Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.4 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.3 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.69622 | −1.65300 | −0.826499 | − | 0.562938i | \(-0.809671\pi\) | ||||
−0.826499 | + | 0.562938i | \(0.809671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.05843i | − 0.620640i | −0.950632 | − | 0.310320i | \(-0.899564\pi\) | ||||
0.950632 | − | 0.310320i | \(-0.100436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.65027i | − 1.28975i | −0.764287 | − | 0.644876i | \(-0.776909\pi\) | ||||
0.764287 | − | 0.644876i | \(-0.223091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.73497i | 1.39094i | 0.718557 | + | 0.695468i | \(0.244803\pi\) | ||||
−0.718557 | + | 0.695468i | \(0.755197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.27215 | −0.750682 | −0.375341 | − | 0.926887i | \(-0.622474\pi\) | ||||
−0.375341 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.45085 | 0.928067 | 0.464033 | − | 0.885818i | \(-0.346402\pi\) | ||||
0.464033 | + | 0.885818i | \(0.346402\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.66201 | 1.73240 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.2594 | 1.90512 | 0.952561 | − | 0.304346i | \(-0.0984380\pi\) | ||||
0.952561 | + | 0.304346i | \(0.0984380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.26066i | − 0.226422i | −0.993571 | − | 0.113211i | \(-0.963886\pi\) | ||||
0.993571 | − | 0.113211i | \(-0.0361136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.69622i | 0.624775i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.25539i | − 0.535183i | −0.963532 | − | 0.267592i | \(-0.913772\pi\) | ||||
0.963532 | − | 0.267592i | \(-0.0862278\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.72747i | 1.36300i | 0.731817 | + | 0.681501i | \(0.238673\pi\) | ||||
−0.731817 | + | 0.681501i | \(0.761327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.56921 | 0.391801 | 0.195901 | − | 0.980624i | \(-0.437237\pi\) | ||||
0.195901 | + | 0.980624i | \(0.437237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.03048 | −0.296176 | −0.148088 | − | 0.988974i | \(-0.547312\pi\) | ||||
−0.148088 | + | 0.988974i | \(0.547312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0794 | 1.38451 | 0.692253 | − | 0.721655i | \(-0.256618\pi\) | ||||
0.692253 | + | 0.721655i | \(0.256618\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.60840i | 1.02592i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.851213i | 0.110818i | 0.998464 | + | 0.0554092i | \(0.0176463\pi\) | ||||
−0.998464 | + | 0.0554092i | \(0.982354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.31448i | 0.296339i | 0.988962 | + | 0.148170i | \(0.0473382\pi\) | ||||
−0.988962 | + | 0.148170i | \(0.952662\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.1884i | 2.13196i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.4289 | −1.88494 | −0.942468 | − | 0.334296i | \(-0.891501\pi\) | ||||
−0.942468 | + | 0.334296i | \(0.891501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.44544 | 0.527576 | 0.263788 | − | 0.964581i | \(-0.415028\pi\) | ||||
0.263788 | + | 0.964581i | \(0.415028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.97349 | −0.816186 | −0.408093 | − | 0.912940i | \(-0.633806\pi\) | ||||
−0.408093 | + | 0.912940i | \(0.633806\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.05843 | −0.234580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 11.6750i | − 1.31354i | −0.754092 | − | 0.656769i | \(-0.771923\pi\) | ||||
0.754092 | − | 0.656769i | \(-0.228077\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 12.8349i | − 1.40882i | −0.709796 | − | 0.704408i | \(-0.751213\pi\) | ||||
0.709796 | − | 0.704408i | \(-0.248787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 21.1977i | − 2.29921i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.35419i | 0.249544i | 0.992185 | + | 0.124772i | \(0.0398200\pi\) | ||||
−0.992185 | + | 0.124772i | \(0.960180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.65027 | −0.487480 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.0946 | 1.24088 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.02539 | 0.408717 | 0.204358 | − | 0.978896i | \(-0.434489\pi\) | ||||
0.204358 | + | 0.978896i | \(0.434489\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.2008 | −1.41303 | −0.706517 | − | 0.707696i | \(-0.749735\pi\) | ||||
−0.706517 | + | 0.707696i | \(0.749735\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.30631i | − 0.522846i | −0.965224 | − | 0.261423i | \(-0.915808\pi\) | ||||
0.965224 | − | 0.261423i | \(-0.0841918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3669i | 1.29223i | 0.763240 | + | 0.646115i | \(0.223608\pi\) | ||||
−0.763240 | + | 0.646115i | \(0.776392\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.91832i | 0.566872i | 0.958991 | + | 0.283436i | \(0.0914743\pi\) | ||||
−0.958991 | + | 0.283436i | \(0.908526\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 18.5535i | − 1.74537i | −0.488287 | − | 0.872683i | \(-0.662378\pi\) | ||||
0.488287 | − | 0.872683i | \(-0.337622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.4513 | −1.53409 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.73497 | 0.525724 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.76287 | 0.614806 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13.5356 | −1.21066 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 9.76963i | − 0.866915i | −0.901174 | − | 0.433457i | \(-0.857293\pi\) | ||||
0.901174 | − | 0.433457i | \(-0.142707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.5661i | − 1.36002i | −0.733204 | − | 0.680009i | \(-0.761976\pi\) | ||||
0.733204 | − | 0.680009i | \(-0.238024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.27215i | 0.283731i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.54964i | 0.730445i | 0.930920 | + | 0.365223i | \(0.119007\pi\) | ||||
−0.930920 | + | 0.365223i | \(0.880993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4607 | 1.31136 | 0.655679 | − | 0.755040i | \(-0.272383\pi\) | ||||
0.655679 | + | 0.755040i | \(0.272383\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.57225 | −0.800472 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −37.9210 | −3.14916 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.91181 | −0.730084 | −0.365042 | − | 0.930991i | \(-0.618945\pi\) | ||||
−0.365042 | + | 0.930991i | \(0.618945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 14.8040i | − 1.20473i | −0.798219 | − | 0.602367i | \(-0.794224\pi\) | ||||
0.798219 | − | 0.602367i | \(-0.205776\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.65968i | 0.374275i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3716i | 1.14698i | 0.819214 | + | 0.573488i | \(0.194410\pi\) | ||||
−0.819214 | + | 0.573488i | \(0.805590\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 4.45085i | − 0.350776i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.7846 | −1.70630 | −0.853149 | − | 0.521667i | \(-0.825310\pi\) | ||||
−0.853149 | + | 0.521667i | \(0.825310\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.4031 | 1.03717 | 0.518583 | − | 0.855027i | \(-0.326460\pi\) | ||||
0.518583 | + | 0.855027i | \(0.326460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.62498 | −0.663460 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.3221 | −1.01286 | −0.506429 | − | 0.862282i | \(-0.669035\pi\) | ||||
−0.506429 | + | 0.862282i | \(0.669035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 8.66201i | − 0.654787i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 12.6787i | − 0.947648i | −0.880619 | − | 0.473824i | \(-0.842873\pi\) | ||||
0.880619 | − | 0.473824i | \(-0.157127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.1255i | 0.826951i | 0.910515 | + | 0.413476i | \(0.135685\pi\) | ||||
−0.910515 | + | 0.413476i | \(0.864315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0326i | 0.884657i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.8050 | 0.863270 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.76387 | −0.561774 | −0.280887 | − | 0.959741i | \(-0.590629\pi\) | ||||
−0.280887 | + | 0.959741i | \(0.590629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.09582 | 0.654731 | 0.327366 | − | 0.944898i | \(-0.393839\pi\) | ||||
0.327366 | + | 0.944898i | \(0.393839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3722 | −0.738988 | −0.369494 | − | 0.929233i | \(-0.620469\pi\) | ||||
−0.369494 | + | 0.929233i | \(0.620469\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 9.92379i | − 0.703479i | −0.936098 | − | 0.351739i | \(-0.885590\pi\) | ||||
0.936098 | − | 0.351739i | \(-0.114410\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 10.2594i | − 0.720069i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 32.2586i | − 2.25304i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.73549i | 0.465903i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9624 | 0.754680 | 0.377340 | − | 0.926075i | \(-0.376839\pi\) | ||||
0.377340 | + | 0.926075i | \(0.376839\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.49637 | −0.647647 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.26066 | −0.0855794 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.6692 | 1.79396 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.18980i | − 0.0796749i | −0.999206 | − | 0.0398375i | \(-0.987316\pi\) | ||||
0.999206 | − | 0.0398375i | \(-0.0126840\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.62724i | 0.638983i | 0.947589 | + | 0.319491i | \(0.103512\pi\) | ||||
−0.947589 | + | 0.319491i | \(0.896488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 21.5143i | − 1.42170i | −0.703343 | − | 0.710851i | \(-0.748310\pi\) | ||||
0.703343 | − | 0.710851i | \(-0.251690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 6.82082i | − 0.446847i | −0.974722 | − | 0.223423i | \(-0.928277\pi\) | ||||
0.974722 | − | 0.223423i | \(-0.0717232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.50510 | 0.489579 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.24506 | 0.403959 | 0.201980 | − | 0.979390i | \(-0.435263\pi\) | ||||
0.201980 | + | 0.979390i | \(0.435263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.5573 | 1.64629 | 0.823145 | − | 0.567831i | \(-0.192217\pi\) | ||||
0.823145 | + | 0.567831i | \(0.192217\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.69622 | 0.236143 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.2164i | 0.968194i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 0.373698i | − 0.0235876i | −0.999930 | − | 0.0117938i | \(-0.996246\pi\) | ||||
0.999930 | − | 0.0117938i | \(-0.00375417\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.16177i | − 0.575995i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 11.0514i | − 0.689369i | −0.938719 | − | 0.344684i | \(-0.887986\pi\) | ||||
0.938719 | − | 0.344684i | \(-0.112014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.25539 | −0.202280 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.6685 | −1.70612 | −0.853058 | − | 0.521817i | \(-0.825255\pi\) | ||||
−0.853058 | + | 0.521817i | \(0.825255\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.2555 | −2.28859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.3247 | −1.78796 | −0.893981 | − | 0.448105i | \(-0.852099\pi\) | ||||
−0.893981 | + | 0.448105i | \(0.852099\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 5.13414i | − 0.311877i | −0.987767 | − | 0.155938i | \(-0.950160\pi\) | ||||
0.987767 | − | 0.155938i | \(-0.0498401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 17.8301i | − 1.07520i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.93089i | 0.356353i | 0.983999 | + | 0.178176i | \(0.0570197\pi\) | ||||
−0.983999 | + | 0.178176i | \(0.942980\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 10.7827i | − 0.643242i | −0.946868 | − | 0.321621i | \(-0.895772\pi\) | ||||
0.946868 | − | 0.321621i | \(-0.104228\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.1556 | 1.07924 | 0.539619 | − | 0.841910i | \(-0.318568\pi\) | ||||
0.539619 | + | 0.841910i | \(0.318568\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.72747 | 0.515166 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8899 | −0.934701 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.8863 | 1.27861 | 0.639306 | − | 0.768953i | \(-0.279222\pi\) | ||||
0.639306 | + | 0.768953i | \(0.279222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 3.14627i | − 0.183183i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 20.6976i | − 1.19698i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.56921i | − 0.148087i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 8.55484i | − 0.489848i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.8301 | −0.960546 | −0.480273 | − | 0.877119i | \(-0.659462\pi\) | ||||
−0.480273 | + | 0.877119i | \(0.659462\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.1293 | −1.87859 | −0.939294 | − | 0.343113i | \(-0.888519\pi\) | ||||
−0.939294 | + | 0.343113i | \(0.888519\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4187 | 0.758469 | 0.379235 | − | 0.925301i | \(-0.376187\pi\) | ||||
0.379235 | + | 0.925301i | \(0.376187\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.764835 | −0.0429574 | −0.0214787 | − | 0.999769i | \(-0.506837\pi\) | ||||
−0.0214787 | + | 0.999769i | \(0.506837\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 21.1183i | − 1.18240i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 18.7657i | − 1.04415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 40.2807i | − 2.23437i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.03048i | 0.111944i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7299 | −1.63410 | −0.817051 | − | 0.576566i | \(-0.804392\pi\) | ||||
−0.817051 | + | 0.576566i | \(0.804392\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 57.0284 | 3.11580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0487 | −1.03765 | −0.518824 | − | 0.854881i | \(-0.673630\pi\) | ||||
−0.518824 | + | 0.854881i | \(0.673630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.59499 | −0.140526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 30.0749i | − 1.61451i | −0.590205 | − | 0.807253i | \(-0.700953\pi\) | ||||
0.590205 | − | 0.807253i | \(-0.299047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 28.7995i | − 1.54160i | −0.637078 | − | 0.770800i | \(-0.719857\pi\) | ||||
0.637078 | − | 0.770800i | \(-0.280143\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 26.2377i | − 1.39649i | −0.715857 | − | 0.698247i | \(-0.753964\pi\) | ||||
0.715857 | − | 0.698247i | \(-0.246036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.4313 | −0.872083 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.4178 | −0.972053 | −0.486027 | − | 0.873944i | \(-0.661554\pi\) | ||||
−0.486027 | + | 0.873944i | \(0.661554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.29305 | −0.436476 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.7755 | 1.34915 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 37.2862i | − 1.94632i | −0.230127 | − | 0.973161i | \(-0.573914\pi\) | ||||
0.230127 | − | 0.973161i | \(-0.426086\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 10.0794i | − 0.523294i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.59095i | 0.237711i | 0.992912 | + | 0.118855i | \(0.0379224\pi\) | ||||
−0.992912 | + | 0.118855i | \(0.962078\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 47.7090i | − 2.45714i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0149 | 1.07947 | 0.539733 | − | 0.841836i | \(-0.318525\pi\) | ||||
0.539733 | + | 0.841836i | \(0.318525\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.09047 | 0.464501 | 0.232251 | − | 0.972656i | \(-0.425391\pi\) | ||||
0.232251 | + | 0.972656i | \(0.425391\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.60840 | 0.387760 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.06330 | 0.104614 | 0.0523068 | − | 0.998631i | \(-0.483343\pi\) | ||||
0.0523068 | + | 0.998631i | \(0.483343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.5255i | 1.29088i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.1533i | 2.17128i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 0.0369436i | − 0.00185415i | −1.00000 | 0.000927073i | \(-0.999705\pi\) | |||||
1.00000 | 0.000927073i | \(-0.000295096\pi\) | ||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.6814i | 0.932906i | 0.884546 | + | 0.466453i | \(0.154468\pi\) | ||||
−0.884546 | + | 0.466453i | \(0.845532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.86242 | −0.292028 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.70100 | −0.332156 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5630 | −0.571755 | −0.285878 | − | 0.958266i | \(-0.592285\pi\) | ||||
−0.285878 | + | 0.958266i | \(0.592285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.851213 | 0.0418854 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.4406i | 2.32877i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.5911i | 0.712822i | 0.934329 | + | 0.356411i | \(0.116000\pi\) | ||||
−0.934329 | + | 0.356411i | \(0.884000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 17.6204i | − 0.858767i | −0.903122 | − | 0.429384i | \(-0.858731\pi\) | ||||
0.903122 | − | 0.429384i | \(-0.141269\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 49.6764i | 2.40966i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.31448 | 0.112006 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6500 | −0.850170 | −0.425085 | − | 0.905153i | \(-0.639756\pi\) | ||||
−0.425085 | + | 0.905153i | \(0.639756\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.31965 | −0.303703 | −0.151852 | − | 0.988403i | \(-0.548524\pi\) | ||||
−0.151852 | + | 0.988403i | \(0.548524\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.5638 | −0.696683 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 10.1993i | − 0.486786i | −0.969928 | − | 0.243393i | \(-0.921739\pi\) | ||||
0.969928 | − | 0.243393i | \(-0.0782605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.46579i | 0.449733i | 0.974390 | + | 0.224867i | \(0.0721947\pi\) | ||||
−0.974390 | + | 0.224867i | \(0.927805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 8.70161i | − 0.412496i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.1482i | 1.32840i | 0.747556 | + | 0.664198i | \(0.231227\pi\) | ||||
−0.747556 | + | 0.664198i | \(0.768773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.9649 | 0.845934 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.1884 | 0.805804 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.9936 | −1.63693 | −0.818465 | − | 0.574556i | \(-0.805175\pi\) | ||||
−0.818465 | + | 0.574556i | \(0.805175\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.2558 | −1.40915 | −0.704577 | − | 0.709628i | \(-0.748863\pi\) | ||||
−0.704577 | + | 0.709628i | \(0.748863\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.87077i | − 0.133416i | −0.997773 | − | 0.0667080i | \(-0.978750\pi\) | ||||
0.997773 | − | 0.0667080i | \(-0.0212496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.1957i | 1.67494i | 0.546484 | + | 0.837469i | \(0.315966\pi\) | ||||
−0.546484 | + | 0.837469i | \(0.684034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4289i | 0.712439i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5.28855i | − 0.243168i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.3434 | −1.30048 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.1156 | −0.782030 | −0.391015 | − | 0.920384i | \(-0.627876\pi\) | ||||
−0.391015 | + | 0.920384i | \(0.627876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1384 | −0.690253 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.8787 | −0.675608 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 26.8336i | − 1.21595i | −0.793957 | − | 0.607974i | \(-0.791982\pi\) | ||||
0.793957 | − | 0.607974i | \(-0.208018\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.17336i | 0.323729i | 0.986813 | + | 0.161865i | \(0.0517508\pi\) | ||||
−0.986813 | + | 0.161865i | \(0.948249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 58.8374i | 2.64990i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4.44544i | − 0.199405i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.8731 | 1.65067 | 0.825334 | − | 0.564646i | \(-0.190987\pi\) | ||||
0.825334 | + | 0.564646i | \(0.190987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.4855 | −0.779642 | −0.389821 | − | 0.920891i | \(-0.627463\pi\) | ||||
−0.389821 | + | 0.920891i | \(0.627463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.4893 | 2.33574 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.6034 | 1.71106 | 0.855532 | − | 0.517750i | \(-0.173230\pi\) | ||||
0.855532 | + | 0.517750i | \(0.173230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.97349i | 0.308489i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.6133i | 0.864264i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.17960i | 0.183819i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3406i | 1.28543i | 0.766104 | + | 0.642716i | \(0.222193\pi\) | ||||
−0.766104 | + | 0.642716i | \(0.777807\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.90612 | 0.345711 | 0.172855 | − | 0.984947i | \(-0.444701\pi\) | ||||
0.172855 | + | 0.984947i | \(0.444701\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.22987 | 0.314938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.18992 | −0.138692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.5851 | 1.75793 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 49.4071i | − 2.13606i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.05843i | 0.0886629i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 6.25573i | − 0.268955i | −0.990917 | − | 0.134477i | \(-0.957064\pi\) | ||||
0.990917 | − | 0.134477i | \(-0.0429356\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 21.8754i | − 0.937038i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.4597 | −0.789279 | −0.394640 | − | 0.918836i | \(-0.629131\pi\) | ||||
−0.394640 | + | 0.918836i | \(0.629131\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −33.5703 | −1.43014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.6750 | −0.496471 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.6497 | 0.451243 | 0.225622 | − | 0.974215i | \(-0.427559\pi\) | ||||
0.225622 | + | 0.974215i | \(0.427559\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 11.9475i | − 0.505327i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.9117i | 0.459874i | 0.973206 | + | 0.229937i | \(0.0738520\pi\) | ||||
−0.973206 | + | 0.229937i | \(0.926148\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 68.5778i | 2.88509i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 10.7145i | − 0.449175i | −0.974454 | − | 0.224588i | \(-0.927896\pi\) | ||||
0.974454 | − | 0.224588i | \(-0.0721035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6134 | 0.904493 | 0.452247 | − | 0.891893i | \(-0.350623\pi\) | ||||
0.452247 | + | 0.891893i | \(0.350623\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 38.5533 | 1.60779 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.2449 | 0.717914 | 0.358957 | − | 0.933354i | \(-0.383133\pi\) | ||||
0.358957 | + | 0.933354i | \(0.383133\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8349 | −0.532482 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 20.7476i | − 0.859279i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.83868i | 0.282263i | 0.989991 | + | 0.141131i | \(0.0450740\pi\) | ||||
−0.989991 | + | 0.141131i | \(0.954926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.12508i | 0.169971i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.2262i | 0.953787i | 0.878961 | + | 0.476893i | \(0.158237\pi\) | ||||
−0.878961 | + | 0.476893i | \(0.841763\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.1977 | −0.869021 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.71919 | 0.192821 | 0.0964105 | − | 0.995342i | \(-0.469264\pi\) | ||||
0.0964105 | + | 0.995342i | \(0.469264\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.230392 | −0.00939787 | −0.00469893 | − | 0.999989i | \(-0.501496\pi\) | ||||
−0.00469893 | + | 0.999989i | \(0.501496\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.9970 | −1.01627 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.43638i | 0.220656i | 0.993895 | + | 0.110328i | \(0.0351901\pi\) | ||||
−0.993895 | + | 0.110328i | \(0.964810\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.44228i | 0.381994i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 24.7976i | − 1.00156i | −0.865573 | − | 0.500782i | \(-0.833046\pi\) | ||||
0.865573 | − | 0.500782i | \(-0.166954\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 13.4024i | − 0.539561i | −0.962922 | − | 0.269781i | \(-0.913049\pi\) | ||||
0.962922 | − | 0.269781i | \(-0.0869512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.8992 | 0.518465 | 0.259232 | − | 0.965815i | \(-0.416530\pi\) | ||||
0.259232 | + | 0.965815i | \(0.416530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.35419 | 0.0943188 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.72041 | 0.268817 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.6696 | 0.744405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 24.0217i | − 0.956288i | −0.878281 | − | 0.478144i | \(-0.841310\pi\) | ||||
0.878281 | − | 0.478144i | \(-0.158690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.1107i | 1.43301i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.65027i | 0.184250i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 10.4176i | − 0.411469i | −0.978608 | − | 0.205735i | \(-0.934042\pi\) | ||||
0.978608 | − | 0.205735i | \(-0.0659583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.2723 | −1.66706 | −0.833528 | − | 0.552477i | \(-0.813683\pi\) | ||||
−0.833528 | + | 0.552477i | \(0.813683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.75700 | 0.304959 | 0.152480 | − | 0.988307i | \(-0.451274\pi\) | ||||
0.152480 | + | 0.988307i | \(0.451274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75216 | 0.0687784 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.9159 | 0.779370 | 0.389685 | − | 0.920948i | \(-0.372584\pi\) | ||||
0.389685 | + | 0.920948i | \(0.372584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.5357i | 2.24811i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.4456i | 1.53658i | 0.640101 | + | 0.768291i | \(0.278892\pi\) | ||||
−0.640101 | + | 0.768291i | \(0.721108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 35.8650i | − 1.39499i | −0.716591 | − | 0.697494i | \(-0.754298\pi\) | ||||
0.716591 | − | 0.697494i | \(-0.245702\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 12.0946i | − 0.469007i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.6631 | 1.76808 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.76420 | 0.183920 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5668 | 1.17827 | 0.589133 | − | 0.808036i | \(-0.299470\pi\) | ||||
0.589133 | + | 0.808036i | \(0.299470\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.14804 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 4.02539i | − 0.154480i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.07293i | 0.0793186i | 0.999213 | + | 0.0396593i | \(0.0126273\pi\) | ||||
−0.999213 | + | 0.0396593i | \(0.987373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 31.6013i | − 1.20742i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 46.8717i | − 1.78567i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.7325 | −1.32129 | −0.660644 | − | 0.750700i | \(-0.729717\pi\) | ||||
−0.660644 | + | 0.750700i | \(0.729717\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −57.1460 | −2.16767 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.0518 | −1.89585 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.1113 | −1.13729 | −0.568643 | − | 0.822584i | \(-0.692531\pi\) | ||||
−0.568643 | + | 0.822584i | \(0.692531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6521i | 0.401752i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.2008i | 0.534077i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 30.7194i | − 1.15369i | −0.816853 | − | 0.576846i | \(-0.804283\pi\) | ||||
0.816853 | − | 0.576846i | \(-0.195717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 5.61102i | − 0.210135i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.3811 | 1.32318 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.93357 | −0.0721099 | −0.0360549 | − | 0.999350i | \(-0.511479\pi\) | ||||
−0.0360549 | + | 0.999350i | \(0.511479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.30631 | −0.197617 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 88.8671 | 3.30044 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 21.4593i | − 0.795881i | −0.917411 | − | 0.397940i | \(-0.869725\pi\) | ||||
0.917411 | − | 0.397940i | \(-0.130275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.7344i | 0.544970i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.43101i | − 0.274471i | −0.990538 | − | 0.137235i | \(-0.956178\pi\) | ||||
0.990538 | − | 0.137235i | \(-0.0438217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.7592i | 1.16987i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.48141 | 0.238423 | 0.119211 | − | 0.992869i | \(-0.461963\pi\) | ||||
0.119211 | + | 0.992869i | \(0.461963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.4752 | 1.85176 | 0.925879 | − | 0.377821i | \(-0.123327\pi\) | ||||
0.925879 | + | 0.377821i | \(0.123327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.9400 | 1.20683 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.3669 | 0.488417 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.8254i | 1.27080i | 0.772185 | + | 0.635398i | \(0.219164\pi\) | ||||
−0.772185 | + | 0.635398i | \(0.780836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 54.7189i | 1.99142i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6422i | 0.568524i | 0.958747 | + | 0.284262i | \(0.0917485\pi\) | ||||
−0.958747 | + | 0.284262i | \(0.908251\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 8.77808i | − 0.318205i | −0.987262 | − | 0.159103i | \(-0.949140\pi\) | ||||
0.987262 | − | 0.159103i | \(-0.0508600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.91832 | 0.214257 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.95837 | 0.142928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.4092 | 0.735975 | 0.367988 | − | 0.929831i | \(-0.380047\pi\) | ||||
0.367988 | + | 0.929831i | \(0.380047\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.204759 | 0.00736468 | 0.00368234 | − | 0.999993i | \(-0.498828\pi\) | ||||
0.00368234 | + | 0.999993i | \(0.498828\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 10.9199i | − 0.392254i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 28.5576i | − 1.02318i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 9.15062i | − 0.327435i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 53.1205i | − 1.89595i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.9705 | −1.85255 | −0.926274 | − | 0.376850i | \(-0.877007\pi\) | ||||
−0.926274 | + | 0.376850i | \(0.877007\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.5535 | −0.659687 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.7630 | 0.382204 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.9252 | −0.599522 | −0.299761 | − | 0.954014i | \(-0.596907\pi\) | ||||
−0.299761 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 11.6448i | − 0.411962i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.3544i | 0.506557i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.4513i | 0.579832i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4440i | 0.367191i | 0.983002 | + | 0.183596i | \(0.0587737\pi\) | ||||
−0.983002 | + | 0.183596i | \(0.941226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.2976 | −0.537170 | −0.268585 | − | 0.963256i | \(-0.586556\pi\) | ||||
−0.268585 | + | 0.963256i | \(0.586556\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 80.5204 | 2.82051 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.40685 | −0.294118 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.7719 | −0.724946 | −0.362473 | − | 0.931994i | \(-0.618067\pi\) | ||||
−0.362473 | + | 0.931994i | \(0.618067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6.01697i | − 0.209738i | −0.994486 | − | 0.104869i | \(-0.966558\pi\) | ||||
0.994486 | − | 0.104869i | \(-0.0334424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 53.8903i | − 1.87395i | −0.349399 | − | 0.936974i | \(-0.613614\pi\) | ||||
0.349399 | − | 0.936974i | \(-0.386386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 5.69863i | − 0.197922i | −0.995091 | − | 0.0989608i | \(-0.968448\pi\) | ||||
0.995091 | − | 0.0989608i | \(-0.0315519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.73497i | − 0.198705i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −49.5409 | −1.71443 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.43315 | 0.325668 | 0.162834 | − | 0.986653i | \(-0.447936\pi\) | ||||
0.162834 | + | 0.986653i | \(0.447936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 76.2553 | 2.62949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.8798 | 1.09670 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 6.76287i | − 0.232375i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 14.4893i | − 0.496686i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.49254i | 0.119582i | 0.998211 | + | 0.0597912i | \(0.0190435\pi\) | ||||
−0.998211 | + | 0.0597912i | \(0.980957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.2047i | 0.382745i | 0.981517 | + | 0.191372i | \(0.0612938\pi\) | ||||
−0.981517 | + | 0.191372i | \(0.938706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.4564 | −1.48271 | −0.741357 | − | 0.671111i | \(-0.765817\pi\) | ||||
−0.741357 | + | 0.671111i | \(0.765817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.8312 | −0.675063 | −0.337532 | − | 0.941314i | \(-0.609592\pi\) | ||||
−0.337532 | + | 0.941314i | \(0.609592\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.2412 | 1.67425 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0321 | −0.815235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 71.7483i | 2.43110i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.5356i | 0.457587i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.6652i | 1.37317i | 0.727051 | + | 0.686584i | \(0.240890\pi\) | ||||
−0.727051 | + | 0.686584i | \(0.759110\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.8298i | 1.57774i | 0.614562 | + | 0.788868i | \(0.289333\pi\) | ||||
−0.614562 | + | 0.788868i | \(0.710667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8388 | 0.633975 | 0.316988 | − | 0.948430i | \(-0.397329\pi\) | ||||
0.316988 | + | 0.948430i | \(0.397329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.52873 | −0.0513297 | −0.0256648 | − | 0.999671i | \(-0.508170\pi\) | ||||
−0.0256648 | + | 0.999671i | \(0.508170\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.76963 | −0.327663 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.64403 | 0.222334 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.8631i | 1.56646i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 12.9336i | − 0.431361i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.8048i | 1.92576i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 41.1222i | − 1.36695i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.5682 | 0.815773 | 0.407886 | − | 0.913033i | \(-0.366266\pi\) | ||||
0.407886 | + | 0.913033i | \(0.366266\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8864 | 0.493209 | 0.246604 | − | 0.969116i | \(-0.420685\pi\) | ||||
0.246604 | + | 0.969116i | \(0.420685\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.4198 | −0.874367 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.5661 | −0.514038 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.6464i | 1.83560i | 0.397038 | + | 0.917802i | \(0.370038\pi\) | ||||
−0.397038 | + | 0.917802i | \(0.629962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 20.6725i | − 0.680443i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 28.1982i | − 0.927153i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 29.3098i | − 0.961623i | −0.876824 | − | 0.480812i | \(-0.840342\pi\) | ||||
0.876824 | − | 0.480812i | \(-0.159658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.27215 | 0.107240 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.6340 | −1.42698 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.6626 | 0.413669 | 0.206834 | − | 0.978376i | \(-0.433684\pi\) | ||||
0.206834 | + | 0.978376i | \(0.433684\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6135 | −0.867575 | −0.433788 | − | 0.901015i | \(-0.642823\pi\) | ||||
−0.433788 | + | 0.901015i | \(0.642823\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.8447i | 1.26496i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.05029i | − 0.131617i | −0.997832 | − | 0.0658084i | \(-0.979037\pi\) | ||||
0.997832 | − | 0.0658084i | \(-0.0209626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.4286i | 1.05268i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 7.19155i | − 0.232957i | −0.993193 | − | 0.116479i | \(-0.962839\pi\) | ||||
0.993193 | − | 0.116479i | \(-0.0371606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6969 | 0.928611 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.54964 | 0.276082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.4107 | 0.948733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.6201 | −1.08227 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.3071i | 1.48914i | 0.667547 | + | 0.744568i | \(0.267344\pi\) | ||||
−0.667547 | + | 0.744568i | \(0.732656\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 22.1689i | − 0.711432i | −0.934594 | − | 0.355716i | \(-0.884237\pi\) | ||||
0.934594 | − | 0.355716i | \(-0.115763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 15.4607i | − 0.495647i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 13.0854i | − 0.418638i | −0.977847 | − | 0.209319i | \(-0.932875\pi\) | ||||
0.977847 | − | 0.209319i | \(-0.0671248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.84594 | 0.154877 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.9454 | 0.476684 | 0.238342 | − | 0.971181i | \(-0.423396\pi\) | ||||
0.238342 | + | 0.971181i | \(0.423396\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.3379 | 1.22155 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4352 | 0.363618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 25.6587i | − 0.815075i | −0.913188 | − | 0.407537i | \(-0.866388\pi\) | ||||
0.913188 | − | 0.407537i | \(-0.133612\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.6805i | 1.16285i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 10.1507i | − 0.321476i | −0.986997 | − | 0.160738i | \(-0.948613\pi\) | ||||
0.986997 | − | 0.160738i | \(-0.0513874\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.j.d.5615.4 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.45 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.33 | yes | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.46 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.15 | ✓ | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.16 | yes | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.34 | yes | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.15 | ✓ | 48 | 8.5 | even | 2 | ||
1512.2.j.d.323.16 | yes | 48 | 12.11 | even | 2 | ||
1512.2.j.d.323.33 | yes | 48 | 4.3 | odd | 2 | ||
1512.2.j.d.323.34 | yes | 48 | 24.5 | odd | 2 | ||
6048.2.j.d.5615.3 | 48 | 24.11 | even | 2 | inner | ||
6048.2.j.d.5615.4 | 48 | 1.1 | even | 1 | trivial | ||
6048.2.j.d.5615.45 | 48 | 3.2 | odd | 2 | inner | ||
6048.2.j.d.5615.46 | 48 | 8.3 | odd | 2 | inner |