Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,1,Mod(167,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([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("1932.167");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.bi (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: | \(0.964193604407\) |
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 | 1343.1 | ||
Root | \(0.654861 + 0.755750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1932.1343 |
Dual form | 1932.1.bi.a.1007.1 |
$q$-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 \(\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times\).
\(n\) | \(829\) | \(925\) | \(967\) | \(1289\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{11}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(3\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(4\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(5\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(6\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(7\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(8\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(9\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(10\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(11\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(12\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(13\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(14\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(15\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(16\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(17\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(18\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(19\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(20\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(21\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(22\) | 0.830830 | 0.830830 | ||||||||
\(23\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(24\) | 1.00000 | 1.00000 | ||||||||
\(25\) | −1.75667 | + | 0.515804i | −1.75667 | + | 0.515804i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(28\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(29\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(30\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(31\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
1.00000 | \(0\) | |||||||||
\(32\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(33\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(34\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(35\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(36\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(37\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
1.00000 | \(0\) | |||||||||
\(38\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(41\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(42\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(43\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(44\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(45\) | 1.68251 | 1.68251 | ||||||||
\(46\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(49\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(50\) | 1.54019 | − | 0.989821i | 1.54019 | − | 0.989821i | ||||
\(51\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(54\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(55\) | −0.198939 | + | 1.38365i | −0.198939 | + | 1.38365i | ||||
\(56\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(57\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(60\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(61\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(62\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(63\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(64\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(67\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(68\) | −1.30972 | −1.30972 | ||||||||
\(69\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(70\) | 1.68251 | 1.68251 | ||||||||
\(71\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(72\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(73\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(74\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(75\) | 1.54019 | + | 0.989821i | 1.54019 | + | 0.989821i | ||||
\(76\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(77\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(80\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(81\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(82\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(83\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(84\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(85\) | −0.915415 | + | 2.00448i | −0.915415 | + | 2.00448i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(89\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(90\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(93\) | −1.30972 | −1.30972 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.11435 | + | 2.44009i | 2.11435 | + | 2.44009i | ||||
\(96\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(97\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(98\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(99\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(100\) | −1.19894 | + | 1.38365i | −1.19894 | + | 1.38365i | ||||
\(101\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
1.00000 | \(0\) | |||||||||
\(102\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(103\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(108\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(109\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(110\) | −0.198939 | − | 1.38365i | −0.198939 | − | 1.38365i | ||||
\(111\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(112\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(113\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(114\) | −1.91899 | −1.91899 | ||||||||
\(115\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(120\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(121\) | −0.260554 | − | 0.167448i | −0.260554 | − | 0.167448i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | ||||
\(124\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(125\) | 0.580699 | + | 1.27155i | 0.580699 | + | 1.27155i | ||||
\(126\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(127\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(128\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(132\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(133\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(136\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 1.00000 | 1.00000 | ||||||||
\(139\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(140\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(148\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(149\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(150\) | −1.75667 | − | 0.515804i | −1.75667 | − | 0.515804i | ||||
\(151\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(152\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(153\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(154\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(155\) | −1.85380 | − | 1.19136i | −1.85380 | − | 1.19136i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.68251 | 1.68251 | ||||||||
\(161\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(162\) | 1.00000 | 1.00000 | ||||||||
\(163\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(164\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(165\) | 1.17597 | − | 0.755750i | 1.17597 | − | 0.755750i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(168\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(169\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(170\) | 0.313607 | − | 2.18119i | 0.313607 | − | 2.18119i | ||||
\(171\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.260554 | + | 1.81219i | −0.260554 | + | 1.81219i | ||||
\(176\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(179\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | 1.00000 | \(0\) | ||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(180\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | ||||
\(181\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(185\) | −0.478891 | −0.478891 | ||||||||
\(186\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(187\) | 0.712591 | + | 0.822373i | 0.712591 | + | 0.822373i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(190\) | −2.71616 | − | 1.74557i | −2.71616 | − | 1.74557i | ||||
\(191\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(192\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(193\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(197\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(198\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(199\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(200\) | 0.760554 | − | 1.66538i | 0.760554 | − | 1.66538i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(205\) | 3.09792 | − | 0.909632i | 3.09792 | − | 0.909632i | ||||
\(206\) | −0.284630 | −0.284630 | ||||||||
\(207\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.52977 | − | 0.449181i | 1.52977 | − | 0.449181i | ||||
\(210\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(211\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(214\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(217\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(218\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.580699 | + | 1.27155i | 0.580699 | + | 1.27155i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(223\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(224\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(225\) | −0.260554 | − | 1.81219i | −0.260554 | − | 1.81219i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(228\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(231\) | 0.830830 | 0.830830 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(239\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(240\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(241\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(242\) | 0.297176 | + | 0.0872586i | 0.297176 | + | 0.0872586i | ||||
\(243\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(246\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.915415 | − | 1.05645i | −0.915415 | − | 1.05645i | ||||
\(251\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(252\) | 1.00000 | 1.00000 | ||||||||
\(253\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.11435 | − | 0.620830i | 2.11435 | − | 0.620830i | ||||
\(256\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(257\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
1.00000 | \(0\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(264\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(267\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
1.00000 | \(0\) | |||||||||
\(270\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(271\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(272\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.52111 | 1.52111 | ||||||||
\(276\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(277\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(278\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(279\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(280\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | ||||
\(281\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
1.00000 | \(0\) | |||||||||
\(284\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(285\) | 0.459493 | − | 3.19584i | 0.459493 | − | 3.19584i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(288\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(289\) | 0.297176 | + | 0.650724i | 0.297176 | + | 0.650724i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(294\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(297\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.83083 | 1.83083 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(304\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(307\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(308\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(309\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(310\) | 2.11435 | + | 0.620830i | 2.11435 | + | 0.620830i | ||||
\(311\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(321\) | −1.91899 | −1.91899 | ||||||||
\(322\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(323\) | 2.51334 | 2.51334 | ||||||||
\(324\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(328\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.915415 | + | 1.05645i | −0.915415 | + | 1.05645i | ||||
\(331\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(337\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(338\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.313607 | + | 2.18119i | 0.313607 | + | 2.18119i | ||||
\(341\) | −0.915415 | + | 0.588302i | −0.915415 | + | 0.588302i | ||||
\(342\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(343\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(346\) | 1.68251 | 1.68251 | ||||||||
\(347\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(350\) | −0.260554 | − | 1.81219i | −0.260554 | − | 1.81219i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(353\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.198939 | − | 0.435615i | −0.198939 | − | 0.435615i | ||||
\(356\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(357\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(358\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(359\) | −0.284630 | + | 1.97964i | −0.284630 | + | 1.97964i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(360\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(361\) | 1.11435 | − | 2.44009i | 1.11435 | − | 2.44009i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0440780 | + | 0.306569i | 0.0440780 | + | 0.306569i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(368\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(369\) | −1.91899 | −1.91899 | ||||||||
\(370\) | 0.459493 | − | 0.134919i | 0.459493 | − | 0.134919i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(373\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(374\) | −0.915415 | − | 0.588302i | −0.915415 | − | 0.588302i | ||||
\(375\) | 0.580699 | − | 1.27155i | 0.580699 | − | 1.27155i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(379\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(380\) | 3.09792 | + | 0.909632i | 3.09792 | + | 0.909632i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(383\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(384\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(385\) | 1.17597 | + | 0.755750i | 1.17597 | + | 0.755750i | ||||
\(386\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.30972 | −1.30972 | ||||||||
\(392\) | 1.00000 | 1.00000 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(397\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(398\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(399\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | ||||
\(400\) | −0.260554 | + | 1.81219i | −0.260554 | + | 1.81219i | ||||
\(401\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(405\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0982369 | + | 0.215109i | −0.0982369 | + | 0.215109i | ||||
\(408\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | ||||
\(409\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(410\) | −2.71616 | + | 1.74557i | −2.71616 | + | 1.74557i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(418\) | −1.34125 | + | 0.861971i | −1.34125 | + | 0.861971i | ||||
\(419\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(420\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(421\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.30075 | + | 0.675560i | 2.30075 | + | 0.675560i | ||||
\(426\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(432\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(433\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(434\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.30972 | −1.30972 | ||||||||
\(437\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(440\) | −0.915415 | − | 1.05645i | −0.915415 | − | 1.05645i | ||||
\(441\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(444\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(445\) | 0.313607 | − | 0.361922i | 0.313607 | − | 0.361922i | ||||
\(446\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(449\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(450\) | 0.760554 | + | 1.66538i | 0.760554 | + | 1.66538i | ||||
\(451\) | 0.226900 | − | 1.57812i | 0.226900 | − | 1.57812i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(457\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.30972 | −1.30972 | ||||||||
\(460\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(461\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(462\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(463\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.313607 | + | 2.18119i | 0.313607 | + | 2.18119i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.30075 | − | 2.65520i | 2.30075 | − | 2.65520i | ||||
\(476\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(479\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(480\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(484\) | −0.309721 | −0.309721 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(487\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(491\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(492\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.34125 | − | 0.393828i | −1.34125 | − | 0.393828i | ||||
\(496\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(497\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(500\) | 1.17597 | + | 0.755750i | 1.17597 | + | 0.755750i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(504\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(505\) | −0.478891 | −0.478891 | ||||||||
\(506\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(507\) | 1.00000 | 1.00000 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | 1.00000 | \(0\) | ||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(510\) | −1.85380 | + | 1.19136i | −1.85380 | + | 1.19136i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(513\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(514\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(515\) | 0.0681534 | − | 0.474017i | 0.0681534 | − | 0.474017i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(519\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.54019 | − | 0.989821i | 1.54019 | − | 0.989821i | ||||
\(526\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(527\) | −1.64589 | + | 0.483276i | −1.64589 | + | 0.483276i | ||||
\(528\) | 0.830830 | 0.830830 | ||||||||
\(529\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(535\) | −2.71616 | − | 1.74557i | −2.71616 | − | 1.74557i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(538\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(539\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(540\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(541\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(542\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(545\) | −0.915415 | + | 2.00448i | −0.915415 | + | 2.00448i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.45949 | + | 0.428546i | −1.45949 | + | 0.428546i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(555\) | 0.313607 | + | 0.361922i | 0.313607 | + | 0.361922i | ||||
\(556\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | ||||
\(557\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(558\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | ||||
\(561\) | 0.154861 | − | 1.07708i | 0.154861 | − | 1.07708i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(567\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(568\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(569\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(570\) | 0.459493 | + | 3.19584i | 0.459493 | + | 3.19584i | ||||
\(571\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(574\) | −1.91899 | −1.91899 | ||||||||
\(575\) | −1.19894 | + | 1.38365i | −1.19894 | + | 1.38365i | ||||
\(576\) | 1.00000 | 1.00000 | ||||||||
\(577\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(578\) | −0.468468 | − | 0.540641i | −0.468468 | − | 0.540641i | ||||
\(579\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(587\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(588\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(589\) | −0.357685 | + | 2.48775i | −0.357685 | + | 2.48775i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(593\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(594\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(595\) | 1.44306 | + | 1.66538i | 1.44306 | + | 1.66538i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.830830 | 0.830830 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(600\) | −1.75667 | + | 0.515804i | −1.75667 | + | 0.515804i | ||||
\(601\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.216476 | + | 0.474017i | −0.216476 | + | 0.474017i | ||||
\(606\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(607\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(608\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(613\) | −1.30972 | + | 1.51150i | −1.30972 | + | 1.51150i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(614\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(615\) | −2.71616 | − | 1.74557i | −2.71616 | − | 1.74557i | ||||
\(616\) | −0.118239 | − | 0.822373i | −0.118239 | − | 0.822373i | ||||
\(617\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(618\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(619\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(620\) | −2.20362 | −2.20362 | ||||||||
\(621\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.438384 | − | 0.281733i | 0.438384 | − | 0.281733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.34125 | − | 0.861971i | −1.34125 | − | 0.861971i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.244123 | + | 0.281733i | −0.244123 | + | 0.281733i | ||||
\(630\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(631\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(640\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | ||||
\(641\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(642\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(643\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(644\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.41153 | + | 0.708089i | −2.41153 | + | 0.708089i | ||||
\(647\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(648\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(654\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
1.00000 | \(0\) | |||||||||
\(660\) | 0.580699 | − | 1.27155i | 0.580699 | − | 1.27155i | ||||
\(661\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.09792 | − | 0.909632i | 3.09792 | − | 0.909632i | ||||
\(666\) | −0.284630 | −0.284630 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(673\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(674\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(675\) | −1.19894 | + | 1.38365i | −1.19894 | + | 1.38365i | ||||
\(676\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(677\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.915415 | − | 2.00448i | −0.915415 | − | 2.00448i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.712591 | − | 0.822373i | 0.712591 | − | 0.822373i | ||||
\(683\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(684\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(691\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(692\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(693\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(694\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(695\) | 0.459493 | + | 3.19584i | 0.459493 | + | 3.19584i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.04408 | − | 2.28621i | 1.04408 | − | 2.28621i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.760554 | + | 1.66538i | 0.760554 | + | 1.66538i | ||||
\(701\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.226900 | + | 0.496841i | 0.226900 | + | 0.496841i | ||||
\(704\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(707\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(710\) | 0.313607 | + | 0.361922i | 0.313607 | + | 0.361922i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.284630 | −0.284630 | ||||||||
\(713\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(714\) | −1.30972 | −1.30972 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(717\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(718\) | −0.284630 | − | 1.97964i | −0.284630 | − | 1.97964i | ||||
\(719\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(720\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(721\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(722\) | −0.381761 | + | 2.65520i | −0.381761 | + | 2.65520i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.128663 | − | 0.281733i | −0.128663 | − | 0.281733i | ||||
\(727\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(734\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(735\) | 1.68251 | 1.68251 | ||||||||
\(736\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(739\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(740\) | −0.402869 | + | 0.258908i | −0.402869 | + | 0.258908i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(744\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.04408 | + | 0.306569i | 1.04408 | + | 0.306569i | ||||
\(749\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(750\) | −0.198939 | + | 1.38365i | −0.198939 | + | 1.38365i | ||||
\(751\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(757\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(760\) | −3.22871 | −3.22871 | ||||||||
\(761\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(764\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(765\) | −1.85380 | − | 1.19136i | −1.85380 | − | 1.19136i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(769\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(770\) | −1.34125 | − | 0.393828i | −1.34125 | − | 0.393828i | ||||
\(771\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(772\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(773\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.996114 | + | 2.18119i | −0.996114 | + | 2.18119i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.41153 | − | 2.78305i | −2.41153 | − | 2.78305i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.236479 | −0.236479 | ||||||||
\(782\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(797\) | −1.30972 | + | 1.51150i | −1.30972 | + | 1.51150i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(798\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.260554 | − | 1.81219i | −0.260554 | − | 1.81219i | ||||
\(801\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(808\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(809\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(810\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(811\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | ||||
\(814\) | 0.0336545 | − | 0.234072i | 0.0336545 | − | 0.234072i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.11435 | − | 2.44009i | 2.11435 | − | 2.44009i | ||||
\(821\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(824\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(825\) | −0.996114 | − | 1.14958i | −0.996114 | − | 1.14958i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(828\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(834\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.04408 | − | 1.20493i | 1.04408 | − | 1.20493i | ||||
\(837\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(840\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(841\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(842\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.260554 | + | 0.167448i | −0.260554 | + | 0.167448i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(850\) | −2.39788 | −2.39788 | ||||||||
\(851\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(852\) | −0.284630 | −0.284630 | ||||||||
\(853\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.71616 | + | 1.74557i | −2.71616 | + | 1.74557i | ||||
\(856\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(857\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(862\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(863\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(864\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(865\) | −0.402869 | + | 2.80202i | −0.402869 | + | 2.80202i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.297176 | − | 0.650724i | 0.297176 | − | 0.650724i | ||||
\(868\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(875\) | 1.39788 | 1.39788 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(878\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(879\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(880\) | 1.17597 | + | 0.755750i | 1.17597 | + | 0.755750i | ||||
\(881\) | 0.830830 | − | 1.81926i | 0.830830 | − | 1.81926i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(882\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(883\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(887\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(888\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.198939 | + | 0.435615i | −0.198939 | + | 0.435615i | ||||
\(891\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(892\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.459493 | − | 0.134919i | 0.459493 | − | 0.134919i | ||||
\(896\) | 1.00000 | 1.00000 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.19894 | − | 1.38365i | −1.19894 | − | 1.38365i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.226900 | + | 1.57812i | 0.226900 | + | 1.57812i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(912\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 1.68251 | 1.68251 | ||||||||
\(921\) | 1.68251 | 1.68251 | ||||||||
\(922\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(925\) | 0.0741615 | + | 0.515804i | 0.0741615 | + | 0.515804i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(930\) | −0.915415 | − | 2.00448i | −0.915415 | − | 2.00448i | ||||
\(931\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.19894 | − | 1.38365i | 1.19894 | − | 1.38365i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
1.00000 | \(0\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.45949 | + | 3.19584i | −1.45949 | + | 3.19584i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(953\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.459493 | + | 0.134919i | 0.459493 | + | 0.134919i | ||||
\(956\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(961\) | −0.101808 | − | 0.708089i | −0.101808 | − | 0.708089i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.83083 | 2.83083 | ||||||||
\(966\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0.297176 | − | 0.0872586i | 0.297176 | − | 0.0872586i | ||||
\(969\) | −1.64589 | − | 1.89945i | −1.64589 | − | 1.89945i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(972\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(973\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0982369 | − | 0.215109i | −0.0982369 | − | 0.215109i | ||||
\(980\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(981\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | ||||
\(982\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(983\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(984\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 1.39788 | 1.39788 | ||||||||
\(991\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(992\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(995\) | 1.17597 | + | 0.755750i | 1.17597 | + | 0.755750i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i |
(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 | 1932.1.bi.a.1343.1 | yes | 10 | |
3.2 | odd | 2 | 1932.1.bi.c.1343.1 | yes | 10 | ||
4.3 | odd | 2 | 1932.1.bi.d.1343.1 | yes | 10 | ||
7.6 | odd | 2 | 1932.1.bi.b.1343.1 | yes | 10 | ||
12.11 | even | 2 | 1932.1.bi.b.1343.1 | yes | 10 | ||
21.20 | even | 2 | 1932.1.bi.d.1343.1 | yes | 10 | ||
23.18 | even | 11 | inner | 1932.1.bi.a.1007.1 | ✓ | 10 | |
28.27 | even | 2 | 1932.1.bi.c.1343.1 | yes | 10 | ||
69.41 | odd | 22 | 1932.1.bi.c.1007.1 | yes | 10 | ||
84.83 | odd | 2 | CM | 1932.1.bi.a.1343.1 | yes | 10 | |
92.87 | odd | 22 | 1932.1.bi.d.1007.1 | yes | 10 | ||
161.41 | odd | 22 | 1932.1.bi.b.1007.1 | yes | 10 | ||
276.179 | even | 22 | 1932.1.bi.b.1007.1 | yes | 10 | ||
483.41 | even | 22 | 1932.1.bi.d.1007.1 | yes | 10 | ||
644.363 | even | 22 | 1932.1.bi.c.1007.1 | yes | 10 | ||
1932.1007 | odd | 22 | inner | 1932.1.bi.a.1007.1 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.1.bi.a.1007.1 | ✓ | 10 | 23.18 | even | 11 | inner | |
1932.1.bi.a.1007.1 | ✓ | 10 | 1932.1007 | odd | 22 | inner | |
1932.1.bi.a.1343.1 | yes | 10 | 1.1 | even | 1 | trivial | |
1932.1.bi.a.1343.1 | yes | 10 | 84.83 | odd | 2 | CM | |
1932.1.bi.b.1007.1 | yes | 10 | 161.41 | odd | 22 | ||
1932.1.bi.b.1007.1 | yes | 10 | 276.179 | even | 22 | ||
1932.1.bi.b.1343.1 | yes | 10 | 7.6 | odd | 2 | ||
1932.1.bi.b.1343.1 | yes | 10 | 12.11 | even | 2 | ||
1932.1.bi.c.1007.1 | yes | 10 | 69.41 | odd | 22 | ||
1932.1.bi.c.1007.1 | yes | 10 | 644.363 | even | 22 | ||
1932.1.bi.c.1343.1 | yes | 10 | 3.2 | odd | 2 | ||
1932.1.bi.c.1343.1 | yes | 10 | 28.27 | even | 2 | ||
1932.1.bi.d.1007.1 | yes | 10 | 92.87 | odd | 22 | ||
1932.1.bi.d.1007.1 | yes | 10 | 483.41 | even | 22 | ||
1932.1.bi.d.1343.1 | yes | 10 | 4.3 | odd | 2 | ||
1932.1.bi.d.1343.1 | yes | 10 | 21.20 | even | 2 |