Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(199,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.22986704741655040229376.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(-0.337183 - 1.25838i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.199 |
Dual form | 1050.3.q.b.649.4 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 1.50000i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | 5.76140 | − | 3.97571i | 0.823057 | − | 0.567958i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −1.50000 | − | 2.59808i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.647280 | − | 1.12112i | 0.0588436 | − | 0.101920i | −0.835103 | − | 0.550094i | \(-0.814592\pi\) |
0.893947 | + | 0.448174i | \(0.147925\pi\) | |||||||
\(12\) | −1.73205 | − | 3.00000i | −0.144338 | − | 0.250000i | ||||
\(13\) | −3.22960 | −0.248431 | −0.124215 | − | 0.992255i | \(-0.539641\pi\) | ||||
−0.124215 | + | 0.992255i | \(0.539641\pi\) | |||||||
\(14\) | −4.24500 | + | 8.94315i | −0.303214 | + | 0.638797i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −15.1826 | + | 26.2970i | −0.893092 | + | 1.54688i | −0.0569439 | + | 0.998377i | \(0.518136\pi\) |
−0.836148 | + | 0.548504i | \(0.815198\pi\) | |||||||
\(18\) | 3.67423 | + | 2.12132i | 0.204124 | + | 0.117851i | ||||
\(19\) | −28.9470 | + | 16.7125i | −1.52352 | + | 0.879607i | −0.523912 | + | 0.851773i | \(0.675528\pi\) |
−0.999613 | + | 0.0278345i | \(0.991139\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.974040 | − | 12.0852i | −0.0463829 | − | 0.575484i | ||||
\(22\) | 1.83078i | 0.0832175i | ||||||||
\(23\) | −30.9462 | + | 17.8668i | −1.34549 | + | 0.776818i | −0.987607 | − | 0.156950i | \(-0.949834\pi\) |
−0.357881 | + | 0.933767i | \(0.616501\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.95544 | − | 2.28367i | 0.152132 | − | 0.0878336i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −1.12472 | − | 13.9547i | −0.0401687 | − | 0.498384i | ||||
\(29\) | 32.8033 | 1.13115 | 0.565574 | − | 0.824697i | \(-0.308655\pi\) | ||||
0.565574 | + | 0.824697i | \(0.308655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 39.5125 | + | 22.8125i | 1.27460 | + | 0.735888i | 0.975849 | − | 0.218444i | \(-0.0700981\pi\) |
0.298747 | + | 0.954332i | \(0.403431\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.12112 | − | 1.94184i | −0.0339734 | − | 0.0588436i | ||||
\(34\) | − | 42.9428i | − | 1.26302i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −34.6873 | + | 20.0267i | −0.937494 | + | 0.541262i | −0.889174 | − | 0.457570i | \(-0.848720\pi\) |
−0.0483201 | + | 0.998832i | \(0.515387\pi\) | |||||||
\(38\) | 23.6351 | − | 40.9372i | 0.621976 | − | 1.07729i | ||||
\(39\) | −2.79692 | + | 4.84440i | −0.0717158 | + | 0.124215i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.2993i | 1.03169i | 0.856682 | + | 0.515845i | \(0.172522\pi\) | ||||
−0.856682 | + | 0.515845i | \(0.827478\pi\) | |||||||
\(42\) | 9.73845 | + | 14.1125i | 0.231868 | + | 0.336012i | ||||
\(43\) | − | 55.4597i | − | 1.28976i | −0.764283 | − | 0.644881i | \(-0.776907\pi\) | ||
0.764283 | − | 0.644881i | \(-0.223093\pi\) | |||||||
\(44\) | −1.29456 | − | 2.24224i | −0.0294218 | − | 0.0509601i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25.2675 | − | 43.7646i | 0.549293 | − | 0.951403i | ||||
\(47\) | 30.3745 | + | 52.6102i | 0.646266 | + | 1.11937i | 0.984008 | + | 0.178127i | \(0.0570037\pi\) |
−0.337741 | + | 0.941239i | \(0.609663\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 17.3875 | − | 45.8113i | 0.354847 | − | 0.934924i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 26.2970 | + | 45.5477i | 0.515627 | + | 0.893092i | ||||
\(52\) | −3.22960 | + | 5.59383i | −0.0621077 | + | 0.107574i | ||||
\(53\) | −47.3438 | − | 27.3340i | −0.893280 | − | 0.515735i | −0.0182660 | − | 0.999833i | \(-0.505815\pi\) |
−0.875014 | + | 0.484098i | \(0.839148\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.2450 | + | 16.2957i | 0.200804 | + | 0.290995i | ||||
\(57\) | 57.8939i | 1.01568i | ||||||||
\(58\) | −40.1757 | + | 23.1954i | −0.692684 | + | 0.399921i | ||||
\(59\) | −11.4277 | − | 6.59780i | −0.193690 | − | 0.111827i | 0.400019 | − | 0.916507i | \(-0.369004\pi\) |
−0.593709 | + | 0.804680i | \(0.702337\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.1684 | − | 19.7271i | 0.560137 | − | 0.323395i | −0.193064 | − | 0.981186i | \(-0.561842\pi\) |
0.753200 | + | 0.657791i | \(0.228509\pi\) | |||||||
\(62\) | −64.5236 | −1.04070 | ||||||||
\(63\) | −18.9713 | − | 9.00500i | −0.301132 | − | 0.142937i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.74618 | + | 1.58551i | 0.0416087 | + | 0.0240228i | ||||
\(67\) | −34.7163 | − | 20.0434i | −0.518153 | − | 0.299156i | 0.218026 | − | 0.975943i | \(-0.430038\pi\) |
−0.736179 | + | 0.676787i | \(0.763372\pi\) | |||||||
\(68\) | 30.3651 | + | 52.5940i | 0.446546 | + | 0.773440i | ||||
\(69\) | 61.8924i | 0.896992i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46.4480 | 0.654198 | 0.327099 | − | 0.944990i | \(-0.393929\pi\) | ||||
0.327099 | + | 0.944990i | \(0.393929\pi\) | |||||||
\(72\) | 7.34847 | − | 4.24264i | 0.102062 | − | 0.0589256i | ||||
\(73\) | −68.2001 | + | 118.126i | −0.934247 | + | 1.61816i | −0.158277 | + | 0.987395i | \(0.550594\pi\) |
−0.775970 | + | 0.630769i | \(0.782739\pi\) | |||||||
\(74\) | 28.3220 | − | 49.0552i | 0.382730 | − | 0.662908i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 66.8501i | 0.879607i | ||||||||
\(77\) | −0.728012 | − | 9.03263i | −0.00945470 | − | 0.117307i | ||||
\(78\) | − | 7.91088i | − | 0.101422i | ||||||
\(79\) | −21.1511 | − | 36.6348i | −0.267736 | − | 0.463732i | 0.700541 | − | 0.713612i | \(-0.252942\pi\) |
−0.968277 | + | 0.249880i | \(0.919609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −29.9101 | − | 51.8059i | −0.364758 | − | 0.631779i | ||||
\(83\) | −1.53725 | −0.0185211 | −0.00926054 | − | 0.999957i | \(-0.502948\pi\) | ||||
−0.00926054 | + | 0.999957i | \(0.502948\pi\) | |||||||
\(84\) | −21.9062 | − | 10.3981i | −0.260788 | − | 0.123787i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 39.2160 | + | 67.9240i | 0.456000 | + | 0.789814i | ||||
\(87\) | 28.4085 | − | 49.2050i | 0.326534 | − | 0.565574i | ||||
\(88\) | 3.17101 | + | 1.83078i | 0.0360342 | + | 0.0208044i | ||||
\(89\) | 30.2844 | − | 17.4847i | 0.340274 | − | 0.196457i | −0.320119 | − | 0.947377i | \(-0.603723\pi\) |
0.660393 | + | 0.750920i | \(0.270390\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.6070 | + | 12.8400i | −0.204473 | + | 0.141098i | ||||
\(92\) | 71.4672i | 0.776818i | ||||||||
\(93\) | 68.4376 | − | 39.5125i | 0.735888 | − | 0.424865i | ||||
\(94\) | −74.4020 | − | 42.9560i | −0.791511 | − | 0.456979i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | − | 4.89898i | 0.0883883 | − | 0.0510310i | ||||
\(97\) | 150.516 | 1.55172 | 0.775858 | − | 0.630907i | \(-0.217317\pi\) | ||||
0.775858 | + | 0.630907i | \(0.217317\pi\) | |||||||
\(98\) | 11.0982 | + | 68.4020i | 0.113247 | + | 0.697979i | ||||
\(99\) | −3.88368 | −0.0392291 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 103.806 | + | 59.9325i | 1.02778 | + | 0.593391i | 0.916349 | − | 0.400381i | \(-0.131122\pi\) |
0.111434 | + | 0.993772i | \(0.464456\pi\) | |||||||
\(102\) | −64.4142 | − | 37.1895i | −0.631511 | − | 0.364603i | ||||
\(103\) | −49.8245 | − | 86.2986i | −0.483733 | − | 0.837851i | 0.516092 | − | 0.856533i | \(-0.327386\pi\) |
−0.999825 | + | 0.0186825i | \(0.994053\pi\) | |||||||
\(104\) | − | 9.13469i | − | 0.0878336i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 77.3122 | 0.729360 | ||||||||
\(107\) | −40.6950 | + | 23.4953i | −0.380327 | + | 0.219582i | −0.677961 | − | 0.735098i | \(-0.737136\pi\) |
0.297634 | + | 0.954680i | \(0.403803\pi\) | |||||||
\(108\) | −5.19615 | + | 9.00000i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −29.0802 | + | 50.3683i | −0.266791 | + | 0.462095i | −0.968031 | − | 0.250830i | \(-0.919297\pi\) |
0.701241 | + | 0.712925i | \(0.252630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 69.3746i | 0.624996i | ||||||||
\(112\) | −25.2951 | − | 12.0067i | −0.225849 | − | 0.107202i | ||||
\(113\) | 211.102i | 1.86816i | 0.357068 | + | 0.934078i | \(0.383776\pi\) | ||||
−0.357068 | + | 0.934078i | \(0.616224\pi\) | |||||||
\(114\) | −40.9372 | − | 70.9053i | −0.359098 | − | 0.621976i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 32.8033 | − | 56.8170i | 0.282787 | − | 0.489802i | ||||
\(117\) | 4.84440 | + | 8.39075i | 0.0414052 | + | 0.0717158i | ||||
\(118\) | 18.6614 | 0.158148 | ||||||||
\(119\) | 17.0762 | + | 211.869i | 0.143498 | + | 1.78041i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 59.6621 | + | 103.338i | 0.493075 | + | 0.854031i | ||||
\(122\) | −27.8983 | + | 48.3213i | −0.228675 | + | 0.396077i | ||||
\(123\) | 63.4490 | + | 36.6323i | 0.515845 | + | 0.297823i | ||||
\(124\) | 79.0250 | − | 45.6251i | 0.637298 | − | 0.367944i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 29.6025 | − | 2.38590i | 0.234940 | − | 0.0189357i | ||||
\(127\) | 90.2615i | 0.710720i | 0.934729 | + | 0.355360i | \(0.115642\pi\) | ||||
−0.934729 | + | 0.355360i | \(0.884358\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −83.1896 | − | 48.0296i | −0.644881 | − | 0.372322i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −174.806 | + | 100.924i | −1.33440 | + | 0.770414i | −0.985970 | − | 0.166923i | \(-0.946617\pi\) |
−0.348426 | + | 0.937336i | \(0.613284\pi\) | |||||||
\(132\) | −4.48449 | −0.0339734 | ||||||||
\(133\) | −100.331 | + | 211.372i | −0.754368 | + | 1.58927i | ||||
\(134\) | 56.6914 | 0.423070 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −74.3791 | − | 42.9428i | −0.546905 | − | 0.315756i | ||||
\(137\) | 0.00352554 | + | 0.00203547i | 2.57339e−5 | + | 1.48575e-5i | 0.500013 | − | 0.866018i | \(-0.333329\pi\) |
−0.499987 | + | 0.866033i | \(0.666662\pi\) | |||||||
\(138\) | −43.7646 | − | 75.8024i | −0.317134 | − | 0.549293i | ||||
\(139\) | − | 115.950i | − | 0.834169i | −0.908868 | − | 0.417085i | \(-0.863052\pi\) | ||
0.908868 | − | 0.417085i | \(-0.136948\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 105.220 | 0.746244 | ||||||||
\(142\) | −56.8870 | + | 32.8437i | −0.400613 | + | 0.231294i | ||||
\(143\) | −2.09046 | + | 3.62078i | −0.0146186 | + | 0.0253201i | ||||
\(144\) | −6.00000 | + | 10.3923i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 192.899i | − | 1.32123i | ||||||
\(147\) | −53.6589 | − | 65.7550i | −0.365027 | − | 0.447313i | ||||
\(148\) | 80.1068i | 0.541262i | ||||||||
\(149\) | −2.59675 | − | 4.49770i | −0.0174278 | − | 0.0301859i | 0.857180 | − | 0.515017i | \(-0.172214\pi\) |
−0.874608 | + | 0.484831i | \(0.838881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 80.3710 | − | 139.207i | 0.532258 | − | 0.921899i | −0.467032 | − | 0.884240i | \(-0.654677\pi\) |
0.999291 | − | 0.0376583i | \(-0.0119898\pi\) | |||||||
\(152\) | −47.2702 | − | 81.8744i | −0.310988 | − | 0.538647i | ||||
\(153\) | 91.0954 | 0.595395 | ||||||||
\(154\) | 7.27866 | + | 10.5479i | 0.0472640 | + | 0.0684928i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.59383 | + | 9.68881i | 0.0358579 | + | 0.0621077i | ||||
\(157\) | 47.6157 | − | 82.4728i | 0.303285 | − | 0.525305i | −0.673593 | − | 0.739102i | \(-0.735250\pi\) |
0.976878 | + | 0.213798i | \(0.0685833\pi\) | |||||||
\(158\) | 51.8095 | + | 29.9122i | 0.327908 | + | 0.189318i | ||||
\(159\) | −82.0019 | + | 47.3438i | −0.515735 | + | 0.297760i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −107.260 | + | 225.971i | −0.666214 | + | 1.40355i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | −213.473 | + | 123.249i | −1.30965 | + | 0.756128i | −0.982038 | − | 0.188683i | \(-0.939578\pi\) |
−0.327615 | + | 0.944811i | \(0.606245\pi\) | |||||||
\(164\) | 73.2645 | + | 42.2993i | 0.446735 | + | 0.257923i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.88274 | − | 1.08700i | 0.0113418 | − | 0.00654819i | ||||
\(167\) | 14.9445 | 0.0894879 | 0.0447439 | − | 0.998998i | \(-0.485753\pi\) | ||||
0.0447439 | + | 0.998998i | \(0.485753\pi\) | |||||||
\(168\) | 34.1820 | − | 2.75500i | 0.203464 | − | 0.0163988i | ||||
\(169\) | −158.570 | −0.938282 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 86.8409 | + | 50.1376i | 0.507841 | + | 0.293202i | ||||
\(172\) | −96.0591 | − | 55.4597i | −0.558483 | − | 0.322440i | ||||
\(173\) | −83.8331 | − | 145.203i | −0.484584 | − | 0.839325i | 0.515259 | − | 0.857035i | \(-0.327696\pi\) |
−0.999843 | + | 0.0177099i | \(0.994362\pi\) | |||||||
\(174\) | 80.3513i | 0.461789i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.17824 | −0.0294218 | ||||||||
\(177\) | −19.7934 | + | 11.4277i | −0.111827 | + | 0.0645635i | ||||
\(178\) | −24.7271 | + | 42.8286i | −0.138916 | + | 0.240610i | ||||
\(179\) | 33.4724 | − | 57.9759i | 0.186997 | − | 0.323888i | −0.757251 | − | 0.653124i | \(-0.773458\pi\) |
0.944248 | + | 0.329236i | \(0.106791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.9109i | − | 0.137629i | −0.997629 | − | 0.0688146i | \(-0.978078\pi\) | ||
0.997629 | − | 0.0688146i | \(-0.0219217\pi\) | |||||||
\(182\) | 13.7097 | − | 28.8828i | 0.0753278 | − | 0.158697i | ||||
\(183\) | − | 68.3367i | − | 0.373425i | ||||||
\(184\) | −50.5350 | − | 87.5291i | −0.274647 | − | 0.475702i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −55.8791 | + | 96.7854i | −0.300425 | + | 0.520352i | ||||
\(187\) | 19.6547 | + | 34.0430i | 0.105106 | + | 0.182048i | ||||
\(188\) | 121.498 | 0.646266 | ||||||||
\(189\) | −29.9371 | + | 20.6584i | −0.158397 | + | 0.109304i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.80231 | + | 11.7819i | 0.0356142 | + | 0.0616856i | 0.883283 | − | 0.468840i | \(-0.155328\pi\) |
−0.847669 | + | 0.530526i | \(0.821995\pi\) | |||||||
\(192\) | −6.92820 | + | 12.0000i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −157.978 | − | 91.2089i | −0.818541 | − | 0.472585i | 0.0313718 | − | 0.999508i | \(-0.490012\pi\) |
−0.849913 | + | 0.526923i | \(0.823346\pi\) | |||||||
\(194\) | −184.344 | + | 106.431i | −0.950228 | + | 0.548615i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −61.9600 | − | 75.9273i | −0.316122 | − | 0.387384i | ||||
\(197\) | 286.679i | 1.45522i | 0.685989 | + | 0.727612i | \(0.259370\pi\) | ||||
−0.685989 | + | 0.727612i | \(0.740630\pi\) | |||||||
\(198\) | 4.75652 | − | 2.74618i | 0.0240228 | − | 0.0138696i | ||||
\(199\) | 2.74117 | + | 1.58262i | 0.0137747 | + | 0.00795285i | 0.506872 | − | 0.862022i | \(-0.330802\pi\) |
−0.493097 | + | 0.869974i | \(0.664135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −60.1303 | + | 34.7163i | −0.299156 | + | 0.172718i | ||||
\(202\) | −169.515 | −0.839181 | ||||||||
\(203\) | 188.993 | − | 130.416i | 0.931000 | − | 0.642445i | ||||
\(204\) | 105.188 | 0.515627 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 122.045 | + | 70.4625i | 0.592450 | + | 0.342051i | ||||
\(207\) | 92.8387 | + | 53.6004i | 0.448496 | + | 0.258939i | ||||
\(208\) | 6.45920 | + | 11.1877i | 0.0310539 | + | 0.0537869i | ||||
\(209\) | 43.2708i | 0.207037i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −179.324 | −0.849878 | −0.424939 | − | 0.905222i | \(-0.639705\pi\) | ||||
−0.424939 | + | 0.905222i | \(0.639705\pi\) | |||||||
\(212\) | −94.6877 | + | 54.6679i | −0.446640 | + | 0.257868i | ||||
\(213\) | 40.2252 | − | 69.6720i | 0.188851 | − | 0.327099i | ||||
\(214\) | 33.2273 | − | 57.5514i | 0.155268 | − | 0.268932i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | 318.343 | − | 25.6578i | 1.46702 | − | 0.118239i | ||||
\(218\) | − | 82.2512i | − | 0.377299i | ||||||
\(219\) | 118.126 | + | 204.600i | 0.539388 | + | 0.934247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 49.0336 | − | 84.9288i | 0.221872 | − | 0.384293i | ||||
\(222\) | −49.0552 | − | 84.9661i | −0.220969 | − | 0.382730i | ||||
\(223\) | 71.3345 | 0.319886 | 0.159943 | − | 0.987126i | \(-0.448869\pi\) | ||||
0.159943 | + | 0.987126i | \(0.448869\pi\) | |||||||
\(224\) | 39.4700 | − | 3.18120i | 0.176205 | − | 0.0142018i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −149.271 | − | 258.546i | −0.660493 | − | 1.14401i | ||||
\(227\) | 71.2698 | − | 123.443i | 0.313964 | − | 0.543802i | −0.665253 | − | 0.746618i | \(-0.731676\pi\) |
0.979217 | + | 0.202817i | \(0.0650096\pi\) | |||||||
\(228\) | 100.275 | + | 57.8939i | 0.439804 | + | 0.253921i | ||||
\(229\) | −109.001 | + | 62.9320i | −0.475989 | + | 0.274812i | −0.718743 | − | 0.695276i | \(-0.755282\pi\) |
0.242755 | + | 0.970088i | \(0.421949\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1794 | − | 6.73047i | −0.0613828 | − | 0.0291362i | ||||
\(232\) | 92.7817i | 0.399921i | ||||||||
\(233\) | −142.258 | + | 82.1326i | −0.610549 | + | 0.352500i | −0.773180 | − | 0.634186i | \(-0.781335\pi\) |
0.162631 | + | 0.986687i | \(0.448002\pi\) | |||||||
\(234\) | −11.8663 | − | 6.85102i | −0.0507108 | − | 0.0292779i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.8555 | + | 13.1956i | −0.0968452 | + | 0.0559136i | ||||
\(237\) | −73.2697 | −0.309155 | ||||||||
\(238\) | −170.728 | − | 247.411i | −0.717344 | − | 1.03954i | ||||
\(239\) | 50.4246 | 0.210982 | 0.105491 | − | 0.994420i | \(-0.466359\pi\) | ||||
0.105491 | + | 0.994420i | \(0.466359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −169.006 | − | 97.5757i | −0.701270 | − | 0.404879i | 0.106550 | − | 0.994307i | \(-0.466020\pi\) |
−0.807820 | + | 0.589429i | \(0.799353\pi\) | |||||||
\(242\) | −146.142 | − | 84.3749i | −0.603891 | − | 0.348657i | ||||
\(243\) | 7.79423 | + | 13.5000i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | − | 78.9084i | − | 0.323395i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −103.612 | −0.421186 | ||||||||
\(247\) | 93.4872 | − | 53.9748i | 0.378491 | − | 0.218522i | ||||
\(248\) | −64.5236 | + | 111.758i | −0.260176 | + | 0.450638i | ||||
\(249\) | −1.33130 | + | 2.30587i | −0.00534657 | + | 0.00926054i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 328.725i | 1.30966i | 0.755775 | + | 0.654832i | \(0.227260\pi\) | ||||
−0.755775 | + | 0.654832i | \(0.772740\pi\) | |||||||
\(252\) | −34.5684 | + | 23.8542i | −0.137176 | + | 0.0946597i | ||||
\(253\) | 46.2593i | 0.182843i | ||||||||
\(254\) | −63.8245 | − | 110.547i | −0.251278 | − | 0.435225i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −201.596 | − | 349.175i | −0.784420 | − | 1.35866i | −0.929345 | − | 0.369213i | \(-0.879627\pi\) |
0.144924 | − | 0.989443i | \(-0.453706\pi\) | |||||||
\(258\) | 135.848 | 0.526543 | ||||||||
\(259\) | −120.227 | + | 253.288i | −0.464197 | + | 0.977947i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −49.2050 | − | 85.2255i | −0.188525 | − | 0.326534i | ||||
\(262\) | 142.728 | − | 247.213i | 0.544765 | − | 0.943560i | ||||
\(263\) | 431.240 | + | 248.977i | 1.63970 | + | 0.946679i | 0.980937 | + | 0.194326i | \(0.0622519\pi\) |
0.658759 | + | 0.752354i | \(0.271081\pi\) | |||||||
\(264\) | 5.49235 | − | 3.17101i | 0.0208044 | − | 0.0120114i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −26.5830 | − | 329.822i | −0.0999360 | − | 1.23993i | ||||
\(267\) | − | 60.5688i | − | 0.226849i | ||||||
\(268\) | −69.4325 | + | 40.0869i | −0.259077 | + | 0.149578i | ||||
\(269\) | 155.357 | + | 89.6952i | 0.577534 | + | 0.333439i | 0.760153 | − | 0.649745i | \(-0.225124\pi\) |
−0.182619 | + | 0.983184i | \(0.558457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −126.057 | + | 72.7792i | −0.465156 | + | 0.268558i | −0.714210 | − | 0.699932i | \(-0.753214\pi\) |
0.249054 | + | 0.968490i | \(0.419880\pi\) | |||||||
\(272\) | 121.461 | 0.446546 | ||||||||
\(273\) | 3.14576 | + | 39.0303i | 0.0115229 | + | 0.142968i | ||||
\(274\) | −0.00575719 | −2.10116e−5 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 107.201 | + | 61.8924i | 0.388409 | + | 0.224248i | ||||
\(277\) | 185.057 | + | 106.843i | 0.668076 | + | 0.385714i | 0.795347 | − | 0.606154i | \(-0.207288\pi\) |
−0.127271 | + | 0.991868i | \(0.540622\pi\) | |||||||
\(278\) | 81.9887 | + | 142.009i | 0.294923 | + | 0.510822i | ||||
\(279\) | − | 136.875i | − | 0.490592i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −349.479 | −1.24370 | −0.621849 | − | 0.783137i | \(-0.713618\pi\) | ||||
−0.621849 | + | 0.783137i | \(0.713618\pi\) | |||||||
\(282\) | −128.868 | + | 74.4020i | −0.456979 | + | 0.263837i | ||||
\(283\) | −47.1253 | + | 81.6234i | −0.166521 | + | 0.288422i | −0.937194 | − | 0.348808i | \(-0.886587\pi\) |
0.770674 | + | 0.637230i | \(0.219920\pi\) | |||||||
\(284\) | 46.4480 | − | 80.4503i | 0.163549 | − | 0.283276i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5.91271i | − | 0.0206738i | ||||||
\(287\) | 168.170 | + | 243.703i | 0.585957 | + | 0.849140i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | −316.521 | − | 548.230i | −1.09523 | − | 1.89699i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 130.351 | − | 225.775i | 0.447942 | − | 0.775858i | ||||
\(292\) | 136.400 | + | 236.252i | 0.467124 | + | 0.809082i | ||||
\(293\) | 195.931 | 0.668707 | 0.334354 | − | 0.942448i | \(-0.391482\pi\) | ||||
0.334354 | + | 0.942448i | \(0.391482\pi\) | |||||||
\(294\) | 112.214 | + | 42.5905i | 0.381681 | + | 0.144866i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −56.6441 | − | 98.1104i | −0.191365 | − | 0.331454i | ||||
\(297\) | −3.36337 | + | 5.82552i | −0.0113245 | + | 0.0196145i | ||||
\(298\) | 6.36070 | + | 3.67235i | 0.0213446 | + | 0.0123233i | ||||
\(299\) | 99.9440 | − | 57.7027i | 0.334261 | − | 0.192986i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −220.492 | − | 319.526i | −0.732531 | − | 1.06155i | ||||
\(302\) | 227.324i | 0.752727i | ||||||||
\(303\) | 179.797 | − | 103.806i | 0.593391 | − | 0.342594i | ||||
\(304\) | 115.788 | + | 66.8501i | 0.380881 | + | 0.219902i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −111.569 | + | 64.4142i | −0.364603 | + | 0.210504i | ||||
\(307\) | 452.419 | 1.47368 | 0.736839 | − | 0.676069i | \(-0.236318\pi\) | ||||
0.736839 | + | 0.676069i | \(0.236318\pi\) | |||||||
\(308\) | −16.3730 | − | 7.77168i | −0.0531590 | − | 0.0252327i | ||||
\(309\) | −172.597 | −0.558567 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −56.8889 | − | 32.8448i | −0.182922 | − | 0.105610i | 0.405743 | − | 0.913987i | \(-0.367013\pi\) |
−0.588665 | + | 0.808377i | \(0.700346\pi\) | |||||||
\(312\) | −13.7020 | − | 7.91088i | −0.0439168 | − | 0.0253554i | ||||
\(313\) | −177.290 | − | 307.075i | −0.566422 | − | 0.981071i | −0.996916 | − | 0.0784776i | \(-0.974994\pi\) |
0.430494 | − | 0.902593i | \(-0.358339\pi\) | |||||||
\(314\) | 134.678i | 0.428909i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84.6045 | −0.267736 | ||||||||
\(317\) | 116.792 | − | 67.4299i | 0.368429 | − | 0.212713i | −0.304343 | − | 0.952563i | \(-0.598437\pi\) |
0.672772 | + | 0.739850i | \(0.265104\pi\) | |||||||
\(318\) | 66.9543 | − | 115.968i | 0.210548 | − | 0.364680i | ||||
\(319\) | 21.2329 | − | 36.7765i | 0.0665609 | − | 0.115287i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 81.3900i | 0.253551i | ||||||||
\(322\) | −28.4190 | − | 352.601i | −0.0882576 | − | 1.09504i | ||||
\(323\) | − | 1014.96i | − | 3.14228i | ||||||
\(324\) | 9.00000 | + | 15.5885i | 0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 174.300 | − | 301.897i | 0.534664 | − | 0.926064i | ||||
\(327\) | 50.3683 | + | 87.2405i | 0.154032 | + | 0.266791i | ||||
\(328\) | −119.641 | −0.364758 | ||||||||
\(329\) | 384.162 | + | 182.348i | 1.16767 | + | 0.554250i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 90.2612 | + | 156.337i | 0.272692 | + | 0.472317i | 0.969550 | − | 0.244892i | \(-0.0787525\pi\) |
−0.696858 | + | 0.717209i | \(0.745419\pi\) | |||||||
\(332\) | −1.53725 | + | 2.66259i | −0.00463027 | + | 0.00801986i | ||||
\(333\) | 104.062 | + | 60.0801i | 0.312498 | + | 0.180421i | ||||
\(334\) | −18.3032 | + | 10.5673i | −0.0547999 | + | 0.0316387i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −39.9162 | + | 27.5445i | −0.118798 | + | 0.0819777i | ||||
\(337\) | − | 5.84677i | − | 0.0173495i | −0.999962 | − | 0.00867473i | \(-0.997239\pi\) | ||
0.999962 | − | 0.00867473i | \(-0.00276129\pi\) | |||||||
\(338\) | 194.207 | − | 112.126i | 0.574578 | − | 0.331733i | ||||
\(339\) | 316.653 | + | 182.819i | 0.934078 | + | 0.539290i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51.1513 | − | 29.5322i | 0.150004 | − | 0.0866047i | ||||
\(342\) | −141.811 | −0.414651 | ||||||||
\(343\) | −81.9559 | − | 333.065i | −0.238938 | − | 0.971035i | ||||
\(344\) | 156.864 | 0.456000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 205.348 | + | 118.558i | 0.593492 | + | 0.342653i | ||||
\(347\) | −339.718 | − | 196.136i | −0.979014 | − | 0.565234i | −0.0770414 | − | 0.997028i | \(-0.524547\pi\) |
−0.901972 | + | 0.431794i | \(0.857881\pi\) | |||||||
\(348\) | −56.8170 | − | 98.4099i | −0.163267 | − | 0.282787i | ||||
\(349\) | − | 230.853i | − | 0.661471i | −0.943724 | − | 0.330735i | \(-0.892703\pi\) | ||
0.943724 | − | 0.330735i | \(-0.107297\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.7815 | 0.0478106 | ||||||||
\(352\) | 6.34202 | − | 3.66157i | 0.0180171 | − | 0.0104022i | ||||
\(353\) | −62.8188 | + | 108.805i | −0.177957 | + | 0.308230i | −0.941181 | − | 0.337904i | \(-0.890282\pi\) |
0.763224 | + | 0.646134i | \(0.223615\pi\) | |||||||
\(354\) | 16.1613 | − | 27.9921i | 0.0456533 | − | 0.0790738i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 69.9388i | − | 0.196457i | ||||||
\(357\) | 332.592 | + | 157.870i | 0.931630 | + | 0.442212i | ||||
\(358\) | 94.6743i | 0.264453i | ||||||||
\(359\) | 215.984 | + | 374.096i | 0.601628 | + | 1.04205i | 0.992575 | + | 0.121637i | \(0.0388143\pi\) |
−0.390947 | + | 0.920413i | \(0.627852\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 378.118 | − | 654.919i | 1.04742 | − | 1.81418i | ||||
\(362\) | 17.6147 | + | 30.5095i | 0.0486593 | + | 0.0842803i | ||||
\(363\) | 206.675 | 0.569354 | ||||||||
\(364\) | 3.63241 | + | 45.0683i | 0.00997916 | + | 0.123814i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 48.3213 | + | 83.6950i | 0.132026 | + | 0.228675i | ||||
\(367\) | 236.049 | − | 408.849i | 0.643185 | − | 1.11403i | −0.341532 | − | 0.939870i | \(-0.610946\pi\) |
0.984717 | − | 0.174159i | \(-0.0557208\pi\) | |||||||
\(368\) | 123.785 | + | 71.4672i | 0.336372 | + | 0.194204i | ||||
\(369\) | 109.897 | − | 63.4490i | 0.297823 | − | 0.171948i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −381.439 | + | 30.7432i | −1.02814 | + | 0.0828658i | ||||
\(372\) | − | 158.050i | − | 0.424865i | ||||||
\(373\) | −75.7963 | + | 43.7610i | −0.203207 | + | 0.117322i | −0.598151 | − | 0.801384i | \(-0.704098\pi\) |
0.394943 | + | 0.918705i | \(0.370764\pi\) | |||||||
\(374\) | −48.1441 | − | 27.7960i | −0.128728 | − | 0.0743209i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −148.804 | + | 85.9121i | −0.395756 | + | 0.228490i | ||||
\(377\) | −105.942 | −0.281012 | ||||||||
\(378\) | 22.0577 | − | 46.4700i | 0.0583536 | − | 0.122936i | ||||
\(379\) | 359.658 | 0.948965 | 0.474483 | − | 0.880265i | \(-0.342635\pi\) | ||||
0.474483 | + | 0.880265i | \(0.342635\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 135.392 | + | 78.1687i | 0.355360 | + | 0.205167i | ||||
\(382\) | −16.6622 | − | 9.61992i | −0.0436183 | − | 0.0251830i | ||||
\(383\) | −242.085 | − | 419.304i | −0.632077 | − | 1.09479i | −0.987126 | − | 0.159942i | \(-0.948869\pi\) |
0.355050 | − | 0.934847i | \(-0.384464\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 257.978 | 0.668336 | ||||||||
\(387\) | −144.089 | + | 83.1896i | −0.372322 | + | 0.214960i | ||||
\(388\) | 150.516 | − | 260.702i | 0.387929 | − | 0.671913i | ||||
\(389\) | −179.791 | + | 311.407i | −0.462188 | + | 0.800533i | −0.999070 | − | 0.0431246i | \(-0.986269\pi\) |
0.536882 | + | 0.843657i | \(0.319602\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1085.06i | − | 2.77508i | ||||||
\(392\) | 129.574 | + | 49.1793i | 0.330546 | + | 0.125457i | ||||
\(393\) | 349.612i | 0.889597i | ||||||||
\(394\) | −202.713 | − | 351.109i | −0.514499 | − | 0.891139i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.88368 | + | 6.72673i | −0.00980727 | + | 0.0169867i | ||||
\(397\) | 90.6969 | + | 157.092i | 0.228456 | + | 0.395697i | 0.957351 | − | 0.288929i | \(-0.0932991\pi\) |
−0.728895 | + | 0.684626i | \(0.759966\pi\) | |||||||
\(398\) | −4.47632 | −0.0112470 | ||||||||
\(399\) | 230.169 | + | 333.550i | 0.576865 | + | 0.835965i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 132.742 | + | 229.916i | 0.331027 | + | 0.573355i | 0.982713 | − | 0.185133i | \(-0.0592716\pi\) |
−0.651687 | + | 0.758488i | \(0.725938\pi\) | |||||||
\(402\) | 49.0962 | − | 85.0371i | 0.122130 | − | 0.211535i | ||||
\(403\) | −127.610 | − | 73.6754i | −0.316649 | − | 0.182817i | ||||
\(404\) | 207.612 | − | 119.865i | 0.513891 | − | 0.296695i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −139.250 | + | 293.365i | −0.342980 | + | 0.722574i | ||||
\(407\) | 51.8516i | 0.127399i | ||||||||
\(408\) | −128.828 | + | 74.3791i | −0.315756 | + | 0.182302i | ||||
\(409\) | 492.567 | + | 284.384i | 1.20432 | + | 0.695315i | 0.961513 | − | 0.274759i | \(-0.0885981\pi\) |
0.242808 | + | 0.970074i | \(0.421931\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.00610642 | − | 0.00352554i | 1.48575e−5 | − | 8.57797e-6i | ||||
\(412\) | −199.298 | −0.483733 | ||||||||
\(413\) | −92.0707 | + | 7.42071i | −0.222931 | + | 0.0179678i | ||||
\(414\) | −151.605 | −0.366195 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −15.8218 | − | 9.13469i | −0.0380331 | − | 0.0219584i | ||||
\(417\) | −173.924 | − | 100.415i | −0.417085 | − | 0.240804i | ||||
\(418\) | −30.5970 | − | 52.9956i | −0.0731987 | − | 0.126784i | ||||
\(419\) | − | 556.041i | − | 1.32707i | −0.748146 | − | 0.663534i | \(-0.769056\pi\) | ||
0.748146 | − | 0.663534i | \(-0.230944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −476.267 | −1.13128 | −0.565638 | − | 0.824654i | \(-0.691370\pi\) | ||||
−0.565638 | + | 0.824654i | \(0.691370\pi\) | |||||||
\(422\) | 219.627 | − | 126.801i | 0.520442 | − | 0.300477i | ||||
\(423\) | 91.1235 | − | 157.831i | 0.215422 | − | 0.373122i | ||||
\(424\) | 77.3122 | − | 133.909i | 0.182340 | − | 0.315822i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 113.774i | 0.267075i | ||||||||
\(427\) | 118.428 | − | 249.499i | 0.277350 | − | 0.584307i | ||||
\(428\) | 93.9810i | 0.219582i | ||||||||
\(429\) | 3.62078 | + | 6.27137i | 0.00844004 | + | 0.0146186i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −229.808 | + | 398.039i | −0.533196 | + | 0.923523i | 0.466052 | + | 0.884757i | \(0.345676\pi\) |
−0.999248 | + | 0.0387660i | \(0.987657\pi\) | |||||||
\(432\) | 10.3923 | + | 18.0000i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −65.9185 | −0.152237 | −0.0761183 | − | 0.997099i | \(-0.524253\pi\) | ||||
−0.0761183 | + | 0.997099i | \(0.524253\pi\) | |||||||
\(434\) | −371.746 | + | 256.527i | −0.856559 | + | 0.591076i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 58.1604 | + | 100.737i | 0.133395 | + | 0.231047i | ||||
\(437\) | 597.199 | − | 1034.38i | 1.36659 | − | 2.36700i | ||||
\(438\) | −289.348 | − | 167.055i | −0.660613 | − | 0.381405i | ||||
\(439\) | 307.619 | − | 177.604i | 0.700727 | − | 0.404565i | −0.106891 | − | 0.994271i | \(-0.534090\pi\) |
0.807618 | + | 0.589706i | \(0.200756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −145.102 | + | 23.5429i | −0.329031 | + | 0.0533852i | ||||
\(442\) | 138.688i | 0.313774i | ||||||||
\(443\) | 656.650 | − | 379.117i | 1.48228 | − | 0.855795i | 0.482482 | − | 0.875906i | \(-0.339735\pi\) |
0.999798 | + | 0.0201113i | \(0.00640205\pi\) | |||||||
\(444\) | 120.160 | + | 69.3746i | 0.270631 | + | 0.156249i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −87.3666 | + | 50.4411i | −0.195889 | + | 0.113097i | ||||
\(447\) | −8.99539 | −0.0201239 | ||||||||
\(448\) | −46.0912 | + | 31.8057i | −0.102882 | + | 0.0709948i | ||||
\(449\) | −668.104 | −1.48798 | −0.743992 | − | 0.668189i | \(-0.767070\pi\) | ||||
−0.743992 | + | 0.668189i | \(0.767070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.4227 | + | 27.3795i | 0.105150 | + | 0.0607084i | ||||
\(452\) | 365.639 | + | 211.102i | 0.808936 | + | 0.467039i | ||||
\(453\) | −139.207 | − | 241.113i | −0.307300 | − | 0.532258i | ||||
\(454\) | 201.581i | 0.444012i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −163.749 | −0.359098 | ||||||||
\(457\) | −645.475 | + | 372.665i | −1.41242 | + | 0.815460i | −0.995616 | − | 0.0935379i | \(-0.970182\pi\) |
−0.416802 | + | 0.908997i | \(0.636849\pi\) | |||||||
\(458\) | 88.9993 | − | 154.151i | 0.194322 | − | 0.336575i | ||||
\(459\) | 78.8909 | − | 136.643i | 0.171876 | − | 0.297697i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 592.937i | − | 1.28620i | −0.765783 | − | 0.643099i | \(-0.777648\pi\) | ||
0.765783 | − | 0.643099i | \(-0.222352\pi\) | |||||||
\(462\) | 22.1253 | − | 1.78326i | 0.0478903 | − | 0.00385987i | ||||
\(463\) | 529.829i | 1.14434i | 0.820136 | + | 0.572169i | \(0.193898\pi\) | ||||
−0.820136 | + | 0.572169i | \(0.806102\pi\) | |||||||
\(464\) | −65.6066 | − | 113.634i | −0.141394 | − | 0.244901i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 116.153 | − | 201.183i | 0.249255 | − | 0.431723i | ||||
\(467\) | −83.6375 | − | 144.864i | −0.179095 | − | 0.310202i | 0.762476 | − | 0.647017i | \(-0.223984\pi\) |
−0.941571 | + | 0.336815i | \(0.890650\pi\) | |||||||
\(468\) | 19.3776 | 0.0414052 | ||||||||
\(469\) | −279.701 | + | 22.5434i | −0.596378 | + | 0.0480669i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −82.4728 | − | 142.847i | −0.175102 | − | 0.303285i | ||||
\(472\) | 18.6614 | − | 32.3225i | 0.0395369 | − | 0.0684799i | ||||
\(473\) | −62.1771 | − | 35.8980i | −0.131453 | − | 0.0758943i | ||||
\(474\) | 89.7367 | − | 51.8095i | 0.189318 | − | 0.109303i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 384.044 | + | 182.292i | 0.806815 | + | 0.382966i | ||||
\(477\) | 164.004i | 0.343824i | ||||||||
\(478\) | −61.7573 | + | 35.6556i | −0.129199 | + | 0.0745933i | ||||
\(479\) | −221.195 | − | 127.707i | −0.461785 | − | 0.266612i | 0.251009 | − | 0.967985i | \(-0.419237\pi\) |
−0.712795 | + | 0.701373i | \(0.752571\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 112.026 | − | 64.6783i | 0.232902 | − | 0.134466i | ||||
\(482\) | 275.986 | 0.572585 | ||||||||
\(483\) | 246.066 | + | 356.587i | 0.509454 | + | 0.738276i | ||||
\(484\) | 238.648 | 0.493075 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | − | 11.0227i | −0.0392837 | − | 0.0226805i | ||||
\(487\) | −525.531 | − | 303.415i | −1.07912 | − | 0.623030i | −0.148460 | − | 0.988918i | \(-0.547432\pi\) |
−0.930659 | + | 0.365889i | \(0.880765\pi\) | |||||||
\(488\) | 55.7967 | + | 96.6427i | 0.114337 | + | 0.198038i | ||||
\(489\) | 426.947i | 0.873102i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 707.855 | 1.44166 | 0.720830 | − | 0.693112i | \(-0.243761\pi\) | ||||
0.720830 | + | 0.693112i | \(0.243761\pi\) | |||||||
\(492\) | 126.898 | − | 73.2645i | 0.257923 | − | 0.148912i | ||||
\(493\) | −498.038 | + | 862.628i | −1.01022 | + | 1.74975i | ||||
\(494\) | −76.3319 | + | 132.211i | −0.154518 | + | 0.267633i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 182.500i | − | 0.367944i | ||||||
\(497\) | 267.606 | − | 184.664i | 0.538442 | − | 0.371557i | ||||
\(498\) | − | 3.76548i | − | 0.00756120i | ||||||
\(499\) | 330.115 | + | 571.776i | 0.661553 | + | 1.14584i | 0.980208 | + | 0.197972i | \(0.0634357\pi\) |
−0.318655 | + | 0.947871i | \(0.603231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9423 | − | 22.4167i | 0.0258329 | − | 0.0447439i | ||||
\(502\) | −232.444 | − | 402.605i | −0.463036 | − | 0.802002i | ||||
\(503\) | −254.083 | −0.505136 | −0.252568 | − | 0.967579i | \(-0.581275\pi\) | ||||
−0.252568 | + | 0.967579i | \(0.581275\pi\) | |||||||
\(504\) | 25.4700 | − | 53.6589i | 0.0505357 | − | 0.106466i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −32.7103 | − | 56.6559i | −0.0646448 | − | 0.111968i | ||||
\(507\) | −137.325 | + | 237.855i | −0.270859 | + | 0.469141i | ||||
\(508\) | 156.337 | + | 90.2615i | 0.307751 | + | 0.177680i | ||||
\(509\) | −222.003 | + | 128.174i | −0.436156 | + | 0.251815i | −0.701966 | − | 0.712211i | \(-0.747694\pi\) |
0.265810 | + | 0.964026i | \(0.414361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 76.7063 | + | 951.715i | 0.150110 | + | 1.86246i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 150.413 | − | 86.8409i | 0.293202 | − | 0.169280i | ||||
\(514\) | 493.807 | + | 285.100i | 0.960715 | + | 0.554669i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −166.379 | + | 96.0591i | −0.322440 | + | 0.186161i | ||||
\(517\) | 78.6433 | 0.152115 | ||||||||
\(518\) | −31.8545 | − | 395.227i | −0.0614952 | − | 0.762986i | ||||
\(519\) | −290.406 | −0.559550 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 164.700 | + | 95.0898i | 0.316124 | + | 0.182514i | 0.649663 | − | 0.760222i | \(-0.274910\pi\) |
−0.333540 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(522\) | 120.527 | + | 69.5863i | 0.230895 | + | 0.133307i | ||||
\(523\) | 173.610 | + | 300.701i | 0.331950 | + | 0.574954i | 0.982894 | − | 0.184171i | \(-0.0589602\pi\) |
−0.650944 | + | 0.759126i | \(0.725627\pi\) | |||||||
\(524\) | 403.697i | 0.770414i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −704.212 | −1.33881 | ||||||||
\(527\) | −1199.80 | + | 692.706i | −2.27666 | + | 1.31443i | ||||
\(528\) | −4.48449 | + | 7.76736i | −0.00849335 | + | 0.0147109i | ||||
\(529\) | 373.946 | − | 647.693i | 0.706891 | − | 1.22437i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.5868i | 0.0745515i | ||||||||
\(532\) | 265.777 | + | 385.151i | 0.499580 | + | 0.723967i | ||||
\(533\) | − | 136.610i | − | 0.256304i | ||||||
\(534\) | 42.8286 | + | 74.1813i | 0.0802033 | + | 0.138916i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 56.6914 | − | 98.1924i | 0.105768 | − | 0.183195i | ||||
\(537\) | −57.9759 | − | 100.417i | −0.107963 | − | 0.186997i | ||||
\(538\) | −253.696 | −0.471554 | ||||||||
\(539\) | −40.1055 | − | 49.1462i | −0.0744072 | − | 0.0911804i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −216.672 | − | 375.287i | −0.400503 | − | 0.693691i | 0.593284 | − | 0.804993i | \(-0.297831\pi\) |
−0.993787 | + | 0.111302i | \(0.964498\pi\) | |||||||
\(542\) | 102.925 | − | 178.272i | 0.189899 | − | 0.328915i | ||||
\(543\) | −37.3663 | − | 21.5735i | −0.0688146 | − | 0.0397301i | ||||
\(544\) | −148.758 | + | 85.8856i | −0.273452 | + | 0.157878i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −31.4513 | − | 45.5777i | −0.0576032 | − | 0.0834757i | ||||
\(547\) | 718.061i | 1.31272i | 0.754446 | + | 0.656362i | \(0.227906\pi\) | ||||
−0.754446 | + | 0.656362i | \(0.772094\pi\) | |||||||
\(548\) | 0.00705109 | − | 0.00407095i | 1.28670e−5 | − | 7.42874e-6i | ||||
\(549\) | −102.505 | − | 59.1813i | −0.186712 | − | 0.107798i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −949.556 | + | 548.226i | −1.72333 | + | 0.994966i | ||||
\(552\) | −175.058 | −0.317134 | ||||||||
\(553\) | −267.510 | − | 126.977i | −0.483742 | − | 0.229615i | ||||
\(554\) | −302.197 | −0.545482 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −200.830 | − | 115.950i | −0.361206 | − | 0.208542i | ||||
\(557\) | −858.396 | − | 495.595i | −1.54111 | − | 0.889758i | −0.998769 | − | 0.0495971i | \(-0.984206\pi\) |
−0.542337 | − | 0.840161i | \(-0.682460\pi\) | |||||||
\(558\) | 96.7854 | + | 167.637i | 0.173451 | + | 0.300425i | ||||
\(559\) | 179.113i | 0.320417i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.0860 | 0.121365 | ||||||||
\(562\) | 428.023 | − | 247.119i | 0.761606 | − | 0.439713i | ||||
\(563\) | −290.108 | + | 502.481i | −0.515289 | + | 0.892506i | 0.484554 | + | 0.874762i | \(0.338982\pi\) |
−0.999843 | + | 0.0177449i | \(0.994351\pi\) | |||||||
\(564\) | 105.220 | − | 182.247i | 0.186561 | − | 0.323133i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 133.291i | − | 0.235496i | ||||||
\(567\) | 5.06126 | + | 62.7964i | 0.00892639 | + | 0.110752i | ||||
\(568\) | 131.375i | 0.231294i | ||||||||
\(569\) | −106.770 | − | 184.931i | −0.187645 | − | 0.325010i | 0.756820 | − | 0.653624i | \(-0.226752\pi\) |
−0.944465 | + | 0.328613i | \(0.893419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 378.751 | − | 656.016i | 0.663311 | − | 1.14889i | −0.316429 | − | 0.948616i | \(-0.602484\pi\) |
0.979740 | − | 0.200273i | \(-0.0641828\pi\) | |||||||
\(572\) | 4.18091 | + | 7.24156i | 0.00730929 | + | 0.0126601i | ||||
\(573\) | 23.5639 | 0.0411237 | ||||||||
\(574\) | −378.289 | − | 179.560i | −0.659040 | − | 0.312823i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 90.7836 | − | 157.242i | 0.157337 | − | 0.272516i | −0.776570 | − | 0.630031i | \(-0.783042\pi\) |
0.933908 | + | 0.357514i | \(0.116376\pi\) | |||||||
\(578\) | 775.314 | + | 447.628i | 1.34137 | + | 0.774442i | ||||
\(579\) | −273.627 | + | 157.978i | −0.472585 | + | 0.272847i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.85671 | + | 6.11165i | −0.0152439 | + | 0.0105192i | ||||
\(582\) | 368.689i | 0.633486i | ||||||||
\(583\) | −61.2894 | + | 35.3855i | −0.105128 | + | 0.0606955i | ||||
\(584\) | −334.111 | − | 192.899i | −0.572107 | − | 0.330306i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −239.966 | + | 138.544i | −0.409498 | + | 0.236424i | ||||
\(587\) | −156.397 | −0.266434 | −0.133217 | − | 0.991087i | \(-0.542531\pi\) | ||||
−0.133217 | + | 0.991087i | \(0.542531\pi\) | |||||||
\(588\) | −167.550 | + | 27.1850i | −0.284949 | + | 0.0462329i | ||||
\(589\) | −1525.02 | −2.58917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 430.019 | + | 248.271i | 0.727612 | + | 0.420087i | ||||
\(592\) | 138.749 | + | 80.1068i | 0.234373 | + | 0.135316i | ||||
\(593\) | 105.889 | + | 183.404i | 0.178564 | + | 0.309282i | 0.941389 | − | 0.337323i | \(-0.109521\pi\) |
−0.762825 | + | 0.646605i | \(0.776188\pi\) | |||||||
\(594\) | − | 9.51303i | − | 0.0160152i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.3870 | −0.0174278 | ||||||||
\(597\) | 4.74785 | − | 2.74117i | 0.00795285 | − | 0.00459158i | ||||
\(598\) | −81.6039 | + | 141.342i | −0.136461 | + | 0.236358i | ||||
\(599\) | 264.528 | − | 458.175i | 0.441616 | − | 0.764901i | −0.556194 | − | 0.831053i | \(-0.687739\pi\) |
0.997810 | + | 0.0661519i | \(0.0210722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 899.473i | 1.49663i | 0.663345 | + | 0.748314i | \(0.269136\pi\) | ||||
−0.663345 | + | 0.748314i | \(0.730864\pi\) | |||||||
\(602\) | 495.985 | + | 235.427i | 0.823895 | + | 0.391074i | ||||
\(603\) | 120.261i | 0.199437i | ||||||||
\(604\) | −160.742 | − | 278.413i | −0.266129 | − | 0.460949i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −146.804 | + | 254.272i | −0.242251 | + | 0.419591i | ||||
\(607\) | 268.038 | + | 464.255i | 0.441578 | + | 0.764835i | 0.997807 | − | 0.0661939i | \(-0.0210856\pi\) |
−0.556229 | + | 0.831029i | \(0.687752\pi\) | |||||||
\(608\) | −189.081 | −0.310988 | ||||||||
\(609\) | −31.9517 | − | 396.433i | −0.0524659 | − | 0.650958i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −98.0976 | − | 169.910i | −0.160552 | − | 0.278085i | ||||
\(612\) | 91.0954 | − | 157.782i | 0.148849 | − | 0.257813i | ||||
\(613\) | 717.977 | + | 414.524i | 1.17125 | + | 0.676222i | 0.953974 | − | 0.299888i | \(-0.0969495\pi\) |
0.217276 | + | 0.976110i | \(0.430283\pi\) | |||||||
\(614\) | −554.098 | + | 319.908i | −0.902439 | + | 0.521024i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.5481 | − | 2.05913i | 0.0414742 | − | 0.00334274i | ||||
\(617\) | 404.320i | 0.655300i | 0.944799 | + | 0.327650i | \(0.106257\pi\) | ||||
−0.944799 | + | 0.327650i | \(0.893743\pi\) | |||||||
\(618\) | 211.388 | − | 122.045i | 0.342051 | − | 0.197483i | ||||
\(619\) | 346.662 | + | 200.145i | 0.560036 | + | 0.323337i | 0.753160 | − | 0.657838i | \(-0.228529\pi\) |
−0.193124 | + | 0.981174i | \(0.561862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 160.801 | − | 92.8387i | 0.258939 | − | 0.149499i | ||||
\(622\) | 92.8991 | 0.149355 | ||||||||
\(623\) | 104.966 | − | 221.138i | 0.168485 | − | 0.354957i | ||||
\(624\) | 22.3753 | 0.0358579 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 434.270 | + | 250.726i | 0.693722 | + | 0.400521i | ||||
\(627\) | 64.9061 | + | 37.4736i | 0.103519 | + | 0.0597665i | ||||
\(628\) | −95.2314 | − | 164.946i | −0.151642 | − | 0.262652i | ||||
\(629\) | − | 1216.23i | − | 1.93359i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 334.639 | 0.530331 | 0.265165 | − | 0.964203i | \(-0.414573\pi\) | ||||
0.265165 | + | 0.964203i | \(0.414573\pi\) | |||||||
\(632\) | 103.619 | − | 59.8244i | 0.163954 | − | 0.0946589i | ||||
\(633\) | −155.299 | + | 268.987i | −0.245339 | + | 0.424939i | ||||
\(634\) | −95.3603 | + | 165.169i | −0.150411 | + | 0.260519i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 189.375i | 0.297760i | ||||||||
\(637\) | −56.1547 | + | 147.952i | −0.0881550 | + | 0.232264i | ||||
\(638\) | 60.0558i | 0.0941313i | ||||||||
\(639\) | −69.6720 | − | 120.676i | −0.109033 | − | 0.188851i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.0084 | − | 62.3683i | 0.0561753 | − | 0.0972984i | −0.836570 | − | 0.547860i | \(-0.815443\pi\) |
0.892746 | + | 0.450561i | \(0.148776\pi\) | |||||||
\(642\) | −57.5514 | − | 99.6819i | −0.0896439 | − | 0.155268i | ||||
\(643\) | 1254.20 | 1.95054 | 0.975269 | − | 0.221020i | \(-0.0709386\pi\) | ||||
0.975269 | + | 0.221020i | \(0.0709386\pi\) | |||||||
\(644\) | 284.133 | + | 411.751i | 0.441200 | + | 0.639366i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 717.683 | + | 1243.06i | 1.11096 | + | 1.92425i | ||||
\(647\) | −73.1699 | + | 126.734i | −0.113091 | + | 0.195879i | −0.917015 | − | 0.398853i | \(-0.869409\pi\) |
0.803924 | + | 0.594732i | \(0.202742\pi\) | |||||||
\(648\) | −22.0454 | − | 12.7279i | −0.0340207 | − | 0.0196419i | ||||
\(649\) | −14.7939 | + | 8.54125i | −0.0227949 | + | 0.0131606i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 237.207 | − | 499.735i | 0.364373 | − | 0.767642i | ||||
\(652\) | 492.996i | 0.756128i | ||||||||
\(653\) | −687.082 | + | 396.687i | −1.05219 | + | 0.607484i | −0.923262 | − | 0.384170i | \(-0.874488\pi\) |
−0.128930 | + | 0.991654i | \(0.541154\pi\) | |||||||
\(654\) | −123.377 | − | 71.2316i | −0.188649 | − | 0.108917i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 146.529 | − | 84.5986i | 0.223368 | − | 0.128961i | ||||
\(657\) | 409.200 | 0.622832 | ||||||||
\(658\) | −599.441 | + | 48.3137i | −0.911004 | + | 0.0734251i | ||||
\(659\) | −35.5649 | −0.0539680 | −0.0269840 | − | 0.999636i | \(-0.508590\pi\) | ||||
−0.0269840 | + | 0.999636i | \(0.508590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 193.509 | + | 111.723i | 0.292752 | + | 0.169021i | 0.639182 | − | 0.769055i | \(-0.279273\pi\) |
−0.346430 | + | 0.938076i | \(0.612606\pi\) | |||||||
\(662\) | −221.094 | − | 127.649i | −0.333979 | − | 0.192823i | ||||
\(663\) | −84.9288 | − | 147.101i | −0.128098 | − | 0.221872i | ||||
\(664\) | − | 4.34800i | − | 0.00654819i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −169.932 | −0.255154 | ||||||||
\(667\) | −1015.14 | + | 586.090i | −1.52195 | + | 0.878696i | ||||
\(668\) | 14.9445 | − | 25.8846i | 0.0223720 | − | 0.0387494i | ||||
\(669\) | 61.7775 | − | 107.002i | 0.0923431 | − | 0.159943i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 51.0759i | − | 0.0761190i | ||||||
\(672\) | 29.4102 | − | 61.9600i | 0.0437652 | − | 0.0922024i | ||||
\(673\) | − | 216.920i | − | 0.322318i | −0.986928 | − | 0.161159i | \(-0.948477\pi\) | ||
0.986928 | − | 0.161159i | \(-0.0515232\pi\) | |||||||
\(674\) | 4.13429 | + | 7.16080i | 0.00613396 | + | 0.0106243i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −158.570 | + | 274.651i | −0.234571 | + | 0.406288i | ||||
\(677\) | 23.4825 | + | 40.6729i | 0.0346861 | + | 0.0600781i | 0.882847 | − | 0.469660i | \(-0.155624\pi\) |
−0.848161 | + | 0.529738i | \(0.822290\pi\) | |||||||
\(678\) | −517.091 | −0.762672 | ||||||||
\(679\) | 867.186 | − | 598.410i | 1.27715 | − | 0.881310i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −123.443 | − | 213.809i | −0.181267 | − | 0.313964i | ||||
\(682\) | −41.7648 | + | 72.3388i | −0.0612388 | + | 0.106069i | ||||
\(683\) | 51.1993 | + | 29.5599i | 0.0749623 | + | 0.0432795i | 0.537013 | − | 0.843574i | \(-0.319553\pi\) |
−0.462050 | + | 0.886854i | \(0.652886\pi\) | |||||||
\(684\) | 173.682 | − | 100.275i | 0.253921 | − | 0.146601i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 335.888 | + | 349.968i | 0.489632 | + | 0.510157i | ||||
\(687\) | 218.003i | 0.317326i | ||||||||
\(688\) | −192.118 | + | 110.919i | −0.279242 | + | 0.161220i | ||||
\(689\) | 152.902 | + | 88.2779i | 0.221918 | + | 0.128125i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 916.389 | − | 529.078i | 1.32618 | − | 0.765669i | 0.341472 | − | 0.939892i | \(-0.389075\pi\) |
0.984706 | + | 0.174222i | \(0.0557412\pi\) | |||||||
\(692\) | −335.332 | −0.484584 | ||||||||
\(693\) | −22.3754 | + | 15.4404i | −0.0322878 | + | 0.0222805i | ||||
\(694\) | 554.757 | 0.799361 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 139.173 | + | 80.3513i | 0.199961 | + | 0.115447i | ||||
\(697\) | −1112.34 | − | 642.212i | −1.59590 | − | 0.921395i | ||||
\(698\) | 163.238 | + | 282.736i | 0.233865 | + | 0.405066i | ||||
\(699\) | 284.516i | 0.407032i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −394.358 | −0.562565 | −0.281283 | − | 0.959625i | \(-0.590760\pi\) | ||||
−0.281283 | + | 0.959625i | \(0.590760\pi\) | |||||||
\(702\) | −20.5531 | + | 11.8663i | −0.0292779 | + | 0.0169036i | ||||
\(703\) | 669.394 | − | 1159.42i | 0.952197 | − | 1.64925i | ||||
\(704\) | −5.17824 | + | 8.96898i | −0.00735546 | + | 0.0127400i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 177.678i | − | 0.251669i | ||||||
\(707\) | 836.342 | − | 67.4075i | 1.18295 | − | 0.0953430i | ||||
\(708\) | 45.7109i | 0.0645635i | ||||||||
\(709\) | −20.7217 | − | 35.8911i | −0.0292267 | − | 0.0506221i | 0.851042 | − | 0.525097i | \(-0.175971\pi\) |
−0.880269 | + | 0.474475i | \(0.842638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −63.4534 | + | 109.905i | −0.0892453 | + | 0.154577i | ||||
\(712\) | 49.4542 | + | 85.6572i | 0.0694581 | + | 0.120305i | ||||
\(713\) | −1630.35 | −2.28660 | ||||||||
\(714\) | −518.971 | + | 41.8280i | −0.726850 | + | 0.0585826i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −66.9449 | − | 115.952i | −0.0934984 | − | 0.161944i | ||||
\(717\) | 43.6690 | − | 75.6369i | 0.0609051 | − | 0.105491i | ||||
\(718\) | −529.052 | − | 305.448i | −0.736841 | − | 0.425415i | ||||
\(719\) | −556.327 | + | 321.195i | −0.773751 | + | 0.446725i | −0.834211 | − | 0.551445i | \(-0.814077\pi\) |
0.0604602 | + | 0.998171i | \(0.480743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −630.157 | − | 299.113i | −0.874004 | − | 0.414859i | ||||
\(722\) | 1069.48i | 1.48127i | ||||||||
\(723\) | −292.727 | + | 169.006i | −0.404879 | + | 0.233757i | ||||
\(724\) | −43.1469 | − | 24.9109i | −0.0595952 | − | 0.0344073i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −253.125 | + | 146.142i | −0.348657 | + | 0.201297i | ||||
\(727\) | −979.168 | −1.34686 | −0.673431 | − | 0.739250i | \(-0.735180\pi\) | ||||
−0.673431 | + | 0.739250i | \(0.735180\pi\) | |||||||
\(728\) | −36.3169 | − | 52.6286i | −0.0498858 | − | 0.0722921i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1458.42 | + | 842.021i | 1.99511 | + | 1.15188i | ||||
\(732\) | −118.363 | − | 68.3367i | −0.161698 | − | 0.0933562i | ||||
\(733\) | 618.862 | + | 1071.90i | 0.844286 | + | 1.46235i | 0.886240 | + | 0.463227i | \(0.153308\pi\) |
−0.0419537 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(734\) | 667.647i | 0.909601i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −202.140 | −0.274647 | ||||||||
\(737\) | −44.9423 | + | 25.9474i | −0.0609800 | + | 0.0352068i | ||||
\(738\) | −89.7304 | + | 155.418i | −0.121586 | + | 0.210593i | ||||
\(739\) | −477.274 | + | 826.662i | −0.645837 | + | 1.11862i | 0.338271 | + | 0.941049i | \(0.390158\pi\) |
−0.984108 | + | 0.177574i | \(0.943175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 186.974i | − | 0.252327i | ||||||
\(742\) | 445.426 | − | 307.370i | 0.600305 | − | 0.414246i | ||||
\(743\) | − | 401.194i | − | 0.539964i | −0.962865 | − | 0.269982i | \(-0.912982\pi\) | ||
0.962865 | − | 0.269982i | \(-0.0870178\pi\) | |||||||
\(744\) | 111.758 | + | 193.571i | 0.150213 | + | 0.260176i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 61.8874 | − | 107.192i | 0.0829590 | − | 0.143689i | ||||
\(747\) | 2.30587 | + | 3.99389i | 0.00308685 | + | 0.00534657i | ||||
\(748\) | 78.6190 | 0.105106 | ||||||||
\(749\) | −141.050 | + | 297.157i | −0.188318 | + | 0.396738i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 420.870 | + | 728.968i | 0.560412 | + | 0.970662i | 0.997460 | + | 0.0712243i | \(0.0226906\pi\) |
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(752\) | 121.498 | − | 210.441i | 0.161567 | − | 0.279841i | ||||
\(753\) | 493.088 | + | 284.685i | 0.654832 | + | 0.378067i | ||||
\(754\) | 129.751 | − | 74.9120i | 0.172084 | − | 0.0993528i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.84424 | + | 72.5110i | 0.00773048 | + | 0.0959140i | ||||
\(757\) | − | 1287.18i | − | 1.70037i | −0.526487 | − | 0.850183i | \(-0.676491\pi\) | ||
0.526487 | − | 0.850183i | \(-0.323509\pi\) | |||||||
\(758\) | −440.489 | + | 254.317i | −0.581120 | + | 0.335510i | ||||
\(759\) | 69.3890 | + | 40.0617i | 0.0914216 | + | 0.0527823i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1237.18 | + | 714.288i | −1.62573 | + | 0.938618i | −0.640387 | + | 0.768052i | \(0.721226\pi\) |
−0.985346 | + | 0.170565i | \(0.945441\pi\) | |||||||
\(762\) | −221.095 | −0.290150 | ||||||||
\(763\) | 32.7072 | + | 405.807i | 0.0428666 | + | 0.531857i | ||||
\(764\) | 27.2092 | 0.0356142 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 592.986 | + | 342.361i | 0.774133 | + | 0.446946i | ||||
\(767\) | 36.9070 | + | 21.3083i | 0.0481187 | + | 0.0277813i | ||||
\(768\) | 13.8564 | + | 24.0000i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | − | 1030.04i | − | 1.33945i | −0.742608 | − | 0.669726i | \(-0.766411\pi\) | ||
0.742608 | − | 0.669726i | \(-0.233589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −698.349 | −0.905771 | ||||||||
\(772\) | −315.957 | + | 182.418i | −0.409271 | + | 0.236293i | ||||
\(773\) | −374.310 | + | 648.324i | −0.484231 | + | 0.838712i | −0.999836 | − | 0.0181142i | \(-0.994234\pi\) |
0.515605 | + | 0.856826i | \(0.327567\pi\) | |||||||
\(774\) | 117.648 | − | 203.772i | 0.152000 | − | 0.263271i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 425.725i | 0.548615i | ||||||||
\(777\) | 275.813 | + | 399.695i | 0.354972 | + | 0.514408i | ||||
\(778\) | − | 508.526i | − | 0.653632i | ||||||
\(779\) | −706.929 | − | 1224.44i | −0.907482 | − | 1.57181i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0649 | − | 52.0739i | 0.0384954 | − | 0.0666759i | ||||
\(782\) | 767.250 | + | 1328.92i | 0.981139 | + | 1.69938i | ||||
\(783\) | −170.451 | −0.217690 | ||||||||
\(784\) | −193.470 | + | 31.3905i | −0.246773 | + | 0.0400389i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −247.213 | − | 428.185i | −0.314520 | − | 0.544765i | ||||
\(787\) | 80.7880 | − | 139.929i | 0.102653 | − | 0.177800i | −0.810124 | − | 0.586259i | \(-0.800600\pi\) |
0.912777 | + | 0.408458i | \(0.133934\pi\) | |||||||
\(788\) | 496.543 | + | 286.679i | 0.630131 | + | 0.363806i | ||||
\(789\) | 746.930 | − | 431.240i | 0.946679 | − | 0.546566i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 839.279 | + | 1216.24i | 1.06103 | + | 1.53760i | ||||
\(792\) | − | 10.9847i | − | 0.0138696i | ||||||
\(793\) | −110.350 | + | 63.7107i | −0.139155 | + | 0.0803414i | ||||
\(794\) | −222.161 | − | 128.265i | −0.279800 | − | 0.161543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.48235 | − | 3.16523i | 0.00688737 | − | 0.00397643i | ||||
\(797\) | −1350.55 | −1.69454 | −0.847269 | − | 0.531164i | \(-0.821755\pi\) | ||||
−0.847269 | + | 0.531164i | \(0.821755\pi\) | |||||||
\(798\) | −517.754 | − | 245.760i | −0.648815 | − | 0.307969i | ||||
\(799\) | −1844.65 | −2.30870 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −90.8531 | − | 52.4541i | −0.113425 | − | 0.0654857i | ||||
\(802\) | −325.150 | − | 187.725i | −0.405423 | − | 0.234071i | ||||
\(803\) | 88.2891 | + | 152.921i | 0.109949 | + | 0.190437i | ||||
\(804\) | 138.865i | 0.172718i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 208.386 | 0.258543 | ||||||||
\(807\) | 269.085 | − | 155.357i | 0.333439 | − | 0.192511i | ||||
\(808\) | −169.515 | + | 293.608i | −0.209795 | + | 0.363376i | ||||
\(809\) | 644.079 | − | 1115.58i | 0.796142 | − | 1.37896i | −0.125969 | − | 0.992034i | \(-0.540204\pi\) |
0.922111 | − | 0.386925i | \(-0.126463\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1097.00i | 1.35265i | 0.736605 | + | 0.676323i | \(0.236428\pi\) | ||||
−0.736605 | + | 0.676323i | \(0.763572\pi\) | |||||||
\(812\) | −36.8947 | − | 457.762i | −0.0454368 | − | 0.563746i | ||||
\(813\) | 252.114i | 0.310104i | ||||||||
\(814\) | −36.6646 | − | 63.5049i | −0.0450425 | − | 0.0780159i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 105.188 | − | 182.191i | 0.128907 | − | 0.223273i | ||||
\(817\) | 926.873 | + | 1605.39i | 1.13448 | + | 1.96498i | ||||
\(818\) | −804.359 | −0.983324 | ||||||||
\(819\) | 61.2697 | + | 29.0826i | 0.0748104 | + | 0.0355099i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −448.083 | − | 776.103i | −0.545778 | − | 0.945315i | −0.998558 | − | 0.0536923i | \(-0.982901\pi\) |
0.452780 | − | 0.891622i | \(-0.350432\pi\) | |||||||
\(822\) | −0.00498587 | + | 0.00863579i | −6.06554e−6 | + | 1.05058e-5i | ||||
\(823\) | −46.8742 | − | 27.0628i | −0.0569553 | − | 0.0328832i | 0.471252 | − | 0.881999i | \(-0.343802\pi\) |
−0.528207 | + | 0.849115i | \(0.677136\pi\) | |||||||
\(824\) | 244.089 | − | 140.925i | 0.296225 | − | 0.171026i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 107.516 | − | 74.1923i | 0.130164 | − | 0.0898212i | ||||
\(827\) | − | 977.965i | − | 1.18255i | −0.806472 | − | 0.591273i | \(-0.798626\pi\) | ||
0.806472 | − | 0.591273i | \(-0.201374\pi\) | |||||||
\(828\) | 185.677 | − | 107.201i | 0.224248 | − | 0.129470i | ||||
\(829\) | 667.395 | + | 385.321i | 0.805061 | + | 0.464802i | 0.845238 | − | 0.534391i | \(-0.179459\pi\) |
−0.0401771 | + | 0.999193i | \(0.512792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 320.528 | − | 185.057i | 0.385714 | − | 0.222692i | ||||
\(832\) | 25.8368 | 0.0310539 | ||||||||
\(833\) | 940.712 | + | 1152.77i | 1.12931 | + | 1.38388i | ||||
\(834\) | 284.017 | 0.340548 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 74.9472 | + | 43.2708i | 0.0896497 | + | 0.0517593i | ||||
\(837\) | −205.313 | − | 118.537i | −0.245296 | − | 0.141622i | ||||
\(838\) | 393.181 | + | 681.009i | 0.469189 | + | 0.812659i | ||||
\(839\) | − | 148.387i | − | 0.176862i | −0.996082 | − | 0.0884308i | \(-0.971815\pi\) | ||
0.996082 | − | 0.0884308i | \(-0.0281852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 235.056 | 0.279496 | ||||||||
\(842\) | 583.306 | − | 336.772i | 0.692762 | − | 0.399966i | ||||
\(843\) | −302.658 | + | 524.218i | −0.359024 | + | 0.621849i | ||||
\(844\) | −179.324 | + | 310.599i | −0.212470 | + | 0.368008i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 257.736i | 0.304653i | ||||||||
\(847\) | 754.578 | + | 358.171i | 0.890883 | + | 0.422870i | ||||
\(848\) | 218.672i | 0.257868i | ||||||||
\(849\) | 81.6234 | + | 141.376i | 0.0961407 | + | 0.166521i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 715.627 | − | 1239.50i | 0.840924 | − | 1.45652i | ||||
\(852\) | −80.4503 | − | 139.344i | −0.0944253 | − | 0.163549i | ||||
\(853\) | 59.1817 | 0.0693807 | 0.0346903 | − | 0.999398i | \(-0.488956\pi\) | ||||
0.0346903 | + | 0.999398i | \(0.488956\pi\) | |||||||
\(854\) | 31.3780 | + | 389.314i | 0.0367423 | + | 0.455872i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −66.4546 | − | 115.103i | −0.0776339 | − | 0.134466i | ||||
\(857\) | −128.218 | + | 222.080i | −0.149613 | + | 0.259137i | −0.931084 | − | 0.364804i | \(-0.881136\pi\) |
0.781472 | + | 0.623941i | \(0.214469\pi\) | |||||||
\(858\) | −8.86906 | − | 5.12055i | −0.0103369 | − | 0.00596801i | ||||
\(859\) | −26.1614 | + | 15.1043i | −0.0304556 | + | 0.0175836i | −0.515151 | − | 0.857100i | \(-0.672264\pi\) |
0.484695 | + | 0.874683i | \(0.338931\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 511.194 | − | 41.2012i | 0.593721 | − | 0.0478528i | ||||
\(862\) | − | 649.994i | − | 0.754054i | ||||||
\(863\) | 1114.24 | − | 643.310i | 1.29113 | − | 0.745434i | 0.312275 | − | 0.949992i | \(-0.398909\pi\) |
0.978855 | + | 0.204558i | \(0.0655756\pi\) | |||||||
\(864\) | −25.4558 | − | 14.6969i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 80.7333 | − | 46.6114i | 0.0932255 | − | 0.0538238i | ||||
\(867\) | −1096.46 | −1.26466 | ||||||||
\(868\) | 273.903 | − | 577.045i | 0.315556 | − | 0.664798i | ||||
\(869\) | −54.7628 | −0.0630182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 112.120 | + | 64.7323i | 0.128725 | + | 0.0743196i | ||||
\(872\) | −142.463 | − | 82.2512i | −0.163375 | − | 0.0943247i | ||||
\(873\) | −225.775 | − | 391.053i | −0.258619 | − | 0.447942i | ||||
\(874\) | 1689.13i | 1.93265i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 472.504 | 0.539388 | ||||||||
\(877\) | −264.177 | + | 152.523i | −0.301228 | + | 0.173914i | −0.642994 | − | 0.765871i | \(-0.722308\pi\) |
0.341767 | + | 0.939785i | \(0.388975\pi\) | |||||||
\(878\) | −251.170 | + | 435.039i | −0.286071 | + | 0.495489i | ||||
\(879\) | 169.681 | − | 293.897i | 0.193039 | − | 0.334354i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 515.564i | − | 0.585204i | −0.956234 | − | 0.292602i | \(-0.905479\pi\) | ||
0.956234 | − | 0.292602i | \(-0.0945210\pi\) | |||||||
\(882\) | 161.066 | − | 131.437i | 0.182615 | − | 0.149022i | ||||
\(883\) | − | 951.802i | − | 1.07792i | −0.842332 | − | 0.538960i | \(-0.818818\pi\) | ||
0.842332 | − | 0.538960i | \(-0.181182\pi\) | |||||||
\(884\) | −98.0673 | − | 169.858i | −0.110936 | − | 0.192147i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −536.152 | + | 928.643i | −0.605138 | + | 1.04813i | ||||
\(887\) | −608.088 | − | 1053.24i | −0.685556 | − | 1.18742i | −0.973262 | − | 0.229699i | \(-0.926226\pi\) |
0.287706 | − | 0.957719i | \(-0.407108\pi\) | |||||||
\(888\) | −196.221 | −0.220969 | ||||||||
\(889\) | 358.853 | + | 520.033i | 0.403659 | + | 0.584963i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.82552 | + | 10.0901i | 0.00653818 | + | 0.0113245i | ||||
\(892\) | 71.3345 | − | 123.555i | 0.0799715 | − | 0.138515i | ||||
\(893\) | −1758.50 | − | 1015.27i | −1.96920 | − | 1.13692i | ||||
\(894\) | 11.0171 | − | 6.36070i | 0.0123233 | − | 0.00711488i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 33.9600 | − | 71.5452i | 0.0379018 | − | 0.0798496i | ||||
\(897\) | − | 199.888i | − | 0.222841i | ||||||
\(898\) | 818.257 | − | 472.421i | 0.911200 | − | 0.526081i | ||||
\(899\) | 1296.14 | + | 748.327i | 1.44176 | + | 0.832399i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1437.60 | − | 830.000i | 1.59556 | − | 0.921198i | ||||
\(902\) | −77.4409 | −0.0858547 | ||||||||
\(903\) | −670.240 | + | 54.0200i | −0.742237 | + | 0.0598228i | ||||
\(904\) | −597.086 | −0.660493 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 340.985 | + | 196.868i | 0.376363 | + | 0.217294i | ||||
\(907\) | −1188.52 | − | 686.190i | −1.31038 | − | 0.756549i | −0.328222 | − | 0.944601i | \(-0.606449\pi\) |
−0.982159 | + | 0.188052i | \(0.939783\pi\) | |||||||
\(908\) | −142.540 | − | 246.886i | −0.156982 | − | 0.271901i | ||||
\(909\) | − | 359.595i | − | 0.395594i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −317.135 | −0.348118 | −0.174059 | − | 0.984735i | \(-0.555688\pi\) | ||||
−0.174059 | + | 0.984735i | \(0.555688\pi\) | |||||||
\(912\) | 200.550 | − | 115.788i | 0.219902 | − | 0.126960i | ||||
\(913\) | −0.995031 | + | 1.72344i | −0.00108985 | + | 0.00188767i | ||||
\(914\) | 527.028 | − | 912.839i | 0.576617 | − | 0.998730i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 251.728i | 0.274812i | ||||||||
\(917\) | −605.882 | + | 1276.44i | −0.660721 | + | 1.39198i | ||||
\(918\) | 223.137i | 0.243069i | ||||||||
\(919\) | 451.409 | + | 781.863i | 0.491195 | + | 0.850775i | 0.999949 | − | 0.0101370i | \(-0.00322675\pi\) |
−0.508753 | + | 0.860912i | \(0.669893\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 391.806 | − | 678.628i | 0.425414 | − | 0.736839i | ||||
\(922\) | 419.270 | + | 726.197i | 0.454740 | + | 0.787632i | ||||
\(923\) | −150.009 | −0.162523 | ||||||||
\(924\) | −25.8369 | + | 17.8290i | −0.0279621 | + | 0.0192955i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −374.645 | − | 648.905i | −0.404585 | − | 0.700761i | ||||
\(927\) | −149.474 | + | 258.896i | −0.161244 | + | 0.279284i | ||||
\(928\) | 160.703 | + | 92.7817i | 0.173171 | + | 0.0999803i | ||||
\(929\) | 291.968 | − | 168.568i | 0.314282 | − | 0.181451i | −0.334559 | − | 0.942375i | \(-0.608587\pi\) |
0.648841 | + | 0.760924i | \(0.275254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 262.307 | + | 1616.69i | 0.281748 | + | 1.73651i | ||||
\(932\) | 328.530i | 0.352500i | ||||||||
\(933\) | −98.5344 | + | 56.8889i | −0.105610 | + | 0.0609741i | ||||
\(934\) | 204.869 | + | 118.281i | 0.219346 | + | 0.126640i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −23.7326 | + | 13.7020i | −0.0253554 | + | 0.0146389i | ||||
\(937\) | 1577.72 | 1.68380 | 0.841900 | − | 0.539634i | \(-0.181438\pi\) | ||||
0.841900 | + | 0.539634i | \(0.181438\pi\) | |||||||
\(938\) | 326.622 | − | 225.388i | 0.348211 | − | 0.240286i | ||||
\(939\) | −614.150 | −0.654047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −711.530 | − | 410.802i | −0.756142 | − | 0.436559i | 0.0717667 | − | 0.997421i | \(-0.477136\pi\) |
−0.827909 | + | 0.560863i | \(0.810470\pi\) | |||||||
\(942\) | 202.016 | + | 116.634i | 0.214455 | + | 0.123815i | ||||
\(943\) | −755.753 | − | 1309.00i | −0.801435 | − | 1.38813i | ||||
\(944\) | 52.7824i | 0.0559136i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 101.535 | 0.107331 | ||||||||
\(947\) | 354.357 | − | 204.588i | 0.374189 | − | 0.216038i | −0.301098 | − | 0.953593i | \(-0.597353\pi\) |
0.675287 | + | 0.737555i | \(0.264020\pi\) | |||||||
\(948\) | −73.2697 | + | 126.907i | −0.0772887 | + | 0.133868i | ||||
\(949\) | 220.259 | − | 381.500i | 0.232096 | − | 0.402002i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 233.584i | − | 0.245619i | ||||||
\(952\) | −599.256 | + | 48.2988i | −0.629470 | + | 0.0507340i | ||||
\(953\) | − | 820.950i | − | 0.861437i | −0.902486 | − | 0.430719i | \(-0.858260\pi\) | ||
0.902486 | − | 0.430719i | \(-0.141740\pi\) | |||||||
\(954\) | −115.968 | − | 200.863i | −0.121560 | − | 0.210548i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 50.4246 | − | 87.3380i | 0.0527454 | − | 0.0913577i | ||||
\(957\) | −36.7765 | − | 63.6988i | −0.0384289 | − | 0.0665609i | ||||
\(958\) | 361.210 | 0.377046 | ||||||||
\(959\) | 0.0284045 | − | 0.00228935i | 2.96189e−5 | − | 2.38722e-6i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 560.324 | + | 970.510i | 0.583063 | + | 1.00990i | ||||
\(962\) | −91.4689 | + | 158.429i | −0.0950820 | + | 0.164687i | ||||
\(963\) | 122.085 | + | 70.4858i | 0.126776 | + | 0.0731940i | ||||
\(964\) | −338.012 | + | 195.151i | −0.350635 | + | 0.202439i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −553.514 | − | 262.733i | −0.572995 | − | 0.271981i | ||||
\(967\) | 1627.11i | 1.68263i | 0.540543 | + | 0.841317i | \(0.318219\pi\) | ||||
−0.540543 | + | 0.841317i | \(0.681781\pi\) | |||||||
\(968\) | −292.283 | + | 168.750i | −0.301945 | + | 0.174328i | ||||
\(969\) | −1522.44 | − | 878.978i | −1.57114 | − | 0.907098i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1074.33 | − | 620.263i | 1.10641 | − | 0.638788i | 0.168515 | − | 0.985699i | \(-0.446103\pi\) |
0.937898 | + | 0.346911i | \(0.112769\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | −460.981 | − | 668.032i | −0.473773 | − | 0.686569i | ||||
\(974\) | 858.188 | 0.881097 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −136.673 | − | 78.9084i | −0.140034 | − | 0.0808488i | ||||
\(977\) | −622.459 | − | 359.377i | −0.637113 | − | 0.367837i | 0.146389 | − | 0.989227i | \(-0.453235\pi\) |
−0.783502 | + | 0.621390i | \(0.786568\pi\) | |||||||
\(978\) | −301.897 | − | 522.901i | −0.308688 | − | 0.534664i | ||||
\(979\) | − | 45.2700i | − | 0.0462410i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 174.481 | 0.177860 | ||||||||
\(982\) | −866.941 | + | 500.529i | −0.882832 | + | 0.509704i | ||||
\(983\) | −201.047 | + | 348.223i | −0.204524 | + | 0.354246i | −0.949981 | − | 0.312308i | \(-0.898898\pi\) |
0.745457 | + | 0.666554i | \(0.232231\pi\) | |||||||
\(984\) | −103.612 | + | 179.461i | −0.105296 | + | 0.182379i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1408.66i | − | 1.42867i | ||||||
\(987\) | 606.217 | − | 418.325i | 0.614202 | − | 0.423835i | ||||
\(988\) | − | 215.899i | − | 0.218522i | ||||||
\(989\) | 990.889 | + | 1716.27i | 1.00191 | + | 1.73536i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 298.270 | − | 516.618i | 0.300979 | − | 0.521310i | −0.675379 | − | 0.737471i | \(-0.736020\pi\) |
0.976358 | + | 0.216160i | \(0.0693534\pi\) | |||||||
\(992\) | 129.047 | + | 223.516i | 0.130088 | + | 0.225319i | ||||
\(993\) | 312.674 | 0.314878 | ||||||||
\(994\) | −197.172 | + | 415.392i | −0.198362 | + | 0.417899i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.66259 | + | 4.61175i | 0.00267329 | + | 0.00463027i | ||||
\(997\) | 680.693 | − | 1178.99i | 0.682741 | − | 1.18254i | −0.291400 | − | 0.956601i | \(-0.594121\pi\) |
0.974141 | − | 0.225941i | \(-0.0725457\pi\) | |||||||
\(998\) | −808.613 | − | 466.853i | −0.810234 | − | 0.467789i | ||||
\(999\) | 180.240 | − | 104.062i | 0.180421 | − | 0.104166i |
(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 | 1050.3.q.b.199.4 | 16 | ||
5.2 | odd | 4 | 1050.3.p.c.451.2 | ✓ | 8 | ||
5.3 | odd | 4 | 1050.3.p.d.451.3 | yes | 8 | ||
5.4 | even | 2 | inner | 1050.3.q.b.199.5 | 16 | ||
7.5 | odd | 6 | inner | 1050.3.q.b.649.5 | 16 | ||
35.12 | even | 12 | 1050.3.p.c.901.2 | yes | 8 | ||
35.19 | odd | 6 | inner | 1050.3.q.b.649.4 | 16 | ||
35.33 | even | 12 | 1050.3.p.d.901.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.c.451.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1050.3.p.c.901.2 | yes | 8 | 35.12 | even | 12 | ||
1050.3.p.d.451.3 | yes | 8 | 5.3 | odd | 4 | ||
1050.3.p.d.901.3 | yes | 8 | 35.33 | even | 12 | ||
1050.3.q.b.199.4 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.q.b.199.5 | 16 | 5.4 | even | 2 | inner | ||
1050.3.q.b.649.4 | 16 | 35.19 | odd | 6 | inner | ||
1050.3.q.b.649.5 | 16 | 7.5 | odd | 6 | inner |