Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4800,2,Mod(2401,4800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4800, 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("4800.2401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4800 = 2^{6} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4800.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(38.3281929702\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2401.8 | ||
Root | \(0.228425 - 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4800.2401 |
Dual form | 4800.2.k.p.2401.3 |
$q$-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 \(\left(\mathbb{Z}/4800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(4351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.58258i | 1.08019i | 0.841605 | + | 0.540094i | \(0.181611\pi\) | ||||
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 7.02355i | − 1.94798i | −0.226584 | − | 0.973992i | \(-0.572756\pi\) | ||||
0.226584 | − | 0.973992i | \(-0.427244\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.58258 | −1.83904 | −0.919522 | − | 0.393038i | \(-0.871424\pi\) | ||||
−0.919522 | + | 0.393038i | \(0.871424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.58258i | − 1.05131i | −0.850696 | − | 0.525657i | \(-0.823819\pi\) | ||||
0.850696 | − | 0.525657i | \(-0.176181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.64575i | 0.577350i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.55040 | 0.531795 | 0.265898 | − | 0.964001i | \(-0.414332\pi\) | ||||
0.265898 | + | 0.964001i | \(0.414332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.37780i | 0.812937i | 0.913665 | + | 0.406469i | \(0.133240\pi\) | ||||
−0.913665 | + | 0.406469i | \(0.866760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.28245 | −0.769151 | −0.384576 | − | 0.923094i | \(-0.625652\pi\) | ||||
−0.384576 | + | 0.923094i | \(0.625652\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.58258 | −0.623646 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92820i | 1.13899i | 0.821995 | + | 0.569495i | \(0.192861\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.02355 | 1.12467 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.58258 | −1.49655 | −0.748273 | − | 0.663390i | \(-0.769117\pi\) | ||||
−0.748273 | + | 0.663390i | \(0.769117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.58258i | 0.698836i | 0.936967 | + | 0.349418i | \(0.113621\pi\) | ||||
−0.936967 | + | 0.349418i | \(0.886379\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.29150 | −0.771845 | −0.385922 | − | 0.922531i | \(-0.626117\pi\) | ||||
−0.385922 | + | 0.922531i | \(0.626117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 7.58258i | − 1.06177i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.66930i | 1.32818i | 0.747652 | + | 0.664091i | \(0.231181\pi\) | ||||
−0.747652 | + | 0.664091i | \(0.768819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.58258 | 0.606977 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.16515i | 1.19320i | 0.802538 | + | 0.596601i | \(0.203482\pi\) | ||||
−0.802538 | + | 0.596601i | \(0.796518\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 0.0953502i | − 0.0122083i | −0.999981 | − | 0.00610417i | \(-0.998057\pi\) | ||||
0.999981 | − | 0.00610417i | \(-0.00194303\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.64575 | −0.333333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.58258i | 0.559851i | 0.960022 | + | 0.279925i | \(0.0903097\pi\) | ||||
−0.960022 | + | 0.279925i | \(0.909690\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.55040i | 0.307032i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.5975 | −1.96976 | −0.984881 | − | 0.173233i | \(-0.944579\pi\) | ||||
−0.984881 | + | 0.173233i | \(0.944579\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.47860i | 1.08019i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.29150 | −0.595341 | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||||
−0.297670 | + | 0.954669i | \(0.596210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.0000i | 1.09764i | 0.835940 | + | 0.548821i | \(0.184923\pi\) | ||||
−0.835940 | + | 0.548821i | \(0.815077\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.37780 | −0.469350 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.16515 | 0.335505 | 0.167753 | − | 0.985829i | \(-0.446349\pi\) | ||||
0.167753 | + | 0.985829i | \(0.446349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 18.5826i | − 1.94798i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.28245i | − 0.444070i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.165151 | 0.0167686 | 0.00838429 | − | 0.999965i | \(-0.497331\pi\) | ||||
0.00838429 | + | 0.999965i | \(0.497331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3.58258i | − 0.360062i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9427i | 1.28785i | 0.765090 | + | 0.643924i | \(0.222695\pi\) | ||||
−0.765090 | + | 0.643924i | \(0.777305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0471 | 1.38410 | 0.692051 | − | 0.721848i | \(-0.256707\pi\) | ||||
0.692051 | + | 0.721848i | \(0.256707\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.58258i | − 0.152993i | −0.997070 | − | 0.0764967i | \(-0.975627\pi\) | ||||
0.997070 | − | 0.0764967i | \(-0.0243735\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1244i | 1.16130i | 0.814152 | + | 0.580651i | \(0.197202\pi\) | ||||
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.92820 | −0.657596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1652 | 1.05033 | 0.525165 | − | 0.851001i | \(-0.324004\pi\) | ||||
0.525165 | + | 0.851001i | \(0.324004\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.02355i | 0.649328i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.0616 | −1.83904 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.83485 | −0.166804 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 9.58258i | − 0.864032i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2197 | −1.08432 | −0.542162 | − | 0.840274i | \(-0.682394\pi\) | ||||
−0.542162 | + | 0.840274i | \(0.682394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.58258 | −0.403473 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 5.58258i | − 0.487752i | −0.969806 | − | 0.243876i | \(-0.921581\pi\) | ||||
0.969806 | − | 0.243876i | \(-0.0784190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 12.1244i | − 1.05131i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 5.29150i | − 0.445625i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.1624 | 2.10419 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 5.29150i | − 0.433497i | −0.976228 | − | 0.216748i | \(-0.930455\pi\) | ||||
0.976228 | − | 0.216748i | \(-0.0695451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6748 | −1.19421 | −0.597107 | − | 0.802161i | \(-0.703683\pi\) | ||||
−0.597107 | + | 0.802161i | \(0.703683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.58258 | 0.613015 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73205i | 0.138233i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) | ||||
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.66930 | −0.766826 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.74773 | 0.531795 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.74773i | − 0.450197i | −0.974336 | − | 0.225098i | \(-0.927730\pi\) | ||||
0.974336 | − | 0.225098i | \(-0.0722703\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.0797 | 1.70858 | 0.854290 | − | 0.519797i | \(-0.173993\pi\) | ||||
0.854290 | + | 0.519797i | \(0.173993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −36.3303 | −2.79464 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.58258i | 0.350438i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 6.20520i | − 0.471773i | −0.971781 | − | 0.235886i | \(-0.924201\pi\) | ||||
0.971781 | − | 0.235886i | \(-0.0757993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.16515 | −0.688895 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 18.0000i | − 1.34538i | −0.739923 | − | 0.672692i | \(-0.765138\pi\) | ||||
0.739923 | − | 0.672692i | \(-0.234862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.2433i | 1.43034i | 0.698950 | + | 0.715170i | \(0.253651\pi\) | ||||
−0.698950 | + | 0.715170i | \(0.746349\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0953502 | 0.00704849 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 27.1652i | − 1.98651i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.64575i | − 0.192450i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.03260 | 0.581219 | 0.290609 | − | 0.956842i | \(-0.406142\pi\) | ||||
0.290609 | + | 0.956842i | \(0.406142\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0000 | 1.22369 | 0.611843 | − | 0.790979i | \(-0.290428\pi\) | ||||
0.611843 | + | 0.790979i | \(0.290428\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.56490i | 0.610224i | 0.952316 | + | 0.305112i | \(0.0986939\pi\) | ||||
−0.952316 | + | 0.305112i | \(0.901306\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.9844 | 1.55843 | 0.779215 | − | 0.626757i | \(-0.215618\pi\) | ||||
0.779215 | + | 0.626757i | \(0.215618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.58258 | −0.323230 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.5826i | 0.812937i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.55040 | −0.177265 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.4174 | 1.13562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7477i | 0.808747i | 0.914594 | + | 0.404373i | \(0.132510\pi\) | ||||
−0.914594 | + | 0.404373i | \(0.867490\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 16.5975i | − 1.13724i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3303 | −0.769151 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 53.2566i | 3.58243i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.76465 | −0.653890 | −0.326945 | − | 0.945043i | \(-0.606019\pi\) | ||||
−0.326945 | + | 0.945043i | \(0.606019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 17.5826i | − 1.16700i | −0.812114 | − | 0.583498i | \(-0.801683\pi\) | ||||
0.812114 | − | 0.583498i | \(-0.198317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.9518i | 0.921958i | 0.887411 | + | 0.460979i | \(0.152502\pi\) | ||||
−0.887411 | + | 0.460979i | \(0.847498\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.47860 | −0.623646 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.5826 | −1.41392 | −0.706961 | − | 0.707253i | \(-0.749934\pi\) | ||||
−0.706961 | + | 0.707253i | \(0.749934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 5.29150i | − 0.343720i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.35970 | −0.152636 | −0.0763182 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763182 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4955 | −1.83555 | −0.917777 | − | 0.397097i | \(-0.870018\pi\) | ||||
−0.917777 | + | 0.397097i | \(0.870018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −32.1860 | −2.04794 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.0000 | −0.633724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 27.1652i | − 1.71465i | −0.514776 | − | 0.857325i | \(-0.672125\pi\) | ||||
0.514776 | − | 0.857325i | \(-0.327875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.13701i | 0.574439i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.83485 | −0.301590 | −0.150795 | − | 0.988565i | \(-0.548183\pi\) | ||||
−0.150795 | + | 0.988565i | \(0.548183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3303i | 1.13899i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 4.37780i | − 0.270979i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.1153 | 0.685399 | 0.342700 | − | 0.939445i | \(-0.388659\pi\) | ||||
0.342700 | + | 0.939445i | \(0.388659\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.16515i | 0.193704i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 7.65120i | − 0.466502i | −0.972417 | − | 0.233251i | \(-0.925064\pi\) | ||||
0.972417 | − | 0.233251i | \(-0.0749364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.9035 | −1.69502 | −0.847509 | − | 0.530781i | \(-0.821899\pi\) | ||||
−0.847509 | + | 0.530781i | \(0.821899\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.5826 | 1.12467 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.55945i | 0.213867i | 0.994266 | + | 0.106933i | \(0.0341032\pi\) | ||||
−0.994266 | + | 0.106933i | \(0.965897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.28245 | 0.256384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4174 | −0.979381 | −0.489691 | − | 0.871896i | \(-0.662890\pi\) | ||||
−0.489691 | + | 0.871896i | \(0.662890\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 14.5826i | − 0.866844i | −0.901191 | − | 0.433422i | \(-0.857306\pi\) | ||||
0.901191 | − | 0.433422i | \(-0.142694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.3531 | −1.49655 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.4955 | 2.38209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.165151i | 0.00968135i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.94630i | − 0.522649i | −0.965251 | − | 0.261324i | \(-0.915841\pi\) | ||||
0.965251 | − | 0.261324i | \(-0.0841592\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.58258 | 0.207882 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 17.9129i | − 1.03593i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.1244i | 0.698836i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9427 | −0.743539 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.5826i | 0.832272i | 0.909302 | + | 0.416136i | \(0.136616\pi\) | ||||
−0.909302 | + | 0.416136i | \(0.863384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0471i | 0.799112i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1479 | 1.08578 | 0.542889 | − | 0.839804i | \(-0.317330\pi\) | ||||
0.542889 | + | 0.839804i | \(0.317330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.16515 | −0.461522 | −0.230761 | − | 0.973011i | \(-0.574121\pi\) | ||||
−0.230761 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.9216i | 1.68057i | 0.542149 | + | 0.840283i | \(0.317611\pi\) | ||||
−0.542149 | + | 0.840283i | \(0.682389\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.6838 | −0.878125 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.58258 | 0.0883308 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.7477i | 1.93342i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1244 | −0.670478 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.0000 | −0.771845 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 7.16515i | − 0.393832i | −0.980420 | − | 0.196916i | \(-0.936907\pi\) | ||||
0.980420 | − | 0.196916i | \(-0.0630927\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.92820i | − 0.379663i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.16515 | 0.226890 | 0.113445 | − | 0.993544i | \(-0.463811\pi\) | ||||
0.113445 | + | 0.993544i | \(0.463811\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.1652i | 0.606408i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 15.3422i | − 0.830827i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.3303i | 1.09139i | 0.837985 | + | 0.545694i | \(0.183734\pi\) | ||||
−0.837985 | + | 0.545694i | \(0.816266\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 21.1660i | − 1.13299i | −0.824065 | − | 0.566495i | \(-0.808299\pi\) | ||||
0.824065 | − | 0.566495i | \(-0.191701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.02355 | −0.374890 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.9129 | −0.740508 | −0.370254 | − | 0.928931i | \(-0.620729\pi\) | ||||
−0.370254 | + | 0.928931i | \(0.620729\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 20.0616i | − 1.06177i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.2813 | −1.70374 | −0.851871 | − | 0.523751i | \(-0.824532\pi\) | ||||
−0.851871 | + | 0.523751i | \(0.824532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.00000 | −0.105263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1.83485i | − 0.0963046i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.83645 | 0.148062 | 0.0740308 | − | 0.997256i | \(-0.476414\pi\) | ||||
0.0740308 | + | 0.997256i | \(0.476414\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.58258 | 0.498849 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.5826i | 1.32818i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 36.5638i | − 1.89320i | −0.322410 | − | 0.946600i | \(-0.604493\pi\) | ||||
0.322410 | − | 0.946600i | \(-0.395507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.7477 | 1.58359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.7477i | − 0.808906i | −0.914559 | − | 0.404453i | \(-0.867462\pi\) | ||||
0.914559 | − | 0.404453i | \(-0.132538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 12.2197i | − 0.626034i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.1950 | 1.69619 | 0.848093 | − | 0.529847i | \(-0.177751\pi\) | ||||
0.848093 | + | 0.529847i | \(0.177751\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 4.58258i | − 0.232945i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4.18710i | − 0.212294i | −0.994350 | − | 0.106147i | \(-0.966149\pi\) | ||||
0.994350 | − | 0.106147i | \(-0.0338515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.3386 | −0.977996 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.58258 | 0.281604 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.38685i | − 0.270358i | −0.990821 | − | 0.135179i | \(-0.956839\pi\) | ||||
0.990821 | − | 0.135179i | \(-0.0431610\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.1244 | 0.606977 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.7477 | −1.23584 | −0.617921 | − | 0.786240i | \(-0.712025\pi\) | ||||
−0.617921 | + | 0.786240i | \(0.712025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.0780i | 1.49829i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.8208 | −1.23032 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.33030 | 0.362460 | 0.181230 | − | 0.983441i | \(-0.441992\pi\) | ||||
0.181230 | + | 0.983441i | \(0.441992\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 6.00000i | − 0.295958i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.2487i | 1.19320i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 29.5826i | − 1.44520i | −0.691265 | − | 0.722602i | \(-0.742946\pi\) | ||||
0.691265 | − | 0.722602i | \(-0.257054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 10.5830i | − 0.515784i | −0.966174 | − | 0.257892i | \(-0.916972\pi\) | ||||
0.966174 | − | 0.257892i | \(-0.0830279\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.29150 | 0.257282 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 0.252273i | − 0.0122083i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.1624i | 1.21485i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.723000 | 0.0348257 | 0.0174128 | − | 0.999848i | \(-0.494457\pi\) | ||||
0.0174128 | + | 0.999848i | \(0.494457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.1652 | 1.44964 | 0.724822 | − | 0.688936i | \(-0.241922\pi\) | ||||
0.724822 | + | 0.688936i | \(0.241922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 11.6874i | − 0.559084i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4485 | −1.21459 | −0.607294 | − | 0.794477i | \(-0.707745\pi\) | ||||
−0.607294 | + | 0.794477i | \(0.707745\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.66970i | 0.0793297i | 0.999213 | + | 0.0396649i | \(0.0126290\pi\) | ||||
−0.999213 | + | 0.0396649i | \(0.987371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.29150 | 0.250279 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.66970 | 0.0787979 | 0.0393989 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393989 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 34.3303i | − 1.61655i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 14.6748i | − 0.689480i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.8348 | 0.506833 | 0.253416 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253416 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.58258i | 0.353924i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.28790i | 0.432581i | 0.976329 | + | 0.216290i | \(0.0693958\pi\) | ||||
−0.976329 | + | 0.216290i | \(0.930604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6657 | −0.635099 | −0.317550 | − | 0.948242i | \(-0.602860\pi\) | ||||
−0.317550 | + | 0.948242i | \(0.602860\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 7.58258i | − 0.350880i | −0.984490 | − | 0.175440i | \(-0.943865\pi\) | ||||
0.984490 | − | 0.175440i | \(-0.0561348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.1244i | 0.559851i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.73205 | −0.0798087 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.4174 | −0.754874 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 9.66930i | − 0.442727i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.190700 | 0.00871332 | 0.00435666 | − | 0.999991i | \(-0.498613\pi\) | ||||
0.00435666 | + | 0.999991i | \(0.498613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.6606 | 2.21873 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.74773i | 0.307032i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.74655 | 0.351030 | 0.175515 | − | 0.984477i | \(-0.443841\pi\) | ||||
0.175515 | + | 0.984477i | \(0.443841\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.74773 | 0.259921 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.1652i | 1.04543i | 0.852508 | + | 0.522714i | \(0.175081\pi\) | ||||
−0.852508 | + | 0.522714i | \(0.824919\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 33.1950i | − 1.49503i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.9129 | −1.96976 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 6.58258i | − 0.294677i | −0.989086 | − | 0.147338i | \(-0.952929\pi\) | ||||
0.989086 | − | 0.147338i | \(-0.0470706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.0797i | 0.986449i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.2095 | 1.74827 | 0.874133 | − | 0.485687i | \(-0.161430\pi\) | ||||
0.874133 | + | 0.485687i | \(0.161430\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 36.3303i | − 1.61349i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 22.8027i | − 1.01071i | −0.862911 | − | 0.505356i | \(-0.831361\pi\) | ||||
0.862911 | − | 0.505356i | \(-0.168639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.29150 | 0.234082 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.58258 | −0.202326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 18.9572i | − 0.833737i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.20520 | 0.272378 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.7477 | −0.996596 | −0.498298 | − | 0.867006i | \(-0.666041\pi\) | ||||
−0.498298 | + | 0.867006i | \(0.666041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 35.7477i | − 1.56314i | −0.623818 | − | 0.781569i | \(-0.714419\pi\) | ||||
0.623818 | − | 0.781569i | \(-0.285581\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.4720 | 1.41450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.4955 | −0.717194 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 9.16515i | − 0.397734i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 67.3037i | 2.91525i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0000 | 0.776757 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 24.1534i | − 1.03843i | −0.854642 | − | 0.519217i | \(-0.826224\pi\) | ||||
0.854642 | − | 0.519217i | \(-0.173776\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.2433 | −0.825807 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 40.6606i | − 1.73852i | −0.494353 | − | 0.869261i | \(-0.664595\pi\) | ||||
0.494353 | − | 0.869261i | \(-0.335405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0953502i | 0.00406945i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0616 | 0.854653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0000 | −0.595341 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 10.3923i | − 0.440336i | −0.975462 | − | 0.220168i | \(-0.929339\pi\) | ||||
0.975462 | − | 0.220168i | \(-0.0706606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.1860 | 1.36132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.1652 | 1.14691 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 41.0780i | − 1.73123i | −0.500708 | − | 0.865616i | \(-0.666927\pi\) | ||||
0.500708 | − | 0.865616i | \(-0.333073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.64575 | 0.111111 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.0780 | −1.72208 | −0.861040 | − | 0.508537i | \(-0.830187\pi\) | ||||
−0.861040 | + | 0.508537i | \(0.830187\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0780i | 1.00763i | 0.863810 | + | 0.503817i | \(0.168071\pi\) | ||||
−0.863810 | + | 0.503817i | \(0.831929\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.03260i | 0.335567i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.1652 | −1.83862 | −0.919310 | − | 0.393535i | \(-0.871252\pi\) | ||||
−0.919310 | + | 0.393535i | \(0.871252\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.0000i | 0.706496i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.4575i | 1.09764i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.6410 | −1.43468 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.4174i | 1.42056i | 0.703920 | + | 0.710280i | \(0.251431\pi\) | ||||
−0.703920 | + | 0.710280i | \(0.748569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.6247i | 0.808620i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.56490 | −0.352313 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.41742 | −0.0992717 | −0.0496359 | − | 0.998767i | \(-0.515806\pi\) | ||||
−0.0496359 | + | 0.998767i | \(0.515806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.9844i | 0.899760i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.8208 | 1.01415 | 0.507075 | − | 0.861902i | \(-0.330727\pi\) | ||||
0.507075 | + | 0.861902i | \(0.330727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.00000 | −0.367118 | −0.183559 | − | 0.983009i | \(-0.558762\pi\) | ||||
−0.183559 | + | 0.983009i | \(0.558762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.58258i | − 0.186617i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8745 | 0.644326 | 0.322163 | − | 0.946684i | \(-0.395590\pi\) | ||||
0.322163 | + | 0.946684i | \(0.395590\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.5826 | −0.469350 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.1652i | 1.50354i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9572i | 0.765674i | 0.923816 | + | 0.382837i | \(0.125053\pi\) | ||||
−0.923816 | + | 0.382837i | \(0.874947\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.58258 | 0.224746 | 0.112373 | − | 0.993666i | \(-0.464155\pi\) | ||||
0.112373 | + | 0.993666i | \(0.464155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.9129i | 1.48365i | 0.670591 | + | 0.741827i | \(0.266040\pi\) | ||||
−0.670591 | + | 0.741827i | \(0.733960\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.55040i | − 0.102344i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.37420 | 0.335505 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.4174i | 0.655649i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 52.5336i | − 2.09465i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0025 | 0.955523 | 0.477761 | − | 0.878490i | \(-0.341448\pi\) | ||||
0.477761 | + | 0.878490i | \(0.341448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.7477 | −0.466930 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.5975 | 0.656587 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.33030 | −0.0920414 | −0.0460207 | − | 0.998940i | \(-0.514654\pi\) | ||||
−0.0460207 | + | 0.998940i | \(0.514654\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.33030i | − 0.249643i | −0.992179 | − | 0.124821i | \(-0.960164\pi\) | ||||
0.992179 | − | 0.124821i | \(-0.0398358\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.27340 | 0.128691 | 0.0643453 | − | 0.997928i | \(-0.479504\pi\) | ||||
0.0643453 | + | 0.997928i | \(0.479504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.8348 | −1.28888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 11.3303i | − 0.444070i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8383i | 0.463269i | 0.972803 | + | 0.231634i | \(0.0744073\pi\) | ||||
−0.972803 | + | 0.231634i | \(0.925593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.74773i | 0.340763i | 0.985378 | + | 0.170382i | \(0.0545000\pi\) | ||||
−0.985378 | + | 0.170382i | \(0.945500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.0652i | 0.624864i | 0.949940 | + | 0.312432i | \(0.101144\pi\) | ||||
−0.949940 | + | 0.312432i | \(0.898856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −53.2566 | −2.06832 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1652i | 0.432316i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 9.76465i | − 0.377523i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.341599 | 0.0131873 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.3303 | 1.24624 | 0.623121 | − | 0.782126i | \(-0.285864\pi\) | ||||
0.623121 | + | 0.782126i | \(0.285864\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.4720i | 1.24800i | 0.781424 | + | 0.624000i | \(0.214494\pi\) | ||||
−0.781424 | + | 0.624000i | \(0.785506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.436950 | 0.0167686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.5826 | 0.673766 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 7.16515i | − 0.274167i | −0.990560 | − | 0.137083i | \(-0.956227\pi\) | ||||
0.990560 | − | 0.137083i | \(-0.0437728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.9518 | −0.532293 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 67.9129 | 2.58727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 19.1652i | − 0.729077i | −0.931188 | − | 0.364538i | \(-0.881227\pi\) | ||||
0.931188 | − | 0.364538i | \(-0.118773\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.47860i | − 0.360062i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 72.6606 | 2.75222 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 21.5826i | − 0.816328i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 3.99640i | − 0.150942i | −0.997148 | − | 0.0754710i | \(-0.975954\pi\) | ||||
0.997148 | − | 0.0754710i | \(-0.0240460\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.7490 | 1.19744 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.2432i | 1.28785i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.66025i | 0.325243i | 0.986689 | + | 0.162621i | \(0.0519949\pi\) | ||||
−0.986689 | + | 0.162621i | \(0.948005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.29150 | 0.198447 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.9220 | −0.409031 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.35970i | − 0.0881246i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.4002 | −1.46938 | −0.734690 | − | 0.678403i | \(-0.762672\pi\) | ||||
−0.734690 | + | 0.678403i | \(0.762672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.1652 | 1.38410 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 28.4955i | − 1.05976i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1570 | 0.747580 | 0.373790 | − | 0.927513i | \(-0.378058\pi\) | ||||
0.373790 | + | 0.927513i | \(0.378058\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 34.7477i | − 1.28519i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 3.65480i | − 0.134993i | −0.997720 | − | 0.0674966i | \(-0.978499\pi\) | ||||
0.997720 | − | 0.0674966i | \(-0.0215012\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.4174 | −0.604744 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.33030i | − 0.0857216i | −0.999081 | − | 0.0428608i | \(-0.986353\pi\) | ||||
0.999081 | − | 0.0428608i | \(-0.0136472\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 32.1860i | − 1.18238i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0290 | 0.441301 | 0.220651 | − | 0.975353i | \(-0.429182\pi\) | ||||
0.220651 | + | 0.975353i | \(0.429182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 10.0000i | − 0.365881i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.18710i | − 0.152993i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.6591 | 1.33771 | 0.668855 | − | 0.743393i | \(-0.266785\pi\) | ||||
0.668855 | + | 0.743393i | \(0.266785\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.1652 | 0.989953 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.9518i | 0.507085i | 0.967324 | + | 0.253543i | \(0.0815958\pi\) | ||||
−0.967324 | + | 0.253543i | \(0.918404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.13701 | −0.331652 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0000 | −0.435000 | −0.217500 | − | 0.976060i | \(-0.569790\pi\) | ||||
−0.217500 | + | 0.976060i | \(0.569790\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.0780i | 1.16130i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 64.3719 | 2.32434 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.8348 | 1.14799 | 0.573997 | − | 0.818857i | \(-0.305392\pi\) | ||||
0.573997 | + | 0.818857i | \(0.305392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4.83485i | − 0.174123i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.6983i | 0.780434i | 0.920723 | + | 0.390217i | \(0.127600\pi\) | ||||
−0.920723 | + | 0.390217i | \(0.872400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.3303 | −0.657596 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.9129i | 1.57334i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 59.4618i | − 2.12771i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.37780 | 0.156450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.9129i | 0.959341i | 0.877449 | + | 0.479670i | \(0.159244\pi\) | ||||
−0.877449 | + | 0.479670i | \(0.840756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.1153i | 0.395715i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.5402 | 1.05033 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.669697 | −0.0237816 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 0.381401i | − 0.0135099i | −0.999977 | − | 0.00675495i | \(-0.997850\pi\) | ||||
0.999977 | − | 0.00675495i | \(-0.00215019\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.1232 | 1.41946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.16515 | −0.111835 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.16515i | 0.252853i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.65120 | 0.269335 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.25227 | −0.114344 | −0.0571719 | − | 0.998364i | \(-0.518208\pi\) | ||||
−0.0571719 | + | 0.998364i | \(0.518208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.4174i | 1.45436i | 0.686446 | + | 0.727181i | \(0.259170\pi\) | ||||
−0.686446 | + | 0.727181i | \(0.740830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 27.9035i | − 0.978619i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.0000 | 0.734697 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.5826i | 0.649328i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 36.6591i | − 1.27941i | −0.768620 | − | 0.639706i | \(-0.779056\pi\) | ||||
0.768620 | − | 0.639706i | \(-0.220944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.12795 | 0.283323 | 0.141661 | − | 0.989915i | \(-0.454756\pi\) | ||||
0.141661 | + | 0.989915i | \(0.454756\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.2523i | 0.391280i | 0.980676 | + | 0.195640i | \(0.0626784\pi\) | ||||
−0.980676 | + | 0.195640i | \(0.937322\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.7062i | 1.76110i | 0.473953 | + | 0.880550i | \(0.342827\pi\) | ||||
−0.473953 | + | 0.880550i | \(0.657173\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.55945 | −0.123476 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.28245i | 0.148023i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.86001 | −0.340405 | −0.170203 | − | 0.985409i | \(-0.554442\pi\) | ||||
−0.170203 | + | 0.985409i | \(0.554442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.83485 | 0.339133 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 16.4174i | − 0.565446i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.85455 | −0.166804 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.5826 | 0.500473 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.6697i | 0.605709i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.5348i | 0.840054i | 0.907512 | + | 0.420027i | \(0.137979\pi\) | ||||
−0.907512 | + | 0.420027i | \(0.862021\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.8348 | 0.848342 | 0.424171 | − | 0.905582i | \(-0.360565\pi\) | ||||
0.424171 | + | 0.905582i | \(0.360565\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.16515i | 0.107994i | 0.998541 | + | 0.0539968i | \(0.0171961\pi\) | ||||
−0.998541 | + | 0.0539968i | \(0.982804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 25.3531i | − 0.864032i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.2668 | −0.894133 | −0.447066 | − | 0.894501i | \(-0.647531\pi\) | ||||
−0.447066 | + | 0.894501i | \(0.647531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.4955i | 1.37530i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 18.9572i | − 0.643079i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.1860 | 1.09058 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.165151 | −0.00558953 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 34.7364i | − 1.17296i | −0.809962 | − | 0.586482i | \(-0.800513\pi\) | ||||
0.809962 | − | 0.586482i | \(-0.199487\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.94630 | 0.301751 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3303 | 1.15662 | 0.578309 | − | 0.815818i | \(-0.303713\pi\) | ||||
0.578309 | + | 0.815818i | \(0.303713\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 7.08712i | − 0.238501i | −0.992864 | − | 0.119250i | \(-0.961951\pi\) | ||||
0.992864 | − | 0.119250i | \(-0.0380491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.3205 | 0.581566 | 0.290783 | − | 0.956789i | \(-0.406084\pi\) | ||||
0.290783 | + | 0.956789i | \(0.406084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.3303 | −1.08432 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.58258i | 0.120021i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.2487i | 0.811452i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.9129 | 0.598094 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 18.7477i | − 0.625272i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 73.3182i | − 2.44258i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.1244 | −0.403473 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6697i | 0.453895i | 0.973907 | + | 0.226947i | \(0.0728746\pi\) | ||||
−0.973907 | + | 0.226947i | \(0.927125\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 12.9427i | − 0.429282i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.1051 | 1.26248 | 0.631239 | − | 0.775588i | \(-0.282547\pi\) | ||||
0.631239 | + | 0.775588i | \(0.282547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.8258 | −1.18566 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 14.7701i | − 0.487752i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.8227 | 1.11571 | 0.557853 | − | 0.829940i | \(-0.311625\pi\) | ||||
0.557853 | + | 0.829940i | \(0.311625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.5826 | −0.480512 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 116.573i | 3.83706i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.0471 | −0.461368 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.2432 | 1.58281 | 0.791404 | − | 0.611294i | \(-0.209351\pi\) | ||||
0.791404 | + | 0.611294i | \(0.209351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.1479i | 0.626874i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8348 | −0.451965 | −0.225982 | − | 0.974131i | \(-0.572559\pi\) | ||||
−0.225982 | + | 0.974131i | \(0.572559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 8.16515i | − 0.266460i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 36.6591i | − 1.19505i | −0.801849 | − | 0.597527i | \(-0.796150\pi\) | ||||
0.801849 | − | 0.597527i | \(-0.203850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.4394 | −0.795857 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 41.0780i | − 1.33486i | −0.744674 | − | 0.667428i | \(-0.767395\pi\) | ||||
0.744674 | − | 0.667428i | \(-0.232605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 14.0471i | − 0.455988i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.9216 | −0.970275 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.6606 | −1.57627 | −0.788136 | − | 0.615501i | \(-0.788954\pi\) | ||||
−0.788136 | + | 0.615501i | \(0.788954\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 15.6838i | − 0.506985i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.8745 | −0.512615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6606 | −0.408407 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.58258i | 0.0509978i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.0405 | −1.19114 | −0.595571 | − | 0.803302i | \(-0.703074\pi\) | ||||
−0.595571 | + | 0.803302i | \(0.703074\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.7477 | −1.11626 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000i | 0.577647i | 0.957382 | + | 0.288824i | \(0.0932642\pi\) | ||||
−0.957382 | + | 0.288824i | \(0.906736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.4955 | 0.495743 | 0.247872 | − | 0.968793i | \(-0.420269\pi\) | ||||
0.247872 | + | 0.968793i | \(0.420269\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.3394i | 0.362409i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 12.1244i | − 0.387101i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.4104 | 0.395830 | 0.197915 | − | 0.980219i | \(-0.436583\pi\) | ||||
0.197915 | + | 0.980219i | \(0.436583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 14.0000i | − 0.445625i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.6874i | 0.371638i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.7153 | −1.64279 | −0.821395 | − | 0.570360i | \(-0.806804\pi\) | ||||
−0.821395 | + | 0.570360i | \(0.806804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.16515 | 0.227379 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.6772i | − 1.22492i | −0.790502 | − | 0.612460i | \(-0.790180\pi\) | ||||
0.790502 | − | 0.612460i | \(-0.209820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.92820 | 0.219199 |
(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 | 4800.2.k.p.2401.8 | yes | 8 | |
4.3 | odd | 2 | inner | 4800.2.k.p.2401.1 | ✓ | 8 | |
5.2 | odd | 4 | 4800.2.d.t.1249.7 | 8 | |||
5.3 | odd | 4 | 4800.2.d.s.1249.3 | 8 | |||
5.4 | even | 2 | 4800.2.k.s.2401.2 | yes | 8 | ||
8.3 | odd | 2 | inner | 4800.2.k.p.2401.6 | yes | 8 | |
8.5 | even | 2 | inner | 4800.2.k.p.2401.3 | yes | 8 | |
20.3 | even | 4 | 4800.2.d.t.1249.6 | 8 | |||
20.7 | even | 4 | 4800.2.d.s.1249.2 | 8 | |||
20.19 | odd | 2 | 4800.2.k.s.2401.7 | yes | 8 | ||
40.3 | even | 4 | 4800.2.d.s.1249.7 | 8 | |||
40.13 | odd | 4 | 4800.2.d.t.1249.2 | 8 | |||
40.19 | odd | 2 | 4800.2.k.s.2401.4 | yes | 8 | ||
40.27 | even | 4 | 4800.2.d.t.1249.3 | 8 | |||
40.29 | even | 2 | 4800.2.k.s.2401.5 | yes | 8 | ||
40.37 | odd | 4 | 4800.2.d.s.1249.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4800.2.d.s.1249.2 | 8 | 20.7 | even | 4 | |||
4800.2.d.s.1249.3 | 8 | 5.3 | odd | 4 | |||
4800.2.d.s.1249.6 | 8 | 40.37 | odd | 4 | |||
4800.2.d.s.1249.7 | 8 | 40.3 | even | 4 | |||
4800.2.d.t.1249.2 | 8 | 40.13 | odd | 4 | |||
4800.2.d.t.1249.3 | 8 | 40.27 | even | 4 | |||
4800.2.d.t.1249.6 | 8 | 20.3 | even | 4 | |||
4800.2.d.t.1249.7 | 8 | 5.2 | odd | 4 | |||
4800.2.k.p.2401.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
4800.2.k.p.2401.3 | yes | 8 | 8.5 | even | 2 | inner | |
4800.2.k.p.2401.6 | yes | 8 | 8.3 | odd | 2 | inner | |
4800.2.k.p.2401.8 | yes | 8 | 1.1 | even | 1 | trivial | |
4800.2.k.s.2401.2 | yes | 8 | 5.4 | even | 2 | ||
4800.2.k.s.2401.4 | yes | 8 | 40.19 | odd | 2 | ||
4800.2.k.s.2401.5 | yes | 8 | 40.29 | even | 2 | ||
4800.2.k.s.2401.7 | yes | 8 | 20.19 | odd | 2 |