Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(163,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.e (of order \(3\), 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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1767277521.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.3 | ||
Root | \(0.0512865 + 1.21608i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.163 |
Dual form | 567.2.e.d.487.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.768262 | − | 1.33067i | 0.543243 | − | 0.940925i | −0.455472 | − | 0.890250i | \(-0.650530\pi\) |
0.998715 | − | 0.0506745i | \(-0.0161371\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.180452 | − | 0.312552i | −0.0902259 | − | 0.156276i | ||||
\(5\) | 1.57880 | − | 2.73457i | 0.706062 | − | 1.22294i | −0.260245 | − | 0.965543i | \(-0.583803\pi\) |
0.966307 | − | 0.257393i | \(-0.0828634\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.28677 | + | 1.33067i | −0.864318 | + | 0.502945i | ||||
\(8\) | 2.51851 | 0.890428 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.42587 | − | 4.20173i | −0.767127 | − | 1.32870i | ||||
\(11\) | −2.87458 | − | 4.97892i | −0.866719 | − | 1.50120i | −0.865330 | − | 0.501202i | \(-0.832891\pi\) |
−0.00138834 | − | 0.999999i | \(-0.500442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.360904 | −0.100097 | −0.0500484 | − | 0.998747i | \(-0.515938\pi\) | ||||
−0.0500484 | + | 0.998747i | \(0.515938\pi\) | |||||||
\(14\) | 0.0138393 | + | 4.06523i | 0.00369871 | + | 1.08648i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.29578 | − | 3.97640i | 0.573945 | − | 0.994101i | ||||
\(17\) | 1.38842 | + | 2.40481i | 0.336741 | + | 0.583253i | 0.983818 | − | 0.179172i | \(-0.0573419\pi\) |
−0.647076 | + | 0.762425i | \(0.724009\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.61533 | − | 6.26193i | 0.829413 | − | 1.43658i | −0.0690869 | − | 0.997611i | \(-0.522009\pi\) |
0.898500 | − | 0.438974i | \(-0.144658\pi\) | |||||||
\(20\) | −1.13959 | −0.254820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.83372 | −1.88336 | ||||||||
\(23\) | −0.412190 | + | 0.713934i | −0.0859476 | + | 0.148866i | −0.905795 | − | 0.423717i | \(-0.860725\pi\) |
0.819847 | + | 0.572583i | \(0.194058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.48524 | − | 4.30456i | −0.497047 | − | 0.860911i | ||||
\(26\) | −0.277269 | + | 0.480243i | −0.0543768 | + | 0.0941834i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.828555 | + | 0.474613i | 0.156582 | + | 0.0896934i | ||||
\(29\) | 4.27819 | 0.794440 | 0.397220 | − | 0.917723i | \(-0.369975\pi\) | ||||
0.397220 | + | 0.917723i | \(0.369975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49099 | + | 4.31453i | 0.447396 | + | 0.774912i | 0.998216 | − | 0.0597122i | \(-0.0190183\pi\) |
−0.550820 | + | 0.834624i | \(0.685685\pi\) | |||||||
\(32\) | −1.00901 | − | 1.74765i | −0.178369 | − | 0.308944i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.26668 | 0.731730 | ||||||||
\(35\) | 0.0284402 | + | 8.35419i | 0.00480728 | + | 1.41212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.74542 | + | 6.48725i | −0.615743 | + | 1.06650i | 0.374511 | + | 0.927222i | \(0.377811\pi\) |
−0.990254 | + | 0.139275i | \(0.955523\pi\) | |||||||
\(38\) | −5.55503 | − | 9.62160i | −0.901145 | − | 1.56083i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.97623 | − | 6.88703i | 0.628697 | − | 1.08894i | ||||
\(41\) | 3.33138 | 0.520274 | 0.260137 | − | 0.965572i | \(-0.416232\pi\) | ||||
0.260137 | + | 0.965572i | \(0.416232\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.86975 | −1.20013 | −0.600063 | − | 0.799953i | \(-0.704858\pi\) | ||||
−0.600063 | + | 0.799953i | \(0.704858\pi\) | |||||||
\(44\) | −1.03745 | + | 1.79691i | −0.156401 | + | 0.270895i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.633340 | + | 1.09698i | 0.0933809 | + | 0.161740i | ||||
\(47\) | −1.74075 | + | 3.01506i | −0.253914 | + | 0.439792i | −0.964600 | − | 0.263718i | \(-0.915051\pi\) |
0.710686 | + | 0.703509i | \(0.248385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.45864 | − | 6.08587i | 0.494092 | − | 0.869410i | ||||
\(50\) | −7.63725 | −1.08007 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0651258 | + | 0.112801i | 0.00903132 | + | 0.0156427i | ||||
\(53\) | −1.45772 | − | 2.52485i | −0.200233 | − | 0.346814i | 0.748370 | − | 0.663281i | \(-0.230837\pi\) |
−0.948604 | + | 0.316467i | \(0.897503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.1536 | −2.44783 | ||||||||
\(56\) | −5.75925 | + | 3.35130i | −0.769613 | + | 0.447836i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.28677 | − | 5.69285i | 0.431574 | − | 0.747508i | ||||
\(59\) | 1.19939 | + | 2.07740i | 0.156147 | + | 0.270455i | 0.933476 | − | 0.358639i | \(-0.116759\pi\) |
−0.777329 | + | 0.629094i | \(0.783426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60056 | + | 2.77226i | −0.204931 | + | 0.354951i | −0.950111 | − | 0.311913i | \(-0.899030\pi\) |
0.745180 | + | 0.666864i | \(0.232364\pi\) | |||||||
\(62\) | 7.65494 | 0.972178 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.08239 | 0.760298 | ||||||||
\(65\) | −0.569796 | + | 0.986916i | −0.0706745 | + | 0.122412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.949637 | − | 1.64482i | −0.116017 | − | 0.200947i | 0.802169 | − | 0.597097i | \(-0.203679\pi\) |
−0.918186 | + | 0.396150i | \(0.870346\pi\) | |||||||
\(68\) | 0.501086 | − | 0.867907i | 0.0607656 | − | 0.105249i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.1385 | + | 6.38036i | 1.33131 | + | 0.762599i | ||||
\(71\) | −1.60957 | −0.191021 | −0.0955104 | − | 0.995428i | \(-0.530448\pi\) | ||||
−0.0955104 | + | 0.995428i | \(0.530448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.70688 | + | 13.3487i | 0.902022 | + | 1.56235i | 0.824865 | + | 0.565330i | \(0.191251\pi\) |
0.0771572 | + | 0.997019i | \(0.475416\pi\) | |||||||
\(74\) | 5.75492 | + | 9.96781i | 0.668996 | + | 1.15873i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.60957 | −0.299338 | ||||||||
\(77\) | 13.1988 | + | 7.56054i | 1.50414 | + | 0.861603i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.73641 | + | 4.73960i | −0.307870 | + | 0.533247i | −0.977896 | − | 0.209091i | \(-0.932950\pi\) |
0.670026 | + | 0.742337i | \(0.266283\pi\) | |||||||
\(80\) | −7.24916 | − | 12.5559i | −0.810481 | − | 1.40379i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.55937 | − | 4.43296i | 0.282635 | − | 0.489538i | ||||
\(83\) | 13.0348 | 1.43076 | 0.715380 | − | 0.698735i | \(-0.246254\pi\) | ||||
0.715380 | + | 0.698735i | \(0.246254\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.76817 | 0.951041 | ||||||||
\(86\) | −6.04603 | + | 10.4720i | −0.651960 | + | 1.12923i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.23966 | − | 12.5395i | −0.771750 | − | 1.33671i | ||||
\(89\) | −7.13384 | + | 12.3562i | −0.756185 | + | 1.30975i | 0.188598 | + | 0.982054i | \(0.439606\pi\) |
−0.944783 | + | 0.327697i | \(0.893728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.825304 | − | 0.480243i | 0.0865154 | − | 0.0503432i | ||||
\(92\) | 0.297522 | 0.0310188 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.67470 | + | 4.63271i | 0.275874 | + | 0.477827i | ||||
\(95\) | −11.4158 | − | 19.7727i | −1.17123 | − | 2.02864i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0053 | 1.62509 | 0.812547 | − | 0.582896i | \(-0.198080\pi\) | ||||
0.812547 | + | 0.582896i | \(0.198080\pi\) | |||||||
\(98\) | −5.44113 | − | 9.27785i | −0.549637 | − | 0.937204i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.896931 | + | 1.55353i | −0.0896931 | + | 0.155353i | ||||
\(101\) | 1.50375 | + | 2.60456i | 0.149628 | + | 0.259164i | 0.931090 | − | 0.364789i | \(-0.118859\pi\) |
−0.781462 | + | 0.623953i | \(0.785526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.86031 | + | 8.41831i | −0.478901 | + | 0.829481i | −0.999707 | − | 0.0241941i | \(-0.992298\pi\) |
0.520806 | + | 0.853675i | \(0.325631\pi\) | |||||||
\(104\) | −0.908940 | −0.0891289 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.47964 | −0.435101 | ||||||||
\(107\) | 5.21214 | − | 9.02770i | 0.503877 | − | 0.872740i | −0.496113 | − | 0.868258i | \(-0.665240\pi\) |
0.999990 | − | 0.00448241i | \(-0.00142680\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.33713 | + | 4.04803i | 0.223857 | + | 0.387731i | 0.955976 | − | 0.293445i | \(-0.0948019\pi\) |
−0.732119 | + | 0.681177i | \(0.761469\pi\) | |||||||
\(110\) | −13.9467 | + | 24.1564i | −1.32977 | + | 2.30322i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.0413557 | + | 12.1480i | 0.00390775 | + | 1.14788i | ||||
\(113\) | −4.68664 | −0.440882 | −0.220441 | − | 0.975400i | \(-0.570750\pi\) | ||||
−0.220441 | + | 0.975400i | \(0.570750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.30153 | + | 2.25432i | 0.121369 | + | 0.210217i | ||||
\(116\) | −0.772008 | − | 1.33716i | −0.0716791 | − | 0.124152i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.68578 | 0.339304 | ||||||||
\(119\) | −6.37501 | − | 3.65173i | −0.584396 | − | 0.334754i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0264 | + | 19.0983i | −1.00240 | + | 1.73621i | ||||
\(122\) | 2.45930 | + | 4.25964i | 0.222655 | + | 0.385649i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.899009 | − | 1.55713i | 0.0807334 | − | 0.139834i | ||||
\(125\) | 0.0932326 | 0.00833898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.15945 | −0.812770 | −0.406385 | − | 0.913702i | \(-0.633211\pi\) | ||||
−0.406385 | + | 0.913702i | \(0.633211\pi\) | |||||||
\(128\) | 6.69088 | − | 11.5889i | 0.591396 | − | 1.02433i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.875505 | + | 1.51642i | 0.0767868 | + | 0.132999i | ||||
\(131\) | 4.60582 | − | 7.97752i | 0.402413 | − | 0.696999i | −0.591604 | − | 0.806229i | \(-0.701505\pi\) |
0.994017 | + | 0.109230i | \(0.0348384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0651258 | + | 19.1304i | 0.00564712 | + | 1.65882i | ||||
\(134\) | −2.91828 | −0.252101 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.49675 | + | 6.05655i | 0.299844 | + | 0.519345i | ||||
\(137\) | 3.41219 | + | 5.91009i | 0.291523 | + | 0.504933i | 0.974170 | − | 0.225815i | \(-0.0725046\pi\) |
−0.682647 | + | 0.730748i | \(0.739171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.68664 | −0.482334 | −0.241167 | − | 0.970484i | \(-0.577530\pi\) | ||||
−0.241167 | + | 0.970484i | \(0.577530\pi\) | |||||||
\(140\) | 2.60599 | − | 1.51642i | 0.220246 | − | 0.128161i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.23657 | + | 2.14180i | −0.103771 | + | 0.179736i | ||||
\(143\) | 1.03745 | + | 1.79691i | 0.0867557 | + | 0.150265i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.75442 | − | 11.6990i | 0.560924 | − | 0.971549i | ||||
\(146\) | 23.6836 | 1.96007 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.70347 | 0.222224 | ||||||||
\(149\) | 10.7943 | − | 18.6962i | 0.884301 | − | 1.53165i | 0.0377873 | − | 0.999286i | \(-0.487969\pi\) |
0.846513 | − | 0.532368i | \(-0.178698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.77776 | + | 4.81123i | 0.226051 | + | 0.391532i | 0.956634 | − | 0.291292i | \(-0.0940850\pi\) |
−0.730583 | + | 0.682824i | \(0.760752\pi\) | |||||||
\(152\) | 9.10523 | − | 15.7707i | 0.738532 | − | 1.27917i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.2007 | − | 11.7548i | 1.62782 | − | 0.947225i | ||||
\(155\) | 15.7311 | 1.26356 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.03560 | − | 5.25781i | −0.242267 | − | 0.419619i | 0.719093 | − | 0.694914i | \(-0.244558\pi\) |
−0.961360 | + | 0.275295i | \(0.911224\pi\) | |||||||
\(158\) | 4.20456 | + | 7.28250i | 0.334496 | + | 0.579365i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.37209 | −0.503758 | ||||||||
\(161\) | −0.00742511 | − | 2.18109i | −0.000585181 | − | 0.171894i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.92630 | − | 3.33644i | 0.150879 | − | 0.261330i | −0.780672 | − | 0.624941i | \(-0.785123\pi\) |
0.931551 | + | 0.363611i | \(0.118456\pi\) | |||||||
\(164\) | −0.601153 | − | 1.04123i | −0.0469422 | − | 0.0813063i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.0142 | − | 17.3451i | 0.777251 | − | 1.34624i | ||||
\(167\) | 3.53837 | 0.273807 | 0.136904 | − | 0.990584i | \(-0.456285\pi\) | ||||
0.136904 | + | 0.990584i | \(0.456285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8697 | −0.989981 | ||||||||
\(170\) | 6.73625 | − | 11.6675i | 0.516647 | − | 0.894858i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.42011 | + | 2.45970i | 0.108282 | + | 0.187551i | ||||
\(173\) | −4.92679 | + | 8.53345i | −0.374577 | + | 0.648786i | −0.990264 | − | 0.139205i | \(-0.955545\pi\) |
0.615687 | + | 0.787991i | \(0.288879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4111 | + | 6.53651i | 0.862598 | + | 0.494114i | ||||
\(176\) | −26.3976 | −1.98979 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.9613 | + | 18.9855i | 0.821585 | + | 1.42303i | ||||
\(179\) | −9.94855 | − | 17.2314i | −0.743590 | − | 1.28794i | −0.950851 | − | 0.309649i | \(-0.899788\pi\) |
0.207261 | − | 0.978286i | \(-0.433545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0930 | 0.898869 | 0.449434 | − | 0.893313i | \(-0.351626\pi\) | ||||
0.449434 | + | 0.893313i | \(0.351626\pi\) | |||||||
\(182\) | −0.00499466 | − | 1.46716i | −0.000370229 | − | 0.108753i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.03811 | + | 1.79805i | −0.0765301 | + | 0.132554i | ||||
\(185\) | 11.8265 | + | 20.4842i | 0.869505 | + | 1.50603i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.98225 | − | 13.8257i | 0.583720 | − | 1.01103i | ||||
\(188\) | 1.25648 | 0.0916385 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.0812 | −2.54506 | ||||||||
\(191\) | 4.85982 | − | 8.41745i | 0.351644 | − | 0.609065i | −0.634894 | − | 0.772600i | \(-0.718956\pi\) |
0.986538 | + | 0.163534i | \(0.0522894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.15093 | + | 1.99346i | 0.0828454 | + | 0.143492i | 0.904471 | − | 0.426535i | \(-0.140266\pi\) |
−0.821626 | + | 0.570027i | \(0.806933\pi\) | |||||||
\(194\) | 12.2963 | − | 21.2978i | 0.882821 | − | 1.52909i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.52627 | + | 0.0172006i | −0.180448 | + | 0.00122861i | ||||
\(197\) | −5.06470 | −0.360845 | −0.180422 | − | 0.983589i | \(-0.557746\pi\) | ||||
−0.180422 | + | 0.983589i | \(0.557746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.97666 | + | 8.61982i | 0.352786 | + | 0.611043i | 0.986736 | − | 0.162330i | \(-0.0519011\pi\) |
−0.633951 | + | 0.773374i | \(0.718568\pi\) | |||||||
\(200\) | −6.25909 | − | 10.8411i | −0.442585 | − | 0.766579i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.62108 | 0.325138 | ||||||||
\(203\) | −9.78325 | + | 5.69285i | −0.686649 | + | 0.399560i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.25959 | − | 9.10987i | 0.367346 | − | 0.636261i | ||||
\(206\) | 7.46798 | + | 12.9349i | 0.520319 | + | 0.901219i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.828555 | + | 1.43510i | −0.0574500 | + | 0.0995062i | ||||
\(209\) | −41.5702 | −2.87547 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3007 | −1.60408 | −0.802042 | − | 0.597267i | \(-0.796253\pi\) | ||||
−0.802042 | + | 0.597267i | \(0.796253\pi\) | |||||||
\(212\) | −0.526097 | + | 0.911226i | −0.0361325 | + | 0.0625833i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00858 | − | 13.8713i | −0.547455 | − | 0.948220i | ||||
\(215\) | −12.4248 | + | 21.5204i | −0.847363 | + | 1.46768i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4375 | − | 6.55165i | −0.776430 | − | 0.444755i | ||||
\(218\) | 7.18212 | 0.486435 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.27585 | + | 5.67394i | 0.220858 | + | 0.382537i | ||||
\(221\) | −0.501086 | − | 0.867907i | −0.0337067 | − | 0.0583817i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8754 | −0.795235 | −0.397618 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397618 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(224\) | 4.63291 | + | 2.65382i | 0.309549 | + | 0.177316i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.60056 | + | 6.23636i | −0.239506 | + | 0.414836i | ||||
\(227\) | 2.98040 | + | 5.16221i | 0.197816 | + | 0.342628i | 0.947820 | − | 0.318806i | \(-0.103282\pi\) |
−0.750004 | + | 0.661434i | \(0.769948\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.8603 | − | 20.5427i | 0.783752 | − | 1.35750i | −0.145990 | − | 0.989286i | \(-0.546637\pi\) |
0.929742 | − | 0.368212i | \(-0.120030\pi\) | |||||||
\(230\) | 3.99968 | 0.263731 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.7747 | 0.707392 | ||||||||
\(233\) | −6.92961 | + | 12.0024i | −0.453974 | + | 0.786306i | −0.998629 | − | 0.0523544i | \(-0.983327\pi\) |
0.544654 | + | 0.838661i | \(0.316661\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.49659 | + | 9.52037i | 0.358558 | + | 0.621040i | ||||
\(236\) | 0.432864 | − | 0.749743i | 0.0281771 | − | 0.0488041i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.75692 | + | 5.67754i | −0.632447 | + | 0.368020i | ||||
\(239\) | −22.3426 | −1.44522 | −0.722610 | − | 0.691256i | \(-0.757058\pi\) | ||||
−0.722610 | + | 0.691256i | \(0.757058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.86031 | − | 8.41831i | −0.313080 | − | 0.542271i | 0.665947 | − | 0.745999i | \(-0.268028\pi\) |
−0.979028 | + | 0.203728i | \(0.934694\pi\) | |||||||
\(242\) | 16.9424 | + | 29.3450i | 1.08910 | + | 1.88637i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.15530 | 0.0739604 | ||||||||
\(245\) | −11.1817 | − | 19.0663i | −0.714372 | − | 1.21810i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.30478 | + | 2.25995i | −0.0830215 | + | 0.143797i | ||||
\(248\) | 6.27359 | + | 10.8662i | 0.398373 | + | 0.690003i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.0716270 | − | 0.124062i | 0.00453009 | − | 0.00784635i | ||||
\(251\) | 6.51950 | 0.411507 | 0.205754 | − | 0.978604i | \(-0.434035\pi\) | ||||
0.205754 | + | 0.978604i | \(0.434035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.73950 | 0.297970 | ||||||||
\(254\) | −7.03686 | + | 12.1882i | −0.441532 | + | 0.764755i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.19830 | − | 7.27167i | −0.262394 | − | 0.454480i | ||||
\(257\) | 2.76501 | − | 4.78914i | 0.172477 | − | 0.298738i | −0.766808 | − | 0.641876i | \(-0.778156\pi\) |
0.939285 | + | 0.343138i | \(0.111490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0674692 | − | 19.8188i | −0.00419233 | − | 1.23148i | ||||
\(260\) | 0.411283 | 0.0255067 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.07696 | − | 12.2576i | −0.437216 | − | 0.757280i | ||||
\(263\) | 4.34749 | + | 7.53008i | 0.268078 | + | 0.464325i | 0.968365 | − | 0.249536i | \(-0.0802782\pi\) |
−0.700288 | + | 0.713861i | \(0.746945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.20581 | −0.565509 | ||||||||
\(266\) | 25.5062 | + | 14.6105i | 1.56389 | + | 0.895827i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.342728 | + | 0.593622i | −0.0209354 | + | 0.0362612i | ||||
\(269\) | −1.88951 | − | 3.27272i | −0.115205 | − | 0.199541i | 0.802657 | − | 0.596442i | \(-0.203419\pi\) |
−0.917862 | + | 0.396900i | \(0.870086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.30995 | + | 5.73300i | −0.201065 | + | 0.348255i | −0.948872 | − | 0.315661i | \(-0.897774\pi\) |
0.747807 | + | 0.663916i | \(0.231107\pi\) | |||||||
\(272\) | 12.7500 | 0.773083 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.4858 | 0.633472 | ||||||||
\(275\) | −14.2880 | + | 24.7476i | −0.861601 | + | 1.49234i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6329 | + | 21.8808i | 0.759038 | + | 1.31469i | 0.943342 | + | 0.331823i | \(0.107664\pi\) |
−0.184303 | + | 0.982869i | \(0.559003\pi\) | |||||||
\(278\) | −4.36882 | + | 7.56703i | −0.262025 | + | 0.453840i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0716270 | + | 21.0401i | 0.00428053 | + | 1.25739i | ||||
\(281\) | −7.42442 | −0.442904 | −0.221452 | − | 0.975171i | \(-0.571080\pi\) | ||||
−0.221452 | + | 0.975171i | \(0.571080\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.71013 | − | 13.3543i | −0.458320 | − | 0.793833i | 0.540553 | − | 0.841310i | \(-0.318215\pi\) |
−0.998872 | + | 0.0474771i | \(0.984882\pi\) | |||||||
\(284\) | 0.290450 | + | 0.503074i | 0.0172350 | + | 0.0298520i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.18812 | 0.188518 | ||||||||
\(287\) | −7.61810 | + | 4.43296i | −0.449682 | + | 0.261669i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.64458 | − | 8.04465i | 0.273211 | − | 0.473215i | ||||
\(290\) | −10.3783 | − | 17.9758i | −0.609436 | − | 1.05557i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.78144 | − | 4.81760i | 0.162772 | − | 0.281929i | ||||
\(293\) | −30.5797 | −1.78649 | −0.893243 | − | 0.449574i | \(-0.851576\pi\) | ||||
−0.893243 | + | 0.449574i | \(0.851576\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.57440 | 0.440999 | ||||||||
\(296\) | −9.43286 | + | 16.3382i | −0.548274 | + | 0.949639i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.5856 | − | 28.7272i | −0.960780 | − | 1.66412i | ||||
\(299\) | 0.148761 | − | 0.257662i | 0.00860307 | − | 0.0149010i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.9963 | − | 10.4720i | 1.03729 | − | 0.603597i | ||||
\(302\) | 8.53620 | 0.491203 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.6000 | − | 28.7520i | −0.952074 | − | 1.64904i | ||||
\(305\) | 5.05395 | + | 8.75369i | 0.289388 | + | 0.501235i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.7794 | −1.64252 | −0.821262 | − | 0.570551i | \(-0.806730\pi\) | ||||
−0.821262 | + | 0.570551i | \(0.806730\pi\) | |||||||
\(308\) | −0.0186884 | − | 5.48962i | −0.00106487 | − | 0.312800i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0856 | − | 20.9329i | 0.686418 | − | 1.18891i | ||||
\(311\) | −1.28628 | − | 2.22789i | −0.0729380 | − | 0.126332i | 0.827250 | − | 0.561834i | \(-0.189904\pi\) |
−0.900188 | + | 0.435502i | \(0.856571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.25724 | − | 16.0340i | 0.523250 | − | 0.906296i | −0.476383 | − | 0.879238i | \(-0.658053\pi\) |
0.999634 | − | 0.0270587i | \(-0.00861409\pi\) | |||||||
\(314\) | −9.32854 | −0.526440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.97516 | 0.111111 | ||||||||
\(317\) | 7.75909 | − | 13.4391i | 0.435794 | − | 0.754817i | −0.561566 | − | 0.827432i | \(-0.689801\pi\) |
0.997360 | + | 0.0726145i | \(0.0231343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2980 | − | 21.3008i | −0.688556 | − | 1.19261i | ||||
\(320\) | 9.60289 | − | 16.6327i | 0.536818 | − | 0.929796i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.90802 | − | 1.66577i | −0.162057 | − | 0.0928297i | ||||
\(323\) | 20.0784 | 1.11719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.896931 | + | 1.55353i | 0.0497528 | + | 0.0861744i | ||||
\(326\) | −2.95980 | − | 5.12652i | −0.163928 | − | 0.283932i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.39011 | 0.463266 | ||||||||
\(329\) | −0.0313574 | − | 9.21110i | −0.00172879 | − | 0.507825i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.7952 | + | 27.3581i | −0.868182 | + | 1.50374i | −0.00432948 | + | 0.999991i | \(0.501378\pi\) |
−0.863853 | + | 0.503745i | \(0.831955\pi\) | |||||||
\(332\) | −2.35216 | − | 4.07407i | −0.129092 | − | 0.223593i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.71839 | − | 4.70840i | 0.148744 | − | 0.257632i | ||||
\(335\) | −5.99716 | −0.327660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4081 | −0.621440 | −0.310720 | − | 0.950502i | \(-0.600570\pi\) | ||||
−0.310720 | + | 0.950502i | \(0.600570\pi\) | |||||||
\(338\) | −9.88733 | + | 17.1254i | −0.537800 | + | 0.931497i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.58223 | − | 2.74051i | −0.0858086 | − | 0.148625i | ||||
\(341\) | 14.3211 | − | 24.8049i | 0.775532 | − | 1.34326i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.189142 | + | 18.5193i | 0.0102127 | + | 0.999948i | ||||
\(344\) | −19.8200 | −1.06862 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.57013 | + | 13.1118i | 0.406973 | + | 0.704897i | ||||
\(347\) | −2.04070 | − | 3.53459i | −0.109550 | − | 0.189747i | 0.806038 | − | 0.591864i | \(-0.201608\pi\) |
−0.915588 | + | 0.402117i | \(0.868274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.2779 | −1.29956 | −0.649782 | − | 0.760120i | \(-0.725140\pi\) | ||||
−0.649782 | + | 0.760120i | \(0.725140\pi\) | |||||||
\(350\) | 17.4646 | − | 10.1626i | 0.933524 | − | 0.543216i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.80094 | + | 10.0475i | −0.309191 | + | 0.535535i | ||||
\(353\) | −17.0395 | − | 29.5133i | −0.906922 | − | 1.57083i | −0.818316 | − | 0.574768i | \(-0.805092\pi\) |
−0.0886057 | − | 0.996067i | \(-0.528241\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.54119 | + | 4.40148i | −0.134873 | + | 0.233606i | ||||
\(356\) | 5.14926 | 0.272910 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.5724 | −1.61580 | ||||||||
\(359\) | 2.74465 | − | 4.75388i | 0.144857 | − | 0.250900i | −0.784462 | − | 0.620176i | \(-0.787061\pi\) |
0.929320 | + | 0.369276i | \(0.120394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.6412 | − | 28.8233i | −0.875851 | − | 1.51702i | ||||
\(362\) | 9.29062 | − | 16.0918i | 0.488304 | − | 0.845768i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.299029 | − | 0.171290i | −0.0156734 | − | 0.00897802i | ||||
\(365\) | 48.6706 | 2.54754 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.81955 | + | 11.8118i | 0.355978 | + | 0.616571i | 0.987285 | − | 0.158962i | \(-0.0508146\pi\) |
−0.631307 | + | 0.775533i | \(0.717481\pi\) | |||||||
\(368\) | 1.89259 | + | 3.27807i | 0.0986583 | + | 0.170881i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36.3435 | 1.88941 | ||||||||
\(371\) | 6.69321 | + | 3.83400i | 0.347494 | + | 0.199051i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.46189 | + | 7.72823i | −0.231028 | + | 0.400153i | −0.958111 | − | 0.286397i | \(-0.907542\pi\) |
0.727083 | + | 0.686550i | \(0.240876\pi\) | |||||||
\(374\) | −12.2649 | − | 21.2435i | −0.634204 | − | 1.09847i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.38408 | + | 7.59346i | −0.226092 | + | 0.391603i | ||||
\(377\) | −1.54402 | −0.0795209 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.7035 | 1.52576 | 0.762882 | − | 0.646537i | \(-0.223784\pi\) | ||||
0.762882 | + | 0.646537i | \(0.223784\pi\) | |||||||
\(380\) | −4.12000 | + | 7.13604i | −0.211351 | + | 0.366071i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.46722 | − | 12.9336i | −0.382056 | − | 0.661741i | ||||
\(383\) | −8.85505 | + | 15.3374i | −0.452472 | + | 0.783705i | −0.998539 | − | 0.0540370i | \(-0.982791\pi\) |
0.546067 | + | 0.837742i | \(0.316124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 41.5131 | − | 24.1564i | 2.11570 | − | 1.23112i | ||||
\(386\) | 3.53685 | 0.180021 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.88819 | − | 5.00249i | −0.146626 | − | 0.253963i | ||||
\(389\) | 10.6628 | + | 18.4685i | 0.540624 | + | 0.936388i | 0.998868 | + | 0.0475619i | \(0.0151451\pi\) |
−0.458244 | + | 0.888826i | \(0.651522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.28917 | −0.115768 | ||||||||
\(392\) | 8.71063 | − | 15.3273i | 0.439953 | − | 0.774146i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.89101 | + | 6.73943i | −0.196026 | + | 0.339528i | ||||
\(395\) | 8.64050 | + | 14.9658i | 0.434751 | + | 0.753010i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.11783 | − | 1.93614i | 0.0561024 | − | 0.0971722i | −0.836610 | − | 0.547799i | \(-0.815466\pi\) |
0.892713 | + | 0.450626i | \(0.148799\pi\) | |||||||
\(398\) | 15.2935 | 0.766594 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.8222 | −1.14111 | ||||||||
\(401\) | 4.36851 | − | 7.56648i | 0.218153 | − | 0.377852i | −0.736090 | − | 0.676883i | \(-0.763330\pi\) |
0.954243 | + | 0.299031i | \(0.0966635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.899009 | − | 1.55713i | −0.0447828 | − | 0.0775661i | ||||
\(404\) | 0.542708 | − | 0.939997i | 0.0270007 | − | 0.0467666i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0592072 | + | 17.3919i | 0.00293841 | + | 0.863143i | ||||
\(407\) | 43.0660 | 2.13470 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3460 | + | 24.8480i | 0.709363 | + | 1.22865i | 0.965094 | + | 0.261905i | \(0.0843506\pi\) |
−0.255731 | + | 0.966748i | \(0.582316\pi\) | |||||||
\(410\) | −8.08148 | − | 13.9975i | −0.399116 | − | 0.691289i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.50821 | 0.172837 | ||||||||
\(413\) | −5.50706 | − | 3.15456i | −0.270985 | − | 0.155226i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.5795 | − | 35.6447i | 1.01021 | − | 1.74973i | ||||
\(416\) | 0.364154 | + | 0.630734i | 0.0178541 | + | 0.0309243i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −31.9368 | + | 55.3161i | −1.56208 | + | 2.70560i | ||||
\(419\) | −8.64442 | −0.422307 | −0.211154 | − | 0.977453i | \(-0.567722\pi\) | ||||
−0.211154 | + | 0.977453i | \(0.567722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4669 | 0.900024 | 0.450012 | − | 0.893022i | \(-0.351420\pi\) | ||||
0.450012 | + | 0.893022i | \(0.351420\pi\) | |||||||
\(422\) | −17.9010 | + | 31.0055i | −0.871408 | + | 1.50932i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.67128 | − | 6.35885i | −0.178293 | − | 0.308813i | ||||
\(425\) | 6.90111 | − | 11.9531i | 0.334753 | − | 0.579809i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0288322 | − | 8.46933i | −0.00139529 | − | 0.409860i | ||||
\(428\) | −3.76216 | −0.181851 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.0910 | + | 33.0665i | 0.920648 | + | 1.59461i | ||||
\(431\) | −2.90368 | − | 5.02932i | −0.139865 | − | 0.242254i | 0.787580 | − | 0.616212i | \(-0.211334\pi\) |
−0.927445 | + | 0.373958i | \(0.878000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.63877 | 0.174868 | 0.0874341 | − | 0.996170i | \(-0.472133\pi\) | ||||
0.0874341 | + | 0.996170i | \(0.472133\pi\) | |||||||
\(434\) | −17.5051 | + | 10.1862i | −0.840271 | + | 0.488952i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.843480 | − | 1.46095i | 0.0403954 | − | 0.0699669i | ||||
\(437\) | 2.98040 | + | 5.16221i | 0.142572 | + | 0.246942i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.33095 | − | 16.1617i | 0.445342 | − | 0.771355i | −0.552734 | − | 0.833358i | \(-0.686415\pi\) |
0.998076 | + | 0.0620029i | \(0.0197488\pi\) | |||||||
\(440\) | −45.7200 | −2.17961 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.53986 | −0.0732437 | ||||||||
\(443\) | −13.0455 | + | 22.5955i | −0.619812 | + | 1.07355i | 0.369708 | + | 0.929148i | \(0.379458\pi\) |
−0.989520 | + | 0.144398i | \(0.953876\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.5258 | + | 39.0159i | 1.06783 | + | 1.84953i | ||||
\(446\) | −9.12341 | + | 15.8022i | −0.432006 | + | 0.748256i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.9090 | + | 8.09364i | −0.657140 | + | 0.382388i | ||||
\(449\) | 5.63824 | 0.266085 | 0.133042 | − | 0.991110i | \(-0.457525\pi\) | ||||
0.133042 | + | 0.991110i | \(0.457525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.57631 | − | 16.5867i | −0.450931 | − | 0.781035i | ||||
\(452\) | 0.845712 | + | 1.46482i | 0.0397790 | + | 0.0688992i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.15892 | 0.429849 | ||||||||
\(455\) | −0.0102642 | − | 3.01506i | −0.000481193 | − | 0.141348i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.99616 | − | 17.3139i | 0.467601 | − | 0.809908i | −0.531714 | − | 0.846924i | \(-0.678452\pi\) |
0.999315 | + | 0.0370159i | \(0.0117852\pi\) | |||||||
\(458\) | −18.2236 | − | 31.5643i | −0.851535 | − | 1.47490i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.469729 | − | 0.813594i | 0.0219012 | − | 0.0379340i | ||||
\(461\) | −37.4495 | −1.74420 | −0.872098 | − | 0.489332i | \(-0.837241\pi\) | ||||
−0.872098 | + | 0.489332i | \(0.837241\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.45513 | 0.114099 | 0.0570497 | − | 0.998371i | \(-0.481831\pi\) | ||||
0.0570497 | + | 0.998371i | \(0.481831\pi\) | |||||||
\(464\) | 9.82178 | − | 17.0118i | 0.455965 | − | 0.789754i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.6475 | + | 18.4420i | 0.493236 | + | 0.854311i | ||||
\(467\) | 16.7054 | − | 28.9345i | 0.773032 | − | 1.33893i | −0.162862 | − | 0.986649i | \(-0.552072\pi\) |
0.935894 | − | 0.352282i | \(-0.114594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.36031 | + | 2.49768i | 0.201341 | + | 0.115332i | ||||
\(470\) | 16.8913 | 0.779136 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.02067 | + | 5.23196i | 0.139038 | + | 0.240821i | ||||
\(473\) | 22.6222 | + | 39.1828i | 1.04017 | + | 1.80163i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.9398 | −1.64903 | ||||||||
\(476\) | 0.00902647 | + | 2.65148i | 0.000413727 | + | 0.121531i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.1649 | + | 29.7305i | −0.785106 | + | 1.35984i | ||||
\(479\) | 17.3468 | + | 30.0455i | 0.792595 | + | 1.37281i | 0.924355 | + | 0.381533i | \(0.124604\pi\) |
−0.131760 | + | 0.991282i | \(0.542063\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.35173 | − | 2.34127i | 0.0616338 | − | 0.106753i | ||||
\(482\) | −14.9360 | −0.680315 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.95896 | 0.361771 | ||||||||
\(485\) | 25.2692 | − | 43.7676i | 1.14742 | − | 1.98739i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.479909 | − | 0.831226i | −0.0217467 | − | 0.0376665i | 0.854947 | − | 0.518715i | \(-0.173589\pi\) |
−0.876694 | + | 0.481049i | \(0.840256\pi\) | |||||||
\(488\) | −4.03103 | + | 6.98195i | −0.182476 | + | 0.316058i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −33.9614 | + | 0.231233i | −1.53422 | + | 0.0104460i | ||||
\(491\) | −15.7738 | −0.711862 | −0.355931 | − | 0.934512i | \(-0.615836\pi\) | ||||
−0.355931 | + | 0.934512i | \(0.615836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.93993 | + | 10.2883i | 0.267521 | + | 0.463360i | ||||
\(494\) | 2.00483 | + | 3.47247i | 0.0902017 | + | 0.156234i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.8751 | 1.02712 | ||||||||
\(497\) | 3.68072 | − | 2.14180i | 0.165103 | − | 0.0960730i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.56437 | − | 16.5660i | 0.428160 | − | 0.741595i | −0.568550 | − | 0.822649i | \(-0.692495\pi\) |
0.996710 | + | 0.0810539i | \(0.0258286\pi\) | |||||||
\(500\) | −0.0168240 | − | 0.0291400i | −0.000752392 | − | 0.00130318i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.00868 | − | 8.67529i | 0.223548 | − | 0.387197i | ||||
\(503\) | 33.3898 | 1.48878 | 0.744388 | − | 0.667747i | \(-0.232741\pi\) | ||||
0.744388 | + | 0.667747i | \(0.232741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.49648 | 0.422588 | ||||||||
\(506\) | 3.64117 | − | 6.30670i | 0.161870 | − | 0.280367i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.65284 | + | 2.86280i | 0.0733330 | + | 0.127016i | ||||
\(509\) | 16.7588 | − | 29.0271i | 0.742822 | − | 1.28660i | −0.208384 | − | 0.978047i | \(-0.566820\pi\) |
0.951206 | − | 0.308558i | \(-0.0998463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.3866 | − | 20.2701i | −1.56541 | − | 0.896698i | ||||
\(512\) | 13.8619 | 0.612617 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.24850 | − | 7.35862i | −0.187393 | − | 0.324575i | ||||
\(515\) | 15.3470 | + | 26.5817i | 0.676268 | + | 1.17133i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.0157 | 0.880287 | ||||||||
\(518\) | −26.4240 | − | 15.1362i | −1.16101 | − | 0.665047i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.43504 | + | 2.48556i | −0.0629305 | + | 0.108999i | ||||
\(521\) | −13.3622 | − | 23.1439i | −0.585407 | − | 1.01395i | −0.994825 | − | 0.101607i | \(-0.967601\pi\) |
0.409418 | − | 0.912347i | \(-0.365732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.53219 | + | 14.7782i | −0.373086 | + | 0.646205i | −0.990039 | − | 0.140796i | \(-0.955034\pi\) |
0.616952 | + | 0.787001i | \(0.288367\pi\) | |||||||
\(524\) | −3.32452 | −0.145232 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.3600 | 0.582526 | ||||||||
\(527\) | −6.91709 | + | 11.9808i | −0.301313 | + | 0.521890i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1602 | + | 19.3300i | 0.485226 | + | 0.840436i | ||||
\(530\) | −7.07247 | + | 12.2499i | −0.307209 | + | 0.532101i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.96749 | − | 3.47247i | 0.258723 | − | 0.150551i | ||||
\(533\) | −1.20231 | −0.0520777 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.4579 | − | 28.5059i | −0.711537 | − | 1.23242i | ||||
\(536\) | −2.39167 | − | 4.14250i | −0.103304 | − | 0.178929i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.80654 | −0.250338 | ||||||||
\(539\) | −40.2432 | + | 0.274004i | −1.73340 | + | 0.0118022i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.17128 | + | 10.6890i | −0.265324 | + | 0.459555i | −0.967648 | − | 0.252302i | \(-0.918812\pi\) |
0.702324 | + | 0.711857i | \(0.252146\pi\) | |||||||
\(542\) | 5.08582 | + | 8.80889i | 0.218455 | + | 0.378374i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.80185 | − | 4.85295i | 0.120128 | − | 0.208068i | ||||
\(545\) | 14.7595 | 0.632227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.4424 | 1.00233 | 0.501163 | − | 0.865353i | \(-0.332906\pi\) | ||||
0.501163 | + | 0.865353i | \(0.332906\pi\) | |||||||
\(548\) | 1.23147 | − | 2.13297i | 0.0526059 | − | 0.0911161i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.9539 | + | 38.0252i | 0.936117 | + | 1.62140i | ||||
\(551\) | 15.4671 | − | 26.7897i | 0.658919 | − | 1.14128i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0492931 | − | 14.4796i | −0.00209616 | − | 0.615736i | ||||
\(554\) | 38.8215 | 1.64937 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.02616 | + | 1.77737i | 0.0435191 | + | 0.0753772i | ||||
\(557\) | −12.2557 | − | 21.2275i | −0.519292 | − | 0.899440i | −0.999749 | − | 0.0224216i | \(-0.992862\pi\) |
0.480457 | − | 0.877018i | \(-0.340471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.84022 | 0.120129 | ||||||||
\(560\) | 33.2849 | + | 19.0663i | 1.40655 | + | 0.805697i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.70390 | + | 9.87944i | −0.240604 | + | 0.416739i | ||||
\(563\) | −6.68571 | − | 11.5800i | −0.281769 | − | 0.488039i | 0.690051 | − | 0.723760i | \(-0.257588\pi\) |
−0.971821 | + | 0.235722i | \(0.924255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.39927 | + | 12.8159i | −0.311290 | + | 0.539170i | ||||
\(566\) | −23.6936 | −0.995916 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.05372 | −0.170090 | ||||||||
\(569\) | −7.12440 | + | 12.3398i | −0.298670 | + | 0.517312i | −0.975832 | − | 0.218522i | \(-0.929876\pi\) |
0.677162 | + | 0.735834i | \(0.263210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6618 | + | 25.3951i | 0.613579 | + | 1.06275i | 0.990632 | + | 0.136559i | \(0.0436042\pi\) |
−0.377053 | + | 0.926192i | \(0.623062\pi\) | |||||||
\(572\) | 0.374419 | − | 0.648512i | 0.0156552 | − | 0.0271157i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0461040 | + | 13.5428i | 0.00192434 | + | 0.565267i | ||||
\(575\) | 4.09756 | 0.170880 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.05004 | + | 15.6751i | 0.376758 | + | 0.652564i | 0.990588 | − | 0.136874i | \(-0.0437055\pi\) |
−0.613830 | + | 0.789438i | \(0.710372\pi\) | |||||||
\(578\) | −7.13650 | − | 12.3608i | −0.296839 | − | 0.514141i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.87539 | −0.202440 | ||||||||
\(581\) | −29.8077 | + | 17.3451i | −1.23663 | + | 0.719594i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.38067 | + | 14.5157i | −0.347092 | + | 0.601181i | ||||
\(584\) | 19.4099 | + | 33.6189i | 0.803186 | + | 1.39116i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.4932 | + | 40.6915i | −0.970496 | + | 1.68095i | ||||
\(587\) | −6.52804 | −0.269441 | −0.134721 | − | 0.990884i | \(-0.543014\pi\) | ||||
−0.134721 | + | 0.990884i | \(0.543014\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0230 | 1.48430 | ||||||||
\(590\) | 5.81912 | − | 10.0790i | 0.239569 | − | 0.414946i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.1973 | + | 29.7866i | 0.706804 | + | 1.22422i | ||||
\(593\) | −12.7202 | + | 22.0321i | −0.522357 | + | 0.904749i | 0.477305 | + | 0.878738i | \(0.341614\pi\) |
−0.999662 | + | 0.0260111i | \(0.991719\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0508 | + | 11.6675i | −0.822002 | + | 0.478322i | ||||
\(596\) | −7.79138 | −0.319147 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.228575 | − | 0.395903i | −0.00934712 | − | 0.0161897i | ||||
\(599\) | 3.08966 | + | 5.35144i | 0.126240 | + | 0.218654i | 0.922217 | − | 0.386673i | \(-0.126376\pi\) |
−0.795977 | + | 0.605327i | \(0.793042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9344 | −0.527607 | −0.263804 | − | 0.964576i | \(-0.584977\pi\) | ||||
−0.263804 | + | 0.964576i | \(0.584977\pi\) | |||||||
\(602\) | −0.108912 | − | 31.9924i | −0.00443892 | − | 1.30391i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.00251 | − | 1.73639i | 0.0407914 | − | 0.0706527i | ||||
\(605\) | 34.8171 | + | 60.3050i | 1.41552 | + | 2.45175i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5378 | − | 19.9840i | 0.468304 | − | 0.811126i | −0.531040 | − | 0.847347i | \(-0.678199\pi\) |
0.999344 | + | 0.0362205i | \(0.0115319\pi\) | |||||||
\(608\) | −14.5916 | −0.591766 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.5310 | 0.628832 | ||||||||
\(611\) | 0.628242 | − | 1.08815i | 0.0254159 | − | 0.0440217i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.81363 | + | 15.2657i | 0.355979 | + | 0.616574i | 0.987285 | − | 0.158960i | \(-0.0508141\pi\) |
−0.631306 | + | 0.775534i | \(0.717481\pi\) | |||||||
\(614\) | −22.1101 | + | 38.2958i | −0.892290 | + | 1.54549i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 33.2413 | + | 19.0413i | 1.33933 | + | 0.767195i | ||||
\(617\) | −21.6441 | −0.871358 | −0.435679 | − | 0.900102i | \(-0.643492\pi\) | ||||
−0.435679 | + | 0.900102i | \(0.643492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.78970 | + | 8.29601i | 0.192514 | + | 0.333445i | 0.946083 | − | 0.323925i | \(-0.105002\pi\) |
−0.753568 | + | 0.657370i | \(0.771669\pi\) | |||||||
\(620\) | −2.83872 | − | 4.91680i | −0.114006 | − | 0.197463i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.95278 | −0.158492 | ||||||||
\(623\) | −0.128508 | − | 37.7485i | −0.00514854 | − | 1.51236i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5734 | − | 21.7777i | 0.502935 | − | 0.871109i | ||||
\(626\) | −14.2240 | − | 24.6366i | −0.568504 | − | 0.984678i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.09556 | + | 1.89756i | −0.0437176 | + | 0.0757211i | ||||
\(629\) | −20.8008 | −0.829384 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1742 | −1.24103 | −0.620514 | − | 0.784196i | \(-0.713076\pi\) | ||||
−0.620514 | + | 0.784196i | \(0.713076\pi\) | |||||||
\(632\) | −6.89167 | + | 11.9367i | −0.274136 | + | 0.474817i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.9220 | − | 20.6496i | −0.473484 | − | 0.820099i | ||||
\(635\) | −14.4610 | + | 25.0471i | −0.573866 | + | 0.993965i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.24824 | + | 2.19641i | −0.0494570 | + | 0.0870250i | ||||
\(638\) | −37.7924 | −1.49621 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.1272 | − | 36.5933i | −0.835124 | − | 1.44648i | ||||
\(641\) | −4.12607 | − | 7.14656i | −0.162970 | − | 0.282272i | 0.772963 | − | 0.634452i | \(-0.218774\pi\) |
−0.935933 | + | 0.352179i | \(0.885441\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.4318 | 0.963495 | 0.481748 | − | 0.876310i | \(-0.340002\pi\) | ||||
0.481748 | + | 0.876310i | \(0.340002\pi\) | |||||||
\(644\) | −0.680365 | + | 0.395903i | −0.0268101 | + | 0.0156008i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.4254 | − | 26.7176i | 0.606906 | − | 1.05119i | ||||
\(647\) | 19.3432 | + | 33.5034i | 0.760461 | + | 1.31716i | 0.942613 | + | 0.333886i | \(0.108360\pi\) |
−0.182153 | + | 0.983270i | \(0.558307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.89548 | − | 11.9433i | 0.270671 | − | 0.468817i | ||||
\(650\) | 2.75631 | 0.108111 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.39041 | −0.0544528 | ||||||||
\(653\) | 3.82715 | − | 6.62882i | 0.149768 | − | 0.259406i | −0.781374 | − | 0.624064i | \(-0.785481\pi\) |
0.931142 | + | 0.364658i | \(0.118814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5434 | − | 25.1899i | −0.568257 | − | 0.984249i | ||||
\(656\) | 7.64810 | − | 13.2469i | 0.298608 | − | 0.517205i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.2810 | − | 7.03481i | −0.478764 | − | 0.274246i | ||||
\(659\) | −38.5145 | −1.50031 | −0.750156 | − | 0.661261i | \(-0.770022\pi\) | ||||
−0.750156 | + | 0.661261i | \(0.770022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1066 | − | 27.8974i | −0.626474 | − | 1.08508i | −0.988254 | − | 0.152821i | \(-0.951164\pi\) |
0.361780 | − | 0.932263i | \(-0.382169\pi\) | |||||||
\(662\) | 24.2697 | + | 42.0363i | 0.943268 | + | 1.63379i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.8284 | 1.27399 | ||||||||
\(665\) | 52.4162 | + | 30.0250i | 2.03261 | + | 1.16432i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.76343 | + | 3.05435i | −0.0682803 | + | 0.118265i | ||||
\(668\) | −0.638506 | − | 1.10592i | −0.0247045 | − | 0.0427895i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.60739 | + | 7.98023i | −0.177999 | + | 0.308303i | ||||
\(671\) | 18.4038 | 0.710470 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26136 | 0.0486218 | 0.0243109 | − | 0.999704i | \(-0.492261\pi\) | ||||
0.0243109 | + | 0.999704i | \(0.492261\pi\) | |||||||
\(674\) | −8.76442 | + | 15.1804i | −0.337593 | + | 0.584728i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.32237 | + | 4.02246i | 0.0893219 | + | 0.154710i | ||||
\(677\) | 7.41589 | − | 12.8447i | 0.285016 | − | 0.493662i | −0.687597 | − | 0.726092i | \(-0.741335\pi\) |
0.972613 | + | 0.232431i | \(0.0746679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.6005 | + | 21.2978i | −1.40460 | + | 0.817333i | ||||
\(680\) | 22.0827 | 0.846833 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.0047 | − | 38.1133i | −0.842605 | − | 1.45943i | ||||
\(683\) | −2.76560 | − | 4.79016i | −0.105823 | − | 0.183290i | 0.808251 | − | 0.588838i | \(-0.200414\pi\) |
−0.914074 | + | 0.405547i | \(0.867081\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5487 | 0.823334 | ||||||||
\(686\) | 24.7883 | + | 13.9760i | 0.946423 | + | 0.533605i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.0672 | + | 31.2933i | −0.688805 | + | 1.19305i | ||||
\(689\) | 0.526097 | + | 0.911226i | 0.0200427 | + | 0.0347150i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.31896 | + | 7.48065i | −0.164301 | + | 0.284577i | −0.936407 | − | 0.350916i | \(-0.885870\pi\) |
0.772106 | + | 0.635494i | \(0.219203\pi\) | |||||||
\(692\) | 3.55620 | 0.135186 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.27116 | −0.238050 | ||||||||
\(695\) | −8.97808 | + | 15.5505i | −0.340558 | + | 0.589864i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.62535 | + | 8.01134i | 0.175198 | + | 0.303451i | ||||
\(698\) | −18.6518 | + | 32.3058i | −0.705979 | + | 1.22279i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0161571 | − | 4.74609i | −0.000610683 | − | 0.179385i | ||||
\(701\) | −26.5897 | −1.00428 | −0.502140 | − | 0.864786i | \(-0.667454\pi\) | ||||
−0.502140 | + | 0.864786i | \(0.667454\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.0818 | + | 46.9070i | 1.02141 | + | 1.76913i | ||||
\(704\) | −17.4843 | − | 30.2837i | −0.658965 | − | 1.14136i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.3632 | −1.97072 | ||||||||
\(707\) | −6.90454 | − | 3.95506i | −0.259672 | − | 0.148745i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.06305 | + | 8.76946i | −0.190147 | + | 0.329344i | −0.945299 | − | 0.326206i | \(-0.894230\pi\) |
0.755152 | + | 0.655550i | \(0.227563\pi\) | |||||||
\(710\) | 3.90460 | + | 6.76297i | 0.146537 | + | 0.253810i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.9666 | + | 31.1191i | −0.673328 | + | 1.16624i | ||||
\(713\) | −4.10705 | −0.153810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.55170 | 0.245020 | ||||||||
\(716\) | −3.59047 | + | 6.21888i | −0.134182 | + | 0.232410i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.21722 | − | 7.30445i | −0.157385 | − | 0.272600i | ||||
\(719\) | 16.1938 | − | 28.0485i | 0.603927 | − | 1.04603i | −0.388293 | − | 0.921536i | \(-0.626935\pi\) |
0.992220 | − | 0.124496i | \(-0.0397315\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0875527 | − | 25.7182i | −0.00326063 | − | 0.957796i | ||||
\(722\) | −51.1391 | −1.90320 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.18221 | − | 3.77970i | −0.0811013 | − | 0.140472i | ||||
\(725\) | −10.6323 | − | 18.4157i | −0.394874 | − | 0.683943i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2348 | 0.935907 | 0.467953 | − | 0.883753i | \(-0.344992\pi\) | ||||
0.467953 | + | 0.883753i | \(0.344992\pi\) | |||||||
\(728\) | 2.07854 | − | 1.20950i | 0.0770357 | − | 0.0448269i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 37.3917 | − | 64.7644i | 1.38393 | − | 2.39704i | ||||
\(731\) | −10.9265 | − | 18.9253i | −0.404132 | − | 0.699977i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.42336 | + | 2.46533i | −0.0525731 | + | 0.0910592i | −0.891114 | − | 0.453779i | \(-0.850076\pi\) |
0.838541 | + | 0.544838i | \(0.183409\pi\) | |||||||
\(734\) | 20.9568 | 0.773529 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.66361 | 0.0613215 | ||||||||
\(737\) | −5.45962 | + | 9.45634i | −0.201108 | + | 0.348329i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2708 | − | 21.2537i | −0.451390 | − | 0.781830i | 0.547083 | − | 0.837078i | \(-0.315738\pi\) |
−0.998473 | + | 0.0552485i | \(0.982405\pi\) | |||||||
\(740\) | 4.26824 | − | 7.39282i | 0.156904 | − | 0.271765i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.2439 | − | 5.96092i | 0.376066 | − | 0.218832i | ||||
\(743\) | −4.59070 | −0.168416 | −0.0842082 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842082 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.0840 | − | 59.0353i | −1.24874 | − | 2.16288i | ||||
\(746\) | 6.85581 | + | 11.8746i | 0.251009 | + | 0.434760i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.76165 | −0.210667 | ||||||||
\(749\) | 0.0938905 | + | 27.5799i | 0.00343068 | + | 1.00775i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.7178 | + | 27.2240i | −0.573551 | + | 0.993419i | 0.422647 | + | 0.906295i | \(0.361101\pi\) |
−0.996197 | + | 0.0871246i | \(0.972232\pi\) | |||||||
\(752\) | 7.99273 | + | 13.8438i | 0.291465 | + | 0.504832i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.18621 | + | 2.05457i | −0.0431992 | + | 0.0748231i | ||||
\(755\) | 17.5422 | 0.638425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5432 | 1.07376 | 0.536882 | − | 0.843657i | \(-0.319602\pi\) | ||||
0.536882 | + | 0.843657i | \(0.319602\pi\) | |||||||
\(758\) | 22.8200 | − | 39.5255i | 0.828861 | − | 1.43563i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.7507 | − | 49.7977i | −1.04290 | − | 1.80635i | ||||
\(761\) | −23.2437 | + | 40.2592i | −0.842582 | + | 1.45940i | 0.0451218 | + | 0.998981i | \(0.485632\pi\) |
−0.887704 | + | 0.460414i | \(0.847701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.7311 | − | 6.14698i | −0.388491 | − | 0.222536i | ||||
\(764\) | −3.50785 | −0.126910 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6060 | + | 23.5663i | 0.491605 | + | 0.851484i | ||||
\(767\) | −0.432864 | − | 0.749743i | −0.0156298 | − | 0.0270716i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.1706 | 0.511006 | 0.255503 | − | 0.966808i | \(-0.417759\pi\) | ||||
0.255503 | + | 0.966808i | \(0.417759\pi\) | |||||||
\(770\) | −0.251233 | − | 73.7986i | −0.00905382 | − | 2.65952i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.415373 | − | 0.719448i | 0.0149496 | − | 0.0258935i | ||||
\(773\) | −17.0042 | − | 29.4522i | −0.611600 | − | 1.05932i | −0.990971 | − | 0.134078i | \(-0.957193\pi\) |
0.379371 | − | 0.925245i | \(-0.376140\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.3814 | − | 21.4452i | 0.444754 | − | 0.770336i | ||||
\(776\) | 40.3096 | 1.44703 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.7672 | 1.17476 | ||||||||
\(779\) | 12.0440 | − | 20.8608i | 0.431522 | − | 0.747417i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.62684 | + | 8.01392i | 0.165561 | + | 0.286761i | ||||
\(782\) | −1.75868 | + | 3.04613i | −0.0628904 | + | 0.108929i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.2596 | − | 27.7248i | −0.580700 | − | 0.990170i | ||||
\(785\) | −19.1705 | −0.684223 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.5530 | + | 25.2065i | 0.518757 | + | 0.898514i | 0.999762 | + | 0.0217964i | \(0.00693855\pi\) |
−0.481005 | + | 0.876718i | \(0.659728\pi\) | |||||||
\(788\) | 0.913934 | + | 1.58298i | 0.0325576 | + | 0.0563914i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.5527 | 0.944701 | ||||||||
\(791\) | 10.7173 | − | 6.23636i | 0.381062 | − | 0.221739i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.577649 | − | 1.00052i | 0.0205129 | − | 0.0355294i | ||||
\(794\) | −1.71757 | − | 2.97493i | −0.0609544 | − | 0.105576i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.79609 | − | 3.11093i | 0.0636609 | − | 0.110264i | ||||
\(797\) | 18.5038 | 0.655439 | 0.327720 | − | 0.944775i | \(-0.393720\pi\) | ||||
0.327720 | + | 0.944775i | \(0.393720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.66754 | −0.342013 | ||||||||
\(800\) | −5.01524 | + | 8.68665i | −0.177316 | + | 0.307120i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.71231 | − | 11.6261i | −0.237020 | − | 0.410531i | ||||
\(803\) | 44.3081 | − | 76.7439i | 1.56360 | − | 2.70823i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.97607 | − | 3.42321i | −0.210629 | − | 0.120652i | ||||
\(806\) | −2.76270 | −0.0973118 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.78720 | + | 6.55962i | 0.133233 | + | 0.230767i | ||||
\(809\) | 20.5407 | + | 35.5775i | 0.722172 | + | 1.25084i | 0.960128 | + | 0.279562i | \(0.0901892\pi\) |
−0.237956 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.1361 | −1.51471 | −0.757357 | − | 0.653001i | \(-0.773510\pi\) | ||||
−0.757357 | + | 0.653001i | \(0.773510\pi\) | |||||||
\(812\) | 3.54472 | + | 2.03049i | 0.124395 | + | 0.0712561i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33.0860 | − | 57.3066i | 1.15966 | − | 2.00859i | ||||
\(815\) | −6.08248 | − | 10.5352i | −0.213060 | − | 0.369031i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.4517 | + | 49.2798i | −0.995399 | + | 1.72408i | ||||
\(818\) | 44.0859 | 1.54143 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.79641 | −0.132576 | ||||||||
\(821\) | 6.58738 | − | 11.4097i | 0.229901 | − | 0.398201i | −0.727877 | − | 0.685707i | \(-0.759493\pi\) |
0.957779 | + | 0.287507i | \(0.0928264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.99083 | + | 10.3764i | 0.208827 | + | 0.361699i | 0.951345 | − | 0.308127i | \(-0.0997020\pi\) |
−0.742518 | + | 0.669826i | \(0.766369\pi\) | |||||||
\(824\) | −12.2407 | + | 21.2016i | −0.426427 | + | 0.738592i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.42854 | + | 4.90455i | −0.293266 | + | 0.170651i | ||||
\(827\) | −29.9879 | −1.04278 | −0.521391 | − | 0.853318i | \(-0.674587\pi\) | ||||
−0.521391 | + | 0.853318i | \(0.674587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.4619 | − | 23.3167i | −0.467551 | − | 0.809822i | 0.531762 | − | 0.846894i | \(-0.321530\pi\) |
−0.999313 | + | 0.0370721i | \(0.988197\pi\) | |||||||
\(830\) | −31.6208 | − | 54.7688i | −1.09757 | − | 1.90105i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.19516 | −0.0761034 | ||||||||
\(833\) | 19.4374 | − | 0.132344i | 0.673467 | − | 0.00458543i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.58639 | − | 9.67591i | 0.193325 | − | 0.334849i | ||||
\(836\) | 7.50142 | + | 12.9928i | 0.259442 | + | 0.449367i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.64117 | + | 11.5029i | −0.229416 | + | 0.397359i | ||||
\(839\) | 11.2238 | 0.387490 | 0.193745 | − | 0.981052i | \(-0.437937\pi\) | ||||
0.193745 | + | 0.981052i | \(0.437937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.6971 | −0.368864 | ||||||||
\(842\) | 14.1874 | − | 24.5734i | 0.488932 | − | 0.846855i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.20465 | + | 7.28267i | 0.144730 | + | 0.250680i | ||||
\(845\) | −20.3188 | + | 35.1932i | −0.698988 | + | 1.21068i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.198628 | − | 58.3460i | −0.00682494 | − | 2.00479i | ||||
\(848\) | −13.3864 | −0.459691 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.6037 | − | 18.3662i | −0.363704 | − | 0.629954i | ||||
\(851\) | −3.08765 | − | 5.34796i | −0.105843 | − | 0.183326i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1934 | −0.417496 | −0.208748 | − | 0.977970i | \(-0.566939\pi\) | ||||
−0.208748 | + | 0.977970i | \(0.566939\pi\) | |||||||
\(854\) | −11.2920 | − | 6.46830i | −0.386405 | − | 0.221341i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.1268 | − | 22.7363i | 0.448666 | − | 0.777112i | ||||
\(857\) | −18.7191 | − | 32.4225i | −0.639433 | − | 1.10753i | −0.985557 | − | 0.169341i | \(-0.945836\pi\) |
0.346125 | − | 0.938188i | \(-0.387497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.378867 | + | 0.656216i | −0.0129268 | + | 0.0223898i | −0.872416 | − | 0.488763i | \(-0.837448\pi\) |
0.859490 | + | 0.511153i | \(0.170781\pi\) | |||||||
\(860\) | 8.96830 | 0.305817 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.92314 | −0.303923 | ||||||||
\(863\) | 11.7796 | − | 20.4029i | 0.400983 | − | 0.694522i | −0.592862 | − | 0.805304i | \(-0.702002\pi\) |
0.993845 | + | 0.110782i | \(0.0353354\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.5569 | + | 26.9453i | 0.528949 | + | 0.916167i | ||||
\(866\) | 2.79553 | − | 4.84200i | 0.0949959 | − | 0.164538i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.0161946 | + | 4.75708i | 0.000549679 | + | 0.161466i | ||||
\(869\) | 31.4641 | 1.06735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.342728 | + | 0.593622i | 0.0116129 | + | 0.0201141i | ||||
\(872\) | 5.88609 | + | 10.1950i | 0.199328 | + | 0.345247i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.15892 | 0.309805 | ||||||||
\(875\) | −0.213202 | + | 0.124062i | −0.00720753 | + | 0.00419405i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.3370 | + | 31.7606i | −0.619196 | + | 1.07248i | 0.370437 | + | 0.928857i | \(0.379208\pi\) |
−0.989633 | + | 0.143621i | \(0.954125\pi\) | |||||||
\(878\) | −14.3372 | − | 24.8328i | −0.483858 | − | 0.838066i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −41.6766 | + | 72.1860i | −1.40492 | + | 2.43339i | ||||
\(881\) | 39.4357 | 1.32862 | 0.664311 | − | 0.747456i | \(-0.268725\pi\) | ||||
0.664311 | + | 0.747456i | \(0.268725\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.76912 | −0.295105 | −0.147552 | − | 0.989054i | \(-0.547139\pi\) | ||||
−0.147552 | + | 0.989054i | \(0.547139\pi\) | |||||||
\(884\) | −0.180844 | + | 0.313231i | −0.00608244 | + | 0.0105351i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0448 | + | 34.7185i | 0.673417 | + | 1.16639i | ||||
\(887\) | 3.91300 | − | 6.77752i | 0.131386 | − | 0.227567i | −0.792825 | − | 0.609449i | \(-0.791391\pi\) |
0.924211 | + | 0.381882i | \(0.124724\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.9456 | − | 12.1882i | 0.702492 | − | 0.408779i | ||||
\(890\) | 69.2230 | 2.32036 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.14294 | + | 3.71168i | 0.0717508 | + | 0.124276i | ||||
\(893\) | 12.5867 | + | 21.8008i | 0.421199 | + | 0.729537i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −62.8272 | −2.10008 | ||||||||
\(896\) | 0.120528 | + | 35.4046i | 0.00402656 | + | 1.18278i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.33164 | − | 7.50263i | 0.144549 | − | 0.250366i | ||||
\(899\) | 10.6569 | + | 18.4584i | 0.355429 | + | 0.615621i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.04786 | − | 7.01109i | 0.134854 | − | 0.233573i | ||||
\(902\) | −29.4285 | −0.979860 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.8033 | −0.392573 | ||||||||
\(905\) | 19.0925 | − | 33.0692i | 0.634657 | − | 1.09926i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.9666 | − | 44.9755i | −0.862208 | − | 1.49339i | −0.869793 | − | 0.493416i | \(-0.835748\pi\) |
0.00758572 | − | 0.999971i | \(-0.497585\pi\) | |||||||
\(908\) | 1.07564 | − | 1.86306i | 0.0356963 | − | 0.0618279i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.01993 | − | 2.30270i | −0.133259 | − | 0.0763336i | ||||
\(911\) | −36.1524 | −1.19778 | −0.598891 | − | 0.800830i | \(-0.704392\pi\) | ||||
−0.598891 | + | 0.800830i | \(0.704392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.4697 | − | 64.8995i | −1.24007 | − | 2.14786i | ||||
\(914\) | −15.3593 | − | 26.6031i | −0.508042 | − | 0.879954i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.56086 | −0.282859 | ||||||||
\(917\) | 0.0829684 | + | 24.3716i | 0.00273986 | + | 0.804821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.58842 | − | 9.67942i | 0.184345 | − | 0.319295i | −0.759011 | − | 0.651078i | \(-0.774317\pi\) |
0.943356 | + | 0.331783i | \(0.107650\pi\) | |||||||
\(920\) | 3.27793 | + | 5.67754i | 0.108070 | + | 0.187183i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.7710 | + | 49.8328i | −0.947522 | + | 1.64116i | ||||
\(923\) | 0.580900 | 0.0191206 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.2330 | 1.22421 | ||||||||
\(926\) | 1.88618 | − | 3.26696i | 0.0619837 | − | 0.107359i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.31673 | − | 7.47679i | −0.141703 | − | 0.245438i | ||||
\(929\) | 16.4192 | − | 28.4389i | 0.538696 | − | 0.933049i | −0.460279 | − | 0.887775i | \(-0.652250\pi\) |
0.998975 | − | 0.0452744i | \(-0.0144162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.6051 | − | 43.6602i | −0.839175 | − | 1.43090i | ||||
\(932\) | 5.00185 | 0.163841 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.6682 | − | 44.4586i | −0.839889 | − | 1.45473i | ||||
\(935\) | −25.2048 | − | 43.6560i | −0.824285 | − | 1.42770i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.9566 | −0.847965 | −0.423983 | − | 0.905670i | \(-0.639368\pi\) | ||||
−0.423983 | + | 0.905670i | \(0.639368\pi\) | |||||||
\(938\) | 6.67344 | − | 3.88326i | 0.217895 | − | 0.126793i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.98374 | − | 3.43594i | 0.0647024 | − | 0.112068i | ||||
\(941\) | 14.7340 | + | 25.5200i | 0.480314 | + | 0.831928i | 0.999745 | − | 0.0225845i | \(-0.00718949\pi\) |
−0.519431 | + | 0.854512i | \(0.673856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.37316 | + | 2.37839i | −0.0447163 | + | 0.0774509i | ||||
\(944\) | 11.0141 | 0.358479 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69.5192 | 2.26026 | ||||||||
\(947\) | −5.76137 | + | 9.97898i | −0.187219 | + | 0.324273i | −0.944322 | − | 0.329022i | \(-0.893281\pi\) |
0.757103 | + | 0.653296i | \(0.226614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.78144 | − | 4.81760i | −0.0902895 | − | 0.156386i | ||||
\(950\) | −27.6111 | + | 47.8239i | −0.895824 | + | 1.55161i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16.0555 | − | 9.19692i | −0.520362 | − | 0.298074i | ||||
\(953\) | −29.2912 | −0.948835 | −0.474417 | − | 0.880300i | \(-0.657341\pi\) | ||||
−0.474417 | + | 0.880300i | \(0.657341\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.3454 | − | 26.5790i | −0.496565 | − | 0.860076i | ||||
\(956\) | 4.03176 | + | 6.98321i | 0.130396 | + | 0.225853i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 53.3075 | 1.72229 | ||||||||
\(959\) | −15.6673 | − | 8.97452i | −0.505922 | − | 0.289802i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.08991 | − | 5.35188i | 0.0996744 | − | 0.172641i | ||||
\(962\) | −2.07697 | − | 3.59742i | −0.0669643 | − | 0.115985i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.75411 | + | 3.03820i | −0.0564959 | + | 0.0978538i | ||||
\(965\) | 7.26834 | 0.233976 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.0803 | 1.35321 | 0.676606 | − | 0.736345i | \(-0.263450\pi\) | ||||
0.676606 | + | 0.736345i | \(0.263450\pi\) | |||||||
\(968\) | −27.7702 | + | 48.0993i | −0.892567 | + | 1.54597i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −38.8268 | − | 67.2500i | −1.24665 | − | 2.15927i | ||||
\(971\) | −17.5774 | + | 30.4450i | −0.564087 | + | 0.977027i | 0.433047 | + | 0.901371i | \(0.357438\pi\) |
−0.997134 | + | 0.0756560i | \(0.975895\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0040 | − | 7.56703i | 0.416890 | − | 0.242588i | ||||
\(974\) | −1.47478 | −0.0472551 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.34907 | + | 12.7290i | 0.235238 | + | 0.407444i | ||||
\(977\) | −2.21513 | − | 3.83671i | −0.0708682 | − | 0.122747i | 0.828414 | − | 0.560117i | \(-0.189244\pi\) |
−0.899282 | + | 0.437369i | \(0.855910\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 82.0271 | 2.62160 | ||||||||
\(980\) | −3.94144 | + | 6.93540i | −0.125905 | + | 0.221543i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.1184 | + | 20.9897i | −0.386714 | + | 0.669809i | ||||
\(983\) | 11.0801 | + | 19.1912i | 0.353399 | + | 0.612105i | 0.986843 | − | 0.161684i | \(-0.0516925\pi\) |
−0.633444 | + | 0.773789i | \(0.718359\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.99616 | + | 13.8498i | −0.254779 | + | 0.441290i | ||||
\(986\) | 18.2537 | 0.581316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.941804 | 0.0299628 | ||||||||
\(989\) | 3.24383 | − | 5.61848i | 0.103148 | − | 0.178657i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.3602 | + | 31.8007i | 0.583229 | + | 1.01018i | 0.995094 | + | 0.0989378i | \(0.0315445\pi\) |
−0.411864 | + | 0.911245i | \(0.635122\pi\) | |||||||
\(992\) | 5.02686 | − | 8.70677i | 0.159603 | − | 0.276440i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.0222753 | − | 6.54328i | −0.000706531 | − | 0.207540i | ||||
\(995\) | 31.4286 | 0.996355 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.9515 | + | 34.5571i | 0.631872 | + | 1.09443i | 0.987169 | + | 0.159681i | \(0.0510464\pi\) |
−0.355297 | + | 0.934753i | \(0.615620\pi\) | |||||||
\(998\) | −14.6959 | − | 25.4540i | −0.465190 | − | 0.805733i | ||||
\(999\) | 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 | 567.2.e.d.163.3 | yes | 8 | |
3.2 | odd | 2 | 567.2.e.c.163.2 | ✓ | 8 | ||
7.2 | even | 3 | 3969.2.a.s.1.2 | 4 | |||
7.4 | even | 3 | inner | 567.2.e.d.487.3 | yes | 8 | |
7.5 | odd | 6 | 3969.2.a.t.1.2 | 4 | |||
9.2 | odd | 6 | 567.2.h.k.352.3 | 8 | |||
9.4 | even | 3 | 567.2.g.k.541.3 | 8 | |||
9.5 | odd | 6 | 567.2.g.j.541.2 | 8 | |||
9.7 | even | 3 | 567.2.h.j.352.2 | 8 | |||
21.2 | odd | 6 | 3969.2.a.x.1.3 | 4 | |||
21.5 | even | 6 | 3969.2.a.w.1.3 | 4 | |||
21.11 | odd | 6 | 567.2.e.c.487.2 | yes | 8 | ||
63.4 | even | 3 | 567.2.h.j.298.2 | 8 | |||
63.11 | odd | 6 | 567.2.g.j.109.2 | 8 | |||
63.25 | even | 3 | 567.2.g.k.109.3 | 8 | |||
63.32 | odd | 6 | 567.2.h.k.298.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.c.163.2 | ✓ | 8 | 3.2 | odd | 2 | ||
567.2.e.c.487.2 | yes | 8 | 21.11 | odd | 6 | ||
567.2.e.d.163.3 | yes | 8 | 1.1 | even | 1 | trivial | |
567.2.e.d.487.3 | yes | 8 | 7.4 | even | 3 | inner | |
567.2.g.j.109.2 | 8 | 63.11 | odd | 6 | |||
567.2.g.j.541.2 | 8 | 9.5 | odd | 6 | |||
567.2.g.k.109.3 | 8 | 63.25 | even | 3 | |||
567.2.g.k.541.3 | 8 | 9.4 | even | 3 | |||
567.2.h.j.298.2 | 8 | 63.4 | even | 3 | |||
567.2.h.j.352.2 | 8 | 9.7 | even | 3 | |||
567.2.h.k.298.3 | 8 | 63.32 | odd | 6 | |||
567.2.h.k.352.3 | 8 | 9.2 | odd | 6 | |||
3969.2.a.s.1.2 | 4 | 7.2 | even | 3 | |||
3969.2.a.t.1.2 | 4 | 7.5 | odd | 6 | |||
3969.2.a.w.1.3 | 4 | 21.5 | even | 6 | |||
3969.2.a.x.1.3 | 4 | 21.2 | odd | 6 |