Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), degree \(4\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Character | \(\chi\) | \(=\) | 210.67 |
Dual form | 210.3.v.a.163.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.183013 | − | 0.683013i | ||||
\(3\) | −0.448288 | − | 1.67303i | −0.149429 | − | 0.557678i | ||||
\(4\) | −1.73205 | − | 1.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | −1.45729 | + | 4.78292i | −0.291457 | + | 0.956584i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −1.05182 | + | 6.92053i | −0.150260 | + | 0.988647i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.288675 | + | 0.166667i | ||||
\(10\) | 6.00018 | + | 3.74136i | 0.600018 | + | 0.374136i | ||||
\(11\) | −6.50271 | + | 11.2630i | −0.591156 | + | 1.02391i | 0.402921 | + | 0.915235i | \(0.367995\pi\) |
−0.994077 | + | 0.108677i | \(0.965339\pi\) | |||||||
\(12\) | −0.896575 | + | 3.34607i | −0.0747146 | + | 0.278839i | ||||
\(13\) | −0.863323 | + | 0.863323i | −0.0664095 | + | 0.0664095i | −0.739531 | − | 0.673122i | \(-0.764953\pi\) |
0.673122 | + | 0.739531i | \(0.264953\pi\) | |||||||
\(14\) | 9.06862 | + | 3.96990i | 0.647759 | + | 0.283564i | ||||
\(15\) | 8.65526 | + | 0.293964i | 0.577018 | + | 0.0195976i | ||||
\(16\) | 2.00000 | + | 3.46410i | 0.125000 | + | 0.216506i | ||||
\(17\) | −0.902729 | + | 0.241886i | −0.0531017 | + | 0.0142286i | −0.285272 | − | 0.958447i | \(-0.592084\pi\) |
0.232170 | + | 0.972675i | \(0.425417\pi\) | |||||||
\(18\) | 1.09808 | + | 4.09808i | 0.0610042 | + | 0.227671i | ||||
\(19\) | −5.84532 | + | 3.37480i | −0.307648 | + | 0.177621i | −0.645874 | − | 0.763444i | \(-0.723507\pi\) |
0.338225 | + | 0.941065i | \(0.390173\pi\) | |||||||
\(20\) | 7.30701 | − | 6.82697i | 0.365351 | − | 0.341349i | ||||
\(21\) | 12.0498 | − | 1.34266i | 0.573799 | − | 0.0639361i | ||||
\(22\) | 13.0054 | + | 13.0054i | 0.591156 | + | 0.591156i | ||||
\(23\) | 14.5886 | + | 3.90901i | 0.634287 | + | 0.169957i | 0.561615 | − | 0.827399i | \(-0.310180\pi\) |
0.0726729 | + | 0.997356i | \(0.476847\pi\) | |||||||
\(24\) | 4.24264 | + | 2.44949i | 0.176777 | + | 0.102062i | ||||
\(25\) | −20.7526 | − | 13.9402i | −0.830105 | − | 0.557607i | ||||
\(26\) | 0.863323 | + | 1.49532i | 0.0332047 | + | 0.0575123i | ||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 8.74233 | − | 10.9349i | 0.312226 | − | 0.390532i | ||||
\(29\) | 31.3119i | 1.07972i | 0.841754 | + | 0.539861i | \(0.181523\pi\) | ||||
−0.841754 | + | 0.539861i | \(0.818477\pi\) | |||||||
\(30\) | 3.56961 | − | 11.7157i | 0.118987 | − | 0.390524i | ||||
\(31\) | 23.4627 | − | 40.6387i | 0.756863 | − | 1.31092i | −0.187580 | − | 0.982249i | \(-0.560064\pi\) |
0.944443 | − | 0.328675i | \(-0.106602\pi\) | |||||||
\(32\) | 5.46410 | − | 1.46410i | 0.170753 | − | 0.0457532i | ||||
\(33\) | 21.7585 | + | 5.83017i | 0.659348 | + | 0.176672i | ||||
\(34\) | 1.32169i | 0.0388732i | ||||||||
\(35\) | −31.5675 | − | 15.1160i | −0.901929 | − | 0.431885i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −9.80457 | + | 36.5911i | −0.264988 | + | 0.988950i | 0.697269 | + | 0.716809i | \(0.254398\pi\) |
−0.962258 | + | 0.272141i | \(0.912268\pi\) | |||||||
\(38\) | 2.47052 | + | 9.22012i | 0.0650138 | + | 0.242635i | ||||
\(39\) | 1.83139 | + | 1.05735i | 0.0469586 | + | 0.0271116i | ||||
\(40\) | −6.65126 | − | 12.4804i | −0.166282 | − | 0.312010i | ||||
\(41\) | −64.3783 | −1.57020 | −0.785101 | − | 0.619368i | \(-0.787389\pi\) | ||||
−0.785101 | + | 0.619368i | \(0.787389\pi\) | |||||||
\(42\) | 2.57642 | − | 16.9518i | 0.0613434 | − | 0.403613i | ||||
\(43\) | 17.7560 | − | 17.7560i | 0.412931 | − | 0.412931i | −0.469827 | − | 0.882758i | \(-0.655684\pi\) |
0.882758 | + | 0.469827i | \(0.155684\pi\) | |||||||
\(44\) | 22.5261 | − | 13.0054i | 0.511956 | − | 0.295578i | ||||
\(45\) | −3.38824 | − | 14.6123i | −0.0752941 | − | 0.324718i | ||||
\(46\) | 10.6796 | − | 18.4976i | 0.232165 | − | 0.402122i | ||||
\(47\) | −12.9084 | + | 48.1749i | −0.274647 | + | 1.02500i | 0.681430 | + | 0.731883i | \(0.261358\pi\) |
−0.956077 | + | 0.293114i | \(0.905308\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | −46.7873 | − | 14.5583i | −0.954844 | − | 0.297108i | ||||
\(50\) | −26.6386 | + | 23.2462i | −0.532772 | + | 0.464923i | ||||
\(51\) | 0.809365 | + | 1.40186i | 0.0158699 | + | 0.0274875i | ||||
\(52\) | 2.35864 | − | 0.631996i | 0.0453585 | − | 0.0121538i | ||||
\(53\) | 19.3489 | + | 72.2110i | 0.365073 | + | 1.36247i | 0.867321 | + | 0.497749i | \(0.165840\pi\) |
−0.502248 | + | 0.864724i | \(0.667494\pi\) | |||||||
\(54\) | 6.36396 | − | 3.67423i | 0.117851 | − | 0.0680414i | ||||
\(55\) | −44.3938 | − | 47.5154i | −0.807161 | − | 0.863917i | ||||
\(56\) | −11.7374 | − | 15.9447i | −0.209597 | − | 0.284727i | ||||
\(57\) | 8.26653 | + | 8.26653i | 0.145027 | + | 0.145027i | ||||
\(58\) | 42.7729 | + | 11.4610i | 0.737464 | + | 0.197603i | ||||
\(59\) | 31.0409 | + | 17.9215i | 0.526117 | + | 0.303754i | 0.739434 | − | 0.673229i | \(-0.235093\pi\) |
−0.213317 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(60\) | −14.6974 | − | 9.16442i | −0.244957 | − | 0.152740i | ||||
\(61\) | −54.5626 | − | 94.5052i | −0.894469 | − | 1.54927i | −0.834460 | − | 0.551068i | \(-0.814220\pi\) |
−0.0600092 | − | 0.998198i | \(-0.519113\pi\) | |||||||
\(62\) | −46.9255 | − | 46.9255i | −0.756863 | − | 0.756863i | ||||
\(63\) | −7.64808 | − | 19.5578i | −0.121398 | − | 0.310441i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −2.87110 | − | 5.38731i | −0.0441707 | − | 0.0828818i | ||||
\(66\) | 15.9283 | − | 27.5887i | 0.241338 | − | 0.418010i | ||||
\(67\) | 60.4832 | − | 16.2064i | 0.902734 | − | 0.241887i | 0.222544 | − | 0.974923i | \(-0.428564\pi\) |
0.680190 | + | 0.733036i | \(0.261897\pi\) | |||||||
\(68\) | 1.80546 | + | 0.483771i | 0.0265509 | + | 0.00711428i | ||||
\(69\) | − | 26.1596i | − | 0.379124i | ||||||
\(70\) | −32.2033 | + | 37.5892i | −0.460047 | + | 0.536989i | ||||
\(71\) | −74.7760 | −1.05318 | −0.526592 | − | 0.850118i | \(-0.676530\pi\) | ||||
−0.526592 | + | 0.850118i | \(0.676530\pi\) | |||||||
\(72\) | 2.19615 | − | 8.19615i | 0.0305021 | − | 0.113835i | ||||
\(73\) | 21.5032 | + | 80.2512i | 0.294565 | + | 1.09933i | 0.941562 | + | 0.336839i | \(0.109358\pi\) |
−0.646997 | + | 0.762492i | \(0.723975\pi\) | |||||||
\(74\) | 46.3957 | + | 26.7866i | 0.626969 | + | 0.361981i | ||||
\(75\) | −14.0192 | + | 40.9690i | −0.186923 | + | 0.546254i | ||||
\(76\) | 13.4992 | 0.177621 | ||||||||
\(77\) | −71.1064 | − | 56.8489i | −0.923460 | − | 0.738297i | ||||
\(78\) | 2.11470 | − | 2.11470i | 0.0271116 | − | 0.0271116i | ||||
\(79\) | 83.9374 | − | 48.4613i | 1.06250 | − | 0.613434i | 0.136377 | − | 0.990657i | \(-0.456454\pi\) |
0.926122 | + | 0.377223i | \(0.123121\pi\) | |||||||
\(80\) | −19.4831 | + | 4.51765i | −0.243539 | + | 0.0564706i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −23.5641 | + | 87.9423i | −0.287367 | + | 1.07247i | ||||
\(83\) | 31.9008 | − | 31.9008i | 0.384347 | − | 0.384347i | −0.488318 | − | 0.872666i | \(-0.662390\pi\) |
0.872666 | + | 0.488318i | \(0.162390\pi\) | |||||||
\(84\) | −22.2135 | − | 9.72423i | −0.264446 | − | 0.115765i | ||||
\(85\) | 0.158616 | − | 4.67018i | 0.00186607 | − | 0.0549433i | ||||
\(86\) | −17.7560 | − | 30.7543i | −0.206465 | − | 0.357609i | ||||
\(87\) | 52.3859 | − | 14.0368i | 0.602137 | − | 0.161342i | ||||
\(88\) | −9.52063 | − | 35.5315i | −0.108189 | − | 0.403767i | ||||
\(89\) | −44.1998 | + | 25.5187i | −0.496627 | + | 0.286727i | −0.727319 | − | 0.686299i | \(-0.759234\pi\) |
0.230693 | + | 0.973027i | \(0.425901\pi\) | |||||||
\(90\) | −21.2010 | − | 0.720063i | −0.235566 | − | 0.00800070i | ||||
\(91\) | −5.06659 | − | 6.88271i | −0.0556768 | − | 0.0756342i | ||||
\(92\) | −21.3592 | − | 21.3592i | −0.232165 | − | 0.232165i | ||||
\(93\) | −78.5079 | − | 21.0361i | −0.844171 | − | 0.226195i | ||||
\(94\) | 61.0833 | + | 35.2664i | 0.649822 | + | 0.375175i | ||||
\(95\) | −7.62307 | − | 32.8757i | −0.0802429 | − | 0.346060i | ||||
\(96\) | −4.89898 | − | 8.48528i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −83.5410 | − | 83.5410i | −0.861248 | − | 0.861248i | 0.130235 | − | 0.991483i | \(-0.458427\pi\) |
−0.991483 | + | 0.130235i | \(0.958427\pi\) | |||||||
\(98\) | −37.0124 | + | 58.5840i | −0.377677 | + | 0.597796i | ||||
\(99\) | − | 39.0163i | − | 0.394104i | ||||||
\(100\) | 22.0044 | + | 44.8977i | 0.220044 | + | 0.448977i | ||||
\(101\) | 80.9688 | − | 140.242i | 0.801671 | − | 1.38854i | −0.116844 | − | 0.993150i | \(-0.537278\pi\) |
0.918516 | − | 0.395385i | \(-0.129389\pi\) | |||||||
\(102\) | 2.21123 | − | 0.592496i | 0.0216787 | − | 0.00580879i | ||||
\(103\) | 80.9886 | + | 21.7008i | 0.786297 | + | 0.210688i | 0.629559 | − | 0.776953i | \(-0.283236\pi\) |
0.156738 | + | 0.987640i | \(0.449902\pi\) | |||||||
\(104\) | − | 3.45329i | − | 0.0332047i | ||||||
\(105\) | −11.1382 | + | 59.5898i | −0.106078 | + | 0.567522i | ||||
\(106\) | 105.724 | 0.997399 | ||||||||
\(107\) | −19.2233 | + | 71.7422i | −0.179657 | + | 0.670488i | 0.816055 | + | 0.577974i | \(0.196157\pi\) |
−0.995711 | + | 0.0925131i | \(0.970510\pi\) | |||||||
\(108\) | −2.68973 | − | 10.0382i | −0.0249049 | − | 0.0929463i | ||||
\(109\) | 106.923 | + | 61.7319i | 0.980942 | + | 0.566347i | 0.902554 | − | 0.430576i | \(-0.141689\pi\) |
0.0783878 | + | 0.996923i | \(0.475023\pi\) | |||||||
\(110\) | −81.1565 | + | 43.2513i | −0.737787 | + | 0.393193i | ||||
\(111\) | 65.6134 | 0.591112 | ||||||||
\(112\) | −26.0770 | + | 10.1974i | −0.232831 | + | 0.0910486i | ||||
\(113\) | −41.6631 | + | 41.6631i | −0.368700 | + | 0.368700i | −0.867003 | − | 0.498303i | \(-0.833957\pi\) |
0.498303 | + | 0.867003i | \(0.333957\pi\) | |||||||
\(114\) | 14.3181 | − | 8.26653i | 0.125597 | − | 0.0725134i | ||||
\(115\) | −39.9563 | + | 64.0796i | −0.347446 | + | 0.557214i | ||||
\(116\) | 31.3119 | − | 54.2339i | 0.269930 | − | 0.467533i | ||||
\(117\) | 0.947995 | − | 3.53796i | 0.00810252 | − | 0.0302390i | ||||
\(118\) | 35.8429 | − | 35.8429i | 0.303754 | − | 0.303754i | ||||
\(119\) | −0.724467 | − | 6.50178i | −0.00608795 | − | 0.0546368i | ||||
\(120\) | −17.8985 | + | 16.7226i | −0.149154 | + | 0.139355i | ||||
\(121\) | −24.0705 | − | 41.6914i | −0.198930 | − | 0.344557i | ||||
\(122\) | −149.068 | + | 39.9426i | −1.22187 | + | 0.327398i | ||||
\(123\) | 28.8600 | + | 107.707i | 0.234634 | + | 0.875666i | ||||
\(124\) | −81.2773 | + | 46.9255i | −0.655462 | + | 0.378431i | ||||
\(125\) | 96.9172 | − | 78.9433i | 0.775338 | − | 0.631547i | ||||
\(126\) | −29.5158 | + | 3.28883i | −0.234253 | + | 0.0261018i | ||||
\(127\) | 105.461 | + | 105.461i | 0.830399 | + | 0.830399i | 0.987571 | − | 0.157172i | \(-0.0502378\pi\) |
−0.157172 | + | 0.987571i | \(0.550238\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | −37.6662 | − | 21.7466i | −0.291986 | − | 0.168578i | ||||
\(130\) | −8.41010 | + | 1.95010i | −0.0646931 | + | 0.0150007i | ||||
\(131\) | 104.890 | + | 181.676i | 0.800690 | + | 1.38684i | 0.919162 | + | 0.393879i | \(0.128867\pi\) |
−0.118472 | + | 0.992957i | \(0.537800\pi\) | |||||||
\(132\) | −31.8567 | − | 31.8567i | −0.241338 | − | 0.241338i | ||||
\(133\) | −17.2071 | − | 44.0024i | −0.129377 | − | 0.330845i | ||||
\(134\) | − | 88.5535i | − | 0.660847i | ||||||
\(135\) | −22.9280 | + | 12.2192i | −0.169837 | + | 0.0905122i | ||||
\(136\) | 1.32169 | − | 2.28923i | 0.00971829 | − | 0.0168326i | ||||
\(137\) | 218.804 | − | 58.6283i | 1.59711 | − | 0.427943i | 0.652940 | − | 0.757410i | \(-0.273536\pi\) |
0.944167 | + | 0.329467i | \(0.106869\pi\) | |||||||
\(138\) | −35.7347 | − | 9.57507i | −0.258947 | − | 0.0693846i | ||||
\(139\) | − | 42.1416i | − | 0.303177i | −0.988444 | − | 0.151588i | \(-0.951561\pi\) | ||
0.988444 | − | 0.151588i | \(-0.0484389\pi\) | |||||||
\(140\) | 39.5606 | + | 57.7491i | 0.282576 | + | 0.412494i | ||||
\(141\) | 86.3848 | 0.612658 | ||||||||
\(142\) | −27.3699 | + | 102.146i | −0.192746 | + | 0.719337i | ||||
\(143\) | −4.10969 | − | 15.3376i | −0.0287391 | − | 0.107256i | ||||
\(144\) | −10.3923 | − | 6.00000i | −0.0721688 | − | 0.0416667i | ||||
\(145\) | −149.762 | − | 45.6305i | −1.03284 | − | 0.314693i | ||||
\(146\) | 117.496 | 0.804766 | ||||||||
\(147\) | −3.38231 | + | 84.8031i | −0.0230089 | + | 0.576892i | ||||
\(148\) | 53.5732 | − | 53.5732i | 0.361981 | − | 0.361981i | ||||
\(149\) | 66.4442 | − | 38.3616i | 0.445934 | − | 0.257460i | −0.260177 | − | 0.965561i | \(-0.583781\pi\) |
0.706112 | + | 0.708101i | \(0.250448\pi\) | |||||||
\(150\) | 50.8334 | + | 34.1463i | 0.338889 | + | 0.227642i | ||||
\(151\) | 15.4393 | − | 26.7416i | 0.102247 | − | 0.177097i | −0.810363 | − | 0.585928i | \(-0.800730\pi\) |
0.912610 | + | 0.408831i | \(0.134064\pi\) | |||||||
\(152\) | 4.94105 | − | 18.4402i | 0.0325069 | − | 0.121317i | ||||
\(153\) | 1.98253 | − | 1.98253i | 0.0129577 | − | 0.0129577i | ||||
\(154\) | −103.684 | + | 76.3250i | −0.673271 | + | 0.495617i | ||||
\(155\) | 160.179 | + | 171.443i | 1.03342 | + | 1.10608i | ||||
\(156\) | −2.11470 | − | 3.66277i | −0.0135558 | − | 0.0234793i | ||||
\(157\) | −62.1560 | + | 16.6546i | −0.395898 | + | 0.106081i | −0.451275 | − | 0.892385i | \(-0.649031\pi\) |
0.0553769 | + | 0.998466i | \(0.482364\pi\) | |||||||
\(158\) | −35.4761 | − | 132.399i | −0.224532 | − | 0.837967i | ||||
\(159\) | 112.138 | − | 64.7426i | 0.705268 | − | 0.407186i | ||||
\(160\) | −0.960084 | + | 28.2680i | −0.00600052 | + | 0.176675i | ||||
\(161\) | −42.3970 | + | 96.8493i | −0.263335 | + | 0.601548i | ||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 90.5074 | + | 24.2514i | 0.555260 | + | 0.148782i | 0.525528 | − | 0.850776i | \(-0.323868\pi\) |
0.0297323 | + | 0.999558i | \(0.490535\pi\) | |||||||
\(164\) | 111.506 | + | 64.3783i | 0.679917 | + | 0.392550i | ||||
\(165\) | −59.5936 | + | 95.5729i | −0.361173 | + | 0.579230i | ||||
\(166\) | −31.9008 | − | 55.2538i | −0.192174 | − | 0.332854i | ||||
\(167\) | −30.1240 | − | 30.1240i | −0.180383 | − | 0.180383i | 0.611140 | − | 0.791523i | \(-0.290711\pi\) |
−0.791523 | + | 0.611140i | \(0.790711\pi\) | |||||||
\(168\) | −21.4143 | + | 26.7849i | −0.127466 | + | 0.159434i | ||||
\(169\) | 167.509i | 0.991180i | ||||||||
\(170\) | −6.32152 | − | 1.92608i | −0.0371854 | − | 0.0113299i | ||||
\(171\) | 10.1244 | − | 17.5360i | 0.0592070 | − | 0.102549i | ||||
\(172\) | −48.5104 | + | 12.9983i | −0.282037 | + | 0.0755716i | ||||
\(173\) | 57.0293 | + | 15.2810i | 0.329649 | + | 0.0883293i | 0.419848 | − | 0.907595i | \(-0.362083\pi\) |
−0.0901984 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(174\) | − | 76.6983i | − | 0.440795i | ||||||
\(175\) | 118.301 | − | 128.957i | 0.676008 | − | 0.736895i | ||||
\(176\) | −52.0217 | −0.295578 | ||||||||
\(177\) | 16.0679 | − | 59.9664i | 0.0907794 | − | 0.338793i | ||||
\(178\) | 18.6810 | + | 69.7185i | 0.104950 | + | 0.391677i | ||||
\(179\) | 185.470 | + | 107.081i | 1.03615 | + | 0.598220i | 0.918740 | − | 0.394864i | \(-0.129208\pi\) |
0.117408 | + | 0.993084i | \(0.462542\pi\) | |||||||
\(180\) | −8.74372 | + | 28.6975i | −0.0485762 | + | 0.159431i | ||||
\(181\) | −265.353 | −1.46604 | −0.733019 | − | 0.680208i | \(-0.761890\pi\) | ||||
−0.733019 | + | 0.680208i | \(0.761890\pi\) | |||||||
\(182\) | −11.2565 | + | 4.40184i | −0.0618487 | + | 0.0241860i | ||||
\(183\) | −133.651 | + | 133.651i | −0.730331 | + | 0.730331i | ||||
\(184\) | −36.9952 | + | 21.3592i | −0.201061 | + | 0.116083i | ||||
\(185\) | −160.724 | − | 100.218i | −0.868781 | − | 0.541720i | ||||
\(186\) | −57.4717 | + | 99.5440i | −0.308988 | + | 0.535183i | ||||
\(187\) | 3.14582 | − | 11.7404i | 0.0168226 | − | 0.0627828i | ||||
\(188\) | 70.5329 | − | 70.5329i | 0.375175 | − | 0.375175i | ||||
\(189\) | −29.2923 | + | 21.5630i | −0.154986 | + | 0.114090i | ||||
\(190\) | −47.6993 | − | 1.62004i | −0.251049 | − | 0.00852655i | ||||
\(191\) | 2.14117 | + | 3.70861i | 0.0112103 | + | 0.0194168i | 0.871576 | − | 0.490260i | \(-0.163098\pi\) |
−0.860366 | + | 0.509677i | \(0.829765\pi\) | |||||||
\(192\) | −13.3843 | + | 3.58630i | −0.0697097 | + | 0.0186787i | ||||
\(193\) | 61.2292 | + | 228.511i | 0.317250 | + | 1.18399i | 0.921877 | + | 0.387484i | \(0.126656\pi\) |
−0.604627 | + | 0.796509i | \(0.706678\pi\) | |||||||
\(194\) | −144.697 | + | 83.5410i | −0.745862 | + | 0.430624i | ||||
\(195\) | −7.72608 | + | 7.21850i | −0.0396209 | + | 0.0370180i | ||||
\(196\) | 66.4798 | + | 72.0031i | 0.339183 | + | 0.367363i | ||||
\(197\) | 6.11514 | + | 6.11514i | 0.0310413 | + | 0.0310413i | 0.722457 | − | 0.691416i | \(-0.243013\pi\) |
−0.691416 | + | 0.722457i | \(0.743013\pi\) | |||||||
\(198\) | −53.2972 | − | 14.2809i | −0.269178 | − | 0.0721260i | ||||
\(199\) | −214.306 | − | 123.729i | −1.07691 | − | 0.621756i | −0.146851 | − | 0.989159i | \(-0.546914\pi\) |
−0.930062 | + | 0.367402i | \(0.880247\pi\) | |||||||
\(200\) | 69.3856 | − | 13.6249i | 0.346928 | − | 0.0681246i | ||||
\(201\) | −54.2277 | − | 93.9252i | −0.269790 | − | 0.467289i | ||||
\(202\) | −161.938 | − | 161.938i | −0.801671 | − | 0.801671i | ||||
\(203\) | −216.695 | − | 32.9345i | −1.06746 | − | 0.162239i | ||||
\(204\) | − | 3.23746i | − | 0.0158699i | ||||||
\(205\) | 93.8176 | − | 307.916i | 0.457647 | − | 1.50203i | ||||
\(206\) | 59.2878 | − | 102.689i | 0.287805 | − | 0.498492i | ||||
\(207\) | −43.7658 | + | 11.7270i | −0.211429 | + | 0.0566523i | ||||
\(208\) | −4.71729 | − | 1.26399i | −0.0226793 | − | 0.00607689i | ||||
\(209\) | − | 87.7813i | − | 0.420006i | ||||||
\(210\) | 77.3243 | + | 37.0264i | 0.368211 | + | 0.176316i | ||||
\(211\) | −299.419 | −1.41905 | −0.709524 | − | 0.704681i | \(-0.751090\pi\) | ||||
−0.709524 | + | 0.704681i | \(0.751090\pi\) | |||||||
\(212\) | 38.6978 | − | 144.422i | 0.182537 | − | 0.681236i | ||||
\(213\) | 33.5212 | + | 125.103i | 0.157376 | + | 0.587337i | ||||
\(214\) | 90.9654 | + | 52.5189i | 0.425072 | + | 0.245415i | ||||
\(215\) | 59.0500 | + | 110.801i | 0.274651 | + | 0.515355i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 256.562 | + | 205.119i | 1.18231 | + | 0.945249i | ||||
\(218\) | 123.464 | − | 123.464i | 0.566347 | − | 0.566347i | ||||
\(219\) | 124.623 | − | 71.9513i | 0.569056 | − | 0.328545i | ||||
\(220\) | 29.3770 | + | 126.693i | 0.133532 | + | 0.575877i | ||||
\(221\) | 0.570522 | − | 0.988172i | 0.00258155 | − | 0.00447137i | ||||
\(222\) | 24.0162 | − | 89.6296i | 0.108181 | − | 0.403737i | ||||
\(223\) | 151.041 | − | 151.041i | 0.677313 | − | 0.677313i | −0.282078 | − | 0.959391i | \(-0.591024\pi\) |
0.959391 | + | 0.282078i | \(0.0910237\pi\) | |||||||
\(224\) | 4.38510 | + | 39.3544i | 0.0195763 | + | 0.175689i | ||||
\(225\) | 74.8272 | + | 5.08868i | 0.332565 | + | 0.0226164i | ||||
\(226\) | 41.6631 | + | 72.1626i | 0.184350 | + | 0.319304i | ||||
\(227\) | 55.4109 | − | 14.8473i | 0.244101 | − | 0.0654066i | −0.134694 | − | 0.990887i | \(-0.543005\pi\) |
0.378795 | + | 0.925481i | \(0.376339\pi\) | |||||||
\(228\) | −6.05152 | − | 22.5846i | −0.0265418 | − | 0.0990552i | ||||
\(229\) | 85.5592 | − | 49.3976i | 0.373621 | − | 0.215710i | −0.301418 | − | 0.953492i | \(-0.597460\pi\) |
0.675039 | + | 0.737782i | \(0.264127\pi\) | |||||||
\(230\) | 72.9094 | + | 78.0360i | 0.316997 | + | 0.339287i | ||||
\(231\) | −63.2339 | + | 144.448i | −0.273740 | + | 0.625316i | ||||
\(232\) | −62.6239 | − | 62.6239i | −0.269930 | − | 0.269930i | ||||
\(233\) | −416.934 | − | 111.717i | −1.78942 | − | 0.479473i | −0.797170 | − | 0.603754i | \(-0.793671\pi\) |
−0.992247 | + | 0.124281i | \(0.960337\pi\) | |||||||
\(234\) | −4.48596 | − | 2.58997i | −0.0191708 | − | 0.0110682i | ||||
\(235\) | −211.605 | − | 131.945i | −0.900448 | − | 0.561466i | ||||
\(236\) | −35.8429 | − | 62.0818i | −0.151877 | − | 0.263058i | ||||
\(237\) | −118.705 | − | 118.705i | −0.500867 | − | 0.500867i | ||||
\(238\) | −9.14677 | − | 1.39018i | −0.0384318 | − | 0.00584108i | ||||
\(239\) | − | 344.565i | − | 1.44169i | −0.693094 | − | 0.720847i | \(-0.743753\pi\) | ||
0.693094 | − | 0.720847i | \(-0.256247\pi\) | |||||||
\(240\) | 16.2922 | + | 30.5706i | 0.0678842 | + | 0.127378i | ||||
\(241\) | 50.1238 | − | 86.8170i | 0.207983 | − | 0.360237i | −0.743096 | − | 0.669185i | \(-0.766644\pi\) |
0.951079 | + | 0.308948i | \(0.0999769\pi\) | |||||||
\(242\) | −65.7619 | + | 17.6209i | −0.271744 | + | 0.0728135i | ||||
\(243\) | −15.0573 | − | 4.03459i | −0.0619642 | − | 0.0166032i | ||||
\(244\) | 218.251i | 0.894469i | ||||||||
\(245\) | 137.814 | − | 202.564i | 0.562505 | − | 0.826794i | ||||
\(246\) | 157.694 | 0.641032 | ||||||||
\(247\) | 2.13286 | − | 7.95994i | 0.00863506 | − | 0.0322265i | ||||
\(248\) | 34.3518 | + | 128.203i | 0.138515 | + | 0.516947i | ||||
\(249\) | −67.6719 | − | 39.0704i | −0.271775 | − | 0.156909i | ||||
\(250\) | −72.3644 | − | 161.287i | −0.289458 | − | 0.645147i | ||||
\(251\) | 404.247 | 1.61054 | 0.805272 | − | 0.592905i | \(-0.202019\pi\) | ||||
0.805272 | + | 0.592905i | \(0.202019\pi\) | |||||||
\(252\) | −6.31092 | + | 41.5232i | −0.0250433 | + | 0.164774i | ||||
\(253\) | −138.893 | + | 138.893i | −0.548983 | + | 0.548983i | ||||
\(254\) | 182.663 | − | 105.461i | 0.719147 | − | 0.415200i | ||||
\(255\) | −7.88446 | + | 1.82821i | −0.0309195 | + | 0.00716946i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.03579 | − | 33.7220i | 0.0351587 | − | 0.131214i | −0.946116 | − | 0.323828i | \(-0.895030\pi\) |
0.981275 | + | 0.192614i | \(0.0616966\pi\) | |||||||
\(258\) | −43.4932 | + | 43.4932i | −0.168578 | + | 0.168578i | ||||
\(259\) | −242.917 | − | 106.340i | −0.937905 | − | 0.410579i | ||||
\(260\) | −0.414431 | + | 12.2022i | −0.00159397 | + | 0.0469315i | ||||
\(261\) | −46.9679 | − | 81.3508i | −0.179954 | − | 0.311689i | ||||
\(262\) | 286.566 | − | 76.7851i | 1.09376 | − | 0.293073i | ||||
\(263\) | −53.2792 | − | 198.841i | −0.202583 | − | 0.756049i | −0.990173 | − | 0.139849i | \(-0.955338\pi\) |
0.787590 | − | 0.616199i | \(-0.211328\pi\) | |||||||
\(264\) | −55.1773 | + | 31.8567i | −0.209005 | + | 0.120669i | ||||
\(265\) | −373.576 | − | 12.6880i | −1.40972 | − | 0.0478793i | ||||
\(266\) | −66.4066 | + | 7.39941i | −0.249649 | + | 0.0278173i | ||||
\(267\) | 62.5079 | + | 62.5079i | 0.234112 | + | 0.234112i | ||||
\(268\) | −120.966 | − | 32.4128i | −0.451367 | − | 0.120943i | ||||
\(269\) | −124.603 | − | 71.9393i | −0.463206 | − | 0.267432i | 0.250185 | − | 0.968198i | \(-0.419509\pi\) |
−0.713392 | + | 0.700766i | \(0.752842\pi\) | |||||||
\(270\) | 8.29945 | + | 35.7927i | 0.0307387 | + | 0.132566i | ||||
\(271\) | 95.3473 | + | 165.146i | 0.351835 | + | 0.609396i | 0.986571 | − | 0.163333i | \(-0.0522245\pi\) |
−0.634736 | + | 0.772729i | \(0.718891\pi\) | |||||||
\(272\) | −2.64337 | − | 2.64337i | −0.00971829 | − | 0.00971829i | ||||
\(273\) | −9.24371 | + | 11.5620i | −0.0338597 | + | 0.0423517i | ||||
\(274\) | − | 320.351i | − | 1.16916i | ||||||
\(275\) | 291.957 | − | 143.089i | 1.06166 | − | 0.520322i | ||||
\(276\) | −26.1596 | + | 45.3097i | −0.0947811 | + | 0.164166i | ||||
\(277\) | 47.5729 | − | 12.7471i | 0.171743 | − | 0.0460185i | −0.171923 | − | 0.985110i | \(-0.554998\pi\) |
0.343666 | + | 0.939092i | \(0.388331\pi\) | |||||||
\(278\) | −57.5665 | − | 15.4249i | −0.207074 | − | 0.0554852i | ||||
\(279\) | 140.776i | 0.504575i | ||||||||
\(280\) | 93.3669 | − | 32.9031i | 0.333453 | − | 0.117511i | ||||
\(281\) | −343.443 | −1.22222 | −0.611109 | − | 0.791546i | \(-0.709276\pi\) | ||||
−0.611109 | + | 0.791546i | \(0.709276\pi\) | |||||||
\(282\) | 31.6190 | − | 118.004i | 0.112124 | − | 0.418453i | ||||
\(283\) | −28.4135 | − | 106.040i | −0.100401 | − | 0.374701i | 0.897382 | − | 0.441255i | \(-0.145466\pi\) |
−0.997783 | + | 0.0665533i | \(0.978800\pi\) | |||||||
\(284\) | 129.516 | + | 74.7760i | 0.456042 | + | 0.263296i | ||||
\(285\) | −51.5849 | + | 27.4914i | −0.181000 | + | 0.0964612i | ||||
\(286\) | −22.4558 | −0.0785167 | ||||||||
\(287\) | 67.7143 | − | 445.531i | 0.235938 | − | 1.55237i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | −249.525 | + | 144.063i | −0.863408 | + | 0.498489i | ||||
\(290\) | −117.149 | + | 187.877i | −0.403963 | + | 0.647853i | ||||
\(291\) | −102.316 | + | 177.217i | −0.351603 | + | 0.608994i | ||||
\(292\) | 43.0065 | − | 160.502i | 0.147282 | − | 0.549666i | ||||
\(293\) | −24.9404 | + | 24.9404i | −0.0851209 | + | 0.0851209i | −0.748385 | − | 0.663264i | \(-0.769171\pi\) |
0.663264 | + | 0.748385i | \(0.269171\pi\) | |||||||
\(294\) | 114.605 | + | 35.6604i | 0.389813 | + | 0.121294i | ||||
\(295\) | −130.952 | + | 122.349i | −0.443906 | + | 0.414744i | ||||
\(296\) | −53.5732 | − | 92.7914i | −0.180990 | − | 0.313485i | ||||
\(297\) | −65.2755 | + | 17.4905i | −0.219783 | + | 0.0588906i | ||||
\(298\) | −28.0826 | − | 104.806i | −0.0942370 | − | 0.351697i | ||||
\(299\) | −15.9694 | + | 9.21995i | −0.0534094 | + | 0.0308360i | ||||
\(300\) | 65.2510 | − | 56.9412i | 0.217503 | − | 0.189804i | ||||
\(301\) | 104.205 | + | 141.557i | 0.346196 | + | 0.470290i | ||||
\(302\) | −30.8785 | − | 30.8785i | −0.102247 | − | 0.102247i | ||||
\(303\) | −270.927 | − | 72.5946i | −0.894148 | − | 0.239586i | ||||
\(304\) | −23.3813 | − | 13.4992i | −0.0769121 | − | 0.0444052i | ||||
\(305\) | 531.524 | − | 123.247i | 1.74270 | − | 0.404090i | ||||
\(306\) | −1.98253 | − | 3.43384i | −0.00647886 | − | 0.0112217i | ||||
\(307\) | 311.194 | + | 311.194i | 1.01366 | + | 1.01366i | 0.999905 | + | 0.0137553i | \(0.00437859\pi\) |
0.0137553 | + | 0.999905i | \(0.495621\pi\) | |||||||
\(308\) | 66.3110 | + | 169.572i | 0.215296 | + | 0.550557i | ||||
\(309\) | − | 145.225i | − | 0.469983i | ||||||
\(310\) | 292.825 | − | 156.057i | 0.944596 | − | 0.503409i | ||||
\(311\) | −226.533 | + | 392.367i | −0.728403 | + | 1.26163i | 0.229155 | + | 0.973390i | \(0.426404\pi\) |
−0.957558 | + | 0.288241i | \(0.906929\pi\) | |||||||
\(312\) | −5.77747 | + | 1.54807i | −0.0185175 | + | 0.00496176i | ||||
\(313\) | 325.203 | + | 87.1378i | 1.03899 | + | 0.278396i | 0.737693 | − | 0.675136i | \(-0.235915\pi\) |
0.301293 | + | 0.953532i | \(0.402582\pi\) | |||||||
\(314\) | 91.0027i | 0.289817i | ||||||||
\(315\) | 104.689 | − | 8.07885i | 0.332345 | − | 0.0256471i | ||||
\(316\) | −193.845 | −0.613434 | ||||||||
\(317\) | −131.216 | + | 489.707i | −0.413932 | + | 1.54482i | 0.373033 | + | 0.927818i | \(0.378318\pi\) |
−0.786965 | + | 0.616998i | \(0.788349\pi\) | |||||||
\(318\) | −47.3949 | − | 176.880i | −0.149041 | − | 0.556227i | ||||
\(319\) | −352.667 | − | 203.613i | −1.10554 | − | 0.638284i | ||||
\(320\) | 38.2634 | + | 11.6583i | 0.119573 | + | 0.0364322i | ||||
\(321\) | 128.645 | 0.400762 | ||||||||
\(322\) | 116.780 | + | 93.3646i | 0.362671 | + | 0.289952i | ||||
\(323\) | 4.46043 | − | 4.46043i | 0.0138094 | − | 0.0138094i | ||||
\(324\) | −15.5885 | + | 9.00000i | −0.0481125 | + | 0.0277778i | ||||
\(325\) | 29.9511 | − | 5.88135i | 0.0921572 | − | 0.0180965i | ||||
\(326\) | 66.2560 | − | 114.759i | 0.203239 | − | 0.352021i | ||||
\(327\) | 55.3473 | − | 206.559i | 0.169258 | − | 0.631678i | ||||
\(328\) | 128.757 | − | 128.757i | 0.392550 | − | 0.392550i | ||||
\(329\) | −319.818 | − | 140.004i | −0.972091 | − | 0.425545i | ||||
\(330\) | 108.742 | + | 116.389i | 0.329522 | + | 0.352692i | ||||
\(331\) | 88.2204 | + | 152.802i | 0.266527 | + | 0.461638i | 0.967963 | − | 0.251095i | \(-0.0807906\pi\) |
−0.701436 | + | 0.712733i | \(0.747457\pi\) | |||||||
\(332\) | −87.1547 | + | 23.3530i | −0.262514 | + | 0.0703404i | ||||
\(333\) | −29.4137 | − | 109.773i | −0.0883294 | − | 0.329650i | ||||
\(334\) | −52.1762 | + | 30.1240i | −0.156216 | + | 0.0901915i | ||||
\(335\) | −10.6274 | + | 312.904i | −0.0317234 | + | 0.934040i | ||||
\(336\) | 28.7507 | + | 39.0564i | 0.0855675 | + | 0.116239i | ||||
\(337\) | 93.6762 | + | 93.6762i | 0.277971 | + | 0.277971i | 0.832299 | − | 0.554328i | \(-0.187025\pi\) |
−0.554328 | + | 0.832299i | \(0.687025\pi\) | |||||||
\(338\) | 228.822 | + | 61.3127i | 0.676988 | + | 0.181398i | ||||
\(339\) | 88.3808 | + | 51.0267i | 0.260710 | + | 0.150521i | ||||
\(340\) | −4.94491 | + | 7.93037i | −0.0145438 | + | 0.0233246i | ||||
\(341\) | 305.143 | + | 528.523i | 0.894847 | + | 1.54992i | ||||
\(342\) | −20.2488 | − | 20.2488i | −0.0592070 | − | 0.0592070i | ||||
\(343\) | 149.963 | − | 308.480i | 0.437210 | − | 0.899360i | ||||
\(344\) | 71.0241i | 0.206465i | ||||||||
\(345\) | 125.119 | + | 38.1220i | 0.362664 | + | 0.110499i | ||||
\(346\) | 41.7484 | − | 72.3103i | 0.120660 | − | 0.208989i | ||||
\(347\) | 462.828 | − | 124.014i | 1.33380 | − | 0.357390i | 0.479668 | − | 0.877450i | \(-0.340757\pi\) |
0.854130 | + | 0.520060i | \(0.174090\pi\) | |||||||
\(348\) | −104.772 | − | 28.0735i | −0.301068 | − | 0.0806710i | ||||
\(349\) | 529.116i | 1.51609i | 0.652201 | + | 0.758046i | \(0.273846\pi\) | ||||
−0.652201 | + | 0.758046i | \(0.726154\pi\) | |||||||
\(350\) | −132.857 | − | 208.804i | −0.379590 | − | 0.596583i | ||||
\(351\) | −6.34410 | −0.0180744 | ||||||||
\(352\) | −19.0413 | + | 71.0630i | −0.0540945 | + | 0.201883i | ||||
\(353\) | −42.6410 | − | 159.138i | −0.120796 | − | 0.450817i | 0.878859 | − | 0.477082i | \(-0.158305\pi\) |
−0.999655 | + | 0.0262647i | \(0.991639\pi\) | |||||||
\(354\) | −76.0343 | − | 43.8984i | −0.214786 | − | 0.124007i | ||||
\(355\) | 108.970 | − | 357.648i | 0.306958 | − | 1.00746i | ||||
\(356\) | 102.075 | 0.286727 | ||||||||
\(357\) | −10.5529 | + | 4.12672i | −0.0295600 | + | 0.0115595i | ||||
\(358\) | 214.163 | − | 214.163i | 0.598220 | − | 0.598220i | ||||
\(359\) | −308.088 | + | 177.875i | −0.858184 | + | 0.495473i | −0.863404 | − | 0.504513i | \(-0.831672\pi\) |
0.00521959 | + | 0.999986i | \(0.498339\pi\) | |||||||
\(360\) | 36.0011 | + | 22.4482i | 0.100003 | + | 0.0623560i | ||||
\(361\) | −157.721 | + | 273.182i | −0.436902 | + | 0.756736i | ||||
\(362\) | −97.1260 | + | 362.479i | −0.268304 | + | 1.00132i | ||||
\(363\) | −58.9605 | + | 58.9605i | −0.162426 | + | 0.162426i | ||||
\(364\) | 1.89288 | + | 16.9878i | 0.00520022 | + | 0.0466698i | ||||
\(365\) | −415.171 | − | 14.1007i | −1.13746 | − | 0.0386322i | ||||
\(366\) | 133.651 | + | 231.490i | 0.365166 | + | 0.632485i | ||||
\(367\) | −367.501 | + | 98.4715i | −1.00136 | + | 0.268315i | −0.722017 | − | 0.691875i | \(-0.756785\pi\) |
−0.279347 | + | 0.960190i | \(0.590118\pi\) | |||||||
\(368\) | 15.6360 | + | 58.3544i | 0.0424892 | + | 0.158572i | ||||
\(369\) | 167.260 | − | 96.5674i | 0.453278 | − | 0.261700i | ||||
\(370\) | −195.730 | + | 182.871i | −0.529000 | + | 0.494247i | ||||
\(371\) | −520.090 | + | 57.9515i | −1.40186 | + | 0.156203i | ||||
\(372\) | 114.943 | + | 114.943i | 0.308988 | + | 0.308988i | ||||
\(373\) | 323.837 | + | 86.7718i | 0.868195 | + | 0.232632i | 0.665307 | − | 0.746570i | \(-0.268301\pi\) |
0.202888 | + | 0.979202i | \(0.434967\pi\) | |||||||
\(374\) | −14.8862 | − | 8.59455i | −0.0398027 | − | 0.0229801i | ||||
\(375\) | −175.522 | − | 126.756i | −0.468058 | − | 0.338017i | ||||
\(376\) | −70.5329 | − | 122.167i | −0.187587 | − | 0.324911i | ||||
\(377\) | −27.0323 | − | 27.0323i | −0.0717038 | − | 0.0717038i | ||||
\(378\) | 18.7339 | + | 47.9066i | 0.0495606 | + | 0.126737i | ||||
\(379\) | 674.043i | 1.77848i | 0.457443 | + | 0.889239i | \(0.348765\pi\) | ||||
−0.457443 | + | 0.889239i | \(0.651235\pi\) | |||||||
\(380\) | −19.6722 | + | 64.5655i | −0.0517689 | + | 0.169909i | ||||
\(381\) | 129.162 | − | 223.716i | 0.339009 | − | 0.587181i | ||||
\(382\) | 5.84978 | − | 1.56744i | 0.0153136 | − | 0.00410326i | ||||
\(383\) | −30.9124 | − | 8.28295i | −0.0807112 | − | 0.0216265i | 0.218237 | − | 0.975896i | \(-0.429969\pi\) |
−0.298949 | + | 0.954269i | \(0.596636\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 375.526 | − | 257.251i | 0.975392 | − | 0.668184i | ||||
\(386\) | 334.563 | 0.866743 | ||||||||
\(387\) | −19.4975 | + | 72.7655i | −0.0503811 | + | 0.188025i | ||||
\(388\) | 61.1563 | + | 228.238i | 0.157619 | + | 0.588243i | ||||
\(389\) | −486.253 | − | 280.738i | −1.25001 | − | 0.721692i | −0.278897 | − | 0.960321i | \(-0.589969\pi\) |
−0.971111 | + | 0.238629i | \(0.923302\pi\) | |||||||
\(390\) | 7.03272 | + | 13.1962i | 0.0180326 | + | 0.0338363i | ||||
\(391\) | −14.1151 | −0.0361000 | ||||||||
\(392\) | 122.691 | − | 64.4581i | 0.312988 | − | 0.164434i | ||||
\(393\) | 256.928 | − | 256.928i | 0.653761 | − | 0.653761i | ||||
\(394\) | 10.5917 | − | 6.11514i | 0.0268826 | − | 0.0155207i | ||||
\(395\) | 109.466 | + | 472.088i | 0.277128 | + | 1.19516i | ||||
\(396\) | −39.0163 | + | 67.5782i | −0.0985259 | + | 0.170652i | ||||
\(397\) | −116.982 | + | 436.584i | −0.294666 | + | 1.09971i | 0.646817 | + | 0.762645i | \(0.276100\pi\) |
−0.941483 | + | 0.337062i | \(0.890567\pi\) | |||||||
\(398\) | −247.459 | + | 247.459i | −0.621756 | + | 0.621756i | ||||
\(399\) | −65.9036 | + | 48.5138i | −0.165172 | + | 0.121589i | ||||
\(400\) | 6.78491 | − | 99.7696i | 0.0169623 | − | 0.249424i | ||||
\(401\) | 77.9394 | + | 134.995i | 0.194363 | + | 0.336646i | 0.946691 | − | 0.322142i | \(-0.104403\pi\) |
−0.752329 | + | 0.658788i | \(0.771070\pi\) | |||||||
\(402\) | −148.153 | + | 39.6975i | −0.368540 | + | 0.0987499i | ||||
\(403\) | 14.8284 | + | 55.3402i | 0.0367950 | + | 0.137321i | ||||
\(404\) | −280.484 | + | 161.938i | −0.694268 | + | 0.400836i | ||||
\(405\) | 30.7214 | + | 32.8816i | 0.0758552 | + | 0.0811890i | ||||
\(406\) | −124.305 | + | 283.956i | −0.306171 | + | 0.699399i | ||||
\(407\) | −348.371 | − | 348.371i | −0.855948 | − | 0.855948i | ||||
\(408\) | −4.42245 | − | 1.18499i | −0.0108393 | − | 0.00290439i | ||||
\(409\) | 109.690 | + | 63.3296i | 0.268191 | + | 0.154840i | 0.628065 | − | 0.778161i | \(-0.283847\pi\) |
−0.359874 | + | 0.933001i | \(0.617180\pi\) | |||||||
\(410\) | −386.281 | − | 240.862i | −0.942150 | − | 0.587469i | ||||
\(411\) | −196.174 | − | 339.783i | −0.477309 | − | 0.826723i | ||||
\(412\) | −118.576 | − | 118.576i | −0.287805 | − | 0.287805i | ||||
\(413\) | −156.675 | + | 195.969i | −0.379359 | + | 0.474502i | ||||
\(414\) | 64.0776i | 0.154777i | ||||||||
\(415\) | 106.090 | + | 199.068i | 0.255640 | + | 0.479681i | ||||
\(416\) | −3.45329 | + | 5.98128i | −0.00830118 | + | 0.0143781i | ||||
\(417\) | −70.5043 | + | 18.8916i | −0.169075 | + | 0.0453035i | ||||
\(418\) | −119.912 | − | 32.1302i | −0.286870 | − | 0.0768665i | ||||
\(419\) | 768.293i | 1.83363i | 0.399307 | + | 0.916817i | \(0.369251\pi\) | ||||
−0.399307 | + | 0.916817i | \(0.630749\pi\) | |||||||
\(420\) | 78.8816 | − | 92.0743i | 0.187813 | − | 0.219225i | ||||
\(421\) | 557.422 | 1.32404 | 0.662021 | − | 0.749485i | \(-0.269699\pi\) | ||||
0.662021 | + | 0.749485i | \(0.269699\pi\) | |||||||
\(422\) | −109.595 | + | 409.014i | −0.259704 | + | 0.969228i | ||||
\(423\) | −38.7252 | − | 144.525i | −0.0915490 | − | 0.341666i | ||||
\(424\) | −183.120 | − | 105.724i | −0.431886 | − | 0.249350i | ||||
\(425\) | 22.1059 | + | 7.56444i | 0.0520140 | + | 0.0177987i | ||||
\(426\) | 183.163 | 0.429960 | ||||||||
\(427\) | 711.416 | − | 278.200i | 1.66608 | − | 0.651521i | ||||
\(428\) | 105.038 | − | 105.038i | 0.245415 | − | 0.245415i | ||||
\(429\) | −23.8179 | + | 13.7513i | −0.0555197 | + | 0.0320543i | ||||
\(430\) | 172.971 | − | 40.1077i | 0.402258 | − | 0.0932738i | ||||
\(431\) | −60.4377 | + | 104.681i | −0.140227 | + | 0.242880i | −0.927582 | − | 0.373620i | \(-0.878116\pi\) |
0.787355 | + | 0.616500i | \(0.211450\pi\) | |||||||
\(432\) | −5.37945 | + | 20.0764i | −0.0124524 | + | 0.0464731i | ||||
\(433\) | 301.713 | − | 301.713i | 0.696797 | − | 0.696797i | −0.266921 | − | 0.963718i | \(-0.586006\pi\) |
0.963718 | + | 0.266921i | \(0.0860063\pi\) | |||||||
\(434\) | 374.106 | − | 275.392i | 0.861996 | − | 0.634543i | ||||
\(435\) | −9.20460 | + | 271.013i | −0.0211600 | + | 0.623018i | ||||
\(436\) | −123.464 | − | 213.845i | −0.283174 | − | 0.490471i | ||||
\(437\) | −98.4672 | + | 26.3842i | −0.225325 | + | 0.0603758i | ||||
\(438\) | −52.6720 | − | 196.574i | −0.120256 | − | 0.448800i | ||||
\(439\) | 428.223 | − | 247.234i | 0.975450 | − | 0.563176i | 0.0745567 | − | 0.997217i | \(-0.476246\pi\) |
0.900893 | + | 0.434040i | \(0.142912\pi\) | |||||||
\(440\) | 183.818 | + | 6.24315i | 0.417769 | + | 0.0141890i | ||||
\(441\) | 143.395 | − | 32.3575i | 0.325158 | − | 0.0733729i | ||||
\(442\) | −1.14104 | − | 1.14104i | −0.00258155 | − | 0.00258155i | ||||
\(443\) | −451.126 | − | 120.879i | −1.01834 | − | 0.272864i | −0.289231 | − | 0.957259i | \(-0.593400\pi\) |
−0.729111 | + | 0.684395i | \(0.760066\pi\) | |||||||
\(444\) | −113.646 | − | 65.6134i | −0.255959 | − | 0.147778i | ||||
\(445\) | −57.6424 | − | 248.592i | −0.129533 | − | 0.558634i | ||||
\(446\) | −151.041 | − | 261.610i | −0.338657 | − | 0.586571i | ||||
\(447\) | −93.9663 | − | 93.9663i | −0.210215 | − | 0.210215i | ||||
\(448\) | 55.3642 | + | 8.41456i | 0.123581 | + | 0.0187825i | ||||
\(449\) | − | 542.409i | − | 1.20804i | −0.796970 | − | 0.604019i | \(-0.793565\pi\) | ||
0.796970 | − | 0.604019i | \(-0.206435\pi\) | |||||||
\(450\) | 34.3399 | − | 100.353i | 0.0763109 | − | 0.223007i | ||||
\(451\) | 418.633 | − | 725.094i | 0.928233 | − | 1.60775i | ||||
\(452\) | 113.826 | − | 30.4995i | 0.251827 | − | 0.0674768i | ||||
\(453\) | −51.6608 | − | 13.8425i | −0.114041 | − | 0.0305573i | ||||
\(454\) | − | 81.1271i | − | 0.178694i | ||||||
\(455\) | 40.3029 | − | 14.2030i | 0.0885779 | − | 0.0312154i | ||||
\(456\) | −33.0661 | −0.0725134 | ||||||||
\(457\) | −113.360 | + | 423.064i | −0.248052 | + | 0.925742i | 0.723773 | + | 0.690038i | \(0.242406\pi\) |
−0.971825 | + | 0.235704i | \(0.924261\pi\) | |||||||
\(458\) | −36.1616 | − | 134.957i | −0.0789554 | − | 0.294665i | ||||
\(459\) | −4.20558 | − | 2.42809i | −0.00916249 | − | 0.00528997i | ||||
\(460\) | 133.286 | − | 71.0329i | 0.289752 | − | 0.154419i | ||||
\(461\) | 418.754 | 0.908360 | 0.454180 | − | 0.890910i | \(-0.349932\pi\) | ||||
0.454180 | + | 0.890910i | \(0.349932\pi\) | |||||||
\(462\) | 174.174 | + | 139.251i | 0.377001 | + | 0.301408i | ||||
\(463\) | 571.669 | − | 571.669i | 1.23471 | − | 1.23471i | 0.272572 | − | 0.962135i | \(-0.412126\pi\) |
0.962135 | − | 0.272572i | \(-0.0878742\pi\) | |||||||
\(464\) | −108.468 | + | 62.6239i | −0.233767 | + | 0.134965i | ||||
\(465\) | 215.023 | − | 344.841i | 0.462414 | − | 0.741594i | ||||
\(466\) | −305.217 | + | 528.651i | −0.654972 | + | 1.13445i | ||||
\(467\) | 114.030 | − | 425.564i | 0.244175 | − | 0.911273i | −0.729622 | − | 0.683851i | \(-0.760304\pi\) |
0.973796 | − | 0.227422i | \(-0.0730295\pi\) | |||||||
\(468\) | −5.17994 | + | 5.17994i | −0.0110682 | + | 0.0110682i | ||||
\(469\) | 48.5395 | + | 435.622i | 0.103496 | + | 0.928831i | ||||
\(470\) | −257.692 | + | 240.763i | −0.548282 | + | 0.512262i | ||||
\(471\) | 55.7275 | + | 96.5229i | 0.118317 | + | 0.204932i | ||||
\(472\) | −97.9247 | + | 26.2388i | −0.207468 | + | 0.0555908i | ||||
\(473\) | 84.5243 | + | 315.449i | 0.178698 | + | 0.666911i | ||||
\(474\) | −205.604 | + | 118.705i | −0.433763 | + | 0.250433i | ||||
\(475\) | 168.351 | + | 11.4488i | 0.354423 | + | 0.0241028i | ||||
\(476\) | −5.24697 | + | 11.9859i | −0.0110230 | + | 0.0251804i | ||||
\(477\) | −158.586 | − | 158.586i | −0.332466 | − | 0.332466i | ||||
\(478\) | −470.684 | − | 126.120i | −0.984696 | − | 0.263848i | ||||
\(479\) | 418.951 | + | 241.882i | 0.874638 | + | 0.504972i | 0.868887 | − | 0.495011i | \(-0.164836\pi\) |
0.00575111 | + | 0.999983i | \(0.498169\pi\) | |||||||
\(480\) | 47.7236 | − | 11.0659i | 0.0994242 | − | 0.0230540i | ||||
\(481\) | −23.1255 | − | 40.0545i | −0.0480779 | − | 0.0832734i | ||||
\(482\) | −100.248 | − | 100.248i | −0.207983 | − | 0.207983i | ||||
\(483\) | 181.038 | + | 27.5152i | 0.374820 | + | 0.0569672i | ||||
\(484\) | 96.2822i | 0.198930i | ||||||||
\(485\) | 521.313 | − | 277.827i | 1.07487 | − | 0.572839i | ||||
\(486\) | −11.0227 | + | 19.0919i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −575.465 | + | 154.195i | −1.18165 | + | 0.316623i | −0.795582 | − | 0.605846i | \(-0.792835\pi\) |
−0.386071 | + | 0.922469i | \(0.626168\pi\) | |||||||
\(488\) | 298.136 | + | 79.8852i | 0.610934 | + | 0.163699i | ||||
\(489\) | − | 162.293i | − | 0.331888i | ||||||
\(490\) | −226.265 | − | 262.401i | −0.461765 | − | 0.535512i | ||||
\(491\) | −493.037 | −1.00415 | −0.502074 | − | 0.864824i | \(-0.667430\pi\) | ||||
−0.502074 | + | 0.864824i | \(0.667430\pi\) | |||||||
\(492\) | 57.7200 | − | 215.414i | 0.117317 | − | 0.437833i | ||||
\(493\) | −7.57390 | − | 28.2662i | −0.0153629 | − | 0.0573351i | ||||
\(494\) | −10.0928 | − | 5.82708i | −0.0204308 | − | 0.0117957i | ||||
\(495\) | 186.612 | + | 56.8579i | 0.376993 | + | 0.114864i | ||||
\(496\) | 187.702 | 0.378431 | ||||||||
\(497\) | 78.6509 | − | 517.489i | 0.158251 | − | 1.04123i | ||||
\(498\) | −78.1407 | + | 78.1407i | −0.156909 | + | 0.156909i | ||||
\(499\) | 327.714 | − | 189.206i | 0.656741 | − | 0.379170i | −0.134293 | − | 0.990942i | \(-0.542876\pi\) |
0.791034 | + | 0.611772i | \(0.209543\pi\) | |||||||
\(500\) | −246.809 | + | 39.8166i | −0.493618 | + | 0.0796332i | ||||
\(501\) | −36.8942 | + | 63.9026i | −0.0736410 | + | 0.127550i | ||||
\(502\) | 147.965 | − | 552.211i | 0.294750 | − | 1.10002i | ||||
\(503\) | −458.146 | + | 458.146i | −0.910826 | + | 0.910826i | −0.996337 | − | 0.0855108i | \(-0.972748\pi\) |
0.0855108 | + | 0.996337i | \(0.472748\pi\) | |||||||
\(504\) | 54.4117 | + | 23.8194i | 0.107960 | + | 0.0472607i | ||||
\(505\) | 552.772 | + | 591.640i | 1.09460 | + | 1.17156i | ||||
\(506\) | 138.893 | + | 240.569i | 0.274492 | + | 0.475434i | ||||
\(507\) | 280.249 | − | 75.0924i | 0.552759 | − | 0.148111i | ||||
\(508\) | −77.2026 | − | 288.124i | −0.151974 | − | 0.567173i | ||||
\(509\) | 602.762 | − | 348.005i | 1.18421 | − | 0.683703i | 0.227224 | − | 0.973843i | \(-0.427035\pi\) |
0.956984 | + | 0.290140i | \(0.0937017\pi\) | |||||||
\(510\) | −0.388529 | + | 11.4396i | −0.000761822 | + | 0.0224305i | ||||
\(511\) | −577.998 | + | 64.4039i | −1.13111 | + | 0.126035i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −33.8769 | − | 9.07728i | −0.0660368 | − | 0.0176945i | ||||
\(514\) | −42.7578 | − | 24.6862i | −0.0831864 | − | 0.0480277i | ||||
\(515\) | −221.817 | + | 355.738i | −0.430712 | + | 0.690753i | ||||
\(516\) | 43.4932 | + | 75.3324i | 0.0842892 | + | 0.145993i | ||||
\(517\) | −458.655 | − | 458.655i | −0.887147 | − | 0.887147i | ||||
\(518\) | −234.177 | + | 292.908i | −0.452079 | + | 0.565460i | ||||
\(519\) | − | 102.262i | − | 0.197037i | ||||||
\(520\) | 16.5168 | + | 5.03244i | 0.0317631 | + | 0.00967777i | ||||
\(521\) | −46.9311 | + | 81.2870i | −0.0900788 | + | 0.156021i | −0.907544 | − | 0.419957i | \(-0.862045\pi\) |
0.817465 | + | 0.575978i | \(0.195379\pi\) | |||||||
\(522\) | −128.319 | + | 34.3829i | −0.245821 | + | 0.0658676i | ||||
\(523\) | −696.690 | − | 186.678i | −1.33210 | − | 0.356936i | −0.478605 | − | 0.878030i | \(-0.658857\pi\) |
−0.853499 | + | 0.521094i | \(0.825524\pi\) | |||||||
\(524\) | − | 419.562i | − | 0.800690i | ||||||
\(525\) | −268.782 | − | 140.112i | −0.511965 | − | 0.266881i | ||||
\(526\) | −291.123 | −0.553466 | ||||||||
\(527\) | −11.3506 | + | 42.3610i | −0.0215381 | + | 0.0803814i | ||||
\(528\) | 23.3207 | + | 87.0340i | 0.0441680 | + | 0.164837i | ||||
\(529\) | −260.580 | − | 150.446i | −0.492590 | − | 0.284397i | ||||
\(530\) | −154.071 | + | 505.671i | −0.290699 | + | 0.954096i | ||||
\(531\) | −107.529 | −0.202502 | ||||||||
\(532\) | −14.1987 | + | 93.4215i | −0.0266893 | + | 0.175604i | ||||
\(533\) | 55.5792 | − | 55.5792i | 0.104276 | − | 0.104276i | ||||
\(534\) | 108.267 | − | 62.5079i | 0.202747 | − | 0.117056i | ||||
\(535\) | −315.123 | − | 196.492i | −0.589015 | − | 0.367275i | ||||
\(536\) | −88.5535 | + | 153.379i | −0.165212 | + | 0.286155i | ||||
\(537\) | 96.0065 | − | 358.301i | 0.178783 | − | 0.667228i | ||||
\(538\) | −143.879 | + | 143.879i | −0.267432 | + | 0.267432i | ||||
\(539\) | 468.215 | − | 432.299i | 0.868674 | − | 0.802039i | ||||
\(540\) | 51.9316 | + | 1.76379i | 0.0961696 | + | 0.00326627i | ||||
\(541\) | −501.633 | − | 868.854i | −0.927233 | − | 1.60601i | −0.787930 | − | 0.615765i | \(-0.788847\pi\) |
−0.139303 | − | 0.990250i | \(-0.544486\pi\) | |||||||
\(542\) | 260.494 | − | 69.7990i | 0.480615 | − | 0.128781i | ||||
\(543\) | 118.955 | + | 443.944i | 0.219069 | + | 0.817577i | ||||
\(544\) | −4.57846 | + | 2.64337i | −0.00841628 | + | 0.00485914i | ||||
\(545\) | −451.076 | + | 421.442i | −0.827662 | + | 0.773287i | ||||
\(546\) | 12.4106 | + | 16.8591i | 0.0227300 | + | 0.0308775i | ||||
\(547\) | −188.091 | − | 188.091i | −0.343860 | − | 0.343860i | 0.513957 | − | 0.857816i | \(-0.328179\pi\) |
−0.857816 | + | 0.513957i | \(0.828179\pi\) | |||||||
\(548\) | −437.607 | − | 117.257i | −0.798553 | − | 0.213972i | ||||
\(549\) | 283.516 | + | 163.688i | 0.516422 | + | 0.298156i | ||||
\(550\) | −88.5989 | − | 451.195i | −0.161089 | − | 0.820354i | ||||
\(551\) | −105.671 | − | 183.028i | −0.191781 | − | 0.332175i | ||||
\(552\) | 52.3192 | + | 52.3192i | 0.0947811 | + | 0.0947811i | ||||
\(553\) | 247.091 | + | 631.864i | 0.446818 | + | 1.14261i | ||||
\(554\) | − | 69.6516i | − | 0.125725i | ||||||
\(555\) | −95.6176 | + | 313.824i | −0.172284 | + | 0.565448i | ||||
\(556\) | −42.1416 | + | 72.9914i | −0.0757942 | + | 0.131279i | ||||
\(557\) | 535.638 | − | 143.524i | 0.961648 | − | 0.257673i | 0.256350 | − | 0.966584i | \(-0.417480\pi\) |
0.705298 | + | 0.708911i | \(0.250813\pi\) | |||||||
\(558\) | 192.304 | + | 51.5278i | 0.344631 | + | 0.0923437i | ||||
\(559\) | 30.6584i | 0.0548450i | ||||||||
\(560\) | −10.7718 | − | 139.585i | −0.0192354 | − | 0.249259i | ||||
\(561\) | −21.0523 | −0.0375263 | ||||||||
\(562\) | −125.709 | + | 469.152i | −0.223681 | + | 0.834791i | ||||
\(563\) | −153.153 | − | 571.577i | −0.272031 | − | 1.01523i | −0.957805 | − | 0.287419i | \(-0.907203\pi\) |
0.685774 | − | 0.727815i | \(-0.259464\pi\) | |||||||
\(564\) | −149.623 | − | 86.3848i | −0.265289 | − | 0.153165i | ||||
\(565\) | −138.556 | − | 259.986i | −0.245232 | − | 0.460153i | ||||
\(566\) | −155.254 | −0.274300 | ||||||||
\(567\) | 49.2070 | + | 39.3405i | 0.0867848 | + | 0.0693836i | ||||
\(568\) | 149.552 | − | 149.552i | 0.263296 | − | 0.263296i | ||||
\(569\) | −337.893 | + | 195.083i | −0.593837 | + | 0.342852i | −0.766613 | − | 0.642109i | \(-0.778060\pi\) |
0.172776 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(570\) | 18.6726 | + | 80.5288i | 0.0327590 | + | 0.141279i | ||||
\(571\) | 5.20468 | − | 9.01477i | 0.00911502 | − | 0.0157877i | −0.861432 | − | 0.507873i | \(-0.830432\pi\) |
0.870547 | + | 0.492085i | \(0.163765\pi\) | |||||||
\(572\) | −8.21938 | + | 30.6752i | −0.0143695 | + | 0.0536279i | ||||
\(573\) | 5.24477 | − | 5.24477i | 0.00915318 | − | 0.00915318i | ||||
\(574\) | −583.822 | − | 255.575i | −1.01711 | − | 0.445253i | ||||
\(575\) | −248.260 | − | 284.490i | −0.431756 | − | 0.494765i | ||||
\(576\) | 12.0000 | + | 20.7846i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | −575.421 | + | 154.184i | −0.997263 | + | 0.267216i | −0.720299 | − | 0.693664i | \(-0.755995\pi\) |
−0.276965 | + | 0.960880i | \(0.589329\pi\) | |||||||
\(578\) | 105.462 | + | 393.588i | 0.182460 | + | 0.680948i | ||||
\(579\) | 354.857 | − | 204.877i | 0.612880 | − | 0.353846i | ||||
\(580\) | 213.766 | + | 228.797i | 0.368562 | + | 0.394477i | ||||
\(581\) | 187.217 | + | 254.324i | 0.322232 | + | 0.437736i | ||||
\(582\) | 204.633 | + | 204.633i | 0.351603 | + | 0.351603i | ||||
\(583\) | −939.135 | − | 251.640i | −1.61087 | − | 0.431630i | ||||
\(584\) | −203.509 | − | 117.496i | −0.348474 | − | 0.201192i | ||||
\(585\) | 15.5403 | + | 9.69001i | 0.0265646 | + | 0.0165641i | ||||
\(586\) | 24.9404 | + | 43.1981i | 0.0425605 | + | 0.0737169i | ||||
\(587\) | −57.7749 | − | 57.7749i | −0.0984239 | − | 0.0984239i | 0.656180 | − | 0.754604i | \(-0.272171\pi\) |
−0.754604 | + | 0.656180i | \(0.772171\pi\) | |||||||
\(588\) | 90.6614 | − | 143.501i | 0.154186 | − | 0.244049i | ||||
\(589\) | 316.728i | 0.537739i | ||||||||
\(590\) | 119.200 | + | 223.667i | 0.202035 | + | 0.379097i | ||||
\(591\) | 7.48949 | − | 12.9722i | 0.0126726 | − | 0.0219495i | ||||
\(592\) | −146.365 | + | 39.2183i | −0.247237 | + | 0.0662471i | ||||
\(593\) | 901.848 | + | 241.650i | 1.52082 | + | 0.407503i | 0.920013 | − | 0.391888i | \(-0.128178\pi\) |
0.600810 | + | 0.799392i | \(0.294845\pi\) | |||||||
\(594\) | 95.5700i | 0.160892i | ||||||||
\(595\) | 32.1532 | + | 6.00989i | 0.0540391 | + | 0.0101007i | ||||
\(596\) | −153.446 | −0.257460 | ||||||||
\(597\) | −110.933 | + | 414.007i | −0.185817 | + | 0.693479i | ||||
\(598\) | 6.74947 | + | 25.1894i | 0.0112867 | + | 0.0421227i | ||||
\(599\) | −811.636 | − | 468.598i | −1.35498 | − | 0.782301i | −0.366042 | − | 0.930598i | \(-0.619287\pi\) |
−0.988943 | + | 0.148297i | \(0.952621\pi\) | |||||||
\(600\) | −53.8996 | − | 109.976i | −0.0898327 | − | 0.183294i | ||||
\(601\) | 89.1175 | 0.148282 | 0.0741410 | − | 0.997248i | \(-0.476379\pi\) | ||||
0.0741410 | + | 0.997248i | \(0.476379\pi\) | |||||||
\(602\) | 231.512 | − | 90.5330i | 0.384572 | − | 0.150387i | ||||
\(603\) | −132.830 | + | 132.830i | −0.220282 | + | 0.220282i | ||||
\(604\) | −53.4832 | + | 30.8785i | −0.0885483 | + | 0.0511234i | ||||
\(605\) | 234.484 | − | 54.3711i | 0.387577 | − | 0.0898696i | ||||
\(606\) | −198.332 | + | 343.521i | −0.327281 | + | 0.566867i | ||||
\(607\) | 214.931 | − | 802.135i | 0.354088 | − | 1.32147i | −0.527540 | − | 0.849530i | \(-0.676886\pi\) |
0.881628 | − | 0.471945i | \(-0.156448\pi\) | |||||||
\(608\) | −26.9984 | + | 26.9984i | −0.0444052 | + | 0.0444052i | ||||
\(609\) | 42.0412 | + | 377.302i | 0.0690332 | + | 0.619544i | ||||
\(610\) | 26.1923 | − | 771.187i | 0.0429383 | − | 1.26424i | ||||
\(611\) | −30.4463 | − | 52.7346i | −0.0498303 | − | 0.0863087i | ||||
\(612\) | −5.41637 | + | 1.45131i | −0.00885029 | + | 0.00237143i | ||||
\(613\) | 259.965 | + | 970.204i | 0.424087 | + | 1.58271i | 0.765909 | + | 0.642949i | \(0.222289\pi\) |
−0.341822 | + | 0.939765i | \(0.611044\pi\) | |||||||
\(614\) | 539.004 | − | 311.194i | 0.877856 | − | 0.506830i | ||||
\(615\) | −557.211 | − | 18.9249i | −0.906034 | − | 0.0307722i | ||||
\(616\) | 255.911 | − | 28.5151i | 0.415439 | − | 0.0462907i | ||||
\(617\) | 92.1769 | + | 92.1769i | 0.149395 | + | 0.149395i | 0.777848 | − | 0.628453i | \(-0.216311\pi\) |
−0.628453 | + | 0.777848i | \(0.716311\pi\) | |||||||
\(618\) | −198.381 | − | 53.1560i | −0.321004 | − | 0.0860129i | ||||
\(619\) | 420.450 | + | 242.747i | 0.679241 | + | 0.392160i | 0.799569 | − | 0.600574i | \(-0.205061\pi\) |
−0.120328 | + | 0.992734i | \(0.538395\pi\) | |||||||
\(620\) | −105.996 | − | 457.127i | −0.170962 | − | 0.737301i | ||||
\(621\) | 39.2394 | + | 67.9646i | 0.0631874 | + | 0.109444i | ||||
\(622\) | 453.067 | + | 453.067i | 0.728403 | + | 0.728403i | ||||
\(623\) | −130.113 | − | 332.727i | −0.208849 | − | 0.534072i | ||||
\(624\) | 8.45881i | 0.0135558i | ||||||||
\(625\) | 236.343 | + | 578.590i | 0.378149 | + | 0.925745i | ||||
\(626\) | 238.065 | − | 412.341i | 0.380295 | − | 0.658691i | ||||
\(627\) | −146.861 | + | 39.3513i | −0.234228 | + | 0.0627612i | ||||
\(628\) | 124.312 | + | 33.3093i | 0.197949 | + | 0.0530403i | ||||
\(629\) | − | 35.4035i | − | 0.0562853i | ||||||
\(630\) | 27.2828 | − | 145.965i | 0.0433061 | − | 0.231690i | ||||
\(631\) | 204.708 | 0.324418 | 0.162209 | − | 0.986756i | \(-0.448138\pi\) | ||||
0.162209 | + | 0.986756i | \(0.448138\pi\) | |||||||
\(632\) | −70.9523 | + | 264.797i | −0.112266 | + | 0.418983i | ||||
\(633\) | 134.226 | + | 500.938i | 0.212047 | + | 0.791372i | ||||
\(634\) | 620.923 | + | 358.490i | 0.979374 | + | 0.565442i | ||||
\(635\) | −658.096 | + | 350.723i | −1.03637 | + | 0.552320i | ||||
\(636\) | −258.971 | −0.407186 | ||||||||
\(637\) | 52.9611 | − | 27.8241i | 0.0831415 | − | 0.0436799i | ||||
\(638\) | −407.225 | + | 407.225i | −0.638284 | + | 0.638284i | ||||
\(639\) | 194.274 | − | 112.164i | 0.304028 | − | 0.175531i | ||||
\(640\) | 29.9309 | − | 48.0015i | 0.0467670 | − | 0.0750023i | ||||
\(641\) | 587.986 | − | 1018.42i | 0.917295 | − | 1.58880i | 0.113788 | − | 0.993505i | \(-0.463701\pi\) |
0.803506 | − | 0.595296i | \(-0.202965\pi\) | |||||||
\(642\) | 47.0872 | − | 175.732i | 0.0733445 | − | 0.273725i | ||||
\(643\) | 395.839 | − | 395.839i | 0.615612 | − | 0.615612i | −0.328791 | − | 0.944403i | \(-0.606641\pi\) |
0.944403 | + | 0.328791i | \(0.106641\pi\) | |||||||
\(644\) | 170.283 | − | 125.351i | 0.264415 | − | 0.194644i | ||||
\(645\) | 158.903 | − | 148.463i | 0.246361 | − | 0.230176i | ||||
\(646\) | −4.46043 | − | 7.72569i | −0.00690468 | − | 0.0119593i | ||||
\(647\) | −445.523 | + | 119.378i | −0.688598 | + | 0.184509i | −0.586118 | − | 0.810226i | \(-0.699344\pi\) |
−0.102480 | + | 0.994735i | \(0.532678\pi\) | |||||||
\(648\) | 6.58846 | + | 24.5885i | 0.0101674 | + | 0.0379452i | ||||
\(649\) | −403.700 | + | 233.076i | −0.622034 | + | 0.359131i | ||||
\(650\) | 2.92878 | − | 43.0667i | 0.00450582 | − | 0.0662564i | ||||
\(651\) | 228.157 | − | 521.189i | 0.350472 | − | 0.800598i | ||||
\(652\) | −132.512 | − | 132.512i | −0.203239 | − | 0.203239i | ||||
\(653\) | 242.537 | + | 64.9876i | 0.371419 | + | 0.0995215i | 0.439700 | − | 0.898145i | \(-0.355085\pi\) |
−0.0682808 | + | 0.997666i | \(0.521751\pi\) | |||||||
\(654\) | −261.906 | − | 151.212i | −0.400468 | − | 0.231210i | ||||
\(655\) | −1021.79 | + | 236.929i | −1.55999 | + | 0.361724i | ||||
\(656\) | −128.757 | − | 223.013i | −0.196275 | − | 0.339959i | ||||
\(657\) | −176.244 | − | 176.244i | −0.268255 | − | 0.268255i | ||||
\(658\) | −308.311 | + | 385.634i | −0.468558 | + | 0.586071i | ||||
\(659\) | 524.406i | 0.795760i | 0.917437 | + | 0.397880i | \(0.130254\pi\) | ||||
−0.917437 | + | 0.397880i | \(0.869746\pi\) | |||||||
\(660\) | 198.792 | − | 105.944i | 0.301200 | − | 0.160520i | ||||
\(661\) | 148.475 | − | 257.165i | 0.224621 | − | 0.389055i | −0.731585 | − | 0.681751i | \(-0.761219\pi\) |
0.956206 | + | 0.292696i | \(0.0945522\pi\) | |||||||
\(662\) | 241.023 | − | 64.5818i | 0.364082 | − | 0.0975556i | ||||
\(663\) | −1.90900 | − | 0.511516i | −0.00287934 | − | 0.000771517i | ||||
\(664\) | 127.603i | 0.192174i | ||||||||
\(665\) | 235.536 | − | 18.1763i | 0.354189 | − | 0.0273328i | ||||
\(666\) | −160.719 | −0.241321 | ||||||||
\(667\) | −122.399 | + | 456.798i | −0.183506 | + | 0.684854i | ||||
\(668\) | 22.0523 | + | 82.3002i | 0.0330124 | + | 0.123204i | ||||
\(669\) | −320.406 | − | 184.987i | −0.478933 | − | 0.276512i | ||||
\(670\) | 423.544 | + | 129.048i | 0.632156 | + | 0.192609i | ||||
\(671\) | 1419.22 | 2.11508 | ||||||||
\(672\) | 63.8755 | − | 24.9785i | 0.0950528 | − | 0.0371704i | ||||
\(673\) | −41.9638 | + | 41.9638i | −0.0623533 | + | 0.0623533i | −0.737596 | − | 0.675243i | \(-0.764039\pi\) |
0.675243 | + | 0.737596i | \(0.264039\pi\) | |||||||
\(674\) | 162.252 | − | 93.6762i | 0.240730 | − | 0.138985i | ||||
\(675\) | −25.0306 | − | 127.469i | −0.0370823 | − | 0.188844i | ||||
\(676\) | 167.509 | − | 290.135i | 0.247795 | − | 0.429193i | ||||
\(677\) | −255.227 | + | 952.520i | −0.376997 | + | 1.40697i | 0.473408 | + | 0.880843i | \(0.343024\pi\) |
−0.850405 | + | 0.526129i | \(0.823643\pi\) | |||||||
\(678\) | 102.053 | − | 102.053i | 0.150521 | − | 0.150521i | ||||
\(679\) | 666.018 | − | 490.278i | 0.980880 | − | 0.722058i | ||||
\(680\) | 9.02312 | + | 9.65759i | 0.0132693 | + | 0.0142023i | ||||
\(681\) | −49.6800 | − | 86.0483i | −0.0729516 | − | 0.126356i | ||||
\(682\) | 833.666 | − | 223.380i | 1.22238 | − | 0.327537i | ||||
\(683\) | 107.123 | + | 399.787i | 0.156841 | + | 0.585339i | 0.998941 | + | 0.0460170i | \(0.0146528\pi\) |
−0.842099 | + | 0.539322i | \(0.818680\pi\) | |||||||
\(684\) | −35.0719 | + | 20.2488i | −0.0512747 | + | 0.0296035i | ||||
\(685\) | −38.4454 | + | 1131.96i | −0.0561247 | + | 1.65249i | ||||
\(686\) | −366.502 | − | 317.765i | −0.534259 | − | 0.463214i | ||||
\(687\) | −120.999 | − | 120.999i | −0.176127 | − | 0.176127i | ||||
\(688\) | 97.0207 | + | 25.9966i | 0.141019 | + | 0.0377858i | ||||
\(689\) | −79.0458 | − | 45.6371i | −0.114725 | − | 0.0662367i | ||||
\(690\) | 97.8724 | − | 156.962i | 0.141844 | − | 0.227482i | ||||
\(691\) | 455.346 | + | 788.682i | 0.658966 | + | 1.14136i | 0.980884 | + | 0.194595i | \(0.0623393\pi\) |
−0.321917 | + | 0.946768i | \(0.604327\pi\) | |||||||
\(692\) | −83.4967 | − | 83.4967i | −0.120660 | − | 0.120660i | ||||
\(693\) | 270.013 | + | 41.0381i | 0.389629 | + | 0.0592180i | ||||
\(694\) | − | 677.627i | − | 0.976408i | ||||||
\(695\) | 201.560 | + | 61.4124i | 0.290014 | + | 0.0883632i | ||||
\(696\) | −76.6983 | + | 132.845i | −0.110199 | + | 0.190870i | ||||
\(697\) | 58.1161 | − | 15.5722i | 0.0833804 | − | 0.0223417i | ||||
\(698\) | 722.786 | + | 193.670i | 1.03551 | + | 0.277464i | ||||
\(699\) | 747.626i | 1.06957i | ||||||||
\(700\) | −333.860 | + | 105.058i | −0.476944 | + | 0.150083i | ||||
\(701\) | 295.328 | 0.421296 | 0.210648 | − | 0.977562i | \(-0.432443\pi\) | ||||
0.210648 | + | 0.977562i | \(0.432443\pi\) | |||||||
\(702\) | −2.32210 | + | 8.66621i | −0.00330784 | + | 0.0123450i | ||||
\(703\) | −66.1769 | − | 246.975i | −0.0941349 | − | 0.351316i | ||||
\(704\) | 90.1042 | + | 52.0217i | 0.127989 | + | 0.0738945i | ||||
\(705\) | −125.887 | + | 413.172i | −0.178564 | + | 0.586059i | ||||
\(706\) | −232.995 | −0.330021 | ||||||||
\(707\) | 885.384 | + | 707.856i | 1.25231 | + | 1.00121i | ||||
\(708\) | −87.7969 | + | 87.7969i | −0.124007 | + | 0.124007i | ||||
\(709\) | 754.639 | − | 435.691i | 1.06437 | − | 0.614515i | 0.137733 | − | 0.990469i | \(-0.456019\pi\) |
0.926638 | + | 0.375955i | \(0.122685\pi\) | |||||||
\(710\) | −448.670 | − | 279.764i | −0.631929 | − | 0.394034i | ||||
\(711\) | −145.384 | + | 251.812i | −0.204478 | + | 0.354166i | ||||
\(712\) | 37.3620 | − | 139.437i | 0.0524748 | − | 0.195838i | ||||
\(713\) | 501.146 | − | 501.146i | 0.702869 | − | 0.702869i | ||||
\(714\) | 1.77457 | + | 15.9260i | 0.00248540 | + | 0.0223054i | ||||
\(715\) | 79.3474 | + | 2.69493i | 0.110975 | + | 0.00376913i | ||||
\(716\) | −214.163 | − | 370.941i | −0.299110 | − | 0.518074i | ||||
\(717\) | −576.468 | + | 154.464i | −0.804001 | + | 0.215431i | ||||
\(718\) | 130.213 | + | 485.963i | 0.181356 | + | 0.676829i | ||||
\(719\) | −783.472 | + | 452.338i | −1.08967 | + | 0.629121i | −0.933488 | − | 0.358607i | \(-0.883252\pi\) |
−0.156181 | + | 0.987728i | \(0.549918\pi\) | |||||||
\(720\) | 43.8421 | − | 40.9618i | 0.0608918 | − | 0.0568914i | ||||
\(721\) | −235.367 | + | 537.658i | −0.326445 | + | 0.745712i | ||||
\(722\) | 315.443 | + | 315.443i | 0.436902 | + | 0.436902i | ||||
\(723\) | −167.718 | − | 44.9398i | −0.231975 | − | 0.0621574i | ||||
\(724\) | 459.605 | + | 265.353i | 0.634813 | + | 0.366510i | ||||
\(725\) | 436.494 | − | 649.805i | 0.602060 | − | 0.896283i | ||||
\(726\) | 58.9605 | + | 102.123i | 0.0812129 | + | 0.140665i | ||||
\(727\) | −155.082 | − | 155.082i | −0.213318 | − | 0.213318i | 0.592357 | − | 0.805675i | \(-0.298197\pi\) |
−0.805675 | + | 0.592357i | \(0.798197\pi\) | |||||||
\(728\) | 23.8986 | + | 3.63224i | 0.0328277 | + | 0.00498934i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −171.225 | + | 561.973i | −0.234555 | + | 0.769827i | ||||
\(731\) | −11.7340 | + | 20.3238i | −0.0160519 | + | 0.0278027i | ||||
\(732\) | 365.140 | − | 97.8390i | 0.498825 | − | 0.133660i | ||||
\(733\) | −297.763 | − | 79.7853i | −0.406225 | − | 0.108848i | 0.0499198 | − | 0.998753i | \(-0.484103\pi\) |
−0.456145 | + | 0.889906i | \(0.650770\pi\) | |||||||
\(734\) | 538.058i | 0.733049i | ||||||||
\(735\) | −400.677 | − | 139.760i | −0.545139 | − | 0.190149i | ||||
\(736\) | 85.4368 | 0.116083 | ||||||||
\(737\) | −210.771 | + | 786.609i | −0.285986 | + | 1.06731i | ||||
\(738\) | −70.6922 | − | 263.827i | −0.0957889 | − | 0.357489i | ||||
\(739\) | 204.986 | + | 118.349i | 0.277383 | + | 0.160147i | 0.632238 | − | 0.774774i | \(-0.282136\pi\) |
−0.354855 | + | 0.934921i | \(0.615470\pi\) | |||||||
\(740\) | 178.165 | + | 334.308i | 0.240763 | + | 0.451767i | ||||
\(741\) | −14.2734 | −0.0192623 | ||||||||
\(742\) | −111.203 | + | 731.668i | −0.149869 | + | 0.986075i | ||||
\(743\) | 605.403 | − | 605.403i | 0.814809 | − | 0.814809i | −0.170541 | − | 0.985351i | \(-0.554552\pi\) |
0.985351 | + | 0.170541i | \(0.0545516\pi\) | |||||||
\(744\) | 199.088 | − | 114.943i | 0.267591 | − | 0.154494i | ||||
\(745\) | 86.6521 | + | 373.701i | 0.116312 | + | 0.501612i | ||||
\(746\) | 237.065 | − | 410.609i | 0.317781 | − | 0.550414i | ||||
\(747\) | −35.0295 | + | 130.732i | −0.0468936 | + | 0.175009i | ||||
\(748\) | −17.1891 | + | 17.1891i | −0.0229801 | + | 0.0229801i | ||||
\(749\) | −476.274 | − | 208.495i | −0.635880 | − | 0.278364i | ||||
\(750\) | −237.398 | + | 193.371i | −0.316530 | + | 0.257828i | ||||
\(751\) | −426.169 | − | 738.147i | −0.567469 | − | 0.982886i | −0.996815 | − | 0.0797456i | \(-0.974589\pi\) |
0.429346 | − | 0.903140i | \(-0.358744\pi\) | |||||||
\(752\) | −192.699 | + | 51.6337i | −0.256249 | + | 0.0686618i | ||||
\(753\) | −181.219 | − | 676.318i | −0.240662 | − | 0.898164i | ||||
\(754\) | −46.8214 | + | 27.0323i | −0.0620973 | + | 0.0358519i | ||||
\(755\) | 105.403 | + | 112.815i | 0.139607 | + | 0.149424i | ||||
\(756\) | 72.2987 | − | 8.05595i | 0.0956332 | − | 0.0106560i | ||||
\(757\) | −61.7687 | − | 61.7687i | −0.0815967 | − | 0.0815967i | 0.665130 | − | 0.746727i | \(-0.268376\pi\) |
−0.746727 | + | 0.665130i | \(0.768376\pi\) | |||||||
\(758\) | 920.760 | + | 246.717i | 1.21472 | + | 0.325484i | ||||
\(759\) | 294.636 | + | 170.108i | 0.388190 | + | 0.224122i | ||||
\(760\) | 80.9976 | + | 50.5053i | 0.106576 | + | 0.0664544i | ||||
\(761\) | 46.4211 | + | 80.4037i | 0.0610002 | + | 0.105655i | 0.894913 | − | 0.446241i | \(-0.147238\pi\) |
−0.833913 | + | 0.551897i | \(0.813904\pi\) | |||||||
\(762\) | −258.325 | − | 258.325i | −0.339009 | − | 0.339009i | ||||
\(763\) | −539.680 | + | 675.031i | −0.707314 | + | 0.884706i | ||||
\(764\) | − | 8.56468i | − | 0.0112103i | ||||||
\(765\) | 6.59317 | + | 12.3714i | 0.00861852 | + | 0.0161718i | ||||
\(766\) | −22.6294 | + | 39.1954i | −0.0295424 | + | 0.0511689i | ||||
\(767\) | −42.2703 | + | 11.3263i | −0.0551113 | + | 0.0147670i | ||||
\(768\) | 26.7685 | + | 7.17260i | 0.0348548 | + | 0.00933933i | ||||
\(769\) | − | 1368.95i | − | 1.78017i | −0.455797 | − | 0.890084i | \(-0.650646\pi\) | ||
0.455797 | − | 0.890084i | \(-0.349354\pi\) | |||||||
\(770\) | −213.959 | − | 607.138i | −0.277869 | − | 0.788491i | ||||
\(771\) | −60.4687 | −0.0784289 | ||||||||
\(772\) | 122.458 | − | 457.021i | 0.158625 | − | 0.591996i | ||||
\(773\) | −154.150 | − | 575.297i | −0.199418 | − | 0.744239i | −0.991079 | − | 0.133278i | \(-0.957450\pi\) |
0.791661 | − | 0.610961i | \(-0.209217\pi\) | |||||||
\(774\) | 92.2630 | + | 53.2681i | 0.119203 | + | 0.0688218i | ||||
\(775\) | −1053.42 | + | 516.284i | −1.35926 | + | 0.666174i | ||||
\(776\) | 334.164 | 0.430624 | ||||||||
\(777\) | −69.0135 | + | 454.080i | −0.0888205 | + | 0.584401i | ||||
\(778\) | −561.476 | + | 561.476i | −0.721692 | + | 0.721692i | ||||
\(779\) | 376.312 | − | 217.264i | 0.483070 | − | 0.278901i | ||||
\(780\) | 20.6005 | − | 4.77674i | 0.0264108 | − | 0.00612402i | ||||
\(781\) | 486.247 | − | 842.204i | 0.622595 | − | 1.07837i | ||||
\(782\) | −5.16648 | + | 19.2816i | −0.00660676 | + | 0.0246568i | ||||
\(783\) | −115.047 | + | 115.047i | −0.146932 | + | 0.146932i | ||||
\(784\) | −43.1433 | − | 191.193i | −0.0550297 | − | 0.243868i | ||||
\(785\) | 10.9213 | − | 321.558i | 0.0139125 | − | 0.409628i | ||||
\(786\) | −256.928 | − | 445.012i | −0.326880 | − | 0.566174i | ||||
\(787\) | −1251.20 | + | 335.257i | −1.58983 | + | 0.425993i | −0.941951 | − | 0.335751i | \(-0.891010\pi\) |
−0.647878 | + | 0.761744i | \(0.724343\pi\) | |||||||
\(788\) | −4.47659 | − | 16.7069i | −0.00568096 | − | 0.0212016i | ||||
\(789\) | −308.783 | + | 178.276i | −0.391360 | + | 0.225952i | ||||
\(790\) | 684.951 | + | 23.2635i | 0.867027 | + | 0.0294474i | ||||
\(791\) | −244.509 | − | 332.153i | −0.309113 | − | 0.419915i | ||||
\(792\) | 78.0325 | + | 78.0325i | 0.0985259 | + | 0.0985259i | ||||
\(793\) | 128.694 | + | 34.4834i | 0.162287 | + | 0.0434847i | ||||
\(794\) | 553.566 | + | 319.601i | 0.697186 | + | 0.402521i | ||||
\(795\) | 146.242 | + | 630.693i | 0.183952 | + | 0.793325i | ||||
\(796\) | 247.459 | + | 428.612i | 0.310878 | + | 0.538457i | ||||
\(797\) | −338.085 | − | 338.085i | −0.424198 | − | 0.424198i | 0.462449 | − | 0.886646i | \(-0.346971\pi\) |
−0.886646 | + | 0.462449i | \(0.846971\pi\) | |||||||
\(798\) | 42.1487 | + | 107.783i | 0.0528180 | + | 0.135067i | ||||
\(799\) | − | 46.6112i | − | 0.0583369i | ||||||
\(800\) | −133.804 | − | 45.7865i | −0.167255 | − | 0.0572332i | ||||
\(801\) | 76.5562 | − | 132.599i | 0.0955758 | − | 0.165542i | ||||
\(802\) | 212.934 | − | 57.0556i | 0.265504 | − | 0.0711416i | ||||
\(803\) | −1043.70 | − | 279.659i | −1.29975 | − | 0.348268i | ||||
\(804\) | 216.911i | 0.269790i | ||||||||
\(805\) | −401.438 | − | 343.918i | −0.498680 | − | 0.427228i | ||||
\(806\) | 81.0237 | 0.100526 | ||||||||
\(807\) | −64.4990 | + | 240.714i | −0.0799244 | + | 0.298282i | ||||
\(808\) | 118.547 | + | 442.422i | 0.146716 | + | 0.547552i | ||||
\(809\) | 226.226 | + | 130.612i | 0.279637 | + | 0.161448i | 0.633259 | − | 0.773940i | \(-0.281717\pi\) |
−0.353622 | + | 0.935388i | \(0.615050\pi\) | |||||||
\(810\) | 56.1619 | − | 29.9307i | 0.0693356 | − | 0.0369515i | ||||
\(811\) | 426.501 | 0.525896 | 0.262948 | − | 0.964810i | \(-0.415305\pi\) | ||||
0.262948 | + | 0.964810i | \(0.415305\pi\) | |||||||
\(812\) | 342.392 | + | 273.739i | 0.421665 | + | 0.337117i | ||||
\(813\) | 233.552 | − | 233.552i | 0.287272 | − | 0.287272i | ||||
\(814\) | −603.396 | + | 348.371i | −0.741273 | + | 0.427974i | ||||
\(815\) | −247.888 | + | 397.548i | −0.304157 | + | 0.487789i | ||||
\(816\) | −3.23746 | + | 5.60744i | −0.00396747 | + | 0.00687187i | ||||
\(817\) | −43.8667 | + | 163.713i | −0.0536924 | + | 0.200383i | ||||
\(818\) | 126.659 | − | 126.659i | 0.154840 | − | 0.154840i | ||||
\(819\) | 23.4875 | + | 10.2819i | 0.0286782 | + | 0.0125542i | ||||
\(820\) | −470.413 | + | 439.509i | −0.573674 | + | 0.535986i | ||||
\(821\) | −320.566 | − | 555.236i | −0.390458 | − | 0.676293i | 0.602052 | − | 0.798457i | \(-0.294350\pi\) |
−0.992510 | + | 0.122164i | \(0.961017\pi\) | |||||||
\(822\) | −535.957 | + | 143.609i | −0.652016 | + | 0.174707i | ||||
\(823\) | 46.6662 | + | 174.161i | 0.0567025 | + | 0.211617i | 0.988464 | − | 0.151453i | \(-0.0483953\pi\) |
−0.931762 | + | 0.363070i | \(0.881729\pi\) | |||||||
\(824\) | −205.379 | + | 118.576i | −0.249246 | + | 0.143902i | ||||
\(825\) | −370.273 | − | 424.309i | −0.448815 | − | 0.514313i | ||||
\(826\) | 210.352 | + | 285.752i | 0.254663 | + | 0.345947i | ||||
\(827\) | −530.376 | − | 530.376i | −0.641325 | − | 0.641325i | 0.309556 | − | 0.950881i | \(-0.399820\pi\) |
−0.950881 | + | 0.309556i | \(0.899820\pi\) | |||||||
\(828\) | 87.5317 | + | 23.4540i | 0.105715 | + | 0.0283261i | ||||
\(829\) | −63.0803 | − | 36.4194i | −0.0760920 | − | 0.0439317i | 0.461471 | − | 0.887155i | \(-0.347322\pi\) |
−0.537563 | + | 0.843223i | \(0.680655\pi\) | |||||||
\(830\) | 310.763 | − | 72.0583i | 0.374414 | − | 0.0868173i | ||||
\(831\) | −42.6527 | − | 73.8766i | −0.0513269 | − | 0.0889009i | ||||
\(832\) | 6.90659 | + | 6.90659i | 0.00830118 | + | 0.00830118i | ||||
\(833\) | 45.7577 | + | 1.82501i | 0.0549313 | + | 0.00219089i | ||||
\(834\) | 103.225i | 0.123771i | ||||||||
\(835\) | 187.980 | − | 100.181i | 0.225125 | − | 0.119977i | ||||
\(836\) | −87.7813 | + | 152.042i | −0.105002 | + | 0.181868i | ||||
\(837\) | 235.524 | − | 63.1084i | 0.281390 | − | 0.0753983i | ||||
\(838\) | 1049.51 | + | 281.215i | 1.25240 | + | 0.335578i | ||||
\(839\) | − | 491.775i | − | 0.586144i | −0.956090 | − | 0.293072i | \(-0.905322\pi\) | ||
0.956090 | − | 0.293072i | \(-0.0946776\pi\) | |||||||
\(840\) | −96.9032 | − | 141.456i | −0.115361 | − | 0.168400i | ||||
\(841\) | −139.437 | −0.165799 | ||||||||
\(842\) | 204.031 | − | 761.452i | 0.242317 | − | 0.904338i | ||||
\(843\) | 153.961 | + | 574.592i | 0.182635 | + | 0.681604i | ||||
\(844\) | 518.609 | + | 299.419i | 0.614466 | + | 0.354762i | ||||
\(845\) | −801.184 | − | 244.109i | −0.948146 | − | 0.288887i | ||||
\(846\) | −211.599 | −0.250117 | ||||||||
\(847\) | 313.844 | − | 122.729i | 0.370536 | − | 0.144898i | ||||
\(848\) | −211.449 | + | 211.449i | −0.249350 | + | 0.249350i | ||||
\(849\) | −164.672 | + | 95.0733i | −0.193960 | + | 0.111983i | ||||
\(850\) | 18.4245 | − | 27.4285i | 0.0216759 | − | 0.0322688i | ||||
\(851\) | −286.070 | + | 495.488i | −0.336158 | + | 0.582242i | ||||
\(852\) | 67.0423 | − | 250.205i | 0.0786882 | − | 0.293668i | ||||
\(853\) | 132.089 | − | 132.089i | 0.154852 | − | 0.154852i | −0.625429 | − | 0.780281i | \(-0.715076\pi\) |
0.780281 | + | 0.625429i | \(0.215076\pi\) | |||||||
\(854\) | −119.631 | − | 1073.64i | −0.140084 | − | 1.25719i | ||||
\(855\) | 69.1189 | + | 73.9791i | 0.0808409 | + | 0.0865252i | ||||
\(856\) | −105.038 | − | 181.931i | −0.122708 | − | 0.212536i | ||||
\(857\) | −444.229 | + | 119.031i | −0.518354 | + | 0.138892i | −0.508505 | − | 0.861059i | \(-0.669802\pi\) |
−0.00984877 | + | 0.999951i | \(0.503135\pi\) | |||||||
\(858\) | 10.0666 | + | 37.5692i | 0.0117327 | + | 0.0437870i | ||||
\(859\) | 552.849 | − | 319.187i | 0.643596 | − | 0.371580i | −0.142402 | − | 0.989809i | \(-0.545483\pi\) |
0.785998 | + | 0.618229i | \(0.212149\pi\) | |||||||
\(860\) | 8.52364 | − | 250.963i | 0.00991121 | − | 0.291818i | ||||
\(861\) | −775.744 | + | 86.4380i | −0.900980 | + | 0.100393i | ||||
\(862\) | 120.875 | + | 120.875i | 0.140227 | + | 0.140227i | ||||
\(863\) | 1222.07 | + | 327.454i | 1.41608 | + | 0.379437i | 0.884090 | − | 0.467316i | \(-0.154779\pi\) |
0.531987 | + | 0.846753i | \(0.321446\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | −156.196 | + | 250.498i | −0.180573 | + | 0.289593i | ||||
\(866\) | −301.713 | − | 522.583i | −0.348399 | − | 0.603444i | ||||
\(867\) | 352.882 | + | 352.882i | 0.407014 | + | 0.407014i | ||||
\(868\) | −239.260 | − | 611.839i | −0.275645 | − | 0.704884i | ||||
\(869\) | 1260.52i | 1.45054i | ||||||||
\(870\) | 366.842 | + | 111.771i | 0.421657 | + | 0.128473i | ||||
\(871\) | −38.2252 | + | 66.2079i | −0.0438865 | + | 0.0760137i | ||||
\(872\) | −337.309 | + | 90.3817i | −0.386822 | + | 0.103649i | ||||
\(873\) | 342.357 | + | 91.7344i | 0.392162 | + | 0.105079i | ||||
\(874\) | 144.166i | 0.164950i | ||||||||
\(875\) | 444.390 | + | 753.752i | 0.507874 | + | 0.861431i | ||||
\(876\) | −287.805 | −0.328545 | ||||||||
\(877\) | 367.071 | − | 1369.93i | 0.418553 | − | 1.56206i | −0.359057 | − | 0.933316i | \(-0.616902\pi\) |
0.777610 | − | 0.628747i | \(-0.216432\pi\) | |||||||
\(878\) | −180.988 | − | 675.457i | −0.206137 | − | 0.769313i | ||||
\(879\) | 52.9066 | + | 30.5457i | 0.0601896 | + | 0.0347505i | ||||
\(880\) | 75.8105 | − | 248.816i | 0.0861483 | − | 0.282745i | ||||
\(881\) | 23.7391 | 0.0269456 | 0.0134728 | − | 0.999909i | \(-0.495711\pi\) | ||||
0.0134728 | + | 0.999909i | \(0.495711\pi\) | |||||||
\(882\) | 8.28492 | − | 207.724i | 0.00939334 | − | 0.235515i | ||||
\(883\) | −783.905 | + | 783.905i | −0.887774 | + | 0.887774i | −0.994309 | − | 0.106535i | \(-0.966024\pi\) |
0.106535 | + | 0.994309i | \(0.466024\pi\) | |||||||
\(884\) | −1.97634 | + | 1.14104i | −0.00223568 | + | 0.00129077i | ||||
\(885\) | 263.399 | + | 164.240i | 0.297626 | + | 0.185582i | ||||
\(886\) | −330.247 | + | 572.005i | −0.372739 | + | 0.645603i | ||||
\(887\) | 354.355 | − | 1322.47i | 0.399499 | − | 1.49095i | −0.414482 | − | 0.910057i | \(-0.636037\pi\) |
0.813981 | − | 0.580892i | \(-0.197296\pi\) | |||||||
\(888\) | −131.227 | + | 131.227i | −0.147778 | + | 0.147778i | ||||
\(889\) | −840.769 | + | 618.918i | −0.945747 | + | 0.696195i | ||||
\(890\) | −360.682 | − | 12.2501i | −0.405260 | − | 0.0137641i | ||||
\(891\) | 58.5244 | + | 101.367i | 0.0656840 | + | 0.113768i | ||||
\(892\) | −412.651 | + | 110.570i | −0.462614 | + | 0.123957i | ||||
\(893\) | −87.1266 | − | 325.161i | −0.0975662 | − | 0.364122i | ||||
\(894\) | −162.754 | + | 93.9663i | −0.182052 | + | 0.105108i | ||||
\(895\) | −782.445 | + | 731.042i | −0.874240 | + | 0.816806i | ||||
\(896\) | 31.7592 | − | 72.5490i | 0.0354455 | − | 0.0809698i | ||||
\(897\) | 22.5842 | + | 22.5842i | 0.0251775 | + | 0.0251775i | ||||
\(898\) | −740.945 | − | 198.536i | −0.825106 | − | 0.221086i | ||||
\(899\) | 1272.48 | + | 734.664i | 1.41543 | + | 0.817201i | ||||
\(900\) | −124.516 | − | 83.6410i | −0.138351 | − | 0.0929345i | ||||
\(901\) | −34.9336 | − | 60.5068i | −0.0387720 | − | 0.0671551i | ||||
\(902\) | −837.267 | − | 837.267i | −0.928233 | − | 0.928233i | ||||
\(903\) | 190.116 | − | 237.797i | 0.210538 | − | 0.263341i | ||||
\(904\) | − | 166.652i | − | 0.184350i | ||||||
\(905\) | 386.696 | − | 1269.16i | 0.427288 | − | 1.40239i | ||||
\(906\) | −37.8183 | + | 65.5032i | −0.0417421 | + | 0.0722994i | ||||
\(907\) | 525.221 | − | 140.732i | 0.579075 | − | 0.155163i | 0.0426195 | − | 0.999091i | \(-0.486430\pi\) |
0.536455 | + | 0.843929i | \(0.319763\pi\) | |||||||
\(908\) | −110.822 | − | 29.6946i | −0.122050 | − | 0.0327033i | ||||
\(909\) | 485.813i | 0.534447i | ||||||||
\(910\) | −4.64977 | − | 60.2535i | −0.00510964 | − | 0.0662126i | ||||
\(911\) | 150.624 | 0.165340 | 0.0826698 | − | 0.996577i | \(-0.473655\pi\) | ||||
0.0826698 | + | 0.996577i | \(0.473655\pi\) | |||||||
\(912\) | −12.1030 | + | 45.1692i | −0.0132709 | + | 0.0495276i | ||||
\(913\) | 151.858 | + | 566.742i | 0.166329 | + | 0.620747i | ||||
\(914\) | 536.424 | + | 309.704i | 0.586897 | + | 0.338845i | ||||
\(915\) | −444.473 | − | 834.007i | −0.485763 | − | 0.911483i | ||||
\(916\) | −197.590 | −0.215710 | ||||||||
\(917\) | −1367.62 | + | 534.807i | −1.49140 | + | 0.583214i | ||||
\(918\) | −4.85619 | + | 4.85619i | −0.00528997 | + | 0.00528997i | ||||
\(919\) | 1466.16 | − | 846.489i | 1.59539 | − | 0.921098i | 0.603029 | − | 0.797719i | \(-0.293960\pi\) |
0.992360 | − | 0.123379i | \(-0.0393731\pi\) | |||||||
\(920\) | −48.2467 | − | 208.072i | −0.0524421 | − | 0.226165i | ||||
\(921\) | 381.133 | − | 660.142i | 0.413825 | − | 0.716766i | ||||
\(922\) | 153.275 | − | 572.029i | 0.166241 | − | 0.620421i | ||||
\(923\) | 64.5559 | − | 64.5559i | 0.0699413 | − | 0.0699413i | ||||
\(924\) | 253.972 | − | 186.957i | 0.274862 | − | 0.202335i | ||||
\(925\) | 713.557 | − | 622.685i | 0.771413 | − | 0.673173i | ||||
\(926\) | −571.669 | − | 990.160i | −0.617354 | − | 1.06929i | ||||
\(927\) | −242.966 | + | 65.1025i | −0.262099 | + | 0.0702292i | ||||
\(928\) | 45.8439 | + | 171.092i | 0.0494007 | + | 0.184366i | ||||
\(929\) | −395.118 | + | 228.122i | −0.425316 | + | 0.245556i | −0.697349 | − | 0.716732i | \(-0.745637\pi\) |
0.272033 | + | 0.962288i | \(0.412304\pi\) | |||||||
\(930\) | −392.358 | − | 419.947i | −0.421890 | − | 0.451556i | ||||
\(931\) | 322.618 | − | 72.7999i | 0.346529 | − | 0.0781954i | ||||
\(932\) | 610.434 | + | 610.434i | 0.654972 | + | 0.654972i | ||||
\(933\) | 757.996 | + | 203.104i | 0.812428 | + | 0.217690i | ||||
\(934\) | −539.594 | − | 311.535i | −0.577724 | − | 0.333549i | ||||
\(935\) | 51.5689 | + | 32.1553i | 0.0551539 | + | 0.0343907i | ||||
\(936\) | 5.17994 | + | 8.97192i | 0.00553412 | + | 0.00958538i | ||||
\(937\) | −804.735 | − | 804.735i | −0.858842 | − | 0.858842i | 0.132360 | − | 0.991202i | \(-0.457745\pi\) |
−0.991202 | + | 0.132360i | \(0.957745\pi\) | |||||||
\(938\) | 612.837 | + | 93.1424i | 0.653344 | + | 0.0992989i | ||||
\(939\) | − | 583.138i | − | 0.621020i | ||||||
\(940\) | 234.566 | + | 440.140i | 0.249539 | + | 0.468234i | ||||
\(941\) | −532.052 | + | 921.541i | −0.565411 | + | 0.979321i | 0.431600 | + | 0.902065i | \(0.357949\pi\) |
−0.997011 | + | 0.0772562i | \(0.975384\pi\) | |||||||
\(942\) | 152.250 | − | 40.7954i | 0.161625 | − | 0.0433072i | ||||
\(943\) | −939.189 | − | 251.655i | −0.995959 | − | 0.266866i | ||||
\(944\) | 143.372i | 0.151877i | ||||||||
\(945\) | −60.4469 | − | 171.526i | −0.0639649 | − | 0.181509i | ||||
\(946\) | 461.849 | 0.488213 | ||||||||
\(947\) | −362.448 | + | 1352.68i | −0.382733 | + | 1.42838i | 0.458976 | + | 0.888448i | \(0.348216\pi\) |
−0.841709 | + | 0.539931i | \(0.818450\pi\) | |||||||
\(948\) | 86.8984 | + | 324.309i | 0.0916650 | + | 0.342098i | ||||
\(949\) | −87.8470 | − | 50.7185i | −0.0925679 | − | 0.0534441i | ||||
\(950\) | 77.2602 | − | 225.781i | 0.0813265 | − | 0.237664i | ||||
\(951\) | 878.118 | 0.923363 | ||||||||
\(952\) | 14.4525 | + | 11.5546i | 0.0151812 | + | 0.0121372i | ||||
\(953\) | 273.440 | − | 273.440i | 0.286926 | − | 0.286926i | −0.548938 | − | 0.835863i | \(-0.684968\pi\) |
0.835863 | + | 0.548938i | \(0.184968\pi\) | |||||||
\(954\) | −274.680 | + | 158.586i | −0.287924 | + | 0.166233i | ||||
\(955\) | −20.8583 | + | 4.83652i | −0.0218411 | + | 0.00506442i | ||||
\(956\) | −344.565 | + | 596.804i | −0.360424 | + | 0.624272i | ||||
\(957\) | −182.554 | + | 681.301i | −0.190757 | + | 0.711913i | ||||
\(958\) | 483.763 | − | 483.763i | 0.504972 | − | 0.504972i | ||||
\(959\) | 175.596 | + | 1575.90i | 0.183104 | + | 1.64328i | ||||
\(960\) | 2.35172 | − | 69.2421i | 0.00244970 | − | 0.0721272i | ||||
\(961\) | −620.501 | − | 1074.74i | −0.645682 | − | 1.11835i | ||||
\(962\) | −63.1800 | + | 16.9290i | −0.0656756 | + | 0.0175977i | ||||
\(963\) | −57.6698 | − | 215.227i | −0.0598855 | − | 0.223496i | ||||
\(964\) | −173.634 | + | 100.248i | −0.180118 | + | 0.103991i | ||||
\(965\) | −1182.18 | − | 40.1510i | −1.22505 | − | 0.0416073i | ||||
\(966\) | 103.851 | − | 237.231i | 0.107506 | − | 0.245581i | ||||
\(967\) | −676.635 | − | 676.635i | −0.699726 | − | 0.699726i | 0.264625 | − | 0.964351i | \(-0.414752\pi\) |
−0.964351 | + | 0.264625i | \(0.914752\pi\) | |||||||
\(968\) | 131.524 | + | 35.2417i | 0.135872 | + | 0.0364067i | ||||
\(969\) | −9.46199 | − | 5.46288i | −0.00976470 | − | 0.00563765i | ||||
\(970\) | −188.704 | − | 813.819i | −0.194541 | − | 0.838988i | ||||
\(971\) | −352.028 | − | 609.730i | −0.362542 | − | 0.627940i | 0.625837 | − | 0.779954i | \(-0.284758\pi\) |
−0.988378 | + | 0.152014i | \(0.951424\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 291.642 | + | 44.3254i | 0.299735 | + | 0.0455554i | ||||
\(974\) | 842.539i | 0.865030i | ||||||||
\(975\) | −23.2664 | − | 47.4726i | −0.0238630 | − | 0.0486899i | ||||
\(976\) | 218.251 | − | 378.021i | 0.223617 | − | 0.387317i | ||||
\(977\) | 1334.20 | − | 357.498i | 1.36561 | − | 0.365914i | 0.499737 | − | 0.866177i | \(-0.333430\pi\) |
0.865873 | + | 0.500263i | \(0.166763\pi\) | |||||||
\(978\) | −221.697 | − | 59.4035i | −0.226684 | − | 0.0607398i | ||||
\(979\) | − | 663.764i | − | 0.678002i | ||||||
\(980\) | −441.265 | + | 213.038i | −0.450270 | + | 0.217386i | ||||
\(981\) | −370.391 | −0.377565 | ||||||||
\(982\) | −180.464 | + | 673.501i | −0.183772 | + | 0.685846i | ||||
\(983\) | −283.127 | − | 1056.64i | −0.288023 | − | 1.07492i | −0.946602 | − | 0.322405i | \(-0.895509\pi\) |
0.658578 | − | 0.752512i | \(-0.271158\pi\) | |||||||
\(984\) | −273.134 | − | 157.694i | −0.277575 | − | 0.160258i | ||||
\(985\) | −38.1597 | + | 20.3367i | −0.0387408 | + | 0.0206464i | ||||
\(986\) | −41.3846 | −0.0419722 | ||||||||
\(987\) | −90.8613 | + | 597.828i | −0.0920580 | + | 0.605702i | ||||
\(988\) | −11.6542 | + | 11.6542i | −0.0117957 | + | 0.0117957i | ||||
\(989\) | 328.444 | − | 189.627i | 0.332097 | − | 0.191736i | ||||
\(990\) | 145.974 | − | 234.105i | 0.147448 | − | 0.236470i | ||||
\(991\) | 229.391 | − | 397.317i | 0.231474 | − | 0.400925i | −0.726768 | − | 0.686883i | \(-0.758978\pi\) |
0.958242 | + | 0.285958i | \(0.0923118\pi\) | |||||||
\(992\) | 68.7037 | − | 256.406i | 0.0692577 | − | 0.258473i | ||||
\(993\) | 216.095 | − | 216.095i | 0.217618 | − | 0.217618i | ||||
\(994\) | −678.115 | − | 296.853i | −0.682208 | − | 0.298645i | ||||
\(995\) | 904.093 | − | 844.698i | 0.908636 | − | 0.848943i | ||||
\(996\) | 78.1407 | + | 135.344i | 0.0784546 | + | 0.135887i | ||||
\(997\) | 934.885 | − | 250.502i | 0.937699 | − | 0.251256i | 0.242564 | − | 0.970135i | \(-0.422012\pi\) |
0.695134 | + | 0.718880i | \(0.255345\pi\) | |||||||
\(998\) | −138.508 | − | 516.920i | −0.138786 | − | 0.517956i | ||||
\(999\) | −170.469 | + | 98.4202i | −0.170639 | + | 0.0985187i |
(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 | 210.3.v.a.67.2 | yes | 32 | |
5.3 | odd | 4 | inner | 210.3.v.a.193.8 | yes | 32 | |
7.2 | even | 3 | inner | 210.3.v.a.37.8 | ✓ | 32 | |
35.23 | odd | 12 | inner | 210.3.v.a.163.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.a.37.8 | ✓ | 32 | 7.2 | even | 3 | inner | |
210.3.v.a.67.2 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.a.163.2 | yes | 32 | 35.23 | odd | 12 | inner | |
210.3.v.a.193.8 | yes | 32 | 5.3 | odd | 4 | inner |