Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(109,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.v (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 109.13 | ||
Character | \(\chi\) | \(=\) | 864.109 |
Dual form | 864.2.v.a.325.13 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.567462 | − | 1.29537i | −0.401256 | − | 0.915966i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.35597 | + | 1.47015i | −0.677987 | + | 0.735073i | ||||
\(5\) | 2.16011 | − | 0.894745i | 0.966029 | − | 0.400142i | 0.156796 | − | 0.987631i | \(-0.449883\pi\) |
0.809232 | + | 0.587489i | \(0.199883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.46314 | − | 1.46314i | 0.553014 | − | 0.553014i | −0.374295 | − | 0.927309i | \(-0.622115\pi\) |
0.927309 | + | 0.374295i | \(0.122115\pi\) | |||||||
\(8\) | 2.67385 | + | 0.922239i | 0.945349 | + | 0.326061i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.38480 | − | 2.29041i | −0.754141 | − | 0.724290i | ||||
\(11\) | 2.39513 | + | 5.78235i | 0.722158 | + | 1.74344i | 0.667108 | + | 0.744961i | \(0.267532\pi\) |
0.0550506 | + | 0.998484i | \(0.482468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0552727 | + | 0.0228947i | 0.0153299 | + | 0.00634985i | 0.390335 | − | 0.920673i | \(-0.372359\pi\) |
−0.375005 | + | 0.927023i | \(0.622359\pi\) | |||||||
\(14\) | −2.72558 | − | 1.06503i | −0.728442 | − | 0.284642i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.322664 | − | 3.98696i | −0.0806661 | − | 0.996741i | ||||
\(17\) | − | 3.26457i | − | 0.791775i | −0.918299 | − | 0.395887i | \(-0.870437\pi\) | ||
0.918299 | − | 0.395887i | \(-0.129563\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.456261 | − | 0.188990i | −0.104674 | − | 0.0433572i | 0.329732 | − | 0.944075i | \(-0.393042\pi\) |
−0.434406 | + | 0.900717i | \(0.643042\pi\) | |||||||
\(20\) | −1.61364 | + | 4.38892i | −0.360821 | + | 0.981393i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.13115 | − | 6.38384i | 1.30717 | − | 1.36104i | ||||
\(23\) | 6.25659 | + | 6.25659i | 1.30459 | + | 1.30459i | 0.925262 | + | 0.379328i | \(0.123845\pi\) |
0.379328 | + | 0.925262i | \(0.376155\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.329954 | − | 0.329954i | 0.0659908 | − | 0.0659908i | ||||
\(26\) | −0.00170799 | − | 0.0845906i | −0.000334964 | − | 0.0165896i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.167050 | + | 4.13501i | 0.0315694 | + | 0.781443i | ||||
\(29\) | −3.28735 | + | 7.93636i | −0.610445 | + | 1.47374i | 0.252068 | + | 0.967710i | \(0.418889\pi\) |
−0.862513 | + | 0.506035i | \(0.831111\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.60653 | 1.18657 | 0.593284 | − | 0.804994i | \(-0.297831\pi\) | ||||
0.593284 | + | 0.804994i | \(0.297831\pi\) | |||||||
\(32\) | −4.98150 | + | 2.68042i | −0.880613 | + | 0.473836i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.22883 | + | 1.85252i | −0.725239 | + | 0.317704i | ||||
\(35\) | 1.85140 | − | 4.46967i | 0.312943 | − | 0.755512i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.590451 | + | 0.244573i | −0.0970696 | + | 0.0402076i | −0.430690 | − | 0.902500i | \(-0.641730\pi\) |
0.333620 | + | 0.942708i | \(0.391730\pi\) | |||||||
\(38\) | 0.0140990 | + | 0.698273i | 0.00228715 | + | 0.113275i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.60097 | − | 0.400280i | 1.04370 | − | 0.0632898i | ||||
\(41\) | 1.11963 | + | 1.11963i | 0.174857 | + | 0.174857i | 0.789110 | − | 0.614252i | \(-0.210542\pi\) |
−0.614252 | + | 0.789110i | \(0.710542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.75382 | − | 9.06253i | −0.572453 | − | 1.38202i | −0.899461 | − | 0.437002i | \(-0.856040\pi\) |
0.327008 | − | 0.945022i | \(-0.393960\pi\) | |||||||
\(44\) | −11.7486 | − | 4.31953i | −1.77117 | − | 0.651194i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.55424 | − | 11.6550i | 0.671486 | − | 1.71843i | ||||
\(47\) | − | 12.0850i | − | 1.76278i | −0.472389 | − | 0.881390i | \(-0.656608\pi\) | ||
0.472389 | − | 0.881390i | \(-0.343392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.71846i | 0.388351i | ||||||||
\(50\) | −0.614649 | − | 0.240177i | −0.0869245 | − | 0.0339661i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.108607 | + | 0.0502144i | −0.0150611 | + | 0.00696348i | ||||
\(53\) | −0.152093 | − | 0.367185i | −0.0208916 | − | 0.0504367i | 0.913090 | − | 0.407759i | \(-0.133690\pi\) |
−0.933981 | + | 0.357322i | \(0.883690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3475 | + | 10.3475i | 1.39525 | + | 1.39525i | ||||
\(56\) | 5.26157 | − | 2.56285i | 0.703107 | − | 0.342475i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.1460 | − | 0.245242i | 1.59484 | − | 0.0322018i | ||||
\(59\) | 4.24644 | − | 1.75893i | 0.552840 | − | 0.228994i | −0.0887336 | − | 0.996055i | \(-0.528282\pi\) |
0.641573 | + | 0.767062i | \(0.278282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.578617 | − | 1.39691i | 0.0740844 | − | 0.178855i | −0.882499 | − | 0.470314i | \(-0.844141\pi\) |
0.956583 | + | 0.291459i | \(0.0941406\pi\) | |||||||
\(62\) | −3.74895 | − | 8.55791i | −0.476117 | − | 1.08686i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.29895 | + | 4.93186i | 0.787369 | + | 0.616482i | ||||
\(65\) | 0.139880 | 0.0173500 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.44098 | − | 8.30727i | 0.420383 | − | 1.01489i | −0.561852 | − | 0.827238i | \(-0.689911\pi\) |
0.982235 | − | 0.187657i | \(-0.0600892\pi\) | |||||||
\(68\) | 4.79940 | + | 4.42667i | 0.582012 | + | 0.536813i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.84048 | + | 0.138117i | −0.817593 | + | 0.0165082i | ||||
\(71\) | −2.39497 | + | 2.39497i | −0.284231 | + | 0.284231i | −0.834794 | − | 0.550563i | \(-0.814413\pi\) |
0.550563 | + | 0.834794i | \(0.314413\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.83836 | − | 9.83836i | −1.15149 | − | 1.15149i | −0.986253 | − | 0.165240i | \(-0.947160\pi\) |
−0.165240 | − | 0.986253i | \(-0.552840\pi\) | |||||||
\(74\) | 0.651871 | + | 0.626068i | 0.0757785 | + | 0.0727790i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.896522 | − | 0.414506i | 0.102838 | − | 0.0475471i | ||||
\(77\) | 11.9648 | + | 4.95597i | 1.36351 | + | 0.564786i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.62239i | − | 0.407550i | −0.979018 | − | 0.203775i | \(-0.934679\pi\) | ||
0.979018 | − | 0.203775i | \(-0.0653212\pi\) | |||||||
\(80\) | −4.26431 | − | 8.32356i | −0.476764 | − | 0.930603i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.814992 | − | 2.08569i | 0.0900008 | − | 0.230326i | ||||
\(83\) | 9.86593 | + | 4.08660i | 1.08293 | + | 0.448563i | 0.851535 | − | 0.524298i | \(-0.175672\pi\) |
0.231392 | + | 0.972861i | \(0.425672\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.92096 | − | 7.05182i | −0.316822 | − | 0.764877i | ||||
\(86\) | −9.60920 | + | 10.0052i | −1.03619 | + | 1.07889i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.07150 | + | 17.6700i | 0.114222 | + | 1.88363i | ||||
\(89\) | 6.31778 | − | 6.31778i | 0.669684 | − | 0.669684i | −0.287959 | − | 0.957643i | \(-0.592977\pi\) |
0.957643 | + | 0.287959i | \(0.0929767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.114370 | − | 0.0473735i | 0.0119892 | − | 0.00496609i | ||||
\(92\) | −17.6819 | + | 0.714329i | −1.84347 | + | 0.0744739i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.6546 | + | 6.85778i | −1.61465 | + | 0.707326i | ||||
\(95\) | −1.15467 | −0.118467 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.47320 | −0.454185 | −0.227093 | − | 0.973873i | \(-0.572922\pi\) | ||||
−0.227093 | + | 0.973873i | \(0.572922\pi\) | |||||||
\(98\) | 3.52141 | − | 1.54262i | 0.355716 | − | 0.155828i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0376715 | + | 0.932490i | 0.00376715 | + | 0.0932490i | ||||
\(101\) | −1.15367 | + | 0.477866i | −0.114794 | + | 0.0475494i | −0.439341 | − | 0.898320i | \(-0.644788\pi\) |
0.324547 | + | 0.945870i | \(0.394788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.51916 | − | 6.51916i | 0.642352 | − | 0.642352i | −0.308781 | − | 0.951133i | \(-0.599921\pi\) |
0.951133 | + | 0.308781i | \(0.0999210\pi\) | |||||||
\(104\) | 0.126677 | + | 0.112192i | 0.0124217 | + | 0.0110013i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.389334 | + | 0.405380i | −0.0378154 | + | 0.0393740i | ||||
\(107\) | −0.262336 | − | 0.633334i | −0.0253609 | − | 0.0612267i | 0.910692 | − | 0.413087i | \(-0.135549\pi\) |
−0.936053 | + | 0.351860i | \(0.885549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6809 | − | 4.42416i | −1.02304 | − | 0.423758i | −0.192846 | − | 0.981229i | \(-0.561772\pi\) |
−0.830196 | + | 0.557471i | \(0.811772\pi\) | |||||||
\(110\) | 7.53202 | − | 19.2756i | 0.718150 | − | 1.83786i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.30558 | − | 5.36138i | −0.595821 | − | 0.506602i | ||||
\(113\) | − | 12.3132i | − | 1.15833i | −0.815210 | − | 0.579166i | \(-0.803378\pi\) | ||
0.815210 | − | 0.579166i | \(-0.196622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.1130 | + | 7.91685i | 1.78229 | + | 0.738250i | ||||
\(116\) | −7.21005 | − | 15.5944i | −0.669437 | − | 1.44790i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.68817 | − | 4.50259i | −0.431581 | − | 0.414497i | ||||
\(119\) | −4.77652 | − | 4.77652i | −0.437862 | − | 0.437862i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.9208 | + | 19.9208i | −1.81098 | + | 1.81098i | ||||
\(122\) | −2.13786 | + | 0.0431659i | −0.193552 | + | 0.00390805i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.95828 | + | 9.71256i | −0.804478 | + | 0.872214i | ||||
\(125\) | −4.05621 | + | 9.79257i | −0.362799 | + | 0.875874i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.9033 | −1.32245 | −0.661226 | − | 0.750186i | \(-0.729964\pi\) | ||||
−0.661226 | + | 0.750186i | \(0.729964\pi\) | |||||||
\(128\) | 2.81418 | − | 10.9581i | 0.248741 | − | 0.968570i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0793765 | − | 0.181196i | −0.00696178 | − | 0.0158920i | ||||
\(131\) | −3.60890 | + | 8.71265i | −0.315311 | + | 0.761227i | 0.684180 | + | 0.729313i | \(0.260160\pi\) |
−0.999491 | + | 0.0319142i | \(0.989840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.944091 | + | 0.391055i | −0.0818631 | + | 0.0339088i | ||||
\(134\) | −12.7136 | + | 0.256703i | −1.09829 | + | 0.0221758i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.01072 | − | 8.72897i | 0.258167 | − | 0.748503i | ||||
\(137\) | 3.61267 | + | 3.61267i | 0.308651 | + | 0.308651i | 0.844386 | − | 0.535735i | \(-0.179965\pi\) |
−0.535735 | + | 0.844386i | \(0.679965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.59533 | + | 13.5083i | 0.474590 | + | 1.14576i | 0.962113 | + | 0.272651i | \(0.0879006\pi\) |
−0.487523 | + | 0.873110i | \(0.662099\pi\) | |||||||
\(140\) | 4.06062 | + | 8.78258i | 0.343185 | + | 0.742264i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.46143 | + | 1.74332i | 0.374395 | + | 0.146296i | ||||
\(143\) | 0.374442i | 0.0313124i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.0847i | 1.66794i | ||||||||
\(146\) | −7.16144 | + | 18.3272i | −0.592685 | + | 1.51677i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.441079 | − | 1.19969i | 0.0362565 | − | 0.0986135i | ||||
\(149\) | −1.25331 | − | 3.02575i | −0.102675 | − | 0.247879i | 0.864191 | − | 0.503164i | \(-0.167831\pi\) |
−0.966866 | + | 0.255285i | \(0.917831\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.224843 | − | 0.224843i | −0.0182974 | − | 0.0182974i | 0.697899 | − | 0.716196i | \(-0.254118\pi\) |
−0.716196 | + | 0.697899i | \(0.754118\pi\) | |||||||
\(152\) | −1.04568 | − | 0.926112i | −0.0848159 | − | 0.0751176i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.369724 | − | 18.3112i | −0.0297932 | − | 1.47556i | ||||
\(155\) | 14.2708 | − | 5.91116i | 1.14626 | − | 0.474796i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.194373 | + | 0.469257i | −0.0155126 | + | 0.0374508i | −0.931446 | − | 0.363879i | \(-0.881452\pi\) |
0.915933 | + | 0.401330i | \(0.131452\pi\) | |||||||
\(158\) | −4.69234 | + | 2.05556i | −0.373302 | + | 0.163532i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.36228 | + | 10.2472i | −0.661096 | + | 0.810109i | ||||
\(161\) | 18.3085 | 1.44291 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.75493 | + | 21.1363i | −0.685739 | + | 1.65552i | 0.0674553 | + | 0.997722i | \(0.478512\pi\) |
−0.753194 | + | 0.657798i | \(0.771488\pi\) | |||||||
\(164\) | −3.16422 | + | 0.127831i | −0.247084 | + | 0.00998191i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.304868 | − | 15.0990i | −0.0236623 | − | 1.17191i | ||||
\(167\) | −14.8393 | + | 14.8393i | −1.14830 | + | 1.14830i | −0.161412 | + | 0.986887i | \(0.551605\pi\) |
−0.986887 | + | 0.161412i | \(0.948395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.18986 | − | 9.18986i | −0.706912 | − | 0.706912i | ||||
\(170\) | −7.47719 | + | 7.78536i | −0.573474 | + | 0.597110i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.4133 | + | 6.76989i | 1.40400 | + | 0.516200i | ||||
\(173\) | 14.0446 | + | 5.81747i | 1.06779 | + | 0.442294i | 0.846211 | − | 0.532848i | \(-0.178878\pi\) |
0.221581 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.965536i | − | 0.0729877i | ||||||
\(176\) | 22.2812 | − | 11.4151i | 1.67951 | − | 0.860442i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.7690 | − | 4.59878i | −0.882122 | − | 0.344693i | ||||
\(179\) | −3.27556 | − | 1.35678i | −0.244827 | − | 0.101411i | 0.256896 | − | 0.966439i | \(-0.417300\pi\) |
−0.501723 | + | 0.865028i | \(0.667300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.13658 | + | 5.15816i | 0.158811 | + | 0.383403i | 0.983177 | − | 0.182653i | \(-0.0584686\pi\) |
−0.824367 | + | 0.566056i | \(0.808469\pi\) | |||||||
\(182\) | −0.126267 | − | 0.121269i | −0.00935951 | − | 0.00898903i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.9591 | + | 22.4993i | 0.807917 | + | 1.65867i | ||||
\(185\) | −1.05661 | + | 1.05661i | −0.0776833 | + | 0.0776833i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8769 | − | 7.81907i | 1.38042 | − | 0.571787i | ||||
\(188\) | 17.7668 | + | 16.3870i | 1.29577 | + | 1.19514i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.655231 | + | 1.49573i | 0.0475355 | + | 0.108511i | ||||
\(191\) | −16.0419 | −1.16075 | −0.580375 | − | 0.814350i | \(-0.697094\pi\) | ||||
−0.580375 | + | 0.814350i | \(0.697094\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.08991 | 0.294398 | 0.147199 | − | 0.989107i | \(-0.452974\pi\) | ||||
0.147199 | + | 0.989107i | \(0.452974\pi\) | |||||||
\(194\) | 2.53837 | + | 5.79446i | 0.182244 | + | 0.416018i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.99653 | − | 3.68616i | −0.285466 | − | 0.263297i | ||||
\(197\) | −11.7515 | + | 4.86763i | −0.837259 | + | 0.346804i | −0.759772 | − | 0.650189i | \(-0.774690\pi\) |
−0.0774867 | + | 0.996993i | \(0.524690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.00147 | − | 5.00147i | 0.354544 | − | 0.354544i | −0.507253 | − | 0.861797i | \(-0.669339\pi\) |
0.861797 | + | 0.507253i | \(0.169339\pi\) | |||||||
\(200\) | 1.18654 | − | 0.577951i | 0.0839013 | − | 0.0408673i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.27368 | + | 1.22326i | 0.0896156 | + | 0.0860683i | ||||
\(203\) | 6.80214 | + | 16.4218i | 0.477417 | + | 1.15259i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.42031 | + | 1.41674i | 0.238885 | + | 0.0989493i | ||||
\(206\) | −12.1441 | − | 4.74536i | −0.846120 | − | 0.330625i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0734459 | − | 0.227758i | 0.00509256 | − | 0.0157922i | ||||
\(209\) | − | 3.09092i | − | 0.213803i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.45453 | + | 3.50198i | 0.582034 | + | 0.241086i | 0.654219 | − | 0.756305i | \(-0.272997\pi\) |
−0.0721855 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(212\) | 0.746050 | + | 0.274294i | 0.0512389 | + | 0.0188386i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.671538 | + | 0.699215i | −0.0459054 | + | 0.0477973i | ||||
\(215\) | −16.2173 | − | 16.2173i | −1.10601 | − | 1.10601i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.66626 | − | 9.66626i | 0.656188 | − | 0.656188i | ||||
\(218\) | 0.330050 | + | 16.3462i | 0.0223538 | + | 1.10711i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −29.2432 | + | 1.18139i | −1.97158 | + | 0.0796494i | ||||
\(221\) | 0.0747414 | − | 0.180442i | 0.00502765 | − | 0.0121378i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0650 | 1.07579 | 0.537896 | − | 0.843011i | \(-0.319219\pi\) | ||||
0.537896 | + | 0.843011i | \(0.319219\pi\) | |||||||
\(224\) | −3.36680 | + | 11.2104i | −0.224954 | + | 0.749029i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.9502 | + | 6.98729i | −1.06099 | + | 0.464787i | ||||
\(227\) | 4.12630 | − | 9.96177i | 0.273872 | − | 0.661186i | −0.725770 | − | 0.687938i | \(-0.758516\pi\) |
0.999642 | + | 0.0267514i | \(0.00851626\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.28112 | + | 1.35908i | −0.216822 | + | 0.0898108i | −0.488451 | − | 0.872591i | \(-0.662438\pi\) |
0.271628 | + | 0.962402i | \(0.412438\pi\) | |||||||
\(230\) | −0.590611 | − | 29.2509i | −0.0389437 | − | 1.92875i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.1091 | + | 18.1889i | −1.05761 | + | 1.19416i | ||||
\(233\) | −17.4031 | − | 17.4031i | −1.14011 | − | 1.14011i | −0.988429 | − | 0.151684i | \(-0.951530\pi\) |
−0.151684 | − | 0.988429i | \(-0.548470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.8130 | − | 26.1049i | −0.705363 | − | 1.70290i | ||||
\(236\) | −3.17218 | + | 8.62797i | −0.206491 | + | 0.561633i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.47687 | + | 8.89785i | −0.225372 | + | 0.576762i | ||||
\(239\) | 13.3610i | 0.864251i | 0.901814 | + | 0.432125i | \(0.142236\pi\) | ||||
−0.901814 | + | 0.432125i | \(0.857764\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.39060i | − | 0.282823i | −0.989951 | − | 0.141412i | \(-0.954836\pi\) | ||
0.989951 | − | 0.141412i | \(-0.0451641\pi\) | |||||||
\(242\) | 37.1091 | + | 14.5005i | 2.38546 | + | 0.932130i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.26907 | + | 2.74482i | 0.0812437 | + | 0.175719i | ||||
\(245\) | 2.43233 | + | 5.87215i | 0.155396 | + | 0.375158i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0208920 | − | 0.0208920i | −0.00132932 | − | 0.00132932i | ||||
\(248\) | 17.6649 | + | 6.09280i | 1.12172 | + | 0.386893i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.9868 | − | 0.302601i | 0.947846 | − | 0.0191381i | ||||
\(251\) | 18.1050 | − | 7.49935i | 1.14278 | − | 0.473355i | 0.270673 | − | 0.962671i | \(-0.412754\pi\) |
0.872106 | + | 0.489317i | \(0.162754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.1925 | + | 51.1632i | −1.33236 | + | 3.21660i | ||||
\(254\) | 8.45704 | + | 19.3053i | 0.530642 | + | 1.21132i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7918 | + | 2.57290i | −0.986986 | + | 0.160806i | ||||
\(257\) | 24.9051 | 1.55354 | 0.776769 | − | 0.629786i | \(-0.216857\pi\) | ||||
0.776769 | + | 0.629786i | \(0.216857\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.506068 | + | 1.22176i | −0.0314455 | + | 0.0759162i | ||||
\(260\) | −0.189674 | + | 0.205644i | −0.0117631 | + | 0.0127535i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.3340 | − | 0.269230i | 0.823779 | − | 0.0166331i | ||||
\(263\) | −0.341086 | + | 0.341086i | −0.0210323 | + | 0.0210323i | −0.717545 | − | 0.696512i | \(-0.754734\pi\) |
0.696512 | + | 0.717545i | \(0.254734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.657074 | − | 0.657074i | −0.0403637 | − | 0.0403637i | ||||
\(266\) | 1.04230 | + | 1.00104i | 0.0639074 | + | 0.0613777i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.54702 | + | 16.3232i | 0.461008 | + | 0.997098i | ||||
\(269\) | −19.0868 | − | 7.90603i | −1.16375 | − | 0.482039i | −0.284625 | − | 0.958639i | \(-0.591869\pi\) |
−0.879120 | + | 0.476600i | \(0.841869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.2155i | 0.802784i | 0.915906 | + | 0.401392i | \(0.131474\pi\) | ||||
−0.915906 | + | 0.401392i | \(0.868526\pi\) | |||||||
\(272\) | −13.0157 | + | 1.05336i | −0.789194 | + | 0.0638693i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.62970 | − | 6.72980i | 0.158866 | − | 0.406562i | ||||
\(275\) | 2.69819 | + | 1.11763i | 0.162707 | + | 0.0673955i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.53617 | − | 23.0223i | −0.572973 | − | 1.38328i | −0.899013 | − | 0.437922i | \(-0.855714\pi\) |
0.326040 | − | 0.945356i | \(-0.394286\pi\) | |||||||
\(278\) | 14.3232 | − | 14.9135i | 0.859047 | − | 0.894452i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.07246 | − | 10.2438i | 0.542183 | − | 0.612183i | ||||
\(281\) | −11.1422 | + | 11.1422i | −0.664686 | + | 0.664686i | −0.956481 | − | 0.291795i | \(-0.905747\pi\) |
0.291795 | + | 0.956481i | \(0.405747\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.4532 | + | 4.32986i | −0.621379 | + | 0.257384i | −0.671085 | − | 0.741380i | \(-0.734172\pi\) |
0.0497061 | + | 0.998764i | \(0.484172\pi\) | |||||||
\(284\) | −0.273439 | − | 6.76848i | −0.0162256 | − | 0.401635i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.485042 | − | 0.212482i | 0.0286811 | − | 0.0125643i | ||||
\(287\) | 3.27635 | 0.193397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.34258 | 0.373093 | ||||||||
\(290\) | 26.0172 | − | 11.3973i | 1.52778 | − | 0.669272i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 27.8044 | − | 1.12327i | 1.62713 | − | 0.0657342i | ||||
\(293\) | −21.1780 | + | 8.77221i | −1.23723 | + | 0.512478i | −0.902848 | − | 0.429959i | \(-0.858528\pi\) |
−0.334383 | + | 0.942437i | \(0.608528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.59897 | − | 7.59897i | 0.442429 | − | 0.442429i | ||||
\(296\) | −1.80433 | + | 0.109414i | −0.104875 | + | 0.00635956i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.20827 | + | 3.34049i | −0.185850 | + | 0.193510i | ||||
\(299\) | 0.202576 | + | 0.489062i | 0.0117153 | + | 0.0282832i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.7521 | − | 7.76737i | −1.08085 | − | 0.447704i | ||||
\(302\) | −0.163665 | + | 0.418844i | −0.00941787 | + | 0.0241018i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.606276 | + | 1.88008i | −0.0347723 | + | 0.107830i | ||||
\(305\) | − | 3.53518i | − | 0.202424i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.30394 | − | 1.78275i | −0.245639 | − | 0.101747i | 0.256468 | − | 0.966553i | \(-0.417441\pi\) |
−0.502106 | + | 0.864806i | \(0.667441\pi\) | |||||||
\(308\) | −23.5100 | + | 10.8698i | −1.33960 | + | 0.619365i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.7553 | − | 15.1316i | −0.894839 | − | 0.859419i | ||||
\(311\) | −13.1986 | − | 13.1986i | −0.748421 | − | 0.748421i | 0.225761 | − | 0.974183i | \(-0.427513\pi\) |
−0.974183 | + | 0.225761i | \(0.927513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.2136 | − | 13.2136i | 0.746877 | − | 0.746877i | −0.227014 | − | 0.973891i | \(-0.572896\pi\) |
0.973891 | + | 0.227014i | \(0.0728964\pi\) | |||||||
\(314\) | 0.718161 | − | 0.0145005i | 0.0405282 | − | 0.000818312i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.32544 | + | 4.91187i | 0.299579 | + | 0.276314i | ||||
\(317\) | −3.77929 | + | 9.12400i | −0.212266 | + | 0.512455i | −0.993771 | − | 0.111444i | \(-0.964452\pi\) |
0.781505 | + | 0.623899i | \(0.214452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −53.7644 | −3.01023 | ||||||||
\(320\) | 18.0192 | + | 5.01739i | 1.00730 | + | 0.280480i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.3894 | − | 23.7163i | −0.578977 | − | 1.32166i | ||||
\(323\) | −0.616970 | + | 1.48950i | −0.0343291 | + | 0.0828779i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0257917 | − | 0.0106833i | 0.00143066 | − | 0.000592600i | ||||
\(326\) | 32.3474 | − | 0.653133i | 1.79156 | − | 0.0361737i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.96116 | + | 4.02630i | 0.108287 | + | 0.222315i | ||||
\(329\) | −17.6820 | − | 17.6820i | −0.974843 | − | 0.974843i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.86478 | − | 6.91618i | −0.157462 | − | 0.380148i | 0.825385 | − | 0.564571i | \(-0.190958\pi\) |
−0.982847 | + | 0.184423i | \(0.940958\pi\) | |||||||
\(332\) | −19.3859 | + | 8.96304i | −1.06394 | + | 0.491911i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.6431 | + | 10.8017i | 1.51256 | + | 0.591041i | ||||
\(335\) | − | 21.0234i | − | 1.14863i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.2162i | − | 0.665461i | −0.943022 | − | 0.332730i | \(-0.892030\pi\) | ||
0.943022 | − | 0.332730i | \(-0.107970\pi\) | |||||||
\(338\) | −6.68939 | + | 17.1192i | −0.363855 | + | 0.931160i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 14.3280 | + | 5.26785i | 0.777042 | + | 0.285689i | ||||
\(341\) | 15.8235 | + | 38.2013i | 0.856889 | + | 2.06871i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2194 | + | 14.2194i | 0.767778 | + | 0.767778i | ||||
\(344\) | −1.67934 | − | 27.6938i | −0.0905438 | − | 1.49315i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.433993 | − | 21.4942i | −0.0233316 | − | 1.15553i | ||||
\(347\) | 13.7143 | − | 5.68066i | 0.736223 | − | 0.304954i | 0.0171166 | − | 0.999854i | \(-0.494551\pi\) |
0.719106 | + | 0.694900i | \(0.244551\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.44624 | + | 17.9768i | −0.398588 | + | 0.962277i | 0.589413 | + | 0.807832i | \(0.299359\pi\) |
−0.988001 | + | 0.154445i | \(0.950641\pi\) | |||||||
\(350\) | −1.25073 | + | 0.547905i | −0.0668542 | + | 0.0292867i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.4305 | − | 22.3848i | −1.46205 | − | 1.19312i | ||||
\(353\) | −26.6175 | −1.41671 | −0.708354 | − | 0.705858i | \(-0.750562\pi\) | ||||
−0.708354 | + | 0.705858i | \(0.750562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.03050 | + | 7.31628i | −0.160842 | + | 0.388308i | ||||
\(356\) | 0.721315 | + | 17.8548i | 0.0382296 | + | 0.946304i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.101218 | + | 5.01299i | 0.00534955 | + | 0.264945i | ||||
\(359\) | 6.75743 | − | 6.75743i | 0.356643 | − | 0.356643i | −0.505931 | − | 0.862574i | \(-0.668851\pi\) |
0.862574 | + | 0.505931i | \(0.168851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2626 | − | 13.2626i | −0.698030 | − | 0.698030i | ||||
\(362\) | 5.46930 | − | 5.69472i | 0.287460 | − | 0.299308i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0854365 | + | 0.232378i | −0.00447809 | + | 0.0121799i | ||||
\(365\) | −30.0547 | − | 12.4491i | −1.57314 | − | 0.651615i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.9220i | − | 0.622322i | −0.950357 | − | 0.311161i | \(-0.899282\pi\) | ||
0.950357 | − | 0.311161i | \(-0.100718\pi\) | |||||||
\(368\) | 22.9260 | − | 26.9636i | 1.19510 | − | 1.40557i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.96828 | + | 0.769115i | 0.102326 | + | 0.0399844i | ||||
\(371\) | −0.759775 | − | 0.314709i | −0.0394455 | − | 0.0163389i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.22670 | + | 17.4468i | 0.374184 | + | 0.903361i | 0.993031 | + | 0.117849i | \(0.0376000\pi\) |
−0.618847 | + | 0.785511i | \(0.712400\pi\) | |||||||
\(374\) | −20.8405 | − | 20.0156i | −1.07764 | − | 1.03498i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.1453 | − | 32.3135i | 0.574774 | − | 1.66644i | ||||
\(377\) | −0.363401 | + | 0.363401i | −0.0187161 | + | 0.0187161i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2575 | − | 8.80513i | 1.09192 | − | 0.452289i | 0.237246 | − | 0.971450i | \(-0.423755\pi\) |
0.854677 | + | 0.519160i | \(0.173755\pi\) | |||||||
\(380\) | 1.56570 | − | 1.69754i | 0.0803189 | − | 0.0870817i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.10314 | + | 20.7802i | 0.465757 | + | 1.06321i | ||||
\(383\) | −32.8281 | −1.67744 | −0.838719 | − | 0.544564i | \(-0.816695\pi\) | ||||
−0.838719 | + | 0.544564i | \(0.816695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.2795 | 1.54319 | ||||||||
\(386\) | −2.32086 | − | 5.29795i | −0.118129 | − | 0.269658i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.06555 | − | 6.57627i | 0.307932 | − | 0.333859i | ||||
\(389\) | 0.635526 | − | 0.263244i | 0.0322225 | − | 0.0133470i | −0.366514 | − | 0.930413i | \(-0.619449\pi\) |
0.398736 | + | 0.917066i | \(0.369449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.4251 | − | 20.4251i | 1.03294 | − | 1.03294i | ||||
\(392\) | −2.50707 | + | 7.26875i | −0.126626 | + | 0.367127i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.9739 | + | 12.4604i | 0.653616 | + | 0.627744i | ||||
\(395\) | −3.24111 | − | 7.82474i | −0.163078 | − | 0.393705i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.42539 | − | 2.66148i | −0.322481 | − | 0.133576i | 0.215570 | − | 0.976488i | \(-0.430839\pi\) |
−0.538051 | + | 0.842912i | \(0.680839\pi\) | |||||||
\(398\) | −9.31689 | − | 3.64062i | −0.467014 | − | 0.182488i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.42198 | − | 1.20905i | −0.0710990 | − | 0.0604525i | ||||
\(401\) | − | 37.6097i | − | 1.87814i | −0.343730 | − | 0.939069i | \(-0.611690\pi\) | ||
0.343730 | − | 0.939069i | \(-0.388310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.365161 | + | 0.151255i | 0.0181900 | + | 0.00753453i | ||||
\(404\) | 0.861814 | − | 2.34404i | 0.0428769 | − | 0.116620i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.4124 | − | 18.1301i | 0.864163 | − | 0.899779i | ||||
\(407\) | −2.82841 | − | 2.82841i | −0.140199 | − | 0.140199i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.67172 | + | 6.67172i | −0.329895 | + | 0.329895i | −0.852547 | − | 0.522651i | \(-0.824943\pi\) |
0.522651 | + | 0.852547i | \(0.324943\pi\) | |||||||
\(410\) | −0.105691 | − | 5.23452i | −0.00521971 | − | 0.258514i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.744307 | + | 18.4239i | 0.0366694 | + | 0.907683i | ||||
\(413\) | 3.63957 | − | 8.78669i | 0.179091 | − | 0.432365i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.9679 | 1.22563 | ||||||||
\(416\) | −0.336709 | + | 0.0341040i | −0.0165085 | + | 0.00167209i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.00389 | + | 1.75398i | −0.195837 | + | 0.0857898i | ||||
\(419\) | −9.24059 | + | 22.3088i | −0.451432 | + | 1.08985i | 0.520346 | + | 0.853956i | \(0.325803\pi\) |
−0.971778 | + | 0.235898i | \(0.924197\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.9531 | − | 10.7501i | 1.26488 | − | 0.523929i | 0.353474 | − | 0.935444i | \(-0.385000\pi\) |
0.911403 | + | 0.411515i | \(0.135000\pi\) | |||||||
\(422\) | −0.261254 | − | 12.9390i | −0.0127176 | − | 0.629860i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0680414 | − | 1.12206i | −0.00330438 | − | 0.0544922i | ||||
\(425\) | −1.07716 | − | 1.07716i | −0.0522498 | − | 0.0522498i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.19727 | − | 2.89046i | −0.0579399 | − | 0.139879i | ||||
\(428\) | 1.28681 | + | 0.473113i | 0.0622005 | + | 0.0228688i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.8047 | + | 30.2101i | −0.569275 | + | 1.45686i | ||||
\(431\) | 34.3112i | 1.65271i | 0.563148 | + | 0.826356i | \(0.309590\pi\) | ||||
−0.563148 | + | 0.826356i | \(0.690410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 21.0166i | − | 1.00999i | −0.863121 | − | 0.504997i | \(-0.831494\pi\) | ||
0.863121 | − | 0.504997i | \(-0.168506\pi\) | |||||||
\(434\) | −18.0066 | − | 7.03617i | −0.864346 | − | 0.337747i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.9872 | − | 9.70340i | 1.00510 | − | 0.464708i | ||||
\(437\) | −1.67221 | − | 4.03707i | −0.0799927 | − | 0.193119i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.73217 | − | 8.73217i | −0.416764 | − | 0.416764i | 0.467323 | − | 0.884087i | \(-0.345219\pi\) |
−0.884087 | + | 0.467323i | \(0.845219\pi\) | |||||||
\(440\) | 18.1247 | + | 37.2104i | 0.864062 | + | 1.77394i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.276152 | + | 0.00557584i | −0.0131352 | + | 0.000265216i | ||||
\(443\) | −20.3275 | + | 8.41993i | −0.965789 | + | 0.400043i | −0.809143 | − | 0.587612i | \(-0.800068\pi\) |
−0.156646 | + | 0.987655i | \(0.550068\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.99427 | − | 19.2999i | 0.378965 | − | 0.914902i | ||||
\(446\) | −9.11627 | − | 20.8102i | −0.431668 | − | 0.985389i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.4322 | − | 2.00024i | 0.776349 | − | 0.0945024i | ||||
\(449\) | −24.6957 | −1.16546 | −0.582730 | − | 0.812666i | \(-0.698016\pi\) | ||||
−0.582730 | + | 0.812666i | \(0.698016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.79244 | + | 9.15577i | −0.178579 | + | 0.431128i | ||||
\(452\) | 18.1023 | + | 16.6964i | 0.851459 | + | 0.785334i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.2457 | + | 0.307829i | −0.715517 | + | 0.0144471i | ||||
\(455\) | 0.204664 | − | 0.204664i | 0.00959477 | − | 0.00959477i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.41902 | − | 9.41902i | −0.440603 | − | 0.440603i | 0.451612 | − | 0.892215i | \(-0.350849\pi\) |
−0.892215 | + | 0.451612i | \(0.850849\pi\) | |||||||
\(458\) | 3.62243 | + | 3.47904i | 0.169265 | + | 0.162565i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −37.5556 | + | 17.3638i | −1.75104 | + | 0.809592i | ||||
\(461\) | −9.14047 | − | 3.78611i | −0.425714 | − | 0.176337i | 0.159531 | − | 0.987193i | \(-0.449002\pi\) |
−0.585245 | + | 0.810856i | \(0.699002\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.9637i | 0.974264i | 0.873328 | + | 0.487132i | \(0.161957\pi\) | ||||
−0.873328 | + | 0.487132i | \(0.838043\pi\) | |||||||
\(464\) | 32.7027 | + | 10.5458i | 1.51818 | + | 0.489574i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.6679 | + | 32.4190i | −0.586828 | + | 1.50178i | ||||
\(467\) | 16.0094 | + | 6.63133i | 0.740829 | + | 0.306861i | 0.720993 | − | 0.692942i | \(-0.243686\pi\) |
0.0198354 | + | 0.999803i | \(0.493686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.12005 | − | 17.1893i | −0.328773 | − | 0.793729i | ||||
\(470\) | −27.6796 | + | 28.8204i | −1.27676 | + | 1.32939i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.9765 | − | 0.786890i | 0.597292 | − | 0.0362195i | ||||
\(473\) | 43.4119 | − | 43.4119i | 1.99608 | − | 1.99608i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.212903 | + | 0.0881874i | −0.00976867 | + | 0.00404632i | ||||
\(476\) | 13.4990 | − | 0.545345i | 0.618726 | − | 0.0249958i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.3074 | − | 7.58185i | 0.791624 | − | 0.346786i | ||||
\(479\) | −11.4416 | −0.522780 | −0.261390 | − | 0.965233i | \(-0.584181\pi\) | ||||
−0.261390 | + | 0.965233i | \(0.584181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0382353 | −0.00174338 | ||||||||
\(482\) | −5.68746 | + | 2.49150i | −0.259057 | + | 0.113485i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.27440 | − | 56.2986i | −0.103382 | − | 2.55903i | ||||
\(485\) | −9.66259 | + | 4.00238i | −0.438756 | + | 0.181739i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.40830 | − | 6.40830i | 0.290388 | − | 0.290388i | −0.546846 | − | 0.837234i | \(-0.684172\pi\) |
0.837234 | + | 0.546846i | \(0.184172\pi\) | |||||||
\(488\) | 2.83542 | − | 3.20149i | 0.128353 | − | 0.144925i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.22637 | − | 6.48299i | 0.281279 | − | 0.292871i | ||||
\(491\) | 1.87362 | + | 4.52331i | 0.0845552 | + | 0.204134i | 0.960502 | − | 0.278274i | \(-0.0897623\pi\) |
−0.875947 | + | 0.482408i | \(0.839762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.9088 | + | 10.7318i | 1.16687 | + | 0.483335i | ||||
\(494\) | −0.0152075 | + | 0.0389182i | −0.000684216 | + | 0.00175101i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.13169 | − | 26.3400i | −0.0957157 | − | 1.18270i | ||||
\(497\) | 7.00834i | 0.314367i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.7568 | + | 11.4973i | 1.24257 | + | 0.514688i | 0.904516 | − | 0.426440i | \(-0.140232\pi\) |
0.338051 | + | 0.941128i | \(0.390232\pi\) | |||||||
\(500\) | −8.89639 | − | 19.2417i | −0.397859 | − | 0.860515i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.9883 | − | 19.1971i | −0.892124 | − | 0.856811i | ||||
\(503\) | −8.03823 | − | 8.03823i | −0.358407 | − | 0.358407i | 0.504819 | − | 0.863225i | \(-0.331559\pi\) |
−0.863225 | + | 0.504819i | \(0.831559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.06448 | + | 2.06448i | −0.0918682 | + | 0.0918682i | ||||
\(506\) | 78.3012 | − | 1.58100i | 3.48092 | − | 0.0702838i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.2085 | − | 21.9100i | 0.896606 | − | 0.972100i | ||||
\(509\) | 3.62960 | − | 8.76263i | 0.160879 | − | 0.388397i | −0.822799 | − | 0.568332i | \(-0.807589\pi\) |
0.983678 | + | 0.179935i | \(0.0575889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.7898 | −1.27358 | ||||||||
\(512\) | 12.2941 | + | 18.9962i | 0.543327 | + | 0.839521i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.1327 | − | 32.2614i | −0.623366 | − | 1.42299i | ||||
\(515\) | 8.24909 | − | 19.9151i | 0.363498 | − | 0.877563i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 69.8798 | − | 28.9452i | 3.07331 | − | 1.27301i | ||||
\(518\) | 1.86980 | − | 0.0377535i | 0.0821544 | − | 0.00165880i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.374018 | + | 0.129003i | 0.0164018 | + | 0.00565714i | ||||
\(521\) | 6.13944 | + | 6.13944i | 0.268974 | + | 0.268974i | 0.828687 | − | 0.559713i | \(-0.189089\pi\) |
−0.559713 | + | 0.828687i | \(0.689089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.64181 | − | 16.0347i | −0.290426 | − | 0.701150i | 0.709568 | − | 0.704637i | \(-0.248890\pi\) |
−0.999994 | + | 0.00348661i | \(0.998890\pi\) | |||||||
\(524\) | −7.91530 | − | 17.1197i | −0.345781 | − | 0.747879i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.635386 | + | 0.248280i | 0.0277041 | + | 0.0108255i | ||||
\(527\) | − | 21.5675i | − | 0.939494i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.2899i | 2.40391i | ||||||||
\(530\) | −0.478290 | + | 1.22402i | −0.0207756 | + | 0.0531680i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.705255 | − | 1.91821i | 0.0305767 | − | 0.0831651i | ||||
\(533\) | 0.0362515 | + | 0.0875188i | 0.00157023 | + | 0.00379086i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.13334 | − | 1.13334i | −0.0489988 | − | 0.0489988i | ||||
\(536\) | 16.8620 | − | 19.0390i | 0.728326 | − | 0.822359i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.589803 | + | 29.2109i | 0.0254282 | + | 1.25937i | ||||
\(539\) | −15.7191 | + | 6.51105i | −0.677068 | + | 0.280451i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.68635 | + | 11.3138i | −0.201482 | + | 0.486420i | −0.992033 | − | 0.125975i | \(-0.959794\pi\) |
0.790552 | + | 0.612396i | \(0.209794\pi\) | |||||||
\(542\) | 17.1190 | − | 7.49929i | 0.735323 | − | 0.322122i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.75042 | + | 16.2625i | 0.375171 | + | 0.697247i | ||||
\(545\) | −27.0303 | −1.15785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1142 | + | 29.2461i | −0.517964 | + | 1.25048i | 0.421188 | + | 0.906973i | \(0.361613\pi\) |
−0.939152 | + | 0.343502i | \(0.888387\pi\) | |||||||
\(548\) | −10.2098 | + | 0.412466i | −0.436143 | + | 0.0176197i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0833770 | − | 4.12937i | −0.00355521 | − | 0.176077i | ||||
\(551\) | 2.99978 | − | 2.99978i | 0.127795 | − | 0.127795i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.30005 | − | 5.30005i | −0.225381 | − | 0.225381i | ||||
\(554\) | −24.4111 | + | 25.4172i | −1.03713 | + | 1.07987i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.4464 | − | 10.0910i | −1.16398 | − | 0.427953i | ||||
\(557\) | 24.2696 | + | 10.0528i | 1.02833 | + | 0.425950i | 0.832111 | − | 0.554609i | \(-0.187132\pi\) |
0.196223 | + | 0.980559i | \(0.437132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.586854i | − | 0.0248213i | ||||||
\(560\) | −18.4178 | − | 5.93925i | −0.778293 | − | 0.250979i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.7560 | + | 8.11049i | 0.875538 | + | 0.342120i | ||||
\(563\) | 18.4201 | + | 7.62986i | 0.776315 | + | 0.321560i | 0.735428 | − | 0.677603i | \(-0.236981\pi\) |
0.0408878 | + | 0.999164i | \(0.486981\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.0172 | − | 26.5979i | −0.463497 | − | 1.11898i | ||||
\(566\) | 11.5406 | + | 11.0838i | 0.485087 | + | 0.465885i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.61253 | + | 4.19506i | −0.361374 | + | 0.176021i | ||||
\(569\) | 25.2695 | − | 25.2695i | 1.05935 | − | 1.05935i | 0.0612266 | − | 0.998124i | \(-0.480499\pi\) |
0.998124 | − | 0.0612266i | \(-0.0195012\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0258 | − | 14.9224i | 1.50763 | − | 0.624482i | 0.532565 | − | 0.846389i | \(-0.321228\pi\) |
0.975068 | + | 0.221907i | \(0.0712281\pi\) | |||||||
\(572\) | −0.550485 | − | 0.507734i | −0.0230169 | − | 0.0212294i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.85920 | − | 4.24409i | −0.0776017 | − | 0.177145i | ||||
\(575\) | 4.12878 | 0.172182 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5817 | 1.23150 | 0.615752 | − | 0.787940i | \(-0.288852\pi\) | ||||
0.615752 | + | 0.787940i | \(0.288852\pi\) | |||||||
\(578\) | −3.59917 | − | 8.21600i | −0.149706 | − | 0.341741i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −29.5275 | − | 27.2344i | −1.22606 | − | 1.13085i | ||||
\(581\) | 20.4145 | − | 8.45595i | 0.846935 | − | 0.350812i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.75891 | − | 1.75891i | 0.0728466 | − | 0.0728466i | ||||
\(584\) | −17.2330 | − | 35.3796i | −0.713106 | − | 1.46402i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.3810 | + | 22.4555i | 0.965859 | + | 0.927627i | ||||
\(587\) | −13.5028 | − | 32.5986i | −0.557319 | − | 1.34549i | −0.911881 | − | 0.410455i | \(-0.865370\pi\) |
0.354561 | − | 0.935033i | \(-0.384630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.01430 | − | 1.24857i | −0.124202 | − | 0.0514462i | ||||
\(590\) | −14.1556 | − | 5.53137i | −0.582777 | − | 0.227723i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.16562 | + | 2.27519i | 0.0479068 | + | 0.0935099i | ||||
\(593\) | 34.7178i | 1.42569i | 0.701323 | + | 0.712844i | \(0.252593\pi\) | ||||
−0.701323 | + | 0.712844i | \(0.747407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.5915 | − | 6.04401i | −0.598195 | − | 0.247780i | ||||
\(596\) | 6.14775 | + | 2.26030i | 0.251822 | + | 0.0925853i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.518563 | − | 0.539935i | 0.0212056 | − | 0.0220796i | ||||
\(599\) | 0.840657 | + | 0.840657i | 0.0343483 | + | 0.0343483i | 0.724072 | − | 0.689724i | \(-0.242268\pi\) |
−0.689724 | + | 0.724072i | \(0.742268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.647523 | + | 0.647523i | −0.0264130 | + | 0.0264130i | −0.720190 | − | 0.693777i | \(-0.755945\pi\) |
0.693777 | + | 0.720190i | \(0.255945\pi\) | |||||||
\(602\) | 0.579459 | + | 28.6986i | 0.0236170 | + | 1.16967i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.635432 | − | 0.0256708i | 0.0258554 | − | 0.00104453i | ||||
\(605\) | −25.2070 | + | 60.8550i | −1.02481 | + | 2.47411i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −46.7752 | −1.89855 | −0.949273 | − | 0.314452i | \(-0.898179\pi\) | ||||
−0.949273 | + | 0.314452i | \(0.898179\pi\) | |||||||
\(608\) | 2.77944 | − | 0.281520i | 0.112721 | − | 0.0114171i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.57937 | + | 2.00608i | −0.185413 | + | 0.0812237i | ||||
\(611\) | 0.276683 | − | 0.667972i | 0.0111934 | − | 0.0270233i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0801 | + | 6.24640i | −0.609081 | + | 0.252290i | −0.665836 | − | 0.746099i | \(-0.731925\pi\) |
0.0567545 | + | 0.998388i | \(0.481925\pi\) | |||||||
\(614\) | 0.132996 | + | 6.58684i | 0.00536729 | + | 0.265823i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.4214 | + | 24.2859i | 1.10484 | + | 0.978508i | ||||
\(617\) | 0.207739 | + | 0.207739i | 0.00836324 | + | 0.00836324i | 0.711276 | − | 0.702913i | \(-0.248118\pi\) |
−0.702913 | + | 0.711276i | \(0.748118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.5663 | − | 30.3378i | −0.505083 | − | 1.21938i | −0.946683 | − | 0.322166i | \(-0.895589\pi\) |
0.441600 | − | 0.897212i | \(-0.354411\pi\) | |||||||
\(620\) | −10.6606 | + | 28.9955i | −0.428139 | + | 1.16449i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.60736 | + | 24.5867i | −0.385220 | + | 0.985837i | ||||
\(623\) | − | 18.4876i | − | 0.740689i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.1154i | 1.08462i | ||||||||
\(626\) | −24.6147 | − | 9.61832i | −0.983803 | − | 0.384425i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.426312 | − | 0.922057i | −0.0170117 | − | 0.0367941i | ||||
\(629\) | 0.798426 | + | 1.92757i | 0.0318353 | + | 0.0768573i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.04178 | − | 1.04178i | −0.0414728 | − | 0.0414728i | 0.686066 | − | 0.727539i | \(-0.259336\pi\) |
−0.727539 | + | 0.686066i | \(0.759336\pi\) | |||||||
\(632\) | 3.34071 | − | 9.68572i | 0.132886 | − | 0.385277i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.9636 | − | 0.281941i | 0.554564 | − | 0.0111973i | ||||
\(635\) | −32.1927 | + | 13.3346i | −1.27753 | + | 0.529169i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0622383 | + | 0.150257i | −0.00246597 | + | 0.00595338i | ||||
\(638\) | 30.5092 | + | 69.6449i | 1.20787 | + | 2.75727i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.72580 | − | 26.1887i | −0.147275 | − | 1.03520i | ||||
\(641\) | −27.9724 | −1.10484 | −0.552421 | − | 0.833565i | \(-0.686296\pi\) | ||||
−0.552421 | + | 0.833565i | \(0.686296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.1230 | + | 41.3386i | −0.675266 | + | 1.63024i | 0.0972657 | + | 0.995258i | \(0.468990\pi\) |
−0.772531 | + | 0.634977i | \(0.781010\pi\) | |||||||
\(644\) | −24.8259 | + | 26.9162i | −0.978277 | + | 1.06065i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.27956 | − | 0.0460270i | 0.0896881 | − | 0.00181091i | ||||
\(647\) | −12.5087 | + | 12.5087i | −0.491766 | + | 0.491766i | −0.908862 | − | 0.417096i | \(-0.863048\pi\) |
0.417096 | + | 0.908862i | \(0.363048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3416 | + | 20.3416i | 0.798476 | + | 0.798476i | ||||
\(650\) | −0.0284746 | − | 0.0273474i | −0.00111686 | − | 0.00107266i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.2020 | − | 41.5313i | −0.752007 | − | 1.62649i | ||||
\(653\) | 37.1822 | + | 15.4014i | 1.45505 | + | 0.602703i | 0.963395 | − | 0.268086i | \(-0.0863912\pi\) |
0.491658 | + | 0.870789i | \(0.336391\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.0493i | 0.861537i | ||||||||
\(656\) | 4.10267 | − | 4.82520i | 0.160182 | − | 0.188392i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.8709 | + | 32.9387i | −0.501761 | + | 1.28408i | ||||
\(659\) | 34.3332 | + | 14.2213i | 1.33743 | + | 0.553982i | 0.932766 | − | 0.360483i | \(-0.117388\pi\) |
0.404665 | + | 0.914465i | \(0.367388\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.1157 | − | 29.2500i | −0.471248 | − | 1.13769i | −0.963612 | − | 0.267304i | \(-0.913867\pi\) |
0.492365 | − | 0.870389i | \(-0.336133\pi\) | |||||||
\(662\) | −7.33338 | + | 7.63562i | −0.285020 | + | 0.296767i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.6112 | + | 20.0257i | 0.877485 | + | 0.777149i | ||||
\(665\) | −1.68944 | + | 1.68944i | −0.0655138 | + | 0.0655138i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −70.2222 | + | 29.0870i | −2.71901 | + | 1.12625i | ||||
\(668\) | −1.69423 | − | 41.9377i | −0.0655519 | − | 1.62262i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −27.2331 | + | 11.9300i | −1.05211 | + | 0.460895i | ||||
\(671\) | 9.46327 | 0.365325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3366 | −0.783917 | −0.391958 | − | 0.919983i | \(-0.628202\pi\) | ||||
−0.391958 | + | 0.919983i | \(0.628202\pi\) | |||||||
\(674\) | −15.8246 | + | 6.93224i | −0.609539 | + | 0.267020i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.9717 | − | 1.04923i | 0.998910 | − | 0.0403548i | ||||
\(677\) | −1.06604 | + | 0.441568i | −0.0409712 | + | 0.0169708i | −0.403075 | − | 0.915167i | \(-0.632059\pi\) |
0.362104 | + | 0.932138i | \(0.382059\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.54491 | + | 6.54491i | −0.251171 | + | 0.251171i | ||||
\(680\) | −1.30674 | − | 21.5493i | −0.0501112 | − | 0.826379i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 40.5056 | − | 42.1750i | 1.55104 | − | 1.61497i | ||||
\(683\) | 9.86389 | + | 23.8135i | 0.377431 | + | 0.911200i | 0.992446 | + | 0.122684i | \(0.0391502\pi\) |
−0.615014 | + | 0.788516i | \(0.710850\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.0362 | + | 4.57133i | 0.421670 | + | 0.174662i | ||||
\(686\) | 10.3505 | − | 26.4884i | 0.395183 | − | 1.01133i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −34.9208 | + | 17.8905i | −1.33134 | + | 0.682070i | ||||
\(689\) | − | 0.0237774i | − | 0.000905848i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2626 | − | 10.4641i | −0.961035 | − | 0.398074i | −0.153667 | − | 0.988123i | \(-0.549108\pi\) |
−0.807367 | + | 0.590049i | \(0.799108\pi\) | |||||||
\(692\) | −27.5967 | + | 12.7593i | −1.04907 | + | 0.485036i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.1409 | − | 14.5416i | −0.574741 | − | 0.551991i | ||||
\(695\) | 24.1730 | + | 24.1730i | 0.916935 | + | 0.916935i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.65512 | − | 3.65512i | 0.138447 | − | 0.138447i | ||||
\(698\) | 27.5121 | − | 0.555503i | 1.04135 | − | 0.0210261i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.41948 | + | 1.30924i | 0.0536513 | + | 0.0494847i | ||||
\(701\) | −1.87688 | + | 4.53118i | −0.0708887 | + | 0.171140i | −0.955353 | − | 0.295468i | \(-0.904524\pi\) |
0.884464 | + | 0.466609i | \(0.154524\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.315622 | 0.0119039 | ||||||||
\(704\) | −13.4310 | + | 48.2352i | −0.506198 | + | 1.81793i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1044 | + | 34.4796i | 0.568462 | + | 1.29766i | ||||
\(707\) | −0.988794 | + | 2.38716i | −0.0371874 | + | 0.0897784i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.6589 | − | 9.79984i | 0.888529 | − | 0.368041i | 0.108730 | − | 0.994071i | \(-0.465322\pi\) |
0.779798 | + | 0.626031i | \(0.215322\pi\) | |||||||
\(710\) | 11.1970 | − | 0.226081i | 0.420215 | − | 0.00848465i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.7193 | − | 11.0663i | 0.851442 | − | 0.414727i | ||||
\(713\) | 41.3344 | + | 41.3344i | 1.54798 | + | 1.54798i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.335030 | + | 0.808835i | 0.0125294 | + | 0.0302487i | ||||
\(716\) | 6.43625 | − | 2.97579i | 0.240534 | − | 0.111211i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.5880 | − | 4.91880i | −0.469778 | − | 0.183568i | ||||
\(719\) | − | 7.42466i | − | 0.276893i | −0.990370 | − | 0.138447i | \(-0.955789\pi\) | ||
0.990370 | − | 0.138447i | \(-0.0442109\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 19.0769i | − | 0.710460i | ||||||
\(722\) | −9.65396 | + | 24.7060i | −0.359283 | + | 0.919460i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.4804 | − | 3.85325i | −0.389501 | − | 0.143205i | ||||
\(725\) | 1.53396 | + | 3.70331i | 0.0569698 | + | 0.137537i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2805 | + | 12.2805i | 0.455457 | + | 0.455457i | 0.897161 | − | 0.441704i | \(-0.145626\pi\) |
−0.441704 | + | 0.897161i | \(0.645626\pi\) | |||||||
\(728\) | 0.349497 | − | 0.0211933i | 0.0129532 | − | 0.000785478i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.928723 | + | 45.9964i | 0.0343736 | + | 1.70240i | ||||
\(731\) | −29.5853 | + | 12.2546i | −1.09425 | + | 0.453254i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.1888 | + | 31.8405i | −0.487138 | + | 1.17606i | 0.469016 | + | 0.883190i | \(0.344609\pi\) |
−0.956154 | + | 0.292865i | \(0.905391\pi\) | |||||||
\(734\) | −15.4434 | + | 6.76526i | −0.570026 | + | 0.249710i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.9375 | − | 14.3969i | −1.76700 | − | 0.530678i | ||||
\(737\) | 56.2772 | 2.07300 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3244 | − | 36.9964i | 0.563717 | − | 1.36093i | −0.343056 | − | 0.939315i | \(-0.611462\pi\) |
0.906773 | − | 0.421619i | \(-0.138538\pi\) | |||||||
\(740\) | −0.120635 | − | 2.98610i | −0.00443463 | − | 0.109771i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0234778 | + | 1.16278i | 0.000861899 | + | 0.0426868i | ||||
\(743\) | 6.80014 | − | 6.80014i | 0.249473 | − | 0.249473i | −0.571281 | − | 0.820754i | \(-0.693554\pi\) |
0.820754 | + | 0.571281i | \(0.193554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.41455 | − | 5.41455i | −0.198374 | − | 0.198374i | ||||
\(746\) | 18.4992 | − | 19.2616i | 0.677304 | − | 0.705219i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.1014 | + | 38.3543i | −0.515599 | + | 1.40237i | ||||
\(749\) | −1.31049 | − | 0.542822i | −0.0478842 | − | 0.0198343i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 44.2155i | − | 1.61345i | −0.590930 | − | 0.806723i | \(-0.701239\pi\) | ||
0.590930 | − | 0.806723i | \(-0.298761\pi\) | |||||||
\(752\) | −48.1825 | + | 3.89940i | −1.75704 | + | 0.142197i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.676956 | + | 0.264523i | 0.0246533 | + | 0.00963338i | ||||
\(755\) | −0.686860 | − | 0.284507i | −0.0249974 | − | 0.0103543i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0190 | + | 33.8448i | 0.509529 | + | 1.23011i | 0.944155 | + | 0.329500i | \(0.106880\pi\) |
−0.434627 | + | 0.900611i | \(0.643120\pi\) | |||||||
\(758\) | −23.4687 | − | 22.5398i | −0.852422 | − | 0.818681i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.08742 | − | 1.06488i | −0.111992 | − | 0.0386274i | ||||
\(761\) | −27.3391 | + | 27.3391i | −0.991041 | + | 0.991041i | −0.999960 | − | 0.00891938i | \(-0.997161\pi\) |
0.00891938 | + | 0.999960i | \(0.497161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.1007 | + | 9.15443i | −0.800100 | + | 0.331412i | ||||
\(764\) | 21.7524 | − | 23.5839i | 0.786973 | − | 0.853236i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.6287 | + | 42.5246i | 0.673082 | + | 1.53648i | ||||
\(767\) | 0.274983 | 0.00992906 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.0566 | 1.48054 | 0.740269 | − | 0.672311i | \(-0.234698\pi\) | ||||
0.740269 | + | 0.672311i | \(0.234698\pi\) | |||||||
\(770\) | −17.1825 | − | 39.2232i | −0.619213 | − | 1.41351i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.54581 | + | 6.01276i | −0.199598 | + | 0.216404i | ||||
\(773\) | 27.0461 | − | 11.2029i | 0.972781 | − | 0.402939i | 0.161034 | − | 0.986949i | \(-0.448517\pi\) |
0.811747 | + | 0.584010i | \(0.198517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17985 | − | 2.17985i | 0.0783025 | − | 0.0783025i | ||||
\(776\) | −11.9607 | − | 4.12537i | −0.429363 | − | 0.148092i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.701635 | − | 0.673862i | −0.0251548 | − | 0.0241591i | ||||
\(779\) | −0.299246 | − | 0.722444i | −0.0107216 | − | 0.0258842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.5848 | − | 8.11230i | −0.700800 | − | 0.290281i | ||||
\(782\) | −38.0485 | − | 14.8676i | −1.36061 | − | 0.531665i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.8384 | − | 0.877149i | 0.387085 | − | 0.0313268i | ||||
\(785\) | 1.18756i | 0.0423858i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.4486 | − | 4.32794i | −0.372452 | − | 0.154275i | 0.188603 | − | 0.982053i | \(-0.439604\pi\) |
−0.561054 | + | 0.827779i | \(0.689604\pi\) | |||||||
\(788\) | 8.77860 | − | 23.8768i | 0.312725 | − | 0.850576i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.29674 | + | 8.63868i | −0.295185 | + | 0.307351i | ||||
\(791\) | −18.0160 | − | 18.0160i | −0.640574 | − | 0.640574i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0639635 | − | 0.0639635i | 0.00227141 | − | 0.00227141i | ||||
\(794\) | 0.198551 | + | 9.83356i | 0.00704632 | + | 0.348980i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.571028 | + | 14.1347i | 0.0202395 | + | 0.500993i | ||||
\(797\) | 13.3448 | − | 32.2171i | 0.472696 | − | 1.14119i | −0.490271 | − | 0.871570i | \(-0.663102\pi\) |
0.962967 | − | 0.269619i | \(-0.0868976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.4524 | −1.39572 | ||||||||
\(800\) | −0.759251 | + | 2.52808i | −0.0268436 | + | 0.0893812i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −48.7185 | + | 21.3420i | −1.72031 | + | 0.753614i | ||||
\(803\) | 33.3247 | − | 80.4530i | 1.17600 | − | 2.83913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.5483 | − | 16.3815i | 1.39390 | − | 0.577370i | ||||
\(806\) | −0.0112839 | − | 0.558850i | −0.000397457 | − | 0.0196847i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.52545 | + | 0.213781i | −0.124025 | + | 0.00752080i | ||||
\(809\) | −2.75554 | − | 2.75554i | −0.0968795 | − | 0.0968795i | 0.657006 | − | 0.753885i | \(-0.271823\pi\) |
−0.753885 | + | 0.657006i | \(0.771823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4234 | − | 44.4780i | −0.646933 | − | 1.56183i | −0.817148 | − | 0.576427i | \(-0.804446\pi\) |
0.170215 | − | 0.985407i | \(-0.445554\pi\) | |||||||
\(812\) | −33.3660 | − | 12.2674i | −1.17092 | − | 0.430502i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.05883 | + | 5.26886i | −0.0721620 | + | 0.184674i | ||||
\(815\) | 53.4900i | 1.87367i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.84432i | 0.169481i | ||||||||
\(818\) | 12.4283 | + | 4.85641i | 0.434545 | + | 0.169800i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.72067 | + | 3.10730i | −0.234696 | + | 0.108511i | ||||
\(821\) | −6.71325 | − | 16.2072i | −0.234294 | − | 0.565636i | 0.762380 | − | 0.647130i | \(-0.224031\pi\) |
−0.996674 | + | 0.0814939i | \(0.974031\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.56436 | + | 3.56436i | 0.124246 | + | 0.124246i | 0.766496 | − | 0.642250i | \(-0.221999\pi\) |
−0.642250 | + | 0.766496i | \(0.721999\pi\) | |||||||
\(824\) | 23.4435 | − | 11.4190i | 0.816693 | − | 0.397801i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4473 | + | 0.271518i | −0.467893 | + | 0.00944732i | ||||
\(827\) | 47.5146 | − | 19.6812i | 1.65225 | − | 0.684382i | 0.654799 | − | 0.755803i | \(-0.272753\pi\) |
0.997446 | + | 0.0714207i | \(0.0227533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.4074 | − | 25.1257i | 0.361463 | − | 0.872650i | −0.633623 | − | 0.773642i | \(-0.718433\pi\) |
0.995087 | − | 0.0990081i | \(-0.0315670\pi\) | |||||||
\(830\) | −14.1683 | − | 32.3427i | −0.491790 | − | 1.12263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.235247 | + | 0.416810i | 0.00815571 | + | 0.0144503i | ||||
\(833\) | 8.87459 | 0.307486 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.7771 | + | 45.3318i | −0.649807 | + | 1.56877i | ||||
\(836\) | 4.54411 | + | 4.19121i | 0.157161 | + | 0.144956i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.1418 | − | 0.689364i | 1.17941 | − | 0.0238137i | ||||
\(839\) | 15.1006 | − | 15.1006i | 0.521330 | − | 0.521330i | −0.396643 | − | 0.917973i | \(-0.629825\pi\) |
0.917973 | + | 0.396643i | \(0.129825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.6730 | − | 31.6730i | −1.09217 | − | 1.09217i | ||||
\(842\) | −28.6528 | − | 27.5186i | −0.987441 | − | 0.948355i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.6126 | + | 7.68080i | −0.571828 | + | 0.264384i | ||||
\(845\) | −28.0736 | − | 11.6285i | −0.965763 | − | 0.400032i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 58.2937i | 2.00299i | ||||||||
\(848\) | −1.41488 | + | 0.724867i | −0.0485871 | + | 0.0248920i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.784074 | + | 2.00657i | −0.0268935 | + | 0.0688246i | ||||
\(851\) | −5.22441 | − | 2.16402i | −0.179090 | − | 0.0741817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.55795 | + | 8.58965i | 0.121822 | + | 0.294104i | 0.973012 | − | 0.230753i | \(-0.0741188\pi\) |
−0.851191 | + | 0.524857i | \(0.824119\pi\) | |||||||
\(854\) | −3.06482 | + | 3.19113i | −0.104876 | + | 0.109198i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.117360 | − | 1.93538i | −0.00401129 | − | 0.0661498i | ||||
\(857\) | 16.1608 | − | 16.1608i | 0.552042 | − | 0.552042i | −0.374988 | − | 0.927030i | \(-0.622353\pi\) |
0.927030 | + | 0.374988i | \(0.122353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.7234 | − | 8.16969i | 0.672953 | − | 0.278746i | −0.0199246 | − | 0.999801i | \(-0.506343\pi\) |
0.692878 | + | 0.721055i | \(0.256343\pi\) | |||||||
\(860\) | 45.8321 | − | 1.85156i | 1.56286 | − | 0.0631378i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.4457 | − | 19.4703i | 1.51383 | − | 0.663160i | ||||
\(863\) | −7.49235 | −0.255042 | −0.127521 | − | 0.991836i | \(-0.540702\pi\) | ||||
−0.127521 | + | 0.991836i | \(0.540702\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.5430 | 1.20850 | ||||||||
\(866\) | −27.2243 | + | 11.9261i | −0.925120 | + | 0.405266i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.10362 | + | 27.3180i | 0.0374592 | + | 0.927234i | ||||
\(869\) | 20.9459 | − | 8.67608i | 0.710541 | − | 0.294316i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.380385 | − | 0.380385i | 0.0128889 | − | 0.0128889i | ||||
\(872\) | −24.4789 | − | 21.6799i | −0.828960 | − | 0.734173i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.28060 | + | 4.45702i | −0.144793 | + | 0.150761i | ||||
\(875\) | 8.39307 | + | 20.2627i | 0.283738 | + | 0.685003i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.4548 | + | 15.1001i | 1.23099 | + | 0.509893i | 0.900888 | − | 0.434052i | \(-0.142916\pi\) |
0.330103 | + | 0.943945i | \(0.392916\pi\) | |||||||
\(878\) | −6.35623 | + | 16.2666i | −0.214512 | + | 0.548970i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 37.9162 | − | 44.5937i | 1.27816 | − | 1.50325i | ||||
\(881\) | − | 22.3181i | − | 0.751915i | −0.926637 | − | 0.375958i | \(-0.877314\pi\) | ||
0.926637 | − | 0.375958i | \(-0.122686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5754 | − | 6.45156i | −0.524155 | − | 0.217112i | 0.104886 | − | 0.994484i | \(-0.466552\pi\) |
−0.629041 | + | 0.777372i | \(0.716552\pi\) | |||||||
\(884\) | 0.163928 | + | 0.354555i | 0.00551351 | + | 0.0119250i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.4420 | + | 21.5537i | 0.753954 | + | 0.724110i | ||||
\(887\) | 12.3188 | + | 12.3188i | 0.413624 | + | 0.413624i | 0.882999 | − | 0.469375i | \(-0.155521\pi\) |
−0.469375 | + | 0.882999i | \(0.655521\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.8056 | + | 21.8056i | −0.731335 | + | 0.731335i | ||||
\(890\) | −29.5370 | + | 0.596387i | −0.990081 | + | 0.0199909i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.7837 | + | 23.6179i | −0.729374 | + | 0.790787i | ||||
\(893\) | −2.28394 | + | 5.51393i | −0.0764293 | + | 0.184517i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.28953 | −0.277088 | ||||||||
\(896\) | −11.9157 | − | 20.1508i | −0.398076 | − | 0.673190i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.0138 | + | 31.9901i | 0.467648 | + | 1.06752i | ||||
\(899\) | −21.7179 | + | 52.4318i | −0.724334 | + | 1.74870i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.19870 | + | 0.496518i | −0.0399345 | + | 0.0165414i | ||||
\(902\) | 14.0122 | − | 0.282923i | 0.466555 | − | 0.00942030i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.3558 | − | 32.9237i | 0.377687 | − | 1.09503i | ||||
\(905\) | 9.23047 | + | 9.23047i | 0.306831 | + | 0.306831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.49309 | − | 8.43307i | −0.115986 | − | 0.280015i | 0.855216 | − | 0.518271i | \(-0.173424\pi\) |
−0.971202 | + | 0.238256i | \(0.923424\pi\) | |||||||
\(908\) | 9.05011 | + | 19.5742i | 0.300338 | + | 0.649592i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.381254 | − | 0.148977i | −0.0126384 | − | 0.00493853i | ||||
\(911\) | 14.1627i | 0.469232i | 0.972088 | + | 0.234616i | \(0.0753833\pi\) | ||||
−0.972088 | + | 0.234616i | \(0.924617\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.8362i | 2.21196i | ||||||||
\(914\) | −6.85620 | + | 17.5461i | −0.226783 | + | 0.580372i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.45106 | − | 6.66661i | 0.0809854 | − | 0.220271i | ||||
\(917\) | 7.46749 | + | 18.0281i | 0.246598 | + | 0.595341i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.1001 | + | 17.1001i | 0.564082 | + | 0.564082i | 0.930464 | − | 0.366383i | \(-0.119404\pi\) |
−0.366383 | + | 0.930464i | \(0.619404\pi\) | |||||||
\(920\) | 43.8040 | + | 38.7952i | 1.44417 | + | 1.27904i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.282450 | + | 13.9888i | 0.00930200 | + | 0.460696i | ||||
\(923\) | −0.187209 | + | 0.0775444i | −0.00616205 | + | 0.00255240i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.114124 | + | 0.275520i | −0.00375237 | + | 0.00905903i | ||||
\(926\) | 27.1557 | − | 11.8961i | 0.892392 | − | 0.390929i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.89684 | − | 48.3464i | −0.160747 | − | 1.58705i | ||||
\(929\) | −0.261586 | −0.00858236 | −0.00429118 | − | 0.999991i | \(-0.501366\pi\) | ||||
−0.00429118 | + | 0.999991i | \(0.501366\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.513760 | − | 1.24033i | 0.0168378 | − | 0.0406501i | ||||
\(932\) | 49.1832 | − | 1.98695i | 1.61105 | − | 0.0650846i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.494709 | − | 24.5012i | −0.0161874 | − | 0.801704i | ||||
\(935\) | 33.7800 | − | 33.7800i | 1.10472 | − | 1.10472i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.0093 | − | 21.0093i | −0.686345 | − | 0.686345i | 0.275077 | − | 0.961422i | \(-0.411297\pi\) |
−0.961422 | + | 0.275077i | \(0.911297\pi\) | |||||||
\(938\) | −18.2262 | + | 18.9774i | −0.595106 | + | 0.619633i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 53.0402 | + | 19.5009i | 1.72998 | + | 0.636049i | ||||
\(941\) | −45.9724 | − | 19.0424i | −1.49866 | − | 0.620765i | −0.525478 | − | 0.850807i | \(-0.676114\pi\) |
−0.973181 | + | 0.230042i | \(0.926114\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.0102i | 0.456234i | ||||||||
\(944\) | −8.38299 | − | 16.3629i | −0.272843 | − | 0.532566i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −80.8690 | − | 31.5999i | −2.62928 | − | 1.02740i | ||||
\(947\) | −7.49492 | − | 3.10450i | −0.243552 | − | 0.100883i | 0.257569 | − | 0.966260i | \(-0.417079\pi\) |
−0.501121 | + | 0.865377i | \(0.667079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.318547 | − | 0.769040i | −0.0103405 | − | 0.0249641i | ||||
\(950\) | 0.235050 | + | 0.225746i | 0.00762602 | + | 0.00732416i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.36659 | − | 17.1768i | −0.271163 | − | 0.556703i | ||||
\(953\) | −25.1462 | + | 25.1462i | −0.814565 | + | 0.814565i | −0.985314 | − | 0.170750i | \(-0.945381\pi\) |
0.170750 | + | 0.985314i | \(0.445381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.6521 | + | 14.3534i | −1.12132 | + | 0.464465i | ||||
\(956\) | −19.6426 | − | 18.1172i | −0.635288 | − | 0.585951i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.49267 | + | 14.8211i | 0.209769 | + | 0.478849i | ||||
\(959\) | 10.5717 | 0.341377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6462 | 0.407942 | ||||||||
\(962\) | 0.0216971 | + | 0.0495289i | 0.000699541 | + | 0.00159688i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.45482 | + | 5.95354i | 0.207896 | + | 0.191751i | ||||
\(965\) | 8.83463 | − | 3.65942i | 0.284397 | − | 0.117801i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5199 | + | 22.5199i | −0.724191 | + | 0.724191i | −0.969456 | − | 0.245265i | \(-0.921125\pi\) |
0.245265 | + | 0.969456i | \(0.421125\pi\) | |||||||
\(968\) | −71.6369 | + | 34.8935i | −2.30250 | + | 1.12152i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.6677 | + | 10.2455i | 0.342520 | + | 0.328962i | ||||
\(971\) | −0.448715 | − | 1.08329i | −0.0143999 | − | 0.0347645i | 0.916516 | − | 0.399998i | \(-0.130989\pi\) |
−0.930916 | + | 0.365233i | \(0.880989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.9513 | + | 11.5778i | 0.896077 | + | 0.371167i | ||||
\(974\) | −11.9376 | − | 4.66467i | −0.382505 | − | 0.149466i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.75611 | − | 1.85620i | −0.184249 | − | 0.0594154i | ||||
\(977\) | 11.9638i | 0.382756i | 0.981516 | + | 0.191378i | \(0.0612957\pi\) | ||||
−0.981516 | + | 0.191378i | \(0.938704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.6635 | + | 21.3997i | 1.65117 | + | 0.683939i | ||||
\(980\) | −11.9311 | − | 4.38662i | −0.381125 | − | 0.140125i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.79616 | − | 4.99384i | 0.153052 | − | 0.159360i | ||||
\(983\) | 33.2465 | + | 33.2465i | 1.06040 | + | 1.06040i | 0.998055 | + | 0.0623428i | \(0.0198572\pi\) |
0.0623428 | + | 0.998055i | \(0.480143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.0292 | + | 21.0292i | −0.670045 | + | 0.670045i | ||||
\(986\) | −0.800609 | − | 39.6514i | −0.0254966 | − | 1.26276i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0590432 | − | 0.00238528i | 0.00187841 | − | 7.58858e-5i | ||||
\(989\) | 33.2144 | − | 80.1867i | 1.05616 | − | 2.54979i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0761252 | 0.00241820 | 0.00120910 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00120910 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(992\) | −32.9104 | + | 17.7083i | −1.04491 | + | 0.562238i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.07841 | − | 3.97696i | 0.287950 | − | 0.126142i | ||||
\(995\) | 6.32866 | − | 15.2787i | 0.200632 | − | 0.484368i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.5849 | + | 20.9529i | −1.60204 | + | 0.663586i | −0.991702 | − | 0.128556i | \(-0.958966\pi\) |
−0.610336 | + | 0.792142i | \(0.708966\pi\) | |||||||
\(998\) | −0.857716 | − | 42.4797i | −0.0271505 | − | 1.34467i | ||||
\(999\) | 0 | 0 |
(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 | 864.2.v.a.109.13 | ✓ | 128 | |
3.2 | odd | 2 | inner | 864.2.v.a.109.20 | yes | 128 | |
32.5 | even | 8 | inner | 864.2.v.a.325.13 | yes | 128 | |
96.5 | odd | 8 | inner | 864.2.v.a.325.20 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
864.2.v.a.109.13 | ✓ | 128 | 1.1 | even | 1 | trivial | |
864.2.v.a.109.20 | yes | 128 | 3.2 | odd | 2 | inner | |
864.2.v.a.325.13 | yes | 128 | 32.5 | even | 8 | inner | |
864.2.v.a.325.20 | yes | 128 | 96.5 | odd | 8 | inner |