Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.796594176.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 83x^{4} - 104x^{3} + 22x^{2} + 24x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.2 | ||
Root | \(1.20711 - 0.0981308i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.67 |
Dual form | 392.3.k.i.275.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.26663 | + | 1.54779i | −0.633316 | + | 0.773893i | ||||
\(3\) | −0.292893 | + | 0.507306i | −0.0976311 | + | 0.169102i | −0.910704 | − | 0.413060i | \(-0.864460\pi\) |
0.813073 | + | 0.582162i | \(0.197793\pi\) | |||||||
\(4\) | −0.791288 | − | 3.92095i | −0.197822 | − | 0.980238i | ||||
\(5\) | −7.82295 | + | 4.51658i | −1.56459 | + | 0.903316i | −0.567807 | + | 0.823162i | \(0.692208\pi\) |
−0.996782 | + | 0.0801541i | \(0.974459\pi\) | |||||||
\(6\) | −0.414214 | − | 1.09591i | −0.0690356 | − | 0.182651i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 7.07107 | + | 3.74166i | 0.883883 | + | 0.467707i | ||||
\(9\) | 4.32843 | + | 7.49706i | 0.480936 | + | 0.833006i | ||||
\(10\) | 2.91809 | − | 17.8291i | 0.291809 | − | 1.78291i | ||||
\(11\) | −6.24264 | + | 10.8126i | −0.567513 | + | 0.982961i | 0.429298 | + | 0.903163i | \(0.358761\pi\) |
−0.996811 | + | 0.0797982i | \(0.974572\pi\) | |||||||
\(12\) | 2.22089 | + | 0.746995i | 0.185074 | + | 0.0622496i | ||||
\(13\) | 9.03316i | 0.694858i | 0.937706 | + | 0.347429i | \(0.112945\pi\) | ||||
−0.937706 | + | 0.347429i | \(0.887055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 5.29150i | − | 0.352767i | ||||||
\(16\) | −14.7477 | + | 6.20520i | −0.921733 | + | 0.387825i | ||||
\(17\) | −6.17157 | + | 10.6895i | −0.363034 | + | 0.628793i | −0.988459 | − | 0.151492i | \(-0.951592\pi\) |
0.625425 | + | 0.780284i | \(0.284926\pi\) | |||||||
\(18\) | −17.0864 | − | 2.79653i | −0.949243 | − | 0.155363i | ||||
\(19\) | −14.4350 | − | 25.0022i | −0.759738 | − | 1.31591i | −0.942984 | − | 0.332838i | \(-0.891994\pi\) |
0.183246 | − | 0.983067i | \(-0.441340\pi\) | |||||||
\(20\) | 23.8995 | + | 27.0995i | 1.19497 | + | 1.35497i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.82843 | − | 23.3578i | −0.401292 | − | 1.06172i | ||||
\(23\) | 21.3404 | − | 12.3209i | 0.927843 | − | 0.535690i | 0.0417142 | − | 0.999130i | \(-0.486718\pi\) |
0.886129 | + | 0.463439i | \(0.153385\pi\) | |||||||
\(24\) | −3.96923 | + | 2.49129i | −0.165385 | + | 0.103804i | ||||
\(25\) | 28.2990 | − | 49.0153i | 1.13196 | − | 1.96061i | ||||
\(26\) | −13.9814 | − | 11.4417i | −0.537746 | − | 0.440065i | ||||
\(27\) | −10.3431 | −0.383079 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 22.4499i | − | 0.774136i | −0.922051 | − | 0.387068i | \(-0.873488\pi\) | ||
0.922051 | − | 0.387068i | \(-0.126512\pi\) | |||||||
\(30\) | 8.19012 | + | 6.70239i | 0.273004 | + | 0.223413i | ||||
\(31\) | −14.5340 | − | 8.39119i | −0.468838 | − | 0.270684i | 0.246915 | − | 0.969037i | \(-0.420583\pi\) |
−0.715753 | + | 0.698353i | \(0.753916\pi\) | |||||||
\(32\) | 9.07561 | − | 30.6860i | 0.283613 | − | 0.958939i | ||||
\(33\) | −3.65685 | − | 6.33386i | −0.110814 | − | 0.191935i | ||||
\(34\) | −8.72792 | − | 23.0919i | −0.256704 | − | 0.679174i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 25.9706 | − | 22.9039i | 0.721405 | − | 0.636219i | ||||
\(37\) | −14.0734 | + | 8.12528i | −0.380362 | + | 0.219602i | −0.677976 | − | 0.735084i | \(-0.737143\pi\) |
0.297614 | + | 0.954686i | \(0.403809\pi\) | |||||||
\(38\) | 56.9819 | + | 9.32624i | 1.49952 | + | 0.245427i | ||||
\(39\) | −4.58258 | − | 2.64575i | −0.117502 | − | 0.0678398i | ||||
\(40\) | −72.2161 | + | 2.66626i | −1.80540 | + | 0.0666565i | ||||
\(41\) | 6.97056 | 0.170014 | 0.0850069 | − | 0.996380i | \(-0.472909\pi\) | ||||
0.0850069 | + | 0.996380i | \(0.472909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.8284 | −0.530894 | −0.265447 | − | 0.964126i | \(-0.585519\pi\) | ||||
−0.265447 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(44\) | 47.3353 | + | 15.9212i | 1.07580 | + | 0.361846i | ||||
\(45\) | −67.7221 | − | 39.0994i | −1.50494 | − | 0.868875i | ||||
\(46\) | −7.96032 | + | 48.6364i | −0.173050 | + | 1.05731i | ||||
\(47\) | 5.36882 | − | 3.09969i | 0.114230 | − | 0.0659509i | −0.441796 | − | 0.897115i | \(-0.645659\pi\) |
0.556027 | + | 0.831165i | \(0.312325\pi\) | |||||||
\(48\) | 1.17157 | − | 9.29907i | 0.0244078 | − | 0.193731i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 40.0208 | + | 105.885i | 0.800416 | + | 2.11770i | ||||
\(51\) | −3.61522 | − | 6.26175i | −0.0708867 | − | 0.122779i | ||||
\(52\) | 35.4186 | − | 7.14783i | 0.681127 | − | 0.137458i | ||||
\(53\) | 6.94131 | + | 4.00757i | 0.130968 | + | 0.0756145i | 0.564053 | − | 0.825739i | \(-0.309241\pi\) |
−0.433084 | + | 0.901353i | \(0.642575\pi\) | |||||||
\(54\) | 13.1010 | − | 16.0090i | 0.242610 | − | 0.296463i | ||||
\(55\) | − | 112.782i | − | 2.05057i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.9117 | 0.296696 | ||||||||
\(58\) | 34.7477 | + | 28.4358i | 0.599099 | + | 0.490273i | ||||
\(59\) | −15.2218 | + | 26.3650i | −0.257997 | + | 0.446864i | −0.965705 | − | 0.259641i | \(-0.916396\pi\) |
0.707708 | + | 0.706505i | \(0.249729\pi\) | |||||||
\(60\) | −20.7477 | + | 4.18710i | −0.345795 | + | 0.0697850i | ||||
\(61\) | 13.1918 | − | 7.61627i | 0.216258 | − | 0.124857i | −0.387958 | − | 0.921677i | \(-0.626819\pi\) |
0.604217 | + | 0.796820i | \(0.293486\pi\) | |||||||
\(62\) | 31.3970 | − | 11.8669i | 0.506403 | − | 0.191402i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36.0000 | + | 52.9150i | 0.562500 | + | 0.826797i | ||||
\(65\) | −40.7990 | − | 70.6659i | −0.627677 | − | 1.08717i | ||||
\(66\) | 14.4353 | + | 2.36263i | 0.218717 | + | 0.0357975i | ||||
\(67\) | 39.3137 | − | 68.0933i | 0.586772 | − | 1.01632i | −0.407880 | − | 0.913035i | \(-0.633732\pi\) |
0.994652 | − | 0.103283i | \(-0.0329348\pi\) | |||||||
\(68\) | 46.7964 | + | 15.7400i | 0.688183 | + | 0.231470i | ||||
\(69\) | 14.4348i | 0.209200i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 17.5345i | 0.246965i | 0.992347 | + | 0.123482i | \(0.0394062\pi\) | ||||
−0.992347 | + | 0.123482i | \(0.960594\pi\) | |||||||
\(72\) | 2.55519 | + | 69.2077i | 0.0354887 | + | 0.961218i | ||||
\(73\) | −23.3431 | + | 40.4315i | −0.319769 | + | 0.553856i | −0.980440 | − | 0.196820i | \(-0.936939\pi\) |
0.660671 | + | 0.750676i | \(0.270272\pi\) | |||||||
\(74\) | 5.24961 | − | 32.0744i | 0.0709407 | − | 0.433437i | ||||
\(75\) | 16.5772 | + | 28.7125i | 0.221029 | + | 0.382833i | ||||
\(76\) | −86.6102 | + | 76.3830i | −1.13961 | + | 1.00504i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.89949 | − | 3.74166i | 0.126917 | − | 0.0479700i | ||||
\(79\) | 70.1762 | − | 40.5163i | 0.888307 | − | 0.512864i | 0.0149184 | − | 0.999889i | \(-0.495251\pi\) |
0.873388 | + | 0.487025i | \(0.161918\pi\) | |||||||
\(80\) | 87.3444 | − | 115.152i | 1.09180 | − | 1.43940i | ||||
\(81\) | −35.9264 | + | 62.2264i | −0.443536 | + | 0.768227i | ||||
\(82\) | −8.82914 | + | 10.7889i | −0.107672 | + | 0.131572i | ||||
\(83\) | 40.3848 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 111.498i | − | 1.31174i | ||||||
\(86\) | 28.9152 | − | 35.3335i | 0.336223 | − | 0.410855i | ||||
\(87\) | 11.3890 | + | 6.57544i | 0.130908 | + | 0.0755797i | ||||
\(88\) | −84.5991 | + | 53.0986i | −0.961353 | + | 0.603393i | ||||
\(89\) | −55.9706 | − | 96.9439i | −0.628883 | − | 1.08926i | −0.987776 | − | 0.155878i | \(-0.950179\pi\) |
0.358894 | − | 0.933379i | \(-0.383154\pi\) | |||||||
\(90\) | 146.296 | − | 55.2949i | 1.62552 | − | 0.614387i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −65.1960 | − | 73.9253i | −0.708652 | − | 0.803536i | ||||
\(93\) | 8.51380 | − | 4.91545i | 0.0915463 | − | 0.0528543i | ||||
\(94\) | −2.00266 | + | 12.2360i | −0.0213049 | + | 0.130170i | ||||
\(95\) | 225.849 | + | 130.394i | 2.37736 | + | 1.37257i | ||||
\(96\) | 12.9090 | + | 13.5918i | 0.134469 | + | 0.141582i | ||||
\(97\) | −164.108 | −1.69183 | −0.845916 | − | 0.533317i | \(-0.820945\pi\) | ||||
−0.845916 | + | 0.533317i | \(0.820945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108.083 | −1.09175 | ||||||||
\(100\) | −214.579 | − | 72.1738i | −2.14579 | − | 0.721738i | ||||
\(101\) | 10.5074 | + | 6.06643i | 0.104033 | + | 0.0600636i | 0.551114 | − | 0.834430i | \(-0.314203\pi\) |
−0.447081 | + | 0.894494i | \(0.647536\pi\) | |||||||
\(102\) | 14.2710 | + | 2.33574i | 0.139912 | + | 0.0228994i | ||||
\(103\) | 92.3029 | − | 53.2911i | 0.896144 | − | 0.517389i | 0.0201970 | − | 0.999796i | \(-0.493571\pi\) |
0.875947 | + | 0.482407i | \(0.160237\pi\) | |||||||
\(104\) | −33.7990 | + | 63.8741i | −0.324990 | + | 0.614174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.9949 | + | 5.66756i | −0.141462 | + | 0.0534675i | ||||
\(107\) | 31.7990 | + | 55.0775i | 0.297187 | + | 0.514743i | 0.975491 | − | 0.220038i | \(-0.0706182\pi\) |
−0.678304 | + | 0.734781i | \(0.737285\pi\) | |||||||
\(108\) | 8.18441 | + | 40.5550i | 0.0757815 | + | 0.375509i | ||||
\(109\) | −113.318 | − | 65.4239i | −1.03961 | − | 0.600220i | −0.119888 | − | 0.992787i | \(-0.538253\pi\) |
−0.919723 | + | 0.392568i | \(0.871587\pi\) | |||||||
\(110\) | 174.562 | + | 142.853i | 1.58693 | + | 1.29866i | ||||
\(111\) | − | 9.51936i | − | 0.0857600i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −138.225 | −1.22323 | −0.611617 | − | 0.791154i | \(-0.709481\pi\) | ||||
−0.611617 | + | 0.791154i | \(0.709481\pi\) | |||||||
\(114\) | −21.4209 | + | 26.1757i | −0.187902 | + | 0.229611i | ||||
\(115\) | −111.296 | + | 192.771i | −0.967795 | + | 1.67627i | ||||
\(116\) | −88.0252 | + | 17.7644i | −0.758838 | + | 0.153141i | ||||
\(117\) | −67.7221 | + | 39.0994i | −0.578821 | + | 0.334183i | ||||
\(118\) | −21.5269 | − | 56.9549i | −0.182431 | − | 0.482668i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 19.7990 | − | 37.4166i | 0.164992 | − | 0.311805i | ||||
\(121\) | −17.4411 | − | 30.2089i | −0.144142 | − | 0.249660i | ||||
\(122\) | −4.92075 | + | 30.0651i | −0.0403340 | + | 0.246435i | ||||
\(123\) | −2.04163 | + | 3.53621i | −0.0165986 | + | 0.0287497i | ||||
\(124\) | −21.4009 | + | 63.6269i | −0.172588 | + | 0.513120i | ||||
\(125\) | 285.430i | 2.28344i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 114.442i | 0.901114i | 0.892748 | + | 0.450557i | \(0.148775\pi\) | ||||
−0.892748 | + | 0.450557i | \(0.851225\pi\) | |||||||
\(128\) | −127.500 | − | 11.3035i | −0.996093 | − | 0.0883088i | ||||
\(129\) | 6.68629 | − | 11.5810i | 0.0518317 | − | 0.0897752i | ||||
\(130\) | 161.053 | + | 26.3596i | 1.23887 | + | 0.202766i | ||||
\(131\) | 84.1751 | + | 145.796i | 0.642558 | + | 1.11294i | 0.984860 | + | 0.173353i | \(0.0554603\pi\) |
−0.342301 | + | 0.939590i | \(0.611206\pi\) | |||||||
\(132\) | −21.9411 | + | 19.3503i | −0.166221 | + | 0.146593i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 55.5980 | + | 147.098i | 0.414910 | + | 1.09775i | ||||
\(135\) | 80.9139 | − | 46.7156i | 0.599362 | − | 0.346042i | ||||
\(136\) | −83.6360 | + | 52.4941i | −0.614970 | + | 0.385986i | ||||
\(137\) | −17.3431 | + | 30.0392i | −0.126592 | + | 0.219264i | −0.922354 | − | 0.386345i | \(-0.873737\pi\) |
0.795762 | + | 0.605610i | \(0.207071\pi\) | |||||||
\(138\) | −22.3420 | − | 18.2836i | −0.161899 | − | 0.132490i | ||||
\(139\) | 107.664 | 0.774561 | 0.387281 | − | 0.921962i | \(-0.373414\pi\) | ||||
0.387281 | + | 0.921962i | \(0.373414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.63151i | 0.0257554i | ||||||||
\(142\) | −27.1397 | − | 22.2098i | −0.191124 | − | 0.156407i | ||||
\(143\) | −97.6717 | − | 56.3908i | −0.683019 | − | 0.394341i | ||||
\(144\) | −110.355 | − | 83.7058i | −0.766356 | − | 0.581290i | ||||
\(145\) | 101.397 | + | 175.625i | 0.699289 | + | 1.21120i | ||||
\(146\) | −33.0122 | − | 87.3421i | −0.226111 | − | 0.598233i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 42.9949 | + | 48.7517i | 0.290506 | + | 0.329403i | ||||
\(149\) | −218.391 | + | 126.088i | −1.46571 | + | 0.846229i | −0.999266 | − | 0.0383198i | \(-0.987799\pi\) |
−0.466447 | + | 0.884549i | \(0.654466\pi\) | |||||||
\(150\) | −65.4380 | − | 10.7102i | −0.436253 | − | 0.0714016i | ||||
\(151\) | −203.071 | − | 117.243i | −1.34484 | − | 0.776444i | −0.357327 | − | 0.933979i | \(-0.616312\pi\) |
−0.987513 | + | 0.157535i | \(0.949645\pi\) | |||||||
\(152\) | −8.52139 | − | 230.803i | −0.0560618 | − | 1.51844i | ||||
\(153\) | −106.853 | −0.698384 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 151.598 | 0.978051 | ||||||||
\(156\) | −6.74773 | + | 20.0616i | −0.0432547 | + | 0.128600i | ||||
\(157\) | −8.74409 | − | 5.04840i | −0.0556948 | − | 0.0321554i | 0.471894 | − | 0.881655i | \(-0.343570\pi\) |
−0.527589 | + | 0.849500i | \(0.676904\pi\) | |||||||
\(158\) | −26.1769 | + | 159.937i | −0.165677 | + | 1.01226i | ||||
\(159\) | −4.06613 | + | 2.34758i | −0.0255731 | + | 0.0147647i | ||||
\(160\) | 67.5980 | + | 281.046i | 0.422487 | + | 1.75654i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −50.8076 | − | 134.424i | −0.313627 | − | 0.829780i | ||||
\(163\) | −52.2670 | − | 90.5291i | −0.320657 | − | 0.555394i | 0.659967 | − | 0.751295i | \(-0.270570\pi\) |
−0.980624 | + | 0.195901i | \(0.937237\pi\) | |||||||
\(164\) | −5.51572 | − | 27.3312i | −0.0336324 | − | 0.166654i | ||||
\(165\) | 57.2147 | + | 33.0329i | 0.346756 | + | 0.200200i | ||||
\(166\) | −51.1526 | + | 62.5070i | −0.308148 | + | 0.376548i | ||||
\(167\) | − | 296.765i | − | 1.77703i | −0.458843 | − | 0.888517i | \(-0.651736\pi\) | ||
0.458843 | − | 0.888517i | \(-0.348264\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.4020 | 0.517172 | ||||||||
\(170\) | 172.575 | + | 141.226i | 1.01514 | + | 0.830744i | ||||
\(171\) | 124.962 | − | 216.440i | 0.730772 | − | 1.26573i | ||||
\(172\) | 18.0639 | + | 89.5092i | 0.105022 | + | 0.520402i | ||||
\(173\) | 34.6671 | − | 20.0150i | 0.200388 | − | 0.115694i | −0.396449 | − | 0.918057i | \(-0.629758\pi\) |
0.596836 | + | 0.802363i | \(0.296424\pi\) | |||||||
\(174\) | −24.6030 | + | 9.29907i | −0.141397 | + | 0.0534429i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 24.9706 | − | 198.198i | 0.141878 | − | 1.12612i | ||||
\(177\) | −8.91674 | − | 15.4442i | −0.0503771 | − | 0.0872556i | ||||
\(178\) | 220.943 | + | 36.1617i | 1.24125 | + | 0.203155i | ||||
\(179\) | −147.397 | + | 255.299i | −0.823447 | + | 1.42625i | 0.0796538 | + | 0.996823i | \(0.474619\pi\) |
−0.903101 | + | 0.429429i | \(0.858715\pi\) | |||||||
\(180\) | −99.7191 | + | 296.474i | −0.553995 | + | 1.64708i | ||||
\(181\) | 40.4706i | 0.223595i | 0.993731 | + | 0.111797i | \(0.0356608\pi\) | ||||
−0.993731 | + | 0.111797i | \(0.964339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.92302i | 0.0487596i | ||||||||
\(184\) | 197.000 | − | 7.27335i | 1.07065 | − | 0.0395291i | ||||
\(185\) | 73.3970 | − | 127.127i | 0.396740 | − | 0.687174i | ||||
\(186\) | −3.17579 | + | 19.4036i | −0.0170741 | + | 0.104321i | ||||
\(187\) | −77.0538 | − | 133.461i | −0.412053 | − | 0.713696i | ||||
\(188\) | −16.4020 | − | 18.5981i | −0.0872448 | − | 0.0989263i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −487.889 | + | 184.405i | −2.56784 | + | 0.970552i | ||||
\(191\) | −135.905 | + | 78.4647i | −0.711543 | + | 0.410810i | −0.811632 | − | 0.584169i | \(-0.801421\pi\) |
0.100089 | + | 0.994979i | \(0.468087\pi\) | |||||||
\(192\) | −37.3883 | + | 2.76456i | −0.194731 | + | 0.0143988i | ||||
\(193\) | 130.652 | − | 226.296i | 0.676952 | − | 1.17252i | −0.298942 | − | 0.954271i | \(-0.596634\pi\) |
0.975894 | − | 0.218245i | \(-0.0700330\pi\) | |||||||
\(194\) | 207.864 | − | 254.004i | 1.07146 | − | 1.30930i | ||||
\(195\) | 47.7990 | 0.245123 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 145.283i | − | 0.737475i | −0.929533 | − | 0.368738i | \(-0.879790\pi\) | ||
0.929533 | − | 0.368738i | \(-0.120210\pi\) | |||||||
\(198\) | 136.902 | − | 167.290i | 0.691423 | − | 0.844898i | ||||
\(199\) | 338.189 | + | 195.254i | 1.69944 | + | 0.981175i | 0.946283 | + | 0.323339i | \(0.104805\pi\) |
0.753161 | + | 0.657836i | \(0.228528\pi\) | |||||||
\(200\) | 383.502 | − | 240.705i | 1.91751 | − | 1.20353i | ||||
\(201\) | 23.0294 | + | 39.8882i | 0.114574 | + | 0.198449i | ||||
\(202\) | −22.6985 | + | 8.57922i | −0.112369 | + | 0.0424714i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −21.6913 | + | 19.1300i | −0.106330 | + | 0.0937743i | ||||
\(205\) | −54.5303 | + | 31.4831i | −0.266002 | + | 0.153576i | ||||
\(206\) | −34.4305 | + | 210.365i | −0.167138 | + | 1.02119i | ||||
\(207\) | 184.741 | + | 106.660i | 0.892467 | + | 0.515266i | ||||
\(208\) | −56.0526 | − | 133.219i | −0.269484 | − | 0.640474i | ||||
\(209\) | 360.451 | 1.72464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −164.049 | −0.777482 | −0.388741 | − | 0.921347i | \(-0.627090\pi\) | ||||
−0.388741 | + | 0.921347i | \(0.627090\pi\) | |||||||
\(212\) | 10.2209 | − | 30.3877i | 0.0482118 | − | 0.143338i | ||||
\(213\) | −8.89535 | − | 5.13574i | −0.0417622 | − | 0.0241114i | ||||
\(214\) | −125.526 | − | 20.5448i | −0.586569 | − | 0.0960038i | ||||
\(215\) | 178.586 | − | 103.106i | 0.830630 | − | 0.479565i | ||||
\(216\) | −73.1371 | − | 38.7005i | −0.338598 | − | 0.179169i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 244.794 | − | 92.5234i | 1.12291 | − | 0.424419i | ||||
\(219\) | −13.6741 | − | 23.6842i | −0.0624388 | − | 0.108147i | ||||
\(220\) | −442.211 | + | 89.2427i | −2.01005 | + | 0.405648i | ||||
\(221\) | −96.5598 | − | 55.7488i | −0.436922 | − | 0.252257i | ||||
\(222\) | 14.7339 | + | 12.0575i | 0.0663691 | + | 0.0543132i | ||||
\(223\) | − | 10.5830i | − | 0.0474574i | −0.999718 | − | 0.0237287i | \(-0.992446\pi\) | ||
0.999718 | − | 0.0237287i | \(-0.00755379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 489.960 | 2.17760 | ||||||||
\(226\) | 175.081 | − | 213.943i | 0.774693 | − | 0.946652i | ||||
\(227\) | 106.903 | − | 185.162i | 0.470939 | − | 0.815690i | −0.528509 | − | 0.848928i | \(-0.677249\pi\) |
0.999447 | + | 0.0332382i | \(0.0105820\pi\) | |||||||
\(228\) | −13.3820 | − | 66.3099i | −0.0586930 | − | 0.290833i | ||||
\(229\) | −200.942 | + | 116.014i | −0.877478 | + | 0.506612i | −0.869826 | − | 0.493359i | \(-0.835769\pi\) |
−0.00765200 | + | 0.999971i | \(0.502436\pi\) | |||||||
\(230\) | −157.397 | − | 416.433i | −0.684335 | − | 1.81058i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 84.0000 | − | 158.745i | 0.362069 | − | 0.684246i | ||||
\(233\) | 96.4315 | + | 167.024i | 0.413869 | + | 0.716842i | 0.995309 | − | 0.0967472i | \(-0.0308439\pi\) |
−0.581440 | + | 0.813589i | \(0.697511\pi\) | |||||||
\(234\) | 25.2615 | − | 154.344i | 0.107955 | − | 0.659589i | ||||
\(235\) | −28.0000 | + | 48.4974i | −0.119149 | + | 0.206372i | ||||
\(236\) | 115.421 | + | 38.8218i | 0.489071 | + | 0.164499i | ||||
\(237\) | 47.4678i | 0.200286i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 327.917i | 1.37204i | 0.727583 | + | 0.686020i | \(0.240644\pi\) | ||||
−0.727583 | + | 0.686020i | \(0.759356\pi\) | |||||||
\(240\) | 32.8348 | + | 78.0376i | 0.136812 | + | 0.325157i | ||||
\(241\) | −35.9361 | + | 62.2431i | −0.149112 | + | 0.258270i | −0.930900 | − | 0.365275i | \(-0.880975\pi\) |
0.781787 | + | 0.623545i | \(0.214308\pi\) | |||||||
\(242\) | 68.8484 | + | 11.2684i | 0.284498 | + | 0.0465638i | ||||
\(243\) | −67.5894 | − | 117.068i | −0.278146 | − | 0.481762i | ||||
\(244\) | −40.3015 | − | 45.6976i | −0.165170 | − | 0.187285i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.88730 | − | 7.63908i | −0.0117370 | − | 0.0310532i | ||||
\(247\) | 225.849 | − | 130.394i | 0.914368 | − | 0.527911i | ||||
\(248\) | −71.3737 | − | 113.716i | −0.287797 | − | 0.458532i | ||||
\(249\) | −11.8284 | + | 20.4874i | −0.0475037 | + | 0.0822789i | ||||
\(250\) | −441.784 | − | 361.534i | −1.76714 | − | 1.44614i | ||||
\(251\) | −256.919 | −1.02358 | −0.511790 | − | 0.859110i | \(-0.671018\pi\) | ||||
−0.511790 | + | 0.859110i | \(0.671018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 307.659i | 1.21604i | ||||||||
\(254\) | −177.131 | − | 144.955i | −0.697367 | − | 0.570690i | ||||
\(255\) | 56.5634 | + | 32.6569i | 0.221817 | + | 0.128066i | ||||
\(256\) | 178.991 | − | 183.025i | 0.699183 | − | 0.714943i | ||||
\(257\) | −159.676 | − | 276.567i | −0.621308 | − | 1.07614i | −0.989242 | − | 0.146285i | \(-0.953268\pi\) |
0.367934 | − | 0.929852i | \(-0.380065\pi\) | |||||||
\(258\) | 9.45584 | + | 25.0178i | 0.0366506 | + | 0.0969683i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −244.794 | + | 215.888i | −0.941515 | + | 0.830338i | ||||
\(261\) | 168.308 | − | 97.1729i | 0.644860 | − | 0.372310i | ||||
\(262\) | −332.279 | − | 54.3842i | −1.26824 | − | 0.207573i | ||||
\(263\) | −326.800 | − | 188.678i | −1.24259 | − | 0.717408i | −0.272967 | − | 0.962023i | \(-0.588005\pi\) |
−0.969620 | + | 0.244615i | \(0.921338\pi\) | |||||||
\(264\) | −2.15874 | − | 58.4698i | −0.00817705 | − | 0.221477i | ||||
\(265\) | −72.4020 | −0.273215 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 65.5736 | 0.245594 | ||||||||
\(268\) | −298.099 | − | 100.266i | −1.11231 | − | 0.374126i | ||||
\(269\) | 24.3900 | + | 14.0816i | 0.0906691 | + | 0.0523478i | 0.544649 | − | 0.838664i | \(-0.316663\pi\) |
−0.453980 | + | 0.891012i | \(0.649996\pi\) | |||||||
\(270\) | −30.1822 | + | 184.409i | −0.111786 | + | 0.682996i | ||||
\(271\) | −346.164 | + | 199.858i | −1.27736 | + | 0.737482i | −0.976362 | − | 0.216143i | \(-0.930652\pi\) |
−0.300995 | + | 0.953626i | \(0.597319\pi\) | |||||||
\(272\) | 24.6863 | − | 195.941i | 0.0907584 | − | 0.720373i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.5269 | − | 64.8921i | −0.0895143 | − | 0.236833i | ||||
\(275\) | 353.321 | + | 611.970i | 1.28480 | + | 2.22534i | ||||
\(276\) | 56.5982 | − | 11.4221i | 0.205066 | − | 0.0413844i | ||||
\(277\) | −89.1579 | − | 51.4753i | −0.321870 | − | 0.185831i | 0.330356 | − | 0.943856i | \(-0.392831\pi\) |
−0.652226 | + | 0.758025i | \(0.726165\pi\) | |||||||
\(278\) | −136.371 | + | 166.641i | −0.490542 | + | 0.599428i | ||||
\(279\) | − | 145.283i | − | 0.520726i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.235 | −0.534646 | −0.267323 | − | 0.963607i | \(-0.586139\pi\) | ||||
−0.267323 | + | 0.963607i | \(0.586139\pi\) | |||||||
\(282\) | −5.62081 | − | 4.59979i | −0.0199319 | − | 0.0163113i | ||||
\(283\) | 89.2807 | − | 154.639i | 0.315480 | − | 0.546427i | −0.664060 | − | 0.747679i | \(-0.731168\pi\) |
0.979539 | + | 0.201253i | \(0.0645013\pi\) | |||||||
\(284\) | 68.7519 | − | 13.8748i | 0.242084 | − | 0.0488551i | ||||
\(285\) | −132.299 | + | 76.3830i | −0.464208 | + | 0.268011i | ||||
\(286\) | 210.995 | − | 79.7486i | 0.737745 | − | 0.278841i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 269.338 | − | 64.7820i | 0.935202 | − | 0.224937i | ||||
\(289\) | 68.3234 | + | 118.340i | 0.236413 | + | 0.409479i | ||||
\(290\) | −400.262 | − | 65.5109i | −1.38021 | − | 0.225900i | ||||
\(291\) | 48.0660 | − | 83.2528i | 0.165175 | − | 0.286092i | ||||
\(292\) | 177.001 | + | 59.5344i | 0.606168 | + | 0.203885i | ||||
\(293\) | 219.189i | 0.748085i | 0.927411 | + | 0.374043i | \(0.122029\pi\) | ||||
−0.927411 | + | 0.374043i | \(0.877971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 275.002i | − | 0.932211i | ||||||
\(296\) | −129.916 | + | 4.79657i | −0.438905 | + | 0.0162046i | ||||
\(297\) | 64.5685 | − | 111.836i | 0.217402 | − | 0.376552i | ||||
\(298\) | 81.4635 | − | 497.730i | 0.273368 | − | 1.67024i | ||||
\(299\) | 111.296 | + | 192.771i | 0.372229 | + | 0.644720i | ||||
\(300\) | 99.4630 | − | 87.7181i | 0.331543 | − | 0.292394i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 438.683 | − | 165.807i | 1.45259 | − | 0.549029i | ||||
\(303\) | −6.15507 | + | 3.55363i | −0.0203138 | + | 0.0117282i | ||||
\(304\) | 368.028 | + | 279.153i | 1.21062 | + | 0.918268i | ||||
\(305\) | −68.7990 | + | 119.163i | −0.225570 | + | 0.390699i | ||||
\(306\) | 135.343 | − | 165.385i | 0.442298 | − | 0.540475i | ||||
\(307\) | 316.669 | 1.03150 | 0.515748 | − | 0.856741i | \(-0.327514\pi\) | ||||
0.515748 | + | 0.856741i | \(0.327514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 62.4344i | 0.202053i | ||||||||
\(310\) | −192.019 | + | 234.641i | −0.619416 | + | 0.756908i | ||||
\(311\) | 62.5836 | + | 36.1326i | 0.201233 | + | 0.116182i | 0.597231 | − | 0.802070i | \(-0.296268\pi\) |
−0.395997 | + | 0.918252i | \(0.629601\pi\) | |||||||
\(312\) | −22.5042 | − | 35.8547i | −0.0721289 | − | 0.114919i | ||||
\(313\) | −40.9756 | − | 70.9718i | −0.130913 | − | 0.226747i | 0.793116 | − | 0.609071i | \(-0.208457\pi\) |
−0.924029 | + | 0.382323i | \(0.875124\pi\) | |||||||
\(314\) | 18.8894 | − | 7.13952i | 0.0601573 | − | 0.0227373i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −214.392 | − | 243.098i | −0.678455 | − | 0.769296i | ||||
\(317\) | 94.5267 | − | 54.5750i | 0.298191 | − | 0.172161i | −0.343439 | − | 0.939175i | \(-0.611592\pi\) |
0.641630 | + | 0.767014i | \(0.278258\pi\) | |||||||
\(318\) | 1.51673 | − | 9.26702i | 0.00476960 | − | 0.0291416i | ||||
\(319\) | 242.742 | + | 140.147i | 0.760945 | + | 0.439332i | ||||
\(320\) | −520.621 | − | 251.355i | −1.62694 | − | 0.785483i | ||||
\(321\) | −37.2548 | −0.116059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 356.347 | 1.10324 | ||||||||
\(324\) | 272.415 | + | 91.6267i | 0.840786 | + | 0.282799i | ||||
\(325\) | 442.763 | + | 255.629i | 1.36235 | + | 0.786552i | ||||
\(326\) | 206.323 | + | 33.7689i | 0.632892 | + | 0.103586i | ||||
\(327\) | 66.3799 | − | 38.3245i | 0.202997 | − | 0.117200i | ||||
\(328\) | 49.2893 | + | 26.0815i | 0.150272 | + | 0.0795166i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −123.598 | + | 46.7156i | −0.374539 | + | 0.141563i | ||||
\(331\) | −160.870 | − | 278.635i | −0.486012 | − | 0.841798i | 0.513858 | − | 0.857875i | \(-0.328216\pi\) |
−0.999871 | + | 0.0160770i | \(0.994882\pi\) | |||||||
\(332\) | −31.9560 | − | 158.347i | −0.0962530 | − | 0.476948i | ||||
\(333\) | −121.831 | − | 70.3394i | −0.365860 | − | 0.211229i | ||||
\(334\) | 459.329 | + | 375.892i | 1.37524 | + | 1.12542i | ||||
\(335\) | 710.254i | 2.12016i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −164.049 | −0.486792 | −0.243396 | − | 0.969927i | \(-0.578261\pi\) | ||||
−0.243396 | + | 0.969927i | \(0.578261\pi\) | |||||||
\(338\) | −110.706 | + | 135.280i | −0.327533 | + | 0.400236i | ||||
\(339\) | 40.4853 | − | 70.1226i | 0.119426 | − | 0.206851i | ||||
\(340\) | −437.177 | + | 88.2267i | −1.28581 | + | 0.259490i | ||||
\(341\) | 181.461 | − | 104.766i | 0.532143 | − | 0.307233i | ||||
\(342\) | 176.723 | + | 467.565i | 0.516734 | + | 1.36715i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −161.421 | − | 85.4162i | −0.469248 | − | 0.248303i | ||||
\(345\) | −65.1960 | − | 112.923i | −0.188974 | − | 0.327312i | ||||
\(346\) | −12.9314 | + | 79.0089i | −0.0373740 | + | 0.228349i | ||||
\(347\) | 165.154 | − | 286.056i | 0.475949 | − | 0.824368i | −0.523671 | − | 0.851920i | \(-0.675438\pi\) |
0.999620 | + | 0.0275524i | \(0.00877132\pi\) | |||||||
\(348\) | 16.7700 | − | 49.8587i | 0.0481897 | − | 0.143272i | ||||
\(349\) | − | 262.402i | − | 0.751869i | −0.926646 | − | 0.375934i | \(-0.877322\pi\) | ||
0.926646 | − | 0.375934i | \(-0.122678\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 93.4313i | − | 0.266186i | ||||||
\(352\) | 275.139 | + | 289.693i | 0.781646 | + | 0.822990i | ||||
\(353\) | 289.049 | − | 500.647i | 0.818835 | − | 1.41826i | −0.0877061 | − | 0.996146i | \(-0.527954\pi\) |
0.906541 | − | 0.422118i | \(-0.138713\pi\) | |||||||
\(354\) | 35.1986 | + | 5.76096i | 0.0994311 | + | 0.0162739i | ||||
\(355\) | −79.1960 | − | 137.171i | −0.223087 | − | 0.386398i | ||||
\(356\) | −335.823 | + | 296.168i | −0.943324 | + | 0.831934i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −208.451 | − | 551.509i | −0.582265 | − | 1.54053i | ||||
\(359\) | −316.198 | + | 182.557i | −0.880774 | + | 0.508515i | −0.870913 | − | 0.491437i | \(-0.836472\pi\) |
−0.00986020 | + | 0.999951i | \(0.503139\pi\) | |||||||
\(360\) | −332.571 | − | 529.867i | −0.923809 | − | 1.47185i | ||||
\(361\) | −236.240 | + | 409.180i | −0.654405 | + | 1.13346i | ||||
\(362\) | −62.6399 | − | 51.2614i | −0.173038 | − | 0.141606i | ||||
\(363\) | 20.4335 | 0.0562908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 421.725i | − | 1.15541i | ||||||
\(366\) | −13.8109 | − | 11.3022i | −0.0377348 | − | 0.0308803i | ||||
\(367\) | −450.395 | − | 260.036i | −1.22723 | − | 0.708544i | −0.260784 | − | 0.965397i | \(-0.583981\pi\) |
−0.966451 | + | 0.256853i | \(0.917314\pi\) | |||||||
\(368\) | −238.269 | + | 314.126i | −0.647469 | + | 0.853604i | ||||
\(369\) | 30.1716 | + | 52.2587i | 0.0817658 | + | 0.141622i | ||||
\(370\) | 103.799 | + | 274.626i | 0.280538 | + | 0.742233i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.0101 | − | 29.4927i | −0.0699196 | − | 0.0792814i | ||||
\(373\) | −456.145 | + | 263.356i | −1.22291 | + | 0.706048i | −0.965537 | − | 0.260265i | \(-0.916190\pi\) |
−0.257373 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(374\) | 304.168 | + | 49.7832i | 0.813284 | + | 0.133110i | ||||
\(375\) | −144.800 | − | 83.6004i | −0.386134 | − | 0.222934i | ||||
\(376\) | 49.5613 | − | 1.82983i | 0.131812 | − | 0.00486657i | ||||
\(377\) | 202.794 | 0.537915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 121.976 | 0.321835 | 0.160918 | − | 0.986968i | \(-0.448555\pi\) | ||||
0.160918 | + | 0.986968i | \(0.448555\pi\) | |||||||
\(380\) | 332.557 | − | 988.722i | 0.875150 | − | 2.60190i | ||||
\(381\) | −58.0569 | − | 33.5191i | −0.152380 | − | 0.0879768i | ||||
\(382\) | 50.6947 | − | 309.737i | 0.132709 | − | 0.810831i | ||||
\(383\) | −274.033 | + | 158.213i | −0.715492 | + | 0.413089i | −0.813091 | − | 0.582136i | \(-0.802217\pi\) |
0.0975993 | + | 0.995226i | \(0.468884\pi\) | |||||||
\(384\) | 43.0782 | − | 61.3707i | 0.112183 | − | 0.159820i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 184.770 | + | 488.854i | 0.478678 | + | 1.26646i | ||||
\(387\) | −98.8112 | − | 171.146i | −0.255326 | − | 0.442238i | ||||
\(388\) | 129.856 | + | 643.458i | 0.334681 | + | 1.65840i | ||||
\(389\) | −79.8020 | − | 46.0737i | −0.205146 | − | 0.118441i | 0.393907 | − | 0.919150i | \(-0.371123\pi\) |
−0.599054 | + | 0.800709i | \(0.704456\pi\) | |||||||
\(390\) | −60.5437 | + | 73.9826i | −0.155240 | + | 0.189699i | ||||
\(391\) | 304.157i | 0.777895i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −98.6173 | −0.250935 | ||||||||
\(394\) | 224.867 | + | 184.020i | 0.570727 | + | 0.467055i | ||||
\(395\) | −365.990 | + | 633.913i | −0.926557 | + | 1.60484i | ||||
\(396\) | 85.5250 | + | 423.789i | 0.215972 | + | 1.07017i | ||||
\(397\) | 486.937 | − | 281.133i | 1.22654 | − | 0.708144i | 0.260237 | − | 0.965545i | \(-0.416199\pi\) |
0.966305 | + | 0.257400i | \(0.0828659\pi\) | |||||||
\(398\) | −730.573 | + | 276.131i | −1.83561 | + | 0.693795i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −113.196 | + | 898.465i | −0.282990 | + | 2.24616i | ||||
\(401\) | −40.6030 | − | 70.3265i | −0.101254 | − | 0.175378i | 0.810947 | − | 0.585119i | \(-0.198952\pi\) |
−0.912202 | + | 0.409741i | \(0.865619\pi\) | |||||||
\(402\) | −90.9082 | − | 14.8789i | −0.226140 | − | 0.0370123i | ||||
\(403\) | 75.7990 | − | 131.288i | 0.188087 | − | 0.325776i | ||||
\(404\) | 15.4718 | − | 45.9991i | 0.0382966 | − | 0.113859i | ||||
\(405\) | − | 649.058i | − | 1.60261i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 202.893i | − | 0.498508i | ||||||
\(408\) | −2.13416 | − | 57.8042i | −0.00523080 | − | 0.141677i | ||||
\(409\) | −225.368 | + | 390.348i | −0.551021 | + | 0.954396i | 0.447180 | + | 0.894444i | \(0.352428\pi\) |
−0.998201 | + | 0.0599523i | \(0.980905\pi\) | |||||||
\(410\) | 20.3407 | − | 124.279i | 0.0496115 | − | 0.303119i | ||||
\(411\) | −10.1594 | − | 17.5966i | −0.0247187 | − | 0.0428140i | ||||
\(412\) | −281.990 | − | 319.746i | −0.684442 | − | 0.776084i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −399.085 | + | 150.840i | −0.963974 | + | 0.364348i | ||||
\(415\) | −315.928 | + | 182.401i | −0.761272 | + | 0.439521i | ||||
\(416\) | 277.192 | + | 81.9814i | 0.666327 | + | 0.197071i | ||||
\(417\) | −31.5341 | + | 54.6186i | −0.0756212 | + | 0.130980i | ||||
\(418\) | −456.558 | + | 557.901i | −1.09225 | + | 1.33469i | ||||
\(419\) | 624.988 | 1.49162 | 0.745809 | − | 0.666160i | \(-0.232063\pi\) | ||||
0.745809 | + | 0.666160i | \(0.232063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 566.476i | 1.34555i | 0.739848 | + | 0.672774i | \(0.234897\pi\) | ||||
−0.739848 | + | 0.672774i | \(0.765103\pi\) | |||||||
\(422\) | 207.789 | − | 253.913i | 0.492392 | − | 0.601688i | ||||
\(423\) | 46.4771 | + | 26.8336i | 0.109875 | + | 0.0634363i | ||||
\(424\) | 34.0875 | + | 54.3098i | 0.0803952 | + | 0.128089i | ||||
\(425\) | 349.299 | + | 605.003i | 0.821879 | + | 1.42354i | ||||
\(426\) | 19.2162 | − | 7.26303i | 0.0451084 | − | 0.0170494i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 190.794 | − | 168.264i | 0.445780 | − | 0.393141i | ||||
\(429\) | 57.2147 | − | 33.0329i | 0.133368 | − | 0.0769999i | ||||
\(430\) | −66.6154 | + | 407.010i | −0.154920 | + | 0.946535i | ||||
\(431\) | −250.739 | − | 144.764i | −0.581761 | − | 0.335880i | 0.180072 | − | 0.983653i | \(-0.442367\pi\) |
−0.761833 | + | 0.647774i | \(0.775700\pi\) | |||||||
\(432\) | 152.538 | − | 64.1813i | 0.353097 | − | 0.148568i | ||||
\(433\) | −597.696 | −1.38036 | −0.690180 | − | 0.723638i | \(-0.742468\pi\) | ||||
−0.690180 | + | 0.723638i | \(0.742468\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −118.794 | −0.273090 | ||||||||
\(436\) | −166.857 | + | 496.082i | −0.382700 | + | 1.13780i | ||||
\(437\) | −616.098 | − | 355.704i | −1.40984 | − | 0.813969i | ||||
\(438\) | 53.9782 | + | 8.83461i | 0.123238 | + | 0.0201704i | ||||
\(439\) | −33.2458 | + | 19.1945i | −0.0757308 | + | 0.0437232i | −0.537387 | − | 0.843336i | \(-0.680589\pi\) |
0.461656 | + | 0.887059i | \(0.347255\pi\) | |||||||
\(440\) | 421.990 | − | 797.486i | 0.959068 | − | 1.81247i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 208.593 | − | 78.8407i | 0.471930 | − | 0.178373i | ||||
\(443\) | −299.529 | − | 518.799i | −0.676138 | − | 1.17110i | −0.976135 | − | 0.217165i | \(-0.930319\pi\) |
0.299997 | − | 0.953940i | \(-0.403014\pi\) | |||||||
\(444\) | −37.3250 | + | 7.53255i | −0.0840652 | + | 0.0169652i | ||||
\(445\) | 875.709 | + | 505.591i | 1.96789 | + | 1.13616i | ||||
\(446\) | 16.3802 | + | 13.4048i | 0.0367270 | + | 0.0300555i | ||||
\(447\) | − | 147.721i | − | 0.330473i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −460.039 | −1.02459 | −0.512293 | − | 0.858811i | \(-0.671204\pi\) | ||||
−0.512293 | + | 0.858811i | \(0.671204\pi\) | |||||||
\(450\) | −620.599 | + | 758.354i | −1.37911 | + | 1.68523i | ||||
\(451\) | −43.5147 | + | 75.3697i | −0.0964850 | + | 0.167117i | ||||
\(452\) | 109.376 | + | 541.975i | 0.241982 | + | 1.19906i | ||||
\(453\) | 118.956 | − | 68.6794i | 0.262596 | − | 0.151610i | ||||
\(454\) | 151.184 | + | 399.995i | 0.333004 | + | 0.881045i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 119.584 | + | 63.2777i | 0.262245 | + | 0.138767i | ||||
\(457\) | −133.161 | − | 230.642i | −0.291382 | − | 0.504688i | 0.682755 | − | 0.730647i | \(-0.260782\pi\) |
−0.974137 | + | 0.225959i | \(0.927448\pi\) | |||||||
\(458\) | 74.9549 | − | 457.963i | 0.163657 | − | 0.999920i | ||||
\(459\) | 63.8335 | − | 110.563i | 0.139071 | − | 0.240878i | ||||
\(460\) | 843.914 | + | 283.851i | 1.83460 | + | 0.617067i | ||||
\(461\) | − | 763.123i | − | 1.65537i | −0.561196 | − | 0.827683i | \(-0.689659\pi\) | ||
0.561196 | − | 0.827683i | \(-0.310341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 123.988i | 0.267792i | 0.990995 | + | 0.133896i | \(0.0427488\pi\) | ||||
−0.990995 | + | 0.133896i | \(0.957251\pi\) | |||||||
\(464\) | 139.306 | + | 331.086i | 0.300229 | + | 0.713547i | ||||
\(465\) | −44.4020 | + | 76.9066i | −0.0954882 | + | 0.165390i | ||||
\(466\) | −380.661 | − | 62.3028i | −0.816869 | − | 0.133697i | ||||
\(467\) | 384.359 | + | 665.729i | 0.823038 | + | 1.42554i | 0.903409 | + | 0.428779i | \(0.141056\pi\) |
−0.0803710 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(468\) | 206.894 | + | 234.596i | 0.442082 | + | 0.501274i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −39.5980 | − | 104.766i | −0.0842510 | − | 0.222907i | ||||
\(471\) | 5.12217 | − | 2.95729i | 0.0108751 | − | 0.00627874i | ||||
\(472\) | −206.283 | + | 129.474i | −0.437041 | + | 0.274309i | ||||
\(473\) | 142.510 | − | 246.834i | 0.301289 | − | 0.521848i | ||||
\(474\) | −73.4700 | − | 60.1242i | −0.155000 | − | 0.126844i | ||||
\(475\) | −1633.99 | −3.43997 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 69.3859i | 0.145463i | ||||||||
\(478\) | −507.546 | − | 415.351i | −1.06181 | − | 0.868934i | ||||
\(479\) | 103.041 | + | 59.4905i | 0.215116 | + | 0.124197i | 0.603687 | − | 0.797222i | \(-0.293698\pi\) |
−0.388571 | + | 0.921419i | \(0.627031\pi\) | |||||||
\(480\) | −162.375 | − | 48.0236i | −0.338282 | − | 0.100049i | ||||
\(481\) | −73.3970 | − | 127.127i | −0.152592 | − | 0.264298i | ||||
\(482\) | −50.8213 | − | 134.460i | −0.105438 | − | 0.278964i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −104.647 | + | 92.2898i | −0.216212 | + | 0.190681i | ||||
\(485\) | 1283.81 | − | 741.205i | 2.64702 | − | 1.52826i | ||||
\(486\) | 266.807 | + | 43.6684i | 0.548987 | + | 0.0898527i | ||||
\(487\) | 244.719 | + | 141.288i | 0.502503 | + | 0.290120i | 0.729746 | − | 0.683718i | \(-0.239638\pi\) |
−0.227244 | + | 0.973838i | \(0.572971\pi\) | |||||||
\(488\) | 121.777 | − | 4.49609i | 0.249544 | − | 0.00921330i | ||||
\(489\) | 61.2346 | 0.125224 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −388.049 | −0.790323 | −0.395162 | − | 0.918612i | \(-0.629311\pi\) | ||||
−0.395162 | + | 0.918612i | \(0.629311\pi\) | |||||||
\(492\) | 15.4808 | + | 5.20698i | 0.0314651 | + | 0.0105833i | ||||
\(493\) | 239.978 | + | 138.551i | 0.486771 | + | 0.281037i | ||||
\(494\) | −84.2454 | + | 514.727i | −0.170537 | + | 1.04196i | ||||
\(495\) | 845.530 | − | 488.167i | 1.70814 | − | 0.986195i | ||||
\(496\) | 266.412 | + | 33.5648i | 0.537121 | + | 0.0676709i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −16.7279 | − | 44.2579i | −0.0335902 | − | 0.0888713i | ||||
\(499\) | 13.8579 | + | 24.0025i | 0.0277713 | + | 0.0481013i | 0.879577 | − | 0.475757i | \(-0.157826\pi\) |
−0.851806 | + | 0.523858i | \(0.824492\pi\) | |||||||
\(500\) | 1119.16 | − | 225.857i | 2.23831 | − | 0.451714i | ||||
\(501\) | 150.551 | + | 86.9204i | 0.300500 | + | 0.173494i | ||||
\(502\) | 325.422 | − | 397.656i | 0.648250 | − | 0.792143i | ||||
\(503\) | 727.477i | 1.44628i | 0.690703 | + | 0.723138i | \(0.257301\pi\) | ||||
−0.690703 | + | 0.723138i | \(0.742699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −109.598 | −0.217026 | ||||||||
\(506\) | −476.191 | − | 389.691i | −0.941089 | − | 0.770140i | ||||
\(507\) | −25.5995 | + | 44.3396i | −0.0504920 | + | 0.0874548i | ||||
\(508\) | 448.720 | − | 90.5562i | 0.883307 | − | 0.178260i | ||||
\(509\) | −549.218 | + | 317.091i | −1.07901 | + | 0.622969i | −0.930630 | − | 0.365961i | \(-0.880740\pi\) |
−0.148384 | + | 0.988930i | \(0.547407\pi\) | |||||||
\(510\) | −122.191 | + | 46.1838i | −0.239590 | + | 0.0905565i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 56.5685 | + | 508.865i | 0.110485 | + | 0.993878i | ||||
\(513\) | 149.304 | + | 258.601i | 0.291040 | + | 0.504096i | ||||
\(514\) | 630.318 | + | 103.164i | 1.22630 | + | 0.200709i | ||||
\(515\) | −481.387 | + | 833.787i | −0.934732 | + | 1.61900i | ||||
\(516\) | −50.6993 | − | 17.0527i | −0.0982545 | − | 0.0330479i | ||||
\(517\) | 77.4010i | 0.149712i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4491i | 0.0451813i | ||||||||
\(520\) | −24.0847 | − | 652.339i | −0.0463168 | − | 1.25450i | ||||
\(521\) | −416.563 | + | 721.509i | −0.799546 | + | 1.38485i | 0.120366 | + | 0.992730i | \(0.461593\pi\) |
−0.919912 | + | 0.392125i | \(0.871740\pi\) | |||||||
\(522\) | −62.7819 | + | 383.588i | −0.120272 | + | 0.734843i | ||||
\(523\) | −438.217 | − | 759.014i | −0.837891 | − | 1.45127i | −0.891655 | − | 0.452715i | \(-0.850455\pi\) |
0.0537645 | − | 0.998554i | \(-0.482878\pi\) | |||||||
\(524\) | 505.051 | − | 445.413i | 0.963838 | − | 0.850025i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 705.970 | − | 266.831i | 1.34215 | − | 0.507284i | ||||
\(527\) | 179.395 | − | 103.574i | 0.340408 | − | 0.196535i | ||||
\(528\) | 93.2332 | + | 70.7185i | 0.176578 | + | 0.133937i | ||||
\(529\) | 39.1081 | − | 67.7372i | 0.0739283 | − | 0.128048i | ||||
\(530\) | 91.7067 | − | 112.063i | 0.173032 | − | 0.211439i | ||||
\(531\) | −263.546 | −0.496321 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 62.9662i | 0.118135i | ||||||||
\(534\) | −83.0576 | + | 101.494i | −0.155539 | + | 0.190064i | ||||
\(535\) | −497.524 | − | 287.245i | −0.929951 | − | 0.536907i | ||||
\(536\) | 532.772 | − | 334.394i | 0.993977 | − | 0.623870i | ||||
\(537\) | −86.3431 | − | 149.551i | −0.160788 | − | 0.278493i | ||||
\(538\) | −52.6884 | + | 19.9143i | −0.0979338 | + | 0.0370155i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −247.196 | − | 280.294i | −0.457770 | − | 0.519063i | ||||
\(541\) | 351.532 | − | 202.957i | 0.649783 | − | 0.375152i | −0.138590 | − | 0.990350i | \(-0.544257\pi\) |
0.788373 | + | 0.615198i | \(0.210924\pi\) | |||||||
\(542\) | 129.125 | − | 788.934i | 0.238238 | − | 1.45560i | ||||
\(543\) | −20.5310 | − | 11.8536i | −0.0378103 | − | 0.0218298i | ||||
\(544\) | 272.007 | + | 286.395i | 0.500013 | + | 0.526461i | ||||
\(545\) | 1181.97 | 2.16875 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −606.024 | −1.10791 | −0.553953 | − | 0.832548i | \(-0.686881\pi\) | ||||
−0.553953 | + | 0.832548i | \(0.686881\pi\) | |||||||
\(548\) | 131.506 | + | 44.2320i | 0.239974 | + | 0.0807153i | ||||
\(549\) | 114.199 | + | 65.9329i | 0.208013 | + | 0.120096i | ||||
\(550\) | −1394.73 | − | 228.275i | −2.53587 | − | 0.415045i | ||||
\(551\) | −561.298 | + | 324.066i | −1.01869 | + | 0.588141i | ||||
\(552\) | −54.0101 | + | 102.069i | −0.0978444 | + | 0.184909i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 192.603 | − | 72.7971i | 0.347659 | − | 0.131403i | ||||
\(555\) | 42.9949 | + | 74.4694i | 0.0774684 | + | 0.134179i | ||||
\(556\) | −85.1932 | − | 422.145i | −0.153225 | − | 0.759254i | ||||
\(557\) | 31.5616 | + | 18.2221i | 0.0566635 | + | 0.0327147i | 0.528064 | − | 0.849204i | \(-0.322918\pi\) |
−0.471401 | + | 0.881919i | \(0.656251\pi\) | |||||||
\(558\) | 224.867 | + | 184.020i | 0.402987 | + | 0.329784i | ||||
\(559\) | − | 206.213i | − | 0.368896i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 90.2742 | 0.160917 | ||||||||
\(562\) | 190.293 | − | 232.533i | 0.338600 | − | 0.413759i | ||||
\(563\) | 93.1945 | − | 161.418i | 0.165532 | − | 0.286710i | −0.771312 | − | 0.636457i | \(-0.780399\pi\) |
0.936844 | + | 0.349747i | \(0.113733\pi\) | |||||||
\(564\) | 14.2390 | − | 2.87357i | 0.0252464 | − | 0.00509499i | ||||
\(565\) | 1081.33 | − | 624.306i | 1.91386 | − | 1.10497i | ||||
\(566\) | 126.262 | + | 334.058i | 0.223078 | + | 0.590208i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −65.6081 | + | 123.988i | −0.115507 | + | 0.218288i | ||||
\(569\) | 335.446 | + | 581.009i | 0.589536 | + | 1.02111i | 0.994293 | + | 0.106682i | \(0.0340225\pi\) |
−0.404758 | + | 0.914424i | \(0.632644\pi\) | |||||||
\(570\) | 49.3498 | − | 301.520i | 0.0865786 | − | 0.528983i | ||||
\(571\) | 338.541 | − | 586.371i | 0.592892 | − | 1.02692i | −0.400949 | − | 0.916100i | \(-0.631320\pi\) |
0.993841 | − | 0.110818i | \(-0.0353471\pi\) | |||||||
\(572\) | −143.819 | + | 427.587i | −0.251432 | + | 0.747530i | ||||
\(573\) | − | 91.9271i | − | 0.160431i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1394.67i | − | 2.42552i | ||||||
\(576\) | −240.884 | + | 498.933i | −0.418201 | + | 0.866203i | ||||
\(577\) | −463.950 | + | 803.586i | −0.804073 | + | 1.39270i | 0.112841 | + | 0.993613i | \(0.464005\pi\) |
−0.916915 | + | 0.399083i | \(0.869329\pi\) | |||||||
\(578\) | −269.705 | − | 44.1426i | −0.466618 | − | 0.0763713i | ||||
\(579\) | 76.5341 | + | 132.561i | 0.132183 | + | 0.228948i | ||||
\(580\) | 608.382 | − | 536.542i | 1.04893 | − | 0.925073i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 67.9756 | + | 179.847i | 0.116797 | + | 0.309015i | ||||
\(583\) | −86.6642 | + | 50.0356i | −0.148652 | + | 0.0858244i | ||||
\(584\) | −316.342 | + | 198.552i | −0.541681 | + | 0.339986i | ||||
\(585\) | 353.191 | − | 611.745i | 0.603745 | − | 1.04572i | ||||
\(586\) | −339.258 | − | 277.632i | −0.578938 | − | 0.473774i | ||||
\(587\) | −321.120 | −0.547053 | −0.273526 | − | 0.961865i | \(-0.588190\pi\) | ||||
−0.273526 | + | 0.961865i | \(0.588190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 484.508i | 0.822595i | ||||||||
\(590\) | 425.645 | + | 348.327i | 0.721432 | + | 0.590384i | ||||
\(591\) | 73.7028 | + | 42.5523i | 0.124709 | + | 0.0720005i | ||||
\(592\) | 157.132 | − | 207.158i | 0.265425 | − | 0.349929i | ||||
\(593\) | 109.627 | + | 189.880i | 0.184869 | + | 0.320203i | 0.943532 | − | 0.331280i | \(-0.107481\pi\) |
−0.758663 | + | 0.651483i | \(0.774147\pi\) | |||||||
\(594\) | 91.3137 | + | 241.593i | 0.153727 | + | 0.406723i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 667.196 | + | 756.529i | 1.11946 | + | 1.26934i | ||||
\(597\) | −198.107 | + | 114.377i | −0.331837 | + | 0.191586i | ||||
\(598\) | −439.340 | − | 71.9068i | −0.734683 | − | 0.120246i | ||||
\(599\) | 134.062 | + | 77.4010i | 0.223811 | + | 0.129217i | 0.607713 | − | 0.794156i | \(-0.292087\pi\) |
−0.383903 | + | 0.923373i | \(0.625420\pi\) | |||||||
\(600\) | 9.78595 | + | 265.054i | 0.0163099 | + | 0.441757i | ||||
\(601\) | 205.862 | 0.342533 | 0.171266 | − | 0.985225i | \(-0.445214\pi\) | ||||
0.171266 | + | 0.985225i | \(0.445214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 680.666 | 1.12880 | ||||||||
\(604\) | −299.017 | + | 889.004i | −0.495061 | + | 1.47186i | ||||
\(605\) | 272.882 | + | 157.548i | 0.451045 | + | 0.260411i | ||||
\(606\) | 2.29594 | − | 14.0279i | 0.00378868 | − | 0.0231483i | ||||
\(607\) | −684.735 | + | 395.332i | −1.12806 | + | 0.651288i | −0.943447 | − | 0.331523i | \(-0.892438\pi\) |
−0.184616 | + | 0.982811i | \(0.559104\pi\) | |||||||
\(608\) | −898.225 | + | 216.044i | −1.47734 | + | 0.355335i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −97.2965 | − | 257.422i | −0.159502 | − | 0.422004i | ||||
\(611\) | 28.0000 | + | 48.4974i | 0.0458265 | + | 0.0793739i | ||||
\(612\) | 84.5513 | + | 418.965i | 0.138156 | + | 0.684583i | ||||
\(613\) | 642.133 | + | 370.736i | 1.04753 | + | 0.604789i | 0.921955 | − | 0.387296i | \(-0.126591\pi\) |
0.125570 | + | 0.992085i | \(0.459924\pi\) | |||||||
\(614\) | −401.103 | + | 490.136i | −0.653262 | + | 0.798267i | ||||
\(615\) | − | 36.8848i | − | 0.0599752i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 171.578 | 0.278084 | 0.139042 | − | 0.990286i | \(-0.455598\pi\) | ||||
0.139042 | + | 0.990286i | \(0.455598\pi\) | |||||||
\(618\) | −96.6351 | − | 79.0814i | −0.156368 | − | 0.127963i | ||||
\(619\) | 270.099 | − | 467.825i | 0.436347 | − | 0.755776i | −0.561057 | − | 0.827777i | \(-0.689605\pi\) |
0.997405 | + | 0.0720012i | \(0.0229386\pi\) | |||||||
\(620\) | −119.958 | − | 594.408i | −0.193480 | − | 0.958723i | ||||
\(621\) | −220.727 | + | 127.437i | −0.355438 | + | 0.205212i | ||||
\(622\) | −135.196 | + | 51.0993i | −0.217357 | + | 0.0821532i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 84.0000 | + | 10.5830i | 0.134615 | + | 0.0169599i | ||||
\(625\) | −581.691 | − | 1007.52i | −0.930705 | − | 1.61203i | ||||
\(626\) | 161.750 | + | 26.4737i | 0.258387 | + | 0.0422902i | ||||
\(627\) | −105.574 | + | 182.859i | −0.168379 | + | 0.291641i | ||||
\(628\) | −12.8755 | + | 38.2799i | −0.0205023 | + | 0.0609552i | ||||
\(629\) | − | 200.583i | − | 0.318892i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 269.399i | − | 0.426940i | −0.976950 | − | 0.213470i | \(-0.931523\pi\) | ||
0.976950 | − | 0.213470i | \(-0.0684766\pi\) | |||||||
\(632\) | 647.819 | − | 23.9178i | 1.02503 | − | 0.0378447i | ||||
\(633\) | 48.0488 | − | 83.2229i | 0.0759064 | − | 0.131474i | ||||
\(634\) | −35.2600 | + | 215.434i | −0.0556152 | + | 0.339801i | ||||
\(635\) | −516.884 | − | 895.270i | −0.813991 | − | 1.40987i | ||||
\(636\) | 12.4222 | + | 14.0855i | 0.0195318 | + | 0.0221470i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −524.382 | + | 198.198i | −0.821915 | + | 0.310655i | ||||
\(639\) | −131.457 | + | 75.8968i | −0.205723 | + | 0.118774i | ||||
\(640\) | 1048.48 | − | 487.437i | 1.63825 | − | 0.761620i | ||||
\(641\) | −18.0934 | + | 31.3386i | −0.0282268 | + | 0.0488902i | −0.879794 | − | 0.475356i | \(-0.842319\pi\) |
0.851567 | + | 0.524246i | \(0.175653\pi\) | |||||||
\(642\) | 47.1882 | − | 57.6625i | 0.0735018 | − | 0.0898170i | ||||
\(643\) | 266.297 | 0.414148 | 0.207074 | − | 0.978325i | \(-0.433606\pi\) | ||||
0.207074 | + | 0.978325i | \(0.433606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 120.797i | 0.187282i | ||||||||
\(646\) | −451.361 | + | 551.550i | −0.698701 | + | 0.853792i | ||||
\(647\) | −940.708 | − | 543.118i | −1.45395 | − | 0.839440i | −0.455250 | − | 0.890363i | \(-0.650450\pi\) |
−0.998703 | + | 0.0509233i | \(0.983784\pi\) | |||||||
\(648\) | −486.868 | + | 305.583i | −0.751339 | + | 0.471578i | ||||
\(649\) | −190.049 | − | 329.174i | −0.292833 | − | 0.507202i | ||||
\(650\) | −956.477 | + | 361.514i | −1.47150 | + | 0.556176i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −313.602 | + | 276.571i | −0.480985 | + | 0.424189i | ||||
\(653\) | −1035.20 | + | 597.674i | −1.58530 | + | 0.915274i | −0.591234 | + | 0.806500i | \(0.701359\pi\) |
−0.994066 | + | 0.108774i | \(0.965307\pi\) | |||||||
\(654\) | −24.7608 | + | 151.285i | −0.0378606 | + | 0.231322i | ||||
\(655\) | −1317.00 | − | 760.368i | −2.01068 | − | 1.16087i | ||||
\(656\) | −102.800 | + | 43.2538i | −0.156707 | + | 0.0659356i | ||||
\(657\) | −404.156 | −0.615154 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −685.220 | −1.03979 | −0.519894 | − | 0.854231i | \(-0.674029\pi\) | ||||
−0.519894 | + | 0.854231i | \(0.674029\pi\) | |||||||
\(660\) | 84.2473 | − | 250.475i | 0.127647 | − | 0.379507i | ||||
\(661\) | −860.294 | − | 496.691i | −1.30150 | − | 0.751423i | −0.320842 | − | 0.947133i | \(-0.603966\pi\) |
−0.980662 | + | 0.195710i | \(0.937299\pi\) | |||||||
\(662\) | 635.031 | + | 103.936i | 0.959261 | + | 0.157002i | ||||
\(663\) | 56.5634 | − | 32.6569i | 0.0853143 | − | 0.0492563i | ||||
\(664\) | 285.563 | + | 151.106i | 0.430065 | + | 0.227569i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 263.186 | − | 99.4749i | 0.395174 | − | 0.149362i | ||||
\(667\) | −276.603 | − | 479.091i | −0.414697 | − | 0.718277i | ||||
\(668\) | −1163.60 | + | 234.826i | −1.74192 | + | 0.351536i | ||||
\(669\) | 5.36882 | + | 3.09969i | 0.00802514 | + | 0.00463332i | ||||
\(670\) | −1099.32 | − | 899.630i | −1.64078 | − | 1.34273i | ||||
\(671\) | 190.183i | 0.283432i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 106.569 | 0.158349 | 0.0791743 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791743 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(674\) | 207.789 | − | 253.913i | 0.308293 | − | 0.376725i | ||||
\(675\) | −292.701 | + | 506.972i | −0.433630 | + | 0.751070i | ||||
\(676\) | −69.1602 | − | 342.699i | −0.102308 | − | 0.506951i | ||||
\(677\) | −869.650 | + | 502.092i | −1.28456 | + | 0.741643i | −0.977679 | − | 0.210103i | \(-0.932620\pi\) |
−0.306885 | + | 0.951747i | \(0.599287\pi\) | |||||||
\(678\) | 57.2548 | + | 151.482i | 0.0844467 | + | 0.223425i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 417.186 | − | 788.407i | 0.613509 | − | 1.15942i | ||||
\(681\) | 62.6224 | + | 108.465i | 0.0919565 | + | 0.159273i | ||||
\(682\) | −67.6879 | + | 413.563i | −0.0992491 | + | 0.606397i | ||||
\(683\) | 339.113 | − | 587.360i | 0.496505 | − | 0.859971i | −0.503487 | − | 0.864003i | \(-0.667950\pi\) |
0.999992 | + | 0.00403135i | \(0.00128322\pi\) | |||||||
\(684\) | −947.533 | − | 318.703i | −1.38528 | − | 0.465940i | ||||
\(685\) | − | 313.327i | − | 0.457411i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 135.919i | − | 0.197844i | ||||||
\(688\) | 336.667 | − | 141.655i | 0.489342 | − | 0.205894i | ||||
\(689\) | −36.2010 | + | 62.7020i | −0.0525414 | + | 0.0910043i | ||||
\(690\) | 257.360 | + | 42.1221i | 0.372985 | + | 0.0610465i | ||||
\(691\) | 182.587 | + | 316.250i | 0.264236 | + | 0.457671i | 0.967363 | − | 0.253394i | \(-0.0815468\pi\) |
−0.703127 | + | 0.711064i | \(0.748213\pi\) | |||||||
\(692\) | −105.910 | − | 120.090i | −0.153049 | − | 0.173541i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 233.563 | + | 617.951i | 0.336547 | + | 0.890419i | ||||
\(695\) | −842.250 | + | 486.273i | −1.21187 | + | 0.699673i | ||||
\(696\) | 55.9293 | + | 89.1091i | 0.0803582 | + | 0.128030i | ||||
\(697\) | −43.0193 | + | 74.5117i | −0.0617207 | + | 0.106903i | ||||
\(698\) | 406.143 | + | 332.367i | 0.581866 | + | 0.476170i | ||||
\(699\) | −112.976 | −0.161626 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 940.292i | − | 1.34136i | −0.741748 | − | 0.670679i | \(-0.766003\pi\) | ||
0.741748 | − | 0.670679i | \(-0.233997\pi\) | |||||||
\(702\) | 144.612 | + | 118.343i | 0.206000 | + | 0.168580i | ||||
\(703\) | 406.300 | + | 234.577i | 0.577951 | + | 0.333680i | ||||
\(704\) | −796.883 | + | 58.9231i | −1.13194 | + | 0.0836975i | ||||
\(705\) | −16.4020 | − | 28.4091i | −0.0232653 | − | 0.0402966i | ||||
\(706\) | 408.777 | + | 1081.52i | 0.579004 | + | 1.53190i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −53.5004 | + | 47.1829i | −0.0755656 | + | 0.0666426i | ||||
\(709\) | 915.785 | − | 528.729i | 1.29166 | − | 0.745738i | 0.312709 | − | 0.949849i | \(-0.398764\pi\) |
0.978948 | + | 0.204110i | \(0.0654302\pi\) | |||||||
\(710\) | 312.624 | + | 51.1672i | 0.440316 | + | 0.0720665i | ||||
\(711\) | 607.505 | + | 350.743i | 0.854438 | + | 0.493310i | ||||
\(712\) | −33.0409 | − | 894.919i | −0.0464058 | − | 1.25691i | ||||
\(713\) | −413.547 | −0.580010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1018.77 | 1.42486 | ||||||||
\(716\) | 1117.65 | + | 375.921i | 1.56096 | + | 0.525030i | ||||
\(717\) | −166.354 | − | 96.0448i | −0.232015 | − | 0.133954i | ||||
\(718\) | 117.947 | − | 720.639i | 0.164272 | − | 1.00368i | ||||
\(719\) | 896.185 | − | 517.412i | 1.24643 | − | 0.719628i | 0.276036 | − | 0.961147i | \(-0.410979\pi\) |
0.970396 | + | 0.241520i | \(0.0776458\pi\) | |||||||
\(720\) | 1241.37 | + | 156.397i | 1.72412 | + | 0.217219i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −334.094 | − | 883.930i | −0.462734 | − | 1.22428i | ||||
\(723\) | −21.0509 | − | 36.4612i | −0.0291160 | − | 0.0504304i | ||||
\(724\) | 158.683 | − | 32.0239i | 0.219176 | − | 0.0442319i | ||||
\(725\) | −1100.39 | − | 635.311i | −1.51778 | − | 0.876291i | ||||
\(726\) | −25.8818 | + | 31.6268i | −0.0356498 | + | 0.0435631i | ||||
\(727\) | 495.145i | 0.681080i | 0.940230 | + | 0.340540i | \(0.110610\pi\) | ||||
−0.940230 | + | 0.340540i | \(0.889390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −567.489 | −0.778449 | ||||||||
\(730\) | 652.740 | + | 534.170i | 0.894164 | + | 0.731740i | ||||
\(731\) | 140.887 | − | 244.024i | 0.192732 | − | 0.333822i | ||||
\(732\) | 34.9867 | − | 7.06067i | 0.0477961 | − | 0.00964573i | ||||
\(733\) | 491.464 | − | 283.747i | 0.670483 | − | 0.387103i | −0.125777 | − | 0.992059i | \(-0.540142\pi\) |
0.796260 | + | 0.604955i | \(0.206809\pi\) | |||||||
\(734\) | 972.965 | − | 367.746i | 1.32556 | − | 0.501016i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −184.402 | − | 766.672i | −0.250546 | − | 1.04167i | ||||
\(737\) | 490.843 | + | 850.165i | 0.666001 | + | 1.15355i | ||||
\(738\) | −119.102 | − | 19.4934i | −0.161384 | − | 0.0264138i | ||||
\(739\) | 272.350 | − | 471.725i | 0.368539 | − | 0.638328i | −0.620798 | − | 0.783970i | \(-0.713191\pi\) |
0.989337 | + | 0.145642i | \(0.0465248\pi\) | |||||||
\(740\) | −556.538 | − | 187.192i | −0.752078 | − | 0.252962i | ||||
\(741\) | 152.766i | 0.206162i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 731.264i | 0.984205i | 0.870537 | + | 0.492102i | \(0.163771\pi\) | ||||
−0.870537 | + | 0.492102i | \(0.836229\pi\) | |||||||
\(744\) | 78.5936 | − | 2.90172i | 0.105637 | − | 0.00390016i | ||||
\(745\) | 1138.97 | − | 1972.76i | 1.52883 | − | 2.64800i | ||||
\(746\) | 170.150 | − | 1039.59i | 0.228083 | − | 1.39355i | ||||
\(747\) | 174.803 | + | 302.767i | 0.234006 | + | 0.405310i | ||||
\(748\) | −462.323 | + | 407.731i | −0.618079 | + | 0.545094i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 312.804 | − | 118.229i | 0.417072 | − | 0.157638i | ||||
\(751\) | 577.000 | − | 333.131i | 0.768309 | − | 0.443583i | −0.0639622 | − | 0.997952i | \(-0.520374\pi\) |
0.832271 | + | 0.554369i | \(0.187040\pi\) | |||||||
\(752\) | −59.9437 | + | 79.0280i | −0.0797124 | + | 0.105090i | ||||
\(753\) | 75.2498 | − | 130.336i | 0.0999333 | − | 0.173090i | ||||
\(754\) | −256.865 | + | 313.882i | −0.340670 | + | 0.416289i | ||||
\(755\) | 2118.15 | 2.80550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 238.623i | − | 0.315222i | −0.987501 | − | 0.157611i | \(-0.949621\pi\) | ||
0.987501 | − | 0.157611i | \(-0.0503791\pi\) | |||||||
\(758\) | −154.498 | + | 188.792i | −0.203823 | + | 0.249066i | ||||
\(759\) | −156.077 | − | 90.1113i | −0.205636 | − | 0.118724i | ||||
\(760\) | 1109.10 | + | 1767.07i | 1.45935 | + | 2.32510i | ||||
\(761\) | −307.465 | − | 532.545i | −0.404028 | − | 0.699797i | 0.590180 | − | 0.807272i | \(-0.299057\pi\) |
−0.994208 | + | 0.107475i | \(0.965723\pi\) | |||||||
\(762\) | 125.417 | − | 47.4032i | 0.164589 | − | 0.0622090i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 415.196 | + | 470.788i | 0.543450 | + | 0.616215i | ||||
\(765\) | 835.904 | − | 482.609i | 1.09268 | − | 0.630862i | ||||
\(766\) | 102.219 | − | 624.543i | 0.133445 | − | 0.815331i | ||||
\(767\) | −238.159 | − | 137.501i | −0.310507 | − | 0.179271i | ||||
\(768\) | 40.4246 | + | 144.410i | 0.0526362 | + | 0.188034i | ||||
\(769\) | 178.950 | 0.232705 | 0.116353 | − | 0.993208i | \(-0.462880\pi\) | ||||
0.116353 | + | 0.993208i | \(0.462880\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 187.072 | 0.242636 | ||||||||
\(772\) | −990.677 | − | 333.215i | −1.28326 | − | 0.431625i | ||||
\(773\) | 546.994 | + | 315.807i | 0.707625 | + | 0.408548i | 0.810181 | − | 0.586180i | \(-0.199369\pi\) |
−0.102556 | + | 0.994727i | \(0.532702\pi\) | |||||||
\(774\) | 390.055 | + | 63.8403i | 0.503947 | + | 0.0824810i | ||||
\(775\) | −822.593 | + | 474.925i | −1.06141 | + | 0.612806i | ||||
\(776\) | −1160.42 | − | 614.035i | −1.49538 | − | 0.791282i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 172.392 | − | 65.1580i | 0.221583 | − | 0.0837507i | ||||
\(779\) | −100.620 | − | 174.279i | −0.129166 | − | 0.223722i | ||||
\(780\) | −37.8228 | − | 187.418i | −0.0484907 | − | 0.240279i | ||||
\(781\) | −189.593 | − | 109.462i | −0.242757 | − | 0.140156i | ||||
\(782\) | −470.770 | − | 385.255i | −0.602007 | − | 0.492653i | ||||
\(783\) | 232.203i | 0.296556i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 91.2061 | 0.116186 | ||||||||
\(786\) | 124.912 | − | 152.639i | 0.158921 | − | 0.194197i | ||||
\(787\) | −228.327 | + | 395.475i | −0.290124 | + | 0.502509i | −0.973839 | − | 0.227240i | \(-0.927030\pi\) |
0.683715 | + | 0.729749i | \(0.260363\pi\) | |||||||
\(788\) | −569.646 | + | 114.960i | −0.722901 | + | 0.145889i | ||||
\(789\) | 191.435 | − | 110.525i | 0.242630 | − | 0.140083i | ||||
\(790\) | −517.588 | − | 1369.41i | −0.655175 | − | 1.73343i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −764.264 | − | 404.411i | −0.964980 | − | 0.510619i | ||||
\(793\) | 68.7990 | + | 119.163i | 0.0867579 | + | 0.150269i | ||||
\(794\) | −181.636 | + | 1109.77i | −0.228760 | + | 1.39769i | ||||
\(795\) | 21.2061 | − | 36.7300i | 0.0266743 | − | 0.0462012i | ||||
\(796\) | 497.975 | − | 1480.53i | 0.625597 | − | 1.85996i | ||||
\(797\) | 218.566i | 0.274236i | 0.990555 | + | 0.137118i | \(0.0437839\pi\) | ||||
−0.990555 | + | 0.137118i | \(0.956216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.5199i | 0.0957695i | ||||||||
\(800\) | −1247.25 | − | 1313.23i | −1.55907 | − | 1.64153i | ||||
\(801\) | 484.529 | − | 839.229i | 0.604905 | − | 1.04773i | ||||
\(802\) | 160.280 | + | 26.2330i | 0.199850 | + | 0.0327094i | ||||
\(803\) | −291.446 | − | 504.799i | −0.362946 | − | 0.628641i | ||||
\(804\) | 138.177 | − | 121.860i | 0.171861 | − | 0.151568i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 107.196 | + | 283.614i | 0.132997 | + | 0.351878i | ||||
\(807\) | −14.2873 | + | 8.24879i | −0.0177042 | + | 0.0102215i | ||||
\(808\) | 51.5997 | + | 82.2110i | 0.0638611 | + | 0.101746i | ||||
\(809\) | −673.730 | + | 1166.93i | −0.832794 | + | 1.44244i | 0.0630207 | + | 0.998012i | \(0.479927\pi\) |
−0.895814 | + | 0.444429i | \(0.853407\pi\) | |||||||
\(810\) | 1004.60 | + | 822.117i | 1.24025 | + | 1.01496i | ||||
\(811\) | −672.620 | −0.829371 | −0.414686 | − | 0.909965i | \(-0.636108\pi\) | ||||
−0.414686 | + | 0.909965i | \(0.636108\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 234.148i | − | 0.288005i | ||||||
\(814\) | 314.035 | + | 256.991i | 0.385792 | + | 0.315713i | ||||
\(815\) | 817.764 | + | 472.136i | 1.00339 | + | 0.579308i | ||||
\(816\) | 92.1718 | + | 69.9134i | 0.112956 | + | 0.0856782i | ||||
\(817\) | 329.529 | + | 570.761i | 0.403340 | + | 0.698606i | ||||
\(818\) | −318.718 | − | 843.248i | −0.389631 | − | 1.03087i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 166.593 | + | 188.899i | 0.203162 | + | 0.230364i | ||||
\(821\) | −1006.82 | + | 581.286i | −1.22633 | + | 0.708022i | −0.966260 | − | 0.257567i | \(-0.917079\pi\) |
−0.260070 | + | 0.965590i | \(0.583746\pi\) | |||||||
\(822\) | 40.1039 | + | 6.56381i | 0.0487882 | + | 0.00798517i | ||||
\(823\) | 902.093 | + | 520.824i | 1.09610 | + | 0.632835i | 0.935195 | − | 0.354134i | \(-0.115224\pi\) |
0.160908 | + | 0.986969i | \(0.448558\pi\) | |||||||
\(824\) | 852.077 | − | 31.4592i | 1.03407 | − | 0.0381786i | ||||
\(825\) | −413.941 | −0.501747 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 278.432 | 0.336678 | 0.168339 | − | 0.985729i | \(-0.446160\pi\) | ||||
0.168339 | + | 0.985729i | \(0.446160\pi\) | |||||||
\(828\) | 272.026 | − | 808.758i | 0.328534 | − | 0.976761i | ||||
\(829\) | 922.956 | + | 532.869i | 1.11334 | + | 0.642785i | 0.939692 | − | 0.342023i | \(-0.111112\pi\) |
0.173645 | + | 0.984808i | \(0.444445\pi\) | |||||||
\(830\) | 117.846 | − | 720.024i | 0.141984 | − | 0.867499i | ||||
\(831\) | 52.2275 | − | 30.1535i | 0.0628489 | − | 0.0362859i | ||||
\(832\) | −477.990 | + | 325.194i | −0.574507 | + | 0.390858i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −44.5959 | − | 117.990i | −0.0534723 | − | 0.141474i | ||||
\(835\) | 1340.36 | + | 2321.57i | 1.60522 | + | 2.78033i | ||||
\(836\) | −285.220 | − | 1413.31i | −0.341173 | − | 1.69056i | ||||
\(837\) | 150.327 | + | 86.7913i | 0.179602 | + | 0.103693i | ||||
\(838\) | −791.629 | + | 967.348i | −0.944665 | + | 1.15435i | ||||
\(839\) | 305.844i | 0.364533i | 0.983249 | + | 0.182267i | \(0.0583434\pi\) | ||||
−0.983249 | + | 0.182267i | \(0.941657\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 337.000 | 0.400713 | ||||||||
\(842\) | −876.783 | − | 717.516i | −1.04131 | − | 0.852157i | ||||
\(843\) | 44.0030 | − | 76.2154i | 0.0521981 | − | 0.0904097i | ||||
\(844\) | 129.810 | + | 643.227i | 0.153803 | + | 0.762118i | ||||
\(845\) | −683.741 | + | 394.758i | −0.809161 | + | 0.467169i | ||||
\(846\) | −100.402 | + | 37.9484i | −0.118679 | + | 0.0448563i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −127.236 | − | 16.0303i | −0.150043 | − | 0.0189036i | ||||
\(849\) | 52.2994 | + | 90.5853i | 0.0616012 | + | 0.106696i | ||||
\(850\) | −1378.85 | − | 225.676i | −1.62217 | − | 0.265501i | ||||
\(851\) | −200.221 | + | 346.793i | −0.235278 | + | 0.407513i | ||||
\(852\) | −13.0982 | + | 38.9421i | −0.0153735 | + | 0.0457067i | ||||
\(853\) | − | 164.018i | − | 0.192283i | −0.995368 | − | 0.0961417i | \(-0.969350\pi\) | ||
0.995368 | − | 0.0961417i | \(-0.0306502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2257.60i | 2.64047i | ||||||||
\(856\) | 18.7718 | + | 508.437i | 0.0219297 | + | 0.593969i | ||||
\(857\) | −425.534 | + | 737.047i | −0.496539 | + | 0.860031i | −0.999992 | − | 0.00399164i | \(-0.998729\pi\) |
0.503453 | + | 0.864023i | \(0.332063\pi\) | |||||||
\(858\) | −21.3421 | + | 130.397i | −0.0248742 | + | 0.151978i | ||||
\(859\) | 589.846 | + | 1021.64i | 0.686666 | + | 1.18934i | 0.972910 | + | 0.231184i | \(0.0742599\pi\) |
−0.286244 | + | 0.958157i | \(0.592407\pi\) | |||||||
\(860\) | −545.588 | − | 618.639i | −0.634405 | − | 0.719347i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 541.658 | − | 204.728i | 0.628374 | − | 0.237503i | ||||
\(863\) | 241.662 | − | 139.524i | 0.280026 | − | 0.161673i | −0.353409 | − | 0.935469i | \(-0.614978\pi\) |
0.633435 | + | 0.773796i | \(0.281644\pi\) | |||||||
\(864\) | −93.8703 | + | 317.390i | −0.108646 | + | 0.367350i | ||||
\(865\) | −180.799 | + | 313.153i | −0.209016 | + | 0.362027i | ||||
\(866\) | 757.060 | − | 925.105i | 0.874203 | − | 1.06825i | ||||
\(867\) | −80.0458 | −0.0923250 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1011.71i | 1.16423i | ||||||||
\(870\) | 150.468 | − | 183.868i | 0.172952 | − | 0.211342i | ||||
\(871\) | 615.098 | + | 355.127i | 0.706198 | + | 0.407723i | ||||
\(872\) | −556.482 | − | 886.613i | −0.638168 | − | 1.01676i | ||||
\(873\) | −710.328 | − | 1230.32i | −0.813663 | − | 1.40931i | ||||
\(874\) | 1330.92 | − | 503.042i | 1.52280 | − | 0.575563i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −82.0446 | + | 72.3565i | −0.0936582 | + | 0.0825988i | ||||
\(877\) | −583.839 | + | 337.080i | −0.665723 | + | 0.384355i | −0.794454 | − | 0.607324i | \(-0.792243\pi\) |
0.128731 | + | 0.991680i | \(0.458910\pi\) | |||||||
\(878\) | 12.4012 | − | 75.7698i | 0.0141244 | − | 0.0862982i | ||||
\(879\) | −111.196 | − | 64.1990i | −0.126503 | − | 0.0730364i | ||||
\(880\) | 699.832 | + | 1663.27i | 0.795264 | + | 1.89008i | ||||
\(881\) | −1001.29 | −1.13654 | −0.568271 | − | 0.822841i | \(-0.692387\pi\) | ||||
−0.568271 | + | 0.822841i | \(0.692387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 882.010 | 0.998879 | 0.499439 | − | 0.866349i | \(-0.333539\pi\) | ||||
0.499439 | + | 0.866349i | \(0.333539\pi\) | |||||||
\(884\) | −142.182 | + | 422.720i | −0.160839 | + | 0.478190i | ||||
\(885\) | 139.510 | + | 80.5463i | 0.157639 | + | 0.0910128i | ||||
\(886\) | 1182.38 | + | 193.521i | 1.33452 | + | 0.218421i | ||||
\(887\) | 6.13192 | − | 3.54027i | 0.00691310 | − | 0.00399128i | −0.496539 | − | 0.868014i | \(-0.665396\pi\) |
0.503453 | + | 0.864023i | \(0.332063\pi\) | |||||||
\(888\) | 35.6182 | − | 67.3120i | 0.0401106 | − | 0.0758018i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1891.75 | + | 715.014i | −2.12556 | + | 0.803386i | ||||
\(891\) | −448.551 | − | 776.914i | −0.503425 | − | 0.871957i | ||||
\(892\) | −41.4955 | + | 8.37420i | −0.0465196 | + | 0.00938812i | ||||
\(893\) | −154.998 | − | 89.4882i | −0.173570 | − | 0.100211i | ||||
\(894\) | 228.641 | + | 187.109i | 0.255751 | + | 0.209294i | ||||
\(895\) | − | 2662.92i | − | 2.97533i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −130.392 | −0.145364 | ||||||||
\(898\) | 582.700 | − | 712.042i | 0.648886 | − | 0.792920i | ||||
\(899\) | −188.382 | + | 326.287i | −0.209546 | + | 0.362944i | ||||
\(900\) | −387.700 | − | 1921.11i | −0.430778 | − | 2.13457i | ||||
\(901\) | −85.6776 | + | 49.4660i | −0.0950917 | + | 0.0549012i | ||||
\(902\) | −61.5391 | − | 162.817i | −0.0682252 | − | 0.180507i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −977.401 | − | 517.192i | −1.08120 | − | 0.572115i | ||||
\(905\) | −182.789 | − | 316.600i | −0.201977 | − | 0.349834i | ||||
\(906\) | −44.3726 | + | 271.110i | −0.0489764 | + | 0.299239i | ||||
\(907\) | −225.186 | + | 390.033i | −0.248275 | + | 0.430026i | −0.963047 | − | 0.269332i | \(-0.913197\pi\) |
0.714772 | + | 0.699358i | \(0.246530\pi\) | |||||||
\(908\) | −810.601 | − | 272.646i | −0.892732 | − | 0.300271i | ||||
\(909\) | 105.032i | 0.115547i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 202.426i | 0.222201i | 0.993809 | + | 0.111101i | \(0.0354376\pi\) | ||||
−0.993809 | + | 0.111101i | \(0.964562\pi\) | |||||||
\(912\) | −249.409 | + | 104.940i | −0.273475 | + | 0.115066i | ||||
\(913\) | −252.108 | + | 436.663i | −0.276131 | + | 0.478273i | ||||
\(914\) | 525.652 | + | 86.0335i | 0.575111 | + | 0.0941285i | ||||
\(915\) | −40.3015 | − | 69.8043i | −0.0440454 | − | 0.0762888i | ||||
\(916\) | 613.889 | + | 696.085i | 0.670185 | + | 0.759918i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 90.2742 | + | 238.843i | 0.0983379 | + | 0.260178i | ||||
\(919\) | 1380.21 | − | 796.863i | 1.50186 | − | 0.867098i | 0.501860 | − | 0.864949i | \(-0.332649\pi\) |
0.999998 | − | 0.00214879i | \(-0.000683983\pi\) | |||||||
\(920\) | −1508.27 | + | 946.665i | −1.63942 | + | 1.02898i | ||||
\(921\) | −92.7502 | + | 160.648i | −0.100706 | + | 0.174428i | ||||
\(922\) | 1181.15 | + | 966.596i | 1.28108 | + | 1.04837i | ||||
\(923\) | −158.392 | −0.171606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 919.749i | 0.994323i | ||||||||
\(926\) | −191.906 | − | 157.047i | −0.207242 | − | 0.169597i | ||||
\(927\) | 799.052 | + | 461.333i | 0.861977 | + | 0.497662i | ||||
\(928\) | −688.900 | − | 203.747i | −0.742349 | − | 0.219555i | ||||
\(929\) | 519.701 | + | 900.148i | 0.559419 | + | 0.968943i | 0.997545 | + | 0.0700290i | \(0.0223092\pi\) |
−0.438126 | + | 0.898914i | \(0.644357\pi\) | |||||||
\(930\) | −62.7939 | − | 166.137i | −0.0675204 | − | 0.178642i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 578.589 | − | 510.267i | 0.620803 | − | 0.547497i | ||||
\(933\) | −36.6606 | + | 21.1660i | −0.0392933 | + | 0.0226860i | ||||
\(934\) | −1517.25 | − | 248.328i | −1.62446 | − | 0.265876i | ||||
\(935\) | 1205.58 | + | 696.040i | 1.28939 | + | 0.744427i | ||||
\(936\) | −625.164 | + | 23.0814i | −0.667910 | + | 0.0246596i | ||||
\(937\) | 881.765 | 0.941051 | 0.470525 | − | 0.882386i | \(-0.344064\pi\) | ||||
0.470525 | + | 0.882386i | \(0.344064\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.0059 | 0.0511245 | ||||||||
\(940\) | 212.312 | + | 71.4112i | 0.225864 | + | 0.0759694i | ||||
\(941\) | −825.620 | − | 476.672i | −0.877386 | − | 0.506559i | −0.00759016 | − | 0.999971i | \(-0.502416\pi\) |
−0.869796 | + | 0.493412i | \(0.835749\pi\) | |||||||
\(942\) | −1.91065 | + | 11.6738i | −0.00202830 | + | 0.0123926i | ||||
\(943\) | 148.755 | − | 85.8835i | 0.157746 | − | 0.0910747i | ||||
\(944\) | 60.8873 | − | 483.278i | 0.0644993 | − | 0.511947i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 201.539 | + | 533.222i | 0.213043 | + | 0.563660i | ||||
\(947\) | −8.44783 | − | 14.6321i | −0.00892063 | − | 0.0154510i | 0.861531 | − | 0.507706i | \(-0.169506\pi\) |
−0.870451 | + | 0.492255i | \(0.836173\pi\) | |||||||
\(948\) | 186.119 | − | 37.5607i | 0.196328 | − | 0.0396209i | ||||
\(949\) | −365.224 | − | 210.862i | −0.384852 | − | 0.222194i | ||||
\(950\) | 2069.66 | − | 2529.06i | 2.17859 | − | 2.66217i | ||||
\(951\) | 63.9386i | 0.0672330i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1526.31 | 1.60159 | 0.800794 | − | 0.598940i | \(-0.204411\pi\) | ||||
0.800794 | + | 0.598940i | \(0.204411\pi\) | |||||||
\(954\) | −107.395 | − | 87.8864i | −0.112573 | − | 0.0921241i | ||||
\(955\) | 708.784 | − | 1227.65i | 0.742182 | − | 1.28550i | ||||
\(956\) | 1285.75 | − | 259.477i | 1.34493 | − | 0.271420i | ||||
\(957\) | −142.195 | + | 82.0962i | −0.148584 | + | 0.0857849i | ||||
\(958\) | −222.593 | + | 84.1322i | −0.232352 | + | 0.0878207i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 280.000 | − | 190.494i | 0.291667 | − | 0.198431i | ||||
\(961\) | −339.676 | − | 588.336i | −0.353461 | − | 0.612212i | ||||
\(962\) | 289.733 | + | 47.4206i | 0.301178 | + | 0.0492938i | ||||
\(963\) | −275.279 | + | 476.798i | −0.285856 | + | 0.495117i | ||||
\(964\) | 272.488 | + | 91.6514i | 0.282664 | + | 0.0950741i | ||||
\(965\) | 2360.40i | 2.44601i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1410.39i | − | 1.45852i | −0.684235 | − | 0.729262i | \(-0.739864\pi\) | ||
0.684235 | − | 0.729262i | \(-0.260136\pi\) | |||||||
\(968\) | −10.2960 | − | 278.868i | −0.0106363 | − | 0.288087i | ||||
\(969\) | −104.372 | + | 180.777i | −0.107711 | + | 0.186560i | ||||
\(970\) | −478.881 | + | 2925.89i | −0.493692 | + | 3.01638i | ||||
\(971\) | 298.248 | + | 516.581i | 0.307156 | + | 0.532009i | 0.977739 | − | 0.209825i | \(-0.0672894\pi\) |
−0.670583 | + | 0.741834i | \(0.733956\pi\) | |||||||
\(972\) | −405.536 | + | 357.649i | −0.417218 | + | 0.367952i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −528.653 | + | 199.812i | −0.542765 | + | 0.205146i | ||||
\(975\) | −259.365 | + | 149.744i | −0.266015 | + | 0.153584i | ||||
\(976\) | −147.288 | + | 194.180i | −0.150910 | + | 0.198955i | ||||
\(977\) | −73.3431 | + | 127.034i | −0.0750698 | + | 0.130025i | −0.901117 | − | 0.433577i | \(-0.857251\pi\) |
0.826047 | + | 0.563601i | \(0.190585\pi\) | |||||||
\(978\) | −77.5617 | + | 94.7782i | −0.0793065 | + | 0.0969102i | ||||
\(979\) | 1397.62 | 1.42760 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1132.73i | − | 1.15467i | ||||||
\(982\) | 491.515 | − | 600.617i | 0.500524 | − | 0.611626i | ||||
\(983\) | 146.754 | + | 84.7286i | 0.149292 | + | 0.0861939i | 0.572785 | − | 0.819705i | \(-0.305863\pi\) |
−0.423493 | + | 0.905899i | \(0.639196\pi\) | |||||||
\(984\) | −27.6678 | + | 17.3657i | −0.0281177 | + | 0.0176481i | ||||
\(985\) | 656.181 | + | 1136.54i | 0.666173 | + | 1.15385i | ||||
\(986\) | −518.412 | + | 195.941i | −0.525773 | + | 0.198723i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −689.980 | − | 782.364i | −0.698360 | − | 0.791866i | ||||
\(989\) | −487.167 | + | 281.266i | −0.492586 | + | 0.284395i | ||||
\(990\) | −315.397 | + | 1927.03i | −0.318582 | + | 1.94649i | ||||
\(991\) | −1460.90 | − | 843.449i | −1.47416 | − | 0.851109i | −0.474588 | − | 0.880208i | \(-0.657403\pi\) |
−0.999577 | + | 0.0290984i | \(0.990736\pi\) | |||||||
\(992\) | −389.397 | + | 369.835i | −0.392537 | + | 0.372817i | ||||
\(993\) | 188.471 | 0.189800 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3527.52 | −3.54524 | ||||||||
\(996\) | 89.6899 | + | 30.1672i | 0.0900501 | + | 0.0302884i | ||||
\(997\) | 1503.54 | + | 868.068i | 1.50806 | + | 0.870680i | 0.999956 | + | 0.00938643i | \(0.00298784\pi\) |
0.508107 | + | 0.861294i | \(0.330345\pi\) | |||||||
\(998\) | −54.7036 | − | 8.95334i | −0.0548132 | − | 0.00897128i | ||||
\(999\) | 145.563 | − | 84.0410i | 0.145709 | − | 0.0841251i |
(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 | 392.3.k.i.67.2 | 8 | ||
7.2 | even | 3 | inner | 392.3.k.i.275.4 | 8 | ||
7.3 | odd | 6 | 392.3.g.h.99.1 | 4 | |||
7.4 | even | 3 | 56.3.g.a.43.1 | ✓ | 4 | ||
7.5 | odd | 6 | 392.3.k.j.275.4 | 8 | |||
7.6 | odd | 2 | 392.3.k.j.67.2 | 8 | |||
8.3 | odd | 2 | inner | 392.3.k.i.67.4 | 8 | ||
21.11 | odd | 6 | 504.3.g.a.379.4 | 4 | |||
28.3 | even | 6 | 1568.3.g.h.687.2 | 4 | |||
28.11 | odd | 6 | 224.3.g.a.15.3 | 4 | |||
56.3 | even | 6 | 392.3.g.h.99.2 | 4 | |||
56.11 | odd | 6 | 56.3.g.a.43.2 | yes | 4 | ||
56.19 | even | 6 | 392.3.k.j.275.2 | 8 | |||
56.27 | even | 2 | 392.3.k.j.67.4 | 8 | |||
56.45 | odd | 6 | 1568.3.g.h.687.1 | 4 | |||
56.51 | odd | 6 | inner | 392.3.k.i.275.2 | 8 | ||
56.53 | even | 6 | 224.3.g.a.15.4 | 4 | |||
84.11 | even | 6 | 2016.3.g.a.1135.4 | 4 | |||
112.11 | odd | 12 | 1792.3.d.g.1023.6 | 8 | |||
112.53 | even | 12 | 1792.3.d.g.1023.4 | 8 | |||
112.67 | odd | 12 | 1792.3.d.g.1023.3 | 8 | |||
112.109 | even | 12 | 1792.3.d.g.1023.5 | 8 | |||
168.11 | even | 6 | 504.3.g.a.379.3 | 4 | |||
168.53 | odd | 6 | 2016.3.g.a.1135.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.a.43.1 | ✓ | 4 | 7.4 | even | 3 | ||
56.3.g.a.43.2 | yes | 4 | 56.11 | odd | 6 | ||
224.3.g.a.15.3 | 4 | 28.11 | odd | 6 | |||
224.3.g.a.15.4 | 4 | 56.53 | even | 6 | |||
392.3.g.h.99.1 | 4 | 7.3 | odd | 6 | |||
392.3.g.h.99.2 | 4 | 56.3 | even | 6 | |||
392.3.k.i.67.2 | 8 | 1.1 | even | 1 | trivial | ||
392.3.k.i.67.4 | 8 | 8.3 | odd | 2 | inner | ||
392.3.k.i.275.2 | 8 | 56.51 | odd | 6 | inner | ||
392.3.k.i.275.4 | 8 | 7.2 | even | 3 | inner | ||
392.3.k.j.67.2 | 8 | 7.6 | odd | 2 | |||
392.3.k.j.67.4 | 8 | 56.27 | even | 2 | |||
392.3.k.j.275.2 | 8 | 56.19 | even | 6 | |||
392.3.k.j.275.4 | 8 | 7.5 | odd | 6 | |||
504.3.g.a.379.3 | 4 | 168.11 | even | 6 | |||
504.3.g.a.379.4 | 4 | 21.11 | odd | 6 | |||
1568.3.g.h.687.1 | 4 | 56.45 | odd | 6 | |||
1568.3.g.h.687.2 | 4 | 28.3 | even | 6 | |||
1792.3.d.g.1023.3 | 8 | 112.67 | odd | 12 | |||
1792.3.d.g.1023.4 | 8 | 112.53 | even | 12 | |||
1792.3.d.g.1023.5 | 8 | 112.109 | even | 12 | |||
1792.3.d.g.1023.6 | 8 | 112.11 | odd | 12 | |||
2016.3.g.a.1135.1 | 4 | 168.53 | odd | 6 | |||
2016.3.g.a.1135.4 | 4 | 84.11 | even | 6 |