Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(100,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + 1005 x^{6} - 544 x^{5} + 811 x^{4} - 312 x^{3} + 195 x^{2} + 13 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.6 | ||
Root | \(0.415625 + 0.719884i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.100 |
Dual form | 273.2.j.b.172.6 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.415625 | + | 0.719884i | 0.293892 | + | 0.509035i | 0.974726 | − | 0.223402i | \(-0.0717162\pi\) |
−0.680835 | + | 0.732437i | \(0.738383\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.654511 | − | 1.13365i | 0.327255 | − | 0.566823i | ||||
\(5\) | −1.30847 | + | 2.26634i | −0.585165 | + | 1.01354i | 0.409690 | + | 0.912225i | \(0.365637\pi\) |
−0.994855 | + | 0.101311i | \(0.967696\pi\) | |||||||
\(6\) | −0.415625 | − | 0.719884i | −0.169678 | − | 0.293892i | ||||
\(7\) | 0.801591 | + | 2.52140i | 0.302973 | + | 0.952999i | ||||
\(8\) | 2.75063 | 0.972494 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.17533 | −0.687901 | ||||||||
\(11\) | −1.84837 | −0.557303 | −0.278652 | − | 0.960392i | \(-0.589887\pi\) | ||||
−0.278652 | + | 0.960392i | \(0.589887\pi\) | |||||||
\(12\) | −0.654511 | + | 1.13365i | −0.188941 | + | 0.327255i | ||||
\(13\) | 2.74506 | + | 2.33765i | 0.761344 | + | 0.648348i | ||||
\(14\) | −1.48195 | + | 1.62501i | −0.396069 | + | 0.434302i | ||||
\(15\) | 1.30847 | − | 2.26634i | 0.337845 | − | 0.585165i | ||||
\(16\) | −0.165791 | − | 0.287158i | −0.0414477 | − | 0.0717896i | ||||
\(17\) | −3.41564 | + | 5.91607i | −0.828415 | + | 1.43486i | 0.0708664 | + | 0.997486i | \(0.477424\pi\) |
−0.899281 | + | 0.437371i | \(0.855910\pi\) | |||||||
\(18\) | 0.415625 | + | 0.719884i | 0.0979639 | + | 0.169678i | ||||
\(19\) | 5.06988 | 1.16311 | 0.581556 | − | 0.813507i | \(-0.302444\pi\) | ||||
0.581556 | + | 0.813507i | \(0.302444\pi\) | |||||||
\(20\) | 1.71281 | + | 2.96668i | 0.382997 | + | 0.663370i | ||||
\(21\) | −0.801591 | − | 2.52140i | −0.174922 | − | 0.550214i | ||||
\(22\) | −0.768228 | − | 1.33061i | −0.163787 | − | 0.283687i | ||||
\(23\) | 0.636428 | + | 1.10233i | 0.132704 | + | 0.229851i | 0.924718 | − | 0.380652i | \(-0.124301\pi\) |
−0.792014 | + | 0.610503i | \(0.790967\pi\) | |||||||
\(24\) | −2.75063 | −0.561470 | ||||||||
\(25\) | −0.924183 | − | 1.60073i | −0.184837 | − | 0.320146i | ||||
\(26\) | −0.541921 | + | 2.94772i | −0.106279 | + | 0.578095i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.38302 | + | 0.741562i | 0.639331 | + | 0.140142i | ||||
\(29\) | 0.724496 | − | 1.25486i | 0.134536 | − | 0.233022i | −0.790884 | − | 0.611966i | \(-0.790379\pi\) |
0.925420 | + | 0.378943i | \(0.123712\pi\) | |||||||
\(30\) | 2.17533 | 0.397160 | ||||||||
\(31\) | −3.09878 | − | 5.36725i | −0.556557 | − | 0.963986i | −0.997781 | − | 0.0665883i | \(-0.978789\pi\) |
0.441223 | − | 0.897397i | \(-0.354545\pi\) | |||||||
\(32\) | 2.88844 | − | 5.00293i | 0.510609 | − | 0.884401i | ||||
\(33\) | 1.84837 | 0.321759 | ||||||||
\(34\) | −5.67851 | −0.973857 | ||||||||
\(35\) | −6.76319 | − | 1.48250i | −1.14319 | − | 0.250588i | ||||
\(36\) | 0.654511 | − | 1.13365i | 0.109085 | − | 0.188941i | ||||
\(37\) | −3.93922 | − | 6.82292i | −0.647603 | − | 1.12168i | −0.983694 | − | 0.179852i | \(-0.942438\pi\) |
0.336090 | − | 0.941830i | \(-0.390895\pi\) | |||||||
\(38\) | 2.10717 | + | 3.64973i | 0.341829 | + | 0.592064i | ||||
\(39\) | −2.74506 | − | 2.33765i | −0.439562 | − | 0.374324i | ||||
\(40\) | −3.59911 | + | 6.23384i | −0.569069 | + | 0.985657i | ||||
\(41\) | 4.41239 | − | 7.64248i | 0.689099 | − | 1.19355i | −0.283031 | − | 0.959111i | \(-0.591340\pi\) |
0.972130 | − | 0.234444i | \(-0.0753268\pi\) | |||||||
\(42\) | 1.48195 | − | 1.62501i | 0.228670 | − | 0.250745i | ||||
\(43\) | 0.109598 | + | 0.189830i | 0.0167136 | + | 0.0289488i | 0.874261 | − | 0.485456i | \(-0.161346\pi\) |
−0.857548 | + | 0.514405i | \(0.828013\pi\) | |||||||
\(44\) | −1.20978 | + | 2.09539i | −0.182381 | + | 0.315892i | ||||
\(45\) | −1.30847 | + | 2.26634i | −0.195055 | + | 0.337845i | ||||
\(46\) | −0.529032 | + | 0.916310i | −0.0780015 | + | 0.135103i | ||||
\(47\) | 0.624016 | − | 1.08083i | 0.0910220 | − | 0.157655i | −0.816919 | − | 0.576752i | \(-0.804320\pi\) |
0.907941 | + | 0.419097i | \(0.137653\pi\) | |||||||
\(48\) | 0.165791 | + | 0.287158i | 0.0239299 | + | 0.0414477i | ||||
\(49\) | −5.71490 | + | 4.04226i | −0.816415 | + | 0.577466i | ||||
\(50\) | 0.768228 | − | 1.33061i | 0.108644 | − | 0.188177i | ||||
\(51\) | 3.41564 | − | 5.91607i | 0.478286 | − | 0.828415i | ||||
\(52\) | 4.44675 | − | 1.58191i | 0.616653 | − | 0.219372i | ||||
\(53\) | 1.33947 | + | 2.32004i | 0.183991 | + | 0.318682i | 0.943236 | − | 0.332123i | \(-0.107765\pi\) |
−0.759245 | + | 0.650805i | \(0.774432\pi\) | |||||||
\(54\) | −0.415625 | − | 0.719884i | −0.0565595 | − | 0.0979639i | ||||
\(55\) | 2.41853 | − | 4.18902i | 0.326114 | − | 0.564847i | ||||
\(56\) | 2.20488 | + | 6.93543i | 0.294639 | + | 0.926786i | ||||
\(57\) | −5.06988 | −0.671522 | ||||||||
\(58\) | 1.20448 | 0.158155 | ||||||||
\(59\) | 6.01804 | − | 10.4236i | 0.783483 | − | 1.35703i | −0.146419 | − | 0.989223i | \(-0.546775\pi\) |
0.929901 | − | 0.367809i | \(-0.119892\pi\) | |||||||
\(60\) | −1.71281 | − | 2.96668i | −0.221123 | − | 0.382997i | ||||
\(61\) | −8.72218 | −1.11676 | −0.558381 | − | 0.829585i | \(-0.688577\pi\) | ||||
−0.558381 | + | 0.829585i | \(0.688577\pi\) | |||||||
\(62\) | 2.57586 | − | 4.46153i | 0.327135 | − | 0.566615i | ||||
\(63\) | 0.801591 | + | 2.52140i | 0.100991 | + | 0.317666i | ||||
\(64\) | 4.13888 | 0.517359 | ||||||||
\(65\) | −8.88974 | + | 3.16249i | −1.10264 | + | 0.392259i | ||||
\(66\) | 0.768228 | + | 1.33061i | 0.0945623 | + | 0.163787i | ||||
\(67\) | 13.8331 | 1.68998 | 0.844992 | − | 0.534779i | \(-0.179605\pi\) | ||||
0.844992 | + | 0.534779i | \(0.179605\pi\) | |||||||
\(68\) | 4.47115 | + | 7.74426i | 0.542207 | + | 0.939129i | ||||
\(69\) | −0.636428 | − | 1.10233i | −0.0766170 | − | 0.132704i | ||||
\(70\) | −1.74373 | − | 5.48488i | −0.208415 | − | 0.655569i | ||||
\(71\) | 1.78833 | + | 3.09749i | 0.212236 | + | 0.367604i | 0.952414 | − | 0.304807i | \(-0.0985920\pi\) |
−0.740178 | + | 0.672411i | \(0.765259\pi\) | |||||||
\(72\) | 2.75063 | 0.324165 | ||||||||
\(73\) | −3.26733 | − | 5.65918i | −0.382412 | − | 0.662357i | 0.608994 | − | 0.793175i | \(-0.291573\pi\) |
−0.991406 | + | 0.130817i | \(0.958240\pi\) | |||||||
\(74\) | 3.27448 | − | 5.67156i | 0.380650 | − | 0.659306i | ||||
\(75\) | 0.924183 | + | 1.60073i | 0.106715 | + | 0.184837i | ||||
\(76\) | 3.31829 | − | 5.74745i | 0.380634 | − | 0.659278i | ||||
\(77\) | −1.48163 | − | 4.66047i | −0.168848 | − | 0.531110i | ||||
\(78\) | 0.541921 | − | 2.94772i | 0.0613605 | − | 0.333763i | ||||
\(79\) | 3.08084 | − | 5.33616i | 0.346621 | − | 0.600365i | −0.639026 | − | 0.769185i | \(-0.720662\pi\) |
0.985647 | + | 0.168820i | \(0.0539956\pi\) | |||||||
\(80\) | 0.867729 | 0.0970151 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.33560 | 0.810082 | ||||||||
\(83\) | −8.67738 | −0.952467 | −0.476233 | − | 0.879319i | \(-0.657998\pi\) | ||||
−0.476233 | + | 0.879319i | \(0.657998\pi\) | |||||||
\(84\) | −3.38302 | − | 0.741562i | −0.369118 | − | 0.0809110i | ||||
\(85\) | −8.93852 | − | 15.4820i | −0.969519 | − | 1.67926i | ||||
\(86\) | −0.0911037 | + | 0.157796i | −0.00982396 | + | 0.0170156i | ||||
\(87\) | −0.724496 | + | 1.25486i | −0.0776741 | + | 0.134536i | ||||
\(88\) | −5.08417 | −0.541974 | ||||||||
\(89\) | 7.57751 | + | 13.1246i | 0.803215 | + | 1.39121i | 0.917490 | + | 0.397760i | \(0.130212\pi\) |
−0.114275 | + | 0.993449i | \(0.536454\pi\) | |||||||
\(90\) | −2.17533 | −0.229300 | ||||||||
\(91\) | −3.69373 | + | 8.79524i | −0.387209 | + | 0.921992i | ||||
\(92\) | 1.66620 | 0.173713 | ||||||||
\(93\) | 3.09878 | + | 5.36725i | 0.321329 | + | 0.556557i | ||||
\(94\) | 1.03743 | 0.107002 | ||||||||
\(95\) | −6.63379 | + | 11.4901i | −0.680612 | + | 1.17885i | ||||
\(96\) | −2.88844 | + | 5.00293i | −0.294800 | + | 0.510609i | ||||
\(97\) | 6.08221 | + | 10.5347i | 0.617554 | + | 1.06964i | 0.989931 | + | 0.141554i | \(0.0452098\pi\) |
−0.372376 | + | 0.928082i | \(0.621457\pi\) | |||||||
\(98\) | −5.28522 | − | 2.43400i | −0.533888 | − | 0.245871i | ||||
\(99\) | −1.84837 | −0.185768 | ||||||||
\(100\) | −2.41955 | −0.241955 | ||||||||
\(101\) | −4.59607 | −0.457326 | −0.228663 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228663 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(102\) | 5.67851 | 0.562256 | ||||||||
\(103\) | −2.22609 | + | 3.85570i | −0.219343 | + | 0.379914i | −0.954607 | − | 0.297867i | \(-0.903725\pi\) |
0.735264 | + | 0.677781i | \(0.237058\pi\) | |||||||
\(104\) | 7.55065 | + | 6.43001i | 0.740402 | + | 0.630515i | ||||
\(105\) | 6.76319 | + | 1.48250i | 0.660020 | + | 0.144677i | ||||
\(106\) | −1.11344 | + | 1.92853i | −0.108147 | + | 0.187316i | ||||
\(107\) | −3.60694 | − | 6.24740i | −0.348696 | − | 0.603959i | 0.637322 | − | 0.770597i | \(-0.280042\pi\) |
−0.986018 | + | 0.166639i | \(0.946709\pi\) | |||||||
\(108\) | −0.654511 | + | 1.13365i | −0.0629803 | + | 0.109085i | ||||
\(109\) | 4.34979 | + | 7.53406i | 0.416635 | + | 0.721632i | 0.995599 | − | 0.0937209i | \(-0.0298761\pi\) |
−0.578964 | + | 0.815353i | \(0.696543\pi\) | |||||||
\(110\) | 4.02081 | 0.383369 | ||||||||
\(111\) | 3.93922 | + | 6.82292i | 0.373894 | + | 0.647603i | ||||
\(112\) | 0.591144 | − | 0.648208i | 0.0558578 | − | 0.0612499i | ||||
\(113\) | 1.82527 | + | 3.16146i | 0.171707 | + | 0.297405i | 0.939017 | − | 0.343871i | \(-0.111738\pi\) |
−0.767310 | + | 0.641277i | \(0.778405\pi\) | |||||||
\(114\) | −2.10717 | − | 3.64973i | −0.197355 | − | 0.341829i | ||||
\(115\) | −3.33099 | −0.310616 | ||||||||
\(116\) | −0.948381 | − | 1.64264i | −0.0880550 | − | 0.152516i | ||||
\(117\) | 2.74506 | + | 2.33765i | 0.253781 | + | 0.216116i | ||||
\(118\) | 10.0050 | 0.921036 | ||||||||
\(119\) | −17.6547 | − | 3.86993i | −1.61840 | − | 0.354756i | ||||
\(120\) | 3.59911 | − | 6.23384i | 0.328552 | − | 0.569069i | ||||
\(121\) | −7.58354 | −0.689413 | ||||||||
\(122\) | −3.62516 | − | 6.27896i | −0.328207 | − | 0.568471i | ||||
\(123\) | −4.41239 | + | 7.64248i | −0.397852 | + | 0.689099i | ||||
\(124\) | −8.11274 | −0.728546 | ||||||||
\(125\) | −8.24763 | −0.737691 | ||||||||
\(126\) | −1.48195 | + | 1.62501i | −0.132023 | + | 0.144767i | ||||
\(127\) | 4.80639 | − | 8.32491i | 0.426498 | − | 0.738716i | −0.570061 | − | 0.821602i | \(-0.693080\pi\) |
0.996559 | + | 0.0828862i | \(0.0264138\pi\) | |||||||
\(128\) | −4.05666 | − | 7.02634i | −0.358562 | − | 0.621047i | ||||
\(129\) | −0.109598 | − | 0.189830i | −0.00964959 | − | 0.0167136i | ||||
\(130\) | −5.97143 | − | 5.08517i | −0.523729 | − | 0.445999i | ||||
\(131\) | 8.28016 | − | 14.3417i | 0.723441 | − | 1.25304i | −0.236172 | − | 0.971711i | \(-0.575893\pi\) |
0.959613 | − | 0.281325i | \(-0.0907738\pi\) | |||||||
\(132\) | 1.20978 | − | 2.09539i | 0.105297 | − | 0.182381i | ||||
\(133\) | 4.06397 | + | 12.7832i | 0.352391 | + | 1.10844i | ||||
\(134\) | 5.74940 | + | 9.95825i | 0.496672 | + | 0.860261i | ||||
\(135\) | 1.30847 | − | 2.26634i | 0.112615 | − | 0.195055i | ||||
\(136\) | −9.39516 | + | 16.2729i | −0.805628 | + | 1.39539i | ||||
\(137\) | 5.27844 | − | 9.14252i | 0.450967 | − | 0.781098i | −0.547479 | − | 0.836819i | \(-0.684412\pi\) |
0.998446 | + | 0.0557212i | \(0.0177458\pi\) | |||||||
\(138\) | 0.529032 | − | 0.916310i | 0.0450342 | − | 0.0780015i | ||||
\(139\) | −4.57749 | − | 7.92845i | −0.388258 | − | 0.672482i | 0.603958 | − | 0.797016i | \(-0.293590\pi\) |
−0.992215 | + | 0.124534i | \(0.960256\pi\) | |||||||
\(140\) | −6.10721 | + | 6.69676i | −0.516154 | + | 0.565979i | ||||
\(141\) | −0.624016 | + | 1.08083i | −0.0525516 | + | 0.0910220i | ||||
\(142\) | −1.48655 | + | 2.57479i | −0.124749 | + | 0.216071i | ||||
\(143\) | −5.07388 | − | 4.32084i | −0.424299 | − | 0.361327i | ||||
\(144\) | −0.165791 | − | 0.287158i | −0.0138159 | − | 0.0239299i | ||||
\(145\) | 1.89596 | + | 3.28390i | 0.157451 | + | 0.272713i | ||||
\(146\) | 2.71597 | − | 4.70420i | 0.224775 | − | 0.389322i | ||||
\(147\) | 5.71490 | − | 4.04226i | 0.471357 | − | 0.333400i | ||||
\(148\) | −10.3130 | −0.847727 | ||||||||
\(149\) | −10.9073 | −0.893565 | −0.446782 | − | 0.894643i | \(-0.647430\pi\) | ||||
−0.446782 | + | 0.894643i | \(0.647430\pi\) | |||||||
\(150\) | −0.768228 | + | 1.33061i | −0.0627255 | + | 0.108644i | ||||
\(151\) | 11.1702 | + | 19.3474i | 0.909018 | + | 1.57447i | 0.815430 | + | 0.578855i | \(0.196500\pi\) |
0.0935880 | + | 0.995611i | \(0.470166\pi\) | |||||||
\(152\) | 13.9454 | 1.13112 | ||||||||
\(153\) | −3.41564 | + | 5.91607i | −0.276138 | + | 0.478286i | ||||
\(154\) | 2.73919 | − | 3.00361i | 0.220730 | − | 0.242038i | ||||
\(155\) | 16.2186 | 1.30271 | ||||||||
\(156\) | −4.44675 | + | 1.58191i | −0.356025 | + | 0.126654i | ||||
\(157\) | −0.329586 | − | 0.570859i | −0.0263038 | − | 0.0455595i | 0.852574 | − | 0.522607i | \(-0.175040\pi\) |
−0.878878 | + | 0.477047i | \(0.841707\pi\) | |||||||
\(158\) | 5.12190 | 0.407476 | ||||||||
\(159\) | −1.33947 | − | 2.32004i | −0.106227 | − | 0.183991i | ||||
\(160\) | 7.55887 | + | 13.0924i | 0.597581 | + | 1.03504i | ||||
\(161\) | −2.26925 | + | 2.48830i | −0.178842 | + | 0.196106i | ||||
\(162\) | 0.415625 | + | 0.719884i | 0.0326546 | + | 0.0565595i | ||||
\(163\) | 18.1851 | 1.42436 | 0.712182 | − | 0.701995i | \(-0.247707\pi\) | ||||
0.712182 | + | 0.701995i | \(0.247707\pi\) | |||||||
\(164\) | −5.77591 | − | 10.0042i | −0.451023 | − | 0.781194i | ||||
\(165\) | −2.41853 | + | 4.18902i | −0.188282 | + | 0.326114i | ||||
\(166\) | −3.60654 | − | 6.24671i | −0.279922 | − | 0.484839i | ||||
\(167\) | −2.21154 | + | 3.83050i | −0.171134 | + | 0.296413i | −0.938817 | − | 0.344417i | \(-0.888076\pi\) |
0.767683 | + | 0.640830i | \(0.221410\pi\) | |||||||
\(168\) | −2.20488 | − | 6.93543i | −0.170110 | − | 0.535080i | ||||
\(169\) | 2.07076 | + | 12.8340i | 0.159289 | + | 0.987232i | ||||
\(170\) | 7.43016 | − | 12.8694i | 0.569867 | − | 0.987039i | ||||
\(171\) | 5.06988 | 0.387704 | ||||||||
\(172\) | 0.286933 | 0.0218784 | ||||||||
\(173\) | 3.52044 | 0.267654 | 0.133827 | − | 0.991005i | \(-0.457273\pi\) | ||||
0.133827 | + | 0.991005i | \(0.457273\pi\) | |||||||
\(174\) | −1.20448 | −0.0913111 | ||||||||
\(175\) | 3.29527 | − | 3.61337i | 0.249099 | − | 0.273145i | ||||
\(176\) | 0.306442 | + | 0.530773i | 0.0230990 | + | 0.0400086i | ||||
\(177\) | −6.01804 | + | 10.4236i | −0.452344 | + | 0.783483i | ||||
\(178\) | −6.29881 | + | 10.9099i | −0.472116 | + | 0.817729i | ||||
\(179\) | 10.8203 | 0.808746 | 0.404373 | − | 0.914594i | \(-0.367490\pi\) | ||||
0.404373 | + | 0.914594i | \(0.367490\pi\) | |||||||
\(180\) | 1.71281 | + | 2.96668i | 0.127666 | + | 0.221123i | ||||
\(181\) | −23.0651 | −1.71441 | −0.857207 | − | 0.514973i | \(-0.827802\pi\) | ||||
−0.857207 | + | 0.514973i | \(0.827802\pi\) | |||||||
\(182\) | −7.86677 | + | 0.996466i | −0.583124 | + | 0.0738630i | ||||
\(183\) | 8.72218 | 0.644762 | ||||||||
\(184\) | 1.75058 | + | 3.03209i | 0.129054 | + | 0.223529i | ||||
\(185\) | 20.6174 | 1.51582 | ||||||||
\(186\) | −2.57586 | + | 4.46153i | −0.188872 | + | 0.327135i | ||||
\(187\) | 6.31336 | − | 10.9351i | 0.461678 | − | 0.799650i | ||||
\(188\) | −0.816850 | − | 1.41483i | −0.0595749 | − | 0.103187i | ||||
\(189\) | −0.801591 | − | 2.52140i | −0.0583072 | − | 0.183405i | ||||
\(190\) | −11.0287 | −0.800105 | ||||||||
\(191\) | −1.82966 | −0.132389 | −0.0661947 | − | 0.997807i | \(-0.521086\pi\) | ||||
−0.0661947 | + | 0.997807i | \(0.521086\pi\) | |||||||
\(192\) | −4.13888 | −0.298698 | ||||||||
\(193\) | 3.15951 | 0.227427 | 0.113713 | − | 0.993514i | \(-0.463725\pi\) | ||||
0.113713 | + | 0.993514i | \(0.463725\pi\) | |||||||
\(194\) | −5.05584 | + | 8.75697i | −0.362988 | + | 0.628714i | ||||
\(195\) | 8.88974 | − | 3.16249i | 0.636607 | − | 0.226471i | ||||
\(196\) | 0.842029 | + | 9.12438i | 0.0601450 | + | 0.651742i | ||||
\(197\) | 5.57597 | − | 9.65786i | 0.397271 | − | 0.688094i | −0.596117 | − | 0.802898i | \(-0.703291\pi\) |
0.993388 | + | 0.114804i | \(0.0366239\pi\) | |||||||
\(198\) | −0.768228 | − | 1.33061i | −0.0545956 | − | 0.0945623i | ||||
\(199\) | −10.3748 | + | 17.9697i | −0.735452 | + | 1.27384i | 0.219072 | + | 0.975709i | \(0.429697\pi\) |
−0.954525 | + | 0.298132i | \(0.903636\pi\) | |||||||
\(200\) | −2.54208 | − | 4.40302i | −0.179752 | − | 0.311340i | ||||
\(201\) | −13.8331 | −0.975713 | ||||||||
\(202\) | −1.91024 | − | 3.30864i | −0.134404 | − | 0.232795i | ||||
\(203\) | 3.74476 | + | 0.820855i | 0.262831 | + | 0.0576127i | ||||
\(204\) | −4.47115 | − | 7.74426i | −0.313043 | − | 0.542207i | ||||
\(205\) | 11.5469 | + | 19.9999i | 0.806474 | + | 1.39685i | ||||
\(206\) | −3.70088 | −0.257853 | ||||||||
\(207\) | 0.636428 | + | 1.10233i | 0.0442348 | + | 0.0766170i | ||||
\(208\) | 0.216169 | − | 1.17583i | 0.0149887 | − | 0.0815291i | ||||
\(209\) | −9.37100 | −0.648206 | ||||||||
\(210\) | 1.74373 | + | 5.48488i | 0.120329 | + | 0.378493i | ||||
\(211\) | 8.16773 | − | 14.1469i | 0.562289 | − | 0.973914i | −0.435007 | − | 0.900427i | \(-0.643254\pi\) |
0.997296 | − | 0.0734866i | \(-0.0234126\pi\) | |||||||
\(212\) | 3.50680 | 0.240848 | ||||||||
\(213\) | −1.78833 | − | 3.09749i | −0.122535 | − | 0.212236i | ||||
\(214\) | 2.99827 | − | 5.19316i | 0.204957 | − | 0.354997i | ||||
\(215\) | −0.573624 | −0.0391208 | ||||||||
\(216\) | −2.75063 | −0.187157 | ||||||||
\(217\) | 11.0490 | − | 12.1156i | 0.750056 | − | 0.822460i | ||||
\(218\) | −3.61577 | + | 6.26270i | −0.244891 | + | 0.424163i | ||||
\(219\) | 3.26733 | + | 5.65918i | 0.220786 | + | 0.382412i | ||||
\(220\) | −3.16591 | − | 5.48351i | −0.213445 | − | 0.369698i | ||||
\(221\) | −23.2059 | + | 8.25540i | −1.56100 | + | 0.555318i | ||||
\(222\) | −3.27448 | + | 5.67156i | −0.219769 | + | 0.380650i | ||||
\(223\) | 9.30867 | − | 16.1231i | 0.623355 | − | 1.07968i | −0.365502 | − | 0.930811i | \(-0.619103\pi\) |
0.988857 | − | 0.148871i | \(-0.0475640\pi\) | |||||||
\(224\) | 14.9297 | + | 3.27261i | 0.997534 | + | 0.218660i | ||||
\(225\) | −0.924183 | − | 1.60073i | −0.0616122 | − | 0.106715i | ||||
\(226\) | −1.51726 | + | 2.62797i | −0.100926 | + | 0.174810i | ||||
\(227\) | 11.2727 | − | 19.5249i | 0.748197 | − | 1.29592i | −0.200489 | − | 0.979696i | \(-0.564253\pi\) |
0.948686 | − | 0.316220i | \(-0.102414\pi\) | |||||||
\(228\) | −3.31829 | + | 5.74745i | −0.219759 | + | 0.380634i | ||||
\(229\) | 9.62713 | − | 16.6747i | 0.636179 | − | 1.10189i | −0.350085 | − | 0.936718i | \(-0.613847\pi\) |
0.986264 | − | 0.165176i | \(-0.0528193\pi\) | |||||||
\(230\) | −1.38444 | − | 2.39793i | −0.0912875 | − | 0.158115i | ||||
\(231\) | 1.48163 | + | 4.66047i | 0.0974844 | + | 0.306636i | ||||
\(232\) | 1.99282 | − | 3.45166i | 0.130835 | − | 0.226613i | ||||
\(233\) | −11.4276 | + | 19.7933i | −0.748650 | + | 1.29670i | 0.199820 | + | 0.979833i | \(0.435964\pi\) |
−0.948470 | + | 0.316867i | \(0.897369\pi\) | |||||||
\(234\) | −0.541921 | + | 2.94772i | −0.0354265 | + | 0.192698i | ||||
\(235\) | 1.63301 | + | 2.82846i | 0.106526 | + | 0.184508i | ||||
\(236\) | −7.87775 | − | 13.6447i | −0.512798 | − | 0.888192i | ||||
\(237\) | −3.08084 | + | 5.33616i | −0.200122 | + | 0.346621i | ||||
\(238\) | −4.55185 | − | 14.3178i | −0.295052 | − | 0.928085i | ||||
\(239\) | −11.2501 | −0.727705 | −0.363853 | − | 0.931457i | \(-0.618539\pi\) | ||||
−0.363853 | + | 0.931457i | \(0.618539\pi\) | |||||||
\(240\) | −0.867729 | −0.0560117 | ||||||||
\(241\) | −9.72305 | + | 16.8408i | −0.626316 | + | 1.08481i | 0.361968 | + | 0.932190i | \(0.382105\pi\) |
−0.988285 | + | 0.152621i | \(0.951228\pi\) | |||||||
\(242\) | −3.15191 | − | 5.45928i | −0.202613 | − | 0.350936i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.70876 | + | 9.88787i | −0.365466 | + | 0.633006i | ||||
\(245\) | −1.68335 | − | 18.2411i | −0.107545 | − | 1.16538i | ||||
\(246\) | −7.33560 | −0.467701 | ||||||||
\(247\) | 13.9172 | + | 11.8516i | 0.885528 | + | 0.754101i | ||||
\(248\) | −8.52359 | − | 14.7633i | −0.541249 | − | 0.937470i | ||||
\(249\) | 8.67738 | 0.549907 | ||||||||
\(250\) | −3.42793 | − | 5.93734i | −0.216801 | − | 0.375510i | ||||
\(251\) | −8.79293 | − | 15.2298i | −0.555005 | − | 0.961297i | −0.997903 | − | 0.0647248i | \(-0.979383\pi\) |
0.442898 | − | 0.896572i | \(-0.353950\pi\) | |||||||
\(252\) | 3.38302 | + | 0.741562i | 0.213110 | + | 0.0467140i | ||||
\(253\) | −1.17635 | − | 2.03750i | −0.0739566 | − | 0.128097i | ||||
\(254\) | 7.99063 | 0.501377 | ||||||||
\(255\) | 8.93852 | + | 15.4820i | 0.559752 | + | 0.969519i | ||||
\(256\) | 7.51098 | − | 13.0094i | 0.469436 | − | 0.813087i | ||||
\(257\) | −7.59362 | − | 13.1525i | −0.473677 | − | 0.820432i | 0.525869 | − | 0.850565i | \(-0.323740\pi\) |
−0.999546 | + | 0.0301333i | \(0.990407\pi\) | |||||||
\(258\) | 0.0911037 | − | 0.157796i | 0.00567187 | − | 0.00982396i | ||||
\(259\) | 14.0457 | − | 15.4015i | 0.872755 | − | 0.957005i | ||||
\(260\) | −2.23328 | + | 12.1477i | −0.138502 | + | 0.753368i | ||||
\(261\) | 0.724496 | − | 1.25486i | 0.0448452 | − | 0.0776741i | ||||
\(262\) | 13.7658 | 0.850453 | ||||||||
\(263\) | −13.9699 | −0.861422 | −0.430711 | − | 0.902490i | \(-0.641737\pi\) | ||||
−0.430711 | + | 0.902490i | \(0.641737\pi\) | |||||||
\(264\) | 5.08417 | 0.312909 | ||||||||
\(265\) | −7.01065 | −0.430661 | ||||||||
\(266\) | −7.51333 | + | 8.23862i | −0.460672 | + | 0.505142i | ||||
\(267\) | −7.57751 | − | 13.1246i | −0.463736 | − | 0.803215i | ||||
\(268\) | 9.05393 | − | 15.6819i | 0.553057 | − | 0.957922i | ||||
\(269\) | 14.4628 | − | 25.0503i | 0.881813 | − | 1.52734i | 0.0324890 | − | 0.999472i | \(-0.489657\pi\) |
0.849324 | − | 0.527872i | \(-0.177010\pi\) | |||||||
\(270\) | 2.17533 | 0.132387 | ||||||||
\(271\) | 5.05875 | + | 8.76202i | 0.307297 | + | 0.532255i | 0.977770 | − | 0.209679i | \(-0.0672421\pi\) |
−0.670473 | + | 0.741934i | \(0.733909\pi\) | |||||||
\(272\) | 2.26513 | 0.137344 | ||||||||
\(273\) | 3.69373 | − | 8.79524i | 0.223555 | − | 0.532312i | ||||
\(274\) | 8.77541 | 0.530142 | ||||||||
\(275\) | 1.70823 | + | 2.95874i | 0.103010 | + | 0.178419i | ||||
\(276\) | −1.66620 | −0.100293 | ||||||||
\(277\) | −1.70320 | + | 2.95002i | −0.102335 | + | 0.177250i | −0.912646 | − | 0.408750i | \(-0.865965\pi\) |
0.810311 | + | 0.586000i | \(0.199298\pi\) | |||||||
\(278\) | 3.80504 | − | 6.59053i | 0.228211 | − | 0.395274i | ||||
\(279\) | −3.09878 | − | 5.36725i | −0.185519 | − | 0.321329i | ||||
\(280\) | −18.6030 | − | 4.07780i | −1.11174 | − | 0.243695i | ||||
\(281\) | 9.40331 | 0.560954 | 0.280477 | − | 0.959861i | \(-0.409507\pi\) | ||||
0.280477 | + | 0.959861i | \(0.409507\pi\) | |||||||
\(282\) | −1.03743 | −0.0617779 | ||||||||
\(283\) | 10.4790 | 0.622911 | 0.311456 | − | 0.950261i | \(-0.399183\pi\) | ||||
0.311456 | + | 0.950261i | \(0.399183\pi\) | |||||||
\(284\) | 4.68194 | 0.277822 | ||||||||
\(285\) | 6.63379 | − | 11.4901i | 0.392952 | − | 0.680612i | ||||
\(286\) | 1.00167 | − | 5.44846i | 0.0592299 | − | 0.322174i | ||||
\(287\) | 22.8067 | + | 4.99924i | 1.34623 | + | 0.295096i | ||||
\(288\) | 2.88844 | − | 5.00293i | 0.170203 | − | 0.294800i | ||||
\(289\) | −14.8332 | − | 25.6919i | −0.872542 | − | 1.51129i | ||||
\(290\) | −1.57602 | + | 2.72975i | −0.0925470 | + | 0.160296i | ||||
\(291\) | −6.08221 | − | 10.5347i | −0.356545 | − | 0.617554i | ||||
\(292\) | −8.55401 | −0.500586 | ||||||||
\(293\) | −4.61007 | − | 7.98488i | −0.269323 | − | 0.466481i | 0.699364 | − | 0.714766i | \(-0.253467\pi\) |
−0.968687 | + | 0.248284i | \(0.920133\pi\) | |||||||
\(294\) | 5.28522 | + | 2.43400i | 0.308240 | + | 0.141954i | ||||
\(295\) | 15.7489 | + | 27.2778i | 0.916934 | + | 1.58818i | ||||
\(296\) | −10.8353 | − | 18.7673i | −0.629790 | − | 1.09083i | ||||
\(297\) | 1.84837 | 0.107253 | ||||||||
\(298\) | −4.53337 | − | 7.85203i | −0.262611 | − | 0.454856i | ||||
\(299\) | −0.829819 | + | 4.51371i | −0.0479897 | + | 0.261034i | ||||
\(300\) | 2.41955 | 0.139693 | ||||||||
\(301\) | −0.390784 | + | 0.428507i | −0.0225244 | + | 0.0246987i | ||||
\(302\) | −9.28524 | + | 16.0825i | −0.534306 | + | 0.925445i | ||||
\(303\) | 4.59607 | 0.264037 | ||||||||
\(304\) | −0.840540 | − | 1.45586i | −0.0482083 | − | 0.0834992i | ||||
\(305\) | 11.4127 | − | 19.7674i | 0.653490 | − | 1.13188i | ||||
\(306\) | −5.67851 | −0.324619 | ||||||||
\(307\) | −16.1499 | −0.921726 | −0.460863 | − | 0.887471i | \(-0.652460\pi\) | ||||
−0.460863 | + | 0.887471i | \(0.652460\pi\) | |||||||
\(308\) | −6.25307 | − | 1.37068i | −0.356302 | − | 0.0781016i | ||||
\(309\) | 2.22609 | − | 3.85570i | 0.126638 | − | 0.219343i | ||||
\(310\) | 6.74088 | + | 11.6755i | 0.382856 | + | 0.663126i | ||||
\(311\) | 15.2138 | + | 26.3510i | 0.862694 | + | 1.49423i | 0.869319 | + | 0.494252i | \(0.164558\pi\) |
−0.00662478 | + | 0.999978i | \(0.502109\pi\) | |||||||
\(312\) | −7.55065 | − | 6.43001i | −0.427471 | − | 0.364028i | ||||
\(313\) | −13.6859 | + | 23.7047i | −0.773574 | + | 1.33987i | 0.162018 | + | 0.986788i | \(0.448200\pi\) |
−0.935592 | + | 0.353082i | \(0.885134\pi\) | |||||||
\(314\) | 0.273968 | − | 0.474527i | 0.0154609 | − | 0.0267791i | ||||
\(315\) | −6.76319 | − | 1.48250i | −0.381063 | − | 0.0835293i | ||||
\(316\) | −4.03288 | − | 6.98516i | −0.226867 | − | 0.392946i | ||||
\(317\) | −6.18424 | + | 10.7114i | −0.347342 | + | 0.601613i | −0.985776 | − | 0.168063i | \(-0.946249\pi\) |
0.638435 | + | 0.769676i | \(0.279582\pi\) | |||||||
\(318\) | 1.11344 | − | 1.92853i | 0.0624386 | − | 0.108147i | ||||
\(319\) | −1.33913 | + | 2.31945i | −0.0749771 | + | 0.129864i | ||||
\(320\) | −5.41559 | + | 9.38008i | −0.302741 | + | 0.524362i | ||||
\(321\) | 3.60694 | + | 6.24740i | 0.201320 | + | 0.348696i | ||||
\(322\) | −2.73445 | − | 0.599394i | −0.152385 | − | 0.0334029i | ||||
\(323\) | −17.3169 | + | 29.9938i | −0.963538 | + | 1.66890i | ||||
\(324\) | 0.654511 | − | 1.13365i | 0.0363617 | − | 0.0629803i | ||||
\(325\) | 1.20501 | − | 6.55453i | 0.0668421 | − | 0.363580i | ||||
\(326\) | 7.55818 | + | 13.0911i | 0.418609 | + | 0.725052i | ||||
\(327\) | −4.34979 | − | 7.53406i | −0.240544 | − | 0.416635i | ||||
\(328\) | 12.1368 | − | 21.0216i | 0.670144 | − | 1.16072i | ||||
\(329\) | 3.22540 | + | 0.707011i | 0.177822 | + | 0.0389788i | ||||
\(330\) | −4.02081 | −0.221338 | ||||||||
\(331\) | −12.4062 | −0.681907 | −0.340954 | − | 0.940080i | \(-0.610750\pi\) | ||||
−0.340954 | + | 0.940080i | \(0.610750\pi\) | |||||||
\(332\) | −5.67944 | + | 9.83708i | −0.311700 | + | 0.539880i | ||||
\(333\) | −3.93922 | − | 6.82292i | −0.215868 | − | 0.373894i | ||||
\(334\) | −3.67669 | −0.201179 | ||||||||
\(335\) | −18.1002 | + | 31.3505i | −0.988920 | + | 1.71286i | ||||
\(336\) | −0.591144 | + | 0.648208i | −0.0322495 | + | 0.0353627i | ||||
\(337\) | −15.8519 | −0.863506 | −0.431753 | − | 0.901992i | \(-0.642105\pi\) | ||||
−0.431753 | + | 0.901992i | \(0.642105\pi\) | |||||||
\(338\) | −8.37835 | + | 6.82485i | −0.455722 | + | 0.371223i | ||||
\(339\) | −1.82527 | − | 3.16146i | −0.0991351 | − | 0.171707i | ||||
\(340\) | −23.4014 | −1.26912 | ||||||||
\(341\) | 5.72768 | + | 9.92063i | 0.310171 | + | 0.537232i | ||||
\(342\) | 2.10717 | + | 3.64973i | 0.113943 | + | 0.197355i | ||||
\(343\) | −14.7732 | − | 11.1693i | −0.797676 | − | 0.603086i | ||||
\(344\) | 0.301464 | + | 0.522151i | 0.0162539 | + | 0.0281525i | ||||
\(345\) | 3.33099 | 0.179334 | ||||||||
\(346\) | 1.46318 | + | 2.53431i | 0.0786613 | + | 0.136245i | ||||
\(347\) | 6.46521 | − | 11.1981i | 0.347071 | − | 0.601144i | −0.638657 | − | 0.769492i | \(-0.720510\pi\) |
0.985728 | + | 0.168347i | \(0.0538430\pi\) | |||||||
\(348\) | 0.948381 | + | 1.64264i | 0.0508386 | + | 0.0880550i | ||||
\(349\) | −1.67254 | + | 2.89693i | −0.0895292 | + | 0.155069i | −0.907312 | − | 0.420458i | \(-0.861870\pi\) |
0.817783 | + | 0.575527i | \(0.195203\pi\) | |||||||
\(350\) | 3.97080 | + | 0.870404i | 0.212248 | + | 0.0465250i | ||||
\(351\) | −2.74506 | − | 2.33765i | −0.146521 | − | 0.124775i | ||||
\(352\) | −5.33890 | + | 9.24724i | −0.284564 | + | 0.492880i | ||||
\(353\) | 6.01463 | 0.320127 | 0.160063 | − | 0.987107i | \(-0.448830\pi\) | ||||
0.160063 | + | 0.987107i | \(0.448830\pi\) | |||||||
\(354\) | −10.0050 | −0.531760 | ||||||||
\(355\) | −9.35992 | −0.496773 | ||||||||
\(356\) | 19.8383 | 1.05143 | ||||||||
\(357\) | 17.6547 | + | 3.86993i | 0.934386 | + | 0.204818i | ||||
\(358\) | 4.49719 | + | 7.78936i | 0.237684 | + | 0.411680i | ||||
\(359\) | 7.44965 | − | 12.9032i | 0.393177 | − | 0.681003i | −0.599689 | − | 0.800233i | \(-0.704709\pi\) |
0.992867 | + | 0.119230i | \(0.0380425\pi\) | |||||||
\(360\) | −3.59911 | + | 6.23384i | −0.189690 | + | 0.328552i | ||||
\(361\) | 6.70372 | 0.352827 | ||||||||
\(362\) | −9.58643 | − | 16.6042i | −0.503852 | − | 0.872697i | ||||
\(363\) | 7.58354 | 0.398033 | ||||||||
\(364\) | 7.55311 | + | 9.94397i | 0.395890 | + | 0.521206i | ||||
\(365\) | 17.1008 | 0.895097 | ||||||||
\(366\) | 3.62516 | + | 6.27896i | 0.189490 | + | 0.328207i | ||||
\(367\) | −8.08153 | −0.421852 | −0.210926 | − | 0.977502i | \(-0.567648\pi\) | ||||
−0.210926 | + | 0.977502i | \(0.567648\pi\) | |||||||
\(368\) | 0.211028 | − | 0.365511i | 0.0110006 | − | 0.0190536i | ||||
\(369\) | 4.41239 | − | 7.64248i | 0.229700 | − | 0.397852i | ||||
\(370\) | 8.56911 | + | 14.8421i | 0.445487 | + | 0.771605i | ||||
\(371\) | −4.77603 | + | 5.23707i | −0.247959 | + | 0.271895i | ||||
\(372\) | 8.11274 | 0.420626 | ||||||||
\(373\) | −11.2771 | −0.583905 | −0.291953 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291953 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(374\) | 10.4960 | 0.542733 | ||||||||
\(375\) | 8.24763 | 0.425906 | ||||||||
\(376\) | 1.71643 | − | 2.97295i | 0.0885184 | − | 0.153318i | ||||
\(377\) | 4.92222 | − | 1.75106i | 0.253507 | − | 0.0901843i | ||||
\(378\) | 1.48195 | − | 1.62501i | 0.0762235 | − | 0.0835815i | ||||
\(379\) | −8.94558 | + | 15.4942i | −0.459504 | + | 0.795884i | −0.998935 | − | 0.0461461i | \(-0.985306\pi\) |
0.539431 | + | 0.842030i | \(0.318639\pi\) | |||||||
\(380\) | 8.68377 | + | 15.0407i | 0.445468 | + | 0.771573i | ||||
\(381\) | −4.80639 | + | 8.32491i | −0.246239 | + | 0.426498i | ||||
\(382\) | −0.760453 | − | 1.31714i | −0.0389081 | − | 0.0673909i | ||||
\(383\) | 0.0381094 | 0.00194730 | 0.000973650 | − | 1.00000i | \(-0.499690\pi\) | ||||
0.000973650 | 1.00000i | \(0.499690\pi\) | ||||||||
\(384\) | 4.05666 | + | 7.02634i | 0.207016 | + | 0.358562i | ||||
\(385\) | 12.5009 | + | 2.74020i | 0.637102 | + | 0.139653i | ||||
\(386\) | 1.31317 | + | 2.27448i | 0.0668388 | + | 0.115768i | ||||
\(387\) | 0.109598 | + | 0.189830i | 0.00557119 | + | 0.00964959i | ||||
\(388\) | 15.9235 | 0.808392 | ||||||||
\(389\) | 19.5855 | + | 33.9231i | 0.993025 | + | 1.71997i | 0.598622 | + | 0.801032i | \(0.295715\pi\) |
0.394403 | + | 0.918938i | \(0.370951\pi\) | |||||||
\(390\) | 5.97143 | + | 5.08517i | 0.302375 | + | 0.257498i | ||||
\(391\) | −8.69525 | −0.439737 | ||||||||
\(392\) | −15.7196 | + | 11.1188i | −0.793958 | + | 0.561582i | ||||
\(393\) | −8.28016 | + | 14.3417i | −0.417679 | + | 0.723441i | ||||
\(394\) | 9.27006 | 0.467019 | ||||||||
\(395\) | 8.06236 | + | 13.9644i | 0.405661 | + | 0.702626i | ||||
\(396\) | −1.20978 | + | 2.09539i | −0.0607935 | + | 0.105297i | ||||
\(397\) | 8.73141 | 0.438217 | 0.219108 | − | 0.975701i | \(-0.429685\pi\) | ||||
0.219108 | + | 0.975701i | \(0.429685\pi\) | |||||||
\(398\) | −17.2482 | −0.864573 | ||||||||
\(399\) | −4.06397 | − | 12.7832i | −0.203453 | − | 0.639960i | ||||
\(400\) | −0.306442 | + | 0.530773i | −0.0153221 | + | 0.0265387i | ||||
\(401\) | −12.1419 | − | 21.0303i | −0.606336 | − | 1.05021i | −0.991839 | − | 0.127498i | \(-0.959305\pi\) |
0.385503 | − | 0.922707i | \(-0.374028\pi\) | |||||||
\(402\) | −5.74940 | − | 9.95825i | −0.286754 | − | 0.496672i | ||||
\(403\) | 4.04040 | − | 21.9773i | 0.201267 | − | 1.09477i | ||||
\(404\) | −3.00818 | + | 5.21031i | −0.149662 | + | 0.259223i | ||||
\(405\) | −1.30847 | + | 2.26634i | −0.0650184 | + | 0.112615i | ||||
\(406\) | 0.965497 | + | 3.03696i | 0.0479168 | + | 0.150722i | ||||
\(407\) | 7.28111 | + | 12.6113i | 0.360911 | + | 0.625117i | ||||
\(408\) | 9.39516 | − | 16.2729i | 0.465130 | − | 0.805628i | ||||
\(409\) | 9.86131 | − | 17.0803i | 0.487610 | − | 0.844566i | −0.512288 | − | 0.858814i | \(-0.671202\pi\) |
0.999898 | + | 0.0142477i | \(0.00453532\pi\) | |||||||
\(410\) | −9.59841 | + | 16.6249i | −0.474032 | + | 0.821047i | ||||
\(411\) | −5.27844 | + | 9.14252i | −0.260366 | + | 0.450967i | ||||
\(412\) | 2.91400 | + | 5.04720i | 0.143563 | + | 0.248658i | ||||
\(413\) | 31.1060 | + | 6.81846i | 1.53062 | + | 0.335514i | ||||
\(414\) | −0.529032 | + | 0.916310i | −0.0260005 | + | 0.0450342i | ||||
\(415\) | 11.3541 | − | 19.6659i | 0.557350 | − | 0.965359i | ||||
\(416\) | 19.6241 | − | 6.98119i | 0.962149 | − | 0.342281i | ||||
\(417\) | 4.57749 | + | 7.92845i | 0.224161 | + | 0.388258i | ||||
\(418\) | −3.89483 | − | 6.74604i | −0.190502 | − | 0.329959i | ||||
\(419\) | 11.0976 | − | 19.2216i | 0.542154 | − | 0.939039i | −0.456626 | − | 0.889659i | \(-0.650942\pi\) |
0.998780 | − | 0.0493798i | \(-0.0157245\pi\) | |||||||
\(420\) | 6.10721 | − | 6.69676i | 0.298001 | − | 0.326768i | ||||
\(421\) | −1.85475 | −0.0903949 | −0.0451974 | − | 0.998978i | \(-0.514392\pi\) | ||||
−0.0451974 | + | 0.998978i | \(0.514392\pi\) | |||||||
\(422\) | 13.5789 | 0.661009 | ||||||||
\(423\) | 0.624016 | − | 1.08083i | 0.0303407 | − | 0.0525516i | ||||
\(424\) | 3.68440 | + | 6.38156i | 0.178930 | + | 0.309916i | ||||
\(425\) | 12.6267 | 0.612485 | ||||||||
\(426\) | 1.48655 | − | 2.57479i | 0.0720238 | − | 0.124749i | ||||
\(427\) | −6.99163 | − | 21.9921i | −0.338349 | − | 1.06427i | ||||
\(428\) | −9.44312 | −0.456450 | ||||||||
\(429\) | 5.07388 | + | 4.32084i | 0.244969 | + | 0.208612i | ||||
\(430\) | −0.238413 | − | 0.412943i | −0.0114973 | − | 0.0199139i | ||||
\(431\) | −37.7871 | −1.82014 | −0.910069 | − | 0.414456i | \(-0.863972\pi\) | ||||
−0.910069 | + | 0.414456i | \(0.863972\pi\) | |||||||
\(432\) | 0.165791 | + | 0.287158i | 0.00797662 | + | 0.0138159i | ||||
\(433\) | 17.5680 | + | 30.4286i | 0.844263 | + | 1.46231i | 0.886259 | + | 0.463189i | \(0.153295\pi\) |
−0.0419959 | + | 0.999118i | \(0.513372\pi\) | |||||||
\(434\) | 13.3141 | + | 2.91846i | 0.639096 | + | 0.140091i | ||||
\(435\) | −1.89596 | − | 3.28390i | −0.0909044 | − | 0.157451i | ||||
\(436\) | 11.3879 | 0.545384 | ||||||||
\(437\) | 3.22662 | + | 5.58867i | 0.154350 | + | 0.267342i | ||||
\(438\) | −2.71597 | + | 4.70420i | −0.129774 | + | 0.224775i | ||||
\(439\) | −7.67375 | − | 13.2913i | −0.366248 | − | 0.634360i | 0.622727 | − | 0.782439i | \(-0.286025\pi\) |
−0.988976 | + | 0.148078i | \(0.952691\pi\) | |||||||
\(440\) | 6.65247 | − | 11.5224i | 0.317144 | − | 0.549310i | ||||
\(441\) | −5.71490 | + | 4.04226i | −0.272138 | + | 0.192489i | ||||
\(442\) | −15.5879 | − | 13.2744i | −0.741440 | − | 0.631398i | ||||
\(443\) | −14.5356 | + | 25.1765i | −0.690609 | + | 1.19617i | 0.281030 | + | 0.959699i | \(0.409324\pi\) |
−0.971639 | + | 0.236471i | \(0.924009\pi\) | |||||||
\(444\) | 10.3130 | 0.489435 | ||||||||
\(445\) | −39.6598 | −1.88005 | ||||||||
\(446\) | 15.4757 | 0.732795 | ||||||||
\(447\) | 10.9073 | 0.515900 | ||||||||
\(448\) | 3.31769 | + | 10.4358i | 0.156746 | + | 0.493043i | ||||
\(449\) | −1.18131 | − | 2.04609i | −0.0557494 | − | 0.0965607i | 0.836804 | − | 0.547503i | \(-0.184421\pi\) |
−0.892553 | + | 0.450942i | \(0.851088\pi\) | |||||||
\(450\) | 0.768228 | − | 1.33061i | 0.0362146 | − | 0.0627255i | ||||
\(451\) | −8.15570 | + | 14.1261i | −0.384037 | + | 0.665172i | ||||
\(452\) | 4.77864 | 0.224768 | ||||||||
\(453\) | −11.1702 | − | 19.3474i | −0.524822 | − | 0.909018i | ||||
\(454\) | 18.7409 | 0.879555 | ||||||||
\(455\) | −15.0998 | − | 19.8795i | −0.707891 | − | 0.931967i | ||||
\(456\) | −13.9454 | −0.653051 | ||||||||
\(457\) | 8.37672 | + | 14.5089i | 0.391846 | + | 0.678698i | 0.992693 | − | 0.120667i | \(-0.0385032\pi\) |
−0.600847 | + | 0.799364i | \(0.705170\pi\) | |||||||
\(458\) | 16.0051 | 0.747871 | ||||||||
\(459\) | 3.41564 | − | 5.91607i | 0.159429 | − | 0.276138i | ||||
\(460\) | −2.18017 | + | 3.77616i | −0.101651 | + | 0.176064i | ||||
\(461\) | 12.5469 | + | 21.7318i | 0.584366 | + | 1.01215i | 0.994954 | + | 0.100330i | \(0.0319900\pi\) |
−0.410588 | + | 0.911821i | \(0.634677\pi\) | |||||||
\(462\) | −2.73919 | + | 3.00361i | −0.127439 | + | 0.139741i | ||||
\(463\) | −0.254256 | −0.0118163 | −0.00590815 | − | 0.999983i | \(-0.501881\pi\) | ||||
−0.00590815 | + | 0.999983i | \(0.501881\pi\) | |||||||
\(464\) | −0.480459 | −0.0223048 | ||||||||
\(465\) | −16.2186 | −0.752121 | ||||||||
\(466\) | −18.9985 | −0.880088 | ||||||||
\(467\) | −5.11155 | + | 8.85346i | −0.236534 | + | 0.409689i | −0.959717 | − | 0.280967i | \(-0.909345\pi\) |
0.723183 | + | 0.690656i | \(0.242678\pi\) | |||||||
\(468\) | 4.44675 | − | 1.58191i | 0.205551 | − | 0.0731240i | ||||
\(469\) | 11.0885 | + | 34.8788i | 0.512020 | + | 1.61055i | ||||
\(470\) | −1.35744 | + | 2.35116i | −0.0626141 | + | 0.108451i | ||||
\(471\) | 0.329586 | + | 0.570859i | 0.0151865 | + | 0.0263038i | ||||
\(472\) | 16.5534 | − | 28.6713i | 0.761932 | − | 1.31970i | ||||
\(473\) | −0.202578 | − | 0.350875i | −0.00931453 | − | 0.0161332i | ||||
\(474\) | −5.12190 | −0.235256 | ||||||||
\(475\) | −4.68550 | − | 8.11552i | −0.214985 | − | 0.372366i | ||||
\(476\) | −15.9423 | + | 17.4813i | −0.730715 | + | 0.801253i | ||||
\(477\) | 1.33947 | + | 2.32004i | 0.0613303 | + | 0.106227i | ||||
\(478\) | −4.67581 | − | 8.09874i | −0.213866 | − | 0.370428i | ||||
\(479\) | −12.7080 | −0.580643 | −0.290322 | − | 0.956929i | \(-0.593762\pi\) | ||||
−0.290322 | + | 0.956929i | \(0.593762\pi\) | |||||||
\(480\) | −7.55887 | − | 13.0924i | −0.345014 | − | 0.597581i | ||||
\(481\) | 5.13622 | − | 27.9379i | 0.234191 | − | 1.27386i | ||||
\(482\) | −16.1646 | −0.736277 | ||||||||
\(483\) | 2.26925 | − | 2.48830i | 0.103254 | − | 0.113222i | ||||
\(484\) | −4.96351 | + | 8.59706i | −0.225614 | + | 0.390775i | ||||
\(485\) | −31.8335 | −1.44549 | ||||||||
\(486\) | −0.415625 | − | 0.719884i | −0.0188532 | − | 0.0326546i | ||||
\(487\) | −10.2410 | + | 17.7379i | −0.464063 | + | 0.803781i | −0.999159 | − | 0.0410108i | \(-0.986942\pi\) |
0.535096 | + | 0.844791i | \(0.320276\pi\) | |||||||
\(488\) | −23.9915 | −1.08604 | ||||||||
\(489\) | −18.1851 | −0.822357 | ||||||||
\(490\) | 12.4318 | − | 8.79327i | 0.561612 | − | 0.397239i | ||||
\(491\) | −9.92098 | + | 17.1836i | −0.447727 | + | 0.775487i | −0.998238 | − | 0.0593417i | \(-0.981100\pi\) |
0.550510 | + | 0.834828i | \(0.314433\pi\) | |||||||
\(492\) | 5.77591 | + | 10.0042i | 0.260398 | + | 0.451023i | ||||
\(493\) | 4.94924 | + | 8.57233i | 0.222902 | + | 0.386078i | ||||
\(494\) | −2.74748 | + | 14.9446i | −0.123615 | + | 0.672389i | ||||
\(495\) | 2.41853 | − | 4.18902i | 0.108705 | − | 0.188282i | ||||
\(496\) | −1.02750 | + | 1.77968i | −0.0461361 | + | 0.0799100i | ||||
\(497\) | −6.37648 | + | 6.99202i | −0.286024 | + | 0.313635i | ||||
\(498\) | 3.60654 | + | 6.24671i | 0.161613 | + | 0.279922i | ||||
\(499\) | −13.9419 | + | 24.1480i | −0.624124 | + | 1.08101i | 0.364585 | + | 0.931170i | \(0.381211\pi\) |
−0.988710 | + | 0.149845i | \(0.952123\pi\) | |||||||
\(500\) | −5.39817 | + | 9.34990i | −0.241413 | + | 0.418140i | ||||
\(501\) | 2.21154 | − | 3.83050i | 0.0988043 | − | 0.171134i | ||||
\(502\) | 7.30913 | − | 12.6598i | 0.326223 | − | 0.565034i | ||||
\(503\) | 6.62277 | + | 11.4710i | 0.295295 | + | 0.511465i | 0.975053 | − | 0.221970i | \(-0.0712489\pi\) |
−0.679759 | + | 0.733436i | \(0.737916\pi\) | |||||||
\(504\) | 2.20488 | + | 6.93543i | 0.0982131 | + | 0.308929i | ||||
\(505\) | 6.01381 | − | 10.4162i | 0.267611 | − | 0.463516i | ||||
\(506\) | 0.977844 | − | 1.69368i | 0.0434705 | − | 0.0752931i | ||||
\(507\) | −2.07076 | − | 12.8340i | −0.0919657 | − | 0.569979i | ||||
\(508\) | −6.29167 | − | 10.8975i | −0.279148 | − | 0.483498i | ||||
\(509\) | −13.5375 | − | 23.4477i | −0.600040 | − | 1.03930i | −0.992814 | − | 0.119665i | \(-0.961818\pi\) |
0.392775 | − | 0.919635i | \(-0.371515\pi\) | |||||||
\(510\) | −7.43016 | + | 12.8694i | −0.329013 | + | 0.569867i | ||||
\(511\) | 11.6500 | − | 12.7746i | 0.515365 | − | 0.565115i | ||||
\(512\) | −3.73962 | −0.165270 | ||||||||
\(513\) | −5.06988 | −0.223841 | ||||||||
\(514\) | 6.31220 | − | 10.9331i | 0.278419 | − | 0.482236i | ||||
\(515\) | −5.82554 | − | 10.0901i | −0.256704 | − | 0.444625i | ||||
\(516\) | −0.286933 | −0.0126315 | ||||||||
\(517\) | −1.15341 | + | 1.99776i | −0.0507269 | + | 0.0878615i | ||||
\(518\) | 16.9251 | + | 3.70999i | 0.743645 | + | 0.163008i | ||||
\(519\) | −3.52044 | −0.154530 | ||||||||
\(520\) | −24.4524 | + | 8.69883i | −1.07231 | + | 0.381469i | ||||
\(521\) | −11.6257 | − | 20.1363i | −0.509331 | − | 0.882187i | −0.999942 | − | 0.0108082i | \(-0.996560\pi\) |
0.490611 | − | 0.871379i | \(-0.336774\pi\) | |||||||
\(522\) | 1.20448 | 0.0527185 | ||||||||
\(523\) | −16.7690 | − | 29.0447i | −0.733256 | − | 1.27004i | −0.955484 | − | 0.295043i | \(-0.904666\pi\) |
0.222228 | − | 0.974995i | \(-0.428667\pi\) | |||||||
\(524\) | −10.8389 | − | 18.7735i | −0.473500 | − | 0.820126i | ||||
\(525\) | −3.29527 | + | 3.61337i | −0.143817 | + | 0.157700i | ||||
\(526\) | −5.80626 | − | 10.0567i | −0.253165 | − | 0.438494i | ||||
\(527\) | 42.3373 | 1.84424 | ||||||||
\(528\) | −0.306442 | − | 0.530773i | −0.0133362 | − | 0.0230990i | ||||
\(529\) | 10.6899 | − | 18.5155i | 0.464779 | − | 0.805021i | ||||
\(530\) | −2.91380 | − | 5.04685i | −0.126568 | − | 0.219221i | ||||
\(531\) | 6.01804 | − | 10.4236i | 0.261161 | − | 0.452344i | ||||
\(532\) | 17.1515 | + | 3.75963i | 0.743614 | + | 0.163001i | ||||
\(533\) | 29.9777 | − | 10.6645i | 1.29848 | − | 0.461929i | ||||
\(534\) | 6.29881 | − | 10.9099i | 0.272576 | − | 0.472116i | ||||
\(535\) | 18.8783 | 0.816178 | ||||||||
\(536\) | 38.0498 | 1.64350 | ||||||||
\(537\) | −10.8203 | −0.466930 | ||||||||
\(538\) | 24.0444 | 1.03663 | ||||||||
\(539\) | 10.5632 | − | 7.47158i | 0.454991 | − | 0.321824i | ||||
\(540\) | −1.71281 | − | 2.96668i | −0.0737078 | − | 0.127666i | ||||
\(541\) | −4.65598 | + | 8.06439i | −0.200176 | + | 0.346715i | −0.948585 | − | 0.316522i | \(-0.897485\pi\) |
0.748409 | + | 0.663238i | \(0.230818\pi\) | |||||||
\(542\) | −4.20509 | + | 7.28343i | −0.180624 | + | 0.312850i | ||||
\(543\) | 23.0651 | 0.989817 | ||||||||
\(544\) | 19.7318 | + | 34.1764i | 0.845992 | + | 1.46530i | ||||
\(545\) | −22.7663 | −0.975200 | ||||||||
\(546\) | 7.86677 | − | 0.996466i | 0.336667 | − | 0.0426448i | ||||
\(547\) | −31.5111 | −1.34732 | −0.673658 | − | 0.739043i | \(-0.735278\pi\) | ||||
−0.673658 | + | 0.739043i | \(0.735278\pi\) | |||||||
\(548\) | −6.90959 | − | 11.9678i | −0.295163 | − | 0.511237i | ||||
\(549\) | −8.72218 | −0.372254 | ||||||||
\(550\) | −1.41997 | + | 2.45945i | −0.0605476 | + | 0.104871i | ||||
\(551\) | 3.67311 | − | 6.36201i | 0.156480 | − | 0.271031i | ||||
\(552\) | −1.75058 | − | 3.03209i | −0.0745095 | − | 0.129054i | ||||
\(553\) | 15.9242 | + | 3.49059i | 0.677165 | + | 0.148435i | ||||
\(554\) | −2.83157 | −0.120302 | ||||||||
\(555\) | −20.6174 | −0.875159 | ||||||||
\(556\) | −11.9841 | −0.508238 | ||||||||
\(557\) | 5.53300 | 0.234441 | 0.117220 | − | 0.993106i | \(-0.462602\pi\) | ||||
0.117220 | + | 0.993106i | \(0.462602\pi\) | |||||||
\(558\) | 2.57586 | − | 4.46153i | 0.109045 | − | 0.188872i | ||||
\(559\) | −0.142902 | + | 0.777298i | −0.00604410 | + | 0.0328762i | ||||
\(560\) | 0.695564 | + | 2.18789i | 0.0293929 | + | 0.0924553i | ||||
\(561\) | −6.31336 | + | 10.9351i | −0.266550 | + | 0.461678i | ||||
\(562\) | 3.90826 | + | 6.76930i | 0.164860 | + | 0.285546i | ||||
\(563\) | −6.18438 | + | 10.7117i | −0.260641 | + | 0.451443i | −0.966412 | − | 0.256997i | \(-0.917267\pi\) |
0.705772 | + | 0.708439i | \(0.250600\pi\) | |||||||
\(564\) | 0.816850 | + | 1.41483i | 0.0343956 | + | 0.0595749i | ||||
\(565\) | −9.55324 | −0.401908 | ||||||||
\(566\) | 4.35534 | + | 7.54366i | 0.183068 | + | 0.317084i | ||||
\(567\) | 0.801591 | + | 2.52140i | 0.0336637 | + | 0.105889i | ||||
\(568\) | 4.91904 | + | 8.52003i | 0.206398 | + | 0.357493i | ||||
\(569\) | −0.997229 | − | 1.72725i | −0.0418060 | − | 0.0724101i | 0.844365 | − | 0.535768i | \(-0.179978\pi\) |
−0.886171 | + | 0.463358i | \(0.846644\pi\) | |||||||
\(570\) | 11.0287 | 0.461941 | ||||||||
\(571\) | −11.0440 | − | 19.1288i | −0.462179 | − | 0.800517i | 0.536891 | − | 0.843652i | \(-0.319599\pi\) |
−0.999069 | + | 0.0431350i | \(0.986265\pi\) | |||||||
\(572\) | −8.21921 | + | 2.92395i | −0.343663 | + | 0.122257i | ||||
\(573\) | 1.82966 | 0.0764351 | ||||||||
\(574\) | 5.88015 | + | 18.4960i | 0.245433 | + | 0.772007i | ||||
\(575\) | 1.17635 | − | 2.03750i | 0.0490573 | − | 0.0849697i | ||||
\(576\) | 4.13888 | 0.172453 | ||||||||
\(577\) | −4.54321 | − | 7.86907i | −0.189136 | − | 0.327594i | 0.755826 | − | 0.654772i | \(-0.227235\pi\) |
−0.944963 | + | 0.327179i | \(0.893902\pi\) | |||||||
\(578\) | 12.3301 | − | 21.3564i | 0.512866 | − | 0.888310i | ||||
\(579\) | −3.15951 | −0.131305 | ||||||||
\(580\) | 4.96371 | 0.206107 | ||||||||
\(581\) | −6.95572 | − | 21.8791i | −0.288572 | − | 0.907700i | ||||
\(582\) | 5.05584 | − | 8.75697i | 0.209571 | − | 0.362988i | ||||
\(583\) | −2.47584 | − | 4.28828i | −0.102539 | − | 0.177602i | ||||
\(584\) | −8.98721 | − | 15.5663i | −0.371893 | − | 0.644138i | ||||
\(585\) | −8.88974 | + | 3.16249i | −0.367545 | + | 0.130753i | ||||
\(586\) | 3.83213 | − | 6.63744i | 0.158304 | − | 0.274190i | ||||
\(587\) | −3.02112 | + | 5.23273i | −0.124695 | + | 0.215978i | −0.921614 | − | 0.388109i | \(-0.873128\pi\) |
0.796919 | + | 0.604086i | \(0.206462\pi\) | |||||||
\(588\) | −0.842029 | − | 9.12438i | −0.0347247 | − | 0.376283i | ||||
\(589\) | −15.7105 | − | 27.2113i | −0.647338 | − | 1.12122i | ||||
\(590\) | −13.0912 | + | 22.6747i | −0.538958 | + | 0.933503i | ||||
\(591\) | −5.57597 | + | 9.65786i | −0.229365 | + | 0.397271i | ||||
\(592\) | −1.30617 | + | 2.26236i | −0.0536834 | + | 0.0929823i | ||||
\(593\) | −6.67095 | + | 11.5544i | −0.273943 | + | 0.474484i | −0.969868 | − | 0.243631i | \(-0.921661\pi\) |
0.695925 | + | 0.718115i | \(0.254995\pi\) | |||||||
\(594\) | 0.768228 | + | 1.33061i | 0.0315208 | + | 0.0545956i | ||||
\(595\) | 31.8712 | − | 34.9478i | 1.30659 | − | 1.43272i | ||||
\(596\) | −7.13898 | + | 12.3651i | −0.292424 | + | 0.506493i | ||||
\(597\) | 10.3748 | − | 17.9697i | 0.424614 | − | 0.735452i | ||||
\(598\) | −3.59424 | + | 1.27864i | −0.146979 | + | 0.0522874i | ||||
\(599\) | −15.0725 | − | 26.1063i | −0.615844 | − | 1.06667i | −0.990236 | − | 0.139402i | \(-0.955482\pi\) |
0.374392 | − | 0.927270i | \(-0.377851\pi\) | |||||||
\(600\) | 2.54208 | + | 4.40302i | 0.103780 | + | 0.179752i | ||||
\(601\) | −18.9159 | + | 32.7634i | −0.771598 | + | 1.33645i | 0.165089 | + | 0.986279i | \(0.447209\pi\) |
−0.936687 | + | 0.350168i | \(0.886125\pi\) | |||||||
\(602\) | −0.470895 | − | 0.103221i | −0.0191922 | − | 0.00420696i | ||||
\(603\) | 13.8331 | 0.563328 | ||||||||
\(604\) | 29.2441 | 1.18992 | ||||||||
\(605\) | 9.92283 | − | 17.1869i | 0.403421 | − | 0.698745i | ||||
\(606\) | 1.91024 | + | 3.30864i | 0.0775983 | + | 0.134404i | ||||
\(607\) | 6.70899 | 0.272309 | 0.136155 | − | 0.990688i | \(-0.456526\pi\) | ||||
0.136155 | + | 0.990688i | \(0.456526\pi\) | |||||||
\(608\) | 14.6441 | − | 25.3643i | 0.593895 | − | 1.02866i | ||||
\(609\) | −3.74476 | − | 0.820855i | −0.151745 | − | 0.0332627i | ||||
\(610\) | 18.9737 | 0.768221 | ||||||||
\(611\) | 4.23956 | − | 1.50821i | 0.171514 | − | 0.0610156i | ||||
\(612\) | 4.47115 | + | 7.74426i | 0.180736 | + | 0.313043i | ||||
\(613\) | −20.1672 | −0.814544 | −0.407272 | − | 0.913307i | \(-0.633520\pi\) | ||||
−0.407272 | + | 0.913307i | \(0.633520\pi\) | |||||||
\(614\) | −6.71233 | − | 11.6261i | −0.270888 | − | 0.469191i | ||||
\(615\) | −11.5469 | − | 19.9999i | −0.465618 | − | 0.806474i | ||||
\(616\) | −4.07542 | − | 12.8192i | −0.164203 | − | 0.516501i | ||||
\(617\) | −2.98249 | − | 5.16582i | −0.120071 | − | 0.207968i | 0.799725 | − | 0.600367i | \(-0.204979\pi\) |
−0.919795 | + | 0.392399i | \(0.871645\pi\) | |||||||
\(618\) | 3.70088 | 0.148871 | ||||||||
\(619\) | 4.31420 | + | 7.47242i | 0.173402 | + | 0.300342i | 0.939607 | − | 0.342255i | \(-0.111191\pi\) |
−0.766205 | + | 0.642596i | \(0.777857\pi\) | |||||||
\(620\) | 10.6153 | − | 18.3862i | 0.426320 | − | 0.738407i | ||||
\(621\) | −0.636428 | − | 1.10233i | −0.0255390 | − | 0.0442348i | ||||
\(622\) | −12.6465 | + | 21.9043i | −0.507077 | + | 0.878283i | ||||
\(623\) | −27.0184 | + | 29.6265i | −1.08247 | + | 1.18696i | ||||
\(624\) | −0.216169 | + | 1.17583i | −0.00865370 | + | 0.0470708i | ||||
\(625\) | 15.4127 | − | 26.6956i | 0.616507 | − | 1.06782i | ||||
\(626\) | −22.7529 | −0.909388 | ||||||||
\(627\) | 9.37100 | 0.374242 | ||||||||
\(628\) | −0.862869 | −0.0344322 | ||||||||
\(629\) | 53.8198 | 2.14594 | ||||||||
\(630\) | −1.74373 | − | 5.48488i | −0.0694718 | − | 0.218523i | ||||
\(631\) | −1.02888 | − | 1.78208i | −0.0409592 | − | 0.0709434i | 0.844819 | − | 0.535052i | \(-0.179708\pi\) |
−0.885778 | + | 0.464109i | \(0.846375\pi\) | |||||||
\(632\) | 8.47423 | − | 14.6778i | 0.337087 | − | 0.583852i | ||||
\(633\) | −8.16773 | + | 14.1469i | −0.324638 | + | 0.562289i | ||||
\(634\) | −10.2813 | −0.408323 | ||||||||
\(635\) | 12.5780 | + | 21.7858i | 0.499144 | + | 0.864542i | ||||
\(636\) | −3.50680 | −0.139054 | ||||||||
\(637\) | −25.1372 | − | 2.26318i | −0.995971 | − | 0.0896706i | ||||
\(638\) | −2.22631 | −0.0881405 | ||||||||
\(639\) | 1.78833 | + | 3.09749i | 0.0707454 | + | 0.122535i | ||||
\(640\) | 21.2321 | 0.839271 | ||||||||
\(641\) | 8.83114 | − | 15.2960i | 0.348809 | − | 0.604155i | −0.637229 | − | 0.770674i | \(-0.719920\pi\) |
0.986038 | + | 0.166519i | \(0.0532529\pi\) | |||||||
\(642\) | −2.99827 | + | 5.19316i | −0.118332 | + | 0.204957i | ||||
\(643\) | −24.6023 | − | 42.6124i | −0.970219 | − | 1.68047i | −0.694885 | − | 0.719121i | \(-0.744545\pi\) |
−0.275334 | − | 0.961349i | \(-0.588788\pi\) | |||||||
\(644\) | 1.33561 | + | 4.20115i | 0.0526304 | + | 0.165548i | ||||
\(645\) | 0.573624 | 0.0225864 | ||||||||
\(646\) | −28.7894 | −1.13270 | ||||||||
\(647\) | −15.4959 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(648\) | 2.75063 | 0.108055 | ||||||||
\(649\) | −11.1235 | + | 19.2666i | −0.436637 | + | 0.756278i | ||||
\(650\) | 5.21934 | − | 1.85676i | 0.204719 | − | 0.0728281i | ||||
\(651\) | −11.0490 | + | 12.1156i | −0.433045 | + | 0.474848i | ||||
\(652\) | 11.9023 | − | 20.6154i | 0.466131 | − | 0.807363i | ||||
\(653\) | 18.3665 | + | 31.8117i | 0.718738 | + | 1.24489i | 0.961500 | + | 0.274804i | \(0.0886130\pi\) |
−0.242763 | + | 0.970086i | \(0.578054\pi\) | |||||||
\(654\) | 3.61577 | − | 6.26270i | 0.141388 | − | 0.244891i | ||||
\(655\) | 21.6687 | + | 37.5312i | 0.846665 | + | 1.46647i | ||||
\(656\) | −2.92613 | −0.114246 | ||||||||
\(657\) | −3.26733 | − | 5.65918i | −0.127471 | − | 0.220786i | ||||
\(658\) | 0.831593 | + | 2.61577i | 0.0324189 | + | 0.101973i | ||||
\(659\) | −5.48070 | − | 9.49284i | −0.213498 | − | 0.369789i | 0.739309 | − | 0.673366i | \(-0.235152\pi\) |
−0.952807 | + | 0.303577i | \(0.901819\pi\) | |||||||
\(660\) | 3.16591 | + | 5.48351i | 0.123233 | + | 0.213445i | ||||
\(661\) | 16.0710 | 0.625091 | 0.312545 | − | 0.949903i | \(-0.398818\pi\) | ||||
0.312545 | + | 0.949903i | \(0.398818\pi\) | |||||||
\(662\) | −5.15634 | − | 8.93104i | −0.200407 | − | 0.347115i | ||||
\(663\) | 23.2059 | − | 8.25540i | 0.901241 | − | 0.320613i | ||||
\(664\) | −23.8682 | −0.926268 | ||||||||
\(665\) | −34.2886 | − | 7.51609i | −1.32965 | − | 0.291462i | ||||
\(666\) | 3.27448 | − | 5.67156i | 0.126883 | − | 0.219769i | ||||
\(667\) | 1.84436 | 0.0714139 | ||||||||
\(668\) | 2.89495 | + | 5.01421i | 0.112009 | + | 0.194005i | ||||
\(669\) | −9.30867 | + | 16.1231i | −0.359894 | + | 0.623355i | ||||
\(670\) | −30.0916 | −1.16254 | ||||||||
\(671\) | 16.1218 | 0.622375 | ||||||||
\(672\) | −14.9297 | − | 3.27261i | −0.575927 | − | 0.126244i | ||||
\(673\) | 14.1074 | − | 24.4348i | 0.543802 | − | 0.941892i | −0.454880 | − | 0.890553i | \(-0.650318\pi\) |
0.998681 | − | 0.0513390i | \(-0.0163489\pi\) | |||||||
\(674\) | −6.58844 | − | 11.4115i | −0.253777 | − | 0.439555i | ||||
\(675\) | 0.924183 | + | 1.60073i | 0.0355718 | + | 0.0616122i | ||||
\(676\) | 15.9046 | + | 6.05249i | 0.611714 | + | 0.232788i | ||||
\(677\) | 17.5358 | − | 30.3729i | 0.673956 | − | 1.16733i | −0.302817 | − | 0.953049i | \(-0.597927\pi\) |
0.976773 | − | 0.214277i | \(-0.0687395\pi\) | |||||||
\(678\) | 1.51726 | − | 2.62797i | 0.0582699 | − | 0.100926i | ||||
\(679\) | −21.6867 | + | 23.7802i | −0.832259 | + | 0.912600i | ||||
\(680\) | −24.5866 | − | 42.5852i | −0.942851 | − | 1.63307i | ||||
\(681\) | −11.2727 | + | 19.5249i | −0.431972 | + | 0.748197i | ||||
\(682\) | −4.76114 | + | 8.24654i | −0.182313 | + | 0.315776i | ||||
\(683\) | −24.1916 | + | 41.9011i | −0.925666 | + | 1.60330i | −0.135181 | + | 0.990821i | \(0.543161\pi\) |
−0.790486 | + | 0.612480i | \(0.790172\pi\) | |||||||
\(684\) | 3.31829 | − | 5.74745i | 0.126878 | − | 0.219759i | ||||
\(685\) | 13.8133 | + | 23.9254i | 0.527781 | + | 0.914143i | ||||
\(686\) | 1.90050 | − | 15.2772i | 0.0725615 | − | 0.583287i | ||||
\(687\) | −9.62713 | + | 16.6747i | −0.367298 | + | 0.636179i | ||||
\(688\) | 0.0363408 | − | 0.0629441i | 0.00138548 | − | 0.00239972i | ||||
\(689\) | −1.74650 | + | 9.49988i | −0.0665363 | + | 0.361917i | ||||
\(690\) | 1.38444 | + | 2.39793i | 0.0527049 | + | 0.0912875i | ||||
\(691\) | 12.0530 | + | 20.8764i | 0.458518 | + | 0.794176i | 0.998883 | − | 0.0472547i | \(-0.0150473\pi\) |
−0.540365 | + | 0.841431i | \(0.681714\pi\) | |||||||
\(692\) | 2.30417 | − | 3.99093i | 0.0875913 | − | 0.151713i | ||||
\(693\) | −1.48163 | − | 4.66047i | −0.0562826 | − | 0.177037i | ||||
\(694\) | 10.7484 | 0.408005 | ||||||||
\(695\) | 23.9580 | 0.908779 | ||||||||
\(696\) | −1.99282 | + | 3.45166i | −0.0755376 | + | 0.130835i | ||||
\(697\) | 30.1423 | + | 52.2079i | 1.14172 | + | 1.97752i | ||||
\(698\) | −2.78061 | −0.105248 | ||||||||
\(699\) | 11.4276 | − | 19.7933i | 0.432233 | − | 0.748650i | ||||
\(700\) | −1.93949 | − | 6.10065i | −0.0733059 | − | 0.230583i | ||||
\(701\) | −3.07792 | −0.116251 | −0.0581257 | − | 0.998309i | \(-0.518512\pi\) | ||||
−0.0581257 | + | 0.998309i | \(0.518512\pi\) | |||||||
\(702\) | 0.541921 | − | 2.94772i | 0.0204535 | − | 0.111254i | ||||
\(703\) | −19.9714 | − | 34.5914i | −0.753235 | − | 1.30464i | ||||
\(704\) | −7.65016 | −0.288326 | ||||||||
\(705\) | −1.63301 | − | 2.82846i | −0.0615027 | − | 0.106526i | ||||
\(706\) | 2.49983 | + | 4.32984i | 0.0940825 | + | 0.162956i | ||||
\(707\) | −3.68417 | − | 11.5885i | −0.138557 | − | 0.435831i | ||||
\(708\) | 7.87775 | + | 13.6447i | 0.296064 | + | 0.512798i | ||||
\(709\) | 35.9444 | 1.34992 | 0.674959 | − | 0.737855i | \(-0.264161\pi\) | ||||
0.674959 | + | 0.737855i | \(0.264161\pi\) | |||||||
\(710\) | −3.89022 | − | 6.73806i | −0.145997 | − | 0.252875i | ||||
\(711\) | 3.08084 | − | 5.33616i | 0.115540 | − | 0.200122i | ||||
\(712\) | 20.8429 | + | 36.1010i | 0.781121 | + | 1.35294i | ||||
\(713\) | 3.94430 | − | 6.83173i | 0.147715 | − | 0.255850i | ||||
\(714\) | 4.55185 | + | 14.3178i | 0.170349 | + | 0.535830i | ||||
\(715\) | 16.4315 | − | 5.84544i | 0.614503 | − | 0.218607i | ||||
\(716\) | 7.08200 | − | 12.2664i | 0.264667 | − | 0.458416i | ||||
\(717\) | 11.2501 | 0.420141 | ||||||||
\(718\) | 12.3851 | 0.462206 | ||||||||
\(719\) | 10.1952 | 0.380217 | 0.190108 | − | 0.981763i | \(-0.439116\pi\) | ||||
0.190108 | + | 0.981763i | \(0.439116\pi\) | |||||||
\(720\) | 0.867729 | 0.0323384 | ||||||||
\(721\) | −11.5062 | − | 2.52217i | −0.428513 | − | 0.0939303i | ||||
\(722\) | 2.78624 | + | 4.82590i | 0.103693 | + | 0.179602i | ||||
\(723\) | 9.72305 | − | 16.8408i | 0.361604 | − | 0.626316i | ||||
\(724\) | −15.0963 | + | 26.1476i | −0.561051 | + | 0.971769i | ||||
\(725\) | −2.67827 | −0.0994683 | ||||||||
\(726\) | 3.15191 | + | 5.45928i | 0.116979 | + | 0.202613i | ||||
\(727\) | −2.32372 | −0.0861821 | −0.0430911 | − | 0.999071i | \(-0.513721\pi\) | ||||
−0.0430911 | + | 0.999071i | \(0.513721\pi\) | |||||||
\(728\) | −10.1601 | + | 24.1924i | −0.376558 | + | 0.896632i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.10753 | + | 12.3106i | 0.263061 | + | 0.455636i | ||||
\(731\) | −1.49739 | −0.0553831 | ||||||||
\(732\) | 5.70876 | − | 9.88787i | 0.211002 | − | 0.365466i | ||||
\(733\) | 2.91958 | − | 5.05685i | 0.107837 | − | 0.186779i | −0.807057 | − | 0.590474i | \(-0.798941\pi\) |
0.914894 | + | 0.403695i | \(0.132274\pi\) | |||||||
\(734\) | −3.35889 | − | 5.81777i | −0.123979 | − | 0.214738i | ||||
\(735\) | 1.68335 | + | 18.2411i | 0.0620912 | + | 0.672832i | ||||
\(736\) | 7.35314 | 0.271040 | ||||||||
\(737\) | −25.5687 | −0.941834 | ||||||||
\(738\) | 7.33560 | 0.270027 | ||||||||
\(739\) | 0.0211428 | 0.000777749 | 0.000388875 | − | 1.00000i | \(-0.499876\pi\) | ||||
0.000388875 | 1.00000i | \(0.499876\pi\) | ||||||||
\(740\) | 13.4943 | − | 23.3728i | 0.496060 | − | 0.859201i | ||||
\(741\) | −13.9172 | − | 11.8516i | −0.511260 | − | 0.435380i | ||||
\(742\) | −5.75513 | − | 1.26153i | −0.211277 | − | 0.0463122i | ||||
\(743\) | −14.8332 | + | 25.6918i | −0.544176 | + | 0.942541i | 0.454482 | + | 0.890756i | \(0.349824\pi\) |
−0.998658 | + | 0.0517853i | \(0.983509\pi\) | |||||||
\(744\) | 8.52359 | + | 14.7633i | 0.312490 | + | 0.541249i | ||||
\(745\) | 14.2719 | − | 24.7197i | 0.522883 | − | 0.905660i | ||||
\(746\) | −4.68704 | − | 8.11819i | −0.171605 | − | 0.297228i | ||||
\(747\) | −8.67738 | −0.317489 | ||||||||
\(748\) | −8.26432 | − | 14.3142i | −0.302173 | − | 0.523380i | ||||
\(749\) | 12.8609 | − | 14.1024i | 0.469927 | − | 0.515290i | ||||
\(750\) | 3.42793 | + | 5.93734i | 0.125170 | + | 0.216801i | ||||
\(751\) | −6.30078 | − | 10.9133i | −0.229919 | − | 0.398231i | 0.727865 | − | 0.685720i | \(-0.240513\pi\) |
−0.957784 | + | 0.287489i | \(0.907179\pi\) | |||||||
\(752\) | −0.413824 | −0.0150906 | ||||||||
\(753\) | 8.79293 | + | 15.2298i | 0.320432 | + | 0.555005i | ||||
\(754\) | 3.30636 | + | 2.81565i | 0.120411 | + | 0.102540i | ||||
\(755\) | −58.4635 | −2.12770 | ||||||||
\(756\) | −3.38302 | − | 0.741562i | −0.123039 | − | 0.0269703i | ||||
\(757\) | −8.13319 | + | 14.0871i | −0.295606 | + | 0.512004i | −0.975126 | − | 0.221653i | \(-0.928855\pi\) |
0.679520 | + | 0.733657i | \(0.262188\pi\) | |||||||
\(758\) | −14.8720 | −0.540177 | ||||||||
\(759\) | 1.17635 | + | 2.03750i | 0.0426989 | + | 0.0739566i | ||||
\(760\) | −18.2471 | + | 31.6049i | −0.661891 | + | 1.14643i | ||||
\(761\) | 46.2551 | 1.67675 | 0.838374 | − | 0.545096i | \(-0.183507\pi\) | ||||
0.838374 | + | 0.545096i | \(0.183507\pi\) | |||||||
\(762\) | −7.99063 | −0.289470 | ||||||||
\(763\) | −15.5096 | + | 17.0068i | −0.561486 | + | 0.615687i | ||||
\(764\) | −1.19753 | + | 2.07419i | −0.0433252 | + | 0.0750414i | ||||
\(765\) | −8.93852 | − | 15.4820i | −0.323173 | − | 0.559752i | ||||
\(766\) | 0.0158392 | + | 0.0274344i | 0.000572295 | + | 0.000991244i | ||||
\(767\) | 40.8866 | − | 14.5452i | 1.47633 | − | 0.525198i | ||||
\(768\) | −7.51098 | + | 13.0094i | −0.271029 | + | 0.469436i | ||||
\(769\) | 19.2803 | − | 33.3944i | 0.695264 | − | 1.20423i | −0.274827 | − | 0.961494i | \(-0.588621\pi\) |
0.970092 | − | 0.242739i | \(-0.0780460\pi\) | |||||||
\(770\) | 3.22305 | + | 10.1381i | 0.116151 | + | 0.365351i | ||||
\(771\) | 7.59362 | + | 13.1525i | 0.273477 | + | 0.473677i | ||||
\(772\) | 2.06794 | − | 3.58177i | 0.0744267 | − | 0.128911i | ||||
\(773\) | 5.17723 | − | 8.96723i | 0.186212 | − | 0.322529i | −0.757772 | − | 0.652519i | \(-0.773712\pi\) |
0.943984 | + | 0.329990i | \(0.107046\pi\) | |||||||
\(774\) | −0.0911037 | + | 0.157796i | −0.00327465 | + | 0.00567187i | ||||
\(775\) | −5.72768 | + | 9.92063i | −0.205744 | + | 0.356360i | ||||
\(776\) | 16.7299 | + | 28.9770i | 0.600568 | + | 1.04021i | ||||
\(777\) | −14.0457 | + | 15.4015i | −0.503886 | + | 0.552527i | ||||
\(778\) | −16.2805 | + | 28.1986i | −0.583683 | + | 1.01097i | ||||
\(779\) | 22.3703 | − | 38.7465i | 0.801499 | − | 1.38824i | ||||
\(780\) | 2.23328 | − | 12.1477i | 0.0799644 | − | 0.434957i | ||||
\(781\) | −3.30550 | − | 5.72529i | −0.118280 | − | 0.204867i | ||||
\(782\) | −3.61397 | − | 6.25957i | −0.129235 | − | 0.223842i | ||||
\(783\) | −0.724496 | + | 1.25486i | −0.0258914 | + | 0.0448452i | ||||
\(784\) | 2.10825 | + | 0.970911i | 0.0752946 | + | 0.0346754i | ||||
\(785\) | 1.72501 | 0.0615683 | ||||||||
\(786\) | −13.7658 | −0.491009 | ||||||||
\(787\) | −17.1440 | + | 29.6942i | −0.611116 | + | 1.05848i | 0.379937 | + | 0.925012i | \(0.375946\pi\) |
−0.991053 | + | 0.133471i | \(0.957388\pi\) | |||||||
\(788\) | −7.29906 | − | 12.6423i | −0.260018 | − | 0.450365i | ||||
\(789\) | 13.9699 | 0.497342 | ||||||||
\(790\) | −6.70184 | + | 11.6079i | −0.238441 | + | 0.412992i | ||||
\(791\) | −6.50818 | + | 7.13643i | −0.231404 | + | 0.253742i | ||||
\(792\) | −5.08417 | −0.180658 | ||||||||
\(793\) | −23.9430 | − | 20.3894i | −0.850239 | − | 0.724050i | ||||
\(794\) | 3.62899 | + | 6.28560i | 0.128788 | + | 0.223068i | ||||
\(795\) | 7.01065 | 0.248642 | ||||||||
\(796\) | 13.5809 | + | 23.5228i | 0.481362 | + | 0.833743i | ||||
\(797\) | 6.60638 | + | 11.4426i | 0.234010 | + | 0.405317i | 0.958984 | − | 0.283459i | \(-0.0914819\pi\) |
−0.724975 | + | 0.688776i | \(0.758149\pi\) | |||||||
\(798\) | 7.51333 | − | 8.23862i | 0.265969 | − | 0.291644i | ||||
\(799\) | 4.26283 | + | 7.38343i | 0.150808 | + | 0.261207i | ||||
\(800\) | −10.6778 | −0.377517 | ||||||||
\(801\) | 7.57751 | + | 13.1246i | 0.267738 | + | 0.463736i | ||||
\(802\) | 10.0929 | − | 17.4815i | 0.356394 | − | 0.617293i | ||||
\(803\) | 6.03922 | + | 10.4602i | 0.213120 | + | 0.369134i | ||||
\(804\) | −9.05393 | + | 15.6819i | −0.319307 | + | 0.553057i | ||||
\(805\) | −2.67009 | − | 8.39875i | −0.0941083 | − | 0.296017i | ||||
\(806\) | 17.5004 | − | 6.22571i | 0.616426 | − | 0.219291i | ||||
\(807\) | −14.4628 | + | 25.0503i | −0.509115 | + | 0.881813i | ||||
\(808\) | −12.6421 | −0.444746 | ||||||||
\(809\) | −50.9750 | −1.79219 | −0.896094 | − | 0.443865i | \(-0.853607\pi\) | ||||
−0.896094 | + | 0.443865i | \(0.853607\pi\) | |||||||
\(810\) | −2.17533 | −0.0764334 | ||||||||
\(811\) | 7.86969 | 0.276342 | 0.138171 | − | 0.990408i | \(-0.455878\pi\) | ||||
0.138171 | + | 0.990408i | \(0.455878\pi\) | |||||||
\(812\) | 3.38155 | − | 3.70798i | 0.118669 | − | 0.130124i | ||||
\(813\) | −5.05875 | − | 8.76202i | −0.177418 | − | 0.307297i | ||||
\(814\) | −6.05243 | + | 10.4831i | −0.212138 | + | 0.367433i | ||||
\(815\) | −23.7946 | + | 41.2135i | −0.833488 | + | 1.44364i | ||||
\(816\) | −2.26513 | −0.0792954 | ||||||||
\(817\) | 0.555650 | + | 0.962415i | 0.0194397 | + | 0.0336706i | ||||
\(818\) | 16.3944 | 0.573218 | ||||||||
\(819\) | −3.69373 | + | 8.79524i | −0.129070 | + | 0.307331i | ||||
\(820\) | 30.2304 | 1.05569 | ||||||||
\(821\) | 20.8357 | + | 36.0885i | 0.727171 | + | 1.25950i | 0.958074 | + | 0.286520i | \(0.0924985\pi\) |
−0.230904 | + | 0.972977i | \(0.574168\pi\) | |||||||
\(822\) | −8.77541 | −0.306078 | ||||||||
\(823\) | 7.85504 | − | 13.6053i | 0.273809 | − | 0.474252i | −0.696025 | − | 0.718018i | \(-0.745050\pi\) |
0.969834 | + | 0.243766i | \(0.0783829\pi\) | |||||||
\(824\) | −6.12315 | + | 10.6056i | −0.213310 | + | 0.369464i | ||||
\(825\) | −1.70823 | − | 2.95874i | −0.0594729 | − | 0.103010i | ||||
\(826\) | 8.01993 | + | 25.2266i | 0.279049 | + | 0.877746i | ||||
\(827\) | 33.6343 | 1.16958 | 0.584789 | − | 0.811185i | \(-0.301177\pi\) | ||||
0.584789 | + | 0.811185i | \(0.301177\pi\) | |||||||
\(828\) | 1.66620 | 0.0579044 | ||||||||
\(829\) | −50.3021 | −1.74706 | −0.873532 | − | 0.486767i | \(-0.838176\pi\) | ||||
−0.873532 | + | 0.486767i | \(0.838176\pi\) | |||||||
\(830\) | 18.8762 | 0.655202 | ||||||||
\(831\) | 1.70320 | − | 2.95002i | 0.0590832 | − | 0.102335i | ||||
\(832\) | 11.3615 | + | 9.67525i | 0.393889 | + | 0.335429i | ||||
\(833\) | −4.39423 | − | 47.6167i | −0.152251 | − | 1.64982i | ||||
\(834\) | −3.80504 | + | 6.59053i | −0.131758 | + | 0.228211i | ||||
\(835\) | −5.78746 | − | 10.0242i | −0.200283 | − | 0.346901i | ||||
\(836\) | −6.13342 | + | 10.6234i | −0.212129 | + | 0.367418i | ||||
\(837\) | 3.09878 | + | 5.36725i | 0.107110 | + | 0.185519i | ||||
\(838\) | 18.4498 | 0.637338 | ||||||||
\(839\) | −19.2875 | − | 33.4069i | −0.665877 | − | 1.15333i | −0.979047 | − | 0.203635i | \(-0.934724\pi\) |
0.313170 | − | 0.949697i | \(-0.398609\pi\) | |||||||
\(840\) | 18.6030 | + | 4.07780i | 0.641865 | + | 0.140697i | ||||
\(841\) | 13.4502 | + | 23.2964i | 0.463800 | + | 0.803326i | ||||
\(842\) | −0.770881 | − | 1.33520i | −0.0265663 | − | 0.0460142i | ||||
\(843\) | −9.40331 | −0.323867 | ||||||||
\(844\) | −10.6917 | − | 18.5186i | −0.368025 | − | 0.637437i | ||||
\(845\) | −31.7957 | − | 12.0999i | −1.09381 | − | 0.416248i | ||||
\(846\) | 1.03743 | 0.0356675 | ||||||||
\(847\) | −6.07890 | − | 19.1211i | −0.208874 | − | 0.657010i | ||||
\(848\) | 0.444145 | − | 0.769282i | 0.0152520 | − | 0.0264173i | ||||
\(849\) | −10.4790 | −0.359638 | ||||||||
\(850\) | 5.24798 | + | 9.08977i | 0.180004 | + | 0.311777i | ||||
\(851\) | 5.01406 | − | 8.68460i | 0.171880 | − | 0.297704i | ||||
\(852\) | −4.68194 | −0.160401 | ||||||||
\(853\) | 22.6889 | 0.776855 | 0.388427 | − | 0.921479i | \(-0.373018\pi\) | ||||
0.388427 | + | 0.921479i | \(0.373018\pi\) | |||||||
\(854\) | 12.9259 | − | 14.1736i | 0.442314 | − | 0.485012i | ||||
\(855\) | −6.63379 | + | 11.4901i | −0.226871 | + | 0.392952i | ||||
\(856\) | −9.92134 | − | 17.1843i | −0.339104 | − | 0.587346i | ||||
\(857\) | 10.2901 | + | 17.8230i | 0.351504 | + | 0.608822i | 0.986513 | − | 0.163682i | \(-0.0523371\pi\) |
−0.635009 | + | 0.772504i | \(0.719004\pi\) | |||||||
\(858\) | −1.00167 | + | 5.44846i | −0.0341964 | + | 0.186007i | ||||
\(859\) | 1.81131 | − | 3.13729i | 0.0618012 | − | 0.107043i | −0.833469 | − | 0.552566i | \(-0.813649\pi\) |
0.895271 | + | 0.445523i | \(0.146982\pi\) | |||||||
\(860\) | −0.375443 | + | 0.650286i | −0.0128025 | + | 0.0221746i | ||||
\(861\) | −22.8067 | − | 4.99924i | −0.777249 | − | 0.170374i | ||||
\(862\) | −15.7053 | − | 27.2023i | −0.534923 | − | 0.926515i | ||||
\(863\) | −3.99010 | + | 6.91105i | −0.135824 | + | 0.235255i | −0.925912 | − | 0.377739i | \(-0.876702\pi\) |
0.790088 | + | 0.612994i | \(0.210035\pi\) | |||||||
\(864\) | −2.88844 | + | 5.00293i | −0.0982668 | + | 0.170203i | ||||
\(865\) | −4.60639 | + | 7.97850i | −0.156622 | + | 0.271277i | ||||
\(866\) | −14.6034 | + | 25.2938i | −0.496244 | + | 0.859520i | ||||
\(867\) | 14.8332 | + | 25.6919i | 0.503763 | + | 0.872542i | ||||
\(868\) | −6.50310 | − | 20.4555i | −0.220730 | − | 0.694304i | ||||
\(869\) | −5.69451 | + | 9.86318i | −0.193173 | + | 0.334586i | ||||
\(870\) | 1.57602 | − | 2.72975i | 0.0534321 | − | 0.0925470i | ||||
\(871\) | 37.9728 | + | 32.3370i | 1.28666 | + | 1.09570i | ||||
\(872\) | 11.9647 | + | 20.7234i | 0.405174 | + | 0.701783i | ||||
\(873\) | 6.08221 | + | 10.5347i | 0.205851 | + | 0.356545i | ||||
\(874\) | −2.68213 | + | 4.64558i | −0.0907244 | + | 0.157139i | ||||
\(875\) | −6.61123 | − | 20.7956i | −0.223500 | − | 0.703019i | ||||
\(876\) | 8.55401 | 0.289013 | ||||||||
\(877\) | −12.6000 | −0.425470 | −0.212735 | − | 0.977110i | \(-0.568237\pi\) | ||||
−0.212735 | + | 0.977110i | \(0.568237\pi\) | |||||||
\(878\) | 6.37881 | − | 11.0484i | 0.215275 | − | 0.372866i | ||||
\(879\) | 4.61007 | + | 7.98488i | 0.155494 | + | 0.269323i | ||||
\(880\) | −1.60388 | −0.0540668 | ||||||||
\(881\) | 0.0834951 | − | 0.144618i | 0.00281302 | − | 0.00487230i | −0.864615 | − | 0.502434i | \(-0.832438\pi\) |
0.867428 | + | 0.497562i | \(0.165771\pi\) | |||||||
\(882\) | −5.28522 | − | 2.43400i | −0.177963 | − | 0.0819571i | ||||
\(883\) | 1.54174 | 0.0518836 | 0.0259418 | − | 0.999663i | \(-0.491742\pi\) | ||||
0.0259418 | + | 0.999663i | \(0.491742\pi\) | |||||||
\(884\) | −5.82979 | + | 31.7105i | −0.196077 | + | 1.06654i | ||||
\(885\) | −15.7489 | − | 27.2778i | −0.529392 | − | 0.916934i | ||||
\(886\) | −24.1655 | −0.811857 | ||||||||
\(887\) | 5.16683 | + | 8.94922i | 0.173485 | + | 0.300485i | 0.939636 | − | 0.342176i | \(-0.111164\pi\) |
−0.766151 | + | 0.642661i | \(0.777830\pi\) | |||||||
\(888\) | 10.8353 | + | 18.7673i | 0.363609 | + | 0.629790i | ||||
\(889\) | 24.8432 | + | 5.44565i | 0.833213 | + | 0.182641i | ||||
\(890\) | −16.4836 | − | 28.5504i | −0.552532 | − | 0.957013i | ||||
\(891\) | −1.84837 | −0.0619226 | ||||||||
\(892\) | −12.1852 | − | 21.1055i | −0.407992 | − | 0.706663i | ||||
\(893\) | 3.16369 | − | 5.47967i | 0.105869 | − | 0.183370i | ||||
\(894\) | 4.53337 | + | 7.85203i | 0.151619 | + | 0.262611i | ||||
\(895\) | −14.1580 | + | 24.5224i | −0.473250 | + | 0.819693i | ||||
\(896\) | 14.4644 | − | 15.8607i | 0.483223 | − | 0.529869i | ||||
\(897\) | 0.829819 | − | 4.51371i | 0.0277068 | − | 0.150708i | ||||
\(898\) | 0.981963 | − | 1.70081i | 0.0327685 | − | 0.0567568i | ||||
\(899\) | −8.98022 | −0.299507 | ||||||||
\(900\) | −2.41955 | −0.0806517 | ||||||||
\(901\) | −18.3007 | −0.609684 | ||||||||
\(902\) | −13.5589 | −0.451461 | ||||||||
\(903\) | 0.390784 | − | 0.428507i | 0.0130045 | − | 0.0142598i | ||||
\(904\) | 5.02064 | + | 8.69600i | 0.166984 | + | 0.289225i | ||||
\(905\) | 30.1799 | − | 52.2732i | 1.00321 | − | 1.73762i | ||||
\(906\) | 9.28524 | − | 16.0825i | 0.308482 | − | 0.534306i | ||||
\(907\) | 23.8992 | 0.793559 | 0.396780 | − | 0.917914i | \(-0.370128\pi\) | ||||
0.396780 | + | 0.917914i | \(0.370128\pi\) | |||||||
\(908\) | −14.7562 | − | 25.5586i | −0.489703 | − | 0.848191i | ||||
\(909\) | −4.59607 | −0.152442 | ||||||||
\(910\) | 8.03510 | − | 19.1326i | 0.266361 | − | 0.634239i | ||||
\(911\) | 14.3304 | 0.474786 | 0.237393 | − | 0.971414i | \(-0.423707\pi\) | ||||
0.237393 | + | 0.971414i | \(0.423707\pi\) | |||||||
\(912\) | 0.840540 | + | 1.45586i | 0.0278331 | + | 0.0482083i | ||||
\(913\) | 16.0390 | 0.530813 | ||||||||
\(914\) | −6.96315 | + | 12.0605i | −0.230321 | + | 0.398927i | ||||
\(915\) | −11.4127 | + | 19.7674i | −0.377293 | + | 0.653490i | ||||
\(916\) | −12.6021 | − | 21.8275i | −0.416386 | − | 0.721202i | ||||
\(917\) | 42.7983 | + | 9.38143i | 1.41333 | + | 0.309802i | ||||
\(918\) | 5.67851 | 0.187419 | ||||||||
\(919\) | −54.3463 | −1.79272 | −0.896359 | − | 0.443329i | \(-0.853797\pi\) | ||||
−0.896359 | + | 0.443329i | \(0.853797\pi\) | |||||||
\(920\) | −9.16231 | −0.302072 | ||||||||
\(921\) | 16.1499 | 0.532159 | ||||||||
\(922\) | −10.4296 | + | 18.0646i | −0.343480 | + | 0.594926i | ||||
\(923\) | −2.33175 | + | 12.6833i | −0.0767506 | + | 0.417476i | ||||
\(924\) | 6.25307 | + | 1.37068i | 0.205711 | + | 0.0450920i | ||||
\(925\) | −7.28111 | + | 12.6113i | −0.239402 | + | 0.414656i | ||||
\(926\) | −0.105675 | − | 0.183035i | −0.00347271 | − | 0.00601491i | ||||
\(927\) | −2.22609 | + | 3.85570i | −0.0731144 | + | 0.126638i | ||||
\(928\) | −4.18533 | − | 7.24920i | −0.137390 | − | 0.237967i | ||||
\(929\) | 16.6711 | 0.546961 | 0.273480 | − | 0.961878i | \(-0.411825\pi\) | ||||
0.273480 | + | 0.961878i | \(0.411825\pi\) | |||||||
\(930\) | −6.74088 | − | 11.6755i | −0.221042 | − | 0.382856i | ||||
\(931\) | −28.9739 | + | 20.4938i | −0.949581 | + | 0.671657i | ||||
\(932\) | 14.9590 | + | 25.9098i | 0.490000 | + | 0.848704i | ||||
\(933\) | −15.2138 | − | 26.3510i | −0.498077 | − | 0.862694i | ||||
\(934\) | −8.49796 | −0.278062 | ||||||||
\(935\) | 16.5217 | + | 28.6164i | 0.540316 | + | 0.935855i | ||||
\(936\) | 7.55065 | + | 6.43001i | 0.246801 | + | 0.210172i | ||||
\(937\) | −2.55078 | −0.0833303 | −0.0416651 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416651 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(938\) | −20.5000 | + | 22.4790i | −0.669350 | + | 0.733964i | ||||
\(939\) | 13.6859 | − | 23.7047i | 0.446623 | − | 0.773574i | ||||
\(940\) | 4.27529 | 0.139445 | ||||||||
\(941\) | 17.3944 | + | 30.1280i | 0.567041 | + | 0.982144i | 0.996857 | + | 0.0792275i | \(0.0252453\pi\) |
−0.429815 | + | 0.902917i | \(0.641421\pi\) | |||||||
\(942\) | −0.273968 | + | 0.474527i | −0.00892637 | + | 0.0154609i | ||||
\(943\) | 11.2327 | 0.365786 | ||||||||
\(944\) | −3.99095 | −0.129894 | ||||||||
\(945\) | 6.76319 | + | 1.48250i | 0.220007 | + | 0.0482257i | ||||
\(946\) | 0.168393 | − | 0.291665i | 0.00547493 | − | 0.00948285i | ||||
\(947\) | −7.49284 | − | 12.9780i | −0.243485 | − | 0.421728i | 0.718220 | − | 0.695816i | \(-0.244957\pi\) |
−0.961704 | + | 0.274088i | \(0.911624\pi\) | |||||||
\(948\) | 4.03288 | + | 6.98516i | 0.130982 | + | 0.226867i | ||||
\(949\) | 4.26017 | − | 23.1727i | 0.138291 | − | 0.752218i | ||||
\(950\) | 3.89483 | − | 6.74604i | 0.126365 | − | 0.218870i | ||||
\(951\) | 6.18424 | − | 10.7114i | 0.200538 | − | 0.347342i | ||||
\(952\) | −48.5615 | − | 10.6447i | −1.57389 | − | 0.344998i | ||||
\(953\) | −6.40858 | − | 11.1000i | −0.207594 | − | 0.359564i | 0.743362 | − | 0.668889i | \(-0.233230\pi\) |
−0.950956 | + | 0.309326i | \(0.899897\pi\) | |||||||
\(954\) | −1.11344 | + | 1.92853i | −0.0360489 | + | 0.0624386i | ||||
\(955\) | 2.39405 | − | 4.14662i | 0.0774697 | − | 0.134181i | ||||
\(956\) | −7.36328 | + | 12.7536i | −0.238146 | + | 0.412480i | ||||
\(957\) | 1.33913 | − | 2.31945i | 0.0432880 | − | 0.0749771i | ||||
\(958\) | −5.28177 | − | 9.14829i | −0.170646 | − | 0.295568i | ||||
\(959\) | 27.2831 | + | 5.98048i | 0.881017 | + | 0.193120i | ||||
\(960\) | 5.41559 | − | 9.38008i | 0.174787 | − | 0.302741i | ||||
\(961\) | −3.70488 | + | 6.41704i | −0.119512 | + | 0.207001i | ||||
\(962\) | 22.2468 | − | 7.91421i | 0.717265 | − | 0.255164i | ||||
\(963\) | −3.60694 | − | 6.24740i | −0.116232 | − | 0.201320i | ||||
\(964\) | 12.7277 | + | 22.0450i | 0.409931 | + | 0.710021i | ||||
\(965\) | −4.13413 | + | 7.16052i | −0.133082 | + | 0.230505i | ||||
\(966\) | 2.73445 | + | 0.599394i | 0.0879795 | + | 0.0192852i | ||||
\(967\) | 17.8560 | 0.574209 | 0.287105 | − | 0.957899i | \(-0.407307\pi\) | ||||
0.287105 | + | 0.957899i | \(0.407307\pi\) | |||||||
\(968\) | −20.8595 | −0.670450 | ||||||||
\(969\) | 17.3169 | − | 29.9938i | 0.556299 | − | 0.963538i | ||||
\(970\) | −13.2308 | − | 22.9165i | −0.424816 | − | 0.735803i | ||||
\(971\) | 35.3067 | 1.13305 | 0.566523 | − | 0.824046i | \(-0.308288\pi\) | ||||
0.566523 | + | 0.824046i | \(0.308288\pi\) | |||||||
\(972\) | −0.654511 | + | 1.13365i | −0.0209934 | + | 0.0363617i | ||||
\(973\) | 16.3215 | − | 17.8971i | 0.523243 | − | 0.573753i | ||||
\(974\) | −17.0256 | −0.545537 | ||||||||
\(975\) | −1.20501 | + | 6.55453i | −0.0385913 | + | 0.209913i | ||||
\(976\) | 1.44606 | + | 2.50465i | 0.0462872 | + | 0.0801718i | ||||
\(977\) | 19.1054 | 0.611237 | 0.305618 | − | 0.952154i | \(-0.401137\pi\) | ||||
0.305618 | + | 0.952154i | \(0.401137\pi\) | |||||||
\(978\) | −7.55818 | − | 13.0911i | −0.241684 | − | 0.418609i | ||||
\(979\) | −14.0060 | − | 24.2591i | −0.447634 | − | 0.775325i | ||||
\(980\) | −21.7807 | − | 10.0307i | −0.695758 | − | 0.320417i | ||||
\(981\) | 4.34979 | + | 7.53406i | 0.138878 | + | 0.240544i | ||||
\(982\) | −16.4936 | −0.526333 | ||||||||
\(983\) | −18.4765 | − | 32.0022i | −0.589308 | − | 1.02071i | −0.994323 | − | 0.106402i | \(-0.966067\pi\) |
0.405015 | − | 0.914310i | \(-0.367266\pi\) | |||||||
\(984\) | −12.1368 | + | 21.0216i | −0.386908 | + | 0.670144i | ||||
\(985\) | 14.5920 | + | 25.2740i | 0.464939 | + | 0.805297i | ||||
\(986\) | −4.11406 | + | 7.12576i | −0.131018 | + | 0.226930i | ||||
\(987\) | −3.22540 | − | 0.707011i | −0.102666 | − | 0.0225044i | ||||
\(988\) | 22.5445 | − | 8.02012i | 0.717236 | − | 0.255154i | ||||
\(989\) | −0.139503 | + | 0.241626i | −0.00443593 | + | 0.00768326i | ||||
\(990\) | 4.02081 | 0.127790 | ||||||||
\(991\) | 55.8372 | 1.77373 | 0.886863 | − | 0.462032i | \(-0.152879\pi\) | ||||
0.886863 | + | 0.462032i | \(0.152879\pi\) | |||||||
\(992\) | −35.8026 | −1.13673 | ||||||||
\(993\) | 12.4062 | 0.393699 | ||||||||
\(994\) | −7.68368 | − | 1.68427i | −0.243711 | − | 0.0534218i | ||||
\(995\) | −27.1503 | − | 47.0257i | −0.860722 | − | 1.49081i | ||||
\(996\) | 5.67944 | − | 9.83708i | 0.179960 | − | 0.311700i | ||||
\(997\) | 11.4391 | − | 19.8131i | 0.362280 | − | 0.627488i | −0.626056 | − | 0.779778i | \(-0.715332\pi\) |
0.988336 | + | 0.152291i | \(0.0486650\pi\) | |||||||
\(998\) | −23.1784 | −0.733699 | ||||||||
\(999\) | 3.93922 | + | 6.82292i | 0.124631 | + | 0.215868i |
(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 | 273.2.j.b.100.6 | ✓ | 16 | |
3.2 | odd | 2 | 819.2.n.e.100.3 | 16 | |||
7.4 | even | 3 | 273.2.l.b.256.3 | yes | 16 | ||
13.3 | even | 3 | 273.2.l.b.16.3 | yes | 16 | ||
21.11 | odd | 6 | 819.2.s.e.802.6 | 16 | |||
39.29 | odd | 6 | 819.2.s.e.289.6 | 16 | |||
91.81 | even | 3 | inner | 273.2.j.b.172.6 | yes | 16 | |
273.263 | odd | 6 | 819.2.n.e.172.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.b.100.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
273.2.j.b.172.6 | yes | 16 | 91.81 | even | 3 | inner | |
273.2.l.b.16.3 | yes | 16 | 13.3 | even | 3 | ||
273.2.l.b.256.3 | yes | 16 | 7.4 | even | 3 | ||
819.2.n.e.100.3 | 16 | 3.2 | odd | 2 | |||
819.2.n.e.172.3 | 16 | 273.263 | odd | 6 | |||
819.2.s.e.289.6 | 16 | 39.29 | odd | 6 | |||
819.2.s.e.802.6 | 16 | 21.11 | odd | 6 |