Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3520,1,Mod(109,3520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3520, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 7, 8, 8]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3520.109");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3520 = 2^{6} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3520.db (of order \(16\), degree \(8\), 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: | \(1.75670884447\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{16})\) |
Coefficient field: | \(\Q(\zeta_{64})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{32} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{32}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{32} - \cdots)\) |
Embedding invariants
Embedding label | 549.4 | ||
Root | \(0.290285 + 0.956940i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3520.549 |
Dual form | 3520.1.db.a.109.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3520\mathbb{Z}\right)^\times\).
\(n\) | \(321\) | \(1541\) | \(2751\) | \(2817\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{9}{16}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.995185 | − | 0.0980171i | 0.995185 | − | 0.0980171i | ||||
\(3\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(4\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(5\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.732410 | − | 1.76820i | 0.732410 | − | 1.76820i | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) |
0.634393 | − | 0.773010i | \(-0.281250\pi\) | |||||||
\(8\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | ||||
\(9\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(10\) | −0.0980171 | + | 0.995185i | −0.0980171 | + | 0.995185i | ||||
\(11\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.301614 | + | 1.51631i | 0.301614 | + | 1.51631i | 0.773010 | + | 0.634393i | \(0.218750\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(14\) | 0.555570 | − | 1.83147i | 0.555570 | − | 1.83147i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(17\) | −1.24723 | + | 1.24723i | −1.24723 | + | 1.24723i | −0.290285 | + | 0.956940i | \(0.593750\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(18\) | −0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | ||||
\(19\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(20\) | 1.00000i | 1.00000i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(23\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(26\) | 0.448786 | + | 1.47945i | 0.448786 | + | 1.47945i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.373380 | − | 1.87711i | 0.373380 | − | 1.87711i | ||||
\(29\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.66294i | − | 1.66294i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||
0.555570 | − | 0.831470i | \(-0.312500\pi\) | |||||||
\(32\) | 0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.11897 | + | 1.36347i | −1.11897 | + | 1.36347i | ||||
\(35\) | 1.59133 | + | 1.06330i | 1.59133 | + | 1.06330i | ||||
\(36\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(37\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0980171 | + | 0.995185i | 0.0980171 | + | 0.995185i | ||||
\(41\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.108911 | + | 0.162997i | 0.108911 | + | 0.162997i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(44\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(45\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.88298 | − | 1.88298i | −1.88298 | − | 1.88298i | ||||
\(50\) | −0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.591637 | + | 1.42834i | 0.591637 | + | 1.42834i | ||||
\(53\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(56\) | 0.187593 | − | 1.90466i | 0.187593 | − | 1.90466i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0761205 | + | 0.382683i | −0.0761205 | + | 0.382683i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(62\) | −0.162997 | − | 1.65493i | −0.162997 | − | 1.65493i | ||||
\(63\) | −1.91388 | −1.91388 | ||||||||
\(64\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(65\) | −1.54602 | −1.54602 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(68\) | −0.979938 | + | 1.46658i | −0.979938 | + | 1.46658i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.68789 | + | 0.902197i | 1.68789 | + | 0.902197i | ||||
\(71\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(72\) | −0.634393 | − | 0.773010i | −0.634393 | − | 0.773010i | ||||
\(73\) | 0.761681 | + | 1.83886i | 0.761681 | + | 1.83886i | 0.471397 | + | 0.881921i | \(0.343750\pi\) |
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.373380 | − | 1.87711i | −0.373380 | − | 1.87711i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(80\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(81\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.51631 | + | 0.301614i | −1.51631 | + | 0.301614i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.979938 | − | 1.46658i | −0.979938 | − | 1.46658i | ||||
\(86\) | 0.124363 | + | 0.151537i | 0.124363 | + | 0.151537i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(89\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(90\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | ||||
\(91\) | 2.90205 | + | 0.577253i | 2.90205 | + | 0.577253i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | −2.05848 | − | 1.68935i | −2.05848 | − | 1.68935i | ||||
\(99\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(100\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(101\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(104\) | 0.728789 | + | 1.36347i | 0.728789 | + | 1.36347i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.523788 | + | 0.783904i | 0.523788 | + | 0.783904i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(110\) | 0.471397 | + | 0.881921i | 0.471397 | + | 0.881921i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.91388i | − | 1.91388i | ||||||
\(113\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28547 | − | 0.858923i | 1.28547 | − | 0.858923i | ||||
\(118\) | −0.0382444 | + | 0.388302i | −0.0382444 | + | 0.388302i | ||||
\(119\) | 1.29186 | + | 3.11882i | 1.29186 | + | 3.11882i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.324423 | − | 1.63099i | −0.324423 | − | 1.63099i | ||||
\(125\) | 0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | ||||
\(126\) | −1.90466 | + | 0.187593i | −1.90466 | + | 0.187593i | ||||
\(127\) | −1.99037 | −1.99037 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(128\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.53858 | + | 0.151537i | −1.53858 | + | 0.151537i | ||||
\(131\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.831470 | + | 1.55557i | −0.831470 | + | 1.55557i | ||||
\(137\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(140\) | 1.76820 | + | 0.732410i | 1.76820 | + | 0.732410i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.222174 | + | 0.732410i | −0.222174 | + | 0.732410i | ||||
\(143\) | 1.09320 | + | 1.09320i | 1.09320 | + | 1.09320i | ||||
\(144\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.938254 | + | 1.75535i | 0.938254 | + | 1.75535i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.62958 | + | 0.674993i | 1.62958 | + | 0.674993i | ||||
\(154\) | −0.555570 | − | 1.83147i | −0.555570 | − | 1.83147i | ||||
\(155\) | 1.63099 | + | 0.324423i | 1.63099 | + | 0.324423i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.290285 | + | 0.956940i | 0.290285 | + | 0.956940i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.634393 | + | 0.773010i | −0.634393 | + | 0.773010i | ||||
\(163\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.47945 | + | 0.448786i | −1.47945 | + | 0.448786i | ||||
\(167\) | −1.17221 | − | 0.485544i | −1.17221 | − | 0.485544i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.28436 | + | 0.531999i | −1.28436 | + | 0.531999i | ||||
\(170\) | −1.11897 | − | 1.36347i | −1.11897 | − | 1.36347i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.138617 | + | 0.138617i | 0.138617 | + | 0.138617i | ||||
\(173\) | 0.924678 | − | 0.183930i | 0.924678 | − | 0.183930i | 0.290285 | − | 0.956940i | \(-0.406250\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.35332 | + | 1.35332i | −1.35332 | + | 1.35332i | ||||
\(176\) | 0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.87711 | + | 0.569414i | 1.87711 | + | 0.569414i | ||||
\(179\) | 0.149316 | + | 0.750661i | 0.149316 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(180\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(181\) | −1.53636 | + | 1.02656i | −1.53636 | + | 1.02656i | −0.555570 | + | 0.831470i | \(0.687500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(182\) | 2.94465 | + | 0.290023i | 2.94465 | + | 0.290023i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.344109 | + | 1.72995i | −0.344109 | + | 1.72995i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.390181 | −0.390181 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.196034 | 0.196034 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.21415 | − | 1.47945i | −2.21415 | − | 1.47945i | ||||
\(197\) | −0.113263 | + | 0.569414i | −0.113263 | + | 0.569414i | 0.881921 | + | 0.471397i | \(0.156250\pi\) |
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(198\) | −0.881921 | − | 0.471397i | −0.881921 | − | 0.471397i | ||||
\(199\) | 0.707107 | − | 1.70711i | 0.707107 | − | 1.70711i | − | 1.00000i | \(-0.5\pi\) | |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(200\) | −0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.858923 | + | 1.28547i | 0.858923 | + | 1.28547i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.598102 | + | 0.728789i | 0.598102 | + | 0.728789i | ||||
\(215\) | −0.181112 | + | 0.0750191i | −0.181112 | + | 0.0750191i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.94040 | − | 1.21795i | −2.94040 | − | 1.21795i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(221\) | −2.26737 | − | 1.51501i | −2.26737 | − | 1.51501i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | −0.187593 | − | 1.90466i | −0.187593 | − | 1.90466i | ||||
\(225\) | 1.00000i | 1.00000i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.05496 | − | 0.704900i | −1.05496 | − | 0.704900i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.08979 | − | 0.216773i | −1.08979 | − | 0.216773i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.536376 | + | 0.222174i | −0.536376 | + | 0.222174i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(234\) | 1.19509 | − | 0.980785i | 1.19509 | − | 0.980785i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.390181i | 0.390181i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.59133 | + | 2.97718i | 1.59133 | + | 2.97718i | ||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(242\) | 0.290285 | − | 0.956940i | 0.290285 | − | 0.956940i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.21415 | − | 1.47945i | 2.21415 | − | 1.47945i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.482726 | − | 1.59133i | −0.482726 | − | 1.59133i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.471397 | − | 0.881921i | 0.471397 | − | 0.881921i | ||||
\(251\) | −0.382683 | + | 1.92388i | −0.382683 | + | 1.92388i | 1.00000i | \(0.5\pi\) | ||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(252\) | −1.87711 | + | 0.373380i | −1.87711 | + | 0.373380i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.98079 | + | 0.195090i | −1.98079 | + | 0.195090i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.51631 | + | 0.301614i | −1.51631 | + | 0.301614i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0750191 | + | 0.181112i | −0.0750191 | + | 0.181112i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.0761205 | + | 0.382683i | 0.0761205 | + | 0.382683i | 1.00000 | \(0\) | ||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(272\) | −0.674993 | + | 1.62958i | −0.674993 | + | 1.62958i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.108911 | + | 0.162997i | 0.108911 | + | 0.162997i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.53636 | + | 0.636379i | −1.53636 | + | 0.636379i | ||||
\(280\) | 1.83147 | + | 0.555570i | 1.83147 | + | 0.555570i | ||||
\(281\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.24441 | + | 0.247528i | 1.24441 | + | 0.247528i | 0.773010 | − | 0.634393i | \(-0.218750\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(284\) | −0.149316 | + | 0.750661i | −0.149316 | + | 0.750661i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.19509 | + | 0.980785i | 1.19509 | + | 0.980785i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.773010 | − | 0.634393i | −0.773010 | − | 0.634393i | ||||
\(289\) | − | 2.11114i | − | 2.11114i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.10579 | + | 1.65493i | 1.10579 | + | 1.65493i | ||||
\(293\) | −1.95213 | − | 0.388302i | −1.95213 | − | 0.388302i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
−0.956940 | − | 0.290285i | \(-0.906250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.360480 | − | 0.149316i | −0.360480 | − | 0.149316i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.367977 | − | 0.0731952i | 0.367977 | − | 0.0731952i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.68789 | + | 0.512016i | 1.68789 | + | 0.512016i | ||||
\(307\) | −0.344109 | − | 1.72995i | −0.344109 | − | 1.72995i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
0.290285 | − | 0.956940i | \(-0.406250\pi\) | |||||||
\(308\) | −0.732410 | − | 1.76820i | −0.732410 | − | 1.76820i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.65493 | + | 0.162997i | 1.65493 | + | 0.162997i | ||||
\(311\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.373380 | − | 1.87711i | 0.373380 | − | 1.87711i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(325\) | 0.301614 | − | 1.51631i | 0.301614 | − | 1.51631i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.17588 | + | 0.785695i | −1.17588 | + | 0.785695i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(332\) | −1.42834 | + | 0.591637i | −1.42834 | + | 0.591637i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.21415 | − | 0.368309i | −1.21415 | − | 0.368309i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.410525 | + | 0.410525i | −0.410525 | + | 0.410525i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(338\) | −1.22603 | + | 0.655327i | −1.22603 | + | 0.655327i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.24723 | − | 1.24723i | −1.24723 | − | 1.24723i | ||||
\(341\) | −0.923880 | − | 1.38268i | −0.923880 | − | 1.38268i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.94040 | + | 1.21795i | −2.94040 | + | 1.21795i | ||||
\(344\) | 0.151537 | + | 0.124363i | 0.151537 | + | 0.124363i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.902197 | − | 0.273678i | 0.902197 | − | 0.273678i | ||||
\(347\) | 1.95213 | + | 0.388302i | 1.95213 | + | 0.388302i | 0.995185 | + | 0.0980171i | \(0.0312500\pi\) |
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(350\) | −1.21415 | + | 1.47945i | −1.21415 | + | 1.47945i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.471397 | − | 0.881921i | 0.471397 | − | 0.881921i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.636379 | − | 0.425215i | −0.636379 | − | 0.425215i | ||||
\(356\) | 1.92388 | + | 0.382683i | 1.92388 | + | 0.382683i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.222174 | + | 0.732410i | 0.222174 | + | 0.732410i | ||||
\(359\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(360\) | 0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | ||||
\(361\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(362\) | −1.42834 | + | 1.17221i | −1.42834 | + | 1.17221i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.95890 | 2.95890 | ||||||||
\(365\) | −1.95213 | + | 0.388302i | −1.95213 | + | 0.388302i | ||||
\(366\) | 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 | ||||||||
\(373\) | 0.482726 | − | 0.322547i | 0.482726 | − | 0.322547i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(374\) | −0.172887 | + | 1.75535i | −0.172887 | + | 1.75535i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.382683 | − | 1.92388i | 0.382683 | − | 1.92388i | − | 1.00000i | \(-0.5\pi\) | |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.388302 | + | 0.0382444i | −0.388302 | + | 0.0382444i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.91388 | 1.91388 | ||||||||
\(386\) | 0.195090 | − | 0.0192147i | 0.195090 | − | 0.0192147i | ||||
\(387\) | 0.108911 | − | 0.162997i | 0.108911 | − | 0.162997i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.216773 | − | 1.08979i | 0.216773 | − | 1.08979i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.34850 | − | 1.25530i | −2.34850 | − | 1.25530i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0569057 | + | 0.577774i | −0.0569057 | + | 0.577774i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(397\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(398\) | 0.536376 | − | 1.76820i | 0.536376 | − | 1.76820i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −1.00000 | ||||||||
\(401\) | −0.275899 | + | 0.275899i | −0.275899 | + | 0.275899i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.52154 | − | 0.501565i | 2.52154 | − | 0.501565i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.620908 | + | 0.414877i | 0.620908 | + | 0.414877i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.54602i | − | 1.54602i | ||||||
\(416\) | 0.980785 | + | 1.19509i | 0.980785 | + | 1.19509i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.17588 | − | 0.785695i | −1.17588 | − | 0.785695i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.81225 | − | 0.360480i | −1.81225 | − | 0.360480i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.62958 | − | 0.674993i | 1.62958 | − | 0.674993i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.666656 | + | 0.666656i | 0.666656 | + | 0.666656i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.172887 | + | 0.0924099i | −0.172887 | + | 0.0924099i | ||||
\(431\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | −3.04562 | − | 0.923880i | −3.04562 | − | 0.923880i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(440\) | 0.634393 | + | 0.773010i | 0.634393 | + | 0.773010i | ||||
\(441\) | −1.01906 | + | 2.46024i | −1.01906 | + | 2.46024i | ||||
\(442\) | −2.40494 | − | 1.28547i | −2.40494 | − | 1.28547i | ||||
\(443\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.08979 | + | 1.63099i | −1.08979 | + | 1.63099i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.373380 | − | 1.87711i | −0.373380 | − | 1.87711i | ||||
\(449\) | 1.11114 | 1.11114 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(450\) | 0.0980171 | + | 0.995185i | 0.0980171 | + | 0.995185i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.11897 | − | 0.598102i | −1.11897 | − | 0.598102i | ||||
\(455\) | −1.13232 | + | 2.73367i | −1.13232 | + | 2.73367i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.485544 | + | 1.17221i | 0.485544 | + | 1.17221i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(458\) | −1.10579 | − | 0.108911i | −1.10579 | − | 0.108911i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.512016 | + | 0.273678i | −0.512016 | + | 0.273678i | ||||
\(467\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(468\) | 1.09320 | − | 1.09320i | 1.09320 | − | 1.09320i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0382444 | + | 0.388302i | 0.0382444 | + | 0.388302i | ||||
\(473\) | 0.181112 | + | 0.0750191i | 0.181112 | + | 0.0750191i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.87549 | + | 2.80686i | 1.87549 | + | 2.80686i | ||||
\(477\) | 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 | 0 | ||||||||
\(484\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.05848 | − | 1.68935i | 2.05848 | − | 1.68935i | ||||
\(491\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(496\) | −0.636379 | − | 1.53636i | −0.636379 | − | 1.53636i | ||||
\(497\) | 1.03578 | + | 1.03578i | 1.03578 | + | 1.03578i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.324423 | + | 1.63099i | 0.324423 | + | 1.63099i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(500\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.192268 | + | 1.95213i | −0.192268 | + | 1.95213i | ||||
\(503\) | 0.674993 | + | 1.62958i | 0.674993 | + | 1.62958i | 0.773010 | + | 0.634393i | \(0.218750\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(504\) | −1.83147 | + | 0.555570i | −1.83147 | + | 0.555570i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.95213 | + | 0.388302i | −1.95213 | + | 0.388302i | ||||
\(509\) | 1.08979 | − | 1.63099i | 1.08979 | − | 1.63099i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.80933 | 3.80933 | ||||||||
\(512\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.47945 | + | 0.448786i | −1.47945 | + | 0.448786i | ||||
\(521\) | 0.425215 | + | 1.02656i | 0.425215 | + | 1.02656i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.482726 | − | 0.322547i | 0.482726 | − | 0.322547i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0569057 | + | 0.187593i | −0.0569057 | + | 0.187593i | ||||
\(527\) | 2.07406 | + | 2.07406i | 2.07406 | + | 2.07406i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.382683 | − | 0.0761205i | 0.382683 | − | 0.0761205i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.871028 | + | 0.360791i | −0.871028 | + | 0.360791i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.113263 | + | 0.373380i | 0.113263 | + | 0.373380i | ||||
\(539\) | −2.61177 | − | 0.519514i | −2.61177 | − | 0.519514i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.512016 | + | 1.68789i | −0.512016 | + | 1.68789i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.783904 | + | 0.523788i | 0.783904 | + | 0.523788i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.956940 | + | 0.290285i | −0.956940 | + | 0.290285i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.124363 | + | 0.151537i | 0.124363 | + | 0.151537i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.192268 | − | 0.0382444i | 0.192268 | − | 0.0382444i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(558\) | −1.46658 | + | 0.783904i | −1.46658 | + | 0.783904i | ||||
\(559\) | −0.214305 | + | 0.214305i | −0.214305 | + | 0.214305i | ||||
\(560\) | 1.87711 | + | 0.373380i | 1.87711 | + | 0.373380i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.113263 | − | 0.569414i | −0.113263 | − | 0.569414i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.26268 | + | 0.124363i | 1.26268 | + | 0.124363i | ||||
\(567\) | 0.732410 | + | 1.76820i | 0.732410 | + | 1.76820i | ||||
\(568\) | −0.0750191 | + | 0.761681i | −0.0750191 | + | 0.761681i | ||||
\(569\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(572\) | 1.28547 | + | 0.858923i | 1.28547 | + | 0.858923i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −0.206928 | − | 2.10097i | −0.206928 | − | 2.10097i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.577253 | + | 2.90205i | −0.577253 | + | 2.90205i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.26268 | + | 1.53858i | 1.26268 | + | 1.53858i | ||||
\(585\) | 0.591637 | + | 1.42834i | 0.591637 | + | 1.42834i | ||||
\(586\) | −1.98079 | − | 0.195090i | −1.98079 | − | 0.195090i | ||||
\(587\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.373380 | − | 0.113263i | −0.373380 | − | 0.113263i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.35332 | + | 1.35332i | −1.35332 | + | 1.35332i | −0.471397 | + | 0.881921i | \(0.656250\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.31092 | + | 0.658583i | −3.31092 | + | 0.658583i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.02656 | − | 0.425215i | 1.02656 | − | 0.425215i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(602\) | 0.359031 | − | 0.108911i | 0.359031 | − | 0.108911i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.831470 | + | 0.555570i | 0.831470 | + | 0.555570i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.76384i | − | 1.76384i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||
0.471397 | − | 0.881921i | \(-0.343750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.72995 | + | 0.344109i | 1.72995 | + | 0.344109i | ||||
\(613\) | 0.924678 | + | 0.183930i | 0.924678 | + | 0.183930i | 0.634393 | − | 0.773010i | \(-0.281250\pi\) |
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(614\) | −0.512016 | − | 1.68789i | −0.512016 | − | 1.68789i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.902197 | − | 1.68789i | −0.902197 | − | 1.68789i | ||||
\(617\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.02656 | + | 1.53636i | 1.02656 | + | 1.53636i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(620\) | 1.66294 | 1.66294 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.65463 | − | 2.65463i | 2.65463 | − | 2.65463i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0.187593 | − | 1.90466i | 0.187593 | − | 1.90466i | ||||
\(631\) | −0.541196 | − | 1.30656i | −0.541196 | − | 1.30656i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.388302 | − | 1.95213i | 0.388302 | − | 1.95213i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.28726 | − | 3.42313i | 2.28726 | − | 3.42313i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.765367 | 0.765367 | ||||||||
\(640\) | 0.471397 | + | 0.881921i | 0.471397 | + | 0.881921i | ||||
\(641\) | −1.96157 | −1.96157 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(648\) | −0.471397 | + | 0.881921i | −0.471397 | + | 0.881921i | ||||
\(649\) | 0.149316 | + | 0.360480i | 0.149316 | + | 0.360480i | ||||
\(650\) | 0.151537 | − | 1.53858i | 0.151537 | − | 1.53858i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.40740 | − | 1.40740i | 1.40740 | − | 1.40740i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.923880 | + | 1.38268i | 0.923880 | + | 1.38268i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | −1.09320 | + | 0.897168i | −1.09320 | + | 0.897168i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.36347 | + | 0.728789i | −1.36347 | + | 0.728789i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.24441 | − | 0.247528i | −1.24441 | − | 0.247528i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 0.580569i | − | 0.580569i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) | ||
0.956940 | − | 0.290285i | \(-0.0937500\pi\) | |||||||
\(674\) | −0.368309 | + | 0.448786i | −0.368309 | + | 0.448786i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.15589 | + | 0.772343i | −1.15589 | + | 0.772343i | ||||
\(677\) | 1.72995 | + | 0.344109i | 1.72995 | + | 0.344109i | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.36347 | − | 1.11897i | −1.36347 | − | 1.11897i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.05496 | − | 1.28547i | −1.05496 | − | 1.28547i | ||||
\(683\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.80686 | + | 1.50030i | −2.80686 | + | 1.50030i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.162997 | + | 0.108911i | 0.162997 | + | 0.108911i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.216773 | + | 1.08979i | 0.216773 | + | 1.08979i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(692\) | 0.871028 | − | 0.360791i | 0.871028 | − | 0.360791i | ||||
\(693\) | −1.59133 | + | 1.06330i | −1.59133 | + | 1.06330i | ||||
\(694\) | 1.98079 | + | 0.195090i | 1.98079 | + | 0.195090i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.06330 | + | 1.59133i | −1.06330 | + | 1.59133i | ||||
\(701\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.275899 | − | 1.38704i | 0.275899 | − | 1.38704i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(710\) | −0.674993 | − | 0.360791i | −0.674993 | − | 0.360791i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.95213 | + | 0.192268i | 1.95213 | + | 0.192268i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.28547 | + | 0.858923i | −1.28547 | + | 0.858923i | ||||
\(716\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.38704 | − | 1.38704i | −1.38704 | − | 1.38704i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.555570 | − | 0.831470i | \(-0.687500\pi\) | |||||||
\(720\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(728\) | 2.94465 | − | 0.290023i | 2.94465 | − | 0.290023i | ||||
\(729\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(730\) | −1.90466 | + | 0.577774i | −1.90466 | + | 0.577774i | ||||
\(731\) | −0.339130 | − | 0.0674571i | −0.339130 | − | 0.0674571i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.59133 | − | 1.06330i | −1.59133 | − | 1.06330i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
−0.634393 | − | 0.773010i | \(-0.718750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.871028 | + | 0.360791i | 0.871028 | + | 0.360791i | 0.773010 | − | 0.634393i | \(-0.218750\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.448786 | − | 0.368309i | 0.448786 | − | 0.368309i | ||||
\(747\) | 0.858923 | + | 1.28547i | 0.858923 | + | 1.28547i | ||||
\(748\) | 1.76384i | 1.76384i | ||||||||
\(749\) | 1.76972 | − | 0.352020i | 1.76972 | − | 0.352020i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(758\) | 0.192268 | − | 1.95213i | 0.192268 | − | 1.95213i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.382683 | + | 0.0761205i | −0.382683 | + | 0.0761205i | ||||
\(765\) | −0.979938 | + | 1.46658i | −0.979938 | + | 1.46658i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.603227 | −0.603227 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 1.90466 | − | 0.187593i | 1.90466 | − | 0.187593i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.192268 | − | 0.0382444i | 0.192268 | − | 0.0382444i | ||||
\(773\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(774\) | 0.0924099 | − | 0.172887i | 0.0924099 | − | 0.172887i | ||||
\(775\) | −0.636379 | + | 1.53636i | −0.636379 | + | 1.53636i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.108911 | − | 1.10579i | 0.108911 | − | 1.10579i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.149316 | + | 0.750661i | 0.149316 | + | 0.750661i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.46024 | − | 1.01906i | −2.46024 | − | 1.01906i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.924678 | + | 0.183930i | −0.924678 | + | 0.183930i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(788\) | 0.580569i | 0.580569i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.360480 | − | 1.81225i | 0.360480 | − | 1.81225i | ||||
\(797\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.995185 | + | 0.0980171i | −0.995185 | + | 0.0980171i | ||||
\(801\) | − | 1.96157i | − | 1.96157i | ||||||
\(802\) | −0.247528 | + | 0.301614i | −0.247528 | + | 0.301614i | ||||
\(803\) | 1.65493 | + | 1.10579i | 1.65493 | + | 1.10579i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.46024 | − | 0.746304i | 2.46024 | − | 0.746304i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(810\) | −0.634393 | − | 0.773010i | −0.634393 | − | 0.773010i | ||||
\(811\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.577253 | − | 2.90205i | −0.577253 | − | 2.90205i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.658583 | + | 0.352020i | 0.658583 | + | 0.352020i | ||||
\(827\) | 0.301614 | − | 1.51631i | 0.301614 | − | 1.51631i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
0.773010 | − | 0.634393i | \(-0.218750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.785695 | − | 1.17588i | 0.785695 | − | 1.17588i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(830\) | −0.151537 | − | 1.53858i | −0.151537 | − | 1.53858i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.09320 | + | 1.09320i | 1.09320 | + | 1.09320i | ||||
\(833\) | 4.69701 | 4.69701 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.704900 | − | 1.05496i | 0.704900 | − | 1.05496i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.24723 | − | 0.666656i | −1.24723 | − | 0.666656i | ||||
\(839\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
1.00000 | \(0\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(842\) | −1.83886 | − | 0.181112i | −1.83886 | − | 0.181112i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.271211 | − | 1.36347i | −0.271211 | − | 1.36347i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.35332 | − | 1.35332i | −1.35332 | − | 1.35332i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.55557 | − | 0.831470i | 1.55557 | − | 0.831470i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.10579 | − | 1.65493i | −1.10579 | − | 1.65493i | −0.634393 | − | 0.773010i | \(-0.718750\pi\) |
−0.471397 | − | 0.881921i | \(-0.656250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.728789 | + | 0.598102i | 0.728789 | + | 0.598102i | ||||
\(857\) | −1.83886 | − | 0.761681i | −1.83886 | − | 0.761681i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
−0.881921 | − | 0.471397i | \(-0.843750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.38704 | + | 0.275899i | 1.38704 | + | 0.275899i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(860\) | −0.162997 | + | 0.108911i | −0.162997 | + | 0.108911i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.942793i | 0.942793i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.12151 | − | 0.620908i | −3.12151 | − | 0.620908i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.06330 | − | 1.59133i | −1.06330 | − | 1.59133i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.72995 | + | 0.344109i | −1.72995 | + | 0.344109i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(881\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(882\) | −0.773010 | + | 2.54827i | −0.773010 | + | 2.54827i | ||||
\(883\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(884\) | −2.51936 | − | 1.04355i | −2.51936 | − | 1.04355i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.485544 | − | 1.17221i | −0.485544 | − | 1.17221i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
0.471397 | − | 0.881921i | \(-0.343750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.45777 | + | 3.51936i | −1.45777 | + | 3.51936i | ||||
\(890\) | −0.924678 | + | 1.72995i | −0.924678 | + | 1.72995i | ||||
\(891\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.765367 | −0.765367 | ||||||||
\(896\) | −0.555570 | − | 1.83147i | −0.555570 | − | 1.83147i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.10579 | − | 0.108911i | 1.10579 | − | 0.108911i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.707107 | − | 1.70711i | −0.707107 | − | 1.70711i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(908\) | −1.17221 | − | 0.485544i | −1.17221 | − | 0.485544i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.858923 | + | 2.83149i | −0.858923 | + | 2.83149i | ||||
\(911\) | 0.785695 | + | 0.785695i | 0.785695 | + | 0.785695i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.09320 | + | 1.09320i | −1.09320 | + | 1.09320i | ||||
\(914\) | 0.598102 | + | 1.11897i | 0.598102 | + | 1.11897i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.11114 | −1.11114 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.16054 | − | 0.230845i | −1.16054 | − | 0.230845i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.482726 | + | 0.322547i | −0.482726 | + | 0.322547i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.62958 | − | 0.674993i | −1.62958 | − | 0.674993i | ||||
\(936\) | 0.980785 | − | 1.19509i | 0.980785 | − | 1.19509i | ||||
\(937\) | −0.871028 | + | 0.360791i | −0.871028 | + | 0.360791i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.0761205 | + | 0.382683i | 0.0761205 | + | 0.382683i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.187593 | + | 0.0569057i | 0.187593 | + | 0.0569057i | ||||
\(947\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.55856 | + | 1.70957i | −2.55856 | + | 1.70957i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.14157 | + | 2.60952i | 2.14157 | + | 2.60952i | ||||
\(953\) | 0.591637 | − | 1.42834i | 0.591637 | − | 1.42834i | −0.290285 | − | 0.956940i | \(-0.593750\pi\) |
0.881921 | − | 0.471397i | \(-0.156250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0761205 | − | 0.382683i | 0.0761205 | − | 0.382683i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.76537 | −1.76537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.523788 | − | 0.783904i | 0.523788 | − | 0.783904i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.0382444 | + | 0.192268i | −0.0382444 | + | 0.192268i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.674993 | − | 1.62958i | 0.674993 | − | 1.62958i | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) |
0.773010 | − | 0.634393i | \(-0.218750\pi\) | |||||||
\(968\) | 0.0980171 | − | 0.995185i | 0.0980171 | − | 0.995185i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.53636 | − | 1.02656i | 1.53636 | − | 1.02656i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.92388 | − | 0.382683i | 1.92388 | − | 0.382683i | ||||
\(980\) | 1.88298 | − | 1.88298i | 1.88298 | − | 1.88298i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.536376 | − | 0.222174i | −0.536376 | − | 0.222174i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | ||||
\(991\) | − | 1.11114i | − | 1.11114i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(992\) | −0.783904 | − | 1.46658i | −0.783904 | − | 1.46658i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.13232 | + | 0.929273i | 1.13232 | + | 0.929273i | ||||
\(995\) | 1.53636 | + | 1.02656i | 1.53636 | + | 1.02656i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.87711 | + | 0.373380i | 1.87711 | + | 0.373380i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(998\) | 0.482726 | + | 1.59133i | 0.482726 | + | 1.59133i | ||||
\(999\) | 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 | 3520.1.db.a.549.4 | yes | 32 | |
5.4 | even | 2 | inner | 3520.1.db.a.549.1 | yes | 32 | |
11.10 | odd | 2 | inner | 3520.1.db.a.549.1 | yes | 32 | |
55.54 | odd | 2 | CM | 3520.1.db.a.549.4 | yes | 32 | |
64.45 | even | 16 | inner | 3520.1.db.a.109.4 | yes | 32 | |
320.109 | even | 16 | inner | 3520.1.db.a.109.1 | ✓ | 32 | |
704.109 | odd | 16 | inner | 3520.1.db.a.109.1 | ✓ | 32 | |
3520.109 | odd | 16 | inner | 3520.1.db.a.109.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3520.1.db.a.109.1 | ✓ | 32 | 320.109 | even | 16 | inner | |
3520.1.db.a.109.1 | ✓ | 32 | 704.109 | odd | 16 | inner | |
3520.1.db.a.109.4 | yes | 32 | 64.45 | even | 16 | inner | |
3520.1.db.a.109.4 | yes | 32 | 3520.109 | odd | 16 | inner | |
3520.1.db.a.549.1 | yes | 32 | 5.4 | even | 2 | inner | |
3520.1.db.a.549.1 | yes | 32 | 11.10 | odd | 2 | inner | |
3520.1.db.a.549.4 | yes | 32 | 1.1 | even | 1 | trivial | |
3520.1.db.a.549.4 | yes | 32 | 55.54 | odd | 2 | CM |