Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,1,Mod(13,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(32))
chi = DirichletCharacter(H, H._module([0, 15, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.bm (of order \(32\), 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: | \(0.447162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{32})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1 \) |
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 | 573.1 | ||
Root | \(-0.195090 - 0.980785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.573 |
Dual form | 896.1.bm.a.405.1 |
$q$-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 \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{19}{32}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | ||||
\(3\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(4\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(5\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(8\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(9\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0924099 | + | 0.938254i | 0.0924099 | + | 0.938254i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) | ||||
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(14\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(17\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(19\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.831470 | + | 0.444430i | 0.831470 | + | 0.444430i | ||||
\(23\) | −0.216773 | − | 0.324423i | −0.216773 | − | 0.324423i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(29\) | −0.577774 | − | 0.0569057i | −0.577774 | − | 0.0569057i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(32\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(37\) | −0.172887 | + | 0.0924099i | −0.172887 | + | 0.0924099i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.53858 | + | 1.26268i | 1.53858 | + | 1.26268i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0.831470 | − | 0.444430i | 0.831470 | − | 0.444430i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.390181 | −0.390181 | ||||||||
\(47\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(50\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.26268 | + | 0.124363i | −1.26268 | + | 0.124363i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −1.00000 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.368309 | + | 0.448786i | −0.368309 | + | 0.448786i | ||||
\(59\) | 0 | 0 | −0.956940 | − | 0.290285i | \(-0.906250\pi\) | ||||
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.634393 | − | 0.773010i | \(-0.718750\pi\) | ||||
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 1.00000i | ||||||
\(64\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.980785 | + | 1.19509i | 0.980785 | + | 1.19509i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.360480 | + | 1.81225i | 0.360480 | + | 1.81225i | 0.555570 | + | 0.831470i | \(0.312500\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(72\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(73\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(74\) | −0.0192147 | + | 0.195090i | −0.0192147 | + | 0.195090i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.273678 | + | 0.902197i | 0.273678 | + | 0.902197i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.53636 | + | 0.636379i | −1.53636 | + | 0.636379i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.90466 | − | 0.577774i | 1.90466 | − | 0.577774i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0924099 | − | 0.938254i | 0.0924099 | − | 0.938254i | ||||
\(89\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.216773 | + | 0.324423i | −0.216773 | + | 0.324423i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(98\) | 0.195090 | − | 0.980785i | 0.195090 | − | 0.980785i | ||||
\(99\) | 0.938254 | + | 0.0924099i | 0.938254 | + | 0.0924099i | ||||
\(100\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(101\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.598102 | + | 1.11897i | −0.598102 | + | 1.11897i | ||||
\(107\) | −0.804910 | + | 0.980785i | −0.804910 | + | 0.980785i | 0.195090 | + | 0.980785i | \(0.437500\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.831470 | − | 1.55557i | 0.831470 | − | 1.55557i | − | 1.00000i | \(-0.5\pi\) | |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(113\) | 0.750661 | + | 1.81225i | 0.750661 | + | 1.81225i | 0.555570 | + | 0.831470i | \(0.312500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.168530 | + | 0.555570i | 0.168530 | + | 0.555570i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.109005 | − | 0.0216824i | 0.109005 | − | 0.0216824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(127\) | −0.765367 | −0.765367 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(128\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.53858 | − | 0.151537i | 1.53858 | − | 0.151537i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.324423 | − | 1.63099i | 0.324423 | − | 1.63099i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.70711 | + | 0.707107i | 1.70711 | + | 0.707107i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.151537 | + | 0.124363i | 0.151537 | + | 0.124363i | ||||
\(149\) | −0.980785 | + | 1.19509i | −0.980785 | + | 1.19509i | 1.00000i | \(0.5\pi\) | ||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.617317 | − | 0.923880i | −0.617317 | − | 0.923880i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.902197 | + | 0.273678i | 0.902197 | + | 0.273678i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(158\) | −0.324423 | + | 1.63099i | −0.324423 | + | 1.63099i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.275899 | − | 0.275899i | −0.275899 | − | 0.275899i | ||||
\(162\) | −0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | ||||
\(163\) | 0.187593 | − | 1.90466i | 0.187593 | − | 1.90466i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.577774 | − | 1.90466i | 0.577774 | − | 1.90466i | ||||
\(173\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(176\) | −0.728789 | − | 0.598102i | −0.728789 | − | 0.598102i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0569057 | − | 0.187593i | −0.0569057 | − | 0.187593i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.149316 | + | 0.360480i | 0.149316 | + | 0.360480i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.11114i | − | 1.11114i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 0.390181i | − | 0.390181i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(197\) | −1.90466 | − | 0.577774i | −1.90466 | − | 0.577774i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.923880 | − | 0.382683i | \(-0.875000\pi\) | |||||||
\(198\) | 0.598102 | − | 0.728789i | 0.598102 | − | 0.728789i | ||||
\(199\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(200\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.577774 | + | 0.0569057i | −0.577774 | + | 0.0569057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.360480 | + | 0.149316i | −0.360480 | + | 0.149316i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.512016 | − | 0.273678i | −0.512016 | − | 0.273678i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(212\) | 0.598102 | + | 1.11897i | 0.598102 | + | 1.11897i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.368309 | + | 1.21415i | 0.368309 | + | 1.21415i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.831470 | − | 1.55557i | −0.831470 | − | 1.55557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(224\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(225\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(226\) | 1.92388 | + | 0.382683i | 1.92388 | + | 0.382683i | ||||
\(227\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.555570 | + | 0.168530i | 0.555570 | + | 0.168530i | ||||
\(233\) | 0.923880 | + | 1.38268i | 0.923880 | + | 1.38268i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.292893 | − | 0.707107i | 0.292893 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
1.00000 | \(0\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(242\) | 0.0425316 | − | 0.102680i | 0.0425316 | − | 0.102680i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(252\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(253\) | 0.284359 | − | 0.233368i | 0.284359 | − | 0.233368i | ||||
\(254\) | −0.425215 | + | 0.636379i | −0.425215 | + | 0.636379i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | − | 1.00000i | − | 1.00000i | ||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.151537 | + | 0.124363i | −0.151537 | + | 0.124363i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.168530 | + | 0.555570i | −0.168530 | + | 0.555570i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.38704 | − | 0.275899i | 1.38704 | − | 0.275899i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.728789 | − | 1.36347i | 0.728789 | − | 1.36347i | ||||
\(269\) | 0 | 0 | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) | ||||
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.17588 | − | 1.17588i | −1.17588 | − | 1.17588i | ||||
\(275\) | 0.444430 | − | 0.831470i | 0.444430 | − | 0.831470i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.11897 | + | 1.36347i | −1.11897 | + | 1.36347i | −0.195090 | + | 0.980785i | \(0.562500\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.923880 | − | 0.617317i | −0.923880 | − | 0.617317i | − | 1.00000i | \(-0.5\pi\) | |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(284\) | 1.53636 | − | 1.02656i | 1.53636 | − | 1.02656i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 1.00000 | ||||||||
\(289\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.187593 | − | 0.0569057i | 0.187593 | − | 0.0569057i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.448786 | + | 1.47945i | 0.448786 | + | 1.47945i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.75535 | + | 0.938254i | 1.75535 | + | 0.938254i | ||||
\(302\) | −1.11114 | −1.11114 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(308\) | 0.728789 | − | 0.598102i | 0.728789 | − | 0.598102i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.17588 | + | 1.17588i | 1.17588 | + | 1.17588i | ||||
\(317\) | −1.21415 | − | 1.47945i | −1.21415 | − | 1.47945i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.547357i | − | 0.547357i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.382683 | + | 0.0761205i | −0.382683 | + | 0.0761205i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000i | 1.00000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.47945 | − | 1.21415i | −1.47945 | − | 1.21415i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.90466 | + | 0.187593i | −1.90466 | + | 0.187593i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0569057 | + | 0.187593i | 0.0569057 | + | 0.187593i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.81225 | + | 0.750661i | 1.81225 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(338\) | − | 1.00000i | − | 1.00000i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(344\) | −1.26268 | − | 1.53858i | −1.26268 | − | 1.53858i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.68789 | + | 0.902197i | −1.68789 | + | 0.902197i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(350\) | −0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.902197 | + | 0.273678i | −0.902197 | + | 0.273678i | ||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.187593 | − | 0.0569057i | −0.187593 | − | 0.0569057i | ||||
\(359\) | −1.63099 | − | 1.08979i | −1.63099 | − | 1.08979i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(368\) | 0.382683 | + | 0.0761205i | 0.382683 | + | 0.0761205i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.21415 | + | 0.368309i | −1.21415 | + | 0.368309i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.0924099 | + | 0.938254i | 0.0924099 | + | 0.938254i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.368309 | − | 1.21415i | 0.368309 | − | 1.21415i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.923880 | − | 0.617317i | −0.923880 | − | 0.617317i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.324423 | − | 0.216773i | −0.324423 | − | 0.216773i | ||||
\(387\) | 1.53858 | − | 1.26268i | 1.53858 | − | 1.26268i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.577774 | − | 1.90466i | 0.577774 | − | 1.90466i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.53858 | + | 1.26268i | −1.53858 | + | 1.26268i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.273678 | − | 0.902197i | −0.273678 | − | 0.902197i | ||||
\(397\) | 0 | 0 | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) | ||||
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.980785 | − | 0.195090i | 0.980785 | − | 0.195090i | ||||
\(401\) | −0.750661 | + | 1.81225i | −0.750661 | + | 1.81225i | −0.195090 | + | 0.980785i | \(0.562500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.273678 | + | 0.512016i | −0.273678 | + | 0.512016i | ||||
\(407\) | −0.102680 | − | 0.153672i | −0.102680 | − | 0.153672i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0761205 | + | 0.382683i | −0.0761205 | + | 0.382683i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68789 | − | 0.902197i | 1.68789 | − | 0.902197i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(422\) | −0.512016 | + | 0.273678i | −0.512016 | + | 0.273678i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.26268 | + | 0.124363i | 1.26268 | + | 0.124363i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.21415 | + | 0.368309i | 1.21415 | + | 0.368309i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.75535 | − | 0.172887i | −1.75535 | − | 0.172887i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.195090 | − | 0.980785i | −0.195090 | − | 0.980785i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.187593 | − | 0.0569057i | −0.187593 | − | 0.0569057i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.980785 | + | 0.195090i | 0.980785 | + | 0.195090i | ||||
\(449\) | − | 1.84776i | − | 1.84776i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(450\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.38704 | − | 1.38704i | 1.38704 | − | 1.38704i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.750661 | + | 0.149316i | 0.750661 | + | 0.149316i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.81225 | + | 0.750661i | −1.81225 | + | 0.750661i | −0.831470 | + | 0.555570i | \(0.812500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(464\) | 0.448786 | − | 0.368309i | 0.448786 | − | 0.368309i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.66294 | 1.66294 | ||||||||
\(467\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.19509 | + | 0.980785i | 1.19509 | + | 0.980785i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.04253 | + | 1.56026i | −1.04253 | + | 1.56026i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.124363 | + | 1.26268i | −0.124363 | + | 1.26268i | ||||
\(478\) | −0.425215 | − | 0.636379i | −0.425215 | − | 0.636379i | ||||
\(479\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.0617463 | − | 0.0924099i | −0.0617463 | − | 0.0924099i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.38268 | + | 0.923880i | 1.38268 | + | 0.923880i | 1.00000 | \(0\) | ||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.980785 | − | 1.19509i | 0.980785 | − | 1.19509i | − | 1.00000i | \(-0.5\pi\) | |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.47945 | + | 0.448786i | −1.47945 | + | 0.448786i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(504\) | −0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0360566 | − | 0.366088i | −0.0360566 | − | 0.366088i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | ||||
\(509\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.0192147 | + | 0.195090i | 0.0192147 | + | 0.195090i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(522\) | 0.368309 | + | 0.448786i | 0.368309 | + | 0.448786i | ||||
\(523\) | 0 | 0 | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.541196 | − | 1.30656i | 0.541196 | − | 1.30656i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.324423 | − | 0.783227i | 0.324423 | − | 0.783227i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.728789 | − | 1.36347i | −0.728789 | − | 1.36347i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.444430 | + | 0.831470i | 0.444430 | + | 0.831470i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.26268 | + | 0.124363i | 1.26268 | + | 0.124363i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0569057 | − | 0.577774i | 0.0569057 | − | 0.577774i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(548\) | −1.63099 | + | 0.324423i | −1.63099 | + | 0.324423i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.444430 | − | 0.831470i | −0.444430 | − | 0.831470i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.38268 | + | 0.923880i | −1.38268 | + | 0.923880i | ||||
\(554\) | 0.512016 | + | 1.68789i | 0.512016 | + | 1.68789i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.55557 | + | 0.831470i | 1.55557 | + | 0.831470i | 1.00000 | \(0\) | ||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.02656 | + | 0.425215i | −1.02656 | + | 0.425215i | ||||
\(563\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(568\) | − | 1.84776i | − | 1.84776i | ||||||
\(569\) | 0.149316 | + | 0.750661i | 0.149316 | + | 0.750661i | 0.980785 | + | 0.195090i | \(0.0625000\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.555570 | + | 0.168530i | 0.555570 | + | 0.168530i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.390181i | 0.390181i | ||||||||
\(576\) | 0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | ||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | −0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.233368 | − | 1.17322i | −0.233368 | − | 1.17322i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0569057 | − | 0.187593i | 0.0569057 | − | 0.187593i | ||||
\(593\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.47945 | + | 0.448786i | 1.47945 | + | 0.448786i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17588 | − | 0.785695i | 1.17588 | − | 0.785695i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(602\) | 1.75535 | − | 0.938254i | 1.75535 | − | 0.938254i | ||||
\(603\) | 1.36347 | − | 0.728789i | 1.36347 | − | 0.728789i | ||||
\(604\) | −0.617317 | + | 0.923880i | −0.617317 | + | 0.923880i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.902197 | + | 1.68789i | 0.902197 | + | 1.68789i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0924099 | − | 0.938254i | −0.0924099 | − | 0.938254i | ||||
\(617\) | 0.425215 | + | 0.636379i | 0.425215 | + | 0.636379i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.634393 | − | 0.773010i | \(-0.281250\pi\) | ||||
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.360480 | + | 1.81225i | −0.360480 | + | 1.81225i | 0.195090 | + | 0.980785i | \(0.437500\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(632\) | 1.63099 | − | 0.324423i | 1.63099 | − | 0.324423i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.90466 | + | 0.187593i | −1.90466 | + | 0.187593i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.455111 | − | 0.304095i | −0.455111 | − | 0.304095i | ||||
\(639\) | 1.84776 | 1.84776 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.390181 | −0.390181 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(644\) | −0.149316 | + | 0.360480i | −0.149316 | + | 0.360480i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(648\) | 0.831470 | + | 0.555570i | 0.831470 | + | 0.555570i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.83147 | + | 0.555570i | −1.83147 | + | 0.555570i | ||||
\(653\) | 0.902197 | − | 0.273678i | 0.902197 | − | 0.273678i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.831470 | − | 1.55557i | 0.831470 | − | 1.55557i | − | 1.00000i | \(-0.5\pi\) | |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.634393 | − | 0.773010i | \(-0.281250\pi\) | ||||
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(662\) | −0.902197 | + | 1.68789i | −0.902197 | + | 1.68789i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.187593 | + | 0.0569057i | 0.187593 | + | 0.0569057i | ||||
\(667\) | 0.106784 | + | 0.199779i | 0.106784 | + | 0.199779i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(674\) | 1.63099 | − | 1.08979i | 1.63099 | − | 1.08979i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.831470 | − | 0.555570i | −0.831470 | − | 0.555570i | ||||
\(677\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.151537 | + | 0.124363i | 0.151537 | + | 0.124363i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1.00000i | − | 1.00000i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.98079 | + | 0.195090i | −1.98079 | + | 0.195090i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.938254 | − | 0.0924099i | 0.938254 | − | 0.0924099i | ||||
\(694\) | −0.187593 | + | 1.90466i | −0.187593 | + | 1.90466i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000i | 1.00000i | ||||||||
\(701\) | −1.26268 | − | 1.53858i | −1.26268 | − | 1.53858i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.555570 | − | 0.831470i | \(-0.687500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.273678 | + | 0.902197i | −0.273678 | + | 0.902197i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.902197 | − | 0.273678i | −0.902197 | − | 0.273678i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.324423 | + | 1.63099i | 0.324423 | + | 1.63099i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.151537 | + | 0.124363i | −0.151537 | + | 0.124363i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.81225 | + | 0.750661i | −1.81225 | + | 0.750661i | ||||
\(719\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −1.00000 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.448786 | + | 0.368309i | 0.448786 | + | 0.368309i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.275899 | − | 0.275899i | 0.275899 | − | 0.275899i | ||||
\(737\) | −1.03066 | + | 1.03066i | −1.03066 | + | 1.03066i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.75535 | − | 0.172887i | −1.75535 | − | 0.172887i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.368309 | + | 1.21415i | −0.368309 | + | 1.21415i | ||||
\(743\) | 0.923880 | + | 0.617317i | 0.923880 | + | 0.617317i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.831470 | + | 0.444430i | 0.831470 | + | 0.444430i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.598102 | + | 1.11897i | −0.598102 | + | 1.11897i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | 1.00000i | \(0.5\pi\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.124363 | − | 1.26268i | −0.124363 | − | 1.26268i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(758\) | −0.804910 | − | 0.980785i | −0.804910 | − | 0.980785i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.512016 | − | 1.68789i | 0.512016 | − | 1.68789i | ||||
\(764\) | −1.02656 | + | 0.425215i | −1.02656 | + | 0.425215i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.360480 | + | 0.149316i | −0.360480 | + | 0.149316i | ||||
\(773\) | 0 | 0 | 0.290285 | − | 0.956940i | \(-0.406250\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(774\) | −0.195090 | − | 1.98079i | −0.195090 | − | 1.98079i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.26268 | − | 1.53858i | −1.26268 | − | 1.53858i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.66704 | + | 0.505692i | −1.66704 | + | 0.505692i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.471397 | − | 0.881921i | \(-0.343750\pi\) | ||||
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(788\) | 0.195090 | + | 1.98079i | 0.195090 | + | 1.98079i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.08979 | + | 1.63099i | 1.08979 | + | 1.63099i | ||||
\(792\) | −0.902197 | − | 0.273678i | −0.902197 | − | 0.273678i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) | ||||
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.08979 | + | 1.63099i | 1.08979 | + | 1.63099i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.636379 | − | 0.425215i | 0.636379 | − | 0.425215i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(812\) | 0.273678 | + | 0.512016i | 0.273678 | + | 0.512016i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.184820 | −0.184820 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.90466 | − | 0.187593i | 1.90466 | − | 0.187593i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.38704 | − | 0.275899i | −1.38704 | − | 0.275899i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.90466 | − | 0.577774i | −1.90466 | − | 0.577774i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.923880 | − | 0.382683i | \(-0.875000\pi\) | |||||||
\(828\) | 0.275899 | + | 0.275899i | 0.275899 | + | 0.275899i | ||||
\(829\) | 0 | 0 | −0.634393 | − | 0.773010i | \(-0.718750\pi\) | ||||
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.650201 | − | 0.129333i | −0.650201 | − | 0.129333i | ||||
\(842\) | 0.187593 | − | 1.90466i | 0.187593 | − | 1.90466i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.0569057 | + | 0.577774i | −0.0569057 | + | 0.577774i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.102680 | − | 0.0425316i | 0.102680 | − | 0.0425316i | ||||
\(848\) | 0.804910 | − | 0.980785i | 0.804910 | − | 0.980785i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0674571 | + | 0.0360566i | 0.0674571 | + | 0.0360566i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.773010 | − | 0.634393i | \(-0.781250\pi\) | ||||
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.980785 | − | 0.804910i | 0.980785 | − | 0.804910i | ||||
\(857\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.17588 | − | 0.785695i | 1.17588 | − | 0.785695i | ||||
\(863\) | 0.785695 | + | 0.785695i | 0.785695 | + | 0.785695i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.739060 | − | 1.38268i | −0.739060 | − | 1.38268i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.11897 | + | 1.36347i | −1.11897 | + | 1.36347i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.938254 | − | 1.75535i | 0.938254 | − | 1.75535i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.555570 | − | 0.831470i | \(-0.312500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(882\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(883\) | −1.83147 | + | 0.555570i | −1.83147 | + | 0.555570i | −0.831470 | + | 0.555570i | \(0.812500\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.151537 | + | 0.124363i | −0.151537 | + | 0.124363i | ||||
\(887\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.750661 | + | 0.149316i | −0.750661 | + | 0.149316i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.273678 | − | 0.902197i | 0.273678 | − | 0.902197i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.53636 | − | 1.02656i | −1.53636 | − | 1.02656i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.382683 | − | 1.92388i | −0.382683 | − | 1.92388i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.172887 | + | 1.75535i | 0.172887 | + | 1.75535i | 0.555570 | + | 0.831470i | \(0.312500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.425215 | − | 0.636379i | −0.425215 | − | 0.636379i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.195090 | + | 0.0192147i | 0.195090 | + | 0.0192147i | ||||
\(926\) | −0.382683 | + | 1.92388i | −0.382683 | + | 1.92388i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.0569057 | − | 0.577774i | −0.0569057 | − | 0.577774i | ||||
\(929\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.923880 | − | 1.38268i | 0.923880 | − | 1.38268i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(938\) | 1.47945 | − | 0.448786i | 1.47945 | − | 0.448786i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.718108 | + | 1.73367i | 0.718108 | + | 1.73367i | ||||
\(947\) | 0.512016 | + | 1.68789i | 0.512016 | + | 1.68789i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.216773 | + | 1.08979i | 0.216773 | + | 1.08979i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(954\) | 0.980785 | + | 0.804910i | 0.980785 | + | 0.804910i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.765367 | −0.765367 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.66294i | − | 1.66294i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 1.00000i | − | 1.00000i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.804910 | + | 0.980785i | 0.804910 | + | 0.980785i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.216773 | + | 1.08979i | 0.216773 | + | 1.08979i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | −0.111140 | −0.111140 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) | ||||
−0.995185 | + | 0.0980171i | \(0.968750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.53636 | − | 0.636379i | 1.53636 | − | 0.636379i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.36347 | − | 1.11897i | −1.36347 | − | 1.11897i | ||||
\(982\) | −0.448786 | − | 1.47945i | −0.448786 | − | 1.47945i | ||||
\(983\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0761205 | − | 0.772864i | 0.0761205 | − | 0.772864i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.38704 | + | 1.38704i | 1.38704 | + | 1.38704i | 0.831470 | + | 0.555570i | \(0.187500\pi\) |
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.81225 | + | 0.360480i | 1.81225 | + | 0.360480i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.471397 | − | 0.881921i | \(-0.656250\pi\) | ||||
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(998\) | −0.448786 | + | 1.47945i | −0.448786 | + | 1.47945i | ||||
\(999\) | 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 | 896.1.bm.a.573.1 | yes | 16 | |
4.3 | odd | 2 | 3584.1.bm.a.2897.1 | 16 | |||
7.6 | odd | 2 | CM | 896.1.bm.a.573.1 | yes | 16 | |
28.27 | even | 2 | 3584.1.bm.a.2897.1 | 16 | |||
128.21 | even | 32 | inner | 896.1.bm.a.405.1 | ✓ | 16 | |
128.107 | odd | 32 | 3584.1.bm.a.433.1 | 16 | |||
896.363 | even | 32 | 3584.1.bm.a.433.1 | 16 | |||
896.405 | odd | 32 | inner | 896.1.bm.a.405.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.1.bm.a.405.1 | ✓ | 16 | 128.21 | even | 32 | inner | |
896.1.bm.a.405.1 | ✓ | 16 | 896.405 | odd | 32 | inner | |
896.1.bm.a.573.1 | yes | 16 | 1.1 | even | 1 | trivial | |
896.1.bm.a.573.1 | yes | 16 | 7.6 | odd | 2 | CM | |
3584.1.bm.a.433.1 | 16 | 128.107 | odd | 32 | |||
3584.1.bm.a.433.1 | 16 | 896.363 | even | 32 | |||
3584.1.bm.a.2897.1 | 16 | 4.3 | odd | 2 | |||
3584.1.bm.a.2897.1 | 16 | 28.27 | even | 2 |