Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,1,Mod(979,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([8, 8, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3332.979");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.bn (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: | \(1.66288462209\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{16}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
Embedding invariants
Embedding label | 2547.1 | ||
Root | \(-0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.2547 |
Dual form | 3332.1.bn.b.1371.1 |
$q$-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 \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(885\) | \(1667\) |
\(\chi(n)\) | \(e\left(\frac{9}{16}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(3\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(4\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(5\) | 1.08979 | + | 1.63099i | 1.08979 | + | 1.63099i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(9\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(10\) | 1.63099 | + | 1.08979i | 1.63099 | + | 1.08979i | ||||
\(11\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 1.00000i | − | 1.00000i | ||||||
\(17\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(18\) | 1.00000 | 1.00000 | ||||||||
\(19\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 1.92388 | + | 0.382683i | 1.92388 | + | 0.382683i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.08979 | + | 2.63099i | −1.08979 | + | 2.63099i | ||||
\(26\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.08979 | − | 1.63099i | −1.08979 | − | 1.63099i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(32\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(37\) | −0.0761205 | + | 0.382683i | −0.0761205 | + | 0.382683i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.92388 | − | 0.382683i | 1.92388 | − | 0.382683i | ||||
\(41\) | 0.617317 | − | 0.923880i | 0.617317 | − | 0.923880i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
1.00000 | \(0\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.382683 | + | 1.92388i | 0.382683 | + | 1.92388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.84776i | 2.84776i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41421i | 1.41421i | ||||||||
\(53\) | −0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.63099 | − | 1.08979i | −1.63099 | − | 1.08979i | ||||
\(59\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.38268 | − | 0.923880i | −1.38268 | − | 0.923880i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(65\) | −2.72078 | − | 0.541196i | −2.72078 | − | 0.541196i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(73\) | 0.216773 | + | 0.324423i | 0.216773 | + | 0.324423i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 0.0761205 | + | 0.382683i | 0.0761205 | + | 0.382683i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(80\) | 1.63099 | − | 1.08979i | 1.63099 | − | 1.08979i | ||||
\(81\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(82\) | 0.216773 | − | 1.08979i | 0.216773 | − | 1.08979i | ||||
\(83\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.08979 | − | 1.63099i | 1.08979 | − | 1.63099i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 1.08979 | + | 1.63099i | 1.08979 | + | 1.63099i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.324423 | − | 0.216773i | 0.324423 | − | 0.216773i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.08979 | + | 2.63099i | 1.08979 | + | 2.63099i | ||||
\(101\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0.541196 | + | 1.30656i | 0.541196 | + | 1.30656i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(107\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.923880 | − | 0.617317i | −0.923880 | − | 0.617317i | − | 1.00000i | \(-0.5\pi\) | |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.63099 | − | 0.324423i | 1.63099 | − | 0.324423i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.92388 | − | 0.382683i | −1.92388 | − | 0.382683i | ||||
\(117\) | −1.30656 | + | 0.541196i | −1.30656 | + | 0.541196i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(122\) | −1.63099 | − | 0.324423i | −1.63099 | − | 0.324423i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.55487 | + | 0.707107i | −3.55487 | + | 0.707107i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(128\) | −0.923880 | − | 0.382683i | −0.923880 | − | 0.382683i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.72078 | + | 0.541196i | −2.72078 | + | 0.541196i | ||||
\(131\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −1.00000 | ||||||||
\(137\) | 0.765367 | 0.765367 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(145\) | 1.47247 | − | 3.55487i | 1.47247 | − | 3.55487i | ||||
\(146\) | 0.324423 | + | 0.216773i | 0.324423 | + | 0.216773i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.216773 | + | 0.324423i | 0.216773 | + | 0.324423i | ||||
\(149\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.00000i | − | 1.00000i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.541196 | − | 0.541196i | −0.541196 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.08979 | − | 1.63099i | 1.08979 | − | 1.63099i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(163\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(164\) | −0.216773 | − | 1.08979i | −0.216773 | − | 1.08979i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.00000i | − | 1.00000i | ||||||
\(170\) | 0.382683 | − | 1.92388i | 0.382683 | − | 1.92388i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.08979 | − | 0.216773i | −1.08979 | − | 0.216773i | −0.382683 | − | 0.923880i | \(-0.625000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(180\) | 1.63099 | + | 1.08979i | 1.63099 | + | 1.08979i | ||||
\(181\) | −0.324423 | − | 1.63099i | −0.324423 | − | 1.63099i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.707107 | + | 0.292893i | −0.707107 | + | 0.292893i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0761205 | − | 0.382683i | −0.0761205 | − | 0.382683i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0.216773 | − | 0.324423i | 0.216773 | − | 0.324423i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.923880 | + | 1.38268i | −0.923880 | + | 1.38268i | 1.00000i | \(0.5\pi\) | ||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(200\) | 2.01367 | + | 2.01367i | 2.01367 | + | 2.01367i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.84776 | − | 0.765367i | 1.84776 | − | 0.765367i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.17958 | 2.17958 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(212\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.08979 | − | 0.216773i | −1.08979 | − | 0.216773i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.01367 | + | 2.01367i | −2.01367 | + | 2.01367i | ||||
\(226\) | 1.38268 | − | 0.923880i | 1.38268 | − | 0.923880i | ||||
\(227\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.92388 | + | 0.382683i | −1.92388 | + | 0.382683i | ||||
\(233\) | 0.617317 | + | 0.923880i | 0.617317 | + | 0.923880i | 1.00000 | \(0\) | ||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(234\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.382683 | − | 0.0761205i | −0.382683 | − | 0.0761205i | − | 1.00000i | \(-0.5\pi\) | |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(242\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.63099 | + | 0.324423i | −1.63099 | + | 0.324423i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.01367 | + | 2.01367i | −3.01367 | + | 2.01367i | ||||
\(251\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.00000 | −1.00000 | ||||||||
\(257\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.30656 | + | 1.54120i | −2.30656 | + | 1.54120i | ||||
\(261\) | −0.382683 | − | 1.92388i | −0.382683 | − | 1.92388i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.24830 | − | 0.834089i | −1.24830 | − | 0.834089i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.0761205 | + | 0.382683i | −0.0761205 | + | 0.382683i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.707107 | − | 0.292893i | 0.707107 | − | 0.292893i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.923880 | − | 0.617317i | 0.923880 | − | 0.617317i | − | 1.00000i | \(-0.5\pi\) | |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | − | 1.00000i | \(-0.5\pi\) | |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 1.00000i | ||||||
\(289\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(290\) | − | 3.84776i | − | 3.84776i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.382683 | + | 0.0761205i | 0.382683 | + | 0.0761205i | ||||
\(293\) | 0.541196 | + | 0.541196i | 0.541196 | + | 0.541196i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.324423 | + | 0.216773i | 0.324423 | + | 0.216773i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 3.26197i | − | 3.26197i | ||||||
\(306\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.923880 | + | 1.38268i | −0.923880 | + | 1.38268i | 1.00000i | \(0.5\pi\) | ||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(314\) | −0.707107 | − | 0.292893i | −0.707107 | − | 0.292893i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.92388 | + | 0.382683i | −1.92388 | + | 0.382683i | −0.923880 | + | 0.382683i | \(0.875000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.382683 | − | 1.92388i | 0.382683 | − | 1.92388i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 1.00000 | ||||||||
\(325\) | −1.54120 | − | 3.72078i | −1.54120 | − | 3.72078i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.617317 | − | 0.923880i | −0.617317 | − | 0.923880i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.216773 | + | 0.324423i | −0.216773 | + | 0.324423i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.63099 | + | 0.324423i | 1.63099 | + | 0.324423i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.382683 | − | 1.92388i | −0.382683 | − | 1.92388i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.08979 | + | 0.216773i | −1.08979 | + | 0.216773i | ||||
\(347\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.30656 | + | 1.30656i | −1.30656 | + | 1.30656i | −0.382683 | + | 0.923880i | \(0.625000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(360\) | 1.92388 | + | 0.382683i | 1.92388 | + | 0.382683i | ||||
\(361\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(362\) | −0.923880 | − | 1.38268i | −0.923880 | − | 1.38268i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.923880 | − | 0.617317i | 0.923880 | − | 0.617317i | ||||
\(370\) | −0.541196 | + | 0.541196i | −0.541196 | + | 0.541196i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.84776i | 1.84776i | 0.382683 | + | 0.923880i | \(0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.72078 | + | 0.541196i | 2.72078 | + | 0.541196i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.216773 | − | 0.324423i | −0.216773 | − | 0.324423i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0761205 | − | 0.382683i | 0.0761205 | − | 0.382683i | ||||
\(389\) | 0.541196 | + | 1.30656i | 0.541196 | + | 1.30656i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.324423 | + | 1.63099i | −0.324423 | + | 1.63099i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.08979 | + | 0.216773i | −1.08979 | + | 0.216773i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.63099 | + | 1.08979i | 2.63099 | + | 1.08979i | ||||
\(401\) | −0.216773 | + | 0.324423i | −0.216773 | + | 0.324423i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.41421 | − | 1.41421i | 1.41421 | − | 1.41421i | ||||
\(405\) | −0.382683 | + | 1.92388i | −0.382683 | + | 1.92388i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.765367i | − | 0.765367i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(410\) | 2.01367 | − | 0.834089i | 2.01367 | − | 0.834089i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.30656 | + | 0.541196i | 1.30656 | + | 0.541196i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.765367i | 0.765367i | ||||||||
\(425\) | 2.84776 | 2.84776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.08979 | + | 0.216773i | −1.08979 | + | 0.216773i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.41421 | 1.41421 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.63099 | − | 1.08979i | −1.63099 | − | 1.08979i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(450\) | −1.08979 | + | 2.63099i | −1.08979 | + | 2.63099i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.923880 | − | 1.38268i | 0.923880 | − | 1.38268i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.541196 | − | 1.30656i | −0.541196 | − | 1.30656i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(458\) | −1.84776 | −1.84776 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.765367 | + | 1.84776i | 0.765367 | + | 1.84776i | 0.382683 | + | 0.923880i | \(0.375000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | −1.63099 | + | 1.08979i | −1.63099 | + | 1.08979i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.923880 | + | 0.617317i | 0.923880 | + | 0.617317i | ||||
\(467\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(468\) | −0.541196 | + | 1.30656i | −0.541196 | + | 1.30656i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.765367 | −0.765367 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.306563 | − | 0.458804i | −0.306563 | − | 0.458804i | ||||
\(482\) | −0.382683 | + | 0.0761205i | −0.382683 | + | 0.0761205i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | ||||
\(485\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(488\) | −1.38268 | + | 0.923880i | −1.38268 | + | 0.923880i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.08979 | + | 1.63099i | −1.08979 | + | 1.63099i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(500\) | −2.01367 | + | 3.01367i | −2.01367 | + | 3.01367i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.17958 | + | 3.26197i | 2.17958 | + | 3.26197i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.84776 | 1.84776 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.30656 | + | 1.30656i | 1.30656 | + | 1.30656i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.54120 | + | 2.30656i | −1.54120 | + | 2.30656i | ||||
\(521\) | −0.216773 | − | 1.08979i | −0.216773 | − | 1.08979i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(522\) | −1.08979 | − | 1.63099i | −1.08979 | − | 1.63099i | ||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(530\) | −1.47247 | − | 0.292893i | −1.47247 | − | 0.292893i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.306563 | + | 1.54120i | 0.306563 | + | 1.54120i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.0761205 | + | 0.382683i | 0.0761205 | + | 0.382683i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.63099 | − | 0.324423i | −1.63099 | − | 0.324423i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(545\) | − | 2.17958i | − | 2.17958i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(548\) | 0.541196 | − | 0.541196i | 0.541196 | − | 0.541196i | ||||
\(549\) | −0.923880 | − | 1.38268i | −0.923880 | − | 1.38268i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.617317 | − | 0.923880i | 0.617317 | − | 0.923880i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.30656 | − | 1.30656i | −1.30656 | − | 1.30656i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.765367 | −0.765367 | ||||||||
\(563\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.30656 | + | 2.30656i | 2.30656 | + | 2.30656i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | 1.00000i | \(0.5\pi\) | ||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(577\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(578\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.47247 | − | 3.55487i | −1.47247 | − | 3.55487i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.382683 | − | 0.0761205i | 0.382683 | − | 0.0761205i | ||||
\(585\) | −2.30656 | − | 1.54120i | −2.30656 | − | 1.54120i | ||||
\(586\) | 0.707107 | + | 0.292893i | 0.707107 | + | 0.292893i | ||||
\(587\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.382683 | + | 0.0761205i | 0.382683 | + | 0.0761205i | ||||
\(593\) | −1.84776 | + | 0.765367i | −1.84776 | + | 0.765367i | −0.923880 | + | 0.382683i | \(0.875000\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.41421 | 1.41421 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.63099 | − | 0.324423i | 1.63099 | − | 0.324423i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.63099 | + | 1.08979i | 1.63099 | + | 1.08979i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.24830 | − | 3.01367i | −1.24830 | − | 3.01367i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(613\) | 1.41421 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.923880 | − | 0.617317i | 0.923880 | − | 0.617317i | − | 1.00000i | \(-0.5\pi\) | |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.01367 | − | 3.01367i | −3.01367 | − | 3.01367i | ||||
\(626\) | −0.324423 | + | 1.63099i | −0.324423 | + | 1.63099i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.765367 | −0.765367 | ||||||||
\(629\) | 0.382683 | − | 0.0761205i | 0.382683 | − | 0.0761205i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.63099 | + | 1.08979i | −1.63099 | + | 1.08979i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.382683 | − | 1.92388i | −0.382683 | − | 1.92388i | ||||
\(641\) | 0.617317 | + | 0.923880i | 0.617317 | + | 0.923880i | 1.00000 | \(0\) | ||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.84776 | − | 2.84776i | −2.84776 | − | 2.84776i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.324423 | + | 0.216773i | 0.324423 | + | 0.216773i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.923880 | − | 0.617317i | −0.923880 | − | 0.617317i | ||||
\(657\) | 0.0761205 | + | 0.382683i | 0.0761205 | + | 0.382683i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.30656 | − | 0.541196i | 1.30656 | − | 0.541196i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0761205 | + | 0.382683i | −0.0761205 | + | 0.382683i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.923880 | + | 1.38268i | −0.923880 | + | 1.38268i | 1.00000i | \(0.5\pi\) | ||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(674\) | 1.63099 | − | 0.324423i | 1.63099 | − | 0.324423i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(677\) | 0.0761205 | − | 0.382683i | 0.0761205 | − | 0.382683i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
1.00000 | \(0\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.08979 | − | 1.63099i | −1.08979 | − | 1.63099i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.834089 | + | 1.24830i | 0.834089 | + | 1.24830i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.414214 | − | 1.00000i | 0.414214 | − | 1.00000i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(692\) | −0.923880 | + | 0.617317i | −0.923880 | + | 0.617317i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08979 | − | 0.216773i | −1.08979 | − | 0.216773i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.30656 | − | 1.30656i | 1.30656 | − | 1.30656i | 0.382683 | − | 0.923880i | \(-0.375000\pi\) |
0.923880 | − | 0.382683i | \(-0.125000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.707107 | + | 1.70711i | −0.707107 | + | 1.70711i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.08979 | + | 1.63099i | 1.08979 | + | 1.63099i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(720\) | 1.92388 | − | 0.382683i | 1.92388 | − | 0.382683i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.38268 | − | 0.923880i | −1.38268 | − | 0.923880i | ||||
\(725\) | 5.47875 | − | 1.08979i | 5.47875 | − | 1.08979i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(730\) | 0.765367i | 0.765367i | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.617317 | − | 0.923880i | 0.617317 | − | 0.923880i | ||||
\(739\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(740\) | −0.292893 | + | 0.707107i | −0.292893 | + | 0.707107i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.541196 | + | 2.72078i | −0.541196 | + | 2.72078i | ||||
\(746\) | 0.707107 | + | 1.70711i | 0.707107 | + | 1.70711i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.72078 | − | 0.541196i | 2.72078 | − | 0.541196i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.63099 | − | 1.08979i | 1.63099 | − | 1.08979i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.41421 | − | 1.41421i | −1.41421 | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.324423 | − | 0.216773i | −0.324423 | − | 0.216773i | ||||
\(773\) | −1.70711 | − | 0.707107i | −1.70711 | − | 0.707107i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0761205 | − | 0.382683i | −0.0761205 | − | 0.382683i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.292893 | − | 1.47247i | 0.292893 | − | 1.47247i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(788\) | 0.324423 | + | 1.63099i | 0.324423 | + | 1.63099i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.30656 | − | 0.458804i | 2.30656 | − | 0.458804i | ||||
\(794\) | −0.923880 | + | 0.617317i | −0.923880 | + | 0.617317i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.30656 | − | 0.541196i | 1.30656 |