Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1408,2,Mod(703,1408)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1408, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1408.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1408 = 2^{7} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1408.g (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: | \(11.2429366046\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 9x^{2} - 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 703.4 | ||
Root | \(0.500000 + 0.0913379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1408.703 |
Dual form | 1408.2.g.d.703.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1408\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(639\) | \(1025\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.64575i | 1.18322i | 0.806226 | + | 0.591608i | \(0.201507\pi\) | ||||
−0.806226 | + | 0.591608i | \(0.798493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.74166 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | + | 1.41421i | −0.904534 | + | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.74166 | −1.03775 | −0.518875 | − | 0.854850i | \(-0.673649\pi\) | ||||
−0.518875 | + | 0.854850i | \(0.673649\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.64575i | 0.683130i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264i | 1.02899i | 0.857493 | + | 0.514496i | \(0.172021\pi\) | ||||
−0.857493 | + | 0.514496i | \(0.827979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264i | 0.973329i | 0.873589 | + | 0.486664i | \(0.161786\pi\) | ||||
−0.873589 | + | 0.486664i | \(0.838214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.74166 | 0.816497 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.64575i | − | 0.551677i | −0.961204 | − | 0.275839i | \(-0.911044\pi\) | ||
0.961204 | − | 0.275839i | \(-0.0889555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.93725i | 1.42557i | 0.701381 | + | 0.712786i | \(0.252567\pi\) | ||||
−0.701381 | + | 0.712786i | \(0.747433\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | + | 1.41421i | −0.522233 | + | 0.246183i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.89949i | 1.67332i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.93725i | − | 1.30488i | −0.757842 | − | 0.652438i | \(-0.773746\pi\) | ||
0.757842 | − | 0.652438i | \(-0.226254\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.74166 | −0.599145 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.41421i | 0.220863i | 0.993884 | + | 0.110432i | \(0.0352233\pi\) | ||||
−0.993884 | + | 0.110432i | \(0.964777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528i | 1.29399i | 0.762493 | + | 0.646997i | \(0.223975\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 5.29150i | − | 0.788811i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.5830i | − | 1.54369i | −0.635811 | − | 0.771845i | \(-0.719334\pi\) | ||
0.635811 | − | 0.771845i | \(-0.280666\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.24264i | 0.594089i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.29150i | 0.726844i | 0.931625 | + | 0.363422i | \(0.118392\pi\) | ||||
−0.931625 | + | 0.363422i | \(0.881608\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.74166 | − | 7.93725i | −0.504525 | − | 1.07026i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.24264i | 0.561951i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.00000 | −1.17170 | −0.585850 | − | 0.810419i | \(-0.699239\pi\) | ||||
−0.585850 | + | 0.810419i | \(0.699239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.9666 | 1.91628 | 0.958140 | − | 0.286299i | \(-0.0924251\pi\) | ||||
0.958140 | + | 0.286299i | \(0.0924251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.48331 | −0.942809 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.89949i | − | 1.22788i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.00000 | 0.366508 | 0.183254 | − | 0.983066i | \(-0.441337\pi\) | ||||
0.183254 | + | 0.983066i | \(0.441337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 2.64575i | − | 0.318511i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.64575i | 0.313993i | 0.987599 | + | 0.156996i | \(0.0501811\pi\) | ||||
−0.987599 | + | 0.156996i | \(0.949819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.7279i | − | 1.48969i | −0.667237 | − | 0.744845i | \(-0.732523\pi\) | ||
0.667237 | − | 0.744845i | \(-0.267477\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | −0.230940 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.2250 | + | 5.29150i | −1.27920 | + | 0.603023i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.48331 | 0.841939 | 0.420969 | − | 0.907075i | \(-0.361690\pi\) | ||||
0.420969 | + | 0.907075i | \(0.361690\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.48528i | 0.931381i | 0.884948 | + | 0.465690i | \(0.154194\pi\) | ||||
−0.884948 | + | 0.465690i | \(0.845806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2250 | −1.21752 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.0000 | −1.46760 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.93725i | 0.823055i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.2250 | −1.15166 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | −0.304604 | −0.152302 | − | 0.988334i | \(-0.548669\pi\) | ||||
−0.152302 | + | 0.988334i | \(0.548669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | − | 2.82843i | 0.603023 | − | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2250 | −1.11693 | −0.558463 | − | 0.829529i | \(-0.688609\pi\) | ||||
−0.558463 | + | 0.829529i | \(0.688609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8745i | 1.56416i | 0.623177 | + | 0.782081i | \(0.285842\pi\) | ||||
−0.623177 | + | 0.782081i | \(0.714158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.89949i | 0.966092i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.07107i | 0.683586i | 0.939775 | + | 0.341793i | \(0.111034\pi\) | ||||
−0.939775 | + | 0.341793i | \(0.888966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.48331 | 0.716772 | 0.358386 | − | 0.933574i | \(-0.383327\pi\) | ||||
0.358386 | + | 0.933574i | \(0.383327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.93725i | − | 0.753371i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | 0.282216 | 0.141108 | − | 0.989994i | \(-0.454933\pi\) | ||||
0.141108 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.00000 | 0.652753 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.48331 | 0.691833 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.8745i | 1.45521i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | − | 8.48528i | 0.636364 | − | 0.771389i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.41421i | 0.127515i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.93725i | 0.709930i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.7083 | 1.66009 | 0.830046 | − | 0.557695i | \(-0.188314\pi\) | ||||
0.830046 | + | 0.557695i | \(0.188314\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.48528i | 0.747087i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.2132i | 1.85341i | 0.375794 | + | 0.926703i | \(0.377370\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.8745i | 1.37649i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 13.2288i | − | 1.13855i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0000 | −1.28154 | −0.640768 | − | 0.767734i | \(-0.721384\pi\) | ||||
−0.640768 | + | 0.767734i | \(0.721384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.7279i | − | 1.07957i | −0.841803 | − | 0.539784i | \(-0.818506\pi\) | ||
0.841803 | − | 0.539784i | \(-0.181494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 10.5830i | − | 0.891250i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2250 | − | 5.29150i | 0.938679 | − | 0.442498i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.00000 | 0.577350 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.2250 | 0.919586 | 0.459793 | − | 0.888026i | \(-0.347924\pi\) | ||||
0.459793 | + | 0.888026i | \(0.347924\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9666 | 1.21797 | 0.608984 | − | 0.793183i | \(-0.291578\pi\) | ||||
0.608984 | + | 0.793183i | \(0.291578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.48528i | − | 0.685994i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.0000 | −1.68676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.93725i | − | 0.633462i | −0.948515 | − | 0.316731i | \(-0.897415\pi\) | ||
0.948515 | − | 0.316731i | \(-0.102585\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.29150i | 0.419643i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.89949i | − | 0.780189i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | −0.156652 | −0.0783260 | − | 0.996928i | \(-0.524958\pi\) | ||||
−0.0783260 | + | 0.996928i | \(0.524958\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.74166 | − | 7.93725i | −0.291288 | − | 0.617914i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.2250 | −0.868614 | −0.434307 | − | 0.900765i | \(-0.643007\pi\) | ||||
−0.434307 | + | 0.900765i | \(0.643007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 8.48528i | − | 0.648886i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.48331 | −0.565685 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.00000 | −0.676481 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.0000 | 1.56961 | 0.784807 | − | 0.619740i | \(-0.212762\pi\) | ||||
0.784807 | + | 0.619740i | \(0.212762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.8118i | − | 1.76991i | −0.465672 | − | 0.884957i | \(-0.654188\pi\) | ||
0.465672 | − | 0.884957i | \(-0.345812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.9666 | 1.10637 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.0000 | 1.54395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | − | 12.7279i | −0.438763 | − | 0.930758i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.7083 | −1.36083 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.64575i | − | 0.191440i | −0.995408 | − | 0.0957199i | \(-0.969485\pi\) | ||
0.995408 | − | 0.0957199i | \(-0.0305153\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.9706i | 1.22157i | 0.791797 | + | 0.610784i | \(0.209146\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 9.89949i | − | 0.708918i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4499 | 1.59949 | 0.799746 | − | 0.600338i | \(-0.204967\pi\) | ||||
0.799746 | + | 0.600338i | \(0.204967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00000 | 0.211604 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.74166 | −0.261329 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.29150i | 0.367785i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | − | 12.7279i | −0.415029 | − | 0.880409i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.64575i | 0.181284i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.4499 | −1.53107 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 29.6985i | 2.01606i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 12.7279i | − | 0.860073i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.8745i | − | 1.06783i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.93725i | 0.531518i | 0.964040 | + | 0.265759i | \(0.0856225\pi\) | ||||
−0.964040 | + | 0.265759i | \(0.914377\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 15.5563i | − | 1.03251i | −0.856435 | − | 0.516256i | \(-0.827325\pi\) | ||
0.856435 | − | 0.516256i | \(-0.172675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.93725i | 0.524509i | 0.964999 | + | 0.262254i | \(0.0844659\pi\) | ||||
−0.964999 | + | 0.262254i | \(0.915534\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.2250 | + | 5.29150i | −0.738549 | + | 0.348155i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65685i | 0.370593i | 0.982683 | + | 0.185296i | \(0.0593245\pi\) | ||||
−0.982683 | + | 0.185296i | \(0.940675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.0000 | 1.82652 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.48331 | 0.486094 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 16.9706i | − | 1.09317i | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||
0.837404 | − | 0.546585i | \(-0.184072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.5203i | 1.18322i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 15.8745i | − | 1.01007i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.48528i | 0.537733i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.74166 | + | 7.93725i | 0.235236 | + | 0.499011i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.2250 | −0.702935 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.0000 | −0.748539 | −0.374270 | − | 0.927320i | \(-0.622107\pi\) | ||||
−0.374270 | + | 0.927320i | \(0.622107\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 29.6985i | − | 1.84537i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.2250 | 0.692161 | 0.346081 | − | 0.938205i | \(-0.387512\pi\) | ||||
0.346081 | + | 0.938205i | \(0.387512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.0000 | −0.860013 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.00000 | 0.183597 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 5.29150i | − | 0.322629i | −0.986903 | − | 0.161314i | \(-0.948427\pi\) | ||
0.986903 | − | 0.161314i | \(-0.0515733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.7083 | −1.13645 | −0.568224 | − | 0.822874i | \(-0.692369\pi\) | ||||
−0.568224 | + | 0.822874i | \(0.692369\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.0000 | −0.847319 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.00000 | − | 2.82843i | 0.361814 | − | 0.170561i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.48331 | −0.449629 | −0.224814 | − | 0.974402i | \(-0.572178\pi\) | ||||
−0.224814 | + | 0.974402i | \(0.572178\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 15.8745i | − | 0.950382i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.48528i | 0.506189i | 0.967442 | + | 0.253095i | \(0.0814484\pi\) | ||||
−0.967442 | + | 0.253095i | \(0.918552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 16.9706i | − | 1.00880i | −0.863472 | − | 0.504398i | \(-0.831715\pi\) | ||
0.863472 | − | 0.504398i | \(-0.168285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.2250 | −0.664910 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.29150i | 0.312348i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.00000 | −0.175863 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.2250 | −0.655770 | −0.327885 | − | 0.944718i | \(-0.606336\pi\) | ||||
−0.327885 | + | 0.944718i | \(0.606336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 23.8118i | − | 1.38637i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.0000 | − | 7.07107i | 0.870388 | − | 0.410305i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.89949i | 0.572503i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.7490i | 1.82998i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.2250 | −0.644858 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.5980i | 2.26737i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.7279i | − | 0.726421i | −0.931707 | − | 0.363210i | \(-0.881681\pi\) | ||
0.931707 | − | 0.363210i | \(-0.118319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.8745i | 0.903069i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5830i | 0.600107i | 0.953922 | + | 0.300054i | \(0.0970046\pi\) | ||||
−0.953922 | + | 0.300054i | \(0.902995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0000 | −0.960897 | −0.480448 | − | 0.877023i | \(-0.659526\pi\) | ||||
−0.480448 | + | 0.877023i | \(0.659526\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 19.7990i | − | 1.11555i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 13.2288i | − | 0.743001i | −0.928433 | − | 0.371500i | \(-0.878843\pi\) | ||
0.928433 | − | 0.371500i | \(-0.121157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.07107i | 0.394669i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0000 | −1.00155 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.48331 | 0.415100 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.48331 | 0.413828 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 39.5980i | − | 2.18311i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0000 | 1.04433 | 0.522167 | − | 0.852843i | \(-0.325124\pi\) | ||||
0.522167 | + | 0.852843i | \(0.325124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.8745i | 0.869918i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.93725i | 0.433659i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4.24264i | − | 0.231111i | −0.993301 | − | 0.115556i | \(-0.963135\pi\) | ||
0.993301 | − | 0.115556i | \(-0.0368649\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | 0.162938 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.2250 | − | 23.8118i | −0.607866 | − | 1.28948i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.00000 | 0.376867 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.7279i | − | 0.683271i | −0.939833 | − | 0.341635i | \(-0.889019\pi\) | ||
0.939833 | − | 0.341635i | \(-0.110981\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.74166 | −0.200286 | −0.100143 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100143 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.7083 | 0.998574 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.0000 | 1.75641 | 0.878206 | − | 0.478282i | \(-0.158740\pi\) | ||||
0.878206 | + | 0.478282i | \(0.158740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.00000 | −0.371521 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.8745i | 0.840168i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.2250 | 0.592431 | 0.296216 | − | 0.955121i | \(-0.404275\pi\) | ||||
0.296216 | + | 0.955121i | \(0.404275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | − | 8.48528i | 0.367405 | − | 0.445362i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.6749 | 1.76263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.93725i | 0.414321i | 0.978307 | + | 0.207161i | \(0.0664223\pi\) | ||||
−0.978307 | + | 0.207161i | \(0.933578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.82843i | − | 0.147242i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.7990i | 1.02791i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.1916 | −1.35615 | −0.678075 | − | 0.734993i | \(-0.737185\pi\) | ||||
−0.678075 | + | 0.734993i | \(0.737185\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.93725i | 0.409878i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0000 | 0.565032 | 0.282516 | − | 0.959263i | \(-0.408831\pi\) | ||||
0.282516 | + | 0.959263i | \(0.408831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.7083 | 0.958455 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 29.1033i | − | 1.48711i | −0.668676 | − | 0.743554i | \(-0.733139\pi\) | ||
0.668676 | − | 0.743554i | \(-0.266861\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.0000 | − | 29.6985i | −0.713506 | − | 1.51357i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 16.9706i | − | 0.862662i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 34.3948i | − | 1.74388i | −0.489609 | − | 0.871942i | \(-0.662861\pi\) | ||
0.489609 | − | 0.871942i | \(-0.337139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2250 | 0.567671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.2132i | 1.07006i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.7990i | 0.996195i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 15.8745i | − | 0.796719i | −0.917229 | − | 0.398359i | \(-0.869580\pi\) | ||
0.917229 | − | 0.398359i | \(-0.130420\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.8745i | 0.794719i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.0000 | 1.79775 | 0.898877 | − | 0.438201i | \(-0.144384\pi\) | ||||
0.898877 | + | 0.438201i | \(0.144384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29.6985i | − | 1.47939i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.64575i | 0.131468i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.2250 | + | 23.8118i | 0.556401 | + | 1.18031i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.4558i | − | 1.25871i | −0.777118 | − | 0.629355i | \(-0.783319\pi\) | ||
0.777118 | − | 0.629355i | \(-0.216681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.0000 | −0.739895 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.6749 | −1.65703 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.4499 | −1.10202 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 12.7279i | − | 0.623289i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000 | 0.293119 | 0.146560 | − | 0.989202i | \(-0.453180\pi\) | ||||
0.146560 | + | 0.989202i | \(0.453180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 15.8745i | − | 0.773676i | −0.922148 | − | 0.386838i | \(-0.873567\pi\) | ||
0.922148 | − | 0.386838i | \(-0.126433\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.1660i | 1.02913i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8.48528i | − | 0.411597i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 56.0000 | 2.71003 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.2250 | − | 5.29150i | 0.541947 | − | 0.255476i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.6749 | 1.62206 | 0.811032 | − | 0.585002i | \(-0.198906\pi\) | ||||
0.811032 | + | 0.585002i | \(0.198906\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0000 | 1.20142 | 0.600712 | − | 0.799466i | \(-0.294884\pi\) | ||||
0.600712 | + | 0.799466i | \(0.294884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.2250 | 0.536963 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.9666 | −0.714318 | −0.357159 | − | 0.934044i | \(-0.616255\pi\) | ||||
−0.357159 | + | 0.934044i | \(0.616255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0000 | −0.666667 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0000 | −0.712672 | −0.356336 | − | 0.934358i | \(-0.615974\pi\) | ||||
−0.356336 | + | 0.934358i | \(0.615974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.93725i | 0.376262i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.2250 | 0.530923 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.0000 | −0.991051 | −0.495526 | − | 0.868593i | \(-0.665025\pi\) | ||||
−0.495526 | + | 0.868593i | \(0.665025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | − | 4.24264i | −0.0941763 | − | 0.199778i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.9666 | 0.703194 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 37.0405i | − | 1.73649i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.9411i | 1.58770i | 0.608114 | + | 0.793849i | \(0.291926\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 21.2132i | − | 0.990148i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.4499 | 1.04560 | 0.522799 | − | 0.852456i | \(-0.324888\pi\) | ||||
0.522799 | + | 0.852456i | \(0.324888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.8118i | 1.10663i | 0.832973 | + | 0.553313i | \(0.186637\pi\) | ||||
−0.832973 | + | 0.553313i | \(0.813363\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.0000 | −0.973852 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.00000 | −0.138823 | −0.0694117 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694117 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2250 | 0.518321 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 7.93725i | − | 0.365729i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | − | 25.4558i | −0.551761 | − | 1.17046i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 8.48528i | − | 0.389331i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 10.5830i | − | 0.484563i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.6749 | 1.53865 | 0.769323 | − | 0.638860i | \(-0.220594\pi\) | ||||
0.769323 | + | 0.638860i | \(0.220594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.6985i | 1.35413i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 9.89949i | − | 0.450443i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7.93725i | − | 0.360412i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.6863i | 1.79836i | 0.437582 | + | 0.899178i | \(0.355835\pi\) | ||||
−0.437582 | + | 0.899178i | \(0.644165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.5980i | 1.78703i | 0.449032 | + | 0.893516i | \(0.351769\pi\) | ||||
−0.449032 | + | 0.893516i | \(0.648231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.48331 | + | 15.8745i | 0.336350 | + | 0.713506i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.89949i | 0.444053i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0000 | −0.984855 | −0.492428 | − | 0.870353i | \(-0.663890\pi\) | ||||
−0.492428 | + | 0.870353i | \(0.663890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.2250 | −0.501495 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4499 | −1.00099 | −0.500497 | − | 0.865738i | \(-0.666849\pi\) | ||||
−0.500497 | + | 0.865738i | \(0.666849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 29.6985i | − | 1.32157i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.64575i | − | 0.117271i | −0.998279 | − | 0.0586354i | \(-0.981325\pi\) | ||
0.998279 | − | 0.0586354i | \(-0.0186749\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 47.6235i | − | 2.10674i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 21.2132i | − | 0.936586i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.0000 | −1.85074 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9666 | + | 31.7490i | 0.658232 | + | 1.39632i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.2132i | 0.927589i | 0.885943 | + | 0.463794i | \(0.153512\pi\) | ||||
−0.885943 | + | 0.463794i | \(0.846488\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.48331 | −0.326599 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.6749 | −1.46690 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0000 | 0.695652 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.0000 | 0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.29150i | − | 0.229200i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.7083 | −0.808830 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.0000 | 0.906217 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.0000 | + | 9.89949i | −0.904534 | + | 0.426401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.74166 | −0.160866 | −0.0804332 | − | 0.996760i | \(-0.525630\pi\) | ||||
−0.0804332 | + | 0.996760i | \(0.525630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 23.8118i | − | 1.02186i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.7990i | 0.848096i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.48528i | − | 0.362804i | −0.983409 | − | 0.181402i | \(-0.941936\pi\) | ||
0.983409 | − | 0.181402i | \(-0.0580636\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.9333 | −1.27752 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | 1.19068 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.0000 | 0.891400 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.6749 | −1.42685 | −0.713426 | − | 0.700731i | \(-0.752858\pi\) | ||||
−0.713426 | + | 0.700731i | \(0.752858\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 31.7490i | − | 1.34284i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | − | 12.7279i | −0.253320 | − | 0.537373i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.1421i | 0.596020i | 0.954563 | + | 0.298010i | \(0.0963229\pi\) | ||||
−0.954563 | + | 0.298010i | \(0.903677\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.93725i | 0.333923i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.74166 | 0.157135 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.4264i | 1.77861i | 0.457317 | + | 0.889304i | \(0.348810\pi\) | ||||
−0.457317 | + | 0.889304i | \(0.651190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.9706i | 0.710196i | 0.934829 | + | 0.355098i | \(0.115552\pi\) | ||||
−0.934829 | + | 0.355098i | \(0.884448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.64575i | − | 0.110528i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.29150i | 0.220671i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0000 | 1.12402 | 0.562012 | − | 0.827129i | \(-0.310027\pi\) | ||||
0.562012 | + | 0.827129i | \(0.310027\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.9706i | 0.705273i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7490i | 1.31717i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.48331 | − | 15.8745i | −0.309927 | − | 0.657455i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.7990i | 0.818587i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.0000 | 0.990586 | 0.495293 | − | 0.868726i | \(-0.335061\pi\) | ||||
0.495293 | + | 0.868726i | \(0.335061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.6749 | −1.38755 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4499 | 0.923467 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 25.4558i | − | 1.04535i | −0.852533 | − | 0.522673i | \(-0.824935\pi\) | ||
0.852533 | − | 0.522673i | \(-0.175065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.0000 | −1.72183 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5830i | 0.432410i | 0.976348 | + | 0.216205i | \(0.0693679\pi\) | ||||
−0.976348 | + | 0.216205i | \(0.930632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.7279i | − | 0.519183i | −0.965719 | − | 0.259591i | \(-0.916412\pi\) | ||
0.965719 | − | 0.259591i | \(-0.0835879\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.00000 | −0.244339 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.4499 | + | 18.5203i | 0.912720 | + | 0.752956i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.9333 | −1.21495 | −0.607477 | − | 0.794337i | \(-0.707818\pi\) | ||||
−0.607477 | + | 0.794337i | \(0.707818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.5980i | 1.60196i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.4166 | 1.51124 | 0.755621 | − | 0.655010i | \(-0.227335\pi\) | ||||
0.755621 | + | 0.655010i | \(0.227335\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.74166 | −0.150878 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.0000 | 1.08522 | 0.542611 | − | 0.839984i | \(-0.317436\pi\) | ||||
0.542611 | + | 0.839984i | \(0.317436\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.2288i | 0.530852i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.2250 | 0.449719 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | − | 12.7279i | −0.239617 | − | 0.508304i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.6749 | 1.34271 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.8118i | 0.947931i | 0.880543 | + | 0.473966i | \(0.157178\pi\) | ||||
−0.880543 | + | 0.473966i | \(0.842822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.4975i | 1.96425i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.1916 | −1.03775 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.29150i | − | 0.209329i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0000 | −0.829450 | −0.414725 | − | 0.909947i | \(-0.636122\pi\) | ||||
−0.414725 | + | 0.909947i | \(0.636122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.0000 | −1.77463 | −0.887313 | − | 0.461167i | \(-0.847431\pi\) | ||||
−0.887313 | + | 0.461167i | \(0.847431\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.4499 | −0.883966 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.64575i | 0.104015i | 0.998647 | + | 0.0520076i | \(0.0165620\pi\) | ||||
−0.998647 | + | 0.0520076i | \(0.983438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.0000 | − | 12.7279i | 1.05984 | − | 0.499615i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.6985i | 1.16398i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 13.2288i | − | 0.517681i | −0.965920 | − | 0.258841i | \(-0.916660\pi\) | ||
0.965920 | − | 0.258841i | \(-0.0833404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.1249 | −2.19298 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.4558i | 0.993127i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.2843i | 1.10180i | 0.834572 | + | 0.550899i | \(0.185715\pi\) | ||||
−0.834572 | + | 0.550899i | \(0.814285\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8118i | 0.926170i | 0.886314 | + | 0.463085i | \(0.153258\pi\) | ||||
−0.886314 | + | 0.463085i | \(0.846742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 15.8745i | − | 0.616515i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −42.0000 | −1.62869 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.93725i | 0.306872i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.8999 | + | 21.1660i | −1.73334 | + | 0.817105i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.48528i | 0.327084i | 0.986536 | + | 0.163542i | \(0.0522919\pi\) | ||||
−0.986536 | + | 0.163542i | \(0.947708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | 0.384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.6749 | −1.29423 | −0.647116 | − | 0.762391i | \(-0.724025\pi\) | ||||
−0.647116 | + | 0.762391i | \(0.724025\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.2250 | −0.430775 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.5563i | − | 0.596121i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.0000 | 0.688751 | 0.344375 | − | 0.938832i | \(-0.388091\pi\) | ||||
0.344375 | + | 0.938832i | \(0.388091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 39.6863i | − | 1.51633i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.93725i | 0.302825i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 19.7990i | − | 0.754281i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.0000 | −1.25538 | −0.627690 | − | 0.778464i | \(-0.715999\pi\) | ||||
−0.627690 | + | 0.778464i | \(0.715999\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.4499 | − | 10.5830i | 0.852803 | − | 0.402015i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.6749 | 1.27736 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.65685i | 0.213962i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.2250 | 0.423961 | 0.211981 | − | 0.977274i | \(-0.432009\pi\) | ||||
0.211981 | + | 0.977274i | \(0.432009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.6749 | 1.27007 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 28.0000 | 1.05454 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −42.0000 | −1.57957 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.93725i | 0.298090i | 0.988830 | + | 0.149045i | \(0.0476199\pi\) | ||||
−0.988830 | + | 0.149045i | \(0.952380\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.9666 | −0.561292 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0000 | 0.786456 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.0000 | + | 29.6985i | 0.523570 | + | 1.11066i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 13.2288i | − | 0.493349i | −0.969098 | − | 0.246675i | \(-0.920662\pi\) | ||
0.969098 | − | 0.246675i | \(-0.0793379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.3970i | 2.21206i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 16.9706i | − | 0.631142i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.93725i | − | 0.294376i | −0.989109 | − | 0.147188i | \(-0.952978\pi\) | ||
0.989109 | − | 0.147188i | \(-0.0470223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.0000 | −1.33151 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.9333 | 1.10561 | 0.552805 | − | 0.833311i | \(-0.313557\pi\) | ||||
0.552805 | + | 0.833311i | \(0.313557\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.5203i | 0.683130i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.00000 | + | 4.24264i | −0.331519 | + | 0.156280i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 16.9706i | − | 0.624272i | −0.950037 | − | 0.312136i | \(-0.898955\pi\) | ||
0.950037 | − | 0.312136i | \(-0.101045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 15.8745i | − | 0.583165i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.4499 | 0.823609 | 0.411804 | − | 0.911272i | \(-0.364899\pi\) | ||||
0.411804 | + | 0.911272i | \(0.364899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.6985i | 1.08807i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 16.9706i | − | 0.620920i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.4575i | 0.966736i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.8118i | 0.868904i | 0.900695 | + | 0.434452i | \(0.143058\pi\) | ||||
−0.900695 | + | 0.434452i | \(0.856942\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.00000 | −0.109326 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.5980i | 1.44112i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 47.6235i | − | 1.73091i | −0.500990 | − | 0.865453i | \(-0.667031\pi\) | ||
0.500990 | − | 0.865453i | \(-0.332969\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.74166 | + | 7.93725i | 0.135814 | + | 0.288104i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1838i | 1.38416i | 0.721821 | + | 0.692080i | \(0.243306\pi\) | ||||
−0.721821 | + | 0.692080i | \(0.756694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0000 | 1.01367 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.4499 | 0.811679 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6749 | 1.21593 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 38.1838i | − | 1.37694i | −0.725264 | − | 0.688471i | \(-0.758282\pi\) | ||
0.725264 | − | 0.688471i | \(-0.241718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.1660i | − | 0.761288i | −0.924722 | − | 0.380644i | \(-0.875702\pi\) | ||
0.924722 | − | 0.380644i | \(-0.124298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 15.8745i | − | 0.570229i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 29.6985i | − | 1.06543i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.74166 | − | 7.93725i | −0.133887 | − | 0.284017i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.0000 | 0.749522 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.9706i | − | 0.604935i | −0.953160 | − | 0.302468i | \(-0.902190\pi\) | ||
0.953160 | − | 0.302468i | \(-0.0978104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.2250 | 0.399620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.2250 | 0.399114 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0000 | −1.98862 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.0000 | −0.496529 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2288i | 0.468587i | 0.972166 | + | 0.234293i | \(0.0752776\pi\) | ||||
−0.972166 | + | 0.234293i | \(0.924722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.8999 | 1.58844 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.0000 | + | 38.1838i | 0.635206 | + | 1.34748i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.1916 | 0.923133 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 5.29150i | − | 0.186270i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.5269i | 1.14359i | 0.820398 | + | 0.571793i | \(0.193752\pi\) | ||||
−0.820398 | + | 0.571793i | \(0.806248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.9117i | 1.78775i | 0.448315 | + | 0.893876i | \(0.352024\pi\) | ||||
−0.448315 | + | 0.893876i | \(0.647976\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.7083 | −0.656128 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 5.29150i | − | 0.185353i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.0000 | 0.978399 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.4499 | −0.783508 | −0.391754 | − | 0.920070i | \(-0.628132\pi\) | ||||
−0.391754 | + | 0.920070i | \(0.628132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 23.8118i | − | 0.830026i | −0.909816 | − | 0.415013i | \(-0.863777\pi\) | ||
0.909816 | − | 0.415013i | \(-0.136223\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.00000 | − | 2.82843i | 0.208893 | − | 0.0984732i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.24264i | − | 0.147531i | −0.997276 | − | 0.0737655i | \(-0.976498\pi\) | ||
0.997276 | − | 0.0737655i | \(-0.0235016\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 23.8118i | − | 0.827017i | −0.910500 | − | 0.413508i | \(-0.864303\pi\) | ||
0.910500 | − | 0.413508i | \(-0.135697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.48331 | −0.259593 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.6985i | 1.02899i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 29.6985i | − | 1.02776i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 39.6863i | − | 1.37176i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 34.3948i | − | 1.18744i | −0.804672 | − | 0.593720i | \(-0.797659\pi\) | ||
0.804672 | − | 0.593720i | \(-0.202341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.48528i | 0.292249i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.64575i | 0.0910166i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.1916 | − | 31.7490i | 0.899954 | − | 1.09091i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 16.9706i | − | 0.582428i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0000 | −0.719871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.9333 | −1.02490 | −0.512448 | − | 0.858718i | \(-0.671261\pi\) | ||||
−0.512448 | + | 0.858718i | \(0.671261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.4499 | 0.767772 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.6274i | − | 0.772938i | −0.922302 | − | 0.386469i | \(-0.873695\pi\) | ||
0.922302 | − | 0.386469i | \(-0.126305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.0000 | −1.05771 | −0.528853 | − | 0.848713i | \(-0.677378\pi\) | ||||
−0.528853 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.29150i | 0.180334i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.9150i | 1.80125i | 0.434599 | + | 0.900624i | \(0.356890\pi\) | ||||
−0.434599 | + | 0.900624i | \(0.643110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.4499 | + | 10.5830i | −0.761562 | + | 0.359004i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2250 | −0.380344 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.6985i | 1.00399i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.74166 | 0.126347 | 0.0631734 | − | 0.998003i | \(-0.479878\pi\) | ||||
0.0631734 | + | 0.998003i | \(0.479878\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.2250 | −0.378609 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | −0.101073 | −0.0505363 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505363 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 23.8118i | − | 0.800424i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.4499 | −0.753795 | −0.376898 | − | 0.926255i | \(-0.623009\pi\) | ||||
−0.376898 | + | 0.926255i | \(0.623009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 70.0000 | 2.34772 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | + | 1.41421i | −0.100504 | + | 0.0473779i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 44.8999 | 1.50252 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.5608i | 1.85719i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.89949i | 0.330535i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.4499 | −0.747916 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.7490i | 1.05654i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 63.0000 | 2.09419 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.0000 | 1.39459 | 0.697294 | − | 0.716786i | \(-0.254387\pi\) | ||||
0.697294 | + | 0.716786i | \(0.254387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.4499 | 0.744618 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.9150i | 1.75315i | 0.481263 | + | 0.876577i | \(0.340178\pi\) | ||||
−0.481263 | + | 0.876577i | \(0.659822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 25.4558i | −0.397142 | − | 0.842465i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 39.5980i | 1.30907i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 79.3725i | 2.62111i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.9666 | 0.493704 | 0.246852 | − | 0.969053i | \(-0.420604\pi\) | ||||
0.246852 | + | 0.969053i | \(0.420604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 12.7279i | − | 0.419399i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 9.89949i | − | 0.325846i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.8745i | 0.521951i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 31.7490i | − | 1.04277i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.0000 | 0.393707 | 0.196854 | − | 0.980433i | \(-0.436928\pi\) | ||||
0.196854 | + | 0.980433i | \(0.436928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.6985i | 0.973329i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.5830i | 0.346472i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.6749 | − | 15.8745i | 1.10129 | − | 0.519152i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 21.2132i | − | 0.693005i | −0.938049 | − | 0.346503i | \(-0.887369\pi\) | ||
0.938049 | − | 0.346503i | \(-0.112631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0000 | −0.554774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4499 | −0.731847 | −0.365924 | − | 0.930645i | \(-0.619247\pi\) | ||||
−0.365924 | + | 0.930645i | \(0.619247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.74166 | 0.121845 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 49.4975i | − | 1.61015i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.00000 | 0.292461 | 0.146230 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146230 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.6235i | 1.54592i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 13.2288i | − | 0.428972i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 43.8406i | − | 1.42014i | −0.704133 | − | 0.710068i | \(-0.748664\pi\) | ||
0.704133 | − | 0.710068i | \(-0.251336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.00000 | 0.226515 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −56.1249 | −1.81237 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.0000 | −1.03226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 14.1421i | − | 0.455724i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −44.8999 | −1.44538 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.48331 | 0.240647 | 0.120324 | − | 0.992735i | \(-0.461607\pi\) | ||||
0.120324 | + | 0.992735i | \(0.461607\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.0000 | −0.578243 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45.0000 | −1.44412 | −0.722059 | − | 0.691831i | \(-0.756804\pi\) | ||||
−0.722059 | + | 0.691831i | \(0.756804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 47.6235i | − | 1.52674i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.48331 | 0.239658 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.0000 | −0.863807 | −0.431903 | − | 0.901920i | \(-0.642158\pi\) | ||||
−0.431903 | + | 0.901920i | \(0.642158\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | + | 4.24264i | −0.287641 | + | 0.135595i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9666 | −0.477848 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.5203i | 0.590705i | 0.955388 | + | 0.295352i | \(0.0954370\pi\) | ||||
−0.955388 | + | 0.295352i | \(0.904563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.3970i | 1.89254i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 39.5980i | − | 1.26042i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.4499 | 0.713867 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.7490i | − | 1.00854i | −0.863546 | − | 0.504270i | \(-0.831762\pi\) | ||
0.863546 | − | 0.504270i | \(-0.168238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.0000 | 0.602947 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48.6415 | 1.54049 | 0.770247 | − | 0.637746i | \(-0.220133\pi\) | ||||
0.770247 | + | 0.637746i | \(0.220133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.6863i | 1.25562i |
(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 | 1408.2.g.d.703.4 | yes | 4 | |
4.3 | odd | 2 | 1408.2.g.a.703.3 | yes | 4 | ||
8.3 | odd | 2 | inner | 1408.2.g.d.703.1 | yes | 4 | |
8.5 | even | 2 | 1408.2.g.a.703.2 | yes | 4 | ||
11.10 | odd | 2 | inner | 1408.2.g.d.703.3 | yes | 4 | |
16.3 | odd | 4 | 2816.2.e.n.2815.4 | 8 | |||
16.5 | even | 4 | 2816.2.e.n.2815.1 | 8 | |||
16.11 | odd | 4 | 2816.2.e.n.2815.6 | 8 | |||
16.13 | even | 4 | 2816.2.e.n.2815.7 | 8 | |||
44.43 | even | 2 | 1408.2.g.a.703.4 | yes | 4 | ||
88.21 | odd | 2 | 1408.2.g.a.703.1 | ✓ | 4 | ||
88.43 | even | 2 | inner | 1408.2.g.d.703.2 | yes | 4 | |
176.21 | odd | 4 | 2816.2.e.n.2815.2 | 8 | |||
176.43 | even | 4 | 2816.2.e.n.2815.5 | 8 | |||
176.109 | odd | 4 | 2816.2.e.n.2815.8 | 8 | |||
176.131 | even | 4 | 2816.2.e.n.2815.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1408.2.g.a.703.1 | ✓ | 4 | 88.21 | odd | 2 | ||
1408.2.g.a.703.2 | yes | 4 | 8.5 | even | 2 | ||
1408.2.g.a.703.3 | yes | 4 | 4.3 | odd | 2 | ||
1408.2.g.a.703.4 | yes | 4 | 44.43 | even | 2 | ||
1408.2.g.d.703.1 | yes | 4 | 8.3 | odd | 2 | inner | |
1408.2.g.d.703.2 | yes | 4 | 88.43 | even | 2 | inner | |
1408.2.g.d.703.3 | yes | 4 | 11.10 | odd | 2 | inner | |
1408.2.g.d.703.4 | yes | 4 | 1.1 | even | 1 | trivial | |
2816.2.e.n.2815.1 | 8 | 16.5 | even | 4 | |||
2816.2.e.n.2815.2 | 8 | 176.21 | odd | 4 | |||
2816.2.e.n.2815.3 | 8 | 176.131 | even | 4 | |||
2816.2.e.n.2815.4 | 8 | 16.3 | odd | 4 | |||
2816.2.e.n.2815.5 | 8 | 176.43 | even | 4 | |||
2816.2.e.n.2815.6 | 8 | 16.11 | odd | 4 | |||
2816.2.e.n.2815.7 | 8 | 16.13 | even | 4 | |||
2816.2.e.n.2815.8 | 8 | 176.109 | odd | 4 |