.952621\pi\) | |||||||
\(278\) | 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 | \(0.0557022\pi\) | ||||
−0.984728 | + | 0.174102i | \(0.944298\pi\) | |||||||
\(294\) | 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 | \(-0.450476\pi\) | ||||
0.154957 | + | 0.987921i | \(0.450476\pi\) | |||||||
\(312\) | 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 | \(0.00998831\pi\) | ||||
−0.999508 | + | 0.0313741i | \(0.990012\pi\) | |||||||
\(318\) | 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 | \(-0.884042\pi\) | ||||
−0.934376 | + | 0.356289i | \(0.884042\pi\) | |||||||
\(350\) | 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 | \(0.149332\pi\) | ||||
−0.891957 | + | 0.452121i | \(0.850668\pi\) | |||||||
\(360\) | 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 | \(0.0289676\pi\) | ||||
−0.995862 | + | 0.0908787i | \(0.971032\pi\) | |||||||
\(368\) | 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 | \(-0.801605\pi\) | ||
0.811970 | − | 0.583699i | \(-0.198395\pi\) | |||||||
\(374\) | 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 | \(-0.912196\pi\) | ||
0.962195 | − | 0.272361i | \(-0.0878045\pi\) | |||||||
\(384\) | 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 | \(-0.764335\pi\) | ||||
−0.738224 | + | 0.674555i | \(0.764335\pi\) | |||||||
\(390\) | 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 | \(-0.552490\pi\) | ||||
−0.164154 | + | 0.986435i | \(0.552490\pi\) | |||||||
\(398\) | 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 | \(-0.467495\pi\) | ||||
0.101942 | + | 0.994790i | \(0.467495\pi\) | |||||||
\(422\) | 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 | \(0.158688\pi\) | ||||
−0.878285 | + | 0.478137i | \(0.841312\pi\) | |||||||
\(432\) | 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 | \(-0.869407\pi\) | ||
0.917014 | − | 0.398856i | \(-0.130593\pi\) | |||||||
\(440\) | 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 | \(0.136647\pi\) | ||||
−0.909261 | + | 0.416226i | \(0.863353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.69526 | −0.218207 | −0.109104 | − | 0.994030i | \(-0.534798\pi\) | ||||
−0.109104 | + | 0.994030i | \(0.534798\pi\) | |||||||
\(464\) | 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 | \(0.281129\pi\) | ||||
−0.634687 | + | 0.772770i | \(0.718871\pi\) | |||||||
\(480\) | 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 | \(-0.408635\pi\) | ||||
0.283106 | + | 0.959089i | \(0.408635\pi\) | |||||||
\(488\) | 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 | \(-0.638550\pi\) | ||||
−0.421654 | + | 0.906757i | \(0.638550\pi\) | |||||||
\(504\) | 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 | \(0.160153\pi\) | ||||
−0.876075 | + | 0.482174i | \(0.839847\pi\) | |||||||
\(510\) | 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 | \(-0.127527\pi\) | ||||
0.920812 | + | 0.390006i | \(0.127527\pi\) | |||||||
\(542\) | 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 | \(-0.763457\pi\) | ||
0.736360 | − | 0.676590i | \(-0.236543\pi\) | |||||||
\(558\) | 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 | \(-0.403363\pi\) | ||||
0.298953 | + | 0.954268i | \(0.403363\pi\) | |||||||
\(600\) | 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 | \(-0.895313\pi\) | ||
0.946403 | − | 0.322988i | \(-0.104687\pi\) | |||||||
\(608\) | 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 | \(-0.554019\pi\) | ||||
−0.168892 | + | 0.985635i | \(0.554019\pi\) | |||||||
\(614\) | 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 | \(-0.413685\pi\) | ||||
0.267856 | + | 0.963459i | \(0.413685\pi\) | |||||||
\(632\) | 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 | \(-0.270797\pi\) | ||||
0.659432 | + | 0.751765i | \(0.270797\pi\) | |||||||
\(648\) | 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 | \(-0.573006\pi\) | ||||
−0.227350 | + | 0.973813i | \(0.573006\pi\) | |||||||
\(654\) | 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 | \(-0.200489\pi\) | ||||
0.808113 | + | 0.589028i | \(0.200489\pi\) | |||||||
\(662\) | 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 | \(-0.506106\pi\) | ||||
−0.0191824 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(678\) | 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 | \(-0.491220\pi\) | ||||
0.0275805 | + | 0.999620i | \(0.491220\pi\) | |||||||
\(702\) | 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 | \(-0.364903\pi\) | ||||
0.411793 | + | 0.911277i | \(0.364903\pi\) | |||||||
\(710\) | 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 | \(-0.590246\pi\) | ||||
−0.279733 | + | 0.960078i | \(0.590246\pi\) | |||||||
\(720\) | 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 | \(-0.850438\pi\) | ||
0.891631 | − | 0.452763i | \(-0.149562\pi\) | |||||||
\(728\) | 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 | \(-0.424643\pi\) | ||||
0.234536 | + | 0.972108i | \(0.424643\pi\) | |||||||
\(734\) | 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 | \(-0.804889\pi\) | ||
0.817948 | − | 0.575292i | \(-0.195111\pi\) | |||||||
\(744\) | 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 | \(0.237123\pi\) | ||||
−0.735127 | + | 0.677930i | \(0.762877\pi\) | |||||||
\(752\) | 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 | \(-0.937360\pi\) | ||
0.980699 | − | 0.195522i | \(-0.0626400\pi\) | |||||||
\(758\) | 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 | \(0.0686851\pi\) | ||||
−0.976810 | + | 0.214110i | \(0.931315\pi\) | |||||||
\(774\) | 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 | \(-0.415693\pi\) | ||||
0.261771 | + | 0.965130i | \(0.415693\pi\) | |||||||
\(798\) | 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 | \(0.277147\pi\) | ||||
−0.644305 | + | 0.764769i | \(0.722853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 41.8348i | − | 1.45827i | −0.684369 | − | 0.729135i | \(-0.739922\pi\) | ||
0.684369 | − | 0.729135i | \(-0.260078\pi\) | |||||||
\(824\) | 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 | \(0.0614356\pi\) | ||||
−0.981432 | + | 0.191810i | \(0.938564\pi\) | |||||||
\(830\) | 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 | \(0.187823\pi\) | ||||
−0.830905 | + | 0.556415i | \(0.812177\pi\) | |||||||
\(840\) | 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 | \(-0.623604\pi\) | ||||
−0.378628 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(854\) | 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 | \(-0.745445\pi\) | ||
0.696917 | − | 0.717152i | \(-0.254555\pi\) | |||||||
\(864\) | 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 | \(-0.725400\pi\) | ||||
−0.650402 | + | 0.759590i | \(0.725400\pi\) | |||||||
\(878\) | 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 | \(-0.699796\pi\) | ||||
−0.587265 | + | 0.809394i | \(0.699796\pi\) | |||||||
\(888\) | 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 | \(-0.661568\pi\) | ||||
−0.486064 | + | 0.873923i | \(0.661568\pi\) | |||||||
\(912\) | 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 | \(-0.829976\pi\) | ||
0.860704 | − | 0.509106i | \(-0.170024\pi\) | |||||||
\(920\) | 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 | \(0.0620229\pi\) | ||||
−0.981077 | + | 0.193620i | \(0.937977\pi\) | |||||||
\(942\) | 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 | \(-0.623258\pi\) | ||||
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(968\) | 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 | \(0.0196740\pi\) | ||||
−0.998091 | + | 0.0617684i | \(0.980326\pi\) | |||||||
\(984\) | 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 | \(0.107829\pi\) | ||||
−0.943169 | + | 0.332313i | \(0.892171\pi\) | |||||||
\(992\) | 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 | \(0.265016\pi\) | ||||
−0.672974 | + | 0.739666i | \(0.734984\pi\) | |||||||
\(998\) | 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.623.21 | 32 | ||
3.2 | odd | 2 | inner | 1248.2.h.c.623.19 | 32 | ||
4.3 | odd | 2 | 312.2.h.c.155.29 | yes | 32 | ||
8.3 | odd | 2 | inner | 1248.2.h.c.623.22 | 32 | ||
8.5 | even | 2 | 312.2.h.c.155.31 | yes | 32 | ||
12.11 | even | 2 | 312.2.h.c.155.4 | yes | 32 | ||
13.12 | even | 2 | inner | 1248.2.h.c.623.24 | 32 | ||
24.5 | odd | 2 | 312.2.h.c.155.2 | yes | 32 | ||
24.11 | even | 2 | inner | 1248.2.h.c.623.20 | 32 | ||
39.38 | odd | 2 | inner | 1248.2.h.c.623.18 | 32 | ||
52.51 | odd | 2 | 312.2.h.c.155.3 | yes | 32 | ||
104.51 | odd | 2 | inner | 1248.2.h.c.623.23 | 32 | ||
104.77 | even | 2 | 312.2.h.c.155.1 | ✓ | 32 | ||
156.155 | even | 2 | 312.2.h.c.155.30 | yes | 32 | ||
312.77 | odd | 2 | 312.2.h.c.155.32 | yes | 32 | ||
312.155 | even | 2 | inner | 1248.2.h.c.623.17 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.h.c.155.1 | ✓ | 32 | 104.77 | even | 2 | ||
312.2.h.c.155.2 | yes | 32 | 24.5 | odd | 2 | ||
312.2.h.c.155.3 | yes | 32 | 52.51 | odd | 2 | ||
312.2.h.c.155.4 | yes | 32 | 12.11 | even | 2 | ||
312.2.h.c.155.29 | yes | 32 | 4.3 | odd | 2 | ||
312.2.h.c.155.30 | yes | 32 | 156.155 | even | 2 | ||
312.2.h.c.155.31 | yes | 32 | 8.5 | even | 2 | ||
312.2.h.c.155.32 | yes | 32 | 312.77 | odd | 2 | ||
1248.2.h.c.623.17 | 32 | 312.155 | even | 2 | inner | ||
1248.2.h.c.623.18 | 32 | 39.38 | odd | 2 | inner | ||
1248.2.h.c.623.19 | 32 | 3.2 | odd | 2 | inner | ||
1248.2.h.c.623.20 | 32 | 24.11 | even | 2 | inner | ||
1248.2.h.c.623.21 | 32 | 1.1 | even | 1 | trivial | ||
1248.2.h.c.623.22 | 32 | 8.3 | odd | 2 | inner | ||
1248.2.h.c.623.23 | 32 | 104.51 | odd | 2 | inner | ||
1248.2.h.c.623.24 | 32 | 13.12 | even | 2 | inner |