Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(17,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.f (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: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 125.2 | ||
Character | \(\chi\) | \(=\) | 162.125 |
Dual form | 162.3.f.a.35.2 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.909039 | − | 1.08335i | −0.454519 | − | 0.541675i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.347296 | + | 1.96962i | −0.0868241 | + | 0.492404i | ||||
\(5\) | −0.387127 | − | 1.06362i | −0.0774254 | − | 0.212724i | 0.894941 | − | 0.446184i | \(-0.147217\pi\) |
−0.972366 | + | 0.233460i | \(0.924995\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.332318 | − | 1.88467i | −0.0474741 | − | 0.269239i | 0.951826 | − | 0.306638i | \(-0.0992039\pi\) |
−0.999300 | + | 0.0373988i | \(0.988093\pi\) | |||||||
\(8\) | 2.44949 | − | 1.41421i | 0.306186 | − | 0.176777i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.800362 | + | 1.38627i | −0.0800362 | + | 0.138627i | ||||
\(11\) | 6.05561 | − | 16.6376i | 0.550510 | − | 1.51251i | −0.282507 | − | 0.959265i | \(-0.591166\pi\) |
0.833017 | − | 0.553248i | \(-0.186612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.14397 | − | 7.67270i | −0.703382 | − | 0.590208i | 0.219351 | − | 0.975646i | \(-0.429606\pi\) |
−0.922734 | + | 0.385438i | \(0.874050\pi\) | |||||||
\(14\) | −1.73967 | + | 2.07326i | −0.124262 | + | 0.148090i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.75877 | − | 1.36808i | −0.234923 | − | 0.0855050i | ||||
\(17\) | 2.93931 | + | 1.69701i | 0.172900 | + | 0.0998241i | 0.583953 | − | 0.811788i | \(-0.301505\pi\) |
−0.411052 | + | 0.911612i | \(0.634839\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.2259 | − | 17.7118i | −0.538206 | − | 0.932200i | −0.999001 | − | 0.0446932i | \(-0.985769\pi\) |
0.460795 | − | 0.887507i | \(-0.347564\pi\) | |||||||
\(20\) | 2.22937 | − | 0.393099i | 0.111469 | − | 0.0196549i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −23.5292 | + | 8.56392i | −1.06951 | + | 0.389269i | ||||
\(23\) | −0.678043 | − | 0.119557i | −0.0294801 | − | 0.00519814i | 0.158889 | − | 0.987297i | \(-0.449209\pi\) |
−0.188369 | + | 0.982098i | \(0.560320\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.1697 | − | 15.2462i | 0.726787 | − | 0.609847i | ||||
\(26\) | 16.8809i | 0.649266i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.82749 | 0.136696 | ||||||||
\(29\) | −34.6788 | − | 41.3286i | −1.19582 | − | 1.42512i | −0.879122 | − | 0.476596i | \(-0.841870\pi\) |
−0.316698 | − | 0.948527i | \(-0.602574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.33824 | + | 41.6172i | −0.236717 | + | 1.34249i | 0.602249 | + | 0.798308i | \(0.294271\pi\) |
−0.838966 | + | 0.544183i | \(0.816840\pi\) | |||||||
\(32\) | 1.93476 | + | 5.31570i | 0.0604612 | + | 0.166116i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.833488 | − | 4.72695i | −0.0245144 | − | 0.139028i | ||||
\(35\) | −1.87593 | + | 1.08307i | −0.0535980 | + | 0.0309448i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24382 | − | 14.2787i | 0.222806 | − | 0.385911i | −0.732853 | − | 0.680387i | \(-0.761812\pi\) |
0.955659 | + | 0.294476i | \(0.0951450\pi\) | |||||||
\(38\) | −9.89233 | + | 27.1790i | −0.260325 | + | 0.715236i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.45245 | − | 2.05785i | −0.0613113 | − | 0.0514463i | ||||
\(41\) | −26.0070 | + | 30.9939i | −0.634317 | + | 0.755950i | −0.983461 | − | 0.181119i | \(-0.942028\pi\) |
0.349144 | + | 0.937069i | \(0.386472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 66.4698 | + | 24.1930i | 1.54581 | + | 0.562628i | 0.967430 | − | 0.253140i | \(-0.0814632\pi\) |
0.578379 | + | 0.815768i | \(0.303685\pi\) | |||||||
\(44\) | 30.6667 | + | 17.7054i | 0.696970 | + | 0.402396i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.486845 | + | 0.843240i | 0.0105836 | + | 0.0183313i | ||||
\(47\) | 62.9822 | − | 11.1055i | 1.34005 | − | 0.236286i | 0.542760 | − | 0.839888i | \(-0.317379\pi\) |
0.797286 | + | 0.603601i | \(0.206268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 42.6034 | − | 15.5064i | 0.869457 | − | 0.316456i | ||||
\(50\) | −33.0339 | − | 5.82477i | −0.660678 | − | 0.116495i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 18.2879 | − | 15.3454i | 0.351691 | − | 0.295104i | ||||
\(53\) | 17.6375i | 0.332783i | 0.986060 | + | 0.166392i | \(0.0532116\pi\) | ||||
−0.986060 | + | 0.166392i | \(0.946788\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.0405 | −0.364372 | ||||||||
\(56\) | −3.47934 | − | 4.14651i | −0.0621310 | − | 0.0740449i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.2490 | + | 75.1385i | −0.228430 | + | 1.29549i | ||||
\(59\) | 19.1264 | + | 52.5494i | 0.324177 | + | 0.890668i | 0.989554 | + | 0.144161i | \(0.0460484\pi\) |
−0.665377 | + | 0.746507i | \(0.731729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5245 | + | 65.3586i | 0.188926 | + | 1.07145i | 0.920807 | + | 0.390020i | \(0.127532\pi\) |
−0.731881 | + | 0.681433i | \(0.761357\pi\) | |||||||
\(62\) | 51.7568 | − | 29.8818i | 0.834787 | − | 0.481965i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | − | 6.92820i | 0.0625000 | − | 0.108253i | ||||
\(65\) | −4.62098 | + | 12.6960i | −0.0710920 | + | 0.195324i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −17.2826 | − | 14.5018i | −0.257949 | − | 0.216445i | 0.504637 | − | 0.863331i | \(-0.331626\pi\) |
−0.762586 | + | 0.646887i | \(0.776071\pi\) | |||||||
\(68\) | −4.36327 | + | 5.19994i | −0.0641657 | + | 0.0764697i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.87864 | + | 1.04774i | 0.0411234 | + | 0.0149677i | ||||
\(71\) | 43.0775 | + | 24.8708i | 0.606726 | + | 0.350293i | 0.771683 | − | 0.636007i | \(-0.219415\pi\) |
−0.164957 | + | 0.986301i | \(0.552749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45.2424 | − | 78.3622i | −0.619759 | − | 1.07345i | −0.989529 | − | 0.144331i | \(-0.953897\pi\) |
0.369770 | − | 0.929123i | \(-0.379436\pi\) | |||||||
\(74\) | −22.9628 | + | 4.04896i | −0.310308 | + | 0.0547157i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 38.4369 | − | 13.9899i | 0.505748 | − | 0.184077i | ||||
\(77\) | −33.3689 | − | 5.88383i | −0.433362 | − | 0.0764134i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −57.2341 | + | 48.0251i | −0.724482 | + | 0.607913i | −0.928621 | − | 0.371029i | \(-0.879005\pi\) |
0.204139 | + | 0.978942i | \(0.434561\pi\) | |||||||
\(80\) | 4.52753i | 0.0565942i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 57.2187 | 0.697789 | ||||||||
\(83\) | −8.15901 | − | 9.72353i | −0.0983014 | − | 0.117151i | 0.714651 | − | 0.699481i | \(-0.246586\pi\) |
−0.812952 | + | 0.582330i | \(0.802141\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.667093 | − | 3.78327i | 0.00784815 | − | 0.0445091i | ||||
\(86\) | −34.2141 | − | 94.0025i | −0.397838 | − | 1.09305i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.69603 | − | 49.3177i | −0.0988186 | − | 0.560428i | ||||
\(89\) | −58.5070 | + | 33.7790i | −0.657382 | + | 0.379540i | −0.791279 | − | 0.611455i | \(-0.790584\pi\) |
0.133897 | + | 0.990995i | \(0.457251\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4218 | + | 19.7832i | −0.125514 | + | 0.217397i | ||||
\(92\) | 0.470964 | − | 1.29396i | 0.00511917 | − | 0.0140648i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −69.2844 | − | 58.1365i | −0.737068 | − | 0.618473i | ||||
\(95\) | −14.8799 | + | 17.7332i | −0.156631 | + | 0.186665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −44.2956 | − | 16.1223i | −0.456655 | − | 0.166209i | 0.103442 | − | 0.994635i | \(-0.467014\pi\) |
−0.560098 | + | 0.828427i | \(0.689236\pi\) | |||||||
\(98\) | −55.5270 | − | 32.0585i | −0.566602 | − | 0.327128i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 23.7188 | + | 41.0822i | 0.237188 | + | 0.410822i | ||||
\(101\) | 9.94227 | − | 1.75309i | 0.0984383 | − | 0.0173573i | −0.124212 | − | 0.992256i | \(-0.539640\pi\) |
0.222650 | + | 0.974898i | \(0.428529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 121.488 | − | 44.2181i | 1.17950 | − | 0.429301i | 0.323472 | − | 0.946238i | \(-0.395150\pi\) |
0.856024 | + | 0.516936i | \(0.172928\pi\) | |||||||
\(104\) | −33.2489 | − | 5.86268i | −0.319701 | − | 0.0563719i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.1076 | − | 16.0332i | 0.180260 | − | 0.151257i | ||||
\(107\) | − | 135.970i | − | 1.27075i | −0.772204 | − | 0.635375i | \(-0.780846\pi\) | ||
0.772204 | − | 0.635375i | \(-0.219154\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −182.307 | −1.67254 | −0.836269 | − | 0.548320i | \(-0.815268\pi\) | ||||
−0.836269 | + | 0.548320i | \(0.815268\pi\) | |||||||
\(110\) | 18.2176 | + | 21.7108i | 0.165614 | + | 0.197371i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.32927 | + | 7.53869i | −0.0118685 | + | 0.0673097i | ||||
\(113\) | −5.48933 | − | 15.0818i | −0.0485781 | − | 0.133467i | 0.913031 | − | 0.407890i | \(-0.133735\pi\) |
−0.961609 | + | 0.274423i | \(0.911513\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.135325 | + | 0.767465i | 0.00117674 | + | 0.00667361i | ||||
\(116\) | 93.4452 | − | 53.9506i | 0.805562 | − | 0.465091i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 39.5428 | − | 68.4901i | 0.335108 | − | 0.580425i | ||||
\(119\) | 2.22152 | − | 6.10358i | 0.0186682 | − | 0.0512905i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −147.449 | − | 123.725i | −1.21859 | − | 1.02252i | ||||
\(122\) | 60.3301 | − | 71.8986i | 0.494509 | − | 0.589333i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −79.4214 | − | 28.9070i | −0.640495 | − | 0.233121i | ||||
\(125\) | −47.7561 | − | 27.5720i | −0.382049 | − | 0.220576i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 81.7231 | + | 141.549i | 0.643489 | + | 1.11456i | 0.984648 | + | 0.174550i | \(0.0558470\pi\) |
−0.341160 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(128\) | −11.1418 | + | 1.96460i | −0.0870455 | + | 0.0153485i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 17.9549 | − | 6.53505i | 0.138115 | − | 0.0502696i | ||||
\(131\) | 194.629 | + | 34.3184i | 1.48572 | + | 0.261972i | 0.856861 | − | 0.515548i | \(-0.172412\pi\) |
0.628858 | + | 0.777520i | \(0.283523\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29.9827 | + | 25.1584i | −0.225434 | + | 0.189161i | ||||
\(134\) | 31.9058i | 0.238103i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.59974 | 0.0705863 | ||||||||
\(137\) | 19.4564 | + | 23.1872i | 0.142017 | + | 0.169250i | 0.832364 | − | 0.554229i | \(-0.186987\pi\) |
−0.690347 | + | 0.723478i | \(0.742542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −26.6334 | + | 151.046i | −0.191607 | + | 1.08666i | 0.725561 | + | 0.688158i | \(0.241580\pi\) |
−0.917168 | + | 0.398500i | \(0.869531\pi\) | |||||||
\(140\) | −1.48172 | − | 4.07100i | −0.0105837 | − | 0.0290786i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.2153 | − | 69.2766i | −0.0860235 | − | 0.487863i | ||||
\(143\) | −183.028 | + | 105.671i | −1.27992 | + | 0.738960i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.5329 | + | 52.8845i | −0.210572 | + | 0.364721i | ||||
\(146\) | −43.7666 | + | 120.248i | −0.299771 | + | 0.823614i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 25.2605 | + | 21.1961i | 0.170679 | + | 0.143217i | ||||
\(149\) | 130.956 | − | 156.067i | 0.878898 | − | 1.04743i | −0.119610 | − | 0.992821i | \(-0.538164\pi\) |
0.998508 | − | 0.0546085i | \(-0.0173911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −124.926 | − | 45.4693i | −0.827324 | − | 0.301121i | −0.106564 | − | 0.994306i | \(-0.533985\pi\) |
−0.720760 | + | 0.693184i | \(0.756207\pi\) | |||||||
\(152\) | −50.0965 | − | 28.9232i | −0.329582 | − | 0.190285i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.9594 | + | 41.4988i | 0.155580 | + | 0.269473i | ||||
\(155\) | 47.1059 | − | 8.30603i | 0.303909 | − | 0.0535873i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 238.313 | − | 86.7387i | 1.51791 | − | 0.552476i | 0.557288 | − | 0.830319i | \(-0.311842\pi\) |
0.960626 | + | 0.277844i | \(0.0896197\pi\) | |||||||
\(158\) | 104.056 | + | 18.3479i | 0.658583 | + | 0.116126i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.90490 | − | 4.11570i | 0.0306557 | − | 0.0257231i | ||||
\(161\) | 1.31762i | 0.00818397i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 261.536 | 1.60451 | 0.802257 | − | 0.596979i | \(-0.203632\pi\) | ||||
0.802257 | + | 0.596979i | \(0.203632\pi\) | |||||||
\(164\) | −52.0140 | − | 61.9879i | −0.317159 | − | 0.377975i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.11713 | + | 17.6781i | −0.0187779 | + | 0.106495i | ||||
\(167\) | 26.5485 | + | 72.9413i | 0.158973 | + | 0.436774i | 0.993450 | − | 0.114268i | \(-0.0364523\pi\) |
−0.834477 | + | 0.551043i | \(0.814230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.60471 | − | 26.1146i | −0.0272468 | − | 0.154524i | ||||
\(170\) | −4.70502 | + | 2.71644i | −0.0276766 | + | 0.0159791i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −70.7357 | + | 122.518i | −0.411254 | + | 0.712313i | ||||
\(173\) | −36.6545 | + | 100.707i | −0.211876 | + | 0.582123i | −0.999417 | − | 0.0341382i | \(-0.989131\pi\) |
0.787542 | + | 0.616262i | \(0.211354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −34.7722 | − | 29.1773i | −0.198698 | − | 0.166727i | ||||
\(176\) | −45.5233 | + | 54.2525i | −0.258655 | + | 0.308253i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 89.7797 | + | 32.6771i | 0.504380 | + | 0.183579i | ||||
\(179\) | −102.022 | − | 58.9024i | −0.569955 | − | 0.329064i | 0.187176 | − | 0.982326i | \(-0.440066\pi\) |
−0.757131 | + | 0.653263i | \(0.773400\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 59.7681 | + | 103.521i | 0.330210 | + | 0.571941i | 0.982553 | − | 0.185983i | \(-0.0595470\pi\) |
−0.652343 | + | 0.757924i | \(0.726214\pi\) | |||||||
\(182\) | 31.8150 | − | 5.60984i | 0.174808 | − | 0.0308233i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.82994 | + | 0.666043i | −0.00994532 | + | 0.00361980i | ||||
\(185\) | −18.3786 | − | 3.24064i | −0.0993436 | − | 0.0175170i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 46.0335 | − | 38.6267i | 0.246169 | − | 0.206560i | ||||
\(188\) | 127.908i | 0.680359i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 32.7377 | 0.172304 | ||||||||
\(191\) | 146.062 | + | 174.070i | 0.764722 | + | 0.911361i | 0.998137 | − | 0.0610168i | \(-0.0194343\pi\) |
−0.233414 | + | 0.972377i | \(0.574990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7566 | − | 72.3465i | 0.0660966 | − | 0.374853i | −0.933760 | − | 0.357901i | \(-0.883493\pi\) |
0.999856 | − | 0.0169519i | \(-0.00539623\pi\) | |||||||
\(194\) | 22.8003 | + | 62.6434i | 0.117527 | + | 0.322904i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7456 | + | 89.2976i | 0.0803346 | + | 0.455600i | ||||
\(197\) | −80.0547 | + | 46.2196i | −0.406369 | + | 0.234617i | −0.689228 | − | 0.724544i | \(-0.742050\pi\) |
0.282859 | + | 0.959161i | \(0.408717\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.97251 | − | 3.41650i | 0.00991214 | − | 0.0171683i | −0.861027 | − | 0.508560i | \(-0.830178\pi\) |
0.870939 | + | 0.491391i | \(0.163511\pi\) | |||||||
\(200\) | 22.9451 | − | 63.0412i | 0.114726 | − | 0.315206i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.9371 | − | 9.17733i | −0.0541441 | − | 0.0454323i | ||||
\(203\) | −66.3664 | + | 79.0923i | −0.326928 | + | 0.389617i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 43.0339 | + | 15.6630i | 0.209921 | + | 0.0764051i | ||||
\(206\) | −158.341 | − | 91.4183i | −0.768646 | − | 0.443778i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.8732 | + | 41.3496i | 0.114775 | + | 0.198796i | ||||
\(209\) | −356.607 | + | 62.8794i | −1.70625 | + | 0.300858i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 57.0834 | − | 20.7767i | 0.270538 | − | 0.0984676i | −0.203189 | − | 0.979139i | \(-0.565131\pi\) |
0.473727 | + | 0.880672i | \(0.342908\pi\) | |||||||
\(212\) | −34.7391 | − | 6.12545i | −0.163864 | − | 0.0288936i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −147.303 | + | 123.602i | −0.688334 | + | 0.577581i | ||||
\(215\) | − | 80.0645i | − | 0.372393i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 80.8735 | 0.372689 | ||||||||
\(218\) | 165.724 | + | 197.502i | 0.760201 | + | 0.905972i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.95998 | − | 39.4720i | 0.0316363 | − | 0.179418i | ||||
\(221\) | −13.8563 | − | 38.0698i | −0.0626981 | − | 0.172262i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.2197 | − | 160.042i | −0.126546 | − | 0.717678i | −0.980378 | − | 0.197129i | \(-0.936838\pi\) |
0.853832 | − | 0.520549i | \(-0.174273\pi\) | |||||||
\(224\) | 9.37540 | − | 5.41289i | 0.0418545 | − | 0.0241647i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.3489 | + | 19.6568i | −0.0502162 | + | 0.0869771i | ||||
\(227\) | 89.6325 | − | 246.263i | 0.394857 | − | 1.08486i | −0.569899 | − | 0.821715i | \(-0.693018\pi\) |
0.964756 | − | 0.263146i | \(-0.0847601\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −93.1242 | − | 78.1405i | −0.406656 | − | 0.341225i | 0.416404 | − | 0.909180i | \(-0.363290\pi\) |
−0.823060 | + | 0.567955i | \(0.807735\pi\) | |||||||
\(230\) | 0.708418 | − | 0.844260i | 0.00308008 | − | 0.00367070i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −143.393 | − | 52.1907i | −0.618072 | − | 0.224960i | ||||
\(233\) | 362.949 | + | 209.549i | 1.55772 | + | 0.899352i | 0.997474 | + | 0.0710267i | \(0.0226275\pi\) |
0.560248 | + | 0.828325i | \(0.310706\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.1941 | − | 62.6900i | −0.154017 | − | 0.266766i | ||||
\(236\) | −110.145 | + | 19.4215i | −0.466715 | + | 0.0822944i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.63176 | + | 3.14170i | −0.0362679 | + | 0.0132004i | ||||
\(239\) | −102.988 | − | 18.1595i | −0.430912 | − | 0.0759813i | −0.0460143 | − | 0.998941i | \(-0.514652\pi\) |
−0.384897 | + | 0.922959i | \(0.625763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 36.2898 | − | 30.4507i | 0.150580 | − | 0.126352i | −0.564385 | − | 0.825511i | \(-0.690887\pi\) |
0.714966 | + | 0.699160i | \(0.246442\pi\) | |||||||
\(242\) | 272.210i | 1.12483i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −132.734 | −0.543991 | ||||||||
\(245\) | −32.9858 | − | 39.3110i | −0.134636 | − | 0.160453i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −42.3919 | + | 240.417i | −0.171627 | + | 0.973346i | ||||
\(248\) | 40.8807 | + | 112.319i | 0.164842 | + | 0.452899i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.5420 | + | 76.8007i | 0.0541681 | + | 0.307203i | ||||
\(251\) | 147.898 | − | 85.3890i | 0.589235 | − | 0.340195i | −0.175560 | − | 0.984469i | \(-0.556174\pi\) |
0.764795 | + | 0.644274i | \(0.222840\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.09511 | + | 10.5570i | −0.0240914 | + | 0.0417274i | ||||
\(254\) | 79.0572 | − | 217.208i | 0.311249 | − | 0.855149i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2567 | + | 10.2846i | 0.0478778 | + | 0.0401742i | ||||
\(257\) | 135.000 | − | 160.886i | 0.525291 | − | 0.626017i | −0.436533 | − | 0.899688i | \(-0.643794\pi\) |
0.961823 | + | 0.273671i | \(0.0882381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.6503 | − | 10.7918i | −0.114480 | − | 0.0416672i | ||||
\(260\) | −23.4015 | − | 13.5108i | −0.0900056 | − | 0.0519648i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −139.747 | − | 242.048i | −0.533384 | − | 0.923848i | ||||
\(263\) | 87.0793 | − | 15.3544i | 0.331100 | − | 0.0583818i | −0.00562710 | − | 0.999984i | \(-0.501791\pi\) |
0.336727 | + | 0.941602i | \(0.390680\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.7597 | − | 6.82796i | 0.0707912 | − | 0.0257659i | ||||
\(266\) | 54.5108 | + | 9.61173i | 0.204928 | + | 0.0361343i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 34.5651 | − | 29.0036i | 0.128974 | − | 0.108222i | ||||
\(269\) | − | 417.890i | − | 1.55350i | −0.629812 | − | 0.776748i | \(-0.716868\pi\) | ||
0.629812 | − | 0.776748i | \(-0.283132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.3344 | 0.108245 | 0.0541226 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541226 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(272\) | −8.72653 | − | 10.3999i | −0.0320828 | − | 0.0382348i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.43326 | − | 42.1561i | 0.0271287 | − | 0.153854i | ||||
\(275\) | −143.632 | − | 394.626i | −0.522298 | − | 1.43500i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.7591 | + | 185.786i | 0.118264 | + | 0.670707i | 0.985082 | + | 0.172083i | \(0.0550499\pi\) |
−0.866819 | + | 0.498624i | \(0.833839\pi\) | |||||||
\(278\) | 187.846 | − | 108.453i | 0.675705 | − | 0.390119i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.06338 | + | 5.30593i | −0.0109406 | + | 0.0189497i | ||||
\(281\) | −16.2664 | + | 44.6916i | −0.0578876 | + | 0.159045i | −0.965266 | − | 0.261271i | \(-0.915858\pi\) |
0.907378 | + | 0.420316i | \(0.138081\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 58.5606 | + | 49.1382i | 0.206928 | + | 0.173633i | 0.740362 | − | 0.672209i | \(-0.234654\pi\) |
−0.533434 | + | 0.845842i | \(0.679099\pi\) | |||||||
\(284\) | −63.9466 | + | 76.2086i | −0.225164 | + | 0.268340i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 280.859 | + | 102.224i | 0.982023 | + | 0.357427i | ||||
\(287\) | 67.0560 | + | 38.7148i | 0.233645 | + | 0.134895i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −138.740 | − | 240.305i | −0.480070 | − | 0.831506i | ||||
\(290\) | 85.0480 | − | 14.9963i | 0.293269 | − | 0.0517113i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 170.056 | − | 61.8953i | 0.582383 | − | 0.211970i | ||||
\(293\) | −321.453 | − | 56.6808i | −1.09711 | − | 0.193450i | −0.404339 | − | 0.914609i | \(-0.632499\pi\) |
−0.692770 | + | 0.721159i | \(0.743610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.4884 | − | 40.6866i | 0.164367 | − | 0.137921i | ||||
\(296\) | − | 46.6341i | − | 0.157548i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −288.119 | −0.966843 | ||||||||
\(299\) | 5.28268 | + | 6.29565i | 0.0176678 | + | 0.0210557i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.5068 | − | 133.314i | 0.0780956 | − | 0.442902i | ||||
\(302\) | 64.3034 | + | 176.672i | 0.212925 | + | 0.585007i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.2057 | + | 80.5645i | 0.0467292 | + | 0.265015i | ||||
\(305\) | 65.0554 | − | 37.5598i | 0.213296 | − | 0.123147i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 135.270 | − | 234.294i | 0.440618 | − | 0.763172i | −0.557118 | − | 0.830434i | \(-0.688093\pi\) |
0.997735 | + | 0.0672612i | \(0.0214261\pi\) | |||||||
\(308\) | 23.1778 | − | 63.6804i | 0.0752525 | − | 0.206755i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −51.8194 | − | 43.4816i | −0.167159 | − | 0.140263i | ||||
\(311\) | −271.552 | + | 323.624i | −0.873159 | + | 1.04059i | 0.125663 | + | 0.992073i | \(0.459894\pi\) |
−0.998822 | + | 0.0485173i | \(0.984550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 314.648 | + | 114.523i | 1.00527 | + | 0.365887i | 0.791613 | − | 0.611023i | \(-0.209242\pi\) |
0.213653 | + | 0.976910i | \(0.431464\pi\) | |||||||
\(314\) | −310.604 | − | 179.327i | −0.989184 | − | 0.571106i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −74.7138 | − | 129.408i | −0.236436 | − | 0.409519i | ||||
\(317\) | −61.1385 | + | 10.7804i | −0.192866 | + | 0.0340075i | −0.269247 | − | 0.963071i | \(-0.586775\pi\) |
0.0763807 | + | 0.997079i | \(0.475664\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −897.611 | + | 326.704i | −2.81383 | + | 1.02415i | ||||
\(320\) | −8.91750 | − | 1.57240i | −0.0278672 | − | 0.00491374i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.42744 | − | 1.19777i | 0.00443305 | − | 0.00371977i | ||||
\(323\) | − | 69.4139i | − | 0.214904i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −283.122 | −0.871146 | ||||||||
\(326\) | −237.746 | − | 283.335i | −0.729283 | − | 0.869125i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.8718 | + | 112.699i | −0.0605849 | + | 0.343594i | ||||
\(329\) | −41.8603 | − | 115.010i | −0.127235 | − | 0.349575i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −47.4950 | − | 269.357i | −0.143489 | − | 0.813768i | −0.968568 | − | 0.248750i | \(-0.919980\pi\) |
0.825078 | − | 0.565018i | \(-0.191131\pi\) | |||||||
\(332\) | 21.9852 | − | 12.6932i | 0.0662205 | − | 0.0382324i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 54.8874 | − | 95.0678i | 0.164334 | − | 0.284634i | ||||
\(335\) | −8.73389 | + | 23.9962i | −0.0260713 | + | 0.0716303i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 420.078 | + | 352.488i | 1.24652 | + | 1.04596i | 0.996985 | + | 0.0775926i | \(0.0247233\pi\) |
0.249538 | + | 0.968365i | \(0.419721\pi\) | |||||||
\(338\) | −24.1054 | + | 28.7277i | −0.0713178 | + | 0.0849932i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.21991 | + | 2.62783i | 0.0212350 | + | 0.00772892i | ||||
\(341\) | 647.975 | + | 374.109i | 1.90022 | + | 1.09709i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −90.2691 | − | 156.351i | −0.263175 | − | 0.455833i | ||||
\(344\) | 197.031 | − | 34.7419i | 0.572765 | − | 0.100994i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 142.422 | − | 51.8373i | 0.411623 | − | 0.149819i | ||||
\(347\) | −12.6788 | − | 2.23561i | −0.0365382 | − | 0.00644267i | 0.155349 | − | 0.987860i | \(-0.450350\pi\) |
−0.191887 | + | 0.981417i | \(0.561461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.25639 | − | 6.92793i | 0.0236573 | − | 0.0198508i | −0.630882 | − | 0.775879i | \(-0.717307\pi\) |
0.654540 | + | 0.756028i | \(0.272863\pi\) | |||||||
\(350\) | 64.1937i | 0.183411i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 100.157 | 0.284537 | ||||||||
\(353\) | −33.8253 | − | 40.3115i | −0.0958225 | − | 0.114197i | 0.716002 | − | 0.698098i | \(-0.245970\pi\) |
−0.811825 | + | 0.583901i | \(0.801526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.77669 | − | 55.4464i | 0.0275400 | − | 0.156187i | ||||
\(356\) | −46.2125 | − | 126.968i | −0.129810 | − | 0.356651i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.9300 | + | 164.070i | 0.0808100 | + | 0.458297i | ||||
\(359\) | −85.6783 | + | 49.4664i | −0.238658 | + | 0.137789i | −0.614560 | − | 0.788870i | \(-0.710666\pi\) |
0.375902 | + | 0.926660i | \(0.377333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −28.6385 | + | 49.6034i | −0.0793311 | + | 0.137405i | ||||
\(362\) | 57.8184 | − | 158.855i | 0.159719 | − | 0.438825i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −34.9985 | − | 29.3672i | −0.0961496 | − | 0.0806791i | ||||
\(365\) | −65.8332 | + | 78.4569i | −0.180365 | + | 0.214951i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −478.024 | − | 173.987i | −1.30252 | − | 0.474078i | −0.404702 | − | 0.914448i | \(-0.632625\pi\) |
−0.897816 | + | 0.440370i | \(0.854847\pi\) | |||||||
\(368\) | 2.38504 | + | 1.37701i | 0.00648110 | + | 0.00374186i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.1961 | + | 22.8563i | 0.0356651 | + | 0.0617738i | ||||
\(371\) | 33.2409 | − | 5.86127i | 0.0895982 | − | 0.0157986i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −412.649 | + | 150.192i | −1.10630 | + | 0.402660i | −0.829634 | − | 0.558307i | \(-0.811451\pi\) |
−0.276664 | + | 0.960967i | \(0.589229\pi\) | |||||||
\(374\) | −83.6925 | − | 14.7573i | −0.223777 | − | 0.0394579i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 138.569 | − | 116.273i | 0.368534 | − | 0.309237i | ||||
\(377\) | 643.987i | 1.70819i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 216.141 | 0.570293 | 0.285147 | − | 0.958484i | \(-0.407958\pi\) | ||||
0.285147 | + | 0.958484i | \(0.407958\pi\) | |||||||
\(380\) | −29.7599 | − | 35.4664i | −0.0783155 | − | 0.0933327i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 55.8027 | − | 316.473i | 0.146080 | − | 0.828462i | ||||
\(383\) | 224.513 | + | 616.845i | 0.586197 | + | 1.61056i | 0.777397 | + | 0.629011i | \(0.216540\pi\) |
−0.191200 | + | 0.981551i | \(0.561238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.65981 | + | 37.7697i | 0.0172982 | + | 0.0981031i | ||||
\(386\) | −89.9729 | + | 51.9459i | −0.233091 | + | 0.134575i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 47.1384 | − | 81.6460i | 0.121491 | − | 0.210428i | ||||
\(389\) | −80.9652 | + | 222.450i | −0.208137 | + | 0.571851i | −0.999205 | − | 0.0398773i | \(-0.987303\pi\) |
0.791068 | + | 0.611729i | \(0.209526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.79009 | − | 1.50206i | −0.00457822 | − | 0.00384159i | ||||
\(392\) | 82.4272 | − | 98.2330i | 0.210274 | − | 0.250594i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 122.845 | + | 44.7119i | 0.311789 | + | 0.113482i | ||||
\(395\) | 73.2374 | + | 42.2836i | 0.185411 | + | 0.107047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 150.540 | + | 260.743i | 0.379194 | + | 0.656783i | 0.990945 | − | 0.134267i | \(-0.0428680\pi\) |
−0.611751 | + | 0.791050i | \(0.709535\pi\) | |||||||
\(398\) | −5.49436 | + | 0.968803i | −0.0138049 | + | 0.00243418i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −89.1537 | + | 32.4493i | −0.222884 | + | 0.0811232i | ||||
\(401\) | −34.8014 | − | 6.13642i | −0.0867864 | − | 0.0153028i | 0.130086 | − | 0.991503i | \(-0.458475\pi\) |
−0.216873 | + | 0.976200i | \(0.569586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 386.417 | − | 324.243i | 0.958852 | − | 0.804572i | ||||
\(404\) | 20.1913i | 0.0499784i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 146.014 | 0.359641 | ||||||||
\(407\) | −187.643 | − | 223.624i | −0.461039 | − | 0.549445i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −46.1552 | + | 261.759i | −0.112849 | + | 0.639998i | 0.874944 | + | 0.484224i | \(0.160898\pi\) |
−0.987793 | + | 0.155773i | \(0.950213\pi\) | |||||||
\(410\) | −22.1509 | − | 60.8591i | −0.0540266 | − | 0.148437i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44.9002 | + | 254.642i | 0.108981 | + | 0.618062i | ||||
\(413\) | 92.6823 | − | 53.5102i | 0.224412 | − | 0.129565i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.18359 | + | 12.4423i | −0.0173099 | + | 0.0299816i | ||||
\(416\) | 23.0944 | − | 63.4515i | 0.0555155 | − | 0.152528i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 392.290 | + | 329.170i | 0.938492 | + | 0.787488i | ||||
\(419\) | −297.132 | + | 354.108i | −0.709145 | + | 0.845127i | −0.993528 | − | 0.113584i | \(-0.963767\pi\) |
0.284383 | + | 0.958711i | \(0.408211\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 744.427 | + | 270.949i | 1.76824 | + | 0.643585i | 0.999994 | + | 0.00342601i | \(0.00109054\pi\) |
0.768242 | + | 0.640159i | \(0.221132\pi\) | |||||||
\(422\) | −74.3995 | − | 42.9546i | −0.176302 | − | 0.101788i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.9432 | + | 43.2029i | 0.0588283 | + | 0.101894i | ||||
\(425\) | 79.2792 | − | 13.9791i | 0.186539 | − | 0.0328919i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 119.350 | − | 43.4397i | 0.279508 | − | 0.101732i | ||||
\(428\) | 267.809 | + | 47.2220i | 0.625722 | + | 0.110332i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −86.7379 | + | 72.7818i | −0.201716 | + | 0.169260i | ||||
\(431\) | − | 213.975i | − | 0.496462i | −0.968701 | − | 0.248231i | \(-0.920151\pi\) | ||
0.968701 | − | 0.248231i | \(-0.0798492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 122.246 | 0.282323 | 0.141162 | − | 0.989987i | \(-0.454916\pi\) | ||||
0.141162 | + | 0.989987i | \(0.454916\pi\) | |||||||
\(434\) | −73.5171 | − | 87.6143i | −0.169394 | − | 0.201876i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63.3144 | − | 359.074i | 0.145217 | − | 0.823564i | ||||
\(437\) | 4.81603 | + | 13.2319i | 0.0110207 | + | 0.0302790i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.1853 | + | 131.490i | 0.0528139 | + | 0.299522i | 0.999761 | − | 0.0218673i | \(-0.00696114\pi\) |
−0.946947 | + | 0.321390i | \(0.895850\pi\) | |||||||
\(440\) | −49.0889 | + | 28.3415i | −0.111566 | + | 0.0644125i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.6471 | + | 49.6182i | −0.0648124 | + | 0.112258i | ||||
\(443\) | 48.3138 | − | 132.741i | 0.109060 | − | 0.299641i | −0.873142 | − | 0.487466i | \(-0.837921\pi\) |
0.982203 | + | 0.187825i | \(0.0601437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 58.5778 | + | 49.1526i | 0.131635 | + | 0.110455i | ||||
\(446\) | −147.729 | + | 176.056i | −0.331231 | + | 0.394745i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −14.3867 | − | 5.23632i | −0.0321131 | − | 0.0116882i | ||||
\(449\) | 14.1480 | + | 8.16837i | 0.0315101 | + | 0.0181924i | 0.515672 | − | 0.856786i | \(-0.327542\pi\) |
−0.484162 | + | 0.874978i | \(0.660876\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 358.178 | + | 620.382i | 0.794186 | + | 1.37557i | ||||
\(452\) | 31.6118 | − | 5.57401i | 0.0699376 | − | 0.0123319i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −348.269 | + | 126.760i | −0.767112 | + | 0.279206i | ||||
\(455\) | 25.4635 | + | 4.48990i | 0.0559637 | + | 0.00986792i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −413.177 | + | 346.697i | −0.904107 | + | 0.758636i | −0.970989 | − | 0.239125i | \(-0.923139\pi\) |
0.0668816 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(458\) | 171.919i | 0.375369i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.55861 | −0.00338828 | ||||||||
\(461\) | 232.751 | + | 277.382i | 0.504882 | + | 0.601696i | 0.956937 | − | 0.290295i | \(-0.0937533\pi\) |
−0.452055 | + | 0.891990i | \(0.649309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.1055 | − | 187.751i | 0.0715022 | − | 0.405509i | −0.927959 | − | 0.372683i | \(-0.878438\pi\) |
0.999461 | − | 0.0328264i | \(-0.0104508\pi\) | |||||||
\(464\) | 73.8088 | + | 202.788i | 0.159071 | + | 0.437043i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −102.920 | − | 583.689i | −0.220859 | − | 1.25255i | ||||
\(467\) | −617.016 | + | 356.234i | −1.32123 | + | 0.762814i | −0.983925 | − | 0.178580i | \(-0.942850\pi\) |
−0.337308 | + | 0.941394i | \(0.609516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.5878 | + | 37.3912i | −0.0460294 | + | 0.0797253i | ||||
\(470\) | −35.0134 | + | 96.1986i | −0.0744966 | + | 0.204678i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 121.166 | + | 101.670i | 0.256708 | + | 0.215403i | ||||
\(473\) | 805.030 | − | 959.397i | 1.70197 | − | 2.02832i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −455.839 | − | 165.912i | −0.959661 | − | 0.349288i | ||||
\(476\) | 11.2502 | + | 6.49529i | 0.0236348 | + | 0.0136456i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 73.9468 | + | 128.080i | 0.154700 | + | 0.267949i | ||||
\(479\) | −224.974 | + | 39.6689i | −0.469674 | + | 0.0828162i | −0.403476 | − | 0.914990i | \(-0.632198\pi\) |
−0.0661981 | + | 0.997807i | \(0.521087\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −184.938 | + | 67.3118i | −0.384486 | + | 0.139941i | ||||
\(482\) | −65.9777 | − | 11.6336i | −0.136883 | − | 0.0241362i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 294.899 | − | 247.450i | 0.609295 | − | 0.511259i | ||||
\(485\) | 53.3551i | 0.110011i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 115.510 | 0.237188 | 0.118594 | − | 0.992943i | \(-0.462161\pi\) | ||||
0.118594 | + | 0.992943i | \(0.462161\pi\) | |||||||
\(488\) | 120.660 | + | 143.797i | 0.247254 | + | 0.294666i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.6022 | + | 71.4704i | −0.0257187 | + | 0.145858i | ||||
\(491\) | −150.903 | − | 414.604i | −0.307339 | − | 0.844406i | −0.993173 | − | 0.116649i | \(-0.962785\pi\) |
0.685834 | − | 0.727758i | \(-0.259437\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.7966 | − | 180.328i | −0.0644962 | − | 0.365776i | ||||
\(494\) | 298.991 | − | 172.623i | 0.605245 | − | 0.349439i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 84.5185 | − | 146.390i | 0.170400 | − | 0.295142i | ||||
\(497\) | 32.5579 | − | 89.4520i | 0.0655088 | − | 0.179984i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 216.247 | + | 181.453i | 0.433361 | + | 0.363633i | 0.833218 | − | 0.552945i | \(-0.186496\pi\) |
−0.399857 | + | 0.916577i | \(0.630940\pi\) | |||||||
\(500\) | 70.8918 | − | 84.4856i | 0.141784 | − | 0.168971i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −226.951 | − | 82.6035i | −0.452094 | − | 0.164549i | ||||
\(503\) | −595.298 | − | 343.696i | −1.18350 | − | 0.683291i | −0.226675 | − | 0.973971i | \(-0.572785\pi\) |
−0.956821 | + | 0.290679i | \(0.906119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.71354 | − | 9.89615i | −0.0113139 | − | 0.0195963i | ||||
\(506\) | 16.9777 | − | 2.99362i | 0.0335527 | − | 0.00591625i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −307.178 | + | 111.804i | −0.604682 | + | 0.220086i | ||||
\(509\) | 440.490 | + | 77.6702i | 0.865402 | + | 0.152594i | 0.588690 | − | 0.808359i | \(-0.299644\pi\) |
0.276712 | + | 0.960953i | \(0.410755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −132.652 | + | 111.308i | −0.259593 | + | 0.217824i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −297.016 | −0.577853 | ||||||||
\(515\) | −94.0626 | − | 112.099i | −0.182646 | − | 0.217669i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 196.627 | − | 1115.13i | 0.380322 | − | 2.15692i | ||||
\(518\) | 15.2619 | + | 41.9318i | 0.0294632 | + | 0.0809494i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.63587 | + | 37.6339i | 0.0127613 | + | 0.0723728i | ||||
\(521\) | 265.555 | − | 153.318i | 0.509703 | − | 0.294277i | −0.223008 | − | 0.974817i | \(-0.571588\pi\) |
0.732712 | + | 0.680539i | \(0.238254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 185.369 | − | 321.068i | 0.354434 | − | 0.613897i | −0.632587 | − | 0.774489i | \(-0.718007\pi\) |
0.987021 | + | 0.160592i | \(0.0513403\pi\) | |||||||
\(524\) | −135.188 | + | 371.426i | −0.257992 | + | 0.708828i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −95.7927 | − | 80.3796i | −0.182115 | − | 0.152813i | ||||
\(527\) | −92.1942 | + | 109.873i | −0.174942 | + | 0.208487i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −496.652 | − | 180.767i | −0.938851 | − | 0.341714i | ||||
\(530\) | −24.4503 | − | 14.1164i | −0.0461327 | − | 0.0266347i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −39.1396 | − | 67.7918i | −0.0735707 | − | 0.127428i | ||||
\(533\) | 475.615 | − | 83.8637i | 0.892335 | − | 0.157343i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −144.621 | + | 52.6377i | −0.270320 | + | 0.0983883i | ||||
\(536\) | −62.8421 | − | 11.0808i | −0.117243 | − | 0.0206731i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −452.722 | + | 379.879i | −0.841490 | + | 0.706094i | ||||
\(539\) | − | 802.720i | − | 1.48928i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −656.732 | −1.21392 | −0.606961 | − | 0.794732i | \(-0.707612\pi\) | ||||
−0.606961 | + | 0.794732i | \(0.707612\pi\) | |||||||
\(542\) | −26.6662 | − | 31.7795i | −0.0491995 | − | 0.0586337i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.33395 | + | 18.9078i | −0.00612859 | + | 0.0347570i | ||||
\(545\) | 70.5758 | + | 193.905i | 0.129497 | + | 0.355790i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −73.1807 | − | 415.029i | −0.133786 | − | 0.758736i | −0.975698 | − | 0.219121i | \(-0.929681\pi\) |
0.841912 | − | 0.539615i | \(-0.181430\pi\) | |||||||
\(548\) | −52.4270 | + | 30.2687i | −0.0956696 | + | 0.0552349i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −296.951 | + | 514.334i | −0.539910 | + | 0.935152i | ||||
\(551\) | −377.381 | + | 1036.85i | −0.684902 | + | 1.88175i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 109.532 | + | 91.9078i | 0.198068 | + | 0.166199i | ||||
\(554\) | 171.492 | − | 204.376i | 0.309552 | − | 0.368910i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −288.252 | − | 104.915i | −0.518439 | − | 0.188696i | ||||
\(557\) | −412.640 | − | 238.238i | −0.740825 | − | 0.427715i | 0.0815442 | − | 0.996670i | \(-0.474015\pi\) |
−0.822369 | + | 0.568954i | \(0.807348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −422.172 | − | 731.223i | −0.755227 | − | 1.30809i | ||||
\(560\) | 8.53291 | − | 1.50458i | 0.0152373 | − | 0.00268675i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 63.2035 | − | 23.0042i | 0.112462 | − | 0.0409327i | ||||
\(563\) | 206.039 | + | 36.3303i | 0.365967 | + | 0.0645298i | 0.353608 | − | 0.935394i | \(-0.384955\pi\) |
0.0123591 | + | 0.999924i | \(0.496066\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.9163 | + | 11.6771i | −0.0246306 | + | 0.0206675i | ||||
\(566\) | − | 108.110i | − | 0.191007i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 140.691 | 0.247695 | ||||||||
\(569\) | −569.179 | − | 678.321i | −1.00031 | − | 1.19213i | −0.981335 | − | 0.192308i | \(-0.938403\pi\) |
−0.0189794 | − | 0.999820i | \(-0.506042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 127.475 | − | 722.948i | 0.223249 | − | 1.26611i | −0.642755 | − | 0.766072i | \(-0.722209\pi\) |
0.866004 | − | 0.500037i | \(-0.166680\pi\) | |||||||
\(572\) | −144.567 | − | 397.194i | −0.252739 | − | 0.694395i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.0148 | − | 107.838i | −0.0331269 | − | 0.187872i | ||||
\(575\) | −14.1426 | + | 8.16524i | −0.0245959 | + | 0.0142004i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −349.289 | + | 604.986i | −0.605353 | + | 1.04850i | 0.386642 | + | 0.922230i | \(0.373635\pi\) |
−0.991996 | + | 0.126273i | \(0.959699\pi\) | |||||||
\(578\) | −134.214 | + | 368.751i | −0.232205 | + | 0.637978i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −93.5582 | − | 78.5047i | −0.161307 | − | 0.135353i | ||||
\(581\) | −15.6143 | + | 18.6084i | −0.0268748 | + | 0.0320282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 293.447 | + | 106.806i | 0.503339 | + | 0.183200i | ||||
\(584\) | −221.642 | − | 127.965i | −0.379523 | − | 0.219118i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 230.808 | + | 399.771i | 0.393870 | + | 0.682204i | ||||
\(587\) | 1118.40 | − | 197.205i | 1.90529 | − | 0.335953i | 0.908626 | − | 0.417610i | \(-0.137132\pi\) |
0.996660 | + | 0.0816570i | \(0.0260212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 812.156 | − | 295.601i | 1.37887 | − | 0.501869i | ||||
\(590\) | −88.1557 | − | 15.5442i | −0.149416 | − | 0.0263461i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −50.5211 | + | 42.3922i | −0.0853396 | + | 0.0716085i | ||||
\(593\) | − | 463.710i | − | 0.781973i | −0.920396 | − | 0.390987i | \(-0.872134\pi\) | ||
0.920396 | − | 0.390987i | \(-0.127866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.35191 | −0.0123561 | ||||||||
\(596\) | 261.911 | + | 312.134i | 0.439449 | + | 0.523715i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.01823 | − | 11.4460i | 0.00337497 | − | 0.0191404i | ||||
\(599\) | −192.617 | − | 529.210i | −0.321564 | − | 0.883489i | −0.990170 | − | 0.139872i | \(-0.955331\pi\) |
0.668606 | − | 0.743617i | \(-0.266891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 122.144 | + | 692.715i | 0.203235 | + | 1.15260i | 0.900193 | + | 0.435492i | \(0.143425\pi\) |
−0.696958 | + | 0.717112i | \(0.745463\pi\) | |||||||
\(602\) | −165.794 | + | 95.7211i | −0.275405 | + | 0.159005i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 132.943 | − | 230.265i | 0.220105 | − | 0.381233i | ||||
\(605\) | −74.5148 | + | 204.728i | −0.123165 | + | 0.338393i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 313.569 | + | 263.116i | 0.516589 | + | 0.433470i | 0.863441 | − | 0.504450i | \(-0.168305\pi\) |
−0.346852 | + | 0.937920i | \(0.612749\pi\) | |||||||
\(608\) | 74.3660 | − | 88.6260i | 0.122313 | − | 0.145766i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −99.8283 | − | 36.3345i | −0.163653 | − | 0.0595648i | ||||
\(611\) | −661.116 | − | 381.696i | −1.08202 | − | 0.624706i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 55.6369 | + | 96.3660i | 0.0907617 | + | 0.157204i | 0.907832 | − | 0.419334i | \(-0.137737\pi\) |
−0.817070 | + | 0.576538i | \(0.804403\pi\) | |||||||
\(614\) | −376.788 | + | 66.4379i | −0.613661 | + | 0.108205i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −90.0577 | + | 32.7783i | −0.146198 | + | 0.0532116i | ||||
\(617\) | −438.710 | − | 77.3564i | −0.711037 | − | 0.125375i | −0.193581 | − | 0.981084i | \(-0.562010\pi\) |
−0.517457 | + | 0.855709i | \(0.673121\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −308.760 | + | 259.080i | −0.498804 | + | 0.418546i | −0.857169 | − | 0.515035i | \(-0.827779\pi\) |
0.358365 | + | 0.933582i | \(0.383334\pi\) | |||||||
\(620\) | 95.6651i | 0.154299i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 597.449 | 0.960530 | ||||||||
\(623\) | 83.1054 | + | 99.0411i | 0.133395 | + | 0.158975i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 92.1298 | − | 522.494i | 0.147408 | − | 0.835991i | ||||
\(626\) | −161.959 | − | 444.980i | −0.258721 | − | 0.710831i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 88.0768 | + | 499.508i | 0.140250 | + | 0.795395i | ||||
\(629\) | 48.4622 | − | 27.9797i | 0.0770465 | − | 0.0444828i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −157.151 | + | 272.194i | −0.249052 | + | 0.431370i | −0.963263 | − | 0.268560i | \(-0.913452\pi\) |
0.714211 | + | 0.699930i | \(0.246786\pi\) | |||||||
\(632\) | −72.2766 | + | 198.578i | −0.114362 | + | 0.314206i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 67.2562 | + | 56.4346i | 0.106082 | + | 0.0890136i | ||||
\(635\) | 118.917 | − | 141.720i | 0.187271 | − | 0.223181i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −508.540 | − | 185.093i | −0.798336 | − | 0.290570i | ||||
\(638\) | 1169.90 | + | 675.441i | 1.83370 | + | 1.05868i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.40290 | + | 11.0901i | 0.0100045 | + | 0.0173284i | ||||
\(641\) | −831.894 | + | 146.685i | −1.29781 | + | 0.228838i | −0.779525 | − | 0.626371i | \(-0.784539\pi\) |
−0.518282 | + | 0.855210i | \(0.673428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 305.658 | − | 111.250i | 0.475363 | − | 0.173018i | −0.0932174 | − | 0.995646i | \(-0.529715\pi\) |
0.568580 | + | 0.822628i | \(0.307493\pi\) | |||||||
\(644\) | −2.59520 | − | 0.457604i | −0.00402982 | − | 0.000710566i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −75.1995 | + | 63.0999i | −0.116408 | + | 0.0976779i | ||||
\(647\) | 1029.91i | 1.59182i | 0.605412 | + | 0.795912i | \(0.293008\pi\) | ||||
−0.605412 | + | 0.795912i | \(0.706992\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 990.121 | 1.52561 | ||||||||
\(650\) | 257.369 | + | 306.721i | 0.395953 | + | 0.471878i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −90.8304 | + | 515.125i | −0.139310 | + | 0.790069i | ||||
\(653\) | 247.063 | + | 678.801i | 0.378351 | + | 1.03951i | 0.972040 | + | 0.234817i | \(0.0754490\pi\) |
−0.593688 | + | 0.804695i | \(0.702329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.8444 | − | 220.297i | −0.0593044 | − | 0.336332i | ||||
\(656\) | 140.157 | − | 80.9194i | 0.213653 | − | 0.123353i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −86.5437 | + | 149.898i | −0.131525 | + | 0.227809i | ||||
\(659\) | 325.530 | − | 894.386i | 0.493975 | − | 1.35719i | −0.403038 | − | 0.915183i | \(-0.632046\pi\) |
0.897014 | − | 0.442003i | \(-0.145732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 149.297 | + | 125.275i | 0.225866 | + | 0.189524i | 0.748697 | − | 0.662912i | \(-0.230680\pi\) |
−0.522831 | + | 0.852436i | \(0.675124\pi\) | |||||||
\(662\) | −248.634 | + | 296.310i | −0.375579 | + | 0.447598i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.7366 | − | 12.2791i | −0.0508081 | − | 0.0184926i | ||||
\(665\) | 38.3662 | + | 22.1507i | 0.0576935 | + | 0.0333094i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5726 | + | 32.1686i | 0.0278449 | + | 0.0482288i | ||||
\(668\) | −152.887 | + | 26.9580i | −0.228872 | + | 0.0403563i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 33.9357 | − | 12.3516i | 0.0506503 | − | 0.0184352i | ||||
\(671\) | 1157.20 | + | 204.046i | 1.72459 | + | 0.304092i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 268.446 | − | 225.253i | 0.398880 | − | 0.334700i | −0.421181 | − | 0.906977i | \(-0.638384\pi\) |
0.820060 | + | 0.572277i | \(0.193940\pi\) | |||||||
\(674\) | − | 775.517i | − | 1.15062i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 53.0349 | 0.0784541 | ||||||||
\(677\) | 722.303 | + | 860.807i | 1.06692 | + | 1.27150i | 0.960828 | + | 0.277145i | \(0.0893883\pi\) |
0.106089 | + | 0.994357i | \(0.466167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.6649 | + | 88.8403i | −0.0230706 | + | 0.130840i | ||||
\(680\) | −3.71632 | − | 10.2105i | −0.00546517 | − | 0.0150154i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −183.744 | − | 1042.06i | −0.269419 | − | 1.52795i | ||||
\(683\) | 132.500 | − | 76.4992i | 0.193998 | − | 0.112005i | −0.399855 | − | 0.916578i | \(-0.630940\pi\) |
0.593853 | + | 0.804574i | \(0.297606\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.1303 | − | 29.6706i | 0.0250078 | − | 0.0433147i | ||||
\(686\) | −87.3244 | + | 239.922i | −0.127295 | + | 0.349740i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −216.747 | − | 181.872i | −0.315039 | − | 0.264349i | ||||
\(689\) | 135.327 | − | 161.277i | 0.196411 | − | 0.234074i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 889.111 | + | 323.610i | 1.28670 | + | 0.468321i | 0.892643 | − | 0.450764i | \(-0.148848\pi\) |
0.394059 | + | 0.919085i | \(0.371071\pi\) | |||||||
\(692\) | −185.625 | − | 107.171i | −0.268244 | − | 0.154871i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.10354 | + | 15.7678i | 0.0131175 | + | 0.0227202i | ||||
\(695\) | 170.966 | − | 30.1459i | 0.245994 | − | 0.0433754i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −129.040 | + | 46.9666i | −0.185136 | + | 0.0673839i | ||||
\(698\) | −15.0108 | − | 2.64680i | −0.0215054 | − | 0.00379198i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 69.5443 | − | 58.3546i | 0.0993490 | − | 0.0833637i | ||||
\(701\) | 250.910i | 0.357932i | 0.983855 | + | 0.178966i | \(0.0572752\pi\) | ||||
−0.983855 | + | 0.178966i | \(0.942725\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −337.202 | −0.479662 | ||||||||
\(704\) | −91.0465 | − | 108.505i | −0.129327 | − | 0.154126i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.9229 | + | 73.2894i | −0.0183044 | + | 0.103809i | ||||
\(707\) | −6.60800 | − | 18.1553i | −0.00934653 | − | 0.0256794i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 228.169 | + | 1294.01i | 0.321818 | + | 1.82512i | 0.531151 | + | 0.847277i | \(0.321760\pi\) |
−0.209333 | + | 0.977844i | \(0.567129\pi\) | |||||||
\(710\) | −68.9553 | + | 39.8113i | −0.0971201 | + | 0.0560723i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −95.5416 | + | 165.483i | −0.134188 | + | 0.232420i | ||||
\(713\) | 9.95128 | − | 27.3409i | 0.0139569 | − | 0.0383463i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 183.249 | + | 153.764i | 0.256293 | + | 0.215055i | ||||
\(716\) | 151.447 | − | 180.487i | 0.211518 | − | 0.252078i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 131.474 | + | 47.8528i | 0.183112 | + | 0.0666473i | ||||
\(719\) | 503.280 | + | 290.569i | 0.699972 | + | 0.404129i | 0.807337 | − | 0.590091i | \(-0.200908\pi\) |
−0.107365 | + | 0.994220i | \(0.534241\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −123.709 | − | 214.271i | −0.171580 | − | 0.297185i | ||||
\(722\) | 79.7714 | − | 14.0658i | 0.110487 | − | 0.0194818i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −224.654 | + | 81.7675i | −0.310296 | + | 0.112939i | ||||
\(725\) | −1260.20 | − | 222.208i | −1.73821 | − | 0.306494i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −516.182 | + | 433.128i | −0.710016 | + | 0.595774i | −0.924604 | − | 0.380931i | \(-0.875604\pi\) |
0.214588 | + | 0.976705i | \(0.431159\pi\) | |||||||
\(728\) | 64.6115i | 0.0887521i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 144.841 | 0.198413 | ||||||||
\(731\) | 154.319 | + | 183.911i | 0.211107 | + | 0.251588i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.1418 | − | 244.669i | 0.0588565 | − | 0.333792i | −0.941134 | − | 0.338032i | \(-0.890239\pi\) |
0.999991 | + | 0.00424043i | \(0.00134977\pi\) | |||||||
\(734\) | 246.054 | + | 676.029i | 0.335224 | + | 0.921020i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.676318 | − | 3.83559i | −0.000918910 | − | 0.00521140i | ||||
\(737\) | −345.932 | + | 199.724i | −0.469379 | + | 0.270996i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.7967 | + | 37.7530i | −0.0294949 | + | 0.0510866i | −0.880396 | − | 0.474239i | \(-0.842723\pi\) |
0.850901 | + | 0.525326i | \(0.176057\pi\) | |||||||
\(740\) | 12.7656 | − | 35.0732i | 0.0172508 | − | 0.0473963i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.5671 | − | 30.6834i | −0.0492818 | − | 0.0413524i | ||||
\(743\) | −805.304 | + | 959.724i | −1.08385 | + | 1.29169i | −0.129968 | + | 0.991518i | \(0.541488\pi\) |
−0.953886 | + | 0.300169i | \(0.902957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −216.693 | − | 78.8697i | −0.290863 | − | 0.105865i | ||||
\(746\) | 537.825 | + | 310.513i | 0.720945 | + | 0.416238i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 60.0925 | + | 104.083i | 0.0803376 | + | 0.139149i | ||||
\(749\) | −256.259 | + | 45.1854i | −0.342135 | + | 0.0603277i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −81.7809 | + | 29.7658i | −0.108896 | + | 0.0396349i | −0.395894 | − | 0.918296i | \(-0.629565\pi\) |
0.286998 | + | 0.957931i | \(0.407343\pi\) | |||||||
\(752\) | −251.929 | − | 44.4218i | −0.335012 | − | 0.0590716i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 697.664 | − | 585.409i | 0.925283 | − | 0.776405i | ||||
\(755\) | 150.476i | 0.199307i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −849.639 | −1.12238 | −0.561188 | − | 0.827688i | \(-0.689656\pi\) | ||||
−0.561188 | + | 0.827688i | \(0.689656\pi\) | |||||||
\(758\) | −196.481 | − | 234.157i | −0.259209 | − | 0.308914i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.3697 | + | 64.4807i | −0.0149601 | + | 0.0848431i | ||||
\(761\) | 218.959 | + | 601.584i | 0.287725 | + | 0.790518i | 0.996384 | + | 0.0849663i | \(0.0270783\pi\) |
−0.708659 | + | 0.705551i | \(0.750700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 60.5838 | + | 343.588i | 0.0794021 | + | 0.450312i | ||||
\(764\) | −393.578 | + | 227.232i | −0.515154 | + | 0.297424i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 464.168 | − | 803.963i | 0.605964 | − | 1.04956i | ||||
\(767\) | 228.305 | − | 627.262i | 0.297659 | − | 0.817812i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −129.861 | − | 108.966i | −0.168869 | − | 0.141698i | 0.554436 | − | 0.832226i | \(-0.312934\pi\) |
−0.723306 | + | 0.690528i | \(0.757378\pi\) | |||||||
\(770\) | 34.8638 | − | 41.5490i | 0.0452776 | − | 0.0539598i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 138.065 | + | 50.2514i | 0.178840 | + | 0.0650925i | ||||
\(773\) | −1141.45 | − | 659.019i | −1.47666 | − | 0.852547i | −0.477003 | − | 0.878902i | \(-0.658277\pi\) |
−0.999653 | + | 0.0263542i | \(0.991610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 501.170 | + | 868.052i | 0.646671 | + | 1.12007i | ||||
\(776\) | −131.302 | + | 23.1521i | −0.169203 | + | 0.0298351i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 314.592 | − | 114.502i | 0.404360 | − | 0.147175i | ||||
\(779\) | 814.904 | + | 143.690i | 1.04609 | + | 0.184454i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 674.652 | − | 566.101i | 0.863832 | − | 0.724841i | ||||
\(782\) | 3.30472i | 0.00422599i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −181.350 | −0.231314 | ||||||||
\(785\) | −184.514 | − | 219.896i | −0.235050 | − | 0.280122i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −199.680 | + | 1132.44i | −0.253723 | + | 1.43893i | 0.545608 | + | 0.838040i | \(0.316299\pi\) |
−0.799331 | + | 0.600891i | \(0.794812\pi\) | |||||||
\(788\) | −63.2321 | − | 173.729i | −0.0802438 | − | 0.220468i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20.7677 | − | 117.779i | −0.0262882 | − | 0.149088i | ||||
\(791\) | −26.6001 | + | 15.3575i | −0.0336284 | + | 0.0194154i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 396.098 | − | 686.061i | 0.499492 | − | 0.865146i | ||||
\(794\) | 145.629 | − | 400.113i | 0.183412 | − | 0.503921i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.04414 | + | 5.07163i | 0.00759314 | + | 0.00637140i | ||||
\(797\) | −97.8409 | + | 116.602i | −0.122762 | + | 0.146301i | −0.823925 | − | 0.566699i | \(-0.808220\pi\) |
0.701163 | + | 0.713001i | \(0.252664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 203.970 | + | 74.2390i | 0.255282 | + | 0.0929149i | ||||
\(800\) | 116.198 | + | 67.0870i | 0.145248 | + | 0.0838588i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.9879 | + | 43.2803i | 0.0311570 | + | 0.0539655i | ||||
\(803\) | −1577.73 | + | 278.197i | −1.96480 | + | 0.346447i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.40145 | − | 0.510086i | 0.00174093 | − | 0.000633647i | ||||
\(806\) | −702.537 | − | 123.876i | −0.871634 | − | 0.153693i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21.8742 | − | 18.3547i | 0.0270721 | − | 0.0227162i | ||||
\(809\) | 1046.40i | 1.29345i | 0.762725 | + | 0.646723i | \(0.223861\pi\) | ||||
−0.762725 | + | 0.646723i | \(0.776139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −360.583 | −0.444615 | −0.222308 | − | 0.974977i | \(-0.571359\pi\) | ||||
−0.222308 | + | 0.974977i | \(0.571359\pi\) | |||||||
\(812\) | −132.733 | − | 158.185i | −0.163464 | − | 0.194809i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −71.6885 | + | 406.566i | −0.0880695 | + | 0.499467i | ||||
\(815\) | −101.248 | − | 278.175i | −0.124230 | − | 0.341319i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −251.212 | − | 1424.70i | −0.307481 | − | 1.74381i | ||||
\(818\) | 325.534 | − | 187.947i | 0.397963 | − | 0.229764i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −45.7957 | + | 79.3204i | −0.0558484 | + | 0.0967322i | ||||
\(821\) | 519.549 | − | 1427.45i | 0.632824 | − | 1.73867i | −0.0403490 | − | 0.999186i | \(-0.512847\pi\) |
0.673173 | − | 0.739485i | \(-0.264931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −647.973 | − | 543.714i | −0.787331 | − | 0.660649i | 0.157753 | − | 0.987479i | \(-0.449575\pi\) |
−0.945083 | + | 0.326830i | \(0.894020\pi\) | |||||||
\(824\) | 235.050 | − | 280.122i | 0.285255 | − | 0.339954i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −142.222 | − | 51.7646i | −0.172182 | − | 0.0626690i | ||||
\(827\) | 939.412 | + | 542.370i | 1.13593 | + | 0.655828i | 0.945419 | − | 0.325858i | \(-0.105653\pi\) |
0.190508 | + | 0.981686i | \(0.438986\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −765.727 | − | 1326.28i | −0.923675 | − | 1.59985i | −0.793678 | − | 0.608338i | \(-0.791836\pi\) |
−0.129997 | − | 0.991514i | \(-0.541497\pi\) | |||||||
\(830\) | 20.0096 | − | 3.52823i | 0.0241079 | − | 0.00425088i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −89.7339 | + | 32.6605i | −0.107853 | + | 0.0392554i | ||||
\(833\) | 151.539 | + | 26.7204i | 0.181919 | + | 0.0320773i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 67.3044 | − | 56.4751i | 0.0806041 | − | 0.0676348i | ||||
\(836\) | − | 724.216i | − | 0.866287i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 653.728 | 0.780105 | ||||||||
\(839\) | −83.5716 | − | 99.5967i | −0.0996085 | − | 0.118709i | 0.713937 | − | 0.700210i | \(-0.246910\pi\) |
−0.813546 | + | 0.581501i | \(0.802466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −359.394 | + | 2038.22i | −0.427341 | + | 2.42357i | ||||
\(842\) | −383.180 | − | 1052.78i | −0.455084 | − | 1.25033i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.0972 | + | 119.648i | 0.0249967 | + | 0.141763i | ||||
\(845\) | −25.9935 | + | 15.0073i | −0.0307615 | + | 0.0177602i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −184.180 | + | 319.010i | −0.217450 | + | 0.376635i | ||||
\(848\) | 24.1295 | − | 66.2954i | 0.0284547 | − | 0.0781785i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −87.2121 | − | 73.1796i | −0.102602 | − | 0.0860937i | ||||
\(851\) | −7.29679 | + | 8.69597i | −0.00857437 | + | 0.0102185i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 440.159 | + | 160.205i | 0.516012 | + | 0.187813i | 0.586882 | − | 0.809672i | \(-0.300355\pi\) |
−0.0708696 | + | 0.997486i | \(0.522577\pi\) | |||||||
\(854\) | −155.554 | − | 89.8091i | −0.182148 | − | 0.105163i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −192.291 | − | 333.058i | −0.224639 | − | 0.389086i | ||||
\(857\) | 871.104 | − | 153.599i | 1.01646 | − | 0.179229i | 0.359491 | − | 0.933149i | \(-0.382950\pi\) |
0.656967 | + | 0.753920i | \(0.271839\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −405.595 | + | 147.624i | −0.472171 | + | 0.171856i | −0.567135 | − | 0.823625i | \(-0.691948\pi\) |
0.0949648 | + | 0.995481i | \(0.469726\pi\) | |||||||
\(860\) | 157.696 | + | 27.8061i | 0.183368 | + | 0.0323327i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −231.810 | + | 194.512i | −0.268921 | + | 0.225652i | ||||
\(863\) | 279.578i | 0.323961i | 0.986794 | + | 0.161980i | \(0.0517881\pi\) | ||||
−0.986794 | + | 0.161980i | \(0.948212\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 121.305 | 0.140236 | ||||||||
\(866\) | −111.126 | − | 132.435i | −0.128321 | − | 0.152927i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −28.0871 | + | 159.290i | −0.0323584 | + | 0.183513i | ||||
\(869\) | 452.437 | + | 1243.06i | 0.520641 | + | 1.43045i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.7633 | + | 265.208i | 0.0536892 | + | 0.304487i | ||||
\(872\) | −446.558 | + | 257.820i | −0.512108 | + | 0.295666i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.95687 | − | 17.2458i | 0.0113923 | − | 0.0197320i | ||||
\(875\) | −36.0940 | + | 99.1673i | −0.0412502 | + | 0.113334i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1227.88 | − | 1030.31i | −1.40009 | − | 1.17482i | −0.961058 | − | 0.276346i | \(-0.910877\pi\) |
−0.439033 | − | 0.898471i | \(-0.644679\pi\) | |||||||
\(878\) | 121.374 | − | 144.648i | 0.138239 | − | 0.164747i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 75.3275 | + | 27.4170i | 0.0855994 | + | 0.0311556i | ||||
\(881\) | −37.7796 | − | 21.8121i | −0.0428827 | − | 0.0247583i | 0.478405 | − | 0.878139i | \(-0.341215\pi\) |
−0.521288 | + | 0.853381i | \(0.674548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −460.205 | − | 797.099i | −0.521184 | − | 0.902717i | −0.999696 | − | 0.0246363i | \(-0.992157\pi\) |
0.478513 | − | 0.878081i | \(-0.341176\pi\) | |||||||
\(884\) | 79.7952 | − | 14.0700i | 0.0902660 | − | 0.0159163i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −187.724 | + | 68.3260i | −0.211878 | + | 0.0771174i | ||||
\(887\) | 233.205 | + | 41.1203i | 0.262914 | + | 0.0463588i | 0.303551 | − | 0.952815i | \(-0.401828\pi\) |
−0.0406372 | + | 0.999174i | \(0.512939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 239.614 | − | 201.060i | 0.269533 | − | 0.226165i | ||||
\(890\) | − | 108.142i | − | 0.121508i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 325.022 | 0.364374 | ||||||||
\(893\) | −840.748 | − | 1001.96i | −0.941487 | − | 1.12202i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.1545 | + | 131.316i | −0.0258709 | + | 0.146721i | ||||
\(896\) | 7.40527 | + | 20.3458i | 0.00826481 | + | 0.0227074i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.01190 | − | 22.7526i | −0.00446760 | − | 0.0253370i | ||||
\(899\) | 1974.46 | − | 1139.96i | 2.19629 | − | 1.26803i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.9310 | + | 51.8421i | −0.0332198 | + | 0.0575384i | ||||
\(902\) | 346.494 | − | 951.984i | 0.384140 | − | 1.05541i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.7750 | − | 29.1797i | −0.0384679 | − | 0.0322784i | ||||
\(905\) | 86.9698 | − | 103.647i | 0.0960992 | − | 0.114527i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 302.489 | + | 110.097i | 0.333505 | + | 0.121386i | 0.503345 | − | 0.864086i | \(-0.332103\pi\) |
−0.169839 | + | 0.985472i | \(0.554325\pi\) | |||||||
\(908\) | 453.915 | + | 262.068i | 0.499907 | + | 0.288621i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −18.2832 | − | 31.6674i | −0.0200914 | − | 0.0347993i | ||||
\(911\) | 1105.64 | − | 194.955i | 1.21366 | − | 0.214001i | 0.470065 | − | 0.882632i | \(-0.344230\pi\) |
0.743595 | + | 0.668631i | \(0.233119\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −211.184 | + | 76.8648i | −0.231308 | + | 0.0841893i | ||||
\(914\) | 751.188 | + | 132.455i | 0.821869 | + | 0.144918i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 186.248 | − | 156.281i | 0.203328 | − | 0.170612i | ||||
\(917\) | − | 378.217i | − | 0.412450i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −486.580 | −0.529467 | −0.264734 | − | 0.964322i | \(-0.585284\pi\) | ||||
−0.264734 | + | 0.964322i | \(0.585284\pi\) | |||||||
\(920\) | 1.41684 | + | 1.68852i | 0.00154004 | + | 0.00183535i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 88.9219 | − | 504.301i | 0.0964446 | − | 0.546965i | ||||
\(923\) | −203.073 | − | 557.939i | −0.220014 | − | 0.604484i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −67.9082 | − | 385.127i | −0.0734143 | − | 0.416353i | ||||
\(926\) | −233.494 | + | 134.808i | −0.252153 | + | 0.145581i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 152.595 | − | 264.303i | 0.164435 | − | 0.284809i | ||||
\(929\) | −264.986 | + | 728.043i | −0.285238 | + | 0.783684i | 0.711478 | + | 0.702708i | \(0.248026\pi\) |
−0.996716 | + | 0.0809762i | \(0.974196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −710.304 | − | 596.016i | −0.762947 | − | 0.640189i | ||||
\(932\) | −538.782 | + | 642.095i | −0.578092 | + | 0.688943i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 946.818 | + | 344.614i | 1.01372 | + | 0.368965i | ||||
\(935\) | −58.9050 | − | 34.0088i | −0.0630000 | − | 0.0363731i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 310.767 | + | 538.264i | 0.331661 | + | 0.574454i | 0.982838 | − | 0.184472i | \(-0.0590575\pi\) |
−0.651176 | + | 0.758926i | \(0.725724\pi\) | |||||||
\(938\) | 60.1319 | − | 10.6029i | 0.0641065 | − | 0.0113037i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 136.045 | − | 49.5165i | 0.144729 | − | 0.0526771i | ||||
\(941\) | −1840.64 | − | 324.554i | −1.95604 | − | 0.344903i | −0.998372 | − | 0.0570327i | \(-0.981836\pi\) |
−0.957669 | − | 0.287870i | \(-0.907053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.3394 | − | 17.9059i | 0.0226293 | − | 0.0189882i | ||||
\(944\) | − | 223.688i | − | 0.236957i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1771.17 | −1.87227 | ||||||||
\(947\) | 339.780 | + | 404.935i | 0.358797 | + | 0.427597i | 0.915003 | − | 0.403447i | \(-0.132188\pi\) |
−0.556206 | + | 0.831044i | \(0.687744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −187.554 | + | 1063.67i | −0.197634 | + | 1.12084i | ||||
\(950\) | 234.635 | + | 644.653i | 0.246984 | + | 0.678583i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.19017 | − | 18.0923i | −0.00335102 | − | 0.0190046i | ||||
\(953\) | −226.233 | + | 130.616i | −0.237391 | + | 0.137058i | −0.613977 | − | 0.789324i | \(-0.710431\pi\) |
0.376586 | + | 0.926382i | \(0.377098\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 128.600 | − | 222.742i | 0.134660 | − | 0.233238i | ||||
\(956\) | 71.5346 | − | 196.540i | 0.0748270 | − | 0.205585i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 247.485 | + | 207.665i | 0.258335 | + | 0.216769i | ||||
\(959\) | 37.2345 | − | 44.3744i | 0.0388264 | − | 0.0462715i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −775.100 | − | 282.113i | −0.806556 | − | 0.293562i | ||||
\(962\) | 241.038 | + | 139.163i | 0.250559 | + | 0.144660i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 47.3730 | + | 82.0524i | 0.0491421 | + | 0.0851166i | ||||
\(965\) | −81.8878 | + | 14.4390i | −0.0848579 | + | 0.0149627i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1645.56 | − | 598.934i | 1.70172 | − | 0.619374i | 0.705696 | − | 0.708515i | \(-0.250634\pi\) |
0.996019 | + | 0.0891408i | \(0.0284121\pi\) | |||||||
\(968\) | −536.149 | − | 94.5375i | −0.553873 | − | 0.0976628i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 57.8023 | − | 48.5019i | 0.0595900 | − | 0.0500019i | ||||
\(971\) | 718.037i | 0.739482i | 0.929135 | + | 0.369741i | \(0.120554\pi\) | ||||
−0.929135 | + | 0.369741i | \(0.879446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 293.522 | 0.301667 | ||||||||
\(974\) | −105.004 | − | 125.138i | −0.107807 | − | 0.128479i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46.0979 | − | 261.434i | 0.0472315 | − | 0.267863i | ||||
\(977\) | −359.573 | − | 987.919i | −0.368038 | − | 1.01118i | −0.976107 | − | 0.217291i | \(-0.930278\pi\) |
0.608069 | − | 0.793884i | \(-0.291944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 207.708 | + | 1177.97i | 0.212164 | + | 1.20324i | ||||
\(980\) | 88.8834 | − | 51.3168i | 0.0906973 | − | 0.0523641i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −311.984 | + | 540.372i | −0.317703 | + | 0.550277i | ||||
\(983\) | 280.070 | − | 769.486i | 0.284913 | − | 0.782793i | −0.711845 | − | 0.702337i | \(-0.752140\pi\) |
0.996758 | − | 0.0804562i | \(-0.0256377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 80.1515 | + | 67.2551i | 0.0813721 | + | 0.0682793i | ||||
\(986\) | −166.454 | + | 198.372i | −0.168817 | + | 0.201188i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −458.806 | − | 166.992i | −0.464378 | − | 0.169020i | ||||
\(989\) | −42.1769 | − | 24.3509i | −0.0426460 | − | 0.0246217i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 433.521 | + | 750.880i | 0.437458 | + | 0.757699i | 0.997493 | − | 0.0707698i | \(-0.0225456\pi\) |
−0.560035 | + | 0.828469i | \(0.689212\pi\) | |||||||
\(992\) | −235.423 | + | 41.5114i | −0.237321 | + | 0.0418461i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −126.504 | + | 46.0438i | −0.127268 | + | 0.0463217i | ||||
\(995\) | −4.39747 | − | 0.775393i | −0.00441957 | − | 0.000779290i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −502.010 | + | 421.237i | −0.503521 | + | 0.422504i | −0.858842 | − | 0.512240i | \(-0.828816\pi\) |
0.355321 | + | 0.934744i | \(0.384371\pi\) | |||||||
\(998\) | − | 399.219i | − | 0.400019i | ||||||
\(999\) | 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 | 162.3.f.a.125.2 | 36 | ||
3.2 | odd | 2 | 54.3.f.a.5.6 | ✓ | 36 | ||
12.11 | even | 2 | 432.3.bc.c.113.2 | 36 | |||
27.4 | even | 9 | 1458.3.b.c.1457.11 | 36 | |||
27.11 | odd | 18 | inner | 162.3.f.a.35.2 | 36 | ||
27.16 | even | 9 | 54.3.f.a.11.6 | yes | 36 | ||
27.23 | odd | 18 | 1458.3.b.c.1457.26 | 36 | |||
108.43 | odd | 18 | 432.3.bc.c.65.2 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.3.f.a.5.6 | ✓ | 36 | 3.2 | odd | 2 | ||
54.3.f.a.11.6 | yes | 36 | 27.16 | even | 9 | ||
162.3.f.a.35.2 | 36 | 27.11 | odd | 18 | inner | ||
162.3.f.a.125.2 | 36 | 1.1 | even | 1 | trivial | ||
432.3.bc.c.65.2 | 36 | 108.43 | odd | 18 | |||
432.3.bc.c.113.2 | 36 | 12.11 | even | 2 | |||
1458.3.b.c.1457.11 | 36 | 27.4 | even | 9 | |||
1458.3.b.c.1457.26 | 36 | 27.23 | odd | 18 |