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 | 1567.5 | ||
Root | \(-0.629640 + 1.09057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1567 |
Dual form | 3024.2.b.v.1567.4 |
$q$-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 | ||||||||
\(5\) | 2.18114i | 0.975434i | 0.873002 | + | 0.487717i | \(0.162170\pi\) | ||||
−0.873002 | + | 0.487717i | \(0.837830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.26573i | − | 1.58768i | −0.608128 | − | 0.793839i | \(-0.708079\pi\) | ||
0.608128 | − | 0.793839i | \(-0.291921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.01461i | 0.281403i | 0.990052 | + | 0.140701i | \(0.0449357\pi\) | ||||
−0.990052 | + | 0.140701i | \(0.955064\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.08459i | 0.748124i | 0.927404 | + | 0.374062i | \(0.122035\pi\) | ||||
−0.927404 | + | 0.374062i | \(0.877965\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.24264 | 0.743913 | 0.371956 | − | 0.928250i | \(-0.378687\pi\) | ||||
0.371956 | + | 0.928250i | \(0.378687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.903457i | − | 0.188384i | −0.995554 | − | 0.0941919i | \(-0.969973\pi\) | ||
0.995554 | − | 0.0941919i | \(-0.0300267\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.242641 | 0.0485281 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.34267 | −0.992109 | −0.496055 | − | 0.868291i | \(-0.665218\pi\) | ||||
−0.496055 | + | 0.868291i | \(0.665218\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.24264 | 0.941606 | 0.470803 | − | 0.882238i | \(-0.343964\pi\) | ||||
0.470803 | + | 0.882238i | \(0.343964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.34267 | + | 2.18114i | 0.903077 | + | 0.368679i | ||||
\(36\) | 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 | ||||||||
\(41\) | − | 8.35032i | − | 1.30410i | −0.758175 | − | 0.652051i | \(-0.773909\pi\) | ||
0.758175 | − | 0.652051i | \(-0.226091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.47871i | − | 0.682997i | −0.939882 | − | 0.341499i | \(-0.889066\pi\) | ||
0.939882 | − | 0.341499i | \(-0.110934\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.8984 | −1.88142 | −0.940709 | − | 0.339214i | \(-0.889839\pi\) | ||||
−0.940709 | + | 0.339214i | \(0.889839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.55568 | 1.03785 | 0.518926 | − | 0.854819i | \(-0.326332\pi\) | ||||
0.518926 | + | 0.854819i | \(0.326332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4853 | 1.54868 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.34267 | −0.695557 | −0.347778 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347778 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.46410i | − | 0.443533i | −0.975100 | − | 0.221766i | \(-0.928818\pi\) | ||
0.975100 | − | 0.221766i | \(-0.0711822\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.21301 | −0.274490 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.88437i | 0.474551i | 0.971442 | + | 0.237276i | \(0.0762544\pi\) | ||||
−0.971442 | + | 0.237276i | \(0.923746\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.18114i | − | 0.258853i | −0.991589 | − | 0.129427i | \(-0.958686\pi\) | ||
0.991589 | − | 0.129427i | \(-0.0413137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 14.2767i | − | 1.67096i | −0.549522 | − | 0.835479i | \(-0.685190\pi\) | ||
0.549522 | − | 0.835479i | \(-0.314810\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.8984 | − | 5.26573i | −1.46990 | − | 0.600086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.37769i | − | 1.05507i | −0.849532 | − | 0.527536i | \(-0.823116\pi\) | ||
0.849532 | − | 0.527536i | \(-0.176884\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8984 | 1.41578 | 0.707889 | − | 0.706324i | \(-0.249648\pi\) | ||||
0.707889 | + | 0.706324i | \(0.249648\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.72792 | −0.729746 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.98805i | 0.422732i | 0.977407 | + | 0.211366i | \(0.0677913\pi\) | ||||
−0.977407 | + | 0.211366i | \(0.932209\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.48528 | + | 1.01461i | 0.260528 | + | 0.106360i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.07264i | 0.725638i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.33386i | − | 0.643106i | −0.946892 | − | 0.321553i | \(-0.895795\pi\) | ||
0.946892 | − | 0.321553i | \(-0.104205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.08459i | − | 0.306929i | −0.988154 | − | 0.153464i | \(-0.950957\pi\) | ||
0.988154 | − | 0.153464i | \(-0.0490430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7279 | 1.35265 | 0.676326 | − | 0.736602i | \(-0.263571\pi\) | ||||
0.676326 | + | 0.736602i | \(0.263571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.08459i | 0.298199i | 0.988822 | + | 0.149099i | \(0.0476375\pi\) | ||||
−0.988822 | + | 0.149099i | \(0.952363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.75736 | −0.264107 | −0.132054 | − | 0.991243i | \(-0.542157\pi\) | ||||
−0.132054 | + | 0.991243i | \(0.542157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.2410 | 1.71597 | 0.857986 | − | 0.513674i | \(-0.171716\pi\) | ||||
0.857986 | + | 0.513674i | \(0.171716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.97056 | 0.183756 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.55568 | + | 3.08459i | 0.692628 | + | 0.282764i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.7279 | −1.52072 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4349i | 1.02277i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.47871i | − | 0.397422i | −0.980058 | − | 0.198711i | \(-0.936325\pi\) | ||
0.980058 | − | 0.198711i | \(-0.0636754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.34267 | −0.466792 | −0.233396 | − | 0.972382i | \(-0.574984\pi\) | ||||
−0.233396 | + | 0.972382i | \(0.574984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.24264 | − | 7.94282i | 0.281173 | − | 0.688729i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4540 | 1.74751 | 0.873753 | − | 0.486370i | \(-0.161679\pi\) | ||||
0.873753 | + | 0.486370i | \(0.161679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4853 | 1.56790 | 0.783951 | − | 0.620823i | \(-0.213202\pi\) | ||||
0.783951 | + | 0.620823i | \(0.213202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.34267 | 0.446777 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 11.6531i | − | 0.967738i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.55568 | −0.618985 | −0.309493 | − | 0.950902i | \(-0.600159\pi\) | ||||
−0.309493 | + | 0.950902i | \(0.600159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.2328i | − | 0.914115i | −0.889437 | − | 0.457058i | \(-0.848903\pi\) | ||
0.889437 | − | 0.457058i | \(-0.151097\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.4349i | 0.918475i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.91359i | − | 0.471956i | −0.971758 | − | 0.235978i | \(-0.924171\pi\) | ||
0.971758 | − | 0.235978i | \(-0.0758293\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.21301 | − | 0.903457i | −0.174409 | − | 0.0712024i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.44949i | − | 0.191859i | −0.995388 | − | 0.0959294i | \(-0.969418\pi\) | ||
0.995388 | − | 0.0959294i | \(-0.0305823\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.6853 | 0.826857 | 0.413428 | − | 0.910537i | \(-0.364331\pi\) | ||||
0.413428 | + | 0.910537i | \(0.364331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9706 | 0.920813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9903i | 1.06366i | 0.846851 | + | 0.531831i | \(0.178496\pi\) | ||||
−0.846851 | + | 0.531831i | \(0.821504\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.242641 | − | 0.594346i | 0.0183419 | − | 0.0449283i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 16.1714i | − | 1.20871i | −0.796716 | − | 0.604354i | \(-0.793431\pi\) | ||
0.796716 | − | 0.604354i | \(-0.206569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1903i | 1.50073i | 0.661023 | + | 0.750365i | \(0.270122\pi\) | ||||
−0.661023 | + | 0.750365i | \(0.729878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.18114i | 0.160360i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.2426 | 1.18778 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3526i | 1.32794i | 0.747757 | + | 0.663972i | \(0.231131\pi\) | ||||
−0.747757 | + | 0.663972i | \(0.768869\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9706 | −1.36553 | −0.682765 | − | 0.730638i | \(-0.739223\pi\) | ||||
−0.682765 | + | 0.730638i | \(0.739223\pi\) | |||||||
\(194\) | 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 | \(-0.372515\pi\) | ||||
0.389885 | + | 0.920864i | \(0.372515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.34267 | + | 13.0868i | −0.374982 | + | 0.918515i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.2132 | 1.27207 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 17.0749i | − | 1.18109i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.36308i | 0.575738i | 0.957670 | + | 0.287869i | \(0.0929468\pi\) | ||||
−0.957670 | + | 0.287869i | \(0.907053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.76869 | 0.666219 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.24264 | − | 12.8418i | 0.355894 | − | 0.871758i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.12967 | −0.210524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9706 | 1.06947 | 0.534734 | − | 0.845020i | \(-0.320412\pi\) | ||||
0.534734 | + | 0.845020i | \(0.320412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.55568 | −0.501488 | −0.250744 | − | 0.968053i | \(-0.580675\pi\) | ||||
−0.250744 | + | 0.968053i | \(0.580675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2195i | 1.46831i | 0.678985 | + | 0.734153i | \(0.262420\pi\) | ||||
−0.678985 | + | 0.734153i | \(0.737580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.2410 | −1.19501 | −0.597505 | − | 0.801865i | \(-0.703841\pi\) | ||||
−0.597505 | + | 0.801865i | \(0.703841\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 28.1331i | − | 1.83520i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 28.5098i | − | 1.84415i | −0.387017 | − | 0.922073i | \(-0.626495\pi\) | ||
0.387017 | − | 0.922073i | \(-0.373505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 27.5387i | − | 1.77393i | −0.461841 | − | 0.886963i | \(-0.652811\pi\) | ||
0.461841 | − | 0.886963i | \(-0.347189\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.6853 | − | 10.9057i | 0.682662 | − | 0.696739i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.29002i | 0.209339i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.7967 | −1.62827 | −0.814137 | − | 0.580673i | \(-0.802789\pi\) | ||||
−0.814137 | + | 0.580673i | \(0.802789\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.75736 | −0.299093 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.9903i | − | 0.872690i | −0.899780 | − | 0.436345i | \(-0.856273\pi\) | ||
0.899780 | − | 0.436345i | \(-0.143727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | − | 2.44949i | 0.0621370 | − | 0.152204i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 20.1595i | − | 1.24309i | −0.783380 | − | 0.621543i | \(-0.786506\pi\) | ||
0.783380 | − | 0.621543i | \(-0.213494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4800i | 1.01236i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.6041i | − | 1.07334i | −0.843792 | − | 0.536671i | \(-0.819682\pi\) | ||
0.843792 | − | 0.536671i | \(-0.180318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.27768i | − | 0.0770470i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.4853 | 1.65143 | 0.825715 | − | 0.564087i | \(-0.190772\pi\) | ||||
0.825715 | + | 0.564087i | \(0.190772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.5837 | −1.40689 | −0.703443 | − | 0.710752i | \(-0.748355\pi\) | ||||
−0.703443 | + | 0.710752i | \(0.748355\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.4540 | − | 8.35032i | −1.20736 | − | 0.492904i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.48528 | 0.440311 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.3406i | 1.30515i | 0.757723 | + | 0.652576i | \(0.226312\pi\) | ||||
−0.757723 | + | 0.652576i | \(0.773688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.6531i | − | 0.678470i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.916658 | 0.0530117 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.9706 | − | 4.47871i | −0.632333 | − | 0.258149i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.55568 | 0.432637 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.75736 | 0.385663 | 0.192831 | − | 0.981232i | \(-0.438233\pi\) | ||||
0.192831 | + | 0.981232i | \(0.438233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.34267 | 0.302955 | 0.151478 | − | 0.988461i | \(-0.451597\pi\) | ||||
0.151478 | + | 0.988461i | \(0.451597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.8418i | − | 0.725861i | −0.931816 | − | 0.362931i | \(-0.881776\pi\) | ||
0.931816 | − | 0.362931i | \(-0.118224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.5837 | −1.32459 | −0.662296 | − | 0.749242i | \(-0.730418\pi\) | ||||
−0.662296 | + | 0.749242i | \(0.730418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.1331i | 1.57515i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0022i | 0.556539i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.246186i | 0.0136559i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.8984 | + | 31.5944i | −0.711109 | + | 1.74185i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.05845i | 0.223072i | 0.993760 | + | 0.111536i | \(0.0355771\pi\) | ||||
−0.993760 | + | 0.111536i | \(0.964423\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.47234 | −0.462893 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.9706 | −1.95944 | −0.979721 | − | 0.200368i | \(-0.935786\pi\) | ||||
−0.979721 | + | 0.200368i | \(0.935786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 27.6063i | − | 1.49497i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.98805i | − | 0.214090i | −0.994254 | − | 0.107045i | \(-0.965861\pi\) | ||
0.994254 | − | 0.107045i | \(-0.0341389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.5826i | 1.63705i | 0.574473 | + | 0.818524i | \(0.305207\pi\) | ||||
−0.574473 | + | 0.818524i | \(0.694793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.4132i | 1.56551i | 0.622330 | + | 0.782755i | \(0.286186\pi\) | ||||
−0.622330 | + | 0.782755i | \(0.713814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.75736 | 0.252494 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0022i | 0.527897i | 0.964537 | + | 0.263949i | \(0.0850250\pi\) | ||||
−0.964537 | + | 0.263949i | \(0.914975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.48528 | −0.446594 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.1394 | 1.62991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.0000 | −1.30499 | −0.652495 | − | 0.757793i | \(-0.726278\pi\) | ||||
−0.652495 | + | 0.757793i | \(0.726278\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.55568 | − | 18.5076i | 0.392271 | − | 0.960865i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.2132 | −1.15016 | −0.575078 | − | 0.818099i | \(-0.695028\pi\) | ||||
−0.575078 | + | 0.818099i | \(0.695028\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.42074i | − | 0.279182i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.1464i | − | 0.880753i | −0.897813 | − | 0.440376i | \(-0.854845\pi\) | ||
0.897813 | − | 0.440376i | \(-0.145155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9264 | 1.47807 | 0.739034 | − | 0.673668i | \(-0.235282\pi\) | ||||
0.739034 | + | 0.673668i | \(0.235282\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.4853 | − | 28.1331i | 0.585344 | − | 1.43379i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.2410 | 0.924857 | 0.462428 | − | 0.886657i | \(-0.346978\pi\) | ||||
0.462428 | + | 0.886657i | \(0.346978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.78680 | 0.140934 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.4540 | 1.02915 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5667i | 0.881647i | 0.897594 | + | 0.440824i | \(0.145314\pi\) | ||||
−0.897594 | + | 0.440824i | \(0.854686\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.8984 | 0.644113 | 0.322057 | − | 0.946720i | \(-0.395626\pi\) | ||||
0.322057 | + | 0.946720i | \(0.395626\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.31925i | 0.264970i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.26573i | − | 0.261013i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.8418i | − | 0.634986i | −0.948261 | − | 0.317493i | \(-0.897159\pi\) | ||
0.948261 | − | 0.317493i | \(-0.102841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.34267 | + | 13.0868i | −0.262896 | + | 0.643960i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.1331i | 1.38100i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.2410 | −0.891132 | −0.445566 | − | 0.895249i | \(-0.646998\pi\) | ||||
−0.445566 | + | 0.895249i | \(0.646998\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.9706 | 1.16825 | 0.584127 | − | 0.811662i | \(-0.301437\pi\) | ||||
0.584127 | + | 0.811662i | \(0.301437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.748448i | 0.0363051i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.48528 | − | 3.46410i | −0.410632 | − | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.5217i | 1.18117i | 0.806975 | + | 0.590585i | \(0.201103\pi\) | ||||
−0.806975 | + | 0.590585i | \(0.798897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.174080i | 0.00836574i | 0.999991 | + | 0.00418287i | \(0.00133145\pi\) | ||||
−0.999991 | + | 0.00418287i | \(0.998669\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.92959i | − | 0.140141i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.4853 | −0.882254 | −0.441127 | − | 0.897445i | \(-0.645421\pi\) | ||||
−0.441127 | + | 0.897445i | \(0.645421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 37.6086i | − | 1.78684i | −0.449225 | − | 0.893418i | \(-0.648300\pi\) | ||
0.449225 | − | 0.893418i | \(-0.351700\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.69848 | −0.412348 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.9706 | −2.07049 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.21301 | + | 5.42074i | −0.103747 | + | 0.254128i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.48528 | 0.0694785 | 0.0347393 | − | 0.999396i | \(-0.488940\pi\) | ||||
0.0347393 | + | 0.999396i | \(0.488940\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.2418i | 0.616734i | 0.951268 | + | 0.308367i | \(0.0997824\pi\) | ||||
−0.951268 | + | 0.308367i | \(0.900218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.4231i | 1.46036i | 0.683257 | + | 0.730178i | \(0.260563\pi\) | ||||
−0.683257 | + | 0.730178i | \(0.739437\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.5654 | 1.64577 | 0.822885 | − | 0.568208i | \(-0.192363\pi\) | ||||
0.822885 | + | 0.568208i | \(0.192363\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.51472 | + | 3.88437i | 0.439349 | + | 0.179363i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.5837 | −1.08438 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.786797 | 0.0361007 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6853 | −0.488226 | −0.244113 | − | 0.969747i | \(-0.578497\pi\) | ||||
−0.244113 | + | 0.969747i | \(0.578497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01461i | 0.0462623i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.8150 | 0.627307 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.07306i | − | 0.229882i | −0.993372 | − | 0.114941i | \(-0.963332\pi\) | ||
0.993372 | − | 0.114941i | \(-0.0366679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.35032i | 0.376845i | 0.982088 | + | 0.188422i | \(0.0603374\pi\) | ||||
−0.982088 | + | 0.188422i | \(0.939663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.4800i | − | 0.742221i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.34267 | − | 2.18114i | −0.239652 | − | 0.0978374i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.04384i | − | 0.136261i | −0.997676 | − | 0.0681304i | \(-0.978297\pi\) | ||
0.997676 | − | 0.0681304i | \(-0.0217034\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4540 | −0.912000 | −0.456000 | − | 0.889980i | \(-0.650718\pi\) | ||||
−0.456000 | + | 0.889980i | \(0.650718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.72792 | 0.299389 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.08459i | 0.136722i | 0.997661 | + | 0.0683611i | \(0.0217770\pi\) | ||||
−0.997661 | + | 0.0683611i | \(0.978223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.9706 | − | 14.2767i | −1.54701 | − | 0.631563i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.9425i | 1.31942i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 67.9193i | 2.98709i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.82109i | − | 0.342648i | −0.985215 | − | 0.171324i | \(-0.945195\pi\) | ||
0.985215 | − | 0.171324i | \(-0.0548045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.00000 | 0.306089 | 0.153044 | − | 0.988219i | \(-0.451092\pi\) | ||||
0.153044 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.1714i | 0.704438i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1838 | 0.964512 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.47234 | 0.366978 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.72792 | −0.290873 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.7967 | + | 26.3287i | −1.11114 | + | 1.13406i | ||||
\(540\) | 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 | ||||||||
\(545\) | − | 6.01418i | − | 0.257619i | ||||||
\(546\) | 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 | ||||||||
\(551\) | −17.3244 | −0.738043 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.9706 | − | 9.37769i | −0.976808 | − | 0.398780i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.42602 | −0.187536 | −0.0937681 | − | 0.995594i | \(-0.529891\pi\) | ||||
−0.0937681 | + | 0.995594i | \(0.529891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.54416 | 0.192197 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.8984 | 0.543601 | 0.271800 | − | 0.962354i | \(-0.412381\pi\) | ||||
0.271800 | + | 0.962354i | \(0.412381\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.7862i | 1.67382i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.1114 | 0.633501 | 0.316751 | − | 0.948509i | \(-0.397408\pi\) | ||||
0.316751 | + | 0.948509i | \(0.397408\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.9749i | 1.71475i | 0.514696 | + | 0.857373i | \(0.327905\pi\) | ||||
−0.514696 | + | 0.857373i | \(0.672095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.219215i | − | 0.00914191i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 28.5533i | − | 1.18869i | −0.804210 | − | 0.594346i | \(-0.797411\pi\) | ||
0.804210 | − | 0.594346i | \(-0.202589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8984 | − | 31.5944i | 0.535114 | − | 1.31076i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 39.7862i | − | 1.64778i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.3524 | 1.37660 | 0.688300 | − | 0.725426i | \(-0.258357\pi\) | ||||
0.688300 | + | 0.725426i | \(0.258357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.0000 | 0.700473 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 26.3287i | − | 1.08119i | −0.841284 | − | 0.540594i | \(-0.818199\pi\) | ||
0.841284 | − | 0.540594i | \(-0.181801\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.72792 | + | 16.4800i | −0.275818 | + | 0.675613i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.07264i | − | 0.288980i | −0.989506 | − | 0.144490i | \(-0.953846\pi\) | ||
0.989506 | − | 0.144490i | \(-0.0461542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.9603i | 1.63001i | 0.579452 | + | 0.815007i | \(0.303267\pi\) | ||||
−0.579452 | + | 0.815007i | \(0.696733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 36.4859i | − | 1.48336i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9411 | −1.05292 | −0.526459 | − | 0.850201i | \(-0.676481\pi\) | ||||
−0.526459 | + | 0.850201i | \(0.676481\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 13.0868i | − | 0.529436i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.21320 | 0.0893904 | 0.0446952 | − | 0.999001i | \(-0.485768\pi\) | ||||
0.0446952 | + | 0.999001i | \(0.485768\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.5837 | −0.949444 | −0.474722 | − | 0.880136i | \(-0.657451\pi\) | ||||
−0.474722 | + | 0.880136i | \(0.657451\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.9411 | −1.56518 | −0.782588 | − | 0.622540i | \(-0.786101\pi\) | ||||
−0.782588 | + | 0.622540i | \(0.786101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.76869 | + | 3.98805i | 0.391374 | + | 0.159778i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7279 | −0.949117 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.08459i | 0.122991i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.5387i | 1.09630i | 0.836380 | + | 0.548150i | \(0.184668\pi\) | ||||
−0.836380 | + | 0.548150i | \(0.815332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.76869 | 0.387659 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.97056 | − | 5.07306i | 0.196941 | − | 0.201002i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.6670 | −0.895294 | −0.447647 | − | 0.894210i | \(-0.647738\pi\) | ||||
−0.447647 | + | 0.894210i | \(0.647738\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7279 | 0.462504 | 0.231252 | − | 0.972894i | \(-0.425718\pi\) | ||||
0.231252 | + | 0.972894i | \(0.425718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.7134 | −1.05021 | −0.525105 | − | 0.851037i | \(-0.675974\pi\) | ||||
−0.525105 | + | 0.851037i | \(0.675974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.1331i | 1.10432i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.1394 | 1.21858 | 0.609289 | − | 0.792948i | \(-0.291455\pi\) | ||||
0.609289 | + | 0.792948i | \(0.291455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 11.6531i | − | 0.455324i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.0771i | 1.05477i | 0.849625 | + | 0.527387i | \(0.176828\pi\) | ||||
−0.849625 | + | 0.527387i | \(0.823172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8141i | 1.15964i | 0.814746 | + | 0.579818i | \(0.196876\pi\) | ||||
−0.814746 | + | 0.579818i | \(0.803124\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.3244 | + | 7.07264i | 0.671810 | + | 0.274265i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.82687i | 0.186897i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.2410 | −0.704187 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.51472 | 0.0583881 | 0.0291941 | − | 0.999574i | \(-0.490706\pi\) | ||||
0.0291941 | + | 0.999574i | \(0.490706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.5195i | 0.558030i | 0.960287 | + | 0.279015i | \(0.0900080\pi\) | ||||
−0.960287 | + | 0.279015i | \(0.909992\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.5147 | − | 6.33386i | −0.595400 | − | 0.243071i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.6041i | − | 0.673602i | −0.941576 | − | 0.336801i | \(-0.890655\pi\) | ||
0.941576 | − | 0.336801i | \(-0.109345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.6131i | 1.70458i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.66608i | 0.292055i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.9411 | −0.910763 | −0.455382 | − | 0.890296i | \(-0.650497\pi\) | ||||
−0.455382 | + | 0.890296i | \(0.650497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.3189i | 1.52938i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.7574 | 0.975630 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.2690 | −1.29432 | −0.647162 | − | 0.762353i | \(-0.724044\pi\) | ||||
−0.647162 | + | 0.762353i | \(0.724044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.24264 | 0.122299 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.55568 | − | 3.08459i | −0.284161 | − | 0.116008i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.2426 | 1.02312 | 0.511559 | − | 0.859248i | \(-0.329068\pi\) | ||||
0.511559 | + | 0.859248i | \(0.329068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.73650i | − | 0.177383i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6531i | 0.435801i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5837 | 0.879524 | 0.439762 | − | 0.898114i | \(-0.355063\pi\) | ||||
0.439762 | + | 0.898114i | \(0.355063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.7279 | − | 33.6264i | 0.511255 | − | 1.25231i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.29635 | −0.0481452 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.97056 | −0.258524 | −0.129262 | − | 0.991610i | \(-0.541261\pi\) | ||||
−0.129262 | + | 0.991610i | \(0.541261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8150 | 0.510967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5664i | 0.390278i | 0.980776 | + | 0.195139i | \(0.0625159\pi\) | ||||
−0.980776 | + | 0.195139i | \(0.937484\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.4540 | 0.753434 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 22.2195i | − | 0.817357i | −0.912678 | − | 0.408679i | \(-0.865990\pi\) | ||
0.912678 | − | 0.408679i | \(-0.134010\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0749i | 0.626416i | 0.949684 | + | 0.313208i | \(0.101404\pi\) | ||||
−0.949684 | + | 0.313208i | \(0.898596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.4800i | − | 0.603780i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.55568 | + | 3.08459i | 0.276079 | + | 0.112709i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.44949i | − | 0.0893832i | −0.999001 | − | 0.0446916i | \(-0.985769\pi\) | ||
0.999001 | − | 0.0446916i | \(-0.0142305\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.5004 | 0.891659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.5147 | 0.636583 | 0.318292 | − | 0.947993i | \(-0.396891\pi\) | ||||
0.318292 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.5098i | 1.03348i | 0.856143 | + | 0.516740i | \(0.172854\pi\) | ||||
−0.856143 | + | 0.516740i | \(0.827146\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.75736 | + | 6.75412i | −0.0998231 | + | 0.244516i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.42074i | − | 0.195732i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.1915i | 1.16086i | 0.814312 | + | 0.580428i | \(0.197115\pi\) | ||||
−0.814312 | + | 0.580428i | \(0.802885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.9447i | 1.43671i | 0.695676 | + | 0.718356i | \(0.255105\pi\) | ||||
−0.695676 | + | 0.718356i | \(0.744895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.27208 | 0.0456944 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 27.0771i | − | 0.970138i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4853 | −0.410976 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.8984 | 0.460362 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.9706 | −1.95949 | −0.979744 | − | 0.200252i | \(-0.935824\pi\) | ||||
−0.979744 | + | 0.200252i | \(0.935824\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.2410 | − | 44.6812i | 0.648576 | − | 1.58868i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.51472 | 0.124811 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.92959i | 0.103771i | 0.998653 | + | 0.0518856i | \(0.0165231\pi\) | ||||
−0.998653 | + | 0.0518856i | \(0.983477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 39.7862i | − | 1.40753i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −75.1771 | −2.65294 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.97056 | − | 4.82687i | 0.0694532 | − | 0.170125i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.4540 | −0.719126 | −0.359563 | − | 0.933121i | \(-0.617074\pi\) | ||||
−0.359563 | + | 0.933121i | \(0.617074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.4853 | −0.894909 | −0.447455 | − | 0.894307i | \(-0.647669\pi\) | ||||
−0.447455 | + | 0.894307i | \(0.647669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.34267 | 0.187146 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.5229i | − | 0.508091i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.5654 | 1.24124 | 0.620620 | − | 0.784111i | \(-0.286881\pi\) | ||||
0.620620 | + | 0.784111i | \(0.286881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.5400i | 1.37828i | 0.724629 | + | 0.689139i | \(0.242011\pi\) | ||||
−0.724629 | + | 0.689139i | \(0.757989\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.4956i | − | 0.782249i | −0.920338 | − | 0.391125i | \(-0.872086\pi\) | ||
0.920338 | − | 0.391125i | \(-0.127914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 19.7700i | − | 0.686640i | −0.939218 | − | 0.343320i | \(-0.888448\pi\) | ||
0.939218 | − | 0.343320i | \(-0.111552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.1114 | − | 15.4230i | 0.523578 | − | 0.534374i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.3062i | 0.806545i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.6951 | 1.33590 | 0.667951 | − | 0.744205i | \(-0.267172\pi\) | ||||
0.667951 | + | 0.744205i | \(0.267172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.455844 | −0.0157188 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.1094i | 0.898192i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.7279 | + | 40.9749i | −0.574778 | + | 1.40791i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.903457i | − | 0.0309701i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8580i | 1.12504i | 0.826785 | + | 0.562518i | \(0.190167\pi\) | ||||
−0.826785 | + | 0.562518i | \(0.809833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.35032i | − | 0.285242i | −0.989777 | − | 0.142621i | \(-0.954447\pi\) | ||
0.989777 | − | 0.142621i | \(-0.0455529\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7574 | 0.435275 | 0.217638 | − | 0.976030i | \(-0.430165\pi\) | ||||
0.217638 | + | 0.976030i | \(0.430165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 40.8482i | − | 1.39049i | −0.718774 | − | 0.695244i | \(-0.755296\pi\) | ||
0.718774 | − | 0.695244i | \(-0.244704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.5147 | −1.03753 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.3804 | −1.67512 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.94113 | −0.133540 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.0097 | + | 11.4349i | 0.946901 | + | 0.386571i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.4853 | −1.23202 | −0.616010 | − | 0.787738i | \(-0.711252\pi\) | ||||
−0.616010 | + | 0.787738i | \(0.711252\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.5001i | 1.43186i | 0.698170 | + | 0.715932i | \(0.253998\pi\) | ||||
−0.698170 | + | 0.715932i | \(0.746002\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 27.1185i | − | 0.912609i | −0.889824 | − | 0.456305i | \(-0.849173\pi\) | ||
0.889824 | − | 0.456305i | \(-0.150827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.9544 | −1.50942 | −0.754710 | − | 0.656058i | \(-0.772223\pi\) | ||||
−0.754710 | + | 0.656058i | \(0.772223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9706 | − | 4.47871i | −0.367941 | − | 0.150211i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.8247 | −1.39961 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.2721 | 1.17902 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.0097 | −0.934176 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.3062i | 0.776442i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.0377 | −1.46386 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.5108i | 1.24552i | 0.782411 | + | 0.622762i | \(0.213990\pi\) | ||||
−0.782411 | + | 0.622762i | \(0.786010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.4274i | − | 1.17376i | −0.809673 | − | 0.586882i | \(-0.800355\pi\) | ||
0.809673 | − | 0.586882i | \(-0.199645\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 67.9193i | − | 2.24780i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.34267 | + | 13.0868i | −0.176431 | + | 0.432165i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.4831i | 1.79723i | 0.438736 | + | 0.898616i | \(0.355426\pi\) | ||||
−0.438736 | + | 0.898616i | \(0.644574\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.21301 | 0.0728420 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.242641 | 0.00797798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.0022i | 0.328162i | 0.986447 | + | 0.164081i | \(0.0524659\pi\) | ||||
−0.986447 | + | 0.164081i | \(0.947534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.2132 | − | 15.8856i | −0.531366 | − | 0.520631i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.4274i | 1.15860i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.8872i | 1.13972i | 0.821743 | + | 0.569858i | \(0.193002\pi\) | ||||
−0.821743 | + | 0.569858i | \(0.806998\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17.0749i | − | 0.556625i | −0.960491 | − | 0.278312i | \(-0.910225\pi\) | ||
0.960491 | − | 0.278312i | \(-0.0897751\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.54416 | −0.245672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 42.5001i | − | 1.38107i | −0.723301 | − | 0.690533i | \(-0.757376\pi\) | ||
0.723301 | − | 0.690533i | \(-0.242624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.4853 | 0.470212 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.2690 | 1.11008 | 0.555042 | − | 0.831823i | \(-0.312702\pi\) | ||||
0.555042 | + | 0.831823i | \(0.312702\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40.0294 | −1.29532 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.4540 | − | 50.1019i | 0.660495 | − | 1.61788i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.51472 | −0.113378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 41.3774i | − | 1.33199i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 7.76874i | − | 0.249826i | −0.992168 | − | 0.124913i | \(-0.960135\pi\) | ||
0.992168 | − | 0.124913i | \(-0.0398651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0280 | −0.514364 | −0.257182 | − | 0.966363i | \(-0.582794\pi\) | ||||
−0.257182 | + | 0.966363i | \(0.582794\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4853 | − | 45.2795i | 0.592611 | − | 1.45159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.3707 | 0.683709 | 0.341855 | − | 0.939753i | \(-0.388945\pi\) | ||||
0.341855 | + | 0.939753i | \(0.388945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.0000 | 0.671163 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.916658 | 0.0292368 | 0.0146184 | − | 0.999893i | \(-0.495347\pi\) | ||||
0.0146184 | + | 0.999893i | \(0.495347\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.04632 | −0.128666 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 52.3818i | − | 1.66396i | −0.554804 | − | 0.831981i | \(-0.687207\pi\) | ||
0.554804 | − | 0.831981i | \(-0.312793\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.9925i | 0.760614i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 6.08767i | − | 0.192798i | −0.995343 | − | 0.0963992i | \(-0.969267\pi\) | ||
0.995343 | − | 0.0963992i | \(-0.0307326\pi\) | |||||||
\(998\) | 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.v.1567.5 | yes | 8 | |
3.2 | odd | 2 | inner | 3024.2.b.v.1567.3 | yes | 8 | |
4.3 | odd | 2 | 3024.2.b.u.1567.6 | yes | 8 | ||
7.6 | odd | 2 | 3024.2.b.u.1567.3 | ✓ | 8 | ||
12.11 | even | 2 | 3024.2.b.u.1567.4 | yes | 8 | ||
21.20 | even | 2 | 3024.2.b.u.1567.5 | yes | 8 | ||
28.27 | even | 2 | inner | 3024.2.b.v.1567.4 | yes | 8 | |
84.83 | odd | 2 | inner | 3024.2.b.v.1567.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3024.2.b.u.1567.3 | ✓ | 8 | 7.6 | odd | 2 | ||
3024.2.b.u.1567.4 | yes | 8 | 12.11 | even | 2 | ||
3024.2.b.u.1567.5 | yes | 8 | 21.20 | even | 2 | ||
3024.2.b.u.1567.6 | yes | 8 | 4.3 | odd | 2 | ||
3024.2.b.v.1567.3 | yes | 8 | 3.2 | odd | 2 | inner | |
3024.2.b.v.1567.4 | yes | 8 | 28.27 | even | 2 | inner | |
3024.2.b.v.1567.5 | yes | 8 | 1.1 | even | 1 | trivial | |
3024.2.b.v.1567.6 | yes | 8 | 84.83 | odd | 2 | inner |