Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(2799,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2800.2799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.e (of order \(2\), degree \(1\), 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: | \(22.3581125660\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2799.8 | ||
Root | \(-0.337637 + 0.337637i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.2799 |
Dual form | 2800.2.e.g.2799.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2800\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(801\) | \(2101\) | \(2577\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.96176i | 1.70997i | 0.518652 | + | 0.854985i | \(0.326434\pi\) | ||||
−0.518652 | + | 0.854985i | \(0.673566\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62412 | + | 0.337637i | 0.991824 | + | 0.127615i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.77200 | −1.92400 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.63703i | 1.09661i | 0.836280 | + | 0.548303i | \(0.184726\pi\) | ||||
−0.836280 | + | 0.548303i | \(0.815274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.77200 | −1.32352 | −0.661758 | − | 0.749718i | \(-0.730189\pi\) | ||||
−0.661758 | + | 0.749718i | \(0.730189\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.77200 | −1.15738 | −0.578690 | − | 0.815547i | \(-0.696436\pi\) | ||||
−0.578690 | + | 0.815547i | \(0.696436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.57296 | 1.04911 | 0.524555 | − | 0.851377i | \(-0.324232\pi\) | ||||
0.524555 | + | 0.851377i | \(0.324232\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | + | 7.77200i | −0.218218 | + | 1.69599i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.24824 | −1.09433 | −0.547167 | − | 0.837024i | \(-0.684294\pi\) | ||||
−0.547167 | + | 0.837024i | \(0.684294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 8.20999i | − | 1.58001i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.77200 | 0.886139 | 0.443069 | − | 0.896487i | \(-0.353890\pi\) | ||||
0.443069 | + | 0.896487i | \(0.353890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92351 | −1.06389 | −0.531947 | − | 0.846778i | \(-0.678540\pi\) | ||||
−0.531947 | + | 0.846778i | \(0.678540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.7720 | −1.87516 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.5440i | − | 1.89782i | −0.315543 | − | 0.948911i | \(-0.602187\pi\) | ||
0.315543 | − | 0.948911i | \(-0.397813\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 14.1335i | − | 2.26317i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.02582 | 0.308935 | 0.154468 | − | 0.987998i | \(-0.450634\pi\) | ||||
0.154468 | + | 0.987998i | \(0.450634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.61121i | 0.235019i | 0.993072 | + | 0.117509i | \(0.0374910\pi\) | ||||
−0.993072 | + | 0.117509i | \(0.962509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.77200 | + | 1.77200i | 0.967429 | + | 0.253143i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 14.1335i | − | 1.97909i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.5440i | 1.79395i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.27406 | −0.947002 | −0.473501 | − | 0.880793i | \(-0.657010\pi\) | ||||
−0.473501 | + | 0.880793i | \(0.657010\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.54400i | 0.453763i | 0.973922 | + | 0.226882i | \(0.0728530\pi\) | ||||
−0.973922 | + | 0.226882i | \(0.927147\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.1464 | − | 1.94884i | −1.90827 | − | 0.245531i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5223 | −1.52984 | −0.764921 | − | 0.644124i | \(-0.777222\pi\) | ||||
−0.764921 | + | 0.644124i | \(0.777222\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 15.5440i | − | 1.87128i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.27406i | − | 0.863272i | −0.902048 | − | 0.431636i | \(-0.857936\pi\) | ||
0.902048 | − | 0.431636i | \(-0.142064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.22800 | + | 9.54400i | −0.139943 | + | 1.08764i | ||||
\(78\) | 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 | ||||||||
\(83\) | 2.02582i | 0.222363i | 0.993800 | + | 0.111182i | \(0.0354635\pi\) | ||||
−0.993800 | + | 0.111182i | \(0.964536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.1335i | 1.51527i | ||||||||
\(88\) | 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 | ||||||||
\(93\) | − | 17.5440i | − | 1.81923i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.7720 | −1.70294 | −0.851469 | − | 0.524404i | \(-0.824288\pi\) | ||||
−0.851469 | + | 0.524404i | \(0.824288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 20.9930i | − | 2.10987i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.54400i | − | 0.949664i | −0.880076 | − | 0.474832i | \(-0.842509\pi\) | ||
0.880076 | − | 0.474832i | \(-0.157491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.31231i | 0.424904i | 0.977171 | + | 0.212452i | \(0.0681449\pi\) | ||||
−0.977171 | + | 0.212452i | \(0.931855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5223 | 1.21058 | 0.605288 | − | 0.796006i | \(-0.293058\pi\) | ||||
0.605288 | + | 0.796006i | \(0.293058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.77200 | −0.648640 | −0.324320 | − | 0.945947i | \(-0.605135\pi\) | ||||
−0.324320 | + | 0.945947i | \(0.605135\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.1905 | 3.24522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.5440i | 1.46226i | 0.682240 | + | 0.731128i | \(0.261006\pi\) | ||||
−0.682240 | + | 0.731128i | \(0.738994\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 27.5440 | 2.54644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.5223 | − | 1.61121i | −1.14792 | − | 0.147699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.22800 | −0.202545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.7705 | −1.60232 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5223 | 1.11117 | 0.555587 | − | 0.831458i | \(-0.312493\pi\) | ||||
0.555587 | + | 0.831458i | \(0.312493\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 12.0000 | + | 1.54400i | 1.04053 | + | 0.133882i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.54400i | − | 0.302785i | −0.988474 | − | 0.151392i | \(-0.951624\pi\) | ||
0.988474 | − | 0.151392i | \(-0.0483757\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.14593 | 0.775747 | 0.387874 | − | 0.921713i | \(-0.373210\pi\) | ||||
0.387874 | + | 0.921713i | \(0.373210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.77200 | −0.401875 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 17.3559i | − | 1.45138i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.24824 | + | 20.0570i | −0.432867 | + | 1.65428i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.54400 | −0.781875 | −0.390938 | − | 0.920417i | \(-0.627849\pi\) | ||||
−0.390938 | + | 0.920417i | \(0.627849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.63703i | 0.295977i | 0.988989 | + | 0.147989i | \(0.0472799\pi\) | ||||
−0.988989 | + | 0.147989i | \(0.952720\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 27.5440 | 2.22680 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.00000 | 0.478852 | 0.239426 | − | 0.970915i | \(-0.423041\pi\) | ||||
0.239426 | + | 0.970915i | \(0.423041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.7705 | −1.40930 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.7720 | − | 1.77200i | −1.08539 | − | 0.139653i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.7447 | −1.23322 | −0.616611 | − | 0.787268i | \(-0.711495\pi\) | ||||
−0.616611 | + | 0.787268i | \(0.711495\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 23.4334i | − | 1.81333i | −0.421851 | − | 0.906665i | \(-0.638619\pi\) | ||
0.421851 | − | 0.906665i | \(-0.361381\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.77200 | 0.751692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −26.3952 | −2.01849 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.31601 | 0.176083 | 0.0880413 | − | 0.996117i | \(-0.471939\pi\) | ||||
0.0880413 | + | 0.996117i | \(0.471939\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 21.5440i | − | 1.61935i | ||||||
\(178\) | 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 | \(-0.884583\pi\) | ||
0.934980 | − | 0.354700i | \(-0.115417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.4965 | −0.775922 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 17.3559i | − | 1.26919i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.77200 | − | 21.5440i | 0.201633 | − | 1.56710i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6300i | 1.78216i | 0.453843 | + | 0.891082i | \(0.350053\pi\) | ||||
−0.453843 | + | 0.891082i | \(0.649947\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.45600i | 0.320750i | 0.987056 | + | 0.160375i | \(0.0512703\pi\) | ||||
−0.987056 | + | 0.160375i | \(0.948730\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.57296 | 0.324169 | 0.162084 | − | 0.986777i | \(-0.448178\pi\) | ||||
0.162084 | + | 0.986777i | \(0.448178\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 37.0880i | − | 2.61599i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.5223 | + | 1.61121i | 0.878893 | + | 0.113085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.2928 | 2.10550 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.6320i | 1.15046i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.3559i | − | 1.19483i | −0.801932 | − | 0.597415i | \(-0.796194\pi\) | ||
0.801932 | − | 0.597415i | \(-0.203806\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.5440 | 1.47617 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.5440 | − | 2.00000i | −1.05520 | − | 0.135769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 17.7705i | − | 1.20082i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.7720 | 1.53181 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.4582i | 0.901230i | 0.892718 | + | 0.450615i | \(0.148795\pi\) | ||||
−0.892718 | + | 0.450615i | \(0.851205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.1593i | 1.07253i | 0.844049 | + | 0.536266i | \(0.180166\pi\) | ||||
−0.844049 | + | 0.536266i | \(0.819834\pi\) | |||||||
\(228\) | 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 | ||||||||
\(233\) | − | 8.45600i | − | 0.553971i | −0.960874 | − | 0.276985i | \(-0.910665\pi\) | ||
0.960874 | − | 0.276985i | \(-0.0893354\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.3160 | 1.31967 | ||||||||
\(238\) | 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 | \(-0.912199\pi\) | ||
0.962198 | − | 0.272349i | \(-0.0878006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 3.89769i | − | 0.250037i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.8222 | −1.38851 | ||||||||
\(248\) | 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 | ||||||||
\(253\) | − | 19.0880i | − | 1.20005i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.0880 | −0.816407 | −0.408204 | − | 0.912891i | \(-0.633845\pi\) | ||||
−0.408204 | + | 0.912891i | \(0.633845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.89769 | − | 30.2928i | 0.242191 | − | 1.88231i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −27.5440 | −1.70493 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.47065 | −0.522323 | −0.261161 | − | 0.965295i | \(-0.584105\pi\) | ||||
−0.261161 | + | 0.965295i | \(0.584105\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.5411 | −2.17508 | ||||||||
\(268\) | 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 | ||||||||
\(273\) | 4.77200 | − | 37.0880i | 0.288815 | − | 2.24467i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.5440i | 1.17429i | 0.809483 | + | 0.587143i | \(0.199747\pi\) | ||||
−0.809483 | + | 0.587143i | \(0.800253\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 23.9547i | 1.42396i | 0.702200 | + | 0.711980i | \(0.252201\pi\) | ||||
−0.702200 | + | 0.711980i | \(0.747799\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.02582 | + | 15.7447i | −0.119581 | + | 0.929381i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.77200 | 0.339530 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 49.6746i | − | 2.91198i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3160 | 0.836350 | 0.418175 | − | 0.908366i | \(-0.362670\pi\) | ||||
0.418175 | + | 0.908366i | \(0.362670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 29.8600 | 1.73265 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.0446 | 1.44837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.31601 | + | 0.683994i | 0.306409 | + | 0.0394248i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.2670 | 1.62390 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 31.2288i | − | 1.78232i | −0.453689 | − | 0.891160i | \(-0.649892\pi\) | ||
0.453689 | − | 0.891160i | \(-0.350108\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | −4.77200 | −0.269729 | −0.134865 | − | 0.990864i | \(-0.543060\pi\) | ||||
−0.134865 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.0880i | 1.40908i | 0.709663 | + | 0.704541i | \(0.248847\pi\) | ||||
−0.709663 | + | 0.704541i | \(0.751153\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.3559i | 0.971745i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 37.0880i | 2.07005i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.8222 | −1.21422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 20.0570i | − | 1.10916i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.544004 | + | 4.22800i | −0.0299919 | + | 0.233097i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 13.7189i | − | 0.754058i | −0.926201 | − | 0.377029i | \(-0.876946\pi\) | ||
0.926201 | − | 0.377029i | \(-0.123054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 66.6320i | 3.65141i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.45600i | 0.242734i | 0.992608 | + | 0.121367i | \(0.0387277\pi\) | ||||
−0.992608 | + | 0.121367i | \(0.961272\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −46.0376 | −2.50042 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 21.5440i | − | 1.16667i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1722 | + | 6.93643i | 0.927214 | + | 0.374532i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.24824 | 0.281740 | 0.140870 | − | 0.990028i | \(-0.455010\pi\) | ||||
0.140870 | + | 0.990028i | \(0.455010\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | −35.8600 | −1.90864 | −0.954318 | − | 0.298793i | \(-0.903416\pi\) | ||||
−0.954318 | + | 0.298793i | \(0.903416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.77200 | − | 37.0880i | 0.252561 | − | 1.96291i | ||||
\(358\) | 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 | ||||||||
\(363\) | − | 6.59879i | − | 0.346347i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8088i | 0.773012i | 0.922287 | + | 0.386506i | \(0.126318\pi\) | ||||
−0.922287 | + | 0.386506i | \(0.873682\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 34.6320i | − | 1.80287i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.02582 | + | 15.7447i | −0.105176 | + | 0.817425i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.45600i | − | 0.230723i | −0.993324 | − | 0.115361i | \(-0.963197\pi\) | ||
0.993324 | − | 0.115361i | \(-0.0368026\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.7720 | −1.17282 | ||||||||
\(378\) | 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 | ||||||||
\(383\) | 8.47065i | 0.432830i | 0.976301 | + | 0.216415i | \(0.0694364\pi\) | ||||
−0.976301 | + | 0.216415i | \(0.930564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.6931 | −0.594392 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.3160 | 1.03006 | 0.515031 | − | 0.857171i | \(-0.327780\pi\) | ||||
0.515031 | + | 0.857171i | \(0.327780\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.0446 | 1.26656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.0880i | 1.56818i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.7720 | −0.841763 | −0.420881 | − | 0.907116i | \(-0.638279\pi\) | ||||
−0.420881 | + | 0.907116i | \(0.638279\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 28.2670 | 1.40808 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.9859 | 2.08116 | ||||||||
\(408\) | 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 | ||||||||
\(413\) | −19.0880 | − | 2.45600i | −0.939259 | − | 0.120852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.0880i | 1.32651i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.7189 | −0.670212 | −0.335106 | − | 0.942181i | \(-0.608772\pi\) | ||||
−0.335106 | + | 0.942181i | \(0.608772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8600 | −0.675496 | −0.337748 | − | 0.941237i | \(-0.609665\pi\) | ||||
−0.337748 | + | 0.941237i | \(0.609665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 9.29989i | − | 0.452176i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19659 | + | 9.29989i | −0.0579070 | + | 0.450053i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 51.4040 | 2.48181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.0748i | 1.49682i | 0.663236 | + | 0.748410i | \(0.269183\pi\) | ||||
−0.663236 | + | 0.748410i | \(0.730817\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0880 | −1.20565 | −0.602826 | − | 0.797872i | \(-0.705959\pi\) | ||||
−0.602826 | + | 0.797872i | \(0.705959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.0000 | −1.14808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.8470 | 0.565428 | 0.282714 | − | 0.959204i | \(-0.408765\pi\) | ||||
0.282714 | + | 0.959204i | \(0.408765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.0880 | − | 10.2280i | −1.86133 | − | 0.487048i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.47065 | 0.402453 | 0.201226 | − | 0.979545i | \(-0.435507\pi\) | ||||
0.201226 | + | 0.979545i | \(0.435507\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 28.2670i | − | 1.33698i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.8600 | −1.40918 | −0.704590 | − | 0.709614i | \(-0.748869\pi\) | ||||
−0.704590 | + | 0.709614i | \(0.748869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.8222 | −1.02757 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.7720 | −0.506113 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1760i | 1.31802i | 0.752135 | + | 0.659009i | \(0.229024\pi\) | ||||
−0.752135 | + | 0.659009i | \(0.770976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39.1781i | 1.82868i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.08801i | 0.330121i | 0.986283 | + | 0.165061i | \(0.0527820\pi\) | ||||
−0.986283 | + | 0.165061i | \(0.947218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.19659 | 0.0556102 | 0.0278051 | − | 0.999613i | \(-0.491148\pi\) | ||||
0.0278051 | + | 0.999613i | \(0.491148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1006i | 1.53171i | 0.643010 | + | 0.765857i | \(0.277685\pi\) | ||||
−0.643010 | + | 0.765857i | \(0.722315\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.8600 | − | 4.22800i | −1.51733 | − | 0.195231i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7705i | 0.818823i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.36799i | 0.338780i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 34.6320i | − | 1.58569i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0963 | 1.32944 | 0.664721 | − | 0.747092i | \(-0.268550\pi\) | ||||
0.664721 | + | 0.747092i | \(0.268550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55.0880i | 2.51180i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.24824 | − | 40.7893i | 0.238803 | − | 1.85598i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7447 | −0.713461 | −0.356731 | − | 0.934207i | \(-0.616109\pi\) | ||||
−0.356731 | + | 0.934207i | \(0.616109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 46.6320i | − | 2.10877i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.6300i | 1.11154i | 0.831338 | + | 0.555768i | \(0.187576\pi\) | ||||
−0.831338 | + | 0.555768i | \(0.812424\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.7720 | −1.02560 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.45600 | − | 19.0880i | 0.110166 | − | 0.856214i | ||||
\(498\) | 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 | ||||||||
\(503\) | − | 8.88527i | − | 0.396175i | −0.980184 | − | 0.198087i | \(-0.936527\pi\) | ||
0.980184 | − | 0.198087i | \(-0.0634730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.9423i | 1.28537i | ||||||||
\(508\) | 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 | ||||||||
\(513\) | − | 37.5440i | − | 1.65761i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.86001 | −0.257723 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.85944i | 0.301096i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5440i | 0.943860i | 0.881636 | + | 0.471930i | \(0.156442\pi\) | ||||
−0.881636 | + | 0.471930i | \(0.843558\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 38.9175i | − | 1.70174i | −0.525375 | − | 0.850871i | \(-0.676075\pi\) | ||
0.525375 | − | 0.850871i | \(-0.323925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.2670 | 1.23133 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.54400 | 0.197565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.9859 | 1.82203 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 28.6320i | − | 1.24019i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.54400 | 0.411854 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 28.2670 | 1.21305 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.19659 | −0.0511624 | −0.0255812 | − | 0.999673i | \(-0.508144\pi\) | ||||
−0.0255812 | + | 0.999673i | \(0.508144\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 20.4560i | − | 0.873041i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.8222 | 0.929657 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.31601 | − | 18.0000i | 0.0984866 | − | 0.765438i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.4560i | 0.866748i | 0.901214 | + | 0.433374i | \(0.142677\pi\) | ||||
−0.901214 | + | 0.433374i | \(0.857323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.66724 | −0.408881 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.4040 | 2.17028 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 8.47065i | − | 0.356995i | −0.983940 | − | 0.178498i | \(-0.942876\pi\) | ||
0.983940 | − | 0.178498i | \(-0.0571237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.3688 | + | 2.36346i | 0.771418 | + | 0.0992561i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.6320 | 0.697250 | 0.348625 | − | 0.937262i | \(-0.386649\pi\) | ||||
0.348625 | + | 0.937262i | \(0.386649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.27406i | 0.304410i | 0.988349 | + | 0.152205i | \(0.0486374\pi\) | ||||
−0.988349 | + | 0.152205i | \(0.951363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −72.9480 | −3.04745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.139991 | 0.00582789 | 0.00291394 | − | 0.999996i | \(-0.499072\pi\) | ||||
0.00291394 | + | 0.999996i | \(0.499072\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.1976 | −0.548473 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.683994 | + | 5.31601i | −0.0283769 | + | 0.220545i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.8222 | −0.903783 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.02582i | 0.0836147i | 0.999126 | + | 0.0418074i | \(0.0133116\pi\) | ||||
−0.999126 | + | 0.0418074i | \(0.986688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.0880 | −1.11614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7705 | 0.730982 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.8600 | −0.487032 | −0.243516 | − | 0.969897i | \(-0.578301\pi\) | ||||
−0.243516 | + | 0.969897i | \(0.578301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5440i | 0.554319i | ||||||||
\(598\) | 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 | \(-0.642843\pi\) | ||
0.433843 | − | 0.900989i | \(-0.357157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 72.2787 | 2.94342 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.7571i | 0.436619i | 0.975880 | + | 0.218309i | \(0.0700542\pi\) | ||||
−0.975880 | + | 0.218309i | \(0.929946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.77200 | + | 37.0880i | −0.193371 | + | 1.50288i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.68868i | − | 0.311051i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.0000i | 1.37325i | 0.727013 | + | 0.686624i | \(0.240908\pi\) | ||||
−0.727013 | + | 0.686624i | \(0.759092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.5440i | − | 0.625778i | −0.949790 | − | 0.312889i | \(-0.898703\pi\) | ||
0.949790 | − | 0.312889i | \(-0.101297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8470 | −0.476172 | −0.238086 | − | 0.971244i | \(-0.576520\pi\) | ||||
−0.238086 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.0880i | 1.72906i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.05165 | + | 31.4894i | −0.162326 | + | 1.26160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −49.2600 | −1.96725 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 55.0880i | 2.19650i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.9111i | − | 0.434364i | −0.976131 | − | 0.217182i | \(-0.930314\pi\) | ||
0.976131 | − | 0.217182i | \(-0.0696865\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 51.4040 | 2.04313 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.3160 | − | 8.45600i | −1.28041 | − | 0.335039i | ||||
\(638\) | 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 | ||||||||
\(643\) | 23.9547i | 0.944682i | 0.881416 | + | 0.472341i | \(0.156591\pi\) | ||||
−0.881416 | + | 0.472341i | \(0.843409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 16.5740i | − | 0.651589i | −0.945441 | − | 0.325795i | \(-0.894368\pi\) | ||
0.945441 | − | 0.325795i | \(-0.105632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 26.4560i | − | 1.03849i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.92351 | − | 46.0376i | 0.232161 | − | 1.80435i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.08801i | 0.0425770i | 0.999773 | + | 0.0212885i | \(0.00677686\pi\) | ||||
−0.999773 | + | 0.0212885i | \(0.993223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.6320 | 1.35112 | ||||||||
\(658\) | 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 | \(-0.902247\pi\) | ||
0.953214 | − | 0.302296i | \(-0.0977530\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 67.4451i | 2.61935i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.0446 | −0.969731 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.8600 | −1.54108 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.8897 | −0.497600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.5440i | 1.37012i | 0.728486 | + | 0.685060i | \(0.240224\pi\) | ||||
−0.728486 | + | 0.685060i | \(0.759776\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.7720 | −0.644600 | −0.322300 | − | 0.946638i | \(-0.604456\pi\) | ||||
−0.322300 | + | 0.946638i | \(0.604456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −44.0117 | − | 5.66286i | −1.68902 | − | 0.217320i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.8600 | −1.83400 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.7377 | 1.40573 | 0.702864 | − | 0.711324i | \(-0.251904\pi\) | ||||
0.702864 | + | 0.711324i | \(0.251904\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −63.8081 | −2.43443 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 7.08801 | − | 55.0880i | 0.269251 | − | 2.09262i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 28.6320i | − | 1.08451i | ||||||
\(698\) | 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 | ||||||||
\(703\) | − | 52.7903i | − | 1.99102i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.22241 | − | 25.0446i | 0.121191 | − | 0.941899i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.6840 | 0.513913 | 0.256957 | − | 0.966423i | \(-0.417280\pi\) | ||||
0.256957 | + | 0.966423i | \(0.417280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.5927i | 1.48484i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.0880 | 1.16426 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −41.8600 | −1.56329 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.44483 | −0.240351 | −0.120176 | − | 0.992753i | \(-0.538346\pi\) | ||||
−0.120176 | + | 0.992753i | \(0.538346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.45600 | + | 11.3160i | −0.0542241 | + | 0.421430i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.0446 | 0.931419 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.3693i | 0.903808i | 0.892066 | + | 0.451904i | \(0.149255\pi\) | ||||
−0.892066 | + | 0.451904i | \(0.850745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 32.5440 | 1.20533 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.66724 | −0.357556 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.2280 | 1.15343 | 0.576716 | − | 0.816945i | \(-0.304334\pi\) | ||||
0.576716 | + | 0.816945i | \(0.304334\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 45.5440i | − | 1.67763i | ||||||
\(738\) | 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 | ||||||||
\(743\) | −4.41900 | −0.162117 | −0.0810587 | − | 0.996709i | \(-0.525830\pi\) | ||||
−0.0810587 | + | 0.996709i | \(0.525830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 11.6931i | − | 0.427827i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.8600 | + | 4.22800i | 1.20068 | + | 0.154488i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.4592i | − | 0.929020i | −0.885568 | − | 0.464510i | \(-0.846230\pi\) | ||
0.885568 | − | 0.464510i | \(-0.153770\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 74.1760i | 2.70312i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5440i | 0.419574i | 0.977747 | + | 0.209787i | \(0.0672770\pi\) | ||||
−0.977747 | + | 0.209787i | \(0.932723\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 56.5340 | 2.05206 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.7705 | − | 2.28648i | −0.643337 | − | 0.0827762i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.7118 | 1.25337 | ||||||||
\(768\) | 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 | ||||||||
\(773\) | 43.2280 | 1.55480 | 0.777402 | − | 0.629005i | \(-0.216537\pi\) | ||||
0.777402 | + | 0.629005i | \(0.216537\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 89.7200 | + | 11.5440i | 3.21869 | + | 0.414139i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.4378i | 0.983060i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.4560 | 0.946670 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 39.1781i | − | 1.40011i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 13.9795i | − | 0.498317i | −0.968463 | − | 0.249159i | \(-0.919846\pi\) | ||
0.968463 | − | 0.249159i | \(-0.0801540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 25.0880i | − | 0.893157i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.24824 | + | 40.7893i | −0.186606 | + | 1.45030i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.9120i | − | 0.600562i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.2280 | 0.681091 | 0.340545 | − | 0.940228i | \(-0.389388\pi\) | ||||
0.340545 | + | 0.940228i | \(0.389388\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7.68868i | − | 0.272006i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 69.2640i | − | 2.44732i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 21.8222i | − | 0.770088i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.0376 | 1.62060 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3160 | −0.503324 | −0.251662 | − | 0.967815i | \(-0.580977\pi\) | ||||
−0.251662 | + | 0.967815i | \(0.580977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2938 | −1.48514 | −0.742569 | − | 0.669770i | \(-0.766393\pi\) | ||||
−0.742569 | + | 0.669770i | \(0.766393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000i | 0.140286i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.26402 | 0.324107 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 18.9671 | 0.661153 | 0.330576 | − | 0.943779i | \(-0.392757\pi\) | ||||
0.330576 | + | 0.943779i | \(0.392757\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.24824 | 0.182499 | 0.0912496 | − | 0.995828i | \(-0.470914\pi\) | ||||
0.0912496 | + | 0.995828i | \(0.470914\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | −32.3160 | − | 8.45600i | −1.11968 | − | 0.292983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.6320i | 1.68097i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.44483 | 0.222500 | 0.111250 | − | 0.993792i | \(-0.464515\pi\) | ||||
0.111250 | + | 0.993792i | \(0.464515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.22800 | −0.214759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 60.1711i | 2.07240i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.84653 | − | 0.752256i | −0.200889 | − | 0.0258478i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.9480 | −2.43493 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.5857i | 2.07685i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.1760 | 0.690814 | 0.345407 | − | 0.938453i | \(-0.387741\pi\) | ||||
0.345407 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.9433 | 1.39697 | 0.698483 | − | 0.715626i | \(-0.253859\pi\) | ||||
0.698483 | + | 0.715626i | \(0.253859\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.6320 | − | 6.00000i | −1.58921 | − | 0.204479i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.07747 | 0.206880 | 0.103440 | − | 0.994636i | \(-0.467015\pi\) | ||||
0.103440 | + | 0.994636i | \(0.467015\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.0953i | 0.580586i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.9480 | 0.846304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59.7564 | 2.02477 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 96.8080 | 3.27646 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 5.08801i | − | 0.171810i | −0.996303 | − | 0.0859049i | \(-0.972622\pi\) | ||
0.996303 | − | 0.0859049i | \(-0.0273781\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.4005i | 1.43013i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.6320i | 1.16678i | 0.812191 | + | 0.583391i | \(0.198274\pi\) | ||||
−0.812191 | + | 0.583391i | \(0.801726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6931 | −0.393503 | −0.196751 | − | 0.980453i | \(-0.563039\pi\) | ||||
−0.196751 | + | 0.980453i | \(0.563039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 54.5082i | − | 1.83021i | −0.403220 | − | 0.915103i | \(-0.632109\pi\) | ||
0.403220 | − | 0.915103i | \(-0.367891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.8600 | + | 4.22800i | 1.10209 | + | 0.141803i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.4592i | 0.852916i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.36799i | 0.246560i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 74.1760i | 2.47667i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.2670 | −0.942758 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 28.6320i | − | 0.953871i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.02582 | + | 15.7447i | −0.0674152 | + | 0.523951i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.7964 | −0.657327 | −0.328664 | − | 0.944447i | \(-0.606598\pi\) | ||||
−0.328664 | + | 0.944447i | \(0.606598\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 55.0880i | 1.82715i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.7118i | 1.15005i | 0.818134 | + | 0.575027i | \(0.195009\pi\) | ||||
−0.818134 | + | 0.575027i | \(0.804991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.36799 | −0.243845 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.5440 | + | 3.54400i | 0.909583 | + | 0.117033i | ||||
\(918\) | 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 | ||||||||
\(923\) | 34.7118i | 1.14255i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 24.8906i | − | 0.817516i | ||||||
\(928\) | 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 | ||||||||
\(933\) | − | 71.7200i | − | 2.34801i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.2280 | 0.628151 | 0.314076 | − | 0.949398i | \(-0.398305\pi\) | ||||
0.314076 | + | 0.949398i | \(0.398305\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14.1335i | − | 0.461230i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.1760i | − | 0.853314i | −0.904414 | − | 0.426657i | \(-0.859691\pi\) | ||
0.904414 | − | 0.426657i | \(-0.140309\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 31.4894i | − | 1.02544i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.5153 | 1.08910 | 0.544550 | − | 0.838729i | \(-0.316701\pi\) | ||||
0.544550 | + | 0.838729i | \(0.316701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.6320 | 0.929434 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.3046 | −2.40949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 6.00000i | − | 0.194359i | −0.995267 | − | 0.0971795i | \(-0.969018\pi\) | ||
0.995267 | − | 0.0971795i | \(-0.0309821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −51.4040 | −1.66166 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.19659 | − | 9.29989i | 0.0386399 | − | 0.300309i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.08801 | 0.131871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −72.2787 | −2.32915 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.6186 | 1.33836 | 0.669181 | − | 0.743099i | \(-0.266645\pi\) | ||||
0.669181 | + | 0.743099i | \(0.266645\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 24.0000 | + | 3.08801i | 0.769405 | + | 0.0989970i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.0880i | 1.18655i | 0.805000 | + | 0.593275i | \(0.202165\pi\) | ||||
−0.805000 | + | 0.593275i | \(0.797835\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.6444 | −1.39488 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.0880 | 1.24798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1593i | 0.515403i | 0.966225 | + | 0.257701i | \(0.0829651\pi\) | ||||
−0.966225 | + | 0.257701i | \(0.917035\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.5223 | − | 1.61121i | −0.398589 | − | 0.0512853i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.6320 | −0.338078 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.8151i | − | 1.36007i | −0.733181 | − | 0.680034i | \(-0.761965\pi\) | ||
0.733181 | − | 0.680034i | \(-0.238035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.6320 | 1.28942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.4040 | 1.05792 | 0.528958 | − | 0.848648i | \(-0.322583\pi\) | ||||
0.528958 | + | 0.848648i | \(0.322583\pi\) | |||||||
\(998\) | 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 | 2800.2.e.g.2799.8 | 8 | ||
4.3 | odd | 2 | inner | 2800.2.e.g.2799.1 | 8 | ||
5.2 | odd | 4 | 2800.2.k.m.2351.8 | 8 | |||
5.3 | odd | 4 | 560.2.k.b.111.1 | ✓ | 8 | ||
5.4 | even | 2 | 2800.2.e.h.2799.1 | 8 | |||
7.6 | odd | 2 | 2800.2.e.h.2799.2 | 8 | |||
15.8 | even | 4 | 5040.2.d.d.4591.7 | 8 | |||
20.3 | even | 4 | 560.2.k.b.111.7 | yes | 8 | ||
20.7 | even | 4 | 2800.2.k.m.2351.1 | 8 | |||
20.19 | odd | 2 | 2800.2.e.h.2799.8 | 8 | |||
28.27 | even | 2 | 2800.2.e.h.2799.7 | 8 | |||
35.13 | even | 4 | 560.2.k.b.111.8 | yes | 8 | ||
35.27 | even | 4 | 2800.2.k.m.2351.2 | 8 | |||
35.34 | odd | 2 | inner | 2800.2.e.g.2799.7 | 8 | ||
40.3 | even | 4 | 2240.2.k.d.1791.2 | 8 | |||
40.13 | odd | 4 | 2240.2.k.d.1791.8 | 8 | |||
60.23 | odd | 4 | 5040.2.d.d.4591.6 | 8 | |||
105.83 | odd | 4 | 5040.2.d.d.4591.2 | 8 | |||
140.27 | odd | 4 | 2800.2.k.m.2351.7 | 8 | |||
140.83 | odd | 4 | 560.2.k.b.111.2 | yes | 8 | ||
140.139 | even | 2 | inner | 2800.2.e.g.2799.2 | 8 | ||
280.13 | even | 4 | 2240.2.k.d.1791.1 | 8 | |||
280.83 | odd | 4 | 2240.2.k.d.1791.7 | 8 | |||
420.83 | even | 4 | 5040.2.d.d.4591.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.k.b.111.1 | ✓ | 8 | 5.3 | odd | 4 | ||
560.2.k.b.111.2 | yes | 8 | 140.83 | odd | 4 | ||
560.2.k.b.111.7 | yes | 8 | 20.3 | even | 4 | ||
560.2.k.b.111.8 | yes | 8 | 35.13 | even | 4 | ||
2240.2.k.d.1791.1 | 8 | 280.13 | even | 4 | |||
2240.2.k.d.1791.2 | 8 | 40.3 | even | 4 | |||
2240.2.k.d.1791.7 | 8 | 280.83 | odd | 4 | |||
2240.2.k.d.1791.8 | 8 | 40.13 | odd | 4 | |||
2800.2.e.g.2799.1 | 8 | 4.3 | odd | 2 | inner | ||
2800.2.e.g.2799.2 | 8 | 140.139 | even | 2 | inner | ||
2800.2.e.g.2799.7 | 8 | 35.34 | odd | 2 | inner | ||
2800.2.e.g.2799.8 | 8 | 1.1 | even | 1 | trivial | ||
2800.2.e.h.2799.1 | 8 | 5.4 | even | 2 | |||
2800.2.e.h.2799.2 | 8 | 7.6 | odd | 2 | |||
2800.2.e.h.2799.7 | 8 | 28.27 | even | 2 | |||
2800.2.e.h.2799.8 | 8 | 20.19 | odd | 2 | |||
2800.2.k.m.2351.1 | 8 | 20.7 | even | 4 | |||
2800.2.k.m.2351.2 | 8 | 35.27 | even | 4 | |||
2800.2.k.m.2351.7 | 8 | 140.27 | odd | 4 | |||
2800.2.k.m.2351.8 | 8 | 5.2 | odd | 4 | |||
5040.2.d.d.4591.2 | 8 | 105.83 | odd | 4 | |||
5040.2.d.d.4591.3 | 8 | 420.83 | even | 4 | |||
5040.2.d.d.4591.6 | 8 | 60.23 | odd | 4 | |||
5040.2.d.d.4591.7 | 8 | 15.8 | even | 4 |