Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(881,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.q (of order \(3\), degree \(2\), not 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.3518667.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 881.1 | ||
Root | \(-1.25351 - 2.17114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.881 |
Dual form | 1520.2.q.j.961.1 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.25351 | − | 2.17114i | −0.723714 | − | 1.25351i | −0.959501 | − | 0.281705i | \(-0.909100\pi\) |
0.235787 | − | 0.971805i | \(-0.424233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.50702 | −1.32553 | −0.662764 | − | 0.748828i | \(-0.730617\pi\) | ||||
−0.662764 | + | 0.748828i | \(0.730617\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.64257 | + | 2.84502i | −0.547524 | + | 0.948339i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50702 | 1.35892 | 0.679459 | − | 0.733714i | \(-0.262215\pi\) | ||||
0.679459 | + | 0.733714i | \(0.262215\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 4.33013i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.25351 | − | 2.17114i | 0.323655 | − | 0.560586i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.0793049 | − | 0.137360i | −0.0192343 | − | 0.0333147i | 0.856248 | − | 0.516565i | \(-0.172790\pi\) |
−0.875482 | + | 0.483250i | \(0.839456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.26053 | + | 0.920816i | 0.977432 | + | 0.211250i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.39608 | + | 7.61423i | 0.959303 | + | 1.66156i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.579305 | − | 1.00339i | 0.120793 | − | 0.209220i | −0.799287 | − | 0.600949i | \(-0.794789\pi\) |
0.920081 | + | 0.391729i | \(0.128123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.714858 | 0.137574 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75351 | − | 3.03717i | 0.325619 | − | 0.563988i | −0.656019 | − | 0.754745i | \(-0.727761\pi\) |
0.981637 | + | 0.190757i | \(0.0610942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.28514 | 0.410424 | 0.205212 | − | 0.978718i | \(-0.434212\pi\) | ||||
0.205212 | + | 0.978718i | \(0.434212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.64959 | − | 9.78538i | −0.983467 | − | 1.70342i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.75351 | − | 3.03717i | −0.296397 | − | 0.513375i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9648 | −1.80260 | −0.901302 | − | 0.433192i | \(-0.857387\pi\) | ||||
−0.901302 | + | 0.433192i | \(0.857387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.5351 | −2.00722 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.03865 | − | 5.26310i | −0.474558 | − | 0.821958i | 0.525018 | − | 0.851091i | \(-0.324059\pi\) |
−0.999576 | + | 0.0291332i | \(0.990725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.67420 | − | 2.89981i | −0.255314 | − | 0.442216i | 0.709667 | − | 0.704537i | \(-0.248845\pi\) |
−0.964981 | + | 0.262321i | \(0.915512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.28514 | −0.489720 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.53163 | − | 2.65287i | 0.223412 | − | 0.386960i | −0.732430 | − | 0.680842i | \(-0.761614\pi\) |
0.955842 | + | 0.293882i | \(0.0949472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.29918 | 0.757026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.198819 | + | 0.344364i | −0.0278402 | + | 0.0482207i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.87147 | − | 4.97353i | 0.394426 | − | 0.683166i | −0.598602 | − | 0.801047i | \(-0.704277\pi\) |
0.993028 | + | 0.117881i | \(0.0376100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.25351 | + | 3.90319i | 0.303863 | + | 0.526306i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.34139 | − | 10.4045i | −0.442578 | − | 1.37810i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.53163 | + | 2.65287i | 0.199402 | + | 0.345374i | 0.948335 | − | 0.317272i | \(-0.102767\pi\) |
−0.748933 | + | 0.662646i | \(0.769433\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.436734 | − | 0.756445i | 0.0559180 | − | 0.0968528i | −0.836711 | − | 0.547644i | \(-0.815525\pi\) |
0.892629 | + | 0.450791i | \(0.148858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.76053 | − | 9.97753i | 0.725758 | − | 1.25705i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.22188 | + | 7.31250i | −0.515784 | + | 0.893365i | 0.484048 | + | 0.875042i | \(0.339166\pi\) |
−0.999832 | + | 0.0183230i | \(0.994167\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.90466 | −0.349680 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.11796 | − | 14.0607i | −0.963424 | − | 1.66870i | −0.713790 | − | 0.700359i | \(-0.753023\pi\) |
−0.249634 | − | 0.968340i | \(-0.580310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.57930 | + | 6.19954i | 0.418926 | + | 0.725601i | 0.995832 | − | 0.0912097i | \(-0.0290733\pi\) |
−0.576906 | + | 0.816811i | \(0.695740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.50702 | 0.289486 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.8062 | −1.80128 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.06327 | − | 8.76983i | −0.569662 | − | 0.986683i | −0.996599 | − | 0.0824022i | \(-0.973741\pi\) |
0.426937 | − | 0.904281i | \(-0.359593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.03163 | + | 6.98299i | 0.447959 | + | 0.775888i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.85543 | −0.532952 | −0.266476 | − | 0.963841i | \(-0.585859\pi\) | ||||
−0.266476 | + | 0.963841i | \(0.585859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0793049 | − | 0.137360i | 0.00860183 | − | 0.0148988i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.79216 | −0.942619 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.556248 | − | 0.963449i | 0.0589621 | − | 0.102125i | −0.835038 | − | 0.550193i | \(-0.814554\pi\) |
0.894000 | + | 0.448067i | \(0.147888\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.76755 | + | 15.1858i | −0.919089 | + | 1.59191i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.86445 | − | 4.96137i | −0.297029 | − | 0.514470i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.33281 | + | 4.15013i | 0.136744 | + | 0.425795i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.809757 | − | 1.40254i | −0.0822184 | − | 0.142406i | 0.821984 | − | 0.569510i | \(-0.192867\pi\) |
−0.904203 | + | 0.427104i | \(0.859534\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.40310 | + | 12.8225i | −0.744039 | + | 1.28871i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.15661 | + | 10.6636i | −0.612605 | + | 1.06106i | 0.378194 | + | 0.925726i | \(0.376545\pi\) |
−0.990800 | + | 0.135337i | \(0.956788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6164 | −1.04606 | −0.523032 | − | 0.852313i | \(-0.675199\pi\) | ||||
−0.523032 | + | 0.852313i | \(0.675199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.39608 | + | 7.61423i | −0.429014 | + | 0.743073i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.17265 | 0.210038 | 0.105019 | − | 0.994470i | \(-0.466510\pi\) | ||||
0.105019 | + | 0.994470i | \(0.466510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.91012 | − | 13.7007i | −0.757652 | − | 1.31229i | −0.944045 | − | 0.329816i | \(-0.893013\pi\) |
0.186393 | − | 0.982475i | \(-0.440320\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.7445 | + | 23.8062i | 1.30457 | + | 2.25958i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.83828 | 0.925507 | 0.462754 | − | 0.886487i | \(-0.346861\pi\) | ||||
0.462754 | + | 0.886487i | \(0.346861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.15861 | 0.108041 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.21286 | + | 14.2251i | 0.759279 | + | 1.31511i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.278124 | + | 0.481725i | 0.0254956 | + | 0.0441596i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.31322 | 0.846656 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.61796 | + | 13.1947i | −0.686888 | + | 1.18972i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.85543 | − | 13.6060i | 0.697056 | − | 1.20734i | −0.272426 | − | 0.962177i | \(-0.587826\pi\) |
0.969483 | − | 0.245160i | \(-0.0788407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.19726 | + | 7.26987i | −0.369548 | + | 0.640076i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.76755 | − | 9.98968i | −0.503913 | − | 0.872803i | −0.999990 | − | 0.00452412i | \(-0.998560\pi\) |
0.496077 | − | 0.868279i | \(-0.334773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.9418 | − | 3.22932i | −1.29561 | − | 0.280017i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.357429 | + | 0.619085i | 0.0307626 | + | 0.0532823i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0546904 | + | 0.0947266i | −0.00467252 | + | 0.00809304i | −0.868352 | − | 0.495948i | \(-0.834821\pi\) |
0.863680 | + | 0.504041i | \(0.168154\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.721876 | − | 1.25033i | 0.0612287 | − | 0.106051i | −0.833786 | − | 0.552088i | \(-0.813831\pi\) |
0.895015 | + | 0.446036i | \(0.147165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.67967 | −0.646745 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.2675 | − | 19.5160i | 0.942240 | − | 1.63201i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.50702 | 0.291242 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.64257 | − | 11.5053i | −0.547870 | − | 0.948939i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.864447 | − | 1.49727i | −0.0708183 | − | 0.122661i | 0.828442 | − | 0.560075i | \(-0.189228\pi\) |
−0.899260 | + | 0.437414i | \(0.855894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.1406 | 1.63902 | 0.819508 | − | 0.573068i | \(-0.194247\pi\) | ||||
0.819508 | + | 0.573068i | \(0.194247\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.521056 | 0.0421249 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.14257 | + | 1.97899i | 0.0917735 | + | 0.158956i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.88906 | − | 3.27195i | −0.150764 | − | 0.261130i | 0.780745 | − | 0.624850i | \(-0.214840\pi\) |
−0.931508 | + | 0.363720i | \(0.881507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.3976 | −1.14181 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.03163 | + | 3.51889i | −0.160115 | + | 0.277328i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.61640 | 0.126606 | 0.0633031 | − | 0.997994i | \(-0.479837\pi\) | ||||
0.0633031 | + | 0.997994i | \(0.479837\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.64959 | − | 9.78538i | 0.439820 | − | 0.761791i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.24649 | − | 5.62309i | 0.251221 | − | 0.435128i | −0.712641 | − | 0.701529i | \(-0.752501\pi\) |
0.963862 | + | 0.266401i | \(0.0858346\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.61796 | + | 10.6088i | −0.735504 | + | 0.811273i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.26053 | − | 7.37945i | −0.323922 | − | 0.561049i | 0.657372 | − | 0.753567i | \(-0.271668\pi\) |
−0.981294 | + | 0.192517i | \(0.938335\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.75351 | − | 3.03717i | 0.132553 | − | 0.229588i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.83983 | − | 6.65079i | 0.288620 | − | 0.499904i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.2711 | 0.767698 | 0.383849 | − | 0.923396i | \(-0.374598\pi\) | ||||
0.383849 | + | 0.923396i | \(0.374598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.13355 | + | 10.6236i | −0.455903 | + | 0.789648i | −0.998740 | − | 0.0501908i | \(-0.984017\pi\) |
0.542836 | + | 0.839838i | \(0.317350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.18980 | −0.161875 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.48240 | − | 9.49580i | −0.403074 | − | 0.698145i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.357429 | − | 0.619085i | −0.0261378 | − | 0.0452720i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50702 | −0.182359 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.71085 | −0.413223 | −0.206611 | − | 0.978423i | \(-0.566244\pi\) | ||||
−0.206611 | + | 0.978423i | \(0.566244\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.07930 | + | 8.79761i | 0.365616 | + | 0.633266i | 0.988875 | − | 0.148750i | \(-0.0475249\pi\) |
−0.623259 | + | 0.782016i | \(0.714192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.26755 | − | 10.8557i | −0.448828 | − | 0.777393i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2038 | 1.15448 | 0.577238 | − | 0.816576i | \(-0.304131\pi\) | ||||
0.577238 | + | 0.816576i | \(0.304131\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.167186 | − | 0.289574i | 0.0118515 | − | 0.0205274i | −0.860039 | − | 0.510229i | \(-0.829561\pi\) |
0.871890 | + | 0.489701i | \(0.162894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.1686 | 1.49312 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.14959 | + | 10.6514i | −0.431617 | + | 0.747582i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.03865 | − | 5.26310i | 0.212229 | − | 0.367591i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.90310 | + | 3.29626i | 0.132275 | + | 0.229106i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.2023 | + | 4.15013i | 1.32825 | + | 0.287071i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01404 | + | 1.75636i | 0.0698092 | + | 0.120913i | 0.898817 | − | 0.438324i | \(-0.144428\pi\) |
−0.829008 | + | 0.559237i | \(0.811094\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.3519 | + | 35.2505i | −1.39449 | + | 2.41532i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.67420 | − | 2.89981i | 0.114180 | − | 0.197765i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.01404 | −0.544028 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.97338 | − | 15.5424i | 0.606365 | − | 1.05026i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.793049 | −0.0533463 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.61596 | − | 16.6553i | −0.643932 | − | 1.11532i | −0.984547 | − | 0.175120i | \(-0.943969\pi\) |
0.340615 | − | 0.940203i | \(-0.389365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.64257 | − | 2.84502i | −0.109505 | − | 0.189668i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9788 | −0.857666 | −0.428833 | − | 0.903384i | \(-0.641075\pi\) | ||||
−0.428833 | + | 0.903384i | \(0.641075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.8132 | + | 34.3175i | 1.30361 | + | 2.25793i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5367 | − | 23.4462i | −0.886815 | − | 1.53601i | −0.843619 | − | 0.536943i | \(-0.819579\pi\) |
−0.0431968 | − | 0.999067i | \(-0.513754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.06327 | 0.199825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6937 | + | 21.9861i | −0.824545 | + | 1.42815i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0602 | −1.29758 | −0.648792 | − | 0.760966i | \(-0.724725\pi\) | ||||
−0.648792 | + | 0.760966i | \(0.724725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7922 | − | 18.6926i | 0.695184 | − | 1.20409i | −0.274934 | − | 0.961463i | \(-0.588656\pi\) |
0.970119 | − | 0.242631i | \(-0.0780105\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.1797 | − | 19.3637i | 0.717176 | − | 1.24219i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.64959 | + | 4.58922i | 0.169276 | + | 0.293195i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.6386 | − | 16.1466i | 0.931430 | − | 1.02738i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.08632 | + | 10.5418i | 0.385705 | + | 0.668061i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.63400 | + | 6.29426i | −0.229376 | + | 0.397290i | −0.957623 | − | 0.288024i | \(-0.907002\pi\) |
0.728248 | + | 0.685314i | \(0.240335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.61094 | − | 4.52228i | 0.164148 | − | 0.284313i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.397638 | −0.0249010 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.53865 | + | 13.0573i | −0.470248 | + | 0.814494i | −0.999421 | − | 0.0340202i | \(-0.989169\pi\) |
0.529173 | + | 0.848514i | \(0.322502\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.4538 | 2.38940 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.76053 | + | 9.97753i | 0.356568 | + | 0.617593i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.0773 | + | 17.4544i | 0.621393 | + | 1.07628i | 0.989227 | + | 0.146393i | \(0.0467663\pi\) |
−0.367833 | + | 0.929892i | \(0.619900\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.74293 | 0.352786 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.78905 | −0.170687 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.86245 | + | 6.68995i | 0.235497 | + | 0.407894i | 0.959417 | − | 0.281991i | \(-0.0909947\pi\) |
−0.723920 | + | 0.689884i | \(0.757661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.64257 | − | 4.57707i | −0.160525 | − | 0.278037i | 0.774532 | − | 0.632534i | \(-0.217985\pi\) |
−0.935057 | + | 0.354497i | \(0.884652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 43.9608 | 2.66063 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.25351 | + | 3.90319i | −0.135892 | + | 0.235371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.6264 | 1.84016 | 0.920082 | − | 0.391726i | \(-0.128122\pi\) | ||||
0.920082 | + | 0.391726i | \(0.128122\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.75351 | + | 6.50127i | −0.224717 | + | 0.389221i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.68122 | + | 11.5722i | −0.398568 | + | 0.690341i | −0.993550 | − | 0.113399i | \(-0.963826\pi\) |
0.594981 | + | 0.803740i | \(0.297159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.04767 | + | 3.54667i | 0.121721 | + | 0.210828i | 0.920447 | − | 0.390868i | \(-0.127825\pi\) |
−0.798725 | + | 0.601696i | \(0.794492\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.33983 | − | 8.09596i | 0.434774 | − | 0.479563i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6566 | + | 18.4578i | 0.629040 | + | 1.08953i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48742 | − | 14.7006i | 0.499260 | − | 0.864744i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.03008 | + | 3.51619i | −0.119005 | + | 0.206123i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1726 | 0.711134 | 0.355567 | − | 0.934651i | \(-0.384288\pi\) | ||||
0.355567 | + | 0.934651i | \(0.384288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.53163 | + | 2.65287i | −0.0891751 | + | 0.154456i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.22188 | 0.186952 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.89652 | − | 5.01693i | −0.167510 | − | 0.290136i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.87147 | + | 10.1697i | 0.338426 | + | 0.586170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 30.8695 | 1.77340 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.873467 | 0.0500146 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2675 | + | 21.2480i | 0.700146 | + | 1.21269i | 0.968415 | + | 0.249344i | \(0.0802150\pi\) |
−0.268269 | + | 0.963344i | \(0.586452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.3078 | + | 23.0497i | 0.757052 | + | 1.31125i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.2038 | 0.578606 | 0.289303 | − | 0.957238i | \(-0.406576\pi\) | ||||
0.289303 | + | 0.957238i | \(0.406576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9910 | − | 27.6972i | 0.903864 | − | 1.56554i | 0.0814282 | − | 0.996679i | \(-0.474052\pi\) |
0.822435 | − | 0.568859i | \(-0.192615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.5211 | 0.649138 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.11796 | + | 1.93636i | −0.0627907 | + | 0.108757i | −0.895712 | − | 0.444635i | \(-0.853333\pi\) |
0.832921 | + | 0.553392i | \(0.186667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.90310 | − | 13.6886i | 0.442489 | − | 0.766413i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.72343 | − | 4.71713i | −0.152007 | − | 0.263284i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.211397 | − | 0.658252i | −0.0117625 | − | 0.0366261i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.50000 | + | 4.33013i | 0.138675 | + | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.8308 | + | 34.3480i | −1.09665 | + | 1.89945i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.37147 | + | 9.30365i | −0.296139 | + | 0.512927i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0913 | 0.554670 | 0.277335 | − | 0.960773i | \(-0.410549\pi\) | ||||
0.277335 | + | 0.960773i | \(0.410549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.0105 | − | 31.1951i | 0.986968 | − | 1.70948i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.44375 | −0.461331 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.80620 | − | 4.86048i | −0.152863 | − | 0.264767i | 0.779416 | − | 0.626507i | \(-0.215516\pi\) |
−0.932279 | + | 0.361740i | \(0.882183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3324 | − | 21.3603i | −0.669802 | − | 1.16013i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2992 | 0.557732 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.96481 | 0.322069 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.45233 | − | 2.51551i | −0.0781907 | − | 0.135430i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.73747 | + | 4.74144i | 0.146955 | + | 0.254534i | 0.930101 | − | 0.367305i | \(-0.119719\pi\) |
−0.783146 | + | 0.621838i | \(0.786386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8202 | −1.00742 | −0.503712 | − | 0.863872i | \(-0.668033\pi\) | ||||
−0.503712 | + | 0.863872i | \(0.668033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.78714 | − | 3.09542i | 0.0953907 | − | 0.165222i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7008 | −0.675996 | −0.337998 | − | 0.941147i | \(-0.609750\pi\) | ||||
−0.337998 | + | 0.941147i | \(0.609750\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.11796 | − | 14.0607i | 0.430856 | − | 0.746265i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.697262 | − | 1.20769i | 0.0369030 | − | 0.0639179i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.54021 | − | 9.59592i | −0.292401 | − | 0.506453i | 0.681976 | − | 0.731375i | \(-0.261121\pi\) |
−0.974377 | + | 0.224921i | \(0.927788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3042 | + | 7.84632i | 0.910747 | + | 0.412964i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.6742 | − | 20.2203i | −0.612737 | − | 1.06129i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.57930 | + | 6.19954i | −0.187349 | + | 0.324499i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3202 | + | 17.8752i | −0.538712 | + | 0.933076i | 0.460262 | + | 0.887783i | \(0.347756\pi\) |
−0.998974 | + | 0.0452932i | \(0.985578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.9648 | 1.03933 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0703 | + | 17.4422i | −0.522823 | + | 0.905556i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.55313 | 0.235752 | 0.117876 | − | 0.993028i | \(-0.462391\pi\) | ||||
0.117876 | + | 0.993028i | \(0.462391\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.25351 | + | 2.17114i | 0.0647309 | + | 0.112117i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.76755 | − | 15.1858i | −0.451552 | − | 0.782110i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.9187 | 1.02315 | 0.511577 | − | 0.859237i | \(-0.329061\pi\) | ||||
0.511577 | + | 0.859237i | \(0.329061\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.3874 | −2.01788 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.98742 | − | 17.2987i | −0.510333 | − | 0.883923i | −0.999928 | − | 0.0119734i | \(-0.996189\pi\) |
0.489595 | − | 0.871950i | \(-0.337145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.90310 | − | 13.6886i | −0.402779 | − | 0.697634i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0000 | 0.559161 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.90110 | + | 11.9531i | −0.349900 | + | 0.606044i | −0.986231 | − | 0.165372i | \(-0.947118\pi\) |
0.636332 | + | 0.771416i | \(0.280451\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.183767 | −0.00929349 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.4593 | + | 25.0443i | −0.729378 | + | 1.26332i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.06327 | − | 8.76983i | 0.254761 | − | 0.441258i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.27457 | + | 14.3320i | 0.415289 | + | 0.719301i | 0.995459 | − | 0.0951945i | \(-0.0303473\pi\) |
−0.580170 | + | 0.814495i | \(0.697014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.7183 | + | 36.4886i | 0.586650 | + | 1.82672i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.26253 | − | 7.38292i | −0.212861 | − | 0.368685i | 0.739748 | − | 0.672884i | \(-0.234945\pi\) |
−0.952609 | + | 0.304199i | \(0.901611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.71286 | − | 9.89496i | 0.284578 | − | 0.492903i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.03163 | + | 6.98299i | −0.200333 | + | 0.346988i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −49.4186 | −2.44959 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.78314 | − | 10.0167i | 0.285958 | − | 0.495294i | −0.686883 | − | 0.726768i | \(-0.741022\pi\) |
0.972841 | + | 0.231474i | \(0.0743549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.274220 | 0.0135263 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.37147 | − | 9.30365i | −0.264313 | − | 0.457803i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.42771 | − | 4.20492i | −0.119172 | − | 0.206412i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.61951 | −0.177248 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.7149 | 1.06084 | 0.530420 | − | 0.847735i | \(-0.322034\pi\) | ||||
0.530420 | + | 0.847735i | \(0.322034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46135 | + | 5.99523i | 0.168696 | + | 0.292190i | 0.937962 | − | 0.346739i | \(-0.112711\pi\) |
−0.769266 | + | 0.638929i | \(0.779378\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.03163 | + | 8.71504i | 0.244646 | + | 0.423740i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.158610 | 0.00769371 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.53163 | + | 2.65287i | −0.0741209 | + | 0.128381i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −56.4959 | −2.72765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.9894 | + | 24.2304i | −0.673847 | + | 1.16714i | 0.302958 | + | 0.953004i | \(0.402026\pi\) |
−0.976805 | + | 0.214133i | \(0.931307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.12698 | + | 5.41608i | −0.150273 | + | 0.260280i | −0.931328 | − | 0.364182i | \(-0.881349\pi\) |
0.781055 | + | 0.624462i | \(0.214682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.39608 | − | 7.61423i | −0.210776 | − | 0.365075i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.39208 | − | 3.74152i | 0.162265 | − | 0.178981i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5988 | + | 27.0179i | 0.744490 | + | 1.28949i | 0.950433 | + | 0.310931i | \(0.100641\pi\) |
−0.205942 | + | 0.978564i | \(0.566026\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.70428 | + | 15.0763i | −0.414490 | + | 0.717917i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.3519 | + | 28.3223i | −0.776901 | + | 1.34563i | 0.156819 | + | 0.987627i | \(0.449876\pi\) |
−0.933720 | + | 0.358004i | \(0.883457\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.11250 | 0.0527373 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.16719 | + | 3.75368i | −0.102504 | + | 0.177543i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.6304 | 1.20958 | 0.604788 | − | 0.796387i | \(-0.293258\pi\) | ||||
0.604788 | + | 0.796387i | \(0.293258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6953 | − | 23.7209i | −0.644885 | − | 1.11697i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.2464 | − | 43.7280i | −1.18618 | − | 2.05452i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.5351 | −0.822058 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.1646 | 1.55138 | 0.775688 | − | 0.631116i | \(-0.217403\pi\) | ||||
0.775688 | + | 0.631116i | \(0.217403\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.0566917 | − | 0.0981929i | −0.00264614 | − | 0.00458325i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.08788 | − | 1.88426i | −0.0506677 | − | 0.0877590i | 0.839579 | − | 0.543237i | \(-0.182802\pi\) |
−0.890247 | + | 0.455478i | \(0.849468\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.20072 | 0.288172 | 0.144086 | − | 0.989565i | \(-0.453976\pi\) | ||||
0.144086 | + | 0.989565i | \(0.453976\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.86445 | − | 4.96137i | 0.132836 | − | 0.230078i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.1546 | 0.793821 | 0.396910 | − | 0.917857i | \(-0.370082\pi\) | ||||
0.396910 | + | 0.917857i | \(0.370082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8062 | − | 25.6451i | 0.683687 | − | 1.18418i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.73591 | + | 8.20284i | −0.218219 | + | 0.377967i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.54567 | − | 13.0695i | −0.346950 | − | 0.600936i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.92771 | + | 3.22932i | −0.134333 | + | 0.148171i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.43318 | + | 16.3387i | 0.431915 | + | 0.748099i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.8891 | + | 30.9848i | −0.817372 | + | 1.41573i | 0.0902399 | + | 0.995920i | \(0.471237\pi\) |
−0.907612 | + | 0.419810i | \(0.862097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.4120 | + | 47.4790i | −1.24988 | + | 2.16486i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1867 | 0.463510 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.809757 | − | 1.40254i | 0.0367692 | − | 0.0636861i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7149 | 1.07462 | 0.537311 | − | 0.843384i | \(-0.319440\pi\) | ||||
0.537311 | + | 0.843384i | \(0.319440\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.02617 | − | 3.50943i | −0.0916267 | − | 0.158702i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.5933 | − | 33.9367i | −0.884235 | − | 1.53154i | −0.846588 | − | 0.532249i | \(-0.821347\pi\) |
−0.0376474 | − | 0.999291i | \(-0.511986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.556248 | −0.0250521 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.8062 | −0.665489 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.4698 | + | 49.3112i | 1.27705 | + | 2.21191i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.68824 | − | 8.12027i | −0.209875 | − | 0.363513i | 0.741800 | − | 0.670621i | \(-0.233972\pi\) |
−0.951675 | + | 0.307107i | \(0.900639\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.2780 | −0.727249 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.74649 | − | 11.6853i | 0.300811 | − | 0.521020i | −0.675509 | − | 0.737352i | \(-0.736076\pi\) |
0.976320 | + | 0.216332i | \(0.0694093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.3132 | −0.547931 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.0421 | + | 26.0537i | −0.668044 | + | 1.15709i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.8534 | + | 22.2628i | −0.569718 | + | 0.986781i | 0.426875 | + | 0.904310i | \(0.359614\pi\) |
−0.996594 | + | 0.0824703i | \(0.973719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5527 | − | 21.7419i | −0.555298 | − | 0.961805i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.04567 | + | 0.658252i | 0.134470 | + | 0.0290625i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.30820 | − | 9.19407i | −0.233907 | − | 0.405139i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.90310 | − | 11.9565i | 0.303598 | − | 0.525847i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.6812 | + | 18.5004i | −0.468854 | + | 0.812078i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.7358 | −1.65324 | −0.826618 | − | 0.562763i | \(-0.809738\pi\) | ||||
−0.826618 | + | 0.562763i | \(0.809738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.2003 | − | 33.2559i | 0.839570 | − | 1.45418i | −0.0506855 | − | 0.998715i | \(-0.516141\pi\) |
0.890255 | − | 0.455462i | \(-0.150526\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.79216 | −0.383721 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.181223 | − | 0.313888i | −0.00789420 | − | 0.0136732i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.8288 | + | 18.7561i | 0.470818 | + | 0.815481i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0633 | −0.436709 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.3865 | −1.31619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.08632 | + | 1.88157i | 0.0469659 | + | 0.0813473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.8749 | − | 22.3000i | −0.555594 | − | 0.962317i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.8835 | 1.02874 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.40310 | − | 11.0905i | 0.275291 | − | 0.476818i | −0.694918 | − | 0.719089i | \(-0.744559\pi\) |
0.970208 | + | 0.242272i | \(0.0778926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.7539 | 1.31977 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.91012 | − | 13.7007i | 0.338832 | − | 0.586875i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.12853 | + | 15.8111i | −0.390308 | + | 0.676033i | −0.992490 | − | 0.122326i | \(-0.960965\pi\) |
0.602182 | + | 0.798359i | \(0.294298\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.43473 | + | 2.48503i | 0.0612329 | + | 0.106058i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.2675 | − | 11.3253i | 0.437412 | − | 0.482473i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.7570 | + | 30.7560i | 0.755103 | + | 1.30788i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.7445 | + | 23.8062i | −0.583421 | + | 1.01051i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.45233 | + | 12.9078i | −0.315765 | + | 0.546922i | −0.979600 | − | 0.200958i | \(-0.935595\pi\) |
0.663835 | + | 0.747879i | \(0.268928\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.7420 | −0.708113 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.896081 | + | 1.55206i | −0.0378326 | + | 0.0655279i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.7810 | −1.92944 | −0.964720 | − | 0.263276i | \(-0.915197\pi\) | ||||
−0.964720 | + | 0.263276i | \(0.915197\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.91914 | + | 8.52020i | 0.206950 | + | 0.358447i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.1390 | − | 24.4895i | −0.593783 | − | 1.02846i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.379598 | 0.0159136 | 0.00795679 | − | 0.999968i | \(-0.497467\pi\) | ||||
0.00795679 | + | 0.999968i | \(0.497467\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8514 | 0.663361 | 0.331681 | − | 0.943392i | \(-0.392384\pi\) | ||||
0.331681 | + | 0.943392i | \(0.392384\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.15861 | + | 12.3991i | 0.299055 | + | 0.517979i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.579305 | + | 1.00339i | 0.0241587 | + | 0.0418441i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.2350 | −0.800765 | −0.400382 | − | 0.916348i | \(-0.631123\pi\) | ||||
−0.400382 | + | 0.916348i | \(0.631123\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.7339 | − | 22.0558i | 0.529203 | − | 0.916607i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.0281 | 0.706444 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9418 | − | 22.4158i | 0.535993 | − | 0.928366i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.21286 | + | 14.2251i | −0.339560 | + | 0.588135i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.4242 | + | 35.3757i | 0.842995 | + | 1.46011i | 0.887351 | + | 0.461095i | \(0.152543\pi\) |
−0.0443559 | + | 0.999016i | \(0.514124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.73591 | + | 2.10419i | 0.401161 | + | 0.0867018i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.3117 | − | 35.1808i | −0.835510 | − | 1.44715i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.12342 | − | 12.3381i | 0.292524 | − | 0.506666i | −0.681882 | − | 0.731462i | \(-0.738838\pi\) |
0.974406 | + | 0.224796i | \(0.0721716\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.278124 | + | 0.481725i | −0.0114020 | + | 0.0197488i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.838276 | −0.0343083 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.92571 | + | 13.7277i | −0.323836 | + | 0.560900i | −0.981276 | − | 0.192607i | \(-0.938306\pi\) |
0.657440 | + | 0.753507i | \(0.271639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4718 | 0.671900 | 0.335950 | − | 0.941880i | \(-0.390943\pi\) | ||||
0.335950 | + | 0.941880i | \(0.390943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.8695 | − | 24.0226i | −0.564808 | − | 0.978277i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.65661 | + | 8.06548i | 0.189318 | + | 0.327908i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3914 | 0.421774 | 0.210887 | − | 0.977510i | \(-0.432365\pi\) | ||||
0.210887 | + | 0.977510i | \(0.432365\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.8343 | 1.24947 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.65817 | − | 13.2643i | −0.309816 | − | 0.536617i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.8925 | + | 18.8664i | 0.439945 | + | 0.762007i | 0.997685 | − | 0.0680090i | \(-0.0216647\pi\) |
−0.557740 | + | 0.830016i | \(0.688331\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.2359 | −0.614371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.3855 | − | 37.0408i | 0.860948 | − | 1.49121i | −0.0100671 | − | 0.999949i | \(-0.503205\pi\) |
0.871015 | − | 0.491256i | \(-0.163462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.7882 | −1.15709 | −0.578547 | − | 0.815649i | \(-0.696380\pi\) | ||||
−0.578547 | + | 0.815649i | \(0.696380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.414120 | − | 0.717278i | 0.0166181 | − | 0.0287834i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.95077 | + | 3.37883i | −0.0781560 | + | 0.135370i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.0597 | − | 46.8931i | −0.601427 | − | 1.87273i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.869563 | + | 1.50613i | 0.0346718 | + | 0.0600532i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.69370 | + | 16.7900i | −0.385900 | + | 0.668399i | −0.991894 | − | 0.127071i | \(-0.959442\pi\) |
0.605993 | + | 0.795470i | \(0.292776\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.54221 | − | 4.40324i | 0.101044 | − | 0.175013i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7109 | 0.623466 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.2479 | − | 22.9461i | 0.524903 | − | 0.909158i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 53.3373 | 2.10999 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3433 | − | 35.2356i | −0.803512 | − | 1.39172i | −0.917291 | − | 0.398217i | \(-0.869629\pi\) |
0.113779 | − | 0.993506i | \(-0.463704\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.0527 | − | 29.5361i | −0.672492 | − | 1.16479i | −0.977195 | − | 0.212344i | \(-0.931890\pi\) |
0.304703 | − | 0.952448i | \(-0.401443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.39452 | −0.330534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.0029 | 1.88719 | 0.943595 | − | 0.331103i | \(-0.107421\pi\) | ||||
0.943595 | + | 0.331103i | \(0.107421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.90310 | + | 11.9565i | 0.270970 | + | 0.469334i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0457 | + | 17.3996i | 0.393721 | + | 0.681945i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.90866 | 0.152958 | 0.0764788 | − | 0.997071i | \(-0.475632\pi\) | ||||
0.0764788 | + | 0.997071i | \(0.475632\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.76755 | − | 9.98968i | 0.225357 | − | 0.390329i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.5171 | −0.917488 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.54411 | − | 11.3347i | 0.254922 | − | 0.441539i | −0.709952 | − | 0.704250i | \(-0.751283\pi\) |
0.964874 | + | 0.262711i | \(0.0846167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9714 | − | 20.7350i | 0.465633 | − | 0.806500i | −0.533597 | − | 0.845739i | \(-0.679160\pi\) |
0.999230 | + | 0.0392391i | \(0.0124934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.994095 | + | 1.72182i | 0.0386074 | + | 0.0668700i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.67420 | − | 14.5546i | −0.181258 | − | 0.564403i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.03163 | − | 3.51889i | −0.0786652 | − | 0.136252i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.1074 | + | 41.7552i | −0.932045 | + | 1.61435i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.96837 | − | 3.40931i | 0.0759880 | − | 0.131615i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.3304 | −0.436754 | −0.218377 | − | 0.975865i | \(-0.570076\pi\) | ||||
−0.218377 | + | 0.975865i | \(0.570076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.357429 | + | 0.619085i | −0.0137574 | + | 0.0238286i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.90466 | 0.342234 | 0.171117 | − | 0.985251i | \(-0.445262\pi\) | ||||
0.171117 | + | 0.985251i | \(0.445262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.83983 | + | 4.91873i | 0.108983 | + | 0.188764i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.01404 | + | 8.68457i | 0.192138 | + | 0.332793i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.6977 | 1.02156 | 0.510780 | − | 0.859712i | \(-0.329357\pi\) | ||||
0.510780 | + | 0.859712i | \(0.329357\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.109381 | −0.00417923 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.2691 | + | 28.1789i | 0.620705 | + | 1.07509i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.3573 | − | 24.8676i | −0.546971 | − | 0.947381i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.9708 | −1.36840 | −0.684198 | − | 0.729297i | \(-0.739847\pi\) | ||||
−0.684198 | + | 0.729297i | \(0.739847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 25.9628 | − | 44.9689i | 0.986245 | − | 1.70823i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.44375 | 0.0547646 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.481960 | + | 0.834779i | −0.0182555 | + | 0.0316195i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −33.9366 | + | 58.7800i | −1.28360 | + | 2.22326i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.22543 | − | 2.12252i | −0.0462840 | − | 0.0801663i | 0.841955 | − | 0.539547i | \(-0.181405\pi\) |
−0.888239 | + | 0.459381i | \(0.848071\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.7159 | − | 10.0966i | −1.76192 | − | 0.380799i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.83983 | − | 6.65079i | −0.144616 | − | 0.250483i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.5913 | − | 37.3973i | 0.812026 | − | 1.40647i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1440 | − | 43.5507i | 0.944304 | − | 1.63558i | 0.187165 | − | 0.982329i | \(-0.440070\pi\) |
0.757139 | − | 0.653254i | \(-0.226597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 33.2671 | 1.24761 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.32379 | − | 2.29288i | 0.0495765 | − | 0.0858690i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.5351 | 0.842765 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.1456 | + | 43.5534i | 0.939079 | + | 1.62653i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0491 | − | 41.6543i | −0.896881 | − | 1.55344i | −0.831459 | − | 0.555586i | \(-0.812494\pi\) |
−0.0654223 | − | 0.997858i | \(-0.520839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.2319 | 1.38659 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.1123 | −2.01246 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.75351 | + | 3.03717i | 0.0651237 | + | 0.112798i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.33983 | − | 14.4450i | −0.309307 | − | 0.535736i | 0.668904 | − | 0.743349i | \(-0.266764\pi\) |
−0.978211 | + | 0.207613i | \(0.933430\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.8655 | −1.18020 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.265545 | + | 0.459938i | −0.00982155 | + | 0.0170114i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.13365 | −0.152680 | −0.0763399 | − | 0.997082i | \(-0.524323\pi\) | ||||
−0.0763399 | + | 0.997082i | \(0.524323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.64257 | − | 11.5053i | 0.245015 | − | 0.424378i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.0281 | + | 32.9576i | −0.700908 | + | 1.21401i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4870 | + | 40.6806i | 0.863982 | + | 1.49646i | 0.868054 | + | 0.496470i | \(0.165371\pi\) |
−0.00407159 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −53.4061 | − | 11.5425i | −1.96192 | − | 0.424025i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.6069 | + | 35.6923i | 0.755995 | + | 1.30942i | 0.944878 | + | 0.327422i | \(0.106180\pi\) |
−0.188883 | + | 0.982000i | \(0.560487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.864447 | − | 1.49727i | 0.0316709 | − | 0.0548556i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.97539 | − | 13.8138i | 0.291804 | − | 0.505420i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.61951 | −0.278411 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.98942 | − | 5.17783i | 0.109086 | − | 0.188942i | −0.806314 | − | 0.591487i | \(-0.798541\pi\) |
0.915400 | + | 0.402545i | \(0.131874\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.2210 | 0.664010 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0703 | + | 17.4422i | 0.366495 | + | 0.634788i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1968 | − | 31.5178i | −0.661375 | − | 1.14553i | −0.980255 | − | 0.197739i | \(-0.936640\pi\) |
0.318880 | − | 0.947795i | \(-0.396693\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.0913 | −0.475186 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.71397 | −0.0983813 | −0.0491907 | − | 0.998789i | \(-0.515664\pi\) | ||||
−0.0491907 | + | 0.998789i | \(0.515664\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.7409 | + | 48.0487i | 1.00429 | + | 1.73948i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.260528 | + | 0.451248i | 0.00941941 | + | 0.0163149i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.3163 | 0.553041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.8995 | + | 34.4670i | −0.717596 | + | 1.24291i | 0.244354 | + | 0.969686i | \(0.421424\pi\) |
−0.961950 | + | 0.273226i | \(0.911909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.7991 | 1.36130 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.4874 | + | 38.9494i | −0.808816 | + | 1.40091i | 0.104868 | + | 0.994486i | \(0.466558\pi\) |
−0.913684 | + | 0.406425i | \(0.866775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.14257 | + | 1.97899i | −0.0410424 | + | 0.0710875i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −48.2022 | − | 83.4886i | −1.72924 | − | 2.99514i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.09992 | − | 25.2216i | −0.290210 | − | 0.903658i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.5878 | − | 63.3719i | −1.30921 | − | 2.26762i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.25351 | − | 2.17114i | 0.0447968 | − | 0.0775903i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.88906 | − | 3.27195i | 0.0674235 | − | 0.116781i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7149 | 0.631466 | 0.315733 | − | 0.948848i | \(-0.397750\pi\) | ||||
0.315733 | + | 0.948848i | \(0.397750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.2640 | − | 43.7585i | 0.899422 | − | 1.55784i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.5030 | −1.22679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.18367 | − | 3.78222i | −0.0775443 | − | 0.134311i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.19882 | − | 12.4687i | −0.255316 | − | 0.442220i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4930 | 0.903008 | 0.451504 | − | 0.892269i | \(-0.350888\pi\) | ||||
0.451504 | + | 0.892269i | \(0.350888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.485864 | −0.0171886 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.82735 | + | 3.16507i | 0.0645663 | + | 0.111832i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.1320 | + | 27.9414i | 0.569286 | + | 0.986032i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.06327 | −0.143211 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.68322 | − | 16.7718i | 0.340866 | − | 0.590397i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.4678 | −0.719610 | −0.359805 | − | 0.933027i | \(-0.617157\pi\) | ||||
−0.359805 | + | 0.933027i | \(0.617157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.4508 | + | 19.8333i | −0.402091 | + | 0.696442i | −0.993978 | − | 0.109579i | \(-0.965050\pi\) |
0.591887 | + | 0.806021i | \(0.298383\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.62498 | + | 11.4748i | −0.232348 | + | 0.402439i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.808200 | + | 1.39984i | 0.0283100 | + | 0.0490344i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.46281 | − | 13.8963i | −0.156134 | − | 0.486171i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.8026 | − | 49.8876i | −1.00645 | − | 1.74322i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.3609 | + | 26.6058i | −0.536099 | + | 0.928550i | 0.463011 | + | 0.886353i | \(0.346769\pi\) |
−0.999109 | + | 0.0421975i | \(0.986564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.09846 | − | 3.63464i | 0.0731476 | − | 0.126695i | −0.827132 | − | 0.562008i | \(-0.810029\pi\) |
0.900279 | + | 0.435313i | \(0.143362\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.2992 | 0.393387 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.6652 | + | 18.4726i | −0.370865 | + | 0.642357i | −0.989699 | − | 0.143165i | \(-0.954272\pi\) |
0.618834 | + | 0.785522i | \(0.287605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0390 | 1.18222 | 0.591112 | − | 0.806590i | \(-0.298689\pi\) | ||||
0.591112 | + | 0.806590i | \(0.298689\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.3905 | − | 66.4943i | −1.33175 | − | 2.30666i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.420251 | − | 0.727896i | −0.0145608 | − | 0.0252201i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.49298 | 0.224699 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.63355 | 0.0564638 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.20584 | + | 9.01678i | 0.179725 | + | 0.311294i | 0.941786 | − | 0.336212i | \(-0.109146\pi\) |
−0.762061 | + | 0.647505i | \(0.775812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.35041 | + | 14.4633i | 0.287945 | + | 0.498736i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.4999 | 1.15380 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.6616 | −1.12227 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.13355 | − | 8.89157i | 0.176183 | − | 0.305158i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.35197 | + | 11.0019i | −0.217743 | + | 0.377141i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.56527 | + | 11.3714i | 0.224790 | + | 0.389349i | 0.956257 | − | 0.292529i | \(-0.0944969\pi\) |
−0.731466 | + | 0.681878i | \(0.761164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.9964 | − | 3.02501i | −0.478668 | − | 0.103453i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.6230 | + | 37.4521i | 0.738627 | + | 1.27934i | 0.953114 | + | 0.302612i | \(0.0978587\pi\) |
−0.214487 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7344 | − | 27.2527i | 0.536849 | − | 0.929850i | −0.462222 | − | 0.886764i | \(-0.652948\pi\) |
0.999071 | − | 0.0430861i | \(-0.0137190\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.7163 | − | 46.2740i | 0.910490 | − | 1.57701i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.7842 | 0.809622 | 0.404811 | − | 0.914400i | \(-0.367337\pi\) | ||||
0.404811 | + | 0.914400i | \(0.367337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.26053 | − | 7.37945i | 0.144862 | − | 0.250909i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −42.5562 | −1.44529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.8202 | − | 39.5258i | −0.774123 | − | 1.34082i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.1094 | + | 36.5625i | 0.715264 | + | 1.23887i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.32033 | 0.180066 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.50702 | 0.118559 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0848 | + | 33.0558i | 0.644447 | + | 1.11621i | 0.984429 | + | 0.175783i | \(0.0562456\pi\) |
−0.339982 | + | 0.940432i | \(0.610421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.2585 | − | 26.4285i | −0.514657 | − | 0.891413i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.49209 | 0.185033 | 0.0925167 | − | 0.995711i | \(-0.470509\pi\) | ||||
0.0925167 | + | 0.995711i | \(0.470509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.1491 | + | 29.7032i | −0.577115 | + | 0.999592i | 0.418694 | + | 0.908128i | \(0.362488\pi\) |
−0.995808 | + | 0.0914644i | \(0.970845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.67967 | 0.258149 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.7585 | + | 32.4907i | −0.629850 | + | 1.09093i | 0.357732 | + | 0.933824i | \(0.383550\pi\) |
−0.987582 | + | 0.157107i | \(0.949783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.5491 | + | 47.7165i | −0.923968 | + | 1.60036i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.1706 | + | 31.4725i | 0.608740 | + | 1.05437i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.96837 | − | 9.89226i | 0.300115 | − | 0.331032i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.13555 | + | 8.89504i | 0.171663 | + | 0.297328i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.26164 | + | 12.5775i | −0.242459 | + | 0.419952i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00702 | − | 6.94036i | 0.133642 | − | 0.231474i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.910886 | −0.0303460 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.7199 | − | 25.4956i | 0.489847 | − | 0.848439i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.2671 | −0.407772 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.1265 | − | 19.2717i | −0.369450 | − | 0.639907i | 0.620029 | − | 0.784579i | \(-0.287121\pi\) |
−0.989480 | + | 0.144672i | \(0.953787\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.2253 | − | 35.0313i | −0.670832 | − | 1.16192i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0421 | −0.332710 | −0.166355 | − | 0.986066i | \(-0.553200\pi\) | ||||
−0.166355 | + | 0.986066i | \(0.553200\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.8835 | −0.724238 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.09490 | − | 1.89642i | −0.0361963 | − | 0.0626938i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 20.2269 | + | 35.0340i | 0.667951 | + | 1.15692i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.06104 | −0.199935 | −0.0999676 | − | 0.994991i | \(-0.531874\pi\) | ||||
−0.0999676 | + | 0.994991i | \(0.531874\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.7550 | − | 53.2692i | 1.01341 | − | 1.75528i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −81.1796 | −2.67206 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.48240 | − | 9.49580i | 0.180260 | − | 0.312220i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.4382 | − | 30.2038i | 0.572745 | − | 0.992024i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.9382 | + | 44.9263i | 0.851004 | + | 1.47398i | 0.880303 | + | 0.474412i | \(0.157339\pi\) |
−0.0292983 | + | 0.999571i | \(0.509327\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5773 | + | 4.87957i | 0.739941 | + | 0.159921i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.7906 | − | 22.1540i | −0.418746 | − | 0.725289i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.357429 | − | 0.619085i | 0.0116892 | − | 0.0202462i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5999 | + | 21.8237i | −0.411621 | + | 0.712949i | −0.995067 | − | 0.0992029i | \(-0.968371\pi\) |
0.583446 | + | 0.812152i | \(0.301704\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.1794 | −2.61655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.967923 | − | 1.67649i | 0.0315534 | − | 0.0546521i | −0.849817 | − | 0.527077i | \(-0.823288\pi\) |
0.881371 | + | 0.472425i | \(0.156621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.04122 | −0.229294 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.25351 | − | 2.17114i | −0.0407767 | − | 0.0706272i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6812 | + | 27.1607i | 0.509571 | + | 0.882603i | 0.999939 | + | 0.0110875i | \(0.00352932\pi\) |
−0.490367 | + | 0.871516i | \(0.663137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.7930 | 1.16189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.60548 | 0.181770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.4542 | − | 45.8201i | −0.856937 | − | 1.48426i | −0.874837 | − | 0.484418i | \(-0.839031\pi\) |
0.0179001 | − | 0.999840i | \(-0.494302\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.85543 | − | 4.94575i | −0.0923995 | − | 0.160041i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −39.6264 | −1.28094 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.191800 | − | 0.332208i | 0.00619355 | − | 0.0107275i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7781 | −0.831552 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.56873 | + | 6.18122i | −0.115001 | + | 0.199187i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.07930 | + | 8.79761i | −0.163509 | + | 0.283205i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.0140 | − | 51.9858i | −0.965186 | − | 1.67175i | −0.709113 | − | 0.705094i | \(-0.750905\pi\) |
−0.256073 | − | 0.966657i | \(-0.582429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.16417 | + | 1.28410i | −0.0373985 | + | 0.0412512i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.875025 | + | 1.51559i | 0.0280809 | + | 0.0486375i | 0.879724 | − | 0.475484i | \(-0.157727\pi\) |
−0.851643 | + | 0.524122i | \(0.824394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.53163 | + | 4.38492i | −0.0811604 | + | 0.140574i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.26755 | − | 10.8557i | 0.200722 | − | 0.347661i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.47583 | 0.175187 | 0.0875937 | − | 0.996156i | \(-0.472082\pi\) | ||||
0.0875937 | + | 0.996156i | \(0.472082\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50702 | − | 4.34228i | 0.0801247 | − | 0.138780i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 51.9717 | 1.65933 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.52963 | + | 4.38145i | 0.0806827 | + | 0.139747i | 0.903543 | − | 0.428497i | \(-0.140957\pi\) |
−0.822861 | + | 0.568243i | \(0.807623\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.10192 | + | 14.0329i | 0.258149 | + | 0.447126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.9327 | 0.857278 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.87950 | −0.123361 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0492290 | + | 0.0852672i | 0.00156381 | + | 0.00270860i | 0.866806 | − | 0.498645i | \(-0.166169\pi\) |
−0.865242 | + | 0.501354i | \(0.832836\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.6496 | − | 21.9097i | −0.401423 | − | 0.695284i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.334372 | 0.0106003 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.17967 | + | 15.8996i | −0.290723 | + | 0.503547i | −0.973981 | − | 0.226630i | \(-0.927229\pi\) |
0.683258 | + | 0.730177i | \(0.260562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.83828 | −0.247992 |
(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 | 1520.2.q.j.881.1 | 6 | ||
4.3 | odd | 2 | 95.2.e.b.26.1 | yes | 6 | ||
12.11 | even | 2 | 855.2.k.g.406.3 | 6 | |||
19.11 | even | 3 | inner | 1520.2.q.j.961.1 | 6 | ||
20.3 | even | 4 | 475.2.j.b.349.2 | 12 | |||
20.7 | even | 4 | 475.2.j.b.349.5 | 12 | |||
20.19 | odd | 2 | 475.2.e.d.26.3 | 6 | |||
76.7 | odd | 6 | 1805.2.a.h.1.3 | 3 | |||
76.11 | odd | 6 | 95.2.e.b.11.1 | ✓ | 6 | ||
76.31 | even | 6 | 1805.2.a.g.1.1 | 3 | |||
228.11 | even | 6 | 855.2.k.g.676.3 | 6 | |||
380.87 | even | 12 | 475.2.j.b.49.2 | 12 | |||
380.159 | odd | 6 | 9025.2.a.z.1.1 | 3 | |||
380.163 | even | 12 | 475.2.j.b.49.5 | 12 | |||
380.239 | odd | 6 | 475.2.e.d.201.3 | 6 | |||
380.259 | even | 6 | 9025.2.a.ba.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.b.11.1 | ✓ | 6 | 76.11 | odd | 6 | ||
95.2.e.b.26.1 | yes | 6 | 4.3 | odd | 2 | ||
475.2.e.d.26.3 | 6 | 20.19 | odd | 2 | |||
475.2.e.d.201.3 | 6 | 380.239 | odd | 6 | |||
475.2.j.b.49.2 | 12 | 380.87 | even | 12 | |||
475.2.j.b.49.5 | 12 | 380.163 | even | 12 | |||
475.2.j.b.349.2 | 12 | 20.3 | even | 4 | |||
475.2.j.b.349.5 | 12 | 20.7 | even | 4 | |||
855.2.k.g.406.3 | 6 | 12.11 | even | 2 | |||
855.2.k.g.676.3 | 6 | 228.11 | even | 6 | |||
1520.2.q.j.881.1 | 6 | 1.1 | even | 1 | trivial | ||
1520.2.q.j.961.1 | 6 | 19.11 | even | 3 | inner | ||
1805.2.a.g.1.1 | 3 | 76.31 | even | 6 | |||
1805.2.a.h.1.3 | 3 | 76.7 | odd | 6 | |||
9025.2.a.z.1.1 | 3 | 380.159 | odd | 6 | |||
9025.2.a.ba.1.3 | 3 | 380.259 | even | 6 |