Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 271.3 | ||
Root | \(1.14412 + 1.98168i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.271 |
Dual form | 324.3.f.o.55.3 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.270091 | + | 1.98168i | 0.135045 | + | 0.990839i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.85410 | + | 1.07047i | −0.963525 | + | 0.267617i | ||||
\(5\) | 0.540182 | − | 0.935622i | 0.108036 | − | 0.187124i | −0.806938 | − | 0.590636i | \(-0.798877\pi\) |
0.914975 | + | 0.403511i | \(0.132210\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.20820 | − | 3.00696i | 0.744029 | − | 0.429565i | −0.0795033 | − | 0.996835i | \(-0.525333\pi\) |
0.823532 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(8\) | −3.16228 | − | 7.34847i | −0.395285 | − | 0.918559i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 0.817763i | 0.200000 | + | 0.0817763i | ||||
\(11\) | 15.3500 | − | 8.86234i | 1.39546 | − | 0.805667i | 0.401544 | − | 0.915840i | \(-0.368474\pi\) |
0.993912 | + | 0.110173i | \(0.0351404\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.20820 | + | 10.7529i | −0.477554 | + | 0.827148i | −0.999669 | − | 0.0257271i | \(-0.991810\pi\) |
0.522115 | + | 0.852875i | \(0.325143\pi\) | |||||||
\(14\) | 7.36551 | + | 9.50884i | 0.526108 | + | 0.679203i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.7082 | − | 8.25137i | 0.856763 | − | 0.515711i | ||||
\(17\) | 26.3786 | 1.55168 | 0.775841 | − | 0.630929i | \(-0.217326\pi\) | ||||
0.775841 | + | 0.630929i | \(0.217326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19615i | 0.273482i | 0.990607 | + | 0.136741i | \(0.0436628\pi\) | ||||
−0.990607 | + | 0.136741i | \(0.956337\pi\) | |||||||
\(20\) | −1.08036 | + | 4.18423i | −0.0540182 | + | 0.209211i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21.7082 | + | 28.0252i | 0.986737 | + | 1.27387i | ||||
\(23\) | −25.8384 | − | 14.9178i | −1.12341 | − | 0.648600i | −0.181140 | − | 0.983457i | \(-0.557979\pi\) |
−0.942269 | + | 0.334857i | \(0.891312\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.9164 | + | 20.6398i | 0.476656 | + | 0.825593i | ||||
\(26\) | −22.9856 | − | 9.39840i | −0.884062 | − | 0.361477i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −16.8541 | + | 17.1643i | −0.601932 | + | 0.613012i | ||||
\(29\) | 2.16073 | + | 3.74249i | 0.0745078 | + | 0.129051i | 0.900872 | − | 0.434085i | \(-0.142928\pi\) |
−0.826364 | + | 0.563136i | \(0.809595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.8328 | + | 22.4201i | 1.25267 | + | 0.723230i | 0.971639 | − | 0.236468i | \(-0.0759899\pi\) |
0.281032 | + | 0.959698i | \(0.409323\pi\) | |||||||
\(32\) | 20.0540 | + | 24.9366i | 0.626688 | + | 0.779270i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.12461 | + | 52.2739i | 0.209547 | + | 1.53747i | ||||
\(35\) | − | 6.49721i | − | 0.185635i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −20.4164 | −0.551795 | −0.275897 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275897 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(38\) | −10.2971 | + | 1.40343i | −0.270976 | + | 0.0369324i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.58359 | − | 1.01081i | −0.214590 | − | 0.0252703i | ||||
\(41\) | 29.6197 | − | 51.3028i | 0.722431 | − | 1.25129i | −0.237592 | − | 0.971365i | \(-0.576358\pi\) |
0.960023 | − | 0.279922i | \(-0.0903087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16.5836 | − | 9.57454i | 0.385665 | − | 0.222664i | −0.294615 | − | 0.955616i | \(-0.595191\pi\) |
0.680280 | + | 0.732952i | \(0.261858\pi\) | |||||||
\(44\) | −49.6737 | + | 50.5880i | −1.12895 | + | 1.14973i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 22.5836 | − | 55.2326i | 0.490948 | − | 1.20071i | ||||
\(47\) | −35.5617 | + | 20.5315i | −0.756631 | + | 0.436841i | −0.828085 | − | 0.560603i | \(-0.810570\pi\) |
0.0714537 | + | 0.997444i | \(0.477236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.41641 | + | 11.1135i | −0.130947 | + | 0.226807i | ||||
\(50\) | −37.6830 | + | 29.1891i | −0.753660 | + | 0.583782i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.4164 | − | 48.0885i | 0.238777 | − | 0.924780i | ||||
\(53\) | 70.0430 | 1.32157 | 0.660783 | − | 0.750577i | \(-0.270224\pi\) | ||||
0.660783 | + | 0.750577i | \(0.270224\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 19.1491i | − | 0.348165i | ||||||
\(56\) | −38.5663 | − | 28.7635i | −0.688684 | − | 0.513634i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.83282 | + | 5.29268i | −0.117807 | + | 0.0912530i | ||||
\(59\) | 25.0733 | + | 14.4761i | 0.424971 | + | 0.245357i | 0.697202 | − | 0.716875i | \(-0.254428\pi\) |
−0.272231 | + | 0.962232i | \(0.587761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.20820 | − | 15.9491i | −0.150954 | − | 0.261460i | 0.780624 | − | 0.625001i | \(-0.214901\pi\) |
−0.931578 | + | 0.363540i | \(0.881568\pi\) | |||||||
\(62\) | −33.9411 | + | 83.0096i | −0.547438 | + | 1.33887i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.0000 | + | 46.4758i | −0.687500 | + | 0.726184i | ||||
\(65\) | 6.70711 | + | 11.6171i | 0.103186 | + | 0.178724i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −82.1656 | − | 47.4383i | −1.22635 | − | 0.708035i | −0.260088 | − | 0.965585i | \(-0.583751\pi\) |
−0.966265 | + | 0.257550i | \(0.917085\pi\) | |||||||
\(68\) | −101.666 | + | 28.2374i | −1.49508 | + | 0.415256i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.8754 | − | 1.75484i | 0.183934 | − | 0.0250691i | ||||
\(71\) | − | 83.8931i | − | 1.18159i | −0.806821 | − | 0.590797i | \(-0.798814\pi\) | ||
0.806821 | − | 0.590797i | \(-0.201186\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55.8328 | 0.764833 | 0.382417 | − | 0.923990i | \(-0.375092\pi\) | ||||
0.382417 | + | 0.923990i | \(0.375092\pi\) | |||||||
\(74\) | −5.51428 | − | 40.4588i | −0.0745173 | − | 0.546740i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.56231 | − | 20.0265i | −0.0731882 | − | 0.263507i | ||||
\(77\) | 53.2974 | − | 92.3137i | 0.692173 | − | 1.19888i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −35.5426 | + | 20.5205i | −0.449906 | + | 0.259753i | −0.707790 | − | 0.706422i | \(-0.750308\pi\) |
0.257885 | + | 0.966176i | \(0.416975\pi\) | |||||||
\(80\) | −0.315246 | − | 17.2829i | −0.00394057 | − | 0.216037i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 109.666 | + | 44.8403i | 1.33739 | + | 0.546833i | ||||
\(83\) | −30.7000 | + | 17.7247i | −0.369880 | + | 0.213550i | −0.673406 | − | 0.739273i | \(-0.735169\pi\) |
0.303526 | + | 0.952823i | \(0.401836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.2492 | − | 24.6804i | 0.167638 | − | 0.290357i | ||||
\(86\) | 23.4527 | + | 30.2774i | 0.272706 | + | 0.352062i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −113.666 | − | 84.7740i | −1.29165 | − | 0.963341i | ||||
\(89\) | 26.3786 | 0.296389 | 0.148194 | − | 0.988958i | \(-0.452654\pi\) | ||||
0.148194 | + | 0.988958i | \(0.452654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 74.6712i | 0.820563i | ||||||||
\(92\) | 115.553 | + | 29.8356i | 1.25601 | + | 0.324300i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −50.2918 | − | 64.9264i | −0.535019 | − | 0.690707i | ||||
\(95\) | 4.86163 | + | 2.80687i | 0.0511751 | + | 0.0295460i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −38.1656 | − | 66.1048i | −0.393460 | − | 0.681493i | 0.599443 | − | 0.800417i | \(-0.295389\pi\) |
−0.992903 | + | 0.118924i | \(0.962055\pi\) | |||||||
\(98\) | −23.7565 | − | 9.71359i | −0.242413 | − | 0.0991183i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −68.0213 | − | 66.7919i | −0.680213 | − | 0.667919i | ||||
\(101\) | 36.1019 | + | 62.5302i | 0.357444 | + | 0.619111i | 0.987533 | − | 0.157412i | \(-0.0503149\pi\) |
−0.630089 | + | 0.776523i | \(0.716982\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 50.2082 | + | 28.9877i | 0.487458 | + | 0.281434i | 0.723519 | − | 0.690304i | \(-0.242523\pi\) |
−0.236061 | + | 0.971738i | \(0.575857\pi\) | |||||||
\(104\) | 98.6496 | + | 11.6171i | 0.948554 | + | 0.111703i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.9180 | + | 138.803i | 0.178471 | + | 1.30946i | ||||
\(107\) | − | 64.4015i | − | 0.601883i | −0.953643 | − | 0.300942i | \(-0.902699\pi\) | ||
0.953643 | − | 0.300942i | \(-0.0973009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −43.1672 | −0.396029 | −0.198015 | − | 0.980199i | \(-0.563449\pi\) | ||||
−0.198015 | + | 0.980199i | \(0.563449\pi\) | |||||||
\(110\) | 37.9473 | − | 5.17199i | 0.344976 | − | 0.0470181i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 46.5836 | − | 84.1948i | 0.415925 | − | 0.751739i | ||||
\(113\) | −40.6482 | + | 70.4048i | −0.359719 | + | 0.623051i | −0.987914 | − | 0.155005i | \(-0.950461\pi\) |
0.628195 | + | 0.778056i | \(0.283794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.9149 | + | 16.1166i | −0.242738 | + | 0.140145i | ||||
\(116\) | −12.3339 | − | 12.1109i | −0.106326 | − | 0.104405i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21.9149 | + | 53.5971i | −0.185719 | + | 0.454212i | ||||
\(119\) | 137.385 | − | 79.3193i | 1.15450 | − | 0.666549i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 96.5820 | − | 167.285i | 0.798199 | − | 1.38252i | ||||
\(122\) | 29.1189 | − | 22.5554i | 0.238679 | − | 0.184880i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −173.666 | − | 44.8403i | −1.40053 | − | 0.361615i | ||||
\(125\) | 52.7572 | 0.422057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 191.968i | − | 1.51156i | −0.654826 | − | 0.755780i | \(-0.727258\pi\) | ||
0.654826 | − | 0.755780i | \(-0.272742\pi\) | |||||||
\(128\) | −103.984 | − | 74.6412i | −0.812376 | − | 0.583134i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −21.2098 | + | 16.4290i | −0.163152 | + | 0.126377i | ||||
\(131\) | −122.800 | − | 70.8987i | −0.937406 | − | 0.541211i | −0.0482596 | − | 0.998835i | \(-0.515367\pi\) |
−0.889146 | + | 0.457623i | \(0.848701\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.6246 | + | 27.0626i | 0.117478 | + | 0.203478i | ||||
\(134\) | 71.8154 | − | 175.639i | 0.535936 | − | 1.31074i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −83.4164 | − | 193.842i | −0.613356 | − | 1.42531i | ||||
\(137\) | −43.8893 | − | 76.0185i | −0.320360 | − | 0.554880i | 0.660202 | − | 0.751088i | \(-0.270471\pi\) |
−0.980562 | + | 0.196208i | \(0.937137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −158.916 | − | 91.7504i | −1.14328 | − | 0.660075i | −0.196042 | − | 0.980596i | \(-0.562809\pi\) |
−0.947242 | + | 0.320520i | \(0.896142\pi\) | |||||||
\(140\) | 6.95505 | + | 25.0409i | 0.0496789 | + | 0.178864i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 166.249 | − | 22.6588i | 1.17077 | − | 0.159569i | ||||
\(143\) | 220.077i | 1.53900i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.66874 | 0.0321982 | ||||||||
\(146\) | 15.0799 | + | 110.643i | 0.103287 | + | 0.757827i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 78.6869 | − | 21.8551i | 0.531668 | − | 0.147669i | ||||
\(149\) | −76.9750 | + | 133.325i | −0.516611 | + | 0.894796i | 0.483203 | + | 0.875508i | \(0.339473\pi\) |
−0.999814 | + | 0.0192880i | \(0.993860\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −160.539 | + | 92.6875i | −1.06318 | + | 0.613825i | −0.926309 | − | 0.376765i | \(-0.877036\pi\) |
−0.136866 | + | 0.990590i | \(0.543703\pi\) | |||||||
\(152\) | 38.1838 | − | 16.4317i | 0.251209 | − | 0.108103i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 197.331 | + | 80.6851i | 1.28137 | + | 0.523930i | ||||
\(155\) | 41.9535 | − | 24.2219i | 0.270668 | − | 0.156270i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.0820 | + | 169.883i | −0.624726 | + | 1.08206i | 0.363867 | + | 0.931451i | \(0.381456\pi\) |
−0.988594 | + | 0.150607i | \(0.951877\pi\) | |||||||
\(158\) | −50.2648 | − | 64.8916i | −0.318132 | − | 0.410706i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 34.1641 | − | 5.29268i | 0.213525 | − | 0.0330792i | ||||
\(161\) | −179.429 | −1.11447 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 129.325i | 0.793403i | 0.917948 | + | 0.396701i | \(0.129845\pi\) | ||||
−0.917948 | + | 0.396701i | \(0.870155\pi\) | |||||||
\(164\) | −59.2393 | + | 229.433i | −0.361216 | + | 1.39898i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −43.4164 | − | 56.0503i | −0.261545 | − | 0.337653i | ||||
\(167\) | 119.469 | + | 68.9753i | 0.715382 | + | 0.413026i | 0.813051 | − | 0.582193i | \(-0.197805\pi\) |
−0.0976688 | + | 0.995219i | \(0.531139\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.41641 | + | 12.8456i | 0.0438841 | + | 0.0760094i | ||||
\(170\) | 52.7572 | + | 21.5714i | 0.310336 | + | 0.126891i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −53.6656 | + | 54.6534i | −0.312009 | + | 0.317753i | ||||
\(173\) | −80.2161 | − | 138.938i | −0.463677 | − | 0.803112i | 0.535464 | − | 0.844558i | \(-0.320137\pi\) |
−0.999141 | + | 0.0414461i | \(0.986804\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 124.126 | + | 71.6643i | 0.709292 | + | 0.409510i | ||||
\(176\) | 137.295 | − | 248.145i | 0.780084 | − | 1.40992i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.12461 | + | 52.2739i | 0.0400259 | + | 0.293673i | ||||
\(179\) | 201.469i | 1.12552i | 0.826619 | + | 0.562762i | \(0.190261\pi\) | ||||
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −48.2523 | −0.266587 | −0.133294 | − | 0.991077i | \(-0.542555\pi\) | ||||
−0.133294 | + | 0.991077i | \(0.542555\pi\) | |||||||
\(182\) | −147.974 | + | 20.1680i | −0.813046 | + | 0.110813i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −27.9149 | + | 237.047i | −0.151711 | + | 1.28830i | ||||
\(185\) | −11.0286 | + | 19.1020i | −0.0596139 | + | 0.103254i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 404.912 | − | 233.776i | 2.16530 | − | 1.25014i | ||||
\(188\) | 115.080 | − | 117.198i | 0.612128 | − | 0.623395i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.24922 | + | 10.3923i | −0.0223643 | + | 0.0546963i | ||||
\(191\) | −127.662 | + | 73.7056i | −0.668386 | + | 0.385893i | −0.795465 | − | 0.606000i | \(-0.792773\pi\) |
0.127079 | + | 0.991893i | \(0.459440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.5820 | + | 21.7927i | −0.0651919 | + | 0.112916i | −0.896779 | − | 0.442479i | \(-0.854099\pi\) |
0.831587 | + | 0.555394i | \(0.187433\pi\) | |||||||
\(194\) | 120.690 | − | 93.4863i | 0.622115 | − | 0.481888i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.8328 | − | 49.7013i | 0.0654735 | − | 0.253578i | ||||
\(197\) | −385.506 | −1.95688 | −0.978441 | − | 0.206528i | \(-0.933784\pi\) | ||||
−0.978441 | + | 0.206528i | \(0.933784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 121.386i | 0.609978i | 0.952356 | + | 0.304989i | \(0.0986528\pi\) | ||||
−0.952356 | + | 0.304989i | \(0.901347\pi\) | |||||||
\(200\) | 113.988 | − | 152.836i | 0.569941 | − | 0.764181i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −114.164 | + | 88.4311i | −0.565169 | + | 0.437778i | ||||
\(203\) | 22.5070 | + | 12.9944i | 0.110872 | + | 0.0640119i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.0000 | − | 55.4256i | −0.156098 | − | 0.270369i | ||||
\(206\) | −43.8836 | + | 107.326i | −0.213027 | + | 0.520999i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.62306 | + | 198.629i | 0.0174186 | + | 0.954949i | ||||
\(209\) | 46.0501 | + | 79.7610i | 0.220335 | + | 0.381632i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 226.579 | + | 130.815i | 1.07383 | + | 0.619978i | 0.929226 | − | 0.369511i | \(-0.120475\pi\) |
0.144607 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(212\) | −269.953 | + | 74.9786i | −1.27336 | + | 0.353673i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 127.623 | − | 17.3942i | 0.596369 | − | 0.0812815i | ||||
\(215\) | − | 20.6880i | − | 0.0962231i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 269.666 | 1.24270 | ||||||||
\(218\) | −11.6591 | − | 85.5435i | −0.0534819 | − | 0.392401i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.4984 | + | 73.8025i | 0.0931748 | + | 0.335466i | ||||
\(221\) | −163.764 | + | 283.647i | −0.741012 | + | 1.28347i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −60.6687 | + | 35.0271i | −0.272057 | + | 0.157072i | −0.629822 | − | 0.776739i | \(-0.716872\pi\) |
0.357765 | + | 0.933812i | \(0.383539\pi\) | |||||||
\(224\) | 179.429 | + | 69.5735i | 0.801022 | + | 0.310596i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −150.498 | − | 61.5361i | −0.665922 | − | 0.272283i | ||||
\(227\) | −258.384 | + | 149.178i | −1.13826 | + | 0.657172i | −0.945998 | − | 0.324172i | \(-0.894914\pi\) |
−0.192258 | + | 0.981344i | \(0.561581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −129.833 | + | 224.877i | −0.566956 | + | 0.981996i | 0.429909 | + | 0.902872i | \(0.358546\pi\) |
−0.996865 | + | 0.0791237i | \(0.974788\pi\) | |||||||
\(230\) | −39.4776 | − | 50.9653i | −0.171642 | − | 0.221588i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.6687 | − | 27.7128i | 0.0890894 | − | 0.119452i | ||||
\(233\) | −7.38192 | −0.0316821 | −0.0158410 | − | 0.999875i | \(-0.505043\pi\) | ||||
−0.0158410 | + | 0.999875i | \(0.505043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44.3630i | 0.188779i | ||||||||
\(236\) | −112.131 | − | 28.9521i | −0.475132 | − | 0.122679i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 194.292 | + | 250.830i | 0.816352 | + | 1.05391i | ||||
\(239\) | 71.1233 | + | 41.0631i | 0.297587 | + | 0.171812i | 0.641358 | − | 0.767241i | \(-0.278371\pi\) |
−0.343771 | + | 0.939053i | \(0.611704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 207.913 | + | 360.116i | 0.862711 | + | 1.49426i | 0.869302 | + | 0.494281i | \(0.164568\pi\) |
−0.00659158 | + | 0.999978i | \(0.502098\pi\) | |||||||
\(242\) | 357.591 | + | 146.212i | 1.47765 | + | 0.604184i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 52.5623 | + | 51.6123i | 0.215419 | + | 0.211526i | ||||
\(245\) | 6.93205 | + | 12.0067i | 0.0282941 | + | 0.0490068i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −55.8738 | − | 32.2588i | −0.226210 | − | 0.130602i | ||||
\(248\) | 41.9535 | − | 356.260i | 0.169167 | − | 1.43653i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.2492 | + | 104.548i | 0.0569969 | + | 0.418191i | ||||
\(251\) | − | 140.030i | − | 0.557890i | −0.960307 | − | 0.278945i | \(-0.910015\pi\) | ||
0.960307 | − | 0.278945i | \(-0.0899847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −528.827 | −2.09022 | ||||||||
\(254\) | 380.419 | − | 51.8488i | 1.49771 | − | 0.204129i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 119.830 | − | 226.223i | 0.468085 | − | 0.883684i | ||||
\(257\) | −33.4913 | + | 58.0086i | −0.130316 | + | 0.225714i | −0.923798 | − | 0.382879i | \(-0.874933\pi\) |
0.793482 | + | 0.608593i | \(0.208266\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −106.333 | + | 61.3913i | −0.410551 | + | 0.237032i | ||||
\(260\) | −38.2856 | − | 37.5936i | −0.147252 | − | 0.144591i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 107.331 | − | 262.500i | 0.409661 | − | 1.00191i | ||||
\(263\) | 32.2303 | − | 18.6082i | 0.122549 | − | 0.0707534i | −0.437473 | − | 0.899232i | \(-0.644126\pi\) |
0.560021 | + | 0.828478i | \(0.310793\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.8359 | − | 65.5337i | 0.142777 | − | 0.247297i | ||||
\(266\) | −49.4094 | + | 38.2723i | −0.185749 | + | 0.143881i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 367.456 | + | 94.8767i | 1.37110 | + | 0.354018i | ||||
\(269\) | −279.092 | −1.03752 | −0.518758 | − | 0.854921i | \(-0.673605\pi\) | ||||
−0.518758 | + | 0.854921i | \(0.673605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 406.305i | − | 1.49928i | −0.661845 | − | 0.749641i | \(-0.730226\pi\) | ||
0.661845 | − | 0.749641i | \(-0.269774\pi\) | |||||||
\(272\) | 361.603 | − | 217.660i | 1.32942 | − | 0.800219i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 138.790 | − | 107.506i | 0.506534 | − | 0.392359i | ||||
\(275\) | 365.834 | + | 211.214i | 1.33031 | + | 0.768053i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.41641 | − | 4.18534i | −0.00872349 | − | 0.0151095i | 0.861631 | − | 0.507536i | \(-0.169443\pi\) |
−0.870354 | + | 0.492426i | \(0.836110\pi\) | |||||||
\(278\) | 138.898 | − | 339.702i | 0.499633 | − | 1.22195i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −47.7446 | + | 20.5460i | −0.170516 | + | 0.0733785i | ||||
\(281\) | 2.16073 | + | 3.74249i | 0.00768942 | + | 0.0133185i | 0.869845 | − | 0.493326i | \(-0.164219\pi\) |
−0.862155 | + | 0.506644i | \(0.830886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −38.4195 | − | 22.1815i | −0.135758 | − | 0.0783799i | 0.430583 | − | 0.902551i | \(-0.358308\pi\) |
−0.566341 | + | 0.824171i | \(0.691641\pi\) | |||||||
\(284\) | 89.8048 | + | 323.333i | 0.316214 | + | 1.13850i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −436.122 | + | 59.4407i | −1.52490 | + | 0.207835i | ||||
\(287\) | − | 356.260i | − | 1.24133i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 406.830 | 1.40772 | ||||||||
\(290\) | 1.26098 | + | 9.25194i | 0.00434822 | + | 0.0319032i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −215.185 | + | 59.7671i | −0.736936 | + | 0.204682i | ||||
\(293\) | 194.464 | − | 336.821i | 0.663699 | − | 1.14956i | −0.315938 | − | 0.948780i | \(-0.602319\pi\) |
0.979636 | − | 0.200780i | \(-0.0643475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.0883 | − | 15.6394i | 0.0918246 | − | 0.0530149i | ||||
\(296\) | 64.5624 | + | 150.029i | 0.218116 | + | 0.506856i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −284.997 | − | 116.530i | −0.956365 | − | 0.391040i | ||||
\(299\) | 320.820 | − | 185.226i | 1.07298 | − | 0.619484i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 57.5805 | − | 99.7323i | 0.191297 | − | 0.331337i | ||||
\(302\) | −227.037 | − | 293.104i | −0.751778 | − | 0.970542i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 42.8754 | + | 71.2299i | 0.141037 | + | 0.234309i | ||||
\(305\) | −19.8964 | −0.0652341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 96.6999i | 0.314983i | 0.987520 | + | 0.157492i | \(0.0503407\pi\) | ||||
−0.987520 | + | 0.157492i | \(0.949659\pi\) | |||||||
\(308\) | −106.595 | + | 412.839i | −0.346087 | + | 1.34039i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 59.3313 | + | 76.5963i | 0.191391 | + | 0.247085i | ||||
\(311\) | −117.939 | − | 68.0918i | −0.379224 | − | 0.218945i | 0.298257 | − | 0.954486i | \(-0.403595\pi\) |
−0.677480 | + | 0.735541i | \(0.736928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −141.080 | − | 244.359i | −0.450736 | − | 0.780698i | 0.547696 | − | 0.836678i | \(-0.315505\pi\) |
−0.998432 | + | 0.0559794i | \(0.982172\pi\) | |||||||
\(314\) | −363.145 | − | 148.483i | −1.15651 | − | 0.472877i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 115.018 | − | 117.135i | 0.363982 | − | 0.370681i | ||||
\(317\) | 137.745 | + | 238.581i | 0.434526 | + | 0.752620i | 0.997257 | − | 0.0740196i | \(-0.0235827\pi\) |
−0.562731 | + | 0.826640i | \(0.690249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 66.3344 | + | 38.2982i | 0.207945 | + | 0.120057i | ||||
\(320\) | 19.7158 | + | 66.2727i | 0.0616118 | + | 0.207102i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −48.4621 | − | 355.570i | −0.150503 | − | 1.10426i | ||||
\(323\) | 137.067i | 0.424356i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −295.918 | −0.910517 | ||||||||
\(326\) | −256.280 | + | 34.9294i | −0.786135 | + | 0.107145i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −470.663 | − | 55.4256i | −1.43495 | − | 0.168981i | ||||
\(329\) | −123.475 | + | 213.865i | −0.375304 | + | 0.650045i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 48.0836 | − | 27.7611i | 0.145268 | − | 0.0838703i | −0.425605 | − | 0.904909i | \(-0.639939\pi\) |
0.570872 | + | 0.821039i | \(0.306605\pi\) | |||||||
\(332\) | 99.3474 | − | 101.176i | 0.299239 | − | 0.304747i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −104.420 | + | 255.378i | −0.312633 | + | 0.764606i | ||||
\(335\) | −88.7687 | + | 51.2506i | −0.264981 | + | 0.152987i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 215.330 | − | 372.962i | 0.638961 | − | 1.10671i | −0.346701 | − | 0.937976i | \(-0.612698\pi\) |
0.985661 | − | 0.168736i | \(-0.0539686\pi\) | |||||||
\(338\) | −23.4527 | + | 18.1664i | −0.0693868 | + | 0.0537468i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −28.4984 | + | 110.374i | −0.0838190 | + | 0.324629i | ||||
\(341\) | 794.779 | 2.33073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 371.857i | 1.08413i | ||||||||
\(344\) | −122.800 | − | 91.5867i | −0.356977 | − | 0.266240i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 253.666 | − | 196.489i | 0.733138 | − | 0.567886i | ||||
\(347\) | −117.668 | − | 67.9354i | −0.339100 | − | 0.195779i | 0.320774 | − | 0.947156i | \(-0.396057\pi\) |
−0.659874 | + | 0.751376i | \(0.729390\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −144.041 | − | 249.486i | −0.412725 | − | 0.714861i | 0.582462 | − | 0.812858i | \(-0.302090\pi\) |
−0.995187 | + | 0.0979975i | \(0.968756\pi\) | |||||||
\(350\) | −108.490 | + | 265.334i | −0.309972 | + | 0.758097i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 528.827 | + | 205.052i | 1.50235 | + | 0.582535i | ||||
\(353\) | −99.4820 | − | 172.308i | −0.281819 | − | 0.488124i | 0.690014 | − | 0.723796i | \(-0.257604\pi\) |
−0.971833 | + | 0.235672i | \(0.924271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −78.4922 | − | 45.3175i | −0.221105 | − | 0.127655i | ||||
\(356\) | −101.666 | + | 28.2374i | −0.285578 | + | 0.0793185i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −399.246 | + | 54.4148i | −1.11521 | + | 0.151997i | ||||
\(359\) | 324.658i | 0.904339i | 0.891932 | + | 0.452170i | \(0.149350\pi\) | ||||
−0.891932 | + | 0.452170i | \(0.850650\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.000 | 0.925208 | ||||||||
\(362\) | −13.0325 | − | 95.6206i | −0.0360014 | − | 0.264145i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −79.9330 | − | 287.791i | −0.219596 | − | 0.790633i | ||||
\(365\) | 30.1599 | − | 52.2384i | 0.0826297 | − | 0.143119i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −152.543 | + | 88.0705i | −0.415647 | + | 0.239974i | −0.693213 | − | 0.720732i | \(-0.743806\pi\) |
0.277566 | + | 0.960707i | \(0.410472\pi\) | |||||||
\(368\) | −477.290 | + | 8.70592i | −1.29699 | + | 0.0236574i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −40.8328 | − | 16.6958i | −0.110359 | − | 0.0451238i | ||||
\(371\) | 364.798 | − | 210.616i | 0.983283 | − | 0.567699i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −298.290 | + | 516.654i | −0.799706 | + | 1.38513i | 0.120102 | + | 0.992762i | \(0.461678\pi\) |
−0.919808 | + | 0.392369i | \(0.871655\pi\) | |||||||
\(374\) | 572.632 | + | 739.264i | 1.53110 | + | 1.97664i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 263.331 | + | 196.397i | 0.700349 | + | 0.522334i | ||||
\(377\) | −53.6569 | −0.142326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.3082i | − | 0.0799689i | −0.999200 | − | 0.0399844i | \(-0.987269\pi\) | ||
0.999200 | − | 0.0399844i | \(-0.0127308\pi\) | |||||||
\(380\) | −21.7419 | − | 5.61373i | −0.0572155 | − | 0.0147730i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −180.541 | − | 233.077i | −0.472620 | − | 0.610150i | ||||
\(383\) | −612.470 | − | 353.610i | −1.59914 | − | 0.923264i | −0.991653 | − | 0.128934i | \(-0.958845\pi\) |
−0.607486 | − | 0.794330i | \(-0.707822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −57.5805 | − | 99.7323i | −0.149560 | − | 0.259045i | ||||
\(386\) | −46.5845 | − | 19.0475i | −0.120685 | − | 0.0493460i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 217.857 | + | 213.920i | 0.561488 | + | 0.551339i | ||||
\(389\) | −288.544 | − | 499.773i | −0.741758 | − | 1.28476i | −0.951694 | − | 0.307048i | \(-0.900659\pi\) |
0.209936 | − | 0.977715i | \(-0.432674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −681.580 | − | 393.511i | −1.74317 | − | 1.00642i | ||||
\(392\) | 101.958 | + | 12.0067i | 0.260097 | + | 0.0306292i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −104.122 | − | 763.948i | −0.264268 | − | 1.93896i | ||||
\(395\) | 44.3392i | 0.112251i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.8266 | 0.0675733 | 0.0337867 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337867 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(398\) | −240.547 | + | 32.7851i | −0.604390 | + | 0.0823747i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 333.659 | + | 184.608i | 0.834149 | + | 0.461520i | ||||
\(401\) | 252.532 | − | 437.399i | 0.629756 | − | 1.09077i | −0.357844 | − | 0.933781i | \(-0.616488\pi\) |
0.987600 | − | 0.156989i | \(-0.0501787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −482.164 | + | 278.378i | −1.19644 | + | 0.690763i | ||||
\(404\) | −206.077 | − | 202.352i | −0.510091 | − | 0.500872i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.6718 | + | 48.1113i | −0.0484528 | + | 0.118501i | ||||
\(407\) | −313.392 | + | 180.937i | −0.770005 | + | 0.444563i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 341.664 | − | 591.780i | 0.835364 | − | 1.44689i | −0.0583688 | − | 0.998295i | \(-0.518590\pi\) |
0.893733 | − | 0.448599i | \(-0.148077\pi\) | |||||||
\(410\) | 101.193 | − | 78.3837i | 0.246812 | − | 0.191180i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −224.538 | − | 57.9754i | −0.544995 | − | 0.140717i | ||||
\(413\) | 174.116 | 0.421588 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.2982i | 0.0922847i | ||||||||
\(416\) | −392.641 | + | 60.8277i | −0.943849 | + | 0.146220i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −145.623 | + | 112.799i | −0.348381 | + | 0.269854i | ||||
\(419\) | −265.541 | − | 153.310i | −0.633749 | − | 0.365895i | 0.148453 | − | 0.988919i | \(-0.452571\pi\) |
−0.782203 | + | 0.623024i | \(0.785904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.29335 | + | 16.0966i | 0.0220745 | + | 0.0382341i | 0.876852 | − | 0.480761i | \(-0.159640\pi\) |
−0.854777 | + | 0.518995i | \(0.826306\pi\) | |||||||
\(422\) | −198.037 | + | 484.339i | −0.469283 | + | 1.14772i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −221.495 | − | 514.709i | −0.522395 | − | 1.21394i | ||||
\(425\) | 314.338 | + | 544.449i | 0.739619 | + | 1.28106i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −95.9164 | − | 55.3774i | −0.224629 | − | 0.129689i | ||||
\(428\) | 68.9396 | + | 248.210i | 0.161074 | + | 0.579930i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 40.9969 | − | 5.58763i | 0.0953416 | − | 0.0129945i | ||||
\(431\) | 308.130i | 0.714918i | 0.933929 | + | 0.357459i | \(0.116357\pi\) | ||||
−0.933929 | + | 0.357459i | \(0.883643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 174.839 | 0.403785 | 0.201893 | − | 0.979408i | \(-0.435291\pi\) | ||||
0.201893 | + | 0.979408i | \(0.435291\pi\) | |||||||
\(434\) | 72.8342 | + | 534.391i | 0.167821 | + | 1.23131i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 166.371 | − | 46.2090i | 0.381584 | − | 0.105984i | ||||
\(437\) | 77.5152 | − | 134.260i | 0.177380 | − | 0.307232i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 415.830 | − | 240.079i | 0.947220 | − | 0.546878i | 0.0550040 | − | 0.998486i | \(-0.482483\pi\) |
0.892216 | + | 0.451608i | \(0.149150\pi\) | |||||||
\(440\) | −140.716 | + | 60.5547i | −0.319810 | + | 0.137624i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −606.328 | − | 247.917i | −1.37178 | − | 0.560897i | ||||
\(443\) | −481.477 | + | 277.981i | −1.08686 | + | 0.627497i | −0.932738 | − | 0.360556i | \(-0.882587\pi\) |
−0.154119 | + | 0.988052i | \(0.549254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.2492 | − | 24.6804i | 0.0320207 | − | 0.0554615i | ||||
\(446\) | −85.7986 | − | 110.765i | −0.192373 | − | 0.248353i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −89.4102 | + | 374.362i | −0.199576 | + | 0.835629i | ||||
\(449\) | 801.711 | 1.78555 | 0.892774 | − | 0.450504i | \(-0.148756\pi\) | ||||
0.892774 | + | 0.450504i | \(0.148756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1050.00i | − | 2.32816i | ||||||
\(452\) | 81.2965 | − | 314.860i | 0.179859 | − | 0.696593i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −365.410 | − | 471.743i | −0.804868 | − | 1.03908i | ||||
\(455\) | 69.8640 | + | 40.3360i | 0.153547 | + | 0.0886506i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 68.9149 | + | 119.364i | 0.150798 | + | 0.261190i | 0.931521 | − | 0.363687i | \(-0.118482\pi\) |
−0.780723 | + | 0.624877i | \(0.785149\pi\) | |||||||
\(458\) | −480.701 | − | 196.550i | −1.04956 | − | 0.429148i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 90.3344 | − | 91.9971i | 0.196379 | − | 0.199994i | ||||
\(461\) | 94.1705 | + | 163.108i | 0.204274 | + | 0.353814i | 0.949901 | − | 0.312550i | \(-0.101183\pi\) |
−0.745627 | + | 0.666364i | \(0.767850\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 474.950 | + | 274.212i | 1.02581 | + | 0.592251i | 0.915781 | − | 0.401677i | \(-0.131573\pi\) |
0.110028 | + | 0.993928i | \(0.464906\pi\) | |||||||
\(464\) | 60.5003 | + | 33.4738i | 0.130389 | + | 0.0721419i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.99379 | − | 14.6286i | −0.00427852 | − | 0.0313918i | ||||
\(467\) | − | 618.597i | − | 1.32462i | −0.749231 | − | 0.662309i | \(-0.769577\pi\) | ||
0.749231 | − | 0.662309i | \(-0.230423\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −570.580 | −1.21659 | ||||||||
\(470\) | −87.9133 | + | 11.9820i | −0.187050 | + | 0.0254937i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 27.0883 | − | 230.028i | 0.0573904 | − | 0.487347i | ||||
\(473\) | 169.706 | − | 293.939i | 0.358786 | − | 0.621435i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −107.248 | + | 61.9195i | −0.225785 | + | 0.130357i | ||||
\(476\) | −444.587 | + | 452.771i | −0.934007 | + | 0.951199i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −62.1641 | + | 152.034i | −0.130050 | + | 0.318064i | ||||
\(479\) | 667.208 | − | 385.213i | 1.39292 | − | 0.804202i | 0.399281 | − | 0.916829i | \(-0.369260\pi\) |
0.993637 | + | 0.112627i | \(0.0359265\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 126.749 | − | 219.536i | 0.263512 | − | 0.456416i | ||||
\(482\) | −657.480 | + | 509.282i | −1.36407 | + | 1.05660i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −193.164 | + | 748.121i | −0.399099 | + | 1.54571i | ||||
\(485\) | −82.4655 | −0.170032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 549.208i | 1.12774i | 0.825865 | + | 0.563868i | \(0.190687\pi\) | ||||
−0.825865 | + | 0.563868i | \(0.809313\pi\) | |||||||
\(488\) | −88.0824 | + | 118.102i | −0.180497 | + | 0.242012i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.9211 | + | 16.9800i | −0.0447369 | + | 0.0346530i | ||||
\(491\) | 19.9407 | + | 11.5128i | 0.0406125 | + | 0.0234476i | 0.520169 | − | 0.854063i | \(-0.325869\pi\) |
−0.479556 | + | 0.877511i | \(0.659202\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 56.9969 | + | 98.7215i | 0.115612 | + | 0.200246i | ||||
\(494\) | 48.8355 | − | 119.437i | 0.0988573 | − | 0.241775i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 717.325 | − | 13.0842i | 1.44622 | − | 0.0263795i | ||||
\(497\) | −252.263 | − | 436.932i | −0.507572 | − | 0.879140i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 542.833 | + | 313.405i | 1.08784 | + | 0.628065i | 0.933001 | − | 0.359874i | \(-0.117180\pi\) |
0.154840 | + | 0.987939i | \(0.450514\pi\) | |||||||
\(500\) | −203.332 | + | 56.4748i | −0.406663 | + | 0.112950i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 277.495 | − | 37.8209i | 0.552780 | − | 0.0753405i | ||||
\(503\) | − | 732.896i | − | 1.45705i | −0.685019 | − | 0.728525i | \(-0.740206\pi\) | ||
0.685019 | − | 0.728525i | \(-0.259794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 78.0062 | 0.154468 | ||||||||
\(506\) | −142.831 | − | 1047.96i | −0.282275 | − | 2.07108i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 205.495 | + | 739.865i | 0.404518 | + | 1.45643i | ||||
\(509\) | 218.682 | − | 378.768i | 0.429630 | − | 0.744140i | −0.567211 | − | 0.823573i | \(-0.691977\pi\) |
0.996840 | + | 0.0794323i | \(0.0253108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 290.789 | − | 167.887i | 0.569058 | − | 0.328546i | ||||
\(512\) | 480.666 | + | 176.363i | 0.938801 | + | 0.344459i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −124.000 | − | 50.7013i | −0.241245 | − | 0.0986407i | ||||
\(515\) | 54.2431 | − | 31.3173i | 0.105326 | − | 0.0608102i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −363.915 | + | 630.319i | −0.703897 | + | 1.21919i | ||||
\(518\) | −150.377 | − | 194.136i | −0.290304 | − | 0.374780i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 64.1579 | − | 86.0234i | 0.123381 | − | 0.165430i | ||||
\(521\) | 385.236 | 0.739417 | 0.369709 | − | 0.929148i | \(-0.379458\pi\) | ||||
0.369709 | + | 0.929148i | \(0.379458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 418.572i | 0.800328i | 0.916443 | + | 0.400164i | \(0.131047\pi\) | ||||
−0.916443 | + | 0.400164i | \(0.868953\pi\) | |||||||
\(524\) | 549.179 | + | 141.797i | 1.04805 | + | 0.270606i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.5805 | + | 58.8442i | 0.0866549 | + | 0.111871i | ||||
\(527\) | 1024.35 | + | 591.411i | 1.94375 | + | 1.12222i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 180.582 | + | 312.777i | 0.341365 | + | 0.591261i | ||||
\(530\) | 140.086 | + | 57.2786i | 0.264313 | + | 0.108073i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −89.1885 | − | 87.5765i | −0.167648 | − | 0.164617i | ||||
\(533\) | 367.770 | + | 636.996i | 0.690000 | + | 1.19511i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −60.2554 | − | 34.7885i | −0.112627 | − | 0.0650252i | ||||
\(536\) | −88.7687 | + | 753.805i | −0.165613 | + | 1.40635i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −75.3800 | − | 553.070i | −0.140112 | − | 1.02801i | ||||
\(539\) | 227.457i | 0.421999i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4257 | −0.0433008 | −0.0216504 | − | 0.999766i | \(-0.506892\pi\) | ||||
−0.0216504 | + | 0.999766i | \(0.506892\pi\) | |||||||
\(542\) | 805.167 | − | 109.739i | 1.48555 | − | 0.202471i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 528.997 | + | 657.793i | 0.972421 | + | 1.20918i | ||||
\(545\) | −23.3181 | + | 40.3882i | −0.0427855 | + | 0.0741067i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −625.412 | + | 361.082i | −1.14335 | + | 0.660113i | −0.947258 | − | 0.320473i | \(-0.896158\pi\) |
−0.196091 | + | 0.980586i | \(0.562825\pi\) | |||||||
\(548\) | 250.529 | + | 246.001i | 0.457170 | + | 0.448907i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −319.751 | + | 782.013i | −0.581365 | + | 1.42184i | ||||
\(551\) | −19.4465 | + | 11.2275i | −0.0352932 | + | 0.0203765i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −123.409 | + | 213.750i | −0.223162 | + | 0.386528i | ||||
\(554\) | 7.64135 | − | 5.91897i | 0.0137931 | − | 0.0106841i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 710.696 | + | 183.501i | 1.27823 | + | 0.330038i | ||||
\(557\) | 2.34135 | 0.00420349 | 0.00210175 | − | 0.999998i | \(-0.499331\pi\) | ||||
0.00210175 | + | 0.999998i | \(0.499331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 237.763i | 0.425336i | ||||||||
\(560\) | −53.6109 | − | 89.0651i | −0.0957338 | − | 0.159045i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.83282 | + | 5.29268i | −0.0121580 | + | 0.00941757i | ||||
\(563\) | −311.591 | − | 179.897i | −0.553448 | − | 0.319533i | 0.197064 | − | 0.980391i | \(-0.436859\pi\) |
−0.750511 | + | 0.660857i | \(0.770193\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 43.9149 | + | 76.0628i | 0.0777254 | + | 0.134624i | ||||
\(566\) | 33.5799 | − | 82.1262i | 0.0593284 | − | 0.145099i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −616.486 | + | 265.293i | −1.08536 | + | 0.467066i | ||||
\(569\) | 9.31771 | + | 16.1388i | 0.0163756 | + | 0.0283634i | 0.874097 | − | 0.485751i | \(-0.161454\pi\) |
−0.857721 | + | 0.514115i | \(0.828121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −246.409 | − | 142.264i | −0.431539 | − | 0.249149i | 0.268463 | − | 0.963290i | \(-0.413484\pi\) |
−0.700002 | + | 0.714141i | \(0.746818\pi\) | |||||||
\(572\) | −235.585 | − | 848.198i | −0.411861 | − | 1.48286i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 705.994 | − | 96.2227i | 1.22995 | − | 0.167635i | ||||
\(575\) | − | 711.067i | − | 1.23664i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 664.823 | 1.15221 | 0.576104 | − | 0.817377i | \(-0.304572\pi\) | ||||
0.576104 | + | 0.817377i | \(0.304572\pi\) | |||||||
\(578\) | 109.881 | + | 806.206i | 0.190105 | + | 1.39482i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.9938 | + | 4.99773i | −0.0310238 | + | 0.00861677i | ||||
\(581\) | −106.595 | + | 184.627i | −0.183468 | + | 0.317775i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1075.16 | − | 620.744i | 1.84419 | − | 1.06474i | ||||
\(584\) | −176.559 | − | 410.286i | −0.302327 | − | 0.702544i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 719.994 | + | 294.392i | 1.22866 | + | 0.502376i | ||||
\(587\) | −653.388 | + | 377.234i | −1.11310 | + | 0.642647i | −0.939630 | − | 0.342193i | \(-0.888830\pi\) |
−0.173467 | + | 0.984840i | \(0.555497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −116.498 | + | 201.781i | −0.197790 | + | 0.342583i | ||||
\(590\) | 38.3086 | + | 49.4562i | 0.0649298 | + | 0.0838240i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −279.872 | + | 168.463i | −0.472757 | + | 0.284567i | ||||
\(593\) | −550.801 | −0.928838 | −0.464419 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464419 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 171.387i | − | 0.288046i | ||||||
\(596\) | 153.950 | − | 596.246i | 0.258305 | − | 1.00041i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 453.708 | + | 585.735i | 0.758709 | + | 0.979490i | ||||
\(599\) | 22.5070 | + | 12.9944i | 0.0375743 | + | 0.0216935i | 0.518669 | − | 0.854975i | \(-0.326428\pi\) |
−0.481095 | + | 0.876668i | \(0.659761\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −93.0851 | − | 161.228i | −0.154884 | − | 0.268267i | 0.778133 | − | 0.628100i | \(-0.216167\pi\) |
−0.933017 | + | 0.359833i | \(0.882834\pi\) | |||||||
\(602\) | 213.189 | + | 87.1693i | 0.354135 | + | 0.144799i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 519.517 | − | 529.079i | 0.860127 | − | 0.875959i | ||||
\(605\) | −104.344 | − | 180.729i | −0.172469 | − | 0.298725i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 86.2082 | + | 49.7723i | 0.142023 | + | 0.0819972i | 0.569328 | − | 0.822110i | \(-0.307203\pi\) |
−0.427305 | + | 0.904108i | \(0.640537\pi\) | |||||||
\(608\) | −129.575 | + | 104.204i | −0.213116 | + | 0.171388i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.37384 | − | 39.4283i | −0.00880957 | − | 0.0646365i | ||||
\(611\) | − | 509.856i | − | 0.834461i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −960.234 | −1.56645 | −0.783225 | − | 0.621739i | \(-0.786427\pi\) | ||||
−0.783225 | + | 0.621739i | \(0.786427\pi\) | |||||||
\(614\) | −191.628 | + | 26.1177i | −0.312098 | + | 0.0425370i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −846.906 | − | 99.7323i | −1.37485 | − | 0.161903i | ||||
\(617\) | 177.312 | − | 307.114i | 0.287378 | − | 0.497754i | −0.685805 | − | 0.727786i | \(-0.740550\pi\) |
0.973183 | + | 0.230032i | \(0.0738829\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 312.330 | − | 180.324i | 0.504571 | − | 0.291314i | −0.226028 | − | 0.974121i | \(-0.572574\pi\) |
0.730599 | + | 0.682806i | \(0.239241\pi\) | |||||||
\(620\) | −135.765 | + | 138.263i | −0.218975 | + | 0.223006i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 103.082 | − | 252.107i | 0.165727 | − | 0.405317i | ||||
\(623\) | 137.385 | − | 79.3193i | 0.220522 | − | 0.127318i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −269.412 | + | 466.635i | −0.431059 | + | 0.746616i | ||||
\(626\) | 446.136 | − | 345.575i | 0.712677 | − | 0.552037i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 196.164 | − | 759.740i | 0.312363 | − | 1.20978i | ||||
\(629\) | −538.556 | −0.856210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 82.7121i | 0.131081i | 0.997850 | + | 0.0655405i | \(0.0208772\pi\) | ||||
−0.997850 | + | 0.0655405i | \(0.979123\pi\) | |||||||
\(632\) | 263.190 | + | 196.292i | 0.416440 | + | 0.310589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −435.587 | + | 337.404i | −0.687045 | + | 0.532183i | ||||
\(635\) | −179.610 | − | 103.698i | −0.282850 | − | 0.163303i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −79.6687 | − | 137.990i | −0.125069 | − | 0.216625i | ||||
\(638\) | −57.9784 | + | 141.797i | −0.0908752 | + | 0.222253i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −126.006 | + | 56.9700i | −0.196885 | + | 0.0890156i | ||||
\(641\) | 380.284 | + | 658.672i | 0.593267 | + | 1.02757i | 0.993789 | + | 0.111282i | \(0.0354957\pi\) |
−0.400521 | + | 0.916287i | \(0.631171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 681.580 | + | 393.511i | 1.06000 | + | 0.611992i | 0.925432 | − | 0.378913i | \(-0.123702\pi\) |
0.134568 | + | 0.990904i | \(0.457035\pi\) | |||||||
\(644\) | 691.537 | − | 192.073i | 1.07382 | − | 0.298249i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −271.623 | + | 37.0206i | −0.420469 | + | 0.0573074i | ||||
\(647\) | 978.962i | 1.51308i | 0.653948 | + | 0.756539i | \(0.273111\pi\) | ||||
−0.653948 | + | 0.756539i | \(0.726889\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 513.167 | 0.790704 | ||||||||
\(650\) | −79.9247 | − | 586.414i | −0.122961 | − | 0.902176i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −138.438 | − | 498.430i | −0.212328 | − | 0.764464i | ||||
\(653\) | −469.774 | + | 813.672i | −0.719409 | + | 1.24605i | 0.241826 | + | 0.970320i | \(0.422254\pi\) |
−0.961234 | + | 0.275733i | \(0.911079\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −132.669 | + | 76.5963i | −0.202548 | + | 0.116941i | ||||
\(656\) | −17.2858 | − | 947.672i | −0.0263503 | − | 1.44462i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −457.161 | − | 186.925i | −0.694774 | − | 0.284080i | ||||
\(659\) | 129.463 | − | 74.7455i | 0.196454 | − | 0.113423i | −0.398547 | − | 0.917148i | \(-0.630485\pi\) |
0.595000 | + | 0.803726i | \(0.297152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −168.710 | + | 292.214i | −0.255234 | + | 0.442078i | −0.964959 | − | 0.262400i | \(-0.915486\pi\) |
0.709725 | + | 0.704479i | \(0.248819\pi\) | |||||||
\(662\) | 68.0005 | + | 87.7882i | 0.102720 | + | 0.132611i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 227.331 | + | 169.548i | 0.342366 | + | 0.255343i | ||||
\(665\) | 33.7605 | 0.0507677 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 128.933i | − | 0.193303i | ||||||
\(668\) | −534.280 | − | 137.951i | −0.799821 | − | 0.206513i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −125.538 | − | 162.069i | −0.187370 | − | 0.241894i | ||||
\(671\) | −282.692 | − | 163.212i | −0.421300 | − | 0.243238i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 160.670 | + | 278.289i | 0.238737 | + | 0.413505i | 0.960352 | − | 0.278789i | \(-0.0899331\pi\) |
−0.721615 | + | 0.692295i | \(0.756600\pi\) | |||||||
\(674\) | 797.249 | + | 325.981i | 1.18286 | + | 0.483651i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.3344 | − | 41.5692i | −0.0626248 | − | 0.0614929i | ||||
\(677\) | −370.921 | − | 642.454i | −0.547889 | − | 0.948971i | −0.998419 | − | 0.0562100i | \(-0.982098\pi\) |
0.450530 | − | 0.892761i | \(-0.351235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −397.549 | − | 229.525i | −0.585492 | − | 0.338034i | ||||
\(680\) | −226.423 | − | 26.6638i | −0.332975 | − | 0.0392114i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 214.663 | + | 1575.00i | 0.314754 | + | 2.30938i | ||||
\(683\) | 1259.02i | 1.84337i | 0.387938 | + | 0.921686i | \(0.373188\pi\) | ||||
−0.387938 | + | 0.921686i | \(0.626812\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −94.8328 | −0.138442 | ||||||||
\(686\) | −736.902 | + | 100.435i | −1.07420 | + | 0.146407i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 148.328 | − | 268.087i | 0.215593 | − | 0.389662i | ||||
\(689\) | −434.841 | + | 753.167i | −0.631119 | + | 1.09313i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −192.924 | + | 111.385i | −0.279196 | + | 0.161194i | −0.633059 | − | 0.774103i | \(-0.718201\pi\) |
0.353864 | + | 0.935297i | \(0.384868\pi\) | |||||||
\(692\) | 457.890 | + | 449.614i | 0.661691 | + | 0.649731i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 102.845 | − | 251.528i | 0.148192 | − | 0.362432i | ||||
\(695\) | −171.687 | + | 99.1238i | −0.247032 | + | 0.142624i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 781.325 | − | 1353.29i | 1.12098 | − | 1.94160i | ||||
\(698\) | 455.498 | − | 352.827i | 0.652575 | − | 0.505483i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −555.109 | − | 143.329i | −0.793013 | − | 0.204755i | ||||
\(701\) | 2.34135 | 0.00334001 | 0.00167000 | − | 0.999999i | \(-0.499468\pi\) | ||||
0.00167000 | + | 0.999999i | \(0.499468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 106.087i | − | 0.150906i | ||||||
\(704\) | −263.517 | + | 1103.35i | −0.374313 | + | 1.56725i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 314.590 | − | 243.680i | 0.445595 | − | 0.345156i | ||||
\(707\) | 376.052 | + | 217.113i | 0.531898 | + | 0.307091i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 247.543 | + | 428.756i | 0.349143 | + | 0.604734i | 0.986098 | − | 0.166168i | \(-0.0531393\pi\) |
−0.636954 | + | 0.770902i | \(0.719806\pi\) | |||||||
\(710\) | 68.6047 | − | 167.786i | 0.0966264 | − | 0.236319i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −83.4164 | − | 193.842i | −0.117158 | − | 0.272250i | ||||
\(713\) | −668.919 | − | 1158.60i | −0.938175 | − | 1.62497i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 205.909 | + | 118.881i | 0.287984 | + | 0.166268i | ||||
\(716\) | −215.665 | − | 776.481i | −0.301209 | − | 1.08447i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −643.368 | + | 87.6871i | −0.896055 | + | 0.122127i | ||||
\(719\) | 962.433i | 1.33857i | 0.743005 | + | 0.669286i | \(0.233400\pi\) | ||||
−0.743005 | + | 0.669286i | \(0.766600\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 348.659 | 0.483578 | ||||||||
\(722\) | 90.2103 | + | 661.881i | 0.124945 | + | 0.916732i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 185.969 | − | 51.6525i | 0.256864 | − | 0.0713432i | ||||
\(725\) | −51.4962 | + | 89.1940i | −0.0710292 | + | 0.123026i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −471.659 | + | 272.313i | −0.648775 | + | 0.374570i | −0.787987 | − | 0.615692i | \(-0.788876\pi\) |
0.139212 | + | 0.990263i | \(0.455543\pi\) | |||||||
\(728\) | 548.719 | − | 236.131i | 0.753735 | − | 0.324356i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 111.666 | + | 45.6580i | 0.152967 | + | 0.0625453i | ||||
\(731\) | 437.452 | − | 252.563i | 0.598429 | − | 0.345503i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 73.0851 | − | 126.587i | 0.0997069 | − | 0.172697i | −0.811856 | − | 0.583857i | \(-0.801543\pi\) |
0.911563 | + | 0.411160i | \(0.134876\pi\) | |||||||
\(734\) | −215.728 | − | 278.503i | −0.293907 | − | 0.379432i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −146.164 | − | 943.485i | −0.198592 | − | 1.28191i | ||||
\(737\) | −1681.66 | −2.28176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1172.87i | − | 1.58710i | −0.608505 | − | 0.793550i | \(-0.708231\pi\) | ||
0.608505 | − | 0.793550i | \(-0.291769\pi\) | |||||||
\(740\) | 22.0571 | − | 85.4269i | 0.0298069 | − | 0.115442i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 515.902 | + | 666.027i | 0.695286 | + | 0.897611i | ||||
\(743\) | −428.541 | − | 247.418i | −0.576771 | − | 0.332999i | 0.183078 | − | 0.983098i | \(-0.441394\pi\) |
−0.759849 | + | 0.650099i | \(0.774727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 83.1610 | + | 144.039i | 0.111625 | + | 0.193341i | ||||
\(746\) | −1104.41 | − | 451.572i | −1.48044 | − | 0.605324i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1310.32 | + | 1334.44i | −1.75177 | + | 1.78401i | ||||
\(749\) | −193.653 | − | 335.416i | −0.258548 | − | 0.447819i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −803.022 | − | 463.625i | −1.06927 | − | 0.617344i | −0.141289 | − | 0.989968i | \(-0.545125\pi\) |
−0.927982 | + | 0.372625i | \(0.878458\pi\) | |||||||
\(752\) | −318.073 | + | 574.883i | −0.422970 | + | 0.764472i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.4922 | − | 106.331i | −0.0192205 | − | 0.141022i | ||||
\(755\) | 200.272i | 0.265261i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −757.748 | −1.00099 | −0.500494 | − | 0.865740i | \(-0.666848\pi\) | ||||
−0.500494 | + | 0.865740i | \(0.666848\pi\) | |||||||
\(758\) | 60.0611 | − | 8.18596i | 0.0792363 | − | 0.0107994i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.25233 | − | 44.6017i | 0.00691096 | − | 0.0586864i | ||||
\(761\) | −476.570 | + | 825.443i | −0.626241 | + | 1.08468i | 0.362058 | + | 0.932156i | \(0.382074\pi\) |
−0.988299 | + | 0.152526i | \(0.951259\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −224.823 | + | 129.802i | −0.294657 | + | 0.170120i | ||||
\(764\) | 413.122 | − | 420.726i | 0.540736 | − | 0.550689i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 535.319 | − | 1309.23i | 0.698850 | − | 1.70917i | ||||
\(767\) | −311.320 | + | 179.741i | −0.405893 | + | 0.234343i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −72.8375 | + | 126.158i | −0.0947171 | + | 0.164055i | −0.909491 | − | 0.415725i | \(-0.863528\pi\) |
0.814773 | + | 0.579780i | \(0.196861\pi\) | |||||||
\(770\) | 182.085 | − | 141.043i | 0.236475 | − | 0.183172i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.1641 | − | 97.4601i | 0.0325960 | − | 0.126244i | ||||
\(773\) | 60.1391 | 0.0777996 | 0.0388998 | − | 0.999243i | \(-0.487615\pi\) | ||||
0.0388998 | + | 0.999243i | \(0.487615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1068.67i | 1.37893i | ||||||||
\(776\) | −365.079 | + | 489.501i | −0.470462 | + | 0.630800i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 912.456 | − | 706.785i | 1.17282 | − | 0.908464i | ||||
\(779\) | 266.577 | + | 153.908i | 0.342204 | + | 0.197572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −743.489 | − | 1287.76i | −0.951971 | − | 1.64886i | ||||
\(782\) | 595.723 | − | 1456.96i | 0.761794 | − | 1.86312i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.74457 | + | 205.291i | 0.00477623 | + | 0.261851i | ||||
\(785\) | 105.964 | + | 183.535i | 0.134986 | + | 0.233803i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 284.327 | + | 164.156i | 0.361279 | + | 0.208585i | 0.669642 | − | 0.742684i | \(-0.266448\pi\) |
−0.308363 | + | 0.951269i | \(0.599781\pi\) | |||||||
\(788\) | 1485.78 | − | 412.671i | 1.88551 | − | 0.523694i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −87.8661 | + | 11.9756i | −0.111223 | + | 0.0151590i | ||||
\(791\) | 488.910i | 0.618091i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 228.666 | 0.288355 | ||||||||
\(794\) | 7.24562 | + | 53.1617i | 0.00912546 | + | 0.0669543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −129.939 | − | 467.833i | −0.163240 | − | 0.587730i | ||||
\(797\) | 223.363 | − | 386.875i | 0.280254 | − | 0.485414i | −0.691193 | − | 0.722670i | \(-0.742915\pi\) |
0.971447 | + | 0.237256i | \(0.0762479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −938.067 | + | 541.593i | −1.17405 | + | 0.677838i | ||||
\(800\) | −275.716 | + | 711.067i | −0.344645 | + | 0.888833i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 934.991 | + | 382.301i | 1.16582 | + | 0.476684i | ||||
\(803\) | 857.035 | − | 494.809i | 1.06729 | − | 0.616201i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −96.9242 | + | 167.878i | −0.120403 | + | 0.208544i | ||||
\(806\) | −681.883 | − | 880.307i | −0.846009 | − | 1.09219i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 345.337 | − | 463.031i | 0.427398 | − | 0.573059i | ||||
\(809\) | −793.341 | −0.980644 | −0.490322 | − | 0.871541i | \(-0.663121\pi\) | ||||
−0.490322 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 788.930i | 0.972787i | 0.873740 | + | 0.486394i | \(0.161688\pi\) | ||||
−0.873740 | + | 0.486394i | \(0.838312\pi\) | |||||||
\(812\) | −100.654 | − | 25.9888i | −0.123959 | − | 0.0320060i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −443.204 | − | 572.173i | −0.544476 | − | 0.702916i | ||||
\(815\) | 120.999 | + | 69.8588i | 0.148465 | + | 0.0857163i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.7508 | + | 86.1709i | 0.0608945 | + | 0.105472i | ||||
\(818\) | 1265.00 | + | 517.234i | 1.54645 | + | 0.632316i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 182.663 | + | 179.361i | 0.222759 | + | 0.218733i | ||||
\(821\) | 724.377 | + | 1254.66i | 0.882310 | + | 1.52821i | 0.848766 | + | 0.528769i | \(0.177346\pi\) |
0.0335444 | + | 0.999437i | \(0.489320\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −112.530 | − | 64.9693i | −0.136732 | − | 0.0789421i | 0.430074 | − | 0.902794i | \(-0.358488\pi\) |
−0.566805 | + | 0.823852i | \(0.691821\pi\) | |||||||
\(824\) | 54.2431 | − | 460.621i | 0.0658290 | − | 0.559006i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 47.0270 | + | 345.041i | 0.0569335 | + | 0.417726i | ||||
\(827\) | − | 350.389i | − | 0.423687i | −0.977304 | − | 0.211843i | \(-0.932053\pi\) | ||
0.977304 | − | 0.211843i | \(-0.0679467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 167.748 | 0.202349 | 0.101175 | − | 0.994869i | \(-0.467740\pi\) | ||||
0.101175 | + | 0.994869i | \(0.467740\pi\) | |||||||
\(830\) | −75.8947 | + | 10.3440i | −0.0914394 | + | 0.0124626i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −226.590 | − | 761.660i | −0.272344 | − | 0.915457i | ||||
\(833\) | −169.256 | + | 293.160i | −0.203188 | + | 0.351932i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 129.070 | − | 74.5184i | 0.154574 | − | 0.0892436i | ||||
\(836\) | −262.863 | − | 258.112i | −0.314430 | − | 0.308747i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 232.091 | − | 567.625i | 0.276959 | − | 0.677356i | ||||
\(839\) | −573.036 | + | 330.842i | −0.682998 | + | 0.394329i | −0.800984 | − | 0.598686i | \(-0.795690\pi\) |
0.117985 | + | 0.993015i | \(0.462356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 411.163 | − | 712.154i | 0.488897 | − | 0.846795i | ||||
\(842\) | −29.3881 | + | 22.7640i | −0.0349028 | + | 0.0270356i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1013.29 | − | 261.631i | −1.20058 | − | 0.309989i | ||||
\(845\) | 16.0248 | 0.0189643 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1161.67i | − | 1.37151i | ||||||
\(848\) | 960.163 | − | 577.951i | 1.13227 | − | 0.681546i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −994.024 | + | 769.968i | −1.16944 | + | 0.905844i | ||||
\(851\) | 527.527 | + | 304.568i | 0.619891 | + | 0.357894i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.53947 | − | 14.7908i | −0.0100111 | − | 0.0173397i | 0.860976 | − | 0.508645i | \(-0.169853\pi\) |
−0.870988 | + | 0.491305i | \(0.836520\pi\) | |||||||
\(854\) | 83.8340 | − | 205.032i | 0.0981663 | − | 0.240085i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −473.252 | + | 203.655i | −0.552865 | + | 0.237915i | ||||
\(857\) | −211.209 | − | 365.825i | −0.246452 | − | 0.426867i | 0.716087 | − | 0.698011i | \(-0.245931\pi\) |
−0.962539 | + | 0.271144i | \(0.912598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1145.91 | − | 661.590i | −1.33400 | − | 0.770186i | −0.348091 | − | 0.937461i | \(-0.613170\pi\) |
−0.985910 | + | 0.167275i | \(0.946503\pi\) | |||||||
\(860\) | 22.1458 | + | 79.7335i | 0.0257509 | + | 0.0927134i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −610.614 | + | 83.2229i | −0.708369 | + | 0.0965463i | ||||
\(863\) | − | 1455.50i | − | 1.68656i | −0.537473 | − | 0.843281i | \(-0.680621\pi\) | ||
0.537473 | − | 0.843281i | \(-0.319379\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −173.325 | −0.200376 | ||||||||
\(866\) | 47.2224 | + | 346.475i | 0.0545293 | + | 0.400086i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1039.32 | + | 288.668i | −1.19737 | + | 0.332567i | ||||
\(869\) | −363.719 | + | 629.981i | −0.418549 | + | 0.724949i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1020.20 | − | 589.014i | 1.17130 | − | 0.676250i | ||||
\(872\) | 136.507 | + | 317.213i | 0.156544 | + | 0.363776i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 286.997 | + | 117.348i | 0.328372 | + | 0.134265i | ||||
\(875\) | 274.770 | − | 158.639i | 0.314023 | − | 0.181301i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 376.543 | − | 652.191i | 0.429353 | − | 0.743661i | −0.567463 | − | 0.823399i | \(-0.692075\pi\) |
0.996816 | + | 0.0797378i | \(0.0254083\pi\) | |||||||
\(878\) | 588.072 | + | 759.198i | 0.669786 | + | 0.864690i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −158.006 | − | 262.500i | −0.179553 | − | 0.298295i | ||||
\(881\) | 996.177 | 1.13073 | 0.565367 | − | 0.824839i | \(-0.308735\pi\) | ||||
0.565367 | + | 0.824839i | \(0.308735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 950.011i | 1.07589i | 0.842980 | + | 0.537945i | \(0.180799\pi\) | ||||
−0.842980 | + | 0.537945i | \(0.819201\pi\) | |||||||
\(884\) | 327.527 | − | 1268.51i | 0.370506 | − | 1.43496i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −680.912 | − | 879.053i | −0.768523 | − | 0.992159i | ||||
\(887\) | −375.063 | − | 216.543i | −0.422845 | − | 0.244129i | 0.273449 | − | 0.961887i | \(-0.411836\pi\) |
−0.696294 | + | 0.717757i | \(0.745169\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −577.240 | − | 999.809i | −0.649314 | − | 1.12464i | ||||
\(890\) | 52.7572 | + | 21.5714i | 0.0592777 | + | 0.0242376i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 196.328 | − | 199.942i | 0.220099 | − | 0.224150i | ||||
\(893\) | −106.685 | − | 184.784i | −0.119468 | − | 0.206925i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 188.498 | + | 108.830i | 0.210613 | + | 0.121597i | ||||
\(896\) | −766.013 | − | 76.0707i | −0.854926 | − | 0.0849003i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 216.535 | + | 1588.73i | 0.241130 | + | 1.76919i | ||||
\(899\) | 193.775i | 0.215545i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1847.63 | 2.05065 | ||||||||
\(902\) | 2080.76 | − | 283.595i | 2.30683 | − | 0.314407i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 645.909 | + | 76.0628i | 0.714501 | + | 0.0841402i | ||||
\(905\) | −26.0650 | + | 45.1459i | −0.0288011 | + | 0.0498850i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 593.837 | − | 342.852i | 0.654727 | − | 0.378007i | −0.135538 | − | 0.990772i | \(-0.543276\pi\) |
0.790265 | + | 0.612765i | \(0.209943\pi\) | |||||||
\(908\) | 836.148 | − | 851.539i | 0.920868 | − | 0.937818i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −61.0634 | + | 149.342i | −0.0671026 | + | 0.164113i | ||||
\(911\) | −31.2419 | + | 18.0375i | −0.0342941 | + | 0.0197997i | −0.517049 | − | 0.855956i | \(-0.672970\pi\) |
0.482755 | + | 0.875755i | \(0.339636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −314.164 | + | 544.148i | −0.344101 | + | 0.596000i | ||||
\(914\) | −217.928 | + | 168.806i | −0.238433 | + | 0.184690i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 259.666 | − | 1005.68i | 0.283478 | − | 1.09790i | ||||
\(917\) | −852.758 | −0.929943 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 953.775i | − | 1.03784i | −0.854823 | − | 0.518920i | \(-0.826334\pi\) | ||
0.854823 | − | 0.518920i | \(-0.173666\pi\) | |||||||
\(920\) | 206.707 | + | 154.166i | 0.224682 | + | 0.167572i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −297.793 | + | 230.670i | −0.322986 | + | 0.250184i | ||||
\(923\) | 902.096 | + | 520.826i | 0.977353 | + | 0.564275i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −243.290 | − | 421.391i | −0.263016 | − | 0.455558i | ||||
\(926\) | −415.121 | + | 1015.26i | −0.448295 | + | 1.09639i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.9938 | + | 128.933i | −0.0538726 | + | 0.138937i | ||||
\(929\) | 74.8143 | + | 129.582i | 0.0805321 | + | 0.139486i | 0.903479 | − | 0.428633i | \(-0.141005\pi\) |
−0.822947 | + | 0.568119i | \(0.807671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −57.7477 | − | 33.3406i | −0.0620276 | − | 0.0358116i | ||||
\(932\) | 28.4507 | − | 7.90210i | 0.0305265 | − | 0.00847865i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1225.86 | − | 167.077i | 1.31248 | − | 0.178884i | ||||
\(935\) | − | 505.126i | − | 0.540241i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −661.158 | −0.705611 | −0.352806 | − | 0.935697i | \(-0.614772\pi\) | ||||
−0.352806 | + | 0.935697i | \(0.614772\pi\) | |||||||
\(938\) | −154.109 | − | 1130.71i | −0.164295 | − | 1.20544i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −47.4891 | − | 170.980i | −0.0505204 | − | 0.181893i | ||||
\(941\) | 233.357 | − | 404.186i | 0.247988 | − | 0.429528i | −0.714979 | − | 0.699145i | \(-0.753564\pi\) |
0.962967 | + | 0.269618i | \(0.0868973\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1530.65 | + | 883.721i | −1.62317 | + | 0.937138i | ||||
\(944\) | 463.157 | − | 8.44812i | 0.490633 | − | 0.00894928i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 628.328 | + | 256.912i | 0.664195 | + | 0.271577i | ||||
\(947\) | −1128.20 | + | 651.368i | −1.19134 | + | 0.687823i | −0.958611 | − | 0.284718i | \(-0.908100\pi\) |
−0.232732 | + | 0.972541i | \(0.574767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −346.622 | + | 600.366i | −0.365249 | + | 0.632630i | ||||
\(950\) | −151.671 | − | 195.807i | −0.159654 | − | 0.206112i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1017.33 | − | 758.740i | −1.06862 | − | 0.796996i | ||||
\(953\) | −21.6959 | −0.0227659 | −0.0113829 | − | 0.999935i | \(-0.503623\pi\) | ||||
−0.0113829 | + | 0.999935i | \(0.503623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 159.258i | 0.166762i | ||||||||
\(956\) | −318.073 | − | 82.1262i | −0.332713 | − | 0.0859060i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 943.574 | + | 1218.15i | 0.984942 | + | 1.27155i | ||||
\(959\) | −457.169 | − | 263.947i | −0.476714 | − | 0.275231i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 524.825 | + | 909.024i | 0.546124 | + | 0.945914i | ||||
\(962\) | 469.284 | + | 191.882i | 0.487821 | + | 0.199461i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1186.81 | − | 1165.36i | −1.23113 | − | 1.20888i | ||||
\(965\) | 13.5932 | + | 23.5441i | 0.0140862 | + | 0.0243980i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −555.035 | − | 320.449i | −0.573976 | − | 0.331385i | 0.184760 | − | 0.982784i | \(-0.440849\pi\) |
−0.758736 | + | 0.651399i | \(0.774183\pi\) | |||||||
\(968\) | −1534.71 | − | 180.729i | −1.58544 | − | 0.186703i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.2732 | − | 163.420i | −0.0229620 | − | 0.168474i | ||||
\(971\) | − | 1396.09i | − | 1.43779i | −0.695121 | − | 0.718893i | \(-0.744649\pi\) | ||
0.695121 | − | 0.718893i | \(-0.255351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1103.56 | −1.13418 | ||||||||
\(974\) | −1088.35 | + | 148.336i | −1.11741 | + | 0.152296i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −257.830 | − | 142.653i | −0.264170 | − | 0.146161i | ||||
\(977\) | 504.976 | − | 874.644i | 0.516864 | − | 0.895235i | −0.482944 | − | 0.875651i | \(-0.660433\pi\) |
0.999808 | − | 0.0195835i | \(-0.00623402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 404.912 | − | 233.776i | 0.413597 | − | 0.238791i | ||||
\(980\) | −39.5696 | − | 38.8544i | −0.0403771 | − | 0.0396473i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.4288 | + | 42.6256i | −0.0177483 | + | 0.0434069i | ||||
\(983\) | 420.348 | − | 242.688i | 0.427618 | − | 0.246885i | −0.270714 | − | 0.962660i | \(-0.587260\pi\) |
0.698331 | + | 0.715775i | \(0.253926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −208.243 | + | 360.687i | −0.211414 | + | 0.366180i | ||||
\(986\) | −180.240 | + | 139.613i | −0.182799 | + | 0.141596i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 249.875 | + | 64.5175i | 0.252910 | + | 0.0653012i | ||||
\(989\) | −571.325 | −0.577679 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 265.720i | 0.268133i | 0.990972 | + | 0.134066i | \(0.0428035\pi\) | ||||
−0.990972 | + | 0.134066i | \(0.957196\pi\) | |||||||
\(992\) | 219.672 | + | 1417.97i | 0.221443 | + | 1.42941i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 797.726 | − | 617.916i | 0.802541 | − | 0.621646i | ||||
\(995\) | 113.571 | + | 65.5703i | 0.114142 | + | 0.0658998i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 857.906 | + | 1485.94i | 0.860487 | + | 1.49041i | 0.871460 | + | 0.490467i | \(0.163174\pi\) |
−0.0109725 | + | 0.999940i | \(0.503493\pi\) | |||||||
\(998\) | −474.453 | + | 1160.37i | −0.475404 | + | 1.16269i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.3.f.o.271.3 | 8 | ||
3.2 | odd | 2 | inner | 324.3.f.o.271.2 | 8 | ||
4.3 | odd | 2 | 324.3.f.p.271.4 | 8 | |||
9.2 | odd | 6 | 324.3.f.p.55.2 | 8 | |||
9.4 | even | 3 | 108.3.d.d.55.1 | ✓ | 8 | ||
9.5 | odd | 6 | 108.3.d.d.55.8 | yes | 8 | ||
9.7 | even | 3 | 324.3.f.p.55.3 | 8 | |||
12.11 | even | 2 | 324.3.f.p.271.1 | 8 | |||
36.7 | odd | 6 | inner | 324.3.f.o.55.3 | 8 | ||
36.11 | even | 6 | inner | 324.3.f.o.55.2 | 8 | ||
36.23 | even | 6 | 108.3.d.d.55.7 | yes | 8 | ||
36.31 | odd | 6 | 108.3.d.d.55.2 | yes | 8 | ||
72.5 | odd | 6 | 1728.3.g.l.703.4 | 8 | |||
72.13 | even | 6 | 1728.3.g.l.703.6 | 8 | |||
72.59 | even | 6 | 1728.3.g.l.703.3 | 8 | |||
72.67 | odd | 6 | 1728.3.g.l.703.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.d.55.1 | ✓ | 8 | 9.4 | even | 3 | ||
108.3.d.d.55.2 | yes | 8 | 36.31 | odd | 6 | ||
108.3.d.d.55.7 | yes | 8 | 36.23 | even | 6 | ||
108.3.d.d.55.8 | yes | 8 | 9.5 | odd | 6 | ||
324.3.f.o.55.2 | 8 | 36.11 | even | 6 | inner | ||
324.3.f.o.55.3 | 8 | 36.7 | odd | 6 | inner | ||
324.3.f.o.271.2 | 8 | 3.2 | odd | 2 | inner | ||
324.3.f.o.271.3 | 8 | 1.1 | even | 1 | trivial | ||
324.3.f.p.55.2 | 8 | 9.2 | odd | 6 | |||
324.3.f.p.55.3 | 8 | 9.7 | even | 3 | |||
324.3.f.p.271.1 | 8 | 12.11 | even | 2 | |||
324.3.f.p.271.4 | 8 | 4.3 | odd | 2 | |||
1728.3.g.l.703.3 | 8 | 72.59 | even | 6 | |||
1728.3.g.l.703.4 | 8 | 72.5 | odd | 6 | |||
1728.3.g.l.703.5 | 8 | 72.67 | odd | 6 | |||
1728.3.g.l.703.6 | 8 | 72.13 | even | 6 |