Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(863,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.863");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.s (of order \(6\), 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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 864) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1727.1 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1727 |
Dual form | 2592.2.s.a.863.1 |
$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | −2.72474 | + | 1.57313i | −1.21854 | + | 0.703526i | −0.964606 | − | 0.263695i | \(-0.915059\pi\) |
−0.253937 | + | 0.967221i | \(0.581726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.98735 | − | 1.72474i | −1.12911 | − | 0.651892i | −0.185399 | − | 0.982663i | \(-0.559358\pi\) |
−0.943711 | + | 0.330771i | \(0.892691\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.28024 | − | 3.94949i | 0.687518 | − | 1.19082i | −0.285120 | − | 0.958492i | \(-0.592034\pi\) |
0.972638 | − | 0.232324i | \(-0.0746331\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.44949 | + | 5.97469i | 0.956716 | + | 1.65708i | 0.730391 | + | 0.683030i | \(0.239338\pi\) |
0.226326 | + | 0.974052i | \(0.427329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898i | 1.12390i | 0.827170 | + | 0.561951i | \(0.189949\pi\) | ||||
−0.827170 | + | 0.561951i | \(0.810051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.41421 | − | 2.44949i | −0.294884 | − | 0.510754i | 0.680074 | − | 0.733144i | \(-0.261948\pi\) |
−0.974958 | + | 0.222390i | \(0.928614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.44949 | − | 4.24264i | 0.489898 | − | 0.848528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.89898 | − | 1.09638i | −0.352632 | − | 0.203592i | 0.313212 | − | 0.949683i | \(-0.398595\pi\) |
−0.665844 | + | 0.746091i | \(0.731928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.20881 | + | 1.27526i | −0.396713 | + | 0.229043i | −0.685065 | − | 0.728482i | \(-0.740226\pi\) |
0.288352 | + | 0.957525i | \(0.406893\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.8530 | 1.83449 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89898 | −0.805387 | −0.402694 | − | 0.915335i | \(-0.631926\pi\) | ||||
−0.402694 | + | 0.915335i | \(0.631926\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.55051 | − | 2.04989i | 0.554497 | − | 0.320139i | −0.196437 | − | 0.980516i | \(-0.562937\pi\) |
0.750934 | + | 0.660378i | \(0.229604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.51059 | − | 1.44949i | −0.382861 | − | 0.221045i | 0.296201 | − | 0.955126i | \(-0.404280\pi\) |
−0.679062 | + | 0.734080i | \(0.737613\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.09638 | − | 1.89898i | 0.159923 | − | 0.276995i | −0.774918 | − | 0.632062i | \(-0.782209\pi\) |
0.934841 | + | 0.355067i | \(0.115542\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.44949 | + | 4.24264i | 0.349927 | + | 0.606092i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 12.9029i | − | 1.77235i | −0.463352 | − | 0.886174i | \(-0.653353\pi\) | ||
0.463352 | − | 0.886174i | \(-0.346647\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.3485i | 1.93475i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.09638 | − | 1.89898i | −0.142736 | − | 0.247226i | 0.785790 | − | 0.618493i | \(-0.212257\pi\) |
−0.928526 | + | 0.371267i | \(0.878923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | + | 3.46410i | −0.256074 | + | 0.443533i | −0.965187 | − | 0.261562i | \(-0.915762\pi\) |
0.709113 | + | 0.705095i | \(0.249096\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18.7980 | − | 10.8530i | −2.33160 | − | 1.34615i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9029 | − | 7.44949i | 1.57634 | − | 0.910100i | 0.580975 | − | 0.813921i | \(-0.302671\pi\) |
0.995364 | − | 0.0961789i | \(-0.0306621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2207 | −1.56901 | −0.784506 | − | 0.620121i | \(-0.787083\pi\) | ||||
−0.784506 | + | 0.620121i | \(0.787083\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.89898 | −0.924506 | −0.462253 | − | 0.886748i | \(-0.652959\pi\) | ||||
−0.462253 | + | 0.886748i | \(0.652959\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.6237 | + | 7.86566i | −1.55257 | + | 0.896375i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.73205 | − | 1.00000i | −0.194871 | − | 0.112509i | 0.399390 | − | 0.916781i | \(-0.369222\pi\) |
−0.594261 | + | 0.804272i | \(0.702555\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.20504 | − | 10.7474i | 0.681092 | − | 1.17969i | −0.293556 | − | 0.955942i | \(-0.594839\pi\) |
0.974648 | − | 0.223744i | \(-0.0718279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.44949 | − | 9.43879i | −0.591080 | − | 1.02378i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.02118i | − | 0.532244i | −0.963939 | − | 0.266122i | \(-0.914258\pi\) | ||
0.963939 | − | 0.266122i | \(-0.0857424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 23.7980i | − | 2.49470i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.70674 | − | 13.3485i | −0.790695 | − | 1.36952i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | − | 4.33013i | 0.253837 | − | 0.439658i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.37628 | + | 0.794593i | 0.136945 | + | 0.0790650i | 0.566907 | − | 0.823782i | \(-0.308140\pi\) |
−0.429962 | + | 0.902847i | \(0.641473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.66025 | + | 5.00000i | −0.853320 | + | 0.492665i | −0.861770 | − | 0.507300i | \(-0.830644\pi\) |
0.00844953 | + | 0.999964i | \(0.497310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.66025 | −0.837218 | −0.418609 | − | 0.908166i | \(-0.637482\pi\) | ||||
−0.418609 | + | 0.908166i | \(0.637482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.89898 | 0.469237 | 0.234619 | − | 0.972088i | \(-0.424616\pi\) | ||||
0.234619 | + | 0.972088i | \(0.424616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2474 | + | 7.07107i | −1.15214 | + | 0.665190i | −0.949409 | − | 0.314044i | \(-0.898316\pi\) |
−0.202735 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.70674 | + | 4.44949i | 0.718657 | + | 0.414917i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.97469 | − | 10.3485i | 0.547699 | − | 0.948643i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.89898 | − | 8.48528i | −0.445362 | − | 0.771389i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 0.317837i | − | 0.0284282i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.24745i | − | 0.820578i | −0.911955 | − | 0.410289i | \(-0.865428\pi\) | ||
0.911955 | − | 0.410289i | \(-0.134572\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.15855 | − | 12.3990i | −0.625446 | − | 1.08330i | −0.988454 | − | 0.151518i | \(-0.951584\pi\) |
0.363009 | − | 0.931786i | \(-0.381750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.44949 | − | 14.6349i | 0.732664 | − | 1.26901i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.2474 | − | 8.80312i | −1.30268 | − | 0.752101i | −0.321815 | − | 0.946803i | \(-0.604293\pi\) |
−0.980863 | + | 0.194701i | \(0.937626\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.3205 | − | 10.0000i | 1.46911 | − | 0.848189i | 0.469706 | − | 0.882823i | \(-0.344360\pi\) |
0.999400 | + | 0.0346338i | \(0.0110265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.4626 | 2.63104 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.89898 | 0.572929 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.72474 | − | 3.30518i | 0.468989 | − | 0.270771i | −0.246827 | − | 0.969060i | \(-0.579388\pi\) |
0.715817 | + | 0.698288i | \(0.246055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.27647 | + | 3.62372i | 0.510772 | + | 0.294895i | 0.733151 | − | 0.680066i | \(-0.238049\pi\) |
−0.222379 | + | 0.974960i | \(0.571382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.01229 | − | 6.94949i | 0.322275 | − | 0.558196i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.89898 | − | 5.02118i | −0.231364 | − | 0.400734i | 0.726846 | − | 0.686801i | \(-0.240985\pi\) |
−0.958210 | + | 0.286067i | \(0.907652\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.75663i | 0.768930i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.00000i | − | 0.469956i | −0.972001 | − | 0.234978i | \(-0.924498\pi\) | ||
0.972001 | − | 0.234978i | \(-0.0755019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.83183 | + | 10.1010i | 0.451280 | + | 0.781640i | 0.998466 | − | 0.0553709i | \(-0.0176341\pi\) |
−0.547186 | + | 0.837011i | \(0.684301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.2980 | + | 29.9609i | −1.33061 | + | 2.30469i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.62372 | − | 4.40156i | −0.579621 | − | 0.334644i | 0.181362 | − | 0.983416i | \(-0.441950\pi\) |
−0.760983 | + | 0.648772i | \(0.775283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.6349 | + | 8.44949i | −1.10630 | + | 0.638721i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.66025 | 0.647298 | 0.323649 | − | 0.946177i | \(-0.395090\pi\) | ||||
0.323649 | + | 0.946177i | \(0.395090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.79796 | 0.728277 | 0.364138 | − | 0.931345i | \(-0.381364\pi\) | ||||
0.364138 | + | 0.931345i | \(0.381364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.3485 | − | 7.70674i | 0.981399 | − | 0.566611i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.6814 | + | 7.89898i | 1.00049 | + | 0.577631i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.33902 | − | 9.24745i | 0.386318 | − | 0.669122i | −0.605633 | − | 0.795744i | \(-0.707080\pi\) |
0.991951 | + | 0.126622i | \(0.0404135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.94949 | − | 10.3048i | −0.428254 | − | 0.741757i | 0.568464 | − | 0.822708i | \(-0.307538\pi\) |
−0.996718 | + | 0.0809508i | \(0.974204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.87492i | − | 0.133582i | −0.997767 | − | 0.0667911i | \(-0.978724\pi\) | ||
0.997767 | − | 0.0667911i | \(-0.0212761\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.65153i | 0.400626i | 0.979732 | + | 0.200313i | \(0.0641960\pi\) | ||||
−0.979732 | + | 0.200313i | \(0.935804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.78194 | + | 6.55051i | 0.265440 | + | 0.459756i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.44949 | + | 11.1708i | −0.450452 | + | 0.780206i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.3485 | + | 11.1708i | 1.33836 | + | 0.772703i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.7491 | + | 10.2474i | −1.22190 | + | 0.705463i | −0.965322 | − | 0.261061i | \(-0.915928\pi\) |
−0.256576 | + | 0.966524i | \(0.582594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.12096 | 0.622044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.79796 | 0.597244 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.6969 | + | 11.9494i | −1.39223 | + | 0.803802i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.1455 | − | 9.89898i | −1.14815 | − | 0.662885i | −0.199714 | − | 0.979854i | \(-0.564001\pi\) |
−0.948436 | + | 0.316969i | \(0.897335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.4887 | + | 19.8990i | −0.762531 | + | 1.32074i | 0.179012 | + | 0.983847i | \(0.442710\pi\) |
−0.941542 | + | 0.336895i | \(0.890623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | − | 1.73205i | −0.0660819 | − | 0.114457i | 0.831092 | − | 0.556136i | \(-0.187717\pi\) |
−0.897173 | + | 0.441679i | \(0.854383\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.56388i | − | 0.495526i | −0.968821 | − | 0.247763i | \(-0.920305\pi\) | ||
0.968821 | − | 0.247763i | \(-0.0796954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.89898i | 0.450040i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.60697 | + | 6.24745i | 0.233315 | + | 0.404114i | 0.958782 | − | 0.284144i | \(-0.0917093\pi\) |
−0.725466 | + | 0.688258i | \(0.758376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.101021 | − | 0.174973i | 0.00650730 | − | 0.0112710i | −0.862753 | − | 0.505625i | \(-0.831262\pi\) |
0.869261 | + | 0.494354i | \(0.164595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.3485 | − | 7.70674i | −0.852802 | − | 0.492366i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.2699 | + | 16.8990i | −1.86240 | + | 1.07526i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8990 | −0.810952 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.8990 | + | 11.4887i | −1.24126 | + | 0.716644i | −0.969352 | − | 0.245678i | \(-0.920990\pi\) |
−0.271913 | + | 0.962322i | \(0.587656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.6349 | + | 8.44949i | 0.909371 | + | 0.525026i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.2706 | − | 26.4495i | 0.941627 | − | 1.63095i | 0.179258 | − | 0.983802i | \(-0.442630\pi\) |
0.762368 | − | 0.647143i | \(-0.224037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.2980 | + | 35.1571i | 1.24689 | + | 2.15968i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3923i | 0.633630i | 0.948487 | + | 0.316815i | \(0.102613\pi\) | ||||
−0.948487 | + | 0.316815i | \(0.897387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4495i | 1.05998i | 0.848004 | + | 0.529991i | \(0.177805\pi\) | ||||
−0.848004 | + | 0.529991i | \(0.822195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1708 | − | 19.3485i | −0.673627 | − | 1.16676i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.89898 | + | 5.02118i | −0.174183 | + | 0.301693i | −0.939878 | − | 0.341510i | \(-0.889062\pi\) |
0.765695 | + | 0.643203i | \(0.222395\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7980 | + | 10.8530i | 1.12139 | + | 0.647436i | 0.941756 | − | 0.336297i | \(-0.109175\pi\) |
0.179636 | + | 0.983733i | \(0.442508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.1708 | − | 6.44949i | 0.664038 | − | 0.383382i | −0.129776 | − | 0.991543i | \(-0.541426\pi\) |
0.793814 | + | 0.608161i | \(0.208092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.1421 | −0.834784 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.7980 | − | 14.3171i | 1.44871 | − | 0.836414i | 0.450307 | − | 0.892874i | \(-0.351314\pi\) |
0.998405 | + | 0.0564592i | \(0.0179811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.97469 | + | 3.44949i | 0.347860 | + | 0.200837i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.75663 | − | 16.8990i | 0.564241 | − | 0.977293i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | + | 8.66025i | 0.288195 | + | 0.499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 12.5851i | − | 0.720618i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.87832 | − | 8.44949i | −0.276624 | − | 0.479127i | 0.693920 | − | 0.720052i | \(-0.255882\pi\) |
−0.970544 | + | 0.240926i | \(0.922549\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.74745 | − | 16.8831i | 0.550958 | − | 0.954288i | −0.447247 | − | 0.894410i | \(-0.647596\pi\) |
0.998206 | − | 0.0598776i | \(-0.0190710\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3763 | − | 7.72280i | −0.751286 | − | 0.433755i | 0.0748721 | − | 0.997193i | \(-0.476145\pi\) |
−0.826159 | + | 0.563438i | \(0.809478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.66025 | + | 5.00000i | −0.484881 | + | 0.279946i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.9706 | −0.944267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.7980 | 1.87477 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.55051 | + | 3.78194i | −0.361141 | + | 0.208505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8523 | − | 14.3485i | −1.36600 | − | 0.788663i | −0.375590 | − | 0.926786i | \(-0.622560\pi\) |
−0.990415 | + | 0.138123i | \(0.955893\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.4381 | + | 40.5959i | −1.28056 | + | 2.21799i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8990 | − | 20.6096i | −0.648179 | − | 1.12268i | −0.983558 | − | 0.180595i | \(-0.942198\pi\) |
0.335379 | − | 0.942083i | \(-0.391136\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6315i | 0.629884i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.24745i | 0.391325i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.4012 | + | 19.7474i | 0.612048 | + | 1.06010i | 0.990895 | + | 0.134639i | \(0.0429875\pi\) |
−0.378847 | + | 0.925460i | \(0.623679\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.55051 | + | 13.0779i | −0.404170 | + | 0.700042i | −0.994224 | − | 0.107321i | \(-0.965773\pi\) |
0.590055 | + | 0.807363i | \(0.299106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2474 | − | 7.07107i | −0.651866 | − | 0.376355i | 0.137305 | − | 0.990529i | \(-0.456156\pi\) |
−0.789171 | + | 0.614174i | \(0.789489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.0231 | − | 20.7980i | 1.91191 | − | 1.10384i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.349945 | −0.0184694 | −0.00923470 | − | 0.999957i | \(-0.502940\pi\) | ||||
−0.00923470 | + | 0.999957i | \(0.502940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.5227 | − | 12.4261i | 1.12655 | − | 0.650414i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6476 | − | 6.72474i | −0.608000 | − | 0.351029i | 0.164182 | − | 0.986430i | \(-0.447501\pi\) |
−0.772182 | + | 0.635401i | \(0.780835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.2542 | + | 38.5454i | −1.15538 | + | 2.00118i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.24745 | + | 12.5529i | 0.375259 | + | 0.649967i | 0.990366 | − | 0.138477i | \(-0.0442205\pi\) |
−0.615107 | + | 0.788444i | \(0.710887\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.1278i | − | 0.779119i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.2672 | − | 21.2474i | −0.626826 | − | 1.08569i | −0.988185 | − | 0.153267i | \(-0.951020\pi\) |
0.361359 | − | 0.932427i | \(-0.382313\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.7474 | − | 42.8638i | 1.26125 | − | 2.18454i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.7702 | + | 10.8370i | 0.951685 | + | 0.549455i | 0.893604 | − | 0.448857i | \(-0.148169\pi\) |
0.0580807 | + | 0.998312i | \(0.481502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.48528 | − | 4.89898i | 0.429119 | − | 0.247752i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.29253 | 0.316611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.6969 | −1.03875 | −0.519375 | − | 0.854547i | \(-0.673835\pi\) | ||||
−0.519375 | + | 0.854547i | \(0.673835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.5959 | − | 11.3137i | 0.978573 | − | 0.564980i | 0.0767343 | − | 0.997052i | \(-0.475551\pi\) |
0.901839 | + | 0.432072i | \(0.142217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.2385 | − | 8.79796i | −0.759084 | − | 0.438258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.1708 | + | 19.3485i | −0.553718 | + | 0.959068i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.56388i | 0.372194i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.0454i | 1.91666i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.58166 | + | 16.5959i | 0.468095 | + | 0.810764i | 0.999335 | − | 0.0364574i | \(-0.0116073\pi\) |
−0.531241 | + | 0.847221i | \(0.678274\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.10102 | − | 8.83523i | 0.248609 | − | 0.430603i | −0.714531 | − | 0.699603i | \(-0.753360\pi\) |
0.963140 | + | 0.269001i | \(0.0866934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.6969 | + | 8.48528i | 0.712906 | + | 0.411597i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9494 | − | 6.89898i | 0.578271 | − | 0.333865i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.57826 | −0.316864 | −0.158432 | − | 0.987370i | \(-0.550644\pi\) | ||||
−0.158432 | + | 0.987370i | \(0.550644\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.3939 | −1.26841 | −0.634204 | − | 0.773165i | \(-0.718672\pi\) | ||||
−0.634204 | + | 0.773165i | \(0.718672\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0000 | − | 6.92820i | 0.574038 | − | 0.331421i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.54442 | − | 2.62372i | −0.216894 | − | 0.125224i | 0.387618 | − | 0.921820i | \(-0.373298\pi\) |
−0.604511 | + | 0.796597i | \(0.706631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.00340 | − | 5.20204i | 0.142696 | − | 0.247156i | −0.785815 | − | 0.618462i | \(-0.787756\pi\) |
0.928511 | + | 0.371305i | \(0.121090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.89898 | + | 13.6814i | 0.374448 | + | 0.648562i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.37113i | − | 0.253479i | −0.991936 | − | 0.126740i | \(-0.959549\pi\) | ||
0.991936 | − | 0.126740i | \(-0.0404512\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 18.6969i | − | 0.880404i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.4373 | + | 64.8434i | 1.75509 | + | 3.03990i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | + | 21.6506i | −0.584725 | + | 1.01277i | 0.410184 | + | 0.912003i | \(0.365464\pi\) |
−0.994910 | + | 0.100771i | \(0.967869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.6237 | + | 6.13361i | 0.494796 | + | 0.285671i | 0.726562 | − | 0.687101i | \(-0.241117\pi\) |
−0.231766 | + | 0.972772i | \(0.574450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7618 | − | 8.52270i | 0.686037 | − | 0.396084i | −0.116089 | − | 0.993239i | \(-0.537036\pi\) |
0.802126 | + | 0.597155i | \(0.203702\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1455 | 0.793401 | 0.396700 | − | 0.917948i | \(-0.370155\pi\) | ||||
0.396700 | + | 0.917948i | \(0.370155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −51.3939 | −2.37315 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4495 | + | 6.61037i | −0.526448 | + | 0.303945i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.7846 | + | 12.0000i | 0.953663 | + | 0.550598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.58166 | + | 16.5959i | −0.437797 | + | 0.758287i | −0.997519 | − | 0.0703935i | \(-0.977575\pi\) |
0.559722 | + | 0.828680i | \(0.310908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.8990 | − | 29.2699i | −0.770527 | − | 1.33459i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.7313i | 0.714323i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.7980i | − | 0.715874i | −0.933746 | − | 0.357937i | \(-0.883480\pi\) | ||
0.933746 | − | 0.357937i | \(-0.116520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.50170 | + | 2.60102i | 0.0677708 | + | 0.117382i | 0.897920 | − | 0.440159i | \(-0.145078\pi\) |
−0.830149 | + | 0.557542i | \(0.811745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.79796 | − | 6.57826i | 0.171051 | − | 0.296270i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.4949 | + | 22.8024i | 1.77159 | + | 1.02283i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.41761 | + | 2.55051i | −0.197760 | + | 0.114177i | −0.595610 | − | 0.803274i | \(-0.703090\pi\) |
0.397850 | + | 0.917450i | \(0.369756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.1127 | −1.38725 | −0.693623 | − | 0.720338i | \(-0.743987\pi\) | ||||
−0.693623 | + | 0.720338i | \(0.743987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00000 | −0.222497 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.1186 | − | 22.0078i | 1.68958 | − | 0.975478i | 0.734742 | − | 0.678347i | \(-0.237303\pi\) |
0.954837 | − | 0.297131i | \(-0.0960299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.5970 | + | 13.6237i | 1.04387 | + | 0.602678i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.7313 | − | 27.2474i | 0.693205 | − | 1.20067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.00000 | − | 8.66025i | −0.219900 | − | 0.380878i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 0.921404i | − | 0.0403674i | −0.999796 | − | 0.0201837i | \(-0.993575\pi\) | ||
0.999796 | − | 0.0201837i | \(-0.00642511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.3939i | 1.37276i | 0.727244 | + | 0.686379i | \(0.240801\pi\) | ||||
−0.727244 | + | 0.686379i | \(0.759199\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.41761 | − | 7.65153i | −0.192434 | − | 0.333306i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.50000 | − | 12.9904i | 0.326087 | − | 0.564799i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.4949 | + | 14.1421i | 1.06099 | + | 0.612564i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.5970 | − | 13.6237i | 1.02019 | − | 0.589005i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.3417 | 0.962325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0000 | −0.859867 | −0.429934 | − | 0.902861i | \(-0.641463\pi\) | ||||
−0.429934 | + | 0.902861i | \(0.641463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.3485 | + | 7.70674i | −0.571786 | + | 0.330121i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.63907 | − | 2.10102i | −0.155596 | − | 0.0898332i | 0.420181 | − | 0.907440i | \(-0.361967\pi\) |
−0.575776 | + | 0.817607i | \(0.695300\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.37113 | − | 9.30306i | 0.228818 | − | 0.396324i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.44949 | + | 5.97469i | 0.146687 | + | 0.254070i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.8735i | 1.26578i | 0.774242 | + | 0.632890i | \(0.218131\pi\) | ||||
−0.774242 | + | 0.632890i | \(0.781869\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.0000i | − | 0.845910i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.74094 | + | 4.74745i | 0.115517 | + | 0.200081i | 0.917986 | − | 0.396612i | \(-0.129814\pi\) |
−0.802469 | + | 0.596693i | \(0.796481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.2474 | − | 38.5337i | 0.935957 | − | 1.62113i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.8990 | + | 9.75663i | 0.708442 | + | 0.409019i | 0.810484 | − | 0.585761i | \(-0.199204\pi\) |
−0.102042 | + | 0.994780i | \(0.532538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.174973 | − | 0.101021i | 0.00732238 | − | 0.00422758i | −0.496334 | − | 0.868131i | \(-0.665321\pi\) |
0.503657 | + | 0.863904i | \(0.331988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8564 | −0.577852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7980 | 0.657678 | 0.328839 | − | 0.944386i | \(-0.393343\pi\) | ||||
0.328839 | + | 0.944386i | \(0.393343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.0732 | + | 21.4042i | −1.53806 | + | 0.887997i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.9599 | − | 29.4217i | −2.11054 | − | 1.21852i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.7402 | + | 28.9949i | −0.690942 | + | 1.19675i | 0.280587 | + | 0.959829i | \(0.409471\pi\) |
−0.971529 | + | 0.236919i | \(0.923862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.24745 | − | 10.8209i | −0.257422 | − | 0.445867i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.7764i | 1.75661i | 0.478097 | + | 0.878307i | \(0.341327\pi\) | ||||
−0.478097 | + | 0.878307i | \(0.658673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.5959i | 1.54128i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.4169 | − | 31.8990i | −0.752493 | − | 1.30336i | −0.946611 | − | 0.322379i | \(-0.895518\pi\) |
0.194117 | − | 0.980978i | \(-0.437816\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8485 | + | 34.3786i | −0.809636 | + | 1.40233i | 0.103480 | + | 0.994631i | \(0.467002\pi\) |
−0.913116 | + | 0.407699i | \(0.866331\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.6969 | + | 15.4135i | 1.08538 | + | 0.626647i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.63907 | − | 2.10102i | 0.147705 | − | 0.0852778i | −0.424326 | − | 0.905510i | \(-0.639489\pi\) |
0.572031 | + | 0.820232i | \(0.306156\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.1278 | 0.612003 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.247449 | − | 0.142865i | 0.00996191 | − | 0.00575151i | −0.495011 | − | 0.868887i | \(-0.664836\pi\) |
0.504973 | + | 0.863135i | \(0.331503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2385 | + | 8.79796i | 0.612488 | + | 0.353620i | 0.773938 | − | 0.633261i | \(-0.218284\pi\) |
−0.161451 | + | 0.986881i | \(0.551617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.66025 | + | 15.0000i | −0.346966 | + | 0.600962i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.7474 | + | 22.0792i | 0.509898 | + | 0.883169i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16.9706i | − | 0.676661i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.7423i | − | 1.10441i | −0.833710 | − | 0.552203i | \(-0.813787\pi\) | ||
0.833710 | − | 0.552203i | \(-0.186213\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.5475 | + | 25.1969i | 0.577298 | + | 0.999910i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.8990 | + | 29.2699i | −0.669562 | + | 1.15972i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.7526 | − | 10.2494i | −0.701184 | − | 0.404829i | 0.106604 | − | 0.994302i | \(-0.466002\pi\) |
−0.807788 | + | 0.589473i | \(0.799335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5276 | − | 10.6969i | 0.730659 | − | 0.421846i | −0.0880043 | − | 0.996120i | \(-0.528049\pi\) |
0.818663 | + | 0.574274i | \(0.194716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | −0.817127 | −0.408564 | − | 0.912730i | \(-0.633970\pi\) | ||||
−0.408564 | + | 0.912730i | \(0.633970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.0000 | −0.392534 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.07321 | + | 0.619620i | −0.0419981 | + | 0.0242476i | −0.520852 | − | 0.853647i | \(-0.674386\pi\) |
0.478854 | + | 0.877895i | \(0.341052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.0105 | + | 22.5227i | 1.52427 | + | 0.880035i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.71563 | + | 15.0959i | −0.339513 | + | 0.588053i | −0.984341 | − | 0.176274i | \(-0.943596\pi\) |
0.644828 | + | 0.764327i | \(0.276929\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.2474 | − | 38.5337i | −0.865325 | − | 1.49879i | −0.866724 | − | 0.498789i | \(-0.833778\pi\) |
0.00139818 | − | 0.999999i | \(-0.499555\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 53.1687i | 2.06179i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.20204i | 0.240144i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.12096 | + | 15.7980i | 0.352111 | + | 0.609873i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.29796 | + | 2.24813i | −0.0500326 | + | 0.0866591i | −0.889957 | − | 0.456044i | \(-0.849266\pi\) |
0.839924 | + | 0.542703i | \(0.182599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.4949 | − | 22.8024i | −1.51791 | − | 0.876367i | −0.999778 | − | 0.0210677i | \(-0.993293\pi\) |
−0.518134 | − | 0.855299i | \(-0.673373\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.9367 | + | 8.62372i | −0.573219 | + | 0.330948i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.3923 | −0.397650 | −0.198825 | − | 0.980035i | \(-0.563713\pi\) | ||||
−0.198825 | + | 0.980035i | \(0.563713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.3939 | 2.11649 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 77.0908 | − | 44.5084i | 2.93693 | − | 1.69564i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.46410 | − | 2.00000i | −0.131781 | − | 0.0760836i | 0.432660 | − | 0.901557i | \(-0.357575\pi\) |
−0.564441 | + | 0.825473i | \(0.690908\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.4626 | + | 54.4949i | −1.19345 | + | 2.06711i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.10102 | + | 12.2993i | 0.268970 | + | 0.465870i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2528i | − | 0.500553i | −0.968174 | − | 0.250276i | \(-0.919478\pi\) | ||
0.968174 | − | 0.250276i | \(-0.0805215\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.0000i | − | 0.905177i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.74094 | − | 4.74745i | −0.103084 | − | 0.178546i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0000 | − | 34.6410i | 0.751116 | − | 1.30097i | −0.196167 | − | 0.980571i | \(-0.562849\pi\) |
0.947282 | − | 0.320400i | \(-0.103817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.24745 | + | 3.60697i | 0.233969 | + | 0.135082i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −85.7277 | + | 49.4949i | −3.20603 | + | 1.85100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.4949 | 1.28466 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.30306 | + | 5.37113i | −0.345507 | + | 0.199479i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.9367 | − | 8.62372i | −0.553973 | − | 0.319836i | 0.196750 | − | 0.980454i | \(-0.436961\pi\) |
−0.750723 | + | 0.660617i | \(0.770295\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.02118 | − | 8.69694i | 0.185715 | − | 0.321668i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2474 | + | 38.5337i | 0.821728 | + | 1.42328i | 0.904394 | + | 0.426698i | \(0.140323\pi\) |
−0.0826660 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 67.9465i | − | 2.50284i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 39.3939i | − | 1.44913i | −0.689208 | − | 0.724564i | \(-0.742041\pi\) | ||
0.689208 | − | 0.724564i | \(-0.257959\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.58919 | + | 2.75255i | 0.0583016 | + | 0.100981i | 0.893703 | − | 0.448659i | \(-0.148098\pi\) |
−0.835402 | + | 0.549640i | \(0.814765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3990 | + | 18.0116i | −0.380989 | + | 0.659893i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.8712 | + | 14.9367i | 0.945312 | + | 0.545776i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.2935 | + | 12.8712i | −0.813502 | + | 0.469676i | −0.848171 | − | 0.529723i | \(-0.822296\pi\) |
0.0346683 | + | 0.999399i | \(0.488963\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.8024 | −0.829864 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.3939 | 0.704882 | 0.352441 | − | 0.935834i | \(-0.385352\pi\) | ||||
0.352441 | + | 0.935834i | \(0.385352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.2020 | − | 15.1278i | 0.949823 | − | 0.548381i | 0.0567972 | − | 0.998386i | \(-0.481911\pi\) |
0.893026 | + | 0.450005i | \(0.148578\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6349 | − | 8.44949i | −0.529821 | − | 0.305892i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.56388 | − | 13.1010i | 0.273116 | − | 0.473050i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.7474 | + | 32.4715i | 0.676050 | + | 1.17095i | 0.976161 | + | 0.217049i | \(0.0696431\pi\) |
−0.300110 | + | 0.953904i | \(0.597024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 0.349945i | − | 0.0125867i | −0.999980 | − | 0.00629333i | \(-0.997997\pi\) | ||
0.999980 | − | 0.00629333i | \(-0.00200324\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.4949i | 0.448830i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.0424 | + | 17.3939i | 0.359805 | + | 0.623200i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.1464 | + | 52.2151i | −1.07872 | + | 1.86840i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.7980 | + | 9.12096i | 0.563853 | + | 0.325541i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.4052 | + | 21.5959i | −1.33335 | + | 0.769811i | −0.985812 | − | 0.167854i | \(-0.946316\pi\) |
−0.347540 | + | 0.937665i | \(0.612983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.7832 | 1.73453 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.5959 | −0.979960 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.72474 | − | 5.03723i | 0.309046 | − | 0.178428i | −0.337453 | − | 0.941342i | \(-0.609566\pi\) |
0.646500 | + | 0.762914i | \(0.276232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.57826 | + | 3.79796i | 0.232722 | + | 0.134362i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0116 | + | 31.1969i | −0.635614 | + | 1.10092i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.3485 | − | 26.5843i | −0.540962 | − | 0.936974i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.02118i | − | 0.176535i | −0.996097 | − | 0.0882676i | \(-0.971867\pi\) | ||
0.996097 | − | 0.0882676i | \(-0.0281331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.4949i | − | 0.860132i | −0.902797 | − | 0.430066i | \(-0.858490\pi\) | ||
0.902797 | − | 0.430066i | \(-0.141510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.43879 | + | 16.3485i | 0.330627 | + | 0.572662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.10102 | − | 12.2993i | 0.248433 | − | 0.430299i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.1010 | + | 5.83183i | 0.352528 | + | 0.203532i | 0.665798 | − | 0.746132i | \(-0.268091\pi\) |
−0.313270 | + | 0.949664i | \(0.601425\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.4069 | − | 22.1742i | 1.33878 | − | 0.772945i | 0.352154 | − | 0.935942i | \(-0.385449\pi\) |
0.986627 | + | 0.162997i | \(0.0521161\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.2616 | −1.78254 | −0.891271 | − | 0.453471i | \(-0.850185\pi\) | ||||
−0.891271 | + | 0.453471i | \(0.850185\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.59592 | 0.0554285 | 0.0277143 | − | 0.999616i | \(-0.491177\pi\) | ||||
0.0277143 | + | 0.999616i | \(0.491177\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.6969 | + | 8.48528i | −0.509219 | + | 0.293998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.7805 | − | 18.3485i | −1.09981 | − | 0.634975i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.7313 | − | 27.2474i | 0.543106 | − | 0.940686i | −0.455618 | − | 0.890175i | \(-0.650582\pi\) |
0.998724 | − | 0.0505110i | \(-0.0160850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0959 | − | 20.9507i | −0.417101 | − | 0.722439i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 108.848i | − | 3.74448i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.7980i | 1.16131i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.92820 | + | 12.0000i | 0.237496 | + | 0.411355i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00000 | + | 8.66025i | −0.171197 | + | 0.296521i | −0.938839 | − | 0.344358i | \(-0.888097\pi\) |
0.767642 | + | 0.640879i | \(0.221430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.8990 | − | 11.4887i | −0.679736 | − | 0.392446i | 0.120019 | − | 0.992772i | \(-0.461704\pi\) |
−0.799756 | + | 0.600326i | \(0.795038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.349945 | + | 0.202041i | −0.0119400 | + | 0.00689355i | −0.505958 | − | 0.862558i | \(-0.668861\pi\) |
0.494018 | + | 0.869452i | \(0.335528\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.92820 | −0.235839 | −0.117919 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117919 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.6969 | 0.941724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.89898 | + | 4.56048i | −0.267955 | + | 0.154704i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 89.0168 | + | 51.3939i | 3.01622 | + | 1.74142i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.548188 | + | 0.949490i | −0.0185321 | + | 0.0320986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.8990 | + | 31.0019i | 0.604406 | + | 1.04686i | 0.992145 | + | 0.125092i | \(0.0399227\pi\) |
−0.387740 | + | 0.921769i | \(0.626744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.2193i | 1.38871i | 0.719631 | + | 0.694356i | \(0.244311\pi\) | ||||
−0.719631 | + | 0.694356i | \(0.755689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.1010i | 1.45046i | 0.688504 | + | 0.725232i | \(0.258268\pi\) | ||||
−0.688504 | + | 0.725232i | \(0.741732\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.51739 | − | 14.7526i | −0.285986 | − | 0.495342i | 0.686862 | − | 0.726788i | \(-0.258988\pi\) |
−0.972848 | + | 0.231446i | \(0.925654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.9495 | + | 27.6253i | −0.534929 | + | 0.926524i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.30306 | + | 5.37113i | 0.311315 | + | 0.179738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.5970 | + | 13.6237i | −0.788760 | + | 0.455391i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.59264 | 0.186525 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.6969 | 1.48907 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.6969 | + | 15.4135i | −0.887436 | + | 0.512362i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5337 | + | 22.2474i | 1.27949 | + | 0.738714i | 0.976755 | − | 0.214360i | \(-0.0687666\pi\) |
0.302736 | + | 0.953074i | \(0.402100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.8530 | − | 18.7980i | 0.359576 | − | 0.622804i | −0.628314 | − | 0.777960i | \(-0.716255\pi\) |
0.987890 | + | 0.155156i | \(0.0495880\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.2980 | − | 49.0135i | −0.936526 | − | 1.62211i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.3867i | 1.63089i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.2474i | − | 0.898810i | −0.893328 | − | 0.449405i | \(-0.851636\pi\) | ||
0.893328 | − | 0.449405i | \(-0.148364\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.6048 | − | 78.9898i | −1.50110 | − | 2.59998i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | + | 20.7846i | −0.394558 | + | 0.683394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.8990 | − | 13.2207i | −0.751291 | − | 0.433758i | 0.0748691 | − | 0.997193i | \(-0.476146\pi\) |
−0.826160 | + | 0.563435i | \(0.809479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7846 | + | 12.0000i | −0.681188 | + | 0.393284i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −49.7046 | −1.62551 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0000 | −0.490029 | −0.245014 | − | 0.969519i | \(-0.578793\pi\) | ||||
−0.245014 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.02781 | + | 5.21221i | −0.294298 | + | 0.169913i | −0.639879 | − | 0.768476i | \(-0.721015\pi\) |
0.345580 | + | 0.938389i | \(0.387682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0424 | − | 5.79796i | −0.327024 | − | 0.188808i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7402 | − | 28.9949i | 0.543984 | − | 0.942208i | −0.454686 | − | 0.890652i | \(-0.650249\pi\) |
0.998670 | − | 0.0515559i | \(-0.0164180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.2474 | − | 47.1940i | −0.884490 | − | 1.53198i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6834i | 1.44744i | 0.690096 | + | 0.723718i | \(0.257568\pi\) | ||||
−0.690096 | + | 0.723718i | \(0.742432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.5959i | 1.08714i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.3663 | + | 52.5959i | 0.980578 | + | 1.69841i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.2474 | + | 21.2132i | −0.395079 | + | 0.684297i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.4217 | + | 18.7187i | 1.04369 | + | 0.602575i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.4363 | − | 12.3763i | 0.689346 | − | 0.397994i | −0.114021 | − | 0.993478i | \(-0.536373\pi\) |
0.803367 | + | 0.595484i | \(0.203040\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.94598 | −0.287090 | −0.143545 | − | 0.989644i | \(-0.545850\pi\) | ||||
−0.143545 | + | 0.989644i | \(0.545850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −68.9898 | −2.21171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.75255 | − | 1.58919i | 0.0880619 | − | 0.0508426i | −0.455322 | − | 0.890327i | \(-0.650476\pi\) |
0.543384 | + | 0.839484i | \(0.317143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.8311 | − | 11.4495i | −0.633805 | − | 0.365927i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.01778 | − | 3.49490i | 0.0643572 | − | 0.111470i | −0.832051 | − | 0.554698i | \(-0.812834\pi\) |
0.896409 | + | 0.443229i | \(0.146167\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.94949 | + | 5.10867i | 0.0939786 | + | 0.162776i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.19955i | 0.260731i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 33.2474i | − | 1.05614i | −0.849201 | − | 0.528070i | \(-0.822916\pi\) | ||
0.849201 | − | 0.528070i | \(-0.177084\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.89060 | − | 15.3990i | −0.281851 | − | 0.488180i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.6515 | − | 27.1092i | 0.495689 | − | 0.858558i | −0.504299 | − | 0.863529i | \(-0.668249\pi\) |
0.999988 | + | 0.00497084i | \(0.00158227\pi\) | |||||||
\(998\) | 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 | 2592.2.s.a.1727.1 | 8 | ||
3.2 | odd | 2 | 2592.2.s.h.1727.3 | 8 | |||
4.3 | odd | 2 | inner | 2592.2.s.a.1727.2 | 8 | ||
9.2 | odd | 6 | 864.2.c.a.863.8 | yes | 8 | ||
9.4 | even | 3 | 2592.2.s.h.863.4 | 8 | |||
9.5 | odd | 6 | inner | 2592.2.s.a.863.2 | 8 | ||
9.7 | even | 3 | 864.2.c.a.863.2 | yes | 8 | ||
12.11 | even | 2 | 2592.2.s.h.1727.4 | 8 | |||
36.7 | odd | 6 | 864.2.c.a.863.1 | ✓ | 8 | ||
36.11 | even | 6 | 864.2.c.a.863.7 | yes | 8 | ||
36.23 | even | 6 | inner | 2592.2.s.a.863.1 | 8 | ||
36.31 | odd | 6 | 2592.2.s.h.863.3 | 8 | |||
72.11 | even | 6 | 1728.2.c.g.1727.1 | 8 | |||
72.29 | odd | 6 | 1728.2.c.g.1727.2 | 8 | |||
72.43 | odd | 6 | 1728.2.c.g.1727.7 | 8 | |||
72.61 | even | 6 | 1728.2.c.g.1727.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.c.a.863.1 | ✓ | 8 | 36.7 | odd | 6 | ||
864.2.c.a.863.2 | yes | 8 | 9.7 | even | 3 | ||
864.2.c.a.863.7 | yes | 8 | 36.11 | even | 6 | ||
864.2.c.a.863.8 | yes | 8 | 9.2 | odd | 6 | ||
1728.2.c.g.1727.1 | 8 | 72.11 | even | 6 | |||
1728.2.c.g.1727.2 | 8 | 72.29 | odd | 6 | |||
1728.2.c.g.1727.7 | 8 | 72.43 | odd | 6 | |||
1728.2.c.g.1727.8 | 8 | 72.61 | even | 6 | |||
2592.2.s.a.863.1 | 8 | 36.23 | even | 6 | inner | ||
2592.2.s.a.863.2 | 8 | 9.5 | odd | 6 | inner | ||
2592.2.s.a.1727.1 | 8 | 1.1 | even | 1 | trivial | ||
2592.2.s.a.1727.2 | 8 | 4.3 | odd | 2 | inner | ||
2592.2.s.h.863.3 | 8 | 36.31 | odd | 6 | |||
2592.2.s.h.863.4 | 8 | 9.4 | even | 3 | |||
2592.2.s.h.1727.3 | 8 | 3.2 | odd | 2 | |||
2592.2.s.h.1727.4 | 8 | 12.11 | even | 2 |