Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.3 | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.z.729.3 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0973732 | + | 0.0707458i | 0.0688532 | + | 0.0500248i | 0.621679 | − | 0.783272i | \(-0.286451\pi\) |
−0.552826 | + | 0.833297i | \(0.686451\pi\) | |||||||
\(3\) | 0.855309 | − | 2.63237i | 0.493813 | − | 1.51980i | −0.324985 | − | 0.945719i | \(-0.605359\pi\) |
0.818798 | − | 0.574081i | \(-0.194641\pi\) | |||||||
\(4\) | −0.613557 | − | 1.88834i | −0.306779 | − | 0.944168i | ||||
\(5\) | 2.27214 | − | 1.65081i | 1.01613 | − | 0.738265i | 0.0506472 | − | 0.998717i | \(-0.483872\pi\) |
0.965487 | + | 0.260452i | \(0.0838716\pi\) | |||||||
\(6\) | 0.269513 | − | 0.195813i | 0.110028 | − | 0.0799403i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | 0.148234 | − | 0.456218i | 0.0524087 | − | 0.161297i | ||||
\(9\) | −3.77078 | − | 2.73963i | −1.25693 | − | 0.913210i | ||||
\(10\) | 0.338034 | 0.106896 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −5.49558 | −1.58644 | ||||||||
\(13\) | 0.873475 | + | 0.634617i | 0.242258 | + | 0.176011i | 0.702289 | − | 0.711892i | \(-0.252162\pi\) |
−0.460030 | + | 0.887903i | \(0.652162\pi\) | |||||||
\(14\) | 0.0371933 | − | 0.114469i | 0.00994031 | − | 0.0305931i | ||||
\(15\) | −2.40216 | − | 7.39308i | −0.620235 | − | 1.90889i | ||||
\(16\) | −3.16592 | + | 2.30017i | −0.791480 | + | 0.575044i | ||||
\(17\) | 5.62937 | − | 4.08998i | 1.36532 | − | 0.991965i | 0.367237 | − | 0.930128i | \(-0.380304\pi\) |
0.998086 | − | 0.0618375i | \(-0.0196961\pi\) | |||||||
\(18\) | −0.173355 | − | 0.533533i | −0.0408603 | − | 0.125755i | ||||
\(19\) | −2.33126 | + | 7.17488i | −0.534828 | + | 1.64603i | 0.209194 | + | 0.977874i | \(0.432916\pi\) |
−0.744021 | + | 0.668156i | \(0.767084\pi\) | |||||||
\(20\) | −4.51137 | − | 3.27771i | −1.00877 | − | 0.732917i | ||||
\(21\) | −2.76784 | −0.603992 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.82552 | 1.00619 | 0.503095 | − | 0.864231i | \(-0.332194\pi\) | ||||
0.503095 | + | 0.864231i | \(0.332194\pi\) | |||||||
\(24\) | −1.07415 | − | 0.780415i | −0.219260 | − | 0.159302i | ||||
\(25\) | 0.892384 | − | 2.74647i | 0.178477 | − | 0.549295i | ||||
\(26\) | 0.0401566 | + | 0.123589i | 0.00787536 | + | 0.0242379i | ||||
\(27\) | −3.71922 | + | 2.70217i | −0.715764 | + | 0.520033i | ||||
\(28\) | −1.60631 | + | 1.16706i | −0.303565 | + | 0.220553i | ||||
\(29\) | −0.379245 | − | 1.16720i | −0.0704241 | − | 0.216743i | 0.909650 | − | 0.415376i | \(-0.136350\pi\) |
−0.980074 | + | 0.198633i | \(0.936350\pi\) | |||||||
\(30\) | 0.289124 | − | 0.889831i | 0.0527865 | − | 0.162460i | ||||
\(31\) | 6.53207 | + | 4.74583i | 1.17319 | + | 0.852376i | 0.991388 | − | 0.130958i | \(-0.0418054\pi\) |
0.181807 | + | 0.983334i | \(0.441805\pi\) | |||||||
\(32\) | −1.43040 | −0.252861 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.837498 | 0.143630 | ||||||||
\(35\) | −2.27214 | − | 1.65081i | −0.384063 | − | 0.279038i | ||||
\(36\) | −2.85975 | + | 8.80141i | −0.476625 | + | 1.46690i | ||||
\(37\) | 0.474419 | + | 1.46011i | 0.0779941 | + | 0.240041i | 0.982450 | − | 0.186526i | \(-0.0597228\pi\) |
−0.904456 | + | 0.426567i | \(0.859723\pi\) | |||||||
\(38\) | −0.734595 | + | 0.533714i | −0.119167 | + | 0.0865799i | ||||
\(39\) | 2.41764 | − | 1.75652i | 0.387132 | − | 0.281268i | ||||
\(40\) | −0.416320 | − | 1.28130i | −0.0658259 | − | 0.202591i | ||||
\(41\) | −2.87381 | + | 8.84469i | −0.448814 | + | 1.38131i | 0.429432 | + | 0.903099i | \(0.358714\pi\) |
−0.878246 | + | 0.478209i | \(0.841286\pi\) | |||||||
\(42\) | −0.269513 | − | 0.195813i | −0.0415868 | − | 0.0302146i | ||||
\(43\) | 5.23402 | 0.798181 | 0.399091 | − | 0.916912i | \(-0.369326\pi\) | ||||
0.399091 | + | 0.916912i | \(0.369326\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.0904 | −1.95140 | ||||||||
\(46\) | 0.469876 | + | 0.341385i | 0.0692795 | + | 0.0503345i | ||||
\(47\) | −0.585237 | + | 1.80117i | −0.0853655 | + | 0.262728i | −0.984623 | − | 0.174691i | \(-0.944107\pi\) |
0.899258 | + | 0.437419i | \(0.144107\pi\) | |||||||
\(48\) | 3.34707 | + | 10.3012i | 0.483109 | + | 1.48686i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 0.281196 | − | 0.204301i | 0.0397671 | − | 0.0288925i | ||||
\(51\) | −5.95149 | − | 18.3168i | −0.833375 | − | 2.56486i | ||||
\(52\) | 0.662442 | − | 2.03879i | 0.0918642 | − | 0.282729i | ||||
\(53\) | 3.09491 | + | 2.24858i | 0.425119 | + | 0.308867i | 0.779694 | − | 0.626161i | \(-0.215375\pi\) |
−0.354575 | + | 0.935027i | \(0.615375\pi\) | |||||||
\(54\) | −0.553319 | −0.0752972 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.479696 | −0.0641021 | ||||||||
\(57\) | 16.8930 | + | 12.2735i | 2.23753 | + | 1.62566i | ||||
\(58\) | 0.0456459 | − | 0.140484i | 0.00599360 | − | 0.0184464i | ||||
\(59\) | −2.05913 | − | 6.33736i | −0.268076 | − | 0.825053i | −0.990969 | − | 0.134093i | \(-0.957188\pi\) |
0.722893 | − | 0.690960i | \(-0.242812\pi\) | |||||||
\(60\) | −12.4868 | + | 9.07216i | −1.61203 | + | 1.17121i | ||||
\(61\) | −7.92798 | + | 5.76001i | −1.01507 | + | 0.737494i | −0.965267 | − | 0.261265i | \(-0.915861\pi\) |
−0.0498066 | + | 0.998759i | \(0.515861\pi\) | |||||||
\(62\) | 0.300302 | + | 0.924233i | 0.0381383 | + | 0.117378i | ||||
\(63\) | −1.44031 | + | 4.43281i | −0.181462 | + | 0.558482i | ||||
\(64\) | 6.19256 | + | 4.49915i | 0.774069 | + | 0.562394i | ||||
\(65\) | 3.03229 | 0.376110 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.06100 | −0.251792 | −0.125896 | − | 0.992043i | \(-0.540181\pi\) | ||||
−0.125896 | + | 0.992043i | \(0.540181\pi\) | |||||||
\(68\) | −11.1772 | − | 8.12070i | −1.35543 | − | 0.984780i | ||||
\(69\) | 4.12731 | − | 12.7026i | 0.496870 | − | 1.52921i | ||||
\(70\) | −0.104458 | − | 0.321489i | −0.0124851 | − | 0.0384253i | ||||
\(71\) | −10.1299 | + | 7.35977i | −1.20219 | + | 0.873444i | −0.994499 | − | 0.104749i | \(-0.966596\pi\) |
−0.207694 | + | 0.978194i | \(0.566596\pi\) | |||||||
\(72\) | −1.80883 | + | 1.31419i | −0.213172 | + | 0.154879i | ||||
\(73\) | −0.793272 | − | 2.44144i | −0.0928454 | − | 0.285749i | 0.893841 | − | 0.448385i | \(-0.148000\pi\) |
−0.986686 | + | 0.162636i | \(0.948000\pi\) | |||||||
\(74\) | −0.0571011 | + | 0.175739i | −0.00663786 | + | 0.0204292i | ||||
\(75\) | −6.46648 | − | 4.69817i | −0.746685 | − | 0.542498i | ||||
\(76\) | 14.9789 | 1.71820 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.359679 | 0.0407257 | ||||||||
\(79\) | −12.4009 | − | 9.00978i | −1.39521 | − | 1.01368i | −0.995271 | − | 0.0971373i | \(-0.969031\pi\) |
−0.399939 | − | 0.916542i | \(-0.630969\pi\) | |||||||
\(80\) | −3.39627 | + | 10.4527i | −0.379715 | + | 1.16864i | ||||
\(81\) | −0.388893 | − | 1.19689i | −0.0432103 | − | 0.132988i | ||||
\(82\) | −0.905557 | + | 0.657925i | −0.100002 | + | 0.0726557i | ||||
\(83\) | 1.65527 | − | 1.20262i | 0.181689 | − | 0.132005i | −0.493223 | − | 0.869903i | \(-0.664181\pi\) |
0.674912 | + | 0.737898i | \(0.264181\pi\) | |||||||
\(84\) | 1.69823 | + | 5.22661i | 0.185292 | + | 0.570270i | ||||
\(85\) | 6.03897 | − | 18.5860i | 0.655018 | − | 2.01594i | ||||
\(86\) | 0.509654 | + | 0.370285i | 0.0549574 | + | 0.0399289i | ||||
\(87\) | −3.39687 | −0.364183 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.76119 | 0.504685 | 0.252342 | − | 0.967638i | \(-0.418799\pi\) | ||||
0.252342 | + | 0.967638i | \(0.418799\pi\) | |||||||
\(90\) | −1.27465 | − | 0.926087i | −0.134360 | − | 0.0976182i | ||||
\(91\) | 0.333638 | − | 1.02683i | 0.0349747 | − | 0.107641i | ||||
\(92\) | −2.96073 | − | 9.11220i | −0.308678 | − | 0.950013i | ||||
\(93\) | 18.0797 | − | 13.1357i | 1.87478 | − | 1.36211i | ||||
\(94\) | −0.184412 | + | 0.133983i | −0.0190206 | + | 0.0138193i | ||||
\(95\) | 6.54740 | + | 20.1508i | 0.671749 | + | 2.06743i | ||||
\(96\) | −1.22343 | + | 3.76533i | −0.124866 | + | 0.384298i | ||||
\(97\) | −7.37429 | − | 5.35773i | −0.748745 | − | 0.543995i | 0.146692 | − | 0.989182i | \(-0.453137\pi\) |
−0.895438 | + | 0.445187i | \(0.853137\pi\) | |||||||
\(98\) | −0.120360 | −0.0121582 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.73379 | −0.573379 | ||||||||
\(101\) | −3.83786 | − | 2.78837i | −0.381881 | − | 0.277453i | 0.380239 | − | 0.924888i | \(-0.375842\pi\) |
−0.762120 | + | 0.647435i | \(0.775842\pi\) | |||||||
\(102\) | 0.716320 | − | 2.20461i | 0.0709263 | − | 0.218289i | ||||
\(103\) | 0.108434 | + | 0.333726i | 0.0106843 | + | 0.0328830i | 0.956257 | − | 0.292529i | \(-0.0944969\pi\) |
−0.945572 | + | 0.325412i | \(0.894497\pi\) | |||||||
\(104\) | 0.419002 | − | 0.304423i | 0.0410866 | − | 0.0298511i | ||||
\(105\) | −6.28893 | + | 4.56918i | −0.613737 | + | 0.445906i | ||||
\(106\) | 0.142284 | + | 0.437904i | 0.0138198 | + | 0.0425330i | ||||
\(107\) | −0.787293 | + | 2.42304i | −0.0761105 | + | 0.234244i | −0.981872 | − | 0.189543i | \(-0.939299\pi\) |
0.905762 | + | 0.423787i | \(0.139299\pi\) | |||||||
\(108\) | 7.38455 | + | 5.36519i | 0.710579 | + | 0.516266i | ||||
\(109\) | 3.81522 | 0.365432 | 0.182716 | − | 0.983166i | \(-0.441511\pi\) | ||||
0.182716 | + | 0.983166i | \(0.441511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.24933 | 0.403329 | ||||||||
\(112\) | 3.16592 | + | 2.30017i | 0.299151 | + | 0.217346i | ||||
\(113\) | 0.715276 | − | 2.20139i | 0.0672875 | − | 0.207090i | −0.911759 | − | 0.410725i | \(-0.865276\pi\) |
0.979047 | + | 0.203635i | \(0.0652757\pi\) | |||||||
\(114\) | 0.776629 | + | 2.39022i | 0.0727379 | + | 0.223864i | ||||
\(115\) | 10.9643 | − | 7.96602i | 1.02242 | − | 0.742835i | ||||
\(116\) | −1.97137 | + | 1.43228i | −0.183037 | + | 0.132984i | ||||
\(117\) | −1.55506 | − | 4.78599i | −0.143766 | − | 0.442465i | ||||
\(118\) | 0.247837 | − | 0.762763i | 0.0228152 | − | 0.0702181i | ||||
\(119\) | −5.62937 | − | 4.08998i | −0.516044 | − | 0.374928i | ||||
\(120\) | −3.72894 | −0.340404 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.17947 | −0.106784 | ||||||||
\(123\) | 20.8245 | + | 15.1299i | 1.87768 | + | 1.36422i | ||||
\(124\) | 4.95392 | − | 15.2466i | 0.444875 | − | 1.36918i | ||||
\(125\) | 1.83313 | + | 5.64179i | 0.163960 | + | 0.504617i | ||||
\(126\) | −0.453850 | + | 0.329741i | −0.0404322 | + | 0.0293757i | ||||
\(127\) | 7.96594 | − | 5.78759i | 0.706863 | − | 0.513566i | −0.175297 | − | 0.984516i | \(-0.556089\pi\) |
0.882160 | + | 0.470950i | \(0.156089\pi\) | |||||||
\(128\) | 1.16873 | + | 3.59697i | 0.103302 | + | 0.317930i | ||||
\(129\) | 4.47671 | − | 13.7779i | 0.394152 | − | 1.21308i | ||||
\(130\) | 0.295264 | + | 0.214522i | 0.0258964 | + | 0.0188148i | ||||
\(131\) | −16.3782 | −1.43097 | −0.715484 | − | 0.698629i | \(-0.753794\pi\) | ||||
−0.715484 | + | 0.698629i | \(0.753794\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.54411 | 0.654158 | ||||||||
\(134\) | −0.200687 | − | 0.145807i | −0.0173367 | − | 0.0125958i | ||||
\(135\) | −3.98983 | + | 12.2794i | −0.343390 | + | 1.05685i | ||||
\(136\) | −1.03146 | − | 3.17449i | −0.0884466 | − | 0.272211i | ||||
\(137\) | 11.4995 | − | 8.35487i | 0.982468 | − | 0.713805i | 0.0242094 | − | 0.999707i | \(-0.492293\pi\) |
0.958259 | + | 0.285902i | \(0.0922931\pi\) | |||||||
\(138\) | 1.30054 | − | 0.944899i | 0.110710 | − | 0.0804352i | ||||
\(139\) | 2.83660 | + | 8.73015i | 0.240597 | + | 0.740481i | 0.996330 | + | 0.0856009i | \(0.0272810\pi\) |
−0.755733 | + | 0.654880i | \(0.772719\pi\) | |||||||
\(140\) | −1.72319 | + | 5.30344i | −0.145636 | + | 0.448222i | ||||
\(141\) | 4.24080 | + | 3.08112i | 0.357140 | + | 0.259477i | ||||
\(142\) | −1.50705 | −0.126469 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 18.2396 | 1.51997 | ||||||||
\(145\) | −2.78852 | − | 2.02598i | −0.231574 | − | 0.168248i | ||||
\(146\) | 0.0954781 | − | 0.293851i | 0.00790182 | − | 0.0243193i | ||||
\(147\) | 0.855309 | + | 2.63237i | 0.0705447 | + | 0.217114i | ||||
\(148\) | 2.46610 | − | 1.79173i | 0.202712 | − | 0.147279i | ||||
\(149\) | 9.40077 | − | 6.83006i | 0.770141 | − | 0.559540i | −0.131863 | − | 0.991268i | \(-0.542096\pi\) |
0.902004 | + | 0.431728i | \(0.142096\pi\) | |||||||
\(150\) | −0.297286 | − | 0.914952i | −0.0242733 | − | 0.0747055i | ||||
\(151\) | −5.53604 | + | 17.0382i | −0.450517 | + | 1.38655i | 0.425802 | + | 0.904816i | \(0.359992\pi\) |
−0.876319 | + | 0.481732i | \(0.840008\pi\) | |||||||
\(152\) | 2.92774 | + | 2.12713i | 0.237471 | + | 0.172533i | ||||
\(153\) | −32.4321 | −2.62198 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.6763 | 1.82140 | ||||||||
\(156\) | −4.80025 | − | 3.48759i | −0.384328 | − | 0.279231i | ||||
\(157\) | 2.29539 | − | 7.06450i | 0.183192 | − | 0.563808i | −0.816720 | − | 0.577034i | \(-0.804210\pi\) |
0.999913 | + | 0.0132257i | \(0.00421001\pi\) | |||||||
\(158\) | −0.570111 | − | 1.75462i | −0.0453556 | − | 0.139590i | ||||
\(159\) | 8.56622 | − | 6.22372i | 0.679345 | − | 0.493573i | ||||
\(160\) | −3.25006 | + | 2.36131i | −0.256940 | + | 0.186678i | ||||
\(161\) | −1.49117 | − | 4.58934i | −0.117520 | − | 0.361691i | ||||
\(162\) | 0.0468071 | − | 0.144057i | 0.00367751 | − | 0.0113182i | ||||
\(163\) | −6.35318 | − | 4.61585i | −0.497619 | − | 0.361542i | 0.310488 | − | 0.950577i | \(-0.399508\pi\) |
−0.808107 | + | 0.589036i | \(0.799508\pi\) | |||||||
\(164\) | 18.4650 | 1.44187 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.246259 | 0.0191134 | ||||||||
\(167\) | −4.37078 | − | 3.17556i | −0.338221 | − | 0.245732i | 0.405690 | − | 0.914011i | \(-0.367031\pi\) |
−0.743911 | + | 0.668279i | \(0.767031\pi\) | |||||||
\(168\) | −0.410289 | + | 1.26274i | −0.0316544 | + | 0.0974224i | ||||
\(169\) | −3.65700 | − | 11.2551i | −0.281308 | − | 0.865776i | ||||
\(170\) | 1.90292 | − | 1.38255i | 0.145947 | − | 0.106037i | ||||
\(171\) | 28.4472 | − | 20.6681i | 2.17541 | − | 1.58053i | ||||
\(172\) | −3.21137 | − | 9.88359i | −0.244865 | − | 0.753617i | ||||
\(173\) | 6.09416 | − | 18.7559i | 0.463331 | − | 1.42599i | −0.397739 | − | 0.917499i | \(-0.630205\pi\) |
0.861070 | − | 0.508487i | \(-0.169795\pi\) | |||||||
\(174\) | −0.330764 | − | 0.240314i | −0.0250751 | − | 0.0182182i | ||||
\(175\) | −2.88781 | −0.218298 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.4435 | −1.38630 | ||||||||
\(178\) | 0.463612 | + | 0.336834i | 0.0347492 | + | 0.0252468i | ||||
\(179\) | −7.20911 | + | 22.1873i | −0.538834 | + | 1.65836i | 0.196382 | + | 0.980527i | \(0.437081\pi\) |
−0.735216 | + | 0.677833i | \(0.762919\pi\) | |||||||
\(180\) | 8.03169 | + | 24.7190i | 0.598646 | + | 1.84244i | ||||
\(181\) | −2.49582 | + | 1.81332i | −0.185513 | + | 0.134783i | −0.676666 | − | 0.736291i | \(-0.736576\pi\) |
0.491153 | + | 0.871073i | \(0.336576\pi\) | |||||||
\(182\) | 0.105131 | − | 0.0763824i | 0.00779285 | − | 0.00566184i | ||||
\(183\) | 8.38162 | + | 25.7960i | 0.619588 | + | 1.90689i | ||||
\(184\) | 0.715307 | − | 2.20149i | 0.0527331 | − | 0.162296i | ||||
\(185\) | 3.48832 | + | 2.53441i | 0.256466 | + | 0.186334i | ||||
\(186\) | 2.68978 | 0.197224 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.76030 | 0.274248 | ||||||||
\(189\) | 3.71922 | + | 2.70217i | 0.270533 | + | 0.196554i | ||||
\(190\) | −0.788045 | + | 2.42535i | −0.0571708 | + | 0.175954i | ||||
\(191\) | 3.88480 | + | 11.9562i | 0.281094 | + | 0.865119i | 0.987542 | + | 0.157354i | \(0.0502964\pi\) |
−0.706448 | + | 0.707765i | \(0.749704\pi\) | |||||||
\(192\) | 17.1400 | − | 12.4529i | 1.23697 | − | 0.898713i | ||||
\(193\) | −16.7212 | + | 12.1487i | −1.20362 | + | 0.874479i | −0.994636 | − | 0.103440i | \(-0.967015\pi\) |
−0.208982 | + | 0.977920i | \(0.567015\pi\) | |||||||
\(194\) | −0.339021 | − | 1.04340i | −0.0243403 | − | 0.0749117i | ||||
\(195\) | 2.59355 | − | 7.98212i | 0.185728 | − | 0.571612i | ||||
\(196\) | 1.60631 | + | 1.16706i | 0.114737 | + | 0.0833611i | ||||
\(197\) | −6.27954 | −0.447399 | −0.223699 | − | 0.974658i | \(-0.571813\pi\) | ||||
−0.223699 | + | 0.974658i | \(0.571813\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.86896 | −0.486927 | −0.243464 | − | 0.969910i | \(-0.578284\pi\) | ||||
−0.243464 | + | 0.969910i | \(0.578284\pi\) | |||||||
\(200\) | −1.12071 | − | 0.814243i | −0.0792461 | − | 0.0575757i | ||||
\(201\) | −1.76280 | + | 5.42533i | −0.124338 | + | 0.382673i | ||||
\(202\) | −0.176439 | − | 0.543024i | −0.0124142 | − | 0.0382070i | ||||
\(203\) | −0.992877 | + | 0.721367i | −0.0696863 | + | 0.0506301i | ||||
\(204\) | −30.9367 | + | 22.4768i | −2.16600 | + | 1.57369i | ||||
\(205\) | 8.07118 | + | 24.8405i | 0.563716 | + | 1.73494i | ||||
\(206\) | −0.0130511 | + | 0.0401673i | −0.000909316 | + | 0.00279859i | ||||
\(207\) | −18.1960 | − | 13.2201i | −1.26471 | − | 0.918863i | ||||
\(208\) | −4.22508 | −0.292957 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.935623 | −0.0645641 | ||||||||
\(211\) | 8.29939 | + | 6.02986i | 0.571354 | + | 0.415113i | 0.835597 | − | 0.549343i | \(-0.185122\pi\) |
−0.264243 | + | 0.964456i | \(0.585122\pi\) | |||||||
\(212\) | 2.34718 | − | 7.22387i | 0.161205 | − | 0.496137i | ||||
\(213\) | 10.7095 | + | 32.9604i | 0.733802 | + | 2.25841i | ||||
\(214\) | −0.248081 | + | 0.180241i | −0.0169585 | + | 0.0123211i | ||||
\(215\) | 11.8925 | − | 8.64038i | 0.811059 | − | 0.589269i | ||||
\(216\) | 0.681463 | + | 2.09733i | 0.0463677 | + | 0.142705i | ||||
\(217\) | 2.49503 | − | 7.67891i | 0.169374 | − | 0.521279i | ||||
\(218\) | 0.371500 | + | 0.269910i | 0.0251611 | + | 0.0182806i | ||||
\(219\) | −7.10527 | −0.480130 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.51268 | 0.505358 | ||||||||
\(222\) | 0.413771 | + | 0.300622i | 0.0277705 | + | 0.0201765i | ||||
\(223\) | −4.17855 | + | 12.8603i | −0.279817 | + | 0.861187i | 0.708088 | + | 0.706124i | \(0.249558\pi\) |
−0.987905 | + | 0.155063i | \(0.950442\pi\) | |||||||
\(224\) | 0.442016 | + | 1.36039i | 0.0295335 | + | 0.0908947i | ||||
\(225\) | −10.8893 | + | 7.91154i | −0.725953 | + | 0.527436i | ||||
\(226\) | 0.225388 | − | 0.163754i | 0.0149926 | − | 0.0108927i | ||||
\(227\) | −4.19535 | − | 12.9120i | −0.278455 | − | 0.856997i | −0.988284 | − | 0.152623i | \(-0.951228\pi\) |
0.709829 | − | 0.704374i | \(-0.248772\pi\) | |||||||
\(228\) | 12.8116 | − | 39.4301i | 0.848471 | − | 2.61133i | ||||
\(229\) | 1.17547 | + | 0.854026i | 0.0776770 | + | 0.0564356i | 0.625946 | − | 0.779866i | \(-0.284713\pi\) |
−0.548269 | + | 0.836302i | \(0.684713\pi\) | |||||||
\(230\) | 1.63119 | 0.107557 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.588713 | −0.0386509 | ||||||||
\(233\) | 6.63707 | + | 4.82211i | 0.434809 | + | 0.315907i | 0.783569 | − | 0.621305i | \(-0.213397\pi\) |
−0.348760 | + | 0.937212i | \(0.613397\pi\) | |||||||
\(234\) | 0.187167 | − | 0.576042i | 0.0122355 | − | 0.0376570i | ||||
\(235\) | 1.64365 | + | 5.05864i | 0.107220 | + | 0.329989i | ||||
\(236\) | −10.7037 | + | 7.77666i | −0.696749 | + | 0.506218i | ||||
\(237\) | −34.3237 | + | 24.9376i | −2.22956 | + | 1.61987i | ||||
\(238\) | −0.258801 | − | 0.796508i | −0.0167756 | − | 0.0516300i | ||||
\(239\) | −3.20869 | + | 9.87533i | −0.207553 | + | 0.638782i | 0.792046 | + | 0.610461i | \(0.209016\pi\) |
−0.999599 | + | 0.0283205i | \(0.990984\pi\) | |||||||
\(240\) | 24.6104 | + | 17.8805i | 1.58860 | + | 1.15418i | ||||
\(241\) | 8.20445 | 0.528495 | 0.264248 | − | 0.964455i | \(-0.414876\pi\) | ||||
0.264248 | + | 0.964455i | \(0.414876\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17.2749 | −1.10818 | ||||||||
\(244\) | 15.7411 | + | 11.4366i | 1.00772 | + | 0.732152i | ||||
\(245\) | −0.867882 | + | 2.67107i | −0.0554470 | + | 0.170648i | ||||
\(246\) | 0.957373 | + | 2.94649i | 0.0610399 | + | 0.187861i | ||||
\(247\) | −6.58959 | + | 4.78762i | −0.419286 | + | 0.304629i | ||||
\(248\) | 3.13341 | − | 2.27655i | 0.198972 | − | 0.144561i | ||||
\(249\) | −1.74998 | − | 5.38589i | −0.110901 | − | 0.341317i | ||||
\(250\) | −0.220635 | + | 0.679045i | −0.0139542 | + | 0.0429466i | ||||
\(251\) | 13.3044 | + | 9.66623i | 0.839768 | + | 0.610127i | 0.922306 | − | 0.386461i | \(-0.126302\pi\) |
−0.0825377 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(252\) | 9.25435 | 0.582969 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.18512 | 0.0743608 | ||||||||
\(255\) | −43.7602 | − | 31.7936i | −2.74037 | − | 1.99099i | ||||
\(256\) | 4.59002 | − | 14.1266i | 0.286876 | − | 0.882915i | ||||
\(257\) | −3.72179 | − | 11.4545i | −0.232159 | − | 0.714511i | −0.997486 | − | 0.0708695i | \(-0.977423\pi\) |
0.765327 | − | 0.643642i | \(-0.222577\pi\) | |||||||
\(258\) | 1.41064 | − | 1.02489i | 0.0878226 | − | 0.0638068i | ||||
\(259\) | 1.24205 | − | 0.902399i | 0.0771770 | − | 0.0560724i | ||||
\(260\) | −1.86049 | − | 5.72599i | −0.115382 | − | 0.355111i | ||||
\(261\) | −1.76764 | + | 5.44023i | −0.109414 | + | 0.336742i | ||||
\(262\) | −1.59479 | − | 1.15869i | −0.0985268 | − | 0.0715839i | ||||
\(263\) | −1.87602 | −0.115681 | −0.0578403 | − | 0.998326i | \(-0.518421\pi\) | ||||
−0.0578403 | + | 0.998326i | \(0.518421\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7441 | 0.660003 | ||||||||
\(266\) | 0.734595 | + | 0.533714i | 0.0450409 | + | 0.0327241i | ||||
\(267\) | 4.07229 | − | 12.5332i | 0.249220 | − | 0.767021i | ||||
\(268\) | 1.26454 | + | 3.89187i | 0.0772443 | + | 0.237734i | ||||
\(269\) | 11.3497 | − | 8.24603i | 0.692003 | − | 0.502769i | −0.185315 | − | 0.982679i | \(-0.559331\pi\) |
0.877318 | + | 0.479910i | \(0.159331\pi\) | |||||||
\(270\) | −1.25722 | + | 0.913424i | −0.0765120 | + | 0.0555892i | ||||
\(271\) | −0.418185 | − | 1.28704i | −0.0254029 | − | 0.0781822i | 0.937551 | − | 0.347847i | \(-0.113087\pi\) |
−0.962954 | + | 0.269665i | \(0.913087\pi\) | |||||||
\(272\) | −8.41447 | + | 25.8971i | −0.510202 | + | 1.57024i | ||||
\(273\) | −2.41764 | − | 1.75652i | −0.146322 | − | 0.106309i | ||||
\(274\) | 1.71081 | 0.103354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −26.5190 | −1.59626 | ||||||||
\(277\) | −10.8275 | − | 7.86663i | −0.650561 | − | 0.472660i | 0.212901 | − | 0.977074i | \(-0.431709\pi\) |
−0.863462 | + | 0.504413i | \(0.831709\pi\) | |||||||
\(278\) | −0.341412 | + | 1.05076i | −0.0204766 | + | 0.0630204i | ||||
\(279\) | −11.6292 | − | 35.7909i | −0.696220 | − | 2.14275i | ||||
\(280\) | −1.08994 | + | 0.791887i | −0.0651363 | + | 0.0473243i | ||||
\(281\) | 1.87600 | − | 1.36300i | 0.111913 | − | 0.0813096i | −0.530421 | − | 0.847734i | \(-0.677966\pi\) |
0.642334 | + | 0.766425i | \(0.277966\pi\) | |||||||
\(282\) | 0.194964 | + | 0.600037i | 0.0116099 | + | 0.0357317i | ||||
\(283\) | 6.88116 | − | 21.1780i | 0.409042 | − | 1.25890i | −0.508430 | − | 0.861103i | \(-0.669774\pi\) |
0.917472 | − | 0.397800i | \(-0.130226\pi\) | |||||||
\(284\) | 20.1130 | + | 14.6129i | 1.19349 | + | 0.867118i | ||||
\(285\) | 58.6445 | 3.47380 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.29986 | 0.548953 | ||||||||
\(288\) | 5.39370 | + | 3.91875i | 0.317827 | + | 0.230915i | ||||
\(289\) | 9.70861 | − | 29.8800i | 0.571095 | − | 1.75765i | ||||
\(290\) | −0.128198 | − | 0.394552i | −0.00752803 | − | 0.0231689i | ||||
\(291\) | −20.4108 | + | 14.8293i | −1.19650 | + | 0.869312i | ||||
\(292\) | −4.12354 | + | 2.99593i | −0.241312 | + | 0.175323i | ||||
\(293\) | 0.753942 | + | 2.32039i | 0.0440457 | + | 0.135559i | 0.970661 | − | 0.240452i | \(-0.0772956\pi\) |
−0.926615 | + | 0.376011i | \(0.877296\pi\) | |||||||
\(294\) | −0.102945 | + | 0.316832i | −0.00600387 | + | 0.0184780i | ||||
\(295\) | −15.1404 | − | 11.0002i | −0.881509 | − | 0.640454i | ||||
\(296\) | 0.736455 | 0.0428056 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.39858 | 0.0810176 | ||||||||
\(299\) | 4.21497 | + | 3.06235i | 0.243758 | + | 0.177101i | ||||
\(300\) | −4.90417 | + | 15.0935i | −0.283142 | + | 0.871422i | ||||
\(301\) | −1.61740 | − | 4.97785i | −0.0932255 | − | 0.286919i | ||||
\(302\) | −1.74444 | + | 1.26741i | −0.100381 | + | 0.0729313i | ||||
\(303\) | −10.6226 | + | 7.71775i | −0.610251 | + | 0.443373i | ||||
\(304\) | −9.12290 | − | 28.0774i | −0.523234 | − | 1.61035i | ||||
\(305\) | −8.50483 | + | 26.1752i | −0.486985 | + | 1.49879i | ||||
\(306\) | −3.15802 | − | 2.29444i | −0.180532 | − | 0.131164i | ||||
\(307\) | 8.89055 | 0.507410 | 0.253705 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253705 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.971237 | 0.0552517 | ||||||||
\(310\) | 2.20806 | + | 1.60425i | 0.125409 | + | 0.0911153i | ||||
\(311\) | −3.65713 | + | 11.2555i | −0.207377 | + | 0.638240i | 0.792231 | + | 0.610222i | \(0.208920\pi\) |
−0.999607 | + | 0.0280183i | \(0.991080\pi\) | |||||||
\(312\) | −0.442978 | − | 1.36335i | −0.0250787 | − | 0.0771843i | ||||
\(313\) | 23.8988 | − | 17.3635i | 1.35084 | − | 0.981443i | 0.351872 | − | 0.936048i | \(-0.385545\pi\) |
0.998969 | − | 0.0453948i | \(-0.0144546\pi\) | |||||||
\(314\) | 0.723293 | − | 0.525503i | 0.0408178 | − | 0.0296559i | ||||
\(315\) | 4.04514 | + | 12.4497i | 0.227918 | + | 0.701459i | ||||
\(316\) | −9.40482 | + | 28.9451i | −0.529063 | + | 1.62829i | ||||
\(317\) | 20.3504 | + | 14.7854i | 1.14299 | + | 0.830433i | 0.987533 | − | 0.157409i | \(-0.0503141\pi\) |
0.155460 | + | 0.987842i | \(0.450314\pi\) | |||||||
\(318\) | 1.27442 | 0.0714660 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 21.4976 | 1.20175 | ||||||||
\(321\) | 5.70496 | + | 4.14490i | 0.318420 | + | 0.231346i | ||||
\(322\) | 0.179477 | − | 0.552373i | 0.0100018 | − | 0.0307825i | ||||
\(323\) | 16.2216 | + | 49.9248i | 0.902592 | + | 2.77789i | ||||
\(324\) | −2.02152 | + | 1.46872i | −0.112307 | + | 0.0815956i | ||||
\(325\) | 2.52243 | − | 1.83265i | 0.139919 | − | 0.101657i | ||||
\(326\) | −0.292077 | − | 0.898921i | −0.0161767 | − | 0.0497866i | ||||
\(327\) | 3.26319 | − | 10.0431i | 0.180455 | − | 0.555383i | ||||
\(328\) | 3.60911 | + | 2.62217i | 0.199280 | + | 0.144785i | ||||
\(329\) | 1.89387 | 0.104412 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.46333 | −0.520152 | −0.260076 | − | 0.965588i | \(-0.583748\pi\) | ||||
−0.260076 | + | 0.965588i | \(0.583748\pi\) | |||||||
\(332\) | −3.28656 | − | 2.38782i | −0.180373 | − | 0.131049i | ||||
\(333\) | 2.21124 | − | 6.80549i | 0.121175 | − | 0.372939i | ||||
\(334\) | −0.200940 | − | 0.618429i | −0.0109949 | − | 0.0338389i | ||||
\(335\) | −4.68290 | + | 3.40233i | −0.255854 | + | 0.185889i | ||||
\(336\) | 8.76276 | − | 6.36651i | 0.478047 | − | 0.347322i | ||||
\(337\) | 5.32277 | + | 16.3818i | 0.289950 | + | 0.892373i | 0.984871 | + | 0.173288i | \(0.0554391\pi\) |
−0.694922 | + | 0.719086i | \(0.744561\pi\) | |||||||
\(338\) | 0.440156 | − | 1.35466i | 0.0239413 | − | 0.0736839i | ||||
\(339\) | −5.18310 | − | 3.76574i | −0.281508 | − | 0.204527i | ||||
\(340\) | −38.8019 | −2.10433 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.23217 | 0.228850 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 0.775861 | − | 2.38786i | 0.0418316 | − | 0.128745i | ||||
\(345\) | −11.5917 | − | 35.6755i | −0.624074 | − | 1.92070i | ||||
\(346\) | 1.92031 | − | 1.39519i | 0.103236 | − | 0.0750057i | ||||
\(347\) | −7.06664 | + | 5.13421i | −0.379357 | + | 0.275619i | −0.761080 | − | 0.648658i | \(-0.775331\pi\) |
0.381723 | + | 0.924277i | \(0.375331\pi\) | |||||||
\(348\) | 2.08417 | + | 6.41443i | 0.111723 | + | 0.343849i | ||||
\(349\) | 9.26589 | − | 28.5175i | 0.495992 | − | 1.52651i | −0.319413 | − | 0.947616i | \(-0.603486\pi\) |
0.815405 | − | 0.578891i | \(-0.196514\pi\) | |||||||
\(350\) | −0.281196 | − | 0.204301i | −0.0150305 | − | 0.0109203i | ||||
\(351\) | −4.96348 | −0.264931 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.31999 | 0.389604 | 0.194802 | − | 0.980843i | \(-0.437594\pi\) | ||||
0.194802 | + | 0.980843i | \(0.437594\pi\) | |||||||
\(354\) | −1.79590 | − | 1.30480i | −0.0954510 | − | 0.0693492i | ||||
\(355\) | −10.8669 | + | 33.4449i | −0.576756 | + | 1.77507i | ||||
\(356\) | −2.92126 | − | 8.99072i | −0.154827 | − | 0.476507i | ||||
\(357\) | −15.5812 | + | 11.3204i | −0.824644 | + | 0.599139i | ||||
\(358\) | −2.27163 | + | 1.65044i | −0.120060 | + | 0.0872284i | ||||
\(359\) | −1.53580 | − | 4.72671i | −0.0810565 | − | 0.249466i | 0.902313 | − | 0.431081i | \(-0.141868\pi\) |
−0.983370 | + | 0.181615i | \(0.941868\pi\) | |||||||
\(360\) | −1.94044 | + | 5.97206i | −0.102270 | + | 0.314755i | ||||
\(361\) | −30.6728 | − | 22.2851i | −1.61436 | − | 1.17290i | ||||
\(362\) | −0.371311 | −0.0195156 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.14371 | −0.112361 | ||||||||
\(365\) | −5.83278 | − | 4.23776i | −0.305302 | − | 0.221815i | ||||
\(366\) | −1.00881 | + | 3.10480i | −0.0527314 | + | 0.162291i | ||||
\(367\) | −4.38935 | − | 13.5090i | −0.229122 | − | 0.705165i | −0.997847 | − | 0.0655858i | \(-0.979108\pi\) |
0.768725 | − | 0.639580i | \(-0.220892\pi\) | |||||||
\(368\) | −15.2772 | + | 11.0995i | −0.796379 | + | 0.578603i | ||||
\(369\) | 35.0677 | − | 25.4782i | 1.82555 | − | 1.32634i | ||||
\(370\) | 0.160370 | + | 0.493567i | 0.00833723 | + | 0.0256593i | ||||
\(371\) | 1.18215 | − | 3.63829i | 0.0613742 | − | 0.188890i | ||||
\(372\) | −35.8975 | − | 26.0811i | −1.86120 | − | 1.35224i | ||||
\(373\) | −8.97781 | −0.464853 | −0.232427 | − | 0.972614i | \(-0.574667\pi\) | ||||
−0.232427 | + | 0.972614i | \(0.574667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.4192 | 0.847883 | ||||||||
\(376\) | 0.734975 | + | 0.533991i | 0.0379035 | + | 0.0275385i | ||||
\(377\) | 0.409461 | − | 1.26019i | 0.0210883 | − | 0.0649032i | ||||
\(378\) | 0.170985 | + | 0.526238i | 0.00879452 | + | 0.0270667i | ||||
\(379\) | −8.72895 | + | 6.34195i | −0.448376 | + | 0.325764i | −0.788954 | − | 0.614452i | \(-0.789377\pi\) |
0.340578 | + | 0.940216i | \(0.389377\pi\) | |||||||
\(380\) | 34.0343 | − | 24.7274i | 1.74592 | − | 1.26849i | ||||
\(381\) | −8.42175 | − | 25.9195i | −0.431459 | − | 1.32790i | ||||
\(382\) | −0.467574 | + | 1.43905i | −0.0239232 | + | 0.0736280i | ||||
\(383\) | 19.0200 | + | 13.8188i | 0.971875 | + | 0.706109i | 0.955878 | − | 0.293763i | \(-0.0949077\pi\) |
0.0159972 | + | 0.999872i | \(0.494908\pi\) | |||||||
\(384\) | 10.4682 | 0.534202 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.48766 | −0.126619 | ||||||||
\(387\) | −19.7363 | − | 14.3393i | −1.00325 | − | 0.728907i | ||||
\(388\) | −5.59265 | + | 17.2124i | −0.283924 | + | 0.873827i | ||||
\(389\) | −3.66944 | − | 11.2934i | −0.186048 | − | 0.572596i | 0.813917 | − | 0.580981i | \(-0.197331\pi\) |
−0.999965 | + | 0.00838486i | \(0.997331\pi\) | |||||||
\(390\) | 0.817243 | − | 0.593762i | 0.0413827 | − | 0.0300663i | ||||
\(391\) | 27.1646 | − | 19.7363i | 1.37377 | − | 0.998106i | ||||
\(392\) | 0.148234 | + | 0.456218i | 0.00748696 | + | 0.0230425i | ||||
\(393\) | −14.0084 | + | 43.1134i | −0.706631 | + | 2.17479i | ||||
\(394\) | −0.611459 | − | 0.444251i | −0.0308048 | − | 0.0223810i | ||||
\(395\) | −43.0501 | −2.16608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7264 | −1.19079 | −0.595397 | − | 0.803431i | \(-0.703005\pi\) | ||||
−0.595397 | + | 0.803431i | \(0.703005\pi\) | |||||||
\(398\) | −0.668852 | − | 0.485950i | −0.0335265 | − | 0.0243585i | ||||
\(399\) | 6.45255 | − | 19.8589i | 0.323032 | − | 0.994189i | ||||
\(400\) | 3.49216 | + | 10.7478i | 0.174608 | + | 0.537388i | ||||
\(401\) | 3.07524 | − | 2.23430i | 0.153570 | − | 0.111575i | −0.508347 | − | 0.861153i | \(-0.669743\pi\) |
0.661917 | + | 0.749577i | \(0.269743\pi\) | |||||||
\(402\) | −0.555468 | + | 0.403571i | −0.0277042 | + | 0.0201283i | ||||
\(403\) | 2.69382 | + | 8.29072i | 0.134189 | + | 0.412990i | ||||
\(404\) | −2.91062 | + | 8.95798i | −0.144809 | + | 0.445676i | ||||
\(405\) | −2.85946 | − | 2.07752i | −0.142088 | − | 0.103233i | ||||
\(406\) | −0.147713 | −0.00733089 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −9.23866 | −0.457382 | ||||||||
\(409\) | −4.84028 | − | 3.51667i | −0.239336 | − | 0.173888i | 0.461651 | − | 0.887062i | \(-0.347257\pi\) |
−0.700988 | + | 0.713174i | \(0.747257\pi\) | |||||||
\(410\) | −0.971446 | + | 2.98980i | −0.0479763 | + | 0.147656i | ||||
\(411\) | −12.1575 | − | 37.4170i | −0.599686 | − | 1.84564i | ||||
\(412\) | 0.563657 | − | 0.409521i | 0.0277694 | − | 0.0201756i | ||||
\(413\) | −5.39088 | + | 3.91670i | −0.265268 | + | 0.192728i | ||||
\(414\) | −0.836530 | − | 2.57457i | −0.0411132 | − | 0.126533i | ||||
\(415\) | 1.77571 | − | 5.46506i | 0.0871660 | − | 0.268269i | ||||
\(416\) | −1.24941 | − | 0.907752i | −0.0612576 | − | 0.0445062i | ||||
\(417\) | 25.4072 | 1.24419 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.16889 | −0.203664 | −0.101832 | − | 0.994802i | \(-0.532470\pi\) | ||||
−0.101832 | + | 0.994802i | \(0.532470\pi\) | |||||||
\(420\) | 12.4868 | + | 9.07216i | 0.609291 | + | 0.442676i | ||||
\(421\) | 7.24814 | − | 22.3075i | 0.353253 | − | 1.08720i | −0.603763 | − | 0.797164i | \(-0.706333\pi\) |
0.957016 | − | 0.290036i | \(-0.0936674\pi\) | |||||||
\(422\) | 0.381551 | + | 1.17429i | 0.0185736 | + | 0.0571637i | ||||
\(423\) | 7.14134 | − | 5.18849i | 0.347224 | − | 0.252273i | ||||
\(424\) | 1.48462 | − | 1.07864i | 0.0720993 | − | 0.0523832i | ||||
\(425\) | −6.20946 | − | 19.1108i | −0.301203 | − | 0.927008i | ||||
\(426\) | −1.28899 | + | 3.96711i | −0.0624519 | + | 0.192207i | ||||
\(427\) | 7.92798 | + | 5.76001i | 0.383662 | + | 0.278747i | ||||
\(428\) | 5.05856 | 0.244515 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.76928 | 0.0853221 | ||||||||
\(431\) | 30.1545 | + | 21.9085i | 1.45249 | + | 1.05530i | 0.985241 | + | 0.171171i | \(0.0547552\pi\) |
0.467250 | + | 0.884125i | \(0.345245\pi\) | |||||||
\(432\) | 5.55928 | − | 17.1097i | 0.267471 | − | 0.823191i | ||||
\(433\) | −7.04136 | − | 21.6711i | −0.338386 | − | 1.04145i | −0.965030 | − | 0.262139i | \(-0.915572\pi\) |
0.626644 | − | 0.779306i | \(-0.284428\pi\) | |||||||
\(434\) | 0.786200 | − | 0.571207i | 0.0377388 | − | 0.0274188i | ||||
\(435\) | −7.71818 | + | 5.60758i | −0.370058 | + | 0.268863i | ||||
\(436\) | −2.34085 | − | 7.20441i | −0.112107 | − | 0.345029i | ||||
\(437\) | −11.2495 | + | 34.6225i | −0.538138 | + | 1.65622i | ||||
\(438\) | −0.691863 | − | 0.502668i | −0.0330585 | − | 0.0240184i | ||||
\(439\) | 1.42974 | 0.0682379 | 0.0341189 | − | 0.999418i | \(-0.489137\pi\) | ||||
0.0341189 | + | 0.999418i | \(0.489137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.66094 | 0.221949 | ||||||||
\(442\) | 0.731534 | + | 0.531490i | 0.0347955 | + | 0.0252804i | ||||
\(443\) | −8.16736 | + | 25.1365i | −0.388043 | + | 1.19427i | 0.546206 | + | 0.837651i | \(0.316072\pi\) |
−0.934249 | + | 0.356622i | \(0.883928\pi\) | |||||||
\(444\) | −2.60721 | − | 8.02417i | −0.123733 | − | 0.380810i | ||||
\(445\) | 10.8181 | − | 7.85982i | 0.512828 | − | 0.372591i | ||||
\(446\) | −1.31669 | + | 0.956630i | −0.0623470 | + | 0.0452978i | ||||
\(447\) | −9.93869 | − | 30.5881i | −0.470084 | − | 1.44677i | ||||
\(448\) | 2.36535 | − | 7.27979i | 0.111752 | − | 0.343938i | ||||
\(449\) | −11.3966 | − | 8.28012i | −0.537839 | − | 0.390763i | 0.285443 | − | 0.958396i | \(-0.407859\pi\) |
−0.823282 | + | 0.567633i | \(0.807859\pi\) | |||||||
\(450\) | −1.62003 | −0.0763691 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.59583 | −0.216170 | ||||||||
\(453\) | 40.1158 | + | 29.1458i | 1.88481 | + | 1.36939i | ||||
\(454\) | 0.504952 | − | 1.55408i | 0.0236986 | − | 0.0729367i | ||||
\(455\) | −0.937030 | − | 2.88388i | −0.0439286 | − | 0.135198i | ||||
\(456\) | 8.10350 | − | 5.88754i | 0.379481 | − | 0.275709i | ||||
\(457\) | 23.8521 | − | 17.3296i | 1.11576 | − | 0.810645i | 0.132196 | − | 0.991224i | \(-0.457797\pi\) |
0.983560 | + | 0.180579i | \(0.0577972\pi\) | |||||||
\(458\) | 0.0540402 | + | 0.166319i | 0.00252513 | + | 0.00777156i | ||||
\(459\) | −9.88504 | + | 30.4230i | −0.461394 | + | 1.42002i | ||||
\(460\) | −21.7697 | − | 15.8166i | −1.01502 | − | 0.737454i | ||||
\(461\) | −31.7282 | −1.47773 | −0.738866 | − | 0.673853i | \(-0.764638\pi\) | ||||
−0.738866 | + | 0.673853i | \(0.764638\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.7839 | −0.594117 | −0.297059 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297059 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(464\) | 3.88542 | + | 2.82292i | 0.180376 | + | 0.131051i | ||||
\(465\) | 19.3952 | − | 59.6924i | 0.899432 | − | 2.76817i | ||||
\(466\) | 0.305129 | + | 0.939089i | 0.0141348 | + | 0.0435025i | ||||
\(467\) | −23.9281 | + | 17.3848i | −1.10726 | + | 0.804472i | −0.982230 | − | 0.187681i | \(-0.939903\pi\) |
−0.125030 | + | 0.992153i | \(0.539903\pi\) | |||||||
\(468\) | −8.08344 | + | 5.87296i | −0.373657 | + | 0.271478i | ||||
\(469\) | 0.636885 | + | 1.96013i | 0.0294086 | + | 0.0905105i | ||||
\(470\) | −0.197830 | + | 0.608857i | −0.00912521 | + | 0.0280845i | ||||
\(471\) | −16.6331 | − | 12.0847i | −0.766413 | − | 0.556832i | ||||
\(472\) | −3.19645 | −0.147129 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.10644 | −0.234546 | ||||||||
\(475\) | 17.6252 | + | 12.8055i | 0.808702 | + | 0.587556i | ||||
\(476\) | −4.26931 | + | 13.1396i | −0.195683 | + | 0.602251i | ||||
\(477\) | −5.50993 | − | 16.9578i | −0.252282 | − | 0.776445i | ||||
\(478\) | −1.01108 | + | 0.734591i | −0.0462456 | + | 0.0335994i | ||||
\(479\) | −23.1034 | + | 16.7856i | −1.05562 | + | 0.766955i | −0.973274 | − | 0.229649i | \(-0.926242\pi\) |
−0.0823493 | + | 0.996604i | \(0.526242\pi\) | |||||||
\(480\) | 3.43604 | + | 10.5750i | 0.156833 | + | 0.482682i | ||||
\(481\) | −0.512218 | + | 1.57645i | −0.0233551 | + | 0.0718797i | ||||
\(482\) | 0.798894 | + | 0.580430i | 0.0363886 | + | 0.0264379i | ||||
\(483\) | −13.3563 | −0.607731 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.6000 | −1.16244 | ||||||||
\(486\) | −1.68211 | − | 1.22213i | −0.0763021 | − | 0.0554367i | ||||
\(487\) | 0.327026 | − | 1.00648i | 0.0148190 | − | 0.0456081i | −0.943374 | − | 0.331732i | \(-0.892367\pi\) |
0.958193 | + | 0.286124i | \(0.0923670\pi\) | |||||||
\(488\) | 1.45262 | + | 4.47072i | 0.0657572 | + | 0.202380i | ||||
\(489\) | −17.5846 | + | 12.7759i | −0.795202 | + | 0.577748i | ||||
\(490\) | −0.273475 | + | 0.198691i | −0.0123543 | + | 0.00897596i | ||||
\(491\) | −5.70102 | − | 17.5459i | −0.257283 | − | 0.791837i | −0.993371 | − | 0.114951i | \(-0.963329\pi\) |
0.736088 | − | 0.676886i | \(-0.236671\pi\) | |||||||
\(492\) | 15.7933 | − | 48.6067i | 0.712016 | − | 2.19136i | ||||
\(493\) | −6.90872 | − | 5.01948i | −0.311153 | − | 0.226066i | ||||
\(494\) | −0.980354 | −0.0441082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.5962 | −1.41871 | ||||||||
\(497\) | 10.1299 | + | 7.35977i | 0.454386 | + | 0.330131i | ||||
\(498\) | 0.210628 | − | 0.648246i | 0.00943846 | − | 0.0290486i | ||||
\(499\) | 9.80490 | + | 30.1764i | 0.438927 | + | 1.35088i | 0.889008 | + | 0.457892i | \(0.151395\pi\) |
−0.450081 | + | 0.892988i | \(0.648605\pi\) | |||||||
\(500\) | 9.52886 | − | 6.92312i | 0.426144 | − | 0.309611i | ||||
\(501\) | −12.0976 | + | 8.78944i | −0.540482 | + | 0.392683i | ||||
\(502\) | 0.611650 | + | 1.88246i | 0.0272993 | + | 0.0840185i | ||||
\(503\) | 8.97024 | − | 27.6076i | 0.399963 | − | 1.23096i | −0.525065 | − | 0.851062i | \(-0.675959\pi\) |
0.925028 | − | 0.379898i | \(-0.124041\pi\) | |||||||
\(504\) | 1.80883 | + | 1.31419i | 0.0805715 | + | 0.0585386i | ||||
\(505\) | −13.3232 | −0.592876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.7555 | −1.45472 | ||||||||
\(508\) | −15.8165 | − | 11.4913i | −0.701743 | − | 0.509846i | ||||
\(509\) | 0.892536 | − | 2.74694i | 0.0395610 | − | 0.121756i | −0.929326 | − | 0.369261i | \(-0.879611\pi\) |
0.968887 | + | 0.247505i | \(0.0796107\pi\) | |||||||
\(510\) | −2.01180 | − | 6.19169i | −0.0890842 | − | 0.274173i | ||||
\(511\) | −2.07681 | + | 1.50889i | −0.0918728 | + | 0.0667495i | ||||
\(512\) | 7.56587 | − | 5.49693i | 0.334367 | − | 0.242932i | ||||
\(513\) | −10.7173 | − | 32.9844i | −0.473179 | − | 1.45630i | ||||
\(514\) | 0.447954 | − | 1.37866i | 0.0197584 | − | 0.0608101i | ||||
\(515\) | 0.797297 | + | 0.579270i | 0.0351331 | + | 0.0255257i | ||||
\(516\) | −28.7640 | −1.26626 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.184783 | 0.00811890 | ||||||||
\(519\) | −44.1601 | − | 32.0842i | −1.93841 | − | 1.40834i | ||||
\(520\) | 0.449489 | − | 1.38339i | 0.0197114 | − | 0.0606655i | ||||
\(521\) | 9.78683 | + | 30.1208i | 0.428769 | + | 1.31961i | 0.899339 | + | 0.437252i | \(0.144048\pi\) |
−0.470570 | + | 0.882362i | \(0.655952\pi\) | |||||||
\(522\) | −0.556994 | + | 0.404680i | −0.0243790 | + | 0.0177123i | ||||
\(523\) | −12.9751 | + | 9.42693i | −0.567359 | + | 0.412211i | −0.834145 | − | 0.551545i | \(-0.814038\pi\) |
0.266786 | + | 0.963756i | \(0.414038\pi\) | |||||||
\(524\) | 10.0489 | + | 30.9275i | 0.438990 | + | 1.35107i | ||||
\(525\) | −2.46997 | + | 7.60180i | −0.107799 | + | 0.331770i | ||||
\(526\) | −0.182674 | − | 0.132721i | −0.00796498 | − | 0.00578690i | ||||
\(527\) | 56.1818 | 2.44732 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.285644 | 0.0124193 | ||||||||
\(530\) | 1.04618 | + | 0.760097i | 0.0454433 | + | 0.0330165i | ||||
\(531\) | −9.59748 | + | 29.5380i | −0.416495 | + | 1.28184i | ||||
\(532\) | −4.62875 | − | 14.2458i | −0.200682 | − | 0.617635i | ||||
\(533\) | −8.12319 | + | 5.90184i | −0.351854 | + | 0.255637i | ||||
\(534\) | 1.28320 | − | 0.932302i | 0.0555297 | − | 0.0403447i | ||||
\(535\) | 2.21113 | + | 6.80517i | 0.0955956 | + | 0.294213i | ||||
\(536\) | −0.305511 | + | 0.940267i | −0.0131961 | + | 0.0406134i | ||||
\(537\) | 52.2393 | + | 37.9541i | 2.25429 | + | 1.63784i | ||||
\(538\) | 1.68853 | 0.0727976 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 25.6357 | 1.10318 | ||||||||
\(541\) | 10.9983 | + | 7.99073i | 0.472854 | + | 0.343549i | 0.798553 | − | 0.601925i | \(-0.205599\pi\) |
−0.325699 | + | 0.945474i | \(0.605599\pi\) | |||||||
\(542\) | 0.0503327 | − | 0.154908i | 0.00216198 | − | 0.00665388i | ||||
\(543\) | 2.63863 | + | 8.12087i | 0.113235 | + | 0.348500i | ||||
\(544\) | −8.05222 | + | 5.85028i | −0.345236 | + | 0.250829i | ||||
\(545\) | 8.66873 | − | 6.29820i | 0.371327 | − | 0.269785i | ||||
\(546\) | −0.111147 | − | 0.342075i | −0.00475665 | − | 0.0146395i | ||||
\(547\) | 2.72703 | − | 8.39294i | 0.116599 | − | 0.358856i | −0.875678 | − | 0.482896i | \(-0.839585\pi\) |
0.992277 | + | 0.124040i | \(0.0395850\pi\) | |||||||
\(548\) | −22.8324 | − | 16.5887i | −0.975352 | − | 0.708635i | ||||
\(549\) | 45.6749 | 1.94936 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.25862 | 0.394430 | ||||||||
\(552\) | −5.18333 | − | 3.76591i | −0.220617 | − | 0.160288i | ||||
\(553\) | −4.73672 | + | 14.5781i | −0.201426 | + | 0.619925i | ||||
\(554\) | −0.497777 | − | 1.53200i | −0.0211485 | − | 0.0650884i | ||||
\(555\) | 9.65510 | − | 7.01484i | 0.409836 | − | 0.297764i | ||||
\(556\) | 14.7450 | − | 10.7129i | 0.625329 | − | 0.454328i | ||||
\(557\) | −10.5041 | − | 32.3284i | −0.445074 | − | 1.36980i | −0.882403 | − | 0.470495i | \(-0.844075\pi\) |
0.437329 | − | 0.899302i | \(-0.355925\pi\) | |||||||
\(558\) | 1.39969 | − | 4.30779i | 0.0592534 | − | 0.182363i | ||||
\(559\) | 4.57179 | + | 3.32160i | 0.193366 | + | 0.140489i | ||||
\(560\) | 10.9906 | 0.464437 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.279099 | 0.0117731 | ||||||||
\(563\) | −16.3628 | − | 11.8883i | −0.689611 | − | 0.501032i | 0.186921 | − | 0.982375i | \(-0.440149\pi\) |
−0.876532 | + | 0.481343i | \(0.840149\pi\) | |||||||
\(564\) | 3.21622 | − | 9.89850i | 0.135427 | − | 0.416802i | ||||
\(565\) | −2.00887 | − | 6.18267i | −0.0845138 | − | 0.260107i | ||||
\(566\) | 2.16830 | − | 1.57536i | 0.0911403 | − | 0.0662173i | ||||
\(567\) | −1.01813 | + | 0.739718i | −0.0427576 | + | 0.0310652i | ||||
\(568\) | 1.85607 | + | 5.71239i | 0.0778789 | + | 0.239687i | ||||
\(569\) | −8.94078 | + | 27.5169i | −0.374817 | + | 1.15357i | 0.568785 | + | 0.822486i | \(0.307414\pi\) |
−0.943602 | + | 0.331082i | \(0.892586\pi\) | |||||||
\(570\) | 5.71041 | + | 4.14885i | 0.239183 | + | 0.173776i | ||||
\(571\) | 7.51312 | 0.314414 | 0.157207 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157207 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 34.7958 | 1.45362 | ||||||||
\(574\) | 0.905557 | + | 0.657925i | 0.0377972 | + | 0.0274613i | ||||
\(575\) | 4.30622 | − | 13.2532i | 0.179582 | − | 0.552695i | ||||
\(576\) | −11.0247 | − | 33.9306i | −0.459364 | − | 1.41378i | ||||
\(577\) | −27.8098 | + | 20.2050i | −1.15774 | + | 0.841145i | −0.989490 | − | 0.144600i | \(-0.953810\pi\) |
−0.168247 | + | 0.985745i | \(0.553810\pi\) | |||||||
\(578\) | 3.05924 | − | 2.22267i | 0.127248 | − | 0.0924509i | ||||
\(579\) | 17.6780 | + | 54.4072i | 0.734672 | + | 2.26109i | ||||
\(580\) | −2.11481 | + | 6.50872i | −0.0878127 | + | 0.270260i | ||||
\(581\) | −1.65527 | − | 1.20262i | −0.0686721 | − | 0.0498932i | ||||
\(582\) | −3.03658 | −0.125870 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.23142 | −0.0509565 | ||||||||
\(585\) | −11.4341 | − | 8.30736i | −0.472742 | − | 0.343467i | ||||
\(586\) | −0.0907443 | + | 0.279282i | −0.00374861 | + | 0.0115370i | ||||
\(587\) | 12.9908 | + | 39.9816i | 0.536188 | + | 1.65022i | 0.741067 | + | 0.671431i | \(0.234320\pi\) |
−0.204879 | + | 0.978787i | \(0.565680\pi\) | |||||||
\(588\) | 4.44602 | − | 3.23022i | 0.183351 | − | 0.133212i | ||||
\(589\) | −49.2787 | + | 35.8031i | −2.03049 | + | 1.47524i | ||||
\(590\) | −0.696056 | − | 2.14224i | −0.0286562 | − | 0.0881946i | ||||
\(591\) | −5.37095 | + | 16.5301i | −0.220931 | + | 0.679957i | ||||
\(592\) | −4.86049 | − | 3.53135i | −0.199765 | − | 0.145138i | ||||
\(593\) | −29.2867 | −1.20266 | −0.601331 | − | 0.799000i | \(-0.705363\pi\) | ||||
−0.601331 | + | 0.799000i | \(0.705363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.5425 | −0.801165 | ||||||||
\(596\) | −18.6654 | − | 13.5612i | −0.764563 | − | 0.555487i | ||||
\(597\) | −5.87508 | + | 18.0817i | −0.240451 | + | 0.740033i | ||||
\(598\) | 0.193776 | + | 0.596383i | 0.00792411 | + | 0.0243879i | ||||
\(599\) | 12.2628 | − | 8.90947i | 0.501046 | − | 0.364031i | −0.308370 | − | 0.951266i | \(-0.599784\pi\) |
0.809416 | + | 0.587235i | \(0.199784\pi\) | |||||||
\(600\) | −3.10194 | + | 2.25369i | −0.126636 | + | 0.0920067i | ||||
\(601\) | −9.84944 | − | 30.3135i | −0.401767 | − | 1.23651i | −0.923565 | − | 0.383443i | \(-0.874738\pi\) |
0.521798 | − | 0.853069i | \(-0.325262\pi\) | |||||||
\(602\) | 0.194670 | − | 0.599134i | 0.00793417 | − | 0.0244189i | ||||
\(603\) | 7.77159 | + | 5.64639i | 0.316483 | + | 0.229939i | ||||
\(604\) | 35.5705 | 1.44734 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.58035 | −0.0641974 | ||||||||
\(607\) | −16.2987 | − | 11.8417i | −0.661545 | − | 0.480640i | 0.205639 | − | 0.978628i | \(-0.434073\pi\) |
−0.867184 | + | 0.497987i | \(0.834073\pi\) | |||||||
\(608\) | 3.33462 | − | 10.2629i | 0.135237 | − | 0.416216i | ||||
\(609\) | 1.04969 | + | 3.23061i | 0.0425356 | + | 0.130911i | ||||
\(610\) | −2.67993 | + | 1.94708i | −0.108507 | + | 0.0788350i | ||||
\(611\) | −1.65424 | + | 1.20188i | −0.0669235 | + | 0.0486228i | ||||
\(612\) | 19.8990 | + | 61.2427i | 0.804368 | + | 2.47559i | ||||
\(613\) | 1.20248 | − | 3.70086i | 0.0485678 | − | 0.149476i | −0.923831 | − | 0.382800i | \(-0.874960\pi\) |
0.972399 | + | 0.233323i | \(0.0749600\pi\) | |||||||
\(614\) | 0.865701 | + | 0.628969i | 0.0349368 | + | 0.0253831i | ||||
\(615\) | 72.2929 | 2.91513 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6122 | 1.15189 | 0.575943 | − | 0.817490i | \(-0.304635\pi\) | ||||
0.575943 | + | 0.817490i | \(0.304635\pi\) | |||||||
\(618\) | 0.0945724 | + | 0.0687109i | 0.00380426 | + | 0.00276396i | ||||
\(619\) | −8.08222 | + | 24.8745i | −0.324852 | + | 0.999791i | 0.646656 | + | 0.762782i | \(0.276167\pi\) |
−0.971507 | + | 0.237009i | \(0.923833\pi\) | |||||||
\(620\) | −13.9132 | − | 42.8204i | −0.558767 | − | 1.71971i | ||||
\(621\) | −17.9472 | + | 13.0394i | −0.720194 | + | 0.523252i | ||||
\(622\) | −1.15238 | + | 0.837256i | −0.0462064 | + | 0.0335709i | ||||
\(623\) | −1.47129 | − | 4.52816i | −0.0589459 | − | 0.181417i | ||||
\(624\) | −3.61375 | + | 11.1220i | −0.144666 | + | 0.445236i | ||||
\(625\) | 25.1601 | + | 18.2799i | 1.00640 | + | 0.731195i | ||||
\(626\) | 3.55550 | 0.142106 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.7485 | −0.588529 | ||||||||
\(629\) | 8.64251 | + | 6.27915i | 0.344599 | + | 0.250366i | ||||
\(630\) | −0.486873 | + | 1.49844i | −0.0193975 | + | 0.0596993i | ||||
\(631\) | −1.75606 | − | 5.40459i | −0.0699075 | − | 0.215153i | 0.909999 | − | 0.414610i | \(-0.136082\pi\) |
−0.979907 | + | 0.199457i | \(0.936082\pi\) | |||||||
\(632\) | −5.94866 | + | 4.32195i | −0.236625 | + | 0.171918i | ||||
\(633\) | 22.9714 | − | 16.6897i | 0.913031 | − | 0.663356i | ||||
\(634\) | 0.935578 | + | 2.87941i | 0.0371565 | + | 0.114356i | ||||
\(635\) | 8.54555 | − | 26.3005i | 0.339120 | − | 1.04370i | ||||
\(636\) | −17.0083 | − | 12.3573i | −0.674424 | − | 0.489998i | ||||
\(637\) | −1.07967 | −0.0427782 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 58.3605 | 2.30870 | ||||||||
\(640\) | 8.59342 | + | 6.24349i | 0.339685 | + | 0.246795i | ||||
\(641\) | −6.40569 | + | 19.7147i | −0.253009 | + | 0.778683i | 0.741206 | + | 0.671278i | \(0.234254\pi\) |
−0.994215 | + | 0.107405i | \(0.965746\pi\) | |||||||
\(642\) | 0.262276 | + | 0.807204i | 0.0103512 | + | 0.0318578i | ||||
\(643\) | −17.2123 | + | 12.5055i | −0.678789 | + | 0.493169i | −0.872956 | − | 0.487800i | \(-0.837800\pi\) |
0.194167 | + | 0.980969i | \(0.437800\pi\) | |||||||
\(644\) | −7.75130 | + | 5.63165i | −0.305444 | + | 0.221918i | ||||
\(645\) | −12.5730 | − | 38.6956i | −0.495060 | − | 1.52364i | ||||
\(646\) | −1.95243 | + | 6.00895i | −0.0768172 | + | 0.236419i | ||||
\(647\) | 13.9732 | + | 10.1521i | 0.549341 | + | 0.399120i | 0.827543 | − | 0.561403i | \(-0.189738\pi\) |
−0.278201 | + | 0.960523i | \(0.589738\pi\) | |||||||
\(648\) | −0.603690 | −0.0237152 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.375270 | 0.0147193 | ||||||||
\(651\) | −18.0797 | − | 13.1357i | −0.708600 | − | 0.514828i | ||||
\(652\) | −4.81824 | + | 14.8290i | −0.188697 | + | 0.580749i | ||||
\(653\) | 12.6940 | + | 39.0682i | 0.496756 | + | 1.52886i | 0.814202 | + | 0.580582i | \(0.197175\pi\) |
−0.317446 | + | 0.948276i | \(0.602825\pi\) | |||||||
\(654\) | 1.02825 | − | 0.747069i | 0.0402078 | − | 0.0292127i | ||||
\(655\) | −37.2136 | + | 27.0372i | −1.45405 | + | 1.05643i | ||||
\(656\) | −11.2461 | − | 34.6118i | −0.439085 | − | 1.35137i | ||||
\(657\) | −3.69739 | + | 11.3794i | −0.144249 | + | 0.443952i | ||||
\(658\) | 0.184412 | + | 0.133983i | 0.00718912 | + | 0.00522320i | ||||
\(659\) | −6.00410 | −0.233887 | −0.116943 | − | 0.993139i | \(-0.537310\pi\) | ||||
−0.116943 | + | 0.993139i | \(0.537310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.83502 | −0.0713739 | −0.0356870 | − | 0.999363i | \(-0.511362\pi\) | ||||
−0.0356870 | + | 0.999363i | \(0.511362\pi\) | |||||||
\(662\) | −0.921475 | − | 0.669491i | −0.0358141 | − | 0.0260205i | ||||
\(663\) | 6.42567 | − | 19.7762i | 0.249552 | − | 0.768043i | ||||
\(664\) | −0.303291 | − | 0.933433i | −0.0117700 | − | 0.0362242i | ||||
\(665\) | 17.1413 | − | 12.4539i | 0.664712 | − | 0.482941i | ||||
\(666\) | 0.696775 | − | 0.506237i | 0.0269995 | − | 0.0196163i | ||||
\(667\) | −1.83006 | − | 5.63233i | −0.0708600 | − | 0.218085i | ||||
\(668\) | −3.31480 | + | 10.2019i | −0.128253 | + | 0.394723i | ||||
\(669\) | 30.2790 | + | 21.9990i | 1.17066 | + | 0.850531i | ||||
\(670\) | −0.696689 | −0.0269154 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.95910 | 0.152726 | ||||||||
\(673\) | 35.9530 | + | 26.1214i | 1.38589 | + | 1.00690i | 0.996303 | + | 0.0859135i | \(0.0273809\pi\) |
0.389583 | + | 0.920991i | \(0.372619\pi\) | |||||||
\(674\) | −0.640648 | + | 1.97171i | −0.0246768 | + | 0.0759475i | ||||
\(675\) | 4.10247 | + | 12.6261i | 0.157904 | + | 0.485979i | ||||
\(676\) | −19.0096 | + | 13.8113i | −0.731139 | + | 0.531203i | ||||
\(677\) | 12.5779 | − | 9.13838i | 0.483408 | − | 0.351216i | −0.319236 | − | 0.947675i | \(-0.603426\pi\) |
0.802644 | + | 0.596459i | \(0.203426\pi\) | |||||||
\(678\) | −0.238285 | − | 0.733365i | −0.00915127 | − | 0.0281647i | ||||
\(679\) | −2.81673 | + | 8.66899i | −0.108096 | + | 0.332685i | ||||
\(680\) | −7.58410 | − | 5.51017i | −0.290837 | − | 0.211305i | ||||
\(681\) | −37.5774 | −1.43997 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.8979 | −1.41186 | −0.705930 | − | 0.708282i | \(-0.749471\pi\) | ||||
−0.705930 | + | 0.708282i | \(0.749471\pi\) | |||||||
\(684\) | −56.4822 | − | 41.0367i | −2.15965 | − | 1.56908i | ||||
\(685\) | 12.3362 | − | 37.9670i | 0.471343 | − | 1.45064i | ||||
\(686\) | 0.0371933 | + | 0.114469i | 0.00142004 | + | 0.00437045i | ||||
\(687\) | 3.25350 | − | 2.36381i | 0.124129 | − | 0.0901849i | ||||
\(688\) | −16.5705 | + | 12.0392i | −0.631744 | + | 0.458989i | ||||
\(689\) | 1.27634 | + | 3.92816i | 0.0486246 | + | 0.149651i | ||||
\(690\) | 1.39517 | − | 4.29390i | 0.0531133 | − | 0.163466i | ||||
\(691\) | 15.1064 | + | 10.9755i | 0.574676 | + | 0.417527i | 0.836801 | − | 0.547507i | \(-0.184423\pi\) |
−0.262125 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(692\) | −39.1566 | −1.48851 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.05133 | −0.0399078 | ||||||||
\(695\) | 20.8570 | + | 15.1535i | 0.791150 | + | 0.574804i | ||||
\(696\) | −0.503532 | + | 1.54971i | −0.0190863 | + | 0.0587417i | ||||
\(697\) | 19.9968 | + | 61.5439i | 0.757433 | + | 2.33114i | ||||
\(698\) | 2.91974 | − | 2.12132i | 0.110514 | − | 0.0802930i | ||||
\(699\) | 18.3703 | − | 13.3468i | 0.694830 | − | 0.504824i | ||||
\(700\) | 1.77184 | + | 5.45316i | 0.0669693 | + | 0.206110i | ||||
\(701\) | 8.07548 | − | 24.8538i | 0.305007 | − | 0.938714i | −0.674668 | − | 0.738121i | \(-0.735713\pi\) |
0.979675 | − | 0.200593i | \(-0.0642868\pi\) | |||||||
\(702\) | −0.483310 | − | 0.351145i | −0.0182414 | − | 0.0132531i | ||||
\(703\) | −11.5821 | −0.436828 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7221 | 0.554465 | ||||||||
\(706\) | 0.712771 | + | 0.517858i | 0.0268255 | + | 0.0194899i | ||||
\(707\) | −1.46593 | + | 4.51167i | −0.0551320 | + | 0.169679i | ||||
\(708\) | 11.3161 | + | 34.8275i | 0.425286 | + | 1.30890i | ||||
\(709\) | 13.3042 | − | 9.66609i | 0.499651 | − | 0.363017i | −0.309233 | − | 0.950986i | \(-0.600072\pi\) |
0.808884 | + | 0.587969i | \(0.200072\pi\) | |||||||
\(710\) | −3.42423 | + | 2.48785i | −0.128509 | + | 0.0933674i | ||||
\(711\) | 22.0776 | + | 67.9477i | 0.827973 | + | 2.54824i | ||||
\(712\) | 0.705771 | − | 2.17214i | 0.0264499 | − | 0.0814044i | ||||
\(713\) | 31.5206 | + | 22.9011i | 1.18046 | + | 0.857653i | ||||
\(714\) | −2.31806 | −0.0867513 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 46.3204 | 1.73107 | ||||||||
\(717\) | 23.2511 | + | 16.8929i | 0.868329 | + | 0.630878i | ||||
\(718\) | 0.184849 | − | 0.568907i | 0.00689850 | − | 0.0212314i | ||||
\(719\) | −2.88904 | − | 8.89155i | −0.107743 | − | 0.331599i | 0.882621 | − | 0.470084i | \(-0.155777\pi\) |
−0.990364 | + | 0.138486i | \(0.955777\pi\) | |||||||
\(720\) | 41.4430 | − | 30.1101i | 1.54449 | − | 1.12214i | ||||
\(721\) | 0.283885 | − | 0.206254i | 0.0105724 | − | 0.00768131i | ||||
\(722\) | −1.41013 | − | 4.33994i | −0.0524797 | − | 0.161516i | ||||
\(723\) | 7.01735 | − | 21.5972i | 0.260978 | − | 0.803207i | ||||
\(724\) | 4.95548 | + | 3.60037i | 0.184169 | + | 0.133807i | ||||
\(725\) | −3.54411 | −0.131625 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7523 | 1.02928 | 0.514638 | − | 0.857408i | \(-0.327927\pi\) | ||||
0.514638 | + | 0.857408i | \(0.327927\pi\) | |||||||
\(728\) | −0.419002 | − | 0.304423i | −0.0155293 | − | 0.0112827i | ||||
\(729\) | −13.6087 | + | 41.8833i | −0.504026 | + | 1.55123i | ||||
\(730\) | −0.268153 | − | 0.825289i | −0.00992478 | − | 0.0305453i | ||||
\(731\) | 29.4643 | − | 21.4070i | 1.08977 | − | 0.791768i | ||||
\(732\) | 43.5689 | − | 31.6546i | 1.61035 | − | 1.16999i | ||||
\(733\) | −0.450021 | − | 1.38502i | −0.0166219 | − | 0.0511569i | 0.942402 | − | 0.334484i | \(-0.108562\pi\) |
−0.959023 | + | 0.283327i | \(0.908562\pi\) | |||||||
\(734\) | 0.528302 | − | 1.62594i | 0.0195000 | − | 0.0600147i | ||||
\(735\) | 6.28893 | + | 4.56918i | 0.231971 | + | 0.168537i | ||||
\(736\) | −6.90240 | −0.254426 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5.21712 | 0.192045 | ||||||||
\(739\) | −22.3261 | − | 16.2209i | −0.821280 | − | 0.596695i | 0.0957991 | − | 0.995401i | \(-0.469459\pi\) |
−0.917079 | + | 0.398706i | \(0.869459\pi\) | |||||||
\(740\) | 2.64554 | − | 8.14212i | 0.0972518 | − | 0.299310i | ||||
\(741\) | 6.96665 | + | 21.4412i | 0.255926 | + | 0.787661i | ||||
\(742\) | 0.372503 | − | 0.270639i | 0.0136750 | − | 0.00993548i | ||||
\(743\) | 22.6341 | − | 16.4446i | 0.830365 | − | 0.603296i | −0.0892975 | − | 0.996005i | \(-0.528462\pi\) |
0.919663 | + | 0.392709i | \(0.128462\pi\) | |||||||
\(744\) | −3.31270 | − | 10.1955i | −0.121450 | − | 0.373784i | ||||
\(745\) | 10.0848 | − | 31.0378i | 0.369478 | − | 1.13714i | ||||
\(746\) | −0.874198 | − | 0.635142i | −0.0320067 | − | 0.0232542i | ||||
\(747\) | −9.53638 | −0.348918 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.54774 | 0.0930922 | ||||||||
\(750\) | 1.59879 | + | 1.16159i | 0.0583795 | + | 0.0424152i | ||||
\(751\) | 10.5361 | − | 32.4269i | 0.384469 | − | 1.18328i | −0.552395 | − | 0.833582i | \(-0.686286\pi\) |
0.936864 | − | 0.349693i | \(-0.113714\pi\) | |||||||
\(752\) | −2.29020 | − | 7.04851i | −0.0835150 | − | 0.257033i | ||||
\(753\) | 36.8245 | − | 26.7546i | 1.34196 | − | 0.974991i | ||||
\(754\) | 0.129024 | − | 0.0937413i | 0.00469877 | − | 0.00341386i | ||||
\(755\) | 15.5481 | + | 47.8522i | 0.565854 | + | 1.74152i | ||||
\(756\) | 2.82065 | − | 8.68106i | 0.102586 | − | 0.315727i | ||||
\(757\) | 32.1689 | + | 23.3721i | 1.16920 | + | 0.849472i | 0.990913 | − | 0.134507i | \(-0.0429451\pi\) |
0.178285 | + | 0.983979i | \(0.442945\pi\) | |||||||
\(758\) | −1.29863 | −0.0471684 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1637 | 0.368677 | ||||||||
\(761\) | −3.09381 | − | 2.24778i | −0.112150 | − | 0.0814820i | 0.530296 | − | 0.847812i | \(-0.322081\pi\) |
−0.642447 | + | 0.766330i | \(0.722081\pi\) | |||||||
\(762\) | 1.01364 | − | 3.11967i | 0.0367203 | − | 0.113014i | ||||
\(763\) | −1.17897 | − | 3.62849i | −0.0426815 | − | 0.131360i | ||||
\(764\) | 20.1937 | − | 14.6716i | 0.730584 | − | 0.530800i | ||||
\(765\) | −73.6905 | + | 53.5393i | −2.66428 | + | 1.93572i | ||||
\(766\) | 0.874413 | + | 2.69117i | 0.0315938 | + | 0.0972358i | ||||
\(767\) | 2.22319 | − | 6.84228i | 0.0802748 | − | 0.247060i | ||||
\(768\) | −33.2607 | − | 24.1653i | −1.20019 | − | 0.871990i | ||||
\(769\) | 19.6583 | 0.708897 | 0.354449 | − | 0.935075i | \(-0.384669\pi\) | ||||
0.354449 | + | 0.935075i | \(0.384669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.3358 | −1.20056 | ||||||||
\(772\) | 33.2001 | + | 24.1213i | 1.19490 | + | 0.868145i | ||||
\(773\) | −5.43764 | + | 16.7353i | −0.195578 | + | 0.601928i | 0.804391 | + | 0.594100i | \(0.202492\pi\) |
−0.999969 | + | 0.00782804i | \(0.997508\pi\) | |||||||
\(774\) | −0.907346 | − | 2.79252i | −0.0326139 | − | 0.100375i | ||||
\(775\) | 18.8634 | − | 13.7051i | 0.677594 | − | 0.492301i | ||||
\(776\) | −3.53742 | + | 2.57008i | −0.126986 | + | 0.0922606i | ||||
\(777\) | −1.31312 | − | 4.04136i | −0.0471078 | − | 0.144983i | ||||
\(778\) | 0.441653 | − | 1.35927i | 0.0158340 | − | 0.0487321i | ||||
\(779\) | −56.7600 | − | 41.2385i | −2.03364 | − | 1.47752i | ||||
\(780\) | −16.6642 | −0.596675 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.04136 | 0.144519 | ||||||||
\(783\) | 4.56446 | + | 3.31627i | 0.163120 | + | 0.118514i | ||||
\(784\) | 1.20927 | − | 3.72176i | 0.0431883 | − | 0.132920i | ||||
\(785\) | −6.44667 | − | 19.8408i | −0.230092 | − | 0.708149i | ||||
\(786\) | −4.41414 | + | 3.20706i | −0.157447 | + | 0.114392i | ||||
\(787\) | −43.7651 | + | 31.7972i | −1.56006 | + | 1.13345i | −0.624098 | + | 0.781346i | \(0.714533\pi\) |
−0.935961 | + | 0.352103i | \(0.885467\pi\) | |||||||
\(788\) | 3.85286 | + | 11.8579i | 0.137252 | + | 0.422419i | ||||
\(789\) | −1.60458 | + | 4.93839i | −0.0571246 | + | 0.175811i | ||||
\(790\) | −4.19192 | − | 3.04561i | −0.149142 | − | 0.108358i | ||||
\(791\) | −2.31468 | −0.0823006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.5803 | −0.375717 | ||||||||
\(794\) | −2.31032 | − | 1.67854i | −0.0819901 | − | 0.0595693i | ||||
\(795\) | 9.18950 | − | 28.2824i | 0.325918 | − | 1.00307i | ||||
\(796\) | 4.21450 | + | 12.9709i | 0.149379 | + | 0.459741i | ||||
\(797\) | −29.5489 | + | 21.4685i | −1.04667 | + | 0.760454i | −0.971577 | − | 0.236722i | \(-0.923927\pi\) |
−0.0750976 | + | 0.997176i | \(0.523927\pi\) | |||||||
\(798\) | 2.03324 | − | 1.47724i | 0.0719759 | − | 0.0522936i | ||||
\(799\) | 4.07224 | + | 12.5331i | 0.144066 | + | 0.443388i | ||||
\(800\) | −1.27646 | + | 3.92854i | −0.0451297 | + | 0.138895i | ||||
\(801\) | −17.9534 | − | 13.0439i | −0.634351 | − | 0.460883i | ||||
\(802\) | 0.457513 | 0.0161554 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.3264 | 0.399452 | ||||||||
\(805\) | −10.9643 | − | 7.96602i | −0.386440 | − | 0.280765i | ||||
\(806\) | −0.324228 | + | 0.997871i | −0.0114204 | + | 0.0351485i | ||||
\(807\) | −11.9991 | − | 36.9295i | −0.422389 | − | 1.29998i | ||||
\(808\) | −1.84100 | + | 1.33757i | −0.0647663 | + | 0.0470555i | ||||
\(809\) | 37.9716 | − | 27.5880i | 1.33501 | − | 0.969941i | 0.335397 | − | 0.942077i | \(-0.391130\pi\) |
0.999612 | − | 0.0278638i | \(-0.00887048\pi\) | |||||||
\(810\) | −0.131459 | − | 0.404589i | −0.00461900 | − | 0.0142158i | ||||
\(811\) | 3.91262 | − | 12.0418i | 0.137391 | − | 0.422845i | −0.858564 | − | 0.512707i | \(-0.828643\pi\) |
0.995954 | + | 0.0898623i | \(0.0286427\pi\) | |||||||
\(812\) | 1.97137 | + | 1.43228i | 0.0691815 | + | 0.0502633i | ||||
\(813\) | −3.74565 | −0.131366 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0552 | −0.772561 | ||||||||
\(816\) | 60.9737 | + | 44.3000i | 2.13451 | + | 1.55081i | ||||
\(817\) | −12.2019 | + | 37.5535i | −0.426889 | + | 1.31383i | ||||
\(818\) | −0.222524 | − | 0.684858i | −0.00778037 | − | 0.0239455i | ||||
\(819\) | −4.07121 | + | 2.95791i | −0.142260 | + | 0.103358i | ||||
\(820\) | 41.9551 | − | 30.4822i | 1.46514 | − | 1.06448i | ||||
\(821\) | 15.2326 | + | 46.8812i | 0.531622 | + | 1.63616i | 0.750837 | + | 0.660488i | \(0.229651\pi\) |
−0.219214 | + | 0.975677i | \(0.570349\pi\) | |||||||
\(822\) | 1.46328 | − | 4.50350i | 0.0510376 | − | 0.157078i | ||||
\(823\) | −15.5541 | − | 11.3007i | −0.542182 | − | 0.393918i | 0.282713 | − | 0.959205i | \(-0.408766\pi\) |
−0.824895 | + | 0.565287i | \(0.808766\pi\) | |||||||
\(824\) | 0.168326 | 0.00586390 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.802017 | −0.0279057 | ||||||||
\(827\) | 35.3070 | + | 25.6521i | 1.22775 | + | 0.892010i | 0.996719 | − | 0.0809378i | \(-0.0257915\pi\) |
0.231027 | + | 0.972947i | \(0.425792\pi\) | |||||||
\(828\) | −13.7998 | + | 42.4714i | −0.479576 | + | 1.47598i | ||||
\(829\) | −11.3432 | − | 34.9106i | −0.393964 | − | 1.21250i | −0.929765 | − | 0.368153i | \(-0.879990\pi\) |
0.535801 | − | 0.844344i | \(-0.320010\pi\) | |||||||
\(830\) | 0.559536 | − | 0.406527i | 0.0194218 | − | 0.0141108i | ||||
\(831\) | −29.9688 | + | 21.7736i | −1.03960 | + | 0.755317i | ||||
\(832\) | 2.55380 | + | 7.85980i | 0.0885372 | + | 0.272489i | ||||
\(833\) | −2.15023 | + | 6.61772i | −0.0745010 | + | 0.229290i | ||||
\(834\) | 2.47398 | + | 1.79745i | 0.0856668 | + | 0.0622406i | ||||
\(835\) | −15.1733 | −0.525094 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −37.1182 | −1.28299 | ||||||||
\(838\) | −0.405939 | − | 0.294932i | −0.0140229 | − | 0.0101882i | ||||
\(839\) | 12.5011 | − | 38.4745i | 0.431587 | − | 1.32829i | −0.464957 | − | 0.885333i | \(-0.653930\pi\) |
0.896544 | − | 0.442955i | \(-0.146070\pi\) | |||||||
\(840\) | 1.15231 | + | 3.54643i | 0.0397583 | + | 0.122364i | ||||
\(841\) | 22.2430 | − | 16.1605i | 0.766999 | − | 0.557257i | ||||
\(842\) | 2.28393 | − | 1.65938i | 0.0787096 | − | 0.0571859i | ||||
\(843\) | −1.98335 | − | 6.10413i | −0.0683102 | − | 0.210237i | ||||
\(844\) | 6.29425 | − | 19.3717i | 0.216657 | − | 0.666802i | ||||
\(845\) | −26.8893 | − | 19.5362i | −0.925018 | − | 0.672065i | ||||
\(846\) | 1.06244 | 0.0365274 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.9704 | −0.514085 | ||||||||
\(849\) | −49.8629 | − | 36.2275i | −1.71129 | − | 1.24333i | ||||
\(850\) | 0.747370 | − | 2.30017i | 0.0256346 | − | 0.0788951i | ||||
\(851\) | 2.28932 | + | 7.04580i | 0.0784769 | + | 0.241527i | ||||
\(852\) | 55.6695 | − | 40.4462i | 1.90720 | − | 1.38567i | ||||
\(853\) | 20.6258 | − | 14.9855i | 0.706213 | − | 0.513094i | −0.175737 | − | 0.984437i | \(-0.556231\pi\) |
0.881950 | + | 0.471344i | \(0.156231\pi\) | |||||||
\(854\) | 0.364476 | + | 1.12174i | 0.0124721 | + | 0.0383852i | ||||
\(855\) | 30.5170 | − | 93.9217i | 1.04366 | − | 3.21206i | ||||
\(856\) | 0.988731 | + | 0.718355i | 0.0337941 | + | 0.0245529i | ||||
\(857\) | −49.4756 | −1.69005 | −0.845027 | − | 0.534723i | \(-0.820416\pi\) | ||||
−0.845027 | + | 0.534723i | \(0.820416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6779 | 0.739641 | 0.369821 | − | 0.929103i | \(-0.379419\pi\) | ||||
0.369821 | + | 0.929103i | \(0.379419\pi\) | |||||||
\(860\) | −23.6126 | − | 17.1556i | −0.805184 | − | 0.585001i | ||||
\(861\) | 7.95426 | − | 24.4807i | 0.271080 | − | 0.834299i | ||||
\(862\) | 1.38630 | + | 4.26661i | 0.0472177 | + | 0.145321i | ||||
\(863\) | −11.0349 | + | 8.01730i | −0.375631 | + | 0.272912i | −0.759542 | − | 0.650458i | \(-0.774577\pi\) |
0.383911 | + | 0.923370i | \(0.374577\pi\) | |||||||
\(864\) | 5.31995 | − | 3.86517i | 0.180988 | − | 0.131496i | ||||
\(865\) | −17.1156 | − | 52.6764i | −0.581948 | − | 1.79105i | ||||
\(866\) | 0.847497 | − | 2.60833i | 0.0287991 | − | 0.0886346i | ||||
\(867\) | −70.3515 | − | 51.1133i | −2.38926 | − | 1.73590i | ||||
\(868\) | −16.0312 | −0.544135 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.14826 | −0.0389295 | ||||||||
\(871\) | −1.80024 | − | 1.30795i | −0.0609986 | − | 0.0443181i | ||||
\(872\) | 0.565546 | − | 1.74057i | 0.0191518 | − | 0.0589432i | ||||
\(873\) | 13.1286 | + | 40.4056i | 0.444335 | + | 1.36752i | ||||
\(874\) | −3.54480 | + | 2.57545i | −0.119905 | + | 0.0871158i | ||||
\(875\) | 4.79919 | − | 3.48682i | 0.162242 | − | 0.117876i | ||||
\(876\) | 4.35949 | + | 13.4171i | 0.147294 | + | 0.453323i | ||||
\(877\) | −9.00137 | + | 27.7034i | −0.303955 | + | 0.935476i | 0.676111 | + | 0.736800i | \(0.263664\pi\) |
−0.980065 | + | 0.198676i | \(0.936336\pi\) | |||||||
\(878\) | 0.139219 | + | 0.101148i | 0.00469840 | + | 0.00341359i | ||||
\(879\) | 6.75299 | 0.227773 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.8256 | −1.64498 | −0.822488 | − | 0.568783i | \(-0.807414\pi\) | ||||
−0.822488 | + | 0.568783i | \(0.807414\pi\) | |||||||
\(882\) | 0.453850 | + | 0.329741i | 0.0152819 | + | 0.0111030i | ||||
\(883\) | −7.48227 | + | 23.0281i | −0.251799 | + | 0.774956i | 0.742645 | + | 0.669685i | \(0.233571\pi\) |
−0.994444 | + | 0.105271i | \(0.966429\pi\) | |||||||
\(884\) | −4.60946 | − | 14.1865i | −0.155033 | − | 0.477142i | ||||
\(885\) | −41.9062 | + | 30.4467i | −1.40866 | + | 1.02345i | ||||
\(886\) | −2.57359 | + | 1.86982i | −0.0864613 | + | 0.0628178i | ||||
\(887\) | −2.05419 | − | 6.32214i | −0.0689729 | − | 0.212277i | 0.910629 | − | 0.413225i | \(-0.135598\pi\) |
−0.979602 | + | 0.200948i | \(0.935598\pi\) | |||||||
\(888\) | 0.629897 | − | 1.93862i | 0.0211380 | − | 0.0650559i | ||||
\(889\) | −7.96594 | − | 5.78759i | −0.267169 | − | 0.194110i | ||||
\(890\) | 1.60944 | 0.0539486 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.8483 | 0.898947 | ||||||||
\(893\) | −11.5589 | − | 8.39800i | −0.386803 | − | 0.281028i | ||||
\(894\) | 1.19622 | − | 3.68158i | 0.0400076 | − | 0.123131i | ||||
\(895\) | 20.2470 | + | 62.3137i | 0.676781 | + | 2.08292i | ||||
\(896\) | 3.05976 | − | 2.22305i | 0.102220 | − | 0.0742668i | ||||
\(897\) | 11.6664 | − | 8.47611i | 0.389528 | − | 0.283009i | ||||
\(898\) | −0.523941 | − | 1.61252i | −0.0174841 | − | 0.0538106i | ||||
\(899\) | 3.06206 | − | 9.42405i | 0.102125 | − | 0.314310i | ||||
\(900\) | 21.6209 | + | 15.7085i | 0.720695 | + | 0.523616i | ||||
\(901\) | 26.6191 | 0.886809 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.4869 | −0.482095 | ||||||||
\(904\) | −0.898287 | − | 0.652643i | −0.0298766 | − | 0.0217066i | ||||
\(905\) | −2.67742 | + | 8.24025i | −0.0890004 | + | 0.273915i | ||||
\(906\) | 1.84426 | + | 5.67605i | 0.0612714 | + | 0.188574i | ||||
\(907\) | 6.77799 | − | 4.92450i | 0.225060 | − | 0.163515i | −0.469542 | − | 0.882910i | \(-0.655581\pi\) |
0.694601 | + | 0.719395i | \(0.255581\pi\) | |||||||
\(908\) | −21.8080 | + | 15.8445i | −0.723725 | + | 0.525817i | ||||
\(909\) | 6.83261 | + | 21.0286i | 0.226623 | + | 0.697475i | ||||
\(910\) | 0.112781 | − | 0.347104i | 0.00373865 | − | 0.0115064i | ||||
\(911\) | 15.1988 | + | 11.0426i | 0.503559 | + | 0.365857i | 0.810375 | − | 0.585912i | \(-0.199263\pi\) |
−0.306816 | + | 0.951769i | \(0.599263\pi\) | |||||||
\(912\) | −81.7130 | −2.70579 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 3.54856 | 0.117376 | ||||||||
\(915\) | 61.6285 | + | 44.7757i | 2.03738 | + | 1.48024i | ||||
\(916\) | 0.891472 | − | 2.74367i | 0.0294551 | − | 0.0906534i | ||||
\(917\) | 5.06113 | + | 15.5766i | 0.167133 | + | 0.514384i | ||||
\(918\) | −3.11484 | + | 2.26306i | −0.102805 | + | 0.0746922i | ||||
\(919\) | 14.5655 | − | 10.5824i | 0.480470 | − | 0.349082i | −0.321038 | − | 0.947066i | \(-0.604032\pi\) |
0.801508 | + | 0.597984i | \(0.204032\pi\) | |||||||
\(920\) | −2.00896 | − | 6.18294i | −0.0662334 | − | 0.203845i | ||||
\(921\) | 7.60417 | − | 23.4032i | 0.250566 | − | 0.771163i | ||||
\(922\) | −3.08948 | − | 2.24464i | −0.101747 | − | 0.0739232i | ||||
\(923\) | −13.5188 | −0.444977 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.43353 | 0.145773 | ||||||||
\(926\) | −1.24481 | − | 0.904405i | −0.0409069 | − | 0.0297206i | ||||
\(927\) | 0.505405 | − | 1.55548i | 0.0165997 | − | 0.0510886i | ||||
\(928\) | 0.542471 | + | 1.66955i | 0.0178075 | + | 0.0548058i | ||||
\(929\) | 8.18928 | − | 5.94986i | 0.268682 | − | 0.195209i | −0.445284 | − | 0.895389i | \(-0.646897\pi\) |
0.713966 | + | 0.700181i | \(0.246897\pi\) | |||||||
\(930\) | 6.11156 | − | 4.44031i | 0.200406 | − | 0.145603i | ||||
\(931\) | −2.33126 | − | 7.17488i | −0.0764039 | − | 0.235147i | ||||
\(932\) | 5.03354 | − | 15.4917i | 0.164879 | − | 0.507446i | ||||
\(933\) | 26.5006 | + | 19.2538i | 0.867592 | + | 0.630343i | ||||
\(934\) | −3.55986 | −0.116482 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.41397 | −0.0789031 | ||||||||
\(937\) | −22.8234 | − | 16.5822i | −0.745608 | − | 0.541716i | 0.148854 | − | 0.988859i | \(-0.452441\pi\) |
−0.894462 | + | 0.447143i | \(0.852441\pi\) | |||||||
\(938\) | −0.0766554 | + | 0.235921i | −0.00250289 | + | 0.00770310i | ||||
\(939\) | −25.2663 | − | 77.7617i | −0.824535 | − | 2.53766i | ||||
\(940\) | 8.54394 | − | 6.20753i | 0.278672 | − | 0.202467i | ||||
\(941\) | −16.3018 | + | 11.8439i | −0.531423 | + | 0.386101i | −0.820890 | − | 0.571087i | \(-0.806522\pi\) |
0.289467 | + | 0.957188i | \(0.406522\pi\) | |||||||
\(942\) | −0.764680 | − | 2.35344i | −0.0249146 | − | 0.0766794i | ||||
\(943\) | −13.8676 | + | 42.6802i | −0.451593 | + | 1.38986i | ||||
\(944\) | 21.0961 | + | 15.3272i | 0.686619 | + | 0.498858i | ||||
\(945\) | 12.9114 | 0.420007 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.125141 | 0.00406653 | 0.00203326 | − | 0.999998i | \(-0.499353\pi\) | ||||
0.00203326 | + | 0.999998i | \(0.499353\pi\) | |||||||
\(948\) | 68.1501 | + | 49.5140i | 2.21341 | + | 1.60814i | ||||
\(949\) | 0.856475 | − | 2.63596i | 0.0278024 | − | 0.0855669i | ||||
\(950\) | 0.810292 | + | 2.49382i | 0.0262894 | + | 0.0809103i | ||||
\(951\) | 56.3267 | − | 40.9237i | 1.82652 | − | 1.32704i | ||||
\(952\) | −2.70039 | + | 1.96195i | −0.0875200 | + | 0.0635870i | ||||
\(953\) | 9.06949 | + | 27.9130i | 0.293790 | + | 0.904192i | 0.983625 | + | 0.180226i | \(0.0576828\pi\) |
−0.689836 | + | 0.723966i | \(0.742317\pi\) | |||||||
\(954\) | 0.663174 | − | 2.04104i | 0.0214711 | − | 0.0660811i | ||||
\(955\) | 28.5642 | + | 20.7531i | 0.924316 | + | 0.671555i | ||||
\(956\) | 20.6166 | 0.666790 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.43717 | −0.111050 | ||||||||
\(959\) | −11.4995 | − | 8.35487i | −0.371338 | − | 0.269793i | ||||
\(960\) | 18.3871 | − | 56.5898i | 0.593442 | − | 1.82643i | ||||
\(961\) | 10.5656 | + | 32.5174i | 0.340824 | + | 1.04895i | ||||
\(962\) | −0.161403 | + | 0.117266i | −0.00520385 | + | 0.00378082i | ||||
\(963\) | 9.60694 | − | 6.97985i | 0.309579 | − | 0.224923i | ||||
\(964\) | −5.03390 | − | 15.4928i | −0.162131 | − | 0.498988i | ||||
\(965\) | −17.9378 | + | 55.2070i | −0.577440 | + | 1.77718i | ||||
\(966\) | −1.30054 | − | 0.944899i | −0.0418443 | − | 0.0304016i | ||||
\(967\) | 51.9463 | 1.67048 | 0.835240 | − | 0.549885i | \(-0.185328\pi\) | ||||
0.835240 | + | 0.549885i | \(0.185328\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 145.295 | 4.66756 | ||||||||
\(970\) | −2.49276 | − | 1.81109i | −0.0800376 | − | 0.0581507i | ||||
\(971\) | −7.72746 | + | 23.7827i | −0.247986 | + | 0.763222i | 0.747145 | + | 0.664661i | \(0.231424\pi\) |
−0.995131 | + | 0.0985614i | \(0.968576\pi\) | |||||||
\(972\) | 10.5991 | + | 32.6208i | 0.339968 | + | 1.04631i | ||||
\(973\) | 7.42631 | − | 5.39553i | 0.238076 | − | 0.172973i | ||||
\(974\) | 0.103048 | − | 0.0748688i | 0.00330187 | − | 0.00239895i | ||||
\(975\) | −2.66677 | − | 8.20747i | −0.0854049 | − | 0.262849i | ||||
\(976\) | 11.8503 | − | 36.4715i | 0.379319 | − | 1.16742i | ||||
\(977\) | 14.0896 | + | 10.2367i | 0.450765 | + | 0.327500i | 0.789898 | − | 0.613239i | \(-0.210134\pi\) |
−0.339133 | + | 0.940738i | \(0.610134\pi\) | |||||||
\(978\) | −2.61611 | −0.0836540 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.57636 | 0.178130 | ||||||||
\(981\) | −14.3863 | − | 10.4523i | −0.459320 | − | 0.333716i | ||||
\(982\) | 0.686174 | − | 2.11183i | 0.0218967 | − | 0.0673911i | ||||
\(983\) | −13.0822 | − | 40.2629i | −0.417258 | − | 1.28419i | −0.910216 | − | 0.414135i | \(-0.864084\pi\) |
0.492958 | − | 0.870053i | \(-0.335916\pi\) | |||||||
\(984\) | 9.98943 | − | 7.25775i | 0.318452 | − | 0.231369i | ||||
\(985\) | −14.2680 | + | 10.3663i | −0.454617 | + | 0.330298i | ||||
\(986\) | −0.317617 | − | 0.977525i | −0.0101150 | − | 0.0311308i | ||||
\(987\) | 1.61984 | − | 4.98536i | 0.0515601 | − | 0.158686i | ||||
\(988\) | 13.0837 | + | 9.50588i | 0.416249 | + | 0.302422i | ||||
\(989\) | 25.2569 | 0.803122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.6263 | 1.76703 | 0.883513 | − | 0.468406i | \(-0.155172\pi\) | ||||
0.883513 | + | 0.468406i | \(0.155172\pi\) | |||||||
\(992\) | −9.34345 | − | 6.78841i | −0.296655 | − | 0.215532i | ||||
\(993\) | −8.09408 | + | 24.9110i | −0.256858 | + | 0.790527i | ||||
\(994\) | 0.465704 | + | 1.43329i | 0.0147712 | + | 0.0454612i | ||||
\(995\) | −15.6073 | + | 11.3393i | −0.494784 | + | 0.359481i | ||||
\(996\) | −9.09666 | + | 6.60911i | −0.288239 | + | 0.209418i | ||||
\(997\) | 5.07614 | + | 15.6228i | 0.160763 | + | 0.494778i | 0.998699 | − | 0.0509905i | \(-0.0162378\pi\) |
−0.837936 | + | 0.545768i | \(0.816238\pi\) | |||||||
\(998\) | −1.18012 | + | 3.63202i | −0.0373559 | + | 0.114970i | ||||
\(999\) | −5.70994 | − | 4.14851i | −0.180654 | − | 0.131253i |
(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 | 847.2.f.z.323.3 | 24 | ||
11.2 | odd | 10 | 847.2.f.y.148.3 | 24 | |||
11.3 | even | 5 | inner | 847.2.f.z.729.3 | 24 | ||
11.4 | even | 5 | inner | 847.2.f.z.372.4 | 24 | ||
11.5 | even | 5 | 847.2.a.m.1.4 | ✓ | 6 | ||
11.6 | odd | 10 | 847.2.a.n.1.3 | yes | 6 | ||
11.7 | odd | 10 | 847.2.f.y.372.3 | 24 | |||
11.8 | odd | 10 | 847.2.f.y.729.4 | 24 | |||
11.9 | even | 5 | inner | 847.2.f.z.148.4 | 24 | ||
11.10 | odd | 2 | 847.2.f.y.323.4 | 24 | |||
33.5 | odd | 10 | 7623.2.a.cs.1.3 | 6 | |||
33.17 | even | 10 | 7623.2.a.cp.1.4 | 6 | |||
77.6 | even | 10 | 5929.2.a.bm.1.3 | 6 | |||
77.27 | odd | 10 | 5929.2.a.bj.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.4 | ✓ | 6 | 11.5 | even | 5 | ||
847.2.a.n.1.3 | yes | 6 | 11.6 | odd | 10 | ||
847.2.f.y.148.3 | 24 | 11.2 | odd | 10 | |||
847.2.f.y.323.4 | 24 | 11.10 | odd | 2 | |||
847.2.f.y.372.3 | 24 | 11.7 | odd | 10 | |||
847.2.f.y.729.4 | 24 | 11.8 | odd | 10 | |||
847.2.f.z.148.4 | 24 | 11.9 | even | 5 | inner | ||
847.2.f.z.323.3 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.z.372.4 | 24 | 11.4 | even | 5 | inner | ||
847.2.f.z.729.3 | 24 | 11.3 | even | 5 | inner | ||
5929.2.a.bj.1.4 | 6 | 77.27 | odd | 10 | |||
5929.2.a.bm.1.3 | 6 | 77.6 | even | 10 | |||
7623.2.a.cp.1.4 | 6 | 33.17 | even | 10 | |||
7623.2.a.cs.1.3 | 6 | 33.5 | odd | 10 |