Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(769,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.769");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.k (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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.10 | ||
Character | \(\chi\) | \(=\) | 1155.769 |
Dual form | 1155.2.k.a.769.9 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.83264 | −1.29587 | −0.647936 | − | 0.761695i | \(-0.724368\pi\) | ||||
−0.647936 | + | 0.761695i | \(0.724368\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.35857 | 0.679284 | ||||||||
\(5\) | −0.538446 | + | 2.17027i | −0.240801 | + | 0.970575i | ||||
\(6\) | 1.83264 | 0.748172 | ||||||||
\(7\) | −0.996474 | − | 2.45093i | −0.376632 | − | 0.926363i | ||||
\(8\) | 1.17551 | 0.415606 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.986778 | − | 3.97732i | 0.312047 | − | 1.25774i | ||||
\(11\) | −2.65195 | + | 1.99178i | −0.799592 | + | 0.600544i | ||||
\(12\) | −1.35857 | −0.392185 | ||||||||
\(13\) | − | 1.25331i | − | 0.347607i | −0.984780 | − | 0.173803i | \(-0.944394\pi\) | ||
0.984780 | − | 0.173803i | \(-0.0556057\pi\) | |||||||
\(14\) | 1.82618 | + | 4.49167i | 0.488066 | + | 1.20045i | ||||
\(15\) | 0.538446 | − | 2.17027i | 0.139026 | − | 0.560362i | ||||
\(16\) | −4.87143 | −1.21786 | ||||||||
\(17\) | 0.900604i | 0.218429i | 0.994018 | + | 0.109214i | \(0.0348335\pi\) | ||||
−0.994018 | + | 0.109214i | \(0.965167\pi\) | |||||||
\(18\) | −1.83264 | −0.431957 | ||||||||
\(19\) | 4.96271 | 1.13852 | 0.569261 | − | 0.822157i | \(-0.307229\pi\) | ||||
0.569261 | + | 0.822157i | \(0.307229\pi\) | |||||||
\(20\) | −0.731517 | + | 2.94846i | −0.163572 | + | 0.659296i | ||||
\(21\) | 0.996474 | + | 2.45093i | 0.217448 | + | 0.534836i | ||||
\(22\) | 4.86006 | − | 3.65021i | 1.03617 | − | 0.778228i | ||||
\(23\) | 0.648612i | 0.135245i | 0.997711 | + | 0.0676225i | \(0.0215413\pi\) | ||||
−0.997711 | + | 0.0676225i | \(0.978459\pi\) | |||||||
\(24\) | −1.17551 | −0.239950 | ||||||||
\(25\) | −4.42015 | − | 2.33715i | −0.884030 | − | 0.467430i | ||||
\(26\) | 2.29687i | 0.450454i | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.35378 | − | 3.32975i | −0.255840 | − | 0.629264i | ||||
\(29\) | − | 8.58387i | − | 1.59398i | −0.603989 | − | 0.796992i | \(-0.706423\pi\) | ||
0.603989 | − | 0.796992i | \(-0.293577\pi\) | |||||||
\(30\) | −0.986778 | + | 3.97732i | −0.180160 | + | 0.726157i | ||||
\(31\) | 0.163881i | 0.0294338i | 0.999892 | + | 0.0147169i | \(0.00468471\pi\) | ||||
−0.999892 | + | 0.0147169i | \(0.995315\pi\) | |||||||
\(32\) | 6.57655 | 1.16258 | ||||||||
\(33\) | 2.65195 | − | 1.99178i | 0.461644 | − | 0.346724i | ||||
\(34\) | − | 1.65048i | − | 0.283055i | ||||||
\(35\) | 5.85572 | − | 0.842925i | 0.989798 | − | 0.142480i | ||||
\(36\) | 1.35857 | 0.226428 | ||||||||
\(37\) | − | 5.80621i | − | 0.954535i | −0.878758 | − | 0.477268i | \(-0.841627\pi\) | ||
0.878758 | − | 0.477268i | \(-0.158373\pi\) | |||||||
\(38\) | −9.09485 | −1.47538 | ||||||||
\(39\) | 1.25331i | 0.200691i | ||||||||
\(40\) | −0.632950 | + | 2.55118i | −0.100078 | + | 0.403377i | ||||
\(41\) | 7.60600 | 1.18786 | 0.593929 | − | 0.804517i | \(-0.297576\pi\) | ||||
0.593929 | + | 0.804517i | \(0.297576\pi\) | |||||||
\(42\) | −1.82618 | − | 4.49167i | −0.281785 | − | 0.693079i | ||||
\(43\) | −10.5561 | −1.60980 | −0.804898 | − | 0.593414i | \(-0.797780\pi\) | ||||
−0.804898 | + | 0.593414i | \(0.797780\pi\) | |||||||
\(44\) | −3.60285 | + | 2.70597i | −0.543150 | + | 0.407940i | ||||
\(45\) | −0.538446 | + | 2.17027i | −0.0802669 | + | 0.323525i | ||||
\(46\) | − | 1.18867i | − | 0.175260i | ||||||
\(47\) | −1.99140 | −0.290475 | −0.145238 | − | 0.989397i | \(-0.546395\pi\) | ||||
−0.145238 | + | 0.989397i | \(0.546395\pi\) | |||||||
\(48\) | 4.87143 | 0.703130 | ||||||||
\(49\) | −5.01408 | + | 4.88457i | −0.716297 | + | 0.697795i | ||||
\(50\) | 8.10054 | + | 4.28315i | 1.14559 | + | 0.605729i | ||||
\(51\) | − | 0.900604i | − | 0.126110i | ||||||
\(52\) | − | 1.70271i | − | 0.236124i | ||||||
\(53\) | 12.1331i | 1.66662i | 0.552809 | + | 0.833308i | \(0.313556\pi\) | ||||
−0.552809 | + | 0.833308i | \(0.686444\pi\) | |||||||
\(54\) | 1.83264 | 0.249391 | ||||||||
\(55\) | −2.89477 | − | 6.82791i | −0.390331 | − | 0.920675i | ||||
\(56\) | −1.17137 | − | 2.88109i | −0.156530 | − | 0.385002i | ||||
\(57\) | −4.96271 | −0.657326 | ||||||||
\(58\) | 15.7311i | 2.06560i | ||||||||
\(59\) | 0.600825i | 0.0782207i | 0.999235 | + | 0.0391104i | \(0.0124524\pi\) | ||||
−0.999235 | + | 0.0391104i | \(0.987548\pi\) | |||||||
\(60\) | 0.731517 | − | 2.94846i | 0.0944384 | − | 0.380645i | ||||
\(61\) | 5.24147 | 0.671102 | 0.335551 | − | 0.942022i | \(-0.391078\pi\) | ||||
0.335551 | + | 0.942022i | \(0.391078\pi\) | |||||||
\(62\) | − | 0.300334i | − | 0.0381425i | ||||||
\(63\) | −0.996474 | − | 2.45093i | −0.125544 | − | 0.308788i | ||||
\(64\) | −2.30959 | −0.288699 | ||||||||
\(65\) | 2.72003 | + | 0.674842i | 0.337378 | + | 0.0837039i | ||||
\(66\) | −4.86006 | + | 3.65021i | −0.598232 | + | 0.449310i | ||||
\(67\) | 6.57395i | 0.803136i | 0.915829 | + | 0.401568i | \(0.131535\pi\) | ||||
−0.915829 | + | 0.401568i | \(0.868465\pi\) | |||||||
\(68\) | 1.22353i | 0.148375i | ||||||||
\(69\) | − | 0.648612i | − | 0.0780837i | ||||||
\(70\) | −10.7314 | + | 1.54478i | −1.28265 | + | 0.184636i | ||||
\(71\) | 10.8708 | 1.29012 | 0.645062 | − | 0.764130i | \(-0.276832\pi\) | ||||
0.645062 | + | 0.764130i | \(0.276832\pi\) | |||||||
\(72\) | 1.17551 | 0.138535 | ||||||||
\(73\) | − | 1.42104i | − | 0.166321i | −0.996536 | − | 0.0831603i | \(-0.973499\pi\) | ||
0.996536 | − | 0.0831603i | \(-0.0265013\pi\) | |||||||
\(74\) | 10.6407i | 1.23696i | ||||||||
\(75\) | 4.42015 | + | 2.33715i | 0.510395 | + | 0.269871i | ||||
\(76\) | 6.74218 | 0.773381 | ||||||||
\(77\) | 7.52430 | + | 4.51497i | 0.857473 | + | 0.514528i | ||||
\(78\) | − | 2.29687i | − | 0.260070i | ||||||
\(79\) | − | 6.04097i | − | 0.679662i | −0.940486 | − | 0.339831i | \(-0.889630\pi\) | ||
0.940486 | − | 0.339831i | \(-0.110370\pi\) | |||||||
\(80\) | 2.62300 | − | 10.5723i | 0.293261 | − | 1.18202i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.9391 | −1.53931 | ||||||||
\(83\) | 6.80883i | 0.747366i | 0.927556 | + | 0.373683i | \(0.121905\pi\) | ||||
−0.927556 | + | 0.373683i | \(0.878095\pi\) | |||||||
\(84\) | 1.35378 | + | 3.32975i | 0.147709 | + | 0.363306i | ||||
\(85\) | −1.95455 | − | 0.484927i | −0.212001 | − | 0.0525977i | ||||
\(86\) | 19.3456 | 2.08609 | ||||||||
\(87\) | 8.58387i | 0.920287i | ||||||||
\(88\) | −3.11739 | + | 2.34136i | −0.332315 | + | 0.249590i | ||||
\(89\) | 13.9385i | 1.47748i | 0.673991 | + | 0.738739i | \(0.264578\pi\) | ||||
−0.673991 | + | 0.738739i | \(0.735422\pi\) | |||||||
\(90\) | 0.986778 | − | 3.97732i | 0.104016 | − | 0.419247i | ||||
\(91\) | −3.07178 | + | 1.24889i | −0.322010 | + | 0.130920i | ||||
\(92\) | 0.881184i | 0.0918698i | ||||||||
\(93\) | − | 0.163881i | − | 0.0169936i | ||||||
\(94\) | 3.64951 | 0.376419 | ||||||||
\(95\) | −2.67215 | + | 10.7704i | −0.274157 | + | 1.10502i | ||||
\(96\) | −6.57655 | −0.671216 | ||||||||
\(97\) | 19.2743 | 1.95700 | 0.978502 | − | 0.206236i | \(-0.0661214\pi\) | ||||
0.978502 | + | 0.206236i | \(0.0661214\pi\) | |||||||
\(98\) | 9.18900 | − | 8.95165i | 0.928230 | − | 0.904253i | ||||
\(99\) | −2.65195 | + | 1.99178i | −0.266531 | + | 0.200181i | ||||
\(100\) | −6.00508 | − | 3.17518i | −0.600508 | − | 0.317518i | ||||
\(101\) | 16.4453 | 1.63637 | 0.818186 | − | 0.574953i | \(-0.194980\pi\) | ||||
0.818186 | + | 0.574953i | \(0.194980\pi\) | |||||||
\(102\) | 1.65048i | 0.163422i | ||||||||
\(103\) | 9.53098 | 0.939116 | 0.469558 | − | 0.882902i | \(-0.344413\pi\) | ||||
0.469558 | + | 0.882902i | \(0.344413\pi\) | |||||||
\(104\) | − | 1.47328i | − | 0.144467i | ||||||
\(105\) | −5.85572 | + | 0.842925i | −0.571460 | + | 0.0822611i | ||||
\(106\) | − | 22.2357i | − | 2.15972i | ||||||
\(107\) | 0.883216 | 0.0853837 | 0.0426919 | − | 0.999088i | \(-0.486407\pi\) | ||||
0.0426919 | + | 0.999088i | \(0.486407\pi\) | |||||||
\(108\) | −1.35857 | −0.130728 | ||||||||
\(109\) | 12.0458i | 1.15378i | 0.816822 | + | 0.576890i | \(0.195734\pi\) | ||||
−0.816822 | + | 0.576890i | \(0.804266\pi\) | |||||||
\(110\) | 5.30507 | + | 12.5131i | 0.505819 | + | 1.19308i | ||||
\(111\) | 5.80621i | 0.551101i | ||||||||
\(112\) | 4.85425 | + | 11.9395i | 0.458684 | + | 1.12818i | ||||
\(113\) | 10.2440i | 0.963673i | 0.876261 | + | 0.481837i | \(0.160030\pi\) | ||||
−0.876261 | + | 0.481837i | \(0.839970\pi\) | |||||||
\(114\) | 9.09485 | 0.851811 | ||||||||
\(115\) | −1.40766 | − | 0.349243i | −0.131265 | − | 0.0325671i | ||||
\(116\) | − | 11.6618i | − | 1.08277i | ||||||
\(117\) | − | 1.25331i | − | 0.115869i | ||||||
\(118\) | − | 1.10110i | − | 0.101364i | ||||||
\(119\) | 2.20731 | − | 0.897428i | 0.202344 | − | 0.0822671i | ||||
\(120\) | 0.632950 | − | 2.55118i | 0.0577802 | − | 0.232890i | ||||
\(121\) | 3.06563 | − | 10.5642i | 0.278694 | − | 0.960380i | ||||
\(122\) | −9.60573 | −0.869662 | ||||||||
\(123\) | −7.60600 | −0.685810 | ||||||||
\(124\) | 0.222643i | 0.0199939i | ||||||||
\(125\) | 7.45226 | − | 8.33449i | 0.666551 | − | 0.745460i | ||||
\(126\) | 1.82618 | + | 4.49167i | 0.162689 | + | 0.400149i | ||||
\(127\) | 1.61785 | 0.143561 | 0.0717807 | − | 0.997420i | \(-0.477132\pi\) | ||||
0.0717807 | + | 0.997420i | \(0.477132\pi\) | |||||||
\(128\) | −8.92045 | −0.788464 | ||||||||
\(129\) | 10.5561 | 0.929416 | ||||||||
\(130\) | −4.98483 | − | 1.23674i | −0.437199 | − | 0.108469i | ||||
\(131\) | −7.90226 | −0.690423 | −0.345212 | − | 0.938525i | \(-0.612193\pi\) | ||||
−0.345212 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(132\) | 3.60285 | − | 2.70597i | 0.313588 | − | 0.235524i | ||||
\(133\) | −4.94521 | − | 12.1632i | −0.428804 | − | 1.05469i | ||||
\(134\) | − | 12.0477i | − | 1.04076i | ||||||
\(135\) | 0.538446 | − | 2.17027i | 0.0463421 | − | 0.186787i | ||||
\(136\) | 1.05867i | 0.0907803i | ||||||||
\(137\) | − | 3.93225i | − | 0.335955i | −0.985791 | − | 0.167977i | \(-0.946276\pi\) | ||
0.985791 | − | 0.167977i | \(-0.0537236\pi\) | |||||||
\(138\) | 1.18867i | 0.101186i | ||||||||
\(139\) | −0.108206 | −0.00917793 | −0.00458897 | − | 0.999989i | \(-0.501461\pi\) | ||||
−0.00458897 | + | 0.999989i | \(0.501461\pi\) | |||||||
\(140\) | 7.95540 | − | 1.14517i | 0.672354 | − | 0.0967847i | ||||
\(141\) | 1.99140 | 0.167706 | ||||||||
\(142\) | −19.9222 | −1.67184 | ||||||||
\(143\) | 2.49632 | + | 3.32372i | 0.208753 | + | 0.277943i | ||||
\(144\) | −4.87143 | −0.405952 | ||||||||
\(145\) | 18.6293 | + | 4.62195i | 1.54708 | + | 0.383832i | ||||
\(146\) | 2.60426i | 0.215530i | ||||||||
\(147\) | 5.01408 | − | 4.88457i | 0.413554 | − | 0.402872i | ||||
\(148\) | − | 7.88814i | − | 0.648401i | ||||||
\(149\) | 4.27007i | 0.349818i | 0.984585 | + | 0.174909i | \(0.0559631\pi\) | ||||
−0.984585 | + | 0.174909i | \(0.944037\pi\) | |||||||
\(150\) | −8.10054 | − | 4.28315i | −0.661407 | − | 0.349718i | ||||
\(151\) | 16.1520i | 1.31443i | 0.753704 | + | 0.657214i | \(0.228265\pi\) | ||||
−0.753704 | + | 0.657214i | \(0.771735\pi\) | |||||||
\(152\) | 5.83372 | 0.473177 | ||||||||
\(153\) | 0.900604i | 0.0728095i | ||||||||
\(154\) | −13.7893 | − | 8.27431i | −1.11118 | − | 0.666763i | ||||
\(155\) | −0.355665 | − | 0.0882409i | −0.0285677 | − | 0.00708768i | ||||
\(156\) | 1.70271i | 0.136326i | ||||||||
\(157\) | 16.5612 | 1.32173 | 0.660863 | − | 0.750506i | \(-0.270190\pi\) | ||||
0.660863 | + | 0.750506i | \(0.270190\pi\) | |||||||
\(158\) | 11.0709i | 0.880755i | ||||||||
\(159\) | − | 12.1331i | − | 0.962221i | ||||||
\(160\) | −3.54112 | + | 14.2729i | −0.279950 | + | 1.12837i | ||||
\(161\) | 1.58970 | − | 0.646325i | 0.125286 | − | 0.0509375i | ||||
\(162\) | −1.83264 | −0.143986 | ||||||||
\(163\) | 17.9624i | 1.40692i | 0.710735 | + | 0.703460i | \(0.248363\pi\) | ||||
−0.710735 | + | 0.703460i | \(0.751637\pi\) | |||||||
\(164\) | 10.3333 | 0.806894 | ||||||||
\(165\) | 2.89477 | + | 6.82791i | 0.225358 | + | 0.531552i | ||||
\(166\) | − | 12.4781i | − | 0.968491i | ||||||
\(167\) | 3.86148i | 0.298810i | 0.988776 | + | 0.149405i | \(0.0477359\pi\) | ||||
−0.988776 | + | 0.149405i | \(0.952264\pi\) | |||||||
\(168\) | 1.17137 | + | 2.88109i | 0.0903729 | + | 0.222281i | ||||
\(169\) | 11.4292 | 0.879170 | ||||||||
\(170\) | 3.58199 | + | 0.888696i | 0.274726 | + | 0.0681599i | ||||
\(171\) | 4.96271 | 0.379508 | ||||||||
\(172\) | −14.3412 | −1.09351 | ||||||||
\(173\) | 9.17271i | 0.697388i | 0.937237 | + | 0.348694i | \(0.113375\pi\) | ||||
−0.937237 | + | 0.348694i | \(0.886625\pi\) | |||||||
\(174\) | − | 15.7311i | − | 1.19257i | ||||||
\(175\) | −1.32362 | + | 13.1624i | −0.100056 | + | 0.994982i | ||||
\(176\) | 12.9188 | − | 9.70281i | 0.973788 | − | 0.731377i | ||||
\(177\) | − | 0.600825i | − | 0.0451608i | ||||||
\(178\) | − | 25.5443i | − | 1.91462i | ||||||
\(179\) | −17.2783 | −1.29144 | −0.645719 | − | 0.763575i | \(-0.723442\pi\) | ||||
−0.645719 | + | 0.763575i | \(0.723442\pi\) | |||||||
\(180\) | −0.731517 | + | 2.94846i | −0.0545240 | + | 0.219765i | ||||
\(181\) | 14.8336i | 1.10257i | 0.834317 | + | 0.551285i | \(0.185862\pi\) | ||||
−0.834317 | + | 0.551285i | \(0.814138\pi\) | |||||||
\(182\) | 5.62946 | − | 2.28877i | 0.417284 | − | 0.169655i | ||||
\(183\) | −5.24147 | −0.387461 | ||||||||
\(184\) | 0.762451i | 0.0562086i | ||||||||
\(185\) | 12.6011 | + | 3.12633i | 0.926448 | + | 0.229853i | ||||
\(186\) | 0.300334i | 0.0220216i | ||||||||
\(187\) | −1.79380 | − | 2.38835i | −0.131176 | − | 0.174654i | ||||
\(188\) | −2.70545 | −0.197315 | ||||||||
\(189\) | 0.996474 | + | 2.45093i | 0.0724828 | + | 0.178279i | ||||
\(190\) | 4.89709 | − | 19.7383i | 0.355272 | − | 1.43197i | ||||
\(191\) | −12.9155 | −0.934532 | −0.467266 | − | 0.884117i | \(-0.654761\pi\) | ||||
−0.467266 | + | 0.884117i | \(0.654761\pi\) | |||||||
\(192\) | 2.30959 | 0.166680 | ||||||||
\(193\) | −1.42077 | −0.102269 | −0.0511347 | − | 0.998692i | \(-0.516284\pi\) | ||||
−0.0511347 | + | 0.998692i | \(0.516284\pi\) | |||||||
\(194\) | −35.3228 | −2.53603 | ||||||||
\(195\) | −2.72003 | − | 0.674842i | −0.194785 | − | 0.0483264i | ||||
\(196\) | −6.81197 | + | 6.63602i | −0.486570 | + | 0.474002i | ||||
\(197\) | 16.4316 | 1.17070 | 0.585351 | − | 0.810780i | \(-0.300957\pi\) | ||||
0.585351 | + | 0.810780i | \(0.300957\pi\) | |||||||
\(198\) | 4.86006 | − | 3.65021i | 0.345390 | − | 0.259409i | ||||
\(199\) | − | 12.7554i | − | 0.904206i | −0.891966 | − | 0.452103i | \(-0.850674\pi\) | ||
0.891966 | − | 0.452103i | \(-0.149326\pi\) | |||||||
\(200\) | −5.19594 | − | 2.74735i | −0.367408 | − | 0.194267i | ||||
\(201\) | − | 6.57395i | − | 0.463691i | ||||||
\(202\) | −30.1384 | −2.12053 | ||||||||
\(203\) | −21.0384 | + | 8.55360i | −1.47661 | + | 0.600345i | ||||
\(204\) | − | 1.22353i | − | 0.0856644i | ||||||
\(205\) | −4.09543 | + | 16.5071i | −0.286037 | + | 1.15291i | ||||
\(206\) | −17.4669 | −1.21697 | ||||||||
\(207\) | 0.648612i | 0.0450816i | ||||||||
\(208\) | 6.10543i | 0.423335i | ||||||||
\(209\) | −13.1608 | + | 9.88462i | −0.910353 | + | 0.683733i | ||||
\(210\) | 10.7314 | − | 1.54478i | 0.740539 | − | 0.106600i | ||||
\(211\) | − | 2.34216i | − | 0.161241i | −0.996745 | − | 0.0806204i | \(-0.974310\pi\) | ||
0.996745 | − | 0.0806204i | \(-0.0256901\pi\) | |||||||
\(212\) | 16.4837i | 1.13211i | ||||||||
\(213\) | −10.8708 | −0.744853 | ||||||||
\(214\) | −1.61862 | −0.110646 | ||||||||
\(215\) | 5.68391 | − | 22.9097i | 0.387640 | − | 1.56243i | ||||
\(216\) | −1.17551 | −0.0799835 | ||||||||
\(217\) | 0.401659 | − | 0.163303i | 0.0272664 | − | 0.0110857i | ||||
\(218\) | − | 22.0757i | − | 1.49515i | ||||||
\(219\) | 1.42104i | 0.0960252i | ||||||||
\(220\) | −3.93274 | − | 9.27618i | −0.265146 | − | 0.625400i | ||||
\(221\) | 1.12874 | 0.0759272 | ||||||||
\(222\) | − | 10.6407i | − | 0.714157i | ||||||
\(223\) | 4.12809 | 0.276437 | 0.138219 | − | 0.990402i | \(-0.455862\pi\) | ||||
0.138219 | + | 0.990402i | \(0.455862\pi\) | |||||||
\(224\) | −6.55336 | − | 16.1186i | −0.437865 | − | 1.07697i | ||||
\(225\) | −4.42015 | − | 2.33715i | −0.294677 | − | 0.155810i | ||||
\(226\) | − | 18.7735i | − | 1.24880i | ||||||
\(227\) | 21.8296i | 1.44888i | 0.689336 | + | 0.724442i | \(0.257902\pi\) | ||||
−0.689336 | + | 0.724442i | \(0.742098\pi\) | |||||||
\(228\) | −6.74218 | −0.446512 | ||||||||
\(229\) | − | 1.37953i | − | 0.0911616i | −0.998961 | − | 0.0455808i | \(-0.985486\pi\) | ||
0.998961 | − | 0.0455808i | \(-0.0145139\pi\) | |||||||
\(230\) | 2.57974 | + | 0.640036i | 0.170103 | + | 0.0422027i | ||||
\(231\) | −7.52430 | − | 4.51497i | −0.495062 | − | 0.297063i | ||||
\(232\) | − | 10.0904i | − | 0.662470i | ||||||
\(233\) | −2.59060 | −0.169716 | −0.0848578 | − | 0.996393i | \(-0.527044\pi\) | ||||
−0.0848578 | + | 0.996393i | \(0.527044\pi\) | |||||||
\(234\) | 2.29687i | 0.150151i | ||||||||
\(235\) | 1.07226 | − | 4.32187i | 0.0699466 | − | 0.281928i | ||||
\(236\) | 0.816262i | 0.0531341i | ||||||||
\(237\) | 6.04097i | 0.392403i | ||||||||
\(238\) | −4.04521 | + | 1.64466i | −0.262212 | + | 0.106608i | ||||
\(239\) | − | 9.02101i | − | 0.583521i | −0.956491 | − | 0.291760i | \(-0.905759\pi\) | ||
0.956491 | − | 0.291760i | \(-0.0942410\pi\) | |||||||
\(240\) | −2.62300 | + | 10.5723i | −0.169314 | + | 0.682440i | ||||
\(241\) | −0.695298 | −0.0447881 | −0.0223940 | − | 0.999749i | \(-0.507129\pi\) | ||||
−0.0223940 | + | 0.999749i | \(0.507129\pi\) | |||||||
\(242\) | −5.61820 | + | 19.3603i | −0.361151 | + | 1.24453i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.12090 | 0.455869 | ||||||||
\(245\) | −7.90102 | − | 13.5120i | −0.504778 | − | 0.863249i | ||||
\(246\) | 13.9391 | 0.888722 | ||||||||
\(247\) | − | 6.21982i | − | 0.395758i | ||||||
\(248\) | 0.192644i | 0.0122329i | ||||||||
\(249\) | − | 6.80883i | − | 0.431492i | ||||||
\(250\) | −13.6573 | + | 15.2741i | −0.863764 | + | 0.966021i | ||||
\(251\) | − | 9.59678i | − | 0.605744i | −0.953031 | − | 0.302872i | \(-0.902055\pi\) | ||
0.953031 | − | 0.302872i | \(-0.0979454\pi\) | |||||||
\(252\) | −1.35378 | − | 3.32975i | −0.0852800 | − | 0.209755i | ||||
\(253\) | −1.29189 | − | 1.72008i | −0.0812205 | − | 0.108141i | ||||
\(254\) | −2.96494 | −0.186037 | ||||||||
\(255\) | 1.95455 | + | 0.484927i | 0.122399 | + | 0.0303673i | ||||
\(256\) | 20.9672 | 1.31045 | ||||||||
\(257\) | −4.38110 | −0.273285 | −0.136643 | − | 0.990620i | \(-0.543631\pi\) | ||||
−0.136643 | + | 0.990620i | \(0.543631\pi\) | |||||||
\(258\) | −19.3456 | −1.20440 | ||||||||
\(259\) | −14.2306 | + | 5.78574i | −0.884246 | + | 0.359508i | ||||
\(260\) | 3.69535 | + | 0.916819i | 0.229176 | + | 0.0568587i | ||||
\(261\) | − | 8.58387i | − | 0.531328i | ||||||
\(262\) | 14.4820 | 0.894700 | ||||||||
\(263\) | 2.67617 | 0.165020 | 0.0825100 | − | 0.996590i | \(-0.473706\pi\) | ||||
0.0825100 | + | 0.996590i | \(0.473706\pi\) | |||||||
\(264\) | 3.11739 | − | 2.34136i | 0.191862 | − | 0.144101i | ||||
\(265\) | −26.3322 | − | 6.53305i | −1.61758 | − | 0.401322i | ||||
\(266\) | 9.06278 | + | 22.2908i | 0.555675 | + | 1.36674i | ||||
\(267\) | − | 13.9385i | − | 0.853023i | ||||||
\(268\) | 8.93117i | 0.545558i | ||||||||
\(269\) | 16.0604i | 0.979219i | 0.871942 | + | 0.489609i | \(0.162861\pi\) | ||||
−0.871942 | + | 0.489609i | \(0.837139\pi\) | |||||||
\(270\) | −0.986778 | + | 3.97732i | −0.0600534 | + | 0.242052i | ||||
\(271\) | −25.5100 | −1.54962 | −0.774812 | − | 0.632192i | \(-0.782155\pi\) | ||||
−0.774812 | + | 0.632192i | \(0.782155\pi\) | |||||||
\(272\) | − | 4.38723i | − | 0.266015i | ||||||
\(273\) | 3.07178 | − | 1.24889i | 0.185912 | − | 0.0755865i | ||||
\(274\) | 7.20640i | 0.435354i | ||||||||
\(275\) | 16.3771 | − | 2.60597i | 0.987575 | − | 0.157146i | ||||
\(276\) | − | 0.881184i | − | 0.0530410i | ||||||
\(277\) | 23.7027 | 1.42416 | 0.712080 | − | 0.702099i | \(-0.247753\pi\) | ||||
0.712080 | + | 0.702099i | \(0.247753\pi\) | |||||||
\(278\) | 0.198303 | 0.0118934 | ||||||||
\(279\) | 0.163881i | 0.00981127i | ||||||||
\(280\) | 6.88347 | − | 0.990869i | 0.411366 | − | 0.0592157i | ||||
\(281\) | − | 24.1777i | − | 1.44232i | −0.692769 | − | 0.721160i | \(-0.743609\pi\) | ||
0.692769 | − | 0.721160i | \(-0.256391\pi\) | |||||||
\(282\) | −3.64951 | −0.217325 | ||||||||
\(283\) | − | 28.5166i | − | 1.69514i | −0.530687 | − | 0.847568i | \(-0.678066\pi\) | ||
0.530687 | − | 0.847568i | \(-0.321934\pi\) | |||||||
\(284\) | 14.7687 | 0.876361 | ||||||||
\(285\) | 2.67215 | − | 10.7704i | 0.158285 | − | 0.637984i | ||||
\(286\) | −4.57486 | − | 6.09118i | −0.270517 | − | 0.360179i | ||||
\(287\) | −7.57918 | − | 18.6418i | −0.447385 | − | 1.10039i | ||||
\(288\) | 6.57655 | 0.387527 | ||||||||
\(289\) | 16.1889 | 0.952289 | ||||||||
\(290\) | −34.1408 | − | 8.47038i | −2.00482 | − | 0.497398i | ||||
\(291\) | −19.2743 | −1.12988 | ||||||||
\(292\) | − | 1.93059i | − | 0.112979i | ||||||
\(293\) | − | 14.6498i | − | 0.855851i | −0.903814 | − | 0.427926i | \(-0.859245\pi\) | ||
0.903814 | − | 0.427926i | \(-0.140755\pi\) | |||||||
\(294\) | −9.18900 | + | 8.95165i | −0.535914 | + | 0.522071i | ||||
\(295\) | −1.30395 | − | 0.323512i | −0.0759190 | − | 0.0188356i | ||||
\(296\) | − | 6.82527i | − | 0.396711i | ||||||
\(297\) | 2.65195 | − | 1.99178i | 0.153881 | − | 0.115575i | ||||
\(298\) | − | 7.82550i | − | 0.453319i | ||||||
\(299\) | 0.812914 | 0.0470120 | ||||||||
\(300\) | 6.00508 | + | 3.17518i | 0.346703 | + | 0.183319i | ||||
\(301\) | 10.5189 | + | 25.8723i | 0.606300 | + | 1.49125i | ||||
\(302\) | − | 29.6007i | − | 1.70333i | ||||||
\(303\) | −16.4453 | −0.944760 | ||||||||
\(304\) | −24.1755 | −1.38656 | ||||||||
\(305\) | −2.82225 | + | 11.3754i | −0.161602 | + | 0.651354i | ||||
\(306\) | − | 1.65048i | − | 0.0943518i | ||||||
\(307\) | − | 27.6470i | − | 1.57790i | −0.614459 | − | 0.788949i | \(-0.710626\pi\) | ||
0.614459 | − | 0.788949i | \(-0.289374\pi\) | |||||||
\(308\) | 10.2223 | + | 6.13390i | 0.582468 | + | 0.349511i | ||||
\(309\) | −9.53098 | −0.542199 | ||||||||
\(310\) | 0.651806 | + | 0.161714i | 0.0370201 | + | 0.00918473i | ||||
\(311\) | − | 14.1431i | − | 0.801981i | −0.916082 | − | 0.400990i | \(-0.868666\pi\) | ||
0.916082 | − | 0.400990i | \(-0.131334\pi\) | |||||||
\(312\) | 1.47328i | 0.0834083i | ||||||||
\(313\) | −26.8476 | −1.51752 | −0.758758 | − | 0.651373i | \(-0.774193\pi\) | ||||
−0.758758 | + | 0.651373i | \(0.774193\pi\) | |||||||
\(314\) | −30.3507 | −1.71279 | ||||||||
\(315\) | 5.85572 | − | 0.842925i | 0.329933 | − | 0.0474934i | ||||
\(316\) | − | 8.20708i | − | 0.461684i | ||||||
\(317\) | 16.0419i | 0.901005i | 0.892775 | + | 0.450503i | \(0.148755\pi\) | ||||
−0.892775 | + | 0.450503i | \(0.851245\pi\) | |||||||
\(318\) | 22.2357i | 1.24692i | ||||||||
\(319\) | 17.0972 | + | 22.7640i | 0.957258 | + | 1.27454i | ||||
\(320\) | 1.24359 | − | 5.01244i | 0.0695188 | − | 0.280204i | ||||
\(321\) | −0.883216 | −0.0492963 | ||||||||
\(322\) | −2.91335 | + | 1.18448i | −0.162355 | + | 0.0660085i | ||||
\(323\) | 4.46943i | 0.248686i | ||||||||
\(324\) | 1.35857 | 0.0754761 | ||||||||
\(325\) | −2.92918 | + | 5.53983i | −0.162482 | + | 0.307295i | ||||
\(326\) | − | 32.9185i | − | 1.82319i | ||||||
\(327\) | − | 12.0458i | − | 0.666136i | ||||||
\(328\) | 8.94095 | 0.493681 | ||||||||
\(329\) | 1.98437 | + | 4.88077i | 0.109402 | + | 0.269085i | ||||
\(330\) | −5.30507 | − | 12.5131i | −0.292035 | − | 0.688823i | ||||
\(331\) | 27.2861 | 1.49978 | 0.749890 | − | 0.661562i | \(-0.230106\pi\) | ||||
0.749890 | + | 0.661562i | \(0.230106\pi\) | |||||||
\(332\) | 9.25026i | 0.507674i | ||||||||
\(333\) | − | 5.80621i | − | 0.318178i | ||||||
\(334\) | − | 7.07671i | − | 0.387220i | ||||||
\(335\) | −14.2673 | − | 3.53972i | −0.779504 | − | 0.193396i | ||||
\(336\) | −4.85425 | − | 11.9395i | −0.264821 | − | 0.651354i | ||||
\(337\) | 7.08104 | 0.385729 | 0.192865 | − | 0.981225i | \(-0.438222\pi\) | ||||
0.192865 | + | 0.981225i | \(0.438222\pi\) | |||||||
\(338\) | −20.9456 | −1.13929 | ||||||||
\(339\) | − | 10.2440i | − | 0.556377i | ||||||
\(340\) | −2.65540 | − | 0.658807i | −0.144009 | − | 0.0357288i | ||||
\(341\) | −0.326414 | − | 0.434602i | −0.0176763 | − | 0.0235350i | ||||
\(342\) | −9.09485 | −0.491793 | ||||||||
\(343\) | 16.9681 | + | 7.42180i | 0.916192 | + | 0.400740i | ||||
\(344\) | −12.4089 | −0.669041 | ||||||||
\(345\) | 1.40766 | + | 0.349243i | 0.0757861 | + | 0.0188026i | ||||
\(346\) | − | 16.8103i | − | 0.903726i | ||||||
\(347\) | 15.8426 | 0.850477 | 0.425239 | − | 0.905081i | \(-0.360190\pi\) | ||||
0.425239 | + | 0.905081i | \(0.360190\pi\) | |||||||
\(348\) | 11.6618i | 0.625137i | ||||||||
\(349\) | 16.4924 | 0.882820 | 0.441410 | − | 0.897305i | \(-0.354478\pi\) | ||||
0.441410 | + | 0.897305i | \(0.354478\pi\) | |||||||
\(350\) | 2.42571 | − | 24.1219i | 0.129660 | − | 1.28937i | ||||
\(351\) | 1.25331i | 0.0668969i | ||||||||
\(352\) | −17.4407 | + | 13.0990i | −0.929590 | + | 0.698181i | ||||
\(353\) | −22.5281 | −1.19905 | −0.599525 | − | 0.800356i | \(-0.704644\pi\) | ||||
−0.599525 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(354\) | 1.10110i | 0.0585226i | ||||||||
\(355\) | −5.85333 | + | 23.5925i | −0.310663 | + | 1.25216i | ||||
\(356\) | 18.9364i | 1.00363i | ||||||||
\(357\) | −2.20731 | + | 0.897428i | −0.116823 | + | 0.0474969i | ||||
\(358\) | 31.6648 | 1.67354 | ||||||||
\(359\) | − | 14.2371i | − | 0.751403i | −0.926741 | − | 0.375702i | \(-0.877402\pi\) | ||
0.926741 | − | 0.375702i | \(-0.122598\pi\) | |||||||
\(360\) | −0.632950 | + | 2.55118i | −0.0333594 | + | 0.134459i | ||||
\(361\) | 5.62845 | 0.296234 | ||||||||
\(362\) | − | 27.1846i | − | 1.42879i | ||||||
\(363\) | −3.06563 | + | 10.5642i | −0.160904 | + | 0.554476i | ||||
\(364\) | −4.17322 | + | 1.69671i | −0.218736 | + | 0.0889317i | ||||
\(365\) | 3.08405 | + | 0.765156i | 0.161427 | + | 0.0400501i | ||||
\(366\) | 9.60573 | 0.502100 | ||||||||
\(367\) | 19.6640 | 1.02645 | 0.513226 | − | 0.858254i | \(-0.328450\pi\) | ||||
0.513226 | + | 0.858254i | \(0.328450\pi\) | |||||||
\(368\) | − | 3.15967i | − | 0.164709i | ||||||
\(369\) | 7.60600 | 0.395953 | ||||||||
\(370\) | −23.0932 | − | 5.72945i | −1.20056 | − | 0.297860i | ||||
\(371\) | 29.7375 | − | 12.0904i | 1.54389 | − | 0.627700i | ||||
\(372\) | − | 0.222643i | − | 0.0115435i | ||||||
\(373\) | −7.37461 | −0.381843 | −0.190922 | − | 0.981605i | \(-0.561148\pi\) | ||||
−0.190922 | + | 0.981605i | \(0.561148\pi\) | |||||||
\(374\) | 3.28740 | + | 4.37699i | 0.169987 | + | 0.226329i | ||||
\(375\) | −7.45226 | + | 8.33449i | −0.384833 | + | 0.430391i | ||||
\(376\) | −2.34091 | −0.120723 | ||||||||
\(377\) | −10.7583 | −0.554079 | ||||||||
\(378\) | −1.82618 | − | 4.49167i | −0.0939284 | − | 0.231026i | ||||
\(379\) | −5.17238 | −0.265687 | −0.132844 | − | 0.991137i | \(-0.542411\pi\) | ||||
−0.132844 | + | 0.991137i | \(0.542411\pi\) | |||||||
\(380\) | −3.63030 | + | 14.6324i | −0.186231 | + | 0.750624i | ||||
\(381\) | −1.61785 | −0.0828852 | ||||||||
\(382\) | 23.6694 | 1.21103 | ||||||||
\(383\) | 19.7084 | 1.00705 | 0.503527 | − | 0.863980i | \(-0.332035\pi\) | ||||
0.503527 | + | 0.863980i | \(0.332035\pi\) | |||||||
\(384\) | 8.92045 | 0.455220 | ||||||||
\(385\) | −13.8501 | + | 13.8987i | −0.705868 | + | 0.708343i | ||||
\(386\) | 2.60376 | 0.132528 | ||||||||
\(387\) | −10.5561 | −0.536598 | ||||||||
\(388\) | 26.1854 | 1.32936 | ||||||||
\(389\) | −36.6557 | −1.85852 | −0.929258 | − | 0.369431i | \(-0.879553\pi\) | ||||
−0.929258 | + | 0.369431i | \(0.879553\pi\) | |||||||
\(390\) | 4.98483 | + | 1.23674i | 0.252417 | + | 0.0626249i | ||||
\(391\) | −0.584142 | −0.0295413 | ||||||||
\(392\) | −5.89411 | + | 5.74187i | −0.297698 | + | 0.290008i | ||||
\(393\) | 7.90226 | 0.398616 | ||||||||
\(394\) | −30.1132 | −1.51708 | ||||||||
\(395\) | 13.1105 | + | 3.25274i | 0.659663 | + | 0.163663i | ||||
\(396\) | −3.60285 | + | 2.70597i | −0.181050 | + | 0.135980i | ||||
\(397\) | −19.4173 | −0.974525 | −0.487263 | − | 0.873255i | \(-0.662005\pi\) | ||||
−0.487263 | + | 0.873255i | \(0.662005\pi\) | |||||||
\(398\) | 23.3760i | 1.17174i | ||||||||
\(399\) | 4.94521 | + | 12.1632i | 0.247570 | + | 0.608923i | ||||
\(400\) | 21.5324 | + | 11.3853i | 1.07662 | + | 0.569263i | ||||
\(401\) | 22.8621 | 1.14168 | 0.570840 | − | 0.821061i | \(-0.306618\pi\) | ||||
0.570840 | + | 0.821061i | \(0.306618\pi\) | |||||||
\(402\) | 12.0477i | 0.600884i | ||||||||
\(403\) | 0.205394 | 0.0102314 | ||||||||
\(404\) | 22.3421 | 1.11156 | ||||||||
\(405\) | −0.538446 | + | 2.17027i | −0.0267556 | + | 0.107842i | ||||
\(406\) | 38.5559 | − | 15.6757i | 1.91350 | − | 0.777970i | ||||
\(407\) | 11.5647 | + | 15.3978i | 0.573241 | + | 0.763239i | ||||
\(408\) | − | 1.05867i | − | 0.0524120i | ||||||
\(409\) | 1.25943 | 0.0622746 | 0.0311373 | − | 0.999515i | \(-0.490087\pi\) | ||||
0.0311373 | + | 0.999515i | \(0.490087\pi\) | |||||||
\(410\) | 7.50544 | − | 30.2515i | 0.370667 | − | 1.49402i | ||||
\(411\) | 3.93225i | 0.193964i | ||||||||
\(412\) | 12.9485 | 0.637927 | ||||||||
\(413\) | 1.47258 | − | 0.598706i | 0.0724608 | − | 0.0294604i | ||||
\(414\) | − | 1.18867i | − | 0.0584200i | ||||||
\(415\) | −14.7770 | − | 3.66619i | −0.725374 | − | 0.179966i | ||||
\(416\) | − | 8.24248i | − | 0.404121i | ||||||
\(417\) | 0.108206 | 0.00529888 | ||||||||
\(418\) | 24.1191 | − | 18.1149i | 1.17970 | − | 0.886031i | ||||
\(419\) | 39.4012i | 1.92487i | 0.271508 | + | 0.962436i | \(0.412478\pi\) | ||||
−0.271508 | + | 0.962436i | \(0.587522\pi\) | |||||||
\(420\) | −7.95540 | + | 1.14517i | −0.388184 | + | 0.0558787i | ||||
\(421\) | 6.21963 | 0.303126 | 0.151563 | − | 0.988448i | \(-0.451569\pi\) | ||||
0.151563 | + | 0.988448i | \(0.451569\pi\) | |||||||
\(422\) | 4.29233i | 0.208947i | ||||||||
\(423\) | −1.99140 | −0.0968250 | ||||||||
\(424\) | 14.2627i | 0.692656i | ||||||||
\(425\) | 2.10485 | − | 3.98080i | 0.102100 | − | 0.193097i | ||||
\(426\) | 19.9222 | 0.965235 | ||||||||
\(427\) | −5.22299 | − | 12.8465i | −0.252758 | − | 0.621684i | ||||
\(428\) | 1.19991 | 0.0579998 | ||||||||
\(429\) | −2.49632 | − | 3.32372i | −0.120524 | − | 0.160471i | ||||
\(430\) | −10.4166 | + | 41.9852i | −0.502331 | + | 2.02470i | ||||
\(431\) | − | 7.39679i | − | 0.356291i | −0.984004 | − | 0.178145i | \(-0.942990\pi\) | ||
0.984004 | − | 0.178145i | \(-0.0570097\pi\) | |||||||
\(432\) | 4.87143 | 0.234377 | ||||||||
\(433\) | 25.6828 | 1.23424 | 0.617118 | − | 0.786870i | \(-0.288300\pi\) | ||||
0.617118 | + | 0.786870i | \(0.288300\pi\) | |||||||
\(434\) | −0.736097 | + | 0.299275i | −0.0353338 | + | 0.0143657i | ||||
\(435\) | −18.6293 | − | 4.62195i | −0.893208 | − | 0.221606i | ||||
\(436\) | 16.3651i | 0.783746i | ||||||||
\(437\) | 3.21887i | 0.153979i | ||||||||
\(438\) | − | 2.60426i | − | 0.124436i | ||||||
\(439\) | 32.2236 | 1.53795 | 0.768975 | − | 0.639278i | \(-0.220767\pi\) | ||||
0.768975 | + | 0.639278i | \(0.220767\pi\) | |||||||
\(440\) | −3.40284 | − | 8.02629i | −0.162224 | − | 0.382638i | ||||
\(441\) | −5.01408 | + | 4.88457i | −0.238766 | + | 0.232598i | ||||
\(442\) | −2.06857 | −0.0983919 | ||||||||
\(443\) | 29.6173i | 1.40716i | 0.710617 | + | 0.703579i | \(0.248416\pi\) | ||||
−0.710617 | + | 0.703579i | \(0.751584\pi\) | |||||||
\(444\) | 7.88814i | 0.374355i | ||||||||
\(445\) | −30.2503 | − | 7.50514i | −1.43400 | − | 0.355778i | ||||
\(446\) | −7.56530 | −0.358227 | ||||||||
\(447\) | − | 4.27007i | − | 0.201967i | ||||||
\(448\) | 2.30145 | + | 5.66064i | 0.108733 | + | 0.267440i | ||||
\(449\) | −3.86846 | −0.182564 | −0.0912819 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912819 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(450\) | 8.10054 | + | 4.28315i | 0.381863 | + | 0.201910i | ||||
\(451\) | −20.1707 | + | 15.1495i | −0.949802 | + | 0.713361i | ||||
\(452\) | 13.9172i | 0.654608i | ||||||||
\(453\) | − | 16.1520i | − | 0.758885i | ||||||
\(454\) | − | 40.0059i | − | 1.87757i | ||||||
\(455\) | −1.05645 | − | 7.33905i | −0.0495271 | − | 0.344060i | ||||
\(456\) | −5.83372 | −0.273189 | ||||||||
\(457\) | −12.1915 | −0.570295 | −0.285148 | − | 0.958484i | \(-0.592043\pi\) | ||||
−0.285148 | + | 0.958484i | \(0.592043\pi\) | |||||||
\(458\) | 2.52817i | 0.118134i | ||||||||
\(459\) | − | 0.900604i | − | 0.0420366i | ||||||
\(460\) | −1.91241 | − | 0.474470i | −0.0891665 | − | 0.0221223i | ||||
\(461\) | 27.4628 | 1.27907 | 0.639534 | − | 0.768763i | \(-0.279127\pi\) | ||||
0.639534 | + | 0.768763i | \(0.279127\pi\) | |||||||
\(462\) | 13.7893 | + | 8.27431i | 0.641538 | + | 0.384956i | ||||
\(463\) | − | 17.1399i | − | 0.796557i | −0.917265 | − | 0.398279i | \(-0.869608\pi\) | ||
0.917265 | − | 0.398279i | \(-0.130392\pi\) | |||||||
\(464\) | 41.8157i | 1.94125i | ||||||||
\(465\) | 0.355665 | + | 0.0882409i | 0.0164936 | + | 0.00409207i | ||||
\(466\) | 4.74763 | 0.219930 | ||||||||
\(467\) | −2.44194 | −0.113000 | −0.0564998 | − | 0.998403i | \(-0.517994\pi\) | ||||
−0.0564998 | + | 0.998403i | \(0.517994\pi\) | |||||||
\(468\) | − | 1.70271i | − | 0.0787079i | ||||||
\(469\) | 16.1123 | − | 6.55077i | 0.743996 | − | 0.302487i | ||||
\(470\) | −1.96507 | + | 7.92043i | −0.0906418 | + | 0.365342i | ||||
\(471\) | −16.5612 | −0.763099 | ||||||||
\(472\) | 0.706277i | 0.0325090i | ||||||||
\(473\) | 27.9943 | − | 21.0255i | 1.28718 | − | 0.966753i | ||||
\(474\) | − | 11.0709i | − | 0.508504i | ||||||
\(475\) | −21.9359 | − | 11.5986i | −1.00649 | − | 0.532180i | ||||
\(476\) | 2.99879 | − | 1.21922i | 0.137449 | − | 0.0558828i | ||||
\(477\) | 12.1331i | 0.555539i | ||||||||
\(478\) | 16.5323i | 0.756168i | ||||||||
\(479\) | −27.3292 | −1.24870 | −0.624352 | − | 0.781143i | \(-0.714637\pi\) | ||||
−0.624352 | + | 0.781143i | \(0.714637\pi\) | |||||||
\(480\) | 3.54112 | − | 14.2729i | 0.161629 | − | 0.651465i | ||||
\(481\) | −7.27700 | −0.331803 | ||||||||
\(482\) | 1.27423 | 0.0580396 | ||||||||
\(483\) | −1.58970 | + | 0.646325i | −0.0723339 | + | 0.0294088i | ||||
\(484\) | 4.16487 | − | 14.3522i | 0.189312 | − | 0.652371i | ||||
\(485\) | −10.3782 | + | 41.8304i | −0.471248 | + | 1.89942i | ||||
\(486\) | 1.83264 | 0.0831302 | ||||||||
\(487\) | − | 34.6540i | − | 1.57032i | −0.619292 | − | 0.785161i | \(-0.712580\pi\) | ||
0.619292 | − | 0.785161i | \(-0.287420\pi\) | |||||||
\(488\) | 6.16142 | 0.278914 | ||||||||
\(489\) | − | 17.9624i | − | 0.812286i | ||||||
\(490\) | 14.4797 | + | 24.7626i | 0.654127 | + | 1.11866i | ||||
\(491\) | 26.4405i | 1.19324i | 0.802522 | + | 0.596622i | \(0.203491\pi\) | ||||
−0.802522 | + | 0.596622i | \(0.796509\pi\) | |||||||
\(492\) | −10.3333 | −0.465860 | ||||||||
\(493\) | 7.73067 | 0.348172 | ||||||||
\(494\) | 11.3987i | 0.512852i | ||||||||
\(495\) | −2.89477 | − | 6.82791i | −0.130110 | − | 0.306892i | ||||
\(496\) | − | 0.798333i | − | 0.0358462i | ||||||
\(497\) | −10.8324 | − | 26.6435i | −0.485901 | − | 1.19512i | ||||
\(498\) | 12.4781i | 0.559158i | ||||||||
\(499\) | 2.98892 | 0.133803 | 0.0669013 | − | 0.997760i | \(-0.478689\pi\) | ||||
0.0669013 | + | 0.997760i | \(0.478689\pi\) | |||||||
\(500\) | 10.1244 | − | 11.3230i | 0.452777 | − | 0.506379i | ||||
\(501\) | − | 3.86148i | − | 0.172518i | ||||||
\(502\) | 17.5874i | 0.784966i | ||||||||
\(503\) | 34.8409i | 1.55348i | 0.629823 | + | 0.776739i | \(0.283127\pi\) | ||||
−0.629823 | + | 0.776739i | \(0.716873\pi\) | |||||||
\(504\) | −1.17137 | − | 2.88109i | −0.0521768 | − | 0.128334i | ||||
\(505\) | −8.85494 | + | 35.6908i | −0.394039 | + | 1.58822i | ||||
\(506\) | 2.36757 | + | 3.15229i | 0.105251 | + | 0.140137i | ||||
\(507\) | −11.4292 | −0.507589 | ||||||||
\(508\) | 2.19797 | 0.0975190 | ||||||||
\(509\) | 20.3471i | 0.901872i | 0.892556 | + | 0.450936i | \(0.148910\pi\) | ||||
−0.892556 | + | 0.450936i | \(0.851090\pi\) | |||||||
\(510\) | −3.58199 | − | 0.888696i | −0.158613 | − | 0.0393521i | ||||
\(511\) | −3.48287 | + | 1.41603i | −0.154073 | + | 0.0626416i | ||||
\(512\) | −20.5843 | −0.909708 | ||||||||
\(513\) | −4.96271 | −0.219109 | ||||||||
\(514\) | 8.02897 | 0.354143 | ||||||||
\(515\) | −5.13193 | + | 20.6848i | −0.226140 | + | 0.911482i | ||||
\(516\) | 14.3412 | 0.631338 | ||||||||
\(517\) | 5.28108 | − | 3.96642i | 0.232261 | − | 0.174443i | ||||
\(518\) | 26.0796 | − | 10.6032i | 1.14587 | − | 0.465877i | ||||
\(519\) | − | 9.17271i | − | 0.402637i | ||||||
\(520\) | 3.19743 | + | 0.793285i | 0.140216 | + | 0.0347878i | ||||
\(521\) | − | 14.1540i | − | 0.620098i | −0.950721 | − | 0.310049i | \(-0.899655\pi\) | ||
0.950721 | − | 0.310049i | \(-0.100345\pi\) | |||||||
\(522\) | 15.7311i | 0.688533i | ||||||||
\(523\) | 32.0815i | 1.40283i | 0.712754 | + | 0.701414i | \(0.247447\pi\) | ||||
−0.712754 | + | 0.701414i | \(0.752553\pi\) | |||||||
\(524\) | −10.7358 | −0.468994 | ||||||||
\(525\) | 1.32362 | − | 13.1624i | 0.0577674 | − | 0.574453i | ||||
\(526\) | −4.90446 | −0.213845 | ||||||||
\(527\) | −0.147591 | −0.00642919 | ||||||||
\(528\) | −12.9188 | + | 9.70281i | −0.562217 | + | 0.422261i | ||||
\(529\) | 22.5793 | 0.981709 | ||||||||
\(530\) | 48.2575 | + | 11.9727i | 2.09617 | + | 0.520062i | ||||
\(531\) | 0.600825i | 0.0260736i | ||||||||
\(532\) | −6.71840 | − | 16.5246i | −0.291280 | − | 0.716432i | ||||
\(533\) | − | 9.53270i | − | 0.412907i | ||||||
\(534\) | 25.5443i | 1.10541i | ||||||||
\(535\) | −0.475565 | + | 1.91682i | −0.0205604 | + | 0.0828713i | ||||
\(536\) | 7.72776i | 0.333788i | ||||||||
\(537\) | 17.2783 | 0.745612 | ||||||||
\(538\) | − | 29.4329i | − | 1.26894i | ||||||
\(539\) | 3.56809 | − | 22.9405i | 0.153688 | − | 0.988119i | ||||
\(540\) | 0.731517 | − | 2.94846i | 0.0314795 | − | 0.126882i | ||||
\(541\) | 40.2041i | 1.72851i | 0.503053 | + | 0.864255i | \(0.332210\pi\) | ||||
−0.503053 | + | 0.864255i | \(0.667790\pi\) | |||||||
\(542\) | 46.7507 | 2.00811 | ||||||||
\(543\) | − | 14.8336i | − | 0.636569i | ||||||
\(544\) | 5.92287i | 0.253941i | ||||||||
\(545\) | −26.1427 | − | 6.48603i | −1.11983 | − | 0.277831i | ||||
\(546\) | −5.62946 | + | 2.28877i | −0.240919 | + | 0.0979504i | ||||
\(547\) | −7.50899 | −0.321061 | −0.160531 | − | 0.987031i | \(-0.551321\pi\) | ||||
−0.160531 | + | 0.987031i | \(0.551321\pi\) | |||||||
\(548\) | − | 5.34223i | − | 0.228209i | ||||||
\(549\) | 5.24147 | 0.223701 | ||||||||
\(550\) | −30.0133 | + | 4.77581i | −1.27977 | + | 0.203641i | ||||
\(551\) | − | 42.5992i | − | 1.81479i | ||||||
\(552\) | − | 0.762451i | − | 0.0324521i | ||||||
\(553\) | −14.8060 | + | 6.01967i | −0.629614 | + | 0.255982i | ||||
\(554\) | −43.4386 | −1.84553 | ||||||||
\(555\) | −12.6011 | − | 3.12633i | −0.534885 | − | 0.132706i | ||||
\(556\) | −0.147006 | −0.00623443 | ||||||||
\(557\) | −1.55694 | −0.0659697 | −0.0329848 | − | 0.999456i | \(-0.510501\pi\) | ||||
−0.0329848 | + | 0.999456i | \(0.510501\pi\) | |||||||
\(558\) | − | 0.300334i | − | 0.0127142i | ||||||
\(559\) | 13.2301i | 0.559575i | ||||||||
\(560\) | −28.5257 | + | 4.10625i | −1.20543 | + | 0.173521i | ||||
\(561\) | 1.79380 | + | 2.38835i | 0.0757345 | + | 0.100836i | ||||
\(562\) | 44.3090i | 1.86906i | ||||||||
\(563\) | 1.41618i | 0.0596847i | 0.999555 | + | 0.0298424i | \(0.00950053\pi\) | ||||
−0.999555 | + | 0.0298424i | \(0.990499\pi\) | |||||||
\(564\) | 2.70545 | 0.113920 | ||||||||
\(565\) | −22.2322 | − | 5.51584i | −0.935317 | − | 0.232053i | ||||
\(566\) | 52.2607i | 2.19668i | ||||||||
\(567\) | −0.996474 | − | 2.45093i | −0.0418480 | − | 0.102929i | ||||
\(568\) | 12.7787 | 0.536184 | ||||||||
\(569\) | − | 43.4668i | − | 1.82222i | −0.412161 | − | 0.911111i | \(-0.635226\pi\) | ||
0.412161 | − | 0.911111i | \(-0.364774\pi\) | |||||||
\(570\) | −4.89709 | + | 19.7383i | −0.205117 | + | 0.826746i | ||||
\(571\) | 0.461909i | 0.0193303i | 0.999953 | + | 0.00966514i | \(0.00307656\pi\) | ||||
−0.999953 | + | 0.00966514i | \(0.996923\pi\) | |||||||
\(572\) | 3.39143 | + | 4.51550i | 0.141803 | + | 0.188803i | ||||
\(573\) | 12.9155 | 0.539552 | ||||||||
\(574\) | 13.8899 | + | 34.1636i | 0.579754 | + | 1.42596i | ||||
\(575\) | 1.51590 | − | 2.86696i | 0.0632175 | − | 0.119561i | ||||
\(576\) | −2.30959 | −0.0962329 | ||||||||
\(577\) | 9.50039 | 0.395506 | 0.197753 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197753 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(578\) | −29.6684 | −1.23404 | ||||||||
\(579\) | 1.42077 | 0.0590452 | ||||||||
\(580\) | 25.3092 | + | 6.27924i | 1.05091 | + | 0.260731i | ||||
\(581\) | 16.6879 | − | 6.78482i | 0.692332 | − | 0.281482i | ||||
\(582\) | 35.3228 | 1.46418 | ||||||||
\(583\) | −24.1666 | − | 32.1765i | −1.00088 | − | 1.33261i | ||||
\(584\) | − | 1.67045i | − | 0.0691239i | ||||||
\(585\) | 2.72003 | + | 0.674842i | 0.112459 | + | 0.0279013i | ||||
\(586\) | 26.8478i | 1.10907i | ||||||||
\(587\) | −5.15760 | −0.212877 | −0.106439 | − | 0.994319i | \(-0.533945\pi\) | ||||
−0.106439 | + | 0.994319i | \(0.533945\pi\) | |||||||
\(588\) | 6.81197 | − | 6.63602i | 0.280921 | − | 0.273665i | ||||
\(589\) | 0.813291i | 0.0335111i | ||||||||
\(590\) | 2.38968 | + | 0.592881i | 0.0983814 | + | 0.0244085i | ||||
\(591\) | −16.4316 | −0.675905 | ||||||||
\(592\) | 28.2845i | 1.16249i | ||||||||
\(593\) | 0.142190i | 0.00583903i | 0.999996 | + | 0.00291951i | \(0.000929311\pi\) | ||||
−0.999996 | + | 0.00291951i | \(0.999071\pi\) | |||||||
\(594\) | −4.86006 | + | 3.65021i | −0.199411 | + | 0.149770i | ||||
\(595\) | 0.759142 | + | 5.27369i | 0.0311218 | + | 0.216200i | ||||
\(596\) | 5.80118i | 0.237626i | ||||||||
\(597\) | 12.7554i | 0.522044i | ||||||||
\(598\) | −1.48978 | −0.0609216 | ||||||||
\(599\) | 47.1360 | 1.92592 | 0.962962 | − | 0.269639i | \(-0.0869043\pi\) | ||||
0.962962 | + | 0.269639i | \(0.0869043\pi\) | |||||||
\(600\) | 5.19594 | + | 2.74735i | 0.212123 | + | 0.112160i | ||||
\(601\) | 33.9280 | 1.38395 | 0.691976 | − | 0.721920i | \(-0.256740\pi\) | ||||
0.691976 | + | 0.721920i | \(0.256740\pi\) | |||||||
\(602\) | −19.2774 | − | 47.4146i | −0.785687 | − | 1.93248i | ||||
\(603\) | 6.57395i | 0.267712i | ||||||||
\(604\) | 21.9435i | 0.892870i | ||||||||
\(605\) | 21.2765 | + | 12.3415i | 0.865011 | + | 0.501753i | ||||
\(606\) | 30.1384 | 1.22429 | ||||||||
\(607\) | 34.6346i | 1.40578i | 0.711300 | + | 0.702888i | \(0.248107\pi\) | ||||
−0.711300 | + | 0.702888i | \(0.751893\pi\) | |||||||
\(608\) | 32.6375 | 1.32362 | ||||||||
\(609\) | 21.0384 | − | 8.55360i | 0.852520 | − | 0.346609i | ||||
\(610\) | 5.17217 | − | 20.8470i | 0.209415 | − | 0.844072i | ||||
\(611\) | 2.49584i | 0.100971i | ||||||||
\(612\) | 1.22353i | 0.0494584i | ||||||||
\(613\) | −5.21722 | −0.210721 | −0.105361 | − | 0.994434i | \(-0.533600\pi\) | ||||
−0.105361 | + | 0.994434i | \(0.533600\pi\) | |||||||
\(614\) | 50.6670i | 2.04475i | ||||||||
\(615\) | 4.09543 | − | 16.5071i | 0.165144 | − | 0.665630i | ||||
\(616\) | 8.84490 | + | 5.30740i | 0.356371 | + | 0.213841i | ||||
\(617\) | − | 2.17670i | − | 0.0876306i | −0.999040 | − | 0.0438153i | \(-0.986049\pi\) | ||
0.999040 | − | 0.0438153i | \(-0.0139513\pi\) | |||||||
\(618\) | 17.4669 | 0.702620 | ||||||||
\(619\) | − | 14.8762i | − | 0.597926i | −0.954265 | − | 0.298963i | \(-0.903359\pi\) | ||
0.954265 | − | 0.298963i | \(-0.0966408\pi\) | |||||||
\(620\) | −0.483196 | − | 0.119881i | −0.0194056 | − | 0.00481455i | ||||
\(621\) | − | 0.648612i | − | 0.0260279i | ||||||
\(622\) | 25.9192i | 1.03926i | ||||||||
\(623\) | 34.1622 | − | 13.8894i | 1.36868 | − | 0.556465i | ||||
\(624\) | − | 6.10543i | − | 0.244413i | ||||||
\(625\) | 14.0755 | + | 20.6611i | 0.563019 | + | 0.826444i | ||||
\(626\) | 49.2019 | 1.96651 | ||||||||
\(627\) | 13.1608 | − | 9.88462i | 0.525593 | − | 0.394754i | ||||
\(628\) | 22.4995 | 0.897829 | ||||||||
\(629\) | 5.22910 | 0.208498 | ||||||||
\(630\) | −10.7314 | + | 1.54478i | −0.427550 | + | 0.0615454i | ||||
\(631\) | −16.6415 | −0.662487 | −0.331243 | − | 0.943545i | \(-0.607468\pi\) | ||||
−0.331243 | + | 0.943545i | \(0.607468\pi\) | |||||||
\(632\) | − | 7.10123i | − | 0.282472i | ||||||
\(633\) | 2.34216i | 0.0930924i | ||||||||
\(634\) | − | 29.3991i | − | 1.16759i | ||||||
\(635\) | −0.871128 | + | 3.51118i | −0.0345697 | + | 0.139337i | ||||
\(636\) | − | 16.4837i | − | 0.653622i | ||||||
\(637\) | 6.12189 | + | 6.28421i | 0.242558 | + | 0.248990i | ||||
\(638\) | −31.3330 | − | 41.7181i | −1.24048 | − | 1.65164i | ||||
\(639\) | 10.8708 | 0.430041 | ||||||||
\(640\) | 4.80319 | − | 19.3598i | 0.189863 | − | 0.765263i | ||||
\(641\) | −39.2533 | −1.55041 | −0.775205 | − | 0.631709i | \(-0.782354\pi\) | ||||
−0.775205 | + | 0.631709i | \(0.782354\pi\) | |||||||
\(642\) | 1.61862 | 0.0638817 | ||||||||
\(643\) | 1.64378 | 0.0648245 | 0.0324122 | − | 0.999475i | \(-0.489681\pi\) | ||||
0.0324122 | + | 0.999475i | \(0.489681\pi\) | |||||||
\(644\) | 2.15972 | − | 0.878077i | 0.0851048 | − | 0.0346011i | ||||
\(645\) | −5.68391 | + | 22.9097i | −0.223804 | + | 0.902067i | ||||
\(646\) | − | 8.19086i | − | 0.322265i | ||||||
\(647\) | 20.1321 | 0.791476 | 0.395738 | − | 0.918363i | \(-0.370489\pi\) | ||||
0.395738 | + | 0.918363i | \(0.370489\pi\) | |||||||
\(648\) | 1.17551 | 0.0461785 | ||||||||
\(649\) | −1.19671 | − | 1.59335i | −0.0469750 | − | 0.0625446i | ||||
\(650\) | 5.36813 | − | 10.1525i | 0.210555 | − | 0.398215i | ||||
\(651\) | −0.401659 | + | 0.163303i | −0.0157423 | + | 0.00640034i | ||||
\(652\) | 24.4031i | 0.955699i | ||||||||
\(653\) | − | 28.2479i | − | 1.10543i | −0.833372 | − | 0.552713i | \(-0.813593\pi\) | ||
0.833372 | − | 0.552713i | \(-0.186407\pi\) | |||||||
\(654\) | 22.0757i | 0.863227i | ||||||||
\(655\) | 4.25494 | − | 17.1500i | 0.166254 | − | 0.670107i | ||||
\(656\) | −37.0521 | −1.44664 | ||||||||
\(657\) | − | 1.42104i | − | 0.0554402i | ||||||
\(658\) | −3.63664 | − | 8.94469i | −0.141771 | − | 0.348700i | ||||
\(659\) | 5.74521i | 0.223801i | 0.993719 | + | 0.111901i | \(0.0356939\pi\) | ||||
−0.993719 | + | 0.111901i | \(0.964306\pi\) | |||||||
\(660\) | 3.93274 | + | 9.27618i | 0.153082 | + | 0.361075i | ||||
\(661\) | 26.7265i | 1.03954i | 0.854307 | + | 0.519769i | \(0.173982\pi\) | ||||
−0.854307 | + | 0.519769i | \(0.826018\pi\) | |||||||
\(662\) | −50.0056 | −1.94352 | ||||||||
\(663\) | −1.12874 | −0.0438366 | ||||||||
\(664\) | 8.00386i | 0.310610i | ||||||||
\(665\) | 29.0602 | − | 4.18319i | 1.12691 | − | 0.162217i | ||||
\(666\) | 10.6407i | 0.412319i | ||||||||
\(667\) | 5.56760 | 0.215578 | ||||||||
\(668\) | 5.24609i | 0.202977i | ||||||||
\(669\) | −4.12809 | −0.159601 | ||||||||
\(670\) | 26.1468 | + | 6.48704i | 1.01014 | + | 0.250616i | ||||
\(671\) | −13.9001 | + | 10.4399i | −0.536607 | + | 0.403026i | ||||
\(672\) | 6.55336 | + | 16.1186i | 0.252801 | + | 0.621790i | ||||
\(673\) | 23.9242 | 0.922210 | 0.461105 | − | 0.887346i | \(-0.347453\pi\) | ||||
0.461105 | + | 0.887346i | \(0.347453\pi\) | |||||||
\(674\) | −12.9770 | −0.499856 | ||||||||
\(675\) | 4.42015 | + | 2.33715i | 0.170132 | + | 0.0899569i | ||||
\(676\) | 15.5274 | 0.597206 | ||||||||
\(677\) | − | 42.9651i | − | 1.65128i | −0.564195 | − | 0.825641i | \(-0.690813\pi\) | ||
0.564195 | − | 0.825641i | \(-0.309187\pi\) | |||||||
\(678\) | 18.7735i | 0.720993i | ||||||||
\(679\) | −19.2063 | − | 47.2398i | −0.737070 | − | 1.81290i | ||||
\(680\) | −2.29760 | − | 0.570037i | −0.0881090 | − | 0.0218599i | ||||
\(681\) | − | 21.8296i | − | 0.836513i | ||||||
\(682\) | 0.598199 | + | 0.796470i | 0.0229062 | + | 0.0304984i | ||||
\(683\) | − | 27.4806i | − | 1.05151i | −0.850635 | − | 0.525757i | \(-0.823782\pi\) | ||
0.850635 | − | 0.525757i | \(-0.176218\pi\) | |||||||
\(684\) | 6.74218 | 0.257794 | ||||||||
\(685\) | 8.53405 | + | 2.11731i | 0.326069 | + | 0.0808981i | ||||
\(686\) | −31.0964 | − | 13.6015i | −1.18727 | − | 0.519307i | ||||
\(687\) | 1.37953i | 0.0526322i | ||||||||
\(688\) | 51.4234 | 1.96050 | ||||||||
\(689\) | 15.2066 | 0.579327 | ||||||||
\(690\) | −2.57974 | − | 0.640036i | −0.0982090 | − | 0.0243658i | ||||
\(691\) | − | 40.6341i | − | 1.54580i | −0.634531 | − | 0.772898i | \(-0.718807\pi\) | ||
0.634531 | − | 0.772898i | \(-0.281193\pi\) | |||||||
\(692\) | 12.4618i | 0.473725i | ||||||||
\(693\) | 7.52430 | + | 4.51497i | 0.285824 | + | 0.171509i | ||||
\(694\) | −29.0339 | −1.10211 | ||||||||
\(695\) | 0.0582633 | − | 0.234837i | 0.00221005 | − | 0.00890787i | ||||
\(696\) | 10.0904i | 0.382477i | ||||||||
\(697\) | 6.85000i | 0.259462i | ||||||||
\(698\) | −30.2247 | −1.14402 | ||||||||
\(699\) | 2.59060 | 0.0979854 | ||||||||
\(700\) | −1.79822 | + | 17.8820i | −0.0679665 | + | 0.675876i | ||||
\(701\) | 41.0535i | 1.55057i | 0.631611 | + | 0.775285i | \(0.282394\pi\) | ||||
−0.631611 | + | 0.775285i | \(0.717606\pi\) | |||||||
\(702\) | − | 2.29687i | − | 0.0866898i | ||||||
\(703\) | − | 28.8145i | − | 1.08676i | ||||||
\(704\) | 6.12491 | − | 4.60019i | 0.230841 | − | 0.173376i | ||||
\(705\) | −1.07226 | + | 4.32187i | −0.0403837 | + | 0.162771i | ||||
\(706\) | 41.2859 | 1.55382 | ||||||||
\(707\) | −16.3873 | − | 40.3063i | −0.616310 | − | 1.51588i | ||||
\(708\) | − | 0.816262i | − | 0.0306770i | ||||||
\(709\) | −18.9113 | −0.710230 | −0.355115 | − | 0.934823i | \(-0.615558\pi\) | ||||
−0.355115 | + | 0.934823i | \(0.615558\pi\) | |||||||
\(710\) | 10.7270 | − | 43.2366i | 0.402579 | − | 1.62264i | ||||
\(711\) | − | 6.04097i | − | 0.226554i | ||||||
\(712\) | 16.3849i | 0.614049i | ||||||||
\(713\) | −0.106295 | −0.00398078 | ||||||||
\(714\) | 4.04521 | − | 1.64466i | 0.151388 | − | 0.0615499i | ||||
\(715\) | −8.55750 | + | 3.62805i | −0.320033 | + | 0.135681i | ||||
\(716\) | −23.4737 | −0.877254 | ||||||||
\(717\) | 9.02101i | 0.336896i | ||||||||
\(718\) | 26.0914i | 0.973723i | ||||||||
\(719\) | − | 15.2306i | − | 0.568005i | −0.958824 | − | 0.284002i | \(-0.908338\pi\) | ||
0.958824 | − | 0.284002i | \(-0.0916624\pi\) | |||||||
\(720\) | 2.62300 | − | 10.5723i | 0.0977536 | − | 0.394007i | ||||
\(721\) | −9.49738 | − | 23.3597i | −0.353701 | − | 0.869962i | ||||
\(722\) | −10.3149 | −0.383882 | ||||||||
\(723\) | 0.695298 | 0.0258584 | ||||||||
\(724\) | 20.1524i | 0.748959i | ||||||||
\(725\) | −20.0618 | + | 37.9420i | −0.745076 | + | 1.40913i | ||||
\(726\) | 5.61820 | − | 19.3603i | 0.208511 | − | 0.718530i | ||||
\(727\) | −6.78304 | −0.251569 | −0.125785 | − | 0.992058i | \(-0.540145\pi\) | ||||
−0.125785 | + | 0.992058i | \(0.540145\pi\) | |||||||
\(728\) | −3.61091 | + | 1.46809i | −0.133829 | + | 0.0544110i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.65195 | − | 1.40226i | −0.209188 | − | 0.0518998i | ||||
\(731\) | − | 9.50689i | − | 0.351625i | ||||||
\(732\) | −7.12090 | −0.263196 | ||||||||
\(733\) | 21.8456i | 0.806886i | 0.915005 | + | 0.403443i | \(0.132187\pi\) | ||||
−0.915005 | + | 0.403443i | \(0.867813\pi\) | |||||||
\(734\) | −36.0370 | −1.33015 | ||||||||
\(735\) | 7.90102 | + | 13.5120i | 0.291434 | + | 0.498397i | ||||
\(736\) | 4.26563i | 0.157233i | ||||||||
\(737\) | −13.0939 | − | 17.4338i | −0.482319 | − | 0.642181i | ||||
\(738\) | −13.9391 | −0.513104 | ||||||||
\(739\) | − | 29.0056i | − | 1.06699i | −0.845804 | − | 0.533493i | \(-0.820879\pi\) | ||
0.845804 | − | 0.533493i | \(-0.179121\pi\) | |||||||
\(740\) | 17.1194 | + | 4.24734i | 0.629322 | + | 0.156135i | ||||
\(741\) | 6.21982i | 0.228491i | ||||||||
\(742\) | −54.4980 | + | 22.1573i | −2.00069 | + | 0.813419i | ||||
\(743\) | −12.8170 | −0.470210 | −0.235105 | − | 0.971970i | \(-0.575543\pi\) | ||||
−0.235105 | + | 0.971970i | \(0.575543\pi\) | |||||||
\(744\) | − | 0.192644i | − | 0.00706266i | ||||||
\(745\) | −9.26721 | − | 2.29920i | −0.339524 | − | 0.0842363i | ||||
\(746\) | 13.5150 | 0.494820 | ||||||||
\(747\) | 6.80883i | 0.249122i | ||||||||
\(748\) | −2.43701 | − | 3.24474i | −0.0891058 | − | 0.118639i | ||||
\(749\) | −0.880101 | − | 2.16470i | −0.0321582 | − | 0.0790963i | ||||
\(750\) | 13.6573 | − | 15.2741i | 0.498695 | − | 0.557732i | ||||
\(751\) | 2.86925 | 0.104701 | 0.0523503 | − | 0.998629i | \(-0.483329\pi\) | ||||
0.0523503 | + | 0.998629i | \(0.483329\pi\) | |||||||
\(752\) | 9.70095 | 0.353757 | ||||||||
\(753\) | 9.59678i | 0.349726i | ||||||||
\(754\) | 19.7160 | 0.718016 | ||||||||
\(755\) | −35.0541 | − | 8.69696i | −1.27575 | − | 0.316515i | ||||
\(756\) | 1.35378 | + | 3.32975i | 0.0492364 | + | 0.121102i | ||||
\(757\) | − | 26.3576i | − | 0.957982i | −0.877820 | − | 0.478991i | \(-0.841003\pi\) | ||
0.877820 | − | 0.478991i | \(-0.158997\pi\) | |||||||
\(758\) | 9.47911 | 0.344297 | ||||||||
\(759\) | 1.29189 | + | 1.72008i | 0.0468927 | + | 0.0624351i | ||||
\(760\) | −3.14115 | + | 12.6608i | −0.113941 | + | 0.459254i | ||||
\(761\) | −22.7063 | −0.823102 | −0.411551 | − | 0.911387i | \(-0.635013\pi\) | ||||
−0.411551 | + | 0.911387i | \(0.635013\pi\) | |||||||
\(762\) | 2.96494 | 0.107409 | ||||||||
\(763\) | 29.5234 | − | 12.0033i | 1.06882 | − | 0.434550i | ||||
\(764\) | −17.5466 | −0.634813 | ||||||||
\(765\) | −1.95455 | − | 0.484927i | −0.0706671 | − | 0.0175326i | ||||
\(766\) | −36.1185 | −1.30501 | ||||||||
\(767\) | 0.753022 | 0.0271900 | ||||||||
\(768\) | −20.9672 | −0.756587 | ||||||||
\(769\) | 23.6591 | 0.853169 | 0.426585 | − | 0.904448i | \(-0.359717\pi\) | ||||
0.426585 | + | 0.904448i | \(0.359717\pi\) | |||||||
\(770\) | 25.3823 | − | 25.4713i | 0.914715 | − | 0.917922i | ||||
\(771\) | 4.38110 | 0.157781 | ||||||||
\(772\) | −1.93021 | −0.0694700 | ||||||||
\(773\) | −54.1026 | −1.94593 | −0.972967 | − | 0.230945i | \(-0.925818\pi\) | ||||
−0.972967 | + | 0.230945i | \(0.925818\pi\) | |||||||
\(774\) | 19.3456 | 0.695363 | ||||||||
\(775\) | 0.383013 | − | 0.724377i | 0.0137582 | − | 0.0260204i | ||||
\(776\) | 22.6571 | 0.813343 | ||||||||
\(777\) | 14.2306 | − | 5.78574i | 0.510520 | − | 0.207562i | ||||
\(778\) | 67.1767 | 2.40840 | ||||||||
\(779\) | 37.7464 | 1.35240 | ||||||||
\(780\) | −3.69535 | − | 0.916819i | −0.132315 | − | 0.0328274i | ||||
\(781\) | −28.8287 | + | 21.6522i | −1.03157 | + | 0.774776i | ||||
\(782\) | 1.07052 | 0.0382818 | ||||||||
\(783\) | 8.58387i | 0.306762i | ||||||||
\(784\) | 24.4257 | − | 23.7948i | 0.872348 | − | 0.849815i | ||||
\(785\) | −8.91731 | + | 35.9423i | −0.318273 | + | 1.28283i | ||||
\(786\) | −14.4820 | −0.516556 | ||||||||
\(787\) | − | 8.62574i | − | 0.307474i | −0.988112 | − | 0.153737i | \(-0.950869\pi\) | ||
0.988112 | − | 0.153737i | \(-0.0491309\pi\) | |||||||
\(788\) | 22.3234 | 0.795239 | ||||||||
\(789\) | −2.67617 | −0.0952743 | ||||||||
\(790\) | −24.0269 | − | 5.96110i | −0.854839 | − | 0.212086i | ||||
\(791\) | 25.1073 | − | 10.2079i | 0.892711 | − | 0.362950i | ||||
\(792\) | −3.11739 | + | 2.34136i | −0.110772 | + | 0.0831966i | ||||
\(793\) | − | 6.56921i | − | 0.233279i | ||||||
\(794\) | 35.5849 | 1.26286 | ||||||||
\(795\) | 26.3322 | + | 6.53305i | 0.933908 | + | 0.231703i | ||||
\(796\) | − | 17.3291i | − | 0.614213i | ||||||
\(797\) | 37.2277 | 1.31867 | 0.659336 | − | 0.751848i | \(-0.270837\pi\) | ||||
0.659336 | + | 0.751848i | \(0.270837\pi\) | |||||||
\(798\) | −9.06278 | − | 22.2908i | −0.320819 | − | 0.789086i | ||||
\(799\) | − | 1.79346i | − | 0.0634480i | ||||||
\(800\) | −29.0693 | − | 15.3704i | −1.02776 | − | 0.543425i | ||||
\(801\) | 13.9385i | 0.492493i | ||||||||
\(802\) | −41.8981 | −1.47947 | ||||||||
\(803\) | 2.83041 | + | 3.76853i | 0.0998828 | + | 0.132989i | ||||
\(804\) | − | 8.93117i | − | 0.314978i | ||||||
\(805\) | 0.546731 | + | 3.79809i | 0.0192697 | + | 0.133865i | ||||
\(806\) | −0.376413 | −0.0132586 | ||||||||
\(807\) | − | 16.0604i | − | 0.565352i | ||||||
\(808\) | 19.3317 | 0.680087 | ||||||||
\(809\) | − | 10.2662i | − | 0.360940i | −0.983581 | − | 0.180470i | \(-0.942238\pi\) | ||
0.983581 | − | 0.180470i | \(-0.0577618\pi\) | |||||||
\(810\) | 0.986778 | − | 3.97732i | 0.0346719 | − | 0.139749i | ||||
\(811\) | −5.33963 | −0.187500 | −0.0937499 | − | 0.995596i | \(-0.529885\pi\) | ||||
−0.0937499 | + | 0.995596i | \(0.529885\pi\) | |||||||
\(812\) | −28.5822 | + | 11.6207i | −1.00304 | + | 0.407805i | ||||
\(813\) | 25.5100 | 0.894676 | ||||||||
\(814\) | −21.1939 | − | 28.2185i | −0.742846 | − | 0.989060i | ||||
\(815\) | −38.9832 | − | 9.67177i | −1.36552 | − | 0.338787i | ||||
\(816\) | 4.38723i | 0.153584i | ||||||||
\(817\) | −52.3870 | −1.83279 | ||||||||
\(818\) | −2.30807 | −0.0806999 | ||||||||
\(819\) | −3.07178 | + | 1.24889i | −0.107337 | + | 0.0436399i | ||||
\(820\) | −5.56392 | + | 22.4260i | −0.194300 | + | 0.783151i | ||||
\(821\) | 17.5107i | 0.611128i | 0.952172 | + | 0.305564i | \(0.0988450\pi\) | ||||
−0.952172 | + | 0.305564i | \(0.901155\pi\) | |||||||
\(822\) | − | 7.20640i | − | 0.251352i | ||||||
\(823\) | 11.7968i | 0.411211i | 0.978635 | + | 0.205606i | \(0.0659164\pi\) | ||||
−0.978635 | + | 0.205606i | \(0.934084\pi\) | |||||||
\(824\) | 11.2038 | 0.390302 | ||||||||
\(825\) | −16.3771 | + | 2.60597i | −0.570177 | + | 0.0907283i | ||||
\(826\) | −2.69870 | + | 1.09721i | −0.0938999 | + | 0.0381769i | ||||
\(827\) | 29.9264 | 1.04064 | 0.520322 | − | 0.853970i | \(-0.325812\pi\) | ||||
0.520322 | + | 0.853970i | \(0.325812\pi\) | |||||||
\(828\) | 0.881184i | 0.0306233i | ||||||||
\(829\) | 37.7348i | 1.31058i | 0.755376 | + | 0.655292i | \(0.227454\pi\) | ||||
−0.755376 | + | 0.655292i | \(0.772546\pi\) | |||||||
\(830\) | 27.0809 | + | 6.71880i | 0.939992 | + | 0.233213i | ||||
\(831\) | −23.7027 | −0.822239 | ||||||||
\(832\) | 2.89464i | 0.100354i | ||||||||
\(833\) | −4.39906 | − | 4.51570i | −0.152418 | − | 0.156460i | ||||
\(834\) | −0.198303 | −0.00686667 | ||||||||
\(835\) | −8.38046 | − | 2.07920i | −0.290018 | − | 0.0719537i | ||||
\(836\) | −17.8799 | + | 13.4289i | −0.618389 | + | 0.464449i | ||||
\(837\) | − | 0.163881i | − | 0.00566454i | ||||||
\(838\) | − | 72.2081i | − | 2.49439i | ||||||
\(839\) | 13.9080i | 0.480156i | 0.970754 | + | 0.240078i | \(0.0771731\pi\) | ||||
−0.970754 | + | 0.240078i | \(0.922827\pi\) | |||||||
\(840\) | −6.88347 | + | 0.990869i | −0.237502 | + | 0.0341882i | ||||
\(841\) | −44.6828 | −1.54079 | ||||||||
\(842\) | −11.3983 | −0.392813 | ||||||||
\(843\) | 24.1777i | 0.832724i | ||||||||
\(844\) | − | 3.18198i | − | 0.109528i | ||||||
\(845\) | −6.15402 | + | 24.8045i | −0.211705 | + | 0.853300i | ||||
\(846\) | 3.64951 | 0.125473 | ||||||||
\(847\) | −28.9468 | + | 3.01329i | −0.994626 | + | 0.103538i | ||||
\(848\) | − | 59.1058i | − | 2.02970i | ||||||
\(849\) | 28.5166i | 0.978687i | ||||||||
\(850\) | −3.85742 | + | 7.29538i | −0.132309 | + | 0.250230i | ||||
\(851\) | 3.76598 | 0.129096 | ||||||||
\(852\) | −14.7687 | −0.505967 | ||||||||
\(853\) | − | 30.0061i | − | 1.02739i | −0.857973 | − | 0.513695i | \(-0.828276\pi\) | ||
0.857973 | − | 0.513695i | \(-0.171724\pi\) | |||||||
\(854\) | 9.57186 | + | 23.5429i | 0.327542 | + | 0.805623i | ||||
\(855\) | −2.67215 | + | 10.7704i | −0.0913857 | + | 0.368340i | ||||
\(856\) | 1.03823 | 0.0354860 | ||||||||
\(857\) | − | 3.51078i | − | 0.119926i | −0.998201 | − | 0.0599630i | \(-0.980902\pi\) | ||
0.998201 | − | 0.0599630i | \(-0.0190983\pi\) | |||||||
\(858\) | 4.57486 | + | 6.09118i | 0.156183 | + | 0.207949i | ||||
\(859\) | − | 8.47192i | − | 0.289058i | −0.989501 | − | 0.144529i | \(-0.953833\pi\) | ||
0.989501 | − | 0.144529i | \(-0.0461667\pi\) | |||||||
\(860\) | 7.72199 | − | 31.1244i | 0.263318 | − | 1.06133i | ||||
\(861\) | 7.57918 | + | 18.6418i | 0.258298 | + | 0.635309i | ||||
\(862\) | 13.5556i | 0.461707i | ||||||||
\(863\) | − | 8.18498i | − | 0.278620i | −0.990249 | − | 0.139310i | \(-0.955512\pi\) | ||
0.990249 | − | 0.139310i | \(-0.0444885\pi\) | |||||||
\(864\) | −6.57655 | −0.223739 | ||||||||
\(865\) | −19.9073 | − | 4.93901i | −0.676867 | − | 0.167931i | ||||
\(866\) | −47.0673 | −1.59941 | ||||||||
\(867\) | −16.1889 | −0.549804 | ||||||||
\(868\) | 0.545682 | − | 0.221858i | 0.0185216 | − | 0.00753035i | ||||
\(869\) | 12.0323 | + | 16.0203i | 0.408167 | + | 0.543452i | ||||
\(870\) | 34.1408 | + | 8.47038i | 1.15748 | + | 0.287173i | ||||
\(871\) | 8.23922 | 0.279175 | ||||||||
\(872\) | 14.1600i | 0.479519i | ||||||||
\(873\) | 19.2743 | 0.652335 | ||||||||
\(874\) | − | 5.89903i | − | 0.199538i | ||||||
\(875\) | −27.8532 | − | 9.95984i | −0.941611 | − | 0.336704i | ||||
\(876\) | 1.93059i | 0.0652285i | ||||||||
\(877\) | 46.2648 | 1.56225 | 0.781126 | − | 0.624373i | \(-0.214646\pi\) | ||||
0.781126 | + | 0.624373i | \(0.214646\pi\) | |||||||
\(878\) | −59.0543 | −1.99299 | ||||||||
\(879\) | 14.6498i | 0.494126i | ||||||||
\(880\) | 14.1017 | + | 33.2617i | 0.475367 | + | 1.12125i | ||||
\(881\) | 38.7271i | 1.30475i | 0.757897 | + | 0.652374i | \(0.226227\pi\) | ||||
−0.757897 | + | 0.652374i | \(0.773773\pi\) | |||||||
\(882\) | 9.18900 | − | 8.95165i | 0.309410 | − | 0.301418i | ||||
\(883\) | 48.1751i | 1.62122i | 0.585585 | + | 0.810611i | \(0.300865\pi\) | ||||
−0.585585 | + | 0.810611i | \(0.699135\pi\) | |||||||
\(884\) | 1.53347 | 0.0515762 | ||||||||
\(885\) | 1.30395 | + | 0.323512i | 0.0438319 | + | 0.0108747i | ||||
\(886\) | − | 54.2778i | − | 1.82350i | ||||||
\(887\) | 6.20413i | 0.208314i | 0.994561 | + | 0.104157i | \(0.0332145\pi\) | ||||
−0.994561 | + | 0.104157i | \(0.966785\pi\) | |||||||
\(888\) | 6.82527i | 0.229041i | ||||||||
\(889\) | −1.61215 | − | 3.96524i | −0.0540698 | − | 0.132990i | ||||
\(890\) | 55.4380 | + | 13.7542i | 1.85828 | + | 0.461042i | ||||
\(891\) | −2.65195 | + | 1.99178i | −0.0888435 | + | 0.0667271i | ||||
\(892\) | 5.60829 | 0.187779 | ||||||||
\(893\) | −9.88272 | −0.330713 | ||||||||
\(894\) | 7.82550i | 0.261724i | ||||||||
\(895\) | 9.30342 | − | 37.4985i | 0.310979 | − | 1.25344i | ||||
\(896\) | 8.88899 | + | 21.8634i | 0.296960 | + | 0.730404i | ||||
\(897\) | −0.812914 | −0.0271424 | ||||||||
\(898\) | 7.08949 | 0.236579 | ||||||||
\(899\) | 1.40673 | 0.0469171 | ||||||||
\(900\) | −6.00508 | − | 3.17518i | −0.200169 | − | 0.105839i | ||||
\(901\) | −10.9272 | −0.364036 | ||||||||
\(902\) | 36.9656 | − | 27.7635i | 1.23082 | − | 0.924425i | ||||
\(903\) | −10.5189 | − | 25.8723i | −0.350047 | − | 0.860976i | ||||
\(904\) | 12.0419i | 0.400509i | ||||||||
\(905\) | −32.1929 | − | 7.98708i | −1.07013 | − | 0.265500i | ||||
\(906\) | 29.6007i | 0.983418i | ||||||||
\(907\) | 25.8651i | 0.858835i | 0.903106 | + | 0.429418i | \(0.141281\pi\) | ||||
−0.903106 | + | 0.429418i | \(0.858719\pi\) | |||||||
\(908\) | 29.6571i | 0.984204i | ||||||||
\(909\) | 16.4453 | 0.545457 | ||||||||
\(910\) | 1.93609 | + | 13.4498i | 0.0641808 | + | 0.445858i | ||||
\(911\) | −31.9293 | −1.05787 | −0.528933 | − | 0.848664i | \(-0.677408\pi\) | ||||
−0.528933 | + | 0.848664i | \(0.677408\pi\) | |||||||
\(912\) | 24.1755 | 0.800530 | ||||||||
\(913\) | −13.5617 | − | 18.0566i | −0.448826 | − | 0.597588i | ||||
\(914\) | 22.3427 | 0.739030 | ||||||||
\(915\) | 2.82225 | − | 11.3754i | 0.0933008 | − | 0.376060i | ||||
\(916\) | − | 1.87418i | − | 0.0619247i | ||||||
\(917\) | 7.87439 | + | 19.3679i | 0.260035 | + | 0.639583i | ||||
\(918\) | 1.65048i | 0.0544740i | ||||||||
\(919\) | − | 15.4795i | − | 0.510621i | −0.966859 | − | 0.255311i | \(-0.917822\pi\) | ||
0.966859 | − | 0.255311i | \(-0.0821777\pi\) | |||||||
\(920\) | −1.65473 | − | 0.410539i | −0.0545547 | − | 0.0135351i | ||||
\(921\) | 27.6470i | 0.911000i | ||||||||
\(922\) | −50.3294 | −1.65751 | ||||||||
\(923\) | − | 13.6245i | − | 0.448455i | ||||||
\(924\) | −10.2223 | − | 6.13390i | −0.336288 | − | 0.201790i | ||||
\(925\) | −13.5700 | + | 25.6643i | −0.446178 | + | 0.843838i | ||||
\(926\) | 31.4112i | 1.03224i | ||||||||
\(927\) | 9.53098 | 0.313039 | ||||||||
\(928\) | − | 56.4522i | − | 1.85314i | ||||||
\(929\) | − | 12.0282i | − | 0.394632i | −0.980340 | − | 0.197316i | \(-0.936778\pi\) | ||
0.980340 | − | 0.197316i | \(-0.0632225\pi\) | |||||||
\(930\) | −0.651806 | − | 0.161714i | −0.0213736 | − | 0.00530281i | ||||
\(931\) | −24.8834 | + | 24.2407i | −0.815521 | + | 0.794456i | ||||
\(932\) | −3.51950 | −0.115285 | ||||||||
\(933\) | 14.1431i | 0.463024i | ||||||||
\(934\) | 4.47520 | 0.146433 | ||||||||
\(935\) | 6.14924 | − | 2.60704i | 0.201102 | − | 0.0852593i | ||||
\(936\) | − | 1.47328i | − | 0.0481558i | ||||||
\(937\) | 26.8317i | 0.876554i | 0.898840 | + | 0.438277i | \(0.144411\pi\) | ||||
−0.898840 | + | 0.438277i | \(0.855589\pi\) | |||||||
\(938\) | −29.5280 | + | 12.0052i | −0.964123 | + | 0.391984i | ||||
\(939\) | 26.8476 | 0.876138 | ||||||||
\(940\) | 1.45674 | − | 5.87156i | 0.0475136 | − | 0.191509i | ||||
\(941\) | −21.7437 | −0.708824 | −0.354412 | − | 0.935089i | \(-0.615319\pi\) | ||||
−0.354412 | + | 0.935089i | \(0.615319\pi\) | |||||||
\(942\) | 30.3507 | 0.988879 | ||||||||
\(943\) | 4.93335i | 0.160652i | ||||||||
\(944\) | − | 2.92687i | − | 0.0952617i | ||||||
\(945\) | −5.85572 | + | 0.842925i | −0.190487 | + | 0.0274204i | ||||
\(946\) | −51.3035 | + | 38.5321i | −1.66802 | + | 1.25279i | ||||
\(947\) | 23.4252i | 0.761216i | 0.924736 | + | 0.380608i | \(0.124285\pi\) | ||||
−0.924736 | + | 0.380608i | \(0.875715\pi\) | |||||||
\(948\) | 8.20708i | 0.266553i | ||||||||
\(949\) | −1.78101 | −0.0578141 | ||||||||
\(950\) | 40.2006 | + | 21.2560i | 1.30428 | + | 0.689637i | ||||
\(951\) | − | 16.0419i | − | 0.520196i | ||||||
\(952\) | 2.59472 | − | 1.05494i | 0.0840955 | − | 0.0341907i | ||||
\(953\) | −27.7086 | −0.897568 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(954\) | − | 22.2357i | − | 0.719907i | ||||||
\(955\) | 6.95430 | − | 28.0301i | 0.225036 | − | 0.907033i | ||||
\(956\) | − | 12.2557i | − | 0.396376i | ||||||
\(957\) | −17.0972 | − | 22.7640i | −0.552673 | − | 0.735854i | ||||
\(958\) | 50.0846 | 1.61816 | ||||||||
\(959\) | −9.63765 | + | 3.91838i | −0.311216 | + | 0.126531i | ||||
\(960\) | −1.24359 | + | 5.01244i | −0.0401367 | + | 0.161776i | ||||
\(961\) | 30.9731 | 0.999134 | ||||||||
\(962\) | 13.3361 | 0.429974 | ||||||||
\(963\) | 0.883216 | 0.0284612 | ||||||||
\(964\) | −0.944610 | −0.0304238 | ||||||||
\(965\) | 0.765009 | − | 3.08346i | 0.0246265 | − | 0.0992600i | ||||
\(966\) | 2.91335 | − | 1.18448i | 0.0937354 | − | 0.0381100i | ||||
\(967\) | −42.1076 | −1.35409 | −0.677044 | − | 0.735942i | \(-0.736739\pi\) | ||||
−0.677044 | + | 0.735942i | \(0.736739\pi\) | |||||||
\(968\) | 3.60369 | − | 12.4183i | 0.115827 | − | 0.399140i | ||||
\(969\) | − | 4.46943i | − | 0.143579i | ||||||
\(970\) | 19.0194 | − | 76.6600i | 0.610677 | − | 2.46140i | ||||
\(971\) | − | 50.6587i | − | 1.62572i | −0.582462 | − | 0.812858i | \(-0.697910\pi\) | ||
0.582462 | − | 0.812858i | \(-0.302090\pi\) | |||||||
\(972\) | −1.35857 | −0.0435761 | ||||||||
\(973\) | 0.107825 | + | 0.265205i | 0.00345670 | + | 0.00850210i | ||||
\(974\) | 63.5083i | 2.03494i | ||||||||
\(975\) | 2.92918 | − | 5.53983i | 0.0938088 | − | 0.177417i | ||||
\(976\) | −25.5335 | −0.817306 | ||||||||
\(977\) | − | 42.2098i | − | 1.35041i | −0.737629 | − | 0.675206i | \(-0.764055\pi\) | ||
0.737629 | − | 0.675206i | \(-0.235945\pi\) | |||||||
\(978\) | 32.9185i | 1.05262i | ||||||||
\(979\) | −27.7624 | − | 36.9642i | −0.887291 | − | 1.18138i | ||||
\(980\) | −10.7341 | − | 18.3570i | −0.342888 | − | 0.586392i | ||||
\(981\) | 12.0458i | 0.384594i | ||||||||
\(982\) | − | 48.4559i | − | 1.54629i | ||||||
\(983\) | 6.75765 | 0.215536 | 0.107768 | − | 0.994176i | \(-0.465630\pi\) | ||||
0.107768 | + | 0.994176i | \(0.465630\pi\) | |||||||
\(984\) | −8.94095 | −0.285027 | ||||||||
\(985\) | −8.84752 | + | 35.6610i | −0.281906 | + | 1.13625i | ||||
\(986\) | −14.1675 | −0.451186 | ||||||||
\(987\) | −1.98437 | − | 4.88077i | −0.0631633 | − | 0.155357i | ||||
\(988\) | − | 8.45006i | − | 0.268832i | ||||||
\(989\) | − | 6.84683i | − | 0.217717i | ||||||
\(990\) | 5.30507 | + | 12.5131i | 0.168606 | + | 0.397692i | ||||
\(991\) | −49.0326 | −1.55757 | −0.778787 | − | 0.627289i | \(-0.784165\pi\) | ||||
−0.778787 | + | 0.627289i | \(0.784165\pi\) | |||||||
\(992\) | 1.07777i | 0.0342192i | ||||||||
\(993\) | −27.2861 | −0.865899 | ||||||||
\(994\) | 19.8520 | + | 48.8279i | 0.629666 | + | 1.54873i | ||||
\(995\) | 27.6827 | + | 6.86810i | 0.877599 | + | 0.217733i | ||||
\(996\) | − | 9.25026i | − | 0.293106i | ||||||
\(997\) | − | 4.20775i | − | 0.133261i | −0.997778 | − | 0.0666304i | \(-0.978775\pi\) | ||
0.997778 | − | 0.0666304i | \(-0.0212248\pi\) | |||||||
\(998\) | −5.47762 | −0.173391 | ||||||||
\(999\) | 5.80621i | 0.183700i |
(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 | 1155.2.k.a.769.10 | yes | 48 | |
5.4 | even | 2 | 1155.2.k.b.769.39 | yes | 48 | ||
7.6 | odd | 2 | 1155.2.k.b.769.9 | yes | 48 | ||
11.10 | odd | 2 | inner | 1155.2.k.a.769.39 | yes | 48 | |
35.34 | odd | 2 | inner | 1155.2.k.a.769.40 | yes | 48 | |
55.54 | odd | 2 | 1155.2.k.b.769.10 | yes | 48 | ||
77.76 | even | 2 | 1155.2.k.b.769.40 | yes | 48 | ||
385.384 | even | 2 | inner | 1155.2.k.a.769.9 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.k.a.769.9 | ✓ | 48 | 385.384 | even | 2 | inner | |
1155.2.k.a.769.10 | yes | 48 | 1.1 | even | 1 | trivial | |
1155.2.k.a.769.39 | yes | 48 | 11.10 | odd | 2 | inner | |
1155.2.k.a.769.40 | yes | 48 | 35.34 | odd | 2 | inner | |
1155.2.k.b.769.9 | yes | 48 | 7.6 | odd | 2 | ||
1155.2.k.b.769.10 | yes | 48 | 55.54 | odd | 2 | ||
1155.2.k.b.769.39 | yes | 48 | 5.4 | even | 2 | ||
1155.2.k.b.769.40 | yes | 48 | 77.76 | even | 2 |