Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(111,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.k (of order \(2\), degree \(1\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.116319195136.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 77x^{4} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 111.2 | ||
Root | \(-0.337637 - 0.337637i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.111 |
Dual form | 560.2.k.b.111.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.96176 | −1.70997 | −0.854985 | − | 0.518652i | \(-0.826434\pi\) | ||||
−0.854985 | + | 0.518652i | \(0.826434\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.337637 | + | 2.62412i | 0.127615 | + | 0.991824i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.77200 | 1.92400 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.63703i | − | 1.09661i | −0.836280 | − | 0.548303i | \(-0.815274\pi\) | ||
0.836280 | − | 0.548303i | \(-0.184726\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.77200i | 1.32352i | 0.749718 | + | 0.661758i | \(0.230189\pi\) | ||||
−0.749718 | + | 0.661758i | \(0.769811\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.96176i | − | 0.764722i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.77200i | − | 1.15738i | −0.815547 | − | 0.578690i | \(-0.803564\pi\) | ||
0.815547 | − | 0.578690i | \(-0.196436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.57296 | −1.04911 | −0.524555 | − | 0.851377i | \(-0.675768\pi\) | ||||
−0.524555 | + | 0.851377i | \(0.675768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | − | 7.77200i | −0.218218 | − | 1.69599i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.24824i | 1.09433i | 0.837024 | + | 0.547167i | \(0.184294\pi\) | ||||
−0.837024 | + | 0.547167i | \(0.815706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.20999 | −1.58001 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.77200 | −0.886139 | −0.443069 | − | 0.896487i | \(-0.646110\pi\) | ||||
−0.443069 | + | 0.896487i | \(0.646110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92351 | −1.06389 | −0.531947 | − | 0.846778i | \(-0.678540\pi\) | ||||
−0.531947 | + | 0.846778i | \(0.678540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.7720i | 1.87516i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.62412 | + | 0.337637i | −0.443557 | + | 0.0570711i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.5440 | −1.89782 | −0.948911 | − | 0.315543i | \(-0.897813\pi\) | ||||
−0.948911 | + | 0.315543i | \(0.897813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 14.1335i | − | 2.26317i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.02582i | − | 0.308935i | −0.987998 | − | 0.154468i | \(-0.950634\pi\) | ||
0.987998 | − | 0.154468i | \(-0.0493663\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.77200i | 0.860439i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.61121 | 0.235019 | 0.117509 | − | 0.993072i | \(-0.462509\pi\) | ||||
0.117509 | + | 0.993072i | \(0.462509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77200 | + | 1.77200i | −0.967429 | + | 0.253143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.1335i | 1.97909i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.63703 | 0.490417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.5440 | 1.79395 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.27406 | 0.947002 | 0.473501 | − | 0.880793i | \(-0.342990\pi\) | ||||
0.473501 | + | 0.880793i | \(0.342990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.54400i | − | 0.453763i | −0.973922 | − | 0.226882i | \(-0.927147\pi\) | ||
0.973922 | − | 0.226882i | \(-0.0728530\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.94884 | + | 15.1464i | 0.245531 | + | 1.90827i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.77200 | −0.591894 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.5223i | − | 1.52984i | −0.644124 | − | 0.764921i | \(-0.722778\pi\) | ||
0.644124 | − | 0.764921i | \(-0.277222\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 15.5440i | − | 1.87128i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.27406i | 0.863272i | 0.902048 | + | 0.431636i | \(0.142064\pi\) | ||||
−0.902048 | + | 0.431636i | \(0.857936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.96176 | 0.341994 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.54400 | − | 1.22800i | 1.08764 | − | 0.139943i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.85944i | − | 0.771748i | −0.922552 | − | 0.385874i | \(-0.873900\pi\) | ||
0.922552 | − | 0.385874i | \(-0.126100\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | 0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.02582 | −0.222363 | −0.111182 | − | 0.993800i | \(-0.535464\pi\) | ||||
−0.111182 | + | 0.993800i | \(0.535464\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.77200 | 0.517596 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.1335 | 1.51527 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5223 | + | 1.61121i | −1.31269 | + | 0.168900i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.5440 | 1.81923 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.57296i | − | 0.469176i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 16.7720i | − | 1.70294i | −0.524404 | − | 0.851469i | \(-0.675712\pi\) | ||
0.524404 | − | 0.851469i | \(-0.324288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 20.9930i | − | 2.10987i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.54400i | 0.949664i | 0.880076 | + | 0.474832i | \(0.157491\pi\) | ||||
−0.880076 | + | 0.474832i | \(0.842509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.31231 | −0.424904 | −0.212452 | − | 0.977171i | \(-0.568145\pi\) | ||||
−0.212452 | + | 0.977171i | \(0.568145\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.77200 | − | 1.00000i | 0.758470 | − | 0.0975900i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5223i | 1.21058i | 0.796006 | + | 0.605288i | \(0.206942\pi\) | ||||
−0.796006 | + | 0.605288i | \(0.793058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.77200 | 0.648640 | 0.324320 | − | 0.945947i | \(-0.394865\pi\) | ||||
0.324320 | + | 0.945947i | \(0.394865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.1905 | 3.24522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.5440 | −1.46226 | −0.731128 | − | 0.682240i | \(-0.761006\pi\) | ||||
−0.731128 | + | 0.682240i | \(0.761006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.24824 | −0.489401 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.5440i | 2.54644i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.5223 | − | 1.61121i | 1.14792 | − | 0.147699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.22800 | −0.202545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.7705i | 1.60232i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5223i | 1.11117i | 0.831458 | + | 0.555587i | \(0.187507\pi\) | ||||
−0.831458 | + | 0.555587i | \(0.812493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000i | 0.528271i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4965 | 0.917081 | 0.458541 | − | 0.888673i | \(-0.348372\pi\) | ||||
0.458541 | + | 0.888673i | \(0.348372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.54400 | − | 12.0000i | −0.133882 | − | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 8.20999i | − | 0.706604i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.54400 | −0.302785 | −0.151392 | − | 0.988474i | \(-0.548376\pi\) | ||||
−0.151392 | + | 0.988474i | \(0.548376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.14593 | −0.775747 | −0.387874 | − | 0.921713i | \(-0.626790\pi\) | ||||
−0.387874 | + | 0.921713i | \(0.626790\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.77200 | −0.401875 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.3559 | 1.45138 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.77200i | − | 0.396293i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.0570 | − | 5.24824i | 1.65428 | − | 0.432867i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.54400 | 0.781875 | 0.390938 | − | 0.920417i | \(-0.372151\pi\) | ||||
0.390938 | + | 0.920417i | \(0.372151\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.63703i | − | 0.295977i | −0.988989 | − | 0.147989i | \(-0.952720\pi\) | ||
0.988989 | − | 0.147989i | \(-0.0472799\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 27.5440i | − | 2.22680i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.92351i | − | 0.475788i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000i | 0.478852i | 0.970915 | + | 0.239426i | \(0.0769593\pi\) | ||||
−0.970915 | + | 0.239426i | \(0.923041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.7705 | 1.40930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.7720 | + | 1.77200i | −1.08539 | + | 0.139653i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7447i | 1.23322i | 0.787268 | + | 0.616611i | \(0.211495\pi\) | ||||
−0.787268 | + | 0.616611i | \(0.788505\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.7720 | −0.838599 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.4334 | −1.81333 | −0.906665 | − | 0.421851i | \(-0.861381\pi\) | ||||
−0.906665 | + | 0.421851i | \(0.861381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.77200 | −0.751692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.3952 | −2.01849 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.31601i | − | 0.176083i | −0.996117 | − | 0.0880413i | \(-0.971939\pi\) | ||
0.996117 | − | 0.0880413i | \(-0.0280608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.337637 | − | 2.62412i | −0.0255230 | − | 0.198365i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.5440 | −1.61935 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3.22241i | − | 0.240854i | −0.992722 | − | 0.120427i | \(-0.961574\pi\) | ||
0.992722 | − | 0.120427i | \(-0.0384264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.54400i | 0.709400i | 0.934980 | + | 0.354700i | \(0.115417\pi\) | ||||
−0.934980 | + | 0.354700i | \(0.884583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4965i | 0.775922i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 11.5440i | − | 0.848732i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3559 | −1.26919 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.77200 | − | 21.5440i | −0.201633 | − | 1.56710i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.6300i | − | 1.78216i | −0.453843 | − | 0.891082i | \(-0.649947\pi\) | ||
0.453843 | − | 0.891082i | \(-0.350053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.45600 | −0.320750 | −0.160375 | − | 0.987056i | \(-0.551270\pi\) | ||||
−0.160375 | + | 0.987056i | \(0.551270\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.1335 | 1.01212 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.57296 | −0.324169 | −0.162084 | − | 0.986777i | \(-0.551822\pi\) | ||||
−0.162084 | + | 0.986777i | \(0.551822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37.0880i | 2.61599i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.61121 | − | 12.5223i | −0.113085 | − | 0.878893i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.2928i | 2.10550i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.6320i | 1.15046i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3559i | 1.19483i | 0.801932 | + | 0.597415i | \(0.203806\pi\) | ||||
−0.801932 | + | 0.597415i | \(0.796194\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 21.5440i | − | 1.47617i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.02582 | 0.138160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | − | 15.5440i | −0.135769 | − | 1.05520i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 17.7705i | − | 1.20082i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.7720 | 1.53181 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.4582 | −0.901230 | −0.450615 | − | 0.892718i | \(-0.648795\pi\) | ||||
−0.450615 | + | 0.892718i | \(0.648795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.77200 | −0.384800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1593 | 1.07253 | 0.536266 | − | 0.844049i | \(-0.319834\pi\) | ||||
0.536266 | + | 0.844049i | \(0.319834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.5440i | 1.42367i | 0.702348 | + | 0.711834i | \(0.252135\pi\) | ||||
−0.702348 | + | 0.711834i | \(0.747865\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.2670 | + | 3.63703i | −1.85983 | + | 0.239299i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.45600 | 0.553971 | 0.276985 | − | 0.960874i | \(-0.410665\pi\) | ||||
0.276985 | + | 0.960874i | \(0.410665\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.61121i | 0.105104i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.3160i | 1.31967i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1335i | 0.914221i | 0.889410 | + | 0.457110i | \(0.151116\pi\) | ||||
−0.889410 | + | 0.457110i | \(0.848884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.45600i | 0.544699i | 0.962198 | + | 0.272349i | \(0.0878006\pi\) | ||||
−0.962198 | + | 0.272349i | \(0.912199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.89769 | 0.250037 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.77200 | − | 6.77200i | −0.113209 | − | 0.432647i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.8222i | − | 1.38851i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.0446 | 1.58080 | 0.790401 | − | 0.612590i | \(-0.209872\pi\) | ||||
0.790401 | + | 0.612590i | \(0.209872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.0880 | 1.20005 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.1335 | −0.885075 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.0880i | − | 0.816407i | −0.912891 | − | 0.408204i | \(-0.866155\pi\) | ||
0.912891 | − | 0.408204i | \(-0.133845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.89769 | − | 30.2928i | −0.242191 | − | 1.88231i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.5440 | −1.70493 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.47065i | 0.522323i | 0.965295 | + | 0.261161i | \(0.0841055\pi\) | ||||
−0.965295 | + | 0.261161i | \(0.915895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.00000i | − | 0.368577i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 35.5411i | − | 2.17508i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.5440i | − | 0.947735i | −0.880596 | − | 0.473867i | \(-0.842858\pi\) | ||
0.880596 | − | 0.473867i | \(-0.157142\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35055 | 0.0820401 | 0.0410200 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410200 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 37.0880 | − | 4.77200i | 2.24467 | − | 0.288815i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.63703i | 0.219321i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5440 | 1.17429 | 0.587143 | − | 0.809483i | \(-0.300253\pi\) | ||||
0.587143 | + | 0.809483i | \(0.300253\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −34.1905 | −2.04693 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3160 | 1.21195 | 0.605976 | − | 0.795483i | \(-0.292783\pi\) | ||||
0.605976 | + | 0.795483i | \(0.292783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.9547 | −1.42396 | −0.711980 | − | 0.702200i | \(-0.752201\pi\) | ||||
−0.711980 | + | 0.702200i | \(0.752201\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.5440i | 0.802278i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.7447 | − | 2.02582i | 0.929381 | − | 0.119581i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.77200 | −0.339530 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 49.6746i | 2.91198i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.3160i | − | 0.836350i | −0.908366 | − | 0.418175i | \(-0.862670\pi\) | ||
0.908366 | − | 0.418175i | \(-0.137330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.27406i | 0.423512i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.8600i | 1.73265i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.0446 | −1.44837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.31601 | − | 0.683994i | 0.306409 | − | 0.0394248i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 28.2670i | − | 1.62390i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.54400 | 0.202929 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.2288 | −1.78232 | −0.891160 | − | 0.453689i | \(-0.850108\pi\) | ||||
−0.891160 | + | 0.453689i | \(0.850108\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.7720 | 0.726574 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.2154 | −1.37313 | −0.686564 | − | 0.727070i | \(-0.740882\pi\) | ||||
−0.686564 | + | 0.727070i | \(0.740882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.77200i | 0.269729i | 0.990864 | + | 0.134865i | \(0.0430600\pi\) | ||||
−0.990864 | + | 0.134865i | \(0.956940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.1464 | + | 1.94884i | −0.853404 | + | 0.109805i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.0880 | 1.40908 | 0.704541 | − | 0.709663i | \(-0.251153\pi\) | ||||
0.704541 | + | 0.709663i | \(0.251153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.3559i | 0.971745i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 37.0880i | − | 2.07005i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.8222i | 1.21422i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.77200i | − | 0.264703i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.0570 | −1.10916 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.544004 | + | 4.22800i | 0.0299919 | + | 0.233097i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7189i | 0.754058i | 0.926201 | + | 0.377029i | \(0.123054\pi\) | ||||
−0.926201 | + | 0.377029i | \(0.876946\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −66.6320 | −3.65141 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5223 | 0.684166 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.45600 | 0.242734 | 0.121367 | − | 0.992608i | \(-0.461272\pi\) | ||||
0.121367 | + | 0.992608i | \(0.461272\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 46.0376 | 2.50042 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.5440i | 1.16667i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.93643 | − | 17.1722i | −0.374532 | − | 0.927214i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.5440 | 0.836861 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.24824i | 0.281740i | 0.990028 | + | 0.140870i | \(0.0449900\pi\) | ||||
−0.990028 | + | 0.140870i | \(0.955010\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.45600i | 0.131466i | 0.997837 | + | 0.0657332i | \(0.0209386\pi\) | ||||
−0.997837 | + | 0.0657332i | \(0.979061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 39.1781i | − | 2.09117i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.8600i | 1.90864i | 0.298793 | + | 0.954318i | \(0.403416\pi\) | ||||
−0.298793 | + | 0.954318i | \(0.596584\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.27406 | −0.386067 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −37.0880 | + | 4.77200i | −1.96291 | + | 0.252561i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.22241i | 0.170072i | 0.996378 | + | 0.0850362i | \(0.0271006\pi\) | ||||
−0.996378 | + | 0.0850362i | \(0.972899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.91199 | 0.100631 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.59879 | 0.346347 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8088 | 0.773012 | 0.386506 | − | 0.922287i | \(-0.373682\pi\) | ||||
0.386506 | + | 0.922287i | \(0.373682\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 34.6320i | − | 1.80287i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.02582 | − | 15.7447i | −0.105176 | − | 0.817425i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.45600 | 0.230723 | 0.115361 | − | 0.993324i | \(-0.463197\pi\) | ||||
0.115361 | + | 0.993324i | \(0.463197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.96176i | 0.152944i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 22.7720i | − | 1.17282i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.22241i | 0.165524i | 0.996569 | + | 0.0827621i | \(0.0263742\pi\) | ||||
−0.996569 | + | 0.0827621i | \(0.973626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 37.0880i | − | 1.90008i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.47065 | −0.432830 | −0.216415 | − | 0.976301i | \(-0.569436\pi\) | ||||
−0.216415 | + | 0.976301i | \(0.569436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.22800 | + | 9.54400i | 0.0625846 | + | 0.486407i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 11.6931i | − | 0.594392i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.3160 | −1.03006 | −0.515031 | − | 0.857171i | \(-0.672220\pi\) | ||||
−0.515031 | + | 0.857171i | \(0.672220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.0446 | 1.26656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.0880 | −1.56818 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.85944 | 0.345136 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.7720i | − | 0.841763i | −0.907116 | − | 0.420881i | \(-0.861721\pi\) | ||
0.907116 | − | 0.420881i | \(-0.138279\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.57296 | + | 35.5411i | 0.228935 | + | 1.77928i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.22800 | −0.360949 | −0.180475 | − | 0.983580i | \(-0.557763\pi\) | ||||
−0.180475 | + | 0.983580i | \(0.557763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 28.2670i | − | 1.40808i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000i | 0.347833i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.9859i | 2.08116i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0880i | 1.83388i | 0.399021 | + | 0.916942i | \(0.369350\pi\) | ||||
−0.399021 | + | 0.916942i | \(0.630650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.4965 | 0.517753 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.45600 | + | 19.0880i | 0.120852 | + | 0.939259i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.02582i | − | 0.0994438i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.0880 | 1.32651 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.7189 | 0.670212 | 0.335106 | − | 0.942181i | \(-0.391228\pi\) | ||||
0.335106 | + | 0.942181i | \(0.391228\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8600 | −0.675496 | −0.337748 | − | 0.941237i | \(-0.609665\pi\) | ||||
−0.337748 | + | 0.941237i | \(0.609665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.29989 | 0.452176 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.77200i | 0.231476i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.29989 | − | 1.19659i | 0.450053 | − | 0.0579070i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −51.4040 | −2.48181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 31.0748i | − | 1.49682i | −0.663236 | − | 0.748410i | \(-0.730817\pi\) | ||
0.663236 | − | 0.748410i | \(-0.269183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0880i | 1.20565i | 0.797872 | + | 0.602826i | \(0.205959\pi\) | ||||
−0.797872 | + | 0.602826i | \(0.794041\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.1335i | 0.677650i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 24.0000i | − | 1.14808i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.8470 | −0.565428 | −0.282714 | − | 0.959204i | \(-0.591235\pi\) | ||||
−0.282714 | + | 0.959204i | \(0.591235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.0880 | + | 10.2280i | −1.86133 | + | 0.487048i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8.47065i | − | 0.402453i | −0.979545 | − | 0.201226i | \(-0.935507\pi\) | ||
0.979545 | − | 0.201226i | \(-0.0644927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.2670 | −1.33698 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.8600 | 1.40918 | 0.704590 | − | 0.709614i | \(-0.251131\pi\) | ||||
0.704590 | + | 0.709614i | \(0.251131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.8222 | −1.02757 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.7720i | 0.506113i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.61121 | − | 12.5223i | −0.0755345 | − | 0.587055i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1760 | 1.31802 | 0.659009 | − | 0.752135i | \(-0.270976\pi\) | ||||
0.659009 | + | 0.752135i | \(0.270976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.1781i | 1.82868i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.08801i | − | 0.330121i | −0.986283 | − | 0.165061i | \(-0.947218\pi\) | ||
0.986283 | − | 0.165061i | \(-0.0527820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.19659i | − | 0.0556102i | −0.999613 | − | 0.0278051i | \(-0.991148\pi\) | ||
0.999613 | − | 0.0278051i | \(-0.00885178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.5440i | 0.813584i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1006 | 1.53171 | 0.765857 | − | 0.643010i | \(-0.222315\pi\) | ||||
0.765857 | + | 0.643010i | \(0.222315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.8600 | − | 4.22800i | 1.51733 | − | 0.195231i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 17.7705i | − | 0.818823i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.36799 | −0.338780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.57296 | 0.209822 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.6320 | −1.58569 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.0963 | −1.32944 | −0.664721 | − | 0.747092i | \(-0.731450\pi\) | ||||
−0.664721 | + | 0.747092i | \(0.731450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 55.0880i | − | 2.51180i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 40.7893 | − | 5.24824i | 1.85598 | − | 0.238803i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.7720 | 0.761577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.7447i | − | 0.713461i | −0.934207 | − | 0.356731i | \(-0.883891\pi\) | ||
0.934207 | − | 0.356731i | \(-0.116109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 46.6320i | − | 2.10877i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 24.6300i | − | 1.11154i | −0.831338 | − | 0.555768i | \(-0.812424\pi\) | ||
0.831338 | − | 0.555768i | \(-0.187576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.7720i | 1.02560i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.9930 | 0.943563 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.0880 | + | 2.45600i | −0.856214 | + | 0.110166i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6816i | 1.28397i | 0.766719 | + | 0.641983i | \(0.221888\pi\) | ||||
−0.766719 | + | 0.641983i | \(0.778112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 69.4040 | 3.10074 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.88527 | 0.396175 | 0.198087 | − | 0.980184i | \(-0.436527\pi\) | ||||
0.198087 | + | 0.980184i | \(0.436527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.54400 | −0.424703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.9423 | 1.28537 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0880i | 0.846061i | 0.906115 | + | 0.423031i | \(0.139034\pi\) | ||||
−0.906115 | + | 0.423031i | \(0.860966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7447 | + | 2.02582i | −0.696505 | + | 0.0896172i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.5440 | 1.65761 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.31231i | − | 0.190023i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5.86001i | − | 0.257723i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.85944i | 0.301096i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.5440i | − | 0.943860i | −0.881636 | − | 0.471930i | \(-0.843558\pi\) | ||
0.881636 | − | 0.471930i | \(-0.156442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.9175 | 1.70174 | 0.850871 | − | 0.525375i | \(-0.176075\pi\) | ||||
0.850871 | + | 0.525375i | \(0.176075\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | + | 7.77200i | 0.0436436 | + | 0.339198i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.2670i | 1.23133i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.54400 | −0.197565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.9859 | 1.82203 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.6320 | 1.24019 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5223 | −0.541386 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.54400i | 0.411854i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.44483 | + | 24.6300i | 0.277598 | + | 1.06089i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2280 | −0.654703 | −0.327351 | − | 0.944903i | \(-0.606156\pi\) | ||||
−0.327351 | + | 0.944903i | \(0.606156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 28.2670i | − | 1.21305i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.77200i | 0.290081i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.19659i | − | 0.0511624i | −0.999673 | − | 0.0255812i | \(-0.991856\pi\) | ||
0.999673 | − | 0.0255812i | \(-0.00814364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 20.4560i | − | 0.873041i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.8222 | 0.929657 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000 | − | 2.31601i | 0.765438 | − | 0.0984866i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.1905i | 1.45131i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4560 | 0.866748 | 0.433374 | − | 0.901214i | \(-0.357323\pi\) | ||||
0.433374 | + | 0.901214i | \(0.357323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.66724 | 0.408881 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.4040 | 2.17028 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.47065 | 0.356995 | 0.178498 | − | 0.983940i | \(-0.442876\pi\) | ||||
0.178498 | + | 0.983940i | \(0.442876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 15.5440i | − | 0.653941i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.36346 | + | 18.3688i | 0.0992561 | + | 0.771418i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6320 | −0.697250 | −0.348625 | − | 0.937262i | \(-0.613351\pi\) | ||||
−0.348625 | + | 0.937262i | \(0.613351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 7.27406i | − | 0.304410i | −0.988349 | − | 0.152205i | \(-0.951363\pi\) | ||
0.988349 | − | 0.152205i | \(-0.0486374\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 72.9480i | 3.04745i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.24824i | − | 0.218867i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.139991i | 0.00582789i | 0.999996 | + | 0.00291394i | \(0.000927538\pi\) | ||||
−0.999996 | + | 0.00291394i | \(0.999072\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.1976 | 0.548473 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.683994 | − | 5.31601i | −0.0283769 | − | 0.220545i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.8222i | 0.903783i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.5440 | −1.13880 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.02582 | 0.0836147 | 0.0418074 | − | 0.999126i | \(-0.486688\pi\) | ||||
0.0418074 | + | 0.999126i | \(0.486688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.0880 | 1.11614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7705 | 0.730982 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8600i | 0.487032i | 0.969897 | + | 0.243516i | \(0.0783009\pi\) | ||||
−0.969897 | + | 0.243516i | \(0.921699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.61121 | + | 12.5223i | 0.0660530 | + | 0.513364i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5440 | 0.554319 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.9627i | − | 0.611361i | −0.952134 | − | 0.305681i | \(-0.901116\pi\) | ||
0.952134 | − | 0.305681i | \(-0.0988840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.1760i | 1.80198i | 0.433843 | + | 0.900989i | \(0.357157\pi\) | ||||
−0.433843 | + | 0.900989i | \(0.642843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 72.2787i | − | 2.94342i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.22800i | − | 0.0905810i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.7571 | 0.436619 | 0.218309 | − | 0.975880i | \(-0.429946\pi\) | ||||
0.218309 | + | 0.975880i | \(0.429946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.77200 | + | 37.0880i | 0.193371 | + | 1.50288i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.68868i | 0.311051i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.0000 | −1.37325 | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||||
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.7705 | −0.716577 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.5440 | −0.625778 | −0.312889 | − | 0.949790i | \(-0.601297\pi\) | ||||
−0.312889 | + | 0.949790i | \(0.601297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8470 | 0.476172 | 0.238086 | − | 0.971244i | \(-0.423480\pi\) | ||||
0.238086 | + | 0.971244i | \(0.423480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 43.0880i | − | 1.72906i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.4894 | + | 4.05165i | −1.26160 | + | 0.162326i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 49.2600i | − | 1.96725i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 55.0880i | 2.19650i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9111i | 0.434364i | 0.976131 | + | 0.217182i | \(0.0696865\pi\) | ||||
−0.976131 | + | 0.217182i | \(0.930314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 51.4040i | − | 2.04313i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.5223 | −0.496932 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.45600 | − | 32.3160i | −0.335039 | − | 1.28041i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 41.9859i | 1.66094i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.63201 | −0.182953 | −0.0914767 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914767 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.9547 | −0.944682 | −0.472341 | − | 0.881416i | \(-0.656591\pi\) | ||||
−0.472341 | + | 0.881416i | \(0.656591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5740 | −0.651589 | −0.325795 | − | 0.945441i | \(-0.605632\pi\) | ||||
−0.325795 | + | 0.945441i | \(0.605632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 26.4560i | − | 1.03849i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.92351 | + | 46.0376i | 0.232161 | + | 1.80435i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.08801 | −0.0425770 | −0.0212885 | − | 0.999773i | \(-0.506777\pi\) | ||||
−0.0212885 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.4965i | 0.410131i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.6320i | 1.35112i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.6746i | 1.93505i | 0.252781 | + | 0.967524i | \(0.418655\pi\) | ||||
−0.252781 | + | 0.967524i | \(0.581345\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5440i | 0.604592i | 0.953214 | + | 0.302296i | \(0.0977530\pi\) | ||||
−0.953214 | + | 0.302296i | \(0.902247\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −67.4451 | −2.61935 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 1.54400i | 0.465340 | − | 0.0598739i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 25.0446i | − | 0.969731i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.8600 | 1.54108 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.8897 | −0.497600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.5440 | −1.37012 | −0.685060 | − | 0.728486i | \(-0.740224\pi\) | ||||
−0.685060 | + | 0.728486i | \(0.740224\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.20999 | 0.316003 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 16.7720i | − | 0.644600i | −0.946638 | − | 0.322300i | \(-0.895544\pi\) | ||
0.946638 | − | 0.322300i | \(-0.104456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44.0117 | − | 5.66286i | 1.68902 | − | 0.217320i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.8600 | −1.83400 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 36.7377i | − | 1.40573i | −0.711324 | − | 0.702864i | \(-0.751904\pi\) | ||
0.711324 | − | 0.702864i | \(-0.248096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.54400i | − | 0.135409i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 63.8081i | − | 2.43443i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 28.6320i | − | 1.09079i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1976 | −0.502059 | −0.251030 | − | 0.967979i | \(-0.580769\pi\) | ||||
−0.251030 | + | 0.967979i | \(0.580769\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 55.0880 | − | 7.08801i | 2.09262 | − | 0.269251i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9.14593i | − | 0.346925i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.6320 | −1.08451 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.0446 | −0.947274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.8600 | −1.12780 | −0.563898 | − | 0.825844i | \(-0.690699\pi\) | ||||
−0.563898 | + | 0.825844i | \(0.690699\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.7903 | 1.99102 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4.77200i | − | 0.179724i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25.0446 | + | 3.22241i | −0.941899 | + | 0.121191i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.6840 | −0.513913 | −0.256957 | − | 0.966423i | \(-0.582720\pi\) | ||||
−0.256957 | + | 0.966423i | \(0.582720\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 39.5927i | − | 1.48484i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 31.0880i | − | 1.16426i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.3559i | 0.649075i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 41.8600i | − | 1.56329i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.44483 | 0.240351 | 0.120176 | − | 0.992753i | \(-0.461654\pi\) | ||||
0.120176 | + | 0.992753i | \(0.461654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.45600 | − | 11.3160i | −0.0542241 | − | 0.421430i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 25.0446i | − | 0.931419i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.77200 | 0.177228 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3693 | 0.903808 | 0.451904 | − | 0.892066i | \(-0.350745\pi\) | ||||
0.451904 | + | 0.892066i | \(0.350745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.5440 | −1.20533 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.66724 | −0.357556 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 31.2280i | − | 1.15343i | −0.816945 | − | 0.576716i | \(-0.804334\pi\) | ||
0.816945 | − | 0.576716i | \(-0.195666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.24824 | + | 20.0570i | 0.193584 | + | 0.739814i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.5440 | −1.67763 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 42.4005i | − | 1.55973i | −0.625949 | − | 0.779864i | \(-0.715288\pi\) | ||
0.625949 | − | 0.779864i | \(-0.284712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 64.6320i | 2.37432i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.41900i | 0.162117i | 0.996709 | + | 0.0810587i | \(0.0258301\pi\) | ||||
−0.996709 | + | 0.0810587i | \(0.974170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.54400i | 0.349665i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.6931 | −0.427827 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32.8600 | + | 4.22800i | −1.20068 | + | 0.154488i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.4592i | 0.929020i | 0.885568 | + | 0.464510i | \(0.153770\pi\) | ||||
−0.885568 | + | 0.464510i | \(0.846230\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −74.1760 | −2.70312 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.63703 | 0.132365 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5440 | 0.419574 | 0.209787 | − | 0.977747i | \(-0.432723\pi\) | ||||
0.209787 | + | 0.977747i | \(0.432723\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −56.5340 | −2.05206 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.28648 | + | 17.7705i | 0.0827762 | + | 0.643337i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 27.5440 | 0.995856 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.7118i | 1.25337i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 28.6320i | − | 1.03250i | −0.856439 | − | 0.516248i | \(-0.827328\pi\) | ||
0.856439 | − | 0.516248i | \(-0.172672\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.7635i | 1.39603i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 43.2280i | − | 1.55480i | −0.629005 | − | 0.777402i | \(-0.716537\pi\) | ||
0.629005 | − | 0.777402i | \(-0.283463\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.92351 | 0.212779 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.5440 | + | 89.7200i | 0.414139 | + | 3.21869i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.4378i | 0.983060i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.4560 | 0.946670 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.1781 | 1.40011 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.9795 | −0.498317 | −0.249159 | − | 0.968463i | \(-0.580154\pi\) | ||||
−0.249159 | + | 0.968463i | \(0.580154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 25.0880i | − | 0.893157i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.24824 | − | 40.7893i | −0.186606 | − | 1.45030i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.9120 | 0.600562 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.7705i | 0.630256i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.2280i | 0.681091i | 0.940228 | + | 0.340545i | \(0.110612\pi\) | ||||
−0.940228 | + | 0.340545i | \(0.889388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.68868i | − | 0.272006i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 69.2640i | 2.44732i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.8222 | 0.770088 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.77200 | − | 13.7720i | −0.0624549 | − | 0.485399i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.0376i | 1.62060i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3160 | 0.503324 | 0.251662 | − | 0.967815i | \(-0.419023\pi\) | ||||
0.251662 | + | 0.967815i | \(0.419023\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2938 | −1.48514 | −0.742569 | − | 0.669770i | \(-0.766393\pi\) | ||||
−0.742569 | + | 0.669770i | \(0.766393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.00000 | −0.140286 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.7447 | −0.551513 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.26402i | 0.324107i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −72.2787 | + | 9.29989i | −2.52562 | + | 0.324964i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.6840 | −0.547375 | −0.273688 | − | 0.961819i | \(-0.588243\pi\) | ||||
−0.273688 | + | 0.961819i | \(0.588243\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.9671i | − | 0.661153i | −0.943779 | − | 0.330576i | \(-0.892757\pi\) | ||
0.943779 | − | 0.330576i | \(-0.107243\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 10.7720i | − | 0.375033i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.24824i | 0.182499i | 0.995828 | + | 0.0912496i | \(0.0290861\pi\) | ||||
−0.995828 | + | 0.0912496i | \(0.970914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.0880i | 1.70490i | 0.522811 | + | 0.852448i | \(0.324883\pi\) | ||||
−0.522811 | + | 0.852448i | \(0.675117\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.8846 | −2.00799 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.45600 | + | 32.3160i | 0.292983 | + | 1.11968i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 23.4334i | − | 0.810946i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.6320 | 1.68097 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.44483 | −0.222500 | −0.111250 | − | 0.993792i | \(-0.535485\pi\) | ||||
−0.111250 | + | 0.993792i | \(0.535485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.22800 | −0.214759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −60.1711 | −2.07240 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 9.77200i | − | 0.336167i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.752256 | − | 5.84653i | −0.0258478 | − | 0.200889i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 70.9480 | 2.43493 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 60.5857i | − | 2.07685i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 20.1760i | − | 0.690814i | −0.938453 | − | 0.345407i | \(-0.887741\pi\) | ||
0.938453 | − | 0.345407i | \(-0.112259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 26.3952i | − | 0.902695i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 6.00000i | − | 0.204956i | −0.994735 | − | 0.102478i | \(-0.967323\pi\) | ||
0.994735 | − | 0.102478i | \(-0.0326771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.9433 | −1.39697 | −0.698483 | − | 0.715626i | \(-0.746141\pi\) | ||||
−0.698483 | + | 0.715626i | \(0.746141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.6320 | + | 6.00000i | −1.58921 | + | 0.204479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.07747i | − | 0.206880i | −0.994636 | − | 0.103440i | \(-0.967015\pi\) | ||
0.994636 | − | 0.103440i | \(-0.0329849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.31601 | 0.0787466 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.0953 | 0.580586 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.9480 | −0.846304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59.7564 | 2.02477 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 96.8080i | − | 3.27646i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.62412 | − | 0.337637i | 0.0887114 | − | 0.0114142i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.08801 | −0.171810 | −0.0859049 | − | 0.996303i | \(-0.527378\pi\) | ||||
−0.0859049 | + | 0.996303i | \(0.527378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.4005i | 1.43013i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 34.6320i | − | 1.16678i | −0.812191 | − | 0.583391i | \(-0.801726\pi\) | ||
0.812191 | − | 0.583391i | \(-0.198274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.6931i | 0.393503i | 0.980453 | + | 0.196751i | \(0.0630392\pi\) | ||||
−0.980453 | + | 0.196751i | \(0.936961\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 21.5440i | − | 0.724194i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.5082 | −1.83021 | −0.915103 | − | 0.403220i | \(-0.867891\pi\) | ||||
−0.915103 | + | 0.403220i | \(0.867891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.8600 | + | 4.22800i | −1.10209 | + | 0.141803i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 25.4592i | − | 0.852916i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.36799 | −0.246560 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.22241 | 0.107713 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 74.1760 | 2.47667 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.2670 | 0.942758 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.6320i | 0.953871i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.7447 | + | 2.02582i | −0.523951 | + | 0.0674152i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.54400 | −0.317253 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 19.7964i | − | 0.657327i | −0.944447 | − | 0.328664i | \(-0.893402\pi\) | ||
0.944447 | − | 0.328664i | \(-0.106598\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 55.0880i | 1.82715i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 34.7118i | − | 1.15005i | −0.818134 | − | 0.575027i | \(-0.804991\pi\) | ||
0.818134 | − | 0.575027i | \(-0.195009\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.36799i | 0.243845i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.4965 | −0.347003 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.54400 | + | 27.5440i | 0.117033 | + | 0.909583i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2368i | 0.733525i | 0.930315 | + | 0.366762i | \(0.119534\pi\) | ||||
−0.930315 | + | 0.366762i | \(0.880466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 92.4920 | 3.04772 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.7118 | −1.14255 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.5440 | 0.379565 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.8906 | −0.817516 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.08801i | 0.0356964i | 0.999841 | + | 0.0178482i | \(0.00568156\pi\) | ||||
−0.999841 | + | 0.0178482i | \(0.994318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.9681 | − | 8.10330i | 1.01494 | − | 0.265575i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 71.7200 | 2.34801 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 17.3559i | − | 0.567599i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.2280i | 0.628151i | 0.949398 | + | 0.314076i | \(0.101695\pi\) | ||||
−0.949398 | + | 0.314076i | \(0.898305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14.1335i | − | 0.461230i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1760i | 0.853314i | 0.904414 | + | 0.426657i | \(0.140309\pi\) | ||||
−0.904414 | + | 0.426657i | \(0.859691\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.4894 | 1.02544 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 21.5440 | − | 2.77200i | 0.700826 | − | 0.0901732i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.5153i | 1.08910i | 0.838729 | + | 0.544550i | \(0.183299\pi\) | ||||
−0.838729 | + | 0.544550i | \(0.816701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.6320 | −0.929434 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.3046 | −2.40949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.6300 | 0.797008 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 51.4040i | − | 1.66166i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.19659 | − | 9.29989i | −0.0386399 | − | 0.300309i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.08801 | 0.131871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 72.2787i | 2.32915i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4.45600i | − | 0.143444i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.6186i | 1.33836i | 0.743099 | + | 0.669181i | \(0.233355\pi\) | ||||
−0.743099 | + | 0.669181i | \(0.766645\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 64.6320i | − | 2.07628i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.3187 | 1.03716 | 0.518578 | − | 0.855031i | \(-0.326462\pi\) | ||||
0.518578 | + | 0.855031i | \(0.326462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.08801 | − | 24.0000i | −0.0989970 | − | 0.769405i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.1335i | 0.452635i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.0880 | 1.18655 | 0.593275 | − | 0.805000i | \(-0.297835\pi\) | ||||
0.593275 | + | 0.805000i | \(0.297835\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.6444 | 1.39488 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.0880 | 1.24798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.1593 | −0.515403 | −0.257701 | − | 0.966225i | \(-0.582965\pi\) | ||||
−0.257701 | + | 0.966225i | \(0.582965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.00000i | − | 0.191176i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.61121 | − | 12.5223i | −0.0512853 | − | 0.398589i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.6320 | 0.338078 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.8151i | 1.36007i | 0.733181 | + | 0.680034i | \(0.238035\pi\) | ||||
−0.733181 | + | 0.680034i | \(0.761965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 40.6320i | − | 1.28942i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.57296i | − | 0.144973i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.4040i | 1.05792i | 0.848648 | + | 0.528958i | \(0.177417\pi\) | ||||
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 94.7762 | 2.99859 |
(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 | 560.2.k.b.111.2 | yes | 8 | |
3.2 | odd | 2 | 5040.2.d.d.4591.3 | 8 | |||
4.3 | odd | 2 | inner | 560.2.k.b.111.8 | yes | 8 | |
5.2 | odd | 4 | 2800.2.e.h.2799.7 | 8 | |||
5.3 | odd | 4 | 2800.2.e.g.2799.2 | 8 | |||
5.4 | even | 2 | 2800.2.k.m.2351.7 | 8 | |||
7.6 | odd | 2 | inner | 560.2.k.b.111.7 | yes | 8 | |
8.3 | odd | 2 | 2240.2.k.d.1791.1 | 8 | |||
8.5 | even | 2 | 2240.2.k.d.1791.7 | 8 | |||
12.11 | even | 2 | 5040.2.d.d.4591.2 | 8 | |||
20.3 | even | 4 | 2800.2.e.g.2799.7 | 8 | |||
20.7 | even | 4 | 2800.2.e.h.2799.2 | 8 | |||
20.19 | odd | 2 | 2800.2.k.m.2351.2 | 8 | |||
21.20 | even | 2 | 5040.2.d.d.4591.6 | 8 | |||
28.27 | even | 2 | inner | 560.2.k.b.111.1 | ✓ | 8 | |
35.13 | even | 4 | 2800.2.e.h.2799.8 | 8 | |||
35.27 | even | 4 | 2800.2.e.g.2799.1 | 8 | |||
35.34 | odd | 2 | 2800.2.k.m.2351.1 | 8 | |||
56.13 | odd | 2 | 2240.2.k.d.1791.2 | 8 | |||
56.27 | even | 2 | 2240.2.k.d.1791.8 | 8 | |||
84.83 | odd | 2 | 5040.2.d.d.4591.7 | 8 | |||
140.27 | odd | 4 | 2800.2.e.g.2799.8 | 8 | |||
140.83 | odd | 4 | 2800.2.e.h.2799.1 | 8 | |||
140.139 | even | 2 | 2800.2.k.m.2351.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.k.b.111.1 | ✓ | 8 | 28.27 | even | 2 | inner | |
560.2.k.b.111.2 | yes | 8 | 1.1 | even | 1 | trivial | |
560.2.k.b.111.7 | yes | 8 | 7.6 | odd | 2 | inner | |
560.2.k.b.111.8 | yes | 8 | 4.3 | odd | 2 | inner | |
2240.2.k.d.1791.1 | 8 | 8.3 | odd | 2 | |||
2240.2.k.d.1791.2 | 8 | 56.13 | odd | 2 | |||
2240.2.k.d.1791.7 | 8 | 8.5 | even | 2 | |||
2240.2.k.d.1791.8 | 8 | 56.27 | even | 2 | |||
2800.2.e.g.2799.1 | 8 | 35.27 | even | 4 | |||
2800.2.e.g.2799.2 | 8 | 5.3 | odd | 4 | |||
2800.2.e.g.2799.7 | 8 | 20.3 | even | 4 | |||
2800.2.e.g.2799.8 | 8 | 140.27 | odd | 4 | |||
2800.2.e.h.2799.1 | 8 | 140.83 | odd | 4 | |||
2800.2.e.h.2799.2 | 8 | 20.7 | even | 4 | |||
2800.2.e.h.2799.7 | 8 | 5.2 | odd | 4 | |||
2800.2.e.h.2799.8 | 8 | 35.13 | even | 4 | |||
2800.2.k.m.2351.1 | 8 | 35.34 | odd | 2 | |||
2800.2.k.m.2351.2 | 8 | 20.19 | odd | 2 | |||
2800.2.k.m.2351.7 | 8 | 5.4 | even | 2 | |||
2800.2.k.m.2351.8 | 8 | 140.139 | even | 2 | |||
5040.2.d.d.4591.2 | 8 | 12.11 | even | 2 | |||
5040.2.d.d.4591.3 | 8 | 3.2 | odd | 2 | |||
5040.2.d.d.4591.6 | 8 | 21.20 | even | 2 | |||
5040.2.d.d.4591.7 | 8 | 84.83 | odd | 2 |