Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Character | \(\chi\) | \(=\) | 1110.43 |
Dual form | 1110.2.l.a.697.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.887844 | + | 2.05225i | −0.397056 | + | 0.917794i | ||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | −1.84414 | + | 1.84414i | −0.697020 | + | 0.697020i | −0.963767 | − | 0.266747i | \(-0.914051\pi\) |
0.266747 | + | 0.963767i | \(0.414051\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.05225 | − | 0.887844i | −0.648979 | − | 0.280761i | ||||
\(11\) | − | 2.12202i | − | 0.639813i | −0.947449 | − | 0.319906i | \(-0.896349\pi\) | ||
0.947449 | − | 0.319906i | \(-0.103651\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | − | 5.07258i | − | 1.40688i | −0.710755 | − | 0.703440i | \(-0.751646\pi\) | ||
0.710755 | − | 0.703440i | \(-0.248354\pi\) | |||||||
\(14\) | −1.84414 | − | 1.84414i | −0.492867 | − | 0.492867i | ||||
\(15\) | −0.823360 | − | 2.07896i | −0.212591 | − | 0.536785i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.93495 | −0.711831 | −0.355916 | − | 0.934518i | \(-0.615831\pi\) | ||||
−0.355916 | + | 0.934518i | \(0.615831\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.28458 | + | 2.28458i | −0.524118 | + | 0.524118i | −0.918813 | − | 0.394694i | \(-0.870851\pi\) |
0.394694 | + | 0.918813i | \(0.370851\pi\) | |||||||
\(20\) | 0.887844 | − | 2.05225i | 0.198528 | − | 0.458897i | ||||
\(21\) | − | 2.60801i | − | 0.569114i | ||||||
\(22\) | 2.12202 | 0.452416 | ||||||||
\(23\) | − | 5.76461i | − | 1.20200i | −0.799248 | − | 0.601002i | \(-0.794768\pi\) | ||
0.799248 | − | 0.601002i | \(-0.205232\pi\) | |||||||
\(24\) | 0.707107 | + | 0.707107i | 0.144338 | + | 0.144338i | ||||
\(25\) | −3.42347 | − | 3.64416i | −0.684693 | − | 0.728831i | ||||
\(26\) | 5.07258 | 0.994814 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1.84414 | − | 1.84414i | 0.348510 | − | 0.348510i | ||||
\(29\) | 5.76649 | + | 5.76649i | 1.07081 | + | 1.07081i | 0.997294 | + | 0.0735173i | \(0.0234224\pi\) |
0.0735173 | + | 0.997294i | \(0.476578\pi\) | |||||||
\(30\) | 2.07896 | − | 0.823360i | 0.379565 | − | 0.150324i | ||||
\(31\) | 1.38171 | − | 1.38171i | 0.248163 | − | 0.248163i | −0.572054 | − | 0.820216i | \(-0.693853\pi\) |
0.820216 | + | 0.572054i | \(0.193853\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.50049 | + | 1.50049i | 0.261203 | + | 0.261203i | ||||
\(34\) | − | 2.93495i | − | 0.503341i | ||||||
\(35\) | −2.14733 | − | 5.42195i | −0.362965 | − | 0.916477i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −5.46669 | + | 2.66745i | −0.898719 | + | 0.438526i | ||||
\(38\) | −2.28458 | − | 2.28458i | −0.370608 | − | 0.370608i | ||||
\(39\) | 3.58685 | + | 3.58685i | 0.574356 | + | 0.574356i | ||||
\(40\) | 2.05225 | + | 0.887844i | 0.324489 | + | 0.140380i | ||||
\(41\) | 6.92685i | 1.08179i | 0.841089 | + | 0.540896i | \(0.181915\pi\) | ||||
−0.841089 | + | 0.540896i | \(0.818085\pi\) | |||||||
\(42\) | 2.60801 | 0.402425 | ||||||||
\(43\) | − | 2.00391i | − | 0.305593i | −0.988258 | − | 0.152797i | \(-0.951172\pi\) | ||
0.988258 | − | 0.152797i | \(-0.0488280\pi\) | |||||||
\(44\) | 2.12202i | 0.319906i | ||||||||
\(45\) | 2.05225 | + | 0.887844i | 0.305931 | + | 0.132352i | ||||
\(46\) | 5.76461 | 0.849945 | ||||||||
\(47\) | 7.27515 | − | 7.27515i | 1.06119 | − | 1.06119i | 0.0631877 | − | 0.998002i | \(-0.479873\pi\) |
0.998002 | − | 0.0631877i | \(-0.0201267\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 0.198289i | 0.0283271i | ||||||||
\(50\) | 3.64416 | − | 3.42347i | 0.515362 | − | 0.484151i | ||||
\(51\) | 2.07533 | − | 2.07533i | 0.290604 | − | 0.290604i | ||||
\(52\) | 5.07258i | 0.703440i | ||||||||
\(53\) | −0.286733 | − | 0.286733i | −0.0393858 | − | 0.0393858i | 0.687140 | − | 0.726525i | \(-0.258866\pi\) |
−0.726525 | + | 0.687140i | \(0.758866\pi\) | |||||||
\(54\) | −0.707107 | + | 0.707107i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | 4.35492 | + | 1.88402i | 0.587217 | + | 0.254041i | ||||
\(56\) | 1.84414 | + | 1.84414i | 0.246434 | + | 0.246434i | ||||
\(57\) | − | 3.23088i | − | 0.427941i | ||||||
\(58\) | −5.76649 | + | 5.76649i | −0.757178 | + | 0.757178i | ||||
\(59\) | 8.25437 | − | 8.25437i | 1.07463 | − | 1.07463i | 0.0776460 | − | 0.996981i | \(-0.475260\pi\) |
0.996981 | − | 0.0776460i | \(-0.0247404\pi\) | |||||||
\(60\) | 0.823360 | + | 2.07896i | 0.106295 | + | 0.268393i | ||||
\(61\) | 2.44633 | − | 2.44633i | 0.313221 | − | 0.313221i | −0.532935 | − | 0.846156i | \(-0.678911\pi\) |
0.846156 | + | 0.532935i | \(0.178911\pi\) | |||||||
\(62\) | 1.38171 | + | 1.38171i | 0.175478 | + | 0.175478i | ||||
\(63\) | 1.84414 | + | 1.84414i | 0.232340 | + | 0.232340i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 10.4102 | + | 4.50366i | 1.29123 | + | 0.558610i | ||||
\(66\) | −1.50049 | + | 1.50049i | −0.184698 | + | 0.184698i | ||||
\(67\) | −9.89884 | − | 9.89884i | −1.20934 | − | 1.20934i | −0.971242 | − | 0.238093i | \(-0.923478\pi\) |
−0.238093 | − | 0.971242i | \(-0.576522\pi\) | |||||||
\(68\) | 2.93495 | 0.355916 | ||||||||
\(69\) | 4.07619 | + | 4.07619i | 0.490716 | + | 0.490716i | ||||
\(70\) | 5.42195 | − | 2.14733i | 0.648047 | − | 0.256655i | ||||
\(71\) | 1.69758 | 0.201465 | 0.100733 | − | 0.994914i | \(-0.467881\pi\) | ||||
0.100733 | + | 0.994914i | \(0.467881\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 5.92047 | − | 5.92047i | 0.692939 | − | 0.692939i | −0.269939 | − | 0.962877i | \(-0.587003\pi\) |
0.962877 | + | 0.269939i | \(0.0870035\pi\) | |||||||
\(74\) | −2.66745 | − | 5.46669i | −0.310085 | − | 0.635490i | ||||
\(75\) | 4.99756 | + | 0.156051i | 0.577069 | + | 0.0180192i | ||||
\(76\) | 2.28458 | − | 2.28458i | 0.262059 | − | 0.262059i | ||||
\(77\) | 3.91330 | + | 3.91330i | 0.445962 | + | 0.445962i | ||||
\(78\) | −3.58685 | + | 3.58685i | −0.406131 | + | 0.406131i | ||||
\(79\) | −5.73733 | + | 5.73733i | −0.645500 | + | 0.645500i | −0.951902 | − | 0.306402i | \(-0.900875\pi\) |
0.306402 | + | 0.951902i | \(0.400875\pi\) | |||||||
\(80\) | −0.887844 | + | 2.05225i | −0.0992640 | + | 0.229449i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −6.92685 | −0.764943 | ||||||||
\(83\) | −7.41007 | − | 7.41007i | −0.813360 | − | 0.813360i | 0.171776 | − | 0.985136i | \(-0.445050\pi\) |
−0.985136 | + | 0.171776i | \(0.945050\pi\) | |||||||
\(84\) | 2.60801i | 0.284557i | ||||||||
\(85\) | 2.60578 | − | 6.02326i | 0.282637 | − | 0.653315i | ||||
\(86\) | 2.00391 | 0.216087 | ||||||||
\(87\) | −8.15506 | −0.874314 | ||||||||
\(88\) | −2.12202 | −0.226208 | ||||||||
\(89\) | −11.9236 | − | 11.9236i | −1.26390 | − | 1.26390i | −0.949187 | − | 0.314714i | \(-0.898092\pi\) |
−0.314714 | − | 0.949187i | \(-0.601908\pi\) | |||||||
\(90\) | −0.887844 | + | 2.05225i | −0.0935870 | + | 0.216326i | ||||
\(91\) | 9.35455 | + | 9.35455i | 0.980623 | + | 0.980623i | ||||
\(92\) | 5.76461i | 0.601002i | ||||||||
\(93\) | 1.95403i | 0.202624i | ||||||||
\(94\) | 7.27515 | + | 7.27515i | 0.750374 | + | 0.750374i | ||||
\(95\) | −2.66018 | − | 6.71688i | −0.272929 | − | 0.689137i | ||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | −7.94678 | −0.806874 | −0.403437 | − | 0.915008i | \(-0.632184\pi\) | ||||
−0.403437 | + | 0.915008i | \(0.632184\pi\) | |||||||
\(98\) | −0.198289 | −0.0200303 | ||||||||
\(99\) | −2.12202 | −0.213271 | ||||||||
\(100\) | 3.42347 | + | 3.64416i | 0.342347 | + | 0.364416i | ||||
\(101\) | − | 15.2228i | − | 1.51472i | −0.652997 | − | 0.757360i | \(-0.726489\pi\) | ||
0.652997 | − | 0.757360i | \(-0.273511\pi\) | |||||||
\(102\) | 2.07533 | + | 2.07533i | 0.205488 | + | 0.205488i | ||||
\(103\) | −13.4988 | −1.33008 | −0.665038 | − | 0.746810i | \(-0.731585\pi\) | ||||
−0.665038 | + | 0.746810i | \(0.731585\pi\) | |||||||
\(104\) | −5.07258 | −0.497407 | ||||||||
\(105\) | 5.35229 | + | 2.31550i | 0.522330 | + | 0.225970i | ||||
\(106\) | 0.286733 | − | 0.286733i | 0.0278500 | − | 0.0278500i | ||||
\(107\) | 2.32171 | − | 2.32171i | 0.224448 | − | 0.224448i | −0.585920 | − | 0.810369i | \(-0.699267\pi\) |
0.810369 | + | 0.585920i | \(0.199267\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | −5.20603 | + | 5.20603i | −0.498647 | + | 0.498647i | −0.911017 | − | 0.412369i | \(-0.864701\pi\) |
0.412369 | + | 0.911017i | \(0.364701\pi\) | |||||||
\(110\) | −1.88402 | + | 4.35492i | −0.179634 | + | 0.415225i | ||||
\(111\) | 1.97936 | − | 5.75171i | 0.187873 | − | 0.545928i | ||||
\(112\) | −1.84414 | + | 1.84414i | −0.174255 | + | 0.174255i | ||||
\(113\) | 16.6356 | 1.56494 | 0.782471 | − | 0.622687i | \(-0.213959\pi\) | ||||
0.782471 | + | 0.622687i | \(0.213959\pi\) | |||||||
\(114\) | 3.23088 | 0.302600 | ||||||||
\(115\) | 11.8304 | + | 5.11807i | 1.10319 | + | 0.477262i | ||||
\(116\) | −5.76649 | − | 5.76649i | −0.535406 | − | 0.535406i | ||||
\(117\) | −5.07258 | −0.468960 | ||||||||
\(118\) | 8.25437 | + | 8.25437i | 0.759876 | + | 0.759876i | ||||
\(119\) | 5.41247 | − | 5.41247i | 0.496160 | − | 0.496160i | ||||
\(120\) | −2.07896 | + | 0.823360i | −0.189782 | + | 0.0751621i | ||||
\(121\) | 6.49703 | 0.590639 | ||||||||
\(122\) | 2.44633 | + | 2.44633i | 0.221481 | + | 0.221481i | ||||
\(123\) | −4.89802 | − | 4.89802i | −0.441640 | − | 0.441640i | ||||
\(124\) | −1.38171 | + | 1.38171i | −0.124081 | + | 0.124081i | ||||
\(125\) | 10.5182 | − | 3.79037i | 0.940779 | − | 0.339021i | ||||
\(126\) | −1.84414 | + | 1.84414i | −0.164289 | + | 0.164289i | ||||
\(127\) | −6.57279 | + | 6.57279i | −0.583241 | + | 0.583241i | −0.935792 | − | 0.352552i | \(-0.885314\pi\) |
0.352552 | + | 0.935792i | \(0.385314\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.41698 | + | 1.41698i | 0.124758 | + | 0.124758i | ||||
\(130\) | −4.50366 | + | 10.4102i | −0.394997 | + | 0.913035i | ||||
\(131\) | −2.67417 | + | 2.67417i | −0.233643 | + | 0.233643i | −0.814212 | − | 0.580568i | \(-0.802830\pi\) |
0.580568 | + | 0.814212i | \(0.302830\pi\) | |||||||
\(132\) | −1.50049 | − | 1.50049i | −0.130601 | − | 0.130601i | ||||
\(133\) | − | 8.42617i | − | 0.730642i | ||||||
\(134\) | 9.89884 | − | 9.89884i | 0.855129 | − | 0.855129i | ||||
\(135\) | −2.07896 | + | 0.823360i | −0.178928 | + | 0.0708636i | ||||
\(136\) | 2.93495i | 0.251670i | ||||||||
\(137\) | 0.925340 | − | 0.925340i | 0.0790571 | − | 0.0790571i | −0.666472 | − | 0.745530i | \(-0.732197\pi\) |
0.745530 | + | 0.666472i | \(0.232197\pi\) | |||||||
\(138\) | −4.07619 | + | 4.07619i | −0.346988 | + | 0.346988i | ||||
\(139\) | −5.44352 | −0.461713 | −0.230857 | − | 0.972988i | \(-0.574153\pi\) | ||||
−0.230857 | + | 0.972988i | \(0.574153\pi\) | |||||||
\(140\) | 2.14733 | + | 5.42195i | 0.181483 | + | 0.458238i | ||||
\(141\) | 10.2886i | 0.866457i | ||||||||
\(142\) | 1.69758i | 0.142457i | ||||||||
\(143\) | −10.7641 | −0.900140 | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −16.9540 | + | 6.71455i | −1.40796 | + | 0.557613i | ||||
\(146\) | 5.92047 | + | 5.92047i | 0.489982 | + | 0.489982i | ||||
\(147\) | −0.140212 | − | 0.140212i | −0.0115645 | − | 0.0115645i | ||||
\(148\) | 5.46669 | − | 2.66745i | 0.449359 | − | 0.219263i | ||||
\(149\) | 16.9497i | 1.38858i | 0.719698 | + | 0.694288i | \(0.244280\pi\) | ||||
−0.719698 | + | 0.694288i | \(0.755720\pi\) | |||||||
\(150\) | −0.156051 | + | 4.99756i | −0.0127415 | + | 0.408049i | ||||
\(151\) | 1.25999i | 0.102536i | 0.998685 | + | 0.0512681i | \(0.0163263\pi\) | ||||
−0.998685 | + | 0.0512681i | \(0.983674\pi\) | |||||||
\(152\) | 2.28458 | + | 2.28458i | 0.185304 | + | 0.185304i | ||||
\(153\) | 2.93495i | 0.237277i | ||||||||
\(154\) | −3.91330 | + | 3.91330i | −0.315343 | + | 0.315343i | ||||
\(155\) | 1.60887 | + | 4.06236i | 0.129228 | + | 0.326297i | ||||
\(156\) | −3.58685 | − | 3.58685i | −0.287178 | − | 0.287178i | ||||
\(157\) | 4.05205 | − | 4.05205i | 0.323389 | − | 0.323389i | −0.526677 | − | 0.850066i | \(-0.676562\pi\) |
0.850066 | + | 0.526677i | \(0.176562\pi\) | |||||||
\(158\) | −5.73733 | − | 5.73733i | −0.456437 | − | 0.456437i | ||||
\(159\) | 0.405502 | 0.0321584 | ||||||||
\(160\) | −2.05225 | − | 0.887844i | −0.162245 | − | 0.0701902i | ||||
\(161\) | 10.6307 | + | 10.6307i | 0.837820 | + | 0.837820i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 0.200876 | 0.0157338 | 0.00786690 | − | 0.999969i | \(-0.497496\pi\) | ||||
0.00786690 | + | 0.999969i | \(0.497496\pi\) | |||||||
\(164\) | − | 6.92685i | − | 0.540896i | ||||||
\(165\) | −4.41160 | + | 1.74719i | −0.343442 | + | 0.136018i | ||||
\(166\) | 7.41007 | − | 7.41007i | 0.575133 | − | 0.575133i | ||||
\(167\) | −7.20812 | −0.557781 | −0.278891 | − | 0.960323i | \(-0.589967\pi\) | ||||
−0.278891 | + | 0.960323i | \(0.589967\pi\) | |||||||
\(168\) | −2.60801 | −0.201212 | ||||||||
\(169\) | −12.7311 | −0.979312 | ||||||||
\(170\) | 6.02326 | + | 2.60578i | 0.461963 | + | 0.199854i | ||||
\(171\) | 2.28458 | + | 2.28458i | 0.174706 | + | 0.174706i | ||||
\(172\) | 2.00391i | 0.152797i | ||||||||
\(173\) | −1.14427 | + | 1.14427i | −0.0869969 | + | 0.0869969i | −0.749266 | − | 0.662269i | \(-0.769594\pi\) |
0.662269 | + | 0.749266i | \(0.269594\pi\) | |||||||
\(174\) | − | 8.15506i | − | 0.618233i | ||||||
\(175\) | 13.0337 | + | 0.406983i | 0.985255 | + | 0.0307650i | ||||
\(176\) | − | 2.12202i | − | 0.159953i | ||||||
\(177\) | 11.6734i | 0.877429i | ||||||||
\(178\) | 11.9236 | − | 11.9236i | 0.893712 | − | 0.893712i | ||||
\(179\) | −9.71351 | − | 9.71351i | −0.726022 | − | 0.726022i | 0.243803 | − | 0.969825i | \(-0.421605\pi\) |
−0.969825 | + | 0.243803i | \(0.921605\pi\) | |||||||
\(180\) | −2.05225 | − | 0.887844i | −0.152966 | − | 0.0661760i | ||||
\(181\) | −1.59280 | −0.118392 | −0.0591961 | − | 0.998246i | \(-0.518854\pi\) | ||||
−0.0591961 | + | 0.998246i | \(0.518854\pi\) | |||||||
\(182\) | −9.35455 | + | 9.35455i | −0.693405 | + | 0.693405i | ||||
\(183\) | 3.45964i | 0.255744i | ||||||||
\(184\) | −5.76461 | −0.424972 | ||||||||
\(185\) | −0.620706 | − | 13.5873i | −0.0456352 | − | 0.998958i | ||||
\(186\) | −1.95403 | −0.143277 | ||||||||
\(187\) | 6.22803i | 0.455439i | ||||||||
\(188\) | −7.27515 | + | 7.27515i | −0.530595 | + | 0.530595i | ||||
\(189\) | −2.60801 | −0.189705 | ||||||||
\(190\) | 6.71688 | − | 2.66018i | 0.487294 | − | 0.192990i | ||||
\(191\) | −14.2911 | − | 14.2911i | −1.03407 | − | 1.03407i | −0.999399 | − | 0.0346716i | \(-0.988961\pi\) |
−0.0346716 | − | 0.999399i | \(-0.511039\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 11.4610i | 0.824978i | 0.910963 | + | 0.412489i | \(0.135340\pi\) | ||||
−0.910963 | + | 0.412489i | \(0.864660\pi\) | |||||||
\(194\) | − | 7.94678i | − | 0.570546i | ||||||
\(195\) | −10.5457 | + | 4.17656i | −0.755193 | + | 0.299090i | ||||
\(196\) | − | 0.198289i | − | 0.0141635i | ||||||
\(197\) | 3.61811 | − | 3.61811i | 0.257780 | − | 0.257780i | −0.566371 | − | 0.824151i | \(-0.691653\pi\) |
0.824151 | + | 0.566371i | \(0.191653\pi\) | |||||||
\(198\) | − | 2.12202i | − | 0.150805i | ||||||
\(199\) | −14.1563 | − | 14.1563i | −1.00351 | − | 1.00351i | −0.999994 | − | 0.00351772i | \(-0.998880\pi\) |
−0.00351772 | − | 0.999994i | \(-0.501120\pi\) | |||||||
\(200\) | −3.64416 | + | 3.42347i | −0.257681 | + | 0.242076i | ||||
\(201\) | 13.9991 | 0.987418 | ||||||||
\(202\) | 15.2228 | 1.07107 | ||||||||
\(203\) | −21.2685 | −1.49275 | ||||||||
\(204\) | −2.07533 | + | 2.07533i | −0.145302 | + | 0.145302i | ||||
\(205\) | −14.2156 | − | 6.14996i | −0.992863 | − | 0.429532i | ||||
\(206\) | − | 13.4988i | − | 0.940505i | ||||||
\(207\) | −5.76461 | −0.400668 | ||||||||
\(208\) | − | 5.07258i | − | 0.351720i | ||||||
\(209\) | 4.84792 | + | 4.84792i | 0.335338 | + | 0.335338i | ||||
\(210\) | −2.31550 | + | 5.35229i | −0.159785 | + | 0.369343i | ||||
\(211\) | 8.13385 | 0.559957 | 0.279979 | − | 0.960006i | \(-0.409673\pi\) | ||||
0.279979 | + | 0.960006i | \(0.409673\pi\) | |||||||
\(212\) | 0.286733 | + | 0.286733i | 0.0196929 | + | 0.0196929i | ||||
\(213\) | −1.20037 | + | 1.20037i | −0.0822478 | + | 0.0822478i | ||||
\(214\) | 2.32171 | + | 2.32171i | 0.158709 | + | 0.158709i | ||||
\(215\) | 4.11252 | + | 1.77916i | 0.280472 | + | 0.121338i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 5.09614i | 0.345949i | ||||||||
\(218\) | −5.20603 | − | 5.20603i | −0.352597 | − | 0.352597i | ||||
\(219\) | 8.37281i | 0.565782i | ||||||||
\(220\) | −4.35492 | − | 1.88402i | −0.293608 | − | 0.127021i | ||||
\(221\) | 14.8878i | 1.00146i | ||||||||
\(222\) | 5.75171 | + | 1.97936i | 0.386029 | + | 0.132846i | ||||
\(223\) | −18.5142 | − | 18.5142i | −1.23980 | − | 1.23980i | −0.960081 | − | 0.279721i | \(-0.909758\pi\) |
−0.279721 | − | 0.960081i | \(-0.590242\pi\) | |||||||
\(224\) | −1.84414 | − | 1.84414i | −0.123217 | − | 0.123217i | ||||
\(225\) | −3.64416 | + | 3.42347i | −0.242944 | + | 0.228231i | ||||
\(226\) | 16.6356i | 1.10658i | ||||||||
\(227\) | 8.71126 | 0.578187 | 0.289093 | − | 0.957301i | \(-0.406646\pi\) | ||||
0.289093 | + | 0.957301i | \(0.406646\pi\) | |||||||
\(228\) | 3.23088i | 0.213970i | ||||||||
\(229\) | 18.0323i | 1.19160i | 0.803131 | + | 0.595802i | \(0.203166\pi\) | ||||
−0.803131 | + | 0.595802i | \(0.796834\pi\) | |||||||
\(230\) | −5.11807 | + | 11.8304i | −0.337476 | + | 0.780075i | ||||
\(231\) | −5.53425 | −0.364127 | ||||||||
\(232\) | 5.76649 | − | 5.76649i | 0.378589 | − | 0.378589i | ||||
\(233\) | −15.7454 | + | 15.7454i | −1.03151 | + | 1.03151i | −0.0320280 | + | 0.999487i | \(0.510197\pi\) |
−0.999487 | + | 0.0320280i | \(0.989803\pi\) | |||||||
\(234\) | − | 5.07258i | − | 0.331605i | ||||||
\(235\) | 8.47123 | + | 21.3896i | 0.552602 | + | 1.39531i | ||||
\(236\) | −8.25437 | + | 8.25437i | −0.537314 | + | 0.537314i | ||||
\(237\) | − | 8.11381i | − | 0.527048i | ||||||
\(238\) | 5.41247 | + | 5.41247i | 0.350838 | + | 0.350838i | ||||
\(239\) | 10.3297 | − | 10.3297i | 0.668170 | − | 0.668170i | −0.289122 | − | 0.957292i | \(-0.593363\pi\) |
0.957292 | + | 0.289122i | \(0.0933635\pi\) | |||||||
\(240\) | −0.823360 | − | 2.07896i | −0.0531477 | − | 0.134196i | ||||
\(241\) | −6.49380 | − | 6.49380i | −0.418303 | − | 0.418303i | 0.466316 | − | 0.884618i | \(-0.345581\pi\) |
−0.884618 | + | 0.466316i | \(0.845581\pi\) | |||||||
\(242\) | 6.49703i | 0.417645i | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −2.44633 | + | 2.44633i | −0.156610 | + | 0.156610i | ||||
\(245\) | −0.406940 | − | 0.176050i | −0.0259984 | − | 0.0112474i | ||||
\(246\) | 4.89802 | − | 4.89802i | 0.312287 | − | 0.312287i | ||||
\(247\) | 11.5887 | + | 11.5887i | 0.737372 | + | 0.737372i | ||||
\(248\) | −1.38171 | − | 1.38171i | −0.0877388 | − | 0.0877388i | ||||
\(249\) | 10.4794 | 0.664106 | ||||||||
\(250\) | 3.79037 | + | 10.5182i | 0.239724 | + | 0.665231i | ||||
\(251\) | −2.81874 | + | 2.81874i | −0.177917 | + | 0.177917i | −0.790447 | − | 0.612530i | \(-0.790152\pi\) |
0.612530 | + | 0.790447i | \(0.290152\pi\) | |||||||
\(252\) | −1.84414 | − | 1.84414i | −0.116170 | − | 0.116170i | ||||
\(253\) | −12.2326 | −0.769057 | ||||||||
\(254\) | −6.57279 | − | 6.57279i | −0.412413 | − | 0.412413i | ||||
\(255\) | 2.41652 | + | 6.10166i | 0.151329 | + | 0.382101i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.1961 | −0.698394 | −0.349197 | − | 0.937049i | \(-0.613546\pi\) | ||||
−0.349197 | + | 0.937049i | \(0.613546\pi\) | |||||||
\(258\) | −1.41698 | + | 1.41698i | −0.0882172 | + | 0.0882172i | ||||
\(259\) | 5.16220 | − | 15.0005i | 0.320763 | − | 0.932086i | ||||
\(260\) | −10.4102 | − | 4.50366i | −0.645613 | − | 0.279305i | ||||
\(261\) | 5.76649 | − | 5.76649i | 0.356937 | − | 0.356937i | ||||
\(262\) | −2.67417 | − | 2.67417i | −0.165211 | − | 0.165211i | ||||
\(263\) | 2.56637 | − | 2.56637i | 0.158249 | − | 0.158249i | −0.623541 | − | 0.781790i | \(-0.714307\pi\) |
0.781790 | + | 0.623541i | \(0.214307\pi\) | |||||||
\(264\) | 1.50049 | − | 1.50049i | 0.0923490 | − | 0.0923490i | ||||
\(265\) | 0.843022 | − | 0.333874i | 0.0517864 | − | 0.0205097i | ||||
\(266\) | 8.42617 | 0.516642 | ||||||||
\(267\) | 16.8625 | 1.03197 | ||||||||
\(268\) | 9.89884 | + | 9.89884i | 0.604668 | + | 0.604668i | ||||
\(269\) | − | 32.1166i | − | 1.95819i | −0.203414 | − | 0.979093i | \(-0.565204\pi\) | ||
0.203414 | − | 0.979093i | \(-0.434796\pi\) | |||||||
\(270\) | −0.823360 | − | 2.07896i | −0.0501081 | − | 0.126522i | ||||
\(271\) | 15.5594 | 0.945166 | 0.472583 | − | 0.881286i | \(-0.343322\pi\) | ||||
0.472583 | + | 0.881286i | \(0.343322\pi\) | |||||||
\(272\) | −2.93495 | −0.177958 | ||||||||
\(273\) | −13.2293 | −0.800675 | ||||||||
\(274\) | 0.925340 | + | 0.925340i | 0.0559018 | + | 0.0559018i | ||||
\(275\) | −7.73297 | + | 7.26466i | −0.466316 | + | 0.438076i | ||||
\(276\) | −4.07619 | − | 4.07619i | −0.245358 | − | 0.245358i | ||||
\(277\) | − | 14.4437i | − | 0.867838i | −0.900952 | − | 0.433919i | \(-0.857130\pi\) | ||
0.900952 | − | 0.433919i | \(-0.142870\pi\) | |||||||
\(278\) | − | 5.44352i | − | 0.326481i | ||||||
\(279\) | −1.38171 | − | 1.38171i | −0.0827209 | − | 0.0827209i | ||||
\(280\) | −5.42195 | + | 2.14733i | −0.324023 | + | 0.128328i | ||||
\(281\) | 10.1736 | + | 10.1736i | 0.606908 | + | 0.606908i | 0.942137 | − | 0.335229i | \(-0.108814\pi\) |
−0.335229 | + | 0.942137i | \(0.608814\pi\) | |||||||
\(282\) | −10.2886 | −0.612678 | ||||||||
\(283\) | −11.7533 | −0.698659 | −0.349330 | − | 0.937000i | \(-0.613591\pi\) | ||||
−0.349330 | + | 0.937000i | \(0.613591\pi\) | |||||||
\(284\) | −1.69758 | −0.100733 | ||||||||
\(285\) | 6.63058 | + | 2.86852i | 0.392762 | + | 0.169916i | ||||
\(286\) | − | 10.7641i | − | 0.636495i | ||||||
\(287\) | −12.7741 | − | 12.7741i | −0.754031 | − | 0.754031i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −8.38604 | −0.493296 | ||||||||
\(290\) | −6.71455 | − | 16.9540i | −0.394292 | − | 0.995576i | ||||
\(291\) | 5.61922 | − | 5.61922i | 0.329405 | − | 0.329405i | ||||
\(292\) | −5.92047 | + | 5.92047i | −0.346469 | + | 0.346469i | ||||
\(293\) | −14.2767 | − | 14.2767i | −0.834051 | − | 0.834051i | 0.154017 | − | 0.988068i | \(-0.450779\pi\) |
−0.988068 | + | 0.154017i | \(0.950779\pi\) | |||||||
\(294\) | 0.140212 | − | 0.140212i | 0.00817732 | − | 0.00817732i | ||||
\(295\) | 9.61144 | + | 24.2686i | 0.559600 | + | 1.41297i | ||||
\(296\) | 2.66745 | + | 5.46669i | 0.155042 | + | 0.317745i | ||||
\(297\) | 1.50049 | − | 1.50049i | 0.0870675 | − | 0.0870675i | ||||
\(298\) | −16.9497 | −0.981871 | ||||||||
\(299\) | −29.2414 | −1.69107 | ||||||||
\(300\) | −4.99756 | − | 0.156051i | −0.288535 | − | 0.00900961i | ||||
\(301\) | 3.69549 | + | 3.69549i | 0.213005 | + | 0.213005i | ||||
\(302\) | −1.25999 | −0.0725041 | ||||||||
\(303\) | 10.7641 | + | 10.7641i | 0.618382 | + | 0.618382i | ||||
\(304\) | −2.28458 | + | 2.28458i | −0.131030 | + | 0.131030i | ||||
\(305\) | 2.84853 | + | 7.19245i | 0.163106 | + | 0.411839i | ||||
\(306\) | −2.93495 | −0.167780 | ||||||||
\(307\) | −16.2628 | − | 16.2628i | −0.928166 | − | 0.928166i | 0.0694214 | − | 0.997587i | \(-0.477885\pi\) |
−0.997587 | + | 0.0694214i | \(0.977885\pi\) | |||||||
\(308\) | −3.91330 | − | 3.91330i | −0.222981 | − | 0.222981i | ||||
\(309\) | 9.54509 | − | 9.54509i | 0.543001 | − | 0.543001i | ||||
\(310\) | −4.06236 | + | 1.60887i | −0.230727 | + | 0.0913779i | ||||
\(311\) | 11.0741 | − | 11.0741i | 0.627952 | − | 0.627952i | −0.319600 | − | 0.947552i | \(-0.603549\pi\) |
0.947552 | + | 0.319600i | \(0.103549\pi\) | |||||||
\(312\) | 3.58685 | − | 3.58685i | 0.203066 | − | 0.203066i | ||||
\(313\) | 4.41462i | 0.249529i | 0.992186 | + | 0.124764i | \(0.0398175\pi\) | ||||
−0.992186 | + | 0.124764i | \(0.960182\pi\) | |||||||
\(314\) | 4.05205 | + | 4.05205i | 0.228671 | + | 0.228671i | ||||
\(315\) | −5.42195 | + | 2.14733i | −0.305492 | + | 0.120988i | ||||
\(316\) | 5.73733 | − | 5.73733i | 0.322750 | − | 0.322750i | ||||
\(317\) | −1.75051 | − | 1.75051i | −0.0983187 | − | 0.0983187i | 0.656237 | − | 0.754555i | \(-0.272147\pi\) |
−0.754555 | + | 0.656237i | \(0.772147\pi\) | |||||||
\(318\) | 0.405502i | 0.0227394i | ||||||||
\(319\) | 12.2366 | − | 12.2366i | 0.685119 | − | 0.685119i | ||||
\(320\) | 0.887844 | − | 2.05225i | 0.0496320 | − | 0.114724i | ||||
\(321\) | 3.28340i | 0.183261i | ||||||||
\(322\) | −10.6307 | + | 10.6307i | −0.592428 | + | 0.592428i | ||||
\(323\) | 6.70514 | − | 6.70514i | 0.373084 | − | 0.373084i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −18.4853 | + | 17.3658i | −1.02538 | + | 0.963281i | ||||
\(326\) | 0.200876i | 0.0111255i | ||||||||
\(327\) | − | 7.36244i | − | 0.407144i | ||||||
\(328\) | 6.92685 | 0.382471 | ||||||||
\(329\) | 26.8328i | 1.47934i | ||||||||
\(330\) | −1.74719 | − | 4.41160i | −0.0961794 | − | 0.242850i | ||||
\(331\) | −17.0019 | − | 17.0019i | −0.934511 | − | 0.934511i | 0.0634724 | − | 0.997984i | \(-0.479783\pi\) |
−0.997984 | + | 0.0634724i | \(0.979783\pi\) | |||||||
\(332\) | 7.41007 | + | 7.41007i | 0.406680 | + | 0.406680i | ||||
\(333\) | 2.66745 | + | 5.46669i | 0.146175 | + | 0.299573i | ||||
\(334\) | − | 7.20812i | − | 0.394411i | ||||||
\(335\) | 29.1035 | − | 11.5263i | 1.59009 | − | 0.629748i | ||||
\(336\) | − | 2.60801i | − | 0.142279i | ||||||
\(337\) | 16.7264 | + | 16.7264i | 0.911145 | + | 0.911145i | 0.996362 | − | 0.0852173i | \(-0.0271584\pi\) |
−0.0852173 | + | 0.996362i | \(0.527158\pi\) | |||||||
\(338\) | − | 12.7311i | − | 0.692478i | ||||||
\(339\) | −11.7631 | + | 11.7631i | −0.638885 | + | 0.638885i | ||||
\(340\) | −2.60578 | + | 6.02326i | −0.141318 | + | 0.326657i | ||||
\(341\) | −2.93202 | − | 2.93202i | −0.158778 | − | 0.158778i | ||||
\(342\) | −2.28458 | + | 2.28458i | −0.123536 | + | 0.123536i | ||||
\(343\) | −13.2747 | − | 13.2747i | −0.716764 | − | 0.716764i | ||||
\(344\) | −2.00391 | −0.108044 | ||||||||
\(345\) | −11.9844 | + | 4.74635i | −0.645218 | + | 0.255535i | ||||
\(346\) | −1.14427 | − | 1.14427i | −0.0615161 | − | 0.0615161i | ||||
\(347\) | 27.1062i | 1.45514i | 0.686036 | + | 0.727568i | \(0.259349\pi\) | ||||
−0.686036 | + | 0.727568i | \(0.740651\pi\) | |||||||
\(348\) | 8.15506 | 0.437157 | ||||||||
\(349\) | − | 1.86734i | − | 0.0999566i | −0.998750 | − | 0.0499783i | \(-0.984085\pi\) | ||
0.998750 | − | 0.0499783i | \(-0.0159152\pi\) | |||||||
\(350\) | −0.406983 | + | 13.0337i | −0.0217541 | + | 0.696680i | ||||
\(351\) | 3.58685 | − | 3.58685i | 0.191452 | − | 0.191452i | ||||
\(352\) | 2.12202 | 0.113104 | ||||||||
\(353\) | 15.2302 | 0.810619 | 0.405310 | − | 0.914179i | \(-0.367164\pi\) | ||||
0.405310 | + | 0.914179i | \(0.367164\pi\) | |||||||
\(354\) | −11.6734 | −0.620436 | ||||||||
\(355\) | −1.50718 | + | 3.48385i | −0.0799929 | + | 0.184904i | ||||
\(356\) | 11.9236 | + | 11.9236i | 0.631950 | + | 0.631950i | ||||
\(357\) | 7.65439i | 0.405113i | ||||||||
\(358\) | 9.71351 | − | 9.71351i | 0.513375 | − | 0.513375i | ||||
\(359\) | − | 18.9718i | − | 1.00129i | −0.865651 | − | 0.500647i | \(-0.833095\pi\) | ||
0.865651 | − | 0.500647i | \(-0.166905\pi\) | |||||||
\(360\) | 0.887844 | − | 2.05225i | 0.0467935 | − | 0.108163i | ||||
\(361\) | 8.56139i | 0.450600i | ||||||||
\(362\) | − | 1.59280i | − | 0.0837159i | ||||||
\(363\) | −4.59410 | + | 4.59410i | −0.241128 | + | 0.241128i | ||||
\(364\) | −9.35455 | − | 9.35455i | −0.490312 | − | 0.490312i | ||||
\(365\) | 6.89384 | + | 17.4067i | 0.360840 | + | 0.911111i | ||||
\(366\) | −3.45964 | −0.180838 | ||||||||
\(367\) | −23.8239 | + | 23.8239i | −1.24360 | + | 1.24360i | −0.285103 | + | 0.958497i | \(0.592028\pi\) |
−0.958497 | + | 0.285103i | \(0.907972\pi\) | |||||||
\(368\) | − | 5.76461i | − | 0.300501i | ||||||
\(369\) | 6.92685 | 0.360598 | ||||||||
\(370\) | 13.5873 | − | 0.620706i | 0.706370 | − | 0.0322690i | ||||
\(371\) | 1.05755 | 0.0549054 | ||||||||
\(372\) | − | 1.95403i | − | 0.101312i | ||||||
\(373\) | −2.47846 | + | 2.47846i | −0.128330 | + | 0.128330i | −0.768354 | − | 0.640025i | \(-0.778924\pi\) |
0.640025 | + | 0.768354i | \(0.278924\pi\) | |||||||
\(374\) | −6.22803 | −0.322044 | ||||||||
\(375\) | −4.75731 | + | 10.1177i | −0.245667 | + | 0.522476i | ||||
\(376\) | −7.27515 | − | 7.27515i | −0.375187 | − | 0.375187i | ||||
\(377\) | 29.2510 | − | 29.2510i | 1.50650 | − | 1.50650i | ||||
\(378\) | − | 2.60801i | − | 0.134142i | ||||||
\(379\) | − | 31.6861i | − | 1.62761i | −0.581139 | − | 0.813804i | \(-0.697393\pi\) | ||
0.581139 | − | 0.813804i | \(-0.302607\pi\) | |||||||
\(380\) | 2.66018 | + | 6.71688i | 0.136464 | + | 0.344569i | ||||
\(381\) | − | 9.29533i | − | 0.476214i | ||||||
\(382\) | 14.2911 | − | 14.2911i | 0.731198 | − | 0.731198i | ||||
\(383\) | 12.7864i | 0.653357i | 0.945136 | + | 0.326678i | \(0.105929\pi\) | ||||
−0.945136 | + | 0.326678i | \(0.894071\pi\) | |||||||
\(384\) | 0.707107 | + | 0.707107i | 0.0360844 | + | 0.0360844i | ||||
\(385\) | −11.5055 | + | 4.55668i | −0.586374 | + | 0.232230i | ||||
\(386\) | −11.4610 | −0.583347 | ||||||||
\(387\) | −2.00391 | −0.101864 | ||||||||
\(388\) | 7.94678 | 0.403437 | ||||||||
\(389\) | 15.4731 | − | 15.4731i | 0.784518 | − | 0.784518i | −0.196071 | − | 0.980590i | \(-0.562818\pi\) |
0.980590 | + | 0.196071i | \(0.0628184\pi\) | |||||||
\(390\) | −4.17656 | − | 10.5457i | −0.211488 | − | 0.534002i | ||||
\(391\) | 16.9189i | 0.855623i | ||||||||
\(392\) | 0.198289 | 0.0100151 | ||||||||
\(393\) | − | 3.78185i | − | 0.190769i | ||||||
\(394\) | 3.61811 | + | 3.61811i | 0.182278 | + | 0.182278i | ||||
\(395\) | −6.68059 | − | 16.8683i | −0.336137 | − | 0.848736i | ||||
\(396\) | 2.12202 | 0.106635 | ||||||||
\(397\) | −11.7358 | − | 11.7358i | −0.589002 | − | 0.589002i | 0.348359 | − | 0.937361i | \(-0.386739\pi\) |
−0.937361 | + | 0.348359i | \(0.886739\pi\) | |||||||
\(398\) | 14.1563 | − | 14.1563i | 0.709590 | − | 0.709590i | ||||
\(399\) | 5.95820 | + | 5.95820i | 0.298283 | + | 0.298283i | ||||
\(400\) | −3.42347 | − | 3.64416i | −0.171173 | − | 0.182208i | ||||
\(401\) | −11.6604 | + | 11.6604i | −0.582291 | + | 0.582291i | −0.935532 | − | 0.353241i | \(-0.885079\pi\) |
0.353241 | + | 0.935532i | \(0.385079\pi\) | |||||||
\(402\) | 13.9991i | 0.698210i | ||||||||
\(403\) | −7.00884 | − | 7.00884i | −0.349135 | − | 0.349135i | ||||
\(404\) | 15.2228i | 0.757360i | ||||||||
\(405\) | 0.887844 | − | 2.05225i | 0.0441173 | − | 0.101977i | ||||
\(406\) | − | 21.2685i | − | 1.05554i | ||||||
\(407\) | 5.66038 | + | 11.6004i | 0.280575 | + | 0.575012i | ||||
\(408\) | −2.07533 | − | 2.07533i | −0.102744 | − | 0.102744i | ||||
\(409\) | 22.9972 | + | 22.9972i | 1.13714 | + | 1.13714i | 0.988961 | + | 0.148176i | \(0.0473403\pi\) |
0.148176 | + | 0.988961i | \(0.452660\pi\) | |||||||
\(410\) | 6.14996 | − | 14.2156i | 0.303725 | − | 0.702060i | ||||
\(411\) | 1.30863i | 0.0645499i | ||||||||
\(412\) | 13.4988 | 0.665038 | ||||||||
\(413\) | 30.4444i | 1.49807i | ||||||||
\(414\) | − | 5.76461i | − | 0.283315i | ||||||
\(415\) | 21.7863 | − | 8.62833i | 1.06945 | − | 0.423548i | ||||
\(416\) | 5.07258 | 0.248704 | ||||||||
\(417\) | 3.84915 | − | 3.84915i | 0.188494 | − | 0.188494i | ||||
\(418\) | −4.84792 | + | 4.84792i | −0.237120 | + | 0.237120i | ||||
\(419\) | 24.2039i | 1.18244i | 0.806512 | + | 0.591218i | \(0.201353\pi\) | ||||
−0.806512 | + | 0.591218i | \(0.798647\pi\) | |||||||
\(420\) | −5.35229 | − | 2.31550i | −0.261165 | − | 0.112985i | ||||
\(421\) | −9.91998 | + | 9.91998i | −0.483470 | + | 0.483470i | −0.906238 | − | 0.422768i | \(-0.861059\pi\) |
0.422768 | + | 0.906238i | \(0.361059\pi\) | |||||||
\(422\) | 8.13385i | 0.395949i | ||||||||
\(423\) | −7.27515 | − | 7.27515i | −0.353730 | − | 0.353730i | ||||
\(424\) | −0.286733 | + | 0.286733i | −0.0139250 | + | 0.0139250i | ||||
\(425\) | 10.0477 | + | 10.6954i | 0.487386 | + | 0.518805i | ||||
\(426\) | −1.20037 | − | 1.20037i | −0.0581580 | − | 0.0581580i | ||||
\(427\) | 9.02276i | 0.436642i | ||||||||
\(428\) | −2.32171 | + | 2.32171i | −0.112224 | + | 0.112224i | ||||
\(429\) | 7.61138 | − | 7.61138i | 0.367481 | − | 0.367481i | ||||
\(430\) | −1.77916 | + | 4.11252i | −0.0857986 | + | 0.198324i | ||||
\(431\) | 18.4635 | − | 18.4635i | 0.889356 | − | 0.889356i | −0.105105 | − | 0.994461i | \(-0.533518\pi\) |
0.994461 | + | 0.105105i | \(0.0335180\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 20.6095 | + | 20.6095i | 0.990427 | + | 0.990427i | 0.999955 | − | 0.00952737i | \(-0.00303270\pi\) |
−0.00952737 | + | 0.999955i | \(0.503033\pi\) | |||||||
\(434\) | −5.09614 | −0.244623 | ||||||||
\(435\) | 7.24042 | − | 16.7362i | 0.347151 | − | 0.802440i | ||||
\(436\) | 5.20603 | − | 5.20603i | 0.249324 | − | 0.249324i | ||||
\(437\) | 13.1697 | + | 13.1697i | 0.629992 | + | 0.629992i | ||||
\(438\) | −8.37281 | −0.400068 | ||||||||
\(439\) | 6.00049 | + | 6.00049i | 0.286388 | + | 0.286388i | 0.835650 | − | 0.549262i | \(-0.185091\pi\) |
−0.549262 | + | 0.835650i | \(0.685091\pi\) | |||||||
\(440\) | 1.88402 | − | 4.35492i | 0.0898172 | − | 0.207612i | ||||
\(441\) | 0.198289 | 0.00944235 | ||||||||
\(442\) | −14.8878 | −0.708140 | ||||||||
\(443\) | −19.3252 | + | 19.3252i | −0.918168 | + | 0.918168i | −0.996896 | − | 0.0787279i | \(-0.974914\pi\) |
0.0787279 | + | 0.996896i | \(0.474914\pi\) | |||||||
\(444\) | −1.97936 | + | 5.75171i | −0.0939364 | + | 0.272964i | ||||
\(445\) | 35.0565 | − | 13.8839i | 1.66184 | − | 0.658162i | ||||
\(446\) | 18.5142 | − | 18.5142i | 0.876673 | − | 0.876673i | ||||
\(447\) | −11.9853 | − | 11.9853i | −0.566884 | − | 0.566884i | ||||
\(448\) | 1.84414 | − | 1.84414i | 0.0871275 | − | 0.0871275i | ||||
\(449\) | −23.5893 | + | 23.5893i | −1.11325 | + | 1.11325i | −0.120538 | + | 0.992709i | \(0.538462\pi\) |
−0.992709 | + | 0.120538i | \(0.961538\pi\) | |||||||
\(450\) | −3.42347 | − | 3.64416i | −0.161384 | − | 0.171787i | ||||
\(451\) | 14.6989 | 0.692145 | ||||||||
\(452\) | −16.6356 | −0.782471 | ||||||||
\(453\) | −0.890945 | − | 0.890945i | −0.0418603 | − | 0.0418603i | ||||
\(454\) | 8.71126i | 0.408840i | ||||||||
\(455\) | −27.5033 | + | 10.8925i | −1.28937 | + | 0.510648i | ||||
\(456\) | −3.23088 | −0.151300 | ||||||||
\(457\) | −10.5479 | −0.493409 | −0.246704 | − | 0.969091i | \(-0.579348\pi\) | ||||
−0.246704 | + | 0.969091i | \(0.579348\pi\) | |||||||
\(458\) | −18.0323 | −0.842592 | ||||||||
\(459\) | −2.07533 | − | 2.07533i | −0.0968679 | − | 0.0968679i | ||||
\(460\) | −11.8304 | − | 5.11807i | −0.551596 | − | 0.238631i | ||||
\(461\) | −26.9418 | − | 26.9418i | −1.25481 | − | 1.25481i | −0.953541 | − | 0.301265i | \(-0.902591\pi\) |
−0.301265 | − | 0.953541i | \(-0.597409\pi\) | |||||||
\(462\) | − | 5.53425i | − | 0.257476i | ||||||
\(463\) | − | 16.5851i | − | 0.770773i | −0.922755 | − | 0.385387i | \(-0.874068\pi\) | ||
0.922755 | − | 0.385387i | \(-0.125932\pi\) | |||||||
\(464\) | 5.76649 | + | 5.76649i | 0.267703 | + | 0.267703i | ||||
\(465\) | −4.01017 | − | 1.73488i | −0.185967 | − | 0.0804530i | ||||
\(466\) | −15.7454 | − | 15.7454i | −0.729391 | − | 0.729391i | ||||
\(467\) | 34.4641 | 1.59481 | 0.797403 | − | 0.603447i | \(-0.206207\pi\) | ||||
0.797403 | + | 0.603447i | \(0.206207\pi\) | |||||||
\(468\) | 5.07258 | 0.234480 | ||||||||
\(469\) | 36.5097 | 1.68586 | ||||||||
\(470\) | −21.3896 | + | 8.47123i | −0.986630 | + | 0.390749i | ||||
\(471\) | 5.73047i | 0.264046i | ||||||||
\(472\) | −8.25437 | − | 8.25437i | −0.379938 | − | 0.379938i | ||||
\(473\) | −4.25233 | −0.195523 | ||||||||
\(474\) | 8.11381 | 0.372680 | ||||||||
\(475\) | 16.1465 | + | 0.504183i | 0.740854 | + | 0.0231335i | ||||
\(476\) | −5.41247 | + | 5.41247i | −0.248080 | + | 0.248080i | ||||
\(477\) | −0.286733 | + | 0.286733i | −0.0131286 | + | 0.0131286i | ||||
\(478\) | 10.3297 | + | 10.3297i | 0.472467 | + | 0.472467i | ||||
\(479\) | 15.9403 | − | 15.9403i | 0.728333 | − | 0.728333i | −0.241954 | − | 0.970288i | \(-0.577788\pi\) |
0.970288 | + | 0.241954i | \(0.0777885\pi\) | |||||||
\(480\) | 2.07896 | − | 0.823360i | 0.0948911 | − | 0.0375811i | ||||
\(481\) | 13.5308 | + | 27.7302i | 0.616953 | + | 1.26439i | ||||
\(482\) | 6.49380 | − | 6.49380i | 0.295785 | − | 0.295785i | ||||
\(483\) | −15.0341 | −0.684077 | ||||||||
\(484\) | −6.49703 | −0.295320 | ||||||||
\(485\) | 7.05550 | − | 16.3088i | 0.320374 | − | 0.740544i | ||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 5.52466 | 0.250346 | 0.125173 | − | 0.992135i | \(-0.460051\pi\) | ||||
0.125173 | + | 0.992135i | \(0.460051\pi\) | |||||||
\(488\) | −2.44633 | − | 2.44633i | −0.110740 | − | 0.110740i | ||||
\(489\) | −0.142041 | + | 0.142041i | −0.00642329 | + | 0.00642329i | ||||
\(490\) | 0.176050 | − | 0.406940i | 0.00795313 | − | 0.0183837i | ||||
\(491\) | 30.9165 | 1.39524 | 0.697621 | − | 0.716467i | \(-0.254242\pi\) | ||||
0.697621 | + | 0.716467i | \(0.254242\pi\) | |||||||
\(492\) | 4.89802 | + | 4.89802i | 0.220820 | + | 0.220820i | ||||
\(493\) | −16.9244 | − | 16.9244i | −0.762237 | − | 0.762237i | ||||
\(494\) | −11.5887 | + | 11.5887i | −0.521401 | + | 0.521401i | ||||
\(495\) | 1.88402 | − | 4.35492i | 0.0846805 | − | 0.195739i | ||||
\(496\) | 1.38171 | − | 1.38171i | 0.0620407 | − | 0.0620407i | ||||
\(497\) | −3.13057 | + | 3.13057i | −0.140425 | + | 0.140425i | ||||
\(498\) | 10.4794i | 0.469594i | ||||||||
\(499\) | 15.3419 | + | 15.3419i | 0.686798 | + | 0.686798i | 0.961523 | − | 0.274725i | \(-0.0885867\pi\) |
−0.274725 | + | 0.961523i | \(0.588587\pi\) | |||||||
\(500\) | −10.5182 | + | 3.79037i | −0.470389 | + | 0.169511i | ||||
\(501\) | 5.09691 | − | 5.09691i | 0.227713 | − | 0.227713i | ||||
\(502\) | −2.81874 | − | 2.81874i | −0.125806 | − | 0.125806i | ||||
\(503\) | 6.97745i | 0.311109i | 0.987827 | + | 0.155555i | \(0.0497164\pi\) | ||||
−0.987827 | + | 0.155555i | \(0.950284\pi\) | |||||||
\(504\) | 1.84414 | − | 1.84414i | 0.0821446 | − | 0.0821446i | ||||
\(505\) | 31.2409 | + | 13.5154i | 1.39020 | + | 0.601429i | ||||
\(506\) | − | 12.2326i | − | 0.543806i | ||||||
\(507\) | 9.00221 | − | 9.00221i | 0.399802 | − | 0.399802i | ||||
\(508\) | 6.57279 | − | 6.57279i | 0.291620 | − | 0.291620i | ||||
\(509\) | −15.9733 | −0.708002 | −0.354001 | − | 0.935245i | \(-0.615179\pi\) | ||||
−0.354001 | + | 0.935245i | \(0.615179\pi\) | |||||||
\(510\) | −6.10166 | + | 2.41652i | −0.270186 | + | 0.107006i | ||||
\(511\) | 21.8364i | 0.965984i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.23088 | −0.142647 | ||||||||
\(514\) | − | 11.1961i | − | 0.493839i | ||||||
\(515\) | 11.9848 | − | 27.7029i | 0.528114 | − | 1.22074i | ||||
\(516\) | −1.41698 | − | 1.41698i | −0.0623790 | − | 0.0623790i | ||||
\(517\) | −15.4380 | − | 15.4380i | −0.678963 | − | 0.678963i | ||||
\(518\) | 15.0005 | + | 5.16220i | 0.659084 | + | 0.226814i | ||||
\(519\) | − | 1.61824i | − | 0.0710327i | ||||||
\(520\) | 4.50366 | − | 10.4102i | 0.197498 | − | 0.456518i | ||||
\(521\) | 38.5368i | 1.68833i | 0.536084 | + | 0.844165i | \(0.319903\pi\) | ||||
−0.536084 | + | 0.844165i | \(0.680097\pi\) | |||||||
\(522\) | 5.76649 | + | 5.76649i | 0.252393 | + | 0.252393i | ||||
\(523\) | − | 14.7060i | − | 0.643047i | −0.946902 | − | 0.321523i | \(-0.895805\pi\) | ||
0.946902 | − | 0.321523i | \(-0.104195\pi\) | |||||||
\(524\) | 2.67417 | − | 2.67417i | 0.116822 | − | 0.116822i | ||||
\(525\) | −9.50399 | + | 8.92843i | −0.414788 | + | 0.389669i | ||||
\(526\) | 2.56637 | + | 2.56637i | 0.111899 | + | 0.111899i | ||||
\(527\) | −4.05526 | + | 4.05526i | −0.176650 | + | 0.176650i | ||||
\(528\) | 1.50049 | + | 1.50049i | 0.0653006 | + | 0.0653006i | ||||
\(529\) | −10.2307 | −0.444812 | ||||||||
\(530\) | 0.333874 | + | 0.843022i | 0.0145026 | + | 0.0366185i | ||||
\(531\) | −8.25437 | − | 8.25437i | −0.358209 | − | 0.358209i | ||||
\(532\) | 8.42617i | 0.365321i | ||||||||
\(533\) | 35.1370 | 1.52195 | ||||||||
\(534\) | 16.8625i | 0.729713i | ||||||||
\(535\) | 2.70342 | + | 6.82606i | 0.116879 | + | 0.295116i | ||||
\(536\) | −9.89884 | + | 9.89884i | −0.427565 | + | 0.427565i | ||||
\(537\) | 13.7370 | 0.592794 | ||||||||
\(538\) | 32.1166 | 1.38465 | ||||||||
\(539\) | 0.420774 | 0.0181240 | ||||||||
\(540\) | 2.07896 | − | 0.823360i | 0.0894642 | − | 0.0354318i | ||||
\(541\) | −24.9509 | − | 24.9509i | −1.07272 | − | 1.07272i | −0.997139 | − | 0.0755841i | \(-0.975918\pi\) |
−0.0755841 | − | 0.997139i | \(-0.524082\pi\) | |||||||
\(542\) | 15.5594i | 0.668333i | ||||||||
\(543\) | 1.12628 | − | 1.12628i | 0.0483334 | − | 0.0483334i | ||||
\(544\) | − | 2.93495i | − | 0.125835i | ||||||
\(545\) | −6.06194 | − | 15.3062i | −0.259665 | − | 0.655646i | ||||
\(546\) | − | 13.2293i | − | 0.566163i | ||||||
\(547\) | − | 36.4914i | − | 1.56026i | −0.625617 | − | 0.780131i | \(-0.715153\pi\) | ||
0.625617 | − | 0.780131i | \(-0.284847\pi\) | |||||||
\(548\) | −0.925340 | + | 0.925340i | −0.0395286 | + | 0.0395286i | ||||
\(549\) | −2.44633 | − | 2.44633i | −0.104407 | − | 0.104407i | ||||
\(550\) | −7.26466 | − | 7.73297i | −0.309766 | − | 0.329735i | ||||
\(551\) | −26.3480 | −1.12246 | ||||||||
\(552\) | 4.07619 | − | 4.07619i | 0.173494 | − | 0.173494i | ||||
\(553\) | − | 21.1609i | − | 0.899852i | ||||||
\(554\) | 14.4437 | 0.613654 | ||||||||
\(555\) | 10.0466 | + | 9.16877i | 0.426453 | + | 0.389192i | ||||
\(556\) | 5.44352 | 0.230857 | ||||||||
\(557\) | 32.6303i | 1.38259i | 0.722572 | + | 0.691296i | \(0.242960\pi\) | ||||
−0.722572 | + | 0.691296i | \(0.757040\pi\) | |||||||
\(558\) | 1.38171 | − | 1.38171i | 0.0584925 | − | 0.0584925i | ||||
\(559\) | −10.1650 | −0.429933 | ||||||||
\(560\) | −2.14733 | − | 5.42195i | −0.0907413 | − | 0.229119i | ||||
\(561\) | −4.40388 | − | 4.40388i | −0.185932 | − | 0.185932i | ||||
\(562\) | −10.1736 | + | 10.1736i | −0.429149 | + | 0.429149i | ||||
\(563\) | 20.4470i | 0.861738i | 0.902415 | + | 0.430869i | \(0.141793\pi\) | ||||
−0.902415 | + | 0.430869i | \(0.858207\pi\) | |||||||
\(564\) | − | 10.2886i | − | 0.433229i | ||||||
\(565\) | −14.7698 | + | 34.1404i | −0.621369 | + | 1.43630i | ||||
\(566\) | − | 11.7533i | − | 0.494027i | ||||||
\(567\) | 1.84414 | − | 1.84414i | 0.0774466 | − | 0.0774466i | ||||
\(568\) | − | 1.69758i | − | 0.0712287i | ||||||
\(569\) | 11.2342 | + | 11.2342i | 0.470964 | + | 0.470964i | 0.902226 | − | 0.431263i | \(-0.141932\pi\) |
−0.431263 | + | 0.902226i | \(0.641932\pi\) | |||||||
\(570\) | −2.86852 | + | 6.63058i | −0.120149 | + | 0.277725i | ||||
\(571\) | 26.4113 | 1.10528 | 0.552639 | − | 0.833421i | \(-0.313621\pi\) | ||||
0.552639 | + | 0.833421i | \(0.313621\pi\) | |||||||
\(572\) | 10.7641 | 0.450070 | ||||||||
\(573\) | 20.2107 | 0.844315 | ||||||||
\(574\) | 12.7741 | − | 12.7741i | 0.533180 | − | 0.533180i | ||||
\(575\) | −21.0071 | + | 19.7349i | −0.876058 | + | 0.823004i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | −7.95386 | −0.331123 | −0.165562 | − | 0.986199i | \(-0.552944\pi\) | ||||
−0.165562 | + | 0.986199i | \(0.552944\pi\) | |||||||
\(578\) | − | 8.38604i | − | 0.348813i | ||||||
\(579\) | −8.10412 | − | 8.10412i | −0.336796 | − | 0.336796i | ||||
\(580\) | 16.9540 | − | 6.71455i | 0.703978 | − | 0.278806i | ||||
\(581\) | 27.3304 | 1.13386 | ||||||||
\(582\) | 5.61922 | + | 5.61922i | 0.232924 | + | 0.232924i | ||||
\(583\) | −0.608453 | + | 0.608453i | −0.0251995 | + | 0.0251995i | ||||
\(584\) | −5.92047 | − | 5.92047i | −0.244991 | − | 0.244991i | ||||
\(585\) | 4.50366 | − | 10.4102i | 0.186203 | − | 0.430409i | ||||
\(586\) | 14.2767 | − | 14.2767i | 0.589763 | − | 0.589763i | ||||
\(587\) | 12.8759i | 0.531445i | 0.964050 | + | 0.265723i | \(0.0856105\pi\) | ||||
−0.964050 | + | 0.265723i | \(0.914389\pi\) | |||||||
\(588\) | 0.140212 | + | 0.140212i | 0.00578224 | + | 0.00578224i | ||||
\(589\) | 6.31326i | 0.260133i | ||||||||
\(590\) | −24.2686 | + | 9.61144i | −0.999123 | + | 0.395697i | ||||
\(591\) | 5.11678i | 0.210476i | ||||||||
\(592\) | −5.46669 | + | 2.66745i | −0.224680 | + | 0.109631i | ||||
\(593\) | 17.6097 | + | 17.6097i | 0.723143 | + | 0.723143i | 0.969244 | − | 0.246102i | \(-0.0791497\pi\) |
−0.246102 | + | 0.969244i | \(0.579150\pi\) | |||||||
\(594\) | 1.50049 | + | 1.50049i | 0.0615660 | + | 0.0615660i | ||||
\(595\) | 6.30232 | + | 15.9132i | 0.258370 | + | 0.652377i | ||||
\(596\) | − | 16.9497i | − | 0.694288i | ||||||
\(597\) | 20.0200 | 0.819364 | ||||||||
\(598\) | − | 29.2414i | − | 1.19577i | ||||||
\(599\) | 28.1341i | 1.14953i | 0.818320 | + | 0.574763i | \(0.194906\pi\) | ||||
−0.818320 | + | 0.574763i | \(0.805094\pi\) | |||||||
\(600\) | 0.156051 | − | 4.99756i | 0.00637076 | − | 0.204025i | ||||
\(601\) | −14.8826 | −0.607072 | −0.303536 | − | 0.952820i | \(-0.598167\pi\) | ||||
−0.303536 | + | 0.952820i | \(0.598167\pi\) | |||||||
\(602\) | −3.69549 | + | 3.69549i | −0.150617 | + | 0.150617i | ||||
\(603\) | −9.89884 | + | 9.89884i | −0.403112 | + | 0.403112i | ||||
\(604\) | − | 1.25999i | − | 0.0512681i | ||||||
\(605\) | −5.76835 | + | 13.3335i | −0.234517 | + | 0.542086i | ||||
\(606\) | −10.7641 | + | 10.7641i | −0.437262 | + | 0.437262i | ||||
\(607\) | − | 5.21022i | − | 0.211476i | −0.994394 | − | 0.105738i | \(-0.966279\pi\) | ||
0.994394 | − | 0.105738i | \(-0.0337205\pi\) | |||||||
\(608\) | −2.28458 | − | 2.28458i | −0.0926519 | − | 0.0926519i | ||||
\(609\) | 15.0391 | − | 15.0391i | 0.609414 | − | 0.609414i | ||||
\(610\) | −7.19245 | + | 2.84853i | −0.291214 | + | 0.115333i | ||||
\(611\) | −36.9038 | − | 36.9038i | −1.49297 | − | 1.49297i | ||||
\(612\) | − | 2.93495i | − | 0.118639i | ||||||
\(613\) | 15.0091 | − | 15.0091i | 0.606211 | − | 0.606211i | −0.335743 | − | 0.941954i | \(-0.608987\pi\) |
0.941954 | + | 0.335743i | \(0.108987\pi\) | |||||||
\(614\) | 16.2628 | − | 16.2628i | 0.656312 | − | 0.656312i | ||||
\(615\) | 14.4007 | − | 5.70329i | 0.580690 | − | 0.229979i | ||||
\(616\) | 3.91330 | − | 3.91330i | 0.157671 | − | 0.157671i | ||||
\(617\) | −6.06777 | − | 6.06777i | −0.244279 | − | 0.244279i | 0.574339 | − | 0.818618i | \(-0.305259\pi\) |
−0.818618 | + | 0.574339i | \(0.805259\pi\) | |||||||
\(618\) | 9.54509 | + | 9.54509i | 0.383960 | + | 0.383960i | ||||
\(619\) | −20.1898 | −0.811495 | −0.405747 | − | 0.913985i | \(-0.632989\pi\) | ||||
−0.405747 | + | 0.913985i | \(0.632989\pi\) | |||||||
\(620\) | −1.60887 | − | 4.06236i | −0.0646139 | − | 0.163148i | ||||
\(621\) | 4.07619 | − | 4.07619i | 0.163572 | − | 0.163572i | ||||
\(622\) | 11.0741 | + | 11.0741i | 0.444029 | + | 0.444029i | ||||
\(623\) | 43.9776 | 1.76193 | ||||||||
\(624\) | 3.58685 | + | 3.58685i | 0.143589 | + | 0.143589i | ||||
\(625\) | −1.55975 | + | 24.9513i | −0.0623900 | + | 0.998052i | ||||
\(626\) | −4.41462 | −0.176444 | ||||||||
\(627\) | −6.85600 | −0.273802 | ||||||||
\(628\) | −4.05205 | + | 4.05205i | −0.161695 | + | 0.161695i | ||||
\(629\) | 16.0445 | − | 7.82884i | 0.639736 | − | 0.312156i | ||||
\(630\) | −2.14733 | − | 5.42195i | −0.0855517 | − | 0.216016i | ||||
\(631\) | 1.59016 | − | 1.59016i | 0.0633034 | − | 0.0633034i | −0.674746 | − | 0.738050i | \(-0.735747\pi\) |
0.738050 | + | 0.674746i | \(0.235747\pi\) | |||||||
\(632\) | 5.73733 | + | 5.73733i | 0.228219 | + | 0.228219i | ||||
\(633\) | −5.75150 | + | 5.75150i | −0.228602 | + | 0.228602i | ||||
\(634\) | 1.75051 | − | 1.75051i | 0.0695218 | − | 0.0695218i | ||||
\(635\) | −7.65340 | − | 19.3246i | −0.303716 | − | 0.766874i | ||||
\(636\) | −0.405502 | −0.0160792 | ||||||||
\(637\) | 1.00584 | 0.0398528 | ||||||||
\(638\) | 12.2366 | + | 12.2366i | 0.484452 | + | 0.484452i | ||||
\(639\) | − | 1.69758i | − | 0.0671550i | ||||||
\(640\) | 2.05225 | + | 0.887844i | 0.0811223 | + | 0.0350951i | ||||
\(641\) | −27.0270 | −1.06750 | −0.533752 | − | 0.845641i | \(-0.679218\pi\) | ||||
−0.533752 | + | 0.845641i | \(0.679218\pi\) | |||||||
\(642\) | −3.28340 | −0.129585 | ||||||||
\(643\) | 18.0452 | 0.711635 | 0.355817 | − | 0.934556i | \(-0.384203\pi\) | ||||
0.355817 | + | 0.934556i | \(0.384203\pi\) | |||||||
\(644\) | −10.6307 | − | 10.6307i | −0.418910 | − | 0.418910i | ||||
\(645\) | −4.16605 | + | 1.64994i | −0.164038 | + | 0.0649663i | ||||
\(646\) | 6.70514 | + | 6.70514i | 0.263810 | + | 0.263810i | ||||
\(647\) | 2.13093i | 0.0837754i | 0.999122 | + | 0.0418877i | \(0.0133372\pi\) | ||||
−0.999122 | + | 0.0418877i | \(0.986663\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −17.5159 | − | 17.5159i | −0.687560 | − | 0.687560i | ||||
\(650\) | −17.3658 | − | 18.4853i | −0.681143 | − | 0.725052i | ||||
\(651\) | −3.60352 | − | 3.60352i | −0.141233 | − | 0.141233i | ||||
\(652\) | −0.200876 | −0.00786690 | ||||||||
\(653\) | 12.1928 | 0.477142 | 0.238571 | − | 0.971125i | \(-0.423321\pi\) | ||||
0.238571 | + | 0.971125i | \(0.423321\pi\) | |||||||
\(654\) | 7.36244 | 0.287894 | ||||||||
\(655\) | −3.11382 | − | 7.86231i | −0.121667 | − | 0.307206i | ||||
\(656\) | 6.92685i | 0.270448i | ||||||||
\(657\) | −5.92047 | − | 5.92047i | −0.230980 | − | 0.230980i | ||||
\(658\) | −26.8328 | −1.04605 | ||||||||
\(659\) | −19.4303 | −0.756898 | −0.378449 | − | 0.925622i | \(-0.623543\pi\) | ||||
−0.378449 | + | 0.925622i | \(0.623543\pi\) | |||||||
\(660\) | 4.41160 | − | 1.74719i | 0.171721 | − | 0.0680091i | ||||
\(661\) | 25.0660 | − | 25.0660i | 0.974956 | − | 0.974956i | −0.0247380 | − | 0.999694i | \(-0.507875\pi\) |
0.999694 | + | 0.0247380i | \(0.00787514\pi\) | |||||||
\(662\) | 17.0019 | − | 17.0019i | 0.660799 | − | 0.660799i | ||||
\(663\) | −10.5273 | − | 10.5273i | −0.408845 | − | 0.408845i | ||||
\(664\) | −7.41007 | + | 7.41007i | −0.287566 | + | 0.287566i | ||||
\(665\) | 17.2926 | + | 7.48113i | 0.670579 | + | 0.290106i | ||||
\(666\) | −5.46669 | + | 2.66745i | −0.211830 | + | 0.103362i | ||||
\(667\) | 33.2416 | − | 33.2416i | 1.28712 | − | 1.28712i | ||||
\(668\) | 7.20812 | 0.278891 | ||||||||
\(669\) | 26.1830 | 1.01229 | ||||||||
\(670\) | 11.5263 | + | 29.1035i | 0.445299 | + | 1.12437i | ||||
\(671\) | −5.19117 | − | 5.19117i | −0.200403 | − | 0.200403i | ||||
\(672\) | 2.60801 | 0.100606 | ||||||||
\(673\) | 25.0421 | + | 25.0421i | 0.965303 | + | 0.965303i | 0.999418 | − | 0.0341149i | \(-0.0108612\pi\) |
−0.0341149 | + | 0.999418i | \(0.510861\pi\) | |||||||
\(674\) | −16.7264 | + | 16.7264i | −0.644277 | + | 0.644277i | ||||
\(675\) | 0.156051 | − | 4.99756i | 0.00600641 | − | 0.192356i | ||||
\(676\) | 12.7311 | 0.489656 | ||||||||
\(677\) | −4.04562 | − | 4.04562i | −0.155486 | − | 0.155486i | 0.625077 | − | 0.780563i | \(-0.285068\pi\) |
−0.780563 | + | 0.625077i | \(0.785068\pi\) | |||||||
\(678\) | −11.7631 | − | 11.7631i | −0.451760 | − | 0.451760i | ||||
\(679\) | 14.6550 | − | 14.6550i | 0.562407 | − | 0.562407i | ||||
\(680\) | −6.02326 | − | 2.60578i | −0.230982 | − | 0.0999272i | ||||
\(681\) | −6.15979 | + | 6.15979i | −0.236044 | + | 0.236044i | ||||
\(682\) | 2.93202 | − | 2.93202i | 0.112273 | − | 0.112273i | ||||
\(683\) | 49.4497i | 1.89214i | 0.323961 | + | 0.946070i | \(0.394985\pi\) | ||||
−0.323961 | + | 0.946070i | \(0.605015\pi\) | |||||||
\(684\) | −2.28458 | − | 2.28458i | −0.0873531 | − | 0.0873531i | ||||
\(685\) | 1.07747 | + | 2.72059i | 0.0411681 | + | 0.103948i | ||||
\(686\) | 13.2747 | − | 13.2747i | 0.506829 | − | 0.506829i | ||||
\(687\) | −12.7507 | − | 12.7507i | −0.486471 | − | 0.486471i | ||||
\(688\) | − | 2.00391i | − | 0.0763983i | ||||||
\(689\) | −1.45448 | + | 1.45448i | −0.0554111 | + | 0.0554111i | ||||
\(690\) | −4.74635 | − | 11.9844i | −0.180690 | − | 0.456238i | ||||
\(691\) | 9.04475i | 0.344078i | 0.985090 | + | 0.172039i | \(0.0550356\pi\) | ||||
−0.985090 | + | 0.172039i | \(0.944964\pi\) | |||||||
\(692\) | 1.14427 | − | 1.14427i | 0.0434985 | − | 0.0434985i | ||||
\(693\) | 3.91330 | − | 3.91330i | 0.148654 | − | 0.148654i | ||||
\(694\) | −27.1062 | −1.02894 | ||||||||
\(695\) | 4.83299 | − | 11.1715i | 0.183326 | − | 0.423758i | ||||
\(696\) | 8.15506i | 0.309117i | ||||||||
\(697\) | − | 20.3300i | − | 0.770054i | ||||||
\(698\) | 1.86734 | 0.0706800 | ||||||||
\(699\) | − | 22.2673i | − | 0.842228i | ||||||
\(700\) | −13.0337 | − | 0.406983i | −0.492627 | − | 0.0153825i | ||||
\(701\) | −6.79801 | − | 6.79801i | −0.256757 | − | 0.256757i | 0.566977 | − | 0.823734i | \(-0.308113\pi\) |
−0.823734 | + | 0.566977i | \(0.808113\pi\) | |||||||
\(702\) | 3.58685 | + | 3.58685i | 0.135377 | + | 0.135377i | ||||
\(703\) | 6.39509 | − | 18.5831i | 0.241195 | − | 0.700875i | ||||
\(704\) | 2.12202i | 0.0799766i | ||||||||
\(705\) | −21.1148 | − | 9.13468i | −0.795230 | − | 0.344032i | ||||
\(706\) | 15.2302i | 0.573194i | ||||||||
\(707\) | 28.0729 | + | 28.0729i | 1.05579 | + | 1.05579i | ||||
\(708\) | − | 11.6734i | − | 0.438715i | ||||||
\(709\) | 12.7014 | − | 12.7014i | 0.477012 | − | 0.477012i | −0.427163 | − | 0.904175i | \(-0.640487\pi\) |
0.904175 | + | 0.427163i | \(0.140487\pi\) | |||||||
\(710\) | −3.48385 | − | 1.50718i | −0.130747 | − | 0.0565635i | ||||
\(711\) | 5.73733 | + | 5.73733i | 0.215167 | + | 0.215167i | ||||
\(712\) | −11.9236 | + | 11.9236i | −0.446856 | + | 0.446856i | ||||
\(713\) | −7.96502 | − | 7.96502i | −0.298292 | − | 0.298292i | ||||
\(714\) | −7.65439 | −0.286458 | ||||||||
\(715\) | 9.55685 | − | 22.0907i | 0.357406 | − | 0.826144i | ||||
\(716\) | 9.71351 | + | 9.71351i | 0.363011 | + | 0.363011i | ||||
\(717\) | 14.6083i | 0.545558i | ||||||||
\(718\) | 18.9718 | 0.708022 | ||||||||
\(719\) | 25.0596i | 0.934567i | 0.884108 | + | 0.467283i | \(0.154767\pi\) | ||||
−0.884108 | + | 0.467283i | \(0.845233\pi\) | |||||||
\(720\) | 2.05225 | + | 0.887844i | 0.0764829 | + | 0.0330880i | ||||
\(721\) | 24.8937 | − | 24.8937i | 0.927089 | − | 0.927089i | ||||
\(722\) | −8.56139 | −0.318622 | ||||||||
\(723\) | 9.18363 | 0.341543 | ||||||||
\(724\) | 1.59280 | 0.0591961 | ||||||||
\(725\) | 1.27261 | − | 40.7554i | 0.0472634 | − | 1.51362i | ||||
\(726\) | −4.59410 | − | 4.59410i | −0.170503 | − | 0.170503i | ||||
\(727\) | − | 28.9528i | − | 1.07380i | −0.843646 | − | 0.536899i | \(-0.819596\pi\) | ||
0.843646 | − | 0.536899i | \(-0.180404\pi\) | |||||||
\(728\) | 9.35455 | − | 9.35455i | 0.346703 | − | 0.346703i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −17.4067 | + | 6.89384i | −0.644253 | + | 0.255152i | ||||
\(731\) | 5.88138i | 0.217531i | ||||||||
\(732\) | − | 3.45964i | − | 0.127872i | ||||||
\(733\) | 12.6845 | − | 12.6845i | 0.468513 | − | 0.468513i | −0.432920 | − | 0.901433i | \(-0.642517\pi\) |
0.901433 | + | 0.432920i | \(0.142517\pi\) | |||||||
\(734\) | −23.8239 | − | 23.8239i | −0.879358 | − | 0.879358i | ||||
\(735\) | 0.412236 | − | 0.163264i | 0.0152055 | − | 0.00602207i | ||||
\(736\) | 5.76461 | 0.212486 | ||||||||
\(737\) | −21.0055 | + | 21.0055i | −0.773748 | + | 0.773748i | ||||
\(738\) | 6.92685i | 0.254981i | ||||||||
\(739\) | −5.09966 | −0.187594 | −0.0937970 | − | 0.995591i | \(-0.529900\pi\) | ||||
−0.0937970 | + | 0.995591i | \(0.529900\pi\) | |||||||
\(740\) | 0.620706 | + | 13.5873i | 0.0228176 | + | 0.499479i | ||||
\(741\) | −16.3889 | −0.602062 | ||||||||
\(742\) | 1.05755i | 0.0388240i | ||||||||
\(743\) | −5.46112 | + | 5.46112i | −0.200349 | + | 0.200349i | −0.800150 | − | 0.599801i | \(-0.795247\pi\) |
0.599801 | + | 0.800150i | \(0.295247\pi\) | |||||||
\(744\) | 1.95403 | 0.0716384 | ||||||||
\(745\) | −34.7851 | − | 15.0487i | −1.27443 | − | 0.551342i | ||||
\(746\) | −2.47846 | − | 2.47846i | −0.0907429 | − | 0.0907429i | ||||
\(747\) | −7.41007 | + | 7.41007i | −0.271120 | + | 0.271120i | ||||
\(748\) | − | 6.22803i | − | 0.227719i | ||||||
\(749\) | 8.56313i | 0.312890i | ||||||||
\(750\) | −10.1177 | − | 4.75731i | −0.369446 | − | 0.173712i | ||||
\(751\) | 50.1472i | 1.82990i | 0.403569 | + | 0.914949i | \(0.367770\pi\) | ||||
−0.403569 | + | 0.914949i | \(0.632230\pi\) | |||||||
\(752\) | 7.27515 | − | 7.27515i | 0.265297 | − | 0.265297i | ||||
\(753\) | − | 3.98630i | − | 0.145269i | ||||||
\(754\) | 29.2510 | + | 29.2510i | 1.06526 | + | 1.06526i | ||||
\(755\) | −2.58581 | − | 1.11867i | −0.0941072 | − | 0.0407126i | ||||
\(756\) | 2.60801 | 0.0948524 | ||||||||
\(757\) | −38.6619 | −1.40519 | −0.702596 | − | 0.711589i | \(-0.747976\pi\) | ||||
−0.702596 | + | 0.711589i | \(0.747976\pi\) | |||||||
\(758\) | 31.6861 | 1.15089 | ||||||||
\(759\) | 8.64976 | − | 8.64976i | 0.313966 | − | 0.313966i | ||||
\(760\) | −6.71688 | + | 2.66018i | −0.243647 | + | 0.0964949i | ||||
\(761\) | − | 2.58952i | − | 0.0938702i | −0.998898 | − | 0.0469351i | \(-0.985055\pi\) | ||
0.998898 | − | 0.0469351i | \(-0.0149454\pi\) | |||||||
\(762\) | 9.29533 | 0.336734 | ||||||||
\(763\) | − | 19.2013i | − | 0.695134i | ||||||
\(764\) | 14.2911 | + | 14.2911i | 0.517035 | + | 0.517035i | ||||
\(765\) | −6.02326 | − | 2.60578i | −0.217772 | − | 0.0942122i | ||||
\(766\) | −12.7864 | −0.461993 | ||||||||
\(767\) | −41.8709 | − | 41.8709i | −1.51187 | − | 1.51187i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 0.970999 | + | 0.970999i | 0.0350151 | + | 0.0350151i | 0.724398 | − | 0.689382i | \(-0.242118\pi\) |
−0.689382 | + | 0.724398i | \(0.742118\pi\) | |||||||
\(770\) | −4.55668 | − | 11.5055i | −0.164211 | − | 0.414629i | ||||
\(771\) | 7.91684 | − | 7.91684i | 0.285118 | − | 0.285118i | ||||
\(772\) | − | 11.4610i | − | 0.412489i | ||||||
\(773\) | 33.8554 | + | 33.8554i | 1.21769 | + | 1.21769i | 0.968438 | + | 0.249255i | \(0.0801859\pi\) |
0.249255 | + | 0.968438i | \(0.419814\pi\) | |||||||
\(774\) | − | 2.00391i | − | 0.0720290i | ||||||
\(775\) | −9.76541 | − | 0.304929i | −0.350784 | − | 0.0109534i | ||||
\(776\) | 7.94678i | 0.285273i | ||||||||
\(777\) | 6.95673 | + | 14.2572i | 0.249571 | + | 0.511473i | ||||
\(778\) | 15.4731 | + | 15.4731i | 0.554738 | + | 0.554738i | ||||
\(779\) | −15.8249 | − | 15.8249i | −0.566988 | − | 0.566988i | ||||
\(780\) | 10.5457 | − | 4.17656i | 0.377596 | − | 0.149545i | ||||
\(781\) | − | 3.60229i | − | 0.128900i | ||||||
\(782\) | −16.9189 | −0.605017 | ||||||||
\(783\) | 8.15506i | 0.291438i | ||||||||
\(784\) | 0.198289i | 0.00708176i | ||||||||
\(785\) | 4.71824 | + | 11.9134i | 0.168401 | + | 0.425208i | ||||
\(786\) | 3.78185 | 0.134894 | ||||||||
\(787\) | 29.0495 | − | 29.0495i | 1.03550 | − | 1.03550i | 0.0361558 | − | 0.999346i | \(-0.488489\pi\) |
0.999346 | − | 0.0361558i | \(-0.0115112\pi\) | |||||||
\(788\) | −3.61811 | + | 3.61811i | −0.128890 | + | 0.128890i | ||||
\(789\) | 3.62939i | 0.129210i | ||||||||
\(790\) | 16.8683 | − | 6.68059i | 0.600147 | − | 0.237685i | ||||
\(791\) | −30.6783 | + | 30.6783i | −1.09080 | + | 1.09080i | ||||
\(792\) | 2.12202i | 0.0754027i | ||||||||
\(793\) | −12.4092 | − | 12.4092i | −0.440664 | − | 0.440664i | ||||
\(794\) | 11.7358 | − | 11.7358i | 0.416487 | − | 0.416487i | ||||
\(795\) | −0.360022 | + | 0.832191i | −0.0127687 | + | 0.0295148i | ||||
\(796\) | 14.1563 | + | 14.1563i | 0.501756 | + | 0.501756i | ||||
\(797\) | − | 46.2735i | − | 1.63909i | −0.573014 | − | 0.819546i | \(-0.694226\pi\) | ||
0.573014 | − | 0.819546i | \(-0.305774\pi\) | |||||||
\(798\) | −5.95820 | + | 5.95820i | −0.210918 | + | 0.210918i | ||||
\(799\) | −21.3522 | + | 21.3522i | −0.755388 | + | 0.755388i | ||||
\(800\) | 3.64416 | − | 3.42347i | 0.128840 | − | 0.121038i | ||||
\(801\) | −11.9236 | + | 11.9236i | −0.421300 | + | 0.421300i | ||||
\(802\) | −11.6604 | − | 11.6604i | −0.411742 | − | 0.411742i | ||||
\(803\) | −12.5634 | − | 12.5634i | −0.443351 | − | 0.443351i | ||||
\(804\) | −13.9991 | −0.493709 | ||||||||
\(805\) | −31.2554 | + | 12.3785i | −1.10161 | + | 0.436285i | ||||
\(806\) | 7.00884 | − | 7.00884i | 0.246876 | − | 0.246876i | ||||
\(807\) | 22.7099 | + | 22.7099i | 0.799426 | + | 0.799426i | ||||
\(808\) | −15.2228 | −0.535535 | ||||||||
\(809\) | −5.77592 | − | 5.77592i | −0.203070 | − | 0.203070i | 0.598244 | − | 0.801314i | \(-0.295865\pi\) |
−0.801314 | + | 0.598244i | \(0.795865\pi\) | |||||||
\(810\) | 2.05225 | + | 0.887844i | 0.0721087 | + | 0.0311957i | ||||
\(811\) | −48.8974 | −1.71702 | −0.858510 | − | 0.512797i | \(-0.828609\pi\) | ||||
−0.858510 | + | 0.512797i | \(0.828609\pi\) | |||||||
\(812\) | 21.2685 | 0.746377 | ||||||||
\(813\) | −11.0022 | + | 11.0022i | −0.385862 | + | 0.385862i | ||||
\(814\) | −11.6004 | + | 5.66038i | −0.406595 | + | 0.198396i | ||||
\(815\) | −0.178346 | + | 0.412247i | −0.00624719 | + | 0.0144404i | ||||
\(816\) | 2.07533 | − | 2.07533i | 0.0726510 | − | 0.0726510i | ||||
\(817\) | 4.57809 | + | 4.57809i | 0.160167 | + | 0.160167i | ||||
\(818\) | −22.9972 | + | 22.9972i | −0.804077 | + | 0.804077i | ||||
\(819\) | 9.35455 | − | 9.35455i | 0.326874 | − | 0.326874i | ||||
\(820\) | 14.2156 | + | 6.14996i | 0.496432 | + | 0.214766i | ||||
\(821\) | 11.8926 | 0.415053 | 0.207527 | − | 0.978229i | \(-0.433459\pi\) | ||||
0.207527 | + | 0.978229i | \(0.433459\pi\) | |||||||
\(822\) | −1.30863 | −0.0456437 | ||||||||
\(823\) | −4.60009 | − | 4.60009i | −0.160349 | − | 0.160349i | 0.622372 | − | 0.782721i | \(-0.286169\pi\) |
−0.782721 | + | 0.622372i | \(0.786169\pi\) | |||||||
\(824\) | 13.4988i | 0.470253i | ||||||||
\(825\) | 0.331144 | − | 10.6049i | 0.0115289 | − | 0.369216i | ||||
\(826\) | −30.4444 | −1.05930 | ||||||||
\(827\) | 1.44766 | 0.0503400 | 0.0251700 | − | 0.999683i | \(-0.491987\pi\) | ||||
0.0251700 | + | 0.999683i | \(0.491987\pi\) | |||||||
\(828\) | 5.76461 | 0.200334 | ||||||||
\(829\) | −17.0831 | − | 17.0831i | −0.593320 | − | 0.593320i | 0.345207 | − | 0.938527i | \(-0.387809\pi\) |
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(830\) | 8.62833 | + | 21.7863i | 0.299494 | + | 0.756213i | ||||
\(831\) | 10.2132 | + | 10.2132i | 0.354293 | + | 0.354293i | ||||
\(832\) | 5.07258i | 0.175860i | ||||||||
\(833\) | − | 0.581970i | − | 0.0201641i | ||||||
\(834\) | 3.84915 | + | 3.84915i | 0.133285 | + | 0.133285i | ||||
\(835\) | 6.39969 | − | 14.7929i | 0.221470 | − | 0.511929i | ||||
\(836\) | −4.84792 | − | 4.84792i | −0.167669 | − | 0.167669i | ||||
\(837\) | 1.95403 | 0.0675413 | ||||||||
\(838\) | −24.2039 | −0.836109 | ||||||||
\(839\) | −24.1753 | −0.834624 | −0.417312 | − | 0.908763i | \(-0.637028\pi\) | ||||
−0.417312 | + | 0.908763i | \(0.637028\pi\) | |||||||
\(840\) | 2.31550 | − | 5.35229i | 0.0798925 | − | 0.184671i | ||||
\(841\) | 37.5049i | 1.29327i | ||||||||
\(842\) | −9.91998 | − | 9.91998i | −0.341865 | − | 0.341865i | ||||
\(843\) | −14.3877 | −0.495538 | ||||||||
\(844\) | −8.13385 | −0.279979 | ||||||||
\(845\) | 11.3032 | − | 26.1273i | 0.388841 | − | 0.898807i | ||||
\(846\) | 7.27515 | − | 7.27515i | 0.250125 | − | 0.250125i | ||||
\(847\) | −11.9814 | + | 11.9814i | −0.411687 | + | 0.411687i | ||||
\(848\) | −0.286733 | − | 0.286733i | −0.00984645 | − | 0.00984645i | ||||
\(849\) | 8.31082 | − | 8.31082i | 0.285226 | − | 0.285226i | ||||
\(850\) | −10.6954 | + | 10.0477i | −0.366850 | + | 0.344634i | ||||
\(851\) | 15.3768 | + | 31.5133i | 0.527110 | + | 1.08026i | ||||
\(852\) | 1.20037 | − | 1.20037i | 0.0411239 | − | 0.0411239i | ||||
\(853\) | −51.8584 | −1.77560 | −0.887799 | − | 0.460232i | \(-0.847766\pi\) | ||||
−0.887799 | + | 0.460232i | \(0.847766\pi\) | |||||||
\(854\) | −9.02276 | −0.308753 | ||||||||
\(855\) | −6.71688 | + | 2.66018i | −0.229712 | + | 0.0909762i | ||||
\(856\) | −2.32171 | − | 2.32171i | −0.0793545 | − | 0.0793545i | ||||
\(857\) | 50.1319 | 1.71247 | 0.856236 | − | 0.516585i | \(-0.172797\pi\) | ||||
0.856236 | + | 0.516585i | \(0.172797\pi\) | |||||||
\(858\) | 7.61138 | + | 7.61138i | 0.259848 | + | 0.259848i | ||||
\(859\) | 22.7307 | − | 22.7307i | 0.775560 | − | 0.775560i | −0.203512 | − | 0.979072i | \(-0.565236\pi\) |
0.979072 | + | 0.203512i | \(0.0652357\pi\) | |||||||
\(860\) | −4.11252 | − | 1.77916i | −0.140236 | − | 0.0606688i | ||||
\(861\) | 18.0653 | 0.615664 | ||||||||
\(862\) | 18.4635 | + | 18.4635i | 0.628869 | + | 0.628869i | ||||
\(863\) | 16.0282 | + | 16.0282i | 0.545605 | + | 0.545605i | 0.925167 | − | 0.379562i | \(-0.123925\pi\) |
−0.379562 | + | 0.925167i | \(0.623925\pi\) | |||||||
\(864\) | −0.707107 | + | 0.707107i | −0.0240563 | + | 0.0240563i | ||||
\(865\) | −1.33239 | − | 3.36425i | −0.0453027 | − | 0.114388i | ||||
\(866\) | −20.6095 | + | 20.6095i | −0.700338 | + | 0.700338i | ||||
\(867\) | 5.92983 | − | 5.92983i | 0.201387 | − | 0.201387i | ||||
\(868\) | − | 5.09614i | − | 0.172974i | ||||||
\(869\) | 12.1747 | + | 12.1747i | 0.412999 | + | 0.412999i | ||||
\(870\) | 16.7362 | + | 7.24042i | 0.567411 | + | 0.245473i | ||||
\(871\) | −50.2126 | + | 50.2126i | −1.70139 | + | 1.70139i | ||||
\(872\) | 5.20603 | + | 5.20603i | 0.176298 | + | 0.176298i | ||||
\(873\) | 7.94678i | 0.268958i | ||||||||
\(874\) | −13.1697 | + | 13.1697i | −0.445472 | + | 0.445472i | ||||
\(875\) | −12.4071 | + | 26.3871i | −0.419437 | + | 0.892046i | ||||
\(876\) | − | 8.37281i | − | 0.282891i | ||||||
\(877\) | 37.8142 | − | 37.8142i | 1.27689 | − | 1.27689i | 0.334498 | − | 0.942396i | \(-0.391433\pi\) |
0.942396 | − | 0.334498i | \(-0.108567\pi\) | |||||||
\(878\) | −6.00049 | + | 6.00049i | −0.202507 | + | 0.202507i | ||||
\(879\) | 20.1902 | 0.681000 | ||||||||
\(880\) | 4.35492 | + | 1.88402i | 0.146804 | + | 0.0635104i | ||||
\(881\) | 44.7156i | 1.50651i | 0.657731 | + | 0.753253i | \(0.271516\pi\) | ||||
−0.657731 | + | 0.753253i | \(0.728484\pi\) | |||||||
\(882\) | 0.198289i | 0.00667675i | ||||||||
\(883\) | 19.8417 | 0.667727 | 0.333863 | − | 0.942621i | \(-0.391648\pi\) | ||||
0.333863 | + | 0.942621i | \(0.391648\pi\) | |||||||
\(884\) | − | 14.8878i | − | 0.500731i | ||||||
\(885\) | −23.9568 | − | 10.3642i | −0.805300 | − | 0.348388i | ||||
\(886\) | −19.3252 | − | 19.3252i | −0.649243 | − | 0.649243i | ||||
\(887\) | −19.6978 | − | 19.6978i | −0.661387 | − | 0.661387i | 0.294320 | − | 0.955707i | \(-0.404907\pi\) |
−0.955707 | + | 0.294320i | \(0.904907\pi\) | |||||||
\(888\) | −5.75171 | − | 1.97936i | −0.193015 | − | 0.0664231i | ||||
\(889\) | − | 24.2423i | − | 0.813060i | ||||||
\(890\) | 13.8839 | + | 35.0565i | 0.465391 | + | 1.17510i | ||||
\(891\) | 2.12202i | 0.0710903i | ||||||||
\(892\) | 18.5142 | + | 18.5142i | 0.619901 | + | 0.619901i | ||||
\(893\) | 33.2413i | 1.11238i | ||||||||
\(894\) | 11.9853 | − | 11.9853i | 0.400847 | − | 0.400847i | ||||
\(895\) | 28.5586 | − | 11.3105i | 0.954610 | − | 0.378068i | ||||
\(896\) | 1.84414 | + | 1.84414i | 0.0616084 | + | 0.0616084i | ||||
\(897\) | 20.6768 | − | 20.6768i | 0.690378 | − | 0.690378i | ||||
\(898\) | −23.5893 | − | 23.5893i | −0.787184 | − | 0.787184i | ||||
\(899\) | 15.9353 | 0.531471 | ||||||||
\(900\) | 3.64416 | − | 3.42347i | 0.121472 | − | 0.114116i | ||||
\(901\) | 0.841548 | + | 0.841548i | 0.0280360 | + | 0.0280360i | ||||
\(902\) | 14.6989i | 0.489420i | ||||||||
\(903\) | −5.22621 | −0.173917 | ||||||||
\(904\) | − | 16.6356i | − | 0.553291i | ||||||
\(905\) | 1.41416 | − | 3.26883i | 0.0470083 | − | 0.108660i | ||||
\(906\) | 0.890945 | − | 0.890945i | 0.0295997 | − | 0.0295997i | ||||
\(907\) | −53.6798 | −1.78241 | −0.891204 | − | 0.453603i | \(-0.850138\pi\) | ||||
−0.891204 | + | 0.453603i | \(0.850138\pi\) | |||||||
\(908\) | −8.71126 | −0.289093 | ||||||||
\(909\) | −15.2228 | −0.504907 | ||||||||
\(910\) | −10.8925 | − | 27.5033i | −0.361083 | − | 0.911724i | ||||
\(911\) | 6.84880 | + | 6.84880i | 0.226911 | + | 0.226911i | 0.811401 | − | 0.584490i | \(-0.198705\pi\) |
−0.584490 | + | 0.811401i | \(0.698705\pi\) | |||||||
\(912\) | − | 3.23088i | − | 0.106985i | ||||||
\(913\) | −15.7243 | + | 15.7243i | −0.520399 | + | 0.520399i | ||||
\(914\) | − | 10.5479i | − | 0.348893i | ||||||
\(915\) | −7.10004 | − | 3.07162i | −0.234720 | − | 0.101545i | ||||
\(916\) | − | 18.0323i | − | 0.595802i | ||||||
\(917\) | − | 9.86309i | − | 0.325708i | ||||||
\(918\) | 2.07533 | − | 2.07533i | 0.0684960 | − | 0.0684960i | ||||
\(919\) | 18.9548 | + | 18.9548i | 0.625261 | + | 0.625261i | 0.946872 | − | 0.321611i | \(-0.104224\pi\) |
−0.321611 | + | 0.946872i | \(0.604224\pi\) | |||||||
\(920\) | 5.11807 | − | 11.8304i | 0.168738 | − | 0.390037i | ||||
\(921\) | 22.9990 | 0.757844 | ||||||||
\(922\) | 26.9418 | − | 26.9418i | 0.887281 | − | 0.887281i | ||||
\(923\) | − | 8.61108i | − | 0.283437i | ||||||
\(924\) | 5.53425 | 0.182063 | ||||||||
\(925\) | 28.4356 | + | 10.7896i | 0.934958 | + | 0.354758i | ||||
\(926\) | 16.5851 | 0.545019 | ||||||||
\(927\) | 13.4988i | 0.443359i | ||||||||
\(928\) | −5.76649 | + | 5.76649i | −0.189294 | + | 0.189294i | ||||
\(929\) | 43.3213 | 1.42133 | 0.710663 | − | 0.703532i | \(-0.248395\pi\) | ||||
0.710663 | + | 0.703532i | \(0.248395\pi\) | |||||||
\(930\) | 1.73488 | − | 4.01017i | 0.0568889 | − | 0.131499i | ||||
\(931\) | −0.453008 | − | 0.453008i | −0.0148467 | − | 0.0148467i | ||||
\(932\) | 15.7454 | − | 15.7454i | 0.515757 | − | 0.515757i | ||||
\(933\) | 15.6611i | 0.512721i | ||||||||
\(934\) | 34.4641i | 1.12770i | ||||||||
\(935\) | −12.7815 | − | 5.52952i | −0.417999 | − | 0.180835i | ||||
\(936\) | 5.07258i | 0.165802i | ||||||||
\(937\) | −4.54929 | + | 4.54929i | −0.148619 | + | 0.148619i | −0.777501 | − | 0.628882i | \(-0.783513\pi\) |
0.628882 | + | 0.777501i | \(0.283513\pi\) | |||||||
\(938\) | 36.5097i | 1.19208i | ||||||||
\(939\) | −3.12160 | − | 3.12160i | −0.101870 | − | 0.101870i | ||||
\(940\) | −8.47123 | − | 21.3896i | −0.276301 | − | 0.697653i | ||||
\(941\) | −59.4050 | −1.93655 | −0.968273 | − | 0.249894i | \(-0.919604\pi\) | ||||
−0.968273 | + | 0.249894i | \(0.919604\pi\) | |||||||
\(942\) | −5.73047 | −0.186709 | ||||||||
\(943\) | 39.9306 | 1.30032 | ||||||||
\(944\) | 8.25437 | − | 8.25437i | 0.268657 | − | 0.268657i | ||||
\(945\) | 2.31550 | − | 5.35229i | 0.0753234 | − | 0.174110i | ||||
\(946\) | − | 4.25233i | − | 0.138255i | ||||||
\(947\) | −22.4238 | −0.728675 | −0.364337 | − | 0.931267i | \(-0.618704\pi\) | ||||
−0.364337 | + | 0.931267i | \(0.618704\pi\) | |||||||
\(948\) | 8.11381i | 0.263524i | ||||||||
\(949\) | −30.0321 | − | 30.0321i | −0.974882 | − | 0.974882i | ||||
\(950\) | −0.504183 | + | 16.1465i | −0.0163579 | + | 0.523863i | ||||
\(951\) | 2.47560 | 0.0802769 | ||||||||
\(952\) | −5.41247 | − | 5.41247i | −0.175419 | − | 0.175419i | ||||
\(953\) | 18.1295 | − | 18.1295i | 0.587272 | − | 0.587272i | −0.349619 | − | 0.936892i | \(-0.613689\pi\) |
0.936892 | + | 0.349619i | \(0.113689\pi\) | |||||||
\(954\) | −0.286733 | − | 0.286733i | −0.00928332 | − | 0.00928332i | ||||
\(955\) | 42.0173 | − | 16.6407i | 1.35965 | − | 0.538480i | ||||
\(956\) | −10.3297 | + | 10.3297i | −0.334085 | + | 0.334085i | ||||
\(957\) | 17.3052i | 0.559397i | ||||||||
\(958\) | 15.9403 | + | 15.9403i | 0.515009 | + | 0.515009i | ||||
\(959\) | 3.41292i | 0.110209i | ||||||||
\(960\) | 0.823360 | + | 2.07896i | 0.0265738 | + | 0.0670982i | ||||
\(961\) | 27.1817i | 0.876831i | ||||||||
\(962\) | −27.7302 | + | 13.5308i | −0.894058 | + | 0.436252i | ||||
\(963\) | −2.32171 | − | 2.32171i | −0.0748162 | − | 0.0748162i | ||||
\(964\) | 6.49380 | + | 6.49380i | 0.209151 | + | 0.209151i | ||||
\(965\) | −23.5208 | − | 10.1755i | −0.757160 | − | 0.327562i | ||||
\(966\) | − | 15.0341i | − | 0.483716i | ||||||
\(967\) | −52.0958 | −1.67529 | −0.837644 | − | 0.546216i | \(-0.816068\pi\) | ||||
−0.837644 | + | 0.546216i | \(0.816068\pi\) | |||||||
\(968\) | − | 6.49703i | − | 0.208823i | ||||||
\(969\) | 9.48250i | 0.304622i | ||||||||
\(970\) | 16.3088 | + | 7.05550i | 0.523644 | + | 0.226539i | ||||
\(971\) | 7.35800 | 0.236129 | 0.118065 | − | 0.993006i | \(-0.462331\pi\) | ||||
0.118065 | + | 0.993006i | \(0.462331\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 10.0386 | − | 10.0386i | 0.321823 | − | 0.321823i | ||||
\(974\) | 5.52466i | 0.177022i | ||||||||
\(975\) | 0.791581 | − | 25.3505i | 0.0253509 | − | 0.811867i | ||||
\(976\) | 2.44633 | − | 2.44633i | 0.0783052 | − | 0.0783052i | ||||
\(977\) | 2.33312i | 0.0746432i | 0.999303 | + | 0.0373216i | \(0.0118826\pi\) | ||||
−0.999303 | + | 0.0373216i | \(0.988117\pi\) | |||||||
\(978\) | −0.142041 | − | 0.142041i | −0.00454196 | − | 0.00454196i | ||||
\(979\) | −25.3021 | + | 25.3021i | −0.808660 | + | 0.808660i | ||||
\(980\) | 0.406940 | + | 0.176050i | 0.0129992 | + | 0.00562371i | ||||
\(981\) | 5.20603 | + | 5.20603i | 0.166216 | + | 0.166216i | ||||
\(982\) | 30.9165i | 0.986585i | ||||||||
\(983\) | −14.6210 | + | 14.6210i | −0.466338 | + | 0.466338i | −0.900726 | − | 0.434388i | \(-0.856965\pi\) |
0.434388 | + | 0.900726i | \(0.356965\pi\) | |||||||
\(984\) | −4.89802 | + | 4.89802i | −0.156143 | + | 0.156143i | ||||
\(985\) | 4.21296 | + | 10.6376i | 0.134236 | + | 0.338942i | ||||
\(986\) | 16.9244 | − | 16.9244i | 0.538983 | − | 0.538983i | ||||
\(987\) | −18.9736 | − | 18.9736i | −0.603938 | − | 0.603938i | ||||
\(988\) | −11.5887 | − | 11.5887i | −0.368686 | − | 0.368686i | ||||
\(989\) | −11.5517 | −0.367324 | ||||||||
\(990\) | 4.35492 | + | 1.88402i | 0.138408 | + | 0.0598781i | ||||
\(991\) | −19.5442 | + | 19.5442i | −0.620841 | + | 0.620841i | −0.945746 | − | 0.324906i | \(-0.894667\pi\) |
0.324906 | + | 0.945746i | \(0.394667\pi\) | |||||||
\(992\) | 1.38171 | + | 1.38171i | 0.0438694 | + | 0.0438694i | ||||
\(993\) | 24.0444 | 0.763025 | ||||||||
\(994\) | −3.13057 | − | 3.13057i | −0.0992956 | − | 0.0992956i | ||||
\(995\) | 41.6208 | − | 16.4837i | 1.31947 | − | 0.522567i | ||||
\(996\) | −10.4794 | −0.332053 | ||||||||
\(997\) | −23.0867 | −0.731162 | −0.365581 | − | 0.930780i | \(-0.619130\pi\) | ||||
−0.365581 | + | 0.930780i | \(0.619130\pi\) | |||||||
\(998\) | −15.3419 | + | 15.3419i | −0.485640 | + | 0.485640i | ||||
\(999\) | −5.75171 | − | 1.97936i | −0.181976 | − | 0.0626243i |
(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 | 1110.2.l.a.43.2 | ✓ | 36 | |
5.2 | odd | 4 | 1110.2.o.a.487.17 | yes | 36 | ||
37.31 | odd | 4 | 1110.2.o.a.253.17 | yes | 36 | ||
185.142 | even | 4 | inner | 1110.2.l.a.697.2 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.2 | ✓ | 36 | 1.1 | even | 1 | trivial | |
1110.2.l.a.697.2 | yes | 36 | 185.142 | even | 4 | inner | |
1110.2.o.a.253.17 | yes | 36 | 37.31 | odd | 4 | ||
1110.2.o.a.487.17 | yes | 36 | 5.2 | odd | 4 |