Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(19,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.j (of order \(18\), degree \(6\), 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(204\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Character | \(\chi\) | \(=\) | 324.19 |
Dual form | 324.3.j.a.307.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91833 | − | 0.565700i | −0.959164 | − | 0.282850i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.35997 | + | 2.17040i | 0.839992 | + | 0.542599i | ||||
\(5\) | 1.66005 | + | 9.41462i | 0.332010 | + | 1.88292i | 0.454962 | + | 0.890511i | \(0.349653\pi\) |
−0.122952 | + | 0.992413i | \(0.539236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.14643 | − | 4.94152i | 0.592347 | − | 0.705932i | −0.383708 | − | 0.923454i | \(-0.625353\pi\) |
0.976055 | + | 0.217523i | \(0.0697976\pi\) | |||||||
\(8\) | −5.21773 | − | 6.06427i | −0.652216 | − | 0.758033i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.14133 | − | 18.9994i | 0.214133 | − | 1.89994i | ||||
\(11\) | 9.17297 | + | 1.61744i | 0.833907 | + | 0.147040i | 0.574270 | − | 0.818666i | \(-0.305286\pi\) |
0.259637 | + | 0.965706i | \(0.416397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.9635 | + | 5.08231i | 1.07412 | + | 0.390947i | 0.817715 | − | 0.575624i | \(-0.195241\pi\) |
0.256402 | + | 0.966570i | \(0.417463\pi\) | |||||||
\(14\) | −10.7496 | + | 7.13382i | −0.767831 | + | 0.509559i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.57875 | + | 14.5849i | 0.411172 | + | 0.911558i | ||||
\(17\) | −2.55788 | − | 4.43037i | −0.150463 | − | 0.260610i | 0.780935 | − | 0.624613i | \(-0.214743\pi\) |
−0.931398 | + | 0.364003i | \(0.881410\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.2181 | − | 5.89945i | −0.537797 | − | 0.310497i | 0.206389 | − | 0.978470i | \(-0.433829\pi\) |
−0.744186 | + | 0.667973i | \(0.767162\pi\) | |||||||
\(20\) | −14.8557 | + | 35.2358i | −0.742787 | + | 1.76179i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −16.6818 | − | 8.29194i | −0.758263 | − | 0.376906i | ||||
\(23\) | 0.496108 | + | 0.591239i | 0.0215699 | + | 0.0257060i | 0.776722 | − | 0.629844i | \(-0.216881\pi\) |
−0.755152 | + | 0.655550i | \(0.772437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −62.3870 | + | 22.7070i | −2.49548 | + | 0.908280i | ||||
\(26\) | −23.9116 | − | 17.6487i | −0.919675 | − | 0.678796i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 24.6569 | − | 7.60395i | 0.880605 | − | 0.271570i | ||||
\(29\) | −11.5797 | + | 4.21465i | −0.399298 | + | 0.145333i | −0.533861 | − | 0.845572i | \(-0.679259\pi\) |
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.5346 | + | 41.1567i | 1.11402 | + | 1.32764i | 0.939331 | + | 0.343013i | \(0.111448\pi\) |
0.174689 | + | 0.984624i | \(0.444108\pi\) | |||||||
\(32\) | −4.36951 | − | 31.7003i | −0.136547 | − | 0.990634i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.40058 | + | 9.94590i | 0.0706054 | + | 0.292526i | ||||
\(35\) | 53.4058 | + | 30.8339i | 1.52588 | + | 0.880968i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8651 | + | 20.5510i | 0.320678 | + | 0.555431i | 0.980628 | − | 0.195878i | \(-0.0627558\pi\) |
−0.659950 | + | 0.751310i | \(0.729422\pi\) | |||||||
\(38\) | 16.2644 | + | 17.0975i | 0.428011 | + | 0.449934i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 48.4311 | − | 59.1899i | 1.21078 | − | 1.47975i | ||||
\(41\) | −14.0864 | − | 5.12705i | −0.343572 | − | 0.125050i | 0.164471 | − | 0.986382i | \(-0.447408\pi\) |
−0.508042 | + | 0.861332i | \(0.669631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 37.1520 | + | 6.55091i | 0.864001 | + | 0.152347i | 0.588049 | − | 0.808825i | \(-0.299896\pi\) |
0.275951 | + | 0.961172i | \(0.411007\pi\) | |||||||
\(44\) | 27.3104 | + | 25.3436i | 0.620691 | + | 0.575990i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.617234 | − | 1.41484i | −0.0134181 | − | 0.0307574i | ||||
\(47\) | −8.14341 | + | 9.70494i | −0.173264 | + | 0.206488i | −0.845687 | − | 0.533679i | \(-0.820809\pi\) |
0.672423 | + | 0.740167i | \(0.265254\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.28300 | + | 7.27625i | 0.0261836 | + | 0.148495i | ||||
\(50\) | 132.524 | − | 8.26716i | 2.65048 | − | 0.165343i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 35.8863 | + | 47.3828i | 0.690122 | + | 0.911207i | ||||
\(53\) | 44.1869 | 0.833715 | 0.416858 | − | 0.908972i | \(-0.363131\pi\) | ||||
0.416858 | + | 0.908972i | \(0.363131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 89.0451i | 1.61900i | ||||||||
\(56\) | −51.6016 | + | 0.638447i | −0.921458 | + | 0.0114008i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.5978 | − | 1.53447i | 0.424100 | − | 0.0264564i | ||||
\(59\) | −24.6079 | + | 4.33904i | −0.417083 | + | 0.0735430i | −0.378252 | − | 0.925703i | \(-0.623475\pi\) |
−0.0388313 | + | 0.999246i | \(0.512363\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −50.4986 | − | 42.3734i | −0.827847 | − | 0.694646i | 0.126949 | − | 0.991909i | \(-0.459482\pi\) |
−0.954795 | + | 0.297263i | \(0.903926\pi\) | |||||||
\(62\) | −42.9663 | − | 98.4884i | −0.693005 | − | 1.58852i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.55069 | + | 63.2834i | −0.149229 | + | 0.988803i | ||||
\(65\) | −24.6678 | + | 139.898i | −0.379505 | + | 2.15228i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.545347 | + | 1.49833i | −0.00813951 | + | 0.0223631i | −0.943696 | − | 0.330814i | \(-0.892677\pi\) |
0.935556 | + | 0.353177i | \(0.114899\pi\) | |||||||
\(68\) | 1.02129 | − | 20.4375i | 0.0150189 | − | 0.300552i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −85.0072 | − | 89.3612i | −1.21439 | − | 1.27659i | ||||
\(71\) | 6.96921 | − | 4.02368i | 0.0981579 | − | 0.0566715i | −0.450117 | − | 0.892969i | \(-0.648618\pi\) |
0.548275 | + | 0.836298i | \(0.315285\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0385 | + | 19.1193i | −0.151213 | + | 0.261908i | −0.931674 | − | 0.363296i | \(-0.881651\pi\) |
0.780461 | + | 0.625205i | \(0.214985\pi\) | |||||||
\(74\) | −11.1355 | − | 46.1356i | −0.150479 | − | 0.623454i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.5285 | − | 41.9994i | −0.283269 | − | 0.552623i | ||||
\(77\) | 46.0277 | − | 38.6218i | 0.597762 | − | 0.501582i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −35.5509 | − | 97.6752i | −0.450011 | − | 1.23639i | −0.932716 | − | 0.360612i | \(-0.882568\pi\) |
0.482705 | − | 0.875783i | \(-0.339654\pi\) | |||||||
\(80\) | −126.390 | + | 86.1482i | −1.57988 | + | 1.07685i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 24.1221 | + | 17.8041i | 0.294171 | + | 0.217123i | ||||
\(83\) | 3.74244 | + | 10.2823i | 0.0450896 | + | 0.123883i | 0.960194 | − | 0.279335i | \(-0.0901140\pi\) |
−0.915104 | + | 0.403218i | \(0.867892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37.4640 | − | 31.4361i | 0.440754 | − | 0.369836i | ||||
\(86\) | −67.5639 | − | 33.5837i | −0.785627 | − | 0.390508i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −38.0535 | − | 64.0667i | −0.432426 | − | 0.728031i | ||||
\(89\) | −59.2666 | + | 102.653i | −0.665916 | + | 1.15340i | 0.313119 | + | 0.949714i | \(0.398626\pi\) |
−0.979036 | + | 0.203687i | \(0.934707\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 83.0131 | − | 47.9276i | 0.912232 | − | 0.526677i | ||||
\(92\) | 0.383684 | + | 3.06329i | 0.00417048 | + | 0.0332967i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 21.1118 | − | 14.0105i | 0.224594 | − | 0.149048i | ||||
\(95\) | 38.5784 | − | 105.993i | 0.406088 | − | 1.11572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.45300 | + | 36.5968i | −0.0665257 | + | 0.377286i | 0.933308 | + | 0.359076i | \(0.116908\pi\) |
−0.999834 | + | 0.0182105i | \(0.994203\pi\) | |||||||
\(98\) | 1.65496 | − | 14.6840i | 0.0168874 | − | 0.149837i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −258.901 | − | 59.1097i | −2.58901 | − | 0.591097i | ||||
\(101\) | 116.941 | + | 98.1248i | 1.15783 | + | 0.971533i | 0.999873 | − | 0.0159135i | \(-0.00506564\pi\) |
0.157954 | + | 0.987446i | \(0.449510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −111.688 | + | 19.6935i | −1.08435 | + | 0.191199i | −0.687136 | − | 0.726528i | \(-0.741133\pi\) |
−0.397210 | + | 0.917728i | \(0.630021\pi\) | |||||||
\(104\) | −42.0374 | − | 111.197i | −0.404205 | − | 1.06920i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −84.7650 | − | 24.9965i | −0.799670 | − | 0.235816i | ||||
\(107\) | − | 187.221i | − | 1.74973i | −0.484368 | − | 0.874864i | \(-0.660951\pi\) | ||
0.484368 | − | 0.874864i | \(-0.339049\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 73.3509 | 0.672944 | 0.336472 | − | 0.941693i | \(-0.390766\pi\) | ||||
0.336472 | + | 0.941693i | \(0.390766\pi\) | |||||||
\(110\) | 50.3728 | − | 170.818i | 0.457935 | − | 1.55289i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 99.3500 | + | 27.9663i | 0.887054 | + | 0.249699i | ||||
\(113\) | −0.634025 | − | 3.59573i | −0.00561084 | − | 0.0318207i | 0.981874 | − | 0.189536i | \(-0.0606983\pi\) |
−0.987485 | + | 0.157715i | \(0.949587\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.74272 | + | 5.65216i | −0.0412411 | + | 0.0491492i | ||||
\(116\) | −48.0547 | − | 10.9714i | −0.414265 | − | 0.0945807i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 49.6606 | + | 5.59699i | 0.420853 | + | 0.0474321i | ||||
\(119\) | −32.4988 | − | 5.73042i | −0.273099 | − | 0.0481548i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −32.1755 | − | 11.7109i | −0.265913 | − | 0.0967844i | ||||
\(122\) | 72.9023 | + | 109.853i | 0.597560 | + | 0.900436i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 26.7087 | + | 213.239i | 0.215392 | + | 1.71967i | ||||
\(125\) | −197.845 | − | 342.678i | −1.58276 | − | 2.74142i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 74.4569 | + | 42.9877i | 0.586274 | + | 0.338486i | 0.763623 | − | 0.645662i | \(-0.223419\pi\) |
−0.177349 | + | 0.984148i | \(0.556752\pi\) | |||||||
\(128\) | 54.1208 | − | 115.995i | 0.422818 | − | 0.906214i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 126.461 | − | 254.416i | 0.972780 | − | 1.95705i | ||||
\(131\) | −26.9506 | − | 32.1185i | −0.205730 | − | 0.245179i | 0.653307 | − | 0.757093i | \(-0.273381\pi\) |
−0.859037 | + | 0.511914i | \(0.828937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −71.5210 | + | 26.0315i | −0.537752 | + | 0.195726i | ||||
\(134\) | 1.89376 | − | 2.56578i | 0.0141325 | − | 0.0191476i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.5207 | + | 38.6281i | −0.0994166 | + | 0.284030i | ||||
\(137\) | 164.469 | − | 59.8617i | 1.20050 | − | 0.436947i | 0.337102 | − | 0.941468i | \(-0.390553\pi\) |
0.863399 | + | 0.504521i | \(0.168331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −162.043 | − | 193.116i | −1.16578 | − | 1.38932i | −0.905799 | − | 0.423707i | \(-0.860729\pi\) |
−0.259980 | − | 0.965614i | \(-0.583716\pi\) | |||||||
\(140\) | 112.520 | + | 219.513i | 0.803715 | + | 1.56795i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.6454 | + | 3.77625i | −0.110179 | + | 0.0265933i | ||||
\(143\) | 119.867 | + | 69.2051i | 0.838229 | + | 0.483951i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −58.9021 | − | 102.021i | −0.406222 | − | 0.703596i | ||||
\(146\) | 31.9914 | − | 30.4326i | 0.219119 | − | 0.208443i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.73739 | + | 94.8025i | −0.0320094 | + | 0.640557i | ||||
\(149\) | −22.1608 | − | 8.06587i | −0.148730 | − | 0.0541333i | 0.266582 | − | 0.963812i | \(-0.414106\pi\) |
−0.415313 | + | 0.909679i | \(0.636328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −137.784 | − | 24.2951i | −0.912480 | − | 0.160895i | −0.302351 | − | 0.953197i | \(-0.597771\pi\) |
−0.610129 | + | 0.792302i | \(0.708882\pi\) | |||||||
\(152\) | 17.5396 | + | 92.7472i | 0.115392 | + | 0.610179i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −110.145 | + | 48.0515i | −0.715225 | + | 0.312023i | ||||
\(155\) | −330.146 | + | 393.452i | −2.12997 | + | 2.53840i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 27.2412 | + | 154.492i | 0.173511 | + | 0.984028i | 0.939849 | + | 0.341591i | \(0.110966\pi\) |
−0.766338 | + | 0.642437i | \(0.777923\pi\) | |||||||
\(158\) | 12.9434 | + | 207.484i | 0.0819200 | + | 1.31319i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 291.192 | − | 93.7614i | 1.81995 | − | 0.586009i | ||||
\(161\) | 4.97870 | 0.0309236 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 61.6254i | 0.378070i | 0.981970 | + | 0.189035i | \(0.0605359\pi\) | ||||
−0.981970 | + | 0.189035i | \(0.939464\pi\) | |||||||
\(164\) | −36.2023 | − | 47.7999i | −0.220746 | − | 0.291463i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.36255 | − | 21.8418i | −0.00820811 | − | 0.131577i | ||||
\(167\) | 164.986 | − | 29.0915i | 0.987940 | − | 0.174200i | 0.343746 | − | 0.939063i | \(-0.388304\pi\) |
0.644194 | + | 0.764862i | \(0.277193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 39.6886 | + | 33.3027i | 0.234844 | + | 0.197057i | ||||
\(170\) | −89.6517 | + | 39.1113i | −0.527363 | + | 0.230066i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 110.612 | + | 102.645i | 0.643090 | + | 0.596776i | ||||
\(173\) | 25.9331 | − | 147.074i | 0.149902 | − | 0.850138i | −0.813397 | − | 0.581709i | \(-0.802384\pi\) |
0.963299 | − | 0.268429i | \(-0.0865046\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −146.476 | + | 402.439i | −0.837005 | + | 2.29965i | ||||
\(176\) | 36.7564 | + | 144.428i | 0.208843 | + | 0.820613i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 171.763 | − | 163.394i | 0.964963 | − | 0.917947i | ||||
\(179\) | 30.5538 | − | 17.6403i | 0.170692 | − | 0.0985490i | −0.412220 | − | 0.911084i | \(-0.635247\pi\) |
0.582912 | + | 0.812535i | \(0.301913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 35.0639 | − | 60.7325i | 0.193723 | − | 0.335539i | −0.752758 | − | 0.658298i | \(-0.771277\pi\) |
0.946481 | + | 0.322759i | \(0.104610\pi\) | |||||||
\(182\) | −186.359 | + | 44.9804i | −1.02395 | + | 0.247145i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.996874 | − | 6.09345i | 0.00541779 | − | 0.0331166i | ||||
\(185\) | −173.783 | + | 145.821i | −0.939366 | + | 0.788222i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.2975 | − | 44.7769i | −0.0871522 | − | 0.239449i | ||||
\(188\) | −48.4252 | + | 14.9338i | −0.257581 | + | 0.0794353i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −133.966 | + | 181.506i | −0.705086 | + | 0.955295i | ||||
\(191\) | −105.068 | − | 288.671i | −0.550092 | − | 1.51137i | −0.833585 | − | 0.552391i | \(-0.813716\pi\) |
0.283493 | − | 0.958974i | \(-0.408507\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 129.962 | − | 109.051i | 0.673379 | − | 0.565032i | −0.240685 | − | 0.970603i | \(-0.577372\pi\) |
0.914063 | + | 0.405572i | \(0.132928\pi\) | |||||||
\(194\) | 33.0818 | − | 66.5541i | 0.170525 | − | 0.343063i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.4815 | + | 27.2326i | −0.0585791 | + | 0.138942i | ||||
\(197\) | 77.3014 | − | 133.890i | 0.392393 | − | 0.679644i | −0.600372 | − | 0.799721i | \(-0.704981\pi\) |
0.992765 | + | 0.120077i | \(0.0383141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 183.949 | − | 106.203i | 0.924364 | − | 0.533682i | 0.0393397 | − | 0.999226i | \(-0.487475\pi\) |
0.885025 | + | 0.465544i | \(0.154141\pi\) | |||||||
\(200\) | 463.219 | + | 259.852i | 2.31610 | + | 1.29926i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −168.821 | − | 254.389i | −0.835749 | − | 1.25935i | ||||
\(203\) | −27.1874 | + | 74.6969i | −0.133928 | + | 0.367965i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.8850 | − | 141.130i | 0.121390 | − | 0.688437i | ||||
\(206\) | 225.394 | + | 25.4030i | 1.09415 | + | 0.123316i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.7375 | + | 237.092i | 0.0852765 | + | 1.13987i | ||||
\(209\) | −84.1887 | − | 70.6427i | −0.402817 | − | 0.338003i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 302.621 | − | 53.3602i | 1.43422 | − | 0.252892i | 0.598094 | − | 0.801426i | \(-0.295925\pi\) |
0.836128 | + | 0.548534i | \(0.184814\pi\) | |||||||
\(212\) | 148.467 | + | 95.9031i | 0.700314 | + | 0.452373i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −105.911 | + | 359.151i | −0.494911 | + | 1.67828i | ||||
\(215\) | 360.647i | 1.67743i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 346.572 | 1.59711 | ||||||||
\(218\) | −140.711 | − | 41.4946i | −0.645464 | − | 0.190342i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −193.263 | + | 299.189i | −0.878469 | + | 1.35995i | ||||
\(221\) | −13.2005 | − | 74.8635i | −0.0597306 | − | 0.338749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 266.463 | − | 317.558i | 1.19490 | − | 1.42403i | 0.314851 | − | 0.949141i | \(-0.398045\pi\) |
0.880048 | − | 0.474884i | \(-0.157510\pi\) | |||||||
\(224\) | −174.765 | − | 109.851i | −0.780203 | − | 0.490406i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.817839 | + | 7.25647i | −0.00361876 | + | 0.0321083i | ||||
\(227\) | 342.743 | + | 60.4349i | 1.50988 | + | 0.266233i | 0.866448 | − | 0.499268i | \(-0.166398\pi\) |
0.643435 | + | 0.765501i | \(0.277509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −155.459 | − | 56.5825i | −0.678861 | − | 0.247085i | −0.0205025 | − | 0.999790i | \(-0.506527\pi\) |
−0.658358 | + | 0.752705i | \(0.728749\pi\) | |||||||
\(230\) | 12.2955 | − | 8.15973i | 0.0534588 | − | 0.0354771i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 85.9782 | + | 48.2312i | 0.370596 | + | 0.207893i | ||||
\(233\) | 141.020 | + | 244.253i | 0.605234 | + | 1.04830i | 0.992014 | + | 0.126125i | \(0.0402539\pi\) |
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −104.887 | − | 60.5564i | −0.446327 | − | 0.257687i | ||||
\(236\) | −92.0991 | − | 38.8299i | −0.390251 | − | 0.164533i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 59.1017 | + | 29.3774i | 0.248327 | + | 0.123435i | ||||
\(239\) | −229.840 | − | 273.912i | −0.961672 | − | 1.14608i | −0.989217 | − | 0.146455i | \(-0.953214\pi\) |
0.0275453 | − | 0.999621i | \(-0.491231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 213.563 | − | 77.7307i | 0.886154 | − | 0.322534i | 0.141464 | − | 0.989943i | \(-0.454819\pi\) |
0.744691 | + | 0.667410i | \(0.232597\pi\) | |||||||
\(242\) | 55.0983 | + | 40.6671i | 0.227679 | + | 0.168046i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −77.7067 | − | 251.975i | −0.318470 | − | 1.03269i | ||||
\(245\) | −66.3732 | + | 24.1579i | −0.270911 | + | 0.0986036i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −112.698 | − | 134.309i | −0.456269 | − | 0.543760i | ||||
\(248\) | 69.3934 | − | 424.172i | 0.279812 | − | 1.71037i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 185.679 | + | 769.289i | 0.742716 | + | 3.07716i | ||||
\(251\) | 102.959 | + | 59.4435i | 0.410196 | + | 0.236827i | 0.690874 | − | 0.722975i | \(-0.257226\pi\) |
−0.280678 | + | 0.959802i | \(0.590559\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.59449 | + | 6.22584i | 0.0142075 | + | 0.0246081i | ||||
\(254\) | −118.515 | − | 124.585i | −0.466593 | − | 0.490491i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −169.440 | + | 191.901i | −0.661875 | + | 0.749614i | ||||
\(257\) | −73.6502 | − | 26.8065i | −0.286577 | − | 0.104305i | 0.194732 | − | 0.980856i | \(-0.437616\pi\) |
−0.481309 | + | 0.876551i | \(0.659838\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 150.751 | + | 26.5814i | 0.582049 | + | 0.102631i | ||||
\(260\) | −386.517 | + | 416.514i | −1.48661 | + | 1.60198i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 33.5307 | + | 76.8598i | 0.127980 | + | 0.293358i | ||||
\(263\) | −27.2928 | + | 32.5263i | −0.103775 | + | 0.123674i | −0.815432 | − | 0.578853i | \(-0.803501\pi\) |
0.711657 | + | 0.702527i | \(0.247945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 73.3525 | + | 416.003i | 0.276802 | + | 1.56982i | ||||
\(266\) | 151.927 | − | 9.47756i | 0.571154 | − | 0.0356299i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.08432 | + | 3.85072i | −0.0189713 | + | 0.0143683i | ||||
\(269\) | 120.901 | 0.449446 | 0.224723 | − | 0.974423i | \(-0.427852\pi\) | ||||
0.224723 | + | 0.974423i | \(0.427852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 167.365i | 0.617583i | 0.951130 | + | 0.308791i | \(0.0999245\pi\) | ||||
−0.951130 | + | 0.308791i | \(0.900076\pi\) | |||||||
\(272\) | 47.7890 | − | 66.4527i | 0.175695 | − | 0.244312i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −349.369 | + | 21.7944i | −1.27507 | + | 0.0795418i | ||||
\(275\) | −609.001 | + | 107.383i | −2.21455 | + | 0.390485i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −263.128 | − | 220.791i | −0.949921 | − | 0.797079i | 0.0293630 | − | 0.999569i | \(-0.490652\pi\) |
−0.979284 | + | 0.202490i | \(0.935097\pi\) | |||||||
\(278\) | 201.607 | + | 462.127i | 0.725204 | + | 1.66233i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −91.6721 | − | 484.750i | −0.327400 | − | 1.73125i | ||||
\(281\) | −14.0638 | + | 79.7600i | −0.0500493 | + | 0.283843i | −0.999552 | − | 0.0299138i | \(-0.990477\pi\) |
0.949503 | + | 0.313757i | \(0.101588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.57602 | − | 12.5725i | 0.0161697 | − | 0.0444259i | −0.931345 | − | 0.364138i | \(-0.881364\pi\) |
0.947515 | + | 0.319712i | \(0.103586\pi\) | |||||||
\(284\) | 32.1493 | + | 1.60654i | 0.113202 | + | 0.00565683i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −190.794 | − | 200.567i | −0.667113 | − | 0.701282i | ||||
\(287\) | −83.7439 | + | 48.3495i | −0.291790 | + | 0.168465i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 131.415 | − | 227.617i | 0.454722 | − | 0.787601i | ||||
\(290\) | 55.2801 | + | 229.032i | 0.190621 | + | 0.789764i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −78.5857 | + | 40.2823i | −0.269129 | + | 0.137953i | ||||
\(293\) | −200.462 | + | 168.207i | −0.684169 | + | 0.574086i | −0.917221 | − | 0.398378i | \(-0.869573\pi\) |
0.233052 | + | 0.972464i | \(0.425129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −81.7007 | − | 224.471i | −0.276952 | − | 0.760918i | ||||
\(296\) | 62.7177 | − | 179.182i | 0.211884 | − | 0.605346i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 37.9488 | + | 28.0093i | 0.127345 | + | 0.0939911i | ||||
\(299\) | 3.92256 | + | 10.7771i | 0.0131189 | + | 0.0360440i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 186.420 | − | 156.425i | 0.619334 | − | 0.519683i | ||||
\(302\) | 250.572 | + | 124.551i | 0.829709 | + | 0.412420i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.8204 | − | 187.842i | 0.0619091 | − | 0.617901i | ||||
\(305\) | 315.099 | − | 545.767i | 1.03311 | − | 1.78940i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −219.994 | + | 127.014i | −0.716594 | + | 0.413726i | −0.813498 | − | 0.581568i | \(-0.802439\pi\) |
0.0969039 | + | 0.995294i | \(0.469106\pi\) | |||||||
\(308\) | 238.476 | − | 29.8697i | 0.774274 | − | 0.0969795i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 855.904 | − | 568.007i | 2.76098 | − | 1.83228i | ||||
\(311\) | 55.4547 | − | 152.361i | 0.178311 | − | 0.489905i | −0.818049 | − | 0.575148i | \(-0.804944\pi\) |
0.996360 | + | 0.0852429i | \(0.0271666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −40.4452 | + | 229.376i | −0.129218 | + | 0.732832i | 0.849495 | + | 0.527597i | \(0.176907\pi\) |
−0.978713 | + | 0.205235i | \(0.934204\pi\) | |||||||
\(314\) | 35.1388 | − | 311.777i | 0.111907 | − | 0.992922i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 92.5442 | − | 405.345i | 0.292862 | − | 1.28274i | ||||
\(317\) | −333.357 | − | 279.720i | −1.05160 | − | 0.882397i | −0.0583393 | − | 0.998297i | \(-0.518581\pi\) |
−0.993261 | + | 0.115899i | \(0.963025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −113.037 | + | 19.9314i | −0.354347 | + | 0.0624810i | ||||
\(320\) | −611.643 | + | 15.1376i | −1.91139 | + | 0.0473049i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.55077 | − | 2.81645i | −0.0296608 | − | 0.00874674i | ||||
\(323\) | 60.3602i | 0.186874i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −986.545 | −3.03552 | ||||||||
\(326\) | 34.8615 | − | 118.218i | 0.106937 | − | 0.362631i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 42.4074 | + | 112.176i | 0.129291 | + | 0.341999i | ||||
\(329\) | 14.1911 | + | 80.4817i | 0.0431340 | + | 0.244625i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −158.081 | + | 188.393i | −0.477585 | + | 0.569164i | −0.950015 | − | 0.312204i | \(-0.898933\pi\) |
0.472430 | + | 0.881368i | \(0.343377\pi\) | |||||||
\(332\) | −9.74212 | + | 42.6706i | −0.0293437 | + | 0.128526i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −332.954 | − | 37.5256i | −0.996869 | − | 0.112352i | ||||
\(335\) | −15.0115 | − | 2.64693i | −0.0448104 | − | 0.00790129i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 155.225 | + | 56.4972i | 0.460607 | + | 0.167647i | 0.561893 | − | 0.827210i | \(-0.310073\pi\) |
−0.101285 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(338\) | −57.2964 | − | 86.3373i | −0.169516 | − | 0.255436i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 194.107 | − | 24.3123i | 0.570902 | − | 0.0715067i | ||||
\(341\) | 250.216 | + | 433.387i | 0.733772 | + | 1.27093i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 315.013 | + | 181.873i | 0.918404 | + | 0.530241i | ||||
\(344\) | −154.123 | − | 259.481i | −0.448031 | − | 0.754304i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −132.948 | + | 267.466i | −0.384243 | + | 0.773022i | ||||
\(347\) | −94.9627 | − | 113.172i | −0.273668 | − | 0.326145i | 0.611652 | − | 0.791127i | \(-0.290505\pi\) |
−0.885320 | + | 0.464982i | \(0.846061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −195.978 | + | 71.3303i | −0.561542 | + | 0.204385i | −0.607167 | − | 0.794574i | \(-0.707694\pi\) |
0.0456250 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(350\) | 508.649 | − | 689.149i | 1.45328 | − | 1.96900i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.1919 | − | 297.853i | 0.0317953 | − | 0.846174i | ||||
\(353\) | 192.471 | − | 70.0538i | 0.545244 | − | 0.198453i | −0.0546879 | − | 0.998503i | \(-0.517416\pi\) |
0.599932 | + | 0.800051i | \(0.295194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.4506 | + | 58.9330i | 0.139298 | + | 0.166008i | ||||
\(356\) | −421.931 | + | 216.278i | −1.18520 | + | 0.607522i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −68.5914 | + | 16.5555i | −0.191596 | + | 0.0462445i | ||||
\(359\) | −311.659 | − | 179.936i | −0.868130 | − | 0.501215i | −0.00140384 | − | 0.999999i | \(-0.500447\pi\) |
−0.866726 | + | 0.498784i | \(0.833780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −110.893 | − | 192.072i | −0.307183 | − | 0.532057i | ||||
\(362\) | −101.621 | + | 96.6693i | −0.280720 | + | 0.267042i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 382.943 | + | 19.1361i | 1.05204 | + | 0.0525718i | ||||
\(365\) | −198.326 | − | 72.1846i | −0.543358 | − | 0.197766i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −519.619 | − | 91.6229i | −1.41586 | − | 0.249654i | −0.587214 | − | 0.809432i | \(-0.699775\pi\) |
−0.828642 | + | 0.559778i | \(0.810886\pi\) | |||||||
\(368\) | −5.35940 | + | 11.1253i | −0.0145636 | + | 0.0302318i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 415.863 | − | 181.424i | 1.12395 | − | 0.490334i | ||||
\(371\) | 183.218 | − | 218.351i | 0.493849 | − | 0.588546i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 58.2221 | + | 330.194i | 0.156091 | + | 0.885238i | 0.957781 | + | 0.287498i | \(0.0928234\pi\) |
−0.801690 | + | 0.597740i | \(0.796065\pi\) | |||||||
\(374\) | 5.93358 | + | 95.1163i | 0.0158652 | + | 0.254322i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 101.343 | − | 1.25388i | 0.269530 | − | 0.00333479i | ||||
\(377\) | −183.113 | −0.485711 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 471.750i | − | 1.24472i | −0.782730 | − | 0.622362i | \(-0.786173\pi\) | ||
0.782730 | − | 0.622362i | \(-0.213827\pi\) | |||||||
\(380\) | 359.670 | − | 272.403i | 0.946499 | − | 0.716851i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 38.2530 | + | 613.202i | 0.100139 | + | 1.60524i | ||||
\(383\) | 692.255 | − | 122.063i | 1.80745 | − | 0.318703i | 0.834728 | − | 0.550662i | \(-0.185625\pi\) |
0.972725 | + | 0.231959i | \(0.0745136\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 440.018 | + | 369.219i | 1.14290 | + | 0.959011i | ||||
\(386\) | −311.000 | + | 135.676i | −0.805700 | + | 0.351493i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −101.111 | + | 108.958i | −0.260596 | + | 0.280820i | ||||
\(389\) | −34.0255 | + | 192.968i | −0.0874691 | + | 0.496062i | 0.909327 | + | 0.416082i | \(0.136597\pi\) |
−0.996796 | + | 0.0799805i | \(0.974514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.35042 | − | 3.71026i | 0.00345377 | − | 0.00948915i | ||||
\(392\) | 37.4308 | − | 45.7459i | 0.0954867 | − | 0.116699i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −224.031 | + | 213.115i | −0.568606 | + | 0.540902i | ||||
\(395\) | 860.558 | − | 496.844i | 2.17863 | − | 1.25783i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 213.100 | − | 369.100i | 0.536775 | − | 0.929722i | −0.462300 | − | 0.886724i | \(-0.652976\pi\) |
0.999075 | − | 0.0429986i | \(-0.0136911\pi\) | |||||||
\(398\) | −412.953 | + | 99.6720i | −1.03757 | + | 0.250432i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −741.608 | − | 760.525i | −1.85402 | − | 1.90131i | ||||
\(401\) | 29.6819 | − | 24.9061i | 0.0740198 | − | 0.0621100i | −0.605027 | − | 0.796205i | \(-0.706838\pi\) |
0.679047 | + | 0.734095i | \(0.262393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 273.054 | + | 750.208i | 0.677552 | + | 1.86156i | ||||
\(404\) | 179.947 | + | 583.504i | 0.445413 | + | 1.44432i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 94.4104 | − | 127.913i | 0.232538 | − | 0.315057i | ||||
\(407\) | 75.5983 | + | 207.704i | 0.185745 | + | 0.510330i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −155.781 | + | 130.715i | −0.380882 | + | 0.319598i | −0.813048 | − | 0.582196i | \(-0.802194\pi\) |
0.432167 | + | 0.901794i | \(0.357749\pi\) | |||||||
\(410\) | −127.575 | + | 256.656i | −0.311158 | + | 0.625989i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −418.010 | − | 176.237i | −1.01459 | − | 0.427759i | ||||
\(413\) | −80.5934 | + | 139.592i | −0.195141 | + | 0.337995i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −90.5909 | + | 52.3027i | −0.218291 | + | 0.126031i | ||||
\(416\) | 100.097 | − | 464.855i | 0.240617 | − | 1.11744i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 121.539 | + | 183.141i | 0.290763 | + | 0.438138i | ||||
\(419\) | −44.1415 | + | 121.278i | −0.105350 | + | 0.289445i | −0.981156 | − | 0.193217i | \(-0.938108\pi\) |
0.875807 | + | 0.482662i | \(0.160330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.2736 | + | 166.019i | −0.0695335 | + | 0.394344i | 0.930101 | + | 0.367304i | \(0.119719\pi\) |
−0.999634 | + | 0.0270398i | \(0.991392\pi\) | |||||||
\(422\) | −610.712 | − | 68.8302i | −1.44718 | − | 0.163105i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −230.555 | − | 267.961i | −0.543762 | − | 0.631984i | ||||
\(425\) | 260.178 | + | 218.316i | 0.612185 | + | 0.513684i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −418.778 | + | 73.8419i | −0.980745 | + | 0.172932i | ||||
\(428\) | 406.344 | − | 629.056i | 0.949401 | − | 1.46976i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 204.018 | − | 691.839i | 0.474461 | − | 1.60893i | ||||
\(431\) | − | 80.4167i | − | 0.186582i | −0.995639 | − | 0.0932909i | \(-0.970261\pi\) | ||
0.995639 | − | 0.0932909i | \(-0.0297387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 794.373 | 1.83458 | 0.917289 | − | 0.398221i | \(-0.130372\pi\) | ||||
0.917289 | + | 0.398221i | \(0.130372\pi\) | |||||||
\(434\) | −664.839 | − | 196.056i | −1.53189 | − | 0.451742i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 246.457 | + | 159.201i | 0.565267 | + | 0.365139i | ||||
\(437\) | −1.58132 | − | 8.96812i | −0.00361859 | − | 0.0205220i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −102.084 | + | 121.659i | −0.232537 | + | 0.277127i | −0.869677 | − | 0.493621i | \(-0.835673\pi\) |
0.637140 | + | 0.770748i | \(0.280117\pi\) | |||||||
\(440\) | 539.993 | − | 464.613i | 1.22726 | − | 1.05594i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.0275 | + | 151.080i | −0.0385237 | + | 0.341811i | ||||
\(443\) | 293.648 | + | 51.7781i | 0.662863 | + | 0.116881i | 0.494950 | − | 0.868921i | \(-0.335186\pi\) |
0.167913 | + | 0.985802i | \(0.446297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1064.82 | − | 387.563i | −2.39286 | − | 0.870929i | ||||
\(446\) | −690.805 | + | 458.442i | −1.54889 | + | 1.02790i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 273.115 | + | 309.595i | 0.609631 | + | 0.691060i | ||||
\(449\) | 357.658 | + | 619.482i | 0.796566 | + | 1.37969i | 0.921840 | + | 0.387571i | \(0.126686\pi\) |
−0.125274 | + | 0.992122i | \(0.539981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −120.922 | − | 69.8143i | −0.268120 | − | 0.154799i | ||||
\(452\) | 5.67387 | − | 13.4576i | 0.0125528 | − | 0.0297735i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −623.306 | − | 309.824i | −1.37292 | − | 0.682431i | ||||
\(455\) | 589.026 | + | 701.974i | 1.29456 | + | 1.54280i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 325.010 | − | 118.294i | 0.711182 | − | 0.258849i | 0.0390042 | − | 0.999239i | \(-0.487581\pi\) |
0.672177 | + | 0.740390i | \(0.265359\pi\) | |||||||
\(458\) | 266.213 | + | 196.487i | 0.581251 | + | 0.429011i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −28.2028 | + | 8.69746i | −0.0613105 | + | 0.0189075i | ||||
\(461\) | 97.9219 | − | 35.6407i | 0.212412 | − | 0.0773116i | −0.233623 | − | 0.972327i | \(-0.575058\pi\) |
0.446035 | + | 0.895016i | \(0.352836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −124.607 | − | 148.501i | −0.269130 | − | 0.320736i | 0.614505 | − | 0.788913i | \(-0.289356\pi\) |
−0.883635 | + | 0.468176i | \(0.844911\pi\) | |||||||
\(464\) | −137.650 | − | 141.161i | −0.296660 | − | 0.304227i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −132.348 | − | 548.332i | −0.284008 | − | 1.17668i | ||||
\(467\) | −486.781 | − | 281.043i | −1.04236 | − | 0.601806i | −0.121858 | − | 0.992548i | \(-0.538885\pi\) |
−0.920500 | + | 0.390742i | \(0.872218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.14278 | + | 8.90756i | 0.0109654 | + | 0.0189927i | ||||
\(470\) | 166.951 | + | 175.502i | 0.355214 | + | 0.373408i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 154.710 | + | 126.589i | 0.327776 | + | 0.268197i | ||||
\(473\) | 330.199 | + | 120.183i | 0.698095 | + | 0.254086i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 771.437 | + | 136.025i | 1.62408 | + | 0.286369i | ||||
\(476\) | −96.7577 | − | 89.7894i | −0.203272 | − | 0.188633i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 285.956 | + | 655.474i | 0.598234 | + | 1.37128i | ||||
\(479\) | −256.804 | + | 306.047i | −0.536125 | + | 0.638929i | −0.964314 | − | 0.264760i | \(-0.914707\pi\) |
0.428189 | + | 0.903689i | \(0.359152\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 61.2323 | + | 347.266i | 0.127302 | + | 0.721966i | ||||
\(482\) | −453.657 | + | 28.3002i | −0.941196 | + | 0.0587141i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −82.6912 | − | 109.182i | −0.170850 | − | 0.225582i | ||||
\(485\) | −355.257 | −0.732488 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 213.387i | − | 0.438167i | −0.975706 | − | 0.219083i | \(-0.929693\pi\) | ||
0.975706 | − | 0.219083i | \(-0.0703067\pi\) | |||||||
\(488\) | 6.52445 | + | 527.330i | 0.0133698 | + | 1.08059i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 140.992 | − | 8.79540i | 0.287738 | − | 0.0179498i | ||||
\(491\) | 279.504 | − | 49.2840i | 0.569254 | − | 0.100375i | 0.118389 | − | 0.992967i | \(-0.462227\pi\) |
0.450865 | + | 0.892592i | \(0.351116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.2918 | + | 40.5216i | 0.0979549 | + | 0.0821939i | ||||
\(494\) | 140.214 | + | 321.402i | 0.283834 | + | 0.650611i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −373.073 | + | 774.445i | −0.752164 | + | 1.56138i | ||||
\(497\) | 9.01426 | − | 51.1224i | 0.0181373 | − | 0.102862i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 54.6097 | − | 150.039i | 0.109438 | − | 0.300679i | −0.872869 | − | 0.487954i | \(-0.837743\pi\) |
0.982308 | + | 0.187275i | \(0.0599655\pi\) | |||||||
\(500\) | 78.9938 | − | 1580.79i | 0.157988 | − | 3.16158i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −163.882 | − | 172.276i | −0.326459 | − | 0.343180i | ||||
\(503\) | −793.165 | + | 457.934i | −1.57687 | + | 0.910405i | −0.581575 | + | 0.813493i | \(0.697563\pi\) |
−0.995293 | + | 0.0969126i | \(0.969103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −729.680 | + | 1263.84i | −1.44491 | + | 2.50266i | ||||
\(506\) | −3.37346 | − | 13.9766i | −0.00666691 | − | 0.0276218i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 156.872 | + | 306.038i | 0.308804 | + | 0.602437i | ||||
\(509\) | 664.450 | − | 557.540i | 1.30540 | − | 1.09536i | 0.316218 | − | 0.948687i | \(-0.397587\pi\) |
0.989185 | − | 0.146676i | \(-0.0468575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.7080 | + | 133.824i | 0.0953190 | + | 0.261887i | ||||
\(512\) | 433.600 | − | 272.277i | 0.846875 | − | 0.531792i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 126.121 | + | 93.0876i | 0.245371 | + | 0.181104i | ||||
\(515\) | −370.814 | − | 1018.80i | −0.720028 | − | 1.97826i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −90.3965 | + | 75.8517i | −0.174848 | + | 0.146715i | ||||
\(518\) | −274.152 | − | 136.272i | −0.529252 | − | 0.263073i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 977.089 | − | 580.358i | 1.87902 | − | 1.11607i | ||||
\(521\) | −467.837 | + | 810.317i | −0.897959 | + | 1.55531i | −0.0678599 | + | 0.997695i | \(0.521617\pi\) |
−0.830099 | + | 0.557616i | \(0.811716\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −74.4213 | + | 42.9672i | −0.142297 | + | 0.0821552i | −0.569458 | − | 0.822020i | \(-0.692847\pi\) |
0.427161 | + | 0.904175i | \(0.359514\pi\) | |||||||
\(524\) | −20.8433 | − | 166.411i | −0.0397773 | − | 0.317577i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 70.7566 | − | 46.9565i | 0.134518 | − | 0.0892710i | ||||
\(527\) | 94.0044 | − | 258.275i | 0.178376 | − | 0.490085i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 91.7564 | − | 520.377i | 0.173453 | − | 0.983699i | ||||
\(530\) | 94.6186 | − | 839.526i | 0.178526 | − | 1.58401i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −296.807 | − | 67.7640i | −0.557908 | − | 0.127376i | ||||
\(533\) | −170.639 | − | 143.183i | −0.320149 | − | 0.268637i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1762.61 | − | 310.796i | 3.29460 | − | 0.580928i | ||||
\(536\) | 11.9317 | − | 4.51074i | 0.0222607 | − | 0.00841555i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −231.928 | − | 68.3938i | −0.431093 | − | 0.127126i | ||||
\(539\) | 68.8200i | 0.127681i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −579.648 | −1.07144 | −0.535719 | − | 0.844396i | \(-0.679959\pi\) | ||||
−0.535719 | + | 0.844396i | \(0.679959\pi\) | |||||||
\(542\) | 94.6784 | − | 321.061i | 0.174683 | − | 0.592363i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −129.267 | + | 100.444i | −0.237624 | + | 0.184640i | ||||
\(545\) | 121.766 | + | 690.571i | 0.223424 | + | 1.26710i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −565.910 | + | 674.425i | −1.03457 | + | 1.23295i | −0.0625529 | + | 0.998042i | \(0.519924\pi\) |
−0.972017 | + | 0.234911i | \(0.924520\pi\) | |||||||
\(548\) | 682.533 | + | 155.829i | 1.24550 | + | 0.284360i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1229.01 | + | 138.516i | 2.23457 | + | 0.251846i | ||||
\(551\) | 143.187 | + | 25.2477i | 0.259867 | + | 0.0458215i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −630.073 | − | 229.328i | −1.13937 | − | 0.414698i | ||||
\(554\) | 379.865 | + | 572.401i | 0.685677 | + | 1.03321i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −125.322 | − | 1000.56i | −0.225400 | − | 1.79957i | ||||
\(557\) | −429.760 | − | 744.366i | −0.771562 | − | 1.33638i | −0.936707 | − | 0.350115i | \(-0.886143\pi\) |
0.165145 | − | 0.986269i | \(-0.447191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 485.479 | + | 280.292i | 0.868478 | + | 0.501416i | ||||
\(560\) | −98.3659 | + | 981.768i | −0.175653 | + | 1.75316i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 72.0993 | − | 145.050i | 0.128291 | − | 0.258096i | ||||
\(563\) | 411.363 | + | 490.243i | 0.730663 | + | 0.870770i | 0.995620 | − | 0.0934901i | \(-0.0298024\pi\) |
−0.264957 | + | 0.964260i | \(0.585358\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.8000 | − | 11.9382i | 0.0580530 | − | 0.0211296i | ||||
\(566\) | −15.8906 | + | 21.5296i | −0.0280753 | + | 0.0380381i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −60.7641 | − | 21.2687i | −0.106979 | − | 0.0374449i | ||||
\(569\) | −774.636 | + | 281.944i | −1.36140 | + | 0.495509i | −0.916487 | − | 0.400066i | \(-0.868987\pi\) |
−0.444912 | + | 0.895574i | \(0.646765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −272.247 | − | 324.452i | −0.476791 | − | 0.568217i | 0.473016 | − | 0.881054i | \(-0.343165\pi\) |
−0.949807 | + | 0.312837i | \(0.898721\pi\) | |||||||
\(572\) | 252.546 | + | 492.685i | 0.441513 | + | 0.861337i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 188.000 | − | 45.3764i | 0.327525 | − | 0.0790529i | ||||
\(575\) | −44.3759 | − | 25.6205i | −0.0771755 | − | 0.0445573i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 239.288 | + | 414.459i | 0.414711 | + | 0.718301i | 0.995398 | − | 0.0958263i | \(-0.0305493\pi\) |
−0.580687 | + | 0.814127i | \(0.697216\pi\) | |||||||
\(578\) | −380.859 | + | 362.302i | −0.658926 | + | 0.626821i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23.5179 | − | 470.630i | 0.0405482 | − | 0.811431i | ||||
\(581\) | 66.3277 | + | 24.1413i | 0.114161 | + | 0.0415513i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 405.325 | + | 71.4698i | 0.695241 | + | 0.122590i | ||||
\(584\) | 173.541 | − | 32.8187i | 0.297159 | − | 0.0561964i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 479.706 | − | 209.276i | 0.818611 | − | 0.357126i | ||||
\(587\) | −52.1927 | + | 62.2008i | −0.0889143 | + | 0.105964i | −0.808667 | − | 0.588266i | \(-0.799811\pi\) |
0.719753 | + | 0.694230i | \(0.244255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −110.077 | − | 624.280i | −0.186889 | − | 1.05990i | ||||
\(590\) | 29.7456 | + | 476.827i | 0.0504163 | + | 0.808181i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −221.677 | + | 308.251i | −0.374454 | + | 0.520695i | ||||
\(593\) | −656.393 | −1.10690 | −0.553451 | − | 0.832881i | \(-0.686690\pi\) | ||||
−0.553451 | + | 0.832881i | \(0.686690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 315.477i | − | 0.530213i | ||||||
\(596\) | −56.9534 | − | 75.1988i | −0.0955594 | − | 0.126172i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.42813 | − | 22.8931i | −0.00238817 | − | 0.0382828i | ||||
\(599\) | −1106.16 | + | 195.046i | −1.84668 | + | 0.325619i | −0.983727 | − | 0.179672i | \(-0.942496\pi\) |
−0.862949 | + | 0.505291i | \(0.831385\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −354.566 | − | 297.517i | −0.589961 | − | 0.495036i | 0.298240 | − | 0.954491i | \(-0.403600\pi\) |
−0.888201 | + | 0.459455i | \(0.848045\pi\) | |||||||
\(602\) | −446.104 | + | 194.616i | −0.741036 | + | 0.323283i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −410.221 | − | 380.678i | −0.679174 | − | 0.630261i | ||||
\(605\) | 56.8409 | − | 322.361i | 0.0939518 | − | 0.532827i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −167.587 | + | 460.442i | −0.276091 | + | 0.758554i | 0.721705 | + | 0.692201i | \(0.243359\pi\) |
−0.997796 | + | 0.0663532i | \(0.978864\pi\) | |||||||
\(608\) | −142.366 | + | 349.696i | −0.234154 | + | 0.575157i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −913.204 | + | 868.710i | −1.49706 | + | 1.42411i | ||||
\(611\) | −163.034 | + | 94.1278i | −0.266832 | + | 0.154055i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 175.664 | − | 304.259i | 0.286564 | − | 0.496344i | −0.686423 | − | 0.727202i | \(-0.740820\pi\) |
0.972987 | + | 0.230859i | \(0.0741535\pi\) | |||||||
\(614\) | 493.873 | − | 119.203i | 0.804353 | − | 0.194142i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −474.373 | − | 77.6062i | −0.770086 | − | 0.125984i | ||||
\(617\) | −108.589 | + | 91.1174i | −0.175996 | + | 0.147678i | −0.726530 | − | 0.687134i | \(-0.758868\pi\) |
0.550535 | + | 0.834812i | \(0.314424\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −244.984 | − | 673.088i | −0.395774 | − | 1.08738i | −0.964323 | − | 0.264730i | \(-0.914717\pi\) |
0.568549 | − | 0.822650i | \(-0.307505\pi\) | |||||||
\(620\) | −1963.23 | + | 605.440i | −3.16650 | + | 0.976516i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −192.571 | + | 260.907i | −0.309599 | + | 0.419464i | ||||
\(623\) | 261.516 | + | 718.509i | 0.419769 | + | 1.15331i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1626.29 | − | 1364.62i | 2.60206 | − | 2.18339i | ||||
\(626\) | 207.345 | − | 417.139i | 0.331223 | − | 0.666356i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −243.780 | + | 578.213i | −0.388185 | + | 0.920722i | ||||
\(629\) | 60.6989 | − | 105.134i | 0.0965006 | − | 0.167144i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −912.443 | + | 526.799i | −1.44603 | + | 0.834864i | −0.998242 | − | 0.0592769i | \(-0.981121\pi\) |
−0.447785 | + | 0.894141i | \(0.647787\pi\) | |||||||
\(632\) | −406.834 | + | 725.232i | −0.643725 | + | 1.14752i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 481.251 | + | 725.175i | 0.759071 | + | 1.14381i | ||||
\(635\) | −281.110 | + | 772.345i | −0.442694 | + | 1.21629i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.0649 | + | 108.123i | −0.0299293 | + | 0.169737i | ||||
\(638\) | 228.117 | + | 25.7099i | 0.357550 | + | 0.0402976i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1181.90 | + | 316.968i | 1.84671 | + | 0.495262i | ||||
\(641\) | 496.119 | + | 416.293i | 0.773977 | + | 0.649444i | 0.941724 | − | 0.336386i | \(-0.109205\pi\) |
−0.167747 | + | 0.985830i | \(0.553649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 876.872 | − | 154.616i | 1.36372 | − | 0.240461i | 0.556567 | − | 0.830802i | \(-0.312118\pi\) |
0.807153 | + | 0.590342i | \(0.201007\pi\) | |||||||
\(644\) | 16.7283 | + | 10.8057i | 0.0259755 | + | 0.0167791i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.1458 | − | 115.791i | 0.0528572 | − | 0.179243i | ||||
\(647\) | 337.800i | 0.522102i | 0.965325 | + | 0.261051i | \(0.0840691\pi\) | ||||
−0.965325 | + | 0.261051i | \(0.915931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −232.746 | −0.358622 | ||||||||
\(650\) | 1892.52 | + | 558.089i | 2.91157 | + | 0.858598i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −133.752 | + | 207.059i | −0.205140 | + | 0.317575i | ||||
\(653\) | −77.4104 | − | 439.016i | −0.118546 | − | 0.672307i | −0.984933 | − | 0.172935i | \(-0.944675\pi\) |
0.866387 | − | 0.499372i | \(-0.166436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 257.644 | − | 307.048i | 0.393349 | − | 0.468776i | ||||
\(656\) | −17.8937 | − | 239.179i | −0.0272769 | − | 0.364603i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.3053 | − | 162.418i | 0.0278196 | − | 0.246836i | ||||
\(659\) | −18.1969 | − | 3.20861i | −0.0276129 | − | 0.00486890i | 0.159825 | − | 0.987145i | \(-0.448907\pi\) |
−0.187438 | + | 0.982277i | \(0.560018\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 218.906 | + | 79.6751i | 0.331173 | + | 0.120537i | 0.502255 | − | 0.864720i | \(-0.332504\pi\) |
−0.171082 | + | 0.985257i | \(0.554726\pi\) | |||||||
\(662\) | 409.825 | − | 271.974i | 0.619071 | − | 0.410837i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42.8274 | − | 76.3451i | 0.0644990 | − | 0.114978i | ||||
\(665\) | −363.805 | − | 630.129i | −0.547076 | − | 0.947563i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.23662 | − | 4.75542i | −0.0123488 | − | 0.00712956i | ||||
\(668\) | 617.487 | + | 260.339i | 0.924382 | + | 0.389728i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.2996 | + | 13.5697i | 0.0407457 | + | 0.0202533i | ||||
\(671\) | −394.686 | − | 470.369i | −0.588206 | − | 0.700997i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −502.586 | + | 182.927i | −0.746785 | + | 0.271808i | −0.687252 | − | 0.726419i | \(-0.741183\pi\) |
−0.0595329 | + | 0.998226i | \(0.518961\pi\) | |||||||
\(674\) | −265.811 | − | 196.191i | −0.394379 | − | 0.291084i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 61.0723 | + | 198.036i | 0.0903436 | + | 0.292952i | ||||
\(677\) | 747.713 | − | 272.145i | 1.10445 | − | 0.401987i | 0.275495 | − | 0.961302i | \(-0.411158\pi\) |
0.828955 | + | 0.559315i | \(0.188936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 154.087 | + | 183.633i | 0.226932 | + | 0.270447i | ||||
\(680\) | −386.114 | − | 63.1672i | −0.567814 | − | 0.0928930i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −234.830 | − | 972.927i | −0.344325 | − | 1.42658i | ||||
\(683\) | 510.054 | + | 294.480i | 0.746785 | + | 0.431156i | 0.824531 | − | 0.565817i | \(-0.191439\pi\) |
−0.0777464 | + | 0.996973i | \(0.524772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 836.602 | + | 1449.04i | 1.22132 | + | 2.11538i | ||||
\(686\) | −501.412 | − | 527.094i | −0.730921 | − | 0.768359i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 148.870 | + | 584.956i | 0.216380 | + | 0.850227i | ||||
\(689\) | 617.005 | + | 224.571i | 0.895508 | + | 0.325938i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −761.202 | − | 134.220i | −1.10159 | − | 0.194241i | −0.406848 | − | 0.913496i | \(-0.633372\pi\) |
−0.694746 | + | 0.719255i | \(0.744483\pi\) | |||||||
\(692\) | 406.343 | − | 437.878i | 0.587201 | − | 0.632772i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 118.148 | + | 270.822i | 0.170242 | + | 0.390233i | ||||
\(695\) | 1549.11 | − | 1846.16i | 2.22894 | − | 2.65634i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.3167 | + | 75.5225i | 0.0191057 | + | 0.108354i | ||||
\(698\) | 416.302 | − | 25.9699i | 0.596422 | − | 0.0372062i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1365.61 | + | 1034.27i | −1.95087 | + | 1.47753i | ||||
\(701\) | 766.488 | 1.09342 | 0.546710 | − | 0.837322i | \(-0.315880\pi\) | ||||
0.546710 | + | 0.837322i | \(0.315880\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 279.990i | − | 0.398279i | ||||||
\(704\) | −189.965 | + | 565.049i | −0.269837 | + | 0.802626i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −408.853 | + | 25.5052i | −0.579111 | + | 0.0361263i | ||||
\(707\) | 969.772 | − | 170.997i | 1.37167 | − | 0.241863i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 850.957 | + | 714.038i | 1.20022 | + | 1.00711i | 0.999624 | + | 0.0274323i | \(0.00873306\pi\) |
0.200598 | + | 0.979674i | \(0.435711\pi\) | |||||||
\(710\) | −61.5241 | − | 141.027i | −0.0866537 | − | 0.198630i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 931.750 | − | 176.205i | 1.30864 | − | 0.247479i | ||||
\(713\) | −7.20056 | + | 40.8364i | −0.0100990 | + | 0.0572740i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −452.554 | + | 1243.38i | −0.632943 | + | 1.73900i | ||||
\(716\) | 140.946 | + | 7.04325i | 0.196852 | + | 0.00983695i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 496.074 | + | 521.482i | 0.690911 | + | 0.726298i | ||||
\(719\) | −540.075 | + | 311.812i | −0.751148 | + | 0.433675i | −0.826108 | − | 0.563511i | \(-0.809450\pi\) |
0.0749608 | + | 0.997186i | \(0.476117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −365.789 | + | 633.565i | −0.507335 | + | 0.878731i | ||||
\(722\) | 104.074 | + | 431.190i | 0.144147 | + | 0.597216i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 249.627 | − | 127.957i | 0.344789 | − | 0.176736i | ||||
\(725\) | 626.717 | − | 525.878i | 0.864438 | − | 0.725349i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −133.681 | − | 367.285i | −0.183880 | − | 0.505206i | 0.813165 | − | 0.582034i | \(-0.197743\pi\) |
−0.997044 | + | 0.0768283i | \(0.975521\pi\) | |||||||
\(728\) | −723.785 | − | 253.340i | −0.994211 | − | 0.347995i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 339.619 | + | 250.667i | 0.465231 | + | 0.343379i | ||||
\(731\) | −66.0073 | − | 181.354i | −0.0902973 | − | 0.248090i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 874.224 | − | 733.561i | 1.19267 | − | 1.00077i | 0.192856 | − | 0.981227i | \(-0.438225\pi\) |
0.999809 | − | 0.0195380i | \(-0.00621954\pi\) | |||||||
\(734\) | 944.969 | + | 469.711i | 1.28742 | + | 0.639934i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.5747 | − | 18.3102i | 0.0225199 | − | 0.0248780i | ||||
\(737\) | −7.42592 | + | 12.8621i | −0.0100759 | + | 0.0174519i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 97.0676 | − | 56.0420i | 0.131350 | − | 0.0758349i | −0.432885 | − | 0.901449i | \(-0.642504\pi\) |
0.564235 | + | 0.825614i | \(0.309171\pi\) | |||||||
\(740\) | −900.394 | + | 112.776i | −1.21675 | + | 0.152400i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −474.993 | + | 315.222i | −0.640152 | + | 0.424827i | ||||
\(743\) | −242.050 | + | 665.027i | −0.325774 | + | 0.895056i | 0.663394 | + | 0.748270i | \(0.269115\pi\) |
−0.989168 | + | 0.146786i | \(0.953107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.1490 | − | 222.025i | 0.0525490 | − | 0.298020i | ||||
\(746\) | 75.1016 | − | 666.356i | 0.100672 | − | 0.893239i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 42.4247 | − | 185.821i | 0.0567176 | − | 0.248424i | ||||
\(749\) | −925.156 | − | 776.298i | −1.23519 | − | 1.03645i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 251.989 | − | 44.4325i | 0.335538 | − | 0.0591645i | −0.00334065 | − | 0.999994i | \(-0.501063\pi\) |
0.338879 | + | 0.940830i | \(0.389952\pi\) | |||||||
\(752\) | −195.119 | − | 54.9246i | −0.259467 | − | 0.0730381i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 351.271 | + | 103.587i | 0.465876 | + | 0.137383i | ||||
\(755\) | − | 1337.52i | − | 1.77155i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 384.164 | 0.507483 | 0.253741 | − | 0.967272i | \(-0.418339\pi\) | ||||
0.253741 | + | 0.967272i | \(0.418339\pi\) | |||||||
\(758\) | −266.869 | + | 904.972i | −0.352070 | + | 1.19389i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −844.063 | + | 319.094i | −1.11061 | + | 0.419861i | ||||
\(761\) | −146.561 | − | 831.191i | −0.192591 | − | 1.09224i | −0.915808 | − | 0.401615i | \(-0.868449\pi\) |
0.723218 | − | 0.690620i | \(-0.242662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 304.144 | − | 362.465i | 0.398616 | − | 0.475052i | ||||
\(764\) | 273.507 | − | 1197.96i | 0.357993 | − | 1.56801i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1397.02 | − | 157.451i | −1.82379 | − | 0.205550i | ||||
\(767\) | −365.665 | − | 64.4766i | −0.476747 | − | 0.0840634i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −371.992 | − | 135.394i | −0.483735 | − | 0.176065i | 0.0886291 | − | 0.996065i | \(-0.471751\pi\) |
−0.572364 | + | 0.820000i | \(0.693974\pi\) | |||||||
\(770\) | −635.232 | − | 957.202i | −0.824977 | − | 1.24312i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 673.352 | − | 84.3388i | 0.872218 | − | 0.109247i | ||||
\(773\) | 74.6477 | + | 129.294i | 0.0965688 | + | 0.167262i | 0.910262 | − | 0.414032i | \(-0.135880\pi\) |
−0.813693 | + | 0.581294i | \(0.802547\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3089.05 | − | 1783.47i | −3.98588 | − | 2.30125i | ||||
\(776\) | 255.603 | − | 151.819i | 0.329385 | − | 0.195643i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 174.434 | − | 350.928i | 0.224208 | − | 0.451064i | ||||
\(779\) | 113.691 | + | 135.491i | 0.145944 | + | 0.173930i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.4365 | − | 25.6368i | 0.0901875 | − | 0.0328256i | ||||
\(782\) | −4.68945 | + | 6.35356i | −0.00599674 | + | 0.00812476i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −97.6830 | + | 66.5811i | −0.124596 | + | 0.0849248i | ||||
\(785\) | −1409.26 | + | 512.931i | −1.79524 | + | 0.653415i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −883.158 | − | 1052.51i | −1.12218 | − | 1.33737i | −0.934839 | − | 0.355071i | \(-0.884457\pi\) |
−0.187343 | − | 0.982295i | \(-0.559988\pi\) | |||||||
\(788\) | 550.324 | − | 282.091i | 0.698381 | − | 0.357983i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1931.90 | + | 466.291i | −2.44544 | + | 0.590242i | ||||
\(791\) | −20.3973 | − | 11.7764i | −0.0257868 | − | 0.0148880i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −489.784 | − | 848.331i | −0.617635 | − | 1.06977i | ||||
\(794\) | −617.595 | + | 587.504i | −0.777828 | + | 0.739929i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 848.563 | + | 42.4037i | 1.06603 | + | 0.0532710i | ||||
\(797\) | −264.891 | − | 96.4123i | −0.332360 | − | 0.120969i | 0.170450 | − | 0.985366i | \(-0.445478\pi\) |
−0.502809 | + | 0.864397i | \(0.667700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 63.8263 | + | 11.2543i | 0.0798828 | + | 0.0140855i | ||||
\(800\) | 992.419 | + | 1878.46i | 1.24052 | + | 2.34808i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −71.0291 | + | 30.9870i | −0.0885649 | + | 0.0386371i | ||||
\(803\) | −132.181 | + | 157.527i | −0.164609 | + | 0.196173i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.26489 | + | 46.8725i | 0.0102669 | + | 0.0582267i | ||||
\(806\) | −99.4133 | − | 1593.61i | −0.123342 | − | 1.97719i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.1088 | − | 1221.15i | −0.0186990 | − | 1.51132i | ||||
\(809\) | 1048.06 | 1.29550 | 0.647749 | − | 0.761854i | \(-0.275711\pi\) | ||||
0.647749 | + | 0.761854i | \(0.275711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 750.843i | 0.925824i | 0.886404 | + | 0.462912i | \(0.153195\pi\) | ||||
−0.886404 | + | 0.462912i | \(0.846805\pi\) | |||||||
\(812\) | −253.471 | + | 191.971i | −0.312156 | + | 0.236418i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.5238 | − | 441.211i | −0.0338130 | − | 0.542029i | ||||
\(815\) | −580.179 | + | 102.301i | −0.711876 | + | 0.125523i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −340.978 | − | 286.114i | −0.417354 | − | 0.350201i | ||||
\(818\) | 372.784 | − | 162.630i | 0.455726 | − | 0.198814i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 389.920 | − | 420.181i | 0.475512 | − | 0.512416i | ||||
\(821\) | 102.983 | − | 584.044i | 0.125436 | − | 0.711382i | −0.855612 | − | 0.517617i | \(-0.826819\pi\) |
0.981048 | − | 0.193764i | \(-0.0620697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 461.497 | − | 1267.95i | 0.560750 | − | 1.54065i | −0.257791 | − | 0.966201i | \(-0.582995\pi\) |
0.818541 | − | 0.574448i | \(-0.194783\pi\) | |||||||
\(824\) | 702.182 | + | 574.548i | 0.852163 | + | 0.697267i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 233.572 | − | 222.191i | 0.282775 | − | 0.268997i | ||||
\(827\) | −771.784 | + | 445.590i | −0.933233 | + | 0.538803i | −0.887833 | − | 0.460166i | \(-0.847790\pi\) |
−0.0454007 | + | 0.998969i | \(0.514456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 440.587 | − | 763.119i | 0.531468 | − | 0.920529i | −0.467857 | − | 0.883804i | \(-0.654974\pi\) |
0.999325 | − | 0.0367255i | \(-0.0116927\pi\) | |||||||
\(830\) | 203.371 | − | 49.0864i | 0.245025 | − | 0.0591403i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −454.987 | + | 835.119i | −0.546859 | + | 1.00375i | ||||
\(833\) | 28.9547 | − | 24.2959i | 0.0347596 | − | 0.0291667i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 547.770 | + | 1504.99i | 0.656012 | + | 1.80238i | ||||
\(836\) | −129.549 | − | 420.080i | −0.154962 | − | 0.502488i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 153.285 | − | 207.680i | 0.182917 | − | 0.247828i | ||||
\(839\) | 381.014 | + | 1046.83i | 0.454129 | + | 1.24771i | 0.929793 | + | 0.368082i | \(0.119985\pi\) |
−0.475665 | + | 0.879627i | \(0.657792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −527.918 | + | 442.976i | −0.627727 | + | 0.526725i | ||||
\(842\) | 150.073 | − | 301.919i | 0.178234 | − | 0.358573i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1132.61 | + | 477.519i | 1.34195 | + | 0.565780i | ||||
\(845\) | −247.647 | + | 428.937i | −0.293073 | + | 0.507618i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −191.283 | + | 110.437i | −0.225836 | + | 0.130386i | ||||
\(848\) | 290.695 | + | 644.463i | 0.342800 | + | 0.759980i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −375.607 | − | 565.984i | −0.441890 | − | 0.665864i | ||||
\(851\) | −6.26415 | + | 17.2106i | −0.00736092 | + | 0.0202240i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 143.568 | − | 814.212i | 0.168309 | − | 0.954528i | −0.777278 | − | 0.629158i | \(-0.783400\pi\) |
0.945587 | − | 0.325370i | \(-0.105489\pi\) | |||||||
\(854\) | 845.126 | + | 95.2499i | 0.989609 | + | 0.111534i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1135.36 | + | 976.867i | −1.32635 | + | 1.14120i | ||||
\(857\) | −178.468 | − | 149.753i | −0.208248 | − | 0.174741i | 0.532698 | − | 0.846305i | \(-0.321178\pi\) |
−0.740946 | + | 0.671565i | \(0.765623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −573.273 | + | 101.083i | −0.667372 | + | 0.117676i | −0.497062 | − | 0.867715i | \(-0.665588\pi\) |
−0.170310 | + | 0.985391i | \(0.554477\pi\) | |||||||
\(860\) | −782.747 | + | 1211.76i | −0.910171 | + | 1.40903i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −45.4918 | + | 154.266i | −0.0527747 | + | 0.178963i | ||||
\(863\) | − | 972.167i | − | 1.12650i | −0.826288 | − | 0.563248i | \(-0.809551\pi\) | ||
0.826288 | − | 0.563248i | \(-0.190449\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1427.70 | 1.65051 | ||||||||
\(866\) | −1523.87 | − | 449.377i | −1.75966 | − | 0.518911i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1164.47 | + | 752.199i | 1.34156 | + | 0.866589i | ||||
\(869\) | −168.123 | − | 953.474i | −0.193467 | − | 1.09721i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.2299 | + | 18.1503i | −0.0174856 | + | 0.0208385i | ||||
\(872\) | −382.725 | − | 444.819i | −0.438905 | − | 0.510114i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.03977 | + | 18.0984i | −0.00233384 | + | 0.0207075i | ||||
\(875\) | −2513.70 | − | 443.233i | −2.87280 | − | 0.506552i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −929.589 | − | 338.343i | −1.05996 | − | 0.385795i | −0.247549 | − | 0.968875i | \(-0.579625\pi\) |
−0.812415 | + | 0.583080i | \(0.801847\pi\) | |||||||
\(878\) | 264.653 | − | 175.633i | 0.301427 | − | 0.200037i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1298.72 | + | 585.806i | −1.47581 | + | 0.665688i | ||||
\(881\) | −162.043 | − | 280.667i | −0.183931 | − | 0.318578i | 0.759285 | − | 0.650759i | \(-0.225549\pi\) |
−0.943216 | + | 0.332181i | \(0.892216\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 638.603 | + | 368.697i | 0.723219 | + | 0.417551i | 0.815936 | − | 0.578142i | \(-0.196222\pi\) |
−0.0927172 | + | 0.995692i | \(0.529555\pi\) | |||||||
\(884\) | 118.130 | − | 280.189i | 0.133632 | − | 0.316956i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −534.023 | − | 265.444i | −0.602735 | − | 0.299599i | ||||
\(887\) | −539.552 | − | 643.013i | −0.608289 | − | 0.724930i | 0.370721 | − | 0.928744i | \(-0.379111\pi\) |
−0.979010 | + | 0.203814i | \(0.934666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 521.155 | − | 189.685i | 0.586226 | − | 0.213369i | ||||
\(890\) | 1823.43 | + | 1345.84i | 2.04880 | + | 1.51218i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1584.53 | − | 488.654i | 1.77638 | − | 0.547818i | ||||
\(893\) | 140.464 | − | 51.1248i | 0.157295 | − | 0.0572506i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 216.797 | + | 258.369i | 0.242232 | + | 0.288680i | ||||
\(896\) | −348.786 | − | 748.406i | −0.389270 | − | 0.835274i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −335.665 | − | 1390.70i | −0.373791 | − | 1.54866i | ||||
\(899\) | −573.360 | − | 331.030i | −0.637775 | − | 0.368220i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −113.025 | − | 195.764i | −0.125444 | − | 0.217275i | ||||
\(902\) | 192.474 | + | 202.332i | 0.213386 | + | 0.224315i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.4973 | + | 22.6065i | −0.0204616 | + | 0.0250071i | ||||
\(905\) | 629.982 | + | 229.295i | 0.696112 | + | 0.253364i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −61.5751 | − | 10.8574i | −0.0678888 | − | 0.0119706i | 0.139601 | − | 0.990208i | \(-0.455418\pi\) |
−0.207489 | + | 0.978237i | \(0.566529\pi\) | |||||||
\(908\) | 1020.44 | + | 946.948i | 1.12383 | + | 1.04289i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −732.839 | − | 1679.83i | −0.805317 | − | 1.84597i | ||||
\(911\) | −142.414 | + | 169.723i | −0.156327 | + | 0.186304i | −0.838523 | − | 0.544866i | \(-0.816581\pi\) |
0.682196 | + | 0.731169i | \(0.261025\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6983 | + | 100.372i | 0.0193848 | + | 0.109937i | ||||
\(914\) | −690.395 | + | 43.0685i | −0.755355 | + | 0.0471209i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −399.531 | − | 527.523i | −0.436169 | − | 0.575899i | ||||
\(917\) | −270.463 | −0.294943 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 610.515i | 0.664326i | 0.943222 | + | 0.332163i | \(0.107778\pi\) | ||||
−0.943222 | + | 0.332163i | \(0.892222\pi\) | |||||||
\(920\) | 59.0224 | − | 0.730261i | 0.0641548 | − | 0.000793762i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −208.008 | + | 12.9760i | −0.225605 | + | 0.0140738i | ||||
\(923\) | 117.764 | − | 20.7650i | 0.127589 | − | 0.0224973i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1206.88 | − | 1012.69i | −1.30473 | − | 1.09480i | ||||
\(926\) | 155.030 | + | 355.364i | 0.167419 | + | 0.383762i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 184.203 | + | 348.662i | 0.198495 | + | 0.375714i | ||||
\(929\) | −101.641 | + | 576.432i | −0.109409 | + | 0.620487i | 0.879959 | + | 0.475050i | \(0.157570\pi\) |
−0.989368 | + | 0.145437i | \(0.953541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.8160 | − | 81.9187i | 0.0320257 | − | 0.0879900i | ||||
\(932\) | −56.3051 | + | 1126.75i | −0.0604132 | + | 1.20896i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 774.820 | + | 814.505i | 0.829572 | + | 0.872061i | ||||
\(935\) | 394.503 | − | 227.766i | 0.421928 | − | 0.243600i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 106.276 | − | 184.075i | 0.113422 | − | 0.196452i | −0.803726 | − | 0.594999i | \(-0.797152\pi\) |
0.917148 | + | 0.398548i | \(0.130486\pi\) | |||||||
\(938\) | −4.82654 | − | 19.9969i | −0.00514556 | − | 0.0213186i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −220.985 | − | 431.114i | −0.235090 | − | 0.458631i | ||||
\(941\) | −277.591 | + | 232.926i | −0.294995 | + | 0.247530i | −0.778258 | − | 0.627945i | \(-0.783896\pi\) |
0.483262 | + | 0.875476i | \(0.339452\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.95709 | − | 10.8720i | −0.00419628 | − | 0.0115292i | ||||
\(944\) | −225.174 | − | 330.359i | −0.238531 | − | 0.349956i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −565.443 | − | 417.343i | −0.597719 | − | 0.441166i | ||||
\(947\) | −262.181 | − | 720.335i | −0.276854 | − | 0.760650i | −0.997715 | − | 0.0675697i | \(-0.978475\pi\) |
0.720861 | − | 0.693080i | \(-0.243747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −251.307 | + | 210.872i | −0.264813 | + | 0.222204i | ||||
\(950\) | −1402.92 | − | 697.343i | −1.47676 | − | 0.734045i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 134.819 | + | 226.981i | 0.141617 | + | 0.238426i | ||||
\(953\) | −649.243 | + | 1124.52i | −0.681262 | + | 1.17998i | 0.293333 | + | 0.956010i | \(0.405235\pi\) |
−0.974596 | + | 0.223971i | \(0.928098\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2543.31 | − | 1468.38i | 2.66315 | − | 1.53757i | ||||
\(956\) | −177.755 | − | 1419.18i | −0.185936 | − | 1.48450i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 665.765 | − | 441.825i | 0.694953 | − | 0.461195i | ||||
\(959\) | 386.150 | − | 1060.94i | 0.402659 | − | 1.10630i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −334.362 | + | 1896.26i | −0.347932 | + | 1.97322i | ||||
\(962\) | 78.9846 | − | 700.809i | 0.0821046 | − | 0.728492i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 886.272 | + | 202.345i | 0.919369 | + | 0.209901i | ||||
\(965\) | 1242.42 | + | 1042.51i | 1.28748 | + | 1.08032i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 589.937 | − | 104.022i | 0.610069 | − | 0.107572i | 0.139926 | − | 0.990162i | \(-0.455314\pi\) |
0.470143 | + | 0.882590i | \(0.344202\pi\) | |||||||
\(968\) | 96.8647 | + | 256.225i | 0.100067 | + | 0.264695i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 681.499 | + | 200.969i | 0.702577 | + | 0.207184i | ||||
\(971\) | 642.416i | 0.661603i | 0.943700 | + | 0.330801i | \(0.107319\pi\) | ||||
−0.943700 | + | 0.330801i | \(0.892681\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1626.19 | −1.67131 | ||||||||
\(974\) | −120.713 | + | 409.347i | −0.123935 | + | 0.420274i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 285.795 | − | 1015.28i | 0.292822 | − | 1.04025i | ||||
\(977\) | −70.1942 | − | 398.091i | −0.0718466 | − | 0.407462i | −0.999427 | − | 0.0338395i | \(-0.989227\pi\) |
0.927581 | − | 0.373623i | \(-0.121885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −709.686 | + | 845.770i | −0.724909 | + | 0.863912i | ||||
\(980\) | −275.444 | − | 62.8866i | −0.281065 | − | 0.0641700i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −564.060 | − | 63.5723i | −0.574399 | − | 0.0647376i | ||||
\(983\) | 1233.41 | + | 217.483i | 1.25474 | + | 0.221245i | 0.761222 | − | 0.648491i | \(-0.224600\pi\) |
0.493518 | + | 0.869736i | \(0.335711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1388.85 | + | 505.499i | 1.41000 | + | 0.513197i | ||||
\(986\) | −69.7164 | − | 105.052i | −0.0707063 | − | 0.106544i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −87.1596 | − | 695.873i | −0.0882182 | − | 0.704325i | ||||
\(989\) | 14.5583 | + | 25.2157i | 0.0147202 | + | 0.0254961i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1340.40 | + | 773.883i | 1.35258 | + | 0.780911i | 0.988610 | − | 0.150501i | \(-0.0480885\pi\) |
0.363968 | + | 0.931412i | \(0.381422\pi\) | |||||||
\(992\) | 1153.78 | − | 1274.59i | 1.16309 | − | 1.28487i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −46.2122 | + | 92.9702i | −0.0464912 | + | 0.0935314i | ||||
\(995\) | 1305.22 | + | 1555.50i | 1.31178 | + | 1.56332i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 690.289 | − | 251.245i | 0.692366 | − | 0.252001i | 0.0282179 | − | 0.999602i | \(-0.491017\pi\) |
0.664148 | + | 0.747601i | \(0.268795\pi\) | |||||||
\(998\) | −189.637 | + | 256.931i | −0.190017 | + | 0.257446i | ||||
\(999\) | 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 | 324.3.j.a.19.4 | 204 | ||
3.2 | odd | 2 | 108.3.j.a.7.31 | yes | 204 | ||
4.3 | odd | 2 | inner | 324.3.j.a.19.11 | 204 | ||
12.11 | even | 2 | 108.3.j.a.7.24 | ✓ | 204 | ||
27.4 | even | 9 | inner | 324.3.j.a.307.11 | 204 | ||
27.23 | odd | 18 | 108.3.j.a.31.24 | yes | 204 | ||
108.23 | even | 18 | 108.3.j.a.31.31 | yes | 204 | ||
108.31 | odd | 18 | inner | 324.3.j.a.307.4 | 204 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.j.a.7.24 | ✓ | 204 | 12.11 | even | 2 | ||
108.3.j.a.7.31 | yes | 204 | 3.2 | odd | 2 | ||
108.3.j.a.31.24 | yes | 204 | 27.23 | odd | 18 | ||
108.3.j.a.31.31 | yes | 204 | 108.23 | even | 18 | ||
324.3.j.a.19.4 | 204 | 1.1 | even | 1 | trivial | ||
324.3.j.a.19.11 | 204 | 4.3 | odd | 2 | inner | ||
324.3.j.a.307.4 | 204 | 108.31 | odd | 18 | inner | ||
324.3.j.a.307.11 | 204 | 27.4 | even | 9 | inner |