Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1127,1,Mod(31,1127)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1127, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([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("1127.31");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1127 = 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1127.v (of order \(66\), degree \(20\), not 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: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 161) |
Projective image: | \(D_{11}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
Embedding invariants
Embedding label | 864.1 | ||
Root | \(0.0475819 + 0.998867i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1127.864 |
Dual form | 1127.1.v.a.1097.1 |
$q$-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 \(\left(\mathbb{Z}/1127\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{11}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0930932 | − | 0.268975i | 0.0930932 | − | 0.268975i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(3\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(4\) | 0.722372 | + | 0.568079i | 0.722372 | + | 0.568079i | ||||
\(5\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.459493 | − | 0.295298i | 0.459493 | − | 0.295298i | ||||
\(9\) | 0.580057 | − | 0.814576i | 0.580057 | − | 0.814576i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.550294 | − | 1.58997i | −0.550294 | − | 1.58997i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.180007 | + | 0.741999i | 0.180007 | + | 0.741999i | ||||
\(17\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(18\) | −0.165101 | − | 0.231852i | −0.165101 | − | 0.231852i | ||||
\(19\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.478891 | −0.478891 | ||||||||
\(23\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(32\) | 0.760064 | + | 0.0725773i | 0.760064 | + | 0.0725773i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.881761 | − | 0.258908i | 0.881761 | − | 0.258908i | ||||
\(37\) | −1.11312 | + | 1.56316i | −1.11312 | + | 1.56316i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(44\) | 0.505713 | − | 1.46116i | 0.505713 | − | 1.46116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0671040 | + | 0.276606i | −0.0671040 | + | 0.276606i | ||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.947890 | + | 0.903811i | −0.947890 | + | 0.903811i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.366049 | + | 0.0705501i | 0.366049 | + | 0.0705501i | ||||
\(59\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.226900 | + | 0.496841i | −0.226900 | + | 0.496841i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.279486 | + | 0.0538665i | −0.279486 | + | 0.0538665i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(72\) | 0.0259893 | − | 0.545582i | 0.0259893 | − | 0.545582i | ||||
\(73\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(74\) | 0.316827 | + | 0.444922i | 0.316827 | + | 0.444922i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.947890 | − | 0.903811i | −0.947890 | − | 0.903811i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.327068 | − | 0.945001i | −0.327068 | − | 0.945001i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.185885 | − | 0.146182i | 0.185885 | − | 0.146182i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.722372 | − | 0.568079i | −0.722372 | − | 0.568079i | ||||
\(89\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.773100 | − | 0.496841i | −0.773100 | − | 0.496841i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(100\) | 0.816827 | + | 0.421104i | 0.816827 | + | 0.421104i | ||||
\(101\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.154861 | + | 0.339098i | 0.154861 | + | 0.339098i | ||||
\(107\) | 1.70566 | + | 0.879330i | 1.70566 | + | 0.879330i | 0.981929 | + | 0.189251i | \(0.0606061\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.264241 | − | 0.105786i | −0.264241 | − | 0.105786i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.601808 | + | 1.04236i | −0.601808 | + | 1.04236i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.43913 | + | 1.13174i | −1.43913 | + | 1.13174i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(128\) | 0.665101 | + | 0.634173i | 0.665101 | + | 0.634173i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.0115295 | + | 0.0801894i | −0.0115295 | + | 0.0801894i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.444587 | + | 0.177986i | −0.444587 | + | 0.177986i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.708829 | + | 0.283772i | 0.708829 | + | 0.283772i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.69209 | + | 0.496841i | −1.69209 | + | 0.496841i | ||||
\(149\) | 0.815816 | + | 0.157236i | 0.815816 | + | 0.157236i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.308779 | + | 1.27280i | −0.308779 | + | 1.27280i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(158\) | −0.331345 | + | 0.170820i | −0.331345 | + | 0.170820i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.284630 | −0.284630 | ||||||||
\(163\) | 0.428368 | − | 1.23769i | 0.428368 | − | 1.23769i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.249723 | + | 0.721528i | 0.249723 | + | 0.721528i | ||||
\(173\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.08070 | − | 0.694523i | 1.08070 | − | 0.694523i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.481929 | + | 0.676774i | 0.481929 | + | 0.676774i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.429342 | + | 0.337639i | −0.429342 | + | 0.337639i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.452418 | − | 1.86489i | −0.452418 | − | 1.86489i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.0475819 | − | 0.998867i | \(-0.484848\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.67489 | − | 0.159932i | −1.67489 | − | 0.159932i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(198\) | −0.277784 | + | 0.390093i | −0.277784 | + | 0.390093i | ||||
\(199\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(200\) | 0.395304 | − | 0.376921i | 0.395304 | − | 0.376921i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.239446 | + | 1.66538i | −0.239446 | + | 1.66538i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(212\) | −1.19817 | + | 0.114411i | −1.19817 | + | 0.114411i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.395304 | − | 0.376921i | 0.395304 | − | 0.376921i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.0530529 | + | 0.0612263i | −0.0530529 | + | 0.0612263i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(226\) | −0.219539 | + | 0.0878903i | −0.219539 | + | 0.0878903i | ||||
\(227\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.468468 | + | 0.540641i | 0.468468 | + | 0.540641i | ||||
\(233\) | −0.0913090 | + | 1.91681i | −0.0913090 | + | 1.91681i | 0.235759 | + | 0.971812i | \(0.424242\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(242\) | 0.170438 | + | 0.492448i | 0.170438 | + | 0.492448i | ||||
\(243\) | 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 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.698939 | + | 1.53046i | 0.698939 | + | 1.53046i | ||||
\(254\) | 0.118239 | + | 0.204797i | 0.118239 | + | 0.204797i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.252989 | + | 0.130425i | −0.252989 | + | 0.130425i | ||||
\(257\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.16413 | + | 0.600149i | 1.16413 | + | 0.600149i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.0671040 | + | 0.276606i | −0.0671040 | + | 0.276606i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.232493 | − | 0.119859i | −0.232493 | − | 0.119859i | ||||
\(269\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0530529 | − | 0.0612263i | −0.0530529 | − | 0.0612263i | ||||
\(275\) | −0.841254 | − | 1.45709i | −0.841254 | − | 1.45709i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
0.723734 | − | 0.690079i | \(-0.242424\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(284\) | −0.0735712 | − | 1.54445i | −0.0735712 | − | 1.54445i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.500000 | − | 0.577031i | 0.500000 | − | 0.577031i | ||||
\(289\) | 0.723734 | + | 0.690079i | 0.723734 | + | 0.690079i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.0498730 | + | 1.04696i | −0.0498730 | + | 1.04696i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.118239 | − | 0.204797i | 0.118239 | − | 0.204797i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.313607 | + | 0.201543i | 0.313607 | + | 0.201543i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.171292 | − | 1.19136i | −0.171292 | − | 1.19136i | ||||
\(317\) | 1.91030 | − | 0.182411i | 1.91030 | − | 0.182411i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.95865 | − | 1.00976i | 1.95865 | − | 1.00976i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.300571 | − | 0.868442i | 0.300571 | − | 0.868442i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.293029 | − | 0.230441i | −0.293029 | − | 0.230441i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.481929 | − | 0.676774i | 0.481929 | − | 0.676774i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.627639 | + | 1.81344i | 0.627639 | + | 1.81344i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
1.00000 | \(0\) | |||||||||
\(338\) | −0.0671040 | − | 0.276606i | −0.0671040 | − | 0.276606i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.453800 | 0.453800 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.88431 | + | 0.363170i | −1.88431 | + | 0.363170i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.302863 | − | 1.24842i | −0.302863 | − | 1.24842i | ||||
\(353\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.226900 | − | 0.0666238i | 0.226900 | − | 0.0666238i | ||||
\(359\) | 0.481929 | − | 0.676774i | 0.481929 | − | 0.676774i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.723734 | − | 0.690079i | 0.723734 | − | 0.690079i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | −0.249723 | − | 0.721528i | −0.249723 | − | 0.721528i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.67489 | + | 0.159932i | −1.67489 | + | 0.159932i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.857685 | − | 0.989821i | 0.857685 | − | 0.989821i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
1.00000 | \(0\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.543727 | − | 0.0519196i | −0.543727 | − | 0.0519196i | ||||
\(383\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.198939 | + | 0.435615i | −0.198939 | + | 0.435615i | ||||
\(387\) | 0.771316 | − | 0.308788i | 0.771316 | − | 0.308788i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.65210 | − | 0.318417i | 1.65210 | − | 0.318417i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0112521 | + | 0.236211i | −0.0112521 | + | 0.236211i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.896884 | − | 1.25950i | −0.896884 | − | 1.25950i | ||||
\(397\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.317178 | + | 0.694523i | 0.317178 | + | 0.694523i | ||||
\(401\) | −1.38884 | − | 1.32425i | −1.38884 | − | 1.32425i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.09792 | + | 0.909632i | 3.09792 | + | 0.909632i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(422\) | 0.425656 | + | 0.219441i | 0.425656 | + | 0.219441i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.168655 | + | 0.695205i | −0.168655 | + | 0.695205i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.732593 | + | 1.60416i | 0.732593 | + | 1.60416i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.771316 | + | 0.308788i | 0.771316 | + | 0.308788i | 0.723734 | − | 0.690079i | \(-0.242424\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.130785 | − | 0.226527i | −0.130785 | − | 0.226527i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.32254 | + | 1.04006i | −1.32254 | + | 1.04006i | −0.327068 | + | 0.945001i | \(0.606061\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(450\) | −0.205996 | − | 0.196417i | −0.205996 | − | 0.196417i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.0363298 | − | 0.762656i | −0.0363298 | − | 0.762656i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0623191 | + | 1.30824i | −0.0623191 | + | 1.30824i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(464\) | −0.928368 | + | 0.371662i | −0.928368 | + | 0.371662i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.507075 | + | 0.203002i | 0.507075 | + | 0.203002i | ||||
\(467\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.329562 | − | 1.35847i | 0.329562 | − | 1.35847i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(478\) | −0.543727 | + | 0.0519196i | −0.543727 | + | 0.0519196i | ||||
\(479\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.68251 | −1.68251 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.653077 | − | 0.513585i | −0.653077 | − | 0.513585i | 0.235759 | − | 0.971812i | \(-0.424242\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0671040 | − | 0.276606i | −0.0671040 | − | 0.276606i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.476723 | − | 0.0455215i | 0.476723 | − | 0.0455215i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.749723 | + | 0.144497i | −0.749723 | + | 0.144497i | ||||
\(509\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(513\) | 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 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(522\) | 0.269798 | − | 0.257252i | 0.269798 | − | 0.257252i | ||||
\(523\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0681534 | + | 0.0437995i | 0.0681534 | + | 0.0437995i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.981929 | − | 0.189251i | 0.981929 | − | 0.189251i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.112515 | + | 0.107283i | −0.112515 | + | 0.107283i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.279486 | − | 0.0538665i | −0.279486 | − | 0.0538665i | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(548\) | 0.242834 | − | 0.0972160i | 0.242834 | − | 0.0972160i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.470237 | + | 0.0906308i | −0.470237 | + | 0.0906308i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.357685 | − | 0.412791i | −0.357685 | − | 0.412791i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.16011 | + | 1.62915i | 1.16011 | + | 1.62915i | 0.580057 | + | 0.814576i | \(0.303030\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.269798 | + | 0.257252i | 0.269798 | + | 0.257252i | ||||
\(563\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.881761 | − | 0.258908i | −0.881761 | − | 0.258908i | ||||
\(569\) | 1.50842 | − | 1.18624i | 1.50842 | − | 1.18624i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
0.928368 | − | 0.371662i | \(-0.121212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.50842 | + | 1.18624i | 1.50842 | + | 1.18624i | 0.928368 | + | 0.371662i | \(0.121212\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(576\) | 0.273100 | + | 0.473023i | 0.273100 | + | 0.473023i | ||||
\(577\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(578\) | 0.252989 | − | 0.130425i | 0.252989 | − | 0.130425i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.95865 | + | 1.00976i | 1.95865 | + | 1.00976i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.36023 | − | 0.544555i | −1.36023 | − | 0.544555i | ||||
\(593\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.500000 | + | 0.577031i | 0.500000 | + | 0.577031i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.142315 | − | 0.246497i | 0.142315 | − | 0.246497i | −0.786053 | − | 0.618159i | \(-0.787879\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(604\) | −0.946106 | + | 0.744026i | −0.946106 | + | 0.744026i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.0135432 | − | 0.284307i | −0.0135432 | − | 0.284307i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.981929 | − | 0.189251i | \(-0.0606061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
1.00000 | \(0\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.928368 | − | 0.371662i | 0.928368 | − | 0.371662i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(632\) | −0.702443 | − | 0.135385i | −0.702443 | − | 0.135385i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.128772 | − | 0.530804i | 0.128772 | − | 0.530804i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.0892619 | − | 0.620830i | −0.0892619 | − | 0.620830i | ||||
\(639\) | −1.67489 | + | 0.159932i | −1.67489 | + | 0.159932i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.77767 | + | 0.916453i | −1.77767 | + | 0.916453i | −0.888835 | + | 0.458227i | \(0.848485\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(648\) | −0.429342 | − | 0.337639i | −0.429342 | − | 0.337639i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.01255 | − | 0.650724i | 1.01255 | − | 0.650724i | ||||
\(653\) | −0.165101 | + | 0.231852i | −0.165101 | + | 0.231852i | −0.888835 | − | 0.458227i | \(-0.848485\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(662\) | −0.137171 | − | 0.192630i | −0.137171 | − | 0.192630i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.546200 | 0.546200 | ||||||||
\(667\) | −0.308779 | − | 1.27280i | −0.308779 | − | 1.27280i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | 1.00000 | \(0\) | ||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(674\) | −0.112903 | − | 0.465392i | −0.112903 | − | 0.465392i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.914825 | + | 0.0873552i | 0.914825 | + | 0.0873552i | ||||
\(677\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.38884 | + | 1.32425i | −1.38884 | + | 1.32425i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.207478 | + | 0.599467i | −0.207478 | + | 0.599467i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.0777324 | + | 0.540641i | −0.0777324 | + | 0.540641i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.914825 | + | 0.0873552i | 0.914825 | + | 0.0873552i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.56199 | − | 0.625325i | 1.56199 | − | 0.625325i | 0.580057 | − | 0.814576i | \(-0.303030\pi\) |
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.28605 | + | 0.247866i | −1.28605 | + | 0.247866i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.0363298 | + | 0.762656i | −0.0363298 | + | 0.762656i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.137171 | − | 0.192630i | −0.137171 | − | 0.192630i | ||||
\(719\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.428368 | + | 1.23769i | 0.428368 | + | 1.23769i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.763521 | −0.763521 | ||||||||
\(737\) | 0.239446 | + | 0.414732i | 0.239446 | + | 0.414732i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.252989 | − | 0.130425i | 0.252989 | − | 0.130425i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.112903 | + | 0.465392i | −0.112903 | + | 0.465392i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.16413 | + | 0.600149i | 1.16413 | + | 0.600149i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(758\) | −0.186393 | − | 0.322842i | −0.186393 | − | 0.322842i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.732593 | − | 1.60416i | 0.732593 | − | 1.60416i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.11904 | − | 1.06700i | −1.11904 | − | 1.06700i | ||||
\(773\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(774\) | −0.0112521 | − | 0.236211i | −0.0112521 | − | 0.236211i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.0681534 | − | 0.474017i | 0.0681534 | − | 0.474017i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.41542 | + | 2.45157i | −1.41542 | + | 2.45157i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(788\) | −0.708829 | − | 0.283772i | −0.708829 | − | 0.283772i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.881761 | + | 0.258908i | −0.881761 | + | 0.258908i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.760064 | − | 0.0725773i | 0.760064 | − | 0.0725773i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.485482 | + | 0.250283i | −0.485482 | + | 0.250283i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.02951 | + | 0.809616i | 1.02951 | + | 0.809616i | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.533064 | − | 0.748584i | 0.533064 | − | 0.748584i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.396666 | + | 1.63508i | 0.396666 | + | 1.63508i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.759713 | − | 1.06687i | −0.759713 | − | 1.06687i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.235759 | − | 0.971812i | \(-0.424242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(828\) | −0.853157 | + | 0.341553i | −0.853157 | + | 0.341553i | ||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | 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 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.686393 | + | 0.201543i | −0.686393 | + | 0.201543i | ||||
\(842\) | −0.137171 | + | 0.192630i | −0.137171 | + | 0.192630i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.11904 | + | 1.06700i | −1.11904 | + | 1.06700i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.959493 | − | 1.66189i | 0.959493 | − | 1.66189i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.04340 | − | 0.0996331i | 1.04340 | − | 0.0996331i | ||||
\(857\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.154861 | − | 0.178719i | 0.154861 | − | 0.178719i | ||||
\(863\) | 1.65210 | + | 0.318417i | 1.65210 | + | 0.318417i | 0.928368 | − | 0.371662i | \(-0.121212\pi\) |
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.915415 | + | 2.00448i | −0.915415 | + | 2.00448i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.152655 | + | 0.0294219i | −0.152655 | + | 0.0294219i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.0800569 | − | 1.68060i | 0.0800569 | − | 1.68060i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.580057 | − | 0.814576i | \(-0.303030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.156630 | + | 0.452553i | 0.156630 | + | 0.452553i | ||||
\(887\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.32254 | + | 1.04006i | −1.32254 | + | 1.04006i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.273100 | − | 0.473023i | −0.273100 | − | 0.473023i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.816827 | − | 0.421104i | 0.816827 | − | 0.421104i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.435418 | − | 0.127850i | −0.435418 | − | 0.127850i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0671040 | + | 0.276606i | −0.0671040 | + | 0.276606i | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) |
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.346082 | + | 0.138550i | 0.346082 | + | 0.138550i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.959493 | + | 1.66189i | 0.959493 | + | 1.66189i | 0.723734 | + | 0.690079i | \(0.242424\pi\) |
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(926\) | −0.0636813 | + | 0.0500796i | −0.0636813 | + | 0.0500796i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.0475819 | + | 0.998867i | 0.0475819 | + | 0.998867i | ||||
\(929\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.15486 | + | 1.33278i | −1.15486 | + | 1.33278i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.334716 | − | 0.215109i | −0.334716 | − | 0.215109i | ||||
\(947\) | −1.78153 | + | 0.713215i | −1.78153 | + | 0.713215i | −0.786053 | + | 0.618159i | \(0.787879\pi\) |
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
1.00000 | \(0\) | |||||||||
\(954\) | 0.366049 | + | 0.0705501i | 0.366049 | + | 0.0705501i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.415766 | − | 1.71381i | 0.415766 | − | 1.71381i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.995472 | + | 0.0950560i | −0.995472 | + | 0.0950560i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.70566 | − | 0.879330i | 1.70566 | − | 0.879330i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(968\) | −0.327068 | + | 0.945001i | −0.327068 | + | 0.945001i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.198939 | + | 0.127850i | −0.198939 | + | 0.127850i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.654136 | − | 1.89000i | −0.654136 | − | 1.89000i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
−0.327068 | − | 0.945001i | \(-0.606061\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.239446 | + | 0.153882i | −0.239446 | + | 0.153882i | ||||
\(982\) | 0.0190998 | + | 0.0787304i | 0.0190998 | + | 0.0787304i | ||||
\(983\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.738471 | − | 0.380708i | −0.738471 | − | 0.380708i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.279486 | + | 0.0538665i | −0.279486 | + | 0.0538665i | −0.327068 | − | 0.945001i | \(-0.606061\pi\) |
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(998\) | −0.0806472 | − | 0.00770088i | −0.0806472 | − | 0.00770088i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))