Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1127,1,Mod(99,1127)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1127, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 19]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1127.99");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1127 = 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1127.o (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: | \(0.562446269237\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{22}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{22} - \cdots)\) |
Embedding invariants
Embedding label | 442.1 | ||
Root | \(0.142315 - 0.989821i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1127.442 |
Dual form | 1127.1.o.a.589.1 |
$q$-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 \(\left(\mathbb{Z}/1127\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{22}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61435 | + | 0.474017i | 1.61435 | + | 0.474017i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(3\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(4\) | 1.54019 | + | 0.989821i | 1.54019 | + | 0.989821i | ||||
\(5\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.915415 | + | 1.05645i | 0.915415 | + | 1.05645i | ||||
\(9\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.425839 | − | 1.45027i | −0.425839 | − | 1.45027i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.216476 | + | 0.474017i | 0.216476 | + | 0.474017i | ||||
\(17\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(18\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | ||||
\(19\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.54311i | − | 2.54311i | ||||||
\(23\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.61435 | + | 1.03748i | −1.61435 | + | 1.03748i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(32\) | −0.0741615 | − | 0.515804i | −0.0741615 | − | 0.515804i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.760554 | + | 1.66538i | −0.760554 | + | 1.66538i | ||||
\(37\) | 1.80075 | − | 0.258908i | 1.80075 | − | 0.258908i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.49611 | − | 1.29639i | −1.49611 | − | 1.29639i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(44\) | 0.779638 | − | 2.65520i | 0.779638 | − | 2.65520i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.41542 | − | 0.909632i | −1.41542 | − | 0.909632i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.512546 | − | 0.234072i | 0.512546 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.09792 | + | 0.909632i | −3.09792 | + | 0.909632i | ||||
\(59\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.198939 | − | 1.38365i | 0.198939 | − | 1.38365i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.304632 | − | 1.03748i | 0.304632 | − | 1.03748i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(72\) | −0.915415 | + | 1.05645i | −0.915415 | + | 1.05645i | ||||
\(73\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(74\) | 3.02977 | + | 0.435615i | 3.02977 | + | 0.435615i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.512546 | − | 0.234072i | −0.512546 | − | 0.234072i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.80075 | − | 2.80202i | −1.80075 | − | 2.80202i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.14231 | − | 1.77748i | 1.14231 | − | 1.77748i | ||||
\(89\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.19894 | + | 1.38365i | −1.19894 | + | 1.38365i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.37491 | − | 0.627899i | 1.37491 | − | 0.627899i | ||||
\(100\) | −1.19894 | − | 1.38365i | −1.19894 | − | 1.38365i | ||||
\(101\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.938384 | − | 0.134919i | 0.938384 | − | 0.134919i | ||||
\(107\) | −1.37491 | + | 1.19136i | −1.37491 | + | 1.19136i | −0.415415 | + | 0.909632i | \(0.636364\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.584585 | + | 0.909632i | 0.584585 | + | 0.909632i | 1.00000 | \(0\) | ||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.557730 | + | 1.89945i | −0.557730 | + | 1.89945i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.51334 | −3.51334 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.08070 | + | 0.694523i | −1.08070 | + | 0.694523i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(128\) | 0.760554 | − | 1.66538i | 0.760554 | − | 1.66538i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.983568 | − | 1.53046i | 0.983568 | − | 1.53046i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.08128i | 1.08128i | 0.841254 | + | 0.540641i | \(0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.85380 | + | 1.19136i | 1.85380 | + | 1.19136i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.438384 | + | 0.281733i | −0.438384 | + | 0.281733i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.02977 | + | 1.38365i | 3.02977 | + | 1.38365i | ||||
\(149\) | −0.557730 | − | 1.89945i | −0.557730 | − | 1.89945i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(158\) | −0.716476 | − | 0.620830i | −0.716476 | − | 0.620830i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.68251 | −1.68251 | ||||||||
\(163\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | 1.00000 | \(0\) | ||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.02111 | − | 3.47758i | −1.02111 | − | 3.47758i | ||||
\(173\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.595270 | − | 0.515804i | 0.595270 | − | 0.515804i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.17597 | + | 0.755750i | −1.17597 | + | 0.755750i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.65486 | − | 0.755750i | 1.65486 | − | 0.755750i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
1.00000 | \(0\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(198\) | 2.51722 | − | 0.361922i | 2.51722 | − | 0.361922i | ||||
\(199\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(200\) | −0.580699 | − | 1.27155i | −0.580699 | − | 1.27155i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −1.00000 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(212\) | 1.02111 | + | 0.146813i | 1.02111 | + | 0.146813i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.78431 | + | 1.27155i | −2.78431 | + | 1.27155i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.512546 | + | 1.74557i | 0.512546 | + | 1.74557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(226\) | −1.80075 | + | 2.80202i | −1.80075 | + | 2.80202i | ||||
\(227\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.57385 | − | 0.755750i | −2.57385 | − | 0.755750i | ||||
\(233\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.118239 | + | 0.822373i | 0.118239 | + | 0.822373i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(242\) | −2.07385 | + | 0.608936i | −2.07385 | + | 0.608936i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.49611 | − | 0.215109i | 1.49611 | − | 0.215109i | ||||
\(254\) | −0.478891 | −0.478891 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | ||||
\(257\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.49611 | − | 1.29639i | 1.49611 | − | 1.29639i | ||||
\(269\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.512546 | + | 1.74557i | −0.512546 | + | 1.74557i | ||||
\(275\) | 1.51150i | 1.51150i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.830830 | −0.830830 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.557730 | − | 0.0801894i | −0.557730 | − | 0.0801894i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(284\) | 1.57028 | + | 1.81219i | 1.57028 | + | 1.81219i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.500000 | − | 0.146813i | 0.500000 | − | 0.146813i | ||||
\(289\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.92195 | + | 1.66538i | 1.92195 | + | 1.66538i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 3.33076i | − | 3.33076i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.11435 | − | 2.44009i | 2.11435 | − | 2.44009i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.557730 | − | 0.867845i | −0.557730 | − | 0.867845i | ||||
\(317\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.19209 | + | 1.89945i | 2.19209 | + | 1.89945i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.75667 | − | 0.515804i | −1.75667 | − | 0.515804i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.71616 | + | 1.74557i | 2.71616 | + | 1.74557i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0405070 | − | 0.281733i | −0.0405070 | − | 0.281733i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.512546 | + | 1.74557i | 0.512546 | + | 1.74557i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.14231 | + | 0.989821i | −1.14231 | + | 0.989821i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 2.76730i | − | 2.76730i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.797176 | + | 0.234072i | 0.797176 | + | 0.234072i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.716476 | + | 0.327204i | −0.716476 | + | 0.327204i | ||||
\(353\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.198939 | + | 0.435615i | −0.198939 | + | 0.435615i | ||||
\(359\) | −1.95949 | + | 0.281733i | −1.95949 | + | 0.281733i | −0.959493 | + | 0.281733i | \(0.909091\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | −0.500000 | + | 0.146813i | −0.500000 | + | 0.146813i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.49611 | + | 0.215109i | 1.49611 | + | 0.215109i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.158746 | − | 0.540641i | −0.158746 | − | 0.540641i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.02977 | − | 0.435615i | 3.02977 | − | 0.435615i | ||||
\(383\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.313607 | + | 2.18119i | −0.313607 | + | 2.18119i | ||||
\(387\) | 1.07028 | − | 1.66538i | 1.07028 | − | 1.66538i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.425839 | − | 1.45027i | 0.425839 | − | 1.45027i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.313607 | + | 0.361922i | −0.313607 | + | 0.361922i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.73913 | + | 0.393828i | 2.73913 | + | 0.393828i | ||||
\(397\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0741615 | − | 0.515804i | −0.0741615 | − | 0.515804i | ||||
\(401\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.14231 | − | 2.50132i | −1.14231 | − | 2.50132i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.80075 | + | 0.822373i | −1.80075 | + | 0.822373i | −0.841254 | + | 0.540641i | \(0.818182\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(422\) | 1.44306 | + | 1.66538i | 1.44306 | + | 1.66538i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.716476 | + | 0.327204i | 0.716476 | + | 0.327204i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.29686 | + | 0.474017i | −3.29686 | + | 0.474017i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.07028 | − | 1.66538i | −1.07028 | − | 1.66538i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.97964i | 1.97964i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.797176 | − | 0.234072i | 0.797176 | − | 0.234072i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(450\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.73913 | + | 2.37347i | −2.73913 | + | 2.37347i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.425839 | − | 0.368991i | −0.425839 | − | 0.368991i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(464\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.17597 | + | 0.755750i | −1.17597 | + | 0.755750i | ||||
\(467\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.24302 | + | 2.72183i | −1.24302 | + | 2.72183i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.304632 | + | 0.474017i | 0.304632 | + | 0.474017i | ||||
\(478\) | −0.198939 | + | 1.38365i | −0.198939 | + | 1.38365i | ||||
\(479\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.35194 | −2.35194 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.51722 | + | 0.361922i | 2.51722 | + | 0.361922i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.500000 | − | 0.146813i | −0.500000 | − | 0.146813i | ||||
\(509\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(522\) | −1.34125 | − | 2.93694i | −1.34125 | − | 2.93694i | ||||
\(523\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.37491 | + | 1.19136i | 1.37491 | + | 1.19136i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.37491 | − | 0.627899i | 1.37491 | − | 0.627899i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(548\) | −1.07028 | + | 1.66538i | −1.07028 | + | 1.66538i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.716476 | + | 2.44009i | −0.716476 | + | 2.44009i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.34125 | − | 0.393828i | −1.34125 | − | 0.393828i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.862362 | − | 0.393828i | −0.862362 | − | 0.393828i | ||||
\(563\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.760554 | + | 1.66538i | 0.760554 | + | 1.66538i | ||||
\(569\) | 0.983568 | + | 1.53046i | 0.983568 | + | 1.53046i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.983568 | − | 1.53046i | 0.983568 | − | 1.53046i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(576\) | 1.39788 | 1.39788 | ||||||||
\(577\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(578\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.557730 | − | 0.643655i | −0.557730 | − | 0.643655i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.512546 | + | 0.797537i | 0.512546 | + | 0.797537i | ||||
\(593\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.02111 | − | 3.47758i | 1.02111 | − | 3.47758i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.07028 | + | 0.153882i | 1.07028 | + | 0.153882i | ||||
\(604\) | 2.95561 | − | 1.89945i | 2.95561 | − | 1.89945i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.817178 | − | 0.708089i | 0.817178 | − | 0.708089i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.584585 | − | 0.909632i | 0.584585 | − | 0.909632i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
1.00000 | \(0\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.80075 | − | 0.822373i | −1.80075 | − | 0.822373i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.841254 | − | 0.540641i | \(-0.818182\pi\) | |||||||
\(632\) | −0.221908 | − | 0.755750i | −0.221908 | − | 0.755750i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.580699 | − | 1.27155i | 0.580699 | − | 1.27155i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.63843 | + | 4.10548i | 2.63843 | + | 4.10548i | ||||
\(639\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(648\) | −1.17597 | − | 0.755750i | −1.17597 | − | 0.755750i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.30075 | + | 2.65520i | 2.30075 | + | 2.65520i | ||||
\(653\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.425839 | − | 0.368991i | 0.425839 | − | 0.368991i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(662\) | 0.0681534 | − | 0.474017i | 0.0681534 | − | 0.474017i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.06092i | 3.06092i | ||||||||
\(667\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
1.00000 | \(0\) | |||||||||
\(674\) | −2.31329 | + | 1.05645i | −2.31329 | + | 1.05645i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.260554 | + | 1.81219i | 0.260554 | + | 1.81219i | ||||
\(677\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.345139 | + | 0.755750i | 0.345139 | + | 0.755750i | 1.00000 | \(0\) | ||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.290638 | − | 0.989821i | 0.290638 | − | 0.989821i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.17597 | + | 0.755750i | 1.17597 | + | 0.755750i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.304632 | − | 1.03748i | −0.304632 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.09138 | + | 0.300696i | −2.09138 | + | 0.300696i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.817178 | − | 1.27155i | 0.817178 | − | 1.27155i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.158746 | − | 0.540641i | 0.158746 | − | 0.540641i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.341254 | + | 0.393828i | −0.341254 | + | 0.393828i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.29686 | − | 0.474017i | −3.29686 | − | 0.474017i | ||||
\(719\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(728\) | 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 | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.521109 | 0.521109 | ||||||||
\(737\) | −1.63436 | −1.63436 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.983568 | + | 0.449181i | −0.983568 | + | 0.449181i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.31329 | + | 1.05645i | 2.31329 | + | 1.05645i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.425839 | − | 0.368991i | 0.425839 | − | 0.368991i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.425839 | + | 1.45027i | −0.425839 | + | 1.45027i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(758\) | − | 0.948034i | − | 0.948034i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.29686 | + | 0.474017i | 3.29686 | + | 0.474017i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.996114 | + | 2.18119i | −0.996114 | + | 2.18119i | ||||
\(773\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(774\) | 2.51722 | − | 2.18119i | 2.51722 | − | 2.18119i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.37491 | − | 2.13940i | 1.37491 | − | 2.13940i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1.97964i | − | 1.97964i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(788\) | −0.438384 | + | 0.281733i | −0.438384 | + | 0.281733i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.92195 | + | 0.877726i | 1.92195 | + | 0.877726i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.0741615 | + | 0.515804i | −0.0741615 | + | 0.515804i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.31329 | − | 2.00448i | −2.31329 | − | 2.00448i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.658432 | − | 4.57949i | −0.658432 | − | 4.57949i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(828\) | −1.54019 | − | 0.989821i | −1.54019 | − | 0.989821i | ||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.11435 | − | 2.44009i | 1.11435 | − | 2.44009i | ||||
\(842\) | −3.29686 | + | 0.474017i | −3.29686 | + | 0.474017i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.996114 | + | 2.18119i | 0.996114 | + | 2.18119i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.221908 | + | 0.192284i | 0.221908 | + | 0.192284i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.81926i | 1.81926i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.51722 | − | 0.361922i | −2.51722 | − | 0.361922i | ||||
\(857\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.938384 | − | 3.19584i | −0.938384 | − | 3.19584i | ||||
\(863\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.121206 | + | 0.843008i | −0.121206 | + | 0.843008i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.425839 | + | 1.45027i | −0.425839 | + | 1.45027i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
1.00000 | \(0\) | |||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.11435 | + | 0.620830i | −2.11435 | + | 0.620830i | ||||
\(887\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.817178 | + | 1.27155i | 0.817178 | + | 1.27155i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.39788 | 1.39788 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.19894 | − | 1.38365i | 1.19894 | − | 1.38365i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.51722 | + | 1.14958i | −2.51722 | + | 1.14958i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.983568 | − | 0.449181i | −0.983568 | − | 0.449181i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.07028 | − | 0.153882i | 1.07028 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.512546 | − | 0.797537i | −0.512546 | − | 0.797537i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.80075 | − | 0.258908i | −1.80075 | − | 0.258908i | ||||
\(926\) | 2.38145 | − | 1.53046i | 2.38145 | − | 1.53046i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(929\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.45949 | + | 0.428546i | −1.45949 | + | 0.428546i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.29686 | + | 3.80478i | −3.29686 | + | 3.80478i | ||||
\(947\) | −0.698939 | − | 0.449181i | −0.698939 | − | 0.449181i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0.267092 | + | 0.909632i | 0.267092 | + | 0.909632i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.631891 | + | 1.38365i | −0.631891 | + | 1.38365i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.37491 | − | 1.19136i | −1.37491 | − | 1.19136i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(968\) | −1.72301 | − | 0.505923i | −1.72301 | − | 0.505923i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.313607 | − | 0.361922i | −0.313607 | − | 0.361922i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.817178 | + | 0.708089i | −0.817178 | + | 0.708089i | ||||
\(982\) | −1.17597 | − | 2.57501i | −1.17597 | − | 2.57501i | ||||
\(983\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.49611 | − | 1.29639i | 1.49611 | − | 1.29639i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(998\) | −0.402869 | − | 2.80202i | −0.402869 | − | 2.80202i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1127.1.o.a.442.1 | ✓ | 10 | |
7.2 | even | 3 | 1127.1.x.a.557.1 | 20 | |||
7.3 | odd | 6 | 1127.1.x.a.373.1 | 20 | |||
7.4 | even | 3 | 1127.1.x.a.373.1 | 20 | |||
7.5 | odd | 6 | 1127.1.x.a.557.1 | 20 | |||
7.6 | odd | 2 | CM | 1127.1.o.a.442.1 | ✓ | 10 | |
23.14 | odd | 22 | inner | 1127.1.o.a.589.1 | yes | 10 | |
161.37 | odd | 66 | 1127.1.x.a.704.1 | 20 | |||
161.60 | odd | 66 | 1127.1.x.a.520.1 | 20 | |||
161.83 | even | 22 | inner | 1127.1.o.a.589.1 | yes | 10 | |
161.129 | even | 66 | 1127.1.x.a.520.1 | 20 | |||
161.152 | even | 66 | 1127.1.x.a.704.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1127.1.o.a.442.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
1127.1.o.a.442.1 | ✓ | 10 | 7.6 | odd | 2 | CM | |
1127.1.o.a.589.1 | yes | 10 | 23.14 | odd | 22 | inner | |
1127.1.o.a.589.1 | yes | 10 | 161.83 | even | 22 | inner | |
1127.1.x.a.373.1 | 20 | 7.3 | odd | 6 | |||
1127.1.x.a.373.1 | 20 | 7.4 | even | 3 | |||
1127.1.x.a.520.1 | 20 | 161.60 | odd | 66 | |||
1127.1.x.a.520.1 | 20 | 161.129 | even | 66 | |||
1127.1.x.a.557.1 | 20 | 7.2 | even | 3 | |||
1127.1.x.a.557.1 | 20 | 7.5 | odd | 6 | |||
1127.1.x.a.704.1 | 20 | 161.37 | odd | 66 | |||
1127.1.x.a.704.1 | 20 | 161.152 | even | 66 |