Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(431,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.h (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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 431.2 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.431 |
Dual form | 720.2.h.a.431.8 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.44949i | − 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.91359 | 1.78301 | 0.891507 | − | 0.453006i | \(-0.149648\pi\) | ||||
0.891507 | + | 0.453006i | \(0.149648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.24264 | −1.73140 | −0.865699 | − | 0.500566i | \(-0.833125\pi\) | ||||
−0.865699 | + | 0.500566i | \(0.833125\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.89898i | − 1.12390i | −0.827170 | − | 0.561951i | \(-0.810051\pi\) | ||||
0.827170 | − | 0.561951i | \(-0.189949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.43488 | −0.299193 | −0.149596 | − | 0.988747i | \(-0.547797\pi\) | ||||
−0.149596 | + | 0.988747i | \(0.547797\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.00000i | − 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.43488i | − 0.257712i | −0.991663 | − | 0.128856i | \(-0.958870\pi\) | ||||
0.991663 | − | 0.128856i | \(-0.0411304\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.44949 | −0.414039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24264 | −0.368688 | −0.184344 | − | 0.982862i | \(-0.559016\pi\) | ||||
−0.184344 | + | 0.982862i | \(0.559016\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 4.24264i | − 0.662589i | −0.943527 | − | 0.331295i | \(-0.892515\pi\) | ||||
0.943527 | − | 0.331295i | \(-0.107485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.8272i | − 1.80363i | −0.432124 | − | 0.901814i | \(-0.642236\pi\) | ||||
0.432124 | − | 0.901814i | \(-0.357764\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.8272 | 1.72517 | 0.862586 | − | 0.505911i | \(-0.168843\pi\) | ||||
0.862586 | + | 0.505911i | \(0.168843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528i | 1.16554i | 0.812636 | + | 0.582772i | \(0.198032\pi\) | ||||
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 5.91359i | − 0.797388i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.91359 | 0.769884 | 0.384942 | − | 0.922941i | \(-0.374221\pi\) | ||||
0.384942 | + | 0.922941i | \(0.374221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.48528 | −0.830355 | −0.415178 | − | 0.909740i | \(-0.636281\pi\) | ||||
−0.415178 | + | 0.909740i | \(0.636281\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.24264i | 0.774304i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.92820i | 0.846415i | 0.906033 | + | 0.423207i | \(0.139096\pi\) | ||||
−0.906033 | + | 0.423207i | \(0.860904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.86976 | 0.340577 | 0.170289 | − | 0.985394i | \(-0.445530\pi\) | ||||
0.170289 | + | 0.985394i | \(0.445530\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.48528 | 0.759045 | 0.379522 | − | 0.925183i | \(-0.376088\pi\) | ||||
0.379522 | + | 0.925183i | \(0.376088\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 14.4853i | − 1.65075i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.36308i | 0.940920i | 0.882421 | + | 0.470460i | \(0.155912\pi\) | ||||
−0.882421 | + | 0.470460i | \(0.844088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.6969 | −1.61320 | −0.806599 | − | 0.591099i | \(-0.798694\pi\) | ||||
−0.806599 | + | 0.591099i | \(0.798694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.75736i | 0.822278i | 0.911573 | + | 0.411139i | \(0.134869\pi\) | ||||
−0.911573 | + | 0.411139i | \(0.865131\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2913i | 1.60296i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.89898 | −0.502625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.48528 | 0.658481 | 0.329240 | − | 0.944246i | \(-0.393207\pi\) | ||||
0.329240 | + | 0.944246i | \(0.393207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 14.4853i | − 1.44134i | −0.693279 | − | 0.720670i | \(-0.743834\pi\) | ||||
0.693279 | − | 0.720670i | \(-0.256166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 11.4069i | − 1.12396i | −0.827152 | − | 0.561978i | \(-0.810040\pi\) | ||||
0.827152 | − | 0.561978i | \(-0.189960\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.95743 | −0.865947 | −0.432974 | − | 0.901407i | \(-0.642536\pi\) | ||||
−0.432974 | + | 0.901407i | \(0.642536\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4853 | −1.00431 | −0.502154 | − | 0.864778i | \(-0.667459\pi\) | ||||
−0.502154 | + | 0.864778i | \(0.667459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.48528i | 0.798228i | 0.916901 | + | 0.399114i | \(0.130682\pi\) | ||||
−0.916901 | + | 0.399114i | \(0.869318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.43488i | 0.133803i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.9706 | 2.17914 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34847i | 0.652071i | 0.945357 | + | 0.326036i | \(0.105713\pi\) | ||||
−0.945357 | + | 0.326036i | \(0.894287\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.6105 | 1.80075 | 0.900375 | − | 0.435114i | \(-0.143292\pi\) | ||||
0.900375 | + | 0.435114i | \(0.143292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | −1.04053 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.4853i | 1.75018i | 0.483964 | + | 0.875088i | \(0.339197\pi\) | ||||
−0.483964 | + | 0.875088i | \(0.660803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.33386i | 0.537231i | 0.963248 | + | 0.268615i | \(0.0865661\pi\) | ||||
−0.963248 | + | 0.268615i | \(0.913434\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −36.9164 | −3.08711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.4853i | 1.18668i | 0.804952 | + | 0.593340i | \(0.202191\pi\) | ||||
−0.804952 | + | 0.593340i | \(0.797809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1903i | 1.64306i | 0.570165 | + | 0.821530i | \(0.306879\pi\) | ||||
−0.570165 | + | 0.821530i | \(0.693121\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.43488 | −0.115252 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.75736 | 0.778722 | 0.389361 | − | 0.921085i | \(-0.372696\pi\) | ||||
0.389361 | + | 0.921085i | \(0.372696\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.51472i | 0.276999i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.76874i | 0.608494i | 0.952593 | + | 0.304247i | \(0.0984049\pi\) | ||||
−0.952593 | + | 0.304247i | \(0.901595\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.43488 | 0.111034 | 0.0555171 | − | 0.998458i | \(-0.482319\pi\) | ||||
0.0555171 | + | 0.998458i | \(0.482319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.9706 | 1.99774 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.51472i | − 0.267219i | −0.991034 | − | 0.133610i | \(-0.957343\pi\) | ||||
0.991034 | − | 0.133610i | \(-0.0426568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.44949i | 0.185164i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.8710 | −1.11151 | −0.555756 | − | 0.831345i | \(-0.687571\pi\) | ||||
−0.555756 | + | 0.831345i | \(0.687571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.4853 | 1.37400 | 0.687000 | − | 0.726657i | \(-0.258927\pi\) | ||||
0.687000 | + | 0.726657i | \(0.258927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.24264i | 0.164882i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6969 | 1.06343 | 0.531717 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531717 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 10.9706i | − 0.781620i | −0.920471 | − | 0.390810i | \(-0.872195\pi\) | ||||
0.920471 | − | 0.390810i | \(-0.127805\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.46410i | 0.245564i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) | ||||
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.6969 | −1.03152 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.24264 | −0.296319 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 28.9706i | − 2.00394i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.8272 | −0.806607 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.51472 | −0.238595 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 4.47871i | − 0.299917i | −0.988692 | − | 0.149958i | \(-0.952086\pi\) | ||||
0.988692 | − | 0.149958i | \(-0.0479140\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.6544 | 1.57000 | 0.784998 | − | 0.619499i | \(-0.212664\pi\) | ||||
0.784998 | + | 0.619499i | \(0.212664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0000i | 1.57229i | 0.618041 | + | 0.786146i | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 11.8272i | − 0.771520i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8272 | 0.765037 | 0.382518 | − | 0.923948i | \(-0.375057\pi\) | ||||
0.382518 | + | 0.923948i | \(0.375057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9706 | −0.835507 | −0.417754 | − | 0.908560i | \(-0.637183\pi\) | ||||
−0.417754 | + | 0.908560i | \(0.637183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.00000i | − 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.5826i | 1.94592i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.8710 | −0.938650 | −0.469325 | − | 0.883025i | \(-0.655503\pi\) | ||||
−0.469325 | + | 0.883025i | \(0.655503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.48528 | −0.533465 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 3.51472i | − 0.219242i | −0.993973 | − | 0.109621i | \(-0.965036\pi\) | ||||
0.993973 | − | 0.109621i | \(-0.0349637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.49333i | 0.341339i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.3497 | 1.19316 | 0.596578 | − | 0.802555i | \(-0.296527\pi\) | ||||
0.596578 | + | 0.802555i | \(0.296527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.48528 | 0.521247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9706i | 0.668887i | 0.942416 | + | 0.334444i | \(0.108548\pi\) | ||||
−0.942416 | + | 0.334444i | \(0.891452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 6.33386i | − 0.384754i | −0.981321 | − | 0.192377i | \(-0.938380\pi\) | ||||
0.981321 | − | 0.192377i | \(-0.0616197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.91359 | −0.356603 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.2426 | 0.855757 | 0.427879 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427879 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 4.24264i | − 0.253095i | −0.991961 | − | 0.126547i | \(-0.959610\pi\) | ||||
0.991961 | − | 0.126547i | \(-0.0403896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.6544i | − 1.40611i | −0.711137 | − | 0.703053i | \(-0.751820\pi\) | ||||
0.711137 | − | 0.703053i | \(-0.248180\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3923 | −0.613438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.9706i | 1.34195i | 0.741478 | + | 0.670977i | \(0.234125\pi\) | ||||
−0.741478 | + | 0.670977i | \(0.765875\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 5.91359i | − 0.344303i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.95743 | 0.518021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.9706 | −1.66984 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.48528i | 0.371346i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 23.6544i | − 1.35003i | −0.737806 | − | 0.675013i | \(-0.764138\pi\) | ||||
0.737806 | − | 0.675013i | \(-0.235862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.95743 | 0.507929 | 0.253965 | − | 0.967214i | \(-0.418265\pi\) | ||||
0.253965 | + | 0.967214i | \(0.418265\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 34.9706i | − 1.96414i | −0.188510 | − | 0.982071i | \(-0.560366\pi\) | ||||
0.188510 | − | 0.982071i | \(-0.439634\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 35.4815i | − 1.98659i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.24264 | 0.346279 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 28.9706i | − 1.59720i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.02922i | 0.111536i | 0.998444 | + | 0.0557681i | \(0.0177608\pi\) | ||||
−0.998444 | + | 0.0557681i | \(0.982239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.92820 | 0.378528 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.4558 | −1.49562 | −0.747808 | − | 0.663916i | \(-0.768893\pi\) | ||||
−0.747808 | + | 0.663916i | \(0.768893\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.48528i | − 0.459504i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 19.5959i | − 1.05808i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7846 | 1.11578 | 0.557888 | − | 0.829916i | \(-0.311612\pi\) | ||||
0.557888 | + | 0.829916i | \(0.311612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.4853 | −0.989494 | −0.494747 | − | 0.869037i | \(-0.664739\pi\) | ||||
−0.494747 | + | 0.869037i | \(0.664739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 12.0000i | − 0.638696i | −0.947638 | − | 0.319348i | \(-0.896536\pi\) | ||||
0.947638 | − | 0.319348i | \(-0.103464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.86976i | − 0.152311i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.95743 | −0.472755 | −0.236377 | − | 0.971661i | \(-0.575960\pi\) | ||||
−0.236377 | + | 0.971661i | \(0.575960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 6.48528i | − 0.339455i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 28.9736i | − 1.51241i | −0.654335 | − | 0.756205i | \(-0.727051\pi\) | ||||
0.654335 | − | 0.756205i | \(-0.272949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7846 | 1.07908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.72792 | 0.141246 | 0.0706232 | − | 0.997503i | \(-0.477501\pi\) | ||||
0.0706232 | + | 0.997503i | \(0.477501\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.4558i | 1.92907i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3205i | 0.889695i | 0.895606 | + | 0.444847i | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.8272 | 0.604341 | 0.302170 | − | 0.953254i | \(-0.402289\pi\) | ||||
0.302170 | + | 0.953254i | \(0.402289\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.4853 | −0.738238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.9706i | 1.16465i | 0.812955 | + | 0.582327i | \(0.197858\pi\) | ||||
−0.812955 | + | 0.582327i | \(0.802142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.36308 | 0.420792 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.7279 | −0.538419 | −0.269209 | − | 0.963082i | \(-0.586762\pi\) | ||||
−0.269209 | + | 0.963082i | \(0.586762\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 28.2426i | − 1.41037i | −0.709023 | − | 0.705185i | \(-0.750864\pi\) | ||||
0.709023 | − | 0.705185i | \(-0.249136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.95743i | 0.446201i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.2621 | −0.657376 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.9706 | −0.938034 | −0.469017 | − | 0.883189i | \(-0.655392\pi\) | ||||
−0.469017 | + | 0.883189i | \(0.655392\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 14.4853i | − 0.712774i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.6969i | 0.721444i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.04384 | 0.148701 | 0.0743506 | − | 0.997232i | \(-0.476312\pi\) | ||||
0.0743506 | + | 0.997232i | \(0.476312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9706 | 1.31446 | 0.657232 | − | 0.753688i | \(-0.271727\pi\) | ||||
0.657232 | + | 0.753688i | \(0.271727\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.8856i | 0.768760i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.8272 | 0.569695 | 0.284848 | − | 0.958573i | \(-0.408057\pi\) | ||||
0.284848 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4558 | −1.12722 | −0.563608 | − | 0.826042i | \(-0.690587\pi\) | ||||
−0.563608 | + | 0.826042i | \(0.690587\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.02944i | 0.336264i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 16.1318i | − 0.769930i | −0.922931 | − | 0.384965i | \(-0.874214\pi\) | ||||
0.922931 | − | 0.384965i | \(-0.125786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.86976 | 0.136346 | 0.0681731 | − | 0.997674i | \(-0.478283\pi\) | ||||
0.0681731 | + | 0.997674i | \(0.478283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.75736 | 0.367734 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 0.727922i | − 0.0343528i | −0.999852 | − | 0.0171764i | \(-0.994532\pi\) | ||||
0.999852 | − | 0.0171764i | \(-0.00546768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 25.0892i | − 1.18141i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.2913 | 0.716866 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.5147 | −0.819304 | −0.409652 | − | 0.912242i | \(-0.634350\pi\) | ||||
−0.409652 | + | 0.912242i | \(0.634350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4558i | 0.906149i | 0.891473 | + | 0.453074i | \(0.149673\pi\) | ||||
−0.891473 | + | 0.453074i | \(0.850327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.37769i | 0.435818i | 0.975969 | + | 0.217909i | \(0.0699237\pi\) | ||||
−0.975969 | + | 0.217909i | \(0.930076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.8272 | −0.547297 | −0.273648 | − | 0.961830i | \(-0.588230\pi\) | ||||
−0.273648 | + | 0.961830i | \(0.588230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.9706 | 0.783628 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 69.9411i | − 3.21590i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898i | 0.224781i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.7846 | 0.949673 | 0.474837 | − | 0.880074i | \(-0.342507\pi\) | ||||
0.474837 | + | 0.880074i | \(0.342507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0000 | 0.638345 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 6.48528i | − 0.294481i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 35.0613i | − 1.58878i | −0.607409 | − | 0.794389i | \(-0.707791\pi\) | ||||
0.607409 | − | 0.794389i | \(-0.292209\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7408 | −0.800630 | −0.400315 | − | 0.916378i | \(-0.631099\pi\) | ||||
−0.400315 | + | 0.916378i | \(0.631099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 7.02944i | − 0.315313i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 29.7420i | − 1.33144i | −0.746203 | − | 0.665718i | \(-0.768125\pi\) | ||||
0.746203 | − | 0.665718i | \(-0.231875\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.08767 | −0.271436 | −0.135718 | − | 0.990748i | \(-0.543334\pi\) | ||||
−0.135718 | + | 0.990748i | \(0.543334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.4853 | −0.644587 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.4853i | 0.642049i | 0.947071 | + | 0.321024i | \(0.104027\pi\) | ||||
−0.947071 | + | 0.321024i | \(0.895973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 15.8856i | − 0.702739i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4069 | −0.502649 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69.9411 | 3.07601 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.2132i | 1.45510i | 0.686056 | + | 0.727548i | \(0.259340\pi\) | ||||
−0.686056 | + | 0.727548i | \(0.740660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.8856i | 0.694630i | 0.937749 | + | 0.347315i | \(0.112907\pi\) | ||||
−0.937749 | + | 0.347315i | \(0.887093\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9411 | −0.910484 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.4853i | 1.14720i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.95743i | 0.387263i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.91359 | 0.254716 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.51472 | −0.237096 | −0.118548 | − | 0.992948i | \(-0.537824\pi\) | ||||
−0.118548 | + | 0.992948i | \(0.537824\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.4853i | 0.449140i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6385i | 0.454869i | 0.973793 | + | 0.227435i | \(0.0730338\pi\) | ||||
−0.973793 | + | 0.227435i | \(0.926966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.3939 | −1.25222 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.4853 | 0.871123 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8.48528i | − 0.359533i | −0.983709 | − | 0.179766i | \(-0.942466\pi\) | ||||
0.983709 | − | 0.179766i | \(-0.0575342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 73.8329i | 3.12280i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.5241 | 1.11786 | 0.558929 | − | 0.829215i | \(-0.311212\pi\) | ||||
0.558929 | + | 0.829215i | \(0.311212\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.48528 | 0.356978 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2426i | 1.18399i | 0.805941 | + | 0.591997i | \(0.201660\pi\) | ||||
−0.805941 | + | 0.591997i | \(0.798340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 25.6836i | − 1.07482i | −0.843320 | − | 0.537412i | \(-0.819402\pi\) | ||||
0.843320 | − | 0.537412i | \(-0.180598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.43488 | 0.0598385 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.4853 | −1.26912 | −0.634559 | − | 0.772874i | \(-0.718818\pi\) | ||||
−0.634559 | + | 0.772874i | \(0.718818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000i | 1.49353i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.1785i | 2.07818i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.6969 | −0.606608 | −0.303304 | − | 0.952894i | \(-0.598090\pi\) | ||||
−0.303304 | + | 0.952894i | \(0.598090\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.02944 | −0.289643 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 20.4853i | − 0.841230i | −0.907239 | − | 0.420615i | \(-0.861814\pi\) | ||||
0.907239 | − | 0.420615i | \(-0.138186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.4815 | −1.44974 | −0.724868 | − | 0.688887i | \(-0.758099\pi\) | ||||
−0.724868 | + | 0.688887i | \(0.758099\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 23.9706i | − 0.974542i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.1623i | 1.22425i | 0.790761 | + | 0.612125i | \(0.209685\pi\) | ||||
−0.790761 | + | 0.612125i | \(0.790315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −73.8329 | −2.98696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2132 | 0.937572 | 0.468786 | − | 0.883312i | \(-0.344691\pi\) | ||||
0.468786 | + | 0.883312i | \(0.344691\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.9411i | 0.883316i | 0.897183 | + | 0.441658i | \(0.145610\pi\) | ||||
−0.897183 | + | 0.441658i | \(0.854390\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 0.594346i | − 0.0238888i | −0.999929 | − | 0.0119444i | \(-0.996198\pi\) | ||||
0.999929 | − | 0.0119444i | \(-0.00380211\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.0016 | 0.761282 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2328i | 0.447172i | 0.974684 | + | 0.223586i | \(0.0717764\pi\) | ||||
−0.974684 | + | 0.223586i | \(0.928224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.34847 | 0.291615 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.24264 | −0.247342 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 24.7279i | − 0.976694i | −0.872649 | − | 0.488347i | \(-0.837600\pi\) | ||||
0.872649 | − | 0.488347i | \(-0.162400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6969i | 0.579591i | 0.957089 | + | 0.289795i | \(0.0935872\pi\) | ||||
−0.957089 | + | 0.289795i | \(0.906413\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.8272 | 0.464975 | 0.232487 | − | 0.972599i | \(-0.425314\pi\) | ||||
0.232487 | + | 0.972599i | \(0.425314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.9706 | 1.37271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.0294i | 0.509881i | 0.966957 | + | 0.254941i | \(0.0820559\pi\) | ||||
−0.966957 | + | 0.254941i | \(0.917944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 20.6105i | − 0.805320i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.6531 | 0.453940 | 0.226970 | − | 0.973902i | \(-0.427118\pi\) | ||||
0.226970 | + | 0.973902i | \(0.427118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.5147 | −0.525662 | −0.262831 | − | 0.964842i | \(-0.584656\pi\) | ||||
−0.262831 | + | 0.964842i | \(0.584656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000i | 0.465340i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.60927i | 0.333352i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.3513 | −1.48054 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.4853 | 1.32931 | 0.664655 | − | 0.747150i | \(-0.268579\pi\) | ||||
0.664655 | + | 0.747150i | \(0.268579\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 27.9411i | − 1.07386i | −0.843625 | − | 0.536932i | \(-0.819583\pi\) | ||||
0.843625 | − | 0.536932i | \(-0.180417\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 15.8856i | − 0.609635i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.2211 | 1.57728 | 0.788640 | − | 0.614855i | \(-0.210786\pi\) | ||||
0.788640 | + | 0.614855i | \(0.210786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.4853 | 0.782702 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 52.9706i | − 2.01802i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6969i | 0.559098i | 0.960131 | + | 0.279549i | \(0.0901849\pi\) | ||||
−0.960131 | + | 0.279549i | \(0.909815\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.33386 | 0.240257 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.4558i | 0.734837i | 0.930056 | + | 0.367419i | \(0.119758\pi\) | ||||
−0.930056 | + | 0.367419i | \(0.880242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9867i | 0.414369i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.4815 | −1.33442 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.9411 | 1.19957 | 0.599787 | − | 0.800160i | \(-0.295252\pi\) | ||||
0.599787 | + | 0.800160i | \(0.295252\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.05887i | 0.0771055i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.9164i | 1.38060i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.3513 | −1.43026 | −0.715131 | − | 0.698990i | \(-0.753633\pi\) | ||||
−0.715131 | + | 0.698990i | \(0.753633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.9411 | −1.04058 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.00000i | 0.222834i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 10.5664i | − 0.391886i | −0.980615 | − | 0.195943i | \(-0.937223\pi\) | ||||
0.980615 | − | 0.195943i | \(-0.0627767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.7574 | 0.655883 | 0.327942 | − | 0.944698i | \(-0.393645\pi\) | ||||
0.327942 | + | 0.944698i | \(0.393645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.9706i | 1.50917i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.08767i | 0.223939i | 0.993712 | + | 0.111969i | \(0.0357158\pi\) | ||||
−0.993712 | + | 0.111969i | \(0.964284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.5667 | 0.644460 | 0.322230 | − | 0.946661i | \(-0.395568\pi\) | ||||
0.322230 | + | 0.946661i | \(0.395568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.4853 | 0.530700 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.9411i | 0.801711i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9723i | 0.619330i | 0.950846 | + | 0.309665i | \(0.100217\pi\) | ||||
−0.950846 | + | 0.309665i | \(0.899783\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.1903 | 0.734799 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.21320 | 0.262168 | 0.131084 | − | 0.991371i | \(-0.458154\pi\) | ||||
0.131084 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.6985i | 0.641570i | 0.947152 | + | 0.320785i | \(0.103947\pi\) | ||||
−0.947152 | + | 0.320785i | \(0.896053\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.6836i | 0.929808i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −36.9164 | −1.33297 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0000 | −0.576975 | −0.288487 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288487 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.9706i | 0.826194i | 0.910687 | + | 0.413097i | \(0.135553\pi\) | ||||
−0.910687 | + | 0.413097i | \(0.864447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.43488i | 0.0515423i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.7846 | −0.744686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.9706 | 0.607254 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 9.75736i | − 0.348255i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.6702i | 1.30715i | 0.756861 | + | 0.653576i | \(0.226732\pi\) | ||||
−0.756861 | + | 0.653576i | \(0.773268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7846 | 0.739016 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.4853 | 1.43767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 44.4853i | 1.57575i | 0.615836 | + | 0.787875i | \(0.288819\pi\) | ||||
−0.615836 | + | 0.787875i | \(0.711181\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.3513 | 1.35339 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.51472 | 0.123878 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 41.6985i | − 1.46604i | −0.680207 | − | 0.733020i | \(-0.738110\pi\) | ||||
0.680207 | − | 0.733020i | \(-0.261890\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 4.65279i | − 0.163382i | −0.996658 | − | 0.0816908i | \(-0.973968\pi\) | ||||
0.996658 | − | 0.0816908i | \(-0.0260320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.76874 | 0.272127 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.9411 | −2.02710 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0000i | 0.628204i | 0.949389 | + | 0.314102i | \(0.101703\pi\) | ||||
−0.949389 | + | 0.314102i | \(0.898297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2767i | 0.497654i | 0.968548 | + | 0.248827i | \(0.0800450\pi\) | ||||
−0.968548 | + | 0.248827i | \(0.919955\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.5241 | −0.922334 | −0.461167 | − | 0.887313i | \(-0.652569\pi\) | ||||
−0.461167 | + | 0.887313i | \(0.652569\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.4853 | −0.364169 | −0.182084 | − | 0.983283i | \(-0.558284\pi\) | ||||
−0.182084 | + | 0.983283i | \(0.558284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.43488i | − 0.0496560i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.95743 | −0.309245 | −0.154622 | − | 0.987974i | \(-0.549416\pi\) | ||||
−0.154622 | + | 0.987974i | \(0.549416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 25.9706i | − 0.893415i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 58.7156i | − 2.01749i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.21792 | 0.110309 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.7574 | −0.608000 | −0.304000 | − | 0.952672i | \(-0.598322\pi\) | ||||
−0.304000 | + | 0.952672i | \(0.598322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.97056i | 0.169791i | 0.996390 | + | 0.0848956i | \(0.0270557\pi\) | ||||
−0.996390 | + | 0.0848956i | \(0.972944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 43.8446i | − 1.49596i | −0.663722 | − | 0.747980i | \(-0.731024\pi\) | ||||
0.663722 | − | 0.747980i | \(-0.268976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.0892 | 0.854048 | 0.427024 | − | 0.904240i | \(-0.359562\pi\) | ||||
0.427024 | + | 0.904240i | \(0.359562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.51472 | −0.119504 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 49.4558i | 1.67767i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 43.2503i | − 1.46548i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.44949 | 0.0828079 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.2426 | 1.02122 | 0.510611 | − | 0.859812i | \(-0.329419\pi\) | ||||
0.510611 | + | 0.859812i | \(0.329419\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 33.2132i | − 1.11898i | −0.828837 | − | 0.559491i | \(-0.810997\pi\) | ||||
0.828837 | − | 0.559491i | \(-0.189003\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.6836i | 0.864322i | 0.901797 | + | 0.432161i | \(0.142249\pi\) | ||||
−0.901797 | + | 0.432161i | \(0.857751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.3497 | 0.649700 | 0.324850 | − | 0.945765i | \(-0.394686\pi\) | ||||
0.324850 | + | 0.945765i | \(0.394686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000 | 0.603701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 57.9411i | − 1.93893i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8710i | 0.497083i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.60927 | −0.287135 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 18.4853i | − 0.614472i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 52.2077i | − 1.73353i | −0.498718 | − | 0.866764i | \(-0.666196\pi\) | ||||
0.498718 | − | 0.866764i | \(-0.333804\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.0482 | −1.75757 | −0.878783 | − | 0.477221i | \(-0.841644\pi\) | ||||
−0.878783 | + | 0.477221i | \(0.841644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −86.9117 | −2.87636 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 50.4853i | − 1.66717i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.43488i | 0.0473323i | 0.999720 | + | 0.0236661i | \(0.00753387\pi\) | ||||
−0.999720 | + | 0.0236661i | \(0.992466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.9149 | −0.589675 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24264 | 0.0737376 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 0.727922i | − 0.0238823i | −0.999929 | − | 0.0119412i | \(-0.996199\pi\) | ||||
0.999929 | − | 0.0119412i | \(-0.00380108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.89898i | − 0.160558i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.02944 | −0.164305 | −0.0821523 | − | 0.996620i | \(-0.526179\pi\) | ||||
−0.0821523 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.9706i | 0.357630i | 0.983883 | + | 0.178815i | \(0.0572264\pi\) | ||||
−0.983883 | + | 0.178815i | \(0.942774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.08767i | 0.198242i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.7846 | −0.675409 | −0.337705 | − | 0.941252i | \(-0.609650\pi\) | ||||
−0.337705 | + | 0.941252i | \(0.609650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.4853 | −1.31421 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 54.4264i | − 1.76304i | −0.472143 | − | 0.881522i | \(-0.656519\pi\) | ||||
0.472143 | − | 0.881522i | \(-0.343481\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14.6969i | − 0.475582i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.1785 | 1.62035 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.9411 | 0.933585 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.0000i | 0.321911i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.4946i | 0.562588i | 0.959622 | + | 0.281294i | \(0.0907636\pi\) | ||||
−0.959622 | + | 0.281294i | \(0.909236\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.7859 | 1.05215 | 0.526074 | − | 0.850439i | \(-0.323663\pi\) | ||||
0.526074 | + | 0.850439i | \(0.323663\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.5147 | 0.497379 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.97056i | 0.159022i | 0.996834 | + | 0.0795112i | \(0.0253359\pi\) | ||||
−0.996834 | + | 0.0795112i | \(0.974664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.8739i | 1.46613i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.8272 | 0.377229 | 0.188614 | − | 0.982051i | \(-0.439600\pi\) | ||||
0.188614 | + | 0.982051i | \(0.439600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.9706 | −0.349551 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.9706i | 0.539633i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 28.7995i | − 0.914847i | −0.889249 | − | 0.457424i | \(-0.848772\pi\) | ||||
0.889249 | − | 0.457424i | \(-0.151228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.46410 | 0.109819 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.78680 | 0.151599 | 0.0757997 | − | 0.997123i | \(-0.475849\pi\) | ||||
0.0757997 | + | 0.997123i | \(0.475849\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.2.h.a.431.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 720.2.h.a.431.5 | yes | 8 | |
4.3 | odd | 2 | inner | 720.2.h.a.431.3 | yes | 8 | |
5.2 | odd | 4 | 3600.2.o.d.3599.8 | 8 | |||
5.3 | odd | 4 | 3600.2.o.c.3599.3 | 8 | |||
5.4 | even | 2 | 3600.2.h.j.1151.8 | 8 | |||
8.3 | odd | 2 | 2880.2.h.f.1151.8 | 8 | |||
8.5 | even | 2 | 2880.2.h.f.1151.5 | 8 | |||
12.11 | even | 2 | inner | 720.2.h.a.431.8 | yes | 8 | |
15.2 | even | 4 | 3600.2.o.c.3599.6 | 8 | |||
15.8 | even | 4 | 3600.2.o.d.3599.1 | 8 | |||
15.14 | odd | 2 | 3600.2.h.j.1151.5 | 8 | |||
20.3 | even | 4 | 3600.2.o.c.3599.5 | 8 | |||
20.7 | even | 4 | 3600.2.o.d.3599.2 | 8 | |||
20.19 | odd | 2 | 3600.2.h.j.1151.1 | 8 | |||
24.5 | odd | 2 | 2880.2.h.f.1151.2 | 8 | |||
24.11 | even | 2 | 2880.2.h.f.1151.3 | 8 | |||
60.23 | odd | 4 | 3600.2.o.d.3599.7 | 8 | |||
60.47 | odd | 4 | 3600.2.o.c.3599.4 | 8 | |||
60.59 | even | 2 | 3600.2.h.j.1151.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.h.a.431.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
720.2.h.a.431.3 | yes | 8 | 4.3 | odd | 2 | inner | |
720.2.h.a.431.5 | yes | 8 | 3.2 | odd | 2 | inner | |
720.2.h.a.431.8 | yes | 8 | 12.11 | even | 2 | inner | |
2880.2.h.f.1151.2 | 8 | 24.5 | odd | 2 | |||
2880.2.h.f.1151.3 | 8 | 24.11 | even | 2 | |||
2880.2.h.f.1151.5 | 8 | 8.5 | even | 2 | |||
2880.2.h.f.1151.8 | 8 | 8.3 | odd | 2 | |||
3600.2.h.j.1151.1 | 8 | 20.19 | odd | 2 | |||
3600.2.h.j.1151.4 | 8 | 60.59 | even | 2 | |||
3600.2.h.j.1151.5 | 8 | 15.14 | odd | 2 | |||
3600.2.h.j.1151.8 | 8 | 5.4 | even | 2 | |||
3600.2.o.c.3599.3 | 8 | 5.3 | odd | 4 | |||
3600.2.o.c.3599.4 | 8 | 60.47 | odd | 4 | |||
3600.2.o.c.3599.5 | 8 | 20.3 | even | 4 | |||
3600.2.o.c.3599.6 | 8 | 15.2 | even | 4 | |||
3600.2.o.d.3599.1 | 8 | 15.8 | even | 4 | |||
3600.2.o.d.3599.2 | 8 | 20.7 | even | 4 | |||
3600.2.o.d.3599.7 | 8 | 60.23 | odd | 4 | |||
3600.2.o.d.3599.8 | 8 | 5.2 | odd | 4 |