Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (of order \(6\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 589.1 | ||
Root | \(1.39564 - 0.228425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.589 |
Dual form | 637.2.q.e.491.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.395644 | − | 0.228425i | −0.279763 | − | 0.161521i | 0.353553 | − | 0.935414i | \(-0.384973\pi\) |
−0.633316 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(3\) | −1.39564 | + | 2.41733i | −0.805775 | + | 1.39564i | 0.109991 | + | 0.993933i | \(0.464918\pi\) |
−0.915766 | + | 0.401711i | \(0.868416\pi\) | |||||||
\(4\) | −0.895644 | − | 1.55130i | −0.447822 | − | 0.775650i | ||||
\(5\) | 0.456850i | 0.204310i | 0.994769 | + | 0.102155i | \(0.0325737\pi\) | ||||
−0.994769 | + | 0.102155i | \(0.967426\pi\) | |||||||
\(6\) | 1.10436 | − | 0.637600i | 0.450851 | − | 0.260299i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | −2.39564 | − | 4.14938i | −0.798548 | − | 1.38313i | ||||
\(10\) | 0.104356 | − | 0.180750i | 0.0330003 | − | 0.0571582i | ||||
\(11\) | −3.39564 | − | 1.96048i | −1.02383 | − | 0.591106i | −0.108616 | − | 0.994084i | \(-0.534642\pi\) |
−0.915210 | + | 0.402978i | \(0.867975\pi\) | |||||||
\(12\) | 5.00000 | 1.44338 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.10436 | − | 0.637600i | −0.285144 | − | 0.164628i | ||||
\(16\) | −1.39564 | + | 2.41733i | −0.348911 | + | 0.604332i | ||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 2.18890i | 0.515929i | ||||||||
\(19\) | 1.18693 | − | 0.685275i | 0.272301 | − | 0.157213i | −0.357632 | − | 0.933863i | \(-0.616416\pi\) |
0.629933 | + | 0.776650i | \(0.283082\pi\) | |||||||
\(20\) | 0.708712 | − | 0.409175i | 0.158473 | − | 0.0914943i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.895644 | + | 1.55130i | 0.190952 | + | 0.330738i | ||||
\(23\) | 0.791288 | − | 1.37055i | 0.164995 | − | 0.285780i | −0.771659 | − | 0.636037i | \(-0.780573\pi\) |
0.936653 | + | 0.350257i | \(0.113906\pi\) | |||||||
\(24\) | −4.18693 | − | 2.41733i | −0.854654 | − | 0.493435i | ||||
\(25\) | 4.79129 | 0.958258 | ||||||||
\(26\) | −1.58258 | − | 0.456850i | −0.310369 | − | 0.0895957i | ||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.39564 | − | 5.88143i | 0.630555 | − | 1.09215i | −0.356883 | − | 0.934149i | \(-0.616161\pi\) |
0.987438 | − | 0.158005i | \(-0.0505061\pi\) | |||||||
\(30\) | 0.291288 | + | 0.504525i | 0.0531816 | + | 0.0921133i | ||||
\(31\) | 8.66025i | 1.55543i | 0.628619 | + | 0.777714i | \(0.283621\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 4.10436 | − | 2.36965i | 0.725555 | − | 0.418899i | ||||
\(33\) | 9.47822 | − | 5.47225i | 1.64995 | − | 0.952597i | ||||
\(34\) | 1.37055i | 0.235048i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.29129 | + | 7.43273i | −0.715215 | + | 1.23879i | ||||
\(37\) | 6.00000 | + | 3.46410i | 0.986394 | + | 0.569495i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | −0.626136 | −0.101573 | ||||||||
\(39\) | −2.79129 | + | 9.66930i | −0.446964 | + | 1.54833i | ||||
\(40\) | −0.791288 | −0.125114 | ||||||||
\(41\) | 6.79129 | + | 3.92095i | 1.06062 | + | 0.612350i | 0.925604 | − | 0.378493i | \(-0.123558\pi\) |
0.135017 | + | 0.990843i | \(0.456891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.68693 | − | 8.11800i | −0.714750 | − | 1.23798i | −0.963056 | − | 0.269302i | \(-0.913207\pi\) |
0.248305 | − | 0.968682i | \(-0.420126\pi\) | |||||||
\(44\) | 7.02355i | 1.05884i | ||||||||
\(45\) | 1.89564 | − | 1.09445i | 0.282586 | − | 0.163151i | ||||
\(46\) | −0.626136 | + | 0.361500i | −0.0923188 | + | 0.0533003i | ||||
\(47\) | − | 9.57395i | − | 1.39650i | −0.715852 | − | 0.698252i | \(-0.753961\pi\) | ||
0.715852 | − | 0.698252i | \(-0.246039\pi\) | |||||||
\(48\) | −3.89564 | − | 6.74745i | −0.562288 | − | 0.973911i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.89564 | − | 1.09445i | −0.268085 | − | 0.154779i | ||||
\(51\) | 8.37386 | 1.17258 | ||||||||
\(52\) | −4.47822 | − | 4.65390i | −0.621017 | − | 0.645380i | ||||
\(53\) | 6.16515 | 0.846849 | 0.423424 | − | 0.905931i | \(-0.360828\pi\) | ||||
0.423424 | + | 0.905931i | \(0.360828\pi\) | |||||||
\(54\) | −1.97822 | − | 1.14213i | −0.269202 | − | 0.155424i | ||||
\(55\) | 0.895644 | − | 1.55130i | 0.120769 | − | 0.209177i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.82560i | 0.506713i | ||||||||
\(58\) | −2.68693 | + | 1.55130i | −0.352811 | + | 0.203696i | ||||
\(59\) | 10.6652 | − | 6.15753i | 1.38848 | − | 0.801642i | 0.395340 | − | 0.918535i | \(-0.370627\pi\) |
0.993145 | + | 0.116893i | \(0.0372935\pi\) | |||||||
\(60\) | 2.28425i | 0.294896i | ||||||||
\(61\) | 7.37386 | + | 12.7719i | 0.944126 | + | 1.63528i | 0.757491 | + | 0.652846i | \(0.226425\pi\) |
0.186636 | + | 0.982429i | \(0.440242\pi\) | |||||||
\(62\) | 1.97822 | − | 3.42638i | 0.251234 | − | 0.435150i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.41742 | 0.427178 | ||||||||
\(65\) | 0.395644 | + | 1.59898i | 0.0490736 | + | 0.198329i | ||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | −3.87386 | − | 2.23658i | −0.473268 | − | 0.273241i | 0.244339 | − | 0.969690i | \(-0.421429\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | −2.68693 | + | 4.65390i | −0.325838 | + | 0.564369i | ||||
\(69\) | 2.20871 | + | 3.82560i | 0.265898 | + | 0.460548i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.79129 | − | 2.18890i | 0.449943 | − | 0.259775i | −0.257863 | − | 0.966181i | \(-0.583018\pi\) |
0.707806 | + | 0.706407i | \(0.249685\pi\) | |||||||
\(72\) | 7.18693 | − | 4.14938i | 0.846988 | − | 0.489009i | ||||
\(73\) | − | 3.46410i | − | 0.405442i | −0.979236 | − | 0.202721i | \(-0.935021\pi\) | ||
0.979236 | − | 0.202721i | \(-0.0649785\pi\) | |||||||
\(74\) | −1.58258 | − | 2.74110i | −0.183971 | − | 0.318647i | ||||
\(75\) | −6.68693 | + | 11.5821i | −0.772140 | + | 1.33739i | ||||
\(76\) | −2.12614 | − | 1.22753i | −0.243885 | − | 0.140807i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.31307 | − | 3.18800i | 0.375131 | − | 0.360970i | ||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | −1.10436 | − | 0.637600i | −0.123471 | − | 0.0712859i | ||||
\(81\) | 0.208712 | − | 0.361500i | 0.0231902 | − | 0.0401667i | ||||
\(82\) | −1.79129 | − | 3.10260i | −0.197815 | − | 0.342625i | ||||
\(83\) | − | 7.02355i | − | 0.770935i | −0.922721 | − | 0.385468i | \(-0.874040\pi\) | ||
0.922721 | − | 0.385468i | \(-0.125960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18693 | − | 0.685275i | 0.128741 | − | 0.0743286i | ||||
\(86\) | 4.28245i | 0.461789i | ||||||||
\(87\) | 9.47822 | + | 16.4168i | 1.01617 | + | 1.76006i | ||||
\(88\) | 3.39564 | − | 5.88143i | 0.361977 | − | 0.626962i | ||||
\(89\) | −13.9782 | − | 8.07033i | −1.48169 | − | 0.855453i | −0.481904 | − | 0.876224i | \(-0.660055\pi\) |
−0.999784 | + | 0.0207708i | \(0.993388\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.83485 | −0.295553 | ||||||||
\(93\) | −20.9347 | − | 12.0866i | −2.17082 | − | 1.25333i | ||||
\(94\) | −2.18693 | + | 3.78788i | −0.225565 | + | 0.390690i | ||||
\(95\) | 0.313068 | + | 0.542250i | 0.0321201 | + | 0.0556337i | ||||
\(96\) | 13.2288i | 1.35015i | ||||||||
\(97\) | −6.31307 | + | 3.64485i | −0.640995 | + | 0.370079i | −0.784998 | − | 0.619499i | \(-0.787336\pi\) |
0.144003 | + | 0.989577i | \(0.454003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.7864i | 1.88811i | ||||||||
\(100\) | −4.29129 | − | 7.43273i | −0.429129 | − | 0.743273i | ||||
\(101\) | −2.60436 | + | 4.51088i | −0.259143 | + | 0.448849i | −0.966013 | − | 0.258495i | \(-0.916773\pi\) |
0.706869 | + | 0.707344i | \(0.250107\pi\) | |||||||
\(102\) | −3.31307 | − | 1.91280i | −0.328043 | − | 0.189396i | ||||
\(103\) | 4.58258 | 0.451535 | 0.225767 | − | 0.974181i | \(-0.427511\pi\) | ||||
0.225767 | + | 0.974181i | \(0.427511\pi\) | |||||||
\(104\) | 1.50000 | + | 6.06218i | 0.147087 | + | 0.594445i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.43920 | − | 1.40828i | −0.236917 | − | 0.136784i | ||||
\(107\) | 2.60436 | − | 4.51088i | 0.251773 | − | 0.436083i | −0.712241 | − | 0.701935i | \(-0.752320\pi\) |
0.964014 | + | 0.265852i | \(0.0856532\pi\) | |||||||
\(108\) | −4.47822 | − | 7.75650i | −0.430917 | − | 0.746370i | ||||
\(109\) | − | 7.93725i | − | 0.760251i | −0.924935 | − | 0.380126i | \(-0.875881\pi\) | ||
0.924935 | − | 0.380126i | \(-0.124119\pi\) | |||||||
\(110\) | −0.708712 | + | 0.409175i | −0.0675731 | + | 0.0390133i | ||||
\(111\) | −16.7477 | + | 9.66930i | −1.58962 | + | 0.917770i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.29129 | − | 9.16478i | −0.497762 | − | 0.862150i | 0.502234 | − | 0.864732i | \(-0.332512\pi\) |
−0.999997 | + | 0.00258173i | \(0.999178\pi\) | |||||||
\(114\) | 0.873864 | − | 1.51358i | 0.0818448 | − | 0.141759i | ||||
\(115\) | 0.626136 | + | 0.361500i | 0.0583875 | + | 0.0337101i | ||||
\(116\) | −12.1652 | −1.12951 | ||||||||
\(117\) | −11.9782 | − | 12.4481i | −1.10739 | − | 1.15083i | ||||
\(118\) | −5.62614 | −0.517928 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.10436 | − | 1.91280i | 0.100813 | − | 0.174614i | ||||
\(121\) | 2.18693 | + | 3.78788i | 0.198812 | + | 0.344352i | ||||
\(122\) | − | 6.73750i | − | 0.609985i | ||||||
\(123\) | −18.9564 | + | 10.9445i | −1.70924 | + | 0.986833i | ||||
\(124\) | 13.4347 | − | 7.75650i | 1.20647 | − | 0.696555i | ||||
\(125\) | 4.47315i | 0.400091i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.47822 | + | 6.02445i | −0.308642 | + | 0.534584i | −0.978066 | − | 0.208297i | \(-0.933208\pi\) |
0.669423 | + | 0.742881i | \(0.266541\pi\) | |||||||
\(128\) | −9.56080 | − | 5.51993i | −0.845063 | − | 0.487897i | ||||
\(129\) | 26.1652 | 2.30371 | ||||||||
\(130\) | 0.208712 | − | 0.723000i | 0.0183053 | − | 0.0634113i | ||||
\(131\) | −17.3739 | −1.51796 | −0.758981 | − | 0.651113i | \(-0.774302\pi\) | ||||
−0.758981 | + | 0.651113i | \(0.774302\pi\) | |||||||
\(132\) | −16.9782 | − | 9.80238i | −1.47776 | − | 0.853188i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.02178 | + | 1.76978i | 0.0882684 | + | 0.152885i | ||||
\(135\) | 2.28425i | 0.196597i | ||||||||
\(136\) | 4.50000 | − | 2.59808i | 0.385872 | − | 0.222783i | ||||
\(137\) | 10.3521 | − | 5.97678i | 0.884438 | − | 0.510631i | 0.0123190 | − | 0.999924i | \(-0.496079\pi\) |
0.872119 | + | 0.489294i | \(0.162745\pi\) | |||||||
\(138\) | − | 2.01810i | − | 0.171792i | ||||||
\(139\) | −1.89564 | − | 3.28335i | −0.160786 | − | 0.278490i | 0.774365 | − | 0.632740i | \(-0.218070\pi\) |
−0.935151 | + | 0.354249i | \(0.884736\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.1434 | + | 13.3618i | 1.94902 | + | 1.12527i | ||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | −13.5826 | − | 3.92095i | −1.13583 | − | 0.327886i | ||||
\(144\) | 13.3739 | 1.11449 | ||||||||
\(145\) | 2.68693 | + | 1.55130i | 0.223138 | + | 0.128829i | ||||
\(146\) | −0.791288 | + | 1.37055i | −0.0654874 | + | 0.113428i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 12.4104i | − | 1.02013i | ||||||
\(149\) | −0.395644 | + | 0.228425i | −0.0324124 | + | 0.0187133i | −0.516119 | − | 0.856517i | \(-0.672624\pi\) |
0.483706 | + | 0.875230i | \(0.339290\pi\) | |||||||
\(150\) | 5.29129 | − | 3.05493i | 0.432032 | − | 0.249434i | ||||
\(151\) | − | 12.1244i | − | 0.986666i | −0.869841 | − | 0.493333i | \(-0.835778\pi\) | ||
0.869841 | − | 0.493333i | \(-0.164222\pi\) | |||||||
\(152\) | 1.18693 | + | 2.05583i | 0.0962729 | + | 0.166750i | ||||
\(153\) | −7.18693 | + | 12.4481i | −0.581029 | + | 1.00637i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.95644 | −0.317789 | ||||||||
\(156\) | 17.5000 | − | 4.33013i | 1.40112 | − | 0.346688i | ||||
\(157\) | −0.956439 | −0.0763322 | −0.0381661 | − | 0.999271i | \(-0.512152\pi\) | ||||
−0.0381661 | + | 0.999271i | \(0.512152\pi\) | |||||||
\(158\) | 2.37386 | + | 1.37055i | 0.188854 | + | 0.109035i | ||||
\(159\) | −8.60436 | + | 14.9032i | −0.682370 | + | 1.18190i | ||||
\(160\) | 1.08258 | + | 1.87508i | 0.0855851 | + | 0.148238i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.165151 | + | 0.0953502i | −0.0129755 | + | 0.00749142i | ||||
\(163\) | 6.00000 | − | 3.46410i | 0.469956 | − | 0.271329i | −0.246265 | − | 0.969202i | \(-0.579203\pi\) |
0.716221 | + | 0.697873i | \(0.245870\pi\) | |||||||
\(164\) | − | 14.0471i | − | 1.09689i | ||||||
\(165\) | 2.50000 | + | 4.33013i | 0.194625 | + | 0.337100i | ||||
\(166\) | −1.60436 | + | 2.77883i | −0.124522 | + | 0.215679i | ||||
\(167\) | 12.7087 | + | 7.33738i | 0.983430 | + | 0.567783i | 0.903304 | − | 0.429001i | \(-0.141134\pi\) |
0.0801258 | + | 0.996785i | \(0.474468\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −0.626136 | −0.0480225 | ||||||||
\(171\) | −5.68693 | − | 3.28335i | −0.434891 | − | 0.251084i | ||||
\(172\) | −8.39564 | + | 14.5417i | −0.640162 | + | 1.10879i | ||||
\(173\) | −9.87386 | − | 17.1020i | −0.750696 | − | 1.30024i | −0.947486 | − | 0.319798i | \(-0.896385\pi\) |
0.196790 | − | 0.980446i | \(-0.436948\pi\) | |||||||
\(174\) | − | 8.66025i | − | 0.656532i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.47822 | − | 5.47225i | 0.714448 | − | 0.412487i | ||||
\(177\) | 34.3749i | 2.58377i | ||||||||
\(178\) | 3.68693 | + | 6.38595i | 0.276347 | + | 0.478647i | ||||
\(179\) | 4.50000 | − | 7.79423i | 0.336346 | − | 0.582568i | −0.647397 | − | 0.762153i | \(-0.724142\pi\) |
0.983742 | + | 0.179585i | \(0.0574756\pi\) | |||||||
\(180\) | −3.39564 | − | 1.96048i | −0.253096 | − | 0.146125i | ||||
\(181\) | −9.16515 | −0.681240 | −0.340620 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340620 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −41.1652 | −3.04302 | ||||||||
\(184\) | 2.37386 | + | 1.37055i | 0.175004 | + | 0.101038i | ||||
\(185\) | −1.58258 | + | 2.74110i | −0.116353 | + | 0.201530i | ||||
\(186\) | 5.52178 | + | 9.56400i | 0.404877 | + | 0.701267i | ||||
\(187\) | 11.7629i | 0.860185i | ||||||||
\(188\) | −14.8521 | + | 8.57485i | −1.08320 | + | 0.625386i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 0.286051i | − | 0.0207523i | ||||||
\(191\) | 7.18693 | + | 12.4481i | 0.520028 | + | 0.900715i | 0.999729 | + | 0.0232830i | \(0.00741188\pi\) |
−0.479701 | + | 0.877432i | \(0.659255\pi\) | |||||||
\(192\) | −4.76951 | + | 8.26103i | −0.344210 | + | 0.596188i | ||||
\(193\) | 16.7477 | + | 9.66930i | 1.20553 | + | 0.696012i | 0.961779 | − | 0.273827i | \(-0.0882895\pi\) |
0.243749 | + | 0.969838i | \(0.421623\pi\) | |||||||
\(194\) | 3.33030 | 0.239102 | ||||||||
\(195\) | −4.41742 | − | 1.27520i | −0.316338 | − | 0.0913190i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.97822 | + | 1.14213i | 0.140942 | + | 0.0813731i | 0.568813 | − | 0.822467i | \(-0.307403\pi\) |
−0.427871 | + | 0.903840i | \(0.640736\pi\) | |||||||
\(198\) | 4.29129 | − | 7.43273i | 0.304969 | − | 0.528221i | ||||
\(199\) | 5.50000 | + | 9.52628i | 0.389885 | + | 0.675300i | 0.992434 | − | 0.122782i | \(-0.0391815\pi\) |
−0.602549 | + | 0.798082i | \(0.705848\pi\) | |||||||
\(200\) | 8.29875i | 0.586811i | ||||||||
\(201\) | 10.8131 | − | 6.24293i | 0.762695 | − | 0.440342i | ||||
\(202\) | 2.06080 | − | 1.18980i | 0.144997 | − | 0.0837141i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.50000 | − | 12.9904i | −0.525105 | − | 0.909509i | ||||
\(205\) | −1.79129 | + | 3.10260i | −0.125109 | + | 0.216695i | ||||
\(206\) | −1.81307 | − | 1.04678i | −0.126322 | − | 0.0729323i | ||||
\(207\) | −7.58258 | −0.527025 | ||||||||
\(208\) | −2.79129 | + | 9.66930i | −0.193541 | + | 0.670446i | ||||
\(209\) | −5.37386 | −0.371718 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.29129 | + | 9.16478i | −0.364267 | + | 0.630929i | −0.988658 | − | 0.150183i | \(-0.952014\pi\) |
0.624391 | + | 0.781112i | \(0.285347\pi\) | |||||||
\(212\) | −5.52178 | − | 9.56400i | −0.379237 | − | 0.656859i | ||||
\(213\) | 12.2197i | 0.837280i | ||||||||
\(214\) | −2.06080 | + | 1.18980i | −0.140873 | + | 0.0813331i | ||||
\(215\) | 3.70871 | − | 2.14123i | 0.252932 | − | 0.146030i | ||||
\(216\) | 8.66025i | 0.589256i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.81307 | + | 3.14033i | −0.122796 | + | 0.212690i | ||||
\(219\) | 8.37386 | + | 4.83465i | 0.565853 | + | 0.326696i | ||||
\(220\) | −3.20871 | −0.216331 | ||||||||
\(221\) | −7.50000 | − | 7.79423i | −0.504505 | − | 0.524297i | ||||
\(222\) | 8.83485 | 0.592956 | ||||||||
\(223\) | 16.4347 | + | 9.48855i | 1.10055 | + | 0.635401i | 0.936364 | − | 0.351029i | \(-0.114168\pi\) |
0.164182 | + | 0.986430i | \(0.447502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4782 | − | 19.8809i | −0.765215 | − | 1.32539i | ||||
\(226\) | 4.83465i | 0.321596i | ||||||||
\(227\) | −7.66515 | + | 4.42548i | −0.508754 | + | 0.293729i | −0.732321 | − | 0.680959i | \(-0.761563\pi\) |
0.223567 | + | 0.974688i | \(0.428230\pi\) | |||||||
\(228\) | 5.93466 | − | 3.42638i | 0.393032 | − | 0.226917i | ||||
\(229\) | − | 6.92820i | − | 0.457829i | −0.973447 | − | 0.228914i | \(-0.926482\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735176\pi\) | |||||||
\(230\) | −0.165151 | − | 0.286051i | −0.0108898 | − | 0.0188616i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.1869 | + | 5.88143i | 0.668805 | + | 0.386135i | ||||
\(233\) | 15.9564 | 1.04534 | 0.522671 | − | 0.852535i | \(-0.324936\pi\) | ||||
0.522671 | + | 0.852535i | \(0.324936\pi\) | |||||||
\(234\) | 1.89564 | + | 7.66115i | 0.123922 | + | 0.500825i | ||||
\(235\) | 4.37386 | 0.285319 | ||||||||
\(236\) | −19.1044 | − | 11.0299i | −1.24359 | − | 0.717986i | ||||
\(237\) | 8.37386 | − | 14.5040i | 0.543941 | − | 0.942133i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2288i | 0.855697i | 0.903850 | + | 0.427849i | \(0.140728\pi\) | ||||
−0.903850 | + | 0.427849i | \(0.859272\pi\) | |||||||
\(240\) | 3.08258 | − | 1.77973i | 0.198979 | − | 0.114881i | ||||
\(241\) | 17.0608 | − | 9.85005i | 1.09898 | − | 0.634498i | 0.163029 | − | 0.986621i | \(-0.447874\pi\) |
0.935954 | + | 0.352123i | \(0.114540\pi\) | |||||||
\(242\) | − | 1.99820i | − | 0.128449i | ||||||
\(243\) | 8.08258 | + | 13.9994i | 0.518497 | + | 0.898064i | ||||
\(244\) | 13.2087 | − | 22.8782i | 0.845601 | − | 1.46462i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 3.56080 | − | 3.42638i | 0.226568 | − | 0.218015i | ||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | 16.9782 | + | 9.80238i | 1.07595 | + | 0.621201i | ||||
\(250\) | 1.02178 | − | 1.76978i | 0.0646231 | − | 0.111930i | ||||
\(251\) | −1.41742 | − | 2.45505i | −0.0894670 | − | 0.154961i | 0.817819 | − | 0.575476i | \(-0.195183\pi\) |
−0.907286 | + | 0.420514i | \(0.861850\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.37386 | + | 3.10260i | −0.337852 | + | 0.195059i | ||||
\(254\) | 2.75227 | − | 1.58903i | 0.172693 | − | 0.0997043i | ||||
\(255\) | 3.82560i | 0.239568i | ||||||||
\(256\) | −0.895644 | − | 1.55130i | −0.0559777 | − | 0.0969563i | ||||
\(257\) | 2.52178 | − | 4.36785i | 0.157304 | − | 0.272459i | −0.776591 | − | 0.630005i | \(-0.783053\pi\) |
0.933896 | + | 0.357546i | \(0.116386\pi\) | |||||||
\(258\) | −10.3521 | − | 5.97678i | −0.644493 | − | 0.372098i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.12614 | − | 2.04588i | 0.131857 | − | 0.126880i | ||||
\(261\) | −32.5390 | −2.01411 | ||||||||
\(262\) | 6.87386 | + | 3.96863i | 0.424669 | + | 0.245183i | ||||
\(263\) | −4.66515 | + | 8.08028i | −0.287666 | + | 0.498251i | −0.973252 | − | 0.229740i | \(-0.926212\pi\) |
0.685587 | + | 0.727991i | \(0.259546\pi\) | |||||||
\(264\) | 9.47822 | + | 16.4168i | 0.583344 | + | 1.01038i | ||||
\(265\) | 2.81655i | 0.173019i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.0172 | − | 22.5266i | 2.38782 | − | 1.37861i | ||||
\(268\) | 8.01270i | 0.489454i | ||||||||
\(269\) | −7.89564 | − | 13.6757i | −0.481406 | − | 0.833819i | 0.518366 | − | 0.855159i | \(-0.326540\pi\) |
−0.999772 | + | 0.0213391i | \(0.993207\pi\) | |||||||
\(270\) | 0.521780 | − | 0.903750i | 0.0317545 | − | 0.0550005i | ||||
\(271\) | 11.1261 | + | 6.42368i | 0.675865 | + | 0.390211i | 0.798295 | − | 0.602266i | \(-0.205736\pi\) |
−0.122430 | + | 0.992477i | \(0.539069\pi\) | |||||||
\(272\) | 8.37386 | 0.507740 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.46099 | −0.329910 | ||||||||
\(275\) | −16.2695 | − | 9.39320i | −0.981088 | − | 0.566432i | ||||
\(276\) | 3.95644 | − | 6.85275i | 0.238150 | − | 0.412487i | ||||
\(277\) | −5.87386 | − | 10.1738i | −0.352926 | − | 0.611286i | 0.633835 | − | 0.773469i | \(-0.281480\pi\) |
−0.986761 | + | 0.162182i | \(0.948147\pi\) | |||||||
\(278\) | 1.73205i | 0.103882i | ||||||||
\(279\) | 35.9347 | − | 20.7469i | 2.15135 | − | 1.24208i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.6446i | 1.82810i | 0.405597 | + | 0.914052i | \(0.367064\pi\) | ||||
−0.405597 | + | 0.914052i | \(0.632936\pi\) | |||||||
\(282\) | −6.10436 | − | 10.5731i | −0.363509 | − | 0.629616i | ||||
\(283\) | 1.37386 | − | 2.37960i | 0.0816677 | − | 0.141453i | −0.822299 | − | 0.569056i | \(-0.807309\pi\) |
0.903966 | + | 0.427603i | \(0.140642\pi\) | |||||||
\(284\) | −6.79129 | − | 3.92095i | −0.402989 | − | 0.232666i | ||||
\(285\) | −1.74773 | −0.103526 | ||||||||
\(286\) | 4.47822 | + | 4.65390i | 0.264803 | + | 0.275191i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −19.6652 | − | 11.3537i | −1.15878 | − | 0.669022i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −0.708712 | − | 1.22753i | −0.0416170 | − | 0.0720828i | ||||
\(291\) | − | 20.3477i | − | 1.19280i | ||||||
\(292\) | −5.37386 | + | 3.10260i | −0.314482 | + | 0.181566i | ||||
\(293\) | −2.20871 | + | 1.27520i | −0.129034 | + | 0.0744980i | −0.563128 | − | 0.826370i | \(-0.690402\pi\) |
0.434093 | + | 0.900868i | \(0.357069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.81307 | + | 4.87238i | 0.163783 | + | 0.283681i | ||||
\(296\) | −6.00000 | + | 10.3923i | −0.348743 | + | 0.604040i | ||||
\(297\) | −16.9782 | − | 9.80238i | −0.985176 | − | 0.568792i | ||||
\(298\) | 0.208712 | 0.0120904 | ||||||||
\(299\) | 1.58258 | − | 5.48220i | 0.0915227 | − | 0.317044i | ||||
\(300\) | 23.9564 | 1.38313 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.76951 | + | 4.79693i | −0.159367 | + | 0.276032i | ||||
\(303\) | −7.26951 | − | 12.5912i | −0.417622 | − | 0.723343i | ||||
\(304\) | 3.82560i | 0.219413i | ||||||||
\(305\) | −5.83485 | + | 3.36875i | −0.334102 | + | 0.192894i | ||||
\(306\) | 5.68693 | − | 3.28335i | 0.325100 | − | 0.187697i | ||||
\(307\) | − | 15.5130i | − | 0.885374i | −0.896676 | − | 0.442687i | \(-0.854025\pi\) | ||
0.896676 | − | 0.442687i | \(-0.145975\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.39564 | + | 11.0776i | −0.363835 | + | 0.630182i | ||||
\(310\) | 1.56534 | + | 0.903750i | 0.0889054 | + | 0.0513296i | ||||
\(311\) | −26.5390 | −1.50489 | −0.752445 | − | 0.658655i | \(-0.771126\pi\) | ||||
−0.752445 | + | 0.658655i | \(0.771126\pi\) | |||||||
\(312\) | −16.7477 | − | 4.83465i | −0.948153 | − | 0.273708i | ||||
\(313\) | 6.74773 | 0.381404 | 0.190702 | − | 0.981648i | \(-0.438924\pi\) | ||||
0.190702 | + | 0.981648i | \(0.438924\pi\) | |||||||
\(314\) | 0.378409 | + | 0.218475i | 0.0213549 | + | 0.0123292i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.37386 | + | 9.30780i | 0.302303 | + | 0.523605i | ||||
\(317\) | − | 18.5203i | − | 1.04020i | −0.854105 | − | 0.520101i | \(-0.825894\pi\) | ||
0.854105 | − | 0.520101i | \(-0.174106\pi\) | |||||||
\(318\) | 6.80852 | − | 3.93090i | 0.381803 | − | 0.220434i | ||||
\(319\) | −23.0608 | + | 13.3142i | −1.29116 | + | 0.745450i | ||||
\(320\) | 1.56125i | 0.0872766i | ||||||||
\(321\) | 7.26951 | + | 12.5912i | 0.405744 | + | 0.702770i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.56080 | − | 2.05583i | −0.198128 | − | 0.114389i | ||||
\(324\) | −0.747727 | −0.0415404 | ||||||||
\(325\) | 16.7695 | − | 4.14938i | 0.930205 | − | 0.230166i | ||||
\(326\) | −3.16515 | −0.175302 | ||||||||
\(327\) | 19.1869 | + | 11.0776i | 1.06104 | + | 0.612592i | ||||
\(328\) | −6.79129 | + | 11.7629i | −0.374986 | + | 0.649495i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 2.28425i | − | 0.125744i | ||||||
\(331\) | 21.5608 | − | 12.4481i | 1.18509 | − | 0.684211i | 0.227902 | − | 0.973684i | \(-0.426813\pi\) |
0.957186 | + | 0.289473i | \(0.0934800\pi\) | |||||||
\(332\) | −10.8956 | + | 6.29060i | −0.597976 | + | 0.345242i | ||||
\(333\) | − | 33.1950i | − | 1.81908i | ||||||
\(334\) | −3.35208 | − | 5.80598i | −0.183418 | − | 0.317689i | ||||
\(335\) | 1.02178 | − | 1.76978i | 0.0558258 | − | 0.0966932i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.95644 | 0.542362 | 0.271181 | − | 0.962528i | \(-0.412586\pi\) | ||||
0.271181 | + | 0.962528i | \(0.412586\pi\) | |||||||
\(338\) | −5.93466 | − | 0.228425i | −0.322803 | − | 0.0124247i | ||||
\(339\) | 29.5390 | 1.60434 | ||||||||
\(340\) | −2.12614 | − | 1.22753i | −0.115306 | − | 0.0665719i | ||||
\(341\) | 16.9782 | − | 29.4071i | 0.919422 | − | 1.59249i | ||||
\(342\) | 1.50000 | + | 2.59808i | 0.0811107 | + | 0.140488i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.0608 | − | 8.11800i | 0.758107 | − | 0.437693i | ||||
\(345\) | −1.74773 | + | 1.00905i | −0.0940945 | + | 0.0543255i | ||||
\(346\) | 9.02175i | 0.485013i | ||||||||
\(347\) | 6.79129 | + | 11.7629i | 0.364575 | + | 0.631463i | 0.988708 | − | 0.149855i | \(-0.0478808\pi\) |
−0.624132 | + | 0.781319i | \(0.714547\pi\) | |||||||
\(348\) | 16.9782 | − | 29.4071i | 0.910128 | − | 1.57639i | ||||
\(349\) | 18.2477 | + | 10.5353i | 0.976778 | + | 0.563943i | 0.901296 | − | 0.433204i | \(-0.142617\pi\) |
0.0754825 | + | 0.997147i | \(0.475950\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.5000 | − | 4.33013i | 0.934081 | − | 0.231125i | ||||
\(352\) | −18.5826 | −0.990455 | ||||||||
\(353\) | −15.7259 | − | 9.07938i | −0.837008 | − | 0.483247i | 0.0192383 | − | 0.999815i | \(-0.493876\pi\) |
−0.856246 | + | 0.516568i | \(0.827209\pi\) | |||||||
\(354\) | 7.85208 | − | 13.6002i | 0.417334 | − | 0.722843i | ||||
\(355\) | 1.00000 | + | 1.73205i | 0.0530745 | + | 0.0919277i | ||||
\(356\) | 28.9126i | 1.53236i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.56080 | + | 2.05583i | −0.188194 | + | 0.108654i | ||||
\(359\) | − | 0.552200i | − | 0.0291440i | −0.999894 | − | 0.0145720i | \(-0.995361\pi\) | ||
0.999894 | − | 0.0145720i | \(-0.00463858\pi\) | |||||||
\(360\) | 1.89564 | + | 3.28335i | 0.0999092 | + | 0.173048i | ||||
\(361\) | −8.56080 | + | 14.8277i | −0.450568 | + | 0.780407i | ||||
\(362\) | 3.62614 | + | 2.09355i | 0.190586 | + | 0.110035i | ||||
\(363\) | −12.2087 | −0.640791 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.58258 | 0.0828358 | ||||||||
\(366\) | 16.2867 | + | 9.40315i | 0.851322 | + | 0.491511i | ||||
\(367\) | −9.00000 | + | 15.5885i | −0.469796 | + | 0.813711i | −0.999404 | − | 0.0345320i | \(-0.989006\pi\) |
0.529607 | + | 0.848243i | \(0.322339\pi\) | |||||||
\(368\) | 2.20871 | + | 3.82560i | 0.115137 | + | 0.199423i | ||||
\(369\) | − | 37.5728i | − | 1.95596i | ||||||
\(370\) | 1.25227 | − | 0.723000i | 0.0651026 | − | 0.0375870i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 43.3013i | 2.24507i | ||||||||
\(373\) | −16.1044 | − | 27.8936i | −0.833852 | − | 1.44427i | −0.894962 | − | 0.446143i | \(-0.852797\pi\) |
0.0611098 | − | 0.998131i | \(-0.480536\pi\) | |||||||
\(374\) | 2.68693 | − | 4.65390i | 0.138938 | − | 0.240648i | ||||
\(375\) | −10.8131 | − | 6.24293i | −0.558384 | − | 0.322383i | ||||
\(376\) | 16.5826 | 0.855181 | ||||||||
\(377\) | 6.79129 | − | 23.5257i | 0.349769 | − | 1.21164i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.5608 | − | 14.1802i | −1.26160 | − | 0.728387i | −0.288219 | − | 0.957565i | \(-0.593063\pi\) |
−0.973385 | + | 0.229178i | \(0.926396\pi\) | |||||||
\(380\) | 0.560795 | − | 0.971326i | 0.0287682 | − | 0.0498280i | ||||
\(381\) | −9.70871 | − | 16.8160i | −0.497392 | − | 0.861509i | ||||
\(382\) | − | 6.56670i | − | 0.335982i | ||||||
\(383\) | −1.10436 | + | 0.637600i | −0.0564300 | + | 0.0325799i | −0.527950 | − | 0.849276i | \(-0.677039\pi\) |
0.471520 | + | 0.881856i | \(0.343706\pi\) | |||||||
\(384\) | 26.6869 | − | 15.4077i | 1.36186 | − | 0.786271i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.41742 | − | 7.65120i | −0.224841 | − | 0.389436i | ||||
\(387\) | −22.4564 | + | 38.8957i | −1.14152 | + | 1.97718i | ||||
\(388\) | 11.3085 | + | 6.52898i | 0.574103 | + | 0.331459i | ||||
\(389\) | −0.330303 | −0.0167470 | −0.00837351 | − | 0.999965i | \(-0.502665\pi\) | ||||
−0.00837351 | + | 0.999965i | \(0.502665\pi\) | |||||||
\(390\) | 1.45644 | + | 1.51358i | 0.0737497 | + | 0.0766429i | ||||
\(391\) | −4.74773 | −0.240103 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.2477 | − | 41.9983i | 1.22314 | − | 2.11853i | ||||
\(394\) | −0.521780 | − | 0.903750i | −0.0262869 | − | 0.0455303i | ||||
\(395\) | − | 2.74110i | − | 0.137920i | ||||||
\(396\) | 29.1434 | − | 16.8259i | 1.46451 | − | 0.845535i | ||||
\(397\) | −28.1216 | + | 16.2360i | −1.41138 | + | 0.814862i | −0.995519 | − | 0.0945652i | \(-0.969854\pi\) |
−0.415864 | + | 0.909427i | \(0.636521\pi\) | |||||||
\(398\) | − | 5.02535i | − | 0.251898i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.68693 | + | 11.5821i | −0.334347 | + | 0.579105i | ||||
\(401\) | 27.0998 | + | 15.6461i | 1.35330 | + | 0.781328i | 0.988710 | − | 0.149840i | \(-0.0478759\pi\) |
0.364590 | + | 0.931168i | \(0.381209\pi\) | |||||||
\(402\) | −5.70417 | −0.284498 | ||||||||
\(403\) | 7.50000 | + | 30.3109i | 0.373602 | + | 1.50989i | ||||
\(404\) | 9.33030 | 0.464200 | ||||||||
\(405\) | 0.165151 | + | 0.0953502i | 0.00820644 | + | 0.00473799i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.5826 | − | 23.5257i | −0.673263 | − | 1.16613i | ||||
\(408\) | 14.5040i | 0.718053i | ||||||||
\(409\) | −7.18693 | + | 4.14938i | −0.355371 | + | 0.205173i | −0.667048 | − | 0.745015i | \(-0.732443\pi\) |
0.311677 | + | 0.950188i | \(0.399109\pi\) | |||||||
\(410\) | 1.41742 | − | 0.818350i | 0.0700016 | − | 0.0404154i | ||||
\(411\) | 33.3658i | 1.64581i | ||||||||
\(412\) | −4.10436 | − | 7.10895i | −0.202207 | − | 0.350233i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.00000 | + | 1.73205i | 0.147442 | + | 0.0851257i | ||||
\(415\) | 3.20871 | 0.157509 | ||||||||
\(416\) | 12.3131 | − | 11.8483i | 0.603698 | − | 0.580909i | ||||
\(417\) | 10.5826 | 0.518231 | ||||||||
\(418\) | 2.12614 | + | 1.22753i | 0.103993 | + | 0.0600402i | ||||
\(419\) | −0.873864 | + | 1.51358i | −0.0426910 | + | 0.0739430i | −0.886581 | − | 0.462573i | \(-0.846926\pi\) |
0.843890 | + | 0.536516i | \(0.180260\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.18710i | 0.204067i | 0.994781 | + | 0.102033i | \(0.0325349\pi\) | ||||
−0.994781 | + | 0.102033i | \(0.967465\pi\) | |||||||
\(422\) | 4.18693 | − | 2.41733i | 0.203817 | − | 0.117674i | ||||
\(423\) | −39.7259 | + | 22.9358i | −1.93154 | + | 1.11518i | ||||
\(424\) | 10.6784i | 0.518587i | ||||||||
\(425\) | −7.18693 | − | 12.4481i | −0.348617 | − | 0.603823i | ||||
\(426\) | 2.79129 | − | 4.83465i | 0.135238 | − | 0.234240i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.33030 | −0.450997 | ||||||||
\(429\) | 28.4347 | − | 27.3613i | 1.37284 | − | 1.32101i | ||||
\(430\) | −1.95644 | −0.0943479 | ||||||||
\(431\) | 30.0172 | + | 17.3305i | 1.44588 | + | 0.834779i | 0.998232 | − | 0.0594316i | \(-0.0189288\pi\) |
0.447647 | + | 0.894210i | \(0.352262\pi\) | |||||||
\(432\) | −6.97822 | + | 12.0866i | −0.335740 | + | 0.581518i | ||||
\(433\) | −16.2477 | − | 28.1419i | −0.780816 | − | 1.35241i | −0.931467 | − | 0.363826i | \(-0.881470\pi\) |
0.150651 | − | 0.988587i | \(-0.451863\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.50000 | + | 4.33013i | −0.359597 | + | 0.207614i | ||||
\(436\) | −12.3131 | + | 7.10895i | −0.589689 | + | 0.340457i | ||||
\(437\) | − | 2.16900i | − | 0.103757i | ||||||
\(438\) | −2.20871 | − | 3.82560i | −0.105536 | − | 0.182794i | ||||
\(439\) | −10.2695 | + | 17.7873i | −0.490137 | + | 0.848942i | −0.999936 | − | 0.0113518i | \(-0.996387\pi\) |
0.509799 | + | 0.860294i | \(0.329720\pi\) | |||||||
\(440\) | 2.68693 | + | 1.55130i | 0.128094 | + | 0.0739554i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.18693 | + | 4.79693i | 0.0564566 | + | 0.228167i | ||||
\(443\) | −15.1652 | −0.720518 | −0.360259 | − | 0.932852i | \(-0.617312\pi\) | ||||
−0.360259 | + | 0.932852i | \(0.617312\pi\) | |||||||
\(444\) | 30.0000 | + | 17.3205i | 1.42374 | + | 0.821995i | ||||
\(445\) | 3.68693 | − | 6.38595i | 0.174777 | − | 0.302723i | ||||
\(446\) | −4.33485 | − | 7.50818i | −0.205261 | − | 0.355523i | ||||
\(447\) | − | 1.27520i | − | 0.0603149i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.7913 | + | 12.5812i | −1.02839 | + | 0.593744i | −0.916524 | − | 0.399979i | \(-0.869017\pi\) |
−0.111870 | + | 0.993723i | \(0.535684\pi\) | |||||||
\(450\) | 10.4877i | 0.494393i | ||||||||
\(451\) | −15.3739 | − | 26.6283i | −0.723927 | − | 1.25388i | ||||
\(452\) | −9.47822 | + | 16.4168i | −0.445818 | + | 0.772179i | ||||
\(453\) | 29.3085 | + | 16.9213i | 1.37703 | + | 0.795031i | ||||
\(454\) | 4.04356 | 0.189774 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.62614 | −0.310297 | ||||||||
\(457\) | 19.7477 | + | 11.4014i | 0.923760 | + | 0.533333i | 0.884833 | − | 0.465909i | \(-0.154273\pi\) |
0.0389271 | + | 0.999242i | \(0.487606\pi\) | |||||||
\(458\) | −1.58258 | + | 2.74110i | −0.0739489 | + | 0.128083i | ||||
\(459\) | −7.50000 | − | 12.9904i | −0.350070 | − | 0.606339i | ||||
\(460\) | − | 1.29510i | − | 0.0603844i | ||||||
\(461\) | −4.02178 | + | 2.32198i | −0.187313 | + | 0.108145i | −0.590724 | − | 0.806874i | \(-0.701158\pi\) |
0.403411 | + | 0.915019i | \(0.367824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.93725i | 0.368875i | 0.982844 | + | 0.184438i | \(0.0590464\pi\) | ||||
−0.982844 | + | 0.184438i | \(0.940954\pi\) | |||||||
\(464\) | 9.47822 | + | 16.4168i | 0.440015 | + | 0.762129i | ||||
\(465\) | 5.52178 | − | 9.56400i | 0.256066 | − | 0.443520i | ||||
\(466\) | −6.31307 | − | 3.64485i | −0.292447 | − | 0.168844i | ||||
\(467\) | −30.1652 | −1.39588 | −0.697938 | − | 0.716158i | \(-0.745899\pi\) | ||||
−0.697938 | + | 0.716158i | \(0.745899\pi\) | |||||||
\(468\) | −8.58258 | + | 29.7309i | −0.396730 | + | 1.37431i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.73049 | − | 0.999100i | −0.0798217 | − | 0.0460851i | ||||
\(471\) | 1.33485 | − | 2.31203i | 0.0615066 | − | 0.106533i | ||||
\(472\) | 10.6652 | + | 18.4726i | 0.490903 | + | 0.850270i | ||||
\(473\) | 36.7545i | 1.68997i | ||||||||
\(474\) | −6.62614 | + | 3.82560i | −0.304349 | + | 0.175716i | ||||
\(475\) | 5.68693 | − | 3.28335i | 0.260934 | − | 0.150651i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.7695 | − | 25.5815i | −0.676249 | − | 1.17130i | ||||
\(478\) | 3.02178 | − | 5.23388i | 0.138213 | − | 0.239392i | ||||
\(479\) | 16.3521 | + | 9.44088i | 0.747146 | + | 0.431365i | 0.824662 | − | 0.565626i | \(-0.191366\pi\) |
−0.0775159 | + | 0.996991i | \(0.524699\pi\) | |||||||
\(480\) | −6.04356 | −0.275850 | ||||||||
\(481\) | 24.0000 | + | 6.92820i | 1.09431 | + | 0.315899i | ||||
\(482\) | −9.00000 | −0.409939 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.91742 | − | 6.78518i | 0.178065 | − | 0.308417i | ||||
\(485\) | −1.66515 | − | 2.88413i | −0.0756106 | − | 0.130961i | ||||
\(486\) | − | 7.38505i | − | 0.334993i | ||||||
\(487\) | 25.4347 | − | 14.6847i | 1.15255 | − | 0.665428i | 0.203046 | − | 0.979169i | \(-0.434916\pi\) |
0.949508 | + | 0.313742i | \(0.101583\pi\) | |||||||
\(488\) | −22.1216 | + | 12.7719i | −1.00140 | + | 0.578157i | ||||
\(489\) | 19.3386i | 0.874522i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.06080 | − | 3.56940i | 0.0930024 | − | 0.161085i | −0.815771 | − | 0.578375i | \(-0.803687\pi\) |
0.908773 | + | 0.417291i | \(0.137020\pi\) | |||||||
\(492\) | 33.9564 | + | 19.6048i | 1.53087 | + | 0.883851i | ||||
\(493\) | −20.3739 | −0.917593 | ||||||||
\(494\) | −2.19148 | + | 0.542250i | −0.0985992 | + | 0.0243970i | ||||
\(495\) | −8.58258 | −0.385758 | ||||||||
\(496\) | −20.9347 | − | 12.0866i | −0.939994 | − | 0.542706i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.47822 | − | 7.75650i | −0.200674 | − | 0.347577i | ||||
\(499\) | 18.4050i | 0.823921i | 0.911202 | + | 0.411961i | \(0.135156\pi\) | ||||
−0.911202 | + | 0.411961i | \(0.864844\pi\) | |||||||
\(500\) | 6.93920 | − | 4.00635i | 0.310331 | − | 0.179169i | ||||
\(501\) | −35.4737 | + | 20.4807i | −1.58485 | + | 0.915012i | ||||
\(502\) | 1.29510i | 0.0578032i | ||||||||
\(503\) | 9.56080 | + | 16.5598i | 0.426295 | + | 0.738364i | 0.996540 | − | 0.0831100i | \(-0.0264853\pi\) |
−0.570246 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.06080 | − | 1.18980i | −0.0917042 | − | 0.0529454i | ||||
\(506\) | 2.83485 | 0.126024 | ||||||||
\(507\) | −1.39564 | + | 36.2599i | −0.0619827 | + | 1.61036i | ||||
\(508\) | 12.4610 | 0.552867 | ||||||||
\(509\) | 13.0390 | + | 7.52808i | 0.577944 | + | 0.333676i | 0.760316 | − | 0.649553i | \(-0.225044\pi\) |
−0.182372 | + | 0.983230i | \(0.558377\pi\) | |||||||
\(510\) | 0.873864 | − | 1.51358i | 0.0386953 | − | 0.0670223i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.8981i | 1.01196i | ||||||||
\(513\) | 5.93466 | − | 3.42638i | 0.262022 | − | 0.151278i | ||||
\(514\) | −1.99545 | + | 1.15208i | −0.0880157 | + | 0.0508159i | ||||
\(515\) | 2.09355i | 0.0922529i | ||||||||
\(516\) | −23.4347 | − | 40.5900i | −1.03165 | − | 1.78688i | ||||
\(517\) | −18.7695 | + | 32.5097i | −0.825482 | + | 1.42978i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55.1216 | 2.41957 | ||||||||
\(520\) | −2.76951 | + | 0.685275i | −0.121451 | + | 0.0300513i | ||||
\(521\) | −16.4174 | −0.719260 | −0.359630 | − | 0.933095i | \(-0.617097\pi\) | ||||
−0.359630 | + | 0.933095i | \(0.617097\pi\) | |||||||
\(522\) | 12.8739 | + | 7.43273i | 0.563474 | + | 0.325322i | ||||
\(523\) | 12.1652 | − | 21.0707i | 0.531945 | − | 0.921356i | −0.467360 | − | 0.884067i | \(-0.654795\pi\) |
0.999305 | − | 0.0372883i | \(-0.0118720\pi\) | |||||||
\(524\) | 15.5608 | + | 26.9521i | 0.679776 | + | 1.17741i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.69148 | − | 2.13128i | 0.160956 | − | 0.0929280i | ||||
\(527\) | 22.5000 | − | 12.9904i | 0.980115 | − | 0.565870i | ||||
\(528\) | 30.5493i | 1.32949i | ||||||||
\(529\) | 10.2477 | + | 17.7496i | 0.445553 | + | 0.771721i | ||||
\(530\) | 0.643371 | − | 1.11435i | 0.0279463 | − | 0.0484043i | ||||
\(531\) | −51.0998 | − | 29.5025i | −2.21754 | − | 1.28030i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.1652 | + | 7.84190i | 1.17665 | + | 0.339671i | ||||
\(534\) | −20.5826 | −0.890695 | ||||||||
\(535\) | 2.06080 | + | 1.18980i | 0.0890960 | + | 0.0514396i | ||||
\(536\) | 3.87386 | − | 6.70973i | 0.167325 | − | 0.289816i | ||||
\(537\) | 12.5608 | + | 21.7559i | 0.542038 | + | 0.938838i | ||||
\(538\) | 7.21425i | 0.311029i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.54356 | − | 2.04588i | 0.152491 | − | 0.0880405i | ||||
\(541\) | 6.28065i | 0.270026i | 0.990844 | + | 0.135013i | \(0.0431077\pi\) | ||||
−0.990844 | + | 0.135013i | \(0.956892\pi\) | |||||||
\(542\) | −2.93466 | − | 5.08298i | −0.126054 | − | 0.218333i | ||||
\(543\) | 12.7913 | − | 22.1552i | 0.548927 | − | 0.950769i | ||||
\(544\) | −12.3131 | − | 7.10895i | −0.527918 | − | 0.304794i | ||||
\(545\) | 3.62614 | 0.155327 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.7477 | −0.502297 | −0.251148 | − | 0.967949i | \(-0.580808\pi\) | ||||
−0.251148 | + | 0.967949i | \(0.580808\pi\) | |||||||
\(548\) | −18.5436 | − | 10.7061i | −0.792142 | − | 0.457343i | ||||
\(549\) | 35.3303 | − | 61.1939i | 1.50786 | − | 2.61169i | ||||
\(550\) | 4.29129 | + | 7.43273i | 0.182981 | + | 0.316933i | ||||
\(551\) | − | 9.30780i | − | 0.396526i | ||||||
\(552\) | −6.62614 | + | 3.82560i | −0.282027 | + | 0.162828i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.36695i | 0.228020i | ||||||||
\(555\) | −4.41742 | − | 7.65120i | −0.187509 | − | 0.324775i | ||||
\(556\) | −3.39564 | + | 5.88143i | −0.144007 | + | 0.249428i | ||||
\(557\) | −28.5998 | − | 16.5121i | −1.21181 | − | 0.699640i | −0.248659 | − | 0.968591i | \(-0.579990\pi\) |
−0.963154 | + | 0.268951i | \(0.913323\pi\) | |||||||
\(558\) | −18.9564 | −0.802490 | ||||||||
\(559\) | −23.4347 | − | 24.3540i | −0.991180 | − | 1.03006i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.4347 | − | 16.4168i | −1.20051 | − | 0.693116i | ||||
\(562\) | 7.00000 | − | 12.1244i | 0.295277 | − | 0.511435i | ||||
\(563\) | 18.1652 | + | 31.4630i | 0.765570 | + | 1.32601i | 0.939945 | + | 0.341327i | \(0.110876\pi\) |
−0.174375 | + | 0.984679i | \(0.555790\pi\) | |||||||
\(564\) | − | 47.8698i | − | 2.01568i | ||||||
\(565\) | 4.18693 | − | 2.41733i | 0.176146 | − | 0.101698i | ||||
\(566\) | −1.08712 | + | 0.627650i | −0.0456951 | + | 0.0263821i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.79129 | + | 6.56670i | 0.159079 | + | 0.275533i | ||||
\(569\) | −8.37386 | + | 14.5040i | −0.351051 | + | 0.608038i | −0.986434 | − | 0.164159i | \(-0.947509\pi\) |
0.635383 | + | 0.772197i | \(0.280842\pi\) | |||||||
\(570\) | 0.691478 | + | 0.399225i | 0.0289628 | + | 0.0167217i | ||||
\(571\) | −2.04356 | −0.0855204 | −0.0427602 | − | 0.999085i | \(-0.513615\pi\) | ||||
−0.0427602 | + | 0.999085i | \(0.513615\pi\) | |||||||
\(572\) | 6.08258 | + | 24.5824i | 0.254325 | + | 1.02784i | ||||
\(573\) | −40.1216 | −1.67610 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.79129 | − | 6.56670i | 0.158108 | − | 0.273850i | ||||
\(576\) | −8.18693 | − | 14.1802i | −0.341122 | − | 0.590841i | ||||
\(577\) | − | 35.6501i | − | 1.48413i | −0.670327 | − | 0.742066i | \(-0.733846\pi\) | ||
0.670327 | − | 0.742066i | \(-0.266154\pi\) | |||||||
\(578\) | −3.16515 | + | 1.82740i | −0.131653 | + | 0.0760099i | ||||
\(579\) | −46.7477 | + | 26.9898i | −1.94277 | + | 1.12166i | ||||
\(580\) | − | 5.55765i | − | 0.230769i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.64792 | + | 8.05043i | −0.192662 | + | 0.333701i | ||||
\(583\) | −20.9347 | − | 12.0866i | −0.867025 | − | 0.500577i | ||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 5.68693 | − | 5.47225i | 0.235126 | − | 0.226250i | ||||
\(586\) | 1.16515 | 0.0481320 | ||||||||
\(587\) | 8.22595 | + | 4.74925i | 0.339521 | + | 0.196023i | 0.660060 | − | 0.751213i | \(-0.270531\pi\) |
−0.320539 | + | 0.947235i | \(0.603864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.93466 | + | 10.2791i | 0.244533 | + | 0.423544i | ||||
\(590\) | − | 2.57030i | − | 0.105818i | ||||||
\(591\) | −5.52178 | + | 3.18800i | −0.227136 | + | 0.131137i | ||||
\(592\) | −16.7477 | + | 9.66930i | −0.688327 | + | 0.397406i | ||||
\(593\) | − | 6.37600i | − | 0.261831i | −0.991394 | − | 0.130916i | \(-0.958208\pi\) | ||
0.991394 | − | 0.130916i | \(-0.0417917\pi\) | |||||||
\(594\) | 4.47822 | + | 7.75650i | 0.183744 | + | 0.318253i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.708712 | + | 0.409175i | 0.0290300 | + | 0.0167605i | ||||
\(597\) | −30.7042 | −1.25664 | ||||||||
\(598\) | −1.87841 | + | 1.80750i | −0.0768139 | + | 0.0739142i | ||||
\(599\) | −6.62614 | −0.270737 | −0.135368 | − | 0.990795i | \(-0.543222\pi\) | ||||
−0.135368 | + | 0.990795i | \(0.543222\pi\) | |||||||
\(600\) | −20.0608 | − | 11.5821i | −0.818979 | − | 0.472837i | ||||
\(601\) | −6.18693 | + | 10.7161i | −0.252370 | + | 0.437118i | −0.964178 | − | 0.265256i | \(-0.914543\pi\) |
0.711808 | + | 0.702374i | \(0.247877\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.4322i | 0.872785i | ||||||||
\(604\) | −18.8085 | + | 10.8591i | −0.765308 | + | 0.441851i | ||||
\(605\) | −1.73049 | + | 0.999100i | −0.0703545 | + | 0.0406192i | ||||
\(606\) | 6.64215i | 0.269819i | ||||||||
\(607\) | −9.87386 | − | 17.1020i | −0.400768 | − | 0.694150i | 0.593051 | − | 0.805165i | \(-0.297923\pi\) |
−0.993819 | + | 0.111015i | \(0.964590\pi\) | |||||||
\(608\) | 3.24773 | − | 5.62523i | 0.131713 | − | 0.228133i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.07803 | 0.124626 | ||||||||
\(611\) | −8.29129 | − | 33.5088i | −0.335430 | − | 1.35562i | ||||
\(612\) | 25.7477 | 1.04079 | ||||||||
\(613\) | −15.8085 | − | 9.12705i | −0.638500 | − | 0.368638i | 0.145536 | − | 0.989353i | \(-0.453509\pi\) |
−0.784037 | + | 0.620715i | \(0.786843\pi\) | |||||||
\(614\) | −3.54356 | + | 6.13763i | −0.143006 | + | 0.247694i | ||||
\(615\) | −5.00000 | − | 8.66025i | −0.201619 | − | 0.349215i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9174 | + | 8.61258i | −0.600553 | + | 0.346729i | −0.769259 | − | 0.638937i | \(-0.779374\pi\) |
0.168706 | + | 0.985666i | \(0.446041\pi\) | |||||||
\(618\) | 5.06080 | − | 2.92185i | 0.203575 | − | 0.117534i | ||||
\(619\) | − | 19.3386i | − | 0.777284i | −0.921389 | − | 0.388642i | \(-0.872944\pi\) | ||
0.921389 | − | 0.388642i | \(-0.127056\pi\) | |||||||
\(620\) | 3.54356 | + | 6.13763i | 0.142313 | + | 0.246493i | ||||
\(621\) | 3.95644 | − | 6.85275i | 0.158766 | − | 0.274992i | ||||
\(622\) | 10.5000 | + | 6.06218i | 0.421012 | + | 0.243071i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −19.4782 | − | 20.2424i | −0.779753 | − | 0.810343i | ||||
\(625\) | 21.9129 | 0.876515 | ||||||||
\(626\) | −2.66970 | − | 1.54135i | −0.106703 | − | 0.0616048i | ||||
\(627\) | 7.50000 | − | 12.9904i | 0.299521 | − | 0.518786i | ||||
\(628\) | 0.856629 | + | 1.48372i | 0.0341832 | + | 0.0592071i | ||||
\(629\) | − | 20.7846i | − | 0.828737i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.9347 | − | 13.8187i | 0.952824 | − | 0.550113i | 0.0588668 | − | 0.998266i | \(-0.481251\pi\) |
0.893957 | + | 0.448153i | \(0.147918\pi\) | |||||||
\(632\) | − | 10.3923i | − | 0.413384i | ||||||
\(633\) | −14.7695 | − | 25.5815i | −0.587035 | − | 1.01677i | ||||
\(634\) | −4.23049 | + | 7.32743i | −0.168014 | + | 0.291009i | ||||
\(635\) | −2.75227 | − | 1.58903i | −0.109221 | − | 0.0630586i | ||||
\(636\) | 30.8258 | 1.22232 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.1652 | 0.481623 | ||||||||
\(639\) | −18.1652 | − | 10.4877i | −0.718602 | − | 0.414885i | ||||
\(640\) | 2.52178 | − | 4.36785i | 0.0996821 | − | 0.172654i | ||||
\(641\) | −14.6869 | − | 25.4385i | −0.580099 | − | 1.00476i | −0.995467 | − | 0.0951074i | \(-0.969681\pi\) |
0.415368 | − | 0.909653i | \(-0.363653\pi\) | |||||||
\(642\) | − | 6.64215i | − | 0.262145i | ||||||
\(643\) | −39.2477 | + | 22.6597i | −1.54778 | + | 0.893611i | −0.549468 | + | 0.835515i | \(0.685170\pi\) |
−0.998311 | + | 0.0580962i | \(0.981497\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.9536i | 0.470671i | ||||||||
\(646\) | 0.939205 | + | 1.62675i | 0.0369525 | + | 0.0640036i | ||||
\(647\) | 17.5390 | − | 30.3785i | 0.689530 | − | 1.19430i | −0.282460 | − | 0.959279i | \(-0.591151\pi\) |
0.971990 | − | 0.235022i | \(-0.0755161\pi\) | |||||||
\(648\) | 0.626136 | + | 0.361500i | 0.0245970 | + | 0.0142011i | ||||
\(649\) | −48.2867 | −1.89542 | ||||||||
\(650\) | −7.58258 | − | 2.18890i | −0.297413 | − | 0.0858558i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.7477 | − | 6.20520i | −0.420913 | − | 0.243015i | ||||
\(653\) | −7.89564 | + | 13.6757i | −0.308980 | + | 0.535170i | −0.978140 | − | 0.207949i | \(-0.933321\pi\) |
0.669159 | + | 0.743119i | \(0.266654\pi\) | |||||||
\(654\) | −5.06080 | − | 8.76555i | −0.197893 | − | 0.342760i | ||||
\(655\) | − | 7.93725i | − | 0.310134i | ||||||
\(656\) | −18.9564 | + | 10.9445i | −0.740125 | + | 0.427311i | ||||
\(657\) | −14.3739 | + | 8.29875i | −0.560778 | + | 0.323765i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.00000 | − | 5.19615i | −0.116863 | − | 0.202413i | 0.801660 | − | 0.597781i | \(-0.203951\pi\) |
−0.918523 | + | 0.395367i | \(0.870617\pi\) | |||||||
\(660\) | 4.47822 | − | 7.75650i | 0.174314 | − | 0.301922i | ||||
\(661\) | 43.7477 | + | 25.2578i | 1.70159 | + | 0.982413i | 0.944155 | + | 0.329502i | \(0.106881\pi\) |
0.757434 | + | 0.652911i | \(0.226453\pi\) | |||||||
\(662\) | −11.3739 | −0.442058 | ||||||||
\(663\) | 29.3085 | − | 7.25198i | 1.13825 | − | 0.281644i | ||||
\(664\) | 12.1652 | 0.472099 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.58258 | + | 13.1334i | −0.293819 | + | 0.508909i | ||||
\(667\) | −5.37386 | − | 9.30780i | −0.208077 | − | 0.360400i | ||||
\(668\) | − | 26.2867i | − | 1.01706i | ||||||
\(669\) | −45.8739 | + | 26.4853i | −1.77359 | + | 1.02398i | ||||
\(670\) | −0.808522 | + | 0.466801i | −0.0312359 | + | 0.0180341i | ||||
\(671\) | − | 57.8251i | − | 2.23231i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2477 | + | 22.9457i | −0.510662 | + | 0.884493i | 0.489261 | + | 0.872137i | \(0.337266\pi\) |
−0.999924 | + | 0.0123559i | \(0.996067\pi\) | |||||||
\(674\) | −3.93920 | − | 2.27430i | −0.151732 | − | 0.0876028i | ||||
\(675\) | 23.9564 | 0.922084 | ||||||||
\(676\) | −19.7042 | − | 12.4104i | −0.757853 | − | 0.477323i | ||||
\(677\) | 29.2087 | 1.12258 | 0.561291 | − | 0.827619i | \(-0.310305\pi\) | ||||
0.561291 | + | 0.827619i | \(0.310305\pi\) | |||||||
\(678\) | −11.6869 | − | 6.74745i | −0.448834 | − | 0.259134i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.18693 | + | 2.05583i | 0.0455168 | + | 0.0788373i | ||||
\(681\) | − | 24.7056i | − | 0.946719i | ||||||
\(682\) | −13.4347 | + | 7.75650i | −0.514440 | + | 0.297012i | ||||
\(683\) | 26.2913 | − | 15.1793i | 1.00601 | − | 0.580819i | 0.0959878 | − | 0.995383i | \(-0.469399\pi\) |
0.910020 | + | 0.414563i | \(0.136066\pi\) | |||||||
\(684\) | 11.7629i | 0.449764i | ||||||||
\(685\) | 2.73049 | + | 4.72935i | 0.104327 | + | 0.180699i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.7477 | + | 9.66930i | 0.638966 | + | 0.368907i | ||||
\(688\) | 26.1652 | 0.997537 | ||||||||
\(689\) | 21.5780 | − | 5.33918i | 0.822057 | − | 0.203406i | ||||
\(690\) | 0.921970 | 0.0350988 | ||||||||
\(691\) | 8.93466 | + | 5.15843i | 0.339890 | + | 0.196236i | 0.660224 | − | 0.751069i | \(-0.270462\pi\) |
−0.320333 | + | 0.947305i | \(0.603795\pi\) | |||||||
\(692\) | −17.6869 | + | 30.6347i | −0.672356 | + | 1.16456i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.20520i | − | 0.235546i | ||||||
\(695\) | 1.50000 | − | 0.866025i | 0.0568982 | − | 0.0328502i | ||||
\(696\) | −28.4347 | + | 16.4168i | −1.07781 | + | 0.622276i | ||||
\(697\) | − | 23.5257i | − | 0.891100i | ||||||
\(698\) | −4.81307 | − | 8.33648i | −0.182177 | − | 0.315540i | ||||
\(699\) | −22.2695 | + | 38.5719i | −0.842310 | + | 1.45892i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9129 | −0.525482 | −0.262741 | − | 0.964866i | \(-0.584627\pi\) | ||||
−0.262741 | + | 0.964866i | \(0.584627\pi\) | |||||||
\(702\) | −7.91288 | − | 2.28425i | −0.298652 | − | 0.0862135i | ||||
\(703\) | 9.49545 | 0.358128 | ||||||||
\(704\) | −11.6044 | − | 6.69978i | −0.437356 | − | 0.252507i | ||||
\(705\) | −6.10436 | + | 10.5731i | −0.229903 | + | 0.398204i | ||||
\(706\) | 4.14792 | + | 7.18440i | 0.156109 | + | 0.270389i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 53.3258 | − | 30.7876i | 2.00410 | − | 1.15707i | ||||
\(709\) | −13.1869 | + | 7.61348i | −0.495246 | + | 0.285930i | −0.726748 | − | 0.686904i | \(-0.758969\pi\) |
0.231502 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(710\) | − | 0.913701i | − | 0.0342906i | ||||||
\(711\) | 14.3739 | + | 24.8963i | 0.539062 | + | 0.933683i | ||||
\(712\) | 13.9782 | − | 24.2110i | 0.523856 | − | 0.907345i | ||||
\(713\) | 11.8693 | + | 6.85275i | 0.444509 | + | 0.256638i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.79129 | − | 6.20520i | 0.0669904 | − | 0.232061i | ||||
\(716\) | −16.1216 | −0.602492 | ||||||||
\(717\) | −31.9782 | − | 18.4626i | −1.19425 | − | 0.689500i | ||||
\(718\) | −0.126136 | + | 0.218475i | −0.00470737 | + | 0.00815341i | ||||
\(719\) | 12.0826 | + | 20.9276i | 0.450604 | + | 0.780469i | 0.998424 | − | 0.0561274i | \(-0.0178753\pi\) |
−0.547820 | + | 0.836597i | \(0.684542\pi\) | |||||||
\(720\) | 6.10985i | 0.227701i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.77405 | − | 3.91100i | 0.252104 | − | 0.145552i | ||||
\(723\) | 54.9887i | 2.04505i | ||||||||
\(724\) | 8.20871 | + | 14.2179i | 0.305074 | + | 0.528404i | ||||
\(725\) | 16.2695 | − | 28.1796i | 0.604234 | − | 1.04656i | ||||
\(726\) | 4.83030 | + | 2.78878i | 0.179269 | + | 0.103501i | ||||
\(727\) | 0.252273 | 0.00935628 | 0.00467814 | − | 0.999989i | \(-0.498511\pi\) | ||||
0.00467814 | + | 0.999989i | \(0.498511\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | −0.626136 | − | 0.361500i | −0.0231744 | − | 0.0133797i | ||||
\(731\) | −14.0608 | + | 24.3540i | −0.520057 | + | 0.900766i | ||||
\(732\) | 36.8693 | + | 63.8595i | 1.36273 | + | 2.36032i | ||||
\(733\) | − | 16.9590i | − | 0.626395i | −0.949688 | − | 0.313198i | \(-0.898600\pi\) | ||
0.949688 | − | 0.313198i | \(-0.101400\pi\) | |||||||
\(734\) | 7.12159 | − | 4.11165i | 0.262863 | − | 0.151764i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.50030i | − | 0.276465i | ||||||
\(737\) | 8.76951 | + | 15.1892i | 0.323029 | + | 0.559503i | ||||
\(738\) | −8.58258 | + | 14.8655i | −0.315929 | + | 0.547205i | ||||
\(739\) | 16.7477 | + | 9.66930i | 0.616075 | + | 0.355691i | 0.775339 | − | 0.631545i | \(-0.217579\pi\) |
−0.159264 | + | 0.987236i | \(0.550912\pi\) | |||||||
\(740\) | 5.66970 | 0.208422 | ||||||||
\(741\) | 3.31307 | + | 13.3896i | 0.121709 | + | 0.491879i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.8521 | + | 17.2351i | 1.09517 | + | 0.632295i | 0.934947 | − | 0.354787i | \(-0.115446\pi\) |
0.160219 | + | 0.987081i | \(0.448780\pi\) | |||||||
\(744\) | 20.9347 | − | 36.2599i | 0.767502 | − | 1.32935i | ||||
\(745\) | −0.104356 | − | 0.180750i | −0.00382331 | − | 0.00662217i | ||||
\(746\) | 14.7146i | 0.538738i | ||||||||
\(747\) | −29.1434 | + | 16.8259i | −1.06630 | + | 0.615629i | ||||
\(748\) | 18.2477 | − | 10.5353i | 0.667203 | − | 0.385210i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.85208 | + | 4.93995i | 0.104143 | + | 0.180382i | ||||
\(751\) | −11.8739 | + | 20.5661i | −0.433283 | + | 0.750469i | −0.997154 | − | 0.0753944i | \(-0.975978\pi\) |
0.563870 | + | 0.825863i | \(0.309312\pi\) | |||||||
\(752\) | 23.1434 | + | 13.3618i | 0.843952 | + | 0.487256i | ||||
\(753\) | 7.91288 | 0.288361 | ||||||||
\(754\) | −8.06080 | + | 7.75650i | −0.293557 | + | 0.282475i | ||||
\(755\) | 5.53901 | 0.201585 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.00000 | + | 5.19615i | −0.109037 | + | 0.188857i | −0.915380 | − | 0.402590i | \(-0.868110\pi\) |
0.806343 | + | 0.591448i | \(0.201443\pi\) | |||||||
\(758\) | 6.47822 | + | 11.2206i | 0.235300 | + | 0.407551i | ||||
\(759\) | − | 17.3205i | − | 0.628695i | ||||||
\(760\) | −0.939205 | + | 0.542250i | −0.0340685 | + | 0.0196695i | ||||
\(761\) | −11.2259 | + | 6.48130i | −0.406940 | + | 0.234947i | −0.689474 | − | 0.724310i | \(-0.742158\pi\) |
0.282534 | + | 0.959257i | \(0.408825\pi\) | |||||||
\(762\) | 8.87086i | 0.321357i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.8739 | − | 22.2982i | 0.465760 | − | 0.806720i | ||||
\(765\) | −5.68693 | − | 3.28335i | −0.205611 | − | 0.118710i | ||||
\(766\) | 0.582576 | 0.0210493 | ||||||||
\(767\) | 31.9955 | − | 30.7876i | 1.15529 | − | 1.11168i | ||||
\(768\) | 5.00000 | 0.180422 | ||||||||
\(769\) | 8.12614 | + | 4.69163i | 0.293036 | + | 0.169184i | 0.639310 | − | 0.768949i | \(-0.279220\pi\) |
−0.346274 | + | 0.938133i | \(0.612553\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.03901 | + | 12.1919i | 0.253504 | + | 0.439082i | ||||
\(772\) | − | 34.6410i | − | 1.24676i | ||||||
\(773\) | −16.8303 | + | 9.71698i | −0.605344 | + | 0.349495i | −0.771141 | − | 0.636664i | \(-0.780314\pi\) |
0.165797 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(774\) | 17.7695 | − | 10.2592i | 0.638712 | − | 0.368760i | ||||
\(775\) | 41.4938i | 1.49050i | ||||||||
\(776\) | −6.31307 | − | 10.9346i | −0.226626 | − | 0.392528i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.130682 | + | 0.0754495i | 0.00468519 | + | 0.00270499i | ||||
\(779\) | 10.7477 | 0.385077 | ||||||||
\(780\) | 1.97822 | + | 7.99488i | 0.0708316 | + | 0.286263i | ||||
\(781\) | −17.1652 | −0.614217 | ||||||||
\(782\) | 1.87841 | + | 1.08450i | 0.0671718 | + | 0.0387816i | ||||
\(783\) | 16.9782 | − | 29.4071i | 0.606752 | − | 1.05093i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 0.436950i | − | 0.0155954i | ||||||
\(786\) | −19.1869 | + | 11.0776i | −0.684375 | + | 0.395124i | ||||
\(787\) | −22.7477 | + | 13.1334i | −0.810869 | + | 0.468155i | −0.847258 | − | 0.531182i | \(-0.821748\pi\) |
0.0363886 | + | 0.999338i | \(0.488415\pi\) | |||||||
\(788\) | − | 4.09175i | − | 0.145763i | ||||||
\(789\) | −13.0218 | − | 22.5544i | −0.463588 | − | 0.802957i | ||||
\(790\) | −0.626136 | + | 1.08450i | −0.0222769 | + | 0.0385848i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −32.5390 | −1.15622 | ||||||||
\(793\) | 36.8693 | + | 38.3157i | 1.30927 | + | 1.36063i | ||||
\(794\) | 14.8348 | 0.526469 | ||||||||
\(795\) | −6.80852 | − | 3.93090i | −0.241473 | − | 0.139415i | ||||
\(796\) | 9.85208 | − | 17.0643i | 0.349198 | − | 0.604828i | ||||
\(797\) | −6.00000 | − | 10.3923i | −0.212531 | − | 0.368114i | 0.739975 | − | 0.672634i | \(-0.234837\pi\) |
−0.952506 | + | 0.304520i | \(0.901504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.8739 | + | 14.3609i | −0.879974 | + | 0.508053i | ||||
\(800\) | 19.6652 | − | 11.3537i | 0.695268 | − | 0.401413i | ||||
\(801\) | 77.3345i | 2.73248i | ||||||||
\(802\) | −7.14792 | − | 12.3806i | −0.252402 | − | 0.437173i | ||||
\(803\) | −6.79129 | + | 11.7629i | −0.239659 | + | 0.415102i | ||||
\(804\) | −19.3693 | − | 11.1829i | −0.683103 | − | 0.394390i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.95644 | − | 13.7055i | 0.139360 | − | 0.482756i | ||||
\(807\) | 44.0780 | 1.55162 | ||||||||
\(808\) | −7.81307 | − | 4.51088i | −0.274863 | − | 0.158692i | ||||
\(809\) | −26.6216 | + | 46.1099i | −0.935965 | + | 1.62114i | −0.163062 | + | 0.986616i | \(0.552137\pi\) |
−0.772904 | + | 0.634524i | \(0.781196\pi\) | |||||||
\(810\) | −0.0435608 | − | 0.0754495i | −0.00153057 | − | 0.00265102i | ||||
\(811\) | − | 27.6374i | − | 0.970479i | −0.874381 | − | 0.485240i | \(-0.838732\pi\) | ||
0.874381 | − | 0.485240i | \(-0.161268\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.0562 | + | 17.9303i | −1.08919 | + | 0.628844i | ||||
\(814\) | 12.4104i | 0.434985i | ||||||||
\(815\) | 1.58258 | + | 2.74110i | 0.0554352 | + | 0.0960166i | ||||
\(816\) | −11.6869 | + | 20.2424i | −0.409124 | + | 0.708624i | ||||
\(817\) | −11.1261 | − | 6.42368i | −0.389254 | − | 0.224736i | ||||
\(818\) | 3.79129 | 0.132559 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.41742 | 0.224106 | ||||||||
\(821\) | 10.9610 | + | 6.32833i | 0.382541 | + | 0.220860i | 0.678923 | − | 0.734209i | \(-0.262447\pi\) |
−0.296382 | + | 0.955069i | \(0.595780\pi\) | |||||||
\(822\) | 7.62159 | − | 13.2010i | 0.265834 | − | 0.460437i | ||||
\(823\) | 11.2477 | + | 19.4816i | 0.392071 | + | 0.679087i | 0.992723 | − | 0.120424i | \(-0.0384254\pi\) |
−0.600651 | + | 0.799511i | \(0.705092\pi\) | |||||||
\(824\) | 7.93725i | 0.276507i | ||||||||
\(825\) | 45.4129 | − | 26.2191i | 1.58107 | − | 0.912833i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 35.3839i | − | 1.23042i | −0.788364 | − | 0.615210i | \(-0.789071\pi\) | ||
0.788364 | − | 0.615210i | \(-0.210929\pi\) | |||||||
\(828\) | 6.79129 | + | 11.7629i | 0.236014 | + | 0.408787i | ||||
\(829\) | 17.1869 | − | 29.7686i | 0.596927 | − | 1.03391i | −0.396345 | − | 0.918102i | \(-0.629722\pi\) |
0.993272 | − | 0.115806i | \(-0.0369451\pi\) | |||||||
\(830\) | −1.26951 | − | 0.732950i | −0.0440652 | − | 0.0254411i | ||||
\(831\) | 32.7913 | 1.13752 | ||||||||
\(832\) | 11.9610 | − | 2.95958i | 0.414673 | − | 0.102605i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.18693 | − | 2.41733i | −0.144982 | − | 0.0837052i | ||||
\(835\) | −3.35208 | + | 5.80598i | −0.116004 | + | 0.200924i | ||||
\(836\) | 4.81307 | + | 8.33648i | 0.166463 | + | 0.288323i | ||||
\(837\) | 43.3013i | 1.49671i | ||||||||
\(838\) | 0.691478 | − | 0.399225i | 0.0238867 | − | 0.0137910i | ||||
\(839\) | 24.2305 | − | 13.9895i | 0.836530 | − | 0.482971i | −0.0195536 | − | 0.999809i | \(-0.506224\pi\) |
0.856083 | + | 0.516838i | \(0.172891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.56080 | − | 14.8277i | −0.295200 | − | 0.511301i | ||||
\(842\) | 0.956439 | − | 1.65660i | 0.0329611 | − | 0.0570903i | ||||
\(843\) | −74.0780 | − | 42.7690i | −2.55138 | − | 1.47304i | ||||
\(844\) | 18.9564 | 0.652508 | ||||||||
\(845\) | 2.76951 | + | 5.25378i | 0.0952740 | + | 0.180735i | ||||
\(846\) | 20.9564 | 0.720497 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.60436 | + | 14.9032i | −0.295475 | + | 0.511777i | ||||
\(849\) | 3.83485 | + | 6.64215i | 0.131612 | + | 0.227958i | ||||
\(850\) | 6.56670i | 0.225236i | ||||||||
\(851\) | 9.49545 | − | 5.48220i | 0.325500 | − | 0.187927i | ||||
\(852\) | 18.9564 | − | 10.9445i | 0.649437 | − | 0.374953i | ||||
\(853\) | 14.1425i | 0.484229i | 0.970248 | + | 0.242114i | \(0.0778409\pi\) | ||||
−0.970248 | + | 0.242114i | \(0.922159\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.50000 | − | 2.59808i | 0.0512989 | − | 0.0888523i | ||||
\(856\) | 7.81307 | + | 4.51088i | 0.267045 | + | 0.154179i | ||||
\(857\) | −15.4610 | −0.528137 | −0.264069 | − | 0.964504i | \(-0.585065\pi\) | ||||
−0.264069 | + | 0.964504i | \(0.585065\pi\) | |||||||
\(858\) | −17.5000 | + | 4.33013i | −0.597440 | + | 0.147828i | ||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | −6.64337 | − | 3.83555i | −0.226537 | − | 0.130791i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.91742 | − | 13.7134i | −0.269669 | − | 0.467080i | ||||
\(863\) | 45.4147i | 1.54594i | 0.634446 | + | 0.772968i | \(0.281228\pi\) | ||||
−0.634446 | + | 0.772968i | \(0.718772\pi\) | |||||||
\(864\) | 20.5218 | − | 11.8483i | 0.698165 | − | 0.403086i | ||||
\(865\) | 7.81307 | − | 4.51088i | 0.265652 | − | 0.153374i | ||||
\(866\) | 14.8456i | 0.504473i | ||||||||
\(867\) | 11.1652 | + | 19.3386i | 0.379188 | + | 0.656774i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.3739 | + | 11.7629i | 0.691136 | + | 0.399028i | ||||
\(870\) | 3.95644 | 0.134136 | ||||||||
\(871\) | −15.4955 | − | 4.47315i | −0.525043 | − | 0.151567i | ||||
\(872\) | 13.7477 | 0.465557 | ||||||||
\(873\) | 30.2477 | + | 17.4635i | 1.02373 | + | 0.591051i | ||||
\(874\) | −0.495454 | + | 0.858152i | −0.0167590 | + | 0.0290274i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 17.3205i | − | 0.585206i | ||||||
\(877\) | 2.75227 | − | 1.58903i | 0.0929377 | − | 0.0536576i | −0.452811 | − | 0.891607i | \(-0.649579\pi\) |
0.545749 | + | 0.837949i | \(0.316245\pi\) | |||||||
\(878\) | 8.12614 | − | 4.69163i | 0.274244 | − | 0.158335i | ||||
\(879\) | − | 7.11890i | − | 0.240115i | ||||||
\(880\) | 2.50000 | + | 4.33013i | 0.0842750 | + | 0.145969i | ||||
\(881\) | 8.29129 | − | 14.3609i | 0.279341 | − | 0.483832i | −0.691880 | − | 0.722012i | \(-0.743217\pi\) |
0.971221 | + | 0.238180i | \(0.0765508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.2432 | 0.984111 | 0.492056 | − | 0.870564i | \(-0.336246\pi\) | ||||
0.492056 | + | 0.870564i | \(0.336246\pi\) | |||||||
\(884\) | −5.37386 | + | 18.6156i | −0.180743 | + | 0.626111i | ||||
\(885\) | −15.7042 | −0.527890 | ||||||||
\(886\) | 6.00000 | + | 3.46410i | 0.201574 | + | 0.116379i | ||||
\(887\) | 11.2087 | − | 19.4141i | 0.376352 | − | 0.651860i | −0.614177 | − | 0.789169i | \(-0.710512\pi\) |
0.990528 | + | 0.137308i | \(0.0438451\pi\) | |||||||
\(888\) | −16.7477 | − | 29.0079i | −0.562017 | − | 0.973442i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.91742 | + | 1.68438i | −0.0977923 | + | 0.0564604i | ||||
\(891\) | −1.41742 | + | 0.818350i | −0.0474855 | + | 0.0274158i | ||||
\(892\) | − | 33.9935i | − | 1.13819i | ||||||
\(893\) | −6.56080 | − | 11.3636i | −0.219549 | − | 0.380269i | ||||
\(894\) | −0.291288 | + | 0.504525i | −0.00974212 | + | 0.0168739i | ||||
\(895\) | 3.56080 | + | 2.05583i | 0.119024 | + | 0.0687187i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.0436 | + | 11.4768i | 0.368734 | + | 0.383199i | ||||
\(898\) | 11.4955 | 0.383608 | ||||||||
\(899\) | 50.9347 | + | 29.4071i | 1.69877 | + | 0.980783i | ||||
\(900\) | −20.5608 | + | 35.6123i | −0.685360 | + | 1.18708i | ||||
\(901\) | −9.24773 | − | 16.0175i | −0.308086 | − | 0.533621i | ||||
\(902\) | 14.0471i | 0.467717i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.8739 | − | 9.16478i | 0.527957 | − | 0.304816i | ||||
\(905\) | − | 4.18710i | − | 0.139184i | ||||||
\(906\) | −7.73049 | − | 13.3896i | −0.256828 | − | 0.444840i | ||||
\(907\) | 20.5390 | − | 35.5746i | 0.681987 | − | 1.18124i | −0.292387 | − | 0.956300i | \(-0.594449\pi\) |
0.974374 | − | 0.224936i | \(-0.0722172\pi\) | |||||||
\(908\) | 13.7305 | + | 7.92730i | 0.455662 | + | 0.263077i | ||||
\(909\) | 24.9564 | 0.827753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.1216 | −1.42868 | −0.714341 | − | 0.699798i | \(-0.753273\pi\) | ||||
−0.714341 | + | 0.699798i | \(0.753273\pi\) | |||||||
\(912\) | −9.24773 | − | 5.33918i | −0.306223 | − | 0.176798i | ||||
\(913\) | −13.7695 | + | 23.8495i | −0.455704 | + | 0.789303i | ||||
\(914\) | −5.20871 | − | 9.02175i | −0.172289 | − | 0.298413i | ||||
\(915\) | − | 18.8063i | − | 0.621717i | ||||||
\(916\) | −10.7477 | + | 6.20520i | −0.355115 | + | 0.205026i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.85275i | 0.226175i | ||||||||
\(919\) | −12.9564 | − | 22.4412i | −0.427393 | − | 0.740267i | 0.569247 | − | 0.822166i | \(-0.307235\pi\) |
−0.996641 | + | 0.0818992i | \(0.973901\pi\) | |||||||
\(920\) | −0.626136 | + | 1.08450i | −0.0206431 | + | 0.0357549i | ||||
\(921\) | 37.5000 | + | 21.6506i | 1.23567 | + | 0.713413i | ||||
\(922\) | 2.12159 | 0.0698709 | ||||||||
\(923\) | 11.3739 | − | 10.9445i | 0.374375 | − | 0.360243i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.7477 | + | 16.5975i | 0.945219 | + | 0.545723i | ||||
\(926\) | 1.81307 | − | 3.14033i | 0.0595811 | − | 0.103198i | ||||
\(927\) | −10.9782 | − | 19.0148i | −0.360572 | − | 0.624529i | ||||
\(928\) | − | 32.1860i | − | 1.05656i | ||||||
\(929\) | 50.1606 | − | 28.9602i | 1.64572 | − | 0.950155i | 0.666969 | − | 0.745086i | \(-0.267592\pi\) |
0.978748 | − | 0.205069i | \(-0.0657418\pi\) | |||||||
\(930\) | −4.36932 | + | 2.52263i | −0.143276 | + | 0.0827202i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.2913 | − | 24.7532i | −0.468127 | − | 0.810819i | ||||
\(933\) | 37.0390 | − | 64.1535i | 1.21260 | − | 2.10029i | ||||
\(934\) | 11.9347 | + | 6.89048i | 0.390514 | + | 0.225463i | ||||
\(935\) | −5.37386 | −0.175744 | ||||||||
\(936\) | 21.5608 | − | 20.7469i | 0.704737 | − | 0.678133i | ||||
\(937\) | −20.4955 | −0.669557 | −0.334779 | − | 0.942297i | \(-0.608662\pi\) | ||||
−0.334779 | + | 0.942297i | \(0.608662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.41742 | + | 16.3115i | −0.307326 | + | 0.532304i | ||||
\(940\) | −3.91742 | − | 6.78518i | −0.127772 | − | 0.221308i | ||||
\(941\) | 39.3049i | 1.28130i | 0.767832 | + | 0.640651i | \(0.221335\pi\) | ||||
−0.767832 | + | 0.640651i | \(0.778665\pi\) | |||||||
\(942\) | −1.05625 | + | 0.609826i | −0.0344145 | + | 0.0198692i | ||||
\(943\) | 10.7477 | − | 6.20520i | 0.349994 | − | 0.202069i | ||||
\(944\) | 34.3749i | 1.11881i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.39564 | − | 14.5417i | 0.272966 | − | 0.472791i | ||||
\(947\) | −33.2305 | − | 19.1856i | −1.07985 | − | 0.623449i | −0.148991 | − | 0.988839i | \(-0.547603\pi\) |
−0.930855 | + | 0.365389i | \(0.880936\pi\) | |||||||
\(948\) | −30.0000 | −0.974355 | ||||||||
\(949\) | −3.00000 | − | 12.1244i | −0.0973841 | − | 0.393573i | ||||
\(950\) | −3.00000 | −0.0973329 | ||||||||
\(951\) | 44.7695 | + | 25.8477i | 1.45175 | + | 0.838169i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.50000 | + | 12.9904i | 0.242949 | + | 0.420800i | 0.961553 | − | 0.274620i | \(-0.0885520\pi\) |
−0.718604 | + | 0.695419i | \(0.755219\pi\) | |||||||
\(954\) | 13.4949i | 0.436914i | ||||||||
\(955\) | −5.68693 | + | 3.28335i | −0.184025 | + | 0.106247i | ||||
\(956\) | 20.5218 | − | 11.8483i | 0.663722 | − | 0.383200i | ||||
\(957\) | − | 74.3273i | − | 2.40266i | ||||||
\(958\) | −4.31307 | − | 7.47045i | −0.139349 | − | 0.241359i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.77405 | − | 2.17895i | −0.121807 | − | 0.0703253i | ||||
\(961\) | −44.0000 | −1.41935 | ||||||||
\(962\) | −7.91288 | − | 8.22330i | −0.255121 | − | 0.265130i | ||||
\(963\) | −24.9564 | −0.804210 | ||||||||
\(964\) | −30.5608 | − | 17.6443i | −0.984297 | − | 0.568284i | ||||
\(965\) | −4.41742 | + | 7.65120i | −0.142202 | + | 0.246301i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.8118i | − | 0.765735i | −0.923803 | − | 0.382867i | \(-0.874937\pi\) | ||
0.923803 | − | 0.382867i | \(-0.125063\pi\) | |||||||
\(968\) | −6.56080 | + | 3.78788i | −0.210872 | + | 0.121747i | ||||
\(969\) | 9.93920 | − | 5.73840i | 0.319293 | − | 0.184344i | ||||
\(970\) | 1.52145i | 0.0488508i | ||||||||
\(971\) | 11.1261 | + | 19.2710i | 0.357055 | + | 0.618437i | 0.987467 | − | 0.157823i | \(-0.0504476\pi\) |
−0.630413 | + | 0.776260i | \(0.717114\pi\) | |||||||
\(972\) | 14.4782 | − | 25.0770i | 0.464389 | − | 0.804346i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −13.4174 | −0.429922 | ||||||||
\(975\) | −13.3739 | + | 46.3284i | −0.428306 | + | 1.48370i | ||||
\(976\) | −41.1652 | −1.31766 | ||||||||
\(977\) | −1.20417 | − | 0.695226i | −0.0385247 | − | 0.0222422i | 0.480614 | − | 0.876932i | \(-0.340414\pi\) |
−0.519139 | + | 0.854690i | \(0.673747\pi\) | |||||||
\(978\) | 4.41742 | − | 7.65120i | 0.141254 | − | 0.244659i | ||||
\(979\) | 31.6434 | + | 54.8079i | 1.01133 | + | 1.75167i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.9347 | + | 19.0148i | −1.05152 | + | 0.607097i | ||||
\(982\) | −1.63068 | + | 0.941475i | −0.0520372 | + | 0.0300437i | ||||
\(983\) | − | 19.8908i | − | 0.634418i | −0.948356 | − | 0.317209i | \(-0.897254\pi\) | ||
0.948356 | − | 0.317209i | \(-0.102746\pi\) | |||||||
\(984\) | −18.9564 | − | 32.8335i | −0.604309 | − | 1.04669i | ||||
\(985\) | −0.521780 | + | 0.903750i | −0.0166253 | + | 0.0287959i | ||||
\(986\) | 8.06080 | + | 4.65390i | 0.256708 | + | 0.148210i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.50455 | − | 2.45505i | −0.270566 | − | 0.0781056i | ||||
\(989\) | −14.8348 | −0.471721 | ||||||||
\(990\) | 3.39564 | + | 1.96048i | 0.107921 | + | 0.0623080i | ||||
\(991\) | 20.1869 | − | 34.9648i | 0.641259 | − | 1.11069i | −0.343893 | − | 0.939009i | \(-0.611746\pi\) |
0.985152 | − | 0.171684i | \(-0.0549209\pi\) | |||||||
\(992\) | 20.5218 | + | 35.5448i | 0.651567 | + | 1.12855i | ||||
\(993\) | 69.4926i | 2.20528i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.35208 | + | 2.51268i | −0.137970 | + | 0.0796572i | ||||
\(996\) | − | 35.1178i | − | 1.11275i | ||||||
\(997\) | −7.03901 | − | 12.1919i | −0.222928 | − | 0.386122i | 0.732768 | − | 0.680479i | \(-0.238228\pi\) |
−0.955696 | + | 0.294356i | \(0.904895\pi\) | |||||||
\(998\) | 4.20417 | − | 7.28183i | 0.133081 | − | 0.230502i | ||||
\(999\) | 30.0000 | + | 17.3205i | 0.949158 | + | 0.547997i |
(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 | 637.2.q.e.589.1 | yes | 4 | |
7.2 | even | 3 | 637.2.k.d.459.2 | 4 | |||
7.3 | odd | 6 | 637.2.u.d.30.2 | 4 | |||
7.4 | even | 3 | 637.2.u.e.30.2 | 4 | |||
7.5 | odd | 6 | 637.2.k.f.459.2 | 4 | |||
7.6 | odd | 2 | 637.2.q.f.589.1 | yes | 4 | ||
13.6 | odd | 12 | 8281.2.a.bs.1.3 | 4 | |||
13.7 | odd | 12 | 8281.2.a.bs.1.2 | 4 | |||
13.10 | even | 6 | inner | 637.2.q.e.491.1 | ✓ | 4 | |
91.6 | even | 12 | 8281.2.a.bq.1.3 | 4 | |||
91.10 | odd | 6 | 637.2.k.f.569.1 | 4 | |||
91.20 | even | 12 | 8281.2.a.bq.1.2 | 4 | |||
91.23 | even | 6 | 637.2.u.e.361.2 | 4 | |||
91.62 | odd | 6 | 637.2.q.f.491.1 | yes | 4 | ||
91.75 | odd | 6 | 637.2.u.d.361.2 | 4 | |||
91.88 | even | 6 | 637.2.k.d.569.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.d.459.2 | 4 | 7.2 | even | 3 | |||
637.2.k.d.569.1 | 4 | 91.88 | even | 6 | |||
637.2.k.f.459.2 | 4 | 7.5 | odd | 6 | |||
637.2.k.f.569.1 | 4 | 91.10 | odd | 6 | |||
637.2.q.e.491.1 | ✓ | 4 | 13.10 | even | 6 | inner | |
637.2.q.e.589.1 | yes | 4 | 1.1 | even | 1 | trivial | |
637.2.q.f.491.1 | yes | 4 | 91.62 | odd | 6 | ||
637.2.q.f.589.1 | yes | 4 | 7.6 | odd | 2 | ||
637.2.u.d.30.2 | 4 | 7.3 | odd | 6 | |||
637.2.u.d.361.2 | 4 | 91.75 | odd | 6 | |||
637.2.u.e.30.2 | 4 | 7.4 | even | 3 | |||
637.2.u.e.361.2 | 4 | 91.23 | even | 6 | |||
8281.2.a.bq.1.2 | 4 | 91.20 | even | 12 | |||
8281.2.a.bq.1.3 | 4 | 91.6 | even | 12 | |||
8281.2.a.bs.1.2 | 4 | 13.7 | odd | 12 | |||
8281.2.a.bs.1.3 | 4 | 13.6 | odd | 12 |