Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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 | 253.17 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.17 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.05225 | + | 0.887844i | 0.917794 | + | 0.397056i | ||||
\(6\) | −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 | \(0.414051\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.05225 | − | 0.887844i | −0.648979 | − | 0.280761i | ||||
\(11\) | 2.12202i | 0.639813i | 0.947449 | + | 0.319906i | \(0.103651\pi\) | ||||
−0.947449 | + | 0.319906i | \(0.896349\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −5.07258 | −1.40688 | −0.703440 | − | 0.710755i | \(-0.748354\pi\) | ||||
−0.703440 | + | 0.710755i | \(0.748354\pi\) | |||||||
\(14\) | 1.84414 | − | 1.84414i | 0.492867 | − | 0.492867i | ||||
\(15\) | 2.07896 | − | 0.823360i | 0.536785 | − | 0.212591i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.93495i | 0.711831i | 0.934518 | + | 0.355916i | \(0.115831\pi\) | ||||
−0.934518 | + | 0.355916i | \(0.884169\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.28458 | + | 2.28458i | 0.524118 | + | 0.524118i | 0.918813 | − | 0.394694i | \(-0.129149\pi\) |
−0.394694 | + | 0.918813i | \(0.629149\pi\) | |||||||
\(20\) | 2.05225 | + | 0.887844i | 0.458897 | + | 0.198528i | ||||
\(21\) | 2.60801i | 0.569114i | ||||||||
\(22\) | − | 2.12202i | − | 0.452416i | ||||||
\(23\) | −5.76461 | −1.20200 | −0.601002 | − | 0.799248i | \(-0.705232\pi\) | ||||
−0.601002 | + | 0.799248i | \(0.705232\pi\) | |||||||
\(24\) | −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 | −0.0735173 | + | 0.997294i | \(0.523422\pi\) |
−0.997294 | + | 0.0735173i | \(0.976578\pi\) | |||||||
\(30\) | −2.07896 | + | 0.823360i | −0.379565 | + | 0.150324i | ||||
\(31\) | 1.38171 | + | 1.38171i | 0.248163 | + | 0.248163i | 0.820216 | − | 0.572054i | \(-0.193853\pi\) |
−0.572054 | + | 0.820216i | \(0.693853\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.50049 | + | 1.50049i | 0.261203 | + | 0.261203i | ||||
\(34\) | − | 2.93495i | − | 0.503341i | ||||||
\(35\) | −5.42195 | + | 2.14733i | −0.916477 | + | 0.362965i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −2.66745 | + | 5.46669i | −0.438526 | + | 0.898719i | ||||
\(38\) | −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 | \(-0.818085\pi\) | ||
0.841089 | − | 0.540896i | \(-0.181915\pi\) | |||||||
\(42\) | − | 2.60801i | − | 0.402425i | ||||||
\(43\) | −2.00391 | −0.305593 | −0.152797 | − | 0.988258i | \(-0.548828\pi\) | ||||
−0.152797 | + | 0.988258i | \(0.548828\pi\) | |||||||
\(44\) | 2.12202i | 0.319906i | ||||||||
\(45\) | 0.887844 | − | 2.05225i | 0.132352 | − | 0.305931i | ||||
\(46\) | 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 | ||||||||
\(50\) | −3.42347 | − | 3.64416i | −0.484151 | − | 0.515362i | ||||
\(51\) | 2.07533 | + | 2.07533i | 0.290604 | + | 0.290604i | ||||
\(52\) | −5.07258 | −0.703440 | ||||||||
\(53\) | −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 | ||||
\(55\) | −1.88402 | + | 4.35492i | −0.254041 | + | 0.587217i | ||||
\(56\) | 1.84414 | − | 1.84414i | 0.246434 | − | 0.246434i | ||||
\(57\) | 3.23088 | 0.427941 | ||||||||
\(58\) | 5.76649 | − | 5.76649i | 0.757178 | − | 0.757178i | ||||
\(59\) | −8.25437 | − | 8.25437i | −1.07463 | − | 1.07463i | −0.996981 | − | 0.0776460i | \(-0.975260\pi\) |
−0.0776460 | − | 0.996981i | \(-0.524740\pi\) | |||||||
\(60\) | 2.07896 | − | 0.823360i | 0.268393 | − | 0.106295i | ||||
\(61\) | 2.44633 | + | 2.44633i | 0.313221 | + | 0.313221i | 0.846156 | − | 0.532935i | \(-0.178911\pi\) |
−0.532935 | + | 0.846156i | \(0.678911\pi\) | |||||||
\(62\) | −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 | \(0.0765222\pi\) |
0.238093 | + | 0.971242i | \(0.423478\pi\) | |||||||
\(68\) | 2.93495i | 0.355916i | ||||||||
\(69\) | −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 | \(0.467881\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −5.92047 | + | 5.92047i | −0.692939 | + | 0.692939i | −0.962877 | − | 0.269939i | \(-0.912997\pi\) |
0.269939 | + | 0.962877i | \(0.412997\pi\) | |||||||
\(74\) | 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 | \(-0.0991253\pi\) |
−0.306402 | + | 0.951902i | \(0.599125\pi\) | |||||||
\(80\) | 2.05225 | + | 0.887844i | 0.229449 | + | 0.0992640i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 6.92685i | 0.764943i | ||||||||
\(83\) | −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 | ||||||||
\(87\) | 8.15506i | 0.874314i | ||||||||
\(88\) | − | 2.12202i | − | 0.226208i | ||||||
\(89\) | 11.9236 | − | 11.9236i | 1.26390 | − | 1.26390i | 0.314714 | − | 0.949187i | \(-0.398092\pi\) |
0.949187 | − | 0.314714i | \(-0.101908\pi\) | |||||||
\(90\) | −0.887844 | + | 2.05225i | −0.0935870 | + | 0.216326i | ||||
\(91\) | 9.35455 | − | 9.35455i | 0.980623 | − | 0.980623i | ||||
\(92\) | −5.76461 | −0.601002 | ||||||||
\(93\) | 1.95403 | 0.202624 | ||||||||
\(94\) | −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 | ||||
\(97\) | 7.94678i | 0.806874i | 0.915008 | + | 0.403437i | \(0.132184\pi\) | ||||
−0.915008 | + | 0.403437i | \(0.867816\pi\) | |||||||
\(98\) | − | 0.198289i | − | 0.0200303i | ||||||
\(99\) | 2.12202 | 0.213271 | ||||||||
\(100\) | 3.42347 | + | 3.64416i | 0.342347 | + | 0.364416i | ||||
\(101\) | 15.2228i | 1.51472i | 0.652997 | + | 0.757360i | \(0.273511\pi\) | ||||
−0.652997 | + | 0.757360i | \(0.726489\pi\) | |||||||
\(102\) | −2.07533 | − | 2.07533i | −0.205488 | − | 0.205488i | ||||
\(103\) | − | 13.4988i | − | 1.33008i | −0.746810 | − | 0.665038i | \(-0.768415\pi\) | ||
0.746810 | − | 0.665038i | \(-0.231585\pi\) | |||||||
\(104\) | 5.07258 | 0.497407 | ||||||||
\(105\) | −2.31550 | + | 5.35229i | −0.225970 | + | 0.522330i | ||||
\(106\) | 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 | \(-0.135299\pi\) |
−0.412369 | + | 0.911017i | \(0.635299\pi\) | |||||||
\(110\) | 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 | ||||
\(113\) | 16.6356i | 1.56494i | 0.622687 | + | 0.782471i | \(0.286041\pi\) | ||||
−0.622687 | + | 0.782471i | \(0.713959\pi\) | |||||||
\(114\) | −3.23088 | −0.302600 | ||||||||
\(115\) | −11.8304 | − | 5.11807i | −1.10319 | − | 0.477262i | ||||
\(116\) | −5.76649 | + | 5.76649i | −0.535406 | + | 0.535406i | ||||
\(117\) | 5.07258i | 0.468960i | ||||||||
\(118\) | 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 | ||||
\(125\) | 3.79037 | + | 10.5182i | 0.339021 | + | 0.940779i | ||||
\(126\) | −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 | \(0.385314\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.41698 | + | 1.41698i | −0.124758 | + | 0.124758i | ||||
\(130\) | 10.4102 | + | 4.50366i | 0.913035 | + | 0.394997i | ||||
\(131\) | −2.67417 | − | 2.67417i | −0.233643 | − | 0.233643i | 0.580568 | − | 0.814212i | \(-0.302830\pi\) |
−0.814212 | + | 0.580568i | \(0.802830\pi\) | |||||||
\(132\) | 1.50049 | + | 1.50049i | 0.130601 | + | 0.130601i | ||||
\(133\) | −8.42617 | −0.730642 | ||||||||
\(134\) | −9.89884 | − | 9.89884i | −0.855129 | − | 0.855129i | ||||
\(135\) | −0.823360 | − | 2.07896i | −0.0708636 | − | 0.178928i | ||||
\(136\) | − | 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 | \(-0.425847\pi\) | ||||
0.230857 | + | 0.972988i | \(0.425847\pi\) | |||||||
\(140\) | −5.42195 | + | 2.14733i | −0.458238 | + | 0.181483i | ||||
\(141\) | − | 10.2886i | − | 0.866457i | ||||||
\(142\) | −1.69758 | −0.142457 | ||||||||
\(143\) | − | 10.7641i | − | 0.900140i | ||||||
\(144\) | − | 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 | ||||
\(148\) | −2.66745 | + | 5.46669i | −0.219263 | + | 0.449359i | ||||
\(149\) | 16.9497i | 1.38858i | 0.719698 | + | 0.694288i | \(0.244280\pi\) | ||||
−0.719698 | + | 0.694288i | \(0.755720\pi\) | |||||||
\(150\) | −4.99756 | − | 0.156051i | −0.408049 | − | 0.0127415i | ||||
\(151\) | − | 1.25999i | − | 0.102536i | −0.998685 | − | 0.0512681i | \(-0.983674\pi\) | ||
0.998685 | − | 0.0512681i | \(-0.0163263\pi\) | |||||||
\(152\) | −2.28458 | − | 2.28458i | −0.185304 | − | 0.185304i | ||||
\(153\) | 2.93495 | 0.237277 | ||||||||
\(154\) | 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 | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 0.200876i | 0.0157338i | 0.999969 | + | 0.00786690i | \(0.00250414\pi\) | ||||
−0.999969 | + | 0.00786690i | \(0.997496\pi\) | |||||||
\(164\) | − | 6.92685i | − | 0.540896i | ||||||
\(165\) | 1.74719 | + | 4.41160i | 0.136018 | + | 0.343442i | ||||
\(166\) | 7.41007 | + | 7.41007i | 0.575133 | + | 0.575133i | ||||
\(167\) | 7.20812i | 0.557781i | 0.960323 | + | 0.278891i | \(0.0899667\pi\) | ||||
−0.960323 | + | 0.278891i | \(0.910033\pi\) | |||||||
\(168\) | − | 2.60801i | − | 0.201212i | ||||||
\(169\) | 12.7311 | 0.979312 | ||||||||
\(170\) | 2.60578 | − | 6.02326i | 0.199854 | − | 0.461963i | ||||
\(171\) | 2.28458 | − | 2.28458i | 0.174706 | − | 0.174706i | ||||
\(172\) | −2.00391 | −0.152797 | ||||||||
\(173\) | 1.14427 | − | 1.14427i | 0.0869969 | − | 0.0869969i | −0.662269 | − | 0.749266i | \(-0.730406\pi\) |
0.749266 | + | 0.662269i | \(0.230406\pi\) | |||||||
\(174\) | − | 8.15506i | − | 0.618233i | ||||||
\(175\) | −13.0337 | − | 0.406983i | −0.985255 | − | 0.0307650i | ||||
\(176\) | 2.12202i | 0.159953i | ||||||||
\(177\) | −11.6734 | −0.877429 | ||||||||
\(178\) | −11.9236 | + | 11.9236i | −0.893712 | + | 0.893712i | ||||
\(179\) | 9.71351 | − | 9.71351i | 0.726022 | − | 0.726022i | −0.243803 | − | 0.969825i | \(-0.578395\pi\) |
0.969825 | + | 0.243803i | \(0.0783950\pi\) | |||||||
\(180\) | 0.887844 | − | 2.05225i | 0.0661760 | − | 0.152966i | ||||
\(181\) | −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 | ||||
\(183\) | 3.45964 | 0.255744 | ||||||||
\(184\) | 5.76461 | 0.424972 | ||||||||
\(185\) | −10.3278 | + | 8.85074i | −0.759318 | + | 0.650720i | ||||
\(186\) | −1.95403 | −0.143277 | ||||||||
\(187\) | −6.22803 | −0.455439 | ||||||||
\(188\) | 7.27515 | − | 7.27515i | 0.530595 | − | 0.530595i | ||||
\(189\) | 2.60801 | 0.189705 | ||||||||
\(190\) | −2.66018 | − | 6.71688i | −0.192990 | − | 0.487294i | ||||
\(191\) | −14.2911 | + | 14.2911i | −1.03407 | + | 1.03407i | −0.0346716 | + | 0.999399i | \(0.511039\pi\) |
−0.999399 | + | 0.0346716i | \(0.988961\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | 11.4610 | 0.824978 | 0.412489 | − | 0.910963i | \(-0.364660\pi\) | ||||
0.412489 | + | 0.910963i | \(0.364660\pi\) | |||||||
\(194\) | − | 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 | \(0.191653\pi\) | |||||||
\(198\) | −2.12202 | −0.150805 | ||||||||
\(199\) | 14.1563 | − | 14.1563i | 1.00351 | − | 1.00351i | 0.00351772 | − | 0.999994i | \(-0.498880\pi\) |
0.999994 | − | 0.00351772i | \(-0.00111973\pi\) | |||||||
\(200\) | −3.42347 | − | 3.64416i | −0.242076 | − | 0.257681i | ||||
\(201\) | 13.9991 | 0.987418 | ||||||||
\(202\) | − | 15.2228i | − | 1.07107i | ||||||
\(203\) | − | 21.2685i | − | 1.49275i | ||||||
\(204\) | 2.07533 | + | 2.07533i | 0.145302 | + | 0.145302i | ||||
\(205\) | 6.14996 | − | 14.2156i | 0.429532 | − | 0.992863i | ||||
\(206\) | 13.4988i | 0.940505i | ||||||||
\(207\) | 5.76461i | 0.400668i | ||||||||
\(208\) | −5.07258 | −0.351720 | ||||||||
\(209\) | −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 | ||||
\(217\) | −5.09614 | −0.345949 | ||||||||
\(218\) | −5.20603 | − | 5.20603i | −0.352597 | − | 0.352597i | ||||
\(219\) | 8.37281i | 0.565782i | ||||||||
\(220\) | −1.88402 | + | 4.35492i | −0.127021 | + | 0.293608i | ||||
\(221\) | − | 14.8878i | − | 1.00146i | ||||||
\(222\) | −1.97936 | − | 5.75171i | −0.132846 | − | 0.386029i | ||||
\(223\) | −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 | ||||||
\(227\) | − | 8.71126i | − | 0.578187i | −0.957301 | − | 0.289093i | \(-0.906646\pi\) | ||
0.957301 | − | 0.289093i | \(-0.0933538\pi\) | |||||||
\(228\) | 3.23088 | 0.213970 | ||||||||
\(229\) | 18.0323i | 1.19160i | 0.803131 | + | 0.595802i | \(0.203166\pi\) | ||||
−0.803131 | + | 0.595802i | \(0.796834\pi\) | |||||||
\(230\) | 11.8304 | + | 5.11807i | 0.780075 | + | 0.337476i | ||||
\(231\) | −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 | \(-0.489803\pi\) |
0.999487 | − | 0.0320280i | \(-0.0101966\pi\) | |||||||
\(234\) | − | 5.07258i | − | 0.331605i | ||||||
\(235\) | 21.3896 | − | 8.47123i | 1.39531 | − | 0.552602i | ||||
\(236\) | −8.25437 | − | 8.25437i | −0.537314 | − | 0.537314i | ||||
\(237\) | 8.11381 | 0.527048 | ||||||||
\(238\) | 5.41247 | + | 5.41247i | 0.350838 | + | 0.350838i | ||||
\(239\) | −10.3297 | − | 10.3297i | −0.668170 | − | 0.668170i | 0.289122 | − | 0.957292i | \(-0.406637\pi\) |
−0.957292 | + | 0.289122i | \(0.906637\pi\) | |||||||
\(240\) | 2.07896 | − | 0.823360i | 0.134196 | − | 0.0531477i | ||||
\(241\) | −6.49380 | + | 6.49380i | −0.418303 | + | 0.418303i | −0.884618 | − | 0.466316i | \(-0.845581\pi\) |
0.466316 | + | 0.884618i | \(0.345581\pi\) | |||||||
\(242\) | −6.49703 | −0.417645 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 2.44633 | + | 2.44633i | 0.156610 | + | 0.156610i | ||||
\(245\) | −0.176050 | + | 0.406940i | −0.0112474 | + | 0.0259984i | ||||
\(246\) | 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 | 0.612530 | − | 0.790447i | \(-0.290152\pi\) |
−0.790447 | + | 0.612530i | \(0.790152\pi\) | |||||||
\(252\) | 1.84414 | + | 1.84414i | 0.116170 | + | 0.116170i | ||||
\(253\) | − | 12.2326i | − | 0.769057i | ||||||
\(254\) | 6.57279 | − | 6.57279i | 0.412413 | − | 0.412413i | ||||
\(255\) | 2.41652 | + | 6.10166i | 0.151329 | + | 0.382101i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.1961i | 0.698394i | 0.937049 | + | 0.349197i | \(0.113546\pi\) | ||||
−0.937049 | + | 0.349197i | \(0.886454\pi\) | |||||||
\(258\) | 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 | −0.781790 | − | 0.623541i | \(-0.785693\pi\) |
0.623541 | + | 0.781790i | \(0.285693\pi\) | |||||||
\(264\) | −1.50049 | − | 1.50049i | −0.0923490 | − | 0.0923490i | ||||
\(265\) | −0.333874 | − | 0.843022i | −0.0205097 | − | 0.0517864i | ||||
\(266\) | 8.42617 | 0.516642 | ||||||||
\(267\) | − | 16.8625i | − | 1.03197i | ||||||
\(268\) | 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 | \(0.343322\pi\) | |||||||
\(272\) | 2.93495i | 0.177958i | ||||||||
\(273\) | − | 13.2293i | − | 0.800675i | ||||||
\(274\) | −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 | ||||
\(277\) | 14.4437 | 0.867838 | 0.433919 | − | 0.900952i | \(-0.357130\pi\) | ||||
0.433919 | + | 0.900952i | \(0.357130\pi\) | |||||||
\(278\) | −5.44352 | −0.326481 | ||||||||
\(279\) | 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 | −0.335229 | − | 0.942137i | \(-0.608814\pi\) |
0.942137 | + | 0.335229i | \(0.108814\pi\) | |||||||
\(282\) | 10.2886i | 0.612678i | ||||||||
\(283\) | − | 11.7533i | − | 0.698659i | −0.937000 | − | 0.349330i | \(-0.886409\pi\) | ||
0.937000 | − | 0.349330i | \(-0.113591\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 8.38604 | 0.493296 | ||||||||
\(290\) | 16.9540 | − | 6.71455i | 0.995576 | − | 0.394292i | ||||
\(291\) | 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 | ||||
\(298\) | − | 16.9497i | − | 0.981871i | ||||||
\(299\) | 29.2414 | 1.69107 | ||||||||
\(300\) | 4.99756 | + | 0.156051i | 0.288535 | + | 0.00900961i | ||||
\(301\) | 3.69549 | − | 3.69549i | 0.213005 | − | 0.213005i | ||||
\(302\) | 1.25999i | 0.0725041i | ||||||||
\(303\) | 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 | 0.997587 | − | 0.0694214i | \(-0.0221153\pi\) |
−0.0694214 | + | 0.997587i | \(0.522115\pi\) | |||||||
\(308\) | −3.91330 | − | 3.91330i | −0.222981 | − | 0.222981i | ||||
\(309\) | −9.54509 | − | 9.54509i | −0.543001 | − | 0.543001i | ||||
\(310\) | −1.60887 | − | 4.06236i | −0.0913779 | − | 0.230727i | ||||
\(311\) | 11.0741 | + | 11.0741i | 0.627952 | + | 0.627952i | 0.947552 | − | 0.319600i | \(-0.103549\pi\) |
−0.319600 | + | 0.947552i | \(0.603549\pi\) | |||||||
\(312\) | 3.58685 | − | 3.58685i | 0.203066 | − | 0.203066i | ||||
\(313\) | 4.41462 | 0.249529 | 0.124764 | − | 0.992186i | \(-0.460182\pi\) | ||||
0.124764 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(314\) | −4.05205 | + | 4.05205i | −0.228671 | + | 0.228671i | ||||
\(315\) | 2.14733 | + | 5.42195i | 0.120988 | + | 0.305492i | ||||
\(316\) | 5.73733 | + | 5.73733i | 0.322750 | + | 0.322750i | ||||
\(317\) | 1.75051 | + | 1.75051i | 0.0983187 | + | 0.0983187i | 0.754555 | − | 0.656237i | \(-0.227853\pi\) |
−0.656237 | + | 0.754555i | \(0.727853\pi\) | |||||||
\(318\) | 0.405502 | 0.0227394 | ||||||||
\(319\) | −12.2366 | − | 12.2366i | −0.685119 | − | 0.685119i | ||||
\(320\) | 2.05225 | + | 0.887844i | 0.114724 | + | 0.0496320i | ||||
\(321\) | − | 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 | ||||||||
\(325\) | −17.3658 | − | 18.4853i | −0.963281 | − | 1.02538i | ||||
\(326\) | − | 0.200876i | − | 0.0111255i | ||||||
\(327\) | 7.36244 | 0.407144 | ||||||||
\(328\) | 6.92685i | 0.382471i | ||||||||
\(329\) | 26.8328i | 1.47934i | ||||||||
\(330\) | −1.74719 | − | 4.41160i | −0.0961794 | − | 0.242850i | ||||
\(331\) | −17.0019 | + | 17.0019i | −0.934511 | + | 0.934511i | −0.997984 | − | 0.0634724i | \(-0.979783\pi\) |
0.0634724 | + | 0.997984i | \(0.479783\pi\) | |||||||
\(332\) | −7.41007 | − | 7.41007i | −0.406680 | − | 0.406680i | ||||
\(333\) | 5.46669 | + | 2.66745i | 0.299573 | + | 0.146175i | ||||
\(334\) | − | 7.20812i | − | 0.394411i | ||||||
\(335\) | 11.5263 | + | 29.1035i | 0.629748 | + | 1.59009i | ||||
\(336\) | 2.60801i | 0.142279i | ||||||||
\(337\) | −16.7264 | − | 16.7264i | −0.911145 | − | 0.911145i | 0.0852173 | − | 0.996362i | \(-0.472842\pi\) |
−0.996362 | + | 0.0852173i | \(0.972842\pi\) | |||||||
\(338\) | −12.7311 | −0.692478 | ||||||||
\(339\) | 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 | ||||
\(347\) | −27.1062 | −1.45514 | −0.727568 | − | 0.686036i | \(-0.759349\pi\) | ||||
−0.727568 | + | 0.686036i | \(0.759349\pi\) | |||||||
\(348\) | 8.15506i | 0.437157i | ||||||||
\(349\) | − | 1.86734i | − | 0.0999566i | −0.998750 | − | 0.0499783i | \(-0.984085\pi\) | ||
0.998750 | − | 0.0499783i | \(-0.0159152\pi\) | |||||||
\(350\) | 13.0337 | + | 0.406983i | 0.696680 | + | 0.0217541i | ||||
\(351\) | 3.58685 | + | 3.58685i | 0.191452 | + | 0.191452i | ||||
\(352\) | − | 2.12202i | − | 0.113104i | ||||||
\(353\) | 15.2302i | 0.810619i | 0.914179 | + | 0.405310i | \(0.132836\pi\) | ||||
−0.914179 | + | 0.405310i | \(0.867164\pi\) | |||||||
\(354\) | 11.6734 | 0.620436 | ||||||||
\(355\) | 3.48385 | + | 1.50718i | 0.184904 | + | 0.0799929i | ||||
\(356\) | 11.9236 | − | 11.9236i | 0.631950 | − | 0.631950i | ||||
\(357\) | −7.65439 | −0.405113 | ||||||||
\(358\) | −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 | ||||||
\(362\) | 1.59280 | 0.0837159 | ||||||||
\(363\) | 4.59410 | − | 4.59410i | 0.241128 | − | 0.241128i | ||||
\(364\) | 9.35455 | − | 9.35455i | 0.490312 | − | 0.490312i | ||||
\(365\) | −17.4067 | + | 6.89384i | −0.911111 | + | 0.360840i | ||||
\(366\) | −3.45964 | −0.180838 | ||||||||
\(367\) | −23.8239 | + | 23.8239i | −1.24360 | + | 1.24360i | −0.285103 | + | 0.958497i | \(0.592028\pi\) |
−0.958497 | + | 0.285103i | \(0.907972\pi\) | |||||||
\(368\) | −5.76461 | −0.300501 | ||||||||
\(369\) | −6.92685 | −0.360598 | ||||||||
\(370\) | 10.3278 | − | 8.85074i | 0.536919 | − | 0.460128i | ||||
\(371\) | 1.05755 | 0.0549054 | ||||||||
\(372\) | 1.95403 | 0.101312 | ||||||||
\(373\) | 2.47846 | − | 2.47846i | 0.128330 | − | 0.128330i | −0.640025 | − | 0.768354i | \(-0.721076\pi\) |
0.768354 | + | 0.640025i | \(0.221076\pi\) | |||||||
\(374\) | 6.22803 | 0.322044 | ||||||||
\(375\) | 10.1177 | + | 4.75731i | 0.522476 | + | 0.245667i | ||||
\(376\) | −7.27515 | + | 7.27515i | −0.375187 | + | 0.375187i | ||||
\(377\) | 29.2510 | − | 29.2510i | 1.50650 | − | 1.50650i | ||||
\(378\) | −2.60801 | −0.134142 | ||||||||
\(379\) | − | 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 | ||||
\(383\) | 12.7864 | 0.653357 | 0.326678 | − | 0.945136i | \(-0.394071\pi\) | ||||
0.326678 | + | 0.945136i | \(0.394071\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −4.55668 | − | 11.5055i | −0.232230 | − | 0.586374i | ||||
\(386\) | −11.4610 | −0.583347 | ||||||||
\(387\) | 2.00391i | 0.101864i | ||||||||
\(388\) | 7.94678i | 0.403437i | ||||||||
\(389\) | −15.4731 | − | 15.4731i | −0.784518 | − | 0.784518i | 0.196071 | − | 0.980590i | \(-0.437182\pi\) |
−0.980590 | + | 0.196071i | \(0.937182\pi\) | |||||||
\(390\) | 10.5457 | − | 4.17656i | 0.534002 | − | 0.211488i | ||||
\(391\) | − | 16.9189i | − | 0.855623i | ||||||
\(392\) | − | 0.198289i | − | 0.0100151i | ||||||
\(393\) | −3.78185 | −0.190769 | ||||||||
\(394\) | −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 | 0.937361 | − | 0.348359i | \(-0.113261\pi\) |
−0.348359 | + | 0.937361i | \(0.613261\pi\) | |||||||
\(398\) | −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 | 0.353241 | − | 0.935532i | \(-0.385079\pi\) |
−0.935532 | + | 0.353241i | \(0.885079\pi\) | |||||||
\(402\) | −13.9991 | −0.698210 | ||||||||
\(403\) | −7.00884 | − | 7.00884i | −0.349135 | − | 0.349135i | ||||
\(404\) | 15.2228i | 0.757360i | ||||||||
\(405\) | −2.05225 | − | 0.887844i | −0.101977 | − | 0.0441173i | ||||
\(406\) | 21.2685i | 1.05554i | ||||||||
\(407\) | −11.6004 | − | 5.66038i | −0.575012 | − | 0.280575i | ||||
\(408\) | −2.07533 | − | 2.07533i | −0.102744 | − | 0.102744i | ||||
\(409\) | −22.9972 | + | 22.9972i | −1.13714 | + | 1.13714i | −0.148176 | + | 0.988961i | \(0.547340\pi\) |
−0.988961 | + | 0.148176i | \(0.952660\pi\) | |||||||
\(410\) | −6.14996 | + | 14.2156i | −0.303725 | + | 0.702060i | ||||
\(411\) | − | 1.30863i | − | 0.0645499i | ||||||
\(412\) | − | 13.4988i | − | 0.665038i | ||||||
\(413\) | 30.4444 | 1.49807 | ||||||||
\(414\) | − | 5.76461i | − | 0.283315i | ||||||
\(415\) | −8.62833 | − | 21.7863i | −0.423548 | − | 1.06945i | ||||
\(416\) | 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 | \(0.798647\pi\) | |||||||
\(420\) | −2.31550 | + | 5.35229i | −0.112985 | + | 0.261165i | ||||
\(421\) | −9.91998 | − | 9.91998i | −0.483470 | − | 0.483470i | 0.422768 | − | 0.906238i | \(-0.361059\pi\) |
−0.906238 | + | 0.422768i | \(0.861059\pi\) | |||||||
\(422\) | −8.13385 | −0.395949 | ||||||||
\(423\) | −7.27515 | − | 7.27515i | −0.353730 | − | 0.353730i | ||||
\(424\) | 0.286733 | + | 0.286733i | 0.0139250 | + | 0.0139250i | ||||
\(425\) | −10.6954 | + | 10.0477i | −0.518805 | + | 0.487386i | ||||
\(426\) | −1.20037 | + | 1.20037i | −0.0581580 | + | 0.0581580i | ||||
\(427\) | −9.02276 | −0.436642 | ||||||||
\(428\) | 2.32171 | − | 2.32171i | 0.112224 | − | 0.112224i | ||||
\(429\) | −7.61138 | − | 7.61138i | −0.367481 | − | 0.367481i | ||||
\(430\) | 4.11252 | + | 1.77916i | 0.198324 | + | 0.0857986i | ||||
\(431\) | 18.4635 | + | 18.4635i | 0.889356 | + | 0.889356i | 0.994461 | − | 0.105105i | \(-0.0335180\pi\) |
−0.105105 | + | 0.994461i | \(0.533518\pi\) | |||||||
\(432\) | −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 | ||||
\(438\) | − | 8.37281i | − | 0.400068i | ||||||
\(439\) | −6.00049 | + | 6.00049i | −0.286388 | + | 0.286388i | −0.835650 | − | 0.549262i | \(-0.814909\pi\) |
0.549262 | + | 0.835650i | \(0.314909\pi\) | |||||||
\(440\) | 1.88402 | − | 4.35492i | 0.0898172 | − | 0.207612i | ||||
\(441\) | 0.198289 | 0.00944235 | ||||||||
\(442\) | 14.8878i | 0.708140i | ||||||||
\(443\) | 19.3252 | − | 19.3252i | 0.918168 | − | 0.918168i | −0.0787279 | − | 0.996896i | \(-0.525086\pi\) |
0.996896 | + | 0.0787279i | \(0.0250858\pi\) | |||||||
\(444\) | 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 | 0.992709 | + | 0.120538i | \(0.0384620\pi\) |
0.120538 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(450\) | −3.64416 | + | 3.42347i | −0.171787 | + | 0.161384i | ||||
\(451\) | 14.6989 | 0.692145 | ||||||||
\(452\) | 16.6356i | 0.782471i | ||||||||
\(453\) | −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 | ||||||||
\(457\) | 10.5479i | 0.493409i | 0.969091 | + | 0.246704i | \(0.0793476\pi\) | ||||
−0.969091 | + | 0.246704i | \(0.920652\pi\) | |||||||
\(458\) | − | 18.0323i | − | 0.842592i | ||||||
\(459\) | 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 | −0.301265 | + | 0.953541i | \(0.597409\pi\) |
−0.953541 | + | 0.301265i | \(0.902591\pi\) | |||||||
\(462\) | 5.53425 | 0.257476 | ||||||||
\(463\) | −16.5851 | −0.770773 | −0.385387 | − | 0.922755i | \(-0.625932\pi\) | ||||
−0.385387 | + | 0.922755i | \(0.625932\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | − | 34.4641i | − | 1.59481i | −0.603447 | − | 0.797403i | \(-0.706207\pi\) | ||
0.603447 | − | 0.797403i | \(-0.293793\pi\) | |||||||
\(468\) | 5.07258i | 0.234480i | ||||||||
\(469\) | −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 | ||||
\(473\) | − | 4.25233i | − | 0.195523i | ||||||
\(474\) | −8.11381 | −0.372680 | ||||||||
\(475\) | −0.504183 | + | 16.1465i | −0.0231335 | + | 0.740854i | ||||
\(476\) | −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 | \(-0.422212\pi\) |
−0.970288 | + | 0.241954i | \(0.922212\pi\) | |||||||
\(480\) | −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 | ||||
\(483\) | − | 15.0341i | − | 0.684077i | ||||||
\(484\) | 6.49703 | 0.295320 | ||||||||
\(485\) | −7.05550 | + | 16.3088i | −0.320374 | + | 0.740544i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | − | 5.52466i | − | 0.250346i | −0.992135 | − | 0.125173i | \(-0.960051\pi\) | ||
0.992135 | − | 0.125173i | \(-0.0399486\pi\) | |||||||
\(488\) | −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 | ||||
\(495\) | 4.35492 | + | 1.88402i | 0.195739 | + | 0.0846805i | ||||
\(496\) | 1.38171 | + | 1.38171i | 0.0620407 | + | 0.0620407i | ||||
\(497\) | −3.13057 | + | 3.13057i | −0.140425 | + | 0.140425i | ||||
\(498\) | 10.4794 | 0.469594 | ||||||||
\(499\) | −15.3419 | + | 15.3419i | −0.686798 | + | 0.686798i | −0.961523 | − | 0.274725i | \(-0.911413\pi\) |
0.274725 | + | 0.961523i | \(0.411413\pi\) | |||||||
\(500\) | 3.79037 | + | 10.5182i | 0.169511 | + | 0.470389i | ||||
\(501\) | 5.09691 | + | 5.09691i | 0.227713 | + | 0.227713i | ||||
\(502\) | 2.81874 | + | 2.81874i | 0.125806 | + | 0.125806i | ||||
\(503\) | 6.97745 | 0.311109 | 0.155555 | − | 0.987827i | \(-0.450284\pi\) | ||||
0.155555 | + | 0.987827i | \(0.450284\pi\) | |||||||
\(504\) | −1.84414 | − | 1.84414i | −0.0821446 | − | 0.0821446i | ||||
\(505\) | −13.5154 | + | 31.2409i | −0.601429 | + | 1.39020i | ||||
\(506\) | 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 | \(-0.384821\pi\) | ||||
0.354001 | + | 0.935245i | \(0.384821\pi\) | |||||||
\(510\) | −2.41652 | − | 6.10166i | −0.107006 | − | 0.270186i | ||||
\(511\) | − | 21.8364i | − | 0.965984i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 3.23088i | − | 0.142647i | ||||||
\(514\) | − | 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 | ||||
\(518\) | 5.16220 | + | 15.0005i | 0.226814 | + | 0.659084i | ||||
\(519\) | − | 1.61824i | − | 0.0710327i | ||||||
\(520\) | 10.4102 | + | 4.50366i | 0.456518 | + | 0.197498i | ||||
\(521\) | − | 38.5368i | − | 1.68833i | −0.536084 | − | 0.844165i | \(-0.680097\pi\) | ||
0.536084 | − | 0.844165i | \(-0.319903\pi\) | |||||||
\(522\) | −5.76649 | − | 5.76649i | −0.252393 | − | 0.252393i | ||||
\(523\) | −14.7060 | −0.643047 | −0.321523 | − | 0.946902i | \(-0.604195\pi\) | ||||
−0.321523 | + | 0.946902i | \(0.604195\pi\) | |||||||
\(524\) | −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 | ||||
\(532\) | −8.42617 | −0.365321 | ||||||||
\(533\) | 35.1370i | 1.52195i | ||||||||
\(534\) | 16.8625i | 0.729713i | ||||||||
\(535\) | 6.82606 | − | 2.70342i | 0.295116 | − | 0.116879i | ||||
\(536\) | −9.89884 | − | 9.89884i | −0.427565 | − | 0.427565i | ||||
\(537\) | − | 13.7370i | − | 0.592794i | ||||||
\(538\) | 32.1166i | 1.38465i | ||||||||
\(539\) | −0.420774 | −0.0181240 | ||||||||
\(540\) | −0.823360 | − | 2.07896i | −0.0354318 | − | 0.0894642i | ||||
\(541\) | −24.9509 | + | 24.9509i | −1.07272 | + | 1.07272i | −0.0755841 | + | 0.997139i | \(0.524082\pi\) |
−0.997139 | + | 0.0755841i | \(0.975918\pi\) | |||||||
\(542\) | −15.5594 | −0.668333 | ||||||||
\(543\) | −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 | ||||||||
\(547\) | 36.4914 | 1.56026 | 0.780131 | − | 0.625617i | \(-0.215153\pi\) | ||||
0.780131 | + | 0.625617i | \(0.215153\pi\) | |||||||
\(548\) | 0.925340 | − | 0.925340i | 0.0395286 | − | 0.0395286i | ||||
\(549\) | 2.44633 | − | 2.44633i | 0.104407 | − | 0.104407i | ||||
\(550\) | 7.73297 | − | 7.26466i | 0.329735 | − | 0.309766i | ||||
\(551\) | −26.3480 | −1.12246 | ||||||||
\(552\) | 4.07619 | − | 4.07619i | 0.173494 | − | 0.173494i | ||||
\(553\) | −21.1609 | −0.899852 | ||||||||
\(554\) | −14.4437 | −0.613654 | ||||||||
\(555\) | −1.04447 | + | 13.5613i | −0.0443351 | + | 0.575645i | ||||
\(556\) | 5.44352 | 0.230857 | ||||||||
\(557\) | −32.6303 | −1.38259 | −0.691296 | − | 0.722572i | \(-0.742960\pi\) | ||||
−0.691296 | + | 0.722572i | \(0.742960\pi\) | |||||||
\(558\) | −1.38171 | + | 1.38171i | −0.0584925 | + | 0.0584925i | ||||
\(559\) | 10.1650 | 0.429933 | ||||||||
\(560\) | −5.42195 | + | 2.14733i | −0.229119 | + | 0.0907413i | ||||
\(561\) | −4.40388 | + | 4.40388i | −0.185932 | + | 0.185932i | ||||
\(562\) | −10.1736 | + | 10.1736i | −0.429149 | + | 0.429149i | ||||
\(563\) | 20.4470 | 0.861738 | 0.430869 | − | 0.902415i | \(-0.358207\pi\) | ||||
0.430869 | + | 0.902415i | \(0.358207\pi\) | |||||||
\(564\) | − | 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 | ||||
\(568\) | −1.69758 | −0.0712287 | ||||||||
\(569\) | −11.2342 | + | 11.2342i | −0.470964 | + | 0.470964i | −0.902226 | − | 0.431263i | \(-0.858068\pi\) |
0.431263 | + | 0.902226i | \(0.358068\pi\) | |||||||
\(570\) | −6.63058 | − | 2.86852i | −0.277725 | − | 0.120149i | ||||
\(571\) | 26.4113 | 1.10528 | 0.552639 | − | 0.833421i | \(-0.313621\pi\) | ||||
0.552639 | + | 0.833421i | \(0.313621\pi\) | |||||||
\(572\) | − | 10.7641i | − | 0.450070i | ||||||
\(573\) | 20.2107i | 0.844315i | ||||||||
\(574\) | −12.7741 | − | 12.7741i | −0.533180 | − | 0.533180i | ||||
\(575\) | −19.7349 | − | 21.0071i | −0.823004 | − | 0.876058i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 7.95386i | 0.331123i | 0.986199 | + | 0.165562i | \(0.0529437\pi\) | ||||
−0.986199 | + | 0.165562i | \(0.947056\pi\) | |||||||
\(578\) | −8.38604 | −0.348813 | ||||||||
\(579\) | 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 | ||||
\(587\) | −12.8759 | −0.531445 | −0.265723 | − | 0.964050i | \(-0.585611\pi\) | ||||
−0.265723 | + | 0.964050i | \(0.585611\pi\) | |||||||
\(588\) | 0.140212 | + | 0.140212i | 0.00578224 | + | 0.00578224i | ||||
\(589\) | 6.31326i | 0.260133i | ||||||||
\(590\) | 9.61144 | + | 24.2686i | 0.395697 | + | 0.999123i | ||||
\(591\) | − | 5.11678i | − | 0.210476i | ||||||
\(592\) | −2.66745 | + | 5.46669i | −0.109631 | + | 0.224680i | ||||
\(593\) | 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 | ||||||||
\(597\) | − | 20.0200i | − | 0.819364i | ||||||
\(598\) | −29.2414 | −1.19577 | ||||||||
\(599\) | 28.1341i | 1.14953i | 0.818320 | + | 0.574763i | \(0.194906\pi\) | ||||
−0.818320 | + | 0.574763i | \(0.805094\pi\) | |||||||
\(600\) | −4.99756 | − | 0.156051i | −0.204025 | − | 0.00637076i | ||||
\(601\) | −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 | ||||||
\(605\) | 13.3335 | + | 5.76835i | 0.542086 | + | 0.234517i | ||||
\(606\) | −10.7641 | − | 10.7641i | −0.437262 | − | 0.437262i | ||||
\(607\) | 5.21022 | 0.211476 | 0.105738 | − | 0.994394i | \(-0.466279\pi\) | ||||
0.105738 | + | 0.994394i | \(0.466279\pi\) | |||||||
\(608\) | −2.28458 | − | 2.28458i | −0.0926519 | − | 0.0926519i | ||||
\(609\) | −15.0391 | − | 15.0391i | −0.609414 | − | 0.609414i | ||||
\(610\) | −2.84853 | − | 7.19245i | −0.115333 | − | 0.291214i | ||||
\(611\) | −36.9038 | + | 36.9038i | −1.49297 | + | 1.49297i | ||||
\(612\) | 2.93495 | 0.118639 | ||||||||
\(613\) | −15.0091 | + | 15.0091i | −0.606211 | + | 0.606211i | −0.941954 | − | 0.335743i | \(-0.891013\pi\) |
0.335743 | + | 0.941954i | \(0.391013\pi\) | |||||||
\(614\) | −16.2628 | − | 16.2628i | −0.656312 | − | 0.656312i | ||||
\(615\) | −5.70329 | − | 14.4007i | −0.229979 | − | 0.580690i | ||||
\(616\) | 3.91330 | + | 3.91330i | 0.157671 | + | 0.157671i | ||||
\(617\) | 6.06777 | + | 6.06777i | 0.244279 | + | 0.244279i | 0.818618 | − | 0.574339i | \(-0.194741\pi\) |
−0.574339 | + | 0.818618i | \(0.694741\pi\) | |||||||
\(618\) | 9.54509 | + | 9.54509i | 0.383960 | + | 0.383960i | ||||
\(619\) | 20.1898 | 0.811495 | 0.405747 | − | 0.913985i | \(-0.367011\pi\) | ||||
0.405747 | + | 0.913985i | \(0.367011\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | 43.9776i | 1.76193i | ||||||||
\(624\) | −3.58685 | + | 3.58685i | −0.143589 | + | 0.143589i | ||||
\(625\) | −1.55975 | + | 24.9513i | −0.0623900 | + | 0.998052i | ||||
\(626\) | −4.41462 | −0.176444 | ||||||||
\(627\) | 6.85600i | 0.273802i | ||||||||
\(628\) | 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 | 0.738050 | − | 0.674746i | \(-0.235747\pi\) |
−0.674746 | + | 0.738050i | \(0.735747\pi\) | |||||||
\(632\) | −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 | ||||
\(635\) | −19.3246 | + | 7.65340i | −0.766874 | + | 0.303716i | ||||
\(636\) | −0.405502 | −0.0160792 | ||||||||
\(637\) | − | 1.00584i | − | 0.0398528i | ||||||
\(638\) | 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 | \(0.679218\pi\) | |||||||
\(642\) | 3.28340i | 0.129585i | ||||||||
\(643\) | 18.0452i | 0.711635i | 0.934556 | + | 0.355817i | \(0.115797\pi\) | ||||
−0.934556 | + | 0.355817i | \(0.884203\pi\) | |||||||
\(644\) | 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 | ||||
\(647\) | −2.13093 | −0.0837754 | −0.0418877 | − | 0.999122i | \(-0.513337\pi\) | ||||
−0.0418877 | + | 0.999122i | \(0.513337\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 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 | ||||
\(652\) | 0.200876i | 0.00786690i | ||||||||
\(653\) | 12.1928i | 0.477142i | 0.971125 | + | 0.238571i | \(0.0766790\pi\) | ||||
−0.971125 | + | 0.238571i | \(0.923321\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | − | 26.8328i | − | 1.04605i | ||||||
\(659\) | 19.4303 | 0.756898 | 0.378449 | − | 0.925622i | \(-0.376457\pi\) | ||||
0.378449 | + | 0.925622i | \(0.376457\pi\) | |||||||
\(660\) | 1.74719 | + | 4.41160i | 0.0680091 | + | 0.171721i | ||||
\(661\) | 25.0660 | + | 25.0660i | 0.974956 | + | 0.974956i | 0.999694 | − | 0.0247380i | \(-0.00787514\pi\) |
−0.0247380 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(662\) | 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 | ||||
\(668\) | 7.20812i | 0.278891i | ||||||||
\(669\) | −26.1830 | −1.01229 | ||||||||
\(670\) | −11.5263 | − | 29.1035i | −0.445299 | − | 1.12437i | ||||
\(671\) | −5.19117 | + | 5.19117i | −0.200403 | + | 0.200403i | ||||
\(672\) | − | 2.60801i | − | 0.100606i | ||||||
\(673\) | 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 | 0.780563 | − | 0.625077i | \(-0.214932\pi\) |
−0.625077 | + | 0.780563i | \(0.714932\pi\) | |||||||
\(678\) | −11.7631 | − | 11.7631i | −0.451760 | − | 0.451760i | ||||
\(679\) | −14.6550 | − | 14.6550i | −0.562407 | − | 0.562407i | ||||
\(680\) | 2.60578 | − | 6.02326i | 0.0999272 | − | 0.230982i | ||||
\(681\) | −6.15979 | − | 6.15979i | −0.236044 | − | 0.236044i | ||||
\(682\) | 2.93202 | − | 2.93202i | 0.112273 | − | 0.112273i | ||||
\(683\) | 49.4497 | 1.89214 | 0.946070 | − | 0.323961i | \(-0.105015\pi\) | ||||
0.946070 | + | 0.323961i | \(0.105015\pi\) | |||||||
\(684\) | 2.28458 | − | 2.28458i | 0.0873531 | − | 0.0873531i | ||||
\(685\) | 2.72059 | − | 1.07747i | 0.103948 | − | 0.0411681i | ||||
\(686\) | 13.2747 | + | 13.2747i | 0.506829 | + | 0.506829i | ||||
\(687\) | 12.7507 | + | 12.7507i | 0.486471 | + | 0.486471i | ||||
\(688\) | −2.00391 | −0.0763983 | ||||||||
\(689\) | 1.45448 | + | 1.45448i | 0.0554111 | + | 0.0554111i | ||||
\(690\) | 11.9844 | − | 4.74635i | 0.456238 | − | 0.180690i | ||||
\(691\) | − | 9.04475i | − | 0.344078i | −0.985090 | − | 0.172039i | \(-0.944964\pi\) | ||
0.985090 | − | 0.172039i | \(-0.0550356\pi\) | |||||||
\(692\) | 1.14427 | − | 1.14427i | 0.0434985 | − | 0.0434985i | ||||
\(693\) | −3.91330 | + | 3.91330i | −0.148654 | + | 0.148654i | ||||
\(694\) | 27.1062 | 1.02894 | ||||||||
\(695\) | 11.1715 | + | 4.83299i | 0.423758 | + | 0.183326i | ||||
\(696\) | − | 8.15506i | − | 0.309117i | ||||||
\(697\) | 20.3300 | 0.770054 | ||||||||
\(698\) | 1.86734i | 0.0706800i | ||||||||
\(699\) | − | 22.2673i | − | 0.842228i | ||||||
\(700\) | −13.0337 | − | 0.406983i | −0.492627 | − | 0.0153825i | ||||
\(701\) | −6.79801 | + | 6.79801i | −0.256757 | + | 0.256757i | −0.823734 | − | 0.566977i | \(-0.808113\pi\) |
0.566977 | + | 0.823734i | \(0.308113\pi\) | |||||||
\(702\) | −3.58685 | − | 3.58685i | −0.135377 | − | 0.135377i | ||||
\(703\) | −18.5831 | + | 6.39509i | −0.700875 | + | 0.241195i | ||||
\(704\) | 2.12202i | 0.0799766i | ||||||||
\(705\) | 9.13468 | − | 21.1148i | 0.344032 | − | 0.795230i | ||||
\(706\) | − | 15.2302i | − | 0.573194i | ||||||
\(707\) | −28.0729 | − | 28.0729i | −1.05579 | − | 1.05579i | ||||
\(708\) | −11.6734 | −0.438715 | ||||||||
\(709\) | −12.7014 | − | 12.7014i | −0.477012 | − | 0.477012i | 0.427163 | − | 0.904175i | \(-0.359513\pi\) |
−0.904175 | + | 0.427163i | \(0.859513\pi\) | |||||||
\(710\) | −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 | ||||
\(717\) | −14.6083 | −0.545558 | ||||||||
\(718\) | 18.9718i | 0.708022i | ||||||||
\(719\) | 25.0596i | 0.934567i | 0.884108 | + | 0.467283i | \(0.154767\pi\) | ||||
−0.884108 | + | 0.467283i | \(0.845233\pi\) | |||||||
\(720\) | 0.887844 | − | 2.05225i | 0.0330880 | − | 0.0764829i | ||||
\(721\) | 24.8937 | + | 24.8937i | 0.927089 | + | 0.927089i | ||||
\(722\) | 8.56139i | 0.318622i | ||||||||
\(723\) | 9.18363i | 0.341543i | ||||||||
\(724\) | −1.59280 | −0.0591961 | ||||||||
\(725\) | −40.7554 | − | 1.27261i | −1.51362 | − | 0.0472634i | ||||
\(726\) | −4.59410 | + | 4.59410i | −0.170503 | + | 0.170503i | ||||
\(727\) | 28.9528 | 1.07380 | 0.536899 | − | 0.843646i | \(-0.319596\pi\) | ||||
0.536899 | + | 0.843646i | \(0.319596\pi\) | |||||||
\(728\) | −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 | ||||||
\(732\) | 3.45964 | 0.127872 | ||||||||
\(733\) | −12.6845 | + | 12.6845i | −0.468513 | + | 0.468513i | −0.901433 | − | 0.432920i | \(-0.857483\pi\) |
0.432920 | + | 0.901433i | \(0.357483\pi\) | |||||||
\(734\) | 23.8239 | − | 23.8239i | 0.879358 | − | 0.879358i | ||||
\(735\) | 0.163264 | + | 0.412236i | 0.00602207 | + | 0.0152055i | ||||
\(736\) | 5.76461 | 0.212486 | ||||||||
\(737\) | −21.0055 | + | 21.0055i | −0.773748 | + | 0.773748i | ||||
\(738\) | 6.92685 | 0.254981 | ||||||||
\(739\) | 5.09966 | 0.187594 | 0.0937970 | − | 0.995591i | \(-0.470100\pi\) | ||||
0.0937970 | + | 0.995591i | \(0.470100\pi\) | |||||||
\(740\) | −10.3278 | + | 8.85074i | −0.379659 | + | 0.325360i | ||||
\(741\) | −16.3889 | −0.602062 | ||||||||
\(742\) | −1.05755 | −0.0388240 | ||||||||
\(743\) | 5.46112 | − | 5.46112i | 0.200349 | − | 0.200349i | −0.599801 | − | 0.800150i | \(-0.704753\pi\) |
0.800150 | + | 0.599801i | \(0.204753\pi\) | |||||||
\(744\) | −1.95403 | −0.0716384 | ||||||||
\(745\) | −15.0487 | + | 34.7851i | −0.551342 | + | 1.27443i | ||||
\(746\) | −2.47846 | + | 2.47846i | −0.0907429 | + | 0.0907429i | ||||
\(747\) | −7.41007 | + | 7.41007i | −0.271120 | + | 0.271120i | ||||
\(748\) | −6.22803 | −0.227719 | ||||||||
\(749\) | 8.56313i | 0.312890i | ||||||||
\(750\) | −10.1177 | − | 4.75731i | −0.369446 | − | 0.173712i | ||||
\(751\) | − | 50.1472i | − | 1.82990i | −0.403569 | − | 0.914949i | \(-0.632230\pi\) | ||
0.403569 | − | 0.914949i | \(-0.367770\pi\) | |||||||
\(752\) | 7.27515 | − | 7.27515i | 0.265297 | − | 0.265297i | ||||
\(753\) | −3.98630 | −0.145269 | ||||||||
\(754\) | −29.2510 | + | 29.2510i | −1.06526 | + | 1.06526i | ||||
\(755\) | 1.11867 | − | 2.58581i | 0.0407126 | − | 0.0941072i | ||||
\(756\) | 2.60801 | 0.0948524 | ||||||||
\(757\) | 38.6619i | 1.40519i | 0.711589 | + | 0.702596i | \(0.247976\pi\) | ||||
−0.711589 | + | 0.702596i | \(0.752024\pi\) | |||||||
\(758\) | 31.6861i | 1.15089i | ||||||||
\(759\) | −8.64976 | − | 8.64976i | −0.313966 | − | 0.313966i | ||||
\(760\) | −2.66018 | − | 6.71688i | −0.0964949 | − | 0.243647i | ||||
\(761\) | 2.58952i | 0.0938702i | 0.998898 | + | 0.0469351i | \(0.0149454\pi\) | ||||
−0.998898 | + | 0.0469351i | \(0.985055\pi\) | |||||||
\(762\) | − | 9.29533i | − | 0.336734i | ||||||
\(763\) | −19.2013 | −0.695134 | ||||||||
\(764\) | −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 | \(-0.757882\pi\) |
0.689382 | + | 0.724398i | \(0.257882\pi\) | |||||||
\(770\) | 4.55668 | + | 11.5055i | 0.164211 | + | 0.414629i | ||||
\(771\) | 7.91684 | + | 7.91684i | 0.285118 | + | 0.285118i | ||||
\(772\) | 11.4610 | 0.412489 | ||||||||
\(773\) | 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 | ||||||
\(775\) | −0.304929 | + | 9.76541i | −0.0109534 | + | 0.350784i | ||||
\(776\) | − | 7.94678i | − | 0.285273i | ||||||
\(777\) | −14.2572 | − | 6.95673i | −0.511473 | − | 0.249571i | ||||
\(778\) | 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 | ||||||||
\(782\) | 16.9189i | 0.605017i | ||||||||
\(783\) | 8.15506 | 0.291438 | ||||||||
\(784\) | 0.198289i | 0.00708176i | ||||||||
\(785\) | 11.9134 | − | 4.71824i | 0.425208 | − | 0.168401i | ||||
\(786\) | 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 | ||||||||
\(790\) | −6.68059 | − | 16.8683i | −0.237685 | − | 0.600147i | ||||
\(791\) | −30.6783 | − | 30.6783i | −1.09080 | − | 1.09080i | ||||
\(792\) | −2.12202 | −0.0754027 | ||||||||
\(793\) | −12.4092 | − | 12.4092i | −0.440664 | − | 0.440664i | ||||
\(794\) | −11.7358 | − | 11.7358i | −0.416487 | − | 0.416487i | ||||
\(795\) | −0.832191 | − | 0.360022i | −0.0295148 | − | 0.0127687i | ||||
\(796\) | 14.1563 | − | 14.1563i | 0.501756 | − | 0.501756i | ||||
\(797\) | 46.2735 | 1.63909 | 0.819546 | − | 0.573014i | \(-0.194226\pi\) | ||||
0.819546 | + | 0.573014i | \(0.194226\pi\) | |||||||
\(798\) | 5.95820 | − | 5.95820i | 0.210918 | − | 0.210918i | ||||
\(799\) | 21.3522 | + | 21.3522i | 0.755388 | + | 0.755388i | ||||
\(800\) | −3.42347 | − | 3.64416i | −0.121038 | − | 0.128840i | ||||
\(801\) | −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 | ||||
\(808\) | − | 15.2228i | − | 0.535535i | ||||||
\(809\) | 5.77592 | − | 5.77592i | 0.203070 | − | 0.203070i | −0.598244 | − | 0.801314i | \(-0.704135\pi\) |
0.801314 | + | 0.598244i | \(0.204135\pi\) | |||||||
\(810\) | 2.05225 | + | 0.887844i | 0.0721087 | + | 0.0311957i | ||||
\(811\) | −48.8974 | −1.71702 | −0.858510 | − | 0.512797i | \(-0.828609\pi\) | ||||
−0.858510 | + | 0.512797i | \(0.828609\pi\) | |||||||
\(812\) | − | 21.2685i | − | 0.746377i | ||||||
\(813\) | 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 | ||||
\(820\) | 6.14996 | − | 14.2156i | 0.214766 | − | 0.496432i | ||||
\(821\) | 11.8926 | 0.415053 | 0.207527 | − | 0.978229i | \(-0.433459\pi\) | ||||
0.207527 | + | 0.978229i | \(0.433459\pi\) | |||||||
\(822\) | 1.30863i | 0.0456437i | ||||||||
\(823\) | −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 | ||||||||
\(827\) | − | 1.44766i | − | 0.0503400i | −0.999683 | − | 0.0251700i | \(-0.991987\pi\) | ||
0.999683 | − | 0.0251700i | \(-0.00801271\pi\) | |||||||
\(828\) | 5.76461i | 0.200334i | ||||||||
\(829\) | 17.0831 | − | 17.0831i | 0.593320 | − | 0.593320i | −0.345207 | − | 0.938527i | \(-0.612191\pi\) |
0.938527 | + | 0.345207i | \(0.112191\pi\) | |||||||
\(830\) | 8.62833 | + | 21.7863i | 0.299494 | + | 0.756213i | ||||
\(831\) | 10.2132 | − | 10.2132i | 0.354293 | − | 0.354293i | ||||
\(832\) | −5.07258 | −0.175860 | ||||||||
\(833\) | −0.581970 | −0.0201641 | ||||||||
\(834\) | −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 | ||||
\(837\) | − | 1.95403i | − | 0.0675413i | ||||||
\(838\) | − | 24.2039i | − | 0.836109i | ||||||
\(839\) | 24.1753 | 0.834624 | 0.417312 | − | 0.908763i | \(-0.362972\pi\) | ||||
0.417312 | + | 0.908763i | \(0.362972\pi\) | |||||||
\(840\) | 2.31550 | − | 5.35229i | 0.0798925 | − | 0.184671i | ||||
\(841\) | − | 37.5049i | − | 1.29327i | ||||||
\(842\) | 9.91998 | + | 9.91998i | 0.341865 | + | 0.341865i | ||||
\(843\) | − | 14.3877i | − | 0.495538i | ||||||
\(844\) | 8.13385 | 0.279979 | ||||||||
\(845\) | 26.1273 | + | 11.3032i | 0.898807 | + | 0.388841i | ||||
\(846\) | 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 | ||||
\(853\) | − | 51.8584i | − | 1.77560i | −0.460232 | − | 0.887799i | \(-0.652234\pi\) | ||
0.460232 | − | 0.887799i | \(-0.347766\pi\) | |||||||
\(854\) | 9.02276 | 0.308753 | ||||||||
\(855\) | 6.71688 | − | 2.66018i | 0.229712 | − | 0.0909762i | ||||
\(856\) | −2.32171 | + | 2.32171i | −0.0793545 | + | 0.0793545i | ||||
\(857\) | − | 50.1319i | − | 1.71247i | −0.516585 | − | 0.856236i | \(-0.672797\pi\) | ||
0.516585 | − | 0.856236i | \(-0.327203\pi\) | |||||||
\(858\) | 7.61138 | + | 7.61138i | 0.259848 | + | 0.259848i | ||||
\(859\) | −22.7307 | − | 22.7307i | −0.775560 | − | 0.775560i | 0.203512 | − | 0.979072i | \(-0.434764\pi\) |
−0.979072 | + | 0.203512i | \(0.934764\pi\) | |||||||
\(860\) | −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 | ||||
\(865\) | 3.36425 | − | 1.33239i | 0.114388 | − | 0.0453027i | ||||
\(866\) | −20.6095 | − | 20.6095i | −0.700338 | − | 0.700338i | ||||
\(867\) | 5.92983 | − | 5.92983i | 0.201387 | − | 0.201387i | ||||
\(868\) | −5.09614 | −0.172974 | ||||||||
\(869\) | −12.1747 | + | 12.1747i | −0.412999 | + | 0.412999i | ||||
\(870\) | 7.24042 | − | 16.7362i | 0.245473 | − | 0.567411i | ||||
\(871\) | −50.2126 | − | 50.2126i | −1.70139 | − | 1.70139i | ||||
\(872\) | −5.20603 | − | 5.20603i | −0.176298 | − | 0.176298i | ||||
\(873\) | 7.94678 | 0.268958 | ||||||||
\(874\) | 13.1697 | + | 13.1697i | 0.445472 | + | 0.445472i | ||||
\(875\) | −26.3871 | − | 12.4071i | −0.892046 | − | 0.419437i | ||||
\(876\) | 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 | ||||||||
\(880\) | −1.88402 | + | 4.35492i | −0.0635104 | + | 0.146804i | ||||
\(881\) | − | 44.7156i | − | 1.50651i | −0.657731 | − | 0.753253i | \(-0.728484\pi\) | ||
0.657731 | − | 0.753253i | \(-0.271516\pi\) | |||||||
\(882\) | −0.198289 | −0.00667675 | ||||||||
\(883\) | 19.8417i | 0.667727i | 0.942621 | + | 0.333863i | \(0.108352\pi\) | ||||
−0.942621 | + | 0.333863i | \(0.891648\pi\) | |||||||
\(884\) | − | 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 | 0.955707 | − | 0.294320i | \(-0.0950930\pi\) |
−0.294320 | + | 0.955707i | \(0.595093\pi\) | |||||||
\(888\) | −1.97936 | − | 5.75171i | −0.0664231 | − | 0.193015i | ||||
\(889\) | − | 24.2423i | − | 0.813060i | ||||||
\(890\) | −35.0565 | + | 13.8839i | −1.17510 | + | 0.465391i | ||||
\(891\) | − | 2.12202i | − | 0.0710903i | ||||||
\(892\) | −18.5142 | − | 18.5142i | −0.619901 | − | 0.619901i | ||||
\(893\) | 33.2413 | 1.11238 | ||||||||
\(894\) | −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 | ||||
\(902\) | −14.6989 | −0.489420 | ||||||||
\(903\) | − | 5.22621i | − | 0.173917i | ||||||
\(904\) | − | 16.6356i | − | 0.553291i | ||||||
\(905\) | −3.26883 | − | 1.41416i | −0.108660 | − | 0.0470083i | ||||
\(906\) | 0.890945 | + | 0.890945i | 0.0295997 | + | 0.0295997i | ||||
\(907\) | 53.6798i | 1.78241i | 0.453603 | + | 0.891204i | \(0.350138\pi\) | ||||
−0.453603 | + | 0.891204i | \(0.649862\pi\) | |||||||
\(908\) | − | 8.71126i | − | 0.289093i | ||||||
\(909\) | 15.2228 | 0.504907 | ||||||||
\(910\) | −27.5033 | + | 10.8925i | −0.911724 | + | 0.361083i | ||||
\(911\) | 6.84880 | − | 6.84880i | 0.226911 | − | 0.226911i | −0.584490 | − | 0.811401i | \(-0.698705\pi\) |
0.811401 | + | 0.584490i | \(0.198705\pi\) | |||||||
\(912\) | 3.23088 | 0.106985 | ||||||||
\(913\) | 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 | ||||||||
\(917\) | 9.86309 | 0.325708 | ||||||||
\(918\) | −2.07533 | + | 2.07533i | −0.0684960 | + | 0.0684960i | ||||
\(919\) | −18.9548 | + | 18.9548i | −0.625261 | + | 0.625261i | −0.946872 | − | 0.321611i | \(-0.895776\pi\) |
0.321611 | + | 0.946872i | \(0.395776\pi\) | |||||||
\(920\) | 11.8304 | + | 5.11807i | 0.390037 | + | 0.168738i | ||||
\(921\) | 22.9990 | 0.757844 | ||||||||
\(922\) | 26.9418 | − | 26.9418i | 0.887281 | − | 0.887281i | ||||
\(923\) | −8.61108 | −0.283437 | ||||||||
\(924\) | −5.53425 | −0.182063 | ||||||||
\(925\) | −29.0534 | + | 8.99444i | −0.955270 | + | 0.295735i | ||||
\(926\) | 16.5851 | 0.545019 | ||||||||
\(927\) | −13.4988 | −0.443359 | ||||||||
\(928\) | 5.76649 | − | 5.76649i | 0.189294 | − | 0.189294i | ||||
\(929\) | −43.3213 | −1.42133 | −0.710663 | − | 0.703532i | \(-0.751605\pi\) | ||||
−0.710663 | + | 0.703532i | \(0.751605\pi\) | |||||||
\(930\) | −4.01017 | − | 1.73488i | −0.131499 | − | 0.0568889i | ||||
\(931\) | −0.453008 | + | 0.453008i | −0.0148467 | + | 0.0148467i | ||||
\(932\) | 15.7454 | − | 15.7454i | 0.515757 | − | 0.515757i | ||||
\(933\) | 15.6611 | 0.512721 | ||||||||
\(934\) | 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 | \(0.283513\pi\) | |||||||
\(938\) | 36.5097 | 1.19208 | ||||||||
\(939\) | 3.12160 | − | 3.12160i | 0.101870 | − | 0.101870i | ||||
\(940\) | 21.3896 | − | 8.47123i | 0.697653 | − | 0.276301i | ||||
\(941\) | −59.4050 | −1.93655 | −0.968273 | − | 0.249894i | \(-0.919604\pi\) | ||||
−0.968273 | + | 0.249894i | \(0.919604\pi\) | |||||||
\(942\) | 5.73047i | 0.186709i | ||||||||
\(943\) | 39.9306i | 1.30032i | ||||||||
\(944\) | −8.25437 | − | 8.25437i | −0.268657 | − | 0.268657i | ||||
\(945\) | 5.35229 | + | 2.31550i | 0.174110 | + | 0.0753234i | ||||
\(946\) | 4.25233i | 0.138255i | ||||||||
\(947\) | 22.4238i | 0.728675i | 0.931267 | + | 0.364337i | \(0.118704\pi\) | ||||
−0.931267 | + | 0.364337i | \(0.881296\pi\) | |||||||
\(948\) | 8.11381 | 0.263524 | ||||||||
\(949\) | 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 | −0.936892 | − | 0.349619i | \(-0.886311\pi\) |
0.349619 | + | 0.936892i | \(0.386311\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | −17.3052 | −0.559397 | ||||||||
\(958\) | 15.9403 | + | 15.9403i | 0.515009 | + | 0.515009i | ||||
\(959\) | 3.41292i | 0.110209i | ||||||||
\(960\) | 2.07896 | − | 0.823360i | 0.0670982 | − | 0.0265738i | ||||
\(961\) | − | 27.1817i | − | 0.876831i | ||||||
\(962\) | −13.5308 | + | 27.7302i | −0.436252 | + | 0.894058i | ||||
\(963\) | −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 | ||||||||
\(967\) | 52.0958i | 1.67529i | 0.546216 | + | 0.837644i | \(0.316068\pi\) | ||||
−0.546216 | + | 0.837644i | \(0.683932\pi\) | |||||||
\(968\) | −6.49703 | −0.208823 | ||||||||
\(969\) | 9.48250i | 0.304622i | ||||||||
\(970\) | 7.05550 | − | 16.3088i | 0.226539 | − | 0.523644i | ||||
\(971\) | 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 | ||||||||
\(975\) | −25.3505 | − | 0.791581i | −0.811867 | − | 0.0253509i | ||||
\(976\) | 2.44633 | + | 2.44633i | 0.0783052 | + | 0.0783052i | ||||
\(977\) | −2.33312 | −0.0746432 | −0.0373216 | − | 0.999303i | \(-0.511883\pi\) | ||||
−0.0373216 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(978\) | −0.142041 | − | 0.142041i | −0.00454196 | − | 0.00454196i | ||||
\(979\) | 25.3021 | + | 25.3021i | 0.808660 | + | 0.808660i | ||||
\(980\) | −0.176050 | + | 0.406940i | −0.00562371 | + | 0.0129992i | ||||
\(981\) | 5.20603 | − | 5.20603i | 0.166216 | − | 0.166216i | ||||
\(982\) | −30.9165 | −0.986585 | ||||||||
\(983\) | 14.6210 | − | 14.6210i | 0.466338 | − | 0.466338i | −0.434388 | − | 0.900726i | \(-0.643035\pi\) |
0.900726 | + | 0.434388i | \(0.143035\pi\) | |||||||
\(984\) | 4.89802 | + | 4.89802i | 0.156143 | + | 0.156143i | ||||
\(985\) | 10.6376 | − | 4.21296i | 0.338942 | − | 0.134236i | ||||
\(986\) | 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 | 0.324906 | − | 0.945746i | \(-0.394667\pi\) |
−0.945746 | + | 0.324906i | \(0.894667\pi\) | |||||||
\(992\) | −1.38171 | − | 1.38171i | −0.0438694 | − | 0.0438694i | ||||
\(993\) | 24.0444i | 0.763025i | ||||||||
\(994\) | 3.13057 | − | 3.13057i | 0.0992956 | − | 0.0992956i | ||||
\(995\) | 41.6208 | − | 16.4837i | 1.31947 | − | 0.522567i | ||||
\(996\) | −10.4794 | −0.332053 | ||||||||
\(997\) | 23.0867i | 0.731162i | 0.930780 | + | 0.365581i | \(0.119130\pi\) | ||||
−0.930780 | + | 0.365581i | \(0.880870\pi\) | |||||||
\(998\) | 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.o.a.253.17 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.2 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.2 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.17 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.2 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.2 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.17 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.17 | yes | 36 | 185.117 | even | 4 | inner |