Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7700,2,Mod(1849,7700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7700.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7700 = 2^{2} \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7700.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: | \(61.4848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 308) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7700.1849 |
Dual form | 7700.2.e.j.1849.4 |
$q$-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 \(\left(\mathbb{Z}/7700\mathbb{Z}\right)^\times\).
\(n\) | \(2201\) | \(3851\) | \(5601\) | \(6777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 2.44949i | − 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.449490i | 0.124666i | 0.998055 | + | 0.0623330i | \(0.0198541\pi\) | ||||
−0.998055 | + | 0.0623330i | \(0.980146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 0.449490i | − 0.109017i | −0.998513 | − | 0.0545086i | \(-0.982641\pi\) | ||||
0.998513 | − | 0.0545086i | \(-0.0173592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.89898 | 1.12390 | 0.561951 | − | 0.827170i | \(-0.310051\pi\) | ||||
0.561951 | + | 0.827170i | \(0.310051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.44949 | −0.534522 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.898979i | 0.187450i | 0.995598 | + | 0.0937251i | \(0.0298775\pi\) | ||||
−0.995598 | + | 0.0937251i | \(0.970123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.89898 | −0.538327 | −0.269163 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269163 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.44949 | 1.15836 | 0.579181 | − | 0.815199i | \(-0.303372\pi\) | ||||
0.579181 | + | 0.815199i | \(0.303372\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.44949i | 0.426401i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.10102 | 0.176304 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.34847 | −1.45999 | −0.729993 | − | 0.683455i | \(-0.760477\pi\) | ||||
−0.729993 | + | 0.683455i | \(0.760477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.89898i | − 0.442090i | −0.975264 | − | 0.221045i | \(-0.929053\pi\) | ||||
0.975264 | − | 0.221045i | \(-0.0709468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 6.44949i | − 0.940755i | −0.882465 | − | 0.470377i | \(-0.844118\pi\) | ||||
0.882465 | − | 0.470377i | \(-0.155882\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.10102 | −0.154174 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.79796i | − 1.34585i | −0.739709 | − | 0.672927i | \(-0.765037\pi\) | ||||
0.739709 | − | 0.672927i | \(-0.234963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 12.0000i | − 1.58944i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.34847 | −0.956689 | −0.478345 | − | 0.878172i | \(-0.658763\pi\) | ||||
−0.478345 | + | 0.878172i | \(0.658763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.34847 | 0.684801 | 0.342401 | − | 0.939554i | \(-0.388760\pi\) | ||||
0.342401 | + | 0.939554i | \(0.388760\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.00000i | 0.377964i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.6969i | − 1.79552i | −0.440488 | − | 0.897758i | \(-0.645195\pi\) | ||||
0.440488 | − | 0.897758i | \(-0.354805\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.20204 | 0.265095 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8990 | −1.53083 | −0.765414 | − | 0.643539i | \(-0.777466\pi\) | ||||
−0.765414 | + | 0.643539i | \(0.777466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.4495i | − 1.45710i | −0.684991 | − | 0.728551i | \(-0.740194\pi\) | ||||
0.684991 | − | 0.728551i | \(-0.259806\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8990 | 1.22623 | 0.613115 | − | 0.789993i | \(-0.289916\pi\) | ||||
0.613115 | + | 0.789993i | \(0.289916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.8990i | 1.85490i | 0.373942 | + | 0.927452i | \(0.378006\pi\) | ||||
−0.373942 | + | 0.927452i | \(0.621994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.10102i | 0.761309i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.449490 | 0.0471193 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 15.7980i | − 1.63817i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.10102i | 0.517930i | 0.965887 | + | 0.258965i | \(0.0833815\pi\) | ||||
−0.965887 | + | 0.258965i | \(0.916619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.44949 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638102\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 14.4495i | − 1.42375i | −0.702306 | − | 0.711875i | \(-0.747846\pi\) | ||||
0.702306 | − | 0.711875i | \(-0.252154\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.8990 | −1.42706 | −0.713532 | − | 0.700623i | \(-0.752906\pi\) | ||||
−0.713532 | + | 0.700623i | \(0.752906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.79796 | 0.929981 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.34847i | − 0.124666i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.449490 | −0.0412047 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.8990i | 2.06473i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.79796i | − 0.159543i | −0.996813 | − | 0.0797715i | \(-0.974581\pi\) | ||||
0.996813 | − | 0.0797715i | \(-0.0254191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.10102 | −0.625210 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.79796 | 0.856052 | 0.428026 | − | 0.903767i | \(-0.359209\pi\) | ||||
0.428026 | + | 0.903767i | \(0.359209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 4.89898i | − 0.424795i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.79796i | 0.837096i | 0.908195 | + | 0.418548i | \(0.137461\pi\) | ||||
−0.908195 | + | 0.418548i | \(0.862539\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.6969 | −1.92513 | −0.962565 | − | 0.271052i | \(-0.912628\pi\) | ||||
−0.962565 | + | 0.271052i | \(0.912628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.7980 | −1.33043 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 0.449490i | − 0.0375882i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.44949i | 0.202031i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.7980 | −0.966526 | −0.483263 | − | 0.875475i | \(-0.660549\pi\) | ||||
−0.483263 | + | 0.875475i | \(0.660549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.69694 | 0.707747 | 0.353873 | − | 0.935293i | \(-0.384864\pi\) | ||||
0.353873 | + | 0.935293i | \(0.384864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.34847i | 0.109017i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −24.0000 | −1.90332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.898979 | 0.0708495 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.89898i | − 0.697022i | −0.937305 | − | 0.348511i | \(-0.886687\pi\) | ||||
0.937305 | − | 0.348511i | \(-0.113313\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.7980i | 1.06772i | 0.845573 | + | 0.533859i | \(0.179259\pi\) | ||||
−0.845573 | + | 0.533859i | \(0.820741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7980 | 0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6969 | −1.12390 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 10.2474i | − 0.779099i | −0.921006 | − | 0.389550i | \(-0.872631\pi\) | ||||
0.921006 | − | 0.389550i | \(-0.127369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.0000i | 1.35296i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.5959 | 1.16569 | 0.582847 | − | 0.812582i | \(-0.301939\pi\) | ||||
0.582847 | + | 0.812582i | \(0.301939\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.10102 | 0.676474 | 0.338237 | − | 0.941061i | \(-0.390170\pi\) | ||||
0.338237 | + | 0.941061i | \(0.390170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 13.1010i | − 0.968455i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.449490i | 0.0328699i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.79796 | −0.130096 | −0.0650479 | − | 0.997882i | \(-0.520720\pi\) | ||||
−0.0650479 | + | 0.997882i | \(0.520720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 21.5959i | − 1.55451i | −0.629187 | − | 0.777254i | \(-0.716612\pi\) | ||||
0.629187 | − | 0.777254i | \(-0.283388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 25.5959i | − 1.82363i | −0.410597 | − | 0.911817i | \(-0.634680\pi\) | ||||
0.410597 | − | 0.911817i | \(-0.365320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.0454 | −1.84631 | −0.923155 | − | 0.384428i | \(-0.874399\pi\) | ||||
−0.923155 | + | 0.384428i | \(0.874399\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.0000 | −2.53924 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.89898i | 0.203468i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.69694i | − 0.187450i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.89898 | −0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31.5959i | 2.16492i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 6.44949i | − 0.437820i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −30.4949 | −2.06065 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.202041 | 0.0135908 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1464i | 0.880350i | 0.897912 | + | 0.440175i | \(0.145084\pi\) | ||||
−0.897912 | + | 0.440175i | \(0.854916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.79796i | 0.119335i | 0.998218 | + | 0.0596674i | \(0.0190040\pi\) | ||||
−0.998218 | + | 0.0596674i | \(0.980996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.10102 | 0.337085 | 0.168542 | − | 0.985694i | \(-0.446094\pi\) | ||||
0.168542 | + | 0.985694i | \(0.446094\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.44949 | 0.161165 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.10102i | 0.0721303i | 0.999349 | + | 0.0360651i | \(0.0114824\pi\) | ||||
−0.999349 | + | 0.0360651i | \(0.988518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 26.6969i | − 1.73415i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34847 | −0.0868625 | −0.0434313 | − | 0.999056i | \(-0.513829\pi\) | ||||
−0.0434313 | + | 0.999056i | \(0.513829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.0454i | 1.41421i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.20204i | 0.140113i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 41.3939 | 2.62323 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.44949 | 0.154610 | 0.0773052 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773052 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.898979i | − 0.0565184i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3.79796i | − 0.236910i | −0.992959 | − | 0.118455i | \(-0.962206\pi\) | ||||
0.992959 | − | 0.118455i | \(-0.0377942\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.69694 | 0.538327 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 19.5959i | − 1.20834i | −0.796857 | − | 0.604168i | \(-0.793506\pi\) | ||||
0.796857 | − | 0.604168i | \(-0.206494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.6969i | 0.899438i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1010 | 0.798783 | 0.399392 | − | 0.916780i | \(-0.369221\pi\) | ||||
0.399392 | + | 0.916780i | \(0.369221\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.30306 | 0.0791554 | 0.0395777 | − | 0.999216i | \(-0.487399\pi\) | ||||
0.0395777 | + | 0.999216i | \(0.487399\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1.10102i | − 0.0666368i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7980i | 0.949207i | 0.880200 | + | 0.474604i | \(0.157409\pi\) | ||||
−0.880200 | + | 0.474604i | \(0.842591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.3485 | −1.15836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.10102 | −0.304301 | −0.152151 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152151 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.0000i | 1.42665i | 0.700832 | + | 0.713326i | \(0.252812\pi\) | ||||
−0.700832 | + | 0.713326i | \(0.747188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.34847i | 0.551823i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7980 | 0.988115 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.4949 | 0.732464 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6515i | 0.622269i | 0.950366 | + | 0.311135i | \(0.100709\pi\) | ||||
−0.950366 | + | 0.311135i | \(0.899291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.404082 | −0.0233687 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.89898 | −0.167094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.6969i | 1.18901i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.79796i | − 0.102615i | −0.998683 | − | 0.0513075i | \(-0.983661\pi\) | ||||
0.998683 | − | 0.0513075i | \(-0.0163388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.3939 | −2.01349 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.55051 | −0.0879214 | −0.0439607 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439607 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5.59592i | − 0.316300i | −0.987415 | − | 0.158150i | \(-0.949447\pi\) | ||||
0.987415 | − | 0.158150i | \(-0.0505530\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.5959i | − 0.763623i | −0.924240 | − | 0.381811i | \(-0.875300\pi\) | ||||
0.924240 | − | 0.381811i | \(-0.124700\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.89898 | 0.162312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.79796 | −0.546869 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.20204i | − 0.122525i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.4949i | 2.01817i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.44949 | −0.355572 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.0000 | −1.75888 | −0.879440 | − | 0.476011i | \(-0.842082\pi\) | ||||
−0.879440 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 12.0000i | − 0.657596i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.6969i | 1.12743i | 0.825968 | + | 0.563717i | \(0.190629\pi\) | ||||
−0.825968 | + | 0.563717i | \(0.809371\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.4949 | 1.33038 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.44949 | −0.349259 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.4949i | 1.42232i | 0.703030 | + | 0.711160i | \(0.251830\pi\) | ||||
−0.703030 | + | 0.711160i | \(0.748170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.75255 | −0.0938119 | −0.0469060 | − | 0.998899i | \(-0.514936\pi\) | ||||
−0.0469060 | + | 0.998899i | \(0.514936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 25.5959i | − 1.36233i | −0.732128 | − | 0.681167i | \(-0.761473\pi\) | ||||
0.732128 | − | 0.681167i | \(-0.238527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.10102i | 0.0582722i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.6969 | 1.30345 | 0.651727 | − | 0.758453i | \(-0.274045\pi\) | ||||
0.651727 | + | 0.758453i | \(0.274045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | 0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.44949i | − 0.128565i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.1464i | 1.10383i | 0.833899 | + | 0.551917i | \(0.186104\pi\) | ||||
−0.833899 | + | 0.551917i | \(0.813896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.0454 | 1.45999 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.79796 | −0.508685 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.20204i | − 0.217573i | −0.994065 | − | 0.108787i | \(-0.965303\pi\) | ||||
0.994065 | − | 0.108787i | \(-0.0346966\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.30306i | − 0.0671111i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.10102 | 0.159289 | 0.0796444 | − | 0.996823i | \(-0.474622\pi\) | ||||
0.0796444 | + | 0.996823i | \(0.474622\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.40408 | −0.225628 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 27.3485i | − 1.39744i | −0.715395 | − | 0.698721i | \(-0.753753\pi\) | ||||
0.715395 | − | 0.698721i | \(-0.246247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.69694i | 0.442090i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.5959 | 0.689340 | 0.344670 | − | 0.938724i | \(-0.387991\pi\) | ||||
0.344670 | + | 0.938724i | \(0.387991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.404082 | 0.0204353 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 24.0000i | − 1.21064i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 25.5959i | − 1.28462i | −0.766444 | − | 0.642311i | \(-0.777976\pi\) | ||||
0.766444 | − | 0.642311i | \(-0.222024\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.0000 | −0.600751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.7980 | −1.38816 | −0.694082 | − | 0.719896i | \(-0.744189\pi\) | ||||
−0.694082 | + | 0.719896i | \(0.744189\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.89898i | 0.144408i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.00000i | − 0.198273i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5505 | 0.571136 | 0.285568 | − | 0.958358i | \(-0.407818\pi\) | ||||
0.285568 | + | 0.958358i | \(0.407818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0000 | 1.18383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.34847i | 0.361595i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 55.5959i | 2.72254i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.4495 | −0.901317 | −0.450658 | − | 0.892697i | \(-0.648811\pi\) | ||||
−0.450658 | + | 0.892697i | \(0.648811\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.79796 | −0.282575 | −0.141288 | − | 0.989969i | \(-0.545124\pi\) | ||||
−0.141288 | + | 0.989969i | \(0.545124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.3485i | 0.940755i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.34847i | − 0.258831i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.10102 | −0.0531578 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.10102 | −0.438381 | −0.219190 | − | 0.975682i | \(-0.570342\pi\) | ||||
−0.219190 | + | 0.975682i | \(0.570342\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 21.1010i | − 1.01405i | −0.861931 | − | 0.507025i | \(-0.830745\pi\) | ||||
0.861931 | − | 0.507025i | \(-0.169255\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.40408i | 0.210676i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8990 | 1.18836 | 0.594182 | − | 0.804331i | \(-0.297476\pi\) | ||||
0.594182 | + | 0.804331i | \(0.297476\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 24.0000i | − 1.14027i | −0.821549 | − | 0.570137i | \(-0.806890\pi\) | ||||
0.821549 | − | 0.570137i | \(-0.193110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.8990i | 1.36687i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5959 | −0.924789 | −0.462394 | − | 0.886674i | \(-0.653010\pi\) | ||||
−0.462394 | + | 0.886674i | \(0.653010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.34847 | 0.440202 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 21.3031i | − 1.00091i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3939i | 0.907207i | 0.891204 | + | 0.453604i | \(0.149862\pi\) | ||||
−0.891204 | + | 0.453604i | \(0.850138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.3485 | −1.73949 | −0.869746 | − | 0.493500i | \(-0.835717\pi\) | ||||
−0.869746 | + | 0.493500i | \(0.835717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.8990i | 1.15715i | 0.815628 | + | 0.578577i | \(0.196392\pi\) | ||||
−0.815628 | + | 0.578577i | \(0.803608\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.34847i | 0.340047i | 0.985440 | + | 0.170023i | \(0.0543843\pi\) | ||||
−0.985440 | + | 0.170023i | \(0.945616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6969 | −0.678642 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.4949 | 1.12867 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.89898i | 0.133295i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.3939i | 1.34585i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.898979 | −0.0410754 | −0.0205377 | − | 0.999789i | \(-0.506538\pi\) | ||||
−0.0205377 | + | 0.999789i | \(0.506538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.79796 | −0.0819799 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.20204i | − 0.100196i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.8990i | 1.67205i | 0.548690 | + | 0.836026i | \(0.315127\pi\) | ||||
−0.548690 | + | 0.836026i | \(0.684873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.7980 | −0.985738 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6969 | 1.47559 | 0.737796 | − | 0.675024i | \(-0.235867\pi\) | ||||
0.737796 | + | 0.675024i | \(0.235867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.30306i | 0.0586869i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8990i | 0.578598i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.6969 | 1.91138 | 0.955689 | − | 0.294379i | \(-0.0951128\pi\) | ||||
0.955689 | + | 0.294379i | \(0.0951128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.7980 | 1.50998 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4949i | 1.09217i | 0.837729 | + | 0.546087i | \(0.183883\pi\) | ||||
−0.837729 | + | 0.546087i | \(0.816117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 31.3485i | − 1.39223i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.6969 | 1.09467 | 0.547336 | − | 0.836913i | \(-0.315642\pi\) | ||||
0.547336 | + | 0.836913i | \(0.315642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4495 | −0.550733 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.44949i | 0.283648i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.1010 | −1.10181 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.10102 | −0.398723 | −0.199361 | − | 0.979926i | \(-0.563887\pi\) | ||||
−0.199361 | + | 0.979926i | \(0.563887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 25.3939i | − 1.11040i | −0.831718 | − | 0.555198i | \(-0.812642\pi\) | ||||
0.831718 | − | 0.555198i | \(-0.187358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.89898i | − 0.126282i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1918 | 0.964862 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.0454 | 0.956689 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.20204i | − 0.182011i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 38.2020i | − 1.64854i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5959 | −0.756508 | −0.378254 | − | 0.925702i | \(-0.623475\pi\) | ||||
−0.378254 | + | 0.925702i | \(0.623475\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 22.2929i | − 0.956678i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12.0000i | − 0.513083i | −0.966533 | − | 0.256541i | \(-0.917417\pi\) | ||||
0.966533 | − | 0.256541i | \(-0.0825830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.0454 | −0.684801 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.2020 | −0.605027 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 10.8990i | − 0.463472i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 43.7980i | − 1.85578i | −0.372855 | − | 0.927890i | \(-0.621621\pi\) | ||||
0.372855 | − | 0.927890i | \(-0.378379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.30306 | 0.0551136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10102 | 0.0464851 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.2929i | 1.10811i | 0.832479 | + | 0.554056i | \(0.186921\pi\) | ||||
−0.832479 | + | 0.554056i | \(0.813079\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.00000i | 0.377964i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.69694 | 0.364595 | 0.182297 | − | 0.983243i | \(-0.441647\pi\) | ||||
0.182297 | + | 0.983243i | \(0.441647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2020 | −0.426942 | −0.213471 | − | 0.976949i | \(-0.568477\pi\) | ||||
−0.213471 | + | 0.976949i | \(0.568477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.40408i | 0.183983i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 22.4949i | − 0.936475i | −0.883603 | − | 0.468237i | \(-0.844889\pi\) | ||||
0.883603 | − | 0.468237i | \(-0.155111\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −52.8990 | −2.19841 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.8990 | 0.701088 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.79796i | 0.405790i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5505i | 0.889485i | 0.895659 | + | 0.444742i | \(0.146705\pi\) | ||||
−0.895659 | + | 0.444742i | \(0.853295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.5959 | 1.30189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −62.6969 | −2.57901 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.853572i | 0.0350520i | 0.999846 | + | 0.0175260i | \(0.00557898\pi\) | ||||
−0.999846 | + | 0.0175260i | \(0.994421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 63.7980i | 2.61108i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.10102 | 0.290140 | 0.145070 | − | 0.989421i | \(-0.453659\pi\) | ||||
0.145070 | + | 0.989421i | \(0.453659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.65153 | 0.271322 | 0.135661 | − | 0.990755i | \(-0.456684\pi\) | ||||
0.135661 | + | 0.990755i | \(0.456684\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.0908i | 1.79552i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.5959i | 0.633019i | 0.948589 | + | 0.316509i | \(0.102511\pi\) | ||||
−0.948589 | + | 0.316509i | \(0.897489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.10102 | 0.287748 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.89898 | 0.117280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6969i | 0.674383i | 0.941436 | + | 0.337191i | \(0.109477\pi\) | ||||
−0.941436 | + | 0.337191i | \(0.890523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 29.3939i | − 1.18335i | −0.806176 | − | 0.591676i | \(-0.798466\pi\) | ||||
0.806176 | − | 0.591676i | \(-0.201534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.55051 | −0.223094 | −0.111547 | − | 0.993759i | \(-0.535581\pi\) | ||||
−0.111547 | + | 0.993759i | \(0.535581\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.00000i | 0.240385i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0000i | 0.479234i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.79796 | 0.0716893 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.20204 | −0.0876619 | −0.0438309 | − | 0.999039i | \(-0.513956\pi\) | ||||
−0.0438309 | + | 0.999039i | \(0.513956\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 48.9898i | 1.94717i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 0.449490i | − 0.0178094i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.6969 | 1.53083 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.59592 | −0.300021 | −0.150010 | − | 0.988684i | \(-0.547931\pi\) | ||||
−0.150010 | + | 0.988684i | \(0.547931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4.24745i | − 0.167503i | −0.996487 | − | 0.0837515i | \(-0.973310\pi\) | ||||
0.996487 | − | 0.0837515i | \(-0.0266902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.247449i | 0.00972821i | 0.999988 | + | 0.00486411i | \(0.00154830\pi\) | ||||
−0.999988 | + | 0.00486411i | \(0.998452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.34847 | 0.288453 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.7980 | −0.619171 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 15.3939i | − 0.602409i | −0.953560 | − | 0.301204i | \(-0.902611\pi\) | ||||
0.953560 | − | 0.301204i | \(-0.0973887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 37.3485i | 1.45710i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.10102 | −0.198708 | −0.0993538 | − | 0.995052i | \(-0.531678\pi\) | ||||
−0.0993538 | + | 0.995052i | \(0.531678\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.5959 | −1.15115 | −0.575574 | − | 0.817750i | \(-0.695221\pi\) | ||||
−0.575574 | + | 0.817750i | \(0.695221\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 0.494897i | − 0.0192202i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.60612i | − 0.100909i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 32.2020 | 1.24500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.34847 | −0.206475 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 7.30306i | − 0.281512i | −0.990044 | − | 0.140756i | \(-0.955047\pi\) | ||||
0.990044 | − | 0.140756i | \(-0.0449534\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.9444i | 1.11242i | 0.831041 | + | 0.556212i | \(0.187746\pi\) | ||||
−0.831041 | + | 0.556212i | \(0.812254\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.10102 | 0.195759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.40408 | 0.168765 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.2020i | 1.00259i | 0.865276 | + | 0.501297i | \(0.167143\pi\) | ||||
−0.865276 | + | 0.501297i | \(0.832857\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 12.4949i | − 0.476710i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.40408 | 0.167782 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.1464 | −1.56528 | −0.782642 | − | 0.622472i | \(-0.786128\pi\) | ||||
−0.782642 | + | 0.622472i | \(0.786128\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.00000i | − 0.113961i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.20204i | 0.159164i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.69694 | 0.102008 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.6969 | −0.781713 | −0.390856 | − | 0.920452i | \(-0.627821\pi\) | ||||
−0.390856 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.5959i | 0.739074i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.44949i | 0.317776i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.79796 | −0.142635 | −0.0713177 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713177 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.6969 | −1.22623 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.79796i | 0.217135i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.1918i | 1.46365i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.1464 | −1.68368 | −0.841839 | − | 0.539729i | \(-0.818527\pi\) | ||||
−0.841839 | + | 0.539729i | \(0.818527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4495 | −0.538127 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.30306i | 0.122842i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.55051i | − 0.0575052i | −0.999587 | − | 0.0287526i | \(-0.990846\pi\) | ||||
0.999587 | − | 0.0287526i | \(-0.00915351\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.30306 | −0.0481955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 45.3485i | − 1.67498i | −0.546450 | − | 0.837492i | \(-0.684021\pi\) | ||||
0.546450 | − | 0.837492i | \(-0.315979\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.6969i | 0.541369i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.3939 | 1.52270 | 0.761349 | − | 0.648342i | \(-0.224537\pi\) | ||||
0.761349 | + | 0.648342i | \(0.224537\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.39388 | 0.198149 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.5959i | 0.718905i | 0.933163 | + | 0.359452i | \(0.117036\pi\) | ||||
−0.933163 | + | 0.359452i | \(0.882964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 50.6969i | − 1.85490i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8990 | −0.470690 | −0.235345 | − | 0.971912i | \(-0.575622\pi\) | ||||
−0.235345 | + | 0.971912i | \(0.575622\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 6.00000i | − 0.218652i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 22.0000i | − 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.20204 | −0.0799290 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.8434 | 1.80682 | 0.903410 | − | 0.428777i | \(-0.141055\pi\) | ||||
0.903410 | + | 0.428777i | \(0.141055\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8990i | 0.539379i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 3.30306i | − 0.119267i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.1464 | −1.41166 | −0.705828 | − | 0.708383i | \(-0.749425\pi\) | ||||
−0.705828 | + | 0.708383i | \(0.749425\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.30306 | −0.335042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.30306i | − 0.118803i | −0.998234 | − | 0.0594014i | \(-0.981081\pi\) | ||||
0.998234 | − | 0.0594014i | \(-0.0189192\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 9.79796i | − 0.351500i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45.7980 | −1.64088 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8990 | 0.461562 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6969i | 0.381305i | 0.981658 | + | 0.190652i | \(0.0610603\pi\) | ||||
−0.981658 | + | 0.190652i | \(0.938940\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.0000 | −1.70885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0000 | 0.355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.40408i | 0.0853715i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 31.7980i | − 1.12634i | −0.826341 | − | 0.563171i | \(-0.809581\pi\) | ||||
0.826341 | − | 0.563171i | \(-0.190419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.89898 | −0.102559 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.0000 | 0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.4495i | 0.439333i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 32.0908i | − 1.12965i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.5959 | 0.899905 | 0.449952 | − | 0.893053i | \(-0.351441\pi\) | ||||
0.449952 | + | 0.893053i | \(0.351441\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5959 | −0.828565 | −0.414282 | − | 0.910148i | \(-0.635967\pi\) | ||||
−0.414282 | + | 0.910148i | \(0.635967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.19184i | − 0.111943i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 14.2020i | − 0.496867i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.34847 | −0.0471193 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7980 | −0.551353 | −0.275676 | − | 0.961251i | \(-0.588902\pi\) | ||||
−0.275676 | + | 0.961251i | \(0.588902\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 35.1918i | − 1.22671i | −0.789807 | − | 0.613355i | \(-0.789819\pi\) | ||||
0.789807 | − | 0.613355i | \(-0.210181\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.6969i | 1.83245i | 0.400662 | + | 0.916226i | \(0.368780\pi\) | ||||
−0.400662 | + | 0.916226i | \(0.631220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.6969 | 1.34238 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.449490i | 0.0155739i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.55051 | −0.329720 | −0.164860 | − | 0.986317i | \(-0.552717\pi\) | ||||
−0.164860 | + | 0.986317i | \(0.552717\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5959 | −0.710204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4949i | 0.430347i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.00000i | − 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 58.7878 | 2.01759 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.59592 | −0.123266 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 43.1464i | − 1.47731i | −0.674086 | − | 0.738653i | \(-0.735462\pi\) | ||||
0.674086 | − | 0.738653i | \(-0.264538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.85357i | 0.302432i | 0.988501 | + | 0.151216i | \(0.0483189\pi\) | ||||
−0.988501 | + | 0.151216i | \(0.951681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.8434 | −0.813525 | −0.406763 | − | 0.913534i | \(-0.633342\pi\) | ||||
−0.406763 | + | 0.913534i | \(0.633342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.8990 | 0.780395 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.0000i | 1.08929i | 0.838666 | + | 0.544646i | \(0.183336\pi\) | ||||
−0.838666 | + | 0.544646i | \(0.816664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 41.1464i | − 1.39741i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8990 | −0.369723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.60612 | 0.223840 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 15.3031i | − 0.517930i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.6969i | 1.23917i | 0.784931 | + | 0.619584i | \(0.212699\pi\) | ||||
−0.784931 | + | 0.619584i | \(0.787301\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.0908 | 0.880021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.6969 | −0.697298 | −0.348649 | − | 0.937253i | \(-0.613359\pi\) | ||||
−0.348649 | + | 0.937253i | \(0.613359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7980i | 1.00278i | 0.865221 | + | 0.501391i | \(0.167178\pi\) | ||||
−0.865221 | + | 0.501391i | \(0.832822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 30.2929i | − 1.01713i | −0.861022 | − | 0.508567i | \(-0.830175\pi\) | ||||
0.861022 | − | 0.508567i | \(-0.169825\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.79796 | −0.0603016 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.00000 | 0.301511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 31.5959i | − 1.05732i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.989795i | 0.0330483i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.6969 | −0.623578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.40408 | −0.146721 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.10102i | 0.236307i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.10102i | 0.102968i | 0.998674 | + | 0.0514838i | \(0.0163951\pi\) | ||||
−0.998674 | + | 0.0514838i | \(0.983605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.3485 | 0.840756 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.4949 | 1.20913 | 0.604565 | − | 0.796556i | \(-0.293347\pi\) | ||||
0.604565 | + | 0.796556i | \(0.293347\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 16.8990i | − 0.559275i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 9.79796i | − 0.323557i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.40408 | −0.145277 | −0.0726386 | − | 0.997358i | \(-0.523142\pi\) | ||||
−0.0726386 | + | 0.997358i | \(0.523142\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.40408 | −0.145119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.79796i | − 0.190842i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 43.3485i | 1.42375i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.2929 | 1.71567 | 0.857836 | − | 0.513923i | \(-0.171808\pi\) | ||||
0.857836 | + | 0.513923i | \(0.171808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.89898 | −0.160558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.79796i | 0.124340i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9444i | 1.07625i | 0.842866 | + | 0.538123i | \(0.180866\pi\) | ||||
−0.842866 | + | 0.538123i | \(0.819134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.7071 | −0.447316 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.5505 | 1.41971 | 0.709853 | − | 0.704350i | \(-0.248761\pi\) | ||||
0.709853 | + | 0.704350i | \(0.248761\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 8.40408i | − 0.273675i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.404082i | 0.0131309i | 0.999978 | + | 0.00656545i | \(0.00208986\pi\) | ||||
−0.999978 | + | 0.00656545i | \(0.997910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.59592 | 0.181651 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.3031 | −1.07993 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.7980i | 1.41876i | 0.704829 | + | 0.709378i | \(0.251024\pi\) | ||||
−0.704829 | + | 0.709378i | \(0.748976\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7.10102i | − 0.229543i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.79796 | 0.316393 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.5959 | 0.341804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0000i | 0.386695i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 38.8990i | − 1.25091i | −0.780262 | − | 0.625453i | \(-0.784914\pi\) | ||||
0.780262 | − | 0.625453i | \(-0.215086\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.39388 | −0.173276 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.0454 | −1.22094 | −0.610468 | − | 0.792041i | \(-0.709018\pi\) | ||||
−0.610468 | + | 0.792041i | \(0.709018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.6969i | 0.727630i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.20204i | 0.134435i | 0.997738 | + | 0.0672176i | \(0.0214122\pi\) | ||||
−0.997738 | + | 0.0672176i | \(0.978588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.6969 | 1.42706 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 19.3485i | − 0.617120i | −0.951205 | − | 0.308560i | \(-0.900153\pi\) | ||||
0.951205 | − | 0.308560i | \(-0.0998471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.7980i | 0.502855i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.60612 | 0.0828699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 60.0908 | 1.90885 | 0.954424 | − | 0.298455i | \(-0.0964711\pi\) | ||||
0.954424 | + | 0.298455i | \(0.0964711\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 78.3837i | 2.48743i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 20.9444i | − 0.663315i | −0.943400 | − | 0.331658i | \(-0.892392\pi\) | ||||
0.943400 | − | 0.331658i | \(-0.107608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 7700.2.e.j.1849.1 | 4 | ||
5.2 | odd | 4 | 7700.2.a.s.1.1 | 2 | |||
5.3 | odd | 4 | 308.2.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 7700.2.e.j.1849.4 | 4 | ||
15.8 | even | 4 | 2772.2.a.n.1.1 | 2 | |||
20.3 | even | 4 | 1232.2.a.n.1.1 | 2 | |||
35.3 | even | 12 | 2156.2.i.i.177.2 | 4 | |||
35.13 | even | 4 | 2156.2.a.c.1.1 | 2 | |||
35.18 | odd | 12 | 2156.2.i.e.177.1 | 4 | |||
35.23 | odd | 12 | 2156.2.i.e.1145.1 | 4 | |||
35.33 | even | 12 | 2156.2.i.i.1145.2 | 4 | |||
40.3 | even | 4 | 4928.2.a.bq.1.2 | 2 | |||
40.13 | odd | 4 | 4928.2.a.bp.1.1 | 2 | |||
55.43 | even | 4 | 3388.2.a.h.1.2 | 2 | |||
140.83 | odd | 4 | 8624.2.a.bj.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
1232.2.a.n.1.1 | 2 | 20.3 | even | 4 | |||
2156.2.a.c.1.1 | 2 | 35.13 | even | 4 | |||
2156.2.i.e.177.1 | 4 | 35.18 | odd | 12 | |||
2156.2.i.e.1145.1 | 4 | 35.23 | odd | 12 | |||
2156.2.i.i.177.2 | 4 | 35.3 | even | 12 | |||
2156.2.i.i.1145.2 | 4 | 35.33 | even | 12 | |||
2772.2.a.n.1.1 | 2 | 15.8 | even | 4 | |||
3388.2.a.h.1.2 | 2 | 55.43 | even | 4 | |||
4928.2.a.bp.1.1 | 2 | 40.13 | odd | 4 | |||
4928.2.a.bq.1.2 | 2 | 40.3 | even | 4 | |||
7700.2.a.s.1.1 | 2 | 5.2 | odd | 4 | |||
7700.2.e.j.1849.1 | 4 | 1.1 | even | 1 | trivial | ||
7700.2.e.j.1849.4 | 4 | 5.4 | even | 2 | inner | ||
8624.2.a.bj.1.2 | 2 | 140.83 | odd | 4 |