Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1567,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4161798144.13 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 29x^{4} + 42x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.8 | ||
Root | \(1.05050 - 1.81952i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1567 |
Dual form | 3024.2.b.u.1567.1 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 3.63904i | 1.62743i | 0.581264 | + | 0.813715i | \(0.302558\pi\) | ||||
−0.581264 | + | 0.813715i | \(0.697442\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 2.44949i | −0.377964 | + | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.50734i | − | 0.454481i | −0.973839 | − | 0.227240i | \(-0.927030\pi\) | ||
0.973839 | − | 0.227240i | \(-0.0729703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.91359i | − | 1.64014i | −0.572267 | − | 0.820068i | \(-0.693936\pi\) | ||
0.572267 | − | 0.820068i | \(-0.306064\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.14639i | − | 1.24818i | −0.781352 | − | 0.624091i | \(-0.785469\pi\) | ||
0.781352 | − | 0.624091i | \(-0.214531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.24264 | 1.20274 | 0.601372 | − | 0.798969i | \(-0.294621\pi\) | ||||
0.601372 | + | 0.798969i | \(0.294621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.78543i | − | 1.83189i | −0.401305 | − | 0.915944i | \(-0.631443\pi\) | ||
0.401305 | − | 0.915944i | \(-0.368557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.24264 | −1.64853 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.91380 | −1.65525 | −0.827626 | − | 0.561281i | \(-0.810309\pi\) | ||||
−0.827626 | + | 0.561281i | \(0.810309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.24264 | 0.582395 | 0.291198 | − | 0.956663i | \(-0.405946\pi\) | ||||
0.291198 | + | 0.956663i | \(0.405946\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.91380 | − | 3.63904i | −1.50671 | − | 0.615111i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.65373i | 1.03914i | 0.854429 | + | 0.519569i | \(0.173907\pi\) | ||||
−0.854429 | + | 0.519569i | \(0.826093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.37769i | − | 1.43008i | −0.699081 | − | 0.715042i | \(-0.746407\pi\) | ||
0.699081 | − | 0.715042i | \(-0.253593\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.69222 | −0.538565 | −0.269283 | − | 0.963061i | \(-0.586787\pi\) | ||||
−0.269283 | + | 0.963061i | \(0.586787\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.6060 | −1.73157 | −0.865785 | − | 0.500416i | \(-0.833180\pi\) | ||||
−0.865785 | + | 0.500416i | \(0.833180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.48528 | 0.739635 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.91380 | 1.16048 | 0.580239 | − | 0.814446i | \(-0.302959\pi\) | ||||
0.580239 | + | 0.814446i | \(0.302959\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.46410i | 0.443533i | 0.975100 | + | 0.221766i | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.5198 | 2.66921 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.8126i | − | 1.32097i | −0.750841 | − | 0.660483i | \(-0.770352\pi\) | ||
0.750841 | − | 0.660483i | \(-0.229648\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.63904i | 0.431875i | 0.976407 | + | 0.215938i | \(0.0692808\pi\) | ||||
−0.976407 | + | 0.215938i | \(0.930719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.420266i | − | 0.0491884i | −0.999698 | − | 0.0245942i | \(-0.992171\pi\) | ||
0.999698 | − | 0.0245942i | \(-0.00782937\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.69222 | + | 1.50734i | 0.420767 | + | 0.171777i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.47871i | − | 0.503895i | −0.967741 | − | 0.251947i | \(-0.918929\pi\) | ||
0.967741 | − | 0.251947i | \(-0.0810710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.69222 | 0.405273 | 0.202637 | − | 0.979254i | \(-0.435049\pi\) | ||||
0.202637 | + | 0.979254i | \(0.435049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.7279 | 2.03133 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.9318i | − | 1.47677i | −0.674380 | − | 0.738385i | \(-0.735589\pi\) | ||
0.674380 | − | 0.738385i | \(-0.264411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4853 | + | 5.91359i | 1.51847 | + | 0.619913i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.0782i | 1.95738i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2621i | − | 1.34656i | −0.739388 | − | 0.673279i | \(-0.764885\pi\) | ||
0.739388 | − | 0.673279i | \(-0.235115\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.14639i | 0.512084i | 0.966666 | + | 0.256042i | \(0.0824186\pi\) | ||||
−0.966666 | + | 0.256042i | \(0.917581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7279 | 1.15559 | 0.577793 | − | 0.816183i | \(-0.303914\pi\) | ||||
0.577793 | + | 0.816183i | \(0.303914\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.14639i | 0.497520i | 0.968565 | + | 0.248760i | \(0.0800230\pi\) | ||||
−0.968565 | + | 0.248760i | \(0.919977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2426 | −1.07685 | −0.538425 | − | 0.842674i | \(-0.680980\pi\) | ||||
−0.538425 | + | 0.842674i | \(0.680980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.22158 | 0.491205 | 0.245603 | − | 0.969371i | \(-0.421014\pi\) | ||||
0.245603 | + | 0.969371i | \(0.421014\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.9706 | 2.98127 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.6060 | + | 5.14639i | 1.15559 | + | 0.471768i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.72792 | 0.793447 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.8001i | − | 1.05543i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.37769i | − | 0.832136i | −0.909334 | − | 0.416068i | \(-0.863408\pi\) | ||
0.909334 | − | 0.416068i | \(-0.136592\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.91380 | 0.778802 | 0.389401 | − | 0.921068i | \(-0.372682\pi\) | ||||
0.389401 | + | 0.921068i | \(0.372682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.24264 | + | 12.8418i | −0.454595 | + | 1.11352i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2982 | −1.39245 | −0.696226 | − | 0.717823i | \(-0.745139\pi\) | ||||
−0.696226 | + | 0.717823i | \(0.745139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.51472 | −0.128477 | −0.0642384 | − | 0.997935i | \(-0.520462\pi\) | ||||
−0.0642384 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.91380 | −0.745409 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 32.4377i | − | 2.69381i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6060 | 1.03273 | 0.516363 | − | 0.856370i | \(-0.327286\pi\) | ||||
0.516363 | + | 0.856370i | \(0.327286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.1610i | 1.47792i | 0.673747 | + | 0.738962i | \(0.264684\pi\) | ||||
−0.673747 | + | 0.738962i | \(0.735316\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8001i | 0.947808i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.01461i | 0.0809748i | 0.999180 | + | 0.0404874i | \(0.0128911\pi\) | ||||
−0.999180 | + | 0.0404874i | \(0.987109\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.5198 | + | 8.78543i | 1.69600 | + | 0.692389i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.44949i | 0.191859i | 0.995388 | + | 0.0959294i | \(0.0305823\pi\) | ||||
−0.995388 | + | 0.0959294i | \(0.969418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.8276 | −1.37954 | −0.689771 | − | 0.724028i | \(-0.742289\pi\) | ||||
−0.689771 | + | 0.724028i | \(0.742289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.9706 | −1.69004 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.0488i | 0.992085i | 0.868298 | + | 0.496042i | \(0.165214\pi\) | ||||
−0.868298 | + | 0.496042i | \(0.834786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.24264 | − | 20.1903i | 0.623085 | − | 1.52624i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6879i | 1.24731i | 0.781699 | + | 0.623655i | \(0.214353\pi\) | ||||
−0.781699 | + | 0.623655i | \(0.785647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.594346i | − | 0.0441774i | −0.999756 | − | 0.0220887i | \(-0.992968\pi\) | ||
0.999756 | − | 0.0220887i | \(-0.00703162\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.63904i | 0.267548i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.75736 | −0.567274 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.3269i | − | 1.47080i | −0.677631 | − | 0.735402i | \(-0.736993\pi\) | ||
0.677631 | − | 0.735402i | \(-0.263007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9706 | 1.07760 | 0.538802 | − | 0.842432i | \(-0.318877\pi\) | ||||
0.538802 | + | 0.842432i | \(0.318877\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0000 | −0.779769 | −0.389885 | − | 0.920864i | \(-0.627485\pi\) | ||||
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.91380 | − | 21.8343i | 0.625626 | − | 1.53246i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.2132 | −1.69112 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 7.90245i | − | 0.546624i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.43488i | − | 0.0987811i | −0.998780 | − | 0.0493905i | \(-0.984272\pi\) | ||
0.998780 | − | 0.0493905i | \(-0.0157279\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 34.1258 | 2.32736 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.24264 | + | 7.94282i | −0.220125 | + | 0.539193i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.4336 | −2.04719 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9706 | 1.20340 | 0.601699 | − | 0.798723i | \(-0.294491\pi\) | ||||
0.601699 | + | 0.798723i | \(0.294491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.6060 | −0.836691 | −0.418345 | − | 0.908288i | \(-0.637390\pi\) | ||||
−0.418345 | + | 0.908288i | \(0.637390\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.4215i | − | 0.820838i | −0.911897 | − | 0.410419i | \(-0.865383\pi\) | ||
0.911897 | − | 0.410419i | \(-0.134617\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.22158 | −0.342077 | −0.171039 | − | 0.985264i | \(-0.554712\pi\) | ||||
−0.171039 | + | 0.985264i | \(0.554712\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.4361i | − | 0.876477i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.89766i | − | 0.252119i | −0.992023 | − | 0.126059i | \(-0.959767\pi\) | ||
0.992023 | − | 0.126059i | \(-0.0402330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.75412i | − | 0.435071i | −0.976052 | − | 0.217536i | \(-0.930198\pi\) | ||
0.976052 | − | 0.217536i | \(-0.0698018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.8276 | − | 18.1952i | 1.13896 | − | 1.16245i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 31.0028i | − | 1.97266i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.38443 | −0.466101 | −0.233051 | − | 0.972465i | \(-0.574871\pi\) | ||||
−0.233051 | + | 0.972465i | \(0.574871\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2426 | −0.832558 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.0488i | − | 0.813964i | −0.913436 | − | 0.406982i | \(-0.866581\pi\) | ||
0.913436 | − | 0.406982i | \(-0.133419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | + | 2.44949i | −0.0621370 | + | 0.152204i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.75606i | 0.169946i | 0.996383 | + | 0.0849731i | \(0.0270804\pi\) | ||||
−0.996383 | + | 0.0849731i | \(0.972920\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 45.8739i | − | 2.81801i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.0929i | 1.34703i | 0.739175 | + | 0.673513i | \(0.235216\pi\) | ||||
−0.739175 | + | 0.673513i | \(0.764784\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.4245i | 0.749224i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.5147 | 0.631768 | 0.315884 | − | 0.948798i | \(-0.397699\pi\) | ||||
0.315884 | + | 0.948798i | \(0.397699\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.1354 | −0.843246 | −0.421623 | − | 0.906771i | \(-0.638539\pi\) | ||||
−0.421623 | + | 0.906771i | \(0.638539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.2982 | − | 6.65373i | −0.962054 | − | 0.392757i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.48528 | −0.557958 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.39511i | 0.373606i | 0.982397 | + | 0.186803i | \(0.0598126\pi\) | ||||
−0.982397 | + | 0.186803i | \(0.940187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.4377i | 1.88860i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −51.9534 | −3.00454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.9706 | + | 9.37769i | 1.32400 | + | 0.540521i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.6060 | −0.721818 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.2426 | −0.869943 | −0.434972 | − | 0.900444i | \(-0.643242\pi\) | ||||
−0.434972 | + | 0.900444i | \(0.643242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.91380 | −0.505455 | −0.252728 | − | 0.967537i | \(-0.581328\pi\) | ||||
−0.252728 | + | 0.967537i | \(0.581328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.94282i | 0.448954i | 0.974479 | + | 0.224477i | \(0.0720674\pi\) | ||||
−0.974479 | + | 0.224477i | \(0.927933\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.1354 | −0.793922 | −0.396961 | − | 0.917835i | \(-0.629935\pi\) | ||||
−0.396961 | + | 0.917835i | \(0.629935\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.4361i | 0.752279i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 26.9806i | − | 1.50124i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 48.7436i | 2.70381i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.69222 | − | 9.04405i | 0.203559 | − | 0.498615i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6544i | 1.30016i | 0.759865 | + | 0.650081i | \(0.225265\pi\) | ||||
−0.759865 | + | 0.650081i | \(0.774735\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39.3474 | 2.14978 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.02944 | −0.110550 | −0.0552752 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552752 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.88777i | − | 0.264687i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.9318i | − | 0.747899i | −0.927449 | − | 0.373949i | \(-0.878003\pi\) | ||
0.927449 | − | 0.373949i | \(-0.121997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.9867i | − | 0.588102i | −0.955790 | − | 0.294051i | \(-0.904996\pi\) | ||
0.955790 | − | 0.294051i | \(-0.0950035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.6831i | − | 0.675053i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2426 | −0.702846 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.9806i | − | 1.42398i | −0.702187 | − | 0.711992i | \(-0.747793\pi\) | ||
0.702187 | − | 0.711992i | \(-0.252207\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.48528 | 0.446594 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52937 | 0.0800507 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.0000 | 1.30499 | 0.652495 | − | 0.757793i | \(-0.273722\pi\) | ||||
0.652495 | + | 0.757793i | \(0.273722\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.6060 | − | 30.8783i | 0.654472 | − | 1.60312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.2132 | 1.04660 | 0.523300 | − | 0.852149i | \(-0.324701\pi\) | ||||
0.523300 | + | 0.852149i | \(0.324701\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 52.7126i | 2.71484i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.1464i | 0.880753i | 0.897813 | + | 0.440376i | \(0.145155\pi\) | ||||
−0.897813 | + | 0.440376i | \(0.854845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.0492 | −1.17776 | −0.588879 | − | 0.808221i | \(-0.700431\pi\) | ||||
−0.588879 | + | 0.808221i | \(0.700431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.48528 | + | 13.4361i | −0.279556 | + | 0.684769i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.22158 | 0.264745 | 0.132372 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132372 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.2132 | −2.28653 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.2982 | 0.820053 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.4231i | 1.57708i | 0.614983 | + | 0.788540i | \(0.289163\pi\) | ||||
−0.614983 | + | 0.788540i | \(0.710837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.69222 | −0.184381 | −0.0921903 | − | 0.995741i | \(-0.529387\pi\) | ||||
−0.0921903 | + | 0.995741i | \(0.529387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 19.1757i | − | 0.955207i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.50734i | − | 0.0747161i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.94282i | 0.392747i | 0.980529 | + | 0.196373i | \(0.0629165\pi\) | ||||
−0.980529 | + | 0.196373i | \(0.937084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.91380 | + | 21.8343i | −0.438619 | + | 1.07439i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4361i | 0.659554i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.22158 | 0.255091 | 0.127546 | − | 0.991833i | \(-0.459290\pi\) | ||||
0.127546 | + | 0.991833i | \(0.459290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.97056 | −0.485935 | −0.242968 | − | 0.970034i | \(-0.578121\pi\) | ||||
−0.242968 | + | 0.970034i | \(0.578121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.4198i | 2.05766i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.48528 | − | 3.46410i | −0.410632 | − | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.0342i | − | 0.483328i | −0.970360 | − | 0.241664i | \(-0.922307\pi\) | ||
0.970360 | − | 0.241664i | \(-0.0776932\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 34.4669i | − | 1.65638i | −0.560451 | − | 0.828188i | \(-0.689372\pi\) | ||
0.560451 | − | 0.828188i | \(-0.310628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 46.0588i | − | 2.20329i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.51472 | 0.0722936 | 0.0361468 | − | 0.999346i | \(-0.488492\pi\) | ||||
0.0361468 | + | 0.999346i | \(0.488492\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.8684i | 1.51411i | 0.653349 | + | 0.757057i | \(0.273364\pi\) | ||||
−0.653349 | + | 0.757057i | \(0.726636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.6985 | 2.40334 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0294 | 0.472268 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.5198 | + | 52.7126i | −1.00886 | + | 2.47120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.4853 | −0.724371 | −0.362185 | − | 0.932106i | \(-0.617969\pi\) | ||||
−0.362185 | + | 0.932106i | \(0.617969\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 29.3710i | − | 1.36794i | −0.729509 | − | 0.683971i | \(-0.760251\pi\) | ||
0.729509 | − | 0.683971i | \(-0.239749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.5667i | − | 0.816394i | −0.912894 | − | 0.408197i | \(-0.866158\pi\) | ||
0.912894 | − | 0.408197i | \(-0.133842\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.5103 | 1.92087 | 0.960433 | − | 0.278511i | \(-0.0898408\pi\) | ||||
0.960433 | + | 0.278511i | \(0.0898408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.4853 | + | 10.8126i | 1.22298 | + | 0.499278i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.1354 | −0.649946 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.2132 | −1.98276 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8276 | 0.814564 | 0.407282 | − | 0.913302i | \(-0.366477\pi\) | ||||
0.407282 | + | 0.913302i | \(0.366477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.91359i | − | 0.269637i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.2612 | 2.19143 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 29.5680i | − | 1.33985i | −0.742428 | − | 0.669926i | \(-0.766326\pi\) | ||
0.742428 | − | 0.669926i | \(-0.233674\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.65373i | 0.300278i | 0.988665 | + | 0.150139i | \(0.0479722\pi\) | ||||
−0.988665 | + | 0.150139i | \(0.952028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 45.8739i | 2.06605i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.91380 | − | 3.63904i | −0.399839 | − | 0.163233i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.7408i | − | 0.794186i | −0.917778 | − | 0.397093i | \(-0.870019\pi\) | ||
0.917778 | − | 0.397093i | \(-0.129981\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.2982 | −0.726702 | −0.363351 | − | 0.931652i | \(-0.618367\pi\) | ||||
−0.363351 | + | 0.931652i | \(0.618367\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.7279 | −0.833382 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5.14639i | − | 0.228110i | −0.993474 | − | 0.114055i | \(-0.963616\pi\) | ||
0.993474 | − | 0.114055i | \(-0.0363839\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.02944 | + | 0.420266i | 0.0455396 | + | 0.0185915i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.6784i | 1.88064i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.56543i | 0.244767i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 23.3416i | − | 1.02261i | −0.859398 | − | 0.511307i | \(-0.829161\pi\) | ||
0.859398 | − | 0.511307i | \(-0.170839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00000 | −0.306089 | −0.153044 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153044 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.6879i | − | 0.726935i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −54.1838 | −2.35582 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.3474 | 1.70433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.7279 | −0.809679 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.38443 | + | 7.53671i | −0.318070 | + | 0.324629i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.0000 | 1.07483 | 0.537417 | − | 0.843317i | \(-0.319400\pi\) | ||||
0.537417 | + | 0.843317i | \(0.319400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 40.9125i | − | 1.75250i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8564i | 0.592457i | 0.955117 | + | 0.296229i | \(0.0957290\pi\) | ||||
−0.955117 | + | 0.296229i | \(0.904271\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −46.7319 | −1.99084 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9706 | + | 4.47871i | 0.466516 | + | 0.190454i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0396 | 1.82365 | 0.911824 | − | 0.410581i | \(-0.134674\pi\) | ||||
0.911824 | + | 0.410581i | \(0.134674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.4558 | −2.34553 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.69222 | 0.155608 | 0.0778042 | − | 0.996969i | \(-0.475209\pi\) | ||||
0.0778042 | + | 0.996969i | \(0.475209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.0016i | 0.799402i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.2120 | −1.05694 | −0.528472 | − | 0.848951i | \(-0.677235\pi\) | ||||
−0.528472 | + | 0.848951i | \(0.677235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.3790i | 0.894681i | 0.894364 | + | 0.447341i | \(0.147629\pi\) | ||||
−0.894364 | + | 0.447341i | \(0.852371\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 72.4151i | 3.01992i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.840532i | − | 0.0349918i | −0.999847 | − | 0.0174959i | \(-0.994431\pi\) | ||
0.999847 | − | 0.0174959i | \(-0.00556940\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.69222 | + | 9.04405i | −0.153179 | + | 0.375210i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0016i | 0.786965i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.9905 | 0.825094 | 0.412547 | − | 0.910936i | \(-0.364639\pi\) | ||||
0.412547 | + | 0.910936i | \(0.364639\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.0000 | 0.700473 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.53671i | 0.309495i | 0.987954 | + | 0.154748i | \(0.0494565\pi\) | ||||
−0.987954 | + | 0.154748i | \(0.950544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.7279 | + | 45.8739i | −0.767770 | + | 1.88064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.0782i | − | 0.779514i | −0.920918 | − | 0.389757i | \(-0.872559\pi\) | ||
0.920918 | − | 0.389757i | \(-0.127441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.4654i | − | 0.630845i | −0.948951 | − | 0.315423i | \(-0.897854\pi\) | ||
0.948951 | − | 0.315423i | \(-0.102146\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 31.7613i | 1.29128i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.9411 | −1.70234 | −0.851169 | − | 0.524892i | \(-0.824106\pi\) | ||||
−0.851169 | + | 0.524892i | \(0.824106\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.8343i | 0.883320i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −40.2132 | −1.62420 | −0.812098 | − | 0.583521i | \(-0.801675\pi\) | ||||
−0.812098 | + | 0.583521i | \(0.801675\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1354 | −0.569069 | −0.284535 | − | 0.958666i | \(-0.591839\pi\) | ||||
−0.284535 | + | 0.958666i | \(0.591839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9411 | −1.16324 | −0.581621 | − | 0.813460i | \(-0.697581\pi\) | ||||
−0.581621 | + | 0.813460i | \(0.697581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.1258 | + | 13.9318i | 1.36722 | + | 0.558166i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.72792 | 0.0691169 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.14639i | − | 0.205200i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.75412i | − | 0.268877i | −0.990922 | − | 0.134439i | \(-0.957077\pi\) | ||
0.990922 | − | 0.134439i | \(-0.0429231\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.1258 | 1.35424 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.9706 | + | 29.5680i | −1.14786 | + | 1.17153i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.8181 | 1.49372 | 0.746862 | − | 0.664979i | \(-0.231560\pi\) | ||||
0.746862 | + | 0.664979i | \(0.231560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7279 | 0.541376 | 0.270688 | − | 0.962667i | \(-0.412749\pi\) | ||||
0.270688 | + | 0.962667i | \(0.412749\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.5690 | 1.75219 | 0.876094 | − | 0.482140i | \(-0.160140\pi\) | ||||
0.876094 | + | 0.482140i | \(0.160140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.4361i | − | 0.527415i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.52937 | 0.0598487 | 0.0299244 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299244 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.4377i | 1.26745i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 34.8831i | − | 1.35885i | −0.733744 | − | 0.679426i | \(-0.762229\pi\) | ||
0.733744 | − | 0.679426i | \(-0.237771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6705i | 1.69859i | 0.527921 | + | 0.849294i | \(0.322972\pi\) | ||||
−0.527921 | + | 0.849294i | \(0.677028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −46.7319 | − | 19.0782i | −1.81218 | − | 0.739821i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 78.3116i | 3.03224i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.22158 | 0.201577 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.4853 | 0.712555 | 0.356278 | − | 0.934380i | \(-0.384046\pi\) | ||||
0.356278 | + | 0.934380i | \(0.384046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.9465i | − | 0.651307i | −0.945489 | − | 0.325653i | \(-0.894416\pi\) | ||
0.945489 | − | 0.325653i | \(-0.105584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.4853 | + | 13.2621i | 1.24667 | + | 0.508951i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22.0929i | − | 0.845361i | −0.906279 | − | 0.422680i | \(-0.861089\pi\) | ||
0.906279 | − | 0.422680i | \(-0.138911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 59.3100i | − | 2.26612i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 74.5468i | 2.84001i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.9411 | −1.67160 | −0.835800 | − | 0.549035i | \(-0.814995\pi\) | ||||
−0.835800 | + | 0.549035i | \(0.814995\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.51213i | − | 0.209087i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.2426 | 1.29703 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.9630 | −1.20723 | −0.603613 | − | 0.797278i | \(-0.706273\pi\) | ||||
−0.603613 | + | 0.797278i | \(0.706273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.24264 | 0.197730 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.6060 | − | 5.14639i | −0.474098 | − | 0.193550i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7574 | 0.704447 | 0.352224 | − | 0.935916i | \(-0.385426\pi\) | ||||
0.352224 | + | 0.935916i | \(0.385426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 28.4880i | − | 1.06688i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 32.4377i | − | 1.21310i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.1354 | −0.527161 | −0.263580 | − | 0.964637i | \(-0.584903\pi\) | ||||
−0.263580 | + | 0.964637i | \(0.584903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.7279 | + | 28.7274i | −0.436771 | + | 1.06987i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 73.4733 | 2.72873 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.9706 | −1.00028 | −0.500141 | − | 0.865944i | \(-0.666719\pi\) | ||||
−0.500141 | + | 0.865944i | \(0.666719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.2612 | −1.78501 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 44.8592i | − | 1.65691i | −0.560053 | − | 0.828457i | \(-0.689219\pi\) | ||
0.560053 | − | 0.828457i | \(-0.310781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.2982 | −0.600353 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.4215i | − | 0.456933i | −0.973552 | − | 0.228467i | \(-0.926629\pi\) | ||
0.973552 | − | 0.228467i | \(-0.0733712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.90245i | − | 0.289913i | −0.989438 | − | 0.144956i | \(-0.953696\pi\) | ||
0.989438 | − | 0.144956i | \(-0.0463042\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.8739i | 1.68069i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.6060 | − | 5.14639i | −0.460614 | − | 0.188045i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.44949i | 0.0893832i | 0.999001 | + | 0.0446916i | \(0.0142305\pi\) | ||||
−0.999001 | + | 0.0446916i | \(0.985769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −66.0888 | −2.40522 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.4853 | 1.25339 | 0.626694 | − | 0.779265i | \(-0.284407\pi\) | ||||
0.626694 | + | 0.779265i | \(0.284407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.89766i | − | 0.141290i | −0.997502 | − | 0.0706451i | \(-0.977494\pi\) | ||
0.997502 | − | 0.0706451i | \(-0.0225058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.2426 | − | 27.5387i | 0.407011 | − | 0.996969i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 52.7126i | − | 1.90334i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.0905i | − | 1.33752i | −0.743479 | − | 0.668759i | \(-0.766826\pi\) | ||
0.743479 | − | 0.668759i | \(-0.233174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 15.6978i | − | 0.564610i | −0.959325 | − | 0.282305i | \(-0.908901\pi\) | ||
0.959325 | − | 0.282305i | \(-0.0910990\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.7279 | −0.960095 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.8831i | 1.24982i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.48528 | 0.196279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.69222 | −0.131781 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.0294 | 0.749618 | 0.374809 | − | 0.927102i | \(-0.377708\pi\) | ||||
0.374809 | + | 0.927102i | \(0.377708\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.22158 | + | 12.7902i | −0.185658 | + | 0.454768i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.4853 | 0.727454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.0588i | 1.63149i | 0.578413 | + | 0.815744i | \(0.303672\pi\) | ||||
−0.578413 | + | 0.815744i | \(0.696328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.0016i | 0.672227i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.633484 | −0.0223552 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.9706 | + | 78.3116i | −1.12681 | + | 2.76012i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.2982 | 0.573015 | 0.286508 | − | 0.958078i | \(-0.407506\pi\) | ||||
0.286508 | + | 0.958078i | \(0.407506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.51472 | 0.298992 | 0.149496 | − | 0.988762i | \(-0.452235\pi\) | ||||
0.149496 | + | 0.988762i | \(0.452235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.91380 | −0.312237 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 49.1639i | − | 1.72003i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.5103 | −1.44872 | −0.724359 | − | 0.689423i | \(-0.757864\pi\) | ||||
−0.724359 | + | 0.689423i | \(0.757864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.7420i | 1.03674i | 0.855156 | + | 0.518371i | \(0.173461\pi\) | ||||
−0.855156 | + | 0.518371i | \(0.826539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 44.8101i | − | 1.55820i | −0.626899 | − | 0.779100i | \(-0.715676\pi\) | ||
0.626899 | − | 0.779100i | \(-0.284324\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8710i | 0.516492i | 0.966079 | + | 0.258246i | \(0.0831445\pi\) | ||||
−0.966079 | + | 0.258246i | \(0.916856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.2120 | + | 25.7319i | −0.873545 | + | 0.891558i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 64.8754i | − | 2.24511i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.0767 | 0.382408 | 0.191204 | − | 0.981550i | \(-0.438761\pi\) | ||||
0.191204 | + | 0.981550i | \(0.438761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.4558 | 1.73986 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 79.9518i | − | 2.75043i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.72792 | + | 21.3790i | −0.299895 | + | 0.734590i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.78543i | − | 0.301161i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.9298i | 0.887819i | 0.896072 | + | 0.443909i | \(0.146409\pi\) | ||||
−0.896072 | + | 0.443909i | \(0.853591\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.65373i | 0.227287i | 0.993522 | + | 0.113643i | \(0.0362522\pi\) | ||||
−0.993522 | + | 0.113643i | \(0.963748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.2426 | −0.724790 | −0.362395 | − | 0.932025i | \(-0.618041\pi\) | ||||
−0.362395 | + | 0.932025i | \(0.618041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.4832i | − | 0.833418i | −0.909040 | − | 0.416709i | \(-0.863183\pi\) | ||
0.909040 | − | 0.416709i | \(-0.136817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.4853 | −1.61455 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.75095 | −0.229010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −63.9411 | −2.16656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.9043 | + | 11.8001i | 0.977142 | + | 0.398917i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5147 | −0.658965 | −0.329483 | − | 0.944162i | \(-0.606874\pi\) | ||||
−0.329483 | + | 0.944162i | \(0.606874\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.15117i | 0.308311i | 0.988047 | + | 0.154155i | \(0.0492656\pi\) | ||||
−0.988047 | + | 0.154155i | \(0.950734\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.52255i | − | 0.253154i | −0.991957 | − | 0.126577i | \(-0.959601\pi\) | ||
0.991957 | − | 0.126577i | \(-0.0403991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.7906 | 1.67180 | 0.835902 | − | 0.548878i | \(-0.184945\pi\) | ||||
0.835902 | + | 0.548878i | \(0.184945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.9706 | + | 9.37769i | 0.770408 | + | 0.314518i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.3570 | −0.647756 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −60.7279 | −2.02991 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.9043 | −0.964011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 64.8754i | 2.16131i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.16285 | 0.0718956 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9149i | 0.594853i | 0.954745 | + | 0.297426i | \(0.0961283\pi\) | ||||
−0.954745 | + | 0.297426i | \(0.903872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.2294i | 0.935281i | 0.883919 | + | 0.467640i | \(0.154896\pi\) | ||||
−0.883919 | + | 0.467640i | \(0.845104\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.56543i | − | 0.184189i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.91380 | + | 21.8343i | −0.294360 | + | 0.721031i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 33.6985i | − | 1.11161i | −0.831312 | − | 0.555806i | \(-0.812410\pi\) | ||
0.831312 | − | 0.555806i | \(-0.187590\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.5198 | 0.708333 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.24264 | −0.271016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.9806i | 0.885206i | 0.896718 | + | 0.442603i | \(0.145945\pi\) | ||||
−0.896718 | + | 0.442603i | \(0.854055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.2132 | − | 25.6836i | −0.859103 | − | 0.841746i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 28.2294i | − | 0.923199i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1026i | 0.460712i | 0.973106 | + | 0.230356i | \(0.0739890\pi\) | ||||
−0.973106 | + | 0.230356i | \(0.926011\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.90245i | − | 0.257612i | −0.991670 | − | 0.128806i | \(-0.958885\pi\) | ||
0.991670 | − | 0.128806i | \(-0.0411145\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.4558 | 1.90358 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.15117i | 0.297373i | 0.988884 | + | 0.148687i | \(0.0475045\pi\) | ||||
−0.988884 | + | 0.148687i | \(0.952495\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.48528 | −0.0806756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.9630 | 1.03538 | 0.517691 | − | 0.855567i | \(-0.326792\pi\) | ||||
0.517691 | + | 0.855567i | \(0.326792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 73.9706 | 2.39363 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.2982 | − | 39.9224i | 0.526297 | − | 1.28916i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4853 | −0.660816 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.4785i | 1.75373i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6251i | 0.695418i | 0.937603 | + | 0.347709i | \(0.113040\pi\) | ||||
−0.937603 | + | 0.347709i | \(0.886960\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.7414 | 0.858172 | 0.429086 | − | 0.903264i | \(-0.358836\pi\) | ||||
0.429086 | + | 0.903264i | \(0.358836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.51472 | − | 3.71029i | 0.0485596 | − | 0.118946i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.6552 | 1.14071 | 0.570356 | − | 0.821398i | \(-0.306805\pi\) | ||||
0.570356 | + | 0.821398i | \(0.306805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.0000 | −0.671163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.9534 | −1.65706 | −0.828529 | − | 0.559947i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559947i | \(0.810822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −82.3871 | −2.61976 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 37.6849i | − | 1.19710i | −0.801086 | − | 0.598549i | \(-0.795744\pi\) | ||
0.801086 | − | 0.598549i | \(-0.204256\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 40.0295i | − | 1.26902i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.4815i | 1.12371i | 0.827235 | + | 0.561856i | \(0.189912\pi\) | ||||
−0.827235 | + | 0.561856i | \(0.810088\pi\) | |||||||
\(998\) | 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 | 3024.2.b.u.1567.8 | yes | 8 | |
3.2 | odd | 2 | inner | 3024.2.b.u.1567.2 | yes | 8 | |
4.3 | odd | 2 | 3024.2.b.v.1567.7 | yes | 8 | ||
7.6 | odd | 2 | 3024.2.b.v.1567.2 | yes | 8 | ||
12.11 | even | 2 | 3024.2.b.v.1567.1 | yes | 8 | ||
21.20 | even | 2 | 3024.2.b.v.1567.8 | yes | 8 | ||
28.27 | even | 2 | inner | 3024.2.b.u.1567.1 | ✓ | 8 | |
84.83 | odd | 2 | inner | 3024.2.b.u.1567.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3024.2.b.u.1567.1 | ✓ | 8 | 28.27 | even | 2 | inner | |
3024.2.b.u.1567.2 | yes | 8 | 3.2 | odd | 2 | inner | |
3024.2.b.u.1567.7 | yes | 8 | 84.83 | odd | 2 | inner | |
3024.2.b.u.1567.8 | yes | 8 | 1.1 | even | 1 | trivial | |
3024.2.b.v.1567.1 | yes | 8 | 12.11 | even | 2 | ||
3024.2.b.v.1567.2 | yes | 8 | 7.6 | odd | 2 | ||
3024.2.b.v.1567.7 | yes | 8 | 4.3 | odd | 2 | ||
3024.2.b.v.1567.8 | yes | 8 | 21.20 | even | 2 |