Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,1,Mod(29,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 11, 11, 18]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2760.29");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.cm (of order \(22\), degree \(10\), 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: | \(1.37741943487\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\Q(\zeta_{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{11}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
Embedding invariants
Embedding label | 1589.1 | ||
Root | \(0.654861 + 0.755750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1589 |
Dual form | 2760.1.cm.b.1829.1 |
$q$-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 \(\left(\mathbb{Z}/2760\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1657\) | \(1841\) | \(2071\) |
\(\chi(n)\) | \(e\left(\frac{1}{11}\right)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(3\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(4\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(5\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(6\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(7\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(8\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(9\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(10\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(11\) | 1.61435 | − | 1.03748i | 1.61435 | − | 1.03748i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(12\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(13\) | −0.857685 | − | 0.989821i | −0.857685 | − | 0.989821i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(16\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(17\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(18\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(19\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(20\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.91899 | 1.91899 | ||||||||
\(23\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(24\) | −1.00000 | −1.00000 | ||||||||
\(25\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(26\) | −0.186393 | − | 1.29639i | −0.186393 | − | 1.29639i | ||||
\(27\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(30\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(31\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(32\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(33\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(34\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(37\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(40\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(41\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.186393 | − | 1.29639i | −0.186393 | − | 1.29639i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(44\) | 1.61435 | + | 1.03748i | 1.61435 | + | 1.03748i | ||||
\(45\) | −1.00000 | −1.00000 | ||||||||
\(46\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(47\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(48\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(49\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(50\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(51\) | −0.273100 | − | 0.0801894i | −0.273100 | − | 0.0801894i | ||||
\(52\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(53\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(54\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(55\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(59\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(60\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(61\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(62\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(65\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(66\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(67\) | −0.698939 | − | 0.449181i | −0.698939 | − | 0.449181i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(68\) | −0.284630 | −0.284630 | ||||||||
\(69\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(72\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(73\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(74\) | 1.61435 | + | 0.474017i | 1.61435 | + | 0.474017i | ||||
\(75\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(79\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(80\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(81\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | ||||
\(86\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(87\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(88\) | 0.797176 | + | 1.74557i | 0.797176 | + | 1.74557i | ||||
\(89\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(90\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(93\) | −0.830830 | −0.830830 | ||||||||
\(94\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(97\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(98\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(99\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | ||||
\(100\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(101\) | 0.797176 | − | 0.234072i | 0.797176 | − | 0.234072i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(102\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | ||||
\(103\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(104\) | 1.10181 | − | 0.708089i | 1.10181 | − | 0.708089i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(108\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(109\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(110\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(111\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −1.00000 | ||||||||
\(116\) | −1.68251 | −1.68251 | ||||||||
\(117\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | ||||
\(118\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(121\) | 1.11435 | − | 2.44009i | 1.11435 | − | 2.44009i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(125\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(128\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(129\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(130\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(131\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(132\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.345139 | − | 0.755750i | −0.345139 | − | 0.755750i | ||||
\(135\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(136\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(137\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(138\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0405070 | − | 0.281733i | −0.0405070 | − | 0.281733i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.41153 | − | 0.708089i | −2.41153 | − | 0.708089i | ||||
\(144\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(145\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(148\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | ||||
\(149\) | −0.698939 | + | 0.449181i | −0.698939 | + | 0.449181i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(150\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(151\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | ||||
\(156\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(157\) | 0.118239 | + | 0.258908i | 0.118239 | + | 0.258908i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(158\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −1.00000 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 1.00000 | ||||||||
\(163\) | 1.61435 | + | 1.03748i | 1.61435 | + | 1.03748i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.797176 | + | 1.74557i | 0.797176 | + | 1.74557i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.101808 | + | 0.708089i | −0.101808 | + | 0.708089i | ||||
\(170\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.10181 | − | 0.708089i | 1.10181 | − | 0.708089i | ||||
\(173\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(174\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.273100 | + | 1.89945i | −0.273100 | + | 1.89945i | ||||
\(177\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(180\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(181\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(185\) | 1.68251 | 1.68251 | ||||||||
\(186\) | −0.698939 | − | 0.449181i | −0.698939 | − | 0.449181i | ||||
\(187\) | 0.0777324 | + | 0.540641i | 0.0777324 | + | 0.540641i | ||||
\(188\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(192\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(193\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.10181 | − | 0.708089i | 1.10181 | − | 0.708089i | ||||
\(196\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(197\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(198\) | −1.84125 | + | 0.540641i | −1.84125 | + | 0.540641i | ||||
\(199\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(200\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(201\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(202\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0405070 | − | 0.281733i | −0.0405070 | − | 0.281733i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(208\) | 1.30972 | 1.30972 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(216\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(221\) | 0.357685 | − | 0.105026i | 0.357685 | − | 0.105026i | ||||
\(222\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(223\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(226\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(227\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.41542 | − | 0.909632i | −1.41542 | − | 0.909632i | ||||
\(233\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(234\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(235\) | −0.273100 | − | 0.0801894i | −0.273100 | − | 0.0801894i | ||||
\(236\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | ||||
\(237\) | 0.544078 | − | 0.627899i | 0.544078 | − | 0.627899i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(240\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(241\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(242\) | 2.25667 | − | 1.45027i | 2.25667 | − | 1.45027i | ||||
\(243\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(251\) | −1.41542 | − | 0.909632i | −1.41542 | − | 0.909632i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(256\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(257\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | 1.00000 | \(0\) | ||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(258\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(261\) | 0.239446 | − | 1.66538i | 0.239446 | − | 1.66538i | ||||
\(262\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | ||||
\(263\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | 1.00000 | \(0\) | ||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(264\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | ||||
\(269\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | −0.415415 | + | 0.909632i | \(0.636364\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(270\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(271\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(272\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(275\) | 1.91899 | 1.91899 | ||||||||
\(276\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(277\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(282\) | 0.118239 | − | 0.258908i | 0.118239 | − | 0.258908i | ||||
\(283\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.64589 | − | 1.89945i | −1.64589 | − | 1.89945i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(289\) | 0.601808 | + | 0.694523i | 0.601808 | + | 0.694523i | ||||
\(290\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(294\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(295\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(296\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | ||||
\(297\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(298\) | −0.830830 | −0.830830 | ||||||||
\(299\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | ||||
\(300\) | −1.00000 | −1.00000 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(303\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(307\) | 0.239446 | − | 1.66538i | 0.239446 | − | 1.66538i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.698939 | + | 0.449181i | −0.698939 | + | 0.449181i | ||||
\(311\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(312\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(313\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(314\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(317\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.459493 | + | 3.19584i | 0.459493 | + | 3.19584i | ||||
\(320\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(325\) | −0.186393 | − | 1.29639i | −0.186393 | − | 1.29639i | ||||
\(326\) | 0.797176 | + | 1.74557i | 0.797176 | + | 1.74557i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.273100 | + | 1.89945i | −0.273100 | + | 1.89945i | ||||
\(331\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(334\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(335\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(338\) | −0.468468 | + | 0.540641i | −0.468468 | + | 0.540641i | ||||
\(339\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | ||||
\(340\) | −0.273100 | − | 0.0801894i | −0.273100 | − | 0.0801894i | ||||
\(341\) | 0.662317 | + | 1.45027i | 0.662317 | + | 1.45027i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.30972 | 1.30972 | ||||||||
\(345\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(348\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(349\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(352\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | ||||
\(353\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(354\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.544078 | + | 0.627899i | 0.544078 | + | 0.627899i | ||||
\(359\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(361\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.57385 | + | 0.755750i | 2.57385 | + | 0.755750i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.345139 | − | 0.755750i | −0.345139 | − | 0.755750i | ||||
\(373\) | −1.25667 | − | 0.368991i | −1.25667 | − | 0.368991i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(374\) | −0.226900 | + | 0.496841i | −0.226900 | + | 0.496841i | ||||
\(375\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(376\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(377\) | 2.11435 | − | 0.620830i | 2.11435 | − | 0.620830i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(384\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.239446 | + | 0.153882i | 0.239446 | + | 0.153882i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(390\) | 1.30972 | 1.30972 | ||||||||
\(391\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(392\) | 1.00000 | 1.00000 | ||||||||
\(393\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.345139 | − | 0.755750i | −0.345139 | − | 0.755750i | ||||
\(396\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | ||||
\(397\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(398\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(401\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(402\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(403\) | 0.915415 | − | 0.588302i | 0.915415 | − | 0.588302i | ||||
\(404\) | 0.544078 | + | 0.627899i | 0.544078 | + | 0.627899i | ||||
\(405\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.11435 | − | 2.44009i | 2.11435 | − | 2.44009i | ||||
\(408\) | 0.118239 | − | 0.258908i | 0.118239 | − | 0.258908i | ||||
\(409\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.118239 | + | 0.822373i | 0.118239 | + | 0.822373i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 1.00000 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.25667 | − | 0.368991i | −1.25667 | − | 0.368991i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.357685 | − | 2.48775i | 0.357685 | − | 2.48775i | ||||
\(430\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(431\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(432\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(433\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41542 | − | 0.909632i | −1.41542 | − | 0.909632i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(440\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(441\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(442\) | 0.357685 | + | 0.105026i | 0.357685 | + | 0.105026i | ||||
\(443\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(444\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(450\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(453\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.284630 | 0.284630 | ||||||||
\(460\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(461\) | 0.284630 | 0.284630 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(464\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | ||||
\(465\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | ||||
\(466\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(467\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(468\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | ||||
\(471\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(472\) | 1.61435 | − | 1.03748i | 1.61435 | − | 1.03748i | ||||
\(473\) | −1.64589 | − | 1.89945i | −1.64589 | − | 1.89945i | ||||
\(474\) | 0.797176 | − | 0.234072i | 0.797176 | − | 0.234072i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(480\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(481\) | −1.85380 | − | 1.19136i | −1.85380 | − | 1.19136i | ||||
\(482\) | −1.91899 | −1.91899 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.68251 | 2.68251 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(487\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(490\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(491\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.313607 | − | 0.361922i | −0.313607 | − | 0.361922i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(496\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(500\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(501\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | ||||
\(502\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | ||||
\(503\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.830830 | 0.830830 | ||||||||
\(506\) | −1.84125 | + | 0.540641i | −1.84125 | + | 0.540641i | ||||
\(507\) | −0.715370 | −0.715370 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(510\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(517\) | −0.459493 | + | 0.295298i | −0.459493 | + | 0.295298i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(521\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(522\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | ||||
\(523\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(524\) | −0.273100 | − | 0.0801894i | −0.273100 | − | 0.0801894i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(527\) | −0.198939 | − | 0.127850i | −0.198939 | − | 0.127850i | ||||
\(528\) | −1.91899 | −1.91899 | ||||||||
\(529\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.61435 | + | 1.03748i | 1.61435 | + | 1.03748i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.544078 | − | 0.627899i | 0.544078 | − | 0.627899i | ||||
\(537\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(538\) | −1.84125 | + | 0.540641i | −1.84125 | + | 0.540641i | ||||
\(539\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(540\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(541\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(542\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.273100 | − | 0.0801894i | −0.273100 | − | 0.0801894i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(548\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.61435 | + | 1.03748i | 1.61435 | + | 1.03748i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.41542 | − | 0.909632i | −1.41542 | − | 0.909632i | ||||
\(555\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(558\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(559\) | −1.12333 | + | 1.29639i | −1.12333 | + | 1.29639i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.524075 | + | 0.153882i | −0.524075 | + | 0.153882i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(564\) | 0.239446 | − | 0.153882i | 0.239446 | − | 0.153882i | ||||
\(565\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | ||||
\(566\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(572\) | −0.357685 | − | 2.48775i | −0.357685 | − | 2.48775i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(576\) | 1.00000 | 1.00000 | ||||||||
\(577\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(578\) | 0.130785 | + | 0.909632i | 0.130785 | + | 0.909632i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(588\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | ||||
\(593\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(594\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.698939 | − | 0.449181i | −0.698939 | − | 0.449181i | ||||
\(597\) | 1.30972 | 1.30972 | ||||||||
\(598\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(601\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | ||||
\(604\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(605\) | 1.75667 | − | 2.02730i | 1.75667 | − | 2.02730i | ||||
\(606\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(607\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.244123 | + | 0.281733i | 0.244123 | + | 0.281733i | ||||
\(612\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(613\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(614\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(620\) | −0.830830 | −0.830830 | ||||||||
\(621\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(625\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | ||||
\(629\) | −0.0681534 | + | 0.474017i | −0.0681534 | + | 0.474017i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(632\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.857685 | + | 0.989821i | −0.857685 | + | 0.989821i | ||||
\(638\) | −1.34125 | + | 2.93694i | −1.34125 | + | 2.93694i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(641\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.30972 | 1.30972 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(648\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(649\) | −3.53334 | − | 1.03748i | −3.53334 | − | 1.03748i | ||||
\(650\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.273100 | + | 1.89945i | −0.273100 | + | 1.89945i | ||||
\(653\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(660\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | ||||
\(661\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.154861 | + | 0.339098i | 0.154861 | + | 0.339098i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.68251 | −1.68251 | ||||||||
\(667\) | 0.239446 | − | 1.66538i | 0.239446 | − | 1.66538i | ||||
\(668\) | −1.91899 | −1.91899 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(676\) | −0.686393 | + | 0.201543i | −0.686393 | + | 0.201543i | ||||
\(677\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(678\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.226900 | + | 1.57812i | −0.226900 | + | 1.57812i | ||||
\(683\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.25667 | + | 0.368991i | −1.25667 | + | 0.368991i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.239446 | − | 0.153882i | 0.239446 | − | 0.153882i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(702\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.84125 | + | 0.540641i | −1.84125 | + | 0.540641i | ||||
\(705\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(706\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(709\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11435 | − | 1.35881i | −2.11435 | − | 1.35881i | ||||
\(716\) | 0.118239 | + | 0.822373i | 0.118239 | + | 0.822373i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(720\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(723\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(726\) | 1.75667 | + | 2.02730i | 1.75667 | + | 2.02730i | ||||
\(727\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.357685 | + | 0.105026i | 0.357685 | + | 0.105026i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | 1.00000 | ||||||||
\(736\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(737\) | −1.59435 | −1.59435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(740\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(744\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | ||||
\(745\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(746\) | −0.857685 | − | 0.989821i | −0.857685 | − | 0.989821i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.459493 | + | 0.295298i | −0.459493 | + | 0.295298i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(751\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(752\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(753\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(754\) | 2.11435 | + | 0.620830i | 2.11435 | + | 0.620830i | ||||
\(755\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.61435 | + | 1.03748i | 1.61435 | + | 1.03748i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.118239 | − | 0.258908i | 0.118239 | − | 0.258908i | ||||
\(766\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(767\) | −0.357685 | + | 2.48775i | −0.357685 | + | 2.48775i | ||||
\(768\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(769\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | 1.00000 | \(0\) | ||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.698939 | + | 0.449181i | −0.698939 | + | 0.449181i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(774\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | ||||
\(775\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.118239 | + | 0.258908i | 0.118239 | + | 0.258908i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(783\) | 1.68251 | 1.68251 | ||||||||
\(784\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(785\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(786\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(787\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.857685 | + | 0.989821i | −0.857685 | + | 0.989821i | ||||
\(790\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.61435 | − | 1.03748i | 1.61435 | − | 1.03748i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(797\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0336545 | − | 0.0736930i | 0.0336545 | − | 0.0736930i | ||||
\(800\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.830830 | 0.830830 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.08816 | 1.08816 | ||||||||
\(807\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(808\) | 0.118239 | + | 0.822373i | 0.118239 | + | 0.822373i | ||||
\(809\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(810\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(811\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | ||||
\(814\) | 3.09792 | − | 0.909632i | 3.09792 | − | 0.909632i | ||||
\(815\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(816\) | 0.239446 | − | 0.153882i | 0.239446 | − | 0.153882i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.857685 | + | 0.989821i | −0.857685 | + | 0.989821i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(822\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | ||||
\(823\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(832\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(833\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.797176 | − | 0.234072i | 0.797176 | − | 0.234072i | ||||
\(838\) | −0.857685 | − | 0.989821i | −0.857685 | − | 0.989821i | ||||
\(839\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.19894 | − | 1.38365i | −1.19894 | − | 1.38365i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.297176 | + | 0.650724i | −0.297176 | + | 0.650724i | ||||
\(846\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(850\) | −0.284630 | −0.284630 | ||||||||
\(851\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.239446 | + | 0.153882i | 0.239446 | + | 0.153882i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(858\) | 1.64589 | − | 1.89945i | 1.64589 | − | 1.89945i | ||||
\(859\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(860\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(864\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.601808 | + | 0.694523i | −0.601808 | + | 0.694523i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.52977 | − | 0.449181i | −1.52977 | − | 0.449181i | ||||
\(870\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | ||||
\(871\) | 0.154861 | + | 1.07708i | 0.154861 | + | 1.07708i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(878\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(881\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(882\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(883\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(884\) | 0.244123 | + | 0.281733i | 0.244123 | + | 0.281733i | ||||
\(885\) | 1.61435 | − | 1.03748i | 1.61435 | − | 1.03748i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(888\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(895\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.17597 | − | 0.755750i | −1.17597 | − | 0.755750i | ||||
\(900\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | ||||
\(907\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.698939 | + | 0.449181i | −0.698939 | + | 0.449181i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.239446 | + | 0.153882i | 0.239446 | + | 0.153882i | ||||
\(919\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(920\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(921\) | 1.68251 | 1.68251 | ||||||||
\(922\) | 0.239446 | + | 0.153882i | 0.239446 | + | 0.153882i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.61435 | + | 0.474017i | 1.61435 | + | 0.474017i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.239446 | − | 1.66538i | 0.239446 | − | 1.66538i | ||||
\(929\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(930\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0777324 | + | 0.540641i | −0.0777324 | + | 0.540641i | ||||
\(936\) | −0.857685 | + | 0.989821i | −0.857685 | + | 0.989821i | ||||
\(937\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0405070 | − | 0.281733i | −0.0405070 | − | 0.281733i | ||||
\(941\) | −0.698939 | − | 0.449181i | −0.698939 | − | 0.449181i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(942\) | −0.284630 | −0.284630 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.91899 | 1.91899 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.357685 | − | 2.48775i | −0.357685 | − | 2.48775i | ||||
\(947\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(948\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.09792 | + | 0.909632i | −3.09792 | + | 0.909632i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(961\) | 0.297176 | + | 0.0872586i | 0.297176 | + | 0.0872586i | ||||
\(962\) | −0.915415 | − | 2.00448i | −0.915415 | − | 2.00448i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 2.25667 | + | 1.45027i | 2.25667 | + | 1.45027i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(972\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(978\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | ||||
\(983\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.0681534 | − | 0.474017i | −0.0681534 | − | 0.474017i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(990\) | −1.91899 | −1.91899 | ||||||||
\(991\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(992\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i |
(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 | 2760.1.cm.b.1589.1 | yes | 10 | |
3.2 | odd | 2 | 2760.1.cm.d.1589.1 | yes | 10 | ||
5.4 | even | 2 | 2760.1.cm.c.1589.1 | yes | 10 | ||
8.5 | even | 2 | 2760.1.cm.a.1589.1 | ✓ | 10 | ||
15.14 | odd | 2 | 2760.1.cm.a.1589.1 | ✓ | 10 | ||
23.12 | even | 11 | inner | 2760.1.cm.b.1829.1 | yes | 10 | |
24.5 | odd | 2 | 2760.1.cm.c.1589.1 | yes | 10 | ||
40.29 | even | 2 | 2760.1.cm.d.1589.1 | yes | 10 | ||
69.35 | odd | 22 | 2760.1.cm.d.1829.1 | yes | 10 | ||
115.104 | even | 22 | 2760.1.cm.c.1829.1 | yes | 10 | ||
120.29 | odd | 2 | CM | 2760.1.cm.b.1589.1 | yes | 10 | |
184.173 | even | 22 | 2760.1.cm.a.1829.1 | yes | 10 | ||
345.104 | odd | 22 | 2760.1.cm.a.1829.1 | yes | 10 | ||
552.173 | odd | 22 | 2760.1.cm.c.1829.1 | yes | 10 | ||
920.909 | even | 22 | 2760.1.cm.d.1829.1 | yes | 10 | ||
2760.1829 | odd | 22 | inner | 2760.1.cm.b.1829.1 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.1.cm.a.1589.1 | ✓ | 10 | 8.5 | even | 2 | ||
2760.1.cm.a.1589.1 | ✓ | 10 | 15.14 | odd | 2 | ||
2760.1.cm.a.1829.1 | yes | 10 | 184.173 | even | 22 | ||
2760.1.cm.a.1829.1 | yes | 10 | 345.104 | odd | 22 | ||
2760.1.cm.b.1589.1 | yes | 10 | 1.1 | even | 1 | trivial | |
2760.1.cm.b.1589.1 | yes | 10 | 120.29 | odd | 2 | CM | |
2760.1.cm.b.1829.1 | yes | 10 | 23.12 | even | 11 | inner | |
2760.1.cm.b.1829.1 | yes | 10 | 2760.1829 | odd | 22 | inner | |
2760.1.cm.c.1589.1 | yes | 10 | 5.4 | even | 2 | ||
2760.1.cm.c.1589.1 | yes | 10 | 24.5 | odd | 2 | ||
2760.1.cm.c.1829.1 | yes | 10 | 115.104 | even | 22 | ||
2760.1.cm.c.1829.1 | yes | 10 | 552.173 | odd | 22 | ||
2760.1.cm.d.1589.1 | yes | 10 | 3.2 | odd | 2 | ||
2760.1.cm.d.1589.1 | yes | 10 | 40.29 | even | 2 | ||
2760.1.cm.d.1829.1 | yes | 10 | 69.35 | odd | 22 | ||
2760.1.cm.d.1829.1 | yes | 10 | 920.909 | even | 22 |