Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(433,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.433");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.w (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40282095616.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 8x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{U}(1)[D_{4}]$ |
Embedding invariants
Embedding label | 433.3 | ||
Root | \(1.03179 + 1.39119i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1120.433 |
Dual form | 1120.2.w.a.657.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | 0.359404 | + | 0.359404i | 0.207502 | + | 0.207502i | 0.803205 | − | 0.595703i | \(-0.203126\pi\) |
−0.595703 | + | 0.803205i | \(0.703126\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.39119 | + | 1.75060i | 0.622160 | + | 0.782890i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.87083 | − | 1.87083i | 0.707107 | − | 0.707107i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.74166i | − | 0.913886i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.48655 | + | 4.48655i | 1.24435 | + | 1.24435i | 0.958180 | + | 0.286166i | \(0.0923810\pi\) |
0.286166 | + | 0.958180i | \(0.407619\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.129171 | + | 1.12917i | −0.0333519 | + | 0.291551i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.62834i | − | 1.75006i | −0.484067 | − | 0.875031i | \(-0.660841\pi\) | ||
0.484067 | − | 0.875031i | \(-0.339159\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.34477 | 0.293452 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.741657 | − | 0.741657i | −0.154646 | − | 0.154646i | 0.625543 | − | 0.780189i | \(-0.284877\pi\) |
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.12917 | + | 4.87083i | −0.225834 | + | 0.974166i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.06358 | − | 2.06358i | 0.397135 | − | 0.397135i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.87775 | + | 0.672384i | 0.993520 | + | 0.113654i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.22497i | 0.516409i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.79953 | − | 3.81417i | 0.715472 | − | 0.568583i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.00000i | − | 1.00000i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.74166 | − | 2.74166i | 0.363141 | − | 0.363141i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.3495i | 1.99834i | 0.0407464 | + | 0.999170i | \(0.487026\pi\) | ||||
−0.0407464 | + | 0.999170i | \(0.512974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6307 | 1.87327 | 0.936636 | − | 0.350304i | \(-0.113922\pi\) | ||||
0.936636 | + | 0.350304i | \(0.113922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.12917 | − | 5.12917i | −0.646215 | − | 0.646215i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.61249 | + | 14.0958i | −0.200004 | + | 1.74837i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 0.533109i | − | 0.0641788i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.22497 | −0.857446 | −0.428723 | − | 0.903436i | \(-0.641036\pi\) | ||||
−0.428723 | + | 0.903436i | \(0.641036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.15642 | + | 1.34477i | −0.249002 | + | 0.155280i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.7417i | 1.77107i | 0.464568 | + | 0.885537i | \(0.346210\pi\) | ||||
−0.464568 | + | 0.885537i | \(0.653790\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.74166 | −0.749073 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.83132 | + | 5.83132i | 0.640071 | + | 0.640071i | 0.950573 | − | 0.310502i | \(-0.100497\pi\) |
−0.310502 | + | 0.950573i | \(0.600497\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.7871 | 1.75977 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.3541 | − | 10.6125i | 1.37011 | − | 1.08882i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1931 | −1.31276 | −0.656382 | − | 0.754429i | \(-0.727914\pi\) | ||||
−0.656382 | + | 0.754429i | \(0.727914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.87083 | + | 2.35414i | 0.182574 | + | 0.229741i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2250 | − | 11.2250i | −1.05596 | − | 1.05596i | −0.998339 | − | 0.0576178i | \(-0.981650\pi\) |
−0.0576178 | − | 0.998339i | \(-0.518350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.266555 | − | 2.33013i | 0.0248564 | − | 0.217286i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.3006 | − | 12.3006i | 1.13719 | − | 1.13719i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0977 | + | 4.79953i | −0.903170 | + | 0.429283i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2250 | − | 12.2250i | 1.08479 | − | 1.08479i | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) |
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.93881 | −0.431506 | −0.215753 | − | 0.976448i | \(-0.569221\pi\) | ||||
−0.215753 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.2713 | − | 14.2713i | −1.23748 | − | 1.23748i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.48331 | + | 0.741657i | 0.557995 | + | 0.0638317i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4833 | − | 16.4833i | 1.40826 | − | 1.40826i | 0.639343 | − | 0.768922i | \(-0.279207\pi\) |
0.768922 | − | 0.639343i | \(-0.220793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.4743i | − | 1.05806i | −0.848604 | − | 0.529028i | \(-0.822557\pi\) | ||
0.848604 | − | 0.529028i | \(-0.177443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.51583 | − | 2.51583i | 0.207502 | − | 0.207502i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.4499 | −1.82695 | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4277 | + | 16.4277i | −1.31108 | + | 1.31108i | −0.390455 | + | 0.920622i | \(0.627682\pi\) |
−0.920622 | + | 0.390455i | \(0.872318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.77503 | −0.218703 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.2583i | 2.09680i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.9143 | −1.59936 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.5525 | + | 13.5525i | 1.03038 | + | 1.03038i | 0.999524 | + | 0.0308546i | \(0.00982288\pi\) |
0.0308546 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.00000 | + | 11.2250i | 0.529150 | + | 0.848528i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.51669 | + | 5.51669i | −0.414659 | + | 0.414659i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.2910 | −1.43389 | −0.716944 | − | 0.697131i | \(-0.754460\pi\) | ||||
−0.716944 | + | 0.697131i | \(0.754460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.25834 | + | 5.25834i | 0.388708 | + | 0.388708i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 7.72119i | − | 0.561634i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.2250 | −1.96993 | −0.984965 | − | 0.172754i | \(-0.944733\pi\) | ||||
−0.984965 | + | 0.172754i | \(0.944733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | − | 6.00000i | −0.431889 | − | 0.431889i | 0.457381 | − | 0.889271i | \(-0.348787\pi\) |
−0.889271 | + | 0.457381i | \(0.848787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.64562 | + | 4.48655i | −0.404291 | + | 0.321289i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.03337 | + | 2.03337i | −0.141329 | + | 0.141329i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.59668 | − | 2.59668i | −0.177922 | − | 0.177922i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.3541 | + | 3.09580i | 0.890276 | + | 0.206387i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.0880 | + | 21.0880i | −1.39966 | + | 1.39966i | −0.598647 | + | 0.801013i | \(0.704295\pi\) |
−0.801013 | + | 0.598647i | \(0.795705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.9436i | − | 1.25183i | −0.779893 | − | 0.625913i | \(-0.784726\pi\) | ||
0.779893 | − | 0.625913i | \(-0.215274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.9666 | − | 17.9666i | −1.17703 | − | 1.17703i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) |
−0.196537 | − | 0.980497i | \(-0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.65762 | + | 5.65762i | −0.367502 | + | 0.367502i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.48331i | 0.484055i | 0.970269 | + | 0.242028i | \(0.0778125\pi\) | ||||
−0.970269 | + | 0.242028i | \(0.922188\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.61370 | − | 8.61370i | −0.552569 | − | 0.552569i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2542 | − | 9.73834i | 0.782890 | − | 0.622160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.2250 | − | 34.2250i | 2.17768 | − | 2.17768i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.19160i | 0.265632i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0367 | −0.696629 | −0.348315 | − | 0.937378i | \(-0.613246\pi\) | ||||
−0.348315 | + | 0.937378i | \(0.613246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2250 | + | 11.2250i | 0.692161 | + | 0.692161i | 0.962707 | − | 0.270546i | \(-0.0872041\pi\) |
−0.270546 | + | 0.962707i | \(0.587204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.8581i | 1.94242i | 0.238215 | + | 0.971212i | \(0.423438\pi\) | ||||
−0.238215 | + | 0.971212i | \(0.576562\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.03337 | + | 6.03337i | 0.365156 | + | 0.365156i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9666 | −0.892834 | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||||
−0.446417 | + | 0.894825i | \(0.647300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3985 | − | 18.3985i | −1.09368 | − | 1.09368i | −0.995133 | − | 0.0985428i | \(-0.968582\pi\) |
−0.0985428 | − | 0.995133i | \(-0.531418\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.61370 | + | 0.985363i | 0.510232 | + | 0.0583679i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 17.0000i | − | 1.00000i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.8654 | − | 17.8654i | −1.04371 | − | 1.04371i | −0.999000 | − | 0.0447054i | \(-0.985765\pi\) |
−0.0447054 | − | 0.999000i | \(-0.514235\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.8708 | + | 21.3541i | −1.56448 | + | 1.24329i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 6.65497i | − | 0.384867i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.74166 | − | 4.74166i | −0.272401 | − | 0.272401i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.3541 | + | 25.6125i | 1.16547 | + | 1.46657i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.452253 | + | 0.452253i | −0.0258115 | + | 0.0258115i | −0.719895 | − | 0.694083i | \(-0.755810\pi\) |
0.694083 | + | 0.719895i | \(0.255810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.84345 | − | 16.1148i | 0.103866 | − | 0.907964i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.9193 | + | 16.7871i | −1.49322 | + | 0.931184i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | − | 18.0000i | 0.980522 | − | 0.980522i | −0.0192914 | − | 0.999814i | \(-0.506141\pi\) |
0.999814 | + | 0.0192914i | \(0.00614103\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.06860i | − | 0.438226i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0958 | − | 13.0958i | −0.707107 | − | 0.707107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.933259 | − | 0.741657i | 0.0502450 | − | 0.0399295i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2224i | 0.600720i | 0.953826 | + | 0.300360i | \(0.0971069\pi\) | ||||
−0.953826 | + | 0.300360i | \(0.902893\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.5167 | 0.988348 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0513 | − | 12.6480i | −0.533469 | − | 0.671286i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.00000i | − | 0.316668i | −0.987386 | − | 0.158334i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158334i | \(-0.0506123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.1916 | −2.06272 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.95345 | + | 3.95345i | 0.207502 | + | 0.207502i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.35414 | − | 1.90420i | −0.276487 | − | 0.0983324i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.78741 | 0.450193 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.77503 | − | 1.77503i | −0.0895383 | − | 0.0895383i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.5573 | + | 21.8997i | −1.38656 | + | 1.10189i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.5842 | − | 18.5842i | 0.932713 | − | 0.932713i | −0.0651619 | − | 0.997875i | \(-0.520756\pi\) |
0.997875 | + | 0.0651619i | \(0.0207564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 10.2583i | − | 0.513559i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.2250 | 1.85893 | 0.929463 | − | 0.368915i | \(-0.120271\pi\) | ||||
0.929463 | + | 0.368915i | \(0.120271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.37894 | − | 11.8019i | −0.466043 | − | 0.586442i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8483 | 0.584436 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.7163 | + | 28.7163i | 1.41304 | + | 1.41304i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.09580 | + | 18.3208i | −0.102879 | + | 0.899331i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.48331 | − | 4.48331i | 0.219549 | − | 0.219549i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.8312i | 1.99474i | 0.0725002 | + | 0.997368i | \(0.476902\pi\) | ||||
−0.0725002 | + | 0.997368i | \(0.523098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.3716 | − | 27.3716i | 1.32460 | − | 1.32460i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.0000 | 0.867029 | 0.433515 | − | 0.901146i | \(-0.357273\pi\) | ||||
0.433515 | + | 0.901146i | \(0.357273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.65762 | + | 5.65762i | −0.270640 | + | 0.270640i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.1916 | −0.913886 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.9333i | 1.41264i | 0.707894 | + | 0.706319i | \(0.249646\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.06860 | − | 8.06860i | −0.379096 | − | 0.379096i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.3541 | + | 29.3875i | 1.09486 | + | 1.37771i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.74166 | + | 3.74166i | −0.175027 | + | 0.175027i | −0.789184 | − | 0.614157i | \(-0.789496\pi\) |
0.614157 | + | 0.789184i | \(0.289496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.9805 | 1.02373 | 0.511867 | − | 0.859064i | \(-0.328954\pi\) | ||||
0.511867 | + | 0.859064i | \(0.328954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | − | 24.0000i | −1.11537 | − | 1.11537i | −0.992411 | − | 0.122963i | \(-0.960760\pi\) |
−0.122963 | − | 0.992411i | \(-0.539240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.3397 | − | 30.3397i | 1.40395 | − | 1.40395i | 0.616949 | − | 0.787003i | \(-0.288368\pi\) |
0.787003 | − | 0.616949i | \(-0.211632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.8084 | −0.544102 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.1563 | + | 8.61370i | 1.70485 | + | 0.395224i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.997356 | − | 0.997356i | −0.0453813 | − | 0.0453813i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.77503 | + | 7.77503i | −0.352320 | + | 0.352320i | −0.860972 | − | 0.508652i | \(-0.830144\pi\) |
0.508652 | + | 0.860972i | \(0.330144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.5167 | + | 13.5167i | −0.606306 | + | 0.606306i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.3541 | − | 23.0958i | −0.816749 | − | 1.02775i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.79676 | + | 9.79676i | −0.435089 | + | 0.435089i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.88026i | 0.393611i | 0.980443 | + | 0.196805i | \(0.0630567\pi\) | ||||
−0.980443 | + | 0.196805i | \(0.936943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.7417 | − | 15.7417i | −0.695011 | − | 0.695011i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.74166i | 0.427611i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.7773 | + | 31.7773i | 1.38952 | + | 1.38952i | 0.826315 | + | 0.563209i | \(0.190433\pi\) |
0.563209 | + | 0.826315i | \(0.309567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.51847 | + | 6.55013i | −0.0662716 | + | 0.285871i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.8999i | − | 0.952169i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 42.0832 | 1.82625 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.93326 | − | 6.93326i | −0.297535 | − | 0.297535i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 40.1124i | − | 1.71196i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.4499 | + | 29.4499i | 1.25234 | + | 1.25234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.1832 | + | 28.1832i | 1.18778 | + | 1.18778i | 0.977679 | + | 0.210103i | \(0.0673798\pi\) |
0.210103 | + | 0.977679i | \(0.432620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.03430 | − | 35.2665i | 0.169724 | − | 1.48367i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.6125 | + | 12.6125i | −0.529675 | + | 0.529675i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.6749i | 1.32788i | 0.747785 | + | 0.663941i | \(0.231117\pi\) | ||||
−0.747785 | + | 0.663941i | \(0.768883\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.78477 | − | 9.78477i | −0.408764 | − | 0.408764i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.44994 | − | 2.77503i | 0.185576 | − | 0.115727i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 4.31285i | − | 0.179236i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.8188 | 0.905197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 38.6459 | + | 4.42088i | 1.59781 | + | 0.182781i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.4961 | + | 32.4961i | −1.34126 | + | 1.34126i | −0.446447 | + | 0.894810i | \(0.647311\pi\) |
−0.894810 | + | 0.446447i | \(0.852689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 41.6749i | − | 1.70279i | −0.524524 | − | 0.851395i | \(-0.675757\pi\) | ||
0.524524 | − | 0.851395i | \(-0.324243\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.3031 | + | 19.2566i | 0.622160 | + | 0.782890i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.6749 | − | 33.6749i | 1.35570 | − | 1.35570i | 0.476558 | − | 0.879143i | \(-0.341884\pi\) |
0.879143 | − | 0.476558i | \(-0.158116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.16145i | 0.328036i | 0.986457 | + | 0.164018i | \(0.0524456\pi\) | ||||
−0.986457 | + | 0.164018i | \(0.947554\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.06093 | −0.122831 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4499 | − | 11.0000i | −0.897998 | − | 0.440000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 50.1916 | 1.99810 | 0.999048 | − | 0.0436231i | \(-0.0138901\pi\) | ||||
0.999048 | + | 0.0436231i | \(0.0138901\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.4083 | + | 4.39371i | 1.52419 | + | 0.174359i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.4059 | − | 31.4059i | 1.24435 | − | 1.24435i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.8084i | 0.783608i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.7750 | −0.899560 | −0.449780 | − | 0.893140i | \(-0.648498\pi\) | ||||
−0.449780 | + | 0.893140i | \(0.648498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.4644 | − | 27.4644i | −1.08309 | − | 1.08309i | −0.996219 | − | 0.0868719i | \(-0.972313\pi\) |
−0.0868719 | − | 0.996219i | \(-0.527687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.87083 | − | 8.64586i | −0.268465 | − | 0.337822i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.4791 | −1.02992 | −0.514958 | − | 0.857215i | \(-0.672193\pi\) | ||||
−0.514958 | + | 0.857215i | \(0.672193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.12917 | − | 44.8375i | 0.198901 | − | 1.73872i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.44994 | + | 9.44994i | 0.364269 | + | 0.364269i | 0.865382 | − | 0.501113i | \(-0.167076\pi\) |
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.72119 | + | 12.3815i | 0.297189 | + | 0.476562i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.0218 | + | 20.0218i | −0.769500 | + | 0.769500i | −0.978018 | − | 0.208519i | \(-0.933136\pi\) |
0.208519 | + | 0.978018i | \(0.433136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.1582 | −0.580865 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.7871 | + | 5.92417i | 1.97868 | + | 0.226351i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.80840 | − | 6.80840i | 0.259757 | − | 0.259757i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6969 | 0.597140 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.8375 | − | 17.3541i | 0.828342 | − | 0.658280i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 12.9146i | − | 0.488474i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.6820 | + | 24.6820i | −0.928264 | + | 0.928264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 43.1582 | 1.61856 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.68953 | + | 2.68953i | −0.100442 | + | 0.100442i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.0334i | 0.519754i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.95847 | + | 9.95847i | 0.367825 | + | 0.367825i | 0.866683 | − | 0.498859i | \(-0.166247\pi\) |
−0.498859 | + | 0.866683i | \(0.666247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.90420 | + | 0.904199i | 0.291551 | + | 0.0333519i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.6012 | 0.903747 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.7417 | − | 30.7417i | −1.12780 | − | 1.12780i | −0.990534 | − | 0.137268i | \(-0.956168\pi\) |
−0.137268 | − | 0.990534i | \(-0.543832\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.9875 | − | 15.9875i | 0.584952 | − | 0.584952i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4499 | −0.819210 | −0.409605 | − | 0.912263i | \(-0.634333\pi\) | ||||
−0.409605 | + | 0.912263i | \(0.634333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.96663 | − | 3.96663i | −0.144552 | − | 0.144552i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −31.2322 | − | 39.3008i | −1.13666 | − | 1.43030i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −68.8665 | + | 68.8665i | −2.48663 | + | 2.48663i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.1223 | + | 25.1223i | 0.903587 | + | 0.903587i | 0.995744 | − | 0.0921578i | \(-0.0293764\pi\) |
−0.0921578 | + | 0.995744i | \(0.529376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −51.6125 | − | 5.90420i | −1.84213 | − | 0.210730i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9337 | − | 33.9337i | 1.20961 | − | 1.20961i | 0.238451 | − | 0.971154i | \(-0.423360\pi\) |
0.971154 | − | 0.238451i | \(-0.0766398\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.06860i | 0.287250i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42.0000 | −1.49335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.6415 | + | 65.6415i | 2.33100 | + | 2.33100i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.86562 | + | 9.86562i | −0.349458 | + | 0.349458i | −0.859908 | − | 0.510449i | \(-0.829479\pi\) |
0.510449 | + | 0.859908i | \(0.329479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.86060 | − | 4.85795i | −0.136068 | − | 0.171220i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.4499 | + | 11.4499i | −0.403057 | + | 0.403057i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.6749i | 0.410468i | 0.978713 | + | 0.205234i | \(0.0657956\pi\) | ||||
−0.978713 | + | 0.205234i | \(0.934204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.2103 | −1.62266 | −0.811332 | − | 0.584586i | \(-0.801257\pi\) | ||||
−0.811332 | + | 0.584586i | \(0.801257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 46.0246i | − | 1.60823i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.0000 | + | 36.0000i | 1.25488 | + | 1.25488i | 0.953506 | + | 0.301376i | \(0.0974458\pi\) |
0.301376 | + | 0.953506i | \(0.402554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.2564i | 0.807729i | 0.914819 | + | 0.403864i | \(0.132333\pi\) | ||||
−0.914819 | + | 0.403864i | \(0.867667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.37907 | − | 5.37907i | −0.185265 | − | 0.185265i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47.7183 | + | 37.9216i | −1.64156 | + | 1.30454i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.5791 | − | 20.5791i | 0.707107 | − | 0.707107i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.2250i | − | 0.453880i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.7406 | + | 20.7406i | 0.710144 | + | 0.710144i | 0.966565 | − | 0.256421i | \(-0.0825433\pi\) |
−0.256421 | + | 0.966565i | \(0.582543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.0958 | − | 36.6125i | −0.995055 | − | 1.25212i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 0.440260i | − | 0.0150215i | −0.999972 | − | 0.00751074i | \(-0.997609\pi\) | ||
0.999972 | − | 0.00751074i | \(-0.00239076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2250 | + | 11.2250i | 0.382102 | + | 0.382102i | 0.871859 | − | 0.489757i | \(-0.162914\pi\) |
−0.489757 | + | 0.871859i | \(0.662914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.87083 | + | 42.5791i | −0.165613 | + | 1.44773i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.10987 | − | 6.10987i | 0.207502 | − | 0.207502i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.91205 | + | 27.8703i | −0.335088 | + | 0.942187i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 12.8418i | − | 0.433142i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.3323 | − | 1.98272i | −0.582617 | − | 0.0666484i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 45.7417i | − | 1.53413i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.39182 | − | 2.39182i | 0.0798607 | − | 0.0798607i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.8375 | − | 33.7707i | −0.892107 | − | 1.12258i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.1710i | 1.19972i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.3832 | 1.73553 | 0.867766 | − | 0.496972i | \(-0.165555\pi\) | ||||
0.867766 | + | 0.496972i | \(0.165555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.88987 | + | 16.5206i | −0.0624772 | + | 0.546154i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.23966 | + | 9.23966i | −0.305121 | + | 0.305121i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.1582i | 1.75353i | 0.480921 | + | 0.876764i | \(0.340303\pi\) | ||||
−0.480921 | + | 0.876764i | \(0.659697\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.325084 | −0.0107119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.4152 | − | 32.4152i | −1.06696 | − | 1.06696i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.3984 | −1.75006 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.9267 | −1.30157 | −0.650787 | − | 0.759260i | \(-0.725561\pi\) | ||||
−0.650787 | + | 0.759260i | \(0.725561\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.5167 | − | 10.7417i | 0.439698 | − | 0.349426i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0334 | + | 12.0334i | 0.389799 | + | 0.389799i | 0.874616 | − | 0.484817i | \(-0.161114\pi\) |
−0.484817 | + | 0.874616i | \(0.661114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.8752 | − | 47.6599i | −1.22561 | − | 1.54224i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 61.6749i | − | 1.99159i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.15642 | − | 18.8507i | 0.0694178 | − | 0.606826i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7750 | + | 17.7750i | −0.571606 | + | 0.571606i | −0.932577 | − | 0.360971i | \(-0.882445\pi\) |
0.360971 | + | 0.932577i | \(0.382445\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9752 | 0.769402 | 0.384701 | − | 0.923041i | \(-0.374305\pi\) | ||||
0.384701 | + | 0.923041i | \(0.374305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.3373 | − | 23.3373i | −0.748159 | − | 0.748159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.7083 | − | 3.64155i | −0.503068 | − | 0.116623i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.9333 | + | 20.9333i | −0.669714 | + | 0.669714i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) |
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.80840 | −0.311574 | −0.155787 | − | 0.987791i | \(-0.549791\pi\) | ||||
−0.155787 | + | 0.987791i | \(0.549791\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.3642 | − | 14.3642i | 0.454918 | − | 0.454918i | −0.442065 | − | 0.896983i | \(-0.645754\pi\) |
0.896983 | + | 0.442065i | \(0.145754\pi\) | |||||||
\(998\) | 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 | 1120.2.w.a.433.3 | 8 | ||
4.3 | odd | 2 | 280.2.s.a.13.2 | ✓ | 8 | ||
5.2 | odd | 4 | inner | 1120.2.w.a.657.3 | 8 | ||
7.6 | odd | 2 | inner | 1120.2.w.a.433.2 | 8 | ||
8.3 | odd | 2 | 280.2.s.a.13.3 | yes | 8 | ||
8.5 | even | 2 | inner | 1120.2.w.a.433.2 | 8 | ||
20.7 | even | 4 | 280.2.s.a.237.2 | yes | 8 | ||
28.27 | even | 2 | 280.2.s.a.13.3 | yes | 8 | ||
35.27 | even | 4 | inner | 1120.2.w.a.657.2 | 8 | ||
40.27 | even | 4 | 280.2.s.a.237.3 | yes | 8 | ||
40.37 | odd | 4 | inner | 1120.2.w.a.657.2 | 8 | ||
56.13 | odd | 2 | CM | 1120.2.w.a.433.3 | 8 | ||
56.27 | even | 2 | 280.2.s.a.13.2 | ✓ | 8 | ||
140.27 | odd | 4 | 280.2.s.a.237.3 | yes | 8 | ||
280.27 | odd | 4 | 280.2.s.a.237.2 | yes | 8 | ||
280.237 | even | 4 | inner | 1120.2.w.a.657.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.s.a.13.2 | ✓ | 8 | 4.3 | odd | 2 | ||
280.2.s.a.13.2 | ✓ | 8 | 56.27 | even | 2 | ||
280.2.s.a.13.3 | yes | 8 | 8.3 | odd | 2 | ||
280.2.s.a.13.3 | yes | 8 | 28.27 | even | 2 | ||
280.2.s.a.237.2 | yes | 8 | 20.7 | even | 4 | ||
280.2.s.a.237.2 | yes | 8 | 280.27 | odd | 4 | ||
280.2.s.a.237.3 | yes | 8 | 40.27 | even | 4 | ||
280.2.s.a.237.3 | yes | 8 | 140.27 | odd | 4 | ||
1120.2.w.a.433.2 | 8 | 7.6 | odd | 2 | inner | ||
1120.2.w.a.433.2 | 8 | 8.5 | even | 2 | inner | ||
1120.2.w.a.433.3 | 8 | 1.1 | even | 1 | trivial | ||
1120.2.w.a.433.3 | 8 | 56.13 | odd | 2 | CM | ||
1120.2.w.a.657.2 | 8 | 35.27 | even | 4 | inner | ||
1120.2.w.a.657.2 | 8 | 40.37 | odd | 4 | inner | ||
1120.2.w.a.657.3 | 8 | 5.2 | odd | 4 | inner | ||
1120.2.w.a.657.3 | 8 | 280.237 | even | 4 | inner |