Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [776,1,Mod(3,776)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(776, base_ring=CyclotomicField(48))
chi = DirichletCharacter(H, H._module([24, 24, 35]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("776.3");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 776 = 2^{3} \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 776.bp (of order \(48\), degree \(16\), 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: | \(0.387274449803\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{48}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{48} + \cdots)\) |
Embedding invariants
Embedding label | 259.1 | ||
Root | \(0.991445 - 0.130526i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 776.259 |
Dual form | 776.1.bp.a.3.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/776\mathbb{Z}\right)^\times\).
\(n\) | \(389\) | \(393\) | \(583\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{48}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.793353 | + | 0.608761i | 0.793353 | + | 0.608761i | ||||
\(3\) | 1.20711 | − | 0.158919i | 1.20711 | − | 0.158919i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(4\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(5\) | 0 | 0 | −0.659346 | − | 0.751840i | \(-0.729167\pi\) | ||||
0.659346 | + | 0.751840i | \(0.270833\pi\) | |||||||
\(6\) | 1.05441 | + | 0.608761i | 1.05441 | + | 0.608761i | ||||
\(7\) | 0 | 0 | −0.321439 | − | 0.946930i | \(-0.604167\pi\) | ||||
0.321439 | + | 0.946930i | \(0.395833\pi\) | |||||||
\(8\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(9\) | 0.465926 | − | 0.124844i | 0.465926 | − | 0.124844i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.17604 | − | 1.53264i | −1.17604 | − | 1.53264i | −0.793353 | − | 0.608761i | \(-0.791667\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(12\) | 0.465926 | + | 1.12484i | 0.465926 | + | 1.12484i | ||||
\(13\) | 0 | 0 | 0.751840 | − | 0.659346i | \(-0.229167\pi\) | ||||
−0.751840 | + | 0.659346i | \(0.770833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(17\) | −1.57469 | − | 0.534534i | −1.57469 | − | 0.534534i | −0.608761 | − | 0.793353i | \(-0.708333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(18\) | 0.445644 | + | 0.184592i | 0.445644 | + | 0.184592i | ||||
\(19\) | 0.382683 | − | 0.0761205i | 0.382683 | − | 0.0761205i | − | 1.00000i | \(-0.5\pi\) | |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 1.93185i | − | 1.93185i | ||||||
\(23\) | 0 | 0 | 0.896873 | − | 0.442289i | \(-0.145833\pi\) | ||||
−0.896873 | + | 0.442289i | \(0.854167\pi\) | |||||||
\(24\) | −0.315118 | + | 1.17604i | −0.315118 | + | 1.17604i | ||||
\(25\) | −0.130526 | + | 0.991445i | −0.130526 | + | 0.991445i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.582262 | + | 0.241181i | −0.582262 | + | 0.241181i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.0654031 | − | 0.997859i | \(-0.479167\pi\) | ||||
−0.0654031 | + | 0.997859i | \(0.520833\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.130526 | − | 0.991445i | \(-0.541667\pi\) | ||||
0.130526 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(32\) | −0.991445 | − | 0.130526i | −0.991445 | − | 0.130526i | ||||
\(33\) | −1.66317 | − | 1.66317i | −1.66317 | − | 1.66317i | ||||
\(34\) | −0.923880 | − | 1.38268i | −0.923880 | − | 1.38268i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.241181 | + | 0.417738i | 0.241181 | + | 0.417738i | ||||
\(37\) | 0 | 0 | 0.442289 | − | 0.896873i | \(-0.354167\pi\) | ||||
−0.442289 | + | 0.896873i | \(0.645833\pi\) | |||||||
\(38\) | 0.349942 | + | 0.172572i | 0.349942 | + | 0.172572i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.95737 | + | 0.128293i | 1.95737 | + | 0.128293i | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.91532 | + | 0.513210i | 1.91532 | + | 0.513210i | 0.991445 | + | 0.130526i | \(0.0416667\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(44\) | 1.17604 | − | 1.53264i | 1.17604 | − | 1.53264i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | −0.965926 | + | 0.741181i | −0.965926 | + | 0.741181i | ||||
\(49\) | −0.793353 | + | 0.608761i | −0.793353 | + | 0.608761i | ||||
\(50\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(51\) | −1.98576 | − | 0.394993i | −1.98576 | − | 0.394993i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.608761 | − | 0.793353i | \(-0.291667\pi\) | ||||
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(54\) | −0.608761 | − | 0.163117i | −0.608761 | − | 0.163117i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.449843 | − | 0.152701i | 0.449843 | − | 0.152701i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.996552 | + | 0.491445i | 0.996552 | + | 0.491445i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.130526 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.307007 | − | 2.33195i | −0.307007 | − | 2.33195i | ||||
\(67\) | −0.389345 | − | 1.95737i | −0.389345 | − | 1.95737i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
−0.130526 | − | 0.991445i | \(-0.541667\pi\) | |||||||
\(68\) | 0.108761 | − | 1.65938i | 0.108761 | − | 1.65938i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.997859 | − | 0.0654031i | \(-0.0208333\pi\) | ||||
−0.997859 | + | 0.0654031i | \(0.979167\pi\) | |||||||
\(72\) | −0.0629609 | + | 0.478235i | −0.0629609 | + | 0.478235i | ||||
\(73\) | −0.366025 | + | 1.36603i | −0.366025 | + | 1.36603i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.21752i | 1.21752i | ||||||||
\(76\) | 0.172572 | + | 0.349942i | 0.172572 | + | 0.349942i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.08226 | + | 0.624844i | −1.08226 | + | 0.624844i | ||||
\(82\) | 1.47479 | + | 1.29335i | 1.47479 | + | 1.29335i | ||||
\(83\) | 0.284338 | − | 0.837633i | 0.284338 | − | 0.837633i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.991445 | − | 0.130526i | \(-0.0416667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.20711 | + | 1.57313i | 1.20711 | + | 1.57313i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.86603 | − | 0.500000i | 1.86603 | − | 0.500000i | ||||
\(89\) | −0.0999004 | + | 0.241181i | −0.0999004 | + | 0.241181i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.21752 | −1.21752 | ||||||||
\(97\) | −0.991445 | + | 0.130526i | −0.991445 | + | 0.130526i | ||||
\(98\) | −1.00000 | −1.00000 | ||||||||
\(99\) | −0.739288 | − | 0.567275i | −0.739288 | − | 0.567275i | ||||
\(100\) | −0.991445 | + | 0.130526i | −0.991445 | + | 0.130526i | ||||
\(101\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(102\) | −1.33496 | − | 1.52222i | −1.33496 | − | 1.52222i | ||||
\(103\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0420463 | − | 0.641502i | −0.0420463 | − | 0.641502i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(108\) | −0.383663 | − | 0.500000i | −0.383663 | − | 0.500000i | ||||
\(109\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.226078 | − | 0.130526i | 0.226078 | − | 0.130526i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.608761 | + | 0.793353i | \(0.291667\pi\) | |||||||
\(114\) | 0.449843 | + | 0.152701i | 0.449843 | + | 0.152701i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.491445 | + | 0.996552i | 0.491445 | + | 0.996552i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.707107 | + | 2.63896i | −0.707107 | + | 2.63896i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.38314 | − | 0.156199i | 2.38314 | − | 0.156199i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(128\) | −0.130526 | − | 0.991445i | −0.130526 | − | 0.991445i | ||||
\(129\) | 2.39356 | + | 0.315118i | 2.39356 | + | 0.315118i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.357164 | + | 0.534534i | 0.357164 | + | 0.534534i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(132\) | 1.17604 | − | 2.03696i | 1.17604 | − | 2.03696i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.882683 | − | 1.78990i | 0.882683 | − | 1.78990i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.09645 | − | 1.25026i | 1.09645 | − | 1.25026i | ||||
\(137\) | −1.42388 | + | 0.483342i | −1.42388 | + | 0.483342i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.293353 | − | 1.47479i | 0.293353 | − | 1.47479i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.793353 | − | 0.608761i | \(-0.208333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.341081 | + | 0.341081i | −0.341081 | + | 0.341081i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.12197 | + | 0.860919i | −1.12197 | + | 0.860919i | ||||
\(147\) | −0.860919 | + | 0.860919i | −0.860919 | + | 0.860919i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(150\) | −0.741181 | + | 0.965926i | −0.741181 | + | 0.965926i | ||||
\(151\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(152\) | −0.0761205 | + | 0.382683i | −0.0761205 | + | 0.382683i | ||||
\(153\) | −0.800421 | − | 0.0524624i | −0.800421 | − | 0.0524624i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.442289 | − | 0.896873i | \(-0.354167\pi\) | ||||
−0.442289 | + | 0.896873i | \(0.645833\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.23900 | − | 0.163117i | −1.23900 | − | 0.163117i | ||||
\(163\) | −0.130526 | − | 0.991445i | −0.130526 | − | 0.991445i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.793353 | − | 0.608761i | \(-0.208333\pi\) | |||||||
\(164\) | 0.382683 | + | 1.92388i | 0.382683 | + | 1.92388i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.735499 | − | 0.491445i | 0.735499 | − | 0.491445i | ||||
\(167\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.130526 | − | 0.991445i | 0.130526 | − | 0.991445i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.168799 | − | 0.0832424i | 0.168799 | − | 0.0832424i | ||||
\(172\) | 1.98289i | 1.98289i | ||||||||
\(173\) | 0 | 0 | −0.442289 | − | 0.896873i | \(-0.645833\pi\) | ||||
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.78480 | + | 0.739288i | 1.78480 | + | 0.739288i | ||||
\(177\) | 1.28104 | + | 0.434856i | 1.28104 | + | 0.434856i | ||||
\(178\) | −0.226078 | + | 0.130526i | −0.226078 | + | 0.130526i | ||||
\(179\) | −0.835400 | − | 0.732626i | −0.835400 | − | 0.732626i | 0.130526 | − | 0.991445i | \(-0.458333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.751840 | − | 0.659346i | \(-0.229167\pi\) | ||||
−0.751840 | + | 0.659346i | \(0.770833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.03264 | + | 3.04206i | 1.03264 | + | 3.04206i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) | ||||
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(192\) | −0.965926 | − | 0.741181i | −0.965926 | − | 0.741181i | ||||
\(193\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(194\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.793353 | − | 0.608761i | −0.793353 | − | 0.608761i | ||||
\(197\) | 0 | 0 | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) | ||||
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(198\) | −0.241181 | − | 0.900100i | −0.241181 | − | 0.900100i | ||||
\(199\) | 0 | 0 | −0.659346 | − | 0.751840i | \(-0.729167\pi\) | ||||
0.659346 | + | 0.751840i | \(0.270833\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(201\) | −0.781044 | − | 2.30088i | −0.781044 | − | 2.30088i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.132420 | − | 2.02033i | −0.132420 | − | 2.02033i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.566715 | − | 0.496996i | −0.566715 | − | 0.496996i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.123864 | − | 0.0420463i | −0.123864 | − | 0.0420463i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.357164 | − | 0.534534i | 0.357164 | − | 0.534534i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 0.630236i | − | 0.630236i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.224745 | + | 1.70711i | −0.224745 | + | 1.70711i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.0654031 | − | 0.997859i | \(-0.479167\pi\) | ||||
−0.0654031 | + | 0.997859i | \(0.520833\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0629609 | + | 0.478235i | 0.0629609 | + | 0.478235i | ||||
\(226\) | 0.258819 | + | 0.0340742i | 0.258819 | + | 0.0340742i | ||||
\(227\) | 1.22474 | + | 1.22474i | 1.22474 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(228\) | 0.263926 | + | 0.394993i | 0.263926 | + | 0.394993i | ||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.18270 | − | 1.34861i | 1.18270 | − | 1.34861i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.216773 | + | 1.08979i | −0.216773 | + | 1.08979i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(242\) | −2.16748 | + | 1.66317i | −2.16748 | + | 1.66317i | ||||
\(243\) | −0.707107 | + | 0.542582i | −0.707107 | + | 0.542582i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.98576 | + | 1.32684i | 1.98576 | + | 1.32684i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.210111 | − | 1.05630i | 0.210111 | − | 1.05630i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.85747 | + | 0.630526i | −1.85747 | + | 0.630526i | −0.866025 | + | 0.500000i | \(0.833333\pi\) |
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(257\) | −1.05217 | − | 1.57469i | −1.05217 | − | 1.57469i | −0.793353 | − | 0.608761i | \(-0.791667\pi\) |
−0.258819 | − | 0.965926i | \(-0.583333\pi\) | |||||||
\(258\) | 1.70711 | + | 1.70711i | 1.70711 | + | 1.70711i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.0420463 | + | 0.641502i | −0.0420463 | + | 0.641502i | ||||
\(263\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(264\) | 2.17303 | − | 0.900100i | 2.17303 | − | 0.900100i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0822623 | + | 0.307007i | −0.0822623 | + | 0.307007i | ||||
\(268\) | 1.78990 | − | 0.882683i | 1.78990 | − | 0.882683i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(272\) | 1.63099 | − | 0.324423i | 1.63099 | − | 0.324423i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.42388 | − | 0.483342i | −1.42388 | − | 0.483342i | ||||
\(275\) | 1.67303 | − | 0.965926i | 1.67303 | − | 0.965926i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.321439 | − | 0.946930i | \(-0.395833\pi\) | ||||
−0.321439 | + | 0.946930i | \(0.604167\pi\) | |||||||
\(278\) | 1.13053 | − | 0.991445i | 1.13053 | − | 0.991445i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.130526 | + | 1.99144i | 0.130526 | + | 1.99144i | 0.130526 | + | 0.991445i | \(0.458333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | 0.382683 | + | 0.923880i | \(0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.478235 | + | 0.0629609i | −0.478235 | + | 0.0629609i | ||||
\(289\) | 1.40056 | + | 1.07469i | 1.40056 | + | 1.07469i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.17604 | + | 0.315118i | −1.17604 | + | 0.315118i | ||||
\(292\) | −1.41421 | −1.41421 | ||||||||
\(293\) | 0 | 0 | −0.793353 | − | 0.608761i | \(-0.791667\pi\) | ||||
0.793353 | + | 0.608761i | \(0.208333\pi\) | |||||||
\(294\) | −1.20711 | + | 0.158919i | −1.20711 | + | 0.158919i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.05441 | + | 0.608761i | 1.05441 | + | 0.608761i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.17604 | + | 0.315118i | −1.17604 | + | 0.315118i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.293353 | + | 0.257264i | −0.293353 | + | 0.257264i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.603080 | − | 0.528887i | −0.603080 | − | 0.528887i | ||||
\(307\) | −1.37413 | + | 0.793353i | −1.37413 | + | 0.793353i | −0.991445 | − | 0.130526i | \(-0.958333\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.98289i | 1.98289i | 0.130526 | + | 0.991445i | \(0.458333\pi\) | ||||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.997859 | − | 0.0654031i | \(-0.0208333\pi\) | ||||
−0.997859 | + | 0.0654031i | \(0.979167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.152701 | − | 0.767680i | −0.152701 | − | 0.767680i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.643296 | − | 0.0846915i | −0.643296 | − | 0.0846915i | ||||
\(324\) | −0.883663 | − | 0.883663i | −0.883663 | − | 0.883663i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.867580 | + | 1.75928i | −0.867580 | + | 1.75928i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.24871 | − | 0.423880i | 1.24871 | − | 0.423880i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(332\) | 0.882683 | + | 0.0578541i | 0.882683 | + | 0.0578541i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.75928 | + | 0.349942i | 1.75928 | + | 0.349942i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.793353 | + | 0.608761i | \(0.208333\pi\) | |||||||
\(338\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(339\) | 0.252157 | − | 0.193487i | 0.252157 | − | 0.193487i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.184592 | + | 0.0367176i | 0.184592 | + | 0.0367176i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.20711 | + | 1.57313i | −1.20711 | + | 1.57313i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.78990 | − | 0.117317i | −1.78990 | − | 0.117317i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.659346 | − | 0.751840i | \(-0.270833\pi\) | ||||
−0.659346 | + | 0.751840i | \(0.729167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.965926 | + | 1.67303i | 0.965926 | + | 1.67303i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0.751597 | + | 1.12484i | 0.751597 | + | 1.12484i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.258819 | − | 0.0340742i | −0.258819 | − | 0.0340742i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.216773 | − | 1.08979i | −0.216773 | − | 1.08979i | ||||
\(359\) | 0 | 0 | 0.0654031 | − | 0.997859i | \(-0.479167\pi\) | ||||
−0.0654031 | + | 0.997859i | \(0.520833\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.783227 | + | 0.324423i | −0.783227 | + | 0.324423i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.434174 | + | 3.29788i | −0.434174 | + | 3.29788i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.442289 | − | 0.896873i | \(-0.645833\pi\) | ||||
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.928006 | − | 0.184592i | 0.928006 | − | 0.184592i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.751840 | − | 0.659346i | \(-0.770833\pi\) | ||||
0.751840 | + | 0.659346i | \(0.229167\pi\) | |||||||
\(374\) | −1.03264 | + | 3.04206i | −1.03264 | + | 3.04206i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.67303 | − | 0.448288i | 1.67303 | − | 0.448288i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.659346 | − | 0.751840i | \(-0.729167\pi\) | ||||
0.659346 | + | 0.751840i | \(0.270833\pi\) | |||||||
\(384\) | −0.315118 | − | 1.17604i | −0.315118 | − | 1.17604i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.793353 | + | 0.608761i | 0.793353 | + | 0.608761i | ||||
\(387\) | 0.956470 | 0.956470 | ||||||||
\(388\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.258819 | − | 0.965926i | −0.258819 | − | 0.965926i | ||||
\(393\) | 0.516083 | + | 0.588480i | 0.516083 | + | 0.588480i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.356604 | − | 0.860919i | 0.356604 | − | 0.860919i | ||||
\(397\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(401\) | 0.991445 | − | 0.869474i | 0.991445 | − | 0.869474i | − | 1.00000i | \(-0.5\pi\) | |
0.991445 | + | 0.130526i | \(0.0416667\pi\) | |||||||
\(402\) | 0.781044 | − | 2.30088i | 0.781044 | − | 2.30088i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.12484 | − | 1.68345i | 1.12484 | − | 1.68345i | ||||
\(409\) | 0.391239 | + | 0.793353i | 0.391239 | + | 0.793353i | 1.00000 | \(0\) | ||
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.64196 | + | 0.809726i | −1.64196 | + | 0.809726i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.119738 | − | 1.82684i | 0.119738 | − | 1.82684i | ||||
\(418\) | −0.147053 | − | 0.739288i | −0.147053 | − | 0.739288i | ||||
\(419\) | 0.207107 | + | 1.57313i | 0.207107 | + | 1.57313i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | −0.0726721 | − | 0.108761i | −0.0726721 | − | 0.108761i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.735499 | − | 1.49144i | 0.735499 | − | 1.49144i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.608761 | − | 0.206647i | 0.608761 | − | 0.206647i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(432\) | 0.383663 | − | 0.500000i | 0.383663 | − | 0.500000i | ||||
\(433\) | −1.65938 | − | 1.10876i | −1.65938 | − | 1.10876i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.793353 | − | 0.608761i | \(-0.791667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.21752 | + | 1.21752i | −1.21752 | + | 1.21752i | ||||
\(439\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.293643 | + | 0.382683i | −0.293643 | + | 0.382683i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.257264 | + | 1.29335i | −0.257264 | + | 1.29335i | 0.608761 | + | 0.793353i | \(0.291667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.793353 | − | 1.37413i | −0.793353 | − | 1.37413i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.130526 | − | 0.991445i | \(-0.458333\pi\) | |||||||
\(450\) | −0.241181 | + | 0.417738i | −0.241181 | + | 0.417738i | ||||
\(451\) | −2.10531 | − | 3.15082i | −2.10531 | − | 3.15082i | ||||
\(452\) | 0.184592 | + | 0.184592i | 0.184592 | + | 0.184592i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.226078 | + | 1.71723i | 0.226078 | + | 1.71723i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0310700 | + | 0.474037i | −0.0310700 | + | 0.474037i | ||||
\(457\) | 1.57469 | − | 1.05217i | 1.57469 | − | 1.05217i | 0.608761 | − | 0.793353i | \(-0.291667\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.04580 | − | 0.0685454i | 1.04580 | − | 0.0685454i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.75928 | − | 0.349942i | 1.75928 | − | 0.349942i | ||||
\(467\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.835400 | + | 0.732626i | −0.835400 | + | 0.732626i | ||||
\(473\) | −1.46593 | − | 3.53906i | −1.46593 | − | 3.53906i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0255190 | + | 0.389345i | 0.0255190 | + | 0.389345i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.73205 | −2.73205 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.891289 | −0.891289 | ||||||||
\(487\) | 0 | 0 | −0.793353 | − | 0.608761i | \(-0.791667\pi\) | ||||
0.793353 | + | 0.608761i | \(0.208333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.315118 | − | 1.17604i | −0.315118 | − | 1.17604i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0.767680 | + | 2.26151i | 0.767680 | + | 2.26151i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.809726 | − | 0.710111i | 0.809726 | − | 0.710111i | ||||
\(499\) | −0.125419 | + | 0.369474i | −0.125419 | + | 0.369474i | −0.991445 | − | 0.130526i | \(-0.958333\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.85747 | − | 0.630526i | −1.85747 | − | 0.630526i | ||||
\(503\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.21752i | − | 1.21752i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(513\) | −0.204463 | + | 0.136618i | −0.204463 | + | 0.136618i | ||||
\(514\) | 0.123864 | − | 1.88981i | 0.123864 | − | 1.88981i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.315118 | + | 2.39356i | 0.315118 | + | 2.39356i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.60876 | − | 0.793353i | −1.60876 | − | 0.793353i | −0.608761 | − | 0.793353i | \(-0.708333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(524\) | −0.423880 | + | 0.483342i | −0.423880 | + | 0.483342i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.27193 | + | 0.608761i | 2.27193 | + | 0.608761i | ||||
\(529\) | 0.608761 | − | 0.793353i | 0.608761 | − | 0.793353i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.525673 | + | 0.104563i | 0.525673 | + | 0.104563i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.252157 | + | 0.193487i | −0.252157 | + | 0.193487i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.95737 | + | 0.389345i | 1.95737 | + | 0.389345i | ||||
\(537\) | −1.12484 | − | 0.751597i | −1.12484 | − | 0.751597i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.86603 | + | 0.500000i | 1.86603 | + | 0.500000i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.997859 | − | 0.0654031i | \(-0.979167\pi\) | ||||
0.997859 | + | 0.0654031i | \(0.0208333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.49144 | + | 0.735499i | 1.49144 | + | 0.735499i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.991445 | − | 1.71723i | 0.991445 | − | 1.71723i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.608761 | − | 0.793353i | \(-0.291667\pi\) | |||||||
\(548\) | −0.835400 | − | 1.25026i | −0.835400 | − | 1.25026i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.91532 | + | 0.252157i | 1.91532 | + | 0.252157i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.50046 | − | 0.0983454i | 1.50046 | − | 0.0983454i | ||||
\(557\) | 0 | 0 | 0.130526 | − | 0.991445i | \(-0.458333\pi\) | ||||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.72995 | + | 3.50799i | 1.72995 | + | 3.50799i | ||||
\(562\) | −1.10876 | + | 1.65938i | −1.10876 | + | 1.65938i | ||||
\(563\) | −1.63099 | + | 0.324423i | −1.63099 | + | 0.324423i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.22474 | + | 0.707107i | −1.22474 | + | 0.707107i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.0983454 | − | 0.0862466i | 0.0983454 | − | 0.0862466i | −0.608761 | − | 0.793353i | \(-0.708333\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.965926 | − | 1.25882i | −0.965926 | − | 1.25882i | −0.965926 | − | 0.258819i | \(-0.916667\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.417738 | − | 0.241181i | −0.417738 | − | 0.241181i | ||||
\(577\) | −0.0862466 | − | 0.0983454i | −0.0862466 | − | 0.0983454i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.793353 | + | 0.608761i | \(0.791667\pi\) | |||||||
\(578\) | 0.456911 | + | 1.70521i | 0.456911 | + | 1.70521i | ||||
\(579\) | 1.20711 | − | 0.158919i | 1.20711 | − | 0.158919i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.12484 | − | 0.465926i | −1.12484 | − | 0.465926i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.12197 | − | 0.860919i | −1.12197 | − | 0.860919i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.869474 | + | 0.991445i | 0.869474 | + | 0.991445i | 1.00000 | \(0\) | ||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(588\) | −1.05441 | − | 0.608761i | −1.05441 | − | 0.608761i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.608761 | − | 0.793353i | −0.608761 | − | 0.793353i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(594\) | 0.465926 | + | 1.12484i | 0.465926 | + | 1.12484i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.946930 | − | 0.321439i | \(-0.895833\pi\) | ||||
0.946930 | + | 0.321439i | \(0.104167\pi\) | |||||||
\(600\) | −1.12484 | − | 0.465926i | −1.12484 | − | 0.465926i | ||||
\(601\) | 1.08979 | − | 0.216773i | 1.08979 | − | 0.216773i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.425773 | − | 0.863382i | −0.425773 | − | 0.863382i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.130526 | − | 0.991445i | \(-0.458333\pi\) | ||||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(608\) | −0.389345 | + | 0.0255190i | −0.389345 | + | 0.0255190i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.156489 | − | 0.786726i | −0.156489 | − | 0.786726i | ||||
\(613\) | 0 | 0 | −0.130526 | − | 0.991445i | \(-0.541667\pi\) | ||||
0.130526 | + | 0.991445i | \(0.458333\pi\) | |||||||
\(614\) | −1.57313 | − | 0.207107i | −1.57313 | − | 0.207107i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.382683 | + | 0.662827i | −0.382683 | + | 0.662827i | −0.991445 | − | 0.130526i | \(-0.958333\pi\) |
0.608761 | + | 0.793353i | \(0.291667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.867580 | − | 1.75928i | 0.867580 | − | 1.75928i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.608761 | − | 0.793353i | \(-0.291667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.965926 | − | 0.258819i | −0.965926 | − | 0.258819i | ||||
\(626\) | −1.20711 | + | 1.57313i | −1.20711 | + | 1.57313i | ||||
\(627\) | −0.763068 | − | 0.509865i | −0.763068 | − | 0.509865i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.793353 | − | 0.608761i | \(-0.208333\pi\) | ||||
−0.793353 | + | 0.608761i | \(0.791667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.156199 | − | 0.0310700i | −0.156199 | − | 0.0310700i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.34861 | + | 0.665060i | 1.34861 | + | 0.665060i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(642\) | 0.346188 | − | 0.702000i | 0.346188 | − | 0.702000i | ||||
\(643\) | 0.382683 | + | 0.662827i | 0.382683 | + | 0.662827i | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) |
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.458804 | − | 0.458804i | −0.458804 | − | 0.458804i | ||||
\(647\) | 0 | 0 | −0.991445 | − | 0.130526i | \(-0.958333\pi\) | ||||
0.991445 | + | 0.130526i | \(0.0416667\pi\) | |||||||
\(648\) | −0.163117 | − | 1.23900i | −0.163117 | − | 1.23900i | ||||
\(649\) | −0.418773 | − | 2.10531i | −0.418773 | − | 2.10531i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(653\) | 0 | 0 | 0.997859 | − | 0.0654031i | \(-0.0208333\pi\) | ||||
−0.997859 | + | 0.0654031i | \(0.979167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.75928 | + | 0.867580i | −1.75928 | + | 0.867580i | ||||
\(657\) | 0.682163i | 0.682163i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.05217 | + | 1.57469i | −1.05217 | + | 1.57469i | −0.258819 | + | 0.965926i | \(0.583333\pi\) |
−0.793353 | + | 0.608761i | \(0.791667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(662\) | 1.24871 | + | 0.423880i | 1.24871 | + | 0.423880i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.665060 | + | 0.583242i | 0.665060 | + | 0.583242i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.37413 | − | 0.793353i | −1.37413 | − | 0.793353i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(674\) | 1.18270 | + | 1.34861i | 1.18270 | + | 1.34861i | ||||
\(675\) | −0.163117 | − | 0.608761i | −0.163117 | − | 0.608761i | ||||
\(676\) | 0.991445 | − | 0.130526i | 0.991445 | − | 0.130526i | ||||
\(677\) | 0 | 0 | −0.793353 | − | 0.608761i | \(-0.791667\pi\) | ||||
0.793353 | + | 0.608761i | \(0.208333\pi\) | |||||||
\(678\) | 0.317837 | 0.317837 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.67303 | + | 1.28376i | 1.67303 | + | 1.28376i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.410670 | − | 1.53264i | −0.410670 | − | 1.53264i | −0.793353 | − | 0.608761i | \(-0.791667\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(684\) | 0.124094 | + | 0.141502i | 0.124094 | + | 0.141502i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.91532 | + | 0.513210i | −1.91532 | + | 0.513210i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.34861 | − | 1.18270i | −1.34861 | − | 1.18270i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.01367 | − | 1.24830i | −3.01367 | − | 1.24830i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.21332 | − | 1.81587i | 1.21332 | − | 1.81587i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.252157 | + | 1.91532i | −0.252157 | + | 1.91532i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.0884799 | + | 1.34994i | −0.0884799 | + | 1.34994i | ||||
\(709\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.184592 | − | 0.184592i | −0.184592 | − | 0.184592i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.491445 | − | 0.996552i | 0.491445 | − | 0.996552i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.946930 | − | 0.321439i | \(-0.104167\pi\) | ||||
−0.946930 | + | 0.321439i | \(0.895833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.818872 | − | 0.219416i | −0.818872 | − | 0.219416i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.35207 | + | 2.35207i | −2.35207 | + | 2.35207i | ||||
\(727\) | 0 | 0 | 0.793353 | − | 0.608761i | \(-0.208333\pi\) | ||||
−0.793353 | + | 0.608761i | \(0.791667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.116337 | − | 0.116337i | 0.116337 | − | 0.116337i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.74171 | − | 1.83195i | −2.74171 | − | 1.83195i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.54206 | + | 2.89867i | −2.54206 | + | 2.89867i | ||||
\(738\) | 0.848609 | + | 0.418488i | 0.848609 | + | 0.418488i | ||||
\(739\) | 0.665060 | − | 1.34861i | 0.665060 | − | 1.34861i | −0.258819 | − | 0.965926i | \(-0.583333\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0279066 | − | 0.425773i | 0.0279066 | − | 0.425773i | ||||
\(748\) | −2.67114 | + | 1.78480i | −2.67114 | + | 1.78480i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.130526 | − | 0.991445i | \(-0.458333\pi\) | ||||
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.14196 | + | 1.05630i | −2.14196 | + | 1.05630i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(758\) | 1.60021 | + | 0.662827i | 1.60021 | + | 0.662827i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.25026 | + | 1.09645i | 1.25026 | + | 1.09645i | 0.991445 | + | 0.130526i | \(0.0416667\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.465926 | − | 1.12484i | 0.465926 | − | 1.12484i | ||||
\(769\) | 0.125419 | + | 0.369474i | 0.125419 | + | 0.369474i | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.52033 | − | 1.73361i | −1.52033 | − | 1.73361i | ||||
\(772\) | 0.258819 | + | 0.965926i | 0.258819 | + | 0.965926i | ||||
\(773\) | 0 | 0 | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) | ||||
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(774\) | 0.758819 | + | 0.582262i | 0.758819 | + | 0.582262i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.758819 | − | 0.0999004i | 0.758819 | − | 0.0999004i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0511923 | + | 0.781044i | 0.0511923 | + | 0.781044i | ||||
\(787\) | −0.465926 | − | 0.607206i | −0.465926 | − | 0.607206i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.807007 | − | 0.465926i | 0.807007 | − | 0.465926i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.442289 | − | 0.896873i | \(-0.645833\pi\) | ||||
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.258819 | − | 0.965926i | 0.258819 | − | 0.965926i | ||||
\(801\) | −0.0164361 | + | 0.124844i | −0.0164361 | + | 0.124844i | ||||
\(802\) | 1.31587 | − | 0.0862466i | 1.31587 | − | 0.0862466i | ||||
\(803\) | 2.52409 | − | 1.04551i | 2.52409 | − | 1.04551i | ||||
\(804\) | 2.02033 | − | 1.34994i | 2.02033 | − | 1.34994i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.130526 | + | 0.226078i | −0.130526 | + | 0.226078i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.793353 | + | 0.608761i | \(0.208333\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.91722 | − | 0.650808i | 1.91722 | − | 0.650808i | ||||
\(817\) | 0.772029 | + | 0.0506014i | 0.772029 | + | 0.0506014i | ||||
\(818\) | −0.172572 | + | 0.867580i | −0.172572 | + | 0.867580i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(822\) | −1.79559 | − | 0.357164i | −1.79559 | − | 0.357164i | ||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.86603 | − | 1.43185i | 1.86603 | − | 1.43185i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.128293 | + | 0.0255190i | 0.128293 | + | 0.0255190i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.130526 | + | 0.991445i | \(0.541667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.608761 | − | 0.793353i | \(-0.291667\pi\) | ||||
−0.608761 | + | 0.793353i | \(0.708333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.57469 | − | 0.534534i | 1.57469 | − | 0.534534i | ||||
\(834\) | 1.20711 | − | 1.37644i | 1.20711 | − | 1.37644i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.333384 | − | 0.676037i | 0.333384 | − | 0.676037i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.793353 | + | 1.37413i | −0.793353 | + | 1.37413i | ||||
\(839\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.991445 | − | 0.130526i | −0.991445 | − | 0.130526i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.474037 | + | 2.38314i | 0.474037 | + | 2.38314i | ||||
\(844\) | 0.00855514 | − | 0.130526i | 0.00855514 | − | 0.130526i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.445644 | + | 1.66317i | −0.445644 | + | 1.66317i | ||||
\(850\) | 1.49144 | − | 0.735499i | 1.49144 | − | 0.735499i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.608761 | + | 0.206647i | 0.608761 | + | 0.206647i | ||||
\(857\) | −1.67303 | + | 0.965926i | −1.67303 | + | 0.965926i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.206647 | + | 0.608761i | −0.206647 | + | 0.608761i | 0.793353 | + | 0.608761i | \(0.208333\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.0654031 | − | 0.997859i | \(-0.520833\pi\) | ||||
0.0654031 | + | 0.997859i | \(0.479167\pi\) | |||||||
\(864\) | 0.608761 | − | 0.163117i | 0.608761 | − | 0.163117i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.641502 | − | 1.88981i | −0.641502 | − | 1.88981i | ||||
\(867\) | 1.86141 | + | 1.07469i | 1.86141 | + | 1.07469i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.445644 | + | 0.184592i | −0.445644 | + | 0.184592i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.70711 | + | 0.224745i | −1.70711 | + | 0.224745i | ||||
\(877\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.662827 | − | 1.60021i | 0.662827 | − | 1.60021i | −0.130526 | − | 0.991445i | \(-0.541667\pi\) |
0.793353 | − | 0.608761i | \(-0.208333\pi\) | |||||||
\(882\) | −0.465926 | + | 0.124844i | −0.465926 | + | 0.124844i | ||||
\(883\) | 0.0420463 | + | 0.641502i | 0.0420463 | + | 0.641502i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.991445 | + | 0.869474i | −0.991445 | + | 0.869474i | ||||
\(887\) | 0 | 0 | 0.321439 | − | 0.946930i | \(-0.395833\pi\) | ||||
−0.321439 | + | 0.946930i | \(0.604167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.23044 | + | 0.923880i | 2.23044 | + | 0.923880i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.207107 | − | 1.57313i | 0.207107 | − | 1.57313i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.445644 | + | 0.184592i | −0.445644 | + | 0.184592i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.247843 | − | 3.78135i | 0.247843 | − | 3.78135i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.0340742 | + | 0.258819i | 0.0340742 | + | 0.258819i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.491445 | + | 0.735499i | 0.491445 | + | 0.735499i | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(908\) | −0.866025 | + | 1.50000i | −0.866025 | + | 1.50000i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.896873 | − | 0.442289i | \(-0.854167\pi\) | ||||
0.896873 | + | 0.442289i | \(0.145833\pi\) | |||||||
\(912\) | −0.313225 | + | 0.357164i | −0.313225 | + | 0.357164i | ||||
\(913\) | −1.61818 | + | 0.549299i | −1.61818 | + | 0.549299i | ||||
\(914\) | 1.88981 | + | 0.123864i | 1.88981 | + | 0.123864i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.871417 | + | 0.582262i | 0.871417 | + | 0.582262i | ||||
\(919\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.53264 | + | 1.17604i | −1.53264 | + | 1.17604i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.88981 | + | 0.123864i | 1.88981 | + | 0.123864i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.257264 | + | 0.293353i | −0.257264 | + | 0.293353i | ||||
\(932\) | 1.60876 | + | 0.793353i | 1.60876 | + | 0.793353i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.923880 | − | 1.60021i | −0.923880 | − | 1.60021i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.22474 | + | 1.22474i | 1.22474 | + | 1.22474i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.315118 | + | 2.39356i | 0.315118 | + | 2.39356i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.0654031 | − | 0.997859i | \(-0.479167\pi\) | ||||
−0.0654031 | + | 0.997859i | \(0.520833\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.10876 | + | 0.0726721i | −1.10876 | + | 0.0726721i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.991445 | − | 3.70012i | 0.991445 | − | 3.70012i | ||||
\(947\) | 0.793353 | − | 0.391239i | 0.793353 | − | 0.391239i | − | 1.00000i | \(-0.5\pi\) | |
0.793353 | + | 0.608761i | \(0.208333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.216773 | + | 0.324423i | −0.216773 | + | 0.324423i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.05217 | + | 0.357164i | 1.05217 | + | 0.357164i | 0.793353 | − | 0.608761i | \(-0.208333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.965926 | + | 0.258819i | −0.965926 | + | 0.258819i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0996785 | − | 0.293643i | −0.0996785 | − | 0.293643i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.991445 | − | 0.130526i | \(-0.0416667\pi\) | ||||
−0.991445 | + | 0.130526i | \(0.958333\pi\) | |||||||
\(968\) | −2.16748 | − | 1.66317i | −2.16748 | − | 1.66317i | ||||
\(969\) | −0.789986 | −0.789986 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.765367 | −0.765367 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(972\) | −0.707107 | − | 0.542582i | −0.707107 | − | 0.542582i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.534534 | + | 1.57469i | 0.534534 | + | 1.57469i | 0.793353 | + | 0.608761i | \(0.208333\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(978\) | 0.465926 | − | 1.12484i | 0.465926 | − | 1.12484i | ||||
\(979\) | 0.487130 | − | 0.130526i | 0.487130 | − | 0.130526i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(983\) | 0 | 0 | 0.751840 | − | 0.659346i | \(-0.229167\pi\) | ||||
−0.751840 | + | 0.659346i | \(0.770833\pi\) | |||||||
\(984\) | −0.767680 | + | 2.26151i | −0.767680 | + | 2.26151i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.442289 | − | 0.896873i | \(-0.645833\pi\) | ||||
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.43996 | − | 0.710111i | 1.43996 | − | 0.710111i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.07469 | − | 0.0704387i | 1.07469 | − | 0.0704387i | ||||
\(997\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(998\) | −0.324423 | + | 0.216773i | −0.324423 | + | 0.216773i | ||||
\(999\) | 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 | 776.1.bp.a.259.1 | yes | 16 | |
4.3 | odd | 2 | 3104.1.et.a.1423.1 | 16 | |||
8.3 | odd | 2 | CM | 776.1.bp.a.259.1 | yes | 16 | |
8.5 | even | 2 | 3104.1.et.a.1423.1 | 16 | |||
97.3 | even | 48 | inner | 776.1.bp.a.3.1 | ✓ | 16 | |
388.3 | odd | 48 | 3104.1.et.a.1167.1 | 16 | |||
776.3 | odd | 48 | inner | 776.1.bp.a.3.1 | ✓ | 16 | |
776.197 | even | 48 | 3104.1.et.a.1167.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
776.1.bp.a.3.1 | ✓ | 16 | 97.3 | even | 48 | inner | |
776.1.bp.a.3.1 | ✓ | 16 | 776.3 | odd | 48 | inner | |
776.1.bp.a.259.1 | yes | 16 | 1.1 | even | 1 | trivial | |
776.1.bp.a.259.1 | yes | 16 | 8.3 | odd | 2 | CM | |
3104.1.et.a.1167.1 | 16 | 388.3 | odd | 48 | |||
3104.1.et.a.1167.1 | 16 | 776.197 | even | 48 | |||
3104.1.et.a.1423.1 | 16 | 4.3 | odd | 2 | |||
3104.1.et.a.1423.1 | 16 | 8.5 | even | 2 |