Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,3,Mod(2,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.n (of order \(6\), degree \(2\), 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: | \(1.71662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2.8 | ||
Character | \(\chi\) | \(=\) | 63.2 |
Dual form | 63.3.n.b.32.8 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.11318 | − | 0.642694i | 0.556589 | − | 0.321347i | −0.195186 | − | 0.980766i | \(-0.562531\pi\) |
0.751775 | + | 0.659419i | \(0.229198\pi\) | |||||||
\(3\) | 2.34935 | − | 1.86563i | 0.783116 | − | 0.621876i | ||||
\(4\) | −1.17389 | + | 2.03324i | −0.293472 | + | 0.508309i | ||||
\(5\) | − | 7.87519i | − | 1.57504i | −0.616291 | − | 0.787519i | \(-0.711365\pi\) | ||
0.616291 | − | 0.787519i | \(-0.288635\pi\) | |||||||
\(6\) | 1.41622 | − | 3.58669i | 0.236036 | − | 0.597781i | ||||
\(7\) | 0.417718 | + | 6.98753i | 0.0596740 | + | 0.998218i | ||||
\(8\) | 8.15936i | 1.01992i | ||||||||
\(9\) | 2.03887 | − | 8.76601i | 0.226541 | − | 0.974002i | ||||
\(10\) | −5.06133 | − | 8.76649i | −0.506133 | − | 0.876649i | ||||
\(11\) | 12.3390i | 1.12173i | 0.827907 | + | 0.560866i | \(0.189532\pi\) | ||||
−0.827907 | + | 0.560866i | \(0.810468\pi\) | |||||||
\(12\) | 1.03539 | + | 6.96682i | 0.0862821 | + | 0.580568i | ||||
\(13\) | −3.39438 | − | 5.87923i | −0.261106 | − | 0.452249i | 0.705430 | − | 0.708779i | \(-0.250754\pi\) |
−0.966536 | + | 0.256531i | \(0.917421\pi\) | |||||||
\(14\) | 4.95583 | + | 7.50990i | 0.353988 | + | 0.536421i | ||||
\(15\) | −14.6922 | − | 18.5016i | −0.979478 | − | 1.23344i | ||||
\(16\) | 0.548409 | + | 0.949873i | 0.0342756 | + | 0.0593671i | ||||
\(17\) | 6.19653 | − | 3.57757i | 0.364502 | − | 0.210445i | −0.306552 | − | 0.951854i | \(-0.599175\pi\) |
0.671054 | + | 0.741409i | \(0.265842\pi\) | |||||||
\(18\) | −3.36423 | − | 11.0685i | −0.186902 | − | 0.614917i | ||||
\(19\) | −15.4920 | + | 26.8330i | −0.815370 | + | 1.41226i | 0.0936913 | + | 0.995601i | \(0.470133\pi\) |
−0.909062 | + | 0.416662i | \(0.863200\pi\) | |||||||
\(20\) | 16.0121 | + | 9.24460i | 0.800606 | + | 0.462230i | ||||
\(21\) | 14.0175 | + | 15.6368i | 0.667499 | + | 0.744611i | ||||
\(22\) | 7.93022 | + | 13.7356i | 0.360465 | + | 0.624343i | ||||
\(23\) | − | 2.16554i | − | 0.0941538i | −0.998891 | − | 0.0470769i | \(-0.985009\pi\) | ||
0.998891 | − | 0.0470769i | \(-0.0149906\pi\) | |||||||
\(24\) | 15.2223 | + | 19.1692i | 0.634263 | + | 0.798715i | ||||
\(25\) | −37.0186 | −1.48074 | ||||||||
\(26\) | −7.55709 | − | 4.36309i | −0.290657 | − | 0.167811i | ||||
\(27\) | −11.5641 | − | 24.3982i | −0.428300 | − | 0.903637i | ||||
\(28\) | −14.6976 | − | 7.35326i | −0.524916 | − | 0.262617i | ||||
\(29\) | −8.97062 | − | 5.17919i | −0.309332 | − | 0.178593i | 0.337296 | − | 0.941399i | \(-0.390488\pi\) |
−0.646627 | + | 0.762806i | \(0.723821\pi\) | |||||||
\(30\) | −28.2458 | − | 11.1530i | −0.941528 | − | 0.371766i | ||||
\(31\) | 10.0973 | − | 17.4891i | 0.325720 | − | 0.564163i | −0.655938 | − | 0.754815i | \(-0.727727\pi\) |
0.981658 | + | 0.190651i | \(0.0610600\pi\) | |||||||
\(32\) | −27.0439 | − | 15.6138i | −0.845121 | − | 0.487931i | ||||
\(33\) | 23.0200 | + | 28.9887i | 0.697577 | + | 0.878446i | ||||
\(34\) | 4.59856 | − | 7.96495i | 0.135252 | − | 0.234263i | ||||
\(35\) | 55.0281 | − | 3.28961i | 1.57223 | − | 0.0939888i | ||||
\(36\) | 15.4300 | + | 14.4358i | 0.428610 | + | 0.400996i | ||||
\(37\) | 2.46193 | − | 4.26419i | 0.0665387 | − | 0.115248i | −0.830837 | − | 0.556516i | \(-0.812138\pi\) |
0.897376 | + | 0.441268i | \(0.145471\pi\) | |||||||
\(38\) | 39.8265i | 1.04807i | ||||||||
\(39\) | −18.9430 | − | 7.47972i | −0.485719 | − | 0.191788i | ||||
\(40\) | 64.2565 | 1.60641 | ||||||||
\(41\) | 28.0117 | − | 16.1725i | 0.683211 | − | 0.394452i | −0.117853 | − | 0.993031i | \(-0.537601\pi\) |
0.801064 | + | 0.598579i | \(0.204268\pi\) | |||||||
\(42\) | 25.6536 | + | 8.39762i | 0.610801 | + | 0.199943i | ||||
\(43\) | 25.5114 | − | 44.1870i | 0.593288 | − | 1.02761i | −0.400498 | − | 0.916298i | \(-0.631163\pi\) |
0.993786 | − | 0.111308i | \(-0.0355039\pi\) | |||||||
\(44\) | −25.0882 | − | 14.4847i | −0.570186 | − | 0.329197i | ||||
\(45\) | −69.0340 | − | 16.0565i | −1.53409 | − | 0.356811i | ||||
\(46\) | −1.39178 | − | 2.41063i | −0.0302560 | − | 0.0524050i | ||||
\(47\) | 18.5364 | − | 10.7020i | 0.394391 | − | 0.227702i | −0.289670 | − | 0.957127i | \(-0.593546\pi\) |
0.684061 | + | 0.729425i | \(0.260212\pi\) | |||||||
\(48\) | 3.06051 | + | 1.20845i | 0.0637607 | + | 0.0251761i | ||||
\(49\) | −48.6510 | + | 5.83763i | −0.992878 | + | 0.119135i | ||||
\(50\) | −41.2083 | + | 23.7916i | −0.824166 | + | 0.475832i | ||||
\(51\) | 7.88340 | − | 19.9654i | 0.154576 | − | 0.391478i | ||||
\(52\) | 15.9385 | 0.306510 | ||||||||
\(53\) | 51.0920 | − | 29.4980i | 0.964000 | − | 0.556566i | 0.0665983 | − | 0.997780i | \(-0.478785\pi\) |
0.897402 | + | 0.441214i | \(0.145452\pi\) | |||||||
\(54\) | −28.5535 | − | 19.7274i | −0.528768 | − | 0.365322i | ||||
\(55\) | 97.1723 | 1.76677 | ||||||||
\(56\) | −57.0137 | + | 3.40831i | −1.01810 | + | 0.0608627i | ||||
\(57\) | 13.6642 | + | 91.9424i | 0.239722 | + | 1.61302i | ||||
\(58\) | −13.3145 | −0.229561 | ||||||||
\(59\) | −89.6310 | − | 51.7485i | −1.51917 | − | 0.877093i | −0.999745 | − | 0.0225767i | \(-0.992813\pi\) |
−0.519425 | − | 0.854516i | \(-0.673854\pi\) | |||||||
\(60\) | 54.8650 | − | 8.15385i | 0.914417 | − | 0.135898i | ||||
\(61\) | −4.46912 | − | 7.74075i | −0.0732643 | − | 0.126898i | 0.827066 | − | 0.562105i | \(-0.190008\pi\) |
−0.900330 | + | 0.435208i | \(0.856675\pi\) | |||||||
\(62\) | − | 25.9579i | − | 0.418676i | ||||||
\(63\) | 62.1044 | + | 10.5849i | 0.985784 | + | 0.168015i | ||||
\(64\) | −44.5268 | −0.695732 | ||||||||
\(65\) | −46.3001 | + | 26.7314i | −0.712309 | + | 0.411252i | ||||
\(66\) | 44.2563 | + | 17.4748i | 0.670550 | + | 0.264769i | ||||
\(67\) | −45.3494 | + | 78.5475i | −0.676857 | + | 1.17235i | 0.299066 | + | 0.954232i | \(0.403325\pi\) |
−0.975922 | + | 0.218118i | \(0.930008\pi\) | |||||||
\(68\) | 16.7987i | 0.247039i | ||||||||
\(69\) | −4.04009 | − | 5.08760i | −0.0585520 | − | 0.0737334i | ||||
\(70\) | 59.1418 | − | 39.0281i | 0.844884 | − | 0.557545i | ||||
\(71\) | 2.12523i | 0.0299328i | 0.999888 | + | 0.0149664i | \(0.00476412\pi\) | ||||
−0.999888 | + | 0.0149664i | \(0.995236\pi\) | |||||||
\(72\) | 71.5250 | + | 16.6359i | 0.993403 | + | 0.231054i | ||||
\(73\) | 35.2282 | + | 61.0170i | 0.482577 | + | 0.835849i | 0.999800 | − | 0.0200023i | \(-0.00636734\pi\) |
−0.517222 | + | 0.855851i | \(0.673034\pi\) | |||||||
\(74\) | − | 6.32907i | − | 0.0855280i | ||||||
\(75\) | −86.9695 | + | 69.0629i | −1.15959 | + | 0.920838i | ||||
\(76\) | −36.3719 | − | 62.9979i | −0.478577 | − | 0.828920i | ||||
\(77\) | −86.2194 | + | 5.15424i | −1.11973 | + | 0.0669382i | ||||
\(78\) | −25.8941 | + | 3.84830i | −0.331976 | + | 0.0493372i | ||||
\(79\) | 72.3404 | + | 125.297i | 0.915701 | + | 1.58604i | 0.805872 | + | 0.592090i | \(0.201697\pi\) |
0.109829 | + | 0.993950i | \(0.464970\pi\) | |||||||
\(80\) | 7.48043 | − | 4.31883i | 0.0935054 | − | 0.0539853i | ||||
\(81\) | −72.6860 | − | 35.7456i | −0.897358 | − | 0.441303i | ||||
\(82\) | 20.7880 | − | 36.0058i | 0.253512 | − | 0.439096i | ||||
\(83\) | −13.6055 | − | 7.85511i | −0.163921 | − | 0.0946399i | 0.415795 | − | 0.909458i | \(-0.363503\pi\) |
−0.579716 | + | 0.814818i | \(0.696837\pi\) | |||||||
\(84\) | −48.2483 | + | 10.1449i | −0.574385 | + | 0.120773i | ||||
\(85\) | −28.1740 | − | 48.7989i | −0.331459 | − | 0.574104i | ||||
\(86\) | − | 65.5840i | − | 0.762605i | ||||||
\(87\) | −30.7375 | + | 4.56811i | −0.353305 | + | 0.0525070i | ||||
\(88\) | −100.679 | −1.14408 | ||||||||
\(89\) | 4.08134 | + | 2.35636i | 0.0458578 | + | 0.0264760i | 0.522754 | − | 0.852484i | \(-0.324905\pi\) |
−0.476896 | + | 0.878960i | \(0.658238\pi\) | |||||||
\(90\) | −87.1666 | + | 26.4940i | −0.968517 | + | 0.294378i | ||||
\(91\) | 39.6634 | − | 26.1742i | 0.435862 | − | 0.287628i | ||||
\(92\) | 4.40305 | + | 2.54210i | 0.0478592 | + | 0.0276315i | ||||
\(93\) | −8.90596 | − | 59.9257i | −0.0957630 | − | 0.644363i | ||||
\(94\) | 13.7562 | − | 23.8264i | 0.146343 | − | 0.253473i | ||||
\(95\) | 211.315 | + | 122.003i | 2.22437 | + | 1.28424i | ||||
\(96\) | −92.6650 | + | 13.7716i | −0.965260 | + | 0.143454i | ||||
\(97\) | −47.0097 | + | 81.4233i | −0.484637 | + | 0.839415i | −0.999844 | − | 0.0176503i | \(-0.994381\pi\) |
0.515208 | + | 0.857065i | \(0.327715\pi\) | |||||||
\(98\) | −50.4055 | + | 37.7660i | −0.514341 | + | 0.385368i | ||||
\(99\) | 108.164 | + | 25.1577i | 1.09257 | + | 0.254118i | ||||
\(100\) | 43.4557 | − | 75.2675i | 0.434557 | − | 0.752675i | ||||
\(101\) | 6.75096i | 0.0668412i | 0.999441 | + | 0.0334206i | \(0.0106401\pi\) | ||||
−0.999441 | + | 0.0334206i | \(0.989360\pi\) | |||||||
\(102\) | −4.05599 | − | 27.2916i | −0.0397646 | − | 0.267565i | ||||
\(103\) | 71.5356 | 0.694520 | 0.347260 | − | 0.937769i | \(-0.387112\pi\) | ||||
0.347260 | + | 0.937769i | \(0.387112\pi\) | |||||||
\(104\) | 47.9708 | − | 27.6959i | 0.461257 | − | 0.266307i | ||||
\(105\) | 123.143 | − | 110.390i | 1.17279 | − | 1.05134i | ||||
\(106\) | 37.9163 | − | 65.6730i | 0.357701 | − | 0.619557i | ||||
\(107\) | 14.2600 | + | 8.23301i | 0.133271 | + | 0.0769440i | 0.565153 | − | 0.824986i | \(-0.308817\pi\) |
−0.431882 | + | 0.901930i | \(0.642150\pi\) | |||||||
\(108\) | 63.1823 | + | 5.12825i | 0.585021 | + | 0.0474838i | ||||
\(109\) | −38.5448 | − | 66.7615i | −0.353622 | − | 0.612491i | 0.633259 | − | 0.773940i | \(-0.281717\pi\) |
−0.986881 | + | 0.161449i | \(0.948383\pi\) | |||||||
\(110\) | 108.170 | − | 62.4520i | 0.983364 | − | 0.567746i | ||||
\(111\) | −2.17146 | − | 14.6111i | −0.0195627 | − | 0.131632i | ||||
\(112\) | −6.40818 | + | 4.22880i | −0.0572159 | + | 0.0377572i | ||||
\(113\) | 5.45295 | − | 3.14826i | 0.0482562 | − | 0.0278607i | −0.475678 | − | 0.879620i | \(-0.657797\pi\) |
0.523934 | + | 0.851759i | \(0.324464\pi\) | |||||||
\(114\) | 74.3015 | + | 93.5664i | 0.651767 | + | 0.820758i | ||||
\(115\) | −17.0540 | −0.148296 | ||||||||
\(116\) | 21.0610 | − | 12.1596i | 0.181561 | − | 0.104824i | ||||
\(117\) | −58.4581 | + | 17.7682i | −0.499642 | + | 0.151865i | ||||
\(118\) | −133.034 | −1.12740 | ||||||||
\(119\) | 27.5868 | + | 41.8040i | 0.231822 | + | 0.351294i | ||||
\(120\) | 150.961 | − | 119.879i | 1.25801 | − | 0.998988i | ||||
\(121\) | −31.2519 | −0.258280 | ||||||||
\(122\) | −9.94986 | − | 5.74456i | −0.0815563 | − | 0.0470865i | ||||
\(123\) | 35.6372 | − | 90.2542i | 0.289733 | − | 0.733774i | ||||
\(124\) | 23.7063 | + | 41.0605i | 0.191180 | + | 0.331133i | ||||
\(125\) | 94.6486i | 0.757189i | ||||||||
\(126\) | 75.9362 | − | 28.1312i | 0.602668 | − | 0.223263i | ||||
\(127\) | −143.267 | −1.12808 | −0.564042 | − | 0.825746i | \(-0.690754\pi\) | ||||
−0.564042 | + | 0.825746i | \(0.690754\pi\) | |||||||
\(128\) | 58.6092 | − | 33.8381i | 0.457885 | − | 0.264360i | ||||
\(129\) | −22.5014 | − | 151.405i | −0.174429 | − | 1.17369i | ||||
\(130\) | −34.3602 | + | 59.5135i | −0.264309 | + | 0.457796i | ||||
\(131\) | − | 178.447i | − | 1.36219i | −0.732194 | − | 0.681096i | \(-0.761504\pi\) | ||
0.732194 | − | 0.681096i | \(-0.238496\pi\) | |||||||
\(132\) | −85.9639 | + | 12.7757i | −0.651241 | + | 0.0967853i | ||||
\(133\) | −193.968 | − | 97.0424i | −1.45840 | − | 0.729642i | ||||
\(134\) | 116.583i | 0.870023i | ||||||||
\(135\) | −192.140 | + | 91.0694i | −1.42326 | + | 0.674588i | ||||
\(136\) | 29.1907 | + | 50.5597i | 0.214637 | + | 0.371763i | ||||
\(137\) | 72.3511i | 0.528110i | 0.964508 | + | 0.264055i | \(0.0850600\pi\) | ||||
−0.964508 | + | 0.264055i | \(0.914940\pi\) | |||||||
\(138\) | −7.76711 | − | 3.06687i | −0.0562834 | − | 0.0222237i | ||||
\(139\) | 96.9860 | + | 167.985i | 0.697741 | + | 1.20852i | 0.969248 | + | 0.246087i | \(0.0791448\pi\) |
−0.271506 | + | 0.962437i | \(0.587522\pi\) | |||||||
\(140\) | −57.9083 | + | 115.747i | −0.413631 | + | 0.826762i | ||||
\(141\) | 23.5825 | − | 59.7247i | 0.167252 | − | 0.423579i | ||||
\(142\) | 1.36587 | + | 2.36576i | 0.00961880 | + | 0.0166602i | ||||
\(143\) | 72.5441 | − | 41.8834i | 0.507301 | − | 0.292891i | ||||
\(144\) | 9.44474 | − | 2.87070i | 0.0655885 | − | 0.0199354i | ||||
\(145\) | −40.7871 | + | 70.6453i | −0.281290 | + | 0.487209i | ||||
\(146\) | 78.4304 | + | 45.2818i | 0.537195 | + | 0.310150i | ||||
\(147\) | −103.407 | + | 104.479i | −0.703451 | + | 0.710743i | ||||
\(148\) | 5.78007 | + | 10.0114i | 0.0390545 | + | 0.0676444i | ||||
\(149\) | 65.1571i | 0.437296i | 0.975804 | + | 0.218648i | \(0.0701646\pi\) | ||||
−0.975804 | + | 0.218648i | \(0.929835\pi\) | |||||||
\(150\) | −52.4263 | + | 132.774i | −0.349509 | + | 0.885160i | ||||
\(151\) | 163.634 | 1.08367 | 0.541834 | − | 0.840486i | \(-0.317730\pi\) | ||||
0.541834 | + | 0.840486i | \(0.317730\pi\) | |||||||
\(152\) | −218.940 | − | 126.405i | −1.44039 | − | 0.831612i | ||||
\(153\) | −18.7271 | − | 61.6131i | −0.122399 | − | 0.402700i | ||||
\(154\) | −92.6649 | + | 61.1502i | −0.601720 | + | 0.397079i | ||||
\(155\) | −137.730 | − | 79.5183i | −0.888579 | − | 0.513021i | ||||
\(156\) | 37.4451 | − | 29.7353i | 0.240032 | − | 0.190611i | ||||
\(157\) | 85.5689 | − | 148.210i | 0.545025 | − | 0.944010i | −0.453581 | − | 0.891215i | \(-0.649854\pi\) |
0.998605 | − | 0.0527952i | \(-0.0168130\pi\) | |||||||
\(158\) | 161.055 | + | 92.9854i | 1.01934 | + | 0.588515i | ||||
\(159\) | 65.0007 | − | 164.620i | 0.408809 | − | 1.03534i | ||||
\(160\) | −122.962 | + | 212.976i | −0.768510 | + | 1.33110i | ||||
\(161\) | 15.1317 | − | 0.904584i | 0.0939860 | − | 0.00561854i | ||||
\(162\) | −103.886 | + | 6.92366i | −0.641271 | + | 0.0427386i | ||||
\(163\) | −33.3826 | + | 57.8203i | −0.204801 | + | 0.354726i | −0.950069 | − | 0.312039i | \(-0.898988\pi\) |
0.745268 | + | 0.666765i | \(0.232321\pi\) | |||||||
\(164\) | 75.9391i | 0.463043i | ||||||||
\(165\) | 228.291 | − | 181.287i | 1.38358 | − | 1.09871i | ||||
\(166\) | −20.1937 | −0.121649 | ||||||||
\(167\) | 12.2509 | − | 7.07305i | 0.0733586 | − | 0.0423536i | −0.462872 | − | 0.886425i | \(-0.653181\pi\) |
0.536231 | + | 0.844072i | \(0.319848\pi\) | |||||||
\(168\) | −127.586 | + | 114.374i | −0.759443 | + | 0.680795i | ||||
\(169\) | 61.4564 | − | 106.446i | 0.363647 | − | 0.629856i | ||||
\(170\) | −62.7254 | − | 36.2145i | −0.368973 | − | 0.213027i | ||||
\(171\) | 203.632 | + | 190.512i | 1.19083 | + | 1.11411i | ||||
\(172\) | 59.8951 | + | 103.741i | 0.348227 | + | 0.603147i | ||||
\(173\) | 42.3431 | − | 24.4468i | 0.244758 | − | 0.141311i | −0.372604 | − | 0.927991i | \(-0.621535\pi\) |
0.617362 | + | 0.786679i | \(0.288202\pi\) | |||||||
\(174\) | −31.2805 | + | 24.8399i | −0.179773 | + | 0.142758i | ||||
\(175\) | −15.4633 | − | 258.668i | −0.0883619 | − | 1.47810i | ||||
\(176\) | −11.7205 | + | 6.76685i | −0.0665939 | + | 0.0384480i | ||||
\(177\) | −307.118 | + | 45.6428i | −1.73513 | + | 0.257869i | ||||
\(178\) | 6.05768 | 0.0340319 | ||||||||
\(179\) | −163.746 | + | 94.5386i | −0.914780 | + | 0.528149i | −0.881966 | − | 0.471313i | \(-0.843780\pi\) |
−0.0328141 | + | 0.999461i | \(0.510447\pi\) | |||||||
\(180\) | 113.685 | − | 121.514i | 0.631583 | − | 0.675077i | ||||
\(181\) | 130.455 | 0.720743 | 0.360372 | − | 0.932809i | \(-0.382650\pi\) | ||||
0.360372 | + | 0.932809i | \(0.382650\pi\) | |||||||
\(182\) | 27.3305 | − | 54.6279i | 0.150167 | − | 0.300153i | ||||
\(183\) | −24.9409 | − | 9.84800i | −0.136289 | − | 0.0538142i | ||||
\(184\) | 17.6694 | 0.0960293 | ||||||||
\(185\) | −33.5813 | − | 19.3882i | −0.181521 | − | 0.104801i | ||||
\(186\) | −48.4278 | − | 60.9842i | −0.260365 | − | 0.327872i | ||||
\(187\) | 44.1438 | + | 76.4593i | 0.236063 | + | 0.408873i | ||||
\(188\) | 50.2518i | 0.267297i | ||||||||
\(189\) | 165.652 | − | 90.9960i | 0.876468 | − | 0.481460i | ||||
\(190\) | 313.641 | 1.65074 | ||||||||
\(191\) | 98.5384 | − | 56.8911i | 0.515908 | − | 0.297859i | −0.219351 | − | 0.975646i | \(-0.570394\pi\) |
0.735259 | + | 0.677787i | \(0.237061\pi\) | |||||||
\(192\) | −104.609 | + | 83.0704i | −0.544839 | + | 0.432659i | ||||
\(193\) | −131.368 | + | 227.536i | −0.680663 | + | 1.17894i | 0.294116 | + | 0.955770i | \(0.404975\pi\) |
−0.974779 | + | 0.223173i | \(0.928359\pi\) | |||||||
\(194\) | 120.851i | 0.622946i | ||||||||
\(195\) | −58.9042 | + | 149.180i | −0.302073 | + | 0.765025i | ||||
\(196\) | 45.2416 | − | 105.772i | 0.230825 | − | 0.539652i | ||||
\(197\) | 184.907i | 0.938615i | 0.883035 | + | 0.469307i | \(0.155496\pi\) | ||||
−0.883035 | + | 0.469307i | \(0.844504\pi\) | |||||||
\(198\) | 136.575 | − | 41.5114i | 0.689772 | − | 0.209654i | ||||
\(199\) | −122.873 | − | 212.822i | −0.617452 | − | 1.06946i | −0.989949 | − | 0.141425i | \(-0.954832\pi\) |
0.372497 | − | 0.928033i | \(-0.378502\pi\) | |||||||
\(200\) | − | 302.048i | − | 1.51024i | ||||||
\(201\) | 39.9987 | + | 269.140i | 0.198999 | + | 1.33901i | ||||
\(202\) | 4.33880 | + | 7.51502i | 0.0214792 | + | 0.0372031i | ||||
\(203\) | 32.4425 | − | 64.8458i | 0.159815 | − | 0.319438i | ||||
\(204\) | 31.3401 | + | 39.4660i | 0.153628 | + | 0.193461i | ||||
\(205\) | −127.362 | − | 220.597i | −0.621277 | − | 1.07608i | ||||
\(206\) | 79.6318 | − | 45.9755i | 0.386562 | − | 0.223182i | ||||
\(207\) | −18.9831 | − | 4.41525i | −0.0917060 | − | 0.0213297i | ||||
\(208\) | 3.72302 | − | 6.44845i | 0.0178991 | − | 0.0310022i | ||||
\(209\) | −331.093 | − | 191.157i | −1.58418 | − | 0.914626i | ||||
\(210\) | 66.1329 | − | 202.027i | 0.314918 | − | 0.962035i | ||||
\(211\) | −23.1354 | − | 40.0718i | −0.109647 | − | 0.189914i | 0.805981 | − | 0.591942i | \(-0.201639\pi\) |
−0.915627 | + | 0.402029i | \(0.868305\pi\) | |||||||
\(212\) | 138.509i | 0.653347i | ||||||||
\(213\) | 3.96488 | + | 4.99290i | 0.0186145 | + | 0.0234408i | ||||
\(214\) | 21.1652 | 0.0989029 | ||||||||
\(215\) | −347.981 | − | 200.907i | −1.61852 | − | 0.934451i | ||||
\(216\) | 199.074 | − | 94.3555i | 0.921637 | − | 0.436831i | ||||
\(217\) | 126.423 | + | 63.2498i | 0.582595 | + | 0.291474i | ||||
\(218\) | −85.8144 | − | 49.5450i | −0.393644 | − | 0.227270i | ||||
\(219\) | 196.598 | + | 77.6275i | 0.897708 | + | 0.354463i | ||||
\(220\) | −114.069 | + | 197.574i | −0.518498 | + | 0.898064i | ||||
\(221\) | −42.0667 | − | 24.2872i | −0.190347 | − | 0.109897i | ||||
\(222\) | −11.8077 | − | 14.8692i | −0.0531878 | − | 0.0669784i | ||||
\(223\) | 55.8857 | − | 96.7968i | 0.250608 | − | 0.434066i | −0.713085 | − | 0.701078i | \(-0.752703\pi\) |
0.963693 | + | 0.267011i | \(0.0860360\pi\) | |||||||
\(224\) | 97.8051 | − | 195.492i | 0.436630 | − | 0.872732i | ||||
\(225\) | −75.4762 | + | 324.505i | −0.335450 | + | 1.44225i | ||||
\(226\) | 4.04674 | − | 7.00915i | 0.0179059 | − | 0.0310139i | ||||
\(227\) | − | 256.634i | − | 1.13055i | −0.824904 | − | 0.565273i | \(-0.808771\pi\) | ||
0.824904 | − | 0.565273i | \(-0.191229\pi\) | |||||||
\(228\) | −202.981 | − | 80.1477i | −0.890267 | − | 0.351525i | ||||
\(229\) | 154.248 | 0.673573 | 0.336787 | − | 0.941581i | \(-0.390660\pi\) | ||||
0.336787 | + | 0.941581i | \(0.390660\pi\) | |||||||
\(230\) | −18.9842 | + | 10.9605i | −0.0825398 | + | 0.0476544i | ||||
\(231\) | −192.943 | + | 172.962i | −0.835253 | + | 0.748754i | ||||
\(232\) | 42.2588 | − | 73.1945i | 0.182150 | − | 0.315493i | ||||
\(233\) | 319.392 | + | 184.401i | 1.37078 | + | 0.791422i | 0.991027 | − | 0.133665i | \(-0.0426746\pi\) |
0.379756 | + | 0.925087i | \(0.376008\pi\) | |||||||
\(234\) | −53.6549 | + | 57.3498i | −0.229294 | + | 0.245085i | ||||
\(235\) | −84.2802 | − | 145.978i | −0.358639 | − | 0.621181i | ||||
\(236\) | 210.434 | − | 121.494i | 0.891669 | − | 0.514805i | ||||
\(237\) | 403.711 | + | 159.407i | 1.70342 | + | 0.672602i | ||||
\(238\) | 57.5762 | + | 28.8055i | 0.241917 | + | 0.121031i | ||||
\(239\) | 172.453 | − | 99.5658i | 0.721561 | − | 0.416593i | −0.0937659 | − | 0.995594i | \(-0.529891\pi\) |
0.815327 | + | 0.579001i | \(0.196557\pi\) | |||||||
\(240\) | 9.51681 | − | 24.1021i | 0.0396534 | − | 0.100425i | ||||
\(241\) | 195.137 | 0.809698 | 0.404849 | − | 0.914384i | \(-0.367324\pi\) | ||||
0.404849 | + | 0.914384i | \(0.367324\pi\) | |||||||
\(242\) | −34.7890 | + | 20.0854i | −0.143756 | + | 0.0829976i | ||||
\(243\) | −237.453 | + | 51.6262i | −0.977171 | + | 0.212453i | ||||
\(244\) | 20.9850 | 0.0860042 | ||||||||
\(245\) | 45.9724 | + | 383.136i | 0.187643 | + | 1.56382i | ||||
\(246\) | −18.3353 | − | 123.373i | −0.0745336 | − | 0.501516i | ||||
\(247\) | 210.343 | 0.851592 | ||||||||
\(248\) | 142.700 | + | 82.3876i | 0.575401 | + | 0.332208i | ||||
\(249\) | −46.6186 | + | 6.92831i | −0.187223 | + | 0.0278245i | ||||
\(250\) | 60.8301 | + | 105.361i | 0.243320 | + | 0.421443i | ||||
\(251\) | − | 194.630i | − | 0.775417i | −0.921782 | − | 0.387709i | \(-0.873267\pi\) | ||
0.921782 | − | 0.387709i | \(-0.126733\pi\) | |||||||
\(252\) | −94.4254 | + | 113.847i | −0.374704 | + | 0.451775i | ||||
\(253\) | 26.7207 | 0.105615 | ||||||||
\(254\) | −159.481 | + | 92.0766i | −0.627879 | + | 0.362506i | ||||
\(255\) | −157.231 | − | 62.0833i | −0.616592 | − | 0.243464i | ||||
\(256\) | 132.549 | − | 229.581i | 0.517768 | − | 0.896801i | ||||
\(257\) | 401.148i | 1.56089i | 0.625226 | + | 0.780444i | \(0.285007\pi\) | ||||
−0.625226 | + | 0.780444i | \(0.714993\pi\) | |||||||
\(258\) | −122.355 | − | 154.080i | −0.474246 | − | 0.597208i | ||||
\(259\) | 30.8245 | + | 15.4216i | 0.119014 | + | 0.0595428i | ||||
\(260\) | − | 125.519i | − | 0.482764i | ||||||
\(261\) | −63.6908 | + | 68.0768i | −0.244026 | + | 0.260831i | ||||
\(262\) | −114.687 | − | 198.643i | −0.437736 | − | 0.758181i | ||||
\(263\) | 292.298i | 1.11140i | 0.831383 | + | 0.555699i | \(0.187549\pi\) | ||||
−0.831383 | + | 0.555699i | \(0.812451\pi\) | |||||||
\(264\) | −236.529 | + | 187.829i | −0.895944 | + | 0.711473i | ||||
\(265\) | −232.302 | − | 402.359i | −0.876612 | − | 1.51834i | ||||
\(266\) | −278.289 | + | 16.6363i | −1.04620 | + | 0.0625424i | ||||
\(267\) | 13.9846 | − | 2.07834i | 0.0523767 | − | 0.00778405i | ||||
\(268\) | −106.470 | − | 184.412i | −0.397277 | − | 0.688105i | ||||
\(269\) | −285.220 | + | 164.672i | −1.06030 | + | 0.612162i | −0.925514 | − | 0.378713i | \(-0.876367\pi\) |
−0.134782 | + | 0.990875i | \(0.543033\pi\) | |||||||
\(270\) | −155.357 | + | 224.864i | −0.575395 | + | 0.832829i | ||||
\(271\) | 25.4109 | − | 44.0130i | 0.0937673 | − | 0.162410i | −0.815326 | − | 0.579002i | \(-0.803442\pi\) |
0.909093 | + | 0.416592i | \(0.136776\pi\) | |||||||
\(272\) | 6.79647 | + | 3.92395i | 0.0249870 | + | 0.0144263i | ||||
\(273\) | 44.3519 | − | 135.489i | 0.162461 | − | 0.496298i | ||||
\(274\) | 46.4996 | + | 80.5396i | 0.169706 | + | 0.293940i | ||||
\(275\) | − | 456.774i | − | 1.66100i | ||||||
\(276\) | 15.0869 | − | 2.24217i | 0.0546627 | − | 0.00812379i | ||||
\(277\) | −13.2632 | −0.0478814 | −0.0239407 | − | 0.999713i | \(-0.507621\pi\) | ||||
−0.0239407 | + | 0.999713i | \(0.507621\pi\) | |||||||
\(278\) | 215.926 | + | 124.665i | 0.776710 | + | 0.448434i | ||||
\(279\) | −132.722 | − | 124.171i | −0.475707 | − | 0.445058i | ||||
\(280\) | 26.8411 | + | 448.994i | 0.0958610 | + | 1.60355i | ||||
\(281\) | −375.796 | − | 216.966i | −1.33735 | − | 0.772120i | −0.350937 | − | 0.936399i | \(-0.614137\pi\) |
−0.986414 | + | 0.164279i | \(0.947470\pi\) | |||||||
\(282\) | −12.1331 | − | 81.6405i | −0.0430253 | − | 0.289505i | ||||
\(283\) | −192.732 | + | 333.822i | −0.681033 | + | 1.17958i | 0.293633 | + | 0.955918i | \(0.405136\pi\) |
−0.974666 | + | 0.223666i | \(0.928198\pi\) | |||||||
\(284\) | −4.32109 | − | 2.49478i | −0.0152151 | − | 0.00878444i | ||||
\(285\) | 724.064 | − | 107.608i | 2.54057 | − | 0.377572i | ||||
\(286\) | 53.8363 | − | 93.2473i | 0.188239 | − | 0.326039i | ||||
\(287\) | 124.707 | + | 188.977i | 0.434519 | + | 0.658455i | ||||
\(288\) | −192.010 | + | 205.233i | −0.666701 | + | 0.712613i | ||||
\(289\) | −118.902 | + | 205.944i | −0.411426 | + | 0.712610i | ||||
\(290\) | 104.854i | 0.361567i | ||||||||
\(291\) | 41.4632 | + | 278.994i | 0.142485 | + | 0.958743i | ||||
\(292\) | −165.416 | −0.566493 | ||||||||
\(293\) | 167.296 | − | 96.5885i | 0.570977 | − | 0.329653i | −0.186563 | − | 0.982443i | \(-0.559735\pi\) |
0.757539 | + | 0.652790i | \(0.226401\pi\) | |||||||
\(294\) | −47.9626 | + | 182.763i | −0.163138 | + | 0.621644i | ||||
\(295\) | −407.529 | + | 705.861i | −1.38145 | + | 2.39275i | ||||
\(296\) | 34.7931 | + | 20.0878i | 0.117544 | + | 0.0678641i | ||||
\(297\) | 301.050 | − | 142.690i | 1.01364 | − | 0.480437i | ||||
\(298\) | 41.8761 | + | 72.5315i | 0.140524 | + | 0.243394i | ||||
\(299\) | −12.7317 | + | 7.35065i | −0.0425809 | + | 0.0245841i | ||||
\(300\) | −38.3285 | − | 257.902i | −0.127762 | − | 0.859673i | ||||
\(301\) | 319.415 | + | 159.804i | 1.06118 | + | 0.530910i | ||||
\(302\) | 182.154 | − | 105.166i | 0.603158 | − | 0.348233i | ||||
\(303\) | 12.5948 | + | 15.8603i | 0.0415669 | + | 0.0523444i | ||||
\(304\) | −33.9839 | −0.111789 | ||||||||
\(305\) | −60.9599 | + | 35.1952i | −0.199868 | + | 0.115394i | ||||
\(306\) | −60.4449 | − | 56.5506i | −0.197532 | − | 0.184806i | ||||
\(307\) | 16.4744 | 0.0536625 | 0.0268313 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268313 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(308\) | 90.7322 | − | 181.355i | 0.294585 | − | 0.588814i | ||||
\(309\) | 168.062 | − | 133.459i | 0.543890 | − | 0.431905i | ||||
\(310\) | −204.424 | −0.659431 | ||||||||
\(311\) | −420.238 | − | 242.625i | −1.35125 | − | 0.780143i | −0.362824 | − | 0.931858i | \(-0.618187\pi\) |
−0.988424 | + | 0.151714i | \(0.951521\pi\) | |||||||
\(312\) | 61.0297 | − | 154.563i | 0.195608 | − | 0.495394i | ||||
\(313\) | −205.370 | − | 355.711i | −0.656134 | − | 1.13646i | −0.981608 | − | 0.190906i | \(-0.938857\pi\) |
0.325475 | − | 0.945551i | \(-0.394476\pi\) | |||||||
\(314\) | − | 219.978i | − | 0.700568i | ||||||
\(315\) | 83.3585 | − | 489.084i | 0.264630 | − | 1.55265i | ||||
\(316\) | −339.678 | −1.07493 | ||||||||
\(317\) | 113.285 | − | 65.4049i | 0.357365 | − | 0.206325i | −0.310559 | − | 0.950554i | \(-0.600516\pi\) |
0.667924 | + | 0.744229i | \(0.267183\pi\) | |||||||
\(318\) | −33.4427 | − | 225.027i | −0.105166 | − | 0.707631i | ||||
\(319\) | 63.9062 | − | 110.689i | 0.200333 | − | 0.346987i | ||||
\(320\) | 350.657i | 1.09580i | ||||||||
\(321\) | 48.8614 | − | 7.26162i | 0.152216 | − | 0.0226219i | ||||
\(322\) | 16.2630 | − | 10.7320i | 0.0505061 | − | 0.0333293i | ||||
\(323\) | 221.695i | 0.686363i | ||||||||
\(324\) | 158.004 | − | 105.826i | 0.487668 | − | 0.326625i | ||||
\(325\) | 125.655 | + | 217.641i | 0.386631 | + | 0.669664i | ||||
\(326\) | 85.8191i | 0.263249i | ||||||||
\(327\) | −215.107 | − | 84.9358i | −0.657820 | − | 0.259743i | ||||
\(328\) | 131.958 | + | 228.557i | 0.402309 | + | 0.696820i | ||||
\(329\) | 82.5234 | + | 125.053i | 0.250831 | + | 0.380100i | ||||
\(330\) | 137.617 | − | 348.526i | 0.417021 | − | 1.05614i | ||||
\(331\) | 120.470 | + | 208.660i | 0.363957 | + | 0.630393i | 0.988608 | − | 0.150512i | \(-0.0480921\pi\) |
−0.624651 | + | 0.780904i | \(0.714759\pi\) | |||||||
\(332\) | 31.9426 | − | 18.4421i | 0.0962126 | − | 0.0555484i | ||||
\(333\) | −32.3604 | − | 30.2755i | −0.0971784 | − | 0.0909173i | ||||
\(334\) | 9.09161 | − | 15.7471i | 0.0272204 | − | 0.0471471i | ||||
\(335\) | 618.576 | + | 357.135i | 1.84650 | + | 1.06607i | ||||
\(336\) | −7.16568 | + | 21.8902i | −0.0213264 | + | 0.0651494i | ||||
\(337\) | −149.637 | − | 259.179i | −0.444026 | − | 0.769076i | 0.553957 | − | 0.832545i | \(-0.313117\pi\) |
−0.997984 | + | 0.0634687i | \(0.979784\pi\) | |||||||
\(338\) | − | 157.991i | − | 0.467428i | ||||||
\(339\) | 6.93739 | − | 17.5695i | 0.0204643 | − | 0.0518275i | ||||
\(340\) | 132.293 | 0.389096 | ||||||||
\(341\) | 215.798 | + | 124.591i | 0.632840 | + | 0.365370i | ||||
\(342\) | 349.120 | + | 81.2012i | 1.02082 | + | 0.237430i | ||||
\(343\) | −61.1130 | − | 337.512i | −0.178172 | − | 0.983999i | ||||
\(344\) | 360.538 | + | 208.157i | 1.04807 | + | 0.605106i | ||||
\(345\) | −40.0658 | + | 31.8164i | −0.116133 | + | 0.0922215i | ||||
\(346\) | 31.4236 | − | 54.4273i | 0.0908198 | − | 0.157304i | ||||
\(347\) | −527.606 | − | 304.613i | −1.52048 | − | 0.877848i | −0.999708 | − | 0.0241511i | \(-0.992312\pi\) |
−0.520770 | − | 0.853697i | \(-0.674355\pi\) | |||||||
\(348\) | 26.7944 | − | 67.8591i | 0.0769955 | − | 0.194997i | ||||
\(349\) | 66.8442 | − | 115.778i | 0.191531 | − | 0.331741i | −0.754227 | − | 0.656614i | \(-0.771988\pi\) |
0.945758 | + | 0.324873i | \(0.105322\pi\) | |||||||
\(350\) | −183.458 | − | 278.006i | −0.524166 | − | 0.794302i | ||||
\(351\) | −104.190 | + | 150.805i | −0.296837 | + | 0.429643i | ||||
\(352\) | 192.659 | − | 333.696i | 0.547327 | − | 0.947999i | ||||
\(353\) | 603.362i | 1.70924i | 0.519252 | + | 0.854621i | \(0.326210\pi\) | ||||
−0.519252 | + | 0.854621i | \(0.673790\pi\) | |||||||
\(354\) | −312.543 | + | 248.191i | −0.882888 | + | 0.701105i | ||||
\(355\) | 16.7366 | 0.0471452 | ||||||||
\(356\) | −9.58209 | + | 5.53222i | −0.0269160 | + | 0.0155399i | ||||
\(357\) | 142.802 | + | 46.7456i | 0.400004 | + | 0.130940i | ||||
\(358\) | −121.519 | + | 210.477i | −0.339438 | + | 0.587924i | ||||
\(359\) | −166.585 | − | 96.1780i | −0.464026 | − | 0.267905i | 0.249710 | − | 0.968321i | \(-0.419665\pi\) |
−0.713736 | + | 0.700415i | \(0.752998\pi\) | |||||||
\(360\) | 131.011 | − | 563.273i | 0.363919 | − | 1.56465i | ||||
\(361\) | −299.506 | − | 518.760i | −0.829658 | − | 1.43701i | ||||
\(362\) | 145.219 | − | 83.8423i | 0.401158 | − | 0.231609i | ||||
\(363\) | −73.4217 | + | 58.3045i | −0.202264 | + | 0.160618i | ||||
\(364\) | 6.65780 | + | 111.371i | 0.0182907 | + | 0.305963i | ||||
\(365\) | 480.520 | − | 277.428i | 1.31649 | − | 0.760078i | ||||
\(366\) | −34.0929 | + | 5.06677i | −0.0931500 | + | 0.0138436i | ||||
\(367\) | 186.792 | 0.508971 | 0.254485 | − | 0.967077i | \(-0.418094\pi\) | ||||
0.254485 | + | 0.967077i | \(0.418094\pi\) | |||||||
\(368\) | 2.05699 | − | 1.18760i | 0.00558964 | − | 0.00322718i | ||||
\(369\) | −84.6565 | − | 278.524i | −0.229421 | − | 0.754809i | ||||
\(370\) | −49.8426 | −0.134710 | ||||||||
\(371\) | 227.460 | + | 344.685i | 0.613100 | + | 0.929070i | ||||
\(372\) | 132.298 | + | 52.2383i | 0.355639 | + | 0.140425i | ||||
\(373\) | −361.251 | −0.968500 | −0.484250 | − | 0.874930i | \(-0.660908\pi\) | ||||
−0.484250 | + | 0.874930i | \(0.660908\pi\) | |||||||
\(374\) | 98.2798 | + | 56.7419i | 0.262780 | + | 0.151716i | ||||
\(375\) | 176.579 | + | 222.363i | 0.470877 | + | 0.592967i | ||||
\(376\) | 87.3213 | + | 151.245i | 0.232238 | + | 0.402247i | ||||
\(377\) | 70.3205i | 0.186526i | ||||||||
\(378\) | 125.918 | − | 207.759i | 0.333117 | − | 0.549626i | ||||
\(379\) | 384.791 | 1.01528 | 0.507640 | − | 0.861569i | \(-0.330518\pi\) | ||||
0.507640 | + | 0.861569i | \(0.330518\pi\) | |||||||
\(380\) | −496.121 | + | 286.435i | −1.30558 | + | 0.753777i | ||||
\(381\) | −336.583 | + | 267.282i | −0.883421 | + | 0.701528i | ||||
\(382\) | 73.1272 | − | 126.660i | 0.191432 | − | 0.331571i | ||||
\(383\) | 422.377i | 1.10281i | 0.834237 | + | 0.551406i | \(0.185909\pi\) | ||||
−0.834237 | + | 0.551406i | \(0.814091\pi\) | |||||||
\(384\) | 74.5643 | − | 188.840i | 0.194178 | − | 0.491772i | ||||
\(385\) | 40.5906 | + | 678.994i | 0.105430 | + | 1.76362i | ||||
\(386\) | 337.717i | 0.874916i | ||||||||
\(387\) | −335.330 | − | 313.725i | −0.866485 | − | 0.810659i | ||||
\(388\) | −110.368 | − | 191.164i | −0.284455 | − | 0.492690i | ||||
\(389\) | − | 719.166i | − | 1.84876i | −0.381478 | − | 0.924378i | \(-0.624585\pi\) | ||
0.381478 | − | 0.924378i | \(-0.375415\pi\) | |||||||
\(390\) | 30.3061 | + | 203.921i | 0.0777079 | + | 0.522875i | ||||
\(391\) | −7.74736 | − | 13.4188i | −0.0198142 | − | 0.0343192i | ||||
\(392\) | −47.6313 | − | 396.961i | −0.121508 | − | 1.01266i | ||||
\(393\) | −332.916 | − | 419.234i | −0.847114 | − | 1.06675i | ||||
\(394\) | 118.839 | + | 205.835i | 0.301621 | + | 0.522423i | ||||
\(395\) | 986.739 | − | 569.694i | 2.49807 | − | 1.44226i | ||||
\(396\) | −178.124 | + | 190.391i | −0.449809 | + | 0.480785i | ||||
\(397\) | −77.9179 | + | 134.958i | −0.196267 | + | 0.339944i | −0.947315 | − | 0.320303i | \(-0.896215\pi\) |
0.751048 | + | 0.660247i | \(0.229548\pi\) | |||||||
\(398\) | −273.559 | − | 157.939i | −0.687334 | − | 0.396832i | ||||
\(399\) | −636.742 | + | 133.885i | −1.59584 | + | 0.335551i | ||||
\(400\) | −20.3013 | − | 35.1630i | −0.0507534 | − | 0.0879074i | ||||
\(401\) | 131.150i | 0.327057i | 0.986539 | + | 0.163528i | \(0.0522875\pi\) | ||||
−0.986539 | + | 0.163528i | \(0.947712\pi\) | |||||||
\(402\) | 217.501 | + | 273.894i | 0.541046 | + | 0.681329i | ||||
\(403\) | −137.096 | −0.340190 | ||||||||
\(404\) | −13.7263 | − | 7.92488i | −0.0339760 | − | 0.0196160i | ||||
\(405\) | −281.503 | + | 572.416i | −0.695069 | + | 1.41337i | ||||
\(406\) | −5.56172 | − | 93.0356i | −0.0136988 | − | 0.229152i | ||||
\(407\) | 52.6160 | + | 30.3779i | 0.129278 | + | 0.0746385i | ||||
\(408\) | 162.905 | + | 64.3235i | 0.399276 | + | 0.157656i | ||||
\(409\) | −106.085 | + | 183.745i | −0.259377 | + | 0.449254i | −0.966075 | − | 0.258261i | \(-0.916850\pi\) |
0.706698 | + | 0.707515i | \(0.250184\pi\) | |||||||
\(410\) | −283.553 | − | 163.709i | −0.691592 | − | 0.399291i | ||||
\(411\) | 134.980 | + | 169.978i | 0.328419 | + | 0.413571i | ||||
\(412\) | −83.9748 | + | 145.449i | −0.203822 | + | 0.353031i | ||||
\(413\) | 324.153 | − | 647.915i | 0.784875 | − | 1.56880i | ||||
\(414\) | −23.9693 | + | 7.28538i | −0.0578968 | + | 0.0175975i | ||||
\(415\) | −61.8605 | + | 107.145i | −0.149061 | + | 0.258182i | ||||
\(416\) | 211.996i | 0.509607i | ||||||||
\(417\) | 541.251 | + | 213.715i | 1.29796 | + | 0.512506i | ||||
\(418\) | −491.421 | −1.17565 | ||||||||
\(419\) | −641.691 | + | 370.481i | −1.53148 | + | 0.884202i | −0.532189 | + | 0.846625i | \(0.678631\pi\) |
−0.999294 | + | 0.0375766i | \(0.988036\pi\) | |||||||
\(420\) | 79.8934 | + | 379.965i | 0.190222 | + | 0.904678i | ||||
\(421\) | 281.034 | − | 486.765i | 0.667539 | − | 1.15621i | −0.311051 | − | 0.950393i | \(-0.600681\pi\) |
0.978590 | − | 0.205819i | \(-0.0659857\pi\) | |||||||
\(422\) | −51.5077 | − | 29.7380i | −0.122056 | − | 0.0704692i | ||||
\(423\) | −56.0204 | − | 184.310i | −0.132436 | − | 0.435722i | ||||
\(424\) | 240.685 | + | 416.878i | 0.567652 | + | 0.983203i | ||||
\(425\) | −229.387 | + | 132.437i | −0.539734 | + | 0.311615i | ||||
\(426\) | 7.62252 | + | 3.00978i | 0.0178932 | + | 0.00706521i | ||||
\(427\) | 52.2219 | − | 34.4616i | 0.122299 | − | 0.0807063i | ||||
\(428\) | −33.4793 | + | 19.3293i | −0.0782227 | + | 0.0451619i | ||||
\(429\) | 92.2926 | − | 233.739i | 0.215134 | − | 0.544846i | ||||
\(430\) | −516.487 | −1.20113 | ||||||||
\(431\) | −290.022 | + | 167.444i | −0.672904 | + | 0.388501i | −0.797176 | − | 0.603747i | \(-0.793674\pi\) |
0.124272 | + | 0.992248i | \(0.460340\pi\) | |||||||
\(432\) | 16.8333 | − | 24.3646i | 0.0389660 | − | 0.0563996i | ||||
\(433\) | 108.934 | 0.251579 | 0.125789 | − | 0.992057i | \(-0.459854\pi\) | ||||
0.125789 | + | 0.992057i | \(0.459854\pi\) | |||||||
\(434\) | 181.382 | − | 10.8431i | 0.417930 | − | 0.0249841i | ||||
\(435\) | 35.9747 | + | 242.064i | 0.0827005 | + | 0.556469i | ||||
\(436\) | 180.989 | 0.415113 | ||||||||
\(437\) | 58.1079 | + | 33.5486i | 0.132970 | + | 0.0767702i | ||||
\(438\) | 268.739 | − | 39.9392i | 0.613560 | − | 0.0911853i | ||||
\(439\) | −291.989 | − | 505.739i | −0.665122 | − | 1.15202i | −0.979252 | − | 0.202645i | \(-0.935046\pi\) |
0.314130 | − | 0.949380i | \(-0.398287\pi\) | |||||||
\(440\) | 792.863i | 1.80196i | ||||||||
\(441\) | −48.0205 | + | 438.378i | −0.108890 | + | 0.994054i | ||||
\(442\) | −62.4370 | −0.141260 | ||||||||
\(443\) | −496.904 | + | 286.888i | −1.12168 | + | 0.647602i | −0.941829 | − | 0.336092i | \(-0.890895\pi\) |
−0.179851 | + | 0.983694i | \(0.557561\pi\) | |||||||
\(444\) | 32.2569 | + | 12.7368i | 0.0726507 | + | 0.0286864i | ||||
\(445\) | 18.5568 | − | 32.1413i | 0.0417007 | − | 0.0722277i | ||||
\(446\) | − | 143.669i | − | 0.322129i | ||||||
\(447\) | 121.559 | + | 153.077i | 0.271944 | + | 0.342453i | ||||
\(448\) | −18.5997 | − | 311.132i | −0.0415171 | − | 0.694492i | ||||
\(449\) | − | 274.994i | − | 0.612459i | −0.951958 | − | 0.306229i | \(-0.900933\pi\) | ||
0.951958 | − | 0.306229i | \(-0.0990675\pi\) | |||||||
\(450\) | 124.539 | + | 409.740i | 0.276754 | + | 0.910534i | ||||
\(451\) | 199.554 | + | 345.637i | 0.442469 | + | 0.766379i | ||||
\(452\) | 14.7828i | 0.0327054i | ||||||||
\(453\) | 384.433 | − | 305.280i | 0.848637 | − | 0.673907i | ||||
\(454\) | −164.937 | − | 285.679i | −0.363297 | − | 0.629249i | ||||
\(455\) | −206.126 | − | 312.357i | −0.453025 | − | 0.686498i | ||||
\(456\) | −750.191 | + | 111.491i | −1.64516 | + | 0.244497i | ||||
\(457\) | 37.2674 | + | 64.5490i | 0.0815479 | + | 0.141245i | 0.903915 | − | 0.427712i | \(-0.140680\pi\) |
−0.822367 | + | 0.568957i | \(0.807347\pi\) | |||||||
\(458\) | 171.706 | − | 99.1344i | 0.374903 | − | 0.216451i | ||||
\(459\) | −158.943 | − | 109.813i | −0.346282 | − | 0.239244i | ||||
\(460\) | 20.0195 | − | 34.6748i | 0.0435207 | − | 0.0753801i | ||||
\(461\) | −602.709 | − | 347.974i | −1.30740 | − | 0.754825i | −0.325735 | − | 0.945461i | \(-0.605612\pi\) |
−0.981661 | + | 0.190636i | \(0.938945\pi\) | |||||||
\(462\) | −103.619 | + | 316.541i | −0.224283 | + | 0.685154i | ||||
\(463\) | 336.870 | + | 583.475i | 0.727580 | + | 1.26021i | 0.957903 | + | 0.287092i | \(0.0926884\pi\) |
−0.230323 | + | 0.973114i | \(0.573978\pi\) | |||||||
\(464\) | − | 11.3613i | − | 0.0244855i | ||||||
\(465\) | −471.926 | + | 70.1361i | −1.01490 | + | 0.150830i | ||||
\(466\) | 474.054 | 1.01728 | ||||||||
\(467\) | −280.524 | − | 161.960i | −0.600693 | − | 0.346810i | 0.168621 | − | 0.985681i | \(-0.446069\pi\) |
−0.769314 | + | 0.638871i | \(0.779402\pi\) | |||||||
\(468\) | 32.4966 | − | 139.717i | 0.0694371 | − | 0.298541i | ||||
\(469\) | −567.796 | − | 284.069i | −1.21065 | − | 0.605692i | ||||
\(470\) | −187.638 | − | 108.333i | −0.399229 | − | 0.230495i | ||||
\(471\) | −75.4728 | − | 507.836i | −0.160240 | − | 1.07821i | ||||
\(472\) | 422.234 | − | 731.331i | 0.894564 | − | 1.54943i | ||||
\(473\) | 545.226 | + | 314.786i | 1.15270 | + | 0.665510i | ||||
\(474\) | 551.852 | − | 82.0143i | 1.16424 | − | 0.173026i | ||||
\(475\) | 573.493 | − | 993.319i | 1.20735 | − | 2.09120i | ||||
\(476\) | −117.381 | + | 7.01711i | −0.246599 | + | 0.0147418i | ||||
\(477\) | −154.410 | − | 508.016i | −0.323710 | − | 1.06502i | ||||
\(478\) | 127.981 | − | 221.669i | 0.267742 | − | 0.463743i | ||||
\(479\) | − | 28.7437i | − | 0.0600077i | −0.999550 | − | 0.0300038i | \(-0.990448\pi\) | ||
0.999550 | − | 0.0300038i | \(-0.00955196\pi\) | |||||||
\(480\) | 108.454 | + | 729.754i | 0.225945 | + | 1.52032i | ||||
\(481\) | −33.4269 | −0.0694946 | ||||||||
\(482\) | 217.222 | − | 125.413i | 0.450669 | − | 0.260194i | ||||
\(483\) | 33.8621 | − | 30.3554i | 0.0701079 | − | 0.0628476i | ||||
\(484\) | 36.6863 | − | 63.5426i | 0.0757982 | − | 0.131286i | ||||
\(485\) | 641.224 | + | 370.211i | 1.32211 | + | 0.763321i | ||||
\(486\) | −231.147 | + | 210.078i | −0.475612 | + | 0.432260i | ||||
\(487\) | 438.026 | + | 758.683i | 0.899437 | + | 1.55787i | 0.828216 | + | 0.560409i | \(0.189356\pi\) |
0.0712210 | + | 0.997461i | \(0.477310\pi\) | |||||||
\(488\) | 63.1595 | − | 36.4652i | 0.129425 | − | 0.0747237i | ||||
\(489\) | 29.4439 | + | 198.120i | 0.0602124 | + | 0.405152i | ||||
\(490\) | 297.415 | + | 396.952i | 0.606969 | + | 0.810107i | ||||
\(491\) | −52.5833 | + | 30.3590i | −0.107094 | + | 0.0618310i | −0.552591 | − | 0.833453i | \(-0.686361\pi\) |
0.445496 | + | 0.895284i | \(0.353027\pi\) | |||||||
\(492\) | 141.674 | + | 178.407i | 0.287955 | + | 0.362617i | ||||
\(493\) | −74.1156 | −0.150336 | ||||||||
\(494\) | 234.150 | − | 135.186i | 0.473987 | − | 0.273656i | ||||
\(495\) | 198.122 | − | 851.813i | 0.400246 | − | 1.72084i | ||||
\(496\) | 22.1499 | 0.0446570 | ||||||||
\(497\) | −14.8501 | + | 0.887745i | −0.0298794 | + | 0.00178621i | ||||
\(498\) | −47.4421 | + | 37.6740i | −0.0952652 | + | 0.0756505i | ||||
\(499\) | 699.521 | 1.40185 | 0.700923 | − | 0.713237i | \(-0.252772\pi\) | ||||
0.700923 | + | 0.713237i | \(0.252772\pi\) | |||||||
\(500\) | −192.443 | − | 111.107i | −0.384886 | − | 0.222214i | ||||
\(501\) | 15.5859 | − | 39.4726i | 0.0311096 | − | 0.0787877i | ||||
\(502\) | −125.087 | − | 216.658i | −0.249178 | − | 0.431589i | ||||
\(503\) | − | 136.689i | − | 0.271747i | −0.990726 | − | 0.135873i | \(-0.956616\pi\) | ||
0.990726 | − | 0.135873i | \(-0.0433840\pi\) | |||||||
\(504\) | −86.3664 | + | 506.732i | −0.171362 | + | 1.00542i | ||||
\(505\) | 53.1651 | 0.105277 | ||||||||
\(506\) | 29.7449 | − | 17.1732i | 0.0587843 | − | 0.0339391i | ||||
\(507\) | −54.2053 | − | 364.733i | −0.106914 | − | 0.719394i | ||||
\(508\) | 168.179 | − | 291.295i | 0.331061 | − | 0.573415i | ||||
\(509\) | − | 172.803i | − | 0.339495i | −0.985488 | − | 0.169747i | \(-0.945705\pi\) | ||
0.985488 | − | 0.169747i | \(-0.0542952\pi\) | |||||||
\(510\) | −214.927 | + | 31.9417i | −0.421425 | + | 0.0626308i | ||||
\(511\) | −411.642 | + | 271.646i | −0.805562 | + | 0.531596i | ||||
\(512\) | − | 70.0483i | − | 0.136813i | ||||||
\(513\) | 833.828 | + | 67.6785i | 1.62540 | + | 0.131927i | ||||
\(514\) | 257.815 | + | 446.549i | 0.501586 | + | 0.868773i | ||||
\(515\) | − | 563.356i | − | 1.09389i | ||||||
\(516\) | 334.257 | + | 131.983i | 0.647785 | + | 0.255780i | ||||
\(517\) | 132.052 | + | 228.721i | 0.255420 | + | 0.442401i | ||||
\(518\) | 44.2246 | − | 2.64377i | 0.0853756 | − | 0.00510380i | ||||
\(519\) | 53.8701 | − | 136.431i | 0.103796 | − | 0.262872i | ||||
\(520\) | −218.111 | − | 377.779i | −0.419444 | − | 0.726498i | ||||
\(521\) | −481.965 | + | 278.263i | −0.925077 | + | 0.534094i | −0.885251 | − | 0.465113i | \(-0.846014\pi\) |
−0.0398260 | + | 0.999207i | \(0.512680\pi\) | |||||||
\(522\) | −27.1466 | + | 116.715i | −0.0520050 | + | 0.223593i | ||||
\(523\) | −155.825 | + | 269.897i | −0.297945 | + | 0.516055i | −0.975666 | − | 0.219264i | \(-0.929634\pi\) |
0.677721 | + | 0.735319i | \(0.262968\pi\) | |||||||
\(524\) | 362.825 | + | 209.477i | 0.692414 | + | 0.399766i | ||||
\(525\) | −518.907 | − | 578.853i | −0.988395 | − | 1.10258i | ||||
\(526\) | 187.858 | + | 325.380i | 0.357144 | + | 0.618592i | ||||
\(527\) | − | 144.495i | − | 0.274185i | ||||||
\(528\) | −14.9112 | + | 37.7638i | −0.0282409 | + | 0.0715223i | ||||
\(529\) | 524.310 | 0.991135 | ||||||||
\(530\) | −517.187 | − | 298.598i | −0.975825 | − | 0.563393i | ||||
\(531\) | −636.374 | + | 680.198i | −1.19844 | + | 1.28098i | ||||
\(532\) | 425.007 | − | 280.465i | 0.798884 | − | 0.527189i | ||||
\(533\) | −190.164 | − | 109.791i | −0.356781 | − | 0.205988i | ||||
\(534\) | 14.2316 | − | 11.3014i | 0.0266509 | − | 0.0211636i | ||||
\(535\) | 64.8365 | − | 112.300i | 0.121190 | − | 0.209907i | ||||
\(536\) | −640.897 | − | 370.022i | −1.19570 | − | 0.690339i | ||||
\(537\) | −208.322 | + | 527.592i | −0.387936 | + | 0.982481i | ||||
\(538\) | −211.667 | + | 366.618i | −0.393433 | + | 0.681446i | ||||
\(539\) | −72.0308 | − | 600.307i | −0.133638 | − | 1.11374i | ||||
\(540\) | 40.3859 | − | 497.572i | 0.0747888 | − | 0.921430i | ||||
\(541\) | −205.505 | + | 355.946i | −0.379862 | + | 0.657941i | −0.991042 | − | 0.133551i | \(-0.957362\pi\) |
0.611180 | + | 0.791492i | \(0.290695\pi\) | |||||||
\(542\) | − | 65.3258i | − | 0.120527i | ||||||
\(543\) | 306.483 | − | 243.380i | 0.564426 | − | 0.448213i | ||||
\(544\) | −223.438 | −0.410731 | ||||||||
\(545\) | −525.759 | + | 303.547i | −0.964696 | + | 0.556967i | ||||
\(546\) | −37.7066 | − | 179.328i | −0.0690596 | − | 0.328440i | ||||
\(547\) | 205.309 | − | 355.605i | 0.375336 | − | 0.650101i | −0.615041 | − | 0.788495i | \(-0.710861\pi\) |
0.990377 | + | 0.138394i | \(0.0441940\pi\) | |||||||
\(548\) | −147.107 | − | 84.9321i | −0.268443 | − | 0.154986i | ||||
\(549\) | −76.9675 | + | 23.3940i | −0.140196 | + | 0.0426120i | ||||
\(550\) | −293.566 | − | 508.471i | −0.533756 | − | 0.924492i | ||||
\(551\) | 277.946 | − | 160.472i | 0.504440 | − | 0.291238i | ||||
\(552\) | 41.5116 | − | 32.9645i | 0.0752021 | − | 0.0597183i | ||||
\(553\) | −845.300 | + | 557.819i | −1.52857 | + | 1.00871i | ||||
\(554\) | −14.7643 | + | 8.52415i | −0.0266503 | + | 0.0153865i | ||||
\(555\) | −115.065 | + | 17.1006i | −0.207325 | + | 0.0308119i | ||||
\(556\) | −455.404 | −0.819071 | ||||||||
\(557\) | −539.330 | + | 311.382i | −0.968276 | + | 0.559034i | −0.898710 | − | 0.438543i | \(-0.855495\pi\) |
−0.0695656 | + | 0.997577i | \(0.522161\pi\) | |||||||
\(558\) | −227.548 | − | 52.9249i | −0.407791 | − | 0.0948475i | ||||
\(559\) | −346.381 | −0.619644 | ||||||||
\(560\) | 33.3026 | + | 50.4656i | 0.0594690 | + | 0.0901172i | ||||
\(561\) | 246.354 | + | 97.2736i | 0.439133 | + | 0.173393i | ||||
\(562\) | −557.770 | −0.992474 | ||||||||
\(563\) | 547.707 | + | 316.219i | 0.972836 | + | 0.561667i | 0.900100 | − | 0.435684i | \(-0.143493\pi\) |
0.0727367 | + | 0.997351i | \(0.476827\pi\) | |||||||
\(564\) | 93.7511 | + | 118.059i | 0.166225 | + | 0.209324i | ||||
\(565\) | −24.7932 | − | 42.9430i | −0.0438817 | − | 0.0760053i | ||||
\(566\) | 495.472i | 0.875391i | ||||||||
\(567\) | 219.411 | − | 522.827i | 0.386968 | − | 0.922093i | ||||
\(568\) | −17.3405 | −0.0305290 | ||||||||
\(569\) | 953.554 | − | 550.535i | 1.67584 | − | 0.967548i | 0.711577 | − | 0.702608i | \(-0.247981\pi\) |
0.964265 | − | 0.264939i | \(-0.0853519\pi\) | |||||||
\(570\) | 736.853 | − | 585.138i | 1.29272 | − | 1.02656i | ||||
\(571\) | 319.146 | − | 552.777i | 0.558924 | − | 0.968086i | −0.438662 | − | 0.898652i | \(-0.644548\pi\) |
0.997587 | − | 0.0694335i | \(-0.0221192\pi\) | |||||||
\(572\) | 196.666i | 0.343821i | ||||||||
\(573\) | 125.363 | − | 317.493i | 0.218784 | − | 0.554089i | ||||
\(574\) | 260.275 | + | 130.216i | 0.453441 | + | 0.226858i | ||||
\(575\) | 80.1651i | 0.139418i | ||||||||
\(576\) | −90.7845 | + | 390.323i | −0.157612 | + | 0.677644i | ||||
\(577\) | 12.4886 | + | 21.6309i | 0.0216441 | + | 0.0374886i | 0.876645 | − | 0.481139i | \(-0.159777\pi\) |
−0.855000 | + | 0.518627i | \(0.826443\pi\) | |||||||
\(578\) | 305.670i | 0.528841i | ||||||||
\(579\) | 115.868 | + | 779.645i | 0.200118 | + | 1.34654i | ||||
\(580\) | −95.7590 | − | 165.860i | −0.165102 | − | 0.285965i | ||||
\(581\) | 49.2045 | − | 98.3497i | 0.0846894 | − | 0.169277i | ||||
\(582\) | 225.464 | + | 283.922i | 0.387395 | + | 0.487839i | ||||
\(583\) | 363.977 | + | 630.426i | 0.624317 | + | 1.08135i | ||||
\(584\) | −497.859 | + | 287.439i | −0.852498 | + | 0.492190i | ||||
\(585\) | 139.928 | + | 460.369i | 0.239192 | + | 0.786955i | ||||
\(586\) | 124.154 | − | 215.040i | 0.211866 | − | 0.366963i | ||||
\(587\) | −192.680 | − | 111.244i | −0.328246 | − | 0.189513i | 0.326816 | − | 0.945088i | \(-0.394024\pi\) |
−0.655062 | + | 0.755575i | \(0.727358\pi\) | |||||||
\(588\) | −91.0423 | − | 332.899i | −0.154834 | − | 0.566154i | ||||
\(589\) | 312.856 | + | 541.883i | 0.531165 | + | 0.920004i | ||||
\(590\) | 1047.67i | 1.77570i | ||||||||
\(591\) | 344.968 | + | 434.411i | 0.583702 | + | 0.735044i | ||||
\(592\) | 5.40059 | 0.00912261 | ||||||||
\(593\) | 326.783 | + | 188.668i | 0.551068 | + | 0.318159i | 0.749553 | − | 0.661945i | \(-0.230269\pi\) |
−0.198485 | + | 0.980104i | \(0.563602\pi\) | |||||||
\(594\) | 243.417 | − | 352.322i | 0.409793 | − | 0.593135i | ||||
\(595\) | 329.214 | − | 217.251i | 0.553302 | − | 0.365128i | ||||
\(596\) | −132.480 | − | 76.4872i | −0.222281 | − | 0.128334i | ||||
\(597\) | −685.718 | − | 270.758i | −1.14861 | − | 0.453531i | ||||
\(598\) | −9.44844 | + | 16.3652i | −0.0158001 | + | 0.0273665i | ||||
\(599\) | 729.103 | + | 420.948i | 1.21720 | + | 0.702751i | 0.964318 | − | 0.264746i | \(-0.0852882\pi\) |
0.252882 | + | 0.967497i | \(0.418621\pi\) | |||||||
\(600\) | −563.509 | − | 709.615i | −0.939181 | − | 1.18269i | ||||
\(601\) | −348.065 | + | 602.867i | −0.579144 | + | 1.00311i | 0.416434 | + | 0.909166i | \(0.363280\pi\) |
−0.995578 | + | 0.0939405i | \(0.970054\pi\) | |||||||
\(602\) | 458.270 | − | 27.3956i | 0.761246 | − | 0.0455077i | ||||
\(603\) | 596.086 | + | 557.682i | 0.988535 | + | 0.924845i | ||||
\(604\) | −192.088 | + | 332.706i | −0.318027 | + | 0.550838i | ||||
\(605\) | 246.115i | 0.406801i | ||||||||
\(606\) | 24.2136 | + | 9.56082i | 0.0399564 | + | 0.0157769i | ||||
\(607\) | −757.947 | −1.24868 | −0.624338 | − | 0.781154i | \(-0.714631\pi\) | ||||
−0.624338 | + | 0.781154i | \(0.714631\pi\) | |||||||
\(608\) | 837.930 | − | 483.779i | 1.37817 | − | 0.795689i | ||||
\(609\) | −44.7594 | − | 212.871i | −0.0734966 | − | 0.349542i | ||||
\(610\) | −45.2395 | + | 78.3571i | −0.0741631 | + | 0.128454i | ||||
\(611\) | −125.839 | − | 72.6532i | −0.205956 | − | 0.118909i | ||||
\(612\) | 147.257 | + | 34.2504i | 0.240617 | + | 0.0559647i | ||||
\(613\) | −110.823 | − | 191.951i | −0.180788 | − | 0.313134i | 0.761361 | − | 0.648328i | \(-0.224532\pi\) |
−0.942149 | + | 0.335194i | \(0.891198\pi\) | |||||||
\(614\) | 18.3389 | − | 10.5880i | 0.0298680 | − | 0.0172443i | ||||
\(615\) | −710.769 | − | 280.650i | −1.15572 | − | 0.456341i | ||||
\(616\) | −42.0553 | − | 703.494i | −0.0682716 | − | 1.14204i | ||||
\(617\) | 713.225 | − | 411.781i | 1.15596 | − | 0.667392i | 0.205625 | − | 0.978631i | \(-0.434077\pi\) |
0.950332 | + | 0.311239i | \(0.100744\pi\) | |||||||
\(618\) | 101.310 | − | 256.576i | 0.163932 | − | 0.415171i | ||||
\(619\) | −156.620 | −0.253021 | −0.126510 | − | 0.991965i | \(-0.540378\pi\) | ||||
−0.126510 | + | 0.991965i | \(0.540378\pi\) | |||||||
\(620\) | 323.359 | − | 186.691i | 0.521547 | − | 0.301115i | ||||
\(621\) | −52.8352 | + | 25.0425i | −0.0850808 | + | 0.0403261i | ||||
\(622\) | −623.733 | −1.00279 | ||||||||
\(623\) | −14.7603 | + | 29.5028i | −0.0236923 | + | 0.0473560i | ||||
\(624\) | −3.28375 | − | 22.0954i | −0.00526242 | − | 0.0354093i | ||||
\(625\) | −180.089 | −0.288142 | ||||||||
\(626\) | −457.227 | − | 263.980i | −0.730394 | − | 0.421693i | ||||
\(627\) | −1134.48 | + | 168.603i | −1.80938 | + | 0.268904i | ||||
\(628\) | 200.897 | + | 347.963i | 0.319899 | + | 0.554082i | ||||
\(629\) | − | 35.2309i | − | 0.0560110i | ||||||
\(630\) | −221.538 | − | 598.012i | −0.351648 | − | 0.949225i | ||||
\(631\) | −857.637 | −1.35917 | −0.679586 | − | 0.733596i | \(-0.737840\pi\) | ||||
−0.679586 | + | 0.733596i | \(0.737840\pi\) | |||||||
\(632\) | −1022.34 | + | 590.251i | −1.61763 | + | 0.933941i | ||||
\(633\) | −129.112 | − | 50.9804i | −0.203969 | − | 0.0805378i | ||||
\(634\) | 84.0707 | − | 145.615i | 0.132604 | − | 0.229676i | ||||
\(635\) | 1128.25i | 1.77677i | ||||||||
\(636\) | 258.407 | + | 325.407i | 0.406300 | + | 0.511646i | ||||
\(637\) | 199.461 | + | 266.216i | 0.313125 | + | 0.417921i | ||||
\(638\) | − | 164.288i | − | 0.257505i | ||||||
\(639\) | 18.6298 | + | 4.33306i | 0.0291546 | + | 0.00678101i | ||||
\(640\) | −266.481 | − | 461.559i | −0.416377 | − | 0.721186i | ||||
\(641\) | 128.273i | 0.200115i | 0.994982 | + | 0.100057i | \(0.0319026\pi\) | ||||
−0.994982 | + | 0.100057i | \(0.968097\pi\) | |||||||
\(642\) | 49.7245 | − | 39.4864i | 0.0774524 | − | 0.0615053i | ||||
\(643\) | 27.7356 | + | 48.0395i | 0.0431347 | + | 0.0747116i | 0.886787 | − | 0.462179i | \(-0.152932\pi\) |
−0.843652 | + | 0.536890i | \(0.819599\pi\) | |||||||
\(644\) | −15.9238 | + | 31.8283i | −0.0247263 | + | 0.0494228i | ||||
\(645\) | −1192.35 | + | 177.203i | −1.84860 | + | 0.274733i | ||||
\(646\) | 142.482 | + | 246.786i | 0.220561 | + | 0.382022i | ||||
\(647\) | 410.064 | − | 236.751i | 0.633794 | − | 0.365921i | −0.148426 | − | 0.988923i | \(-0.547421\pi\) |
0.782220 | + | 0.623003i | \(0.214087\pi\) | |||||||
\(648\) | 291.661 | − | 593.071i | 0.450094 | − | 0.915233i | ||||
\(649\) | 638.527 | − | 1105.96i | 0.983862 | − | 1.70410i | ||||
\(650\) | 279.753 | + | 161.515i | 0.430389 | + | 0.248485i | ||||
\(651\) | 415.012 | − | 87.2627i | 0.637500 | − | 0.134044i | ||||
\(652\) | −78.3749 | − | 135.749i | −0.120207 | − | 0.208205i | ||||
\(653\) | − | 482.186i | − | 0.738416i | −0.929347 | − | 0.369208i | \(-0.879629\pi\) | ||
0.929347 | − | 0.369208i | \(-0.120371\pi\) | |||||||
\(654\) | −294.040 | + | 43.6993i | −0.449603 | + | 0.0668185i | ||||
\(655\) | −1405.30 | −2.14550 | ||||||||
\(656\) | 30.7237 | + | 17.7383i | 0.0468349 | + | 0.0270402i | ||||
\(657\) | 606.701 | − | 184.405i | 0.923442 | − | 0.280677i | ||||
\(658\) | 172.234 | + | 86.1691i | 0.261754 | + | 0.130956i | ||||
\(659\) | 900.528 | + | 519.920i | 1.36651 | + | 0.788953i | 0.990480 | − | 0.137655i | \(-0.0439566\pi\) |
0.376027 | + | 0.926609i | \(0.377290\pi\) | |||||||
\(660\) | 100.611 | + | 676.982i | 0.152441 | + | 1.02573i | ||||
\(661\) | −173.864 | + | 301.141i | −0.263031 | + | 0.455584i | −0.967046 | − | 0.254602i | \(-0.918056\pi\) |
0.704015 | + | 0.710186i | \(0.251389\pi\) | |||||||
\(662\) | 268.209 | + | 154.850i | 0.405149 | + | 0.233913i | ||||
\(663\) | −144.140 | + | 21.4217i | −0.217406 | + | 0.0323102i | ||||
\(664\) | 64.0926 | − | 111.012i | 0.0965251 | − | 0.167186i | ||||
\(665\) | −764.227 | + | 1527.53i | −1.14921 | + | 2.29704i | ||||
\(666\) | −55.4807 | − | 12.9042i | −0.0833044 | − | 0.0193756i | ||||
\(667\) | −11.2157 | + | 19.4262i | −0.0168152 | + | 0.0291247i | ||||
\(668\) | 33.2119i | 0.0497184i | ||||||||
\(669\) | −49.2919 | − | 331.671i | −0.0736799 | − | 0.495772i | ||||
\(670\) | 918.114 | 1.37032 | ||||||||
\(671\) | 95.5134 | − | 55.1447i | 0.142345 | − | 0.0821829i | ||||
\(672\) | −134.937 | − | 641.746i | −0.200799 | − | 0.954980i | ||||
\(673\) | −123.764 | + | 214.366i | −0.183899 | + | 0.318523i | −0.943205 | − | 0.332211i | \(-0.892205\pi\) |
0.759306 | + | 0.650734i | \(0.225539\pi\) | |||||||
\(674\) | −333.145 | − | 192.341i | −0.494281 | − | 0.285373i | ||||
\(675\) | 428.086 | + | 903.187i | 0.634202 | + | 1.33805i | ||||
\(676\) | 144.286 | + | 249.911i | 0.213441 | + | 0.369690i | ||||
\(677\) | 574.625 | − | 331.760i | 0.848782 | − | 0.490045i | −0.0114577 | − | 0.999934i | \(-0.503647\pi\) |
0.860240 | + | 0.509890i | \(0.170314\pi\) | |||||||
\(678\) | −3.56927 | − | 24.0166i | −0.00526441 | − | 0.0354228i | ||||
\(679\) | −588.584 | − | 294.470i | −0.866839 | − | 0.433682i | ||||
\(680\) | 398.167 | − | 229.882i | 0.585540 | − | 0.338062i | ||||
\(681\) | −478.783 | − | 602.922i | −0.703059 | − | 0.885348i | ||||
\(682\) | 320.296 | 0.469642 | ||||||||
\(683\) | −54.4337 | + | 31.4273i | −0.0796979 | + | 0.0460136i | −0.539319 | − | 0.842101i | \(-0.681318\pi\) |
0.459621 | + | 0.888115i | \(0.347985\pi\) | |||||||
\(684\) | −626.398 | + | 190.392i | −0.915787 | + | 0.278350i | ||||
\(685\) | 569.778 | 0.831793 | ||||||||
\(686\) | −284.946 | − | 336.434i | −0.415374 | − | 0.490428i | ||||
\(687\) | 362.383 | − | 287.770i | 0.527486 | − | 0.418879i | ||||
\(688\) | 55.9628 | 0.0813412 | ||||||||
\(689\) | −346.851 | − | 200.255i | −0.503412 | − | 0.290645i | ||||
\(690\) | −24.1522 | + | 61.1674i | −0.0350032 | + | 0.0886484i | ||||
\(691\) | 163.978 | + | 284.018i | 0.237305 | + | 0.411024i | 0.959940 | − | 0.280205i | \(-0.0904026\pi\) |
−0.722635 | + | 0.691230i | \(0.757069\pi\) | |||||||
\(692\) | 114.791i | 0.165884i | ||||||||
\(693\) | −130.608 | + | 766.309i | −0.188468 | + | 1.10578i | ||||
\(694\) | −783.092 | −1.12838 | ||||||||
\(695\) | 1322.91 | − | 763.783i | 1.90347 | − | 1.09897i | ||||
\(696\) | −37.2728 | − | 250.798i | −0.0535529 | − | 0.360343i | ||||
\(697\) | 115.717 | − | 200.427i | 0.166021 | − | 0.287557i | ||||
\(698\) | − | 171.841i | − | 0.246191i | ||||||
\(699\) | 1094.39 | − | 162.644i | 1.56565 | − | 0.232681i | ||||
\(700\) | 544.086 | + | 272.207i | 0.777266 | + | 0.388868i | ||||
\(701\) | 93.8066i | 0.133818i | 0.997759 | + | 0.0669091i | \(0.0213138\pi\) | ||||
−0.997759 | + | 0.0669091i | \(0.978686\pi\) | |||||||
\(702\) | −19.0606 | + | 234.835i | −0.0271518 | + | 0.334522i | ||||
\(703\) | 76.2807 | + | 132.122i | 0.108507 | + | 0.187940i | ||||
\(704\) | − | 549.418i | − | 0.780424i | ||||||
\(705\) | −470.343 | − | 185.717i | −0.667153 | − | 0.263428i | ||||
\(706\) | 387.777 | + | 671.650i | 0.549260 | + | 0.951345i | ||||
\(707\) | −47.1725 | + | 2.82000i | −0.0667220 | + | 0.00398868i | ||||
\(708\) | 267.720 | − | 678.023i | 0.378135 | − | 0.957659i | ||||
\(709\) | −545.930 | − | 945.578i | −0.770000 | − | 1.33368i | −0.937562 | − | 0.347817i | \(-0.886923\pi\) |
0.167563 | − | 0.985861i | \(-0.446410\pi\) | |||||||
\(710\) | 18.6308 | − | 10.7565i | 0.0262405 | − | 0.0151500i | ||||
\(711\) | 1245.85 | − | 378.672i | 1.75225 | − | 0.532590i | ||||
\(712\) | −19.2264 | + | 33.3011i | −0.0270034 | + | 0.0467712i | ||||
\(713\) | −37.8732 | − | 21.8661i | −0.0531181 | − | 0.0306678i | ||||
\(714\) | 189.007 | − | 39.7415i | 0.264715 | − | 0.0556604i | ||||
\(715\) | −329.839 | − | 571.298i | −0.461314 | − | 0.799019i | ||||
\(716\) | − | 443.911i | − | 0.619988i | ||||||
\(717\) | 219.400 | − | 555.648i | 0.305997 | − | 0.774962i | ||||
\(718\) | −247.252 | −0.344362 | ||||||||
\(719\) | −158.261 | − | 91.3719i | −0.220112 | − | 0.127082i | 0.385890 | − | 0.922545i | \(-0.373894\pi\) |
−0.606002 | + | 0.795463i | \(0.707228\pi\) | |||||||
\(720\) | −22.6073 | − | 74.3791i | −0.0313990 | − | 0.103304i | ||||
\(721\) | 29.8817 | + | 499.856i | 0.0414448 | + | 0.693282i | ||||
\(722\) | −666.808 | − | 384.982i | −0.923557 | − | 0.533216i | ||||
\(723\) | 458.445 | − | 364.053i | 0.634087 | − | 0.503531i | ||||
\(724\) | −153.139 | + | 265.245i | −0.211518 | + | 0.366360i | ||||
\(725\) | 332.080 | + | 191.726i | 0.458041 | + | 0.264450i | ||||
\(726\) | −44.2595 | + | 112.091i | −0.0609635 | + | 0.154395i | ||||
\(727\) | −186.677 | + | 323.334i | −0.256777 | + | 0.444750i | −0.965377 | − | 0.260860i | \(-0.915994\pi\) |
0.708600 | + | 0.705611i | \(0.249327\pi\) | |||||||
\(728\) | 213.564 | + | 323.628i | 0.293358 | + | 0.444544i | ||||
\(729\) | −461.544 | + | 564.286i | −0.633119 | + | 0.774055i | ||||
\(730\) | 356.603 | − | 617.654i | 0.488497 | − | 0.846102i | ||||
\(731\) | − | 365.075i | − | 0.499419i | ||||||
\(732\) | 49.3011 | − | 39.1502i | 0.0673513 | − | 0.0534839i | ||||
\(733\) | 694.476 | 0.947443 | 0.473722 | − | 0.880675i | \(-0.342910\pi\) | ||||
0.473722 | + | 0.880675i | \(0.342910\pi\) | |||||||
\(734\) | 207.933 | − | 120.050i | 0.283288 | − | 0.163556i | ||||
\(735\) | 822.794 | + | 814.352i | 1.11945 | + | 1.10796i | ||||
\(736\) | −33.8123 | + | 58.5645i | −0.0459406 | + | 0.0795714i | ||||
\(737\) | −969.200 | − | 559.568i | −1.31506 | − | 0.759251i | ||||
\(738\) | −273.244 | − | 255.639i | −0.370249 | − | 0.346394i | ||||
\(739\) | 143.041 | + | 247.755i | 0.193560 | + | 0.335256i | 0.946428 | − | 0.322916i | \(-0.104663\pi\) |
−0.752867 | + | 0.658172i | \(0.771330\pi\) | |||||||
\(740\) | 78.8415 | − | 45.5192i | 0.106543 | − | 0.0615124i | ||||
\(741\) | 494.170 | − | 392.422i | 0.666895 | − | 0.529584i | ||||
\(742\) | 474.730 | + | 237.509i | 0.639798 | + | 0.320092i | ||||
\(743\) | −700.673 | + | 404.534i | −0.943033 | + | 0.544460i | −0.890910 | − | 0.454180i | \(-0.849932\pi\) |
−0.0521232 | + | 0.998641i | \(0.516599\pi\) | |||||||
\(744\) | 488.955 | − | 72.6669i | 0.657198 | − | 0.0976706i | ||||
\(745\) | 513.124 | 0.688757 | ||||||||
\(746\) | −402.136 | + | 232.174i | −0.539057 | + | 0.311225i | ||||
\(747\) | −96.5978 | + | 103.250i | −0.129314 | + | 0.138220i | ||||
\(748\) | −207.280 | −0.277112 | ||||||||
\(749\) | −51.5717 | + | 103.081i | −0.0688541 | + | 0.137625i | ||||
\(750\) | 339.475 | + | 134.043i | 0.452633 | + | 0.178724i | ||||
\(751\) | −263.348 | −0.350663 | −0.175332 | − | 0.984509i | \(-0.556100\pi\) | ||||
−0.175332 | + | 0.984509i | \(0.556100\pi\) | |||||||
\(752\) | 20.3311 | + | 11.7381i | 0.0270360 | + | 0.0156092i | ||||
\(753\) | −363.106 | − | 457.253i | −0.482213 | − | 0.607242i | ||||
\(754\) | 45.1945 | + | 78.2792i | 0.0599397 | + | 0.103819i | ||||
\(755\) | − | 1288.65i | − | 1.70682i | ||||||
\(756\) | −9.44141 | + | 443.630i | −0.0124886 | + | 0.586812i | ||||
\(757\) | 946.293 | 1.25006 | 0.625028 | − | 0.780602i | \(-0.285087\pi\) | ||||
0.625028 | + | 0.780602i | \(0.285087\pi\) | |||||||
\(758\) | 428.341 | − | 247.303i | 0.565094 | − | 0.326257i | ||||
\(759\) | 62.7761 | − | 49.8508i | 0.0827090 | − | 0.0656796i | ||||
\(760\) | −995.463 | + | 1724.19i | −1.30982 | + | 2.26868i | ||||
\(761\) | − | 646.797i | − | 0.849930i | −0.905210 | − | 0.424965i | \(-0.860286\pi\) | ||
0.905210 | − | 0.424965i | \(-0.139714\pi\) | |||||||
\(762\) | −202.897 | + | 513.853i | −0.266269 | + | 0.674347i | ||||
\(763\) | 450.397 | − | 297.220i | 0.590297 | − | 0.389541i | ||||
\(764\) | 267.136i | 0.349654i | ||||||||
\(765\) | −485.215 | + | 147.479i | −0.634268 | + | 0.192783i | ||||
\(766\) | 271.459 | + | 470.181i | 0.354385 | + | 0.613814i | ||||
\(767\) | 702.616i | 0.916057i | ||||||||
\(768\) | −116.910 | − | 786.652i | −0.152226 | − | 1.02429i | ||||
\(769\) | −212.086 | − | 367.344i | −0.275795 | − | 0.477691i | 0.694541 | − | 0.719454i | \(-0.255608\pi\) |
−0.970335 | + | 0.241763i | \(0.922274\pi\) | |||||||
\(770\) | 481.570 | + | 729.754i | 0.625415 | + | 0.947732i | ||||
\(771\) | 748.393 | + | 942.437i | 0.970678 | + | 1.22236i | ||||
\(772\) | −308.423 | − | 534.204i | −0.399511 | − | 0.691974i | ||||
\(773\) | −359.361 | + | 207.477i | −0.464891 | + | 0.268405i | −0.714099 | − | 0.700045i | \(-0.753163\pi\) |
0.249208 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(774\) | −574.911 | − | 133.717i | −0.742779 | − | 0.172762i | ||||
\(775\) | −373.788 | + | 647.420i | −0.482308 | + | 0.835381i | ||||
\(776\) | −664.361 | − | 383.569i | −0.856136 | − | 0.494290i | ||||
\(777\) | 101.188 | − | 21.2764i | 0.130230 | − | 0.0273828i | ||||
\(778\) | −462.204 | − | 800.560i | −0.594092 | − | 1.02900i | ||||
\(779\) | 1002.18i | 1.28650i | ||||||||
\(780\) | −234.171 | − | 294.887i | −0.300219 | − | 0.378060i | ||||
\(781\) | −26.2232 | −0.0335765 | ||||||||
\(782\) | −17.2484 | − | 9.95836i | −0.0220568 | − | 0.0127345i | ||||
\(783\) | −22.6258 | + | 278.759i | −0.0288963 | + | 0.356015i | ||||
\(784\) | −32.2257 | − | 43.0109i | −0.0411042 | − | 0.0548608i | ||||
\(785\) | −1167.18 | − | 673.871i | −1.48685 | − | 0.858434i | ||||
\(786\) | −640.034 | − | 252.720i | −0.814292 | − | 0.321526i | ||||
\(787\) | 316.288 | − | 547.827i | 0.401891 | − | 0.696095i | −0.592063 | − | 0.805891i | \(-0.701686\pi\) |
0.993954 | + | 0.109796i | \(0.0350198\pi\) | |||||||
\(788\) | −375.960 | − | 217.061i | −0.477106 | − | 0.275458i | ||||
\(789\) | 545.319 | + | 686.709i | 0.691152 | + | 0.870354i | ||||
\(790\) | 732.278 | − | 1268.34i | 0.926934 | − | 1.60550i | ||||
\(791\) | 24.2764 | + | 36.7875i | 0.0306907 | + | 0.0465076i | ||||
\(792\) | −205.271 | + | 882.550i | −0.259180 | + | 1.11433i | ||||
\(793\) | −30.3398 | + | 52.5501i | −0.0382595 | + | 0.0662674i | ||||
\(794\) | 200.309i | 0.252279i | ||||||||
\(795\) | −1296.41 | − | 511.892i | −1.63071 | − | 0.643890i | ||||
\(796\) | 576.957 | 0.724820 | ||||||||
\(797\) | −242.578 | + | 140.052i | −0.304364 | + | 0.175724i | −0.644401 | − | 0.764687i | \(-0.722893\pi\) |
0.340038 | + | 0.940412i | \(0.389560\pi\) | |||||||
\(798\) | −622.761 | + | 558.268i | −0.780402 | + | 0.699584i | ||||
\(799\) | 76.5742 | − | 132.630i | 0.0958376 | − | 0.165996i | ||||
\(800\) | 1001.13 | + | 578.001i | 1.25141 | + | 0.722501i | ||||
\(801\) | 28.9772 | − | 30.9728i | 0.0361763 | − | 0.0386676i | ||||
\(802\) | 84.2891 | + | 145.993i | 0.105099 | + | 0.182036i | ||||
\(803\) | −752.891 | + | 434.682i | −0.937597 | + | 0.541322i | ||||
\(804\) | −594.180 | − | 234.614i | −0.739030 | − | 0.291809i | ||||
\(805\) | −7.12377 | − | 119.165i | −0.00884941 | − | 0.148032i | ||||
\(806\) | −152.613 | + | 88.1110i | −0.189346 | + | 0.109319i | ||||
\(807\) | −362.864 | + | 918.985i | −0.449646 | + | 1.13877i | ||||
\(808\) | −55.0835 | −0.0681726 | ||||||||
\(809\) | −300.584 | + | 173.543i | −0.371551 | + | 0.214515i | −0.674136 | − | 0.738608i | \(-0.735484\pi\) |
0.302585 | + | 0.953122i | \(0.402150\pi\) | |||||||
\(810\) | 54.5251 | + | 818.121i | 0.0673149 | + | 1.01003i | ||||
\(811\) | 101.532 | 0.125193 | 0.0625965 | − | 0.998039i | \(-0.480062\pi\) | ||||
0.0625965 | + | 0.998039i | \(0.480062\pi\) | |||||||
\(812\) | 93.7630 | + | 142.085i | 0.115472 | + | 0.174982i | ||||
\(813\) | −22.4128 | − | 150.809i | −0.0275680 | − | 0.185497i | ||||
\(814\) | 78.0947 | 0.0959394 | ||||||||
\(815\) | 455.346 | + | 262.894i | 0.558707 | + | 0.322569i | ||||
\(816\) | 23.2879 | − | 3.46097i | 0.0285391 | − | 0.00424138i | ||||
\(817\) | 790.447 | + | 1369.09i | 0.967499 | + | 1.67576i | ||||
\(818\) | 272.721i | 0.333400i | ||||||||
\(819\) | −148.574 | − | 401.056i | −0.181410 | − | 0.489690i | ||||
\(820\) | 598.035 | 0.729311 | ||||||||
\(821\) | −471.102 | + | 271.991i | −0.573815 | + | 0.331292i | −0.758672 | − | 0.651473i | \(-0.774151\pi\) |
0.184856 | + | 0.982766i | \(0.440818\pi\) | |||||||
\(822\) | 259.501 | + | 102.465i | 0.315694 | + | 0.124653i | ||||
\(823\) | 218.442 | − | 378.353i | 0.265422 | − | 0.459724i | −0.702252 | − | 0.711928i | \(-0.747822\pi\) |
0.967674 | + | 0.252204i | \(0.0811555\pi\) | |||||||
\(824\) | 583.684i | 0.708354i | ||||||||
\(825\) | −852.170 | − | 1073.12i | −1.03293 | − | 1.30075i | ||||
\(826\) | −55.5706 | − | 929.577i | −0.0672767 | − | 1.12540i | ||||
\(827\) | 571.254i | 0.690754i | 0.938464 | + | 0.345377i | \(0.112249\pi\) | ||||
−0.938464 | + | 0.345377i | \(0.887751\pi\) | |||||||
\(828\) | 31.2614 | − | 33.4142i | 0.0377553 | − | 0.0403553i | ||||
\(829\) | −497.006 | − | 860.840i | −0.599525 | − | 1.03841i | −0.992891 | − | 0.119026i | \(-0.962023\pi\) |
0.393366 | − | 0.919382i | \(-0.371310\pi\) | |||||||
\(830\) | 159.029i | 0.191602i | ||||||||
\(831\) | −31.1598 | + | 24.7441i | −0.0374967 | + | 0.0297763i | ||||
\(832\) | 151.141 | + | 261.784i | 0.181660 | + | 0.314644i | ||||
\(833\) | −280.583 | + | 210.225i | −0.336834 | + | 0.252372i | ||||
\(834\) | 739.862 | − | 109.956i | 0.887125 | − | 0.131841i | ||||
\(835\) | −55.7016 | − | 96.4780i | −0.0667085 | − | 0.115542i | ||||
\(836\) | 777.334 | − | 448.794i | 0.929826 | − | 0.536835i | ||||
\(837\) | −543.468 | − | 44.1111i | −0.649305 | − | 0.0527014i | ||||
\(838\) | −476.211 | + | 824.822i | −0.568271 | + | 0.984275i | ||||
\(839\) | −397.098 | − | 229.265i | −0.473299 | − | 0.273259i | 0.244321 | − | 0.969695i | \(-0.421435\pi\) |
−0.717620 | + | 0.696435i | \(0.754768\pi\) | |||||||
\(840\) | 900.714 | + | 1004.77i | 1.07228 | + | 1.19615i | ||||
\(841\) | −366.852 | − | 635.406i | −0.436209 | − | 0.755537i | ||||
\(842\) | − | 722.475i | − | 0.858047i | ||||||
\(843\) | −1287.65 | + | 191.367i | −1.52746 | + | 0.227007i | ||||
\(844\) | 108.634 | 0.128713 | ||||||||
\(845\) | −838.279 | − | 483.981i | −0.992046 | − | 0.572758i | ||||
\(846\) | −180.816 | − | 169.166i | −0.213730 | − | 0.199960i | ||||
\(847\) | −13.0545 | − | 218.374i | −0.0154126 | − | 0.257820i | ||||
\(848\) | 56.0387 | + | 32.3539i | 0.0660833 | + | 0.0381532i | ||||
\(849\) | 169.992 | + | 1143.83i | 0.200227 | + | 1.34727i | ||||
\(850\) | −170.232 | + | 294.851i | −0.200273 | + | 0.346884i | ||||
\(851\) | −9.23427 | − | 5.33141i | −0.0108511 | − | 0.00626487i | ||||
\(852\) | −14.8061 | + | 2.20043i | −0.0173780 | + | 0.00258266i | ||||
\(853\) | −119.513 | + | 207.002i | −0.140109 | + | 0.242676i | −0.927537 | − | 0.373730i | \(-0.878079\pi\) |
0.787429 | + | 0.616406i | \(0.211412\pi\) | |||||||
\(854\) | 35.9840 | − | 71.9245i | 0.0421358 | − | 0.0842208i | ||||
\(855\) | 1500.32 | − | 1603.64i | 1.75476 | − | 1.87560i | ||||
\(856\) | −67.1760 | + | 116.352i | −0.0784767 | + | 0.135926i | ||||
\(857\) | − | 1577.33i | − | 1.84053i | −0.391299 | − | 0.920263i | \(-0.627974\pi\) | ||
0.391299 | − | 0.920263i | \(-0.372026\pi\) | |||||||
\(858\) | −47.4843 | − | 319.509i | −0.0553431 | − | 0.372388i | ||||
\(859\) | −929.635 | −1.08223 | −0.541115 | − | 0.840949i | \(-0.681998\pi\) | ||||
−0.541115 | + | 0.840949i | \(0.681998\pi\) | |||||||
\(860\) | 816.983 | − | 471.685i | 0.949980 | − | 0.548471i | ||||
\(861\) | 645.540 | + | 211.315i | 0.749756 | + | 0.245430i | ||||
\(862\) | −215.231 | + | 372.790i | −0.249687 | + | 0.432471i | ||||
\(863\) | −169.007 | − | 97.5764i | −0.195837 | − | 0.113066i | 0.398875 | − | 0.917005i | \(-0.369401\pi\) |
−0.594712 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(864\) | −68.2104 | + | 840.381i | −0.0789472 | + | 0.972663i | ||||
\(865\) | −192.523 | − | 333.460i | −0.222570 | − | 0.385503i | ||||
\(866\) | 121.262 | − | 70.0109i | 0.140026 | − | 0.0808440i | ||||
\(867\) | 104.873 | + | 705.662i | 0.120961 | + | 0.813912i | ||||
\(868\) | −277.008 | + | 182.800i | −0.319134 | + | 0.210599i | ||||
\(869\) | −1546.05 | + | 892.611i | −1.77911 | + | 1.02717i | ||||
\(870\) | 195.619 | + | 246.339i | 0.224850 | + | 0.283149i | ||||
\(871\) | 615.732 | 0.706925 | ||||||||
\(872\) | 544.731 | − | 314.500i | 0.624691 | − | 0.360666i | ||||
\(873\) | 617.911 | + | 578.100i | 0.707801 | + | 0.662199i | ||||
\(874\) | 86.2459 | 0.0986795 | ||||||||
\(875\) | −661.360 | + | 39.5364i | −0.755839 | + | 0.0451845i | ||||
\(876\) | −388.619 | + | 308.604i | −0.443629 | + | 0.352288i | ||||
\(877\) | 1129.67 | 1.28811 | 0.644053 | − | 0.764981i | \(-0.277252\pi\) | ||||
0.644053 | + | 0.764981i | \(0.277252\pi\) | |||||||
\(878\) | −650.071 | − | 375.318i | −0.740399 | − | 0.427470i | ||||
\(879\) | 212.839 | − | 539.032i | 0.242137 | − | 0.613233i | ||||
\(880\) | 53.2902 | + | 92.3013i | 0.0605570 | + | 0.104888i | ||||
\(881\) | − | 1585.64i | − | 1.79982i | −0.436075 | − | 0.899910i | \(-0.643632\pi\) | ||
0.436075 | − | 0.899910i | \(-0.356368\pi\) | |||||||
\(882\) | 228.287 | + | 518.855i | 0.258829 | + | 0.588271i | ||||
\(883\) | 1194.30 | 1.35255 | 0.676273 | − | 0.736651i | \(-0.263594\pi\) | ||||
0.676273 | + | 0.736651i | \(0.263594\pi\) | |||||||
\(884\) | 98.7634 | − | 57.0211i | 0.111723 | − | 0.0645035i | ||||
\(885\) | 359.446 | + | 2418.61i | 0.406153 | + | 2.73289i | ||||
\(886\) | −368.762 | + | 638.715i | −0.416210 | + | 0.720897i | ||||
\(887\) | − | 1526.52i | − | 1.72099i | −0.509457 | − | 0.860496i | \(-0.670154\pi\) | ||
0.509457 | − | 0.860496i | \(-0.329846\pi\) | |||||||
\(888\) | 119.217 | − | 17.7177i | 0.134254 | − | 0.0199523i | ||||
\(889\) | −59.8451 | − | 1001.08i | −0.0673173 | − | 1.12607i | ||||
\(890\) | − | 47.7054i | − | 0.0536015i | ||||||
\(891\) | 441.066 | − | 896.876i | 0.495024 | − | 1.00659i | ||||
\(892\) | 131.207 | + | 227.258i | 0.147093 | + | 0.254773i | ||||
\(893\) | 663.182i | 0.742645i | ||||||||
\(894\) | 233.698 | + | 92.2765i | 0.261407 | + | 0.103218i | ||||
\(895\) | 744.509 | + | 1289.53i | 0.831854 | + | 1.44081i | ||||
\(896\) | 260.926 | + | 395.399i | 0.291213 | + | 0.441293i | ||||
\(897\) | −16.1976 | + | 41.0218i | −0.0180576 | + | 0.0457323i | ||||
\(898\) | −176.737 | − | 306.117i | −0.196812 | − | 0.340888i | ||||
\(899\) | −181.158 | + | 104.592i | −0.201511 | + | 0.116342i | ||||
\(900\) | −571.195 | − | 534.394i | −0.634662 | − | 0.593771i | ||||
\(901\) | 211.062 | − | 365.570i | 0.234253 | − | 0.405739i | ||||
\(902\) | 444.278 | + | 256.504i | 0.492547 | + | 0.284372i | ||||
\(903\) | 1048.55 | − | 220.474i | 1.16119 | − | 0.244157i | ||||
\(904\) | 25.6878 | + | 44.4926i | 0.0284157 | + | 0.0492174i | ||||
\(905\) | − | 1027.35i | − | 1.13520i | ||||||
\(906\) | 231.741 | − | 586.903i | 0.255785 | − | 0.647796i | ||||
\(907\) | −922.718 | −1.01733 | −0.508665 | − | 0.860965i | \(-0.669861\pi\) | ||||
−0.508665 | + | 0.860965i | \(0.669861\pi\) | |||||||
\(908\) | 521.797 | + | 301.260i | 0.574666 | + | 0.331784i | ||||
\(909\) | 59.1790 | + | 13.7643i | 0.0651034 | + | 0.0151423i | ||||
\(910\) | −430.205 | − | 215.233i | −0.472753 | − | 0.236519i | ||||
\(911\) | 1137.89 | + | 656.958i | 1.24905 | + | 0.721140i | 0.970920 | − | 0.239404i | \(-0.0769519\pi\) |
0.278131 | + | 0.960543i | \(0.410285\pi\) | |||||||
\(912\) | −79.8400 | + | 63.4013i | −0.0875439 | + | 0.0695190i | ||||
\(913\) | 96.9245 | − | 167.878i | 0.106161 | − | 0.183875i | ||||
\(914\) | 82.9705 | + | 47.9030i | 0.0907773 | + | 0.0524103i | ||||
\(915\) | −77.5548 | + | 196.414i | −0.0847594 | + | 0.214660i | ||||
\(916\) | −181.070 | + | 313.623i | −0.197675 | + | 0.342383i | ||||
\(917\) | 1246.90 | − | 74.5406i | 1.35976 | − | 0.0812874i | ||||
\(918\) | −247.508 | − | 20.0893i | −0.269617 | − | 0.0218837i | ||||
\(919\) | 507.584 | − | 879.162i | 0.552322 | − | 0.956651i | −0.445784 | − | 0.895141i | \(-0.647075\pi\) |
0.998106 | − | 0.0615100i | \(-0.0195916\pi\) | |||||||
\(920\) | − | 139.150i | − | 0.151250i | ||||||
\(921\) | 38.7041 | − | 30.7351i | 0.0420240 | − | 0.0333714i | ||||
\(922\) | −894.564 | −0.970243 | ||||||||
\(923\) | 12.4947 | − | 7.21382i | 0.0135371 | − | 0.00781562i | ||||
\(924\) | −125.179 | − | 595.338i | −0.135475 | − | 0.644305i | ||||
\(925\) | −91.1372 | + | 157.854i | −0.0985267 | + | 0.170653i | ||||
\(926\) | 749.992 | + | 433.008i | 0.809926 | + | 0.467611i | ||||
\(927\) | 145.852 | − | 627.082i | 0.157337 | − | 0.676463i | ||||
\(928\) | 161.734 | + | 280.131i | 0.174282 | + | 0.301865i | ||||
\(929\) | 239.568 | − | 138.314i | 0.257877 | − | 0.148885i | −0.365489 | − | 0.930816i | \(-0.619098\pi\) |
0.623366 | + | 0.781930i | \(0.285765\pi\) | |||||||
\(930\) | −480.262 | + | 381.378i | −0.516411 | + | 0.410084i | ||||
\(931\) | 597.062 | − | 1395.89i | 0.641313 | − | 1.49934i | ||||
\(932\) | −749.863 | + | 432.933i | −0.804574 | + | 0.464521i | ||||
\(933\) | −1439.93 | + | 213.998i | −1.54334 | + | 0.229365i | ||||
\(934\) | −416.364 | −0.445785 | ||||||||
\(935\) | 602.131 | − | 347.641i | 0.643990 | − | 0.371808i | ||||
\(936\) | −144.977 | − | 476.981i | −0.154890 | − | 0.509595i | ||||
\(937\) | 114.886 | 0.122610 | 0.0613051 | − | 0.998119i | \(-0.480474\pi\) | ||||
0.0613051 | + | 0.998119i | \(0.480474\pi\) | |||||||
\(938\) | −814.627 | + | 48.6989i | −0.868473 | + | 0.0519178i | ||||
\(939\) | −1146.11 | − | 452.545i | −1.22056 | − | 0.481944i | ||||
\(940\) | 395.742 | 0.421003 | ||||||||
\(941\) | 489.279 | + | 282.485i | 0.519957 | + | 0.300197i | 0.736917 | − | 0.675983i | \(-0.236281\pi\) |
−0.216960 | + | 0.976180i | \(0.569614\pi\) | |||||||
\(942\) | −410.397 | − | 516.806i | −0.435666 | − | 0.548626i | ||||
\(943\) | −35.0222 | − | 60.6603i | −0.0371392 | − | 0.0643269i | ||||
\(944\) | − | 113.517i | − | 0.120252i | ||||||
\(945\) | −716.610 | − | 1304.54i | −0.758318 | − | 1.38047i | ||||
\(946\) | 809.244 | 0.855438 | ||||||||
\(947\) | −432.763 | + | 249.856i | −0.456983 | + | 0.263839i | −0.710775 | − | 0.703420i | \(-0.751656\pi\) |
0.253792 | + | 0.967259i | \(0.418322\pi\) | |||||||
\(948\) | −798.023 | + | 633.713i | −0.841796 | + | 0.668474i | ||||
\(949\) | 239.155 | − | 414.229i | 0.252008 | − | 0.436490i | ||||
\(950\) | − | 1474.32i | − | 1.55192i | ||||||
\(951\) | 144.124 | − | 365.006i | 0.151550 | − | 0.383813i | ||||
\(952\) | −341.094 | + | 225.090i | −0.358292 | + | 0.236439i | ||||
\(953\) | − | 75.9158i | − | 0.0796598i | −0.999206 | − | 0.0398299i | \(-0.987318\pi\) | ||
0.999206 | − | 0.0398299i | \(-0.0126816\pi\) | |||||||
\(954\) | −498.384 | − | 466.274i | −0.522415 | − | 0.488757i | ||||
\(955\) | −448.028 | − | 776.008i | −0.469140 | − | 0.812574i | ||||
\(956\) | 467.517i | 0.489035i | ||||||||
\(957\) | −56.3661 | − | 379.272i | −0.0588987 | − | 0.396313i | ||||
\(958\) | −18.4734 | − | 31.9968i | −0.0192833 | − | 0.0333996i | ||||
\(959\) | −505.555 | + | 30.2223i | −0.527169 | + | 0.0315144i | ||||
\(960\) | 654.195 | + | 823.816i | 0.681454 | + | 0.858141i | ||||
\(961\) | 276.588 | + | 479.065i | 0.287813 | + | 0.498507i | ||||
\(962\) | −37.2101 | + | 21.4833i | −0.0386799 | + | 0.0223319i | ||||
\(963\) | 101.245 | − | 108.217i | 0.105135 | − | 0.112375i | ||||
\(964\) | −229.069 | + | 396.760i | −0.237624 | + | 0.411577i | ||||
\(965\) | 1791.89 | + | 1034.55i | 1.85688 | + | 1.07207i | ||||
\(966\) | 18.1854 | − | 55.5539i | 0.0188254 | − | 0.0575092i | ||||
\(967\) | −427.761 | − | 740.905i | −0.442359 | − | 0.766189i | 0.555505 | − | 0.831513i | \(-0.312525\pi\) |
−0.997864 | + | 0.0653246i | \(0.979192\pi\) | |||||||
\(968\) | − | 254.996i | − | 0.263425i | ||||||
\(969\) | 413.601 | + | 520.840i | 0.426833 | + | 0.537502i | ||||
\(970\) | 951.728 | 0.981163 | ||||||||
\(971\) | 361.225 | + | 208.553i | 0.372013 | + | 0.214782i | 0.674338 | − | 0.738423i | \(-0.264429\pi\) |
−0.302324 | + | 0.953205i | \(0.597763\pi\) | |||||||
\(972\) | 173.775 | − | 543.401i | 0.178781 | − | 0.559054i | ||||
\(973\) | −1133.28 | + | 747.863i | −1.16473 | + | 0.768615i | ||||
\(974\) | 975.201 | + | 563.033i | 1.00123 | + | 0.578062i | ||||
\(975\) | 701.244 | + | 276.889i | 0.719225 | + | 0.283989i | ||||
\(976\) | 4.90182 | − | 8.49020i | 0.00502236 | − | 0.00869898i | ||||
\(977\) | 1130.11 | + | 652.468i | 1.15671 | + | 0.667828i | 0.950514 | − | 0.310683i | \(-0.100558\pi\) |
0.206198 | + | 0.978510i | \(0.433891\pi\) | |||||||
\(978\) | 160.106 | + | 201.619i | 0.163708 | + | 0.206154i | ||||
\(979\) | −29.0753 | + | 50.3598i | −0.0296989 | + | 0.0514401i | ||||
\(980\) | −832.972 | − | 356.286i | −0.849972 | − | 0.363558i | ||||
\(981\) | −663.820 | + | 201.766i | −0.676677 | + | 0.205674i | ||||
\(982\) | −39.0231 | + | 67.5900i | −0.0397384 | + | 0.0688289i | ||||
\(983\) | 850.301i | 0.865006i | 0.901632 | + | 0.432503i | \(0.142370\pi\) | ||||
−0.901632 | + | 0.432503i | \(0.857630\pi\) | |||||||
\(984\) | 736.416 | + | 290.777i | 0.748391 | + | 0.295505i | ||||
\(985\) | 1456.18 | 1.47835 | ||||||||
\(986\) | −82.5039 | + | 47.6336i | −0.0836753 | + | 0.0483100i | ||||
\(987\) | 427.179 | + | 139.835i | 0.432805 | + | 0.141677i | ||||
\(988\) | −246.920 | + | 427.678i | −0.249919 | + | 0.432872i | ||||
\(989\) | −95.6887 | − | 55.2459i | −0.0967530 | − | 0.0558603i | ||||
\(990\) | −326.910 | − | 1075.55i | −0.330212 | − | 1.08642i | ||||
\(991\) | −68.1967 | − | 118.120i | −0.0688161 | − | 0.119193i | 0.829564 | − | 0.558411i | \(-0.188589\pi\) |
−0.898380 | + | 0.439218i | \(0.855255\pi\) | |||||||
\(992\) | −546.141 | + | 315.315i | −0.550546 | + | 0.317858i | ||||
\(993\) | 672.307 | + | 265.463i | 0.677047 | + | 0.267334i | ||||
\(994\) | −15.9602 | + | 10.5323i | −0.0160566 | + | 0.0105958i | ||||
\(995\) | −1676.01 | + | 967.647i | −1.68444 | + | 0.972510i | ||||
\(996\) | 40.6383 | − | 102.920i | 0.0408015 | − | 0.103333i | ||||
\(997\) | −664.806 | −0.666806 | −0.333403 | − | 0.942784i | \(-0.608197\pi\) | ||||
−0.333403 | + | 0.942784i | \(0.608197\pi\) | |||||||
\(998\) | 778.692 | − | 449.578i | 0.780252 | − | 0.450479i | ||||
\(999\) | −132.509 | − | 10.7552i | −0.132641 | − | 0.0107660i |
(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 | 63.3.n.b.2.8 | yes | 22 | |
3.2 | odd | 2 | 189.3.n.b.170.4 | 22 | |||
7.2 | even | 3 | 441.3.r.g.344.4 | 22 | |||
7.3 | odd | 6 | 441.3.j.f.263.8 | 22 | |||
7.4 | even | 3 | 63.3.j.b.11.8 | ✓ | 22 | ||
7.5 | odd | 6 | 441.3.r.f.344.4 | 22 | |||
7.6 | odd | 2 | 441.3.n.f.128.8 | 22 | |||
9.4 | even | 3 | 189.3.j.b.44.8 | 22 | |||
9.5 | odd | 6 | 63.3.j.b.23.4 | yes | 22 | ||
21.11 | odd | 6 | 189.3.j.b.116.4 | 22 | |||
63.4 | even | 3 | 189.3.n.b.179.4 | 22 | |||
63.5 | even | 6 | 441.3.r.f.50.4 | 22 | |||
63.23 | odd | 6 | 441.3.r.g.50.4 | 22 | |||
63.32 | odd | 6 | inner | 63.3.n.b.32.8 | yes | 22 | |
63.41 | even | 6 | 441.3.j.f.275.4 | 22 | |||
63.59 | even | 6 | 441.3.n.f.410.8 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.j.b.11.8 | ✓ | 22 | 7.4 | even | 3 | ||
63.3.j.b.23.4 | yes | 22 | 9.5 | odd | 6 | ||
63.3.n.b.2.8 | yes | 22 | 1.1 | even | 1 | trivial | |
63.3.n.b.32.8 | yes | 22 | 63.32 | odd | 6 | inner | |
189.3.j.b.44.8 | 22 | 9.4 | even | 3 | |||
189.3.j.b.116.4 | 22 | 21.11 | odd | 6 | |||
189.3.n.b.170.4 | 22 | 3.2 | odd | 2 | |||
189.3.n.b.179.4 | 22 | 63.4 | even | 3 | |||
441.3.j.f.263.8 | 22 | 7.3 | odd | 6 | |||
441.3.j.f.275.4 | 22 | 63.41 | even | 6 | |||
441.3.n.f.128.8 | 22 | 7.6 | odd | 2 | |||
441.3.n.f.410.8 | 22 | 63.59 | even | 6 | |||
441.3.r.f.50.4 | 22 | 63.5 | even | 6 | |||
441.3.r.f.344.4 | 22 | 7.5 | odd | 6 | |||
441.3.r.g.50.4 | 22 | 63.23 | odd | 6 | |||
441.3.r.g.344.4 | 22 | 7.2 | even | 3 |