Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), degree \(2\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} + 28x^{5} + 14x^{4} - 52x^{3} + 306x^{2} + 1052x + 1051 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.1 | ||
Root | \(-1.54823 + 0.711712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.o.865.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −1.99232 | + | 3.45080i | −0.890994 | + | 1.54325i | −0.0523084 | + | 0.998631i | \(0.516658\pi\) |
−0.838686 | + | 0.544616i | \(0.816675\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.657753 | + | 2.56269i | −0.248607 | + | 0.968604i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.444095 | + | 0.769196i | 0.133900 | + | 0.231921i | 0.925177 | − | 0.379537i | \(-0.123917\pi\) |
−0.791277 | + | 0.611458i | \(0.790583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.98465 | −1.93719 | −0.968596 | − | 0.248639i | \(-0.920017\pi\) | ||||
−0.968596 | + | 0.248639i | \(0.920017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.342247 | + | 0.592789i | 0.0830071 | + | 0.143773i | 0.904540 | − | 0.426388i | \(-0.140214\pi\) |
−0.821533 | + | 0.570161i | \(0.806881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73272 | − | 3.00116i | 0.397514 | − | 0.688514i | −0.595905 | − | 0.803055i | \(-0.703206\pi\) |
0.993419 | + | 0.114541i | \(0.0365398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.94638 | + | 5.10328i | −0.614363 | + | 1.06411i | 0.376133 | + | 0.926566i | \(0.377253\pi\) |
−0.990496 | + | 0.137542i | \(0.956080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.43870 | − | 9.42011i | −1.08774 | − | 1.88402i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.87741 | 1.09141 | 0.545703 | − | 0.837978i | \(-0.316263\pi\) | ||||
0.545703 | + | 0.837978i | \(0.316263\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.604133 | − | 1.04639i | −0.108505 | − | 0.187937i | 0.806660 | − | 0.591016i | \(-0.201273\pi\) |
−0.915165 | + | 0.403079i | \(0.867940\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.53287 | − | 7.37548i | −1.27329 | − | 1.24668i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.32689 | − | 7.49440i | 0.711337 | − | 1.23207i | −0.253019 | − | 0.967461i | \(-0.581423\pi\) |
0.964355 | − | 0.264610i | \(-0.0852433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.30015 | 0.983918 | 0.491959 | − | 0.870618i | \(-0.336281\pi\) | ||||
0.491959 | + | 0.870618i | \(0.336281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.888190 | 0.135448 | 0.0677239 | − | 0.997704i | \(-0.478426\pi\) | ||||
0.0677239 | + | 0.997704i | \(0.478426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.59417 | + | 2.76119i | −0.232534 | + | 0.402760i | −0.958553 | − | 0.284914i | \(-0.908035\pi\) |
0.726019 | + | 0.687674i | \(0.241368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.13472 | − | 3.37123i | −0.876389 | − | 0.481604i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.890475 | + | 1.54235i | 0.122316 | + | 0.211858i | 0.920681 | − | 0.390317i | \(-0.127634\pi\) |
−0.798365 | + | 0.602174i | \(0.794301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.53912 | −0.477215 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.11552 | − | 8.86034i | −0.665984 | − | 1.15352i | −0.979018 | − | 0.203776i | \(-0.934679\pi\) |
0.313034 | − | 0.949742i | \(-0.398655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.882798 | − | 1.52905i | 0.113031 | − | 0.195775i | −0.803960 | − | 0.594683i | \(-0.797277\pi\) |
0.916991 | + | 0.398908i | \(0.130611\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.9157 | − | 24.1027i | 1.72603 | − | 2.98957i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.83457 | − | 10.1058i | −0.712806 | − | 1.23462i | −0.963800 | − | 0.266628i | \(-0.914091\pi\) |
0.250993 | − | 0.967989i | \(-0.419243\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.50385 | 1.00922 | 0.504611 | − | 0.863347i | \(-0.331636\pi\) | ||||
0.504611 | + | 0.863347i | \(0.331636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.14240 | + | 8.90690i | 0.601872 | + | 1.04247i | 0.992537 | + | 0.121941i | \(0.0389117\pi\) |
−0.390665 | + | 0.920533i | \(0.627755\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.26331 | + | 0.632136i | −0.257928 | + | 0.0720386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64011 | + | 4.57281i | −0.297036 | + | 0.514482i | −0.975456 | − | 0.220192i | \(-0.929332\pi\) |
0.678420 | + | 0.734674i | \(0.262665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.4120 | −1.25263 | −0.626313 | − | 0.779572i | \(-0.715437\pi\) | ||||
−0.626313 | + | 0.779572i | \(0.715437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.72747 | −0.295835 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.77099 | + | 9.99565i | −0.611724 | + | 1.05954i | 0.379226 | + | 0.925304i | \(0.376190\pi\) |
−0.990950 | + | 0.134232i | \(0.957143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.59417 | − | 17.8995i | 0.481600 | − | 1.87637i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.90428 | + | 11.9586i | 0.708365 | + | 1.22692i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6003 | −1.07630 | −0.538149 | − | 0.842850i | \(-0.680876\pi\) | ||||
−0.538149 | + | 0.842850i | \(0.680876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.29248 | − | 12.6309i | −0.725628 | − | 1.25683i | −0.958715 | − | 0.284369i | \(-0.908216\pi\) |
0.233086 | − | 0.972456i | \(-0.425117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.88280 | + | 13.6534i | −0.776715 | + | 1.34531i | 0.157110 | + | 0.987581i | \(0.449782\pi\) |
−0.933825 | + | 0.357729i | \(0.883551\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.869126 | + | 1.50537i | −0.0840216 | + | 0.145530i | −0.904974 | − | 0.425467i | \(-0.860110\pi\) |
0.820952 | + | 0.570997i | \(0.193443\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.31551 | − | 5.74262i | −0.317568 | − | 0.550044i | 0.662412 | − | 0.749140i | \(-0.269533\pi\) |
−0.979980 | + | 0.199096i | \(0.936199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.17299 | 0.204418 | 0.102209 | − | 0.994763i | \(-0.467409\pi\) | ||||
0.102209 | + | 0.994763i | \(0.467409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.7403 | − | 20.3348i | −1.09479 | − | 1.89623i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.74425 | + | 0.487163i | −0.159895 | + | 0.0446582i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.10556 | − | 8.84309i | 0.464142 | − | 0.803917i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 23.4194 | 2.09469 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.2387 | −1.70716 | −0.853581 | − | 0.520960i | \(-0.825574\pi\) | ||||
−0.853581 | + | 0.520960i | \(0.825574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5198 | + | 18.2208i | −0.919120 | + | 1.59196i | −0.118364 | + | 0.992970i | \(0.537765\pi\) |
−0.800755 | + | 0.598992i | \(0.795568\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.55134 | + | 6.41445i | 0.568073 | + | 0.556203i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.66914 | + | 6.35514i | 0.313476 | + | 0.542956i | 0.979112 | − | 0.203320i | \(-0.0651732\pi\) |
−0.665637 | + | 0.746276i | \(0.731840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.17756 | 0.778430 | 0.389215 | − | 0.921147i | \(-0.372746\pi\) | ||||
0.389215 | + | 0.921147i | \(0.372746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.10185 | − | 5.37256i | −0.259390 | − | 0.449276i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.7097 | + | 20.2818i | −0.972437 | + | 1.68431i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1002 | + | 19.2261i | −0.909361 | + | 1.57506i | −0.0944073 | + | 0.995534i | \(0.530096\pi\) |
−0.814954 | + | 0.579526i | \(0.803238\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.326893 | + | 0.566196i | 0.0266022 | + | 0.0460764i | 0.879020 | − | 0.476785i | \(-0.158198\pi\) |
−0.852418 | + | 0.522861i | \(0.824865\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.81451 | 0.386711 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.48236 | + | 4.29958i | 0.198114 | + | 0.343144i | 0.947917 | − | 0.318518i | \(-0.103185\pi\) |
−0.749803 | + | 0.661661i | \(0.769852\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.1401 | − | 10.9073i | −0.877964 | − | 0.859619i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.93642 | + | 12.0142i | −0.543302 | + | 0.941027i | 0.455409 | + | 0.890282i | \(0.349493\pi\) |
−0.998712 | + | 0.0507449i | \(0.983840\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.1084 | −1.55604 | −0.778019 | − | 0.628241i | \(-0.783775\pi\) | ||||
−0.778019 | + | 0.628241i | \(0.783775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.7853 | 2.75271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.730438 | + | 1.26516i | −0.0555341 | + | 0.0961880i | −0.892456 | − | 0.451134i | \(-0.851019\pi\) |
0.836922 | + | 0.547322i | \(0.184353\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 27.7181 | − | 7.74159i | 2.09529 | − | 0.585209i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.88508 | − | 8.46121i | −0.365128 | − | 0.632421i | 0.623669 | − | 0.781689i | \(-0.285642\pi\) |
−0.988797 | + | 0.149268i | \(0.952308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.83928 | 0.136712 | 0.0683562 | − | 0.997661i | \(-0.478225\pi\) | ||||
0.0683562 | + | 0.997661i | \(0.478225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.2411 | + | 29.8625i | 1.26759 | + | 2.19554i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.303981 | + | 0.526510i | −0.0222293 | + | 0.0385022i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.44410 | + | 2.50125i | −0.104491 | + | 0.180984i | −0.913530 | − | 0.406771i | \(-0.866655\pi\) |
0.809039 | + | 0.587755i | \(0.199988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.849924 | − | 1.47211i | −0.0611789 | − | 0.105965i | 0.833814 | − | 0.552046i | \(-0.186153\pi\) |
−0.894993 | + | 0.446081i | \(0.852819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5465 | 1.10765 | 0.553823 | − | 0.832635i | \(-0.313169\pi\) | ||||
0.553823 | + | 0.832635i | \(0.313169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.59646 | − | 9.69335i | −0.396722 | − | 0.687143i | 0.596597 | − | 0.802541i | \(-0.296519\pi\) |
−0.993319 | + | 0.115398i | \(0.963186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.86588 | + | 15.0619i | −0.271332 | + | 1.05714i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.5519 | + | 21.7406i | −0.876665 | + | 1.51843i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.07797 | 0.212908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3155 | 1.19205 | 0.596024 | − | 0.802966i | \(-0.296746\pi\) | ||||
0.596024 | + | 0.802966i | \(0.296746\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.76956 | + | 3.06497i | −0.120683 | + | 0.209029i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.07894 | − | 0.859937i | 0.209012 | − | 0.0583764i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.39048 | − | 4.14042i | −0.160801 | − | 0.278515i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.595735 | 0.0398934 | 0.0199467 | − | 0.999801i | \(-0.493650\pi\) | ||||
0.0199467 | + | 0.999801i | \(0.493650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.4310 | − | 19.7991i | −0.758704 | − | 1.31411i | −0.943512 | − | 0.331339i | \(-0.892500\pi\) |
0.184808 | − | 0.982775i | \(-0.440834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4830 | − | 19.8891i | 0.758816 | − | 1.31431i | −0.184639 | − | 0.982806i | \(-0.559112\pi\) |
0.943455 | − | 0.331501i | \(-0.107555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.41735 | − | 9.38313i | 0.354903 | − | 0.614709i | −0.632199 | − | 0.774806i | \(-0.717847\pi\) |
0.987101 | + | 0.160097i | \(0.0511807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.35221 | − | 11.0023i | −0.414372 | − | 0.717714i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.60003 | −0.297551 | −0.148776 | − | 0.988871i | \(-0.547533\pi\) | ||||
−0.148776 | + | 0.988871i | \(0.547533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.68834 | − | 8.12045i | −0.302003 | − | 0.523084i | 0.674587 | − | 0.738196i | \(-0.264322\pi\) |
−0.976589 | + | 0.215112i | \(0.930988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.8558 | − | 14.4532i | 1.52409 | − | 0.923378i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.1025 | + | 20.9621i | −0.770061 | + | 1.33378i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.88819 | −0.119182 | −0.0595908 | − | 0.998223i | \(-0.518980\pi\) | ||||
−0.0595908 | + | 0.998223i | \(0.518980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.23389 | −0.329052 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9747 | − | 19.0087i | 0.684582 | − | 1.18573i | −0.288986 | − | 0.957333i | \(-0.593318\pi\) |
0.973568 | − | 0.228398i | \(-0.0733486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.3598 | + | 16.0179i | 1.01655 | + | 0.995306i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.92106 | − | 17.1838i | −0.611759 | − | 1.05960i | −0.990944 | − | 0.134277i | \(-0.957129\pi\) |
0.379185 | − | 0.925321i | \(-0.376204\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.09646 | −0.435932 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.51139 | − | 11.2781i | −0.397006 | − | 0.687635i | 0.596349 | − | 0.802725i | \(-0.296618\pi\) |
−0.993355 | + | 0.115090i | \(0.963284\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.4211 | + | 24.9780i | −0.876017 | + | 1.51731i | −0.0203422 | + | 0.999793i | \(0.506476\pi\) |
−0.855675 | + | 0.517513i | \(0.826858\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.83060 | − | 8.36685i | 0.291296 | − | 0.504540i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2051 | − | 19.4078i | −0.673251 | − | 1.16610i | −0.976977 | − | 0.213345i | \(-0.931564\pi\) |
0.303726 | − | 0.952759i | \(-0.401769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.0965 | −0.960234 | −0.480117 | − | 0.877204i | \(-0.659406\pi\) | ||||
−0.480117 | + | 0.877204i | \(0.659406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4279 | + | 26.7219i | 0.917095 | + | 1.58845i | 0.803805 | + | 0.594892i | \(0.202805\pi\) |
0.113289 | + | 0.993562i | \(0.463861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.14394 | + | 16.1453i | −0.244609 | + | 0.953028i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.26573 | − | 14.3167i | 0.486220 | − | 0.842157i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.154783 | 0.00904250 | 0.00452125 | − | 0.999990i | \(-0.498561\pi\) | ||||
0.00452125 | + | 0.999990i | \(0.498561\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 40.7671 | 2.37355 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.5794 | − | 35.6446i | 1.19014 | − | 2.06138i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.584210 | + | 2.27615i | −0.0336733 | + | 0.131195i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.51764 | + | 6.09273i | 0.201419 | + | 0.348869i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.6430 | 0.835720 | 0.417860 | − | 0.908511i | \(-0.362780\pi\) | ||||
0.417860 | + | 0.908511i | \(0.362780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7702 | + | 22.1186i | 0.724130 | + | 1.25423i | 0.959331 | + | 0.282283i | \(0.0910916\pi\) |
−0.235202 | + | 0.971947i | \(0.575575\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.48465 | + | 16.4279i | −0.536104 | + | 0.928559i | 0.463005 | + | 0.886356i | \(0.346771\pi\) |
−0.999109 | + | 0.0422036i | \(0.986562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.395867 | + | 0.685662i | −0.0222341 | + | 0.0385106i | −0.876928 | − | 0.480621i | \(-0.840411\pi\) |
0.854694 | + | 0.519132i | \(0.173745\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.61013 | + | 4.52087i | 0.146139 | + | 0.253120i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.37208 | 0.131986 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.9874 | + | 65.7961i | 2.10716 | + | 3.64971i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.02748 | − | 5.90154i | −0.332306 | − | 0.325362i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.25253 | + | 16.0258i | −0.508565 | + | 0.880860i | 0.491386 | + | 0.870942i | \(0.336490\pi\) |
−0.999951 | + | 0.00991827i | \(0.996843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 46.4974 | 2.54042 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.41169 | −0.131373 | −0.0656865 | − | 0.997840i | \(-0.520924\pi\) | ||||
−0.0656865 | + | 0.997840i | \(0.520924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.536585 | − | 0.929392i | 0.0290577 | − | 0.0503294i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6745 | − | 13.5039i | 0.684360 | − | 0.729144i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.60185 | − | 11.4347i | −0.354406 | − | 0.613849i | 0.632610 | − | 0.774470i | \(-0.281984\pi\) |
−0.987016 | + | 0.160621i | \(0.948650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0885 | −1.28943 | −0.644715 | − | 0.764423i | \(-0.723024\pi\) | ||||
−0.644715 | + | 0.764423i | \(0.723024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0550 | + | 17.4159i | 0.535176 | + | 0.926952i | 0.999155 | + | 0.0411059i | \(0.0130881\pi\) |
−0.463979 | + | 0.885846i | \(0.653579\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.9424 | + | 29.3451i | −0.899210 | + | 1.55748i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.67514 | + | 16.7578i | −0.510634 | + | 0.884444i | 0.489290 | + | 0.872121i | \(0.337256\pi\) |
−0.999924 | + | 0.0123231i | \(0.996077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.49535 | + | 6.05412i | 0.183966 | + | 0.318638i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.9813 | −2.14506 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3982 | + | 21.4742i | 0.647178 | + | 1.12095i | 0.983794 | + | 0.179303i | \(0.0573844\pi\) |
−0.336616 | + | 0.941642i | \(0.609282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.53827 | + | 1.26752i | −0.235615 | + | 0.0658066i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.19291 | − | 15.9226i | 0.475991 | − | 0.824440i | −0.523631 | − | 0.851945i | \(-0.675423\pi\) |
0.999622 | + | 0.0275049i | \(0.00875618\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.0516 | −2.11426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.23588 | −0.423049 | −0.211524 | − | 0.977373i | \(-0.567843\pi\) | ||||
−0.211524 | + | 0.977373i | \(0.567843\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.47554 | − | 14.6801i | 0.433080 | − | 0.750117i | −0.564057 | − | 0.825736i | \(-0.690760\pi\) |
0.997137 | + | 0.0756194i | \(0.0240934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.32787 | − | 9.06967i | 0.118639 | − | 0.462233i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.00371 | + | 10.3987i | 0.304400 | + | 0.527237i | 0.977128 | − | 0.212654i | \(-0.0682106\pi\) |
−0.672727 | + | 0.739890i | \(0.734877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.03356 | −0.203986 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.5199 | − | 18.2210i | −0.529315 | − | 0.916800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.77939 | + | 6.54609i | −0.189682 | + | 0.328539i | −0.945144 | − | 0.326653i | \(-0.894079\pi\) |
0.755462 | + | 0.655192i | \(0.227412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.32306 | + | 9.21982i | −0.265821 | + | 0.460416i | −0.967778 | − | 0.251803i | \(-0.918976\pi\) |
0.701957 | + | 0.712219i | \(0.252310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.21965 | + | 7.30865i | 0.210196 | + | 0.364070i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.68621 | 0.380991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.45177 | + | 5.97864i | 0.170679 | + | 0.295625i | 0.938657 | − | 0.344851i | \(-0.112071\pi\) |
−0.767978 | + | 0.640476i | \(0.778737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.0710 | − | 7.28156i | 1.28287 | − | 0.358302i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.7363 | − | 39.3805i | 1.11608 | − | 1.93311i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2205 | −1.03669 | −0.518345 | − | 0.855171i | \(-0.673452\pi\) | ||||
−0.518345 | + | 0.855171i | \(0.673452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8529 | 0.967572 | 0.483786 | − | 0.875186i | \(-0.339261\pi\) | ||||
0.483786 | + | 0.875186i | \(0.339261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.72276 | − | 6.44801i | 0.180580 | − | 0.312774i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.33782 | + | 3.26807i | 0.161528 | + | 0.158153i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.7923 | + | 23.8890i | 0.664354 | + | 1.15069i | 0.979460 | + | 0.201638i | \(0.0646264\pi\) |
−0.315107 | + | 0.949056i | \(0.602040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.90046 | 0.0913301 | 0.0456650 | − | 0.998957i | \(-0.485459\pi\) | ||||
0.0456650 | + | 0.998957i | \(0.485459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.2105 | + | 17.6851i | 0.488435 | + | 0.845995i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0604 | − | 26.0853i | 0.718792 | − | 1.24498i | −0.242687 | − | 0.970105i | \(-0.578029\pi\) |
0.961479 | − | 0.274879i | \(-0.0886378\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.3154 | + | 29.9911i | −0.822679 | + | 1.42492i | 0.0810014 | + | 0.996714i | \(0.474188\pi\) |
−0.903680 | + | 0.428208i | \(0.859145\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.9953 | − | 39.8291i | −1.09008 | − | 1.88808i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.2342 | −1.09649 | −0.548244 | − | 0.836318i | \(-0.684704\pi\) | ||||
−0.548244 | + | 0.836318i | \(0.684704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.79787 | + | 4.84605i | 0.131746 | + | 0.228192i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 52.6145 | + | 51.5151i | 2.46660 | + | 2.41506i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.01367 | − | 1.75573i | 0.0474176 | − | 0.0821297i | −0.841342 | − | 0.540502i | \(-0.818234\pi\) |
0.888760 | + | 0.458373i | \(0.151568\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.2371 | −1.64115 | −0.820577 | − | 0.571535i | \(-0.806348\pi\) | ||||
−0.820577 | + | 0.571535i | \(0.806348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.28195 | 0.291947 | 0.145973 | − | 0.989289i | \(-0.453369\pi\) | ||||
0.145973 | + | 0.989289i | \(0.453369\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.74579 | + | 13.4161i | −0.358432 | + | 0.620823i | −0.987699 | − | 0.156366i | \(-0.950022\pi\) |
0.629267 | + | 0.777189i | \(0.283355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.7356 | − | 8.30507i | 1.37306 | − | 0.383493i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.394441 | + | 0.683192i | 0.0181364 | + | 0.0314132i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −37.6950 | −1.72957 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.2119 | + | 31.5439i | 0.832121 | + | 1.44128i | 0.896353 | + | 0.443341i | \(0.146207\pi\) |
−0.0642320 | + | 0.997935i | \(0.520460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.2218 | + | 52.3457i | −1.37800 | + | 2.38676i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.1192 | − | 36.5796i | 0.958975 | − | 1.66099i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.6178 | − | 21.8547i | −0.571767 | − | 0.990330i | −0.996385 | − | 0.0849571i | \(-0.972925\pi\) |
0.424617 | − | 0.905373i | \(-0.360409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0305 | −1.35526 | −0.677628 | − | 0.735405i | \(-0.736992\pi\) | ||||
−0.677628 | + | 0.735405i | \(0.736992\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.01153 | + | 3.48406i | 0.0905945 | + | 0.156914i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.59343 | + | 21.7927i | −0.250900 | + | 0.977536i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.96247 | − | 8.59526i | 0.222151 | − | 0.384777i | −0.733310 | − | 0.679894i | \(-0.762026\pi\) |
0.955461 | + | 0.295118i | \(0.0953589\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.12095 | 0.228332 | 0.114166 | − | 0.993462i | \(-0.463580\pi\) | ||||
0.114166 | + | 0.993462i | \(0.463580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 58.1159 | 2.58612 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.14851 | + | 3.72133i | −0.0952311 | + | 0.164945i | −0.909705 | − | 0.415255i | \(-0.863692\pi\) |
0.814474 | + | 0.580200i | \(0.197026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.2080 | + | 7.31982i | −1.15937 | + | 0.323810i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31.4102 | − | 54.4040i | −1.38410 | − | 2.39733i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.83186 | −0.124545 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.52520 | + | 11.3020i | 0.285874 | + | 0.495148i | 0.972821 | − | 0.231559i | \(-0.0743828\pi\) |
−0.686947 | + | 0.726708i | \(0.741049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.16543 | + | 5.48269i | −0.138415 | + | 0.239741i | −0.926897 | − | 0.375317i | \(-0.877534\pi\) |
0.788482 | + | 0.615058i | \(0.210867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.413525 | − | 0.716247i | 0.0180134 | − | 0.0312002i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.86231 | − | 10.1538i | −0.254883 | − | 0.441470i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −44.0043 | −1.90604 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.46316 | − | 5.99837i | −0.149725 | − | 0.259332i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.131267 | − | 6.21595i | −0.00565407 | − | 0.267740i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.2043 | + | 17.6744i | −0.438717 | + | 0.759880i | −0.997591 | − | 0.0693725i | \(-0.977900\pi\) |
0.558874 | + | 0.829253i | \(0.311234\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 26.4222 | 1.13180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.08732 | 0.345789 | 0.172894 | − | 0.984940i | \(-0.444688\pi\) | ||||
0.172894 | + | 0.984940i | \(0.444688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1839 | − | 17.6391i | 0.433849 | − | 0.751449i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.98214 | − | 9.77357i | −0.424484 | − | 0.415614i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.99018 | + | 5.17914i | 0.126698 | + | 0.219447i | 0.922395 | − | 0.386247i | \(-0.126229\pi\) |
−0.795698 | + | 0.605694i | \(0.792895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.20370 | −0.262388 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.20059 | − | 12.4718i | −0.303469 | − | 0.525623i | 0.673451 | − | 0.739232i | \(-0.264811\pi\) |
−0.976919 | + | 0.213609i | \(0.931478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.32930 | + | 7.49856i | −0.182135 | + | 0.315467i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.36830 | + | 7.56612i | −0.183129 | + | 0.317188i | −0.942944 | − | 0.332950i | \(-0.891956\pi\) |
0.759816 | + | 0.650139i | \(0.225289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.123197 | + | 0.213384i | 0.00515564 | + | 0.00892983i | 0.868592 | − | 0.495528i | \(-0.165026\pi\) |
−0.863436 | + | 0.504458i | \(0.831692\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 64.0979 | 2.67307 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.74257 | − | 6.48231i | −0.155805 | − | 0.269862i | 0.777547 | − | 0.628825i | \(-0.216464\pi\) |
−0.933352 | + | 0.358963i | \(0.883130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.50625 | − | 29.2453i | 0.311412 | − | 1.21330i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.790911 | + | 1.36990i | −0.0327562 | + | 0.0567354i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.2800 | 0.465574 | 0.232787 | − | 0.972528i | \(-0.425216\pi\) | ||||
0.232787 | + | 0.972528i | \(0.425216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.18718 | −0.172530 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.51846 | + | 2.63005i | −0.0623557 | + | 0.108003i | −0.895518 | − | 0.445025i | \(-0.853195\pi\) |
0.833162 | + | 0.553029i | \(0.186528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.79400 | − | 6.98964i | 0.0735468 | − | 0.286547i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.22901 | − | 5.59281i | −0.131934 | − | 0.228516i | 0.792488 | − | 0.609887i | \(-0.208785\pi\) |
−0.924422 | + | 0.381371i | \(0.875452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.0578 | 1.43004 | 0.715019 | − | 0.699105i | \(-0.246418\pi\) | ||||
0.715019 | + | 0.699105i | \(0.246418\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.3438 | + | 35.2366i | 0.827095 | + | 1.43257i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.04055 | − | 12.1946i | 0.285767 | − | 0.494963i | −0.687028 | − | 0.726631i | \(-0.741085\pi\) |
0.972795 | + | 0.231668i | \(0.0744183\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.1347 | − | 19.2859i | 0.450463 | − | 0.780224i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.160037 | + | 0.277193i | 0.00646385 | + | 0.0111957i | 0.869239 | − | 0.494392i | \(-0.164609\pi\) |
−0.862775 | + | 0.505587i | \(0.831276\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.2145 | −0.894321 | −0.447161 | − | 0.894454i | \(-0.647565\pi\) | ||||
−0.447161 | + | 0.894454i | \(0.647565\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.754894 | + | 1.30752i | 0.0303418 | + | 0.0525535i | 0.880798 | − | 0.473493i | \(-0.157007\pi\) |
−0.850456 | + | 0.526047i | \(0.823674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.8198 | − | 21.3639i | −0.874193 | − | 0.855927i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.4655 | + | 33.7152i | −0.778619 | + | 1.34861i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.92347 | 0.236184 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.55733 | −0.101806 | −0.0509029 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509029 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.3298 | − | 66.3891i | 1.52107 | − | 2.63457i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 42.8489 | + | 23.5468i | 1.69773 | + | 0.932960i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3160 | − | 21.3319i | −0.486452 | − | 0.842559i | 0.513427 | − | 0.858133i | \(-0.328376\pi\) |
−0.999879 | + | 0.0155743i | \(0.995042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.7486 | −1.21261 | −0.606303 | − | 0.795234i | \(-0.707348\pi\) | ||||
−0.606303 | + | 0.795234i | \(0.707348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.2787 | − | 24.7314i | −0.561352 | − | 0.972291i | −0.997379 | − | 0.0723568i | \(-0.976948\pi\) |
0.436027 | − | 0.899934i | \(-0.356385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.54356 | − | 7.86967i | 0.178350 | − | 0.308912i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.8545 | + | 23.9967i | −0.542169 | + | 0.939064i | 0.456610 | + | 0.889667i | \(0.349063\pi\) |
−0.998779 | + | 0.0493974i | \(0.984270\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.9177 | − | 72.6036i | −1.63786 | − | 2.83686i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.7244 | 1.35267 | 0.676335 | − | 0.736594i | \(-0.263567\pi\) | ||||
0.676335 | + | 0.736594i | \(0.263567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.1254 | − | 34.8582i | −0.782786 | − | 1.35582i | −0.930313 | − | 0.366767i | \(-0.880465\pi\) |
0.147527 | − | 0.989058i | \(-0.452869\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −35.1874 | + | 9.82773i | −1.36451 | + | 0.381103i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3171 | + | 29.9940i | −0.670520 | + | 1.16137i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.56819 | 0.0605391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.6202 | −0.756304 | −0.378152 | − | 0.925743i | \(-0.623440\pi\) | ||||
−0.378152 | + | 0.925743i | \(0.623440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.22290 | + | 10.7784i | −0.239165 | + | 0.414247i | −0.960475 | − | 0.278366i | \(-0.910207\pi\) |
0.721310 | + | 0.692613i | \(0.243540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.97238 | − | 27.1653i | 0.267575 | − | 1.04251i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.36602 | + | 5.83011i | 0.128797 | + | 0.223083i | 0.923211 | − | 0.384294i | \(-0.125555\pi\) |
−0.794414 | + | 0.607377i | \(0.792222\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.2405 | −1.11722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.21965 | − | 10.7728i | −0.236950 | − | 0.410409i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1891 | + | 41.8967i | −0.920196 | + | 1.59383i | −0.121086 | + | 0.992642i | \(0.538638\pi\) |
−0.799110 | + | 0.601184i | \(0.794696\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.2847 | + | 31.6700i | −0.693577 | + | 1.20131i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.15621 | + | 3.73466i | 0.0816722 | + | 0.141460i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.6903 | −0.781461 | −0.390730 | − | 0.920505i | \(-0.627778\pi\) | ||||
−0.390730 | + | 0.920505i | \(0.627778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9946 | − | 25.9714i | −0.565532 | − | 0.979531i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.1658 | − | 10.3803i | 1.39776 | − | 0.390391i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4717 | + | 23.3337i | −0.505941 | + | 0.876315i | 0.494036 | + | 0.869442i | \(0.335521\pi\) |
−0.999976 | + | 0.00687356i | \(0.997812\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.12002 | 0.266647 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.7195 | 0.924458 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.48080 | + | 7.76097i | −0.167106 | + | 0.289435i | −0.937401 | − | 0.348252i | \(-0.886775\pi\) |
0.770295 | + | 0.637687i | \(0.220109\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.8045 | − | 29.1817i | −1.10998 | − | 1.08678i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.9655 | − | 55.3658i | −1.18717 | − | 2.05623i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.86854 | −0.0693004 | −0.0346502 | − | 0.999400i | \(-0.511032\pi\) | ||||
−0.0346502 | + | 0.999400i | \(0.511032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.303981 | + | 0.526510i | 0.0112431 | + | 0.0194737i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2585 | − | 28.1606i | 0.600522 | − | 1.04014i | −0.392220 | − | 0.919872i | \(-0.628293\pi\) |
0.992742 | − | 0.120263i | \(-0.0383739\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.18221 | − | 8.97585i | 0.190889 | − | 0.330630i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.8522 | − | 32.6530i | −0.693490 | − | 1.20116i | −0.970687 | − | 0.240347i | \(-0.922739\pi\) |
0.277197 | − | 0.960813i | \(-0.410595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.3073 | 0.781689 | 0.390844 | − | 0.920457i | \(-0.372183\pi\) | ||||
0.390844 | + | 0.920457i | \(0.372183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.2302 | − | 76.6090i | −1.62047 | − | 2.80674i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.28612 | − | 3.21746i | −0.120072 | − | 0.117563i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.24028 | − | 3.88028i | 0.0817490 | − | 0.141593i | −0.822252 | − | 0.569123i | \(-0.807283\pi\) |
0.904001 | + | 0.427530i | \(0.140616\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.60511 | −0.0948096 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.1970 | −1.53367 | −0.766837 | − | 0.641841i | \(-0.778171\pi\) | ||||
−0.766837 | + | 0.641841i | \(0.778171\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9791 | − | 27.6766i | 0.579243 | − | 1.00328i | −0.416324 | − | 0.909216i | \(-0.636682\pi\) |
0.995566 | − | 0.0940611i | \(-0.0299849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.8973 | − | 4.71937i | 0.611724 | − | 0.170853i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.7301 | + | 61.8863i | 1.29014 | + | 2.23459i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.12716 | −0.0767075 | −0.0383537 | − | 0.999264i | \(-0.512211\pi\) | ||||
−0.0383537 | + | 0.999264i | \(0.512211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.11167 | + | 7.12162i | 0.147887 | + | 0.256147i | 0.930446 | − | 0.366429i | \(-0.119420\pi\) |
−0.782560 | + | 0.622576i | \(0.786086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.57140 | + | 11.3820i | −0.236052 | + | 0.408853i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.9164 | − | 18.9078i | 0.391121 | − | 0.677442i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.77652 | + | 6.54112i | 0.135134 | + | 0.234060i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.7827 | −0.706074 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.86744 | + | 10.1627i | 0.209152 | + | 0.362262i | 0.951448 | − | 0.307811i | \(-0.0995964\pi\) |
−0.742296 | + | 0.670072i | \(0.766263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.42929 | + | 5.56869i | −0.0508197 | + | 0.198000i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.16603 | + | 10.6799i | −0.218962 | + | 0.379254i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.3167 | 0.755077 | 0.377538 | − | 0.925994i | \(-0.376771\pi\) | ||||
0.377538 | + | 0.925994i | \(0.376771\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.18240 | −0.0772078 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.56743 | + | 7.91102i | −0.161181 | + | 0.279174i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 59.8338 | − | 16.7114i | 2.10887 | − | 0.589000i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.9632 | + | 31.1131i | 0.631551 | + | 1.09388i | 0.987235 | + | 0.159272i | \(0.0509147\pi\) |
−0.355684 | + | 0.934606i | \(0.615752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.7179 | −0.867962 | −0.433981 | − | 0.900922i | \(-0.642892\pi\) | ||||
−0.433981 | + | 0.900922i | \(0.642892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.6392 | − | 47.8725i | −0.968158 | − | 1.67690i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.53899 | − | 2.66560i | 0.0538423 | − | 0.0932577i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.4426 | − | 18.0870i | 0.364448 | − | 0.631242i | −0.624240 | − | 0.781233i | \(-0.714591\pi\) |
0.988687 | + | 0.149991i | \(0.0479245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.60341 | + | 11.4374i | 0.230180 | + | 0.398684i | 0.957861 | − | 0.287232i | \(-0.0927350\pi\) |
−0.727681 | + | 0.685916i | \(0.759402\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.29125 | 0.149221 | 0.0746107 | − | 0.997213i | \(-0.476229\pi\) | ||||
0.0746107 | + | 0.997213i | \(0.476229\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.9754 | − | 24.2061i | −0.485387 | − | 0.840714i | 0.514472 | − | 0.857507i | \(-0.327988\pi\) |
−0.999859 | + | 0.0167927i | \(0.994654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.101162 | − | 4.79039i | −0.00350507 | − | 0.165977i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.0625 | − | 69.3903i | 1.38642 | − | 2.40135i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.5189 | −1.08815 | −0.544077 | − | 0.839035i | \(-0.683120\pi\) | ||||
−0.544077 | + | 0.839035i | \(0.683120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.54390 | 0.191169 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −71.2958 | + | 123.488i | −2.45265 | + | 4.24812i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.3039 | + | 18.9005i | 0.663289 | + | 0.649429i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.4973 | + | 44.1627i | 0.874038 | + | 1.51388i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.81650 | 0.336111 | 0.168055 | − | 0.985778i | \(-0.446251\pi\) | ||||
0.168055 | + | 0.985778i | \(0.446251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.3443 | − | 23.1130i | −0.455832 | − | 0.789524i | 0.542904 | − | 0.839795i | \(-0.317325\pi\) |
−0.998736 | + | 0.0502711i | \(0.983991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0349 | − | 29.5053i | 0.581223 | − | 1.00671i | −0.414111 | − | 0.910226i | \(-0.635908\pi\) |
0.995335 | − | 0.0964822i | \(-0.0307591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.66218 | − | 8.07514i | 0.158703 | − | 0.274881i | −0.775698 | − | 0.631104i | \(-0.782602\pi\) |
0.934401 | + | 0.356223i | \(0.115936\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.91054 | − | 5.04120i | −0.0989612 | − | 0.171406i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.68985 | −0.159092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.7524 | + | 70.5852i | 1.38084 | + | 2.39169i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.4042 | + | 60.0165i | −0.520756 | + | 2.02893i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.592608 | − | 1.02643i | 0.0200109 | − | 0.0346600i | −0.855847 | − | 0.517230i | \(-0.826963\pi\) |
0.875857 | + | 0.482570i | \(0.160297\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.2538 | 1.32249 | 0.661247 | − | 0.750168i | \(-0.270027\pi\) | ||||
0.661247 | + | 0.750168i | \(0.270027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.4854 | −0.790346 | −0.395173 | − | 0.918607i | \(-0.629315\pi\) | ||||
−0.395173 | + | 0.918607i | \(0.629315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.86542 | − | 17.0874i | 0.331248 | − | 0.573739i | −0.651509 | − | 0.758641i | \(-0.725864\pi\) |
0.982757 | + | 0.184902i | \(0.0591969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.6543 | − | 49.3028i | 0.424413 | − | 1.65356i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.52451 | + | 9.56873i | 0.184871 | + | 0.320205i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.9307 | 1.30131 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.55073 | − | 6.15005i | −0.118424 | − | 0.205116i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.609525 | + | 1.05573i | −0.0203062 | + | 0.0351714i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.66443 | + | 6.34699i | −0.121810 | + | 0.210981i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.707545 | + | 1.22550i | 0.0234936 | + | 0.0406922i | 0.877533 | − | 0.479516i | \(-0.159188\pi\) |
−0.854040 | + | 0.520208i | \(0.825854\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4256 | 0.709862 | 0.354931 | − | 0.934893i | \(-0.384504\pi\) | ||||
0.354931 | + | 0.934893i | \(0.384504\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.06800 | − | 8.77803i | −0.167726 | − | 0.290510i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.7749 | − | 38.9438i | −1.31348 | − | 1.28604i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.48008 | + | 12.9559i | −0.246745 | + | 0.427375i | −0.962621 | − | 0.270853i | \(-0.912694\pi\) |
0.715876 | + | 0.698228i | \(0.246028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −59.3964 | −1.95506 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −94.1307 | −3.09500 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.9699 | + | 20.7325i | −0.392720 | + | 0.680210i | −0.992807 | − | 0.119724i | \(-0.961799\pi\) |
0.600088 | + | 0.799934i | \(0.295132\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.7474 | + | 12.5699i | −0.679968 | + | 0.411962i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.21126 | − | 2.09796i | −0.0396123 | − | 0.0686105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.81330 | −0.124575 | −0.0622876 | − | 0.998058i | \(-0.519840\pi\) | ||||
−0.0622876 | + | 0.998058i | \(0.519840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.5406 | + | 47.7016i | 0.897796 | + | 1.55503i | 0.830305 | + | 0.557309i | \(0.188166\pi\) |
0.0674911 | + | 0.997720i | \(0.478501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.5626 | + | 32.1514i | −0.604483 | + | 1.04699i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.6905 | + | 35.8370i | −0.672351 | + | 1.16455i | 0.304884 | + | 0.952389i | \(0.401382\pi\) |
−0.977236 | + | 0.212157i | \(0.931951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.9178 | − | 62.2115i | −1.16594 | − | 2.01947i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.2037 | 0.881215 | 0.440608 | − | 0.897700i | \(-0.354763\pi\) | ||||
0.440608 | + | 0.897700i | \(0.354763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.75421 | − | 9.96658i | −0.186202 | − | 0.322511i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.6996 | + | 5.22275i | −0.603842 | + | 0.168651i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7700 | − | 25.5825i | 0.476453 | − | 0.825241i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.77329 | 0.218040 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.0322 | −0.804981 | −0.402490 | − | 0.915424i | \(-0.631855\pi\) | ||||
−0.402490 | + | 0.915424i | \(0.631855\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.28109 | + | 7.41506i | −0.137387 | + | 0.237961i | −0.926507 | − | 0.376278i | \(-0.877204\pi\) |
0.789120 | + | 0.614239i | \(0.210537\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.03657 | + | 23.5192i | −0.193523 | + | 0.753991i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.3744 | − | 19.7011i | −0.363900 | − | 0.630294i | 0.624699 | − | 0.780866i | \(-0.285222\pi\) |
−0.988599 | + | 0.150572i | \(0.951888\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.2515 | −0.327639 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.4945 | + | 26.8372i | 0.494197 | + | 0.855975i | 0.999978 | − | 0.00668727i | \(-0.00212864\pi\) |
−0.505780 | + | 0.862662i | \(0.668795\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.9737 | + | 53.6481i | −0.986906 | + | 1.70937i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.61695 | + | 4.53268i | −0.0832141 | + | 0.144131i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.37667 | + | 11.0447i | 0.202561 | + | 0.350847i | 0.949353 | − | 0.314211i | \(-0.101740\pi\) |
−0.746792 | + | 0.665058i | \(0.768407\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.5998 | 1.41391 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.92720 | + | 15.4624i | 0.282727 | + | 0.489698i | 0.972055 | − | 0.234751i | \(-0.0754276\pi\) |
−0.689328 | + | 0.724449i | \(0.742094\pi\) | |||||||
\(998\) | 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 | 1512.2.s.o.1297.1 | yes | 8 | |
3.2 | odd | 2 | 1512.2.s.n.1297.4 | yes | 8 | ||
7.4 | even | 3 | inner | 1512.2.s.o.865.1 | yes | 8 | |
21.11 | odd | 6 | 1512.2.s.n.865.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.n.865.4 | ✓ | 8 | 21.11 | odd | 6 | ||
1512.2.s.n.1297.4 | yes | 8 | 3.2 | odd | 2 | ||
1512.2.s.o.865.1 | yes | 8 | 7.4 | even | 3 | inner | |
1512.2.s.o.1297.1 | yes | 8 | 1.1 | even | 1 | trivial |