Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [979,1,Mod(10,979)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(979, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([22, 43]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("979.10");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 979 = 11 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 979.v (of order \(44\), degree \(20\), 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: | \(0.488584647368\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{44})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{44}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\) |
Embedding invariants
Embedding label | 450.1 | ||
Root | \(-0.989821 + 0.142315i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 979.450 |
Dual form | 979.1.v.a.285.1 |
$q$-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 \(\left(\mathbb{Z}/979\mathbb{Z}\right)^\times\).
\(n\) | \(90\) | \(804\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{35}{44}\right)\) |
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 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(3\) | 0.959493 | − | 0.718267i | 0.959493 | − | 0.718267i | − | 1.00000i | \(-0.5\pi\) | |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(4\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(5\) | −0.153882 | + | 0.239446i | −0.153882 | + | 0.239446i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.122986 | − | 0.418852i | 0.122986 | − | 0.418852i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(12\) | −0.847507 | − | 0.847507i | −0.847507 | − | 0.847507i | ||||
\(13\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0243370 | + | 0.340275i | 0.0243370 | + | 0.340275i | ||||
\(16\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(17\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(20\) | 0.258908 | + | 0.118239i | 0.258908 | + | 0.118239i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.936593 | − | 1.71524i | −0.936593 | − | 1.71524i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.281733 | − | 0.959493i | \(-0.590909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.381761 | + | 0.835939i | 0.381761 | + | 0.835939i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.236009 | + | 0.632763i | 0.236009 | + | 0.632763i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.956056 | + | 1.75089i | −0.956056 | + | 1.75089i | −0.415415 | + | 0.909632i | \(0.636364\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.418852 | − | 1.12299i | 0.418852 | − | 1.12299i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.432092 | − | 0.0621254i | −0.432092 | − | 0.0621254i | ||||
\(37\) | 1.13214 | − | 1.13214i | 1.13214 | − | 1.13214i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(44\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(45\) | 0.0813670 | + | 0.0939025i | 0.0813670 | + | 0.0939025i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.80075 | + | 0.258908i | −1.80075 | + | 0.258908i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(48\) | −0.718267 | + | 0.959493i | −0.718267 | + | 0.959493i | ||||
\(49\) | −0.909632 | + | 0.415415i | −0.909632 | + | 0.415415i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.66538 | + | 0.239446i | 1.66538 | + | 0.239446i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.284630i | 0.284630i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.767317 | + | 0.574406i | 0.767317 | + | 0.574406i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(60\) | 0.333348 | − | 0.0725155i | 0.333348 | − | 0.0725155i | ||||
\(61\) | 0 | 0 | 0.936950 | − | 0.349464i | \(-0.113636\pi\) | ||||
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.215109 | + | 1.49611i | −0.215109 | + | 1.49611i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.13066 | − | 0.973039i | −2.13066 | − | 0.973039i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.708089 | − | 1.10181i | −0.708089 | − | 1.10181i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.281733 | − | 0.959493i | \(-0.409091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.966724 | + | 0.527871i | 0.966724 | + | 0.527871i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(80\) | 0.0801894 | − | 0.273100i | 0.0801894 | − | 0.273100i | ||||
\(81\) | 1.04818 | + | 0.673623i | 1.04818 | + | 0.673623i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.56449 | + | 1.17116i | −1.56449 | + | 1.17116i | ||||
\(93\) | 0.340275 | + | 2.36667i | 0.340275 | + | 2.36667i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.909632 | + | 0.584585i | 0.909632 | + | 0.584585i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.122986 | − | 0.418852i | −0.122986 | − | 0.418852i | ||||
\(100\) | 0.773100 | − | 0.496841i | 0.773100 | − | 0.496841i | ||||
\(101\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.75089 | + | 0.956056i | 1.75089 | + | 0.956056i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(108\) | 0.592735 | − | 0.323658i | 0.592735 | − | 0.323658i | ||||
\(109\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.94931 | − | 0.139418i | 1.94931 | − | 0.139418i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.554833 | + | 0.0396824i | 0.554833 | + | 0.0396824i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.86912 | + | 0.697148i | 1.86912 | + | 0.697148i | ||||
\(125\) | −0.540641 | − | 0.0777324i | −0.540641 | − | 0.0777324i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.212565 | − | 0.977147i | \(-0.431818\pi\) | ||||
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(132\) | −1.17116 | − | 0.254771i | −1.17116 | − | 0.254771i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.187830 | − | 0.0408599i | −0.187830 | − | 0.0408599i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.12299 | + | 1.50013i | −1.12299 | + | 1.50013i | −0.281733 | + | 0.959493i | \(0.590909\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.54184 | + | 1.54184i | −1.54184 | + | 1.54184i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.436535i | 0.436535i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.574406 | + | 1.05195i | −0.574406 | + | 1.05195i | ||||
\(148\) | −1.28173 | − | 0.959493i | −1.28173 | − | 0.959493i | ||||
\(149\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.272122 | − | 0.498354i | −0.272122 | − | 0.498354i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.49611 | − | 1.29639i | −1.49611 | − | 1.29639i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.76991 | − | 0.966443i | 1.76991 | − | 0.966443i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.100889 | − | 1.41061i | −0.100889 | − | 1.41061i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.204440 | + | 0.273100i | 0.204440 | + | 0.273100i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.281733 | + | 0.959493i | −0.281733 | + | 0.959493i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(177\) | 1.14881 | 1.14881 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.97964 | −1.97964 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(180\) | 0.0813670 | − | 0.0939025i | 0.0813670 | − | 0.0939025i | ||||
\(181\) | −0.340335 | + | 0.254771i | −0.340335 | + | 0.254771i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0968693 | + | 0.445301i | 0.0968693 | + | 0.445301i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.512546 | + | 1.74557i | 0.512546 | + | 1.74557i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.418852 | − | 0.559521i | −0.418852 | − | 0.559521i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(192\) | 1.05195 | + | 0.574406i | 1.05195 | + | 0.574406i | ||||
\(193\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.540641 | + | 0.841254i | 0.540641 | + | 0.841254i | ||||
\(197\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.45027 | − | 1.25667i | −1.45027 | − | 1.25667i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.540641 | − | 0.841254i | \(-0.681818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.868215 | + | 1.59002i | 0.868215 | + | 1.59002i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.833621 | + | 0.181343i | −0.833621 | + | 0.181343i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(212\) | − | 1.68251i | − | 1.68251i | ||||||
\(213\) | −1.47080 | − | 0.548580i | −1.47080 | − | 0.548580i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.281733 | − | 0.0405070i | 0.281733 | − | 0.0405070i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.397086 | − | 0.0570924i | 0.397086 | − | 0.0570924i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.373128 | + | 1.71524i | −0.373128 | + | 1.71524i | 0.281733 | + | 0.959493i | \(0.409091\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.215109 | − | 0.471022i | 0.215109 | − | 0.471022i | ||||
\(236\) | 0.459359 | − | 0.841254i | 0.459359 | − | 0.841254i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.936950 | − | 0.349464i | \(-0.113636\pi\) | ||||
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(240\) | −0.119218 | − | 0.319635i | −0.119218 | − | 0.319635i | ||||
\(241\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.815938 | − | 0.0583571i | 0.815938 | − | 0.0583571i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0405070 | − | 0.281733i | 0.0405070 | − | 0.281733i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.25667 | + | 0.368991i | −1.25667 | + | 0.368991i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.71524 | − | 0.936593i | −1.71524 | − | 0.936593i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(257\) | −0.158746 | − | 0.540641i | −0.158746 | − | 0.540641i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.313607 | + | 0.361922i | −0.313607 | + | 0.361922i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.19550 | + | 0.0855040i | −1.19550 | + | 0.0855040i | ||||
\(268\) | 1.51150 | 1.51150 | ||||||||
\(269\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.773100 | + | 0.496841i | 0.773100 | + | 0.496841i | ||||
\(276\) | −0.659910 | + | 2.24745i | −0.659910 | + | 2.24745i | ||||
\(277\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.615781 | + | 0.615781i | 0.615781 | + | 0.615781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.877679 | − | 0.479249i | \(-0.840909\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(284\) | −0.989821 | + | 0.857685i | −0.989821 | + | 0.857685i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.29267 | − | 0.0924539i | 1.29267 | − | 0.0924539i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.255616 | + | 0.0953398i | −0.255616 | + | 0.0953398i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.540641 | + | 0.404719i | 0.540641 | + | 0.404719i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.384919 | − | 1.03201i | 0.384919 | − | 1.03201i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.36667 | − | 0.340275i | 2.36667 | − | 0.340275i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.708089 | − | 0.817178i | −0.708089 | − | 0.817178i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.415415 | − | 0.0903680i | −0.415415 | − | 0.0903680i | − | 1.00000i | \(-0.5\pi\) | |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.281733 | − | 0.0405070i | −0.281733 | − | 0.0405070i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.517596 | − | 1.13338i | 0.517596 | − | 1.13338i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.627899 | − | 1.37491i | −0.627899 | − | 1.37491i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.281733 | − | 0.959493i | \(-0.409091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.334961 | − | 0.613435i | −0.334961 | − | 0.613435i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.325137 | − | 0.281733i | −0.325137 | − | 0.281733i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.77021 | − | 1.53390i | 1.77021 | − | 1.53390i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.142315 | + | 1.98982i | 0.142315 | + | 1.98982i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.560861 | − | 0.360443i | 0.560861 | − | 0.360443i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.559521 | − | 0.418852i | 0.559521 | − | 0.418852i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.372786 | 0.372786 | ||||||||
\(356\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.540641 | − | 0.841254i | 0.540641 | − | 0.841254i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.254771 | − | 1.17116i | −0.254771 | − | 1.17116i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(368\) | 1.38189 | + | 1.38189i | 1.38189 | + | 1.38189i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.29415 | − | 0.673623i | 2.29415 | − | 0.673623i | ||||
\(373\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.574574 | + | 0.313741i | −0.574574 | + | 0.313741i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.334961 | − | 0.613435i | −0.334961 | − | 0.613435i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.613435 | − | 1.64468i | −0.613435 | − | 1.64468i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.449181 | − | 0.983568i | 0.449181 | − | 0.983568i | ||||
\(389\) | 0.0498610 | − | 0.133682i | 0.0498610 | − | 0.133682i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.397086 | + | 0.181343i | −0.397086 | + | 0.181343i | ||||
\(397\) | −0.574406 | + | 0.767317i | −0.574406 | + | 0.767317i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.601808 | − | 0.694523i | −0.601808 | − | 0.694523i | ||||
\(401\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.322592 | + | 0.147323i | −0.322592 | + | 0.147323i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.340335 | − | 1.56449i | 0.340335 | − | 1.56449i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.24597i | 2.24597i | ||||||||
\(412\) | 0.697148 | − | 1.86912i | 0.697148 | − | 1.86912i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.424047 | + | 0.0303285i | 0.424047 | + | 0.0303285i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.142315 | + | 0.0101786i | −0.142315 | + | 0.0101786i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.113022 | + | 0.786089i | −0.113022 | + | 0.786089i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.877679 | − | 0.479249i | \(-0.840909\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(432\) | −0.404719 | − | 0.540641i | −0.404719 | − | 0.540641i | ||||
\(433\) | 0.677760 | + | 0.677760i | 0.677760 | + | 0.677760i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0621254 | + | 0.432092i | 0.0621254 | + | 0.432092i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(444\) | −1.91899 | −1.91899 | ||||||||
\(445\) | 0.258908 | − | 0.118239i | 0.258908 | − | 0.118239i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.415415 | − | 1.90963i | −0.415415 | − | 1.90963i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0396824 | − | 0.554833i | −0.0396824 | − | 0.554833i | ||||
\(461\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.909632 | + | 1.41542i | 0.909632 | + | 1.41542i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.619050 | − | 0.282711i | −0.619050 | − | 0.282711i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.215109 | − | 1.49611i | 0.215109 | − | 1.49611i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
0.755750 | − | 0.654861i | \(-0.227273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.36667 | − | 0.169267i | −2.36667 | − | 0.169267i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.305111 | − | 0.668100i | 0.305111 | − | 0.668100i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(485\) | −0.279953 | + | 0.127850i | −0.279953 | + | 0.127850i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.95949 | − | 0.281733i | 1.95949 | − | 0.281733i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
1.00000 | \(0\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.11000 | − | 1.28101i | −1.11000 | − | 1.28101i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.119218 | + | 0.0350055i | 0.119218 | + | 0.0350055i | ||||
\(496\) | 0.424047 | − | 1.94931i | 0.424047 | − | 1.94931i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.898064 | + | 0.334961i | 0.898064 | + | 0.334961i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(500\) | 0.546200i | 0.546200i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.479249 | − | 0.877679i | \(-0.340909\pi\) | ||||
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.418852 | + | 1.12299i | 0.418852 | + | 1.12299i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.822373 | + | 1.80075i | 0.822373 | + | 1.80075i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.498354 | + | 0.272122i | −0.498354 | + | 0.272122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.37491 | + | 1.19136i | −1.37491 | + | 1.19136i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.959493 | − | 1.28173i | −0.959493 | − | 1.28173i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.0855040 | + | 1.19550i | −0.0855040 | + | 1.19550i | ||||
\(529\) | −1.52421 | + | 2.37172i | −1.52421 | + | 2.37172i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.334961 | − | 0.250748i | 0.334961 | − | 0.250748i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.89945 | + | 1.42191i | −1.89945 | + | 1.42191i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.540641 | + | 0.841254i | −0.540641 | + | 0.841254i | ||||
\(540\) | −0.0137130 | + | 0.191733i | −0.0137130 | + | 0.191733i | ||||
\(541\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.143555 | + | 0.488902i | −0.143555 | + | 0.488902i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(548\) | 1.64468 | + | 0.898064i | 1.64468 | + | 0.898064i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.412791 | + | 0.357685i | 0.412791 | + | 0.357685i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(564\) | 1.74557 | + | 1.30672i | 1.74557 | + | 1.30672i | ||||
\(565\) | −0.266582 | + | 0.488209i | −0.266582 | + | 0.488209i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.803771 | − | 0.236009i | −0.803771 | − | 0.236009i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.07628 | − | 1.43775i | 1.07628 | − | 1.43775i | ||||
\(576\) | 0.432092 | − | 0.0621254i | 0.432092 | − | 0.0621254i | ||||
\(577\) | 0.139418 | + | 0.0303285i | 0.139418 | + | 0.0303285i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.53046 | − | 0.698939i | 1.53046 | − | 0.698939i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.07028 | + | 0.153882i | 1.07028 | + | 0.153882i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(588\) | 1.12299 | + | 0.418852i | 1.12299 | + | 0.418852i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.767317 | + | 1.40524i | −0.767317 | + | 1.40524i | ||||
\(593\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.29415 | − | 0.164081i | −2.29415 | − | 0.164081i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.59700 | + | 0.114220i | −1.59700 | + | 0.114220i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.600195 | + | 0.274100i | 0.600195 | + | 0.274100i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.153882 | + | 0.239446i | 0.153882 | + | 0.239446i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.0498610 | + | 0.697148i | −0.0498610 | + | 0.697148i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.258908 | + | 1.80075i | 0.258908 | + | 1.80075i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(620\) | −0.454554 | + | 0.340275i | −0.454554 | + | 0.340275i | ||||
\(621\) | 0.864299 | − | 0.997454i | 0.864299 | − | 0.997454i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.577031i | −0.500000 | + | 0.577031i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.07028 | + | 1.66538i | −1.07028 | + | 1.66538i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.698939 | − | 0.449181i | −0.698939 | − | 0.449181i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.20849 | − | 1.61435i | −1.20849 | − | 1.61435i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.548580 | + | 0.161078i | −0.548580 | + | 0.161078i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.584585 | − | 0.909632i | −0.584585 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.19136 | − | 0.544078i | −1.19136 | − | 0.544078i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.75089 | − | 0.125226i | 1.75089 | − | 0.125226i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.956056 | + | 0.0683785i | 0.956056 | + | 0.0683785i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.38189 | + | 0.300613i | −1.38189 | + | 0.300613i | ||||
\(653\) | −0.340335 | − | 0.254771i | −0.340335 | − | 0.254771i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(660\) | 0.241226 | − | 0.241226i | 0.241226 | − | 0.241226i | ||||
\(661\) | −0.254771 | + | 1.17116i | −0.254771 | + | 1.17116i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.438853 | + | 0.438853i | −0.438853 | + | 0.438853i | ||||
\(676\) | 0.989821 | + | 0.142315i | 0.989821 | + | 0.142315i | ||||
\(677\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.17116 | − | 0.254771i | 1.17116 | − | 0.254771i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.186393 | − | 0.499738i | −0.186393 | − | 0.499738i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.873989 | + | 1.91377i | 0.873989 | + | 1.91377i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.37491 | − | 1.19136i | −1.37491 | − | 1.19136i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(705\) | −0.131925 | − | 0.606448i | −0.131925 | − | 0.606448i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.163493 | − | 1.13712i | −0.163493 | − | 1.13712i | ||||
\(709\) | −1.50013 | + | 1.12299i | −1.50013 | + | 1.12299i | −0.540641 | + | 0.841254i | \(0.681818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.89863 | 3.89863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.281733 | + | 1.95949i | 0.281733 | + | 1.95949i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.424047 | + | 1.94931i | 0.424047 | + | 1.94931i | 0.281733 | + | 0.959493i | \(0.409091\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(720\) | −0.104526 | − | 0.0671750i | −0.104526 | − | 0.0671750i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.300613 | + | 0.300613i | 0.300613 | + | 0.300613i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.0303285 | − | 0.424047i | −0.0303285 | − | 0.424047i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.200672 | + | 0.173883i | −0.200672 | + | 0.173883i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.163493 | − | 0.299415i | −0.163493 | − | 0.299415i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.627899 | + | 1.37491i | 0.627899 | + | 1.37491i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(740\) | 0.426983 | − | 0.159256i | 0.426983 | − | 0.159256i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.479249 | − | 0.877679i | \(-0.340909\pi\) | ||||
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(752\) | 1.65486 | − | 0.755750i | 1.65486 | − | 0.755750i | ||||
\(753\) | −0.940730 | + | 1.25667i | −0.940730 | + | 1.25667i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.989821 | + | 1.14231i | 0.989821 | + | 1.14231i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.31849 | + | 0.333348i | −2.31849 | + | 0.333348i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.494217 | + | 0.494217i | −0.494217 | + | 0.494217i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.418852 | − | 1.12299i | 0.418852 | − | 1.12299i | ||||
\(769\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.540641 | − | 0.404719i | −0.540641 | − | 0.404719i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.133682 | + | 0.0498610i | −0.133682 | + | 0.0498610i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.82862 | − | 0.130785i | −1.82862 | − | 0.130785i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.19136 | − | 0.544078i | −1.19136 | − | 0.544078i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.755750 | − | 0.654861i | 0.755750 | − | 0.654861i | ||||
\(785\) | 0.540641 | − | 0.158746i | 0.540641 | − | 0.158746i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.877679 | − | 0.479249i | \(-0.840909\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0409471 | + | 0.572515i | −0.0409471 | + | 0.572515i | ||||
\(796\) | −1.03748 | + | 1.61435i | −1.03748 | + | 1.61435i | ||||
\(797\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | 1.00000 | \(0\) | ||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.329911 | + | 0.285870i | −0.329911 | + | 0.285870i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.45027 | − | 1.08566i | 1.45027 | − | 1.08566i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.143861 | − | 2.01144i | 0.143861 | − | 2.01144i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.353290 | + | 0.192911i | 0.353290 | + | 0.192911i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.281733 | − | 1.95949i | 0.281733 | − | 1.95949i | − | 1.00000i | \(-0.5\pi\) | |
0.281733 | − | 0.959493i | \(-0.409091\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.09865 | − | 0.0785769i | 1.09865 | − | 0.0785769i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(828\) | 0.298134 | + | 0.799328i | 0.298134 | + | 0.799328i | ||||
\(829\) | 1.75575 | − | 0.654861i | 1.75575 | − | 0.654861i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
1.00000 | \(0\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.33353 | − | 0.191733i | −1.33353 | − | 0.191733i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.398326 | + | 1.83107i | −0.398326 | + | 1.83107i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.909632 | − | 0.415415i | 0.909632 | − | 0.415415i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.66538 | + | 0.239446i | −1.66538 | + | 0.239446i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00224 | − | 0.881537i | −3.00224 | − | 0.881537i | ||||
\(852\) | −0.333679 | + | 1.53390i | −0.333679 | + | 1.53390i | ||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.767317 | − | 1.40524i | 0.767317 | − | 1.40524i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.697148 | − | 1.86912i | −0.697148 | − | 1.86912i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.281733 | − | 0.959493i | \(-0.590909\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.574406 | − | 1.05195i | −0.574406 | − | 1.05195i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.356727 | − | 0.309106i | 0.356727 | − | 0.309106i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0801894 | − | 0.273100i | −0.0801894 | − | 0.273100i | ||||
\(881\) | 0.234072 | − | 0.797176i | 0.234072 | − | 0.797176i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.373128 | + | 1.71524i | 0.373128 | + | 1.71524i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.176782 | + | 0.275078i | −0.176782 | + | 0.275078i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.24597 | 1.24597 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.304632 | − | 0.474017i | 0.304632 | − | 0.474017i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.113022 | − | 0.384919i | −0.113022 | − | 0.384919i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.00863238 | − | 0.120696i | −0.00863238 | − | 0.120696i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.627899 | + | 0.544078i | −0.627899 | + | 0.544078i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.45027 | + | 1.25667i | 1.45027 | + | 1.25667i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.75089 | + | 0.125226i | 1.75089 | + | 0.125226i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.37860 | + | 0.514192i | 1.37860 | + | 0.514192i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.615781 | − | 0.615781i | 0.615781 | − | 0.615781i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.74557 | + | 0.512546i | 1.74557 | + | 0.512546i | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.26636 | − | 0.275479i | −1.26636 | − | 0.275479i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.463496 | + | 0.211672i | −0.463496 | + | 0.211672i | ||||
\(940\) | −0.496841 | − | 0.145886i | −0.496841 | − | 0.145886i | ||||
\(941\) | 0 | 0 | 0.212565 | − | 0.977147i | \(-0.431818\pi\) | ||||
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.898064 | − | 0.334961i | −0.898064 | − | 0.334961i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.933011 | + | 0.347995i | −0.933011 | + | 0.347995i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.198429 | − | 0.0141919i | 0.198429 | − | 0.0141919i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.299415 | + | 0.163493i | −0.299415 | + | 0.163493i | ||||
\(961\) | −1.61092 | − | 2.50664i | −1.61092 | − | 2.50664i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.909632 | − | 0.584585i | −0.909632 | − | 0.584585i | − | 1.00000i | \(-0.5\pi\) | |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(972\) | −0.173883 | − | 0.799328i | −0.173883 | − | 0.799328i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.00000 | −1.00000 | ||||||||
\(980\) | −0.284630 | −0.284630 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.847507 | + | 0.847507i | 0.847507 | + | 0.847507i | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.59002 | − | 0.868215i | −1.59002 | − | 0.868215i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.524075 | − | 0.153882i | 0.524075 | − | 0.153882i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i |
(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 | 979.1.v.a.450.1 | yes | 20 | |
11.10 | odd | 2 | CM | 979.1.v.a.450.1 | yes | 20 | |
89.18 | even | 44 | inner | 979.1.v.a.285.1 | ✓ | 20 | |
979.285 | odd | 44 | inner | 979.1.v.a.285.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
979.1.v.a.285.1 | ✓ | 20 | 89.18 | even | 44 | inner | |
979.1.v.a.285.1 | ✓ | 20 | 979.285 | odd | 44 | inner | |
979.1.v.a.450.1 | yes | 20 | 1.1 | even | 1 | trivial | |
979.1.v.a.450.1 | yes | 20 | 11.10 | odd | 2 | CM |