Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(91,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.e (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.7465802011608416256.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.5 | ||
Root | \(1.37379 - 0.335728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.91 |
Dual form | 460.2.e.a.91.8 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.637910 | − | 1.26217i | −0.451071 | − | 0.892488i | ||||
\(3\) | 2.87247i | 1.65842i | 0.558936 | + | 0.829211i | \(0.311210\pi\) | ||||
−0.558936 | + | 0.829211i | \(0.688790\pi\) | |||||||
\(4\) | −1.18614 | + | 1.61030i | −0.593070 | + | 0.805151i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 3.62554 | − | 1.83238i | 1.48012 | − | 0.748065i | ||||
\(7\) | −2.68161 | −1.01355 | −0.506777 | − | 0.862077i | \(-0.669163\pi\) | ||||
−0.506777 | + | 0.862077i | \(0.669163\pi\) | |||||||
\(8\) | 2.78912 | + | 0.469882i | 0.986104 | + | 0.166128i | ||||
\(9\) | −5.25109 | −1.75036 | ||||||||
\(10\) | −1.26217 | + | 0.637910i | −0.399133 | + | 0.201725i | ||||
\(11\) | −4.89140 | −1.47481 | −0.737406 | − | 0.675449i | \(-0.763950\pi\) | ||||
−0.737406 | + | 0.675449i | \(0.763950\pi\) | |||||||
\(12\) | −4.62554 | − | 3.40715i | −1.33528 | − | 0.983561i | ||||
\(13\) | 0.727591 | 0.201797 | 0.100899 | − | 0.994897i | \(-0.467828\pi\) | ||||
0.100899 | + | 0.994897i | \(0.467828\pi\) | |||||||
\(14\) | 1.71063 | + | 3.38465i | 0.457185 | + | 0.904586i | ||||
\(15\) | 2.87247 | 0.741669 | ||||||||
\(16\) | −1.18614 | − | 3.82009i | −0.296535 | − | 0.955022i | ||||
\(17\) | − | 6.34755i | − | 1.53951i | −0.638342 | − | 0.769753i | \(-0.720379\pi\) | ||
0.638342 | − | 0.769753i | \(-0.279621\pi\) | |||||||
\(18\) | 3.34972 | + | 6.62776i | 0.789537 | + | 1.56218i | ||||
\(19\) | 2.68161 | 0.615204 | 0.307602 | − | 0.951515i | \(-0.400473\pi\) | ||||
0.307602 | + | 0.951515i | \(0.400473\pi\) | |||||||
\(20\) | 1.61030 | + | 1.18614i | 0.360074 | + | 0.265229i | ||||
\(21\) | − | 7.70285i | − | 1.68090i | ||||||
\(22\) | 3.12027 | + | 6.17377i | 0.665245 | + | 1.31625i | ||||
\(23\) | 2.20979 | − | 4.25639i | 0.460772 | − | 0.887518i | ||||
\(24\) | −1.34972 | + | 8.01167i | −0.275511 | + | 1.63538i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.464138 | − | 0.918342i | −0.0910249 | − | 0.180102i | ||||
\(27\) | − | 6.46618i | − | 1.24442i | ||||||
\(28\) | 3.18077 | − | 4.31821i | 0.601109 | − | 0.816064i | ||||
\(29\) | −4.27582 | −0.794000 | −0.397000 | − | 0.917819i | \(-0.629949\pi\) | ||||
−0.397000 | + | 0.917819i | \(0.629949\pi\) | |||||||
\(30\) | −1.83238 | − | 3.62554i | −0.334545 | − | 0.661930i | ||||
\(31\) | 6.13645i | 1.10214i | 0.834459 | + | 0.551070i | \(0.185780\pi\) | ||||
−0.834459 | + | 0.551070i | \(0.814220\pi\) | |||||||
\(32\) | −4.06494 | + | 3.93398i | −0.718587 | + | 0.695437i | ||||
\(33\) | − | 14.0504i | − | 2.44586i | ||||||
\(34\) | −8.01167 | + | 4.04917i | −1.37399 | + | 0.694426i | ||||
\(35\) | 2.68161i | 0.453275i | ||||||||
\(36\) | 6.22853 | − | 8.45583i | 1.03809 | − | 1.40930i | ||||
\(37\) | − | 3.87539i | − | 0.637111i | −0.947904 | − | 0.318555i | \(-0.896802\pi\) | ||
0.947904 | − | 0.318555i | \(-0.103198\pi\) | |||||||
\(38\) | −1.71063 | − | 3.38465i | −0.277501 | − | 0.549063i | ||||
\(39\) | 2.08998i | 0.334665i | ||||||||
\(40\) | 0.469882 | − | 2.78912i | 0.0742949 | − | 0.440999i | ||||
\(41\) | −8.07172 | −1.26059 | −0.630296 | − | 0.776355i | \(-0.717066\pi\) | ||||
−0.630296 | + | 0.776355i | \(0.717066\pi\) | |||||||
\(42\) | −9.72230 | + | 4.91373i | −1.50018 | + | 0.758205i | ||||
\(43\) | −11.1319 | −1.69761 | −0.848803 | − | 0.528709i | \(-0.822676\pi\) | ||||
−0.848803 | + | 0.528709i | \(0.822676\pi\) | |||||||
\(44\) | 5.80189 | − | 7.87663i | 0.874668 | − | 1.18745i | ||||
\(45\) | 5.25109i | 0.782786i | ||||||||
\(46\) | −6.78193 | − | 0.0739292i | −0.999941 | − | 0.0109003i | ||||
\(47\) | − | 9.80928i | − | 1.43083i | −0.698699 | − | 0.715416i | \(-0.746237\pi\) | ||
0.698699 | − | 0.715416i | \(-0.253763\pi\) | |||||||
\(48\) | 10.9731 | − | 3.40715i | 1.58383 | − | 0.491780i | ||||
\(49\) | 0.191051 | 0.0272930 | ||||||||
\(50\) | 0.637910 | + | 1.26217i | 0.0902142 | + | 0.178498i | ||||
\(51\) | 18.2331 | 2.55315 | ||||||||
\(52\) | −0.863025 | + | 1.17164i | −0.119680 | + | 0.162477i | ||||
\(53\) | 11.1565i | 1.53246i | 0.642565 | + | 0.766231i | \(0.277870\pi\) | ||||
−0.642565 | + | 0.766231i | \(0.722130\pi\) | |||||||
\(54\) | −8.16141 | + | 4.12484i | −1.11063 | + | 0.561320i | ||||
\(55\) | 4.89140i | 0.659556i | ||||||||
\(56\) | −7.47935 | − | 1.26004i | −0.999470 | − | 0.168380i | ||||
\(57\) | 7.70285i | 1.02027i | ||||||||
\(58\) | 2.72759 | + | 5.39681i | 0.358150 | + | 0.708636i | ||||
\(59\) | − | 1.87953i | − | 0.244694i | −0.992487 | − | 0.122347i | \(-0.960958\pi\) | ||
0.992487 | − | 0.122347i | \(-0.0390420\pi\) | |||||||
\(60\) | −3.40715 | + | 4.62554i | −0.439862 | + | 0.597155i | ||||
\(61\) | 6.93356i | 0.887751i | 0.896088 | + | 0.443875i | \(0.146397\pi\) | ||||
−0.896088 | + | 0.443875i | \(0.853603\pi\) | |||||||
\(62\) | 7.74524 | − | 3.91451i | 0.983646 | − | 0.497143i | ||||
\(63\) | 14.0814 | 1.77409 | ||||||||
\(64\) | 7.55842 | + | 2.62112i | 0.944803 | + | 0.327640i | ||||
\(65\) | − | 0.727591i | − | 0.0902465i | ||||||
\(66\) | −17.7340 | + | 8.96290i | −2.18290 | + | 1.10326i | ||||
\(67\) | −10.5224 | −1.28552 | −0.642761 | − | 0.766067i | \(-0.722211\pi\) | ||||
−0.642761 | + | 0.766067i | \(0.722211\pi\) | |||||||
\(68\) | 10.2215 | + | 7.52908i | 1.23953 | + | 0.913035i | ||||
\(69\) | 12.2263 | + | 6.34755i | 1.47188 | + | 0.764155i | ||||
\(70\) | 3.38465 | − | 1.71063i | 0.404543 | − | 0.204459i | ||||
\(71\) | 7.24866i | 0.860258i | 0.902767 | + | 0.430129i | \(0.141532\pi\) | ||||
−0.902767 | + | 0.430129i | \(0.858468\pi\) | |||||||
\(72\) | −14.6459 | − | 2.46739i | −1.72604 | − | 0.290785i | ||||
\(73\) | 7.90882 | 0.925657 | 0.462829 | − | 0.886448i | \(-0.346834\pi\) | ||||
0.462829 | + | 0.886448i | \(0.346834\pi\) | |||||||
\(74\) | −4.89140 | + | 2.47215i | −0.568614 | + | 0.287382i | ||||
\(75\) | − | 2.87247i | − | 0.331684i | ||||||
\(76\) | −3.18077 | + | 4.31821i | −0.364859 | + | 0.495332i | ||||
\(77\) | 13.1168 | 1.49480 | ||||||||
\(78\) | 2.63791 | − | 1.33322i | 0.298685 | − | 0.150958i | ||||
\(79\) | −3.67993 | −0.414024 | −0.207012 | − | 0.978338i | \(-0.566374\pi\) | ||||
−0.207012 | + | 0.978338i | \(0.566374\pi\) | |||||||
\(80\) | −3.82009 | + | 1.18614i | −0.427099 | + | 0.132615i | ||||
\(81\) | 2.82064 | 0.313404 | ||||||||
\(82\) | 5.14904 | + | 10.1879i | 0.568616 | + | 1.12506i | ||||
\(83\) | 4.75372 | 0.521789 | 0.260894 | − | 0.965367i | \(-0.415983\pi\) | ||||
0.260894 | + | 0.965367i | \(0.415983\pi\) | |||||||
\(84\) | 12.4039 | + | 9.13667i | 1.35338 | + | 0.996892i | ||||
\(85\) | −6.34755 | −0.688488 | ||||||||
\(86\) | 7.10119 | + | 14.0504i | 0.765741 | + | 1.51509i | ||||
\(87\) | − | 12.2822i | − | 1.31679i | ||||||
\(88\) | −13.6427 | − | 2.29838i | −1.45432 | − | 0.245008i | ||||
\(89\) | − | 8.12461i | − | 0.861207i | −0.902541 | − | 0.430603i | \(-0.858301\pi\) | ||
0.902541 | − | 0.430603i | \(-0.141699\pi\) | |||||||
\(90\) | 6.62776 | − | 3.34972i | 0.698627 | − | 0.353092i | ||||
\(91\) | −1.95112 | −0.204533 | ||||||||
\(92\) | 4.23295 | + | 8.60710i | 0.441316 | + | 0.897352i | ||||
\(93\) | −17.6268 | −1.82781 | ||||||||
\(94\) | −12.3810 | + | 6.25744i | −1.27700 | + | 0.645406i | ||||
\(95\) | − | 2.68161i | − | 0.275128i | ||||||
\(96\) | −11.3003 | − | 11.6764i | −1.15333 | − | 1.19172i | ||||
\(97\) | − | 2.68434i | − | 0.272554i | −0.990671 | − | 0.136277i | \(-0.956486\pi\) | ||
0.990671 | − | 0.136277i | \(-0.0435137\pi\) | |||||||
\(98\) | −0.121873 | − | 0.241138i | −0.0123111 | − | 0.0243587i | ||||
\(99\) | 25.6852 | 2.58146 | ||||||||
\(100\) | 1.18614 | − | 1.61030i | 0.118614 | − | 0.161030i | ||||
\(101\) | 1.53860 | 0.153096 | 0.0765480 | − | 0.997066i | \(-0.475610\pi\) | ||||
0.0765480 | + | 0.997066i | \(0.475610\pi\) | |||||||
\(102\) | −11.6311 | − | 23.0133i | −1.15165 | − | 2.27866i | ||||
\(103\) | −18.1121 | −1.78464 | −0.892321 | − | 0.451401i | \(-0.850924\pi\) | ||||
−0.892321 | + | 0.451401i | \(0.850924\pi\) | |||||||
\(104\) | 2.02934 | + | 0.341882i | 0.198993 | + | 0.0335243i | ||||
\(105\) | −7.70285 | −0.751722 | ||||||||
\(106\) | 14.0814 | − | 7.11684i | 1.36770 | − | 0.691249i | ||||
\(107\) | 11.1319 | 1.07617 | 0.538083 | − | 0.842892i | \(-0.319149\pi\) | ||||
0.538083 | + | 0.842892i | \(0.319149\pi\) | |||||||
\(108\) | 10.4125 | + | 7.66979i | 1.00194 | + | 0.738026i | ||||
\(109\) | 10.6447i | 1.01958i | 0.860300 | + | 0.509788i | \(0.170276\pi\) | ||||
−0.860300 | + | 0.509788i | \(0.829724\pi\) | |||||||
\(110\) | 6.17377 | − | 3.12027i | 0.588646 | − | 0.297507i | ||||
\(111\) | 11.1319 | 1.05660 | ||||||||
\(112\) | 3.18077 | + | 10.2440i | 0.300555 | + | 0.967967i | ||||
\(113\) | − | 5.41399i | − | 0.509305i | −0.967033 | − | 0.254653i | \(-0.918039\pi\) | ||
0.967033 | − | 0.254653i | \(-0.0819611\pi\) | |||||||
\(114\) | 9.72230 | − | 4.91373i | 0.910577 | − | 0.460213i | ||||
\(115\) | −4.25639 | − | 2.20979i | −0.396910 | − | 0.206064i | ||||
\(116\) | 5.07172 | − | 6.88536i | 0.470898 | − | 0.639290i | ||||
\(117\) | −3.82064 | −0.353218 | ||||||||
\(118\) | −2.37228 | + | 1.19897i | −0.218386 | + | 0.110374i | ||||
\(119\) | 17.0217i | 1.56037i | ||||||||
\(120\) | 8.01167 | + | 1.34972i | 0.731362 | + | 0.123212i | ||||
\(121\) | 12.9258 | 1.17507 | ||||||||
\(122\) | 8.75132 | − | 4.42299i | 0.792307 | − | 0.400439i | ||||
\(123\) | − | 23.1858i | − | 2.09059i | ||||||
\(124\) | −9.88154 | − | 7.27870i | −0.887388 | − | 0.653646i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −8.98266 | − | 17.7731i | −0.800239 | − | 1.58335i | ||||
\(127\) | 3.05353i | 0.270957i | 0.990780 | + | 0.135478i | \(0.0432571\pi\) | ||||
−0.990780 | + | 0.135478i | \(0.956743\pi\) | |||||||
\(128\) | −1.51330 | − | 11.2120i | −0.133758 | − | 0.991014i | ||||
\(129\) | − | 31.9762i | − | 2.81535i | ||||||
\(130\) | −0.918342 | + | 0.464138i | −0.0805439 | + | 0.0407076i | ||||
\(131\) | 3.09691i | 0.270578i | 0.990806 | + | 0.135289i | \(0.0431963\pi\) | ||||
−0.990806 | + | 0.135289i | \(0.956804\pi\) | |||||||
\(132\) | 22.6254 | + | 16.6658i | 1.96929 | + | 1.45057i | ||||
\(133\) | −7.19105 | −0.623543 | ||||||||
\(134\) | 6.71238 | + | 13.2811i | 0.579861 | + | 1.14731i | ||||
\(135\) | −6.46618 | −0.556520 | ||||||||
\(136\) | 2.98260 | − | 17.7041i | 0.255756 | − | 1.51811i | ||||
\(137\) | 5.92579i | 0.506275i | 0.967430 | + | 0.253137i | \(0.0814625\pi\) | ||||
−0.967430 | + | 0.253137i | \(0.918538\pi\) | |||||||
\(138\) | 0.212359 | − | 19.4809i | 0.0180772 | − | 1.65832i | ||||
\(139\) | 3.32470i | 0.281997i | 0.990010 | + | 0.140999i | \(0.0450313\pi\) | ||||
−0.990010 | + | 0.140999i | \(0.954969\pi\) | |||||||
\(140\) | −4.31821 | − | 3.18077i | −0.364955 | − | 0.268824i | ||||
\(141\) | 28.1769 | 2.37292 | ||||||||
\(142\) | 9.14904 | − | 4.62400i | 0.767770 | − | 0.388037i | ||||
\(143\) | −3.55894 | −0.297613 | ||||||||
\(144\) | 6.22853 | + | 20.0596i | 0.519044 | + | 1.67163i | ||||
\(145\) | 4.27582i | 0.355088i | ||||||||
\(146\) | −5.04512 | − | 9.98227i | −0.417537 | − | 0.826138i | ||||
\(147\) | 0.548788i | 0.0452633i | ||||||||
\(148\) | 6.24055 | + | 4.59676i | 0.512970 | + | 0.377851i | ||||
\(149\) | 14.4242i | 1.18168i | 0.806789 | + | 0.590839i | \(0.201203\pi\) | ||||
−0.806789 | + | 0.590839i | \(0.798797\pi\) | |||||||
\(150\) | −3.62554 | + | 1.83238i | −0.296024 | + | 0.149613i | ||||
\(151\) | 13.3082i | 1.08300i | 0.840700 | + | 0.541501i | \(0.182144\pi\) | ||||
−0.840700 | + | 0.541501i | \(0.817856\pi\) | |||||||
\(152\) | 7.47935 | + | 1.26004i | 0.606656 | + | 0.102203i | ||||
\(153\) | 33.3315i | 2.69469i | ||||||||
\(154\) | −8.36737 | − | 16.5557i | −0.674262 | − | 1.33409i | ||||
\(155\) | 6.13645 | 0.492892 | ||||||||
\(156\) | −3.36550 | − | 2.47901i | −0.269456 | − | 0.198480i | ||||
\(157\) | − | 3.66320i | − | 0.292356i | −0.989258 | − | 0.146178i | \(-0.953303\pi\) | ||
0.989258 | − | 0.146178i | \(-0.0466971\pi\) | |||||||
\(158\) | 2.34746 | + | 4.64469i | 0.186754 | + | 0.369512i | ||||
\(159\) | −32.0467 | −2.54147 | ||||||||
\(160\) | 3.93398 | + | 4.06494i | 0.311009 | + | 0.321362i | ||||
\(161\) | −5.92579 | + | 11.4140i | −0.467018 | + | 0.899548i | ||||
\(162\) | −1.79932 | − | 3.56012i | −0.141368 | − | 0.279710i | ||||
\(163\) | − | 16.6589i | − | 1.30483i | −0.757864 | − | 0.652413i | \(-0.773757\pi\) | ||
0.757864 | − | 0.652413i | \(-0.226243\pi\) | |||||||
\(164\) | 9.57420 | − | 12.9979i | 0.747620 | − | 1.01497i | ||||
\(165\) | −14.0504 | −1.09382 | ||||||||
\(166\) | −3.03245 | − | 6.00000i | −0.235364 | − | 0.465690i | ||||
\(167\) | 1.87953i | 0.145442i | 0.997352 | + | 0.0727211i | \(0.0231683\pi\) | ||||
−0.997352 | + | 0.0727211i | \(0.976832\pi\) | |||||||
\(168\) | 3.61943 | − | 21.4842i | 0.279245 | − | 1.65754i | ||||
\(169\) | −12.4706 | −0.959278 | ||||||||
\(170\) | 4.04917 | + | 8.01167i | 0.310557 | + | 0.614467i | ||||
\(171\) | −14.0814 | −1.07683 | ||||||||
\(172\) | 13.2041 | − | 17.9258i | 1.00680 | − | 1.36683i | ||||
\(173\) | 6.34755 | 0.482595 | 0.241297 | − | 0.970451i | \(-0.422427\pi\) | ||||
0.241297 | + | 0.970451i | \(0.422427\pi\) | |||||||
\(174\) | −15.5022 | + | 7.83492i | −1.17522 | + | 0.593964i | ||||
\(175\) | 2.68161 | 0.202711 | ||||||||
\(176\) | 5.80189 | + | 18.6856i | 0.437334 | + | 1.40848i | ||||
\(177\) | 5.39889 | 0.405805 | ||||||||
\(178\) | −10.2546 | + | 5.18277i | −0.768617 | + | 0.388465i | ||||
\(179\) | − | 3.09691i | − | 0.231474i | −0.993280 | − | 0.115737i | \(-0.963077\pi\) | ||
0.993280 | − | 0.115737i | \(-0.0369229\pi\) | |||||||
\(180\) | −8.45583 | − | 6.22853i | −0.630260 | − | 0.464247i | ||||
\(181\) | − | 10.7610i | − | 0.799860i | −0.916546 | − | 0.399930i | \(-0.869034\pi\) | ||
0.916546 | − | 0.399930i | \(-0.130966\pi\) | |||||||
\(182\) | 1.24464 | + | 2.46264i | 0.0922587 | + | 0.182543i | ||||
\(183\) | −19.9164 | −1.47227 | ||||||||
\(184\) | 8.16337 | − | 10.8333i | 0.601811 | − | 0.798638i | ||||
\(185\) | −3.87539 | −0.284925 | ||||||||
\(186\) | 11.2443 | + | 22.2480i | 0.824472 | + | 1.63130i | ||||
\(187\) | 31.0484i | 2.27048i | ||||||||
\(188\) | 15.7959 | + | 11.6352i | 1.15203 | + | 0.848584i | ||||
\(189\) | 17.3398i | 1.26128i | ||||||||
\(190\) | −3.38465 | + | 1.71063i | −0.245548 | + | 0.124102i | ||||
\(191\) | −4.75372 | −0.343967 | −0.171984 | − | 0.985100i | \(-0.555018\pi\) | ||||
−0.171984 | + | 0.985100i | \(0.555018\pi\) | |||||||
\(192\) | −7.52908 | + | 21.7113i | −0.543365 | + | 1.56688i | ||||
\(193\) | 21.3640 | 1.53781 | 0.768907 | − | 0.639360i | \(-0.220801\pi\) | ||||
0.768907 | + | 0.639360i | \(0.220801\pi\) | |||||||
\(194\) | −3.38809 | + | 1.71237i | −0.243251 | + | 0.122941i | ||||
\(195\) | 2.08998 | 0.149667 | ||||||||
\(196\) | −0.226613 | + | 0.307650i | −0.0161867 | + | 0.0219750i | ||||
\(197\) | 20.4988 | 1.46048 | 0.730238 | − | 0.683193i | \(-0.239409\pi\) | ||||
0.730238 | + | 0.683193i | \(0.239409\pi\) | |||||||
\(198\) | −16.3848 | − | 32.4190i | −1.16442 | − | 2.30392i | ||||
\(199\) | −15.2762 | −1.08290 | −0.541449 | − | 0.840733i | \(-0.682124\pi\) | ||||
−0.541449 | + | 0.840733i | \(0.682124\pi\) | |||||||
\(200\) | −2.78912 | − | 0.469882i | −0.197221 | − | 0.0332257i | ||||
\(201\) | − | 30.2254i | − | 2.13194i | ||||||
\(202\) | −0.981487 | − | 1.94197i | −0.0690572 | − | 0.136636i | ||||
\(203\) | 11.4661 | 0.804762 | ||||||||
\(204\) | −21.6271 | + | 29.3608i | −1.51420 | + | 2.05567i | ||||
\(205\) | 8.07172i | 0.563754i | ||||||||
\(206\) | 11.5539 | + | 22.8606i | 0.805000 | + | 1.59277i | ||||
\(207\) | −11.6038 | + | 22.3507i | −0.806518 | + | 1.55348i | ||||
\(208\) | −0.863025 | − | 2.77946i | −0.0598400 | − | 0.192721i | ||||
\(209\) | −13.1168 | −0.907311 | ||||||||
\(210\) | 4.91373 | + | 9.72230i | 0.339080 | + | 0.670903i | ||||
\(211\) | − | 26.0740i | − | 1.79501i | −0.441008 | − | 0.897503i | \(-0.645379\pi\) | ||
0.441008 | − | 0.897503i | \(-0.354621\pi\) | |||||||
\(212\) | −17.9653 | − | 13.2332i | −1.23386 | − | 0.908858i | ||||
\(213\) | −20.8216 | −1.42667 | ||||||||
\(214\) | −7.10119 | − | 14.0504i | −0.485427 | − | 0.960466i | ||||
\(215\) | 11.1319i | 0.759193i | ||||||||
\(216\) | 3.03834 | − | 18.0350i | 0.206733 | − | 1.22712i | ||||
\(217\) | − | 16.4556i | − | 1.11708i | ||||||
\(218\) | 13.4354 | − | 6.79036i | 0.909960 | − | 0.459901i | ||||
\(219\) | 22.7179i | 1.53513i | ||||||||
\(220\) | −7.87663 | − | 5.80189i | −0.531042 | − | 0.391163i | ||||
\(221\) | − | 4.61841i | − | 0.310668i | ||||||
\(222\) | −7.10119 | − | 14.0504i | −0.476600 | − | 0.943001i | ||||
\(223\) | − | 1.47929i | − | 0.0990606i | −0.998773 | − | 0.0495303i | \(-0.984228\pi\) | ||
0.998773 | − | 0.0495303i | \(-0.0157724\pi\) | |||||||
\(224\) | 10.9006 | − | 10.5494i | 0.728328 | − | 0.704863i | ||||
\(225\) | 5.25109 | 0.350072 | ||||||||
\(226\) | −6.83337 | + | 3.45364i | −0.454549 | + | 0.229733i | ||||
\(227\) | 2.20064 | 0.146062 | 0.0730308 | − | 0.997330i | \(-0.476733\pi\) | ||||
0.0730308 | + | 0.997330i | \(0.476733\pi\) | |||||||
\(228\) | −12.4039 | − | 9.13667i | −0.821469 | − | 0.605091i | ||||
\(229\) | 17.4140i | 1.15075i | 0.817890 | + | 0.575374i | \(0.195144\pi\) | ||||
−0.817890 | + | 0.575374i | \(0.804856\pi\) | |||||||
\(230\) | −0.0739292 | + | 6.78193i | −0.00487475 | + | 0.447187i | ||||
\(231\) | 37.6777i | 2.47901i | ||||||||
\(232\) | −11.9258 | − | 2.00913i | −0.782967 | − | 0.131906i | ||||
\(233\) | −26.7931 | −1.75527 | −0.877637 | − | 0.479326i | \(-0.840881\pi\) | ||||
−0.877637 | + | 0.479326i | \(0.840881\pi\) | |||||||
\(234\) | 2.43723 | + | 4.82229i | 0.159326 | + | 0.315243i | ||||
\(235\) | −9.80928 | −0.639887 | ||||||||
\(236\) | 3.02661 | + | 2.22938i | 0.197015 | + | 0.145121i | ||||
\(237\) | − | 10.5705i | − | 0.686627i | ||||||
\(238\) | 21.4842 | − | 10.8583i | 1.39261 | − | 0.703839i | ||||
\(239\) | − | 23.5866i | − | 1.52569i | −0.646583 | − | 0.762844i | \(-0.723802\pi\) | ||
0.646583 | − | 0.762844i | \(-0.276198\pi\) | |||||||
\(240\) | −3.40715 | − | 10.9731i | −0.219931 | − | 0.708310i | ||||
\(241\) | − | 0.212188i | − | 0.0136683i | −0.999977 | − | 0.00683413i | \(-0.997825\pi\) | ||
0.999977 | − | 0.00683413i | \(-0.00217539\pi\) | |||||||
\(242\) | −8.24550 | − | 16.3145i | −0.530041 | − | 1.04874i | ||||
\(243\) | − | 11.2963i | − | 0.724659i | ||||||
\(244\) | −11.1651 | − | 8.22417i | −0.714773 | − | 0.526499i | ||||
\(245\) | − | 0.191051i | − | 0.0122058i | ||||||
\(246\) | −29.2644 | + | 14.7905i | −1.86583 | + | 0.943005i | ||||
\(247\) | 1.95112 | 0.124147 | ||||||||
\(248\) | −2.88341 | + | 17.1153i | −0.183097 | + | 1.08682i | ||||
\(249\) | 13.6549i | 0.865346i | ||||||||
\(250\) | 1.26217 | − | 0.637910i | 0.0798266 | − | 0.0403450i | ||||
\(251\) | −11.1153 | −0.701589 | −0.350795 | − | 0.936452i | \(-0.614088\pi\) | ||||
−0.350795 | + | 0.936452i | \(0.614088\pi\) | |||||||
\(252\) | −16.7025 | + | 22.6753i | −1.05216 | + | 1.42841i | ||||
\(253\) | −10.8089 | + | 20.8197i | −0.679553 | + | 1.30892i | ||||
\(254\) | 3.85407 | − | 1.94788i | 0.241826 | − | 0.122221i | ||||
\(255\) | − | 18.2331i | − | 1.14180i | ||||||
\(256\) | −13.1861 | + | 9.06232i | −0.824134 | + | 0.566395i | ||||
\(257\) | 1.25450 | 0.0782533 | 0.0391267 | − | 0.999234i | \(-0.487542\pi\) | ||||
0.0391267 | + | 0.999234i | \(0.487542\pi\) | |||||||
\(258\) | −40.3594 | + | 20.3979i | −2.51266 | + | 1.26992i | ||||
\(259\) | 10.3923i | 0.645746i | ||||||||
\(260\) | 1.17164 | + | 0.863025i | 0.0726620 | + | 0.0535225i | ||||
\(261\) | 22.4527 | 1.38979 | ||||||||
\(262\) | 3.90882 | − | 1.97555i | 0.241488 | − | 0.122050i | ||||
\(263\) | −25.6760 | −1.58325 | −0.791625 | − | 0.611007i | \(-0.790765\pi\) | ||||
−0.791625 | + | 0.611007i | \(0.790765\pi\) | |||||||
\(264\) | 6.60203 | − | 39.1883i | 0.406327 | − | 2.41187i | ||||
\(265\) | 11.1565 | 0.685338 | ||||||||
\(266\) | 4.58725 | + | 9.07632i | 0.281262 | + | 0.556505i | ||||
\(267\) | 23.3377 | 1.42824 | ||||||||
\(268\) | 12.4811 | − | 16.9443i | 0.762404 | − | 1.03504i | ||||
\(269\) | 20.4193 | 1.24498 | 0.622492 | − | 0.782626i | \(-0.286120\pi\) | ||||
0.622492 | + | 0.782626i | \(0.286120\pi\) | |||||||
\(270\) | 4.12484 | + | 8.16141i | 0.251030 | + | 0.496687i | ||||
\(271\) | 3.08711i | 0.187529i | 0.995594 | + | 0.0937643i | \(0.0298900\pi\) | ||||
−0.995594 | + | 0.0937643i | \(0.970110\pi\) | |||||||
\(272\) | −24.2482 | + | 7.52908i | −1.47026 | + | 0.456518i | ||||
\(273\) | − | 5.60452i | − | 0.339201i | ||||||
\(274\) | 7.47935 | − | 3.78012i | 0.451844 | − | 0.228366i | ||||
\(275\) | 4.89140 | 0.294963 | ||||||||
\(276\) | −24.7236 | + | 12.1590i | −1.48819 | + | 0.731887i | ||||
\(277\) | 2.96451 | 0.178120 | 0.0890602 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890602 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(278\) | 4.19633 | − | 2.12086i | 0.251679 | − | 0.127201i | ||||
\(279\) | − | 32.2230i | − | 1.92914i | ||||||
\(280\) | −1.26004 | + | 7.47935i | −0.0753019 | + | 0.446977i | ||||
\(281\) | 8.93603i | 0.533079i | 0.963824 | + | 0.266539i | \(0.0858802\pi\) | ||||
−0.963824 | + | 0.266539i | \(0.914120\pi\) | |||||||
\(282\) | −17.9743 | − | 35.5640i | −1.07036 | − | 2.11780i | ||||
\(283\) | 17.2348 | 1.02450 | 0.512252 | − | 0.858835i | \(-0.328811\pi\) | ||||
0.512252 | + | 0.858835i | \(0.328811\pi\) | |||||||
\(284\) | −11.6725 | − | 8.59793i | −0.692637 | − | 0.510194i | ||||
\(285\) | 7.70285 | 0.456278 | ||||||||
\(286\) | 2.27028 | + | 4.49198i | 0.134245 | + | 0.265616i | ||||
\(287\) | 21.6452 | 1.27768 | ||||||||
\(288\) | 21.3454 | − | 20.6577i | 1.25779 | − | 1.21727i | ||||
\(289\) | −23.2913 | −1.37008 | ||||||||
\(290\) | 5.39681 | − | 2.72759i | 0.316911 | − | 0.160170i | ||||
\(291\) | 7.71069 | 0.452009 | ||||||||
\(292\) | −9.38097 | + | 12.7356i | −0.548980 | + | 0.745294i | ||||
\(293\) | − | 20.3500i | − | 1.18886i | −0.804147 | − | 0.594430i | \(-0.797378\pi\) | ||
0.804147 | − | 0.594430i | \(-0.202622\pi\) | |||||||
\(294\) | 0.692663 | − | 0.350078i | 0.0403969 | − | 0.0204169i | ||||
\(295\) | −1.87953 | −0.109430 | ||||||||
\(296\) | 1.82098 | − | 10.8089i | 0.105842 | − | 0.628257i | ||||
\(297\) | 31.6286i | 1.83528i | ||||||||
\(298\) | 18.2058 | − | 9.20136i | 1.05463 | − | 0.533021i | ||||
\(299\) | 1.60782 | − | 3.09691i | 0.0929826 | − | 0.179099i | ||||
\(300\) | 4.62554 | + | 3.40715i | 0.267056 | + | 0.196712i | ||||
\(301\) | 29.8516 | 1.72062 | ||||||||
\(302\) | 16.7971 | − | 8.48941i | 0.966567 | − | 0.488511i | ||||
\(303\) | 4.41957i | 0.253898i | ||||||||
\(304\) | −3.18077 | − | 10.2440i | −0.182430 | − | 0.587534i | ||||
\(305\) | 6.93356 | 0.397014 | ||||||||
\(306\) | 42.0700 | − | 21.2625i | 2.40498 | − | 1.21550i | ||||
\(307\) | 32.9240i | 1.87907i | 0.342449 | + | 0.939537i | \(0.388744\pi\) | ||||
−0.342449 | + | 0.939537i | \(0.611256\pi\) | |||||||
\(308\) | −15.5584 | + | 21.1221i | −0.886523 | + | 1.20354i | ||||
\(309\) | − | 52.0266i | − | 2.95969i | ||||||
\(310\) | −3.91451 | − | 7.74524i | −0.222329 | − | 0.439900i | ||||
\(311\) | − | 31.6677i | − | 1.79571i | −0.440291 | − | 0.897855i | \(-0.645125\pi\) | ||
0.440291 | − | 0.897855i | \(-0.354875\pi\) | |||||||
\(312\) | −0.982045 | + | 5.82922i | −0.0555973 | + | 0.330015i | ||||
\(313\) | − | 5.92579i | − | 0.334946i | −0.985877 | − | 0.167473i | \(-0.946439\pi\) | ||
0.985877 | − | 0.167473i | \(-0.0535606\pi\) | |||||||
\(314\) | −4.62358 | + | 2.33680i | −0.260924 | + | 0.131873i | ||||
\(315\) | − | 14.0814i | − | 0.793396i | ||||||
\(316\) | 4.36491 | − | 5.92579i | 0.245546 | − | 0.333352i | ||||
\(317\) | 14.3079 | 0.803611 | 0.401806 | − | 0.915725i | \(-0.368383\pi\) | ||||
0.401806 | + | 0.915725i | \(0.368383\pi\) | |||||||
\(318\) | 20.4429 | + | 40.4483i | 1.14638 | + | 2.26823i | ||||
\(319\) | 20.9147 | 1.17100 | ||||||||
\(320\) | 2.62112 | − | 7.55842i | 0.146525 | − | 0.422529i | ||||
\(321\) | 31.9762i | 1.78474i | ||||||||
\(322\) | 18.1865 | + | 0.198249i | 1.01349 | + | 0.0110480i | ||||
\(323\) | − | 17.0217i | − | 0.947111i | ||||||
\(324\) | −3.34568 | + | 4.54208i | −0.185871 | + | 0.252338i | ||||
\(325\) | −0.727591 | −0.0403595 | ||||||||
\(326\) | −21.0263 | + | 10.6269i | −1.16454 | + | 0.588569i | ||||
\(327\) | −30.5766 | −1.69089 | ||||||||
\(328\) | −22.5130 | − | 3.79276i | −1.24307 | − | 0.209420i | ||||
\(329\) | 26.3047i | 1.45023i | ||||||||
\(330\) | 8.96290 | + | 17.7340i | 0.493391 | + | 0.976223i | ||||
\(331\) | − | 15.1629i | − | 0.833430i | −0.909037 | − | 0.416715i | \(-0.863181\pi\) | ||
0.909037 | − | 0.416715i | \(-0.136819\pi\) | |||||||
\(332\) | −5.63858 | + | 7.65492i | −0.309457 | + | 0.420119i | ||||
\(333\) | 20.3500i | 1.11517i | ||||||||
\(334\) | 2.37228 | − | 1.19897i | 0.129805 | − | 0.0656047i | ||||
\(335\) | 10.5224i | 0.574903i | ||||||||
\(336\) | −29.4256 | + | 9.13667i | −1.60530 | + | 0.498446i | ||||
\(337\) | 11.5520i | 0.629276i | 0.949212 | + | 0.314638i | \(0.101883\pi\) | ||||
−0.949212 | + | 0.314638i | \(0.898117\pi\) | |||||||
\(338\) | 7.95513 | + | 15.7400i | 0.432702 | + | 0.856144i | ||||
\(339\) | 15.5515 | 0.844643 | ||||||||
\(340\) | 7.52908 | − | 10.2215i | 0.408322 | − | 0.554337i | ||||
\(341\) | − | 30.0158i | − | 1.62545i | ||||||
\(342\) | 8.98266 | + | 17.7731i | 0.485727 | + | 0.961058i | ||||
\(343\) | 18.2590 | 0.985892 | ||||||||
\(344\) | −31.0484 | − | 5.23070i | −1.67402 | − | 0.282021i | ||||
\(345\) | 6.34755 | − | 12.2263i | 0.341740 | − | 0.658245i | ||||
\(346\) | −4.04917 | − | 8.01167i | −0.217684 | − | 0.430710i | ||||
\(347\) | − | 3.94249i | − | 0.211644i | −0.994385 | − | 0.105822i | \(-0.966253\pi\) | ||
0.994385 | − | 0.105822i | \(-0.0337474\pi\) | |||||||
\(348\) | 19.7780 | + | 14.5684i | 1.06021 | + | 0.780947i | ||||
\(349\) | −14.2826 | −0.764532 | −0.382266 | − | 0.924052i | \(-0.624856\pi\) | ||||
−0.382266 | + | 0.924052i | \(0.624856\pi\) | |||||||
\(350\) | −1.71063 | − | 3.38465i | −0.0914370 | − | 0.180917i | ||||
\(351\) | − | 4.70473i | − | 0.251120i | ||||||
\(352\) | 19.8833 | − | 19.2427i | 1.05978 | − | 1.02564i | ||||
\(353\) | −24.2520 | −1.29080 | −0.645402 | − | 0.763843i | \(-0.723310\pi\) | ||||
−0.645402 | + | 0.763843i | \(0.723310\pi\) | |||||||
\(354\) | −3.44401 | − | 6.81431i | −0.183047 | − | 0.362176i | ||||
\(355\) | 7.24866 | 0.384719 | ||||||||
\(356\) | 13.0831 | + | 9.63693i | 0.693401 | + | 0.510756i | ||||
\(357\) | −48.8942 | −2.58776 | ||||||||
\(358\) | −3.90882 | + | 1.97555i | −0.206588 | + | 0.104411i | ||||
\(359\) | 35.2093 | 1.85828 | 0.929138 | − | 0.369734i | \(-0.120551\pi\) | ||||
0.929138 | + | 0.369734i | \(0.120551\pi\) | |||||||
\(360\) | −2.46739 | + | 14.6459i | −0.130043 | + | 0.771908i | ||||
\(361\) | −11.8089 | −0.621524 | ||||||||
\(362\) | −13.5822 | + | 6.86457i | −0.713866 | + | 0.360794i | ||||
\(363\) | 37.1290i | 1.94876i | ||||||||
\(364\) | 2.31430 | − | 3.14189i | 0.121302 | − | 0.164680i | ||||
\(365\) | − | 7.90882i | − | 0.413967i | ||||||
\(366\) | 12.7049 | + | 25.1379i | 0.664096 | + | 1.31398i | ||||
\(367\) | 4.51174 | 0.235511 | 0.117755 | − | 0.993043i | \(-0.462430\pi\) | ||||
0.117755 | + | 0.993043i | \(0.462430\pi\) | |||||||
\(368\) | −18.8809 | − | 3.39290i | −0.984235 | − | 0.176867i | ||||
\(369\) | 42.3853 | 2.20649 | ||||||||
\(370\) | 2.47215 | + | 4.89140i | 0.128521 | + | 0.254292i | ||||
\(371\) | − | 29.9174i | − | 1.55323i | ||||||
\(372\) | 20.9078 | − | 28.3844i | 1.08402 | − | 1.47166i | ||||
\(373\) | − | 1.05569i | − | 0.0546617i | −0.999626 | − | 0.0273309i | \(-0.991299\pi\) | ||
0.999626 | − | 0.0273309i | \(-0.00870077\pi\) | |||||||
\(374\) | 39.1883 | − | 19.8061i | 2.02638 | − | 1.02415i | ||||
\(375\) | −2.87247 | −0.148334 | ||||||||
\(376\) | 4.60921 | − | 27.3593i | 0.237702 | − | 1.41095i | ||||
\(377\) | −3.11105 | −0.160227 | ||||||||
\(378\) | 21.8857 | − | 11.0612i | 1.12568 | − | 0.568928i | ||||
\(379\) | 6.48253 | 0.332985 | 0.166493 | − | 0.986043i | \(-0.446756\pi\) | ||||
0.166493 | + | 0.986043i | \(0.446756\pi\) | |||||||
\(380\) | 4.31821 | + | 3.18077i | 0.221519 | + | 0.163170i | ||||
\(381\) | −8.77117 | −0.449361 | ||||||||
\(382\) | 3.03245 | + | 6.00000i | 0.155154 | + | 0.306987i | ||||
\(383\) | −1.34915 | −0.0689383 | −0.0344692 | − | 0.999406i | \(-0.510974\pi\) | ||||
−0.0344692 | + | 0.999406i | \(0.510974\pi\) | |||||||
\(384\) | 32.2063 | − | 4.34692i | 1.64352 | − | 0.221828i | ||||
\(385\) | − | 13.1168i | − | 0.668496i | ||||||
\(386\) | −13.6283 | − | 26.9650i | −0.693663 | − | 1.37248i | ||||
\(387\) | 58.4548 | 2.97143 | ||||||||
\(388\) | 4.32260 | + | 3.18401i | 0.219447 | + | 0.161643i | ||||
\(389\) | − | 10.3846i | − | 0.526519i | −0.964725 | − | 0.263259i | \(-0.915203\pi\) | ||
0.964725 | − | 0.263259i | \(-0.0847975\pi\) | |||||||
\(390\) | −1.33322 | − | 2.63791i | −0.0675103 | − | 0.133576i | ||||
\(391\) | −27.0176 | − | 14.0267i | −1.36634 | − | 0.709362i | ||||
\(392\) | 0.532865 | + | 0.0897714i | 0.0269137 | + | 0.00453414i | ||||
\(393\) | −8.89578 | −0.448733 | ||||||||
\(394\) | −13.0764 | − | 25.8729i | −0.658778 | − | 1.30346i | ||||
\(395\) | 3.67993i | 0.185157i | ||||||||
\(396\) | −30.4662 | + | 41.3608i | −1.53098 | + | 2.07846i | ||||
\(397\) | −23.4623 | −1.17754 | −0.588770 | − | 0.808300i | \(-0.700388\pi\) | ||||
−0.588770 | + | 0.808300i | \(0.700388\pi\) | |||||||
\(398\) | 9.74483 | + | 19.2811i | 0.488464 | + | 0.966474i | ||||
\(399\) | − | 20.6561i | − | 1.03410i | ||||||
\(400\) | 1.18614 | + | 3.82009i | 0.0593070 | + | 0.191004i | ||||
\(401\) | − | 26.3500i | − | 1.31586i | −0.753080 | − | 0.657929i | \(-0.771433\pi\) | ||
0.753080 | − | 0.657929i | \(-0.228567\pi\) | |||||||
\(402\) | −38.1496 | + | 19.2811i | −1.90273 | + | 0.961654i | ||||
\(403\) | 4.46482i | 0.222409i | ||||||||
\(404\) | −1.82499 | + | 2.47760i | −0.0907967 | + | 0.123265i | ||||
\(405\) | − | 2.82064i | − | 0.140159i | ||||||
\(406\) | −7.31434 | − | 14.4722i | −0.363005 | − | 0.718241i | ||||
\(407\) | 18.9561i | 0.939619i | ||||||||
\(408\) | 50.8545 | + | 8.56742i | 2.51767 | + | 0.424151i | ||||
\(409\) | 18.3538 | 0.907535 | 0.453768 | − | 0.891120i | \(-0.350080\pi\) | ||||
0.453768 | + | 0.891120i | \(0.350080\pi\) | |||||||
\(410\) | 10.1879 | − | 5.14904i | 0.503144 | − | 0.254293i | ||||
\(411\) | −17.0217 | −0.839617 | ||||||||
\(412\) | 21.4836 | − | 29.1660i | 1.05842 | − | 1.43691i | ||||
\(413\) | 5.04017i | 0.248010i | ||||||||
\(414\) | 35.6125 | + | 0.388208i | 1.75026 | + | 0.0190794i | ||||
\(415\) | − | 4.75372i | − | 0.233351i | ||||||
\(416\) | −2.95762 | + | 2.86233i | −0.145009 | + | 0.140337i | ||||
\(417\) | −9.55010 | −0.467670 | ||||||||
\(418\) | 8.36737 | + | 16.5557i | 0.409261 | + | 0.809764i | ||||
\(419\) | −20.3386 | −0.993606 | −0.496803 | − | 0.867863i | \(-0.665493\pi\) | ||||
−0.496803 | + | 0.867863i | \(0.665493\pi\) | |||||||
\(420\) | 9.13667 | − | 12.4039i | 0.445824 | − | 0.605249i | ||||
\(421\) | 9.22242i | 0.449473i | 0.974420 | + | 0.224737i | \(0.0721522\pi\) | ||||
−0.974420 | + | 0.224737i | \(0.927848\pi\) | |||||||
\(422\) | −32.9098 | + | 16.6329i | −1.60202 | + | 0.809675i | ||||
\(423\) | 51.5094i | 2.50447i | ||||||||
\(424\) | −5.24224 | + | 31.1168i | −0.254585 | + | 1.51117i | ||||
\(425\) | 6.34755i | 0.307901i | ||||||||
\(426\) | 13.2823 | + | 26.2803i | 0.643529 | + | 1.27329i | ||||
\(427\) | − | 18.5931i | − | 0.899784i | ||||||
\(428\) | −13.2041 | + | 17.9258i | −0.638242 | + | 0.866476i | ||||
\(429\) | − | 10.2229i | − | 0.493568i | ||||||
\(430\) | 14.0504 | − | 7.10119i | 0.677570 | − | 0.342450i | ||||
\(431\) | 10.2805 | 0.495192 | 0.247596 | − | 0.968863i | \(-0.420359\pi\) | ||||
0.247596 | + | 0.968863i | \(0.420359\pi\) | |||||||
\(432\) | −24.7014 | + | 7.66979i | −1.18844 | + | 0.369013i | ||||
\(433\) | − | 17.8095i | − | 0.855868i | −0.903810 | − | 0.427934i | \(-0.859242\pi\) | ||
0.903810 | − | 0.427934i | \(-0.140758\pi\) | |||||||
\(434\) | −20.7697 | + | 10.4972i | −0.996979 | + | 0.503881i | ||||
\(435\) | −12.2822 | −0.588885 | ||||||||
\(436\) | −17.1412 | − | 12.6261i | −0.820913 | − | 0.604681i | ||||
\(437\) | 5.92579 | − | 11.4140i | 0.283469 | − | 0.546005i | ||||
\(438\) | 28.6738 | − | 14.4920i | 1.37009 | − | 0.692452i | ||||
\(439\) | 14.9756i | 0.714746i | 0.933962 | + | 0.357373i | \(0.116328\pi\) | ||||
−0.933962 | + | 0.357373i | \(0.883672\pi\) | |||||||
\(440\) | −2.29838 | + | 13.6427i | −0.109571 | + | 0.650391i | ||||
\(441\) | −1.00322 | −0.0477726 | ||||||||
\(442\) | −5.82922 | + | 2.94613i | −0.277268 | + | 0.140133i | ||||
\(443\) | 14.0082i | 0.665548i | 0.943007 | + | 0.332774i | \(0.107985\pi\) | ||||
−0.943007 | + | 0.332774i | \(0.892015\pi\) | |||||||
\(444\) | −13.2041 | + | 17.9258i | −0.626637 | + | 0.850720i | ||||
\(445\) | −8.12461 | −0.385143 | ||||||||
\(446\) | −1.86711 | + | 0.943654i | −0.0884104 | + | 0.0446833i | ||||
\(447\) | −41.4332 | −1.95972 | ||||||||
\(448\) | −20.2688 | − | 7.02882i | −0.957609 | − | 0.332081i | ||||
\(449\) | −28.3872 | −1.33967 | −0.669837 | − | 0.742508i | \(-0.733636\pi\) | ||||
−0.669837 | + | 0.742508i | \(0.733636\pi\) | |||||||
\(450\) | −3.34972 | − | 6.62776i | −0.157907 | − | 0.312435i | ||||
\(451\) | 39.4820 | 1.85914 | ||||||||
\(452\) | 8.71815 | + | 6.42175i | 0.410067 | + | 0.302054i | ||||
\(453\) | −38.2273 | −1.79607 | ||||||||
\(454\) | −1.40381 | − | 2.77758i | −0.0658841 | − | 0.130358i | ||||
\(455\) | 1.95112i | 0.0914698i | ||||||||
\(456\) | −3.61943 | + | 21.4842i | −0.169495 | + | 1.00609i | ||||
\(457\) | 35.6394i | 1.66714i | 0.552413 | + | 0.833570i | \(0.313707\pi\) | ||||
−0.552413 | + | 0.833570i | \(0.686293\pi\) | |||||||
\(458\) | 21.9794 | − | 11.1086i | 1.02703 | − | 0.519069i | ||||
\(459\) | −41.0443 | −1.91579 | ||||||||
\(460\) | 8.60710 | − | 4.23295i | 0.401308 | − | 0.197362i | ||||
\(461\) | −1.09286 | −0.0508997 | −0.0254498 | − | 0.999676i | \(-0.508102\pi\) | ||||
−0.0254498 | + | 0.999676i | \(0.508102\pi\) | |||||||
\(462\) | 47.5557 | − | 24.0350i | 2.21249 | − | 1.11821i | ||||
\(463\) | 20.3766i | 0.946980i | 0.880799 | + | 0.473490i | \(0.157006\pi\) | ||||
−0.880799 | + | 0.473490i | \(0.842994\pi\) | |||||||
\(464\) | 5.07172 | + | 16.3340i | 0.235449 | + | 0.758287i | ||||
\(465\) | 17.6268i | 0.817422i | ||||||||
\(466\) | 17.0916 | + | 33.8174i | 0.791753 | + | 1.56656i | ||||
\(467\) | −30.8277 | −1.42654 | −0.713268 | − | 0.700892i | \(-0.752786\pi\) | ||||
−0.713268 | + | 0.700892i | \(0.752786\pi\) | |||||||
\(468\) | 4.53182 | − | 6.15238i | 0.209483 | − | 0.284394i | ||||
\(469\) | 28.2171 | 1.30295 | ||||||||
\(470\) | 6.25744 | + | 12.3810i | 0.288634 | + | 0.571092i | ||||
\(471\) | 10.5224 | 0.484849 | ||||||||
\(472\) | 0.883156 | − | 5.24224i | 0.0406506 | − | 0.241293i | ||||
\(473\) | 54.4508 | 2.50365 | ||||||||
\(474\) | −13.3417 | + | 6.74302i | −0.612806 | + | 0.309717i | ||||
\(475\) | −2.68161 | −0.123041 | ||||||||
\(476\) | −27.4100 | − | 20.1901i | −1.25634 | − | 0.925411i | ||||
\(477\) | − | 58.5837i | − | 2.68236i | ||||||
\(478\) | −29.7702 | + | 15.0461i | −1.36166 | + | 0.688193i | ||||
\(479\) | −14.5699 | −0.665715 | −0.332858 | − | 0.942977i | \(-0.608013\pi\) | ||||
−0.332858 | + | 0.942977i | \(0.608013\pi\) | |||||||
\(480\) | −11.6764 | + | 11.3003i | −0.532954 | + | 0.515784i | ||||
\(481\) | − | 2.81970i | − | 0.128567i | ||||||
\(482\) | −0.267818 | + | 0.135357i | −0.0121988 | + | 0.00616535i | ||||
\(483\) | −32.7863 | − | 17.0217i | −1.49183 | − | 0.774513i | ||||
\(484\) | −15.3318 | + | 20.8144i | −0.696900 | + | 0.946110i | ||||
\(485\) | −2.68434 | −0.121890 | ||||||||
\(486\) | −14.2579 | + | 7.20604i | −0.646750 | + | 0.326873i | ||||
\(487\) | − | 2.18374i | − | 0.0989549i | −0.998775 | − | 0.0494774i | \(-0.984244\pi\) | ||
0.998775 | − | 0.0494774i | \(-0.0157556\pi\) | |||||||
\(488\) | −3.25795 | + | 19.3385i | −0.147481 | + | 0.875415i | ||||
\(489\) | 47.8522 | 2.16395 | ||||||||
\(490\) | −0.241138 | + | 0.121873i | −0.0108935 | + | 0.00550568i | ||||
\(491\) | 7.55568i | 0.340983i | 0.985359 | + | 0.170491i | \(0.0545355\pi\) | ||||
−0.985359 | + | 0.170491i | \(0.945464\pi\) | |||||||
\(492\) | 37.3361 | + | 27.5016i | 1.68324 | + | 1.23987i | ||||
\(493\) | 27.1410i | 1.22237i | ||||||||
\(494\) | −1.24464 | − | 2.46264i | −0.0559989 | − | 0.110799i | ||||
\(495\) | − | 25.6852i | − | 1.15446i | ||||||
\(496\) | 23.4418 | − | 7.27870i | 1.05257 | − | 0.326823i | ||||
\(497\) | − | 19.4381i | − | 0.871919i | ||||||
\(498\) | 17.2348 | − | 8.71062i | 0.772311 | − | 0.390332i | ||||
\(499\) | − | 10.0079i | − | 0.448015i | −0.974587 | − | 0.224007i | \(-0.928086\pi\) | ||
0.974587 | − | 0.224007i | \(-0.0719140\pi\) | |||||||
\(500\) | −1.61030 | − | 1.18614i | −0.0720149 | − | 0.0530458i | ||||
\(501\) | −5.39889 | −0.241204 | ||||||||
\(502\) | 7.09054 | + | 14.0293i | 0.316466 | + | 0.626160i | ||||
\(503\) | 32.7697 | 1.46113 | 0.730563 | − | 0.682845i | \(-0.239258\pi\) | ||||
0.730563 | + | 0.682845i | \(0.239258\pi\) | |||||||
\(504\) | 39.2747 | + | 6.61659i | 1.74943 | + | 0.294726i | ||||
\(505\) | − | 1.53860i | − | 0.0684666i | ||||||
\(506\) | 33.1731 | + | 0.361617i | 1.47472 | + | 0.0160758i | ||||
\(507\) | − | 35.8215i | − | 1.59089i | ||||||
\(508\) | −4.91710 | − | 3.62191i | −0.218161 | − | 0.160696i | ||||
\(509\) | −4.89723 | −0.217066 | −0.108533 | − | 0.994093i | \(-0.534615\pi\) | ||||
−0.108533 | + | 0.994093i | \(0.534615\pi\) | |||||||
\(510\) | −23.0133 | + | 11.6311i | −1.01905 | + | 0.515034i | ||||
\(511\) | −21.2084 | −0.938204 | ||||||||
\(512\) | 19.8498 | + | 10.8622i | 0.877244 | + | 0.480045i | ||||
\(513\) | − | 17.3398i | − | 0.765570i | ||||||
\(514\) | −0.800256 | − | 1.58339i | −0.0352978 | − | 0.0698402i | ||||
\(515\) | 18.1121i | 0.798116i | ||||||||
\(516\) | 51.4913 | + | 37.9283i | 2.26678 | + | 1.66970i | ||||
\(517\) | 47.9811i | 2.11021i | ||||||||
\(518\) | 13.1168 | − | 6.62936i | 0.576321 | − | 0.291277i | ||||
\(519\) | 18.2331i | 0.800346i | ||||||||
\(520\) | 0.341882 | − | 2.02934i | 0.0149925 | − | 0.0889924i | ||||
\(521\) | 31.5065i | 1.38033i | 0.723654 | + | 0.690163i | \(0.242461\pi\) | ||||
−0.723654 | + | 0.690163i | \(0.757539\pi\) | |||||||
\(522\) | −14.3228 | − | 28.3391i | −0.626892 | − | 1.24037i | ||||
\(523\) | −29.1444 | −1.27440 | −0.637198 | − | 0.770700i | \(-0.719906\pi\) | ||||
−0.637198 | + | 0.770700i | \(0.719906\pi\) | |||||||
\(524\) | −4.98696 | − | 3.67337i | −0.217856 | − | 0.160472i | ||||
\(525\) | 7.70285i | 0.336180i | ||||||||
\(526\) | 16.3790 | + | 32.4075i | 0.714158 | + | 1.41303i | ||||
\(527\) | 38.9514 | 1.69675 | ||||||||
\(528\) | −53.6738 | + | 16.6658i | −2.33585 | + | 0.725284i | ||||
\(529\) | −13.2337 | − | 18.8114i | −0.575378 | − | 0.817888i | ||||
\(530\) | −7.11684 | − | 14.0814i | −0.309136 | − | 0.611656i | ||||
\(531\) | 9.86956i | 0.428302i | ||||||||
\(532\) | 8.52960 | − | 11.5798i | 0.369805 | − | 0.502046i | ||||
\(533\) | −5.87291 | −0.254384 | ||||||||
\(534\) | −14.8874 | − | 29.4561i | −0.644239 | − | 1.27469i | ||||
\(535\) | − | 11.1319i | − | 0.481276i | ||||||
\(536\) | −29.3484 | − | 4.94431i | −1.26766 | − | 0.213562i | ||||
\(537\) | 8.89578 | 0.383881 | ||||||||
\(538\) | −13.0257 | − | 25.7726i | −0.561576 | − | 1.11113i | ||||
\(539\) | −0.934506 | −0.0402520 | ||||||||
\(540\) | 7.66979 | − | 10.4125i | 0.330055 | − | 0.448082i | ||||
\(541\) | 10.0459 | 0.431906 | 0.215953 | − | 0.976404i | \(-0.430714\pi\) | ||||
0.215953 | + | 0.976404i | \(0.430714\pi\) | |||||||
\(542\) | 3.89645 | − | 1.96930i | 0.167367 | − | 0.0845886i | ||||
\(543\) | 30.9107 | 1.32651 | ||||||||
\(544\) | 24.9711 | + | 25.8024i | 1.07063 | + | 1.10627i | ||||
\(545\) | 10.6447 | 0.455968 | ||||||||
\(546\) | −7.07386 | + | 3.57518i | −0.302733 | + | 0.153004i | ||||
\(547\) | − | 40.9194i | − | 1.74959i | −0.484495 | − | 0.874794i | \(-0.660997\pi\) | ||
0.484495 | − | 0.874794i | \(-0.339003\pi\) | |||||||
\(548\) | −9.54231 | − | 7.02882i | −0.407627 | − | 0.300256i | ||||
\(549\) | − | 36.4087i | − | 1.55389i | ||||||
\(550\) | −3.12027 | − | 6.17377i | −0.133049 | − | 0.263251i | ||||
\(551\) | −11.4661 | −0.488472 | ||||||||
\(552\) | 31.1182 | + | 23.4490i | 1.32448 | + | 0.998057i | ||||
\(553\) | 9.86814 | 0.419636 | ||||||||
\(554\) | −1.89109 | − | 3.74172i | −0.0803449 | − | 0.158970i | ||||
\(555\) | − | 11.1319i | − | 0.472525i | ||||||
\(556\) | −5.35377 | − | 3.94356i | −0.227050 | − | 0.167244i | ||||
\(557\) | 5.20180i | 0.220407i | 0.993909 | + | 0.110204i | \(0.0351503\pi\) | ||||
−0.993909 | + | 0.110204i | \(0.964850\pi\) | |||||||
\(558\) | −40.6709 | + | 20.5554i | −1.72174 | + | 0.870180i | ||||
\(559\) | −8.09950 | −0.342572 | ||||||||
\(560\) | 10.2440 | − | 3.18077i | 0.432888 | − | 0.134412i | ||||
\(561\) | −89.1856 | −3.76542 | ||||||||
\(562\) | 11.2788 | − | 5.70038i | 0.475766 | − | 0.240456i | ||||
\(563\) | 22.2639 | 0.938311 | 0.469156 | − | 0.883115i | \(-0.344558\pi\) | ||||
0.469156 | + | 0.883115i | \(0.344558\pi\) | |||||||
\(564\) | −33.4217 | + | 45.3733i | −1.40731 | + | 1.91056i | ||||
\(565\) | −5.41399 | −0.227768 | ||||||||
\(566\) | −10.9943 | − | 21.7533i | −0.462124 | − | 0.914358i | ||||
\(567\) | −7.56387 | −0.317652 | ||||||||
\(568\) | −3.40602 | + | 20.2174i | −0.142913 | + | 0.848304i | ||||
\(569\) | − | 33.1614i | − | 1.39020i | −0.718913 | − | 0.695100i | \(-0.755360\pi\) | ||
0.718913 | − | 0.695100i | \(-0.244640\pi\) | |||||||
\(570\) | −4.91373 | − | 9.72230i | −0.205814 | − | 0.407222i | ||||
\(571\) | −3.20810 | −0.134255 | −0.0671274 | − | 0.997744i | \(-0.521383\pi\) | ||||
−0.0671274 | + | 0.997744i | \(0.521383\pi\) | |||||||
\(572\) | 4.22140 | − | 5.73096i | 0.176506 | − | 0.239623i | ||||
\(573\) | − | 13.6549i | − | 0.570443i | ||||||
\(574\) | −13.8077 | − | 27.3200i | −0.576323 | − | 1.14031i | ||||
\(575\) | −2.20979 | + | 4.25639i | −0.0921545 | + | 0.177504i | ||||
\(576\) | −39.6899 | − | 13.7637i | −1.65375 | − | 0.573488i | ||||
\(577\) | 12.3249 | 0.513091 | 0.256545 | − | 0.966532i | \(-0.417416\pi\) | ||||
0.256545 | + | 0.966532i | \(0.417416\pi\) | |||||||
\(578\) | 14.8578 | + | 29.3976i | 0.618002 | + | 1.22278i | ||||
\(579\) | 61.3675i | 2.55034i | ||||||||
\(580\) | −6.88536 | − | 5.07172i | −0.285899 | − | 0.210592i | ||||
\(581\) | −12.7476 | −0.528861 | ||||||||
\(582\) | −4.91873 | − | 9.73219i | −0.203888 | − | 0.403412i | ||||
\(583\) | − | 54.5709i | − | 2.26009i | ||||||
\(584\) | 22.0587 | + | 3.71621i | 0.912795 | + | 0.153778i | ||||
\(585\) | 3.82064i | 0.157964i | ||||||||
\(586\) | −25.6852 | + | 12.9815i | −1.06104 | + | 0.536260i | ||||
\(587\) | 8.83980i | 0.364857i | 0.983219 | + | 0.182429i | \(0.0583959\pi\) | ||||
−0.983219 | + | 0.182429i | \(0.941604\pi\) | |||||||
\(588\) | −0.883714 | − | 0.650940i | −0.0364438 | − | 0.0268443i | ||||
\(589\) | 16.4556i | 0.678041i | ||||||||
\(590\) | 1.19897 | + | 2.37228i | 0.0493608 | + | 0.0976653i | ||||
\(591\) | 58.8821i | 2.42208i | ||||||||
\(592\) | −14.8043 | + | 4.59676i | −0.608455 | + | 0.188926i | ||||
\(593\) | 2.38210 | 0.0978212 | 0.0489106 | − | 0.998803i | \(-0.484425\pi\) | ||||
0.0489106 | + | 0.998803i | \(0.484425\pi\) | |||||||
\(594\) | 39.9207 | − | 20.1762i | 1.63797 | − | 0.827841i | ||||
\(595\) | 17.0217 | 0.697820 | ||||||||
\(596\) | −23.2273 | − | 17.1092i | −0.951429 | − | 0.700818i | ||||
\(597\) | − | 43.8803i | − | 1.79590i | ||||||
\(598\) | −4.93447 | − | 0.0537902i | −0.201785 | − | 0.00219964i | ||||
\(599\) | 8.38036i | 0.342412i | 0.985235 | + | 0.171206i | \(0.0547664\pi\) | ||||
−0.985235 | + | 0.171206i | \(0.945234\pi\) | |||||||
\(600\) | 1.34972 | − | 8.01167i | 0.0551022 | − | 0.327075i | ||||
\(601\) | 29.2981 | 1.19509 | 0.597547 | − | 0.801834i | \(-0.296142\pi\) | ||||
0.597547 | + | 0.801834i | \(0.296142\pi\) | |||||||
\(602\) | −19.0426 | − | 37.6777i | −0.776120 | − | 1.53563i | ||||
\(603\) | 55.2543 | 2.25013 | ||||||||
\(604\) | −21.4301 | − | 15.7853i | −0.871980 | − | 0.642297i | ||||
\(605\) | − | 12.9258i | − | 0.525508i | ||||||
\(606\) | 5.57825 | − | 2.81929i | 0.226601 | − | 0.114526i | ||||
\(607\) | 6.58224i | 0.267165i | 0.991038 | + | 0.133582i | \(0.0426481\pi\) | ||||
−0.991038 | + | 0.133582i | \(0.957352\pi\) | |||||||
\(608\) | −10.9006 | + | 10.5494i | −0.442078 | + | 0.427836i | ||||
\(609\) | 32.9360i | 1.33464i | ||||||||
\(610\) | −4.42299 | − | 8.75132i | −0.179082 | − | 0.354331i | ||||
\(611\) | − | 7.13714i | − | 0.288738i | ||||||
\(612\) | −53.6738 | − | 39.5359i | −2.16963 | − | 1.59814i | ||||
\(613\) | − | 31.7187i | − | 1.28111i | −0.767914 | − | 0.640553i | \(-0.778705\pi\) | ||
0.767914 | − | 0.640553i | \(-0.221295\pi\) | |||||||
\(614\) | 41.5557 | − | 21.0026i | 1.67705 | − | 0.847595i | ||||
\(615\) | −23.1858 | −0.934941 | ||||||||
\(616\) | 36.5845 | + | 6.16337i | 1.47403 | + | 0.248329i | ||||
\(617\) | − | 41.9737i | − | 1.68980i | −0.534925 | − | 0.844899i | \(-0.679660\pi\) | ||
0.534925 | − | 0.844899i | \(-0.320340\pi\) | |||||||
\(618\) | −65.6663 | + | 33.1883i | −2.64149 | + | 1.33503i | ||||
\(619\) | 40.4232 | 1.62474 | 0.812372 | − | 0.583139i | \(-0.198176\pi\) | ||||
0.812372 | + | 0.583139i | \(0.198176\pi\) | |||||||
\(620\) | −7.27870 | + | 9.88154i | −0.292319 | + | 0.396852i | ||||
\(621\) | −27.5226 | − | 14.2889i | −1.10444 | − | 0.573392i | ||||
\(622\) | −39.9700 | + | 20.2011i | −1.60265 | + | 0.809992i | ||||
\(623\) | 21.7871i | 0.872880i | ||||||||
\(624\) | 7.98391 | − | 2.47901i | 0.319612 | − | 0.0992399i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.47935 | + | 3.78012i | −0.298935 | + | 0.151084i | ||||
\(627\) | − | 37.6777i | − | 1.50470i | ||||||
\(628\) | 5.89886 | + | 4.34508i | 0.235390 | + | 0.173387i | ||||
\(629\) | −24.5992 | −0.980836 | ||||||||
\(630\) | −17.7731 | + | 8.98266i | −0.708096 | + | 0.357878i | ||||
\(631\) | 3.27191 | 0.130253 | 0.0651263 | − | 0.997877i | \(-0.479255\pi\) | ||||
0.0651263 | + | 0.997877i | \(0.479255\pi\) | |||||||
\(632\) | −10.2638 | − | 1.72913i | −0.408271 | − | 0.0687812i | ||||
\(633\) | 74.8967 | 2.97688 | ||||||||
\(634\) | −9.12715 | − | 18.0590i | −0.362486 | − | 0.717214i | ||||
\(635\) | 3.05353 | 0.121176 | ||||||||
\(636\) | 38.0119 | − | 51.6048i | 1.50727 | − | 2.04627i | ||||
\(637\) | 0.139007 | 0.00550765 | ||||||||
\(638\) | −13.3417 | − | 26.3979i | −0.528204 | − | 1.04510i | ||||
\(639\) | − | 38.0633i | − | 1.50576i | ||||||
\(640\) | −11.2120 | + | 1.51330i | −0.443195 | + | 0.0598185i | ||||
\(641\) | 2.70337i | 0.106777i | 0.998574 | + | 0.0533884i | \(0.0170021\pi\) | ||||
−0.998574 | + | 0.0533884i | \(0.982998\pi\) | |||||||
\(642\) | 40.3594 | − | 20.3979i | 1.59286 | − | 0.805043i | ||||
\(643\) | −3.81007 | −0.150254 | −0.0751272 | − | 0.997174i | \(-0.523936\pi\) | ||||
−0.0751272 | + | 0.997174i | \(0.523936\pi\) | |||||||
\(644\) | −11.3511 | − | 23.0809i | −0.447297 | − | 0.909515i | ||||
\(645\) | −31.9762 | −1.25906 | ||||||||
\(646\) | −21.4842 | + | 10.8583i | −0.845285 | + | 0.427214i | ||||
\(647\) | − | 5.11436i | − | 0.201066i | −0.994934 | − | 0.100533i | \(-0.967945\pi\) | ||
0.994934 | − | 0.100533i | \(-0.0320548\pi\) | |||||||
\(648\) | 7.86711 | + | 1.32537i | 0.309049 | + | 0.0520654i | ||||
\(649\) | 9.19352i | 0.360877i | ||||||||
\(650\) | 0.464138 | + | 0.918342i | 0.0182050 | + | 0.0360203i | ||||
\(651\) | 47.2682 | 1.85259 | ||||||||
\(652\) | 26.8258 | + | 19.7598i | 1.05058 | + | 0.773853i | ||||
\(653\) | −27.5197 | −1.07693 | −0.538465 | − | 0.842648i | \(-0.680996\pi\) | ||||
−0.538465 | + | 0.842648i | \(0.680996\pi\) | |||||||
\(654\) | 19.5051 | + | 38.5928i | 0.762710 | + | 1.50910i | ||||
\(655\) | 3.09691 | 0.121006 | ||||||||
\(656\) | 9.57420 | + | 30.8347i | 0.373810 | + | 1.20389i | ||||
\(657\) | −41.5299 | −1.62024 | ||||||||
\(658\) | 33.2010 | − | 16.7800i | 1.29431 | − | 0.654154i | ||||
\(659\) | 31.4372 | 1.22462 | 0.612310 | − | 0.790618i | \(-0.290241\pi\) | ||||
0.612310 | + | 0.790618i | \(0.290241\pi\) | |||||||
\(660\) | 16.6658 | − | 22.6254i | 0.648713 | − | 0.880692i | ||||
\(661\) | − | 0.251685i | − | 0.00978943i | −0.999988 | − | 0.00489471i | \(-0.998442\pi\) | ||
0.999988 | − | 0.00489471i | \(-0.00155804\pi\) | |||||||
\(662\) | −19.1382 | + | 9.67259i | −0.743826 | + | 0.375936i | ||||
\(663\) | 13.2663 | 0.515219 | ||||||||
\(664\) | 13.2587 | + | 2.23369i | 0.514538 | + | 0.0866839i | ||||
\(665\) | 7.19105i | 0.278857i | ||||||||
\(666\) | 25.6852 | − | 12.9815i | 0.995280 | − | 0.503022i | ||||
\(667\) | −9.44865 | + | 18.1996i | −0.365853 | + | 0.704690i | ||||
\(668\) | −3.02661 | − | 2.22938i | −0.117103 | − | 0.0862575i | ||||
\(669\) | 4.24921 | 0.164284 | ||||||||
\(670\) | 13.2811 | − | 6.71238i | 0.513094 | − | 0.259322i | ||||
\(671\) | − | 33.9148i | − | 1.30927i | ||||||
\(672\) | 30.3029 | + | 31.3117i | 1.16896 | + | 1.20787i | ||||
\(673\) | −9.56375 | −0.368655 | −0.184328 | − | 0.982865i | \(-0.559011\pi\) | ||||
−0.184328 | + | 0.982865i | \(0.559011\pi\) | |||||||
\(674\) | 14.5805 | − | 7.36912i | 0.561621 | − | 0.283848i | ||||
\(675\) | 6.46618i | 0.248883i | ||||||||
\(676\) | 14.7919 | − | 20.0814i | 0.568919 | − | 0.772363i | ||||
\(677\) | 48.6951i | 1.87150i | 0.352658 | + | 0.935752i | \(0.385278\pi\) | ||||
−0.352658 | + | 0.935752i | \(0.614722\pi\) | |||||||
\(678\) | −9.92048 | − | 19.6286i | −0.380994 | − | 0.753834i | ||||
\(679\) | 7.19837i | 0.276248i | ||||||||
\(680\) | −17.7041 | − | 2.98260i | −0.678921 | − | 0.114377i | ||||
\(681\) | 6.32127i | 0.242232i | ||||||||
\(682\) | −37.8851 | + | 19.1474i | −1.45069 | + | 0.733193i | ||||
\(683\) | − | 23.9040i | − | 0.914662i | −0.889297 | − | 0.457331i | \(-0.848805\pi\) | ||
0.889297 | − | 0.457331i | \(-0.151195\pi\) | |||||||
\(684\) | 16.7025 | − | 22.6753i | 0.638636 | − | 0.867010i | ||||
\(685\) | 5.92579 | 0.226413 | ||||||||
\(686\) | −11.6476 | − | 23.0459i | −0.444707 | − | 0.879897i | ||||
\(687\) | −50.0212 | −1.90843 | ||||||||
\(688\) | 13.2041 | + | 42.5250i | 0.503400 | + | 1.62125i | ||||
\(689\) | 8.11736i | 0.309247i | ||||||||
\(690\) | −19.4809 | − | 0.212359i | −0.741625 | − | 0.00808438i | ||||
\(691\) | 32.6562i | 1.24230i | 0.783691 | + | 0.621150i | \(0.213334\pi\) | ||||
−0.783691 | + | 0.621150i | \(0.786666\pi\) | |||||||
\(692\) | −7.52908 | + | 10.2215i | −0.286213 | + | 0.388562i | ||||
\(693\) | −68.8777 | −2.61645 | ||||||||
\(694\) | −4.97609 | + | 2.51495i | −0.188890 | + | 0.0954664i | ||||
\(695\) | 3.32470 | 0.126113 | ||||||||
\(696\) | 5.77117 | − | 34.2565i | 0.218756 | − | 1.29849i | ||||
\(697\) | 51.2356i | 1.94069i | ||||||||
\(698\) | 9.11105 | + | 18.0271i | 0.344858 | + | 0.682336i | ||||
\(699\) | − | 76.9624i | − | 2.91098i | ||||||
\(700\) | −3.18077 | + | 4.31821i | −0.120222 | + | 0.163213i | ||||
\(701\) | 6.51180i | 0.245947i | 0.992410 | + | 0.122974i | \(0.0392431\pi\) | ||||
−0.992410 | + | 0.122974i | \(0.960757\pi\) | |||||||
\(702\) | −5.93816 | + | 3.00119i | −0.224121 | + | 0.113273i | ||||
\(703\) | − | 10.3923i | − | 0.391953i | ||||||
\(704\) | −36.9713 | − | 12.8209i | −1.39341 | − | 0.483207i | ||||
\(705\) | − | 28.1769i | − | 1.06120i | ||||||
\(706\) | 15.4706 | + | 30.6101i | 0.582244 | + | 1.15203i | ||||
\(707\) | −4.12592 | −0.155171 | ||||||||
\(708\) | −6.40384 | + | 8.69384i | −0.240671 | + | 0.326734i | ||||
\(709\) | 8.35583i | 0.313810i | 0.987614 | + | 0.156905i | \(0.0501516\pi\) | ||||
−0.987614 | + | 0.156905i | \(0.949848\pi\) | |||||||
\(710\) | −4.62400 | − | 9.14904i | −0.173536 | − | 0.343357i | ||||
\(711\) | 19.3236 | 0.724692 | ||||||||
\(712\) | 3.81761 | − | 22.6605i | 0.143071 | − | 0.849239i | ||||
\(713\) | 26.1191 | + | 13.5602i | 0.978169 | + | 0.507835i | ||||
\(714\) | 31.1901 | + | 61.7128i | 1.16726 | + | 2.30954i | ||||
\(715\) | 3.55894i | 0.133097i | ||||||||
\(716\) | 4.98696 | + | 3.67337i | 0.186371 | + | 0.137280i | ||||
\(717\) | 67.7517 | 2.53023 | ||||||||
\(718\) | −22.4604 | − | 44.4401i | −0.838214 | − | 1.65849i | ||||
\(719\) | − | 3.98961i | − | 0.148787i | −0.997229 | − | 0.0743937i | \(-0.976298\pi\) | ||
0.997229 | − | 0.0743937i | \(-0.0237021\pi\) | |||||||
\(720\) | 20.0596 | − | 6.22853i | 0.747577 | − | 0.232123i | ||||
\(721\) | 48.5698 | 1.80883 | ||||||||
\(722\) | 7.53305 | + | 14.9049i | 0.280351 | + | 0.554703i | ||||
\(723\) | 0.609505 | 0.0226677 | ||||||||
\(724\) | 17.3285 | + | 12.7641i | 0.644008 | + | 0.474373i | ||||
\(725\) | 4.27582 | 0.158800 | ||||||||
\(726\) | 46.8630 | − | 23.6849i | 1.73925 | − | 0.879031i | ||||
\(727\) | 26.1403 | 0.969490 | 0.484745 | − | 0.874656i | \(-0.338912\pi\) | ||||
0.484745 | + | 0.874656i | \(0.338912\pi\) | |||||||
\(728\) | −5.44191 | − | 0.916794i | −0.201690 | − | 0.0339787i | ||||
\(729\) | 40.9103 | 1.51520 | ||||||||
\(730\) | −9.98227 | + | 5.04512i | −0.369460 | + | 0.186728i | ||||
\(731\) | 70.6606i | 2.61348i | ||||||||
\(732\) | 23.6237 | − | 32.0715i | 0.873157 | − | 1.18540i | ||||
\(733\) | 46.1008i | 1.70277i | 0.524540 | + | 0.851386i | \(0.324237\pi\) | ||||
−0.524540 | + | 0.851386i | \(0.675763\pi\) | |||||||
\(734\) | −2.87808 | − | 5.69458i | −0.106232 | − | 0.210191i | ||||
\(735\) | 0.548788 | 0.0202424 | ||||||||
\(736\) | 7.76190 | + | 25.9952i | 0.286108 | + | 0.958198i | ||||
\(737\) | 51.4695 | 1.89590 | ||||||||
\(738\) | −27.0380 | − | 53.4974i | −0.995284 | − | 1.96927i | ||||
\(739\) | 32.2296i | 1.18559i | 0.805355 | + | 0.592793i | \(0.201975\pi\) | ||||
−0.805355 | + | 0.592793i | \(0.798025\pi\) | |||||||
\(740\) | 4.59676 | − | 6.24055i | 0.168980 | − | 0.229407i | ||||
\(741\) | 5.60452i | 0.205887i | ||||||||
\(742\) | −37.7608 | + | 19.0846i | −1.38624 | + | 0.700619i | ||||
\(743\) | −33.3792 | −1.22456 | −0.612281 | − | 0.790640i | \(-0.709748\pi\) | ||||
−0.612281 | + | 0.790640i | \(0.709748\pi\) | |||||||
\(744\) | −49.1633 | − | 8.28250i | −1.80241 | − | 0.303651i | ||||
\(745\) | 14.4242 | 0.528463 | ||||||||
\(746\) | −1.33246 | + | 0.673438i | −0.0487850 | + | 0.0246563i | ||||
\(747\) | −24.9622 | −0.913319 | ||||||||
\(748\) | −49.9973 | − | 36.8278i | −1.82808 | − | 1.34656i | ||||
\(749\) | −29.8516 | −1.09075 | ||||||||
\(750\) | 1.83238 | + | 3.62554i | 0.0669090 | + | 0.132386i | ||||
\(751\) | −1.95865 | −0.0714723 | −0.0357362 | − | 0.999361i | \(-0.511378\pi\) | ||||
−0.0357362 | + | 0.999361i | \(0.511378\pi\) | |||||||
\(752\) | −37.4723 | + | 11.6352i | −1.36648 | + | 0.424292i | ||||
\(753\) | − | 31.9283i | − | 1.16353i | ||||||
\(754\) | 1.98457 | + | 3.92667i | 0.0722737 | + | 0.143001i | ||||
\(755\) | 13.3082 | 0.484333 | ||||||||
\(756\) | −27.9223 | − | 20.5674i | −1.01552 | − | 0.748030i | ||||
\(757\) | − | 16.8031i | − | 0.610721i | −0.952237 | − | 0.305360i | \(-0.901223\pi\) | ||
0.952237 | − | 0.305360i | \(-0.0987769\pi\) | |||||||
\(758\) | −4.13528 | − | 8.18205i | −0.150200 | − | 0.297186i | ||||
\(759\) | −59.8040 | − | 31.0484i | −2.17075 | − | 1.12698i | ||||
\(760\) | 1.26004 | − | 7.47935i | 0.0457065 | − | 0.271305i | ||||
\(761\) | −44.9975 | −1.63116 | −0.815579 | − | 0.578646i | \(-0.803581\pi\) | ||||
−0.815579 | + | 0.578646i | \(0.803581\pi\) | |||||||
\(762\) | 5.59522 | + | 11.0707i | 0.202693 | + | 0.401049i | ||||
\(763\) | − | 28.5449i | − | 1.03340i | ||||||
\(764\) | 5.63858 | − | 7.65492i | 0.203997 | − | 0.276945i | ||||
\(765\) | 33.3315 | 1.20510 | ||||||||
\(766\) | 0.860637 | + | 1.70285i | 0.0310961 | + | 0.0615266i | ||||
\(767\) | − | 1.36753i | − | 0.0493785i | ||||||
\(768\) | −26.0313 | − | 37.8768i | −0.939322 | − | 1.36676i | ||||
\(769\) | 19.8146i | 0.714531i | 0.934003 | + | 0.357266i | \(0.116291\pi\) | ||||
−0.934003 | + | 0.357266i | \(0.883709\pi\) | |||||||
\(770\) | −16.5557 | + | 8.36737i | −0.596625 | + | 0.301539i | ||||
\(771\) | 3.60350i | 0.129777i | ||||||||
\(772\) | −25.3407 | + | 34.4025i | −0.912032 | + | 1.23817i | ||||
\(773\) | 47.4024i | 1.70494i | 0.522772 | + | 0.852472i | \(0.324898\pi\) | ||||
−0.522772 | + | 0.852472i | \(0.675102\pi\) | |||||||
\(774\) | −37.2889 | − | 73.7798i | −1.34032 | − | 2.65196i | ||||
\(775\) | − | 6.13645i | − | 0.220428i | ||||||
\(776\) | 1.26132 | − | 7.48696i | 0.0452789 | − | 0.268766i | ||||
\(777\) | −29.8516 | −1.07092 | ||||||||
\(778\) | −13.1071 | + | 6.62443i | −0.469912 | + | 0.237497i | ||||
\(779\) | −21.6452 | −0.775521 | ||||||||
\(780\) | −2.47901 | + | 3.36550i | −0.0887629 | + | 0.120504i | ||||
\(781\) | − | 35.4561i | − | 1.26872i | ||||||
\(782\) | −0.469269 | + | 43.0486i | −0.0167810 | + | 1.53941i | ||||
\(783\) | 27.6482i | 0.988066i | ||||||||
\(784\) | −0.226613 | − | 0.729831i | −0.00809333 | − | 0.0260654i | ||||
\(785\) | −3.66320 | −0.130745 | ||||||||
\(786\) | 5.67471 | + | 11.2280i | 0.202410 | + | 0.400488i | ||||
\(787\) | 28.8128 | 1.02706 | 0.513532 | − | 0.858070i | \(-0.328337\pi\) | ||||
0.513532 | + | 0.858070i | \(0.328337\pi\) | |||||||
\(788\) | −24.3144 | + | 33.0092i | −0.866165 | + | 1.17590i | ||||
\(789\) | − | 73.7536i | − | 2.62570i | ||||||
\(790\) | 4.64469 | − | 2.34746i | 0.165251 | − | 0.0835190i | ||||
\(791\) | 14.5182i | 0.516209i | ||||||||
\(792\) | 71.6391 | + | 12.0690i | 2.54558 | + | 0.428853i | ||||
\(793\) | 5.04479i | 0.179146i | ||||||||
\(794\) | 14.9669 | + | 29.6134i | 0.531154 | + | 1.05094i | ||||
\(795\) | 32.0467i | 1.13658i | ||||||||
\(796\) | 18.1197 | − | 24.5992i | 0.642235 | − | 0.871897i | ||||
\(797\) | − | 29.1492i | − | 1.03252i | −0.856432 | − | 0.516260i | \(-0.827324\pi\) | ||
0.856432 | − | 0.516260i | \(-0.172676\pi\) | |||||||
\(798\) | −26.0715 | + | 13.1767i | −0.922920 | + | 0.466451i | ||||
\(799\) | −62.2649 | −2.20277 | ||||||||
\(800\) | 4.06494 | − | 3.93398i | 0.143717 | − | 0.139087i | ||||
\(801\) | 42.6630i | 1.50742i | ||||||||
\(802\) | −33.2582 | + | 16.8089i | −1.17439 | + | 0.593545i | ||||
\(803\) | −38.6852 | −1.36517 | ||||||||
\(804\) | 48.6720 | + | 35.8516i | 1.71653 | + | 1.26439i | ||||
\(805\) | 11.4140 | + | 5.92579i | 0.402290 | + | 0.208857i | ||||
\(806\) | 5.63536 | − | 2.84816i | 0.198497 | − | 0.100322i | ||||
\(807\) | 58.6537i | 2.06471i | ||||||||
\(808\) | 4.29134 | + | 0.722959i | 0.150969 | + | 0.0254336i | ||||
\(809\) | −39.3289 | −1.38273 | −0.691365 | − | 0.722506i | \(-0.742990\pi\) | ||||
−0.691365 | + | 0.722506i | \(0.742990\pi\) | |||||||
\(810\) | −3.56012 | + | 1.79932i | −0.125090 | + | 0.0632215i | ||||
\(811\) | − | 25.2461i | − | 0.886510i | −0.896396 | − | 0.443255i | \(-0.853824\pi\) | ||
0.896396 | − | 0.443255i | \(-0.146176\pi\) | |||||||
\(812\) | −13.6004 | + | 18.4639i | −0.477281 | + | 0.647955i | ||||
\(813\) | −8.86763 | −0.311001 | ||||||||
\(814\) | 23.9258 | − | 12.0923i | 0.838599 | − | 0.423835i | ||||
\(815\) | −16.6589 | −0.583536 | ||||||||
\(816\) | −21.6271 | − | 69.6522i | −0.757099 | − | 2.43831i | ||||
\(817\) | −29.8516 | −1.04437 | ||||||||
\(818\) | −11.7081 | − | 23.1656i | −0.409363 | − | 0.809965i | ||||
\(819\) | 10.2455 | 0.358006 | ||||||||
\(820\) | −12.9979 | − | 9.57420i | −0.453907 | − | 0.334346i | ||||
\(821\) | 11.0606 | 0.386019 | 0.193009 | − | 0.981197i | \(-0.438175\pi\) | ||||
0.193009 | + | 0.981197i | \(0.438175\pi\) | |||||||
\(822\) | 10.8583 | + | 21.4842i | 0.378727 | + | 0.749348i | ||||
\(823\) | − | 9.36041i | − | 0.326283i | −0.986603 | − | 0.163142i | \(-0.947837\pi\) | ||
0.986603 | − | 0.163142i | \(-0.0521628\pi\) | |||||||
\(824\) | −50.5170 | − | 8.51057i | −1.75984 | − | 0.296480i | ||||
\(825\) | 14.0504i | 0.489172i | ||||||||
\(826\) | 6.36154 | − | 3.21517i | 0.221346 | − | 0.111870i | ||||
\(827\) | −50.8347 | −1.76770 | −0.883848 | − | 0.467775i | \(-0.845056\pi\) | ||||
−0.883848 | + | 0.467775i | \(0.845056\pi\) | |||||||
\(828\) | −22.2276 | − | 45.1966i | −0.772462 | − | 1.57069i | ||||
\(829\) | 6.23369 | 0.216505 | 0.108252 | − | 0.994123i | \(-0.465475\pi\) | ||||
0.108252 | + | 0.994123i | \(0.465475\pi\) | |||||||
\(830\) | −6.00000 | + | 3.03245i | −0.208263 | + | 0.105258i | ||||
\(831\) | 8.51548i | 0.295399i | ||||||||
\(832\) | 5.49944 | + | 1.90710i | 0.190659 | + | 0.0661168i | ||||
\(833\) | − | 1.21270i | − | 0.0420177i | ||||||
\(834\) | 6.09211 | + | 12.0538i | 0.210952 | + | 0.417390i | ||||
\(835\) | 1.87953 | 0.0650437 | ||||||||
\(836\) | 15.5584 | − | 21.1221i | 0.538099 | − | 0.730522i | ||||
\(837\) | 39.6794 | 1.37152 | ||||||||
\(838\) | 12.9742 | + | 25.6708i | 0.448187 | + | 0.886782i | ||||
\(839\) | −14.6079 | −0.504320 | −0.252160 | − | 0.967686i | \(-0.581141\pi\) | ||||
−0.252160 | + | 0.967686i | \(0.581141\pi\) | |||||||
\(840\) | −21.4842 | − | 3.61943i | −0.741276 | − | 0.124882i | ||||
\(841\) | −10.7174 | −0.369564 | ||||||||
\(842\) | 11.6403 | − | 5.88308i | 0.401150 | − | 0.202744i | ||||
\(843\) | −25.6685 | −0.884069 | ||||||||
\(844\) | 41.9869 | + | 30.9274i | 1.44525 | + | 1.06456i | ||||
\(845\) | 12.4706i | 0.429002i | ||||||||
\(846\) | 65.0135 | − | 32.8584i | 2.23521 | − | 1.12969i | ||||
\(847\) | −34.6620 | −1.19100 | ||||||||
\(848\) | 42.6188 | − | 13.2332i | 1.46354 | − | 0.454429i | ||||
\(849\) | 49.5065i | 1.69906i | ||||||||
\(850\) | 8.01167 | − | 4.04917i | 0.274798 | − | 0.138885i | ||||
\(851\) | −16.4952 | − | 8.56379i | −0.565447 | − | 0.293563i | ||||
\(852\) | 24.6973 | − | 33.5290i | 0.846116 | − | 1.14868i | ||||
\(853\) | 33.5602 | 1.14908 | 0.574541 | − | 0.818476i | \(-0.305181\pi\) | ||||
0.574541 | + | 0.818476i | \(0.305181\pi\) | |||||||
\(854\) | −23.4677 | + | 11.8607i | −0.803047 | + | 0.405866i | ||||
\(855\) | 14.0814i | 0.481573i | ||||||||
\(856\) | 31.0484 | + | 5.23070i | 1.06121 | + | 0.178782i | ||||
\(857\) | −51.6052 | −1.76280 | −0.881400 | − | 0.472372i | \(-0.843398\pi\) | ||||
−0.881400 | + | 0.472372i | \(0.843398\pi\) | |||||||
\(858\) | −12.9031 | + | 6.52132i | −0.440504 | + | 0.222634i | ||||
\(859\) | 27.1505i | 0.926365i | 0.886263 | + | 0.463182i | \(0.153292\pi\) | ||||
−0.886263 | + | 0.463182i | \(0.846708\pi\) | |||||||
\(860\) | −17.9258 | − | 13.2041i | −0.611264 | − | 0.450255i | ||||
\(861\) | 62.1753i | 2.11893i | ||||||||
\(862\) | −6.55801 | − | 12.9757i | −0.223367 | − | 0.441953i | ||||
\(863\) | 8.73671i | 0.297401i | 0.988882 | + | 0.148701i | \(0.0475091\pi\) | ||||
−0.988882 | + | 0.148701i | \(0.952491\pi\) | |||||||
\(864\) | 25.4378 | + | 26.2846i | 0.865412 | + | 0.894222i | ||||
\(865\) | − | 6.34755i | − | 0.215823i | ||||||
\(866\) | −22.4786 | + | 11.3608i | −0.763852 | + | 0.386057i | ||||
\(867\) | − | 66.9037i | − | 2.27217i | ||||||
\(868\) | 26.4985 | + | 19.5186i | 0.899417 | + | 0.662506i | ||||
\(869\) | 18.0000 | 0.610608 | ||||||||
\(870\) | 7.83492 | + | 15.5022i | 0.265629 | + | 0.525573i | ||||
\(871\) | −7.65603 | −0.259415 | ||||||||
\(872\) | −5.00175 | + | 29.6894i | −0.169381 | + | 1.00541i | ||||
\(873\) | 14.0957i | 0.477067i | ||||||||
\(874\) | −18.1865 | − | 0.198249i | −0.615168 | − | 0.00670589i | ||||
\(875\) | − | 2.68161i | − | 0.0906551i | ||||||
\(876\) | −36.5826 | − | 26.9466i | −1.23601 | − | 0.910440i | ||||
\(877\) | 15.0426 | 0.507954 | 0.253977 | − | 0.967210i | \(-0.418261\pi\) | ||||
0.253977 | + | 0.967210i | \(0.418261\pi\) | |||||||
\(878\) | 18.9017 | − | 9.55309i | 0.637903 | − | 0.322401i | ||||
\(879\) | 58.4548 | 1.97163 | ||||||||
\(880\) | 18.6856 | − | 5.80189i | 0.629891 | − | 0.195582i | ||||
\(881\) | 18.6951i | 0.629854i | 0.949116 | + | 0.314927i | \(0.101980\pi\) | ||||
−0.949116 | + | 0.314927i | \(0.898020\pi\) | |||||||
\(882\) | 0.639967 | + | 1.26624i | 0.0215488 | + | 0.0426365i | ||||
\(883\) | − | 0.220695i | − | 0.00742699i | −0.999993 | − | 0.00371350i | \(-0.998818\pi\) | ||
0.999993 | − | 0.00371350i | \(-0.00118205\pi\) | |||||||
\(884\) | 7.43704 | + | 5.47809i | 0.250135 | + | 0.184248i | ||||
\(885\) | − | 5.39889i | − | 0.181482i | ||||||
\(886\) | 17.6807 | − | 8.93595i | 0.593994 | − | 0.300209i | ||||
\(887\) | − | 36.1252i | − | 1.21297i | −0.795096 | − | 0.606483i | \(-0.792580\pi\) | ||
0.795096 | − | 0.606483i | \(-0.207420\pi\) | |||||||
\(888\) | 31.0484 | + | 5.23070i | 1.04192 | + | 0.175531i | ||||
\(889\) | − | 8.18838i | − | 0.274630i | ||||||
\(890\) | 5.18277 | + | 10.2546i | 0.173727 | + | 0.343736i | ||||
\(891\) | −13.7969 | −0.462213 | ||||||||
\(892\) | 2.38210 | + | 1.75465i | 0.0797587 | + | 0.0587499i | ||||
\(893\) | − | 26.3047i | − | 0.880254i | ||||||
\(894\) | 26.4306 | + | 52.2956i | 0.883973 | + | 1.74903i | ||||
\(895\) | −3.09691 | −0.103518 | ||||||||
\(896\) | 4.05809 | + | 30.0664i | 0.135571 | + | 1.00445i | ||||
\(897\) | 8.89578 | + | 4.61841i | 0.297021 | + | 0.154204i | ||||
\(898\) | 18.1085 | + | 35.8294i | 0.604288 | + | 1.19564i | ||||
\(899\) | − | 26.2384i | − | 0.875099i | ||||||
\(900\) | −6.22853 | + | 8.45583i | −0.207618 | + | 0.281861i | ||||
\(901\) | 70.8164 | 2.35924 | ||||||||
\(902\) | −25.1860 | − | 49.8330i | −0.838602 | − | 1.65926i | ||||
\(903\) | 85.7478i | 2.85351i | ||||||||
\(904\) | 2.54394 | − | 15.1003i | 0.0846100 | − | 0.502228i | ||||
\(905\) | −10.7610 | −0.357708 | ||||||||
\(906\) | 24.3856 | + | 48.2493i | 0.810157 | + | 1.60298i | ||||
\(907\) | 17.3062 | 0.574642 | 0.287321 | − | 0.957834i | \(-0.407235\pi\) | ||||
0.287321 | + | 0.957834i | \(0.407235\pi\) | |||||||
\(908\) | −2.61027 | + | 3.54369i | −0.0866248 | + | 0.117602i | ||||
\(909\) | −8.07930 | −0.267974 | ||||||||
\(910\) | 2.46264 | − | 1.24464i | 0.0816357 | − | 0.0412593i | ||||
\(911\) | 36.3949 | 1.20582 | 0.602909 | − | 0.797810i | \(-0.294008\pi\) | ||||
0.602909 | + | 0.797810i | \(0.294008\pi\) | |||||||
\(912\) | 29.4256 | − | 9.13667i | 0.974378 | − | 0.302545i | ||||
\(913\) | −23.2524 | −0.769541 | ||||||||
\(914\) | 44.9829 | − | 22.7347i | 1.48790 | − | 0.751998i | ||||
\(915\) | 19.9164i | 0.658417i | ||||||||
\(916\) | −28.0418 | − | 20.6554i | −0.926526 | − | 0.682475i | ||||
\(917\) | − | 8.30471i | − | 0.274246i | ||||||
\(918\) | 26.1826 | + | 51.8049i | 0.864155 | + | 1.70982i | ||||
\(919\) | 11.5400 | 0.380668 | 0.190334 | − | 0.981719i | \(-0.439043\pi\) | ||||
0.190334 | + | 0.981719i | \(0.439043\pi\) | |||||||
\(920\) | −10.8333 | − | 8.16337i | −0.357162 | − | 0.269138i | ||||
\(921\) | −94.5733 | −3.11630 | ||||||||
\(922\) | 0.697148 | + | 1.37938i | 0.0229594 | + | 0.0454274i | ||||
\(923\) | 5.27406i | 0.173598i | ||||||||
\(924\) | −60.6725 | − | 44.6911i | −1.99598 | − | 1.47023i | ||||
\(925\) | 3.87539i | 0.127422i | ||||||||
\(926\) | 25.7187 | − | 12.9984i | 0.845169 | − | 0.427155i | ||||
\(927\) | 95.1084 | 3.12377 | ||||||||
\(928\) | 17.3810 | − | 16.8210i | 0.570558 | − | 0.552177i | ||||
\(929\) | 14.6414 | 0.480368 | 0.240184 | − | 0.970727i | \(-0.422792\pi\) | ||||
0.240184 | + | 0.970727i | \(0.422792\pi\) | |||||||
\(930\) | 22.2480 | − | 11.2443i | 0.729540 | − | 0.368715i | ||||
\(931\) | 0.512325 | 0.0167908 | ||||||||
\(932\) | 31.7804 | − | 43.1450i | 1.04100 | − | 1.41326i | ||||
\(933\) | 90.9645 | 2.97804 | ||||||||
\(934\) | 19.6653 | + | 38.9098i | 0.643468 | + | 1.27317i | ||||
\(935\) | 31.0484 | 1.01539 | ||||||||
\(936\) | −10.6562 | − | 1.79525i | −0.348310 | − | 0.0586796i | ||||
\(937\) | 10.9207i | 0.356762i | 0.983961 | + | 0.178381i | \(0.0570860\pi\) | ||||
−0.983961 | + | 0.178381i | \(0.942914\pi\) | |||||||
\(938\) | −18.0000 | − | 35.6148i | −0.587721 | − | 1.16286i | ||||
\(939\) | 17.0217 | 0.555481 | ||||||||
\(940\) | 11.6352 | − | 15.7959i | 0.379498 | − | 0.515206i | ||||
\(941\) | 24.4113i | 0.795786i | 0.917432 | + | 0.397893i | \(0.130259\pi\) | ||||
−0.917432 | + | 0.397893i | \(0.869741\pi\) | |||||||
\(942\) | −6.71238 | − | 13.2811i | −0.218701 | − | 0.432722i | ||||
\(943\) | −17.8368 | + | 34.3564i | −0.580846 | + | 1.11880i | ||||
\(944\) | −7.17996 | + | 2.22938i | −0.233688 | + | 0.0725603i | ||||
\(945\) | 17.3398 | 0.564063 | ||||||||
\(946\) | −34.7347 | − | 68.7261i | −1.12932 | − | 2.23448i | ||||
\(947\) | − | 11.9194i | − | 0.387327i | −0.981068 | − | 0.193664i | \(-0.937963\pi\) | ||
0.981068 | − | 0.193664i | \(-0.0620371\pi\) | |||||||
\(948\) | 17.0217 | + | 12.5381i | 0.552838 | + | 0.407218i | ||||
\(949\) | 5.75438 | 0.186795 | ||||||||
\(950\) | 1.71063 | + | 3.38465i | 0.0555001 | + | 0.109813i | ||||
\(951\) | 41.0990i | 1.33273i | ||||||||
\(952\) | −7.99817 | + | 47.4755i | −0.259222 | + | 1.53869i | ||||
\(953\) | − | 56.4533i | − | 1.82870i | −0.404923 | − | 0.914351i | \(-0.632702\pi\) | ||
0.404923 | − | 0.914351i | \(-0.367298\pi\) | |||||||
\(954\) | −73.9425 | + | 37.3712i | −2.39398 | + | 1.20994i | ||||
\(955\) | 4.75372i | 0.153827i | ||||||||
\(956\) | 37.9815 | + | 27.9770i | 1.22841 | + | 0.904840i | ||||
\(957\) | 60.0770i | 1.94201i | ||||||||
\(958\) | 9.29429 | + | 18.3897i | 0.300285 | + | 0.594143i | ||||
\(959\) | − | 15.8907i | − | 0.513137i | ||||||
\(960\) | 21.7113 | + | 7.52908i | 0.700731 | + | 0.243000i | ||||
\(961\) | −6.65605 | −0.214711 | ||||||||
\(962\) | −3.55894 | + | 1.79872i | −0.114745 | + | 0.0579929i | ||||
\(963\) | −58.4548 | −1.88368 | ||||||||
\(964\) | 0.341687 | + | 0.251685i | 0.0110050 | + | 0.00810624i | ||||
\(965\) | − | 21.3640i | − | 0.687732i | ||||||
\(966\) | −0.569466 | + | 52.2402i | −0.0183223 | + | 1.68080i | ||||
\(967\) | − | 23.1460i | − | 0.744324i | −0.928168 | − | 0.372162i | \(-0.878617\pi\) | ||
0.928168 | − | 0.372162i | \(-0.121383\pi\) | |||||||
\(968\) | 36.0516 | + | 6.07360i | 1.15874 | + | 0.195213i | ||||
\(969\) | 48.8942 | 1.57071 | ||||||||
\(970\) | 1.71237 | + | 3.38809i | 0.0549809 | + | 0.108785i | ||||
\(971\) | −9.18083 | −0.294627 | −0.147313 | − | 0.989090i | \(-0.547063\pi\) | ||||
−0.147313 | + | 0.989090i | \(0.547063\pi\) | |||||||
\(972\) | 18.1905 | + | 13.3990i | 0.583460 | + | 0.429774i | ||||
\(973\) | − | 8.91556i | − | 0.285820i | ||||||
\(974\) | −2.75625 | + | 1.39303i | −0.0883161 | + | 0.0446356i | ||||
\(975\) | − | 2.08998i | − | 0.0669330i | ||||||
\(976\) | 26.4868 | − | 8.22417i | 0.847822 | − | 0.263249i | ||||
\(977\) | − | 56.3849i | − | 1.80391i | −0.431827 | − | 0.901956i | \(-0.642131\pi\) | ||
0.431827 | − | 0.901956i | \(-0.357869\pi\) | |||||||
\(978\) | −30.5254 | − | 60.3975i | −0.976095 | − | 1.93130i | ||||
\(979\) | 39.7407i | 1.27012i | ||||||||
\(980\) | 0.307650 | + | 0.226613i | 0.00982750 | + | 0.00723889i | ||||
\(981\) | − | 55.8962i | − | 1.78463i | ||||||
\(982\) | 9.53654 | − | 4.81984i | 0.304323 | − | 0.153807i | ||||
\(983\) | −22.0549 | −0.703441 | −0.351721 | − | 0.936105i | \(-0.614403\pi\) | ||||
−0.351721 | + | 0.936105i | \(0.614403\pi\) | |||||||
\(984\) | 10.8946 | − | 64.6680i | 0.347307 | − | 2.06154i | ||||
\(985\) | − | 20.4988i | − | 0.653145i | ||||||
\(986\) | 34.2565 | − | 17.3135i | 1.09095 | − | 0.551374i | ||||
\(987\) | −75.5595 | −2.40509 | ||||||||
\(988\) | −2.31430 | + | 3.14189i | −0.0736276 | + | 0.0999567i | ||||
\(989\) | −24.5992 | + | 47.3819i | −0.782210 | + | 1.50666i | ||||
\(990\) | −32.4190 | + | 16.3848i | −1.03034 | + | 0.520744i | ||||
\(991\) | − | 14.4702i | − | 0.459661i | −0.973231 | − | 0.229830i | \(-0.926183\pi\) | ||
0.973231 | − | 0.229830i | \(-0.0738171\pi\) | |||||||
\(992\) | −24.1407 | − | 24.9443i | −0.766468 | − | 0.791984i | ||||
\(993\) | 43.5550 | 1.38218 | ||||||||
\(994\) | −24.5342 | + | 12.3998i | −0.778177 | + | 0.393297i | ||||
\(995\) | 15.2762i | 0.484287i | ||||||||
\(996\) | −21.9885 | − | 16.1967i | −0.696734 | − | 0.513211i | ||||
\(997\) | −33.2358 | −1.05259 | −0.526294 | − | 0.850303i | \(-0.676419\pi\) | ||||
−0.526294 | + | 0.850303i | \(0.676419\pi\) | |||||||
\(998\) | −12.6316 | + | 6.38414i | −0.399848 | + | 0.202086i | ||||
\(999\) | −25.0590 | −0.792831 |
(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 | 460.2.e.a.91.5 | ✓ | 16 | |
4.3 | odd | 2 | inner | 460.2.e.a.91.7 | yes | 16 | |
23.22 | odd | 2 | inner | 460.2.e.a.91.6 | yes | 16 | |
92.91 | even | 2 | inner | 460.2.e.a.91.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.e.a.91.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
460.2.e.a.91.6 | yes | 16 | 23.22 | odd | 2 | inner | |
460.2.e.a.91.7 | yes | 16 | 4.3 | odd | 2 | inner | |
460.2.e.a.91.8 | yes | 16 | 92.91 | even | 2 | inner |