Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,2,Mod(361,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3528.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.s (of order \(3\), degree \(2\), 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: | \(28.1712218331\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1176) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.361 |
Dual form | 3528.2.s.bc.3313.2 |
$q$-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 \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.292893 | − | 0.507306i | −0.130986 | − | 0.226874i | 0.793071 | − | 0.609129i | \(-0.208481\pi\) |
−0.924057 | + | 0.382255i | \(0.875148\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.41421 | + | 4.18154i | −0.727913 | + | 1.26078i | 0.229851 | + | 0.973226i | \(0.426176\pi\) |
−0.957764 | + | 0.287556i | \(0.907157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.29289 | + | 3.97141i | −0.556108 | + | 0.963208i | 0.441708 | + | 0.897159i | \(0.354373\pi\) |
−0.997816 | + | 0.0660490i | \(0.978961\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.585786 | + | 1.01461i | 0.134389 | + | 0.232768i | 0.925364 | − | 0.379080i | \(-0.123760\pi\) |
−0.790975 | + | 0.611848i | \(0.790426\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.414214 | + | 0.717439i | 0.0863695 | + | 0.149596i | 0.905974 | − | 0.423333i | \(-0.139140\pi\) |
−0.819604 | + | 0.572930i | \(0.805807\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32843 | − | 4.03295i | 0.465685 | − | 0.806591i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41421 | − | 2.44949i | 0.254000 | − | 0.439941i | −0.710623 | − | 0.703573i | \(-0.751587\pi\) |
0.964623 | + | 0.263631i | \(0.0849203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.82843 | − | 8.36308i | −0.793789 | − | 1.37488i | −0.923606 | − | 0.383344i | \(-0.874772\pi\) |
0.129817 | − | 0.991538i | \(-0.458561\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.75736 | 0.274453 | 0.137227 | − | 0.990540i | \(-0.456181\pi\) | ||||
0.137227 | + | 0.990540i | \(0.456181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3137 | 1.72532 | 0.862662 | − | 0.505781i | \(-0.168795\pi\) | ||||
0.862662 | + | 0.505781i | \(0.168795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.24264 | − | 10.8126i | −0.910583 | − | 1.57718i | −0.813243 | − | 0.581924i | \(-0.802300\pi\) |
−0.0973398 | − | 0.995251i | \(-0.531033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | + | 1.73205i | −0.137361 | + | 0.237915i | −0.926497 | − | 0.376303i | \(-0.877195\pi\) |
0.789136 | + | 0.614218i | \(0.210529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24264 | − | 7.34847i | 0.552345 | − | 0.956689i | −0.445760 | − | 0.895152i | \(-0.647067\pi\) |
0.998105 | − | 0.0615367i | \(-0.0196001\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.53553 | − | 2.65962i | −0.196605 | − | 0.340530i | 0.750821 | − | 0.660506i | \(-0.229658\pi\) |
−0.947425 | + | 0.319976i | \(0.896325\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.24264 | + | 2.15232i | 0.154131 | + | 0.266962i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.65685 | − | 9.79796i | 0.691095 | − | 1.19701i | −0.280385 | − | 0.959888i | \(-0.590462\pi\) |
0.971480 | − | 0.237124i | \(-0.0762046\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.48528 | −0.769661 | −0.384831 | − | 0.922987i | \(-0.625740\pi\) | ||||
−0.384831 | + | 0.922987i | \(0.625740\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.12132 | − | 14.0665i | 0.950529 | − | 1.64636i | 0.206245 | − | 0.978500i | \(-0.433876\pi\) |
0.744284 | − | 0.667864i | \(-0.232791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.17157 | − | 2.02922i | −0.131812 | − | 0.228306i | 0.792563 | − | 0.609790i | \(-0.208746\pi\) |
−0.924375 | + | 0.381485i | \(0.875413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.68629 | 0.291369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.12132 | − | 12.3345i | −0.754858 | − | 1.30745i | −0.945445 | − | 0.325783i | \(-0.894372\pi\) |
0.190586 | − | 0.981670i | \(-0.438961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.343146 | − | 0.594346i | 0.0352060 | − | 0.0609786i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.24264 | −0.836913 | −0.418457 | − | 0.908237i | \(-0.637429\pi\) | ||||
−0.418457 | + | 0.908237i | \(0.637429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.36396 | + | 12.7548i | −0.732742 | + | 1.26915i | 0.222966 | + | 0.974826i | \(0.428426\pi\) |
−0.955707 | + | 0.294319i | \(0.904907\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.07107 | − | 12.2474i | −0.696733 | − | 1.20678i | −0.969593 | − | 0.244723i | \(-0.921303\pi\) |
0.272860 | − | 0.962054i | \(-0.412030\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.58579 | + | 6.21076i | 0.346651 | + | 0.600417i | 0.985652 | − | 0.168788i | \(-0.0539855\pi\) |
−0.639001 | + | 0.769206i | \(0.720652\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.65685 | + | 16.7262i | −0.924959 | + | 1.60208i | −0.133332 | + | 0.991071i | \(0.542568\pi\) |
−0.791627 | + | 0.611004i | \(0.790766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.242641 | − | 0.420266i | 0.0226264 | − | 0.0391900i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.15685 | − | 10.6640i | −0.559714 | − | 0.969453i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | + | 3.46410i | 0.174741 | + | 0.302660i | 0.940072 | − | 0.340977i | \(-0.110758\pi\) |
−0.765331 | + | 0.643637i | \(0.777425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.41421 | + | 12.8418i | −0.633439 | + | 1.09715i | 0.353405 | + | 0.935471i | \(0.385024\pi\) |
−0.986844 | + | 0.161678i | \(0.948309\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.9706 | −1.10015 | −0.550074 | − | 0.835116i | \(-0.685401\pi\) | ||||
−0.550074 | + | 0.835116i | \(0.685401\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2426 | − | 17.7408i | 0.856533 | − | 1.48356i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.828427 | − | 1.43488i | −0.0687971 | − | 0.119160i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.6569 | − | 18.4582i | −0.873044 | − | 1.51216i | −0.858832 | − | 0.512257i | \(-0.828810\pi\) |
−0.0142111 | − | 0.999899i | \(-0.504524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.828427 | + | 1.43488i | −0.0674164 | + | 0.116769i | −0.897763 | − | 0.440478i | \(-0.854809\pi\) |
0.830347 | + | 0.557247i | \(0.188142\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.65685 | −0.133082 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.12132 | + | 7.13834i | −0.328917 | + | 0.569701i | −0.982297 | − | 0.187329i | \(-0.940017\pi\) |
0.653380 | + | 0.757030i | \(0.273350\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.82843 | + | 4.89898i | 0.221540 | + | 0.383718i | 0.955276 | − | 0.295717i | \(-0.0955585\pi\) |
−0.733736 | + | 0.679435i | \(0.762225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.17157 | −0.709718 | −0.354859 | − | 0.934920i | \(-0.615471\pi\) | ||||
−0.354859 | + | 0.934920i | \(0.615471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.70711 | + | 16.8132i | 0.738018 | + | 1.27828i | 0.953387 | + | 0.301751i | \(0.0975712\pi\) |
−0.215369 | + | 0.976533i | \(0.569095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.24264 | − | 9.08052i | 0.391853 | − | 0.678710i | −0.600841 | − | 0.799369i | \(-0.705167\pi\) |
0.992694 | + | 0.120659i | \(0.0385007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.07107 | −0.525588 | −0.262794 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262794 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.82843 | + | 4.89898i | −0.207950 | + | 0.360180i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0711 | − | 19.1757i | −0.809597 | − | 1.40226i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.07107 | − | 13.9795i | −0.584002 | − | 1.01152i | −0.994999 | − | 0.0998844i | \(-0.968153\pi\) |
0.410997 | − | 0.911637i | \(-0.365181\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.0719816 | + | 0.124676i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.3137 | 1.80353 | 0.901764 | − | 0.432230i | \(-0.142273\pi\) | ||||
0.901764 | + | 0.432230i | \(0.142273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.82843 | − | 4.89898i | 0.200502 | − | 0.347279i | −0.748188 | − | 0.663486i | \(-0.769076\pi\) |
0.948690 | + | 0.316207i | \(0.102409\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.514719 | − | 0.891519i | −0.0359495 | − | 0.0622664i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.65685 | −0.664805 | −0.332403 | − | 0.943138i | \(-0.607859\pi\) | ||||
−0.332403 | + | 0.943138i | \(0.607859\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.31371 | − | 5.73951i | −0.225993 | − | 0.391431i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.72792 | − | 16.8493i | 0.654371 | − | 1.13340i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.34315 | −0.156909 | −0.0784543 | − | 0.996918i | \(-0.524998\pi\) | ||||
−0.0784543 | + | 0.996918i | \(0.524998\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.41421 | − | 9.37769i | 0.359354 | − | 0.622419i | −0.628499 | − | 0.777810i | \(-0.716330\pi\) |
0.987853 | + | 0.155391i | \(0.0496637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2929 | − | 19.5599i | −0.746255 | − | 1.29255i | −0.949606 | − | 0.313446i | \(-0.898516\pi\) |
0.203351 | − | 0.979106i | \(-0.434817\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.58579 | − | 7.94282i | −0.300425 | − | 0.520351i | 0.675807 | − | 0.737078i | \(-0.263795\pi\) |
−0.976232 | + | 0.216727i | \(0.930462\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.65685 | + | 6.33386i | −0.238547 | + | 0.413175i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.17157 | 0.463890 | 0.231945 | − | 0.972729i | \(-0.425491\pi\) | ||||
0.231945 | + | 0.972729i | \(0.425491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.94975 | + | 5.10911i | −0.190010 | + | 0.329107i | −0.945253 | − | 0.326338i | \(-0.894185\pi\) |
0.755243 | + | 0.655445i | \(0.227519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.48528 | − | 4.30463i | −0.158135 | − | 0.273897i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.1421 | 1.39760 | 0.698800 | − | 0.715317i | \(-0.253718\pi\) | ||||
0.698800 | + | 0.715317i | \(0.253718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.292893 | + | 0.507306i | 0.0182702 | + | 0.0316449i | 0.875016 | − | 0.484094i | \(-0.160851\pi\) |
−0.856746 | + | 0.515739i | \(0.827517\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.07107 | − | 7.05130i | 0.251033 | − | 0.434802i | −0.712778 | − | 0.701390i | \(-0.752563\pi\) |
0.963810 | + | 0.266589i | \(0.0858965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.17157 | 0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.94975 | − | 17.2335i | 0.606647 | − | 1.05074i | −0.385142 | − | 0.922857i | \(-0.625848\pi\) |
0.991789 | − | 0.127886i | \(-0.0408191\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0711 | − | 19.1757i | −0.672519 | − | 1.16484i | −0.977187 | − | 0.212379i | \(-0.931879\pi\) |
0.304668 | − | 0.952459i | \(-0.401455\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.2426 | + | 19.4728i | 0.677957 | + | 1.17426i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.31371 | + | 14.3998i | −0.499522 | + | 0.865198i | −1.00000 | 0.000551476i | \(-0.999824\pi\) | |
0.500478 | + | 0.865750i | \(0.333158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.82843 | −0.407350 | −0.203675 | − | 0.979039i | \(-0.565289\pi\) | ||||
−0.203675 | + | 0.979039i | \(0.565289\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.07107 | − | 1.85514i | 0.0636684 | − | 0.110277i | −0.832434 | − | 0.554124i | \(-0.813053\pi\) |
0.896103 | + | 0.443847i | \(0.146387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.01472 | − | 3.48960i | −0.118513 | − | 0.205270i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.2426 | −0.598381 | −0.299191 | − | 0.954193i | \(-0.596717\pi\) | ||||
−0.299191 | + | 0.954193i | \(0.596717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.97056 | −0.289397 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.75736 | − | 3.04384i | −0.101631 | − | 0.176030i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.899495 | + | 1.55797i | −0.0515049 | + | 0.0892092i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.4853 | 1.62574 | 0.812870 | − | 0.582445i | \(-0.197904\pi\) | ||||
0.812870 | + | 0.582445i | \(0.197904\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.89949 | − | 13.6823i | 0.447939 | − | 0.775854i | −0.550312 | − | 0.834959i | \(-0.685491\pi\) |
0.998252 | + | 0.0591052i | \(0.0188247\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.63604 | + | 2.83370i | 0.0924744 | + | 0.160170i | 0.908552 | − | 0.417772i | \(-0.137189\pi\) |
−0.816077 | + | 0.577943i | \(0.803856\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0000 | − | 19.0526i | −0.617822 | − | 1.07010i | −0.989882 | − | 0.141890i | \(-0.954682\pi\) |
0.372061 | − | 0.928208i | \(-0.378651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.82843 | + | 11.8272i | −0.382319 | + | 0.662195i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.37258 | −0.298939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.87868 | + | 17.1104i | −0.547971 | + | 0.949113i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.65685 | + | 13.2621i | 0.420859 | + | 0.728949i | 0.996024 | − | 0.0890887i | \(-0.0283955\pi\) |
−0.575165 | + | 0.818037i | \(0.695062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.62742 | −0.362094 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6569 | 1.17972 | 0.589862 | − | 0.807504i | \(-0.299182\pi\) | ||||
0.589862 | + | 0.807504i | \(0.299182\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.82843 | + | 11.8272i | 0.369780 | + | 0.640478i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.24264 | − | 12.5446i | 0.388805 | − | 0.673431i | −0.603484 | − | 0.797375i | \(-0.706221\pi\) |
0.992289 | + | 0.123945i | \(0.0395545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4142 | −0.718046 | −0.359023 | − | 0.933329i | \(-0.616890\pi\) | ||||
−0.359023 | + | 0.933329i | \(0.616890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8492 | + | 27.4517i | −0.843570 | + | 1.46111i | 0.0432872 | + | 0.999063i | \(0.486217\pi\) |
−0.886857 | + | 0.462044i | \(0.847116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.89949 | + | 3.29002i | 0.100815 | + | 0.174616i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.5858 | + | 20.0672i | 0.611474 | + | 1.05910i | 0.990992 | + | 0.133920i | \(0.0427566\pi\) |
−0.379518 | + | 0.925184i | \(0.623910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.81371 | − | 15.2658i | 0.463879 | − | 0.803463i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.51472 | −0.498023 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.6569 | − | 23.6544i | 0.712882 | − | 1.23475i | −0.250889 | − | 0.968016i | \(-0.580723\pi\) |
0.963771 | − | 0.266732i | \(-0.0859438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.65685 | + | 14.9941i | 0.448235 | + | 0.776366i | 0.998271 | − | 0.0587751i | \(-0.0187195\pi\) |
−0.550036 | + | 0.835141i | \(0.685386\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.686292 | −0.0352524 | −0.0176262 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176262 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.4853 | − | 21.6251i | −0.637968 | − | 1.10499i | −0.985878 | − | 0.167465i | \(-0.946442\pi\) |
0.347910 | − | 0.937528i | \(-0.386892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.89949 | − | 3.29002i | 0.0963082 | − | 0.166811i | −0.813846 | − | 0.581081i | \(-0.802630\pi\) |
0.910154 | + | 0.414270i | \(0.135963\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.79899 | −0.192123 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.686292 | + | 1.18869i | −0.0345311 | + | 0.0598096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.87868 | − | 6.71807i | −0.194665 | − | 0.337170i | 0.752125 | − | 0.659020i | \(-0.229029\pi\) |
−0.946791 | + | 0.321850i | \(0.895695\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.41421 | + | 5.91359i | 0.170498 | + | 0.295311i | 0.938594 | − | 0.345024i | \(-0.112129\pi\) |
−0.768096 | + | 0.640334i | \(0.778796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | + | 10.3923i | −0.298881 | + | 0.517678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.6274 | 2.31124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.121320 | − | 0.210133i | 0.00599890 | − | 0.0103904i | −0.863010 | − | 0.505186i | \(-0.831424\pi\) |
0.869009 | + | 0.494796i | \(0.164757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.17157 | + | 2.02922i | 0.0575103 | + | 0.0996107i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4853 | 1.19618 | 0.598092 | − | 0.801427i | \(-0.295926\pi\) | ||||
0.598092 | + | 0.801427i | \(0.295926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68629 | −0.130922 | −0.0654609 | − | 0.997855i | \(-0.520852\pi\) | ||||
−0.0654609 | + | 0.997855i | \(0.520852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.6777 | + | 18.4943i | 0.517943 | + | 0.897104i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0711 | − | 17.4436i | 0.485106 | − | 0.840229i | −0.514747 | − | 0.857342i | \(-0.672114\pi\) |
0.999854 | + | 0.0171133i | \(0.00544758\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0711 | −0.724269 | −0.362135 | − | 0.932126i | \(-0.617952\pi\) | ||||
−0.362135 | + | 0.932126i | \(0.617952\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.485281 | + | 0.840532i | −0.0232142 | + | 0.0402081i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6569 | + | 30.5826i | 0.842716 | + | 1.45963i | 0.887590 | + | 0.460634i | \(0.152378\pi\) |
−0.0448746 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.41421 | − | 14.5738i | −0.399771 | − | 0.692424i | 0.593926 | − | 0.804520i | \(-0.297577\pi\) |
−0.993697 | + | 0.112095i | \(0.964244\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.17157 | + | 7.22538i | −0.197752 | + | 0.342516i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6274 | −1.35101 | −0.675506 | − | 0.737355i | \(-0.736075\pi\) | ||||
−0.675506 | + | 0.737355i | \(0.736075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.24264 | + | 7.34847i | −0.199778 | + | 0.346026i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3137 | − | 17.8639i | −0.482455 | − | 0.835636i | 0.517342 | − | 0.855779i | \(-0.326921\pi\) |
−0.999797 | + | 0.0201422i | \(0.993588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.3848 | −0.949414 | −0.474707 | − | 0.880144i | \(-0.657446\pi\) | ||||
−0.474707 | + | 0.880144i | \(0.657446\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.65685 | −0.448792 | −0.224396 | − | 0.974498i | \(-0.572041\pi\) | ||||
−0.224396 | + | 0.974498i | \(0.572041\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.58579 | + | 11.4069i | 0.304754 | + | 0.527849i | 0.977206 | − | 0.212291i | \(-0.0680925\pi\) |
−0.672453 | + | 0.740140i | \(0.734759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.3137 | + | 47.3087i | −1.25589 | + | 2.17526i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.45584 | 0.250331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.58579 | + | 14.8710i | −0.392295 | + | 0.679474i | −0.992752 | − | 0.120183i | \(-0.961652\pi\) |
0.600457 | + | 0.799657i | \(0.294985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.4853 | + | 35.4815i | 0.934048 | + | 1.61782i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.41421 | + | 4.18154i | 0.109624 | + | 0.189874i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4853 | − | 25.0892i | 0.656391 | − | 1.13690i | −0.325152 | − | 0.945662i | \(-0.605416\pi\) |
0.981543 | − | 0.191241i | \(-0.0612510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8284 | −1.12049 | −0.560246 | − | 0.828327i | \(-0.689293\pi\) | ||||
−0.560246 | + | 0.828327i | \(0.689293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.48528 | + | 11.2328i | −0.292082 | + | 0.505902i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.48528 | − | 7.76874i | −0.200789 | − | 0.347776i | 0.747994 | − | 0.663705i | \(-0.231017\pi\) |
−0.948783 | + | 0.315929i | \(0.897684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.31371 | 0.147751 | 0.0738755 | − | 0.997267i | \(-0.476463\pi\) | ||||
0.0738755 | + | 0.997267i | \(0.476463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.62742 | 0.383915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.192388 | − | 0.333226i | −0.00852746 | − | 0.0147700i | 0.861730 | − | 0.507367i | \(-0.169381\pi\) |
−0.870258 | + | 0.492597i | \(0.836048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.14214 | + | 7.17439i | −0.182524 | + | 0.316141i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.2843 | 2.65130 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.87868 | + | 4.98602i | −0.126117 | + | 0.218441i | −0.922169 | − | 0.386787i | \(-0.873585\pi\) |
0.796052 | + | 0.605228i | \(0.206918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4853 | + | 25.0892i | 0.633397 | + | 1.09708i | 0.986852 | + | 0.161625i | \(0.0516734\pi\) |
−0.353455 | + | 0.935451i | \(0.614993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.48528 | + | 11.2328i | 0.282503 | + | 0.489310i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1569 | − | 19.3242i | 0.485081 | − | 0.840184i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.45584 | −0.322948 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.10051 | − | 3.63818i | 0.0908128 | − | 0.157292i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | + | 15.5885i | 0.386940 | + | 0.670200i | 0.992036 | − | 0.125952i | \(-0.0401986\pi\) |
−0.605096 | + | 0.796152i | \(0.706865\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.3137 | 0.484626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9706 | −1.58075 | −0.790374 | − | 0.612625i | \(-0.790114\pi\) | ||||
−0.790374 | + | 0.612625i | \(0.790114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.65685 | + | 2.86976i | 0.0705844 | + | 0.122256i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.31371 | + | 10.9357i | −0.267520 | + | 0.463359i | −0.968221 | − | 0.250097i | \(-0.919538\pi\) |
0.700700 | + | 0.713456i | \(0.252871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.0000 | −2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0711 | + | 26.1039i | −0.635170 | + | 1.10015i | 0.351309 | + | 0.936259i | \(0.385737\pi\) |
−0.986479 | + | 0.163887i | \(0.947597\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.92893 | − | 5.07306i | −0.123221 | − | 0.213425i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.0711 | − | 29.5680i | −0.715656 | − | 1.23955i | −0.962706 | − | 0.270550i | \(-0.912794\pi\) |
0.247049 | − | 0.969003i | \(-0.420539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.1716 | − | 26.2779i | 0.634911 | − | 1.09970i | −0.351624 | − | 0.936141i | \(-0.614370\pi\) |
0.986534 | − | 0.163556i | \(-0.0522964\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.85786 | 0.160884 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.6066 | + | 25.2994i | −0.608081 | + | 1.05323i | 0.383476 | + | 0.923551i | \(0.374727\pi\) |
−0.991556 | + | 0.129676i | \(0.958606\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.82843 | − | 8.36308i | −0.199973 | − | 0.346363i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.79899 | 0.156801 | 0.0784005 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0784005 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31371 | 0.136539 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.2929 | − | 38.6124i | −0.915459 | − | 1.58562i | −0.806227 | − | 0.591606i | \(-0.798494\pi\) |
−0.109232 | − | 0.994016i | \(-0.534839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.7279 | + | 23.7775i | −0.560908 | + | 0.971521i | 0.436510 | + | 0.899699i | \(0.356214\pi\) |
−0.997418 | + | 0.0718211i | \(0.977119\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.75736 | 0.153266 | 0.0766329 | − | 0.997059i | \(-0.475583\pi\) | ||||
0.0766329 | + | 0.997059i | \(0.475583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.60660 | + | 6.24682i | −0.146629 | + | 0.253969i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.48528 | − | 7.76874i | −0.182052 | − | 0.315323i | 0.760527 | − | 0.649306i | \(-0.224941\pi\) |
−0.942579 | + | 0.333983i | \(0.891607\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.4853 | + | 45.8739i | 1.07148 | + | 1.85586i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8284 | − | 18.7554i | 0.437356 | − | 0.757523i | −0.560129 | − | 0.828406i | \(-0.689248\pi\) |
0.997485 | + | 0.0708828i | \(0.0225816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.4853 | −0.502639 | −0.251319 | − | 0.967904i | \(-0.580864\pi\) | ||||
−0.251319 | + | 0.967904i | \(0.580864\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1716 | − | 19.3497i | 0.449023 | − | 0.777731i | −0.549299 | − | 0.835626i | \(-0.685105\pi\) |
0.998323 | + | 0.0578943i | \(0.0184386\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.98528 | − | 17.2950i | −0.399411 | − | 0.691801i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.2843 | 1.76573 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.9706 | −1.47177 | −0.735887 | − | 0.677104i | \(-0.763235\pi\) | ||||
−0.735887 | + | 0.677104i | \(0.763235\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.85786 | − | 10.1461i | −0.232462 | − | 0.402636i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5563 | + | 23.4803i | −0.535444 | + | 0.927416i | 0.463698 | + | 0.885993i | \(0.346522\pi\) |
−0.999142 | + | 0.0414223i | \(0.986811\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.79899 | 0.307562 | 0.153781 | − | 0.988105i | \(-0.450855\pi\) | ||||
0.153781 | + | 0.988105i | \(0.450855\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.8995 | − | 34.4669i | 0.782330 | − | 1.35504i | −0.148251 | − | 0.988950i | \(-0.547364\pi\) |
0.930581 | − | 0.366085i | \(-0.119302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.4853 | + | 35.4815i | 0.804118 | + | 1.39277i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.92893 | + | 15.4654i | 0.349416 | + | 0.605206i | 0.986146 | − | 0.165881i | \(-0.0530466\pi\) |
−0.636730 | + | 0.771087i | \(0.719713\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.17157 | − | 2.02922i | 0.0457771 | − | 0.0792883i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.4853 | −1.49917 | −0.749587 | − | 0.661906i | \(-0.769748\pi\) | ||||
−0.749587 | + | 0.661906i | \(0.769748\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.53553 | − | 16.5160i | 0.370889 | − | 0.642399i | −0.618813 | − | 0.785538i | \(-0.712386\pi\) |
0.989703 | + | 0.143139i | \(0.0457196\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.17157 | + | 2.02922i | 0.0453635 | + | 0.0785719i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.8284 | 0.572445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.686292 | −0.0264546 | −0.0132273 | − | 0.999913i | \(-0.504211\pi\) | ||||
−0.0132273 | + | 0.999913i | \(0.504211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8492 | + | 27.4517i | 0.609136 | + | 1.05505i | 0.991383 | + | 0.130994i | \(0.0418169\pi\) |
−0.382247 | + | 0.924060i | \(0.624850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.8995 | − | 32.7349i | 0.723169 | − | 1.25257i | −0.236554 | − | 0.971618i | \(-0.576018\pi\) |
0.959723 | − | 0.280947i | \(-0.0906486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.68629 | 0.331886 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.24264 | − | 7.34847i | 0.161632 | − | 0.279954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6569 | + | 27.1185i | 0.595615 | + | 1.03164i | 0.993460 | + | 0.114182i | \(0.0364248\pi\) |
−0.397845 | + | 0.917453i | \(0.630242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.79899 | + | 6.58004i | 0.144104 | + | 0.249595i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.02944 | + | 6.97919i | −0.152626 | + | 0.264356i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.1421 | −0.836297 | −0.418148 | − | 0.908379i | \(-0.637321\pi\) | ||||
−0.418148 | + | 0.908379i | \(0.637321\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.65685 | − | 9.79796i | 0.213352 | − | 0.369537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3137 | + | 33.4523i | 0.725342 | + | 1.25633i | 0.958833 | + | 0.283970i | \(0.0916515\pi\) |
−0.233492 | + | 0.972359i | \(0.575015\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.34315 | 0.0877515 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | −0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3137 | − | 33.4523i | −0.720280 | − | 1.24756i | −0.960888 | − | 0.276939i | \(-0.910680\pi\) |
0.240608 | − | 0.970622i | \(-0.422653\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.58579 | − | 11.4069i | 0.244590 | − | 0.423642i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1421 | 1.41461 | 0.707307 | − | 0.706907i | \(-0.249910\pi\) | ||||
0.707307 | + | 0.706907i | \(0.249910\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.9411 | + | 44.9313i | −0.959467 | + | 1.66185i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0208 | + | 34.6771i | 0.739486 | + | 1.28083i | 0.952727 | + | 0.303827i | \(0.0982646\pi\) |
−0.213241 | + | 0.977000i | \(0.568402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.3137 | + | 47.3087i | 1.00611 | + | 1.74264i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.485281 | − | 0.840532i | 0.0178514 | − | 0.0309195i | −0.856962 | − | 0.515380i | \(-0.827651\pi\) |
0.874813 | + | 0.484461i | \(0.160984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.828427 | −0.0303920 | −0.0151960 | − | 0.999885i | \(-0.504837\pi\) | ||||
−0.0151960 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.24264 | + | 10.8126i | −0.228713 | + | 0.396142i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1421 | + | 31.4231i | 0.662016 | + | 1.14665i | 0.980085 | + | 0.198578i | \(0.0636322\pi\) |
−0.318069 | + | 0.948067i | \(0.603034\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.970563 | 0.0353224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.9411 | −0.942846 | −0.471423 | − | 0.881907i | \(-0.656260\pi\) | ||||
−0.471423 | + | 0.881907i | \(0.656260\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.05025 | + | 10.4793i | 0.219321 | + | 0.379876i | 0.954601 | − | 0.297888i | \(-0.0962823\pi\) |
−0.735279 | + | 0.677764i | \(0.762949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.0000 | + | 31.1769i | −0.649942 | + | 1.12573i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8701 | 0.680472 | 0.340236 | − | 0.940340i | \(-0.389493\pi\) | ||||
0.340236 | + | 0.940340i | \(0.389493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.6777 | − | 32.3507i | 0.671789 | − | 1.16357i | −0.305607 | − | 0.952158i | \(-0.598859\pi\) |
0.977396 | − | 0.211415i | \(-0.0678072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.58579 | − | 11.4069i | −0.236568 | − | 0.409749i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.02944 | + | 1.78304i | 0.0368834 | + | 0.0638840i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.6569 | − | 27.1185i | 0.560246 | − | 0.970375i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.82843 | 0.172334 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.65685 | + | 6.33386i | −0.130353 | + | 0.225778i | −0.923813 | − | 0.382845i | \(-0.874944\pi\) |
0.793460 | + | 0.608623i | \(0.208278\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.51472 | + | 11.2838i | 0.231344 | + | 0.400700i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.5858 | −1.29594 | −0.647968 | − | 0.761668i | \(-0.724381\pi\) | ||||
−0.647968 | + | 0.761668i | \(0.724381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 57.2548 | 2.02553 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.2132 | + | 67.9193i | 1.38380 | + | 2.39682i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.3137 | − | 35.1844i | 0.714192 | − | 1.23702i | −0.249078 | − | 0.968483i | \(-0.580128\pi\) |
0.963270 | − | 0.268533i | \(-0.0865390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3431 | −0.503656 | −0.251828 | − | 0.967772i | \(-0.581032\pi\) | ||||
−0.251828 | + | 0.967772i | \(0.581032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.65685 | − | 2.86976i | 0.0580371 | − | 0.100523i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.62742 | + | 11.4790i | 0.231864 | + | 0.401600i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6569 | − | 28.8505i | −0.581328 | − | 1.00689i | −0.995322 | − | 0.0966104i | \(-0.969200\pi\) |
0.413994 | − | 0.910280i | \(-0.364133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.48528 | + | 7.76874i | −0.156347 | + | 0.270801i | −0.933549 | − | 0.358451i | \(-0.883305\pi\) |
0.777202 | + | 0.629252i | \(0.216639\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8579 | −0.412338 | −0.206169 | − | 0.978516i | \(-0.566100\pi\) | ||||
−0.206169 | + | 0.978516i | \(0.566100\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.19239 | + | 2.06528i | −0.0414134 | + | 0.0717300i | −0.885989 | − | 0.463706i | \(-0.846519\pi\) |
0.844576 | + | 0.535436i | \(0.179853\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.68629 | + | 4.65279i | 0.0929630 | + | 0.161017i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7990 | −0.545442 | −0.272721 | − | 0.962093i | \(-0.587924\pi\) | ||||
−0.272721 | + | 0.962093i | \(0.587924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.46447 | − | 2.53653i | −0.0503792 | − | 0.0872593i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | − | 6.92820i | 0.137118 | − | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0711 | −0.652981 | −0.326490 | − | 0.945200i | \(-0.605866\pi\) | ||||
−0.326490 | + | 0.945200i | \(0.605866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6066 | + | 27.0314i | −0.533111 | + | 0.923376i | 0.466141 | + | 0.884711i | \(0.345644\pi\) |
−0.999252 | + | 0.0386654i | \(0.987689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.7279 | + | 46.2941i | 0.911945 | + | 1.57953i | 0.811314 | + | 0.584611i | \(0.198753\pi\) |
0.100631 | + | 0.994924i | \(0.467914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.0416 | − | 36.4452i | −0.716265 | − | 1.24061i | −0.962469 | − | 0.271390i | \(-0.912517\pi\) |
0.246204 | − | 0.969218i | \(-0.420817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.68629 | − | 9.84895i | 0.193340 | − | 0.334874i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3137 | 0.383791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | + | 41.5692i | −0.813209 | + | 1.40852i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.1421 | − | 24.4949i | −0.477546 | − | 0.827134i | 0.522123 | − | 0.852870i | \(-0.325140\pi\) |
−0.999669 | + | 0.0257364i | \(0.991807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0416 | −0.607838 | −0.303919 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303919 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.6569 | −0.728811 | −0.364406 | − | 0.931240i | \(-0.618728\pi\) | ||||
−0.364406 | + | 0.931240i | \(0.618728\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.100505 | + | 0.174080i | 0.00337463 | + | 0.00584503i | 0.867708 | − | 0.497075i | \(-0.165592\pi\) |
−0.864333 | + | 0.502920i | \(0.832259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.31371 | − | 12.6677i | 0.244744 | − | 0.423909i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.14214 | −0.205309 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000 | − | 6.92820i | 0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.58579 | − | 7.94282i | −0.152775 | − | 0.264614i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.07107 | + | 3.58719i | 0.0688446 | + | 0.119242i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1716 | + | 36.6702i | −0.702991 | + | 1.21762i | 0.264421 | + | 0.964407i | \(0.414819\pi\) |
−0.967412 | + | 0.253208i | \(0.918514\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.4853 | 0.347393 | 0.173696 | − | 0.984799i | \(-0.444429\pi\) | ||||
0.173696 | + | 0.984799i | \(0.444429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.65685 | − | 16.7262i | 0.319595 | − | 0.553555i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.34315 | − | 7.52255i | −0.143267 | − | 0.248146i | 0.785458 | − | 0.618915i | \(-0.212427\pi\) |
−0.928725 | + | 0.370769i | \(0.879094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.5147 | 0.905658 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.9706 | −1.47862 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.94975 | − | 3.37706i | −0.0639691 | − | 0.110798i | 0.832267 | − | 0.554375i | \(-0.187043\pi\) |
−0.896236 | + | 0.443577i | \(0.853709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.48528 | + | 11.2328i | −0.212091 | + | 0.367353i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3553 | 0.632311 | 0.316156 | − | 0.948707i | \(-0.397608\pi\) | ||||
0.316156 | + | 0.948707i | \(0.397608\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.36396 | + | 9.29065i | −0.174860 | + | 0.302867i | −0.940113 | − | 0.340863i | \(-0.889281\pi\) |
0.765253 | + | 0.643730i | \(0.222614\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.727922 | + | 1.26080i | 0.0237044 | + | 0.0410572i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.38478 | + | 12.7908i | 0.239973 | + | 0.415645i | 0.960706 | − | 0.277567i | \(-0.0895281\pi\) |
−0.720733 | + | 0.693212i | \(0.756195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.4558 | + | 59.6793i | −1.11848 | + | 1.93727i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.72792 | + | 8.18900i | −0.152992 | + | 0.264990i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.5000 | + | 19.9186i | 0.370968 | + | 0.642535i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.17157 | 0.0377143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.68629 | −0.279332 | −0.139666 | − | 0.990199i | \(-0.544603\pi\) | ||||
−0.139666 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.0000 | + | 17.3205i | 0.320915 | + | 0.555842i | 0.980677 | − | 0.195633i | \(-0.0626762\pi\) |
−0.659762 | + | 0.751475i | \(0.729343\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.8995 | − | 27.5387i | 0.508670 | − | 0.881042i | −0.491280 | − | 0.871002i | \(-0.663471\pi\) |
0.999950 | − | 0.0100402i | \(-0.00319596\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.7696 | 2.19788 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.3137 | + | 40.3805i | −0.743592 | + | 1.28794i | 0.207258 | + | 0.978286i | \(0.433546\pi\) |
−0.950850 | + | 0.309652i | \(0.899787\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.41421 | − | 12.8418i | −0.236236 | − | 0.409174i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.68629 | + | 8.11689i | 0.149015 | + | 0.258102i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3137 | + | 23.0600i | −0.422924 | + | 0.732526i | −0.996224 | − | 0.0868198i | \(-0.972330\pi\) |
0.573300 | + | 0.819345i | \(0.305663\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.31371 | −0.105052 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.80761 | + | 15.2552i | −0.278940 | + | 0.483138i | −0.971122 | − | 0.238585i | \(-0.923316\pi\) |
0.692182 | + | 0.721723i | \(0.256650\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3528.2.s.bc.361.2 | 4 | ||
3.2 | odd | 2 | 1176.2.q.m.361.1 | 4 | |||
7.2 | even | 3 | inner | 3528.2.s.bc.3313.2 | 4 | ||
7.3 | odd | 6 | 3528.2.a.bc.1.2 | 2 | |||
7.4 | even | 3 | 3528.2.a.bm.1.1 | 2 | |||
7.5 | odd | 6 | 3528.2.s.bl.3313.1 | 4 | |||
7.6 | odd | 2 | 3528.2.s.bl.361.1 | 4 | |||
12.11 | even | 2 | 2352.2.q.bg.1537.1 | 4 | |||
21.2 | odd | 6 | 1176.2.q.m.961.1 | 4 | |||
21.5 | even | 6 | 1176.2.q.n.961.2 | 4 | |||
21.11 | odd | 6 | 1176.2.a.m.1.2 | yes | 2 | ||
21.17 | even | 6 | 1176.2.a.l.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 1176.2.q.n.361.2 | 4 | |||
28.3 | even | 6 | 7056.2.a.ce.1.2 | 2 | |||
28.11 | odd | 6 | 7056.2.a.cw.1.1 | 2 | |||
84.11 | even | 6 | 2352.2.a.z.1.2 | 2 | |||
84.23 | even | 6 | 2352.2.q.bg.961.1 | 4 | |||
84.47 | odd | 6 | 2352.2.q.ba.961.2 | 4 | |||
84.59 | odd | 6 | 2352.2.a.bg.1.1 | 2 | |||
84.83 | odd | 2 | 2352.2.q.ba.1537.2 | 4 | |||
168.11 | even | 6 | 9408.2.a.ed.1.1 | 2 | |||
168.53 | odd | 6 | 9408.2.a.dr.1.1 | 2 | |||
168.59 | odd | 6 | 9408.2.a.dh.1.2 | 2 | |||
168.101 | even | 6 | 9408.2.a.dv.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.2.a.l.1.1 | ✓ | 2 | 21.17 | even | 6 | ||
1176.2.a.m.1.2 | yes | 2 | 21.11 | odd | 6 | ||
1176.2.q.m.361.1 | 4 | 3.2 | odd | 2 | |||
1176.2.q.m.961.1 | 4 | 21.2 | odd | 6 | |||
1176.2.q.n.361.2 | 4 | 21.20 | even | 2 | |||
1176.2.q.n.961.2 | 4 | 21.5 | even | 6 | |||
2352.2.a.z.1.2 | 2 | 84.11 | even | 6 | |||
2352.2.a.bg.1.1 | 2 | 84.59 | odd | 6 | |||
2352.2.q.ba.961.2 | 4 | 84.47 | odd | 6 | |||
2352.2.q.ba.1537.2 | 4 | 84.83 | odd | 2 | |||
2352.2.q.bg.961.1 | 4 | 84.23 | even | 6 | |||
2352.2.q.bg.1537.1 | 4 | 12.11 | even | 2 | |||
3528.2.a.bc.1.2 | 2 | 7.3 | odd | 6 | |||
3528.2.a.bm.1.1 | 2 | 7.4 | even | 3 | |||
3528.2.s.bc.361.2 | 4 | 1.1 | even | 1 | trivial | ||
3528.2.s.bc.3313.2 | 4 | 7.2 | even | 3 | inner | ||
3528.2.s.bl.361.1 | 4 | 7.6 | odd | 2 | |||
3528.2.s.bl.3313.1 | 4 | 7.5 | odd | 6 | |||
7056.2.a.ce.1.2 | 2 | 28.3 | even | 6 | |||
7056.2.a.cw.1.1 | 2 | 28.11 | odd | 6 | |||
9408.2.a.dh.1.2 | 2 | 168.59 | odd | 6 | |||
9408.2.a.dr.1.1 | 2 | 168.53 | odd | 6 | |||
9408.2.a.dv.1.2 | 2 | 168.101 | even | 6 | |||
9408.2.a.ed.1.1 | 2 | 168.11 | even | 6 |