Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(141,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.b (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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 141.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.141 |
Dual form | 280.2.b.b.141.1 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | ||||
\(3\) | 2.00000i | 1.15470i | 0.816497 | + | 0.577350i | \(0.195913\pi\) | ||||
−0.816497 | + | 0.577350i | \(0.804087\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −2.00000 | + | 2.00000i | −0.816497 | + | 0.816497i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.00000 | + | 1.00000i | −0.316228 | + | 0.316228i | ||||
\(11\) | − | 4.00000i | − | 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(12\) | −4.00000 | −1.15470 | ||||||||
\(13\) | − | 6.00000i | − | 1.66410i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||
0.554700 | − | 0.832050i | \(-0.312833\pi\) | |||||||
\(14\) | 1.00000 | + | 1.00000i | 0.267261 | + | 0.267261i | ||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.00000 | − | 1.00000i | −0.235702 | − | 0.235702i | ||||
\(19\) | 8.00000i | 1.83533i | 0.397360 | + | 0.917663i | \(0.369927\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | 4.00000 | − | 4.00000i | 0.852803 | − | 0.852803i | ||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | −4.00000 | − | 4.00000i | −0.816497 | − | 0.816497i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 6.00000 | − | 6.00000i | 1.17670 | − | 1.17670i | ||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | −2.00000 | − | 2.00000i | −0.365148 | − | 0.365148i | ||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.707107 | − | 0.707107i | ||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000i | 0.169031i | ||||||||
\(36\) | − | 2.00000i | − | 0.333333i | ||||||
\(37\) | − | 10.0000i | − | 1.64399i | −0.569495 | − | 0.821995i | \(-0.692861\pi\) | ||
0.569495 | − | 0.821995i | \(-0.307139\pi\) | |||||||
\(38\) | −8.00000 | + | 8.00000i | −1.29777 | + | 1.29777i | ||||
\(39\) | 12.0000 | 1.92154 | ||||||||
\(40\) | −2.00000 | − | 2.00000i | −0.316228 | − | 0.316228i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | −2.00000 | + | 2.00000i | −0.308607 | + | 0.308607i | ||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 8.00000 | 1.20605 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 8.00000 | + | 8.00000i | 1.17954 | + | 1.17954i | ||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | − | 8.00000i | − | 1.15470i | ||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | − | 1.00000i | −0.141421 | − | 0.141421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.0000 | 1.66410 | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | −4.00000 | + | 4.00000i | −0.544331 | + | 0.544331i | ||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | −2.00000 | + | 2.00000i | −0.267261 | + | 0.267261i | ||||
\(57\) | −16.0000 | −2.11925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | − | 4.00000i | − | 0.516398i | ||||||
\(61\) | 2.00000i | 0.256074i | 0.991769 | + | 0.128037i | \(0.0408676\pi\) | ||||
−0.991769 | + | 0.128037i | \(0.959132\pi\) | |||||||
\(62\) | −8.00000 | − | 8.00000i | −1.01600 | − | 1.01600i | ||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 8.00000 | + | 8.00000i | 0.984732 | + | 0.984732i | ||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.0000i | 1.92617i | ||||||||
\(70\) | −1.00000 | + | 1.00000i | −0.119523 | + | 0.119523i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 2.00000 | − | 2.00000i | 0.235702 | − | 0.235702i | ||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 10.0000 | − | 10.0000i | 1.16248 | − | 1.16248i | ||||
\(75\) | − | 2.00000i | − | 0.230940i | ||||||
\(76\) | −16.0000 | −1.83533 | ||||||||
\(77\) | − | 4.00000i | − | 0.455842i | ||||||
\(78\) | 12.0000 | + | 12.0000i | 1.35873 | + | 1.35873i | ||||
\(79\) | −2.00000 | −0.225018 | −0.112509 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112509 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(80\) | − | 4.00000i | − | 0.447214i | ||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −2.00000 | − | 2.00000i | −0.220863 | − | 0.220863i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | + | 4.00000i | −0.431331 | + | 0.431331i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.00000 | + | 8.00000i | 0.852803 | + | 0.852803i | ||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 1.00000 | − | 1.00000i | 0.105409 | − | 0.105409i | ||||
\(91\) | − | 6.00000i | − | 0.628971i | ||||||
\(92\) | 16.0000i | 1.66812i | ||||||||
\(93\) | − | 16.0000i | − | 1.65912i | ||||||
\(94\) | 8.00000 | + | 8.00000i | 0.825137 | + | 0.825137i | ||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 8.00000 | − | 8.00000i | 0.816497 | − | 0.816497i | ||||
\(97\) | −16.0000 | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(98\) | 1.00000 | + | 1.00000i | 0.101015 | + | 0.101015i | ||||
\(99\) | 4.00000i | 0.402015i | ||||||||
\(100\) | − | 2.00000i | − | 0.200000i | ||||||
\(101\) | − | 2.00000i | − | 0.199007i | −0.995037 | − | 0.0995037i | \(-0.968274\pi\) | ||
0.995037 | − | 0.0995037i | \(-0.0317255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 12.0000 | + | 12.0000i | 1.17670 | + | 1.17670i | ||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 2.00000 | − | 2.00000i | 0.194257 | − | 0.194257i | ||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | −8.00000 | −0.769800 | ||||||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 4.00000 | + | 4.00000i | 0.381385 | + | 0.381385i | ||||
\(111\) | 20.0000 | 1.89832 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | −16.0000 | − | 16.0000i | −1.49854 | − | 1.49854i | ||||
\(115\) | 8.00000i | 0.746004i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000i | 0.554700i | ||||||||
\(118\) | −4.00000 | + | 4.00000i | −0.368230 | + | 0.368230i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.00000 | − | 4.00000i | 0.365148 | − | 0.365148i | ||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | −2.00000 | + | 2.00000i | −0.181071 | + | 0.181071i | ||||
\(123\) | − | 4.00000i | − | 0.360668i | ||||||
\(124\) | − | 16.0000i | − | 1.43684i | ||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −1.00000 | − | 1.00000i | −0.0890871 | − | 0.0890871i | ||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 6.00000 | + | 6.00000i | 0.526235 | + | 0.526235i | ||||
\(131\) | − | 12.0000i | − | 1.04844i | −0.851581 | − | 0.524222i | \(-0.824356\pi\) | ||
0.851581 | − | 0.524222i | \(-0.175644\pi\) | |||||||
\(132\) | 16.0000i | 1.39262i | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | 12.0000 | − | 12.0000i | 1.03664 | − | 1.03664i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.0000 | 1.87959 | 0.939793 | − | 0.341743i | \(-0.111017\pi\) | ||||
0.939793 | + | 0.341743i | \(0.111017\pi\) | |||||||
\(138\) | −16.0000 | + | 16.0000i | −1.36201 | + | 1.36201i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 16.0000i | 1.34744i | ||||||||
\(142\) | 2.00000 | + | 2.00000i | 0.167836 | + | 0.167836i | ||||
\(143\) | −24.0000 | −2.00698 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | + | 4.00000i | 0.331042 | + | 0.331042i | ||||
\(147\) | 2.00000i | 0.164957i | ||||||||
\(148\) | 20.0000 | 1.64399 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | 2.00000 | − | 2.00000i | 0.163299 | − | 0.163299i | ||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | −16.0000 | − | 16.0000i | −1.29777 | − | 1.29777i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.00000 | − | 4.00000i | 0.322329 | − | 0.322329i | ||||
\(155\) | − | 8.00000i | − | 0.642575i | ||||||
\(156\) | 24.0000i | 1.92154i | ||||||||
\(157\) | − | 2.00000i | − | 0.159617i | −0.996810 | − | 0.0798087i | \(-0.974569\pi\) | ||
0.996810 | − | 0.0798087i | \(-0.0254309\pi\) | |||||||
\(158\) | −2.00000 | − | 2.00000i | −0.159111 | − | 0.159111i | ||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 4.00000 | − | 4.00000i | 0.316228 | − | 0.316228i | ||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | −11.0000 | − | 11.0000i | −0.864242 | − | 0.864242i | ||||
\(163\) | 16.0000i | 1.25322i | 0.779334 | + | 0.626608i | \(0.215557\pi\) | ||||
−0.779334 | + | 0.626608i | \(0.784443\pi\) | |||||||
\(164\) | − | 4.00000i | − | 0.312348i | ||||||
\(165\) | 8.00000i | 0.622799i | ||||||||
\(166\) | 6.00000 | − | 6.00000i | 0.465690 | − | 0.465690i | ||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | −4.00000 | − | 4.00000i | −0.308607 | − | 0.308607i | ||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 8.00000i | − | 0.611775i | ||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | − | 14.0000i | − | 1.06440i | −0.846619 | − | 0.532200i | \(-0.821365\pi\) | ||
0.846619 | − | 0.532200i | \(-0.178635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 16.0000i | 1.20605i | ||||||||
\(177\) | −8.00000 | −0.601317 | ||||||||
\(178\) | 2.00000 | + | 2.00000i | 0.149906 | + | 0.149906i | ||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 2.00000 | 0.149071 | ||||||||
\(181\) | 2.00000i | 0.148659i | 0.997234 | + | 0.0743294i | \(0.0236816\pi\) | ||||
−0.997234 | + | 0.0743294i | \(0.976318\pi\) | |||||||
\(182\) | 6.00000 | − | 6.00000i | 0.444750 | − | 0.444750i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −16.0000 | + | 16.0000i | −1.17954 | + | 1.17954i | ||||
\(185\) | 10.0000 | 0.735215 | ||||||||
\(186\) | 16.0000 | − | 16.0000i | 1.17318 | − | 1.17318i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 16.0000i | 1.16692i | ||||||||
\(189\) | 4.00000i | 0.290957i | ||||||||
\(190\) | −8.00000 | − | 8.00000i | −0.580381 | − | 0.580381i | ||||
\(191\) | −2.00000 | −0.144715 | −0.0723575 | − | 0.997379i | \(-0.523052\pi\) | ||||
−0.0723575 | + | 0.997379i | \(0.523052\pi\) | |||||||
\(192\) | 16.0000 | 1.15470 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | −16.0000 | − | 16.0000i | −1.14873 | − | 1.14873i | ||||
\(195\) | 12.0000i | 0.859338i | ||||||||
\(196\) | 2.00000i | 0.142857i | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | −4.00000 | + | 4.00000i | −0.284268 | + | 0.284268i | ||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | 2.00000 | − | 2.00000i | 0.141421 | − | 0.141421i | ||||
\(201\) | 24.0000 | 1.69283 | ||||||||
\(202\) | 2.00000 | − | 2.00000i | 0.140720 | − | 0.140720i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 2.00000i | − | 0.139686i | ||||||
\(206\) | −8.00000 | − | 8.00000i | −0.557386 | − | 0.557386i | ||||
\(207\) | −8.00000 | −0.556038 | ||||||||
\(208\) | 24.0000i | 1.66410i | ||||||||
\(209\) | 32.0000 | 2.21349 | ||||||||
\(210\) | −2.00000 | − | 2.00000i | −0.138013 | − | 0.138013i | ||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 4.00000i | 0.274075i | ||||||||
\(214\) | −8.00000 | + | 8.00000i | −0.546869 | + | 0.546869i | ||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | −8.00000 | − | 8.00000i | −0.544331 | − | 0.544331i | ||||
\(217\) | −8.00000 | −0.543075 | ||||||||
\(218\) | 4.00000 | − | 4.00000i | 0.270914 | − | 0.270914i | ||||
\(219\) | 8.00000i | 0.540590i | ||||||||
\(220\) | 8.00000i | 0.539360i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 20.0000 | + | 20.0000i | 1.34231 | + | 1.34231i | ||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | −4.00000 | − | 4.00000i | −0.267261 | − | 0.267261i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.00000 | − | 6.00000i | −0.399114 | − | 0.399114i | ||||
\(227\) | − | 18.0000i | − | 1.19470i | −0.801980 | − | 0.597351i | \(-0.796220\pi\) | ||
0.801980 | − | 0.597351i | \(-0.203780\pi\) | |||||||
\(228\) | − | 32.0000i | − | 2.11925i | ||||||
\(229\) | 10.0000i | 0.660819i | 0.943838 | + | 0.330409i | \(0.107187\pi\) | ||||
−0.943838 | + | 0.330409i | \(0.892813\pi\) | |||||||
\(230\) | −8.00000 | + | 8.00000i | −0.527504 | + | 0.527504i | ||||
\(231\) | 8.00000 | 0.526361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | −6.00000 | + | 6.00000i | −0.392232 | + | 0.392232i | ||||
\(235\) | 8.00000i | 0.521862i | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | − | 4.00000i | − | 0.259828i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.00000 | −0.129369 | −0.0646846 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646846 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(240\) | 8.00000 | 0.516398 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | −5.00000 | − | 5.00000i | −0.321412 | − | 0.321412i | ||||
\(243\) | − | 10.0000i | − | 0.641500i | ||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 4.00000 | − | 4.00000i | 0.255031 | − | 0.255031i | ||||
\(247\) | 48.0000 | 3.05417 | ||||||||
\(248\) | 16.0000 | − | 16.0000i | 1.01600 | − | 1.01600i | ||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 1.00000 | − | 1.00000i | 0.0632456 | − | 0.0632456i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | − | 32.0000i | − | 2.01182i | ||||||
\(254\) | −12.0000 | − | 12.0000i | −0.752947 | − | 0.752947i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 16.0000 | 0.998053 | 0.499026 | − | 0.866587i | \(-0.333691\pi\) | ||||
0.499026 | + | 0.866587i | \(0.333691\pi\) | |||||||
\(258\) | −8.00000 | − | 8.00000i | −0.498058 | − | 0.498058i | ||||
\(259\) | − | 10.0000i | − | 0.621370i | ||||||
\(260\) | 12.0000i | 0.744208i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000 | − | 12.0000i | 0.741362 | − | 0.741362i | ||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | −16.0000 | + | 16.0000i | −0.984732 | + | 0.984732i | ||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | −8.00000 | + | 8.00000i | −0.490511 | + | 0.490511i | ||||
\(267\) | 4.00000i | 0.244796i | ||||||||
\(268\) | 24.0000 | 1.46603 | ||||||||
\(269\) | 14.0000i | 0.853595i | 0.904347 | + | 0.426798i | \(0.140358\pi\) | ||||
−0.904347 | + | 0.426798i | \(0.859642\pi\) | |||||||
\(270\) | −4.00000 | − | 4.00000i | −0.243432 | − | 0.243432i | ||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0000 | 0.726273 | ||||||||
\(274\) | 22.0000 | + | 22.0000i | 1.32907 | + | 1.32907i | ||||
\(275\) | 4.00000i | 0.241209i | ||||||||
\(276\) | −32.0000 | −1.92617 | ||||||||
\(277\) | 22.0000i | 1.32185i | 0.750451 | + | 0.660926i | \(0.229836\pi\) | ||||
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(278\) | −4.00000 | + | 4.00000i | −0.239904 | + | 0.239904i | ||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | −2.00000 | − | 2.00000i | −0.119523 | − | 0.119523i | ||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | −16.0000 | + | 16.0000i | −0.952786 | + | 0.952786i | ||||
\(283\) | − | 2.00000i | − | 0.118888i | −0.998232 | − | 0.0594438i | \(-0.981067\pi\) | ||
0.998232 | − | 0.0594438i | \(-0.0189327\pi\) | |||||||
\(284\) | 4.00000i | 0.237356i | ||||||||
\(285\) | − | 16.0000i | − | 0.947758i | ||||||
\(286\) | −24.0000 | − | 24.0000i | −1.41915 | − | 1.41915i | ||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 4.00000 | + | 4.00000i | 0.235702 | + | 0.235702i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 32.0000i | − | 1.87587i | ||||||
\(292\) | 8.00000i | 0.468165i | ||||||||
\(293\) | − | 22.0000i | − | 1.28525i | −0.766179 | − | 0.642627i | \(-0.777845\pi\) | ||
0.766179 | − | 0.642627i | \(-0.222155\pi\) | |||||||
\(294\) | −2.00000 | + | 2.00000i | −0.116642 | + | 0.116642i | ||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 20.0000 | + | 20.0000i | 1.16248 | + | 1.16248i | ||||
\(297\) | 16.0000 | 0.928414 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 48.0000i | − | 2.77591i | ||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 4.00000i | 0.230556i | ||||||||
\(302\) | −2.00000 | − | 2.00000i | −0.115087 | − | 0.115087i | ||||
\(303\) | 4.00000 | 0.229794 | ||||||||
\(304\) | − | 32.0000i | − | 1.83533i | ||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000i | 0.114146i | 0.998370 | + | 0.0570730i | \(0.0181768\pi\) | ||||
−0.998370 | + | 0.0570730i | \(0.981823\pi\) | |||||||
\(308\) | 8.00000 | 0.455842 | ||||||||
\(309\) | − | 16.0000i | − | 0.910208i | ||||||
\(310\) | 8.00000 | − | 8.00000i | 0.454369 | − | 0.454369i | ||||
\(311\) | 20.0000 | 1.13410 | 0.567048 | − | 0.823685i | \(-0.308085\pi\) | ||||
0.567048 | + | 0.823685i | \(0.308085\pi\) | |||||||
\(312\) | −24.0000 | + | 24.0000i | −1.35873 | + | 1.35873i | ||||
\(313\) | 12.0000 | 0.678280 | 0.339140 | − | 0.940736i | \(-0.389864\pi\) | ||||
0.339140 | + | 0.940736i | \(0.389864\pi\) | |||||||
\(314\) | 2.00000 | − | 2.00000i | 0.112867 | − | 0.112867i | ||||
\(315\) | − | 1.00000i | − | 0.0563436i | ||||||
\(316\) | − | 4.00000i | − | 0.225018i | ||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 4.00000 | + | 4.00000i | 0.224309 | + | 0.224309i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | −16.0000 | −0.893033 | ||||||||
\(322\) | 8.00000 | + | 8.00000i | 0.445823 | + | 0.445823i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 22.0000i | − | 1.22222i | ||||||
\(325\) | 6.00000i | 0.332820i | ||||||||
\(326\) | −16.0000 | + | 16.0000i | −0.886158 | + | 0.886158i | ||||
\(327\) | 8.00000 | 0.442401 | ||||||||
\(328\) | 4.00000 | − | 4.00000i | 0.220863 | − | 0.220863i | ||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | −8.00000 | + | 8.00000i | −0.440386 | + | 0.440386i | ||||
\(331\) | 20.0000i | 1.09930i | 0.835395 | + | 0.549650i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549650i | \(0.814761\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | 10.0000i | 0.547997i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | − | 8.00000i | − | 0.436436i | ||||||
\(337\) | 30.0000 | 1.63420 | 0.817102 | − | 0.576493i | \(-0.195579\pi\) | ||||
0.817102 | + | 0.576493i | \(0.195579\pi\) | |||||||
\(338\) | −23.0000 | − | 23.0000i | −1.25104 | − | 1.25104i | ||||
\(339\) | − | 12.0000i | − | 0.651751i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.0000i | 1.73290i | ||||||||
\(342\) | 8.00000 | − | 8.00000i | 0.432590 | − | 0.432590i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.00000 | − | 8.00000i | −0.431331 | − | 0.431331i | ||||
\(345\) | −16.0000 | −0.861411 | ||||||||
\(346\) | 14.0000 | − | 14.0000i | 0.752645 | − | 0.752645i | ||||
\(347\) | − | 16.0000i | − | 0.858925i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | −1.00000 | − | 1.00000i | −0.0534522 | − | 0.0534522i | ||||
\(351\) | 24.0000 | 1.28103 | ||||||||
\(352\) | −16.0000 | + | 16.0000i | −0.852803 | + | 0.852803i | ||||
\(353\) | −24.0000 | −1.27739 | −0.638696 | − | 0.769460i | \(-0.720526\pi\) | ||||
−0.638696 | + | 0.769460i | \(0.720526\pi\) | |||||||
\(354\) | −8.00000 | − | 8.00000i | −0.425195 | − | 0.425195i | ||||
\(355\) | 2.00000i | 0.106149i | ||||||||
\(356\) | 4.00000i | 0.212000i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | + | 12.0000i | −0.634220 | + | 0.634220i | ||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 2.00000 | + | 2.00000i | 0.105409 | + | 0.105409i | ||||
\(361\) | −45.0000 | −2.36842 | ||||||||
\(362\) | −2.00000 | + | 2.00000i | −0.105118 | + | 0.105118i | ||||
\(363\) | − | 10.0000i | − | 0.524864i | ||||||
\(364\) | 12.0000 | 0.628971 | ||||||||
\(365\) | 4.00000i | 0.209370i | ||||||||
\(366\) | −4.00000 | − | 4.00000i | −0.209083 | − | 0.209083i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | −32.0000 | −1.66812 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 10.0000 | + | 10.0000i | 0.519875 | + | 0.519875i | ||||
\(371\) | − | 2.00000i | − | 0.103835i | ||||||
\(372\) | 32.0000 | 1.65912 | ||||||||
\(373\) | 34.0000i | 1.76045i | 0.474554 | + | 0.880227i | \(0.342610\pi\) | ||||
−0.474554 | + | 0.880227i | \(0.657390\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000 | 0.103280 | ||||||||
\(376\) | −16.0000 | + | 16.0000i | −0.825137 | + | 0.825137i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.00000 | + | 4.00000i | −0.205738 | + | 0.205738i | ||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | − | 16.0000i | − | 0.820783i | ||||||
\(381\) | − | 24.0000i | − | 1.22956i | ||||||
\(382\) | −2.00000 | − | 2.00000i | −0.102329 | − | 0.102329i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 16.0000 | + | 16.0000i | 0.816497 | + | 0.816497i | ||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | −2.00000 | − | 2.00000i | −0.101797 | − | 0.101797i | ||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | − | 32.0000i | − | 1.62455i | ||||||
\(389\) | 20.0000i | 1.01404i | 0.861934 | + | 0.507020i | \(0.169253\pi\) | ||||
−0.861934 | + | 0.507020i | \(0.830747\pi\) | |||||||
\(390\) | −12.0000 | + | 12.0000i | −0.607644 | + | 0.607644i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.00000 | + | 2.00000i | −0.101015 | + | 0.101015i | ||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | −10.0000 | + | 10.0000i | −0.503793 | + | 0.503793i | ||||
\(395\) | − | 2.00000i | − | 0.100631i | ||||||
\(396\) | −8.00000 | −0.402015 | ||||||||
\(397\) | − | 2.00000i | − | 0.100377i | −0.998740 | − | 0.0501886i | \(-0.984018\pi\) | ||
0.998740 | − | 0.0501886i | \(-0.0159822\pi\) | |||||||
\(398\) | −24.0000 | − | 24.0000i | −1.20301 | − | 1.20301i | ||||
\(399\) | −16.0000 | −0.801002 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 24.0000 | + | 24.0000i | 1.19701 | + | 1.19701i | ||||
\(403\) | 48.0000i | 2.39105i | ||||||||
\(404\) | 4.00000 | 0.199007 | ||||||||
\(405\) | − | 11.0000i | − | 0.546594i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.0000 | −1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 2.00000 | − | 2.00000i | 0.0987730 | − | 0.0987730i | ||||
\(411\) | 44.0000i | 2.17036i | ||||||||
\(412\) | − | 16.0000i | − | 0.788263i | ||||||
\(413\) | 4.00000i | 0.196827i | ||||||||
\(414\) | −8.00000 | − | 8.00000i | −0.393179 | − | 0.393179i | ||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −24.0000 | + | 24.0000i | −1.17670 | + | 1.17670i | ||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 32.0000 | + | 32.0000i | 1.56517 | + | 1.56517i | ||||
\(419\) | 4.00000i | 0.195413i | 0.995215 | + | 0.0977064i | \(0.0311506\pi\) | ||||
−0.995215 | + | 0.0977064i | \(0.968849\pi\) | |||||||
\(420\) | − | 4.00000i | − | 0.195180i | ||||||
\(421\) | 4.00000i | 0.194948i | 0.995238 | + | 0.0974740i | \(0.0310763\pi\) | ||||
−0.995238 | + | 0.0974740i | \(0.968924\pi\) | |||||||
\(422\) | 12.0000 | − | 12.0000i | 0.584151 | − | 0.584151i | ||||
\(423\) | −8.00000 | −0.388973 | ||||||||
\(424\) | 4.00000 | + | 4.00000i | 0.194257 | + | 0.194257i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.00000 | + | 4.00000i | −0.193801 | + | 0.193801i | ||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | −16.0000 | −0.773389 | ||||||||
\(429\) | − | 48.0000i | − | 2.31746i | ||||||
\(430\) | −4.00000 | − | 4.00000i | −0.192897 | − | 0.192897i | ||||
\(431\) | −18.0000 | −0.867029 | −0.433515 | − | 0.901146i | \(-0.642727\pi\) | ||||
−0.433515 | + | 0.901146i | \(0.642727\pi\) | |||||||
\(432\) | − | 16.0000i | − | 0.769800i | ||||||
\(433\) | 20.0000 | 0.961139 | 0.480569 | − | 0.876957i | \(-0.340430\pi\) | ||||
0.480569 | + | 0.876957i | \(0.340430\pi\) | |||||||
\(434\) | −8.00000 | − | 8.00000i | −0.384012 | − | 0.384012i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 64.0000i | 3.06154i | ||||||||
\(438\) | −8.00000 | + | 8.00000i | −0.382255 | + | 0.382255i | ||||
\(439\) | −28.0000 | −1.33637 | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||||
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(440\) | −8.00000 | + | 8.00000i | −0.381385 | + | 0.381385i | ||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000i | 0.950229i | 0.879924 | + | 0.475114i | \(0.157593\pi\) | ||||
−0.879924 | + | 0.475114i | \(0.842407\pi\) | |||||||
\(444\) | 40.0000i | 1.89832i | ||||||||
\(445\) | 2.00000i | 0.0948091i | ||||||||
\(446\) | −8.00000 | − | 8.00000i | −0.378811 | − | 0.378811i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 8.00000i | − | 0.377964i | ||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 1.00000 | + | 1.00000i | 0.0471405 | + | 0.0471405i | ||||
\(451\) | 8.00000i | 0.376705i | ||||||||
\(452\) | − | 12.0000i | − | 0.564433i | ||||||
\(453\) | − | 4.00000i | − | 0.187936i | ||||||
\(454\) | 18.0000 | − | 18.0000i | 0.844782 | − | 0.844782i | ||||
\(455\) | 6.00000 | 0.281284 | ||||||||
\(456\) | 32.0000 | − | 32.0000i | 1.49854 | − | 1.49854i | ||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | −10.0000 | + | 10.0000i | −0.467269 | + | 0.467269i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.0000 | −0.746004 | ||||||||
\(461\) | − | 26.0000i | − | 1.21094i | −0.795868 | − | 0.605470i | \(-0.792985\pi\) | ||
0.795868 | − | 0.605470i | \(-0.207015\pi\) | |||||||
\(462\) | 8.00000 | + | 8.00000i | 0.372194 | + | 0.372194i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.0000 | 0.741982 | ||||||||
\(466\) | 18.0000 | + | 18.0000i | 0.833834 | + | 0.833834i | ||||
\(467\) | 26.0000i | 1.20314i | 0.798821 | + | 0.601568i | \(0.205457\pi\) | ||||
−0.798821 | + | 0.601568i | \(0.794543\pi\) | |||||||
\(468\) | −12.0000 | −0.554700 | ||||||||
\(469\) | − | 12.0000i | − | 0.554109i | ||||||
\(470\) | −8.00000 | + | 8.00000i | −0.369012 | + | 0.369012i | ||||
\(471\) | 4.00000 | 0.184310 | ||||||||
\(472\) | −8.00000 | − | 8.00000i | −0.368230 | − | 0.368230i | ||||
\(473\) | 16.0000 | 0.735681 | ||||||||
\(474\) | 4.00000 | − | 4.00000i | 0.183726 | − | 0.183726i | ||||
\(475\) | − | 8.00000i | − | 0.367065i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | −2.00000 | − | 2.00000i | −0.0914779 | − | 0.0914779i | ||||
\(479\) | 28.0000 | 1.27935 | 0.639676 | − | 0.768644i | \(-0.279068\pi\) | ||||
0.639676 | + | 0.768644i | \(0.279068\pi\) | |||||||
\(480\) | 8.00000 | + | 8.00000i | 0.365148 | + | 0.365148i | ||||
\(481\) | −60.0000 | −2.73576 | ||||||||
\(482\) | 18.0000 | + | 18.0000i | 0.819878 | + | 0.819878i | ||||
\(483\) | 16.0000i | 0.728025i | ||||||||
\(484\) | − | 10.0000i | − | 0.454545i | ||||||
\(485\) | − | 16.0000i | − | 0.726523i | ||||||
\(486\) | 10.0000 | − | 10.0000i | 0.453609 | − | 0.453609i | ||||
\(487\) | −12.0000 | −0.543772 | −0.271886 | − | 0.962329i | \(-0.587647\pi\) | ||||
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(488\) | −4.00000 | − | 4.00000i | −0.181071 | − | 0.181071i | ||||
\(489\) | −32.0000 | −1.44709 | ||||||||
\(490\) | −1.00000 | + | 1.00000i | −0.0451754 | + | 0.0451754i | ||||
\(491\) | 28.0000i | 1.26362i | 0.775122 | + | 0.631811i | \(0.217688\pi\) | ||||
−0.775122 | + | 0.631811i | \(0.782312\pi\) | |||||||
\(492\) | 8.00000 | 0.360668 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 48.0000 | + | 48.0000i | 2.15962 | + | 2.15962i | ||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | 2.00000 | 0.0897123 | ||||||||
\(498\) | 12.0000 | + | 12.0000i | 0.537733 | + | 0.537733i | ||||
\(499\) | − | 28.0000i | − | 1.25345i | −0.779240 | − | 0.626726i | \(-0.784395\pi\) | ||
0.779240 | − | 0.626726i | \(-0.215605\pi\) | |||||||
\(500\) | 2.00000 | 0.0894427 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 2.00000 | − | 2.00000i | 0.0890871 | − | 0.0890871i | ||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 32.0000 | − | 32.0000i | 1.42257 | − | 1.42257i | ||||
\(507\) | − | 46.0000i | − | 2.04293i | ||||||
\(508\) | − | 24.0000i | − | 1.06483i | ||||||
\(509\) | 30.0000i | 1.32973i | 0.746965 | + | 0.664863i | \(0.231510\pi\) | ||||
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | −32.0000 | −1.41283 | ||||||||
\(514\) | 16.0000 | + | 16.0000i | 0.705730 | + | 0.705730i | ||||
\(515\) | − | 8.00000i | − | 0.352522i | ||||||
\(516\) | − | 16.0000i | − | 0.704361i | ||||||
\(517\) | − | 32.0000i | − | 1.40736i | ||||||
\(518\) | 10.0000 | − | 10.0000i | 0.439375 | − | 0.439375i | ||||
\(519\) | 28.0000 | 1.22906 | ||||||||
\(520\) | −12.0000 | + | 12.0000i | −0.526235 | + | 0.526235i | ||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.0000i | − | 1.48672i | −0.668894 | − | 0.743358i | \(-0.733232\pi\) | ||
0.668894 | − | 0.743358i | \(-0.266768\pi\) | |||||||
\(524\) | 24.0000 | 1.04844 | ||||||||
\(525\) | − | 2.00000i | − | 0.0872872i | ||||||
\(526\) | −12.0000 | − | 12.0000i | −0.523225 | − | 0.523225i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −32.0000 | −1.39262 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 2.00000 | + | 2.00000i | 0.0868744 | + | 0.0868744i | ||||
\(531\) | − | 4.00000i | − | 0.173585i | ||||||
\(532\) | −16.0000 | −0.693688 | ||||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | −4.00000 | + | 4.00000i | −0.173097 | + | 0.173097i | ||||
\(535\) | −8.00000 | −0.345870 | ||||||||
\(536\) | 24.0000 | + | 24.0000i | 1.03664 | + | 1.03664i | ||||
\(537\) | −24.0000 | −1.03568 | ||||||||
\(538\) | −14.0000 | + | 14.0000i | −0.603583 | + | 0.603583i | ||||
\(539\) | − | 4.00000i | − | 0.172292i | ||||||
\(540\) | − | 8.00000i | − | 0.344265i | ||||||
\(541\) | − | 40.0000i | − | 1.71973i | −0.510518 | − | 0.859867i | \(-0.670546\pi\) | ||
0.510518 | − | 0.859867i | \(-0.329454\pi\) | |||||||
\(542\) | −8.00000 | − | 8.00000i | −0.343629 | − | 0.343629i | ||||
\(543\) | −4.00000 | −0.171656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.00000 | 0.171341 | ||||||||
\(546\) | 12.0000 | + | 12.0000i | 0.513553 | + | 0.513553i | ||||
\(547\) | − | 32.0000i | − | 1.36822i | −0.729378 | − | 0.684111i | \(-0.760191\pi\) | ||
0.729378 | − | 0.684111i | \(-0.239809\pi\) | |||||||
\(548\) | 44.0000i | 1.87959i | ||||||||
\(549\) | − | 2.00000i | − | 0.0853579i | ||||||
\(550\) | −4.00000 | + | 4.00000i | −0.170561 | + | 0.170561i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −32.0000 | − | 32.0000i | −1.36201 | − | 1.36201i | ||||
\(553\) | −2.00000 | −0.0850487 | ||||||||
\(554\) | −22.0000 | + | 22.0000i | −0.934690 | + | 0.934690i | ||||
\(555\) | 20.0000i | 0.848953i | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | − | 42.0000i | − | 1.77960i | −0.456354 | − | 0.889799i | \(-0.650845\pi\) | ||
0.456354 | − | 0.889799i | \(-0.349155\pi\) | |||||||
\(558\) | 8.00000 | + | 8.00000i | 0.338667 | + | 0.338667i | ||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | − | 4.00000i | − | 0.169031i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.0000 | − | 22.0000i | −0.928014 | − | 0.928014i | ||||
\(563\) | 30.0000i | 1.26435i | 0.774826 | + | 0.632175i | \(0.217837\pi\) | ||||
−0.774826 | + | 0.632175i | \(0.782163\pi\) | |||||||
\(564\) | −32.0000 | −1.34744 | ||||||||
\(565\) | − | 6.00000i | − | 0.252422i | ||||||
\(566\) | 2.00000 | − | 2.00000i | 0.0840663 | − | 0.0840663i | ||||
\(567\) | −11.0000 | −0.461957 | ||||||||
\(568\) | −4.00000 | + | 4.00000i | −0.167836 | + | 0.167836i | ||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 16.0000 | − | 16.0000i | 0.670166 | − | 0.670166i | ||||
\(571\) | 20.0000i | 0.836974i | 0.908223 | + | 0.418487i | \(0.137439\pi\) | ||||
−0.908223 | + | 0.418487i | \(0.862561\pi\) | |||||||
\(572\) | − | 48.0000i | − | 2.00698i | ||||||
\(573\) | − | 4.00000i | − | 0.167102i | ||||||
\(574\) | −2.00000 | − | 2.00000i | −0.0834784 | − | 0.0834784i | ||||
\(575\) | −8.00000 | −0.333623 | ||||||||
\(576\) | 8.00000i | 0.333333i | ||||||||
\(577\) | −44.0000 | −1.83174 | −0.915872 | − | 0.401470i | \(-0.868499\pi\) | ||||
−0.915872 | + | 0.401470i | \(0.868499\pi\) | |||||||
\(578\) | −17.0000 | − | 17.0000i | −0.707107 | − | 0.707107i | ||||
\(579\) | − | 4.00000i | − | 0.166234i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.00000i | − | 0.248922i | ||||||
\(582\) | 32.0000 | − | 32.0000i | 1.32644 | − | 1.32644i | ||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | −8.00000 | + | 8.00000i | −0.331042 | + | 0.331042i | ||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | 22.0000 | − | 22.0000i | 0.908812 | − | 0.908812i | ||||
\(587\) | 42.0000i | 1.73353i | 0.498721 | + | 0.866763i | \(0.333803\pi\) | ||||
−0.498721 | + | 0.866763i | \(0.666197\pi\) | |||||||
\(588\) | −4.00000 | −0.164957 | ||||||||
\(589\) | − | 64.0000i | − | 2.63707i | ||||||
\(590\) | −4.00000 | − | 4.00000i | −0.164677 | − | 0.164677i | ||||
\(591\) | −20.0000 | −0.822690 | ||||||||
\(592\) | 40.0000i | 1.64399i | ||||||||
\(593\) | 4.00000 | 0.164260 | 0.0821302 | − | 0.996622i | \(-0.473828\pi\) | ||||
0.0821302 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(594\) | 16.0000 | + | 16.0000i | 0.656488 | + | 0.656488i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 48.0000i | − | 1.96451i | ||||||
\(598\) | 48.0000 | − | 48.0000i | 1.96287 | − | 1.96287i | ||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 4.00000 | + | 4.00000i | 0.163299 | + | 0.163299i | ||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | −4.00000 | + | 4.00000i | −0.163028 | + | 0.163028i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | − | 4.00000i | − | 0.162758i | ||||||
\(605\) | − | 5.00000i | − | 0.203279i | ||||||
\(606\) | 4.00000 | + | 4.00000i | 0.162489 | + | 0.162489i | ||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 32.0000 | − | 32.0000i | 1.29777 | − | 1.29777i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00000 | − | 2.00000i | −0.0809776 | − | 0.0809776i | ||||
\(611\) | − | 48.0000i | − | 1.94187i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 10.0000i | − | 0.403896i | −0.979396 | − | 0.201948i | \(-0.935273\pi\) | ||
0.979396 | − | 0.201948i | \(-0.0647272\pi\) | |||||||
\(614\) | −2.00000 | + | 2.00000i | −0.0807134 | + | 0.0807134i | ||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | 8.00000 | + | 8.00000i | 0.322329 | + | 0.322329i | ||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 16.0000 | − | 16.0000i | 0.643614 | − | 0.643614i | ||||
\(619\) | − | 8.00000i | − | 0.321547i | −0.986991 | − | 0.160774i | \(-0.948601\pi\) | ||
0.986991 | − | 0.160774i | \(-0.0513989\pi\) | |||||||
\(620\) | 16.0000 | 0.642575 | ||||||||
\(621\) | 32.0000i | 1.28412i | ||||||||
\(622\) | 20.0000 | + | 20.0000i | 0.801927 | + | 0.801927i | ||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | −48.0000 | −1.92154 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 12.0000 | + | 12.0000i | 0.479616 | + | 0.479616i | ||||
\(627\) | 64.0000i | 2.55591i | ||||||||
\(628\) | 4.00000 | 0.159617 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.00000 | − | 1.00000i | 0.0398410 | − | 0.0398410i | ||||
\(631\) | 18.0000 | 0.716569 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(632\) | 4.00000 | − | 4.00000i | 0.159111 | − | 0.159111i | ||||
\(633\) | 24.0000 | 0.953914 | ||||||||
\(634\) | −18.0000 | + | 18.0000i | −0.714871 | + | 0.714871i | ||||
\(635\) | − | 12.0000i | − | 0.476205i | ||||||
\(636\) | 8.00000i | 0.317221i | ||||||||
\(637\) | − | 6.00000i | − | 0.237729i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 8.00000 | + | 8.00000i | 0.316228 | + | 0.316228i | ||||
\(641\) | 38.0000 | 1.50091 | 0.750455 | − | 0.660922i | \(-0.229834\pi\) | ||||
0.750455 | + | 0.660922i | \(0.229834\pi\) | |||||||
\(642\) | −16.0000 | − | 16.0000i | −0.631470 | − | 0.631470i | ||||
\(643\) | 6.00000i | 0.236617i | 0.992977 | + | 0.118308i | \(0.0377472\pi\) | ||||
−0.992977 | + | 0.118308i | \(0.962253\pi\) | |||||||
\(644\) | 16.0000i | 0.630488i | ||||||||
\(645\) | − | 8.00000i | − | 0.315000i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 22.0000 | − | 22.0000i | 0.864242 | − | 0.864242i | ||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | −6.00000 | + | 6.00000i | −0.235339 | + | 0.235339i | ||||
\(651\) | − | 16.0000i | − | 0.627089i | ||||||
\(652\) | −32.0000 | −1.25322 | ||||||||
\(653\) | 30.0000i | 1.17399i | 0.809590 | + | 0.586995i | \(0.199689\pi\) | ||||
−0.809590 | + | 0.586995i | \(0.800311\pi\) | |||||||
\(654\) | 8.00000 | + | 8.00000i | 0.312825 | + | 0.312825i | ||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 8.00000 | 0.312348 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 8.00000 | + | 8.00000i | 0.311872 | + | 0.311872i | ||||
\(659\) | 12.0000i | 0.467454i | 0.972302 | + | 0.233727i | \(0.0750921\pi\) | ||||
−0.972302 | + | 0.233727i | \(0.924908\pi\) | |||||||
\(660\) | −16.0000 | −0.622799 | ||||||||
\(661\) | − | 2.00000i | − | 0.0777910i | −0.999243 | − | 0.0388955i | \(-0.987616\pi\) | ||
0.999243 | − | 0.0388955i | \(-0.0123839\pi\) | |||||||
\(662\) | −20.0000 | + | 20.0000i | −0.777322 | + | 0.777322i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.0000 | + | 12.0000i | 0.465690 | + | 0.465690i | ||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | −10.0000 | + | 10.0000i | −0.387492 | + | 0.387492i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 16.0000i | − | 0.618596i | ||||||
\(670\) | 12.0000 | + | 12.0000i | 0.463600 | + | 0.463600i | ||||
\(671\) | 8.00000 | 0.308837 | ||||||||
\(672\) | 8.00000 | − | 8.00000i | 0.308607 | − | 0.308607i | ||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 30.0000 | + | 30.0000i | 1.15556 | + | 1.15556i | ||||
\(675\) | − | 4.00000i | − | 0.153960i | ||||||
\(676\) | − | 46.0000i | − | 1.76923i | ||||||
\(677\) | 14.0000i | 0.538064i | 0.963131 | + | 0.269032i | \(0.0867037\pi\) | ||||
−0.963131 | + | 0.269032i | \(0.913296\pi\) | |||||||
\(678\) | 12.0000 | − | 12.0000i | 0.460857 | − | 0.460857i | ||||
\(679\) | −16.0000 | −0.614024 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.0000 | 1.37952 | ||||||||
\(682\) | −32.0000 | + | 32.0000i | −1.22534 | + | 1.22534i | ||||
\(683\) | − | 24.0000i | − | 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(684\) | 16.0000 | 0.611775 | ||||||||
\(685\) | 22.0000i | 0.840577i | ||||||||
\(686\) | 1.00000 | + | 1.00000i | 0.0381802 | + | 0.0381802i | ||||
\(687\) | −20.0000 | −0.763048 | ||||||||
\(688\) | − | 16.0000i | − | 0.609994i | ||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | −16.0000 | − | 16.0000i | −0.609110 | − | 0.609110i | ||||
\(691\) | 36.0000i | 1.36950i | 0.728776 | + | 0.684752i | \(0.240090\pi\) | ||||
−0.728776 | + | 0.684752i | \(0.759910\pi\) | |||||||
\(692\) | 28.0000 | 1.06440 | ||||||||
\(693\) | 4.00000i | 0.151947i | ||||||||
\(694\) | 16.0000 | − | 16.0000i | 0.607352 | − | 0.607352i | ||||
\(695\) | −4.00000 | −0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.00000 | − | 2.00000i | 0.0757011 | − | 0.0757011i | ||||
\(699\) | 36.0000i | 1.36165i | ||||||||
\(700\) | − | 2.00000i | − | 0.0755929i | ||||||
\(701\) | 16.0000i | 0.604312i | 0.953259 | + | 0.302156i | \(0.0977063\pi\) | ||||
−0.953259 | + | 0.302156i | \(0.902294\pi\) | |||||||
\(702\) | 24.0000 | + | 24.0000i | 0.905822 | + | 0.905822i | ||||
\(703\) | 80.0000 | 3.01726 | ||||||||
\(704\) | −32.0000 | −1.20605 | ||||||||
\(705\) | −16.0000 | −0.602595 | ||||||||
\(706\) | −24.0000 | − | 24.0000i | −0.903252 | − | 0.903252i | ||||
\(707\) | − | 2.00000i | − | 0.0752177i | ||||||
\(708\) | − | 16.0000i | − | 0.601317i | ||||||
\(709\) | 40.0000i | 1.50223i | 0.660171 | + | 0.751116i | \(0.270484\pi\) | ||||
−0.660171 | + | 0.751116i | \(0.729516\pi\) | |||||||
\(710\) | −2.00000 | + | 2.00000i | −0.0750587 | + | 0.0750587i | ||||
\(711\) | 2.00000 | 0.0750059 | ||||||||
\(712\) | −4.00000 | + | 4.00000i | −0.149906 | + | 0.149906i | ||||
\(713\) | −64.0000 | −2.39682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.0000i | − | 0.897549i | ||||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | − | 4.00000i | − | 0.149383i | ||||||
\(718\) | 6.00000 | + | 6.00000i | 0.223918 | + | 0.223918i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 4.00000i | 0.149071i | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | −45.0000 | − | 45.0000i | −1.67473 | − | 1.67473i | ||||
\(723\) | 36.0000i | 1.33885i | ||||||||
\(724\) | −4.00000 | −0.148659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.0000 | − | 10.0000i | 0.371135 | − | 0.371135i | ||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 12.0000 | + | 12.0000i | 0.444750 | + | 0.444750i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | −4.00000 | + | 4.00000i | −0.148047 | + | 0.148047i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 8.00000i | − | 0.295689i | ||||||
\(733\) | 6.00000i | 0.221615i | 0.993842 | + | 0.110808i | \(0.0353437\pi\) | ||||
−0.993842 | + | 0.110808i | \(0.964656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.00000 | −0.0737711 | ||||||||
\(736\) | −32.0000 | − | 32.0000i | −1.17954 | − | 1.17954i | ||||
\(737\) | −48.0000 | −1.76810 | ||||||||
\(738\) | 2.00000 | + | 2.00000i | 0.0736210 | + | 0.0736210i | ||||
\(739\) | − | 12.0000i | − | 0.441427i | −0.975339 | − | 0.220714i | \(-0.929161\pi\) | ||
0.975339 | − | 0.220714i | \(-0.0708386\pi\) | |||||||
\(740\) | 20.0000i | 0.735215i | ||||||||
\(741\) | 96.0000i | 3.52665i | ||||||||
\(742\) | 2.00000 | − | 2.00000i | 0.0734223 | − | 0.0734223i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 32.0000 | + | 32.0000i | 1.17318 | + | 1.17318i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.0000 | + | 34.0000i | −1.24483 | + | 1.24483i | ||||
\(747\) | 6.00000i | 0.219529i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000i | 0.292314i | ||||||||
\(750\) | 2.00000 | + | 2.00000i | 0.0730297 | + | 0.0730297i | ||||
\(751\) | 50.0000 | 1.82453 | 0.912263 | − | 0.409605i | \(-0.134333\pi\) | ||||
0.912263 | + | 0.409605i | \(0.134333\pi\) | |||||||
\(752\) | −32.0000 | −1.16692 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.00000i | − | 0.0727875i | ||||||
\(756\) | −8.00000 | −0.290957 | ||||||||
\(757\) | 38.0000i | 1.38113i | 0.723269 | + | 0.690567i | \(0.242639\pi\) | ||||
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(758\) | −12.0000 | + | 12.0000i | −0.435860 | + | 0.435860i | ||||
\(759\) | 64.0000 | 2.32305 | ||||||||
\(760\) | 16.0000 | − | 16.0000i | 0.580381 | − | 0.580381i | ||||
\(761\) | 34.0000 | 1.23250 | 0.616250 | − | 0.787551i | \(-0.288651\pi\) | ||||
0.616250 | + | 0.787551i | \(0.288651\pi\) | |||||||
\(762\) | 24.0000 | − | 24.0000i | 0.869428 | − | 0.869428i | ||||
\(763\) | − | 4.00000i | − | 0.144810i | ||||||
\(764\) | − | 4.00000i | − | 0.144715i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000 | 0.866590 | ||||||||
\(768\) | 32.0000i | 1.15470i | ||||||||
\(769\) | 42.0000 | 1.51456 | 0.757279 | − | 0.653091i | \(-0.226528\pi\) | ||||
0.757279 | + | 0.653091i | \(0.226528\pi\) | |||||||
\(770\) | 4.00000 | + | 4.00000i | 0.144150 | + | 0.144150i | ||||
\(771\) | 32.0000i | 1.15245i | ||||||||
\(772\) | − | 4.00000i | − | 0.143963i | ||||||
\(773\) | 6.00000i | 0.215805i | 0.994161 | + | 0.107903i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107903i | \(0.965587\pi\) | |||||||
\(774\) | 4.00000 | − | 4.00000i | 0.143777 | − | 0.143777i | ||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 32.0000 | − | 32.0000i | 1.14873 | − | 1.14873i | ||||
\(777\) | 20.0000 | 0.717496 | ||||||||
\(778\) | −20.0000 | + | 20.0000i | −0.717035 | + | 0.717035i | ||||
\(779\) | − | 16.0000i | − | 0.573259i | ||||||
\(780\) | −24.0000 | −0.859338 | ||||||||
\(781\) | − | 8.00000i | − | 0.286263i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | 2.00000 | 0.0713831 | ||||||||
\(786\) | 24.0000 | + | 24.0000i | 0.856052 | + | 0.856052i | ||||
\(787\) | − | 46.0000i | − | 1.63972i | −0.572562 | − | 0.819861i | \(-0.694050\pi\) | ||
0.572562 | − | 0.819861i | \(-0.305950\pi\) | |||||||
\(788\) | −20.0000 | −0.712470 | ||||||||
\(789\) | − | 24.0000i | − | 0.854423i | ||||||
\(790\) | 2.00000 | − | 2.00000i | 0.0711568 | − | 0.0711568i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | −8.00000 | − | 8.00000i | −0.284268 | − | 0.284268i | ||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 2.00000 | − | 2.00000i | 0.0709773 | − | 0.0709773i | ||||
\(795\) | 4.00000i | 0.141865i | ||||||||
\(796\) | − | 48.0000i | − | 1.70131i | ||||||
\(797\) | − | 18.0000i | − | 0.637593i | −0.947823 | − | 0.318796i | \(-0.896721\pi\) | ||
0.947823 | − | 0.318796i | \(-0.103279\pi\) | |||||||
\(798\) | −16.0000 | − | 16.0000i | −0.566394 | − | 0.566394i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | + | 4.00000i | 0.141421 | + | 0.141421i | ||||
\(801\) | −2.00000 | −0.0706665 | ||||||||
\(802\) | −18.0000 | − | 18.0000i | −0.635602 | − | 0.635602i | ||||
\(803\) | − | 16.0000i | − | 0.564628i | ||||||
\(804\) | 48.0000i | 1.69283i | ||||||||
\(805\) | 8.00000i | 0.281963i | ||||||||
\(806\) | −48.0000 | + | 48.0000i | −1.69073 | + | 1.69073i | ||||
\(807\) | −28.0000 | −0.985647 | ||||||||
\(808\) | 4.00000 | + | 4.00000i | 0.140720 | + | 0.140720i | ||||
\(809\) | −38.0000 | −1.33601 | −0.668004 | − | 0.744157i | \(-0.732851\pi\) | ||||
−0.668004 | + | 0.744157i | \(0.732851\pi\) | |||||||
\(810\) | 11.0000 | − | 11.0000i | 0.386501 | − | 0.386501i | ||||
\(811\) | − | 20.0000i | − | 0.702295i | −0.936320 | − | 0.351147i | \(-0.885792\pi\) | ||
0.936320 | − | 0.351147i | \(-0.114208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | −40.0000 | − | 40.0000i | −1.40200 | − | 1.40200i | ||||
\(815\) | −16.0000 | −0.560456 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | −6.00000 | − | 6.00000i | −0.209785 | − | 0.209785i | ||||
\(819\) | 6.00000i | 0.209657i | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | − | 44.0000i | − | 1.53561i | −0.640683 | − | 0.767805i | \(-0.721349\pi\) | ||
0.640683 | − | 0.767805i | \(-0.278651\pi\) | |||||||
\(822\) | −44.0000 | + | 44.0000i | −1.53468 | + | 1.53468i | ||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 16.0000 | − | 16.0000i | 0.557386 | − | 0.557386i | ||||
\(825\) | −8.00000 | −0.278524 | ||||||||
\(826\) | −4.00000 | + | 4.00000i | −0.139178 | + | 0.139178i | ||||
\(827\) | 28.0000i | 0.973655i | 0.873498 | + | 0.486828i | \(0.161846\pi\) | ||||
−0.873498 | + | 0.486828i | \(0.838154\pi\) | |||||||
\(828\) | − | 16.0000i | − | 0.556038i | ||||||
\(829\) | 2.00000i | 0.0694629i | 0.999397 | + | 0.0347314i | \(0.0110576\pi\) | ||||
−0.999397 | + | 0.0347314i | \(0.988942\pi\) | |||||||
\(830\) | 6.00000 | + | 6.00000i | 0.208263 | + | 0.208263i | ||||
\(831\) | −44.0000 | −1.52634 | ||||||||
\(832\) | −48.0000 | −1.66410 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.00000 | − | 8.00000i | −0.277017 | − | 0.277017i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 64.0000i | 2.21349i | ||||||||
\(837\) | − | 32.0000i | − | 1.10608i | ||||||
\(838\) | −4.00000 | + | 4.00000i | −0.138178 | + | 0.138178i | ||||
\(839\) | −20.0000 | −0.690477 | −0.345238 | − | 0.938515i | \(-0.612202\pi\) | ||||
−0.345238 | + | 0.938515i | \(0.612202\pi\) | |||||||
\(840\) | 4.00000 | − | 4.00000i | 0.138013 | − | 0.138013i | ||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | −4.00000 | + | 4.00000i | −0.137849 | + | 0.137849i | ||||
\(843\) | − | 44.0000i | − | 1.51544i | ||||||
\(844\) | 24.0000 | 0.826114 | ||||||||
\(845\) | − | 23.0000i | − | 0.791224i | ||||||
\(846\) | −8.00000 | − | 8.00000i | −0.275046 | − | 0.275046i | ||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | 8.00000i | 0.274721i | ||||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 80.0000i | − | 2.74236i | ||||||
\(852\) | −8.00000 | −0.274075 | ||||||||
\(853\) | − | 10.0000i | − | 0.342393i | −0.985237 | − | 0.171197i | \(-0.945237\pi\) | ||
0.985237 | − | 0.171197i | \(-0.0547634\pi\) | |||||||
\(854\) | −2.00000 | + | 2.00000i | −0.0684386 | + | 0.0684386i | ||||
\(855\) | 8.00000 | 0.273594 | ||||||||
\(856\) | −16.0000 | − | 16.0000i | −0.546869 | − | 0.546869i | ||||
\(857\) | 12.0000 | 0.409912 | 0.204956 | − | 0.978771i | \(-0.434295\pi\) | ||||
0.204956 | + | 0.978771i | \(0.434295\pi\) | |||||||
\(858\) | 48.0000 | − | 48.0000i | 1.63869 | − | 1.63869i | ||||
\(859\) | 20.0000i | 0.682391i | 0.939992 | + | 0.341196i | \(0.110832\pi\) | ||||
−0.939992 | + | 0.341196i | \(0.889168\pi\) | |||||||
\(860\) | − | 8.00000i | − | 0.272798i | ||||||
\(861\) | − | 4.00000i | − | 0.136320i | ||||||
\(862\) | −18.0000 | − | 18.0000i | −0.613082 | − | 0.613082i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 16.0000 | − | 16.0000i | 0.544331 | − | 0.544331i | ||||
\(865\) | 14.0000 | 0.476014 | ||||||||
\(866\) | 20.0000 | + | 20.0000i | 0.679628 | + | 0.679628i | ||||
\(867\) | − | 34.0000i | − | 1.15470i | ||||||
\(868\) | − | 16.0000i | − | 0.543075i | ||||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.0000 | −2.43963 | ||||||||
\(872\) | 8.00000 | + | 8.00000i | 0.270914 | + | 0.270914i | ||||
\(873\) | 16.0000 | 0.541518 | ||||||||
\(874\) | −64.0000 | + | 64.0000i | −2.16483 | + | 2.16483i | ||||
\(875\) | − | 1.00000i | − | 0.0338062i | ||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | 22.0000i | 0.742887i | 0.928456 | + | 0.371444i | \(0.121137\pi\) | ||||
−0.928456 | + | 0.371444i | \(0.878863\pi\) | |||||||
\(878\) | −28.0000 | − | 28.0000i | −0.944954 | − | 0.944954i | ||||
\(879\) | 44.0000 | 1.48408 | ||||||||
\(880\) | −16.0000 | −0.539360 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | −1.00000 | − | 1.00000i | −0.0336718 | − | 0.0336718i | ||||
\(883\) | 40.0000i | 1.34611i | 0.739594 | + | 0.673054i | \(0.235018\pi\) | ||||
−0.739594 | + | 0.673054i | \(0.764982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 8.00000i | − | 0.268917i | ||||||
\(886\) | −20.0000 | + | 20.0000i | −0.671913 | + | 0.671913i | ||||
\(887\) | −8.00000 | −0.268614 | −0.134307 | − | 0.990940i | \(-0.542881\pi\) | ||||
−0.134307 | + | 0.990940i | \(0.542881\pi\) | |||||||
\(888\) | −40.0000 | + | 40.0000i | −1.34231 | + | 1.34231i | ||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | −2.00000 | + | 2.00000i | −0.0670402 | + | 0.0670402i | ||||
\(891\) | 44.0000i | 1.47406i | ||||||||
\(892\) | − | 16.0000i | − | 0.535720i | ||||||
\(893\) | 64.0000i | 2.14168i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 8.00000 | − | 8.00000i | 0.267261 | − | 0.267261i | ||||
\(897\) | 96.0000 | 3.20535 | ||||||||
\(898\) | −6.00000 | − | 6.00000i | −0.200223 | − | 0.200223i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.00000i | 0.0666667i | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −8.00000 | + | 8.00000i | −0.266371 | + | 0.266371i | ||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | 12.0000 | − | 12.0000i | 0.399114 | − | 0.399114i | ||||
\(905\) | −2.00000 | −0.0664822 | ||||||||
\(906\) | 4.00000 | − | 4.00000i | 0.132891 | − | 0.132891i | ||||
\(907\) | − | 44.0000i | − | 1.46100i | −0.682915 | − | 0.730498i | \(-0.739288\pi\) | ||
0.682915 | − | 0.730498i | \(-0.260712\pi\) | |||||||
\(908\) | 36.0000 | 1.19470 | ||||||||
\(909\) | 2.00000i | 0.0663358i | ||||||||
\(910\) | 6.00000 | + | 6.00000i | 0.198898 | + | 0.198898i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 64.0000 | 2.11925 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | −6.00000 | − | 6.00000i | −0.198462 | − | 0.198462i | ||||
\(915\) | − | 4.00000i | − | 0.132236i | ||||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | − | 12.0000i | − | 0.396275i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.0000 | −0.461817 | −0.230909 | − | 0.972975i | \(-0.574170\pi\) | ||||
−0.230909 | + | 0.972975i | \(0.574170\pi\) | |||||||
\(920\) | −16.0000 | − | 16.0000i | −0.527504 | − | 0.527504i | ||||
\(921\) | −4.00000 | −0.131804 | ||||||||
\(922\) | 26.0000 | − | 26.0000i | 0.856264 | − | 0.856264i | ||||
\(923\) | − | 12.0000i | − | 0.394985i | ||||||
\(924\) | 16.0000i | 0.526361i | ||||||||
\(925\) | 10.0000i | 0.328798i | ||||||||
\(926\) | 20.0000 | + | 20.0000i | 0.657241 | + | 0.657241i | ||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.0000 | 1.50921 | 0.754606 | − | 0.656179i | \(-0.227828\pi\) | ||||
0.754606 | + | 0.656179i | \(0.227828\pi\) | |||||||
\(930\) | 16.0000 | + | 16.0000i | 0.524661 | + | 0.524661i | ||||
\(931\) | 8.00000i | 0.262189i | ||||||||
\(932\) | 36.0000i | 1.17922i | ||||||||
\(933\) | 40.0000i | 1.30954i | ||||||||
\(934\) | −26.0000 | + | 26.0000i | −0.850746 | + | 0.850746i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0000 | − | 12.0000i | −0.392232 | − | 0.392232i | ||||
\(937\) | −32.0000 | −1.04539 | −0.522697 | − | 0.852518i | \(-0.675074\pi\) | ||||
−0.522697 | + | 0.852518i | \(0.675074\pi\) | |||||||
\(938\) | 12.0000 | − | 12.0000i | 0.391814 | − | 0.391814i | ||||
\(939\) | 24.0000i | 0.783210i | ||||||||
\(940\) | −16.0000 | −0.521862 | ||||||||
\(941\) | − | 22.0000i | − | 0.717180i | −0.933495 | − | 0.358590i | \(-0.883258\pi\) | ||
0.933495 | − | 0.358590i | \(-0.116742\pi\) | |||||||
\(942\) | 4.00000 | + | 4.00000i | 0.130327 | + | 0.130327i | ||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | − | 16.0000i | − | 0.520756i | ||||||
\(945\) | −4.00000 | −0.130120 | ||||||||
\(946\) | 16.0000 | + | 16.0000i | 0.520205 | + | 0.520205i | ||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 8.00000 | 0.259828 | ||||||||
\(949\) | − | 24.0000i | − | 0.779073i | ||||||
\(950\) | 8.00000 | − | 8.00000i | 0.259554 | − | 0.259554i | ||||
\(951\) | −36.0000 | −1.16738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0000 | −0.453504 | −0.226752 | − | 0.973952i | \(-0.572811\pi\) | ||||
−0.226752 | + | 0.973952i | \(0.572811\pi\) | |||||||
\(954\) | −2.00000 | + | 2.00000i | −0.0647524 | + | 0.0647524i | ||||
\(955\) | − | 2.00000i | − | 0.0647185i | ||||||
\(956\) | − | 4.00000i | − | 0.129369i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.0000 | + | 28.0000i | 0.904639 | + | 0.904639i | ||||
\(959\) | 22.0000 | 0.710417 | ||||||||
\(960\) | 16.0000i | 0.516398i | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | −60.0000 | − | 60.0000i | −1.93448 | − | 1.93448i | ||||
\(963\) | − | 8.00000i | − | 0.257796i | ||||||
\(964\) | 36.0000i | 1.15948i | ||||||||
\(965\) | − | 2.00000i | − | 0.0643823i | ||||||
\(966\) | −16.0000 | + | 16.0000i | −0.514792 | + | 0.514792i | ||||
\(967\) | 40.0000 | 1.28631 | 0.643157 | − | 0.765735i | \(-0.277624\pi\) | ||||
0.643157 | + | 0.765735i | \(0.277624\pi\) | |||||||
\(968\) | 10.0000 | − | 10.0000i | 0.321412 | − | 0.321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.0000 | − | 16.0000i | 0.513729 | − | 0.513729i | ||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | 20.0000 | 0.641500 | ||||||||
\(973\) | 4.00000i | 0.128234i | ||||||||
\(974\) | −12.0000 | − | 12.0000i | −0.384505 | − | 0.384505i | ||||
\(975\) | −12.0000 | −0.384308 | ||||||||
\(976\) | − | 8.00000i | − | 0.256074i | ||||||
\(977\) | 50.0000 | 1.59964 | 0.799821 | − | 0.600239i | \(-0.204928\pi\) | ||||
0.799821 | + | 0.600239i | \(0.204928\pi\) | |||||||
\(978\) | −32.0000 | − | 32.0000i | −1.02325 | − | 1.02325i | ||||
\(979\) | − | 8.00000i | − | 0.255681i | ||||||
\(980\) | −2.00000 | −0.0638877 | ||||||||
\(981\) | 4.00000i | 0.127710i | ||||||||
\(982\) | −28.0000 | + | 28.0000i | −0.893516 | + | 0.893516i | ||||
\(983\) | −8.00000 | −0.255160 | −0.127580 | − | 0.991828i | \(-0.540721\pi\) | ||||
−0.127580 | + | 0.991828i | \(0.540721\pi\) | |||||||
\(984\) | 8.00000 | + | 8.00000i | 0.255031 | + | 0.255031i | ||||
\(985\) | −10.0000 | −0.318626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.0000i | 0.509286i | ||||||||
\(988\) | 96.0000i | 3.05417i | ||||||||
\(989\) | 32.0000i | 1.01754i | ||||||||
\(990\) | −4.00000 | − | 4.00000i | −0.127128 | − | 0.127128i | ||||
\(991\) | 50.0000 | 1.58830 | 0.794151 | − | 0.607720i | \(-0.207916\pi\) | ||||
0.794151 | + | 0.607720i | \(0.207916\pi\) | |||||||
\(992\) | 32.0000 | + | 32.0000i | 1.01600 | + | 1.01600i | ||||
\(993\) | −40.0000 | −1.26936 | ||||||||
\(994\) | 2.00000 | + | 2.00000i | 0.0634361 | + | 0.0634361i | ||||
\(995\) | − | 24.0000i | − | 0.760851i | ||||||
\(996\) | 24.0000i | 0.760469i | ||||||||
\(997\) | 10.0000i | 0.316703i | 0.987383 | + | 0.158352i | \(0.0506179\pi\) | ||||
−0.987383 | + | 0.158352i | \(0.949382\pi\) | |||||||
\(998\) | 28.0000 | − | 28.0000i | 0.886325 | − | 0.886325i | ||||
\(999\) | 40.0000 | 1.26554 |
(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 | 280.2.b.b.141.2 | yes | 2 | |
4.3 | odd | 2 | 1120.2.b.a.561.1 | 2 | |||
8.3 | odd | 2 | 1120.2.b.a.561.2 | 2 | |||
8.5 | even | 2 | inner | 280.2.b.b.141.1 | ✓ | 2 | |
16.3 | odd | 4 | 8960.2.a.t.1.1 | 1 | |||
16.5 | even | 4 | 8960.2.a.n.1.1 | 1 | |||
16.11 | odd | 4 | 8960.2.a.b.1.1 | 1 | |||
16.13 | even | 4 | 8960.2.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.b.b.141.1 | ✓ | 2 | 8.5 | even | 2 | inner | |
280.2.b.b.141.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1120.2.b.a.561.1 | 2 | 4.3 | odd | 2 | |||
1120.2.b.a.561.2 | 2 | 8.3 | odd | 2 | |||
8960.2.a.b.1.1 | 1 | 16.11 | odd | 4 | |||
8960.2.a.f.1.1 | 1 | 16.13 | even | 4 | |||
8960.2.a.n.1.1 | 1 | 16.5 | even | 4 | |||
8960.2.a.t.1.1 | 1 | 16.3 | odd | 4 |