Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(91,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, 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("276.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.9 | ||
Character | \(\chi\) | \(=\) | 276.91 |
Dual form | 276.2.e.a.91.12 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.279557 | − | 1.38631i | −0.197677 | − | 0.980267i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.84370 | + | 0.775104i | −0.921848 | + | 0.387552i | ||||
\(5\) | − | 1.27568i | − | 0.570499i | −0.958453 | − | 0.285250i | \(-0.907923\pi\) | ||
0.958453 | − | 0.285250i | \(-0.0920765\pi\) | |||||||
\(6\) | 1.38631 | − | 0.279557i | 0.565958 | − | 0.114129i | ||||
\(7\) | 2.49131 | 0.941627 | 0.470814 | − | 0.882233i | \(-0.343960\pi\) | ||||
0.470814 | + | 0.882233i | \(0.343960\pi\) | |||||||
\(8\) | 1.58995 | + | 2.33924i | 0.562133 | + | 0.827047i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.76848 | + | 0.356624i | −0.559242 | + | 0.112774i | ||||
\(11\) | 5.92184 | 1.78550 | 0.892751 | − | 0.450550i | \(-0.148772\pi\) | ||||
0.892751 | + | 0.450550i | \(0.148772\pi\) | |||||||
\(12\) | −0.775104 | − | 1.84370i | −0.223753 | − | 0.532229i | ||||
\(13\) | −2.46678 | −0.684162 | −0.342081 | − | 0.939670i | \(-0.611132\pi\) | ||||
−0.342081 | + | 0.939670i | \(0.611132\pi\) | |||||||
\(14\) | −0.696464 | − | 3.45372i | −0.186138 | − | 0.923047i | ||||
\(15\) | 1.27568 | 0.329378 | ||||||||
\(16\) | 2.79843 | − | 2.85811i | 0.699607 | − | 0.714528i | ||||
\(17\) | − | 6.74152i | − | 1.63506i | −0.575887 | − | 0.817529i | \(-0.695343\pi\) | ||
0.575887 | − | 0.817529i | \(-0.304657\pi\) | |||||||
\(18\) | 0.279557 | + | 1.38631i | 0.0658923 | + | 0.326756i | ||||
\(19\) | −2.53999 | −0.582714 | −0.291357 | − | 0.956614i | \(-0.594107\pi\) | ||||
−0.291357 | + | 0.956614i | \(0.594107\pi\) | |||||||
\(20\) | 0.988782 | + | 2.35196i | 0.221098 | + | 0.525914i | ||||
\(21\) | 2.49131i | 0.543649i | ||||||||
\(22\) | −1.65549 | − | 8.20949i | −0.352952 | − | 1.75027i | ||||
\(23\) | 4.75259 | − | 0.642542i | 0.990984 | − | 0.133979i | ||||
\(24\) | −2.33924 | + | 1.58995i | −0.477496 | + | 0.324547i | ||||
\(25\) | 3.37265 | 0.674530 | ||||||||
\(26\) | 0.689606 | + | 3.41972i | 0.135243 | + | 0.670662i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −4.59322 | + | 1.93103i | −0.868037 | + | 0.364930i | ||||
\(29\) | 5.45110 | 1.01224 | 0.506122 | − | 0.862462i | \(-0.331079\pi\) | ||||
0.506122 | + | 0.862462i | \(0.331079\pi\) | |||||||
\(30\) | −0.356624 | − | 1.76848i | −0.0651104 | − | 0.322878i | ||||
\(31\) | 3.02410i | 0.543144i | 0.962418 | + | 0.271572i | \(0.0875436\pi\) | ||||
−0.962418 | + | 0.271572i | \(0.912456\pi\) | |||||||
\(32\) | −4.74454 | − | 3.08047i | −0.838725 | − | 0.544556i | ||||
\(33\) | 5.92184i | 1.03086i | ||||||||
\(34\) | −9.34581 | + | 1.88464i | −1.60279 | + | 0.323213i | ||||
\(35\) | − | 3.17811i | − | 0.537198i | ||||||
\(36\) | 1.84370 | − | 0.775104i | 0.307283 | − | 0.129184i | ||||
\(37\) | 4.92988i | 0.810468i | 0.914213 | + | 0.405234i | \(0.132810\pi\) | ||||
−0.914213 | + | 0.405234i | \(0.867190\pi\) | |||||||
\(38\) | 0.710072 | + | 3.52121i | 0.115189 | + | 0.571215i | ||||
\(39\) | − | 2.46678i | − | 0.395001i | ||||||
\(40\) | 2.98411 | − | 2.02826i | 0.471830 | − | 0.320696i | ||||
\(41\) | −9.26643 | −1.44717 | −0.723587 | − | 0.690233i | \(-0.757508\pi\) | ||||
−0.723587 | + | 0.690233i | \(0.757508\pi\) | |||||||
\(42\) | 3.45372 | − | 0.696464i | 0.532921 | − | 0.107467i | ||||
\(43\) | −10.1120 | −1.54207 | −0.771033 | − | 0.636795i | \(-0.780260\pi\) | ||||
−0.771033 | + | 0.636795i | \(0.780260\pi\) | |||||||
\(44\) | −10.9181 | + | 4.59004i | −1.64596 | + | 0.691975i | ||||
\(45\) | 1.27568i | 0.190166i | ||||||||
\(46\) | −2.21938 | − | 6.40893i | −0.327230 | − | 0.944945i | ||||
\(47\) | 9.93569i | 1.44927i | 0.689133 | + | 0.724635i | \(0.257992\pi\) | ||||
−0.689133 | + | 0.724635i | \(0.742008\pi\) | |||||||
\(48\) | 2.85811 | + | 2.79843i | 0.412533 | + | 0.403918i | ||||
\(49\) | −0.793365 | −0.113338 | ||||||||
\(50\) | −0.942849 | − | 4.67553i | −0.133339 | − | 0.661220i | ||||
\(51\) | 6.74152 | 0.944001 | ||||||||
\(52\) | 4.54799 | − | 1.91201i | 0.630693 | − | 0.265148i | ||||
\(53\) | 2.08399i | 0.286258i | 0.989704 | + | 0.143129i | \(0.0457164\pi\) | ||||
−0.989704 | + | 0.143129i | \(0.954284\pi\) | |||||||
\(54\) | −1.38631 | + | 0.279557i | −0.188653 | + | 0.0380429i | ||||
\(55\) | − | 7.55435i | − | 1.01863i | ||||||
\(56\) | 3.96106 | + | 5.82778i | 0.529319 | + | 0.778770i | ||||
\(57\) | − | 2.53999i | − | 0.336430i | ||||||
\(58\) | −1.52389 | − | 7.55690i | −0.200097 | − | 0.992269i | ||||
\(59\) | 7.43825i | 0.968378i | 0.874963 | + | 0.484189i | \(0.160885\pi\) | ||||
−0.874963 | + | 0.484189i | \(0.839115\pi\) | |||||||
\(60\) | −2.35196 | + | 0.988782i | −0.303636 | + | 0.127651i | ||||
\(61\) | 2.14403i | 0.274515i | 0.990535 | + | 0.137257i | \(0.0438287\pi\) | ||||
−0.990535 | + | 0.137257i | \(0.956171\pi\) | |||||||
\(62\) | 4.19233 | − | 0.845409i | 0.532427 | − | 0.107367i | ||||
\(63\) | −2.49131 | −0.313876 | ||||||||
\(64\) | −2.94411 | + | 7.43856i | −0.368014 | + | 0.929820i | ||||
\(65\) | 3.14681i | 0.390314i | ||||||||
\(66\) | 8.20949 | − | 1.65549i | 1.01052 | − | 0.203777i | ||||
\(67\) | 3.96649 | 0.484584 | 0.242292 | − | 0.970203i | \(-0.422101\pi\) | ||||
0.242292 | + | 0.970203i | \(0.422101\pi\) | |||||||
\(68\) | 5.22538 | + | 12.4293i | 0.633670 | + | 1.50727i | ||||
\(69\) | 0.642542 | + | 4.75259i | 0.0773529 | + | 0.572145i | ||||
\(70\) | −4.40583 | + | 0.888462i | −0.526598 | + | 0.106192i | ||||
\(71\) | − | 12.1146i | − | 1.43773i | −0.695148 | − | 0.718867i | \(-0.744661\pi\) | ||
0.695148 | − | 0.718867i | \(-0.255339\pi\) | |||||||
\(72\) | −1.58995 | − | 2.33924i | −0.187378 | − | 0.275682i | ||||
\(73\) | −4.45034 | −0.520873 | −0.260436 | − | 0.965491i | \(-0.583866\pi\) | ||||
−0.260436 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(74\) | 6.83433 | − | 1.37818i | 0.794475 | − | 0.160211i | ||||
\(75\) | 3.37265i | 0.389440i | ||||||||
\(76\) | 4.68297 | − | 1.96876i | 0.537173 | − | 0.225832i | ||||
\(77\) | 14.7532 | 1.68128 | ||||||||
\(78\) | −3.41972 | + | 0.689606i | −0.387207 | + | 0.0780825i | ||||
\(79\) | 3.65421 | 0.411131 | 0.205565 | − | 0.978643i | \(-0.434097\pi\) | ||||
0.205565 | + | 0.978643i | \(0.434097\pi\) | |||||||
\(80\) | −3.64602 | − | 3.56988i | −0.407638 | − | 0.399125i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.59050 | + | 12.8461i | 0.286073 | + | 1.41862i | ||||
\(83\) | −3.03863 | −0.333533 | −0.166766 | − | 0.985996i | \(-0.553333\pi\) | ||||
−0.166766 | + | 0.985996i | \(0.553333\pi\) | |||||||
\(84\) | −1.93103 | − | 4.59322i | −0.210692 | − | 0.501161i | ||||
\(85\) | −8.59999 | −0.932800 | ||||||||
\(86\) | 2.82688 | + | 14.0184i | 0.304831 | + | 1.51164i | ||||
\(87\) | 5.45110i | 0.584419i | ||||||||
\(88\) | 9.41544 | + | 13.8526i | 1.00369 | + | 1.47669i | ||||
\(89\) | − | 5.81313i | − | 0.616190i | −0.951356 | − | 0.308095i | \(-0.900309\pi\) | ||
0.951356 | − | 0.308095i | \(-0.0996915\pi\) | |||||||
\(90\) | 1.76848 | − | 0.356624i | 0.186414 | − | 0.0375915i | ||||
\(91\) | −6.14552 | −0.644226 | ||||||||
\(92\) | −8.26430 | + | 4.86841i | −0.861613 | + | 0.507566i | ||||
\(93\) | −3.02410 | −0.313585 | ||||||||
\(94\) | 13.7739 | − | 2.77759i | 1.42067 | − | 0.286487i | ||||
\(95\) | 3.24020i | 0.332438i | ||||||||
\(96\) | 3.08047 | − | 4.74454i | 0.314400 | − | 0.484238i | ||||
\(97\) | − | 4.52256i | − | 0.459197i | −0.973285 | − | 0.229598i | \(-0.926259\pi\) | ||
0.973285 | − | 0.229598i | \(-0.0737412\pi\) | |||||||
\(98\) | 0.221791 | + | 1.09985i | 0.0224042 | + | 0.111101i | ||||
\(99\) | −5.92184 | −0.595168 | ||||||||
\(100\) | −6.21814 | + | 2.61416i | −0.621814 | + | 0.261416i | ||||
\(101\) | −9.44751 | −0.940062 | −0.470031 | − | 0.882650i | \(-0.655757\pi\) | ||||
−0.470031 | + | 0.882650i | \(0.655757\pi\) | |||||||
\(102\) | −1.88464 | − | 9.34581i | −0.186607 | − | 0.925373i | ||||
\(103\) | −1.68300 | −0.165831 | −0.0829154 | − | 0.996557i | \(-0.526423\pi\) | ||||
−0.0829154 | + | 0.996557i | \(0.526423\pi\) | |||||||
\(104\) | −3.92206 | − | 5.77040i | −0.384590 | − | 0.565834i | ||||
\(105\) | 3.17811 | 0.310151 | ||||||||
\(106\) | 2.88905 | − | 0.582594i | 0.280609 | − | 0.0565865i | ||||
\(107\) | −14.4223 | −1.39425 | −0.697126 | − | 0.716949i | \(-0.745538\pi\) | ||||
−0.697126 | + | 0.716949i | \(0.745538\pi\) | |||||||
\(108\) | 0.775104 | + | 1.84370i | 0.0745844 | + | 0.177410i | ||||
\(109\) | 11.3390i | 1.08608i | 0.839707 | + | 0.543040i | \(0.182727\pi\) | ||||
−0.839707 | + | 0.543040i | \(0.817273\pi\) | |||||||
\(110\) | −10.4726 | + | 2.11187i | −0.998528 | + | 0.201359i | ||||
\(111\) | −4.92988 | −0.467924 | ||||||||
\(112\) | 6.97175 | − | 7.12045i | 0.658769 | − | 0.672819i | ||||
\(113\) | − | 17.9670i | − | 1.69019i | −0.534612 | − | 0.845097i | \(-0.679542\pi\) | ||
0.534612 | − | 0.845097i | \(-0.320458\pi\) | |||||||
\(114\) | −3.52121 | + | 0.710072i | −0.329791 | + | 0.0665044i | ||||
\(115\) | −0.819675 | − | 6.06277i | −0.0764351 | − | 0.565356i | ||||
\(116\) | −10.0502 | + | 4.22517i | −0.933135 | + | 0.392297i | ||||
\(117\) | 2.46678 | 0.228054 | ||||||||
\(118\) | 10.3117 | − | 2.07942i | 0.949269 | − | 0.191426i | ||||
\(119\) | − | 16.7952i | − | 1.53962i | ||||||
\(120\) | 2.02826 | + | 2.98411i | 0.185154 | + | 0.272411i | ||||
\(121\) | 24.0682 | 2.18802 | ||||||||
\(122\) | 2.97228 | − | 0.599378i | 0.269098 | − | 0.0542652i | ||||
\(123\) | − | 9.26643i | − | 0.835526i | ||||||
\(124\) | −2.34399 | − | 5.57552i | −0.210497 | − | 0.500696i | ||||
\(125\) | − | 10.6808i | − | 0.955319i | ||||||
\(126\) | 0.696464 | + | 3.45372i | 0.0620460 | + | 0.307682i | ||||
\(127\) | 0.555947i | 0.0493323i | 0.999696 | + | 0.0246662i | \(0.00785228\pi\) | ||||
−0.999696 | + | 0.0246662i | \(0.992148\pi\) | |||||||
\(128\) | 11.1352 | + | 2.00194i | 0.984220 | + | 0.176948i | ||||
\(129\) | − | 10.1120i | − | 0.890313i | ||||||
\(130\) | 4.36245 | − | 0.879714i | 0.382612 | − | 0.0771560i | ||||
\(131\) | 0.593855i | 0.0518854i | 0.999663 | + | 0.0259427i | \(0.00825874\pi\) | ||||
−0.999663 | + | 0.0259427i | \(0.991741\pi\) | |||||||
\(132\) | −4.59004 | − | 10.9181i | −0.399512 | − | 0.950296i | ||||
\(133\) | −6.32791 | −0.548699 | ||||||||
\(134\) | −1.10886 | − | 5.49877i | −0.0957909 | − | 0.475021i | ||||
\(135\) | −1.27568 | −0.109793 | ||||||||
\(136\) | 15.7700 | − | 10.7187i | 1.35227 | − | 0.919119i | ||||
\(137\) | − | 12.1761i | − | 1.04027i | −0.854083 | − | 0.520136i | \(-0.825881\pi\) | ||
0.854083 | − | 0.520136i | \(-0.174119\pi\) | |||||||
\(138\) | 6.40893 | − | 2.21938i | 0.545564 | − | 0.188926i | ||||
\(139\) | 12.5827i | 1.06725i | 0.845721 | + | 0.533626i | \(0.179171\pi\) | ||||
−0.845721 | + | 0.533626i | \(0.820829\pi\) | |||||||
\(140\) | 2.46336 | + | 5.85946i | 0.208192 | + | 0.495215i | ||||
\(141\) | −9.93569 | −0.836736 | ||||||||
\(142\) | −16.7945 | + | 3.38671i | −1.40936 | + | 0.284206i | ||||
\(143\) | −14.6079 | −1.22157 | ||||||||
\(144\) | −2.79843 | + | 2.85811i | −0.233202 | + | 0.238176i | ||||
\(145\) | − | 6.95383i | − | 0.577485i | ||||||
\(146\) | 1.24412 | + | 6.16954i | 0.102964 | + | 0.510595i | ||||
\(147\) | − | 0.793365i | − | 0.0654356i | ||||||
\(148\) | −3.82117 | − | 9.08921i | −0.314099 | − | 0.747128i | ||||
\(149\) | 17.4838i | 1.43233i | 0.697932 | + | 0.716164i | \(0.254104\pi\) | ||||
−0.697932 | + | 0.716164i | \(0.745896\pi\) | |||||||
\(150\) | 4.67553 | − | 0.942849i | 0.381756 | − | 0.0769833i | ||||
\(151\) | 22.2343i | 1.80940i | 0.426046 | + | 0.904701i | \(0.359906\pi\) | ||||
−0.426046 | + | 0.904701i | \(0.640094\pi\) | |||||||
\(152\) | −4.03846 | − | 5.94165i | −0.327562 | − | 0.481932i | ||||
\(153\) | 6.74152i | 0.545019i | ||||||||
\(154\) | −4.12435 | − | 20.4524i | −0.332350 | − | 1.64810i | ||||
\(155\) | 3.85777 | 0.309864 | ||||||||
\(156\) | 1.91201 | + | 4.54799i | 0.153084 | + | 0.364131i | ||||
\(157\) | − | 18.2974i | − | 1.46029i | −0.683290 | − | 0.730147i | \(-0.739452\pi\) | ||
0.683290 | − | 0.730147i | \(-0.260548\pi\) | |||||||
\(158\) | −1.02156 | − | 5.06586i | −0.0812710 | − | 0.403018i | ||||
\(159\) | −2.08399 | −0.165271 | ||||||||
\(160\) | −3.92969 | + | 6.05250i | −0.310669 | + | 0.478492i | ||||
\(161\) | 11.8402 | − | 1.60077i | 0.933138 | − | 0.126158i | ||||
\(162\) | −0.279557 | − | 1.38631i | −0.0219641 | − | 0.108919i | ||||
\(163\) | 2.10553i | 0.164918i | 0.996594 | + | 0.0824591i | \(0.0262774\pi\) | ||||
−0.996594 | + | 0.0824591i | \(0.973723\pi\) | |||||||
\(164\) | 17.0845 | − | 7.18245i | 1.33407 | − | 0.560855i | ||||
\(165\) | 7.55435 | 0.588105 | ||||||||
\(166\) | 0.849471 | + | 4.21247i | 0.0659317 | + | 0.326951i | ||||
\(167\) | 4.43024i | 0.342823i | 0.985200 | + | 0.171411i | \(0.0548327\pi\) | ||||
−0.985200 | + | 0.171411i | \(0.945167\pi\) | |||||||
\(168\) | −5.82778 | + | 3.96106i | −0.449623 | + | 0.305603i | ||||
\(169\) | −6.91499 | −0.531922 | ||||||||
\(170\) | 2.40419 | + | 11.9222i | 0.184393 | + | 0.914393i | ||||
\(171\) | 2.53999 | 0.194238 | ||||||||
\(172\) | 18.6435 | − | 7.83786i | 1.42155 | − | 0.597631i | ||||
\(173\) | −5.29846 | −0.402835 | −0.201417 | − | 0.979505i | \(-0.564555\pi\) | ||||
−0.201417 | + | 0.979505i | \(0.564555\pi\) | |||||||
\(174\) | 7.55690 | − | 1.52389i | 0.572887 | − | 0.115526i | ||||
\(175\) | 8.40233 | 0.635156 | ||||||||
\(176\) | 16.5718 | − | 16.9253i | 1.24915 | − | 1.27579i | ||||
\(177\) | −7.43825 | −0.559093 | ||||||||
\(178\) | −8.05878 | + | 1.62510i | −0.604031 | + | 0.121806i | ||||
\(179\) | 6.37775i | 0.476696i | 0.971180 | + | 0.238348i | \(0.0766058\pi\) | ||||
−0.971180 | + | 0.238348i | \(0.923394\pi\) | |||||||
\(180\) | −0.988782 | − | 2.35196i | −0.0736994 | − | 0.175305i | ||||
\(181\) | 20.8442i | 1.54934i | 0.632368 | + | 0.774668i | \(0.282083\pi\) | ||||
−0.632368 | + | 0.774668i | \(0.717917\pi\) | |||||||
\(182\) | 1.71802 | + | 8.51958i | 0.127348 | + | 0.631513i | ||||
\(183\) | −2.14403 | −0.158491 | ||||||||
\(184\) | 9.05945 | + | 10.0959i | 0.667872 | + | 0.744277i | ||||
\(185\) | 6.28893 | 0.462372 | ||||||||
\(186\) | 0.845409 | + | 4.19233i | 0.0619884 | + | 0.307397i | ||||
\(187\) | − | 39.9222i | − | 2.91940i | ||||||
\(188\) | −7.70120 | − | 18.3184i | −0.561668 | − | 1.33601i | ||||
\(189\) | − | 2.49131i | − | 0.181216i | ||||||
\(190\) | 4.49192 | − | 0.905822i | 0.325878 | − | 0.0657152i | ||||
\(191\) | 0.120078 | 0.00868856 | 0.00434428 | − | 0.999991i | \(-0.498617\pi\) | ||||
0.00434428 | + | 0.999991i | \(0.498617\pi\) | |||||||
\(192\) | −7.43856 | − | 2.94411i | −0.536832 | − | 0.212473i | ||||
\(193\) | −5.99420 | −0.431472 | −0.215736 | − | 0.976452i | \(-0.569215\pi\) | ||||
−0.215736 | + | 0.976452i | \(0.569215\pi\) | |||||||
\(194\) | −6.26966 | + | 1.26431i | −0.450135 | + | 0.0907725i | ||||
\(195\) | −3.14681 | −0.225348 | ||||||||
\(196\) | 1.46272 | − | 0.614940i | 0.104480 | − | 0.0439243i | ||||
\(197\) | −12.4182 | −0.884761 | −0.442380 | − | 0.896827i | \(-0.645866\pi\) | ||||
−0.442380 | + | 0.896827i | \(0.645866\pi\) | |||||||
\(198\) | 1.65549 | + | 8.20949i | 0.117651 | + | 0.583423i | ||||
\(199\) | 9.56523 | 0.678061 | 0.339030 | − | 0.940775i | \(-0.389901\pi\) | ||||
0.339030 | + | 0.940775i | \(0.389901\pi\) | |||||||
\(200\) | 5.36235 | + | 7.88945i | 0.379175 | + | 0.557868i | ||||
\(201\) | 3.96649i | 0.279774i | ||||||||
\(202\) | 2.64112 | + | 13.0971i | 0.185828 | + | 0.921512i | ||||
\(203\) | 13.5804 | 0.953157 | ||||||||
\(204\) | −12.4293 | + | 5.22538i | −0.870225 | + | 0.365850i | ||||
\(205\) | 11.8210i | 0.825612i | ||||||||
\(206\) | 0.470494 | + | 2.33315i | 0.0327809 | + | 0.162558i | ||||
\(207\) | −4.75259 | + | 0.642542i | −0.330328 | + | 0.0446597i | ||||
\(208\) | −6.90311 | + | 7.05034i | −0.478644 | + | 0.488853i | ||||
\(209\) | −15.0414 | −1.04044 | ||||||||
\(210\) | −0.888462 | − | 4.40583i | −0.0613097 | − | 0.304031i | ||||
\(211\) | − | 2.54447i | − | 0.175169i | −0.996157 | − | 0.0875843i | \(-0.972085\pi\) | ||
0.996157 | − | 0.0875843i | \(-0.0279147\pi\) | |||||||
\(212\) | −1.61531 | − | 3.84224i | −0.110940 | − | 0.263886i | ||||
\(213\) | 12.1146 | 0.830076 | ||||||||
\(214\) | 4.03184 | + | 19.9937i | 0.275611 | + | 1.36674i | ||||
\(215\) | 12.8996i | 0.879748i | ||||||||
\(216\) | 2.33924 | − | 1.58995i | 0.159165 | − | 0.108182i | ||||
\(217\) | 7.53398i | 0.511440i | ||||||||
\(218\) | 15.7193 | − | 3.16990i | 1.06465 | − | 0.214693i | ||||
\(219\) | − | 4.45034i | − | 0.300726i | ||||||
\(220\) | 5.85541 | + | 13.9279i | 0.394772 | + | 0.939020i | ||||
\(221\) | 16.6298i | 1.11864i | ||||||||
\(222\) | 1.37818 | + | 6.83433i | 0.0924977 | + | 0.458691i | ||||
\(223\) | 8.25462i | 0.552770i | 0.961047 | + | 0.276385i | \(0.0891365\pi\) | ||||
−0.961047 | + | 0.276385i | \(0.910864\pi\) | |||||||
\(224\) | −11.8201 | − | 7.67442i | −0.789766 | − | 0.512769i | ||||
\(225\) | −3.37265 | −0.224843 | ||||||||
\(226\) | −24.9078 | + | 5.02281i | −1.65684 | + | 0.334112i | ||||
\(227\) | 10.9045 | 0.723755 | 0.361877 | − | 0.932226i | \(-0.382136\pi\) | ||||
0.361877 | + | 0.932226i | \(0.382136\pi\) | |||||||
\(228\) | 1.96876 | + | 4.68297i | 0.130384 | + | 0.310137i | ||||
\(229\) | 14.3196i | 0.946264i | 0.880992 | + | 0.473132i | \(0.156877\pi\) | ||||
−0.880992 | + | 0.473132i | \(0.843123\pi\) | |||||||
\(230\) | −8.17571 | + | 2.83121i | −0.539090 | + | 0.186685i | ||||
\(231\) | 14.7532i | 0.970686i | ||||||||
\(232\) | 8.66698 | + | 12.7514i | 0.569015 | + | 0.837173i | ||||
\(233\) | 10.5570 | 0.691615 | 0.345808 | − | 0.938305i | \(-0.387605\pi\) | ||||
0.345808 | + | 0.938305i | \(0.387605\pi\) | |||||||
\(234\) | −0.689606 | − | 3.41972i | −0.0450810 | − | 0.223554i | ||||
\(235\) | 12.6747 | 0.826808 | ||||||||
\(236\) | −5.76542 | − | 13.7139i | −0.375297 | − | 0.892697i | ||||
\(237\) | 3.65421i | 0.237366i | ||||||||
\(238\) | −23.2833 | + | 4.69522i | −1.50923 | + | 0.304346i | ||||
\(239\) | − | 4.84386i | − | 0.313323i | −0.987652 | − | 0.156662i | \(-0.949927\pi\) | ||
0.987652 | − | 0.156662i | \(-0.0500732\pi\) | |||||||
\(240\) | 3.56988 | − | 3.64602i | 0.230435 | − | 0.235350i | ||||
\(241\) | − | 22.0218i | − | 1.41855i | −0.704933 | − | 0.709274i | \(-0.749023\pi\) | ||
0.704933 | − | 0.709274i | \(-0.250977\pi\) | |||||||
\(242\) | −6.72844 | − | 33.3659i | −0.432521 | − | 2.14484i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −1.66185 | − | 3.95294i | −0.106389 | − | 0.253061i | ||||
\(245\) | 1.01208i | 0.0646592i | ||||||||
\(246\) | −12.8461 | + | 2.59050i | −0.819039 | + | 0.165164i | ||||
\(247\) | 6.26560 | 0.398671 | ||||||||
\(248\) | −7.07410 | + | 4.80817i | −0.449206 | + | 0.305319i | ||||
\(249\) | − | 3.03863i | − | 0.192565i | ||||||
\(250\) | −14.8069 | + | 2.98589i | −0.936468 | + | 0.188844i | ||||
\(251\) | −1.49664 | −0.0944669 | −0.0472334 | − | 0.998884i | \(-0.515040\pi\) | ||||
−0.0472334 | + | 0.998884i | \(0.515040\pi\) | |||||||
\(252\) | 4.59322 | − | 1.93103i | 0.289346 | − | 0.121643i | ||||
\(253\) | 28.1441 | − | 3.80503i | 1.76940 | − | 0.239220i | ||||
\(254\) | 0.770713 | − | 0.155419i | 0.0483588 | − | 0.00975185i | ||||
\(255\) | − | 8.59999i | − | 0.538552i | ||||||
\(256\) | −0.337613 | − | 15.9964i | −0.0211008 | − | 0.999777i | ||||
\(257\) | 15.3146 | 0.955301 | 0.477650 | − | 0.878550i | \(-0.341489\pi\) | ||||
0.477650 | + | 0.878550i | \(0.341489\pi\) | |||||||
\(258\) | −14.0184 | + | 2.82688i | −0.872744 | + | 0.175994i | ||||
\(259\) | 12.2819i | 0.763159i | ||||||||
\(260\) | −2.43911 | − | 5.80176i | −0.151267 | − | 0.359810i | ||||
\(261\) | −5.45110 | −0.337415 | ||||||||
\(262\) | 0.823266 | − | 0.166016i | 0.0508615 | − | 0.0102565i | ||||
\(263\) | 2.19677 | 0.135458 | 0.0677292 | − | 0.997704i | \(-0.478425\pi\) | ||||
0.0677292 | + | 0.997704i | \(0.478425\pi\) | |||||||
\(264\) | −13.8526 | + | 9.41544i | −0.852570 | + | 0.579480i | ||||
\(265\) | 2.65849 | 0.163310 | ||||||||
\(266\) | 1.76901 | + | 8.77242i | 0.108465 | + | 0.537872i | ||||
\(267\) | 5.81313 | 0.355757 | ||||||||
\(268\) | −7.31299 | + | 3.07444i | −0.446712 | + | 0.187801i | ||||
\(269\) | −8.15180 | −0.497024 | −0.248512 | − | 0.968629i | \(-0.579942\pi\) | ||||
−0.248512 | + | 0.968629i | \(0.579942\pi\) | |||||||
\(270\) | 0.356624 | + | 1.76848i | 0.0217035 | + | 0.107626i | ||||
\(271\) | − | 17.0762i | − | 1.03731i | −0.854984 | − | 0.518654i | \(-0.826433\pi\) | ||
0.854984 | − | 0.518654i | \(-0.173567\pi\) | |||||||
\(272\) | −19.2680 | − | 18.8656i | −1.16829 | − | 1.14390i | ||||
\(273\) | − | 6.14552i | − | 0.371944i | ||||||
\(274\) | −16.8798 | + | 3.40391i | −1.01975 | + | 0.205638i | ||||
\(275\) | 19.9723 | 1.20438 | ||||||||
\(276\) | −4.86841 | − | 8.26430i | −0.293044 | − | 0.497452i | ||||
\(277\) | 13.9801 | 0.839982 | 0.419991 | − | 0.907528i | \(-0.362033\pi\) | ||||
0.419991 | + | 0.907528i | \(0.362033\pi\) | |||||||
\(278\) | 17.4435 | − | 3.51759i | 1.04619 | − | 0.210971i | ||||
\(279\) | − | 3.02410i | − | 0.181048i | ||||||
\(280\) | 7.43436 | − | 5.05303i | 0.444288 | − | 0.301976i | ||||
\(281\) | 22.1413i | 1.32084i | 0.750896 | + | 0.660420i | \(0.229622\pi\) | ||||
−0.750896 | + | 0.660420i | \(0.770378\pi\) | |||||||
\(282\) | 2.77759 | + | 13.7739i | 0.165403 | + | 0.820225i | ||||
\(283\) | −14.2647 | −0.847946 | −0.423973 | − | 0.905675i | \(-0.639365\pi\) | ||||
−0.423973 | + | 0.905675i | \(0.639365\pi\) | |||||||
\(284\) | 9.39004 | + | 22.3356i | 0.557197 | + | 1.32537i | ||||
\(285\) | −3.24020 | −0.191933 | ||||||||
\(286\) | 4.08374 | + | 20.2510i | 0.241477 | + | 1.19747i | ||||
\(287\) | −23.0856 | −1.36270 | ||||||||
\(288\) | 4.74454 | + | 3.08047i | 0.279575 | + | 0.181519i | ||||
\(289\) | −28.4481 | −1.67341 | ||||||||
\(290\) | −9.64015 | + | 1.94399i | −0.566089 | + | 0.114155i | ||||
\(291\) | 4.52256 | 0.265117 | ||||||||
\(292\) | 8.20507 | − | 3.44948i | 0.480166 | − | 0.201865i | ||||
\(293\) | − | 9.44315i | − | 0.551675i | −0.961204 | − | 0.275837i | \(-0.911045\pi\) | ||
0.961204 | − | 0.275837i | \(-0.0889552\pi\) | |||||||
\(294\) | −1.09985 | + | 0.221791i | −0.0641444 | + | 0.0129351i | ||||
\(295\) | 9.48880 | 0.552459 | ||||||||
\(296\) | −11.5322 | + | 7.83827i | −0.670295 | + | 0.455590i | ||||
\(297\) | − | 5.92184i | − | 0.343620i | ||||||
\(298\) | 24.2379 | − | 4.88772i | 1.40407 | − | 0.283138i | ||||
\(299\) | −11.7236 | + | 1.58501i | −0.677994 | + | 0.0916635i | ||||
\(300\) | −2.61416 | − | 6.21814i | −0.150928 | − | 0.359005i | ||||
\(301\) | −25.1922 | −1.45205 | ||||||||
\(302\) | 30.8236 | − | 6.21576i | 1.77370 | − | 0.357677i | ||||
\(303\) | − | 9.44751i | − | 0.542745i | ||||||
\(304\) | −7.10798 | + | 7.25958i | −0.407670 | + | 0.416365i | ||||
\(305\) | 2.73508 | 0.156610 | ||||||||
\(306\) | 9.34581 | − | 1.88464i | 0.534265 | − | 0.107738i | ||||
\(307\) | 16.9520i | 0.967504i | 0.875205 | + | 0.483752i | \(0.160726\pi\) | ||||
−0.875205 | + | 0.483752i | \(0.839274\pi\) | |||||||
\(308\) | −27.2003 | + | 11.4352i | −1.54988 | + | 0.651583i | ||||
\(309\) | − | 1.68300i | − | 0.0957424i | ||||||
\(310\) | −1.07847 | − | 5.34805i | −0.0612528 | − | 0.303749i | ||||
\(311\) | − | 19.6873i | − | 1.11636i | −0.829719 | − | 0.558182i | \(-0.811499\pi\) | ||
0.829719 | − | 0.558182i | \(-0.188501\pi\) | |||||||
\(312\) | 5.77040 | − | 3.92206i | 0.326685 | − | 0.222043i | ||||
\(313\) | 1.61663i | 0.0913772i | 0.998956 | + | 0.0456886i | \(0.0145482\pi\) | ||||
−0.998956 | + | 0.0456886i | \(0.985452\pi\) | |||||||
\(314\) | −25.3658 | + | 5.11518i | −1.43148 | + | 0.288666i | ||||
\(315\) | 3.17811i | 0.179066i | ||||||||
\(316\) | −6.73725 | + | 2.83239i | −0.379000 | + | 0.159335i | ||||
\(317\) | −24.6211 | −1.38286 | −0.691430 | − | 0.722444i | \(-0.743019\pi\) | ||||
−0.691430 | + | 0.722444i | \(0.743019\pi\) | |||||||
\(318\) | 0.582594 | + | 2.88905i | 0.0326703 | + | 0.162010i | ||||
\(319\) | 32.2806 | 1.80736 | ||||||||
\(320\) | 9.48919 | + | 3.75573i | 0.530462 | + | 0.209952i | ||||
\(321\) | − | 14.4223i | − | 0.804972i | ||||||
\(322\) | −5.52917 | − | 15.9666i | −0.308129 | − | 0.889786i | ||||
\(323\) | 17.1234i | 0.952771i | ||||||||
\(324\) | −1.84370 | + | 0.775104i | −0.102428 | + | 0.0430613i | ||||
\(325\) | −8.31959 | −0.461488 | ||||||||
\(326\) | 2.91892 | − | 0.588617i | 0.161664 | − | 0.0326005i | ||||
\(327\) | −11.3390 | −0.627048 | ||||||||
\(328\) | −14.7332 | − | 21.6764i | −0.813503 | − | 1.19688i | ||||
\(329\) | 24.7529i | 1.36467i | ||||||||
\(330\) | −2.11187 | − | 10.4726i | −0.116255 | − | 0.576500i | ||||
\(331\) | 24.9576i | 1.37179i | 0.727699 | + | 0.685896i | \(0.240590\pi\) | ||||
−0.727699 | + | 0.685896i | \(0.759410\pi\) | |||||||
\(332\) | 5.60231 | − | 2.35525i | 0.307467 | − | 0.129261i | ||||
\(333\) | − | 4.92988i | − | 0.270156i | ||||||
\(334\) | 6.14168 | − | 1.23851i | 0.336058 | − | 0.0677681i | ||||
\(335\) | − | 5.05995i | − | 0.276455i | ||||||
\(336\) | 7.12045 | + | 6.97175i | 0.388452 | + | 0.380340i | ||||
\(337\) | − | 16.3446i | − | 0.890347i | −0.895444 | − | 0.445173i | \(-0.853142\pi\) | ||
0.895444 | − | 0.445173i | \(-0.146858\pi\) | |||||||
\(338\) | 1.93314 | + | 9.58630i | 0.105149 | + | 0.521426i | ||||
\(339\) | 17.9670 | 0.975834 | ||||||||
\(340\) | 15.8558 | − | 6.66589i | 0.859899 | − | 0.361508i | ||||
\(341\) | 17.9082i | 0.969786i | ||||||||
\(342\) | −0.710072 | − | 3.52121i | −0.0383963 | − | 0.190405i | ||||
\(343\) | −19.4157 | −1.04835 | ||||||||
\(344\) | −16.0776 | − | 23.6544i | −0.866846 | − | 1.27536i | ||||
\(345\) | 6.06277 | − | 0.819675i | 0.326408 | − | 0.0441298i | ||||
\(346\) | 1.48122 | + | 7.34530i | 0.0796311 | + | 0.394886i | ||||
\(347\) | − | 18.8134i | − | 1.00995i | −0.863133 | − | 0.504977i | \(-0.831501\pi\) | ||
0.863133 | − | 0.504977i | \(-0.168499\pi\) | |||||||
\(348\) | −4.22517 | − | 10.0502i | −0.226493 | − | 0.538746i | ||||
\(349\) | 13.5829 | 0.727078 | 0.363539 | − | 0.931579i | \(-0.381568\pi\) | ||||
0.363539 | + | 0.931579i | \(0.381568\pi\) | |||||||
\(350\) | −2.34893 | − | 11.6482i | −0.125556 | − | 0.622623i | ||||
\(351\) | 2.46678i | 0.131667i | ||||||||
\(352\) | −28.0964 | − | 18.2421i | −1.49754 | − | 0.972306i | ||||
\(353\) | 31.5063 | 1.67691 | 0.838456 | − | 0.544969i | \(-0.183459\pi\) | ||||
0.838456 | + | 0.544969i | \(0.183459\pi\) | |||||||
\(354\) | 2.07942 | + | 10.3117i | 0.110520 | + | 0.548061i | ||||
\(355\) | −15.4542 | −0.820226 | ||||||||
\(356\) | 4.50578 | + | 10.7176i | 0.238806 | + | 0.568033i | ||||
\(357\) | 16.7952 | 0.888897 | ||||||||
\(358\) | 8.84152 | − | 1.78295i | 0.467289 | − | 0.0942316i | ||||
\(359\) | 18.4884 | 0.975779 | 0.487890 | − | 0.872905i | \(-0.337767\pi\) | ||||
0.487890 | + | 0.872905i | \(0.337767\pi\) | |||||||
\(360\) | −2.98411 | + | 2.02826i | −0.157277 | + | 0.106899i | ||||
\(361\) | −12.5485 | −0.660445 | ||||||||
\(362\) | 28.8965 | − | 5.82714i | 1.51876 | − | 0.306268i | ||||
\(363\) | 24.0682i | 1.26325i | ||||||||
\(364\) | 11.3305 | − | 4.76342i | 0.593878 | − | 0.249671i | ||||
\(365\) | 5.67719i | 0.297158i | ||||||||
\(366\) | 0.599378 | + | 2.97228i | 0.0313300 | + | 0.155364i | ||||
\(367\) | 3.17955 | 0.165971 | 0.0829855 | − | 0.996551i | \(-0.473554\pi\) | ||||
0.0829855 | + | 0.996551i | \(0.473554\pi\) | |||||||
\(368\) | 11.4633 | − | 15.3816i | 0.597567 | − | 0.801819i | ||||
\(369\) | 9.26643 | 0.482391 | ||||||||
\(370\) | −1.75812 | − | 8.71839i | −0.0914001 | − | 0.453248i | ||||
\(371\) | 5.19187i | 0.269548i | ||||||||
\(372\) | 5.57552 | − | 2.34399i | 0.289077 | − | 0.121530i | ||||
\(373\) | − | 17.7910i | − | 0.921186i | −0.887612 | − | 0.460593i | \(-0.847637\pi\) | ||
0.887612 | − | 0.460593i | \(-0.152363\pi\) | |||||||
\(374\) | −55.3444 | + | 11.1605i | −2.86179 | + | 0.577098i | ||||
\(375\) | 10.6808 | 0.551553 | ||||||||
\(376\) | −23.2420 | + | 15.7973i | −1.19861 | + | 0.814682i | ||||
\(377\) | −13.4467 | −0.692539 | ||||||||
\(378\) | −3.45372 | + | 0.696464i | −0.177640 | + | 0.0358222i | ||||
\(379\) | 13.2435 | 0.680273 | 0.340136 | − | 0.940376i | \(-0.389527\pi\) | ||||
0.340136 | + | 0.940376i | \(0.389527\pi\) | |||||||
\(380\) | −2.51150 | − | 5.97395i | −0.128837 | − | 0.306457i | ||||
\(381\) | −0.555947 | −0.0284820 | ||||||||
\(382\) | −0.0335687 | − | 0.166465i | −0.00171753 | − | 0.00851711i | ||||
\(383\) | 9.71405 | 0.496365 | 0.248182 | − | 0.968713i | \(-0.420167\pi\) | ||||
0.248182 | + | 0.968713i | \(0.420167\pi\) | |||||||
\(384\) | −2.00194 | + | 11.1352i | −0.102161 | + | 0.568240i | ||||
\(385\) | − | 18.8202i | − | 0.959168i | ||||||
\(386\) | 1.67572 | + | 8.30980i | 0.0852920 | + | 0.422958i | ||||
\(387\) | 10.1120 | 0.514022 | ||||||||
\(388\) | 3.50546 | + | 8.33823i | 0.177963 | + | 0.423309i | ||||
\(389\) | 27.6072i | 1.39974i | 0.714271 | + | 0.699870i | \(0.246759\pi\) | ||||
−0.714271 | + | 0.699870i | \(0.753241\pi\) | |||||||
\(390\) | 0.879714 | + | 4.36245i | 0.0445460 | + | 0.220901i | ||||
\(391\) | −4.33171 | − | 32.0397i | −0.219064 | − | 1.62032i | ||||
\(392\) | −1.26141 | − | 1.85587i | −0.0637109 | − | 0.0937357i | ||||
\(393\) | −0.593855 | −0.0299560 | ||||||||
\(394\) | 3.47160 | + | 17.2155i | 0.174897 | + | 0.867302i | ||||
\(395\) | − | 4.66159i | − | 0.234550i | ||||||
\(396\) | 10.9181 | − | 4.59004i | 0.548654 | − | 0.230658i | ||||
\(397\) | 12.2838 | 0.616508 | 0.308254 | − | 0.951304i | \(-0.400255\pi\) | ||||
0.308254 | + | 0.951304i | \(0.400255\pi\) | |||||||
\(398\) | −2.67403 | − | 13.2603i | −0.134037 | − | 0.664681i | ||||
\(399\) | − | 6.32791i | − | 0.316792i | ||||||
\(400\) | 9.43812 | − | 9.63942i | 0.471906 | − | 0.481971i | ||||
\(401\) | 17.1714i | 0.857499i | 0.903423 | + | 0.428750i | \(0.141046\pi\) | ||||
−0.903423 | + | 0.428750i | \(0.858954\pi\) | |||||||
\(402\) | 5.49877 | − | 1.10886i | 0.274254 | − | 0.0553049i | ||||
\(403\) | − | 7.45979i | − | 0.371599i | ||||||
\(404\) | 17.4183 | − | 7.32280i | 0.866594 | − | 0.364323i | ||||
\(405\) | − | 1.27568i | − | 0.0633888i | ||||||
\(406\) | −3.79650 | − | 18.8266i | −0.188417 | − | 0.934348i | ||||
\(407\) | 29.1940i | 1.44709i | ||||||||
\(408\) | 10.7187 | + | 15.7700i | 0.530654 | + | 0.780734i | ||||
\(409\) | 24.7976 | 1.22616 | 0.613082 | − | 0.790019i | \(-0.289930\pi\) | ||||
0.613082 | + | 0.790019i | \(0.289930\pi\) | |||||||
\(410\) | 16.3875 | − | 3.30463i | 0.809320 | − | 0.163204i | ||||
\(411\) | 12.1761 | 0.600602 | ||||||||
\(412\) | 3.10294 | − | 1.30450i | 0.152871 | − | 0.0642681i | ||||
\(413\) | 18.5310i | 0.911851i | ||||||||
\(414\) | 2.21938 | + | 6.40893i | 0.109077 | + | 0.314982i | ||||
\(415\) | 3.87631i | 0.190280i | ||||||||
\(416\) | 11.7037 | + | 7.59885i | 0.573823 | + | 0.372564i | ||||
\(417\) | −12.5827 | −0.616178 | ||||||||
\(418\) | 4.20494 | + | 20.8520i | 0.205670 | + | 1.01991i | ||||
\(419\) | 14.3462 | 0.700856 | 0.350428 | − | 0.936590i | \(-0.386036\pi\) | ||||
0.350428 | + | 0.936590i | \(0.386036\pi\) | |||||||
\(420\) | −5.85946 | + | 2.46336i | −0.285912 | + | 0.120200i | ||||
\(421\) | − | 34.0216i | − | 1.65811i | −0.559166 | − | 0.829056i | \(-0.688879\pi\) | ||
0.559166 | − | 0.829056i | \(-0.311121\pi\) | |||||||
\(422\) | −3.52742 | + | 0.711325i | −0.171712 | + | 0.0346267i | ||||
\(423\) | − | 9.93569i | − | 0.483090i | ||||||
\(424\) | −4.87496 | + | 3.31344i | −0.236749 | + | 0.160915i | ||||
\(425\) | − | 22.7368i | − | 1.10290i | ||||||
\(426\) | −3.38671 | − | 16.7945i | −0.164087 | − | 0.813696i | ||||
\(427\) | 5.34144i | 0.258491i | ||||||||
\(428\) | 26.5902 | − | 11.1787i | 1.28529 | − | 0.540345i | ||||
\(429\) | − | 14.6079i | − | 0.705275i | ||||||
\(430\) | 17.8829 | − | 3.60619i | 0.862388 | − | 0.173906i | ||||
\(431\) | −24.1892 | −1.16515 | −0.582575 | − | 0.812777i | \(-0.697955\pi\) | ||||
−0.582575 | + | 0.812777i | \(0.697955\pi\) | |||||||
\(432\) | −2.85811 | − | 2.79843i | −0.137511 | − | 0.134639i | ||||
\(433\) | 26.3588i | 1.26672i | 0.773856 | + | 0.633362i | \(0.218325\pi\) | ||||
−0.773856 | + | 0.633362i | \(0.781675\pi\) | |||||||
\(434\) | 10.4444 | − | 2.10618i | 0.501347 | − | 0.101100i | ||||
\(435\) | 6.95383 | 0.333411 | ||||||||
\(436\) | −8.78891 | − | 20.9057i | −0.420912 | − | 1.00120i | ||||
\(437\) | −12.0715 | + | 1.63205i | −0.577460 | + | 0.0780715i | ||||
\(438\) | −6.16954 | + | 1.24412i | −0.294792 | + | 0.0594466i | ||||
\(439\) | 3.36175i | 0.160448i | 0.996777 | + | 0.0802238i | \(0.0255635\pi\) | ||||
−0.996777 | + | 0.0802238i | \(0.974437\pi\) | |||||||
\(440\) | 17.6715 | − | 12.0110i | 0.842454 | − | 0.572604i | ||||
\(441\) | 0.793365 | 0.0377793 | ||||||||
\(442\) | 23.0541 | − | 4.64899i | 1.09657 | − | 0.221130i | ||||
\(443\) | − | 24.2964i | − | 1.15436i | −0.816618 | − | 0.577179i | \(-0.804154\pi\) | ||
0.816618 | − | 0.577179i | \(-0.195846\pi\) | |||||||
\(444\) | 9.08921 | − | 3.82117i | 0.431355 | − | 0.181345i | ||||
\(445\) | −7.41566 | −0.351536 | ||||||||
\(446\) | 11.4434 | − | 2.30764i | 0.541862 | − | 0.109270i | ||||
\(447\) | −17.4838 | −0.826955 | ||||||||
\(448\) | −7.33470 | + | 18.5318i | −0.346532 | + | 0.875544i | ||||
\(449\) | −2.97429 | −0.140365 | −0.0701826 | − | 0.997534i | \(-0.522358\pi\) | ||||
−0.0701826 | + | 0.997534i | \(0.522358\pi\) | |||||||
\(450\) | 0.942849 | + | 4.67553i | 0.0444463 | + | 0.220407i | ||||
\(451\) | −54.8744 | −2.58393 | ||||||||
\(452\) | 13.9263 | + | 33.1257i | 0.655039 | + | 1.55810i | ||||
\(453\) | −22.2343 | −1.04466 | ||||||||
\(454\) | −3.04842 | − | 15.1169i | −0.143070 | − | 0.709473i | ||||
\(455\) | 7.83969i | 0.367530i | ||||||||
\(456\) | 5.94165 | − | 4.03846i | 0.278243 | − | 0.189118i | ||||
\(457\) | − | 30.9823i | − | 1.44929i | −0.689123 | − | 0.724644i | \(-0.742004\pi\) | ||
0.689123 | − | 0.724644i | \(-0.257996\pi\) | |||||||
\(458\) | 19.8513 | − | 4.00314i | 0.927592 | − | 0.187054i | ||||
\(459\) | −6.74152 | −0.314667 | ||||||||
\(460\) | 6.21051 | + | 10.5426i | 0.289566 | + | 0.491550i | ||||
\(461\) | 42.5845 | 1.98336 | 0.991679 | − | 0.128738i | \(-0.0410925\pi\) | ||||
0.991679 | + | 0.128738i | \(0.0410925\pi\) | |||||||
\(462\) | 20.4524 | − | 4.12435i | 0.951532 | − | 0.191882i | ||||
\(463\) | − | 28.2192i | − | 1.31146i | −0.754997 | − | 0.655728i | \(-0.772362\pi\) | ||
0.754997 | − | 0.655728i | \(-0.227638\pi\) | |||||||
\(464\) | 15.2545 | − | 15.5799i | 0.708173 | − | 0.723277i | ||||
\(465\) | 3.85777i | 0.178900i | ||||||||
\(466\) | −2.95130 | − | 14.6353i | −0.136716 | − | 0.677968i | ||||
\(467\) | 16.9236 | 0.783130 | 0.391565 | − | 0.920150i | \(-0.371934\pi\) | ||||
0.391565 | + | 0.920150i | \(0.371934\pi\) | |||||||
\(468\) | −4.54799 | + | 1.91201i | −0.210231 | + | 0.0883828i | ||||
\(469\) | 9.88176 | 0.456297 | ||||||||
\(470\) | −3.54331 | − | 17.5711i | −0.163441 | − | 0.810492i | ||||
\(471\) | 18.2974 | 0.843101 | ||||||||
\(472\) | −17.3999 | + | 11.8265i | −0.800894 | + | 0.544357i | ||||
\(473\) | −59.8817 | −2.75336 | ||||||||
\(474\) | 5.06586 | − | 1.02156i | 0.232683 | − | 0.0469218i | ||||
\(475\) | −8.56650 | −0.393058 | ||||||||
\(476\) | 13.0180 | + | 30.9653i | 0.596681 | + | 1.41929i | ||||
\(477\) | − | 2.08399i | − | 0.0954193i | ||||||
\(478\) | −6.71508 | + | 1.35414i | −0.307141 | + | 0.0619368i | ||||
\(479\) | −25.7641 | −1.17719 | −0.588595 | − | 0.808428i | \(-0.700319\pi\) | ||||
−0.588595 | + | 0.808428i | \(0.700319\pi\) | |||||||
\(480\) | −6.05250 | − | 3.92969i | −0.276257 | − | 0.179365i | ||||
\(481\) | − | 12.1609i | − | 0.554491i | ||||||
\(482\) | −30.5290 | + | 6.15635i | −1.39056 | + | 0.280414i | ||||
\(483\) | 1.60077 | + | 11.8402i | 0.0728376 | + | 0.538747i | ||||
\(484\) | −44.3745 | + | 18.6554i | −2.01702 | + | 0.847972i | ||||
\(485\) | −5.76932 | −0.261971 | ||||||||
\(486\) | 1.38631 | − | 0.279557i | 0.0628842 | − | 0.0126810i | ||||
\(487\) | 21.2924i | 0.964850i | 0.875937 | + | 0.482425i | \(0.160244\pi\) | ||||
−0.875937 | + | 0.482425i | \(0.839756\pi\) | |||||||
\(488\) | −5.01540 | + | 3.40890i | −0.227037 | + | 0.154314i | ||||
\(489\) | −2.10553 | −0.0952156 | ||||||||
\(490\) | 1.40305 | − | 0.282933i | 0.0633833 | − | 0.0127816i | ||||
\(491\) | 7.54351i | 0.340434i | 0.985407 | + | 0.170217i | \(0.0544468\pi\) | ||||
−0.985407 | + | 0.170217i | \(0.945553\pi\) | |||||||
\(492\) | 7.18245 | + | 17.0845i | 0.323810 | + | 0.770228i | ||||
\(493\) | − | 36.7487i | − | 1.65508i | ||||||
\(494\) | −1.75159 | − | 8.68605i | −0.0788079 | − | 0.390804i | ||||
\(495\) | 7.55435i | 0.339543i | ||||||||
\(496\) | 8.64322 | + | 8.46272i | 0.388092 | + | 0.379987i | ||||
\(497\) | − | 30.1811i | − | 1.35381i | ||||||
\(498\) | −4.21247 | + | 0.849471i | −0.188765 | + | 0.0380657i | ||||
\(499\) | − | 18.4954i | − | 0.827970i | −0.910284 | − | 0.413985i | \(-0.864137\pi\) | ||
0.910284 | − | 0.413985i | \(-0.135863\pi\) | |||||||
\(500\) | 8.27872 | + | 19.6921i | 0.370236 | + | 0.880658i | ||||
\(501\) | −4.43024 | −0.197929 | ||||||||
\(502\) | 0.418395 | + | 2.07480i | 0.0186739 | + | 0.0926028i | ||||
\(503\) | −41.5195 | −1.85126 | −0.925632 | − | 0.378425i | \(-0.876466\pi\) | ||||
−0.925632 | + | 0.378425i | \(0.876466\pi\) | |||||||
\(504\) | −3.96106 | − | 5.82778i | −0.176440 | − | 0.259590i | ||||
\(505\) | 12.0520i | 0.536305i | ||||||||
\(506\) | −13.1428 | − | 37.9527i | −0.584270 | − | 1.68720i | ||||
\(507\) | − | 6.91499i | − | 0.307106i | ||||||
\(508\) | −0.430917 | − | 1.02500i | −0.0191188 | − | 0.0454769i | ||||
\(509\) | −0.524721 | −0.0232579 | −0.0116289 | − | 0.999932i | \(-0.503702\pi\) | ||||
−0.0116289 | + | 0.999932i | \(0.503702\pi\) | |||||||
\(510\) | −11.9222 | + | 2.40419i | −0.527925 | + | 0.106459i | ||||
\(511\) | −11.0872 | −0.490468 | ||||||||
\(512\) | −22.0816 | + | 4.93995i | −0.975878 | + | 0.218317i | ||||
\(513\) | 2.53999i | 0.112143i | ||||||||
\(514\) | −4.28131 | − | 21.2308i | −0.188841 | − | 0.936450i | ||||
\(515\) | 2.14696i | 0.0946064i | ||||||||
\(516\) | 7.83786 | + | 18.6435i | 0.345043 | + | 0.820733i | ||||
\(517\) | 58.8376i | 2.58767i | ||||||||
\(518\) | 17.0265 | − | 3.43349i | 0.748100 | − | 0.150859i | ||||
\(519\) | − | 5.29846i | − | 0.232577i | ||||||
\(520\) | −7.36116 | + | 5.00328i | −0.322808 | + | 0.219408i | ||||
\(521\) | 14.1174i | 0.618493i | 0.950982 | + | 0.309247i | \(0.100077\pi\) | ||||
−0.950982 | + | 0.309247i | \(0.899923\pi\) | |||||||
\(522\) | 1.52389 | + | 7.55690i | 0.0666990 | + | 0.330756i | ||||
\(523\) | −26.2501 | −1.14784 | −0.573918 | − | 0.818913i | \(-0.694577\pi\) | ||||
−0.573918 | + | 0.818913i | \(0.694577\pi\) | |||||||
\(524\) | −0.460300 | − | 1.09489i | −0.0201083 | − | 0.0478304i | ||||
\(525\) | 8.40233i | 0.366708i | ||||||||
\(526\) | −0.614122 | − | 3.04539i | −0.0267770 | − | 0.132786i | ||||
\(527\) | 20.3870 | 0.888072 | ||||||||
\(528\) | 16.9253 | + | 16.5718i | 0.736579 | + | 0.721197i | ||||
\(529\) | 22.1743 | − | 6.10748i | 0.964099 | − | 0.265543i | ||||
\(530\) | −0.743201 | − | 3.68549i | −0.0322826 | − | 0.160087i | ||||
\(531\) | − | 7.43825i | − | 0.322793i | ||||||
\(532\) | 11.6667 | − | 4.90479i | 0.505817 | − | 0.212650i | ||||
\(533\) | 22.8583 | 0.990101 | ||||||||
\(534\) | −1.62510 | − | 8.05878i | −0.0703250 | − | 0.348737i | ||||
\(535\) | 18.3981i | 0.795420i | ||||||||
\(536\) | 6.30652 | + | 9.27858i | 0.272400 | + | 0.400773i | ||||
\(537\) | −6.37775 | −0.275220 | ||||||||
\(538\) | 2.27889 | + | 11.3009i | 0.0982501 | + | 0.487216i | ||||
\(539\) | −4.69818 | −0.202365 | ||||||||
\(540\) | 2.35196 | − | 0.988782i | 0.101212 | − | 0.0425504i | ||||
\(541\) | 22.3639 | 0.961498 | 0.480749 | − | 0.876858i | \(-0.340365\pi\) | ||||
0.480749 | + | 0.876858i | \(0.340365\pi\) | |||||||
\(542\) | −23.6729 | + | 4.77378i | −1.01684 | + | 0.205052i | ||||
\(543\) | −20.8442 | −0.894510 | ||||||||
\(544\) | −20.7671 | + | 31.9854i | −0.890381 | + | 1.37136i | ||||
\(545\) | 14.4649 | 0.619608 | ||||||||
\(546\) | −8.51958 | + | 1.71802i | −0.364604 | + | 0.0735247i | ||||
\(547\) | − | 20.2548i | − | 0.866033i | −0.901386 | − | 0.433017i | \(-0.857449\pi\) | ||
0.901386 | − | 0.433017i | \(-0.142551\pi\) | |||||||
\(548\) | 9.43773 | + | 22.4490i | 0.403160 | + | 0.958973i | ||||
\(549\) | − | 2.14403i | − | 0.0915049i | ||||||
\(550\) | −5.58340 | − | 27.6878i | −0.238077 | − | 1.18061i | ||||
\(551\) | −13.8457 | −0.589848 | ||||||||
\(552\) | −10.0959 | + | 9.05945i | −0.429708 | + | 0.385596i | ||||
\(553\) | 9.10378 | 0.387132 | ||||||||
\(554\) | −3.90823 | − | 19.3807i | −0.166045 | − | 0.823407i | ||||
\(555\) | 6.28893i | 0.266950i | ||||||||
\(556\) | −9.75291 | − | 23.1987i | −0.413616 | − | 0.983843i | ||||
\(557\) | − | 28.8162i | − | 1.22098i | −0.792023 | − | 0.610491i | \(-0.790972\pi\) | ||
0.792023 | − | 0.610491i | \(-0.209028\pi\) | |||||||
\(558\) | −4.19233 | + | 0.845409i | −0.177476 | + | 0.0357890i | ||||
\(559\) | 24.9441 | 1.05502 | ||||||||
\(560\) | −9.08338 | − | 8.89370i | −0.383843 | − | 0.375827i | ||||
\(561\) | 39.9222 | 1.68552 | ||||||||
\(562\) | 30.6947 | − | 6.18977i | 1.29478 | − | 0.261100i | ||||
\(563\) | −20.5741 | −0.867095 | −0.433548 | − | 0.901131i | \(-0.642738\pi\) | ||||
−0.433548 | + | 0.901131i | \(0.642738\pi\) | |||||||
\(564\) | 18.3184 | − | 7.70120i | 0.771343 | − | 0.324279i | ||||
\(565\) | −22.9201 | −0.964255 | ||||||||
\(566\) | 3.98779 | + | 19.7752i | 0.167619 | + | 0.831214i | ||||
\(567\) | 2.49131 | 0.104625 | ||||||||
\(568\) | 28.3389 | − | 19.2616i | 1.18907 | − | 0.808197i | ||||
\(569\) | 33.7758i | 1.41596i | 0.706234 | + | 0.707979i | \(0.250393\pi\) | ||||
−0.706234 | + | 0.707979i | \(0.749607\pi\) | |||||||
\(570\) | 0.905822 | + | 4.49192i | 0.0379407 | + | 0.188146i | ||||
\(571\) | −34.0122 | −1.42337 | −0.711684 | − | 0.702500i | \(-0.752067\pi\) | ||||
−0.711684 | + | 0.702500i | \(0.752067\pi\) | |||||||
\(572\) | 26.9325 | − | 11.3226i | 1.12610 | − | 0.473423i | ||||
\(573\) | 0.120078i | 0.00501634i | ||||||||
\(574\) | 6.45374 | + | 32.0037i | 0.269374 | + | 1.33581i | ||||
\(575\) | 16.0288 | − | 2.16707i | 0.668449 | − | 0.0903730i | ||||
\(576\) | 2.94411 | − | 7.43856i | 0.122671 | − | 0.309940i | ||||
\(577\) | −32.4491 | −1.35088 | −0.675438 | − | 0.737417i | \(-0.736045\pi\) | ||||
−0.675438 | + | 0.737417i | \(0.736045\pi\) | |||||||
\(578\) | 7.95286 | + | 39.4377i | 0.330795 | + | 1.64039i | ||||
\(579\) | − | 5.99420i | − | 0.249110i | ||||||
\(580\) | 5.38995 | + | 12.8208i | 0.223805 | + | 0.532353i | ||||
\(581\) | −7.57017 | −0.314064 | ||||||||
\(582\) | −1.26431 | − | 6.26966i | −0.0524075 | − | 0.259886i | ||||
\(583\) | 12.3411i | 0.511114i | ||||||||
\(584\) | −7.07582 | − | 10.4104i | −0.292800 | − | 0.430787i | ||||
\(585\) | − | 3.14681i | − | 0.130105i | ||||||
\(586\) | −13.0911 | + | 2.63990i | −0.540789 | + | 0.109053i | ||||
\(587\) | − | 4.92756i | − | 0.203382i | −0.994816 | − | 0.101691i | \(-0.967575\pi\) | ||
0.994816 | − | 0.101691i | \(-0.0324254\pi\) | |||||||
\(588\) | 0.614940 | + | 1.46272i | 0.0253597 | + | 0.0603217i | ||||
\(589\) | − | 7.68118i | − | 0.316498i | ||||||
\(590\) | −2.65266 | − | 13.1544i | −0.109208 | − | 0.541558i | ||||
\(591\) | − | 12.4182i | − | 0.510817i | ||||||
\(592\) | 14.0902 | + | 13.7959i | 0.579102 | + | 0.567009i | ||||
\(593\) | −19.1860 | −0.787875 | −0.393938 | − | 0.919137i | \(-0.628887\pi\) | ||||
−0.393938 | + | 0.919137i | \(0.628887\pi\) | |||||||
\(594\) | −8.20949 | + | 1.65549i | −0.336840 | + | 0.0679257i | ||||
\(595\) | −21.4253 | −0.878350 | ||||||||
\(596\) | −13.5518 | − | 32.2348i | −0.555102 | − | 1.32039i | ||||
\(597\) | 9.56523i | 0.391479i | ||||||||
\(598\) | 5.47473 | + | 15.8094i | 0.223878 | + | 0.646495i | ||||
\(599\) | 35.3094i | 1.44270i | 0.692568 | + | 0.721352i | \(0.256479\pi\) | ||||
−0.692568 | + | 0.721352i | \(0.743521\pi\) | |||||||
\(600\) | −7.88945 | + | 5.36235i | −0.322085 | + | 0.218917i | ||||
\(601\) | −35.4004 | −1.44401 | −0.722006 | − | 0.691887i | \(-0.756780\pi\) | ||||
−0.722006 | + | 0.691887i | \(0.756780\pi\) | |||||||
\(602\) | 7.04265 | + | 34.9241i | 0.287037 | + | 1.42340i | ||||
\(603\) | −3.96649 | −0.161528 | ||||||||
\(604\) | −17.2339 | − | 40.9933i | −0.701238 | − | 1.66799i | ||||
\(605\) | − | 30.7032i | − | 1.24826i | ||||||
\(606\) | −13.0971 | + | 2.64112i | −0.532035 | + | 0.107288i | ||||
\(607\) | 41.3927i | 1.68008i | 0.542525 | + | 0.840039i | \(0.317468\pi\) | ||||
−0.542525 | + | 0.840039i | \(0.682532\pi\) | |||||||
\(608\) | 12.0511 | + | 7.82437i | 0.488736 | + | 0.317320i | ||||
\(609\) | 13.5804i | 0.550305i | ||||||||
\(610\) | −0.764612 | − | 3.79167i | −0.0309583 | − | 0.153520i | ||||
\(611\) | − | 24.5092i | − | 0.991535i | ||||||
\(612\) | −5.22538 | − | 12.4293i | −0.211223 | − | 0.502425i | ||||
\(613\) | 21.8461i | 0.882354i | 0.897420 | + | 0.441177i | \(0.145439\pi\) | ||||
−0.897420 | + | 0.441177i | \(0.854561\pi\) | |||||||
\(614\) | 23.5007 | − | 4.73906i | 0.948413 | − | 0.191253i | ||||
\(615\) | −11.8210 | −0.476667 | ||||||||
\(616\) | 23.4568 | + | 34.5112i | 0.945101 | + | 1.39050i | ||||
\(617\) | − | 23.4324i | − | 0.943354i | −0.881771 | − | 0.471677i | \(-0.843649\pi\) | ||
0.881771 | − | 0.471677i | \(-0.156351\pi\) | |||||||
\(618\) | −2.33315 | + | 0.470494i | −0.0938532 | + | 0.0189261i | ||||
\(619\) | 18.8898 | 0.759247 | 0.379624 | − | 0.925141i | \(-0.376054\pi\) | ||||
0.379624 | + | 0.925141i | \(0.376054\pi\) | |||||||
\(620\) | −7.11255 | + | 2.99017i | −0.285647 | + | 0.120088i | ||||
\(621\) | −0.642542 | − | 4.75259i | −0.0257843 | − | 0.190715i | ||||
\(622\) | −27.2926 | + | 5.50372i | −1.09433 | + | 0.220679i | ||||
\(623\) | − | 14.4823i | − | 0.580221i | ||||||
\(624\) | −7.05034 | − | 6.90311i | −0.282239 | − | 0.276345i | ||||
\(625\) | 3.23804 | 0.129522 | ||||||||
\(626\) | 2.24114 | − | 0.451940i | 0.0895741 | − | 0.0180631i | ||||
\(627\) | − | 15.0414i | − | 0.600696i | ||||||
\(628\) | 14.1824 | + | 33.7349i | 0.565940 | + | 1.34617i | ||||
\(629\) | 33.2349 | 1.32516 | ||||||||
\(630\) | 4.40583 | − | 0.888462i | 0.175533 | − | 0.0353972i | ||||
\(631\) | 17.4008 | 0.692717 | 0.346358 | − | 0.938102i | \(-0.387418\pi\) | ||||
0.346358 | + | 0.938102i | \(0.387418\pi\) | |||||||
\(632\) | 5.81001 | + | 8.54808i | 0.231110 | + | 0.340024i | ||||
\(633\) | 2.54447 | 0.101134 | ||||||||
\(634\) | 6.88301 | + | 34.1324i | 0.273359 | + | 1.35557i | ||||
\(635\) | 0.709208 | 0.0281441 | ||||||||
\(636\) | 3.84224 | − | 1.61531i | 0.152355 | − | 0.0640512i | ||||
\(637\) | 1.95706 | 0.0775414 | ||||||||
\(638\) | −9.02426 | − | 44.7508i | −0.357274 | − | 1.77170i | ||||
\(639\) | 12.1146i | 0.479244i | ||||||||
\(640\) | 2.55383 | − | 14.2049i | 0.100949 | − | 0.561497i | ||||
\(641\) | − | 7.29894i | − | 0.288291i | −0.989557 | − | 0.144145i | \(-0.953957\pi\) | ||
0.989557 | − | 0.144145i | \(-0.0460433\pi\) | |||||||
\(642\) | −19.9937 | + | 4.03184i | −0.789087 | + | 0.159124i | ||||
\(643\) | 6.74160 | 0.265863 | 0.132931 | − | 0.991125i | \(-0.457561\pi\) | ||||
0.132931 | + | 0.991125i | \(0.457561\pi\) | |||||||
\(644\) | −20.5889 | + | 12.1287i | −0.811318 | + | 0.477938i | ||||
\(645\) | −12.8996 | −0.507923 | ||||||||
\(646\) | 23.7383 | − | 4.78697i | 0.933970 | − | 0.188341i | ||||
\(647\) | − | 4.47981i | − | 0.176120i | −0.996115 | − | 0.0880598i | \(-0.971933\pi\) | ||
0.996115 | − | 0.0880598i | \(-0.0280667\pi\) | |||||||
\(648\) | 1.58995 | + | 2.33924i | 0.0624592 | + | 0.0918941i | ||||
\(649\) | 44.0482i | 1.72904i | ||||||||
\(650\) | 2.32580 | + | 11.5335i | 0.0912255 | + | 0.452382i | ||||
\(651\) | −7.53398 | −0.295280 | ||||||||
\(652\) | −1.63201 | − | 3.88196i | −0.0639144 | − | 0.152029i | ||||
\(653\) | 0.978338 | 0.0382853 | 0.0191427 | − | 0.999817i | \(-0.493906\pi\) | ||||
0.0191427 | + | 0.999817i | \(0.493906\pi\) | |||||||
\(654\) | 3.16990 | + | 15.7193i | 0.123953 | + | 0.614675i | ||||
\(655\) | 0.757567 | 0.0296006 | ||||||||
\(656\) | −25.9314 | + | 26.4845i | −1.01245 | + | 1.03405i | ||||
\(657\) | 4.45034 | 0.173624 | ||||||||
\(658\) | 34.3151 | − | 6.91985i | 1.33774 | − | 0.269764i | ||||
\(659\) | 33.2279 | 1.29437 | 0.647187 | − | 0.762331i | \(-0.275945\pi\) | ||||
0.647187 | + | 0.762331i | \(0.275945\pi\) | |||||||
\(660\) | −13.9279 | + | 5.85541i | −0.542144 | + | 0.227921i | ||||
\(661\) | 10.6444i | 0.414021i | 0.978339 | + | 0.207010i | \(0.0663734\pi\) | ||||
−0.978339 | + | 0.207010i | \(0.933627\pi\) | |||||||
\(662\) | 34.5989 | − | 6.97707i | 1.34472 | − | 0.271172i | ||||
\(663\) | −16.6298 | −0.645850 | ||||||||
\(664\) | −4.83127 | − | 7.10809i | −0.187490 | − | 0.275847i | ||||
\(665\) | 8.07236i | 0.313033i | ||||||||
\(666\) | −6.83433 | + | 1.37818i | −0.264825 | + | 0.0534036i | ||||
\(667\) | 25.9069 | − | 3.50256i | 1.00312 | − | 0.135620i | ||||
\(668\) | −3.43390 | − | 8.16802i | −0.132862 | − | 0.316030i | ||||
\(669\) | −8.25462 | −0.319142 | ||||||||
\(670\) | −7.01465 | + | 1.41455i | −0.270999 | + | 0.0546487i | ||||
\(671\) | 12.6966i | 0.490147i | ||||||||
\(672\) | 7.67442 | − | 11.8201i | 0.296047 | − | 0.455972i | ||||
\(673\) | 15.5105 | 0.597885 | 0.298943 | − | 0.954271i | \(-0.403366\pi\) | ||||
0.298943 | + | 0.954271i | \(0.403366\pi\) | |||||||
\(674\) | −22.6586 | + | 4.56925i | −0.872778 | + | 0.176001i | ||||
\(675\) | − | 3.37265i | − | 0.129813i | ||||||
\(676\) | 12.7491 | − | 5.35984i | 0.490352 | − | 0.206148i | ||||
\(677\) | 10.7034i | 0.411365i | 0.978619 | + | 0.205683i | \(0.0659415\pi\) | ||||
−0.978619 | + | 0.205683i | \(0.934059\pi\) | |||||||
\(678\) | −5.02281 | − | 24.9078i | −0.192900 | − | 0.956579i | ||||
\(679\) | − | 11.2671i | − | 0.432392i | ||||||
\(680\) | −13.6736 | − | 20.1175i | −0.524357 | − | 0.771469i | ||||
\(681\) | 10.9045i | 0.417860i | ||||||||
\(682\) | 24.8263 | − | 5.00638i | 0.950649 | − | 0.191704i | ||||
\(683\) | − | 36.5249i | − | 1.39759i | −0.715324 | − | 0.698793i | \(-0.753721\pi\) | ||
0.715324 | − | 0.698793i | \(-0.246279\pi\) | |||||||
\(684\) | −4.68297 | + | 1.96876i | −0.179058 | + | 0.0752773i | ||||
\(685\) | −15.5327 | −0.593475 | ||||||||
\(686\) | 5.42780 | + | 26.9161i | 0.207234 | + | 1.02766i | ||||
\(687\) | −14.3196 | −0.546326 | ||||||||
\(688\) | −28.2977 | + | 28.9013i | −1.07884 | + | 1.10185i | ||||
\(689\) | − | 5.14075i | − | 0.195847i | ||||||
\(690\) | −2.83121 | − | 8.17571i | −0.107782 | − | 0.311244i | ||||
\(691\) | − | 47.9613i | − | 1.82453i | −0.409596 | − | 0.912267i | \(-0.634330\pi\) | ||
0.409596 | − | 0.912267i | \(-0.365670\pi\) | |||||||
\(692\) | 9.76876 | − | 4.10686i | 0.371352 | − | 0.156119i | ||||
\(693\) | −14.7532 | −0.560426 | ||||||||
\(694\) | −26.0811 | + | 5.25941i | −0.990025 | + | 0.199645i | ||||
\(695\) | 16.0515 | 0.608866 | ||||||||
\(696\) | −12.7514 | + | 8.66698i | −0.483342 | + | 0.328521i | ||||
\(697\) | 62.4698i | 2.36621i | ||||||||
\(698\) | −3.79721 | − | 18.8301i | −0.143726 | − | 0.712731i | ||||
\(699\) | 10.5570i | 0.399304i | ||||||||
\(700\) | −15.4913 | + | 6.51268i | −0.585517 | + | 0.246156i | ||||
\(701\) | − | 35.8504i | − | 1.35405i | −0.735960 | − | 0.677025i | \(-0.763269\pi\) | ||
0.735960 | − | 0.677025i | \(-0.236731\pi\) | |||||||
\(702\) | 3.41972 | − | 0.689606i | 0.129069 | − | 0.0260275i | ||||
\(703\) | − | 12.5219i | − | 0.472271i | ||||||
\(704\) | −17.4346 | + | 44.0500i | −0.657090 | + | 1.66020i | ||||
\(705\) | 12.6747i | 0.477358i | ||||||||
\(706\) | −8.80782 | − | 43.6774i | −0.331486 | − | 1.64382i | ||||
\(707\) | −23.5367 | −0.885188 | ||||||||
\(708\) | 13.7139 | − | 5.76542i | 0.515399 | − | 0.216678i | ||||
\(709\) | − | 18.1038i | − | 0.679902i | −0.940443 | − | 0.339951i | \(-0.889590\pi\) | ||
0.940443 | − | 0.339951i | \(-0.110410\pi\) | |||||||
\(710\) | 4.32034 | + | 21.4243i | 0.162140 | + | 0.804041i | ||||
\(711\) | −3.65421 | −0.137044 | ||||||||
\(712\) | 13.5983 | − | 9.24258i | 0.509618 | − | 0.346380i | ||||
\(713\) | 1.94311 | + | 14.3723i | 0.0727700 | + | 0.538247i | ||||
\(714\) | −4.69522 | − | 23.2833i | −0.175714 | − | 0.871357i | ||||
\(715\) | 18.6349i | 0.696907i | ||||||||
\(716\) | −4.94342 | − | 11.7586i | −0.184744 | − | 0.439441i | ||||
\(717\) | 4.84386 | 0.180897 | ||||||||
\(718\) | −5.16856 | − | 25.6306i | −0.192889 | − | 0.956525i | ||||
\(719\) | − | 4.13110i | − | 0.154064i | −0.997029 | − | 0.0770319i | \(-0.975456\pi\) | ||
0.997029 | − | 0.0770319i | \(-0.0245443\pi\) | |||||||
\(720\) | 3.64602 | + | 3.56988i | 0.135879 | + | 0.133042i | ||||
\(721\) | −4.19287 | −0.156151 | ||||||||
\(722\) | 3.50801 | + | 17.3960i | 0.130555 | + | 0.647412i | ||||
\(723\) | 22.0218 | 0.818999 | ||||||||
\(724\) | −16.1564 | − | 38.4303i | −0.600449 | − | 1.42825i | ||||
\(725\) | 18.3847 | 0.682789 | ||||||||
\(726\) | 33.3659 | − | 6.72844i | 1.23833 | − | 0.249716i | ||||
\(727\) | 47.9031 | 1.77663 | 0.888314 | − | 0.459237i | \(-0.151877\pi\) | ||||
0.888314 | + | 0.459237i | \(0.151877\pi\) | |||||||
\(728\) | −9.77108 | − | 14.3759i | −0.362140 | − | 0.532805i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 7.87033 | − | 1.58710i | 0.291294 | − | 0.0587412i | ||||
\(731\) | 68.1703i | 2.52137i | ||||||||
\(732\) | 3.95294 | − | 1.66185i | 0.146105 | − | 0.0614236i | ||||
\(733\) | 15.5853i | 0.575657i | 0.957682 | + | 0.287829i | \(0.0929334\pi\) | ||||
−0.957682 | + | 0.287829i | \(0.907067\pi\) | |||||||
\(734\) | −0.888865 | − | 4.40783i | −0.0328086 | − | 0.162696i | ||||
\(735\) | −1.01208 | −0.0373310 | ||||||||
\(736\) | −24.5282 | − | 11.5917i | −0.904122 | − | 0.427275i | ||||
\(737\) | 23.4889 | 0.865225 | ||||||||
\(738\) | −2.59050 | − | 12.8461i | −0.0953575 | − | 0.472872i | ||||
\(739\) | − | 1.51685i | − | 0.0557982i | −0.999611 | − | 0.0278991i | \(-0.991118\pi\) | ||
0.999611 | − | 0.0278991i | \(-0.00888172\pi\) | |||||||
\(740\) | −11.5949 | + | 4.87458i | −0.426236 | + | 0.179193i | ||||
\(741\) | 6.26560i | 0.230173i | ||||||||
\(742\) | 7.19752 | − | 1.45142i | 0.264229 | − | 0.0532834i | ||||
\(743\) | −13.3402 | −0.489406 | −0.244703 | − | 0.969598i | \(-0.578690\pi\) | ||||
−0.244703 | + | 0.969598i | \(0.578690\pi\) | |||||||
\(744\) | −4.80817 | − | 7.07410i | −0.176276 | − | 0.259349i | ||||
\(745\) | 22.3037 | 0.817143 | ||||||||
\(746\) | −24.6639 | + | 4.97362i | −0.903008 | + | 0.182097i | ||||
\(747\) | 3.03863 | 0.111178 | ||||||||
\(748\) | 30.9439 | + | 73.6044i | 1.13142 | + | 2.69124i | ||||
\(749\) | −35.9303 | −1.31287 | ||||||||
\(750\) | −2.98589 | − | 14.8069i | −0.109029 | − | 0.540670i | ||||
\(751\) | 2.46508 | 0.0899519 | 0.0449760 | − | 0.998988i | \(-0.485679\pi\) | ||||
0.0449760 | + | 0.998988i | \(0.485679\pi\) | |||||||
\(752\) | 28.3973 | + | 27.8043i | 1.03554 | + | 1.01392i | ||||
\(753\) | − | 1.49664i | − | 0.0545405i | ||||||
\(754\) | 3.75911 | + | 18.6412i | 0.136899 | + | 0.678873i | ||||
\(755\) | 28.3638 | 1.03226 | ||||||||
\(756\) | 1.93103 | + | 4.59322i | 0.0702308 | + | 0.167054i | ||||
\(757\) | 4.61509i | 0.167738i | 0.996477 | + | 0.0838692i | \(0.0267278\pi\) | ||||
−0.996477 | + | 0.0838692i | \(0.973272\pi\) | |||||||
\(758\) | −3.70231 | − | 18.3596i | −0.134474 | − | 0.666849i | ||||
\(759\) | 3.80503 | + | 28.1441i | 0.138114 | + | 1.02157i | ||||
\(760\) | −7.57962 | + | 5.15176i | −0.274942 | + | 0.186874i | ||||
\(761\) | −35.9097 | −1.30172 | −0.650862 | − | 0.759196i | \(-0.725592\pi\) | ||||
−0.650862 | + | 0.759196i | \(0.725592\pi\) | |||||||
\(762\) | 0.155419 | + | 0.770713i | 0.00563023 | + | 0.0279200i | ||||
\(763\) | 28.2490i | 1.02268i | ||||||||
\(764\) | −0.221388 | + | 0.0930732i | −0.00800953 | + | 0.00336727i | ||||
\(765\) | 8.59999 | 0.310933 | ||||||||
\(766\) | −2.71563 | − | 13.4667i | −0.0981198 | − | 0.486570i | ||||
\(767\) | − | 18.3485i | − | 0.662527i | ||||||
\(768\) | 15.9964 | − | 0.337613i | 0.577222 | − | 0.0121826i | ||||
\(769\) | 22.0207i | 0.794087i | 0.917800 | + | 0.397044i | \(0.129964\pi\) | ||||
−0.917800 | + | 0.397044i | \(0.870036\pi\) | |||||||
\(770\) | −26.0906 | + | 5.26133i | −0.940241 | + | 0.189605i | ||||
\(771\) | 15.3146i | 0.551543i | ||||||||
\(772\) | 11.0515 | − | 4.64613i | 0.397751 | − | 0.167218i | ||||
\(773\) | − | 26.2098i | − | 0.942700i | −0.881946 | − | 0.471350i | \(-0.843767\pi\) | ||
0.881946 | − | 0.471350i | \(-0.156233\pi\) | |||||||
\(774\) | −2.82688 | − | 14.0184i | −0.101610 | − | 0.503879i | ||||
\(775\) | 10.1992i | 0.366367i | ||||||||
\(776\) | 10.5794 | − | 7.19065i | 0.379777 | − | 0.258129i | ||||
\(777\) | −12.2819 | −0.440610 | ||||||||
\(778\) | 38.2720 | − | 7.71778i | 1.37212 | − | 0.276696i | ||||
\(779\) | 23.5366 | 0.843288 | ||||||||
\(780\) | 5.80176 | − | 2.43911i | 0.207736 | − | 0.0873341i | ||||
\(781\) | − | 71.7405i | − | 2.56708i | ||||||
\(782\) | −43.2059 | + | 14.9620i | −1.54504 | + | 0.535040i | ||||
\(783\) | − | 5.45110i | − | 0.194806i | ||||||
\(784\) | −2.22017 | + | 2.26753i | −0.0792919 | + | 0.0809830i | ||||
\(785\) | −23.3416 | −0.833097 | ||||||||
\(786\) | 0.166016 | + | 0.823266i | 0.00592161 | + | 0.0293649i | ||||
\(787\) | −30.7607 | −1.09650 | −0.548250 | − | 0.836315i | \(-0.684706\pi\) | ||||
−0.548250 | + | 0.836315i | \(0.684706\pi\) | |||||||
\(788\) | 22.8954 | − | 9.62541i | 0.815615 | − | 0.342891i | ||||
\(789\) | 2.19677i | 0.0782070i | ||||||||
\(790\) | −6.46239 | + | 1.30318i | −0.229922 | + | 0.0463650i | ||||
\(791\) | − | 44.7614i | − | 1.59153i | ||||||
\(792\) | −9.41544 | − | 13.8526i | −0.334563 | − | 0.492232i | ||||
\(793\) | − | 5.28885i | − | 0.187813i | ||||||
\(794\) | −3.43403 | − | 17.0292i | −0.121869 | − | 0.604343i | ||||
\(795\) | 2.65849i | 0.0942871i | ||||||||
\(796\) | −17.6354 | + | 7.41405i | −0.625069 | + | 0.262784i | ||||
\(797\) | − | 54.7924i | − | 1.94085i | −0.241408 | − | 0.970424i | \(-0.577609\pi\) | ||
0.241408 | − | 0.970424i | \(-0.422391\pi\) | |||||||
\(798\) | −8.77242 | + | 1.76901i | −0.310540 | + | 0.0626223i | ||||
\(799\) | 66.9816 | 2.36964 | ||||||||
\(800\) | −16.0017 | − | 10.3894i | −0.565745 | − | 0.367320i | ||||
\(801\) | 5.81313i | 0.205397i | ||||||||
\(802\) | 23.8048 | − | 4.80039i | 0.840578 | − | 0.169508i | ||||
\(803\) | −26.3542 | −0.930020 | ||||||||
\(804\) | −3.07444 | − | 7.31299i | −0.108427 | − | 0.257909i | ||||
\(805\) | −2.04207 | − | 15.1042i | −0.0719734 | − | 0.532355i | ||||
\(806\) | −10.3416 | + | 2.08544i | −0.364266 | + | 0.0734564i | ||||
\(807\) | − | 8.15180i | − | 0.286957i | ||||||
\(808\) | −15.0211 | − | 22.1000i | −0.528440 | − | 0.777476i | ||||
\(809\) | 42.9727 | 1.51084 | 0.755421 | − | 0.655240i | \(-0.227433\pi\) | ||||
0.755421 | + | 0.655240i | \(0.227433\pi\) | |||||||
\(810\) | −1.76848 | + | 0.356624i | −0.0621380 | + | 0.0125305i | ||||
\(811\) | 1.35261i | 0.0474966i | 0.999718 | + | 0.0237483i | \(0.00756003\pi\) | ||||
−0.999718 | + | 0.0237483i | \(0.992440\pi\) | |||||||
\(812\) | −25.0381 | + | 10.5262i | −0.878665 | + | 0.369398i | ||||
\(813\) | 17.0762 | 0.598890 | ||||||||
\(814\) | 40.4719 | − | 8.16139i | 1.41854 | − | 0.286057i | ||||
\(815\) | 2.68598 | 0.0940857 | ||||||||
\(816\) | 18.8656 | − | 19.2680i | 0.660430 | − | 0.674515i | ||||
\(817\) | 25.6844 | 0.898583 | ||||||||
\(818\) | −6.93235 | − | 34.3771i | −0.242384 | − | 1.20197i | ||||
\(819\) | 6.14552 | 0.214742 | ||||||||
\(820\) | −9.16248 | − | 21.7943i | −0.319968 | − | 0.761088i | ||||
\(821\) | −8.46867 | −0.295559 | −0.147779 | − | 0.989020i | \(-0.547213\pi\) | ||||
−0.147779 | + | 0.989020i | \(0.547213\pi\) | |||||||
\(822\) | −3.40391 | − | 16.8798i | −0.118725 | − | 0.588750i | ||||
\(823\) | − | 28.1188i | − | 0.980160i | −0.871677 | − | 0.490080i | \(-0.836967\pi\) | ||
0.871677 | − | 0.490080i | \(-0.163033\pi\) | |||||||
\(824\) | −2.67588 | − | 3.93694i | −0.0932189 | − | 0.137150i | ||||
\(825\) | 19.9723i | 0.695347i | ||||||||
\(826\) | 25.6897 | − | 5.18047i | 0.893858 | − | 0.180252i | ||||
\(827\) | 9.58345 | 0.333249 | 0.166625 | − | 0.986020i | \(-0.446713\pi\) | ||||
0.166625 | + | 0.986020i | \(0.446713\pi\) | |||||||
\(828\) | 8.26430 | − | 4.86841i | 0.287204 | − | 0.169189i | ||||
\(829\) | −16.3484 | −0.567803 | −0.283902 | − | 0.958853i | \(-0.591629\pi\) | ||||
−0.283902 | + | 0.958853i | \(0.591629\pi\) | |||||||
\(830\) | 5.37375 | − | 1.08365i | 0.186526 | − | 0.0376140i | ||||
\(831\) | 13.9801i | 0.484964i | ||||||||
\(832\) | 7.26248 | − | 18.3493i | 0.251781 | − | 0.636148i | ||||
\(833\) | 5.34848i | 0.185314i | ||||||||
\(834\) | 3.51759 | + | 17.4435i | 0.121804 | + | 0.604019i | ||||
\(835\) | 5.65155 | 0.195580 | ||||||||
\(836\) | 27.7318 | − | 11.6587i | 0.959124 | − | 0.403223i | ||||
\(837\) | 3.02410 | 0.104528 | ||||||||
\(838\) | −4.01057 | − | 19.8882i | −0.138543 | − | 0.687026i | ||||
\(839\) | 46.3381 | 1.59977 | 0.799884 | − | 0.600155i | \(-0.204894\pi\) | ||||
0.799884 | + | 0.600155i | \(0.204894\pi\) | |||||||
\(840\) | 5.05303 | + | 7.43436i | 0.174346 | + | 0.256510i | ||||
\(841\) | 0.714489 | 0.0246376 | ||||||||
\(842\) | −47.1644 | + | 9.51098i | −1.62539 | + | 0.327770i | ||||
\(843\) | −22.1413 | −0.762588 | ||||||||
\(844\) | 1.97223 | + | 4.69123i | 0.0678869 | + | 0.161479i | ||||
\(845\) | 8.82129i | 0.303461i | ||||||||
\(846\) | −13.7739 | + | 2.77759i | −0.473557 | + | 0.0954956i | ||||
\(847\) | 59.9614 | 2.06030 | ||||||||
\(848\) | 5.95628 | + | 5.83189i | 0.204539 | + | 0.200268i | ||||
\(849\) | − | 14.2647i | − | 0.489562i | ||||||
\(850\) | −31.5202 | + | 6.35623i | −1.08113 | + | 0.218017i | ||||
\(851\) | 3.16766 | + | 23.4297i | 0.108586 | + | 0.803161i | ||||
\(852\) | −22.3356 | + | 9.39004i | −0.765204 | + | 0.321698i | ||||
\(853\) | −22.0557 | −0.755173 | −0.377587 | − | 0.925974i | \(-0.623246\pi\) | ||||
−0.377587 | + | 0.925974i | \(0.623246\pi\) | |||||||
\(854\) | 7.40488 | − | 1.49324i | 0.253390 | − | 0.0510976i | ||||
\(855\) | − | 3.24020i | − | 0.110813i | ||||||
\(856\) | −22.9307 | − | 33.7371i | −0.783754 | − | 1.15311i | ||||
\(857\) | 44.6464 | 1.52509 | 0.762546 | − | 0.646935i | \(-0.223949\pi\) | ||||
0.762546 | + | 0.646935i | \(0.223949\pi\) | |||||||
\(858\) | −20.2510 | + | 4.08374i | −0.691358 | + | 0.139417i | ||||
\(859\) | 28.3561i | 0.967496i | 0.875207 | + | 0.483748i | \(0.160725\pi\) | ||||
−0.875207 | + | 0.483748i | \(0.839275\pi\) | |||||||
\(860\) | −9.99857 | − | 23.7830i | −0.340948 | − | 0.810994i | ||||
\(861\) | − | 23.0856i | − | 0.786754i | ||||||
\(862\) | 6.76225 | + | 33.5336i | 0.230323 | + | 1.14216i | ||||
\(863\) | 48.0292i | 1.63493i | 0.575975 | + | 0.817467i | \(0.304623\pi\) | ||||
−0.575975 | + | 0.817467i | \(0.695377\pi\) | |||||||
\(864\) | −3.08047 | + | 4.74454i | −0.104800 | + | 0.161413i | ||||
\(865\) | 6.75912i | 0.229817i | ||||||||
\(866\) | 36.5414 | − | 7.36879i | 1.24173 | − | 0.250402i | ||||
\(867\) | − | 28.4481i | − | 0.966146i | ||||||
\(868\) | −5.83962 | − | 13.8904i | −0.198209 | − | 0.471469i | ||||
\(869\) | 21.6397 | 0.734075 | ||||||||
\(870\) | −1.94399 | − | 9.64015i | −0.0659076 | − | 0.326832i | ||||
\(871\) | −9.78445 | −0.331534 | ||||||||
\(872\) | −26.5247 | + | 18.0285i | −0.898239 | + | 0.610521i | ||||
\(873\) | 4.52256i | 0.153066i | ||||||||
\(874\) | 5.63721 | + | 16.2786i | 0.190681 | + | 0.550632i | ||||
\(875\) | − | 26.6092i | − | 0.899554i | ||||||
\(876\) | 3.44948 | + | 8.20507i | 0.116547 | + | 0.277224i | ||||
\(877\) | −36.8661 | −1.24488 | −0.622440 | − | 0.782668i | \(-0.713858\pi\) | ||||
−0.622440 | + | 0.782668i | \(0.713858\pi\) | |||||||
\(878\) | 4.66042 | − | 0.939801i | 0.157281 | − | 0.0317167i | ||||
\(879\) | 9.44315 | 0.318510 | ||||||||
\(880\) | −21.5912 | − | 21.1403i | −0.727839 | − | 0.712639i | ||||
\(881\) | − | 39.9739i | − | 1.34675i | −0.739299 | − | 0.673377i | \(-0.764843\pi\) | ||
0.739299 | − | 0.673377i | \(-0.235157\pi\) | |||||||
\(882\) | −0.221791 | − | 1.09985i | −0.00746808 | − | 0.0370338i | ||||
\(883\) | 27.9445i | 0.940406i | 0.882558 | + | 0.470203i | \(0.155819\pi\) | ||||
−0.882558 | + | 0.470203i | \(0.844181\pi\) | |||||||
\(884\) | −12.8899 | − | 30.6604i | −0.433533 | − | 1.03122i | ||||
\(885\) | 9.48880i | 0.318962i | ||||||||
\(886\) | −33.6823 | + | 6.79223i | −1.13158 | + | 0.228190i | ||||
\(887\) | − | 20.8547i | − | 0.700233i | −0.936706 | − | 0.350117i | \(-0.886142\pi\) | ||
0.936706 | − | 0.350117i | \(-0.113858\pi\) | |||||||
\(888\) | −7.83827 | − | 11.5322i | −0.263035 | − | 0.386995i | ||||
\(889\) | 1.38504i | 0.0464526i | ||||||||
\(890\) | 2.07310 | + | 10.2804i | 0.0694905 | + | 0.344599i | ||||
\(891\) | 5.92184 | 0.198389 | ||||||||
\(892\) | −6.39819 | − | 15.2190i | −0.214227 | − | 0.509570i | ||||
\(893\) | − | 25.2366i | − | 0.844509i | ||||||
\(894\) | 4.88772 | + | 24.2379i | 0.163470 | + | 0.810637i | ||||
\(895\) | 8.13594 | 0.271955 | ||||||||
\(896\) | 27.7412 | + | 4.98746i | 0.926769 | + | 0.166619i | ||||
\(897\) | −1.58501 | − | 11.7236i | −0.0529219 | − | 0.391440i | ||||
\(898\) | 0.831483 | + | 4.12327i | 0.0277469 | + | 0.137595i | ||||
\(899\) | 16.4847i | 0.549794i | ||||||||
\(900\) | 6.21814 | − | 2.61416i | 0.207271 | − | 0.0871386i | ||||
\(901\) | 14.0492 | 0.468048 | ||||||||
\(902\) | 15.3405 | + | 76.0727i | 0.510783 | + | 2.53294i | ||||
\(903\) | − | 25.1922i | − | 0.838343i | ||||||
\(904\) | 42.0292 | − | 28.5667i | 1.39787 | − | 0.950114i | ||||
\(905\) | 26.5904 | 0.883896 | ||||||||
\(906\) | 6.21576 | + | 30.8236i | 0.206505 | + | 1.02405i | ||||
\(907\) | 12.8699 | 0.427337 | 0.213669 | − | 0.976906i | \(-0.431459\pi\) | ||||
0.213669 | + | 0.976906i | \(0.431459\pi\) | |||||||
\(908\) | −20.1045 | + | 8.45210i | −0.667192 | + | 0.280493i | ||||
\(909\) | 9.44751 | 0.313354 | ||||||||
\(910\) | 10.8682 | − | 2.19164i | 0.360278 | − | 0.0726522i | ||||
\(911\) | −12.5529 | −0.415896 | −0.207948 | − | 0.978140i | \(-0.566678\pi\) | ||||
−0.207948 | + | 0.978140i | \(0.566678\pi\) | |||||||
\(912\) | −7.25958 | − | 7.10798i | −0.240389 | − | 0.235369i | ||||
\(913\) | −17.9943 | −0.595524 | ||||||||
\(914\) | −42.9509 | + | 8.66131i | −1.42069 | + | 0.286491i | ||||
\(915\) | 2.73508i | 0.0904191i | ||||||||
\(916\) | −11.0992 | − | 26.4009i | −0.366727 | − | 0.872311i | ||||
\(917\) | 1.47948i | 0.0488567i | ||||||||
\(918\) | 1.88464 | + | 9.34581i | 0.0622024 | + | 0.308458i | ||||
\(919\) | −25.9215 | −0.855070 | −0.427535 | − | 0.903999i | \(-0.640618\pi\) | ||||
−0.427535 | + | 0.903999i | \(0.640618\pi\) | |||||||
\(920\) | 12.8790 | − | 11.5569i | 0.424609 | − | 0.381020i | ||||
\(921\) | −16.9520 | −0.558589 | ||||||||
\(922\) | −11.9048 | − | 59.0352i | −0.392064 | − | 1.94422i | ||||
\(923\) | 29.8840i | 0.983643i | ||||||||
\(924\) | −11.4352 | − | 27.2003i | −0.376192 | − | 0.894825i | ||||
\(925\) | 16.6268i | 0.546685i | ||||||||
\(926\) | −39.1204 | + | 7.88887i | −1.28558 | + | 0.259244i | ||||
\(927\) | 1.68300 | 0.0552769 | ||||||||
\(928\) | −25.8630 | − | 16.7920i | −0.848994 | − | 0.551223i | ||||
\(929\) | −40.8765 | −1.34111 | −0.670557 | − | 0.741858i | \(-0.733945\pi\) | ||||
−0.670557 | + | 0.741858i | \(0.733945\pi\) | |||||||
\(930\) | 5.34805 | − | 1.07847i | 0.175370 | − | 0.0353643i | ||||
\(931\) | 2.01514 | 0.0660435 | ||||||||
\(932\) | −19.4640 | + | 8.18281i | −0.637564 | + | 0.268037i | ||||
\(933\) | 19.6873 | 0.644533 | ||||||||
\(934\) | −4.73111 | − | 23.4613i | −0.154807 | − | 0.767676i | ||||
\(935\) | −50.9278 | −1.66552 | ||||||||
\(936\) | 3.92206 | + | 5.77040i | 0.128197 | + | 0.188611i | ||||
\(937\) | − | 14.6250i | − | 0.477778i | −0.971047 | − | 0.238889i | \(-0.923217\pi\) | ||
0.971047 | − | 0.238889i | \(-0.0767832\pi\) | |||||||
\(938\) | −2.76252 | − | 13.6992i | −0.0901993 | − | 0.447293i | ||||
\(939\) | −1.61663 | −0.0527566 | ||||||||
\(940\) | −23.3683 | + | 9.82423i | −0.762191 | + | 0.320431i | ||||
\(941\) | − | 6.12552i | − | 0.199686i | −0.995003 | − | 0.0998431i | \(-0.968166\pi\) | ||
0.995003 | − | 0.0998431i | \(-0.0318341\pi\) | |||||||
\(942\) | −5.11518 | − | 25.3658i | −0.166661 | − | 0.826464i | ||||
\(943\) | −44.0396 | + | 5.95407i | −1.43413 | + | 0.193891i | ||||
\(944\) | 21.2594 | + | 20.8154i | 0.691933 | + | 0.677484i | ||||
\(945\) | −3.17811 | −0.103384 | ||||||||
\(946\) | 16.7404 | + | 83.0145i | 0.544276 | + | 2.69903i | ||||
\(947\) | 6.15274i | 0.199937i | 0.994991 | + | 0.0999686i | \(0.0318742\pi\) | ||||
−0.994991 | + | 0.0999686i | \(0.968126\pi\) | |||||||
\(948\) | −2.83239 | − | 6.73725i | −0.0919918 | − | 0.218816i | ||||
\(949\) | 10.9780 | 0.356361 | ||||||||
\(950\) | 2.39483 | + | 11.8758i | 0.0776984 | + | 0.385302i | ||||
\(951\) | − | 24.6211i | − | 0.798394i | ||||||
\(952\) | 39.2881 | − | 26.7036i | 1.27333 | − | 0.865468i | ||||
\(953\) | 10.5440i | 0.341552i | 0.985310 | + | 0.170776i | \(0.0546275\pi\) | ||||
−0.985310 | + | 0.170776i | \(0.945373\pi\) | |||||||
\(954\) | −2.88905 | + | 0.582594i | −0.0935364 | + | 0.0188622i | ||||
\(955\) | − | 0.153181i | − | 0.00495682i | ||||||
\(956\) | 3.75450 | + | 8.93061i | 0.121429 | + | 0.288837i | ||||
\(957\) | 32.2806i | 1.04348i | ||||||||
\(958\) | 7.20253 | + | 35.7169i | 0.232703 | + | 1.15396i | ||||
\(959\) | − | 30.3344i | − | 0.979549i | ||||||
\(960\) | −3.75573 | + | 9.48919i | −0.121216 | + | 0.306262i | ||||
\(961\) | 21.8548 | 0.704994 | ||||||||
\(962\) | −16.8588 | + | 3.39968i | −0.543550 | + | 0.109610i | ||||
\(963\) | 14.4223 | 0.464751 | ||||||||
\(964\) | 17.0692 | + | 40.6015i | 0.549761 | + | 1.30769i | ||||
\(965\) | 7.64665i | 0.246154i | ||||||||
\(966\) | 15.9666 | − | 5.52917i | 0.513718 | − | 0.177898i | ||||
\(967\) | − | 13.7270i | − | 0.441430i | −0.975338 | − | 0.220715i | \(-0.929161\pi\) | ||
0.975338 | − | 0.220715i | \(-0.0708391\pi\) | |||||||
\(968\) | 38.2673 | + | 56.3014i | 1.22996 | + | 1.80960i | ||||
\(969\) | −17.1234 | −0.550082 | ||||||||
\(970\) | 1.61286 | + | 7.99805i | 0.0517857 | + | 0.256802i | ||||
\(971\) | 4.43428 | 0.142303 | 0.0711514 | − | 0.997466i | \(-0.477333\pi\) | ||||
0.0711514 | + | 0.997466i | \(0.477333\pi\) | |||||||
\(972\) | −0.775104 | − | 1.84370i | −0.0248615 | − | 0.0591366i | ||||
\(973\) | 31.3475i | 1.00495i | ||||||||
\(974\) | 29.5178 | − | 5.95244i | 0.945811 | − | 0.190728i | ||||
\(975\) | − | 8.31959i | − | 0.266440i | ||||||
\(976\) | 6.12787 | + | 5.99991i | 0.196148 | + | 0.192052i | ||||
\(977\) | 7.21336i | 0.230776i | 0.993321 | + | 0.115388i | \(0.0368111\pi\) | ||||
−0.993321 | + | 0.115388i | \(0.963189\pi\) | |||||||
\(978\) | 0.588617 | + | 2.91892i | 0.0188219 | + | 0.0933367i | ||||
\(979\) | − | 34.4244i | − | 1.10021i | ||||||
\(980\) | −0.784464 | − | 1.86596i | −0.0250588 | − | 0.0596059i | ||||
\(981\) | − | 11.3390i | − | 0.362027i | ||||||
\(982\) | 10.4576 | − | 2.10884i | 0.333716 | − | 0.0672959i | ||||
\(983\) | 51.7339 | 1.65006 | 0.825028 | − | 0.565092i | \(-0.191159\pi\) | ||||
0.825028 | + | 0.565092i | \(0.191159\pi\) | |||||||
\(984\) | 21.6764 | − | 14.7332i | 0.691020 | − | 0.469676i | ||||
\(985\) | 15.8416i | 0.504756i | ||||||||
\(986\) | −50.9450 | + | 10.2734i | −1.62242 | + | 0.327170i | ||||
\(987\) | −24.7529 | −0.787894 | ||||||||
\(988\) | −11.5519 | + | 4.85649i | −0.367514 | + | 0.154506i | ||||
\(989\) | −48.0583 | + | 6.49739i | −1.52816 | + | 0.206605i | ||||
\(990\) | 10.4726 | − | 2.11187i | 0.332843 | − | 0.0671197i | ||||
\(991\) | 5.11827i | 0.162587i | 0.996690 | + | 0.0812936i | \(0.0259051\pi\) | ||||
−0.996690 | + | 0.0812936i | \(0.974095\pi\) | |||||||
\(992\) | 9.31566 | − | 14.3480i | 0.295772 | − | 0.455548i | ||||
\(993\) | −24.9576 | −0.792005 | ||||||||
\(994\) | −41.8403 | + | 8.43735i | −1.32709 | + | 0.267617i | ||||
\(995\) | − | 12.2021i | − | 0.386833i | ||||||
\(996\) | 2.35525 | + | 5.60231i | 0.0746291 | + | 0.177516i | ||||
\(997\) | 30.9514 | 0.980242 | 0.490121 | − | 0.871654i | \(-0.336953\pi\) | ||||
0.490121 | + | 0.871654i | \(0.336953\pi\) | |||||||
\(998\) | −25.6404 | + | 5.17053i | −0.811632 | + | 0.163670i | ||||
\(999\) | 4.92988 | 0.155975 |
(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 | 276.2.e.a.91.9 | ✓ | 24 | |
3.2 | odd | 2 | 828.2.e.f.91.16 | 24 | |||
4.3 | odd | 2 | inner | 276.2.e.a.91.11 | yes | 24 | |
8.3 | odd | 2 | 4416.2.i.d.1471.11 | 24 | |||
8.5 | even | 2 | 4416.2.i.d.1471.10 | 24 | |||
12.11 | even | 2 | 828.2.e.f.91.14 | 24 | |||
23.22 | odd | 2 | inner | 276.2.e.a.91.10 | yes | 24 | |
69.68 | even | 2 | 828.2.e.f.91.15 | 24 | |||
92.91 | even | 2 | inner | 276.2.e.a.91.12 | yes | 24 | |
184.45 | odd | 2 | 4416.2.i.d.1471.9 | 24 | |||
184.91 | even | 2 | 4416.2.i.d.1471.12 | 24 | |||
276.275 | odd | 2 | 828.2.e.f.91.13 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.e.a.91.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
276.2.e.a.91.10 | yes | 24 | 23.22 | odd | 2 | inner | |
276.2.e.a.91.11 | yes | 24 | 4.3 | odd | 2 | inner | |
276.2.e.a.91.12 | yes | 24 | 92.91 | even | 2 | inner | |
828.2.e.f.91.13 | 24 | 276.275 | odd | 2 | |||
828.2.e.f.91.14 | 24 | 12.11 | even | 2 | |||
828.2.e.f.91.15 | 24 | 69.68 | even | 2 | |||
828.2.e.f.91.16 | 24 | 3.2 | odd | 2 | |||
4416.2.i.d.1471.9 | 24 | 184.45 | odd | 2 | |||
4416.2.i.d.1471.10 | 24 | 8.5 | even | 2 | |||
4416.2.i.d.1471.11 | 24 | 8.3 | odd | 2 | |||
4416.2.i.d.1471.12 | 24 | 184.91 | even | 2 |