Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(79,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.4868829729.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - x^{6} + 5x^{5} - 8x^{4} + 15x^{3} - 9x^{2} - 54x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Root | \(1.25184 - 1.19703i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.79 |
Dual form | 273.2.i.d.235.2 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.410741 | + | 0.711425i | −0.290438 | + | 0.503053i | −0.973913 | − | 0.226920i | \(-0.927134\pi\) |
0.683475 | + | 0.729974i | \(0.260468\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.662583 | + | 1.14763i | 0.331292 | + | 0.573814i | ||||
\(5\) | −0.910741 | + | 1.57745i | −0.407296 | + | 0.705457i | −0.994586 | − | 0.103920i | \(-0.966862\pi\) |
0.587290 | + | 0.809377i | \(0.300195\pi\) | |||||||
\(6\) | 0.821482 | 0.335369 | ||||||||
\(7\) | 0.589259 | + | 2.57930i | 0.222719 | + | 0.974883i | ||||
\(8\) | −2.73157 | −0.965754 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.748158 | − | 1.29585i | −0.236588 | − | 0.409783i | ||||
\(11\) | −2.57332 | − | 4.45713i | −0.775887 | − | 1.34387i | −0.934295 | − | 0.356501i | \(-0.883970\pi\) |
0.158408 | − | 0.987374i | \(-0.449364\pi\) | |||||||
\(12\) | 0.662583 | − | 1.14763i | 0.191271 | − | 0.331292i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.07701 | − | 0.640210i | −0.555104 | − | 0.171103i | ||||
\(15\) | 1.82148 | 0.470305 | ||||||||
\(16\) | −0.203200 | + | 0.351952i | −0.0507999 | + | 0.0879881i | ||||
\(17\) | 2.43911 | + | 4.22466i | 0.591570 | + | 1.02463i | 0.994021 | + | 0.109188i | \(0.0348252\pi\) |
−0.402451 | + | 0.915442i | \(0.631841\pi\) | |||||||
\(18\) | −0.410741 | − | 0.711425i | −0.0968126 | − | 0.167684i | ||||
\(19\) | −3.82517 | + | 6.62538i | −0.877553 | + | 1.51997i | −0.0235358 | + | 0.999723i | \(0.507492\pi\) |
−0.854018 | + | 0.520244i | \(0.825841\pi\) | |||||||
\(20\) | −2.41377 | −0.539735 | ||||||||
\(21\) | 1.93911 | − | 1.79996i | 0.423148 | − | 0.392784i | ||||
\(22\) | 4.22788 | 0.901387 | ||||||||
\(23\) | −1.11763 | + | 1.93578i | −0.233041 | + | 0.403639i | −0.958702 | − | 0.284414i | \(-0.908201\pi\) |
0.725661 | + | 0.688053i | \(0.241534\pi\) | |||||||
\(24\) | 1.36578 | + | 2.36561i | 0.278789 | + | 0.482877i | ||||
\(25\) | 0.841101 | + | 1.45683i | 0.168220 | + | 0.291366i | ||||
\(26\) | 0.410741 | − | 0.711425i | 0.0805530 | − | 0.139522i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.56964 | + | 2.38525i | −0.485616 | + | 0.450770i | ||||
\(29\) | 1.82885 | 0.339609 | 0.169805 | − | 0.985478i | \(-0.445686\pi\) | ||||
0.169805 | + | 0.985478i | \(0.445686\pi\) | |||||||
\(30\) | −0.748158 | + | 1.29585i | −0.136594 | + | 0.236588i | ||||
\(31\) | −0.865783 | − | 1.49958i | −0.155499 | − | 0.269333i | 0.777741 | − | 0.628584i | \(-0.216365\pi\) |
−0.933241 | + | 0.359252i | \(0.883032\pi\) | |||||||
\(32\) | −2.89849 | − | 5.02033i | −0.512386 | − | 0.887478i | ||||
\(33\) | −2.57332 | + | 4.45713i | −0.447958 | + | 0.775887i | ||||
\(34\) | −4.00737 | −0.687258 | ||||||||
\(35\) | −4.60537 | − | 1.41955i | −0.778450 | − | 0.239947i | ||||
\(36\) | −1.32517 | −0.220861 | ||||||||
\(37\) | 5.53711 | − | 9.59056i | 0.910296 | − | 1.57668i | 0.0966498 | − | 0.995318i | \(-0.469187\pi\) |
0.813646 | − | 0.581360i | \(-0.197479\pi\) | |||||||
\(38\) | −3.14231 | − | 5.44264i | −0.509750 | − | 0.882912i | ||||
\(39\) | 0.500000 | + | 0.866025i | 0.0800641 | + | 0.138675i | ||||
\(40\) | 2.48775 | − | 4.30891i | 0.393348 | − | 0.681298i | ||||
\(41\) | 5.37453 | 0.839361 | 0.419680 | − | 0.907672i | \(-0.362142\pi\) | ||||
0.419680 | + | 0.907672i | \(0.362142\pi\) | |||||||
\(42\) | 0.484066 | + | 2.11885i | 0.0746930 | + | 0.326945i | ||||
\(43\) | 11.2426 | 1.71448 | 0.857242 | − | 0.514914i | \(-0.172176\pi\) | ||||
0.857242 | + | 0.514914i | \(0.172176\pi\) | |||||||
\(44\) | 3.41008 | − | 5.90644i | 0.514089 | − | 0.890429i | ||||
\(45\) | −0.910741 | − | 1.57745i | −0.135765 | − | 0.235152i | ||||
\(46\) | −0.918109 | − | 1.59021i | −0.135368 | − | 0.234464i | ||||
\(47\) | −4.09801 | + | 7.09796i | −0.597756 | + | 1.03534i | 0.395396 | + | 0.918511i | \(0.370607\pi\) |
−0.993152 | + | 0.116832i | \(0.962726\pi\) | |||||||
\(48\) | 0.406399 | 0.0586587 | ||||||||
\(49\) | −6.30555 | + | 3.03975i | −0.900793 | + | 0.434250i | ||||
\(50\) | −1.38190 | −0.195430 | ||||||||
\(51\) | 2.43911 | − | 4.22466i | 0.341543 | − | 0.591570i | ||||
\(52\) | −0.662583 | − | 1.14763i | −0.0918838 | − | 0.159147i | ||||
\(53\) | 3.25553 | + | 5.63874i | 0.447181 | + | 0.774540i | 0.998201 | − | 0.0599517i | \(-0.0190947\pi\) |
−0.551020 | + | 0.834492i | \(0.685761\pi\) | |||||||
\(54\) | −0.410741 | + | 0.711425i | −0.0558948 | + | 0.0968126i | ||||
\(55\) | 9.37453 | 1.26406 | ||||||||
\(56\) | −1.60960 | − | 7.04552i | −0.215092 | − | 0.941497i | ||||
\(57\) | 7.65033 | 1.01331 | ||||||||
\(58\) | −0.751184 | + | 1.30109i | −0.0986353 | + | 0.170841i | ||||
\(59\) | −4.18727 | − | 7.25256i | −0.545136 | − | 0.944202i | −0.998598 | − | 0.0529273i | \(-0.983145\pi\) |
0.453463 | − | 0.891275i | \(-0.350188\pi\) | |||||||
\(60\) | 1.20688 | + | 2.09038i | 0.155808 | + | 0.269867i | ||||
\(61\) | 1.26059 | − | 2.18341i | 0.161402 | − | 0.279556i | −0.773970 | − | 0.633223i | \(-0.781732\pi\) |
0.935372 | + | 0.353666i | \(0.115065\pi\) | |||||||
\(62\) | 1.42245 | 0.180651 | ||||||||
\(63\) | −2.52837 | − | 0.779336i | −0.318544 | − | 0.0981870i | ||||
\(64\) | 3.94932 | 0.493665 | ||||||||
\(65\) | 0.910741 | − | 1.57745i | 0.112964 | − | 0.195659i | ||||
\(66\) | −2.11394 | − | 3.66145i | −0.260208 | − | 0.450694i | ||||
\(67\) | −0.248158 | − | 0.429822i | −0.0303173 | − | 0.0525111i | 0.850469 | − | 0.526026i | \(-0.176318\pi\) |
−0.880786 | + | 0.473515i | \(0.842985\pi\) | |||||||
\(68\) | −3.23222 | + | 5.59838i | −0.391965 | + | 0.678903i | ||||
\(69\) | 2.23525 | 0.269092 | ||||||||
\(70\) | 2.90152 | − | 2.69331i | 0.346798 | − | 0.321912i | ||||
\(71\) | −2.27580 | −0.270088 | −0.135044 | − | 0.990840i | \(-0.543118\pi\) | ||||
−0.135044 | + | 0.990840i | \(0.543118\pi\) | |||||||
\(72\) | 1.36578 | − | 2.36561i | 0.160959 | − | 0.278789i | ||||
\(73\) | 1.68727 | + | 2.92243i | 0.197479 | + | 0.342045i | 0.947711 | − | 0.319131i | \(-0.103391\pi\) |
−0.750231 | + | 0.661176i | \(0.770058\pi\) | |||||||
\(74\) | 4.54864 | + | 7.87848i | 0.528769 | + | 0.915855i | ||||
\(75\) | 0.841101 | − | 1.45683i | 0.0971220 | − | 0.168220i | ||||
\(76\) | −10.1380 | −1.16290 | ||||||||
\(77\) | 9.97991 | − | 9.26377i | 1.13732 | − | 1.05570i | ||||
\(78\) | −0.821482 | −0.0930146 | ||||||||
\(79\) | 4.01243 | − | 6.94974i | 0.451434 | − | 0.781906i | −0.547041 | − | 0.837105i | \(-0.684246\pi\) |
0.998475 | + | 0.0551991i | \(0.0175793\pi\) | |||||||
\(80\) | −0.370125 | − | 0.641075i | −0.0413812 | − | 0.0716744i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.20754 | + | 3.82357i | −0.243782 | + | 0.422243i | ||||
\(83\) | 16.1614 | 1.77394 | 0.886971 | − | 0.461825i | \(-0.152805\pi\) | ||||
0.886971 | + | 0.461825i | \(0.152805\pi\) | |||||||
\(84\) | 3.35051 | + | 1.03275i | 0.365570 | + | 0.112682i | ||||
\(85\) | −8.88558 | −0.963777 | ||||||||
\(86\) | −4.61781 | + | 7.99828i | −0.497951 | + | 0.862476i | ||||
\(87\) | −0.914425 | − | 1.58383i | −0.0980367 | − | 0.169805i | ||||
\(88\) | 7.02921 | + | 12.1749i | 0.749316 | + | 1.29785i | ||||
\(89\) | −6.52468 | + | 11.3011i | −0.691615 | + | 1.19791i | 0.279694 | + | 0.960089i | \(0.409767\pi\) |
−0.971309 | + | 0.237823i | \(0.923566\pi\) | |||||||
\(90\) | 1.49632 | 0.157726 | ||||||||
\(91\) | −0.589259 | − | 2.57930i | −0.0617711 | − | 0.270384i | ||||
\(92\) | −2.96208 | −0.308818 | ||||||||
\(93\) | −0.865783 | + | 1.49958i | −0.0897775 | + | 0.155499i | ||||
\(94\) | −3.36644 | − | 5.83085i | −0.347222 | − | 0.601406i | ||||
\(95\) | −6.96747 | − | 12.0680i | −0.714848 | − | 1.23815i | ||||
\(96\) | −2.89849 | + | 5.02033i | −0.295826 | + | 0.512386i | ||||
\(97\) | 13.0742 | 1.32749 | 0.663743 | − | 0.747960i | \(-0.268967\pi\) | ||||
0.663743 | + | 0.747960i | \(0.268967\pi\) | |||||||
\(98\) | 0.427398 | − | 5.73447i | 0.0431737 | − | 0.579269i | ||||
\(99\) | 5.14665 | 0.517258 | ||||||||
\(100\) | −1.11460 | + | 1.93054i | −0.111460 | + | 0.193054i | ||||
\(101\) | 5.10675 | + | 8.84516i | 0.508141 | + | 0.880126i | 0.999956 | + | 0.00942616i | \(0.00300049\pi\) |
−0.491814 | + | 0.870700i | \(0.663666\pi\) | |||||||
\(102\) | 2.00368 | + | 3.47048i | 0.198394 | + | 0.343629i | ||||
\(103\) | 2.27284 | − | 3.93667i | 0.223950 | − | 0.387892i | −0.732054 | − | 0.681246i | \(-0.761438\pi\) |
0.956004 | + | 0.293354i | \(0.0947716\pi\) | |||||||
\(104\) | 2.73157 | 0.267852 | ||||||||
\(105\) | 1.07332 | + | 4.69814i | 0.104746 | + | 0.458492i | ||||
\(106\) | −5.34872 | −0.519513 | ||||||||
\(107\) | 3.25691 | − | 5.64113i | 0.314857 | − | 0.545348i | −0.664550 | − | 0.747244i | \(-0.731377\pi\) |
0.979407 | + | 0.201895i | \(0.0647101\pi\) | |||||||
\(108\) | 0.662583 | + | 1.14763i | 0.0637571 | + | 0.110431i | ||||
\(109\) | −1.80048 | − | 3.11853i | −0.172455 | − | 0.298701i | 0.766823 | − | 0.641859i | \(-0.221837\pi\) |
−0.939278 | + | 0.343158i | \(0.888503\pi\) | |||||||
\(110\) | −3.85051 | + | 6.66927i | −0.367131 | + | 0.635890i | ||||
\(111\) | −11.0742 | −1.05112 | ||||||||
\(112\) | −1.02753 | − | 0.316722i | −0.0970922 | − | 0.0299274i | ||||
\(113\) | −0.396272 | −0.0372781 | −0.0186391 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186391 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(114\) | −3.14231 | + | 5.44264i | −0.294304 | + | 0.509750i | ||||
\(115\) | −2.03573 | − | 3.52600i | −0.189833 | − | 0.328801i | ||||
\(116\) | 1.21177 | + | 2.09884i | 0.112510 | + | 0.194872i | ||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 6.87953 | 0.633312 | ||||||||
\(119\) | −9.45938 | + | 8.78060i | −0.867140 | + | 0.804916i | ||||
\(120\) | −4.97550 | −0.454199 | ||||||||
\(121\) | −7.74400 | + | 13.4130i | −0.704000 | + | 1.21936i | ||||
\(122\) | 1.03555 | + | 1.79363i | 0.0937545 | + | 0.162388i | ||||
\(123\) | −2.68727 | − | 4.65448i | −0.242303 | − | 0.419680i | ||||
\(124\) | 1.14731 | − | 1.98719i | 0.103031 | − | 0.178455i | ||||
\(125\) | −12.1715 | −1.08865 | ||||||||
\(126\) | 1.59294 | − | 1.47864i | 0.141911 | − | 0.131727i | ||||
\(127\) | −15.8132 | −1.40319 | −0.701596 | − | 0.712575i | \(-0.747529\pi\) | ||||
−0.701596 | + | 0.712575i | \(0.747529\pi\) | |||||||
\(128\) | 4.17483 | − | 7.23102i | 0.369007 | − | 0.639138i | ||||
\(129\) | −5.62131 | − | 9.73639i | −0.494929 | − | 0.857242i | ||||
\(130\) | 0.748158 | + | 1.29585i | 0.0656178 | + | 0.113653i | ||||
\(131\) | −1.10585 | + | 1.91539i | −0.0966186 | + | 0.167348i | −0.910283 | − | 0.413987i | \(-0.864136\pi\) |
0.813664 | + | 0.581335i | \(0.197469\pi\) | |||||||
\(132\) | −6.82017 | −0.593619 | ||||||||
\(133\) | −19.3428 | − | 5.96218i | −1.67724 | − | 0.516986i | ||||
\(134\) | 0.407715 | 0.0352212 | ||||||||
\(135\) | −0.910741 | + | 1.57745i | −0.0783841 | + | 0.135765i | ||||
\(136\) | −6.66258 | − | 11.5399i | −0.571312 | − | 0.989541i | ||||
\(137\) | 10.3210 | + | 17.8765i | 0.881783 | + | 1.52729i | 0.849357 | + | 0.527819i | \(0.176990\pi\) |
0.0324262 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(138\) | −0.918109 | + | 1.59021i | −0.0781547 | + | 0.135368i | ||||
\(139\) | −10.0249 | −0.850298 | −0.425149 | − | 0.905123i | \(-0.639778\pi\) | ||||
−0.425149 | + | 0.905123i | \(0.639778\pi\) | |||||||
\(140\) | −1.42233 | − | 6.22582i | −0.120209 | − | 0.526178i | ||||
\(141\) | 8.19601 | 0.690229 | ||||||||
\(142\) | 0.934766 | − | 1.61906i | 0.0784438 | − | 0.135869i | ||||
\(143\) | 2.57332 | + | 4.45713i | 0.215192 | + | 0.372724i | ||||
\(144\) | −0.203200 | − | 0.351952i | −0.0169333 | − | 0.0293294i | ||||
\(145\) | −1.66561 | + | 2.88492i | −0.138321 | + | 0.239580i | ||||
\(146\) | −2.77212 | −0.229422 | ||||||||
\(147\) | 5.78527 | + | 3.94089i | 0.477161 | + | 0.325039i | ||||
\(148\) | 14.6752 | 1.20629 | ||||||||
\(149\) | −2.22788 | + | 3.85880i | −0.182515 | + | 0.316126i | −0.942736 | − | 0.333539i | \(-0.891757\pi\) |
0.760221 | + | 0.649664i | \(0.225091\pi\) | |||||||
\(150\) | 0.690950 | + | 1.19676i | 0.0564158 | + | 0.0977150i | ||||
\(151\) | −8.10537 | − | 14.0389i | −0.659606 | − | 1.14247i | −0.980718 | − | 0.195430i | \(-0.937390\pi\) |
0.321112 | − | 0.947041i | \(-0.395944\pi\) | |||||||
\(152\) | 10.4487 | − | 18.0977i | 0.847501 | − | 1.46791i | ||||
\(153\) | −4.87822 | −0.394380 | ||||||||
\(154\) | 2.49132 | + | 10.9050i | 0.200756 | + | 0.878747i | ||||
\(155\) | 3.15402 | 0.253337 | ||||||||
\(156\) | −0.662583 | + | 1.14763i | −0.0530491 | + | 0.0918838i | ||||
\(157\) | 1.00875 | + | 1.74720i | 0.0805069 | + | 0.139442i | 0.903468 | − | 0.428656i | \(-0.141013\pi\) |
−0.822961 | + | 0.568098i | \(0.807679\pi\) | |||||||
\(158\) | 3.29614 | + | 5.70909i | 0.262227 | + | 0.454191i | ||||
\(159\) | 3.25553 | − | 5.63874i | 0.258180 | − | 0.447181i | ||||
\(160\) | 10.5591 | 0.834770 | ||||||||
\(161\) | −5.65153 | − | 1.74201i | −0.445403 | − | 0.137290i | ||||
\(162\) | 0.821482 | 0.0645418 | ||||||||
\(163\) | −6.97688 | + | 12.0843i | −0.546471 | + | 0.946516i | 0.452041 | + | 0.891997i | \(0.350696\pi\) |
−0.998513 | + | 0.0545192i | \(0.982637\pi\) | |||||||
\(164\) | 3.56107 | + | 6.16796i | 0.278073 | + | 0.481637i | ||||
\(165\) | −4.68727 | − | 8.11858i | −0.364903 | − | 0.632031i | ||||
\(166\) | −6.63815 | + | 11.4976i | −0.515220 | + | 0.892387i | ||||
\(167\) | −5.65033 | −0.437236 | −0.218618 | − | 0.975811i | \(-0.570155\pi\) | ||||
−0.218618 | + | 0.975811i | \(0.570155\pi\) | |||||||
\(168\) | −5.29680 | + | 4.91671i | −0.408657 | + | 0.379333i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 3.64968 | − | 6.32142i | 0.279917 | − | 0.484831i | ||||
\(171\) | −3.82517 | − | 6.62538i | −0.292518 | − | 0.506656i | ||||
\(172\) | 7.44917 | + | 12.9023i | 0.567994 | + | 0.983794i | ||||
\(173\) | 3.99632 | − | 6.92182i | 0.303834 | − | 0.526256i | −0.673167 | − | 0.739491i | \(-0.735066\pi\) |
0.977001 | + | 0.213234i | \(0.0683998\pi\) | |||||||
\(174\) | 1.50237 | 0.113894 | ||||||||
\(175\) | −3.26197 | + | 3.02790i | −0.246582 | + | 0.228888i | ||||
\(176\) | 2.09160 | 0.157660 | ||||||||
\(177\) | −4.18727 | + | 7.25256i | −0.314734 | + | 0.545136i | ||||
\(178\) | −5.35991 | − | 9.28364i | −0.401742 | − | 0.695838i | ||||
\(179\) | 5.44786 | + | 9.43596i | 0.407192 | + | 0.705277i | 0.994574 | − | 0.104033i | \(-0.0331747\pi\) |
−0.587382 | + | 0.809310i | \(0.699841\pi\) | |||||||
\(180\) | 1.20688 | − | 2.09038i | 0.0899558 | − | 0.155808i | ||||
\(181\) | −3.80579 | −0.282882 | −0.141441 | − | 0.989947i | \(-0.545174\pi\) | ||||
−0.141441 | + | 0.989947i | \(0.545174\pi\) | |||||||
\(182\) | 2.07701 | + | 0.640210i | 0.153958 | + | 0.0474556i | ||||
\(183\) | −2.52118 | −0.186371 | ||||||||
\(184\) | 3.05287 | − | 5.28772i | 0.225060 | − | 0.389816i | ||||
\(185\) | 10.0858 | + | 17.4690i | 0.741520 | + | 1.28435i | ||||
\(186\) | −0.711226 | − | 1.23188i | −0.0521496 | − | 0.0903257i | ||||
\(187\) | 12.5532 | − | 21.7428i | 0.917983 | − | 1.58999i | ||||
\(188\) | −10.8611 | −0.792126 | ||||||||
\(189\) | 0.589259 | + | 2.57930i | 0.0428623 | + | 0.187616i | ||||
\(190\) | 11.4473 | 0.830476 | ||||||||
\(191\) | 7.50434 | − | 12.9979i | 0.542995 | − | 0.940495i | −0.455735 | − | 0.890115i | \(-0.650624\pi\) |
0.998730 | − | 0.0503796i | \(-0.0160431\pi\) | |||||||
\(192\) | −1.97466 | − | 3.42021i | −0.142509 | − | 0.246833i | ||||
\(193\) | 10.8747 | + | 18.8356i | 0.782779 | + | 1.35581i | 0.930317 | + | 0.366757i | \(0.119532\pi\) |
−0.147538 | + | 0.989056i | \(0.547135\pi\) | |||||||
\(194\) | −5.37012 | + | 9.30133i | −0.385552 | + | 0.667796i | ||||
\(195\) | −1.82148 | −0.130439 | ||||||||
\(196\) | −7.66645 | − | 5.22234i | −0.547604 | − | 0.373024i | ||||
\(197\) | 2.12359 | 0.151300 | 0.0756499 | − | 0.997134i | \(-0.475897\pi\) | ||||
0.0756499 | + | 0.997134i | \(0.475897\pi\) | |||||||
\(198\) | −2.11394 | + | 3.66145i | −0.150231 | + | 0.260208i | ||||
\(199\) | −0.976040 | − | 1.69055i | −0.0691896 | − | 0.119840i | 0.829355 | − | 0.558722i | \(-0.188708\pi\) |
−0.898545 | + | 0.438882i | \(0.855375\pi\) | |||||||
\(200\) | −2.29752 | − | 3.97943i | −0.162459 | − | 0.281388i | ||||
\(201\) | −0.248158 | + | 0.429822i | −0.0175037 | + | 0.0303173i | ||||
\(202\) | −8.39022 | −0.590334 | ||||||||
\(203\) | 1.07767 | + | 4.71715i | 0.0756373 | + | 0.331079i | ||||
\(204\) | 6.46445 | 0.452602 | ||||||||
\(205\) | −4.89481 | + | 8.47805i | −0.341868 | + | 0.592133i | ||||
\(206\) | 1.86710 | + | 3.23391i | 0.130087 | + | 0.225317i | ||||
\(207\) | −1.11763 | − | 1.93578i | −0.0776803 | − | 0.134546i | ||||
\(208\) | 0.203200 | − | 0.351952i | 0.0140894 | − | 0.0244035i | ||||
\(209\) | 39.3736 | 2.72353 | ||||||||
\(210\) | −3.78323 | − | 1.16613i | −0.261068 | − | 0.0804708i | ||||
\(211\) | −0.481943 | −0.0331783 | −0.0165892 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165892 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(212\) | −4.31411 | + | 7.47227i | −0.296295 | + | 0.513197i | ||||
\(213\) | 1.13790 | + | 1.97090i | 0.0779677 | + | 0.135044i | ||||
\(214\) | 2.67549 | + | 4.63409i | 0.182893 | + | 0.316780i | ||||
\(215\) | −10.2391 | + | 17.7347i | −0.698302 | + | 1.20949i | ||||
\(216\) | −2.73157 | −0.185860 | ||||||||
\(217\) | 3.35769 | − | 3.11675i | 0.227935 | − | 0.211579i | ||||
\(218\) | 2.95813 | 0.200350 | ||||||||
\(219\) | 1.68727 | − | 2.92243i | 0.114015 | − | 0.197479i | ||||
\(220\) | 6.21141 | + | 10.7585i | 0.418773 | + | 0.725336i | ||||
\(221\) | −2.43911 | − | 4.22466i | −0.164072 | − | 0.284181i | ||||
\(222\) | 4.54864 | − | 7.87848i | 0.305285 | − | 0.528769i | ||||
\(223\) | −12.2061 | −0.817384 | −0.408692 | − | 0.912672i | \(-0.634015\pi\) | ||||
−0.408692 | + | 0.912672i | \(0.634015\pi\) | |||||||
\(224\) | 11.2410 | − | 10.4343i | 0.751069 | − | 0.697174i | ||||
\(225\) | −1.68220 | −0.112147 | ||||||||
\(226\) | 0.162765 | − | 0.281917i | 0.0108270 | − | 0.0187529i | ||||
\(227\) | 0.503684 | + | 0.872406i | 0.0334307 | + | 0.0579036i | 0.882257 | − | 0.470769i | \(-0.156023\pi\) |
−0.848826 | + | 0.528672i | \(0.822690\pi\) | |||||||
\(228\) | 5.06898 | + | 8.77974i | 0.335702 | + | 0.581452i | ||||
\(229\) | −10.0191 | + | 17.3537i | −0.662084 | + | 1.14676i | 0.317984 | + | 0.948096i | \(0.396994\pi\) |
−0.980067 | + | 0.198666i | \(0.936339\pi\) | |||||||
\(230\) | 3.34464 | 0.220539 | ||||||||
\(231\) | −13.0126 | − | 4.01097i | −0.856167 | − | 0.263902i | ||||
\(232\) | −4.99563 | −0.327979 | ||||||||
\(233\) | 10.8704 | − | 18.8280i | 0.712142 | − | 1.23347i | −0.251910 | − | 0.967751i | \(-0.581059\pi\) |
0.964052 | − | 0.265715i | \(-0.0856080\pi\) | |||||||
\(234\) | 0.410741 | + | 0.711425i | 0.0268510 | + | 0.0465073i | ||||
\(235\) | −7.46445 | − | 12.9288i | −0.486927 | − | 0.843382i | ||||
\(236\) | 5.54882 | − | 9.61085i | 0.361198 | − | 0.625613i | ||||
\(237\) | −8.02486 | −0.521271 | ||||||||
\(238\) | −2.36138 | − | 10.3362i | −0.153065 | − | 0.669996i | ||||
\(239\) | 3.43534 | 0.222214 | 0.111107 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111107 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(240\) | −0.370125 | + | 0.641075i | −0.0238915 | + | 0.0413812i | ||||
\(241\) | −2.26041 | − | 3.91514i | −0.145606 | − | 0.252196i | 0.783993 | − | 0.620770i | \(-0.213180\pi\) |
−0.929599 | + | 0.368573i | \(0.879846\pi\) | |||||||
\(242\) | −6.36156 | − | 11.0185i | −0.408936 | − | 0.708299i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.34098 | 0.213885 | ||||||||
\(245\) | 0.947674 | − | 12.7151i | 0.0605446 | − | 0.812339i | ||||
\(246\) | 4.41508 | 0.281495 | ||||||||
\(247\) | 3.82517 | − | 6.62538i | 0.243390 | − | 0.421563i | ||||
\(248\) | 2.36494 | + | 4.09620i | 0.150174 | + | 0.260109i | ||||
\(249\) | −8.08069 | − | 13.9962i | −0.512093 | − | 0.886971i | ||||
\(250\) | 4.99934 | − | 8.65911i | 0.316186 | − | 0.547651i | ||||
\(251\) | −11.3343 | −0.715417 | −0.357709 | − | 0.933833i | \(-0.616442\pi\) | ||||
−0.357709 | + | 0.933833i | \(0.616442\pi\) | |||||||
\(252\) | −0.780866 | − | 3.41800i | −0.0491899 | − | 0.215314i | ||||
\(253\) | 11.5040 | 0.723253 | ||||||||
\(254\) | 6.49512 | − | 11.2499i | 0.407540 | − | 0.705880i | ||||
\(255\) | 4.44279 | + | 7.69514i | 0.278218 | + | 0.481888i | ||||
\(256\) | 7.37887 | + | 12.7806i | 0.461180 | + | 0.798786i | ||||
\(257\) | 5.59450 | − | 9.68997i | 0.348976 | − | 0.604443i | −0.637092 | − | 0.770788i | \(-0.719863\pi\) |
0.986068 | + | 0.166344i | \(0.0531963\pi\) | |||||||
\(258\) | 9.23561 | 0.574984 | ||||||||
\(259\) | 27.9997 | + | 8.63054i | 1.73982 | + | 0.536276i | ||||
\(260\) | 2.41377 | 0.149696 | ||||||||
\(261\) | −0.914425 | + | 1.58383i | −0.0566015 | + | 0.0980367i | ||||
\(262\) | −0.908437 | − | 1.57346i | −0.0561234 | − | 0.0972086i | ||||
\(263\) | −2.34110 | − | 4.05491i | −0.144358 | − | 0.250036i | 0.784775 | − | 0.619781i | \(-0.212779\pi\) |
−0.929133 | + | 0.369745i | \(0.879445\pi\) | |||||||
\(264\) | 7.02921 | − | 12.1749i | 0.432618 | − | 0.749316i | ||||
\(265\) | −11.8598 | −0.728540 | ||||||||
\(266\) | 12.1865 | − | 11.3121i | 0.747205 | − | 0.693587i | ||||
\(267\) | 13.0494 | 0.798608 | ||||||||
\(268\) | 0.328851 | − | 0.569586i | 0.0200877 | − | 0.0347930i | ||||
\(269\) | −9.67942 | − | 16.7652i | −0.590165 | − | 1.02220i | −0.994210 | − | 0.107456i | \(-0.965729\pi\) |
0.404045 | − | 0.914739i | \(-0.367604\pi\) | |||||||
\(270\) | −0.748158 | − | 1.29585i | −0.0455314 | − | 0.0788628i | ||||
\(271\) | 8.68238 | − | 15.0383i | 0.527417 | − | 0.913513i | −0.472072 | − | 0.881560i | \(-0.656494\pi\) |
0.999489 | − | 0.0319535i | \(-0.0101729\pi\) | |||||||
\(272\) | −1.98250 | −0.120207 | ||||||||
\(273\) | −1.93911 | + | 1.79996i | −0.117360 | + | 0.108939i | ||||
\(274\) | −16.9571 | −1.02441 | ||||||||
\(275\) | 4.32885 | − | 7.49779i | 0.261040 | − | 0.452134i | ||||
\(276\) | 1.48104 | + | 2.56524i | 0.0891481 | + | 0.154409i | ||||
\(277\) | −1.15890 | − | 2.00727i | −0.0696315 | − | 0.120605i | 0.829108 | − | 0.559089i | \(-0.188849\pi\) |
−0.898739 | + | 0.438484i | \(0.855516\pi\) | |||||||
\(278\) | 4.11763 | − | 7.13194i | 0.246959 | − | 0.427745i | ||||
\(279\) | 1.73157 | 0.103666 | ||||||||
\(280\) | 12.5799 | + | 3.87758i | 0.751792 | + | 0.231730i | ||||
\(281\) | −26.8071 | −1.59918 | −0.799589 | − | 0.600548i | \(-0.794949\pi\) | ||||
−0.799589 | + | 0.600548i | \(0.794949\pi\) | |||||||
\(282\) | −3.36644 | + | 5.83085i | −0.200469 | + | 0.347222i | ||||
\(283\) | −7.36090 | − | 12.7495i | −0.437560 | − | 0.757876i | 0.559941 | − | 0.828533i | \(-0.310824\pi\) |
−0.997501 | + | 0.0706564i | \(0.977491\pi\) | |||||||
\(284\) | −1.50791 | − | 2.61177i | −0.0894779 | − | 0.154980i | ||||
\(285\) | −6.96747 | + | 12.0680i | −0.412718 | + | 0.714848i | ||||
\(286\) | −4.22788 | −0.250000 | ||||||||
\(287\) | 3.16699 | + | 13.8625i | 0.186941 | + | 0.818278i | ||||
\(288\) | 5.79698 | 0.341590 | ||||||||
\(289\) | −3.39849 | + | 5.88636i | −0.199911 | + | 0.346256i | ||||
\(290\) | −1.36827 | − | 2.36991i | −0.0803475 | − | 0.139166i | ||||
\(291\) | −6.53711 | − | 11.3226i | −0.383212 | − | 0.663743i | ||||
\(292\) | −2.23591 | + | 3.87271i | −0.130847 | + | 0.226633i | ||||
\(293\) | −10.0599 | −0.587703 | −0.293852 | − | 0.955851i | \(-0.594937\pi\) | ||||
−0.293852 | + | 0.955851i | \(0.594937\pi\) | |||||||
\(294\) | −5.17990 | + | 2.49710i | −0.302098 | + | 0.145634i | ||||
\(295\) | 15.2541 | 0.888126 | ||||||||
\(296\) | −15.1250 | + | 26.1973i | −0.879122 | + | 1.52268i | ||||
\(297\) | −2.57332 | − | 4.45713i | −0.149319 | − | 0.258629i | ||||
\(298\) | −1.83017 | − | 3.16994i | −0.106019 | − | 0.183630i | ||||
\(299\) | 1.11763 | − | 1.93578i | 0.0646339 | − | 0.111949i | ||||
\(300\) | 2.22920 | 0.128703 | ||||||||
\(301\) | 6.62481 | + | 28.9981i | 0.381848 | + | 1.67142i | ||||
\(302\) | 13.3168 | 0.766298 | ||||||||
\(303\) | 5.10675 | − | 8.84516i | 0.293375 | − | 0.508141i | ||||
\(304\) | −1.55455 | − | 2.69255i | −0.0891593 | − | 0.154428i | ||||
\(305\) | 2.29614 | + | 3.97704i | 0.131477 | + | 0.227724i | ||||
\(306\) | 2.00368 | − | 3.47048i | 0.114543 | − | 0.198394i | ||||
\(307\) | 9.33398 | 0.532718 | 0.266359 | − | 0.963874i | \(-0.414179\pi\) | ||||
0.266359 | + | 0.963874i | \(0.414179\pi\) | |||||||
\(308\) | 17.2439 | + | 5.31520i | 0.982561 | + | 0.302862i | ||||
\(309\) | −4.54568 | −0.258595 | ||||||||
\(310\) | −1.29548 | + | 2.24385i | −0.0735786 | + | 0.127442i | ||||
\(311\) | 7.67574 | + | 13.2948i | 0.435251 | + | 0.753877i | 0.997316 | − | 0.0732160i | \(-0.0233262\pi\) |
−0.562065 | + | 0.827093i | \(0.689993\pi\) | |||||||
\(312\) | −1.36578 | − | 2.36561i | −0.0773222 | − | 0.133926i | ||||
\(313\) | 5.64617 | − | 9.77946i | 0.319141 | − | 0.552768i | −0.661168 | − | 0.750238i | \(-0.729939\pi\) |
0.980309 | + | 0.197470i | \(0.0632725\pi\) | |||||||
\(314\) | −1.65734 | −0.0935290 | ||||||||
\(315\) | 3.53205 | − | 3.27860i | 0.199008 | − | 0.184728i | ||||
\(316\) | 10.6343 | 0.598225 | ||||||||
\(317\) | −12.3166 | + | 21.3330i | −0.691769 | + | 1.19818i | 0.279489 | + | 0.960149i | \(0.409835\pi\) |
−0.971258 | + | 0.238030i | \(0.923498\pi\) | |||||||
\(318\) | 2.67436 | + | 4.63212i | 0.149971 | + | 0.259757i | ||||
\(319\) | −4.70623 | − | 8.15142i | −0.263498 | − | 0.456392i | ||||
\(320\) | −3.59681 | + | 6.22986i | −0.201068 | + | 0.348260i | ||||
\(321\) | −6.51381 | −0.363566 | ||||||||
\(322\) | 3.56063 | − | 3.30512i | 0.198426 | − | 0.184187i | ||||
\(323\) | −37.3200 | −2.07654 | ||||||||
\(324\) | 0.662583 | − | 1.14763i | 0.0368102 | − | 0.0637571i | ||||
\(325\) | −0.841101 | − | 1.45683i | −0.0466559 | − | 0.0808104i | ||||
\(326\) | −5.73138 | − | 9.92705i | −0.317432 | − | 0.549808i | ||||
\(327\) | −1.80048 | + | 3.11853i | −0.0995670 | + | 0.172455i | ||||
\(328\) | −14.6809 | −0.810616 | ||||||||
\(329\) | −20.7225 | − | 6.38744i | −1.14247 | − | 0.352151i | ||||
\(330\) | 7.70101 | 0.423927 | ||||||||
\(331\) | 13.7774 | − | 23.8632i | 0.757276 | − | 1.31164i | −0.186959 | − | 0.982368i | \(-0.559863\pi\) |
0.944235 | − | 0.329273i | \(-0.106804\pi\) | |||||||
\(332\) | 10.7083 | + | 18.5473i | 0.587692 | + | 1.01791i | ||||
\(333\) | 5.53711 | + | 9.59056i | 0.303432 | + | 0.525560i | ||||
\(334\) | 2.32082 | − | 4.01979i | 0.126990 | − | 0.219953i | ||||
\(335\) | 0.904031 | 0.0493925 | ||||||||
\(336\) | 0.239474 | + | 1.04823i | 0.0130644 | + | 0.0571854i | ||||
\(337\) | −25.3034 | −1.37837 | −0.689183 | − | 0.724588i | \(-0.742030\pi\) | ||||
−0.689183 | + | 0.724588i | \(0.742030\pi\) | |||||||
\(338\) | −0.410741 | + | 0.711425i | −0.0223414 | + | 0.0386964i | ||||
\(339\) | 0.198136 | + | 0.343181i | 0.0107613 | + | 0.0186391i | ||||
\(340\) | −5.88744 | − | 10.1973i | −0.319291 | − | 0.553029i | ||||
\(341\) | −4.45588 | + | 7.71781i | −0.241300 | + | 0.417943i | ||||
\(342\) | 6.28461 | 0.339833 | ||||||||
\(343\) | −11.5560 | − | 14.4727i | −0.623966 | − | 0.781452i | ||||
\(344\) | −30.7100 | −1.65577 | ||||||||
\(345\) | −2.03573 | + | 3.52600i | −0.109600 | + | 0.189833i | ||||
\(346\) | 3.28290 | + | 5.68616i | 0.176490 | + | 0.305690i | ||||
\(347\) | 9.17502 | + | 15.8916i | 0.492541 | + | 0.853105i | 0.999963 | − | 0.00859203i | \(-0.00273496\pi\) |
−0.507422 | + | 0.861697i | \(0.669402\pi\) | |||||||
\(348\) | 1.21177 | − | 2.09884i | 0.0649575 | − | 0.112510i | ||||
\(349\) | 28.0427 | 1.50109 | 0.750546 | − | 0.660818i | \(-0.229790\pi\) | ||||
0.750546 | + | 0.660818i | \(0.229790\pi\) | |||||||
\(350\) | −0.814296 | − | 3.56433i | −0.0435260 | − | 0.190521i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −14.9175 | + | 25.8379i | −0.795106 | + | 1.37716i | ||||
\(353\) | 9.32010 | + | 16.1429i | 0.496059 | + | 0.859199i | 0.999990 | − | 0.00454470i | \(-0.00144663\pi\) |
−0.503931 | + | 0.863744i | \(0.668113\pi\) | |||||||
\(354\) | −3.43977 | − | 5.95785i | −0.182821 | − | 0.316656i | ||||
\(355\) | 2.07267 | − | 3.58996i | 0.110006 | − | 0.190536i | ||||
\(356\) | −17.2926 | −0.916505 | ||||||||
\(357\) | 12.3339 | + | 3.80177i | 0.652780 | + | 0.201211i | ||||
\(358\) | −8.95064 | −0.473056 | ||||||||
\(359\) | 17.4434 | − | 30.2129i | 0.920630 | − | 1.59458i | 0.122187 | − | 0.992507i | \(-0.461009\pi\) |
0.798443 | − | 0.602071i | \(-0.205658\pi\) | |||||||
\(360\) | 2.48775 | + | 4.30891i | 0.131116 | + | 0.227099i | ||||
\(361\) | −19.7638 | − | 34.2319i | −1.04020 | − | 1.80168i | ||||
\(362\) | 1.56320 | − | 2.70754i | 0.0821598 | − | 0.142305i | ||||
\(363\) | 15.4880 | 0.812909 | ||||||||
\(364\) | 2.56964 | − | 2.38525i | 0.134686 | − | 0.125021i | ||||
\(365\) | −6.14665 | −0.321730 | ||||||||
\(366\) | 1.03555 | − | 1.79363i | 0.0541292 | − | 0.0937545i | ||||
\(367\) | 12.7077 | + | 22.0104i | 0.663338 | + | 1.14893i | 0.979733 | + | 0.200307i | \(0.0641940\pi\) |
−0.316395 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(368\) | −0.454202 | − | 0.786701i | −0.0236769 | − | 0.0410096i | ||||
\(369\) | −2.68727 | + | 4.65448i | −0.139893 | + | 0.242303i | ||||
\(370\) | −16.5705 | −0.861462 | ||||||||
\(371\) | −12.6256 | + | 11.7196i | −0.655490 | + | 0.608454i | ||||
\(372\) | −2.29461 | −0.118970 | ||||||||
\(373\) | −5.29974 | + | 9.17942i | −0.274410 | + | 0.475292i | −0.969986 | − | 0.243160i | \(-0.921816\pi\) |
0.695576 | + | 0.718453i | \(0.255149\pi\) | |||||||
\(374\) | 10.3123 | + | 17.8614i | 0.533234 | + | 0.923589i | ||||
\(375\) | 6.08576 | + | 10.5408i | 0.314267 | + | 0.544327i | ||||
\(376\) | 11.1940 | − | 19.3885i | 0.577285 | − | 0.999887i | ||||
\(377\) | −1.82885 | −0.0941906 | ||||||||
\(378\) | −2.07701 | − | 0.640210i | −0.106830 | − | 0.0329289i | ||||
\(379\) | 27.7743 | 1.42667 | 0.713335 | − | 0.700824i | \(-0.247184\pi\) | ||||
0.713335 | + | 0.700824i | \(0.247184\pi\) | |||||||
\(380\) | 9.23306 | − | 15.9921i | 0.473646 | − | 0.820379i | ||||
\(381\) | 7.90658 | + | 13.6946i | 0.405066 | + | 0.701596i | ||||
\(382\) | 6.16469 | + | 10.6775i | 0.315413 | + | 0.546311i | ||||
\(383\) | −3.81732 | + | 6.61180i | −0.195056 | + | 0.337847i | −0.946919 | − | 0.321473i | \(-0.895822\pi\) |
0.751863 | + | 0.659320i | \(0.229156\pi\) | |||||||
\(384\) | −8.34967 | −0.426092 | ||||||||
\(385\) | 5.52402 | + | 24.1797i | 0.281530 | + | 1.23231i | ||||
\(386\) | −17.8668 | −0.909395 | ||||||||
\(387\) | −5.62131 | + | 9.73639i | −0.285747 | + | 0.494929i | ||||
\(388\) | 8.66277 | + | 15.0043i | 0.439785 | + | 0.761730i | ||||
\(389\) | −1.43845 | − | 2.49147i | −0.0729323 | − | 0.126322i | 0.827253 | − | 0.561830i | \(-0.189902\pi\) |
−0.900185 | + | 0.435507i | \(0.856569\pi\) | |||||||
\(390\) | 0.748158 | − | 1.29585i | 0.0378845 | − | 0.0656178i | ||||
\(391\) | −10.9040 | −0.551441 | ||||||||
\(392\) | 17.2240 | − | 8.30327i | 0.869944 | − | 0.419378i | ||||
\(393\) | 2.21170 | 0.111566 | ||||||||
\(394\) | −0.872247 | + | 1.51078i | −0.0439432 | + | 0.0761118i | ||||
\(395\) | 7.30857 | + | 12.6588i | 0.367734 | + | 0.636934i | ||||
\(396\) | 3.41008 | + | 5.90644i | 0.171363 | + | 0.296810i | ||||
\(397\) | 13.3899 | − | 23.1920i | 0.672021 | − | 1.16397i | −0.305309 | − | 0.952253i | \(-0.598760\pi\) |
0.977330 | − | 0.211721i | \(-0.0679069\pi\) | |||||||
\(398\) | 1.60360 | 0.0803812 | ||||||||
\(399\) | 4.50803 | + | 19.7325i | 0.225684 | + | 0.987860i | ||||
\(400\) | −0.683646 | −0.0341823 | ||||||||
\(401\) | 2.32076 | − | 4.01967i | 0.115893 | − | 0.200733i | −0.802243 | − | 0.596997i | \(-0.796360\pi\) |
0.918136 | + | 0.396264i | \(0.129694\pi\) | |||||||
\(402\) | −0.203857 | − | 0.353091i | −0.0101675 | − | 0.0176106i | ||||
\(403\) | 0.865783 | + | 1.49958i | 0.0431277 | + | 0.0746994i | ||||
\(404\) | −6.76730 | + | 11.7213i | −0.336686 | + | 0.583157i | ||||
\(405\) | 1.82148 | 0.0905102 | ||||||||
\(406\) | −3.79854 | − | 1.17085i | −0.188518 | − | 0.0581083i | ||||
\(407\) | −56.9952 | −2.82515 | ||||||||
\(408\) | −6.66258 | + | 11.5399i | −0.329847 | + | 0.571312i | ||||
\(409\) | −3.01153 | − | 5.21612i | −0.148910 | − | 0.257921i | 0.781915 | − | 0.623386i | \(-0.214243\pi\) |
−0.930825 | + | 0.365465i | \(0.880910\pi\) | |||||||
\(410\) | −4.02100 | − | 6.96457i | −0.198583 | − | 0.343956i | ||||
\(411\) | 10.3210 | − | 17.8765i | 0.509098 | − | 0.881783i | ||||
\(412\) | 6.02378 | 0.296771 | ||||||||
\(413\) | 16.2391 | − | 15.0738i | 0.799075 | − | 0.741735i | ||||
\(414\) | 1.83622 | 0.0902452 | ||||||||
\(415\) | −14.7188 | + | 25.4938i | −0.722519 | + | 1.25144i | ||||
\(416\) | 2.89849 | + | 5.02033i | 0.142110 | + | 0.246142i | ||||
\(417\) | 5.01243 | + | 8.68179i | 0.245460 | + | 0.425149i | ||||
\(418\) | −16.1724 | + | 28.0113i | −0.791016 | + | 1.37008i | ||||
\(419\) | 6.96718 | 0.340369 | 0.170185 | − | 0.985412i | \(-0.445564\pi\) | ||||
0.170185 | + | 0.985412i | \(0.445564\pi\) | |||||||
\(420\) | −4.68056 | + | 4.34469i | −0.228388 | + | 0.211999i | ||||
\(421\) | −5.53279 | −0.269652 | −0.134826 | − | 0.990869i | \(-0.543048\pi\) | ||||
−0.134826 | + | 0.990869i | \(0.543048\pi\) | |||||||
\(422\) | 0.197954 | − | 0.342866i | 0.00963625 | − | 0.0166905i | ||||
\(423\) | −4.09801 | − | 7.09796i | −0.199252 | − | 0.345114i | ||||
\(424\) | −8.89268 | − | 15.4026i | −0.431867 | − | 0.748015i | ||||
\(425\) | −4.10307 | + | 7.10673i | −0.199028 | + | 0.344727i | ||||
\(426\) | −1.86953 | −0.0905791 | ||||||||
\(427\) | 6.37447 | + | 1.96485i | 0.308482 | + | 0.0950855i | ||||
\(428\) | 8.63189 | 0.417238 | ||||||||
\(429\) | 2.57332 | − | 4.45713i | 0.124241 | − | 0.215192i | ||||
\(430\) | −8.41125 | − | 14.5687i | −0.405627 | − | 0.702566i | ||||
\(431\) | 9.51612 | + | 16.4824i | 0.458375 | + | 0.793929i | 0.998875 | − | 0.0474148i | \(-0.0150983\pi\) |
−0.540500 | + | 0.841344i | \(0.681765\pi\) | |||||||
\(432\) | −0.203200 | + | 0.351952i | −0.00977645 | + | 0.0169333i | ||||
\(433\) | 24.1903 | 1.16251 | 0.581256 | − | 0.813720i | \(-0.302561\pi\) | ||||
0.581256 | + | 0.813720i | \(0.302561\pi\) | |||||||
\(434\) | 0.838192 | + | 3.66892i | 0.0402345 | + | 0.176114i | ||||
\(435\) | 3.33122 | 0.159720 | ||||||||
\(436\) | 2.38594 | − | 4.13257i | 0.114266 | − | 0.197914i | ||||
\(437\) | −8.55020 | − | 14.8094i | −0.409012 | − | 0.708429i | ||||
\(438\) | 1.38606 | + | 2.40072i | 0.0662285 | + | 0.114711i | ||||
\(439\) | −7.03277 | + | 12.1811i | −0.335656 | + | 0.581373i | −0.983611 | − | 0.180306i | \(-0.942291\pi\) |
0.647955 | + | 0.761679i | \(0.275625\pi\) | |||||||
\(440\) | −25.6072 | −1.22077 | ||||||||
\(441\) | 0.520276 | − | 6.98064i | 0.0247750 | − | 0.332411i | ||||
\(442\) | 4.00737 | 0.190611 | ||||||||
\(443\) | 5.26197 | − | 9.11400i | 0.250004 | − | 0.433019i | −0.713523 | − | 0.700632i | \(-0.752901\pi\) |
0.963527 | + | 0.267613i | \(0.0862348\pi\) | |||||||
\(444\) | −7.33760 | − | 12.7091i | −0.348227 | − | 0.603147i | ||||
\(445\) | −11.8846 | − | 20.5847i | −0.563384 | − | 0.975809i | ||||
\(446\) | 5.01357 | − | 8.68375i | 0.237399 | − | 0.411187i | ||||
\(447\) | 4.45576 | 0.210750 | ||||||||
\(448\) | 2.32717 | + | 10.1865i | 0.109949 | + | 0.481266i | ||||
\(449\) | 12.7159 | 0.600099 | 0.300050 | − | 0.953924i | \(-0.402997\pi\) | ||||
0.300050 | + | 0.953924i | \(0.402997\pi\) | |||||||
\(450\) | 0.690950 | − | 1.19676i | 0.0325717 | − | 0.0564158i | ||||
\(451\) | −13.8304 | − | 23.9550i | −0.651249 | − | 1.12800i | ||||
\(452\) | −0.262563 | − | 0.454772i | −0.0123499 | − | 0.0213907i | ||||
\(453\) | −8.10537 | + | 14.0389i | −0.380824 | + | 0.659606i | ||||
\(454\) | −0.827535 | −0.0388382 | ||||||||
\(455\) | 4.60537 | + | 1.41955i | 0.215903 | + | 0.0665493i | ||||
\(456\) | −20.8974 | −0.978610 | ||||||||
\(457\) | −0.960106 | + | 1.66295i | −0.0449118 | + | 0.0777896i | −0.887607 | − | 0.460601i | \(-0.847634\pi\) |
0.842696 | + | 0.538390i | \(0.180967\pi\) | |||||||
\(458\) | −8.23055 | − | 14.2557i | −0.384588 | − | 0.666127i | ||||
\(459\) | 2.43911 | + | 4.22466i | 0.113848 | + | 0.197190i | ||||
\(460\) | 2.69769 | − | 4.67253i | 0.125780 | − | 0.217858i | ||||
\(461\) | 24.8320 | 1.15654 | 0.578270 | − | 0.815845i | \(-0.303728\pi\) | ||||
0.578270 | + | 0.815845i | \(0.303728\pi\) | |||||||
\(462\) | 8.19832 | − | 7.61003i | 0.381420 | − | 0.354050i | ||||
\(463\) | 9.05949 | 0.421030 | 0.210515 | − | 0.977591i | \(-0.432486\pi\) | ||||
0.210515 | + | 0.977591i | \(0.432486\pi\) | |||||||
\(464\) | −0.371622 | + | 0.643668i | −0.0172521 | + | 0.0298815i | ||||
\(465\) | −1.57701 | − | 2.73146i | −0.0731320 | − | 0.126668i | ||||
\(466\) | 8.92982 | + | 15.4669i | 0.413666 | + | 0.716490i | ||||
\(467\) | 4.03253 | − | 6.98454i | 0.186603 | − | 0.323206i | −0.757512 | − | 0.652821i | \(-0.773586\pi\) |
0.944116 | + | 0.329615i | \(0.106919\pi\) | |||||||
\(468\) | 1.32517 | 0.0612558 | ||||||||
\(469\) | 0.962410 | − | 0.893350i | 0.0444400 | − | 0.0412511i | ||||
\(470\) | 12.2638 | 0.565688 | ||||||||
\(471\) | 1.00875 | − | 1.74720i | 0.0464807 | − | 0.0805069i | ||||
\(472\) | 11.4378 | + | 19.8108i | 0.526467 | + | 0.911868i | ||||
\(473\) | −28.9309 | − | 50.1098i | −1.33024 | − | 2.30405i | ||||
\(474\) | 3.29614 | − | 5.70909i | 0.151397 | − | 0.262227i | ||||
\(475\) | −12.8694 | −0.590489 | ||||||||
\(476\) | −16.3445 | − | 5.03797i | −0.749149 | − | 0.230915i | ||||
\(477\) | −6.51105 | −0.298121 | ||||||||
\(478\) | −1.41104 | + | 2.44398i | −0.0645392 | + | 0.111785i | ||||
\(479\) | −4.73941 | − | 8.20890i | −0.216549 | − | 0.375074i | 0.737202 | − | 0.675673i | \(-0.236147\pi\) |
−0.953751 | + | 0.300599i | \(0.902813\pi\) | |||||||
\(480\) | −5.27955 | − | 9.14445i | −0.240977 | − | 0.417385i | ||||
\(481\) | −5.53711 | + | 9.59056i | −0.252471 | + | 0.437292i | ||||
\(482\) | 3.71377 | 0.169158 | ||||||||
\(483\) | 1.31714 | + | 5.76537i | 0.0599320 | + | 0.262334i | ||||
\(484\) | −20.5242 | −0.932917 | ||||||||
\(485\) | −11.9072 | + | 20.6239i | −0.540680 | + | 0.936485i | ||||
\(486\) | −0.410741 | − | 0.711425i | −0.0186316 | − | 0.0322709i | ||||
\(487\) | 8.41008 | + | 14.5667i | 0.381097 | + | 0.660080i | 0.991219 | − | 0.132228i | \(-0.0422130\pi\) |
−0.610122 | + | 0.792307i | \(0.708880\pi\) | |||||||
\(488\) | −3.44338 | + | 5.96412i | −0.155875 | + | 0.269983i | ||||
\(489\) | 13.9538 | 0.631011 | ||||||||
\(490\) | 8.65659 | + | 5.89682i | 0.391065 | + | 0.266391i | ||||
\(491\) | −14.8117 | −0.668443 | −0.334222 | − | 0.942494i | \(-0.608473\pi\) | ||||
−0.334222 | + | 0.942494i | \(0.608473\pi\) | |||||||
\(492\) | 3.56107 | − | 6.16796i | 0.160546 | − | 0.278073i | ||||
\(493\) | 4.46076 | + | 7.72627i | 0.200903 | + | 0.347974i | ||||
\(494\) | 3.14231 | + | 5.44264i | 0.141379 | + | 0.244876i | ||||
\(495\) | −4.68727 | + | 8.11858i | −0.210677 | + | 0.364903i | ||||
\(496\) | 0.703708 | 0.0315974 | ||||||||
\(497\) | −1.34104 | − | 5.86997i | −0.0601537 | − | 0.263304i | ||||
\(498\) | 13.2763 | 0.594925 | ||||||||
\(499\) | −19.4893 | + | 33.7565i | −0.872461 | + | 1.51115i | −0.0130188 | + | 0.999915i | \(0.504144\pi\) |
−0.859443 | + | 0.511232i | \(0.829189\pi\) | |||||||
\(500\) | −8.06464 | − | 13.9684i | −0.360662 | − | 0.624684i | ||||
\(501\) | 2.82517 | + | 4.89333i | 0.126219 | + | 0.218618i | ||||
\(502\) | 4.65548 | − | 8.06353i | 0.207784 | − | 0.359893i | ||||
\(503\) | −27.7246 | −1.23618 | −0.618089 | − | 0.786108i | \(-0.712093\pi\) | ||||
−0.618089 | + | 0.786108i | \(0.712093\pi\) | |||||||
\(504\) | 6.90640 | + | 2.12881i | 0.307635 | + | 0.0948246i | ||||
\(505\) | −18.6037 | −0.827855 | ||||||||
\(506\) | −4.72519 | + | 8.18426i | −0.210060 | + | 0.363835i | ||||
\(507\) | −0.500000 | − | 0.866025i | −0.0222058 | − | 0.0384615i | ||||
\(508\) | −10.4775 | − | 18.1476i | −0.464866 | − | 0.805171i | ||||
\(509\) | 15.5011 | − | 26.8487i | 0.687074 | − | 1.19005i | −0.285707 | − | 0.958317i | \(-0.592228\pi\) |
0.972780 | − | 0.231729i | \(-0.0744383\pi\) | |||||||
\(510\) | −7.29935 | −0.323221 | ||||||||
\(511\) | −6.54358 | + | 6.07403i | −0.289471 | + | 0.268699i | ||||
\(512\) | 4.57610 | 0.202237 | ||||||||
\(513\) | −3.82517 | + | 6.62538i | −0.168885 | + | 0.292518i | ||||
\(514\) | 4.59579 | + | 7.96014i | 0.202711 | + | 0.351107i | ||||
\(515\) | 4.13994 | + | 7.17058i | 0.182427 | + | 0.315974i | ||||
\(516\) | 7.44917 | − | 12.9023i | 0.327931 | − | 0.567994i | ||||
\(517\) | 42.1820 | 1.85516 | ||||||||
\(518\) | −17.6406 | + | 16.3748i | −0.775084 | + | 0.719466i | ||||
\(519\) | −7.99263 | −0.350838 | ||||||||
\(520\) | −2.48775 | + | 4.30891i | −0.109095 | + | 0.188958i | ||||
\(521\) | −5.43983 | − | 9.42206i | −0.238323 | − | 0.412788i | 0.721910 | − | 0.691987i | \(-0.243264\pi\) |
−0.960233 | + | 0.279199i | \(0.909931\pi\) | |||||||
\(522\) | −0.751184 | − | 1.30109i | −0.0328784 | − | 0.0569471i | ||||
\(523\) | −5.11347 | + | 8.85678i | −0.223596 | + | 0.387280i | −0.955897 | − | 0.293701i | \(-0.905113\pi\) |
0.732301 | + | 0.680981i | \(0.238446\pi\) | |||||||
\(524\) | −2.93087 | −0.128036 | ||||||||
\(525\) | 4.25322 | + | 1.31100i | 0.185626 | + | 0.0572167i | ||||
\(526\) | 3.84635 | 0.167709 | ||||||||
\(527\) | 4.22348 | − | 7.31527i | 0.183977 | − | 0.318658i | ||||
\(528\) | −1.04580 | − | 1.81137i | −0.0455125 | − | 0.0788300i | ||||
\(529\) | 9.00183 | + | 15.5916i | 0.391384 | + | 0.677897i | ||||
\(530\) | 4.87130 | − | 8.43733i | 0.211596 | − | 0.366494i | ||||
\(531\) | 8.37453 | 0.363424 | ||||||||
\(532\) | −5.97389 | − | 26.1488i | −0.259001 | − | 1.13370i | ||||
\(533\) | −5.37453 | −0.232797 | ||||||||
\(534\) | −5.35991 | + | 9.28364i | −0.231946 | + | 0.401742i | ||||
\(535\) | 5.93240 | + | 10.2752i | 0.256480 | + | 0.444236i | ||||
\(536\) | 0.677860 | + | 1.17409i | 0.0292791 | + | 0.0507129i | ||||
\(537\) | 5.44786 | − | 9.43596i | 0.235092 | − | 0.407192i | ||||
\(538\) | 15.9030 | 0.685625 | ||||||||
\(539\) | 29.7748 | + | 20.2824i | 1.28249 | + | 0.873624i | ||||
\(540\) | −2.41377 | −0.103872 | ||||||||
\(541\) | 0.200420 | − | 0.347137i | 0.00861671 | − | 0.0149246i | −0.861685 | − | 0.507444i | \(-0.830591\pi\) |
0.870302 | + | 0.492519i | \(0.163924\pi\) | |||||||
\(542\) | 7.13243 | + | 12.3537i | 0.306364 | + | 0.530638i | ||||
\(543\) | 1.90290 | + | 3.29591i | 0.0816611 | + | 0.141441i | ||||
\(544\) | 14.1395 | − | 24.4903i | 0.606224 | − | 1.05001i | ||||
\(545\) | 6.55910 | 0.280961 | ||||||||
\(546\) | −0.484066 | − | 2.11885i | −0.0207161 | − | 0.0906783i | ||||
\(547\) | 45.5549 | 1.94779 | 0.973893 | − | 0.227010i | \(-0.0728949\pi\) | ||||
0.973893 | + | 0.227010i | \(0.0728949\pi\) | |||||||
\(548\) | −13.6771 | + | 23.6894i | −0.584255 | + | 1.01196i | ||||
\(549\) | 1.26059 | + | 2.18341i | 0.0538007 | + | 0.0931855i | ||||
\(550\) | 3.55607 | + | 6.15930i | 0.151632 | + | 0.262634i | ||||
\(551\) | −6.99566 | + | 12.1168i | −0.298025 | + | 0.516195i | ||||
\(552\) | −6.10573 | −0.259877 | ||||||||
\(553\) | 20.2898 | + | 6.25406i | 0.862810 | + | 0.265950i | ||||
\(554\) | 1.90403 | 0.0808945 | ||||||||
\(555\) | 10.0858 | − | 17.4690i | 0.428117 | − | 0.741520i | ||||
\(556\) | −6.64231 | − | 11.5048i | −0.281697 | − | 0.487913i | ||||
\(557\) | 8.36276 | + | 14.4847i | 0.354341 | + | 0.613737i | 0.987005 | − | 0.160689i | \(-0.0513718\pi\) |
−0.632664 | + | 0.774427i | \(0.718038\pi\) | |||||||
\(558\) | −0.711226 | + | 1.23188i | −0.0301086 | + | 0.0521496i | ||||
\(559\) | −11.2426 | −0.475512 | ||||||||
\(560\) | 1.43542 | − | 1.33242i | 0.0606577 | − | 0.0563051i | ||||
\(561\) | −25.1065 | −1.06000 | ||||||||
\(562\) | 11.0108 | − | 19.0712i | 0.464462 | − | 0.804472i | ||||
\(563\) | −12.7080 | − | 22.0108i | −0.535577 | − | 0.927647i | −0.999135 | − | 0.0415802i | \(-0.986761\pi\) |
0.463558 | − | 0.886067i | \(-0.346573\pi\) | |||||||
\(564\) | 5.43054 | + | 9.40597i | 0.228667 | + | 0.396063i | ||||
\(565\) | 0.360901 | − | 0.625099i | 0.0151832 | − | 0.0262981i | ||||
\(566\) | 12.0937 | 0.508336 | ||||||||
\(567\) | 1.93911 | − | 1.79996i | 0.0814349 | − | 0.0755913i | ||||
\(568\) | 6.21650 | 0.260839 | ||||||||
\(569\) | 10.0903 | − | 17.4770i | 0.423009 | − | 0.732674i | −0.573223 | − | 0.819399i | \(-0.694307\pi\) |
0.996232 | + | 0.0867259i | \(0.0276404\pi\) | |||||||
\(570\) | −5.72366 | − | 9.91367i | −0.239738 | − | 0.415238i | ||||
\(571\) | −13.0255 | − | 22.5609i | −0.545101 | − | 0.944143i | −0.998601 | − | 0.0528863i | \(-0.983158\pi\) |
0.453499 | − | 0.891257i | \(-0.350175\pi\) | |||||||
\(572\) | −3.41008 | + | 5.90644i | −0.142583 | + | 0.246961i | ||||
\(573\) | −15.0087 | −0.626997 | ||||||||
\(574\) | −11.1629 | − | 3.44083i | −0.465932 | − | 0.143618i | ||||
\(575\) | −3.76014 | −0.156809 | ||||||||
\(576\) | −1.97466 | + | 3.42021i | −0.0822775 | + | 0.142509i | ||||
\(577\) | 2.75553 | + | 4.77271i | 0.114714 | + | 0.198691i | 0.917665 | − | 0.397354i | \(-0.130071\pi\) |
−0.802951 | + | 0.596045i | \(0.796738\pi\) | |||||||
\(578\) | −2.79180 | − | 4.83554i | −0.116124 | − | 0.201132i | ||||
\(579\) | 10.8747 | − | 18.8356i | 0.451938 | − | 0.782779i | ||||
\(580\) | −4.41442 | −0.183299 | ||||||||
\(581\) | 9.52324 | + | 41.6850i | 0.395090 | + | 1.72939i | ||||
\(582\) | 10.7402 | 0.445198 | ||||||||
\(583\) | 16.7551 | − | 29.0206i | 0.693923 | − | 1.20191i | ||||
\(584\) | −4.60888 | − | 7.98281i | −0.190717 | − | 0.330331i | ||||
\(585\) | 0.910741 | + | 1.57745i | 0.0376545 | + | 0.0652195i | ||||
\(586\) | 4.13200 | − | 7.15683i | 0.170691 | − | 0.295646i | ||||
\(587\) | −10.7694 | −0.444499 | −0.222249 | − | 0.974990i | \(-0.571340\pi\) | ||||
−0.222249 | + | 0.974990i | \(0.571340\pi\) | |||||||
\(588\) | −0.689452 | + | 9.25051i | −0.0284325 | + | 0.381485i | ||||
\(589\) | 13.2471 | 0.545835 | ||||||||
\(590\) | −6.26547 | + | 10.8521i | −0.257945 | + | 0.446775i | ||||
\(591\) | −1.06180 | − | 1.83909i | −0.0436765 | − | 0.0756499i | ||||
\(592\) | 2.25028 | + | 3.89760i | 0.0924860 | + | 0.160190i | ||||
\(593\) | 19.0491 | − | 32.9940i | 0.782252 | − | 1.35490i | −0.148376 | − | 0.988931i | \(-0.547404\pi\) |
0.930627 | − | 0.365968i | \(-0.119262\pi\) | |||||||
\(594\) | 4.22788 | 0.173472 | ||||||||
\(595\) | −5.23591 | − | 22.9186i | −0.214651 | − | 0.939569i | ||||
\(596\) | −5.90463 | −0.241863 | ||||||||
\(597\) | −0.976040 | + | 1.69055i | −0.0399467 | + | 0.0691896i | ||||
\(598\) | 0.918109 | + | 1.59021i | 0.0375443 | + | 0.0650286i | ||||
\(599\) | 8.80073 | + | 15.2433i | 0.359588 | + | 0.622825i | 0.987892 | − | 0.155143i | \(-0.0495839\pi\) |
−0.628304 | + | 0.777968i | \(0.716251\pi\) | |||||||
\(600\) | −2.29752 | + | 3.97943i | −0.0937960 | + | 0.162459i | ||||
\(601\) | 16.9127 | 0.689884 | 0.344942 | − | 0.938624i | \(-0.387899\pi\) | ||||
0.344942 | + | 0.938624i | \(0.387899\pi\) | |||||||
\(602\) | −23.3510 | − | 7.19764i | −0.951716 | − | 0.293354i | ||||
\(603\) | 0.496316 | 0.0202115 | ||||||||
\(604\) | 10.7410 | − | 18.6039i | 0.437044 | − | 0.756982i | ||||
\(605\) | −14.1056 | − | 24.4315i | −0.573472 | − | 0.993283i | ||||
\(606\) | 4.19511 | + | 7.26614i | 0.170415 | + | 0.295167i | ||||
\(607\) | −12.2398 | + | 21.1999i | −0.496797 | + | 0.860478i | −0.999993 | − | 0.00369446i | \(-0.998824\pi\) |
0.503196 | + | 0.864172i | \(0.332157\pi\) | |||||||
\(608\) | 44.3488 | 1.79858 | ||||||||
\(609\) | 3.54634 | − | 3.29186i | 0.143705 | − | 0.133393i | ||||
\(610\) | −3.77248 | −0.152743 | ||||||||
\(611\) | 4.09801 | − | 7.09796i | 0.165788 | − | 0.287153i | ||||
\(612\) | −3.23222 | − | 5.59838i | −0.130655 | − | 0.226301i | ||||
\(613\) | −16.5097 | − | 28.5956i | −0.666819 | − | 1.15496i | −0.978789 | − | 0.204872i | \(-0.934322\pi\) |
0.311970 | − | 0.950092i | \(-0.399011\pi\) | |||||||
\(614\) | −3.83385 | + | 6.64042i | −0.154722 | + | 0.267986i | ||||
\(615\) | 9.78961 | 0.394755 | ||||||||
\(616\) | −27.2608 | + | 25.3046i | −1.09837 | + | 1.01955i | ||||
\(617\) | 2.65783 | 0.107000 | 0.0535001 | − | 0.998568i | \(-0.482962\pi\) | ||||
0.0535001 | + | 0.998568i | \(0.482962\pi\) | |||||||
\(618\) | 1.86710 | − | 3.23391i | 0.0751057 | − | 0.130087i | ||||
\(619\) | 5.26942 | + | 9.12691i | 0.211796 | + | 0.366841i | 0.952277 | − | 0.305236i | \(-0.0987354\pi\) |
−0.740481 | + | 0.672078i | \(0.765402\pi\) | |||||||
\(620\) | 2.08980 | + | 3.61964i | 0.0839283 | + | 0.145368i | ||||
\(621\) | −1.11763 | + | 1.93578i | −0.0448487 | + | 0.0776803i | ||||
\(622\) | −12.6110 | −0.505654 | ||||||||
\(623\) | −32.9936 | − | 10.1698i | −1.32186 | − | 0.407446i | ||||
\(624\) | −0.406399 | −0.0162690 | ||||||||
\(625\) | 6.87959 | − | 11.9158i | 0.275184 | − | 0.476632i | ||||
\(626\) | 4.63823 | + | 8.03365i | 0.185381 | + | 0.321089i | ||||
\(627\) | −19.6868 | − | 34.0985i | −0.786215 | − | 1.36176i | ||||
\(628\) | −1.33676 | + | 2.31533i | −0.0533425 | + | 0.0923919i | ||||
\(629\) | 54.0225 | 2.15402 | ||||||||
\(630\) | 0.881717 | + | 3.85944i | 0.0351285 | + | 0.153764i | ||||
\(631\) | 7.56729 | 0.301249 | 0.150625 | − | 0.988591i | \(-0.451872\pi\) | ||||
0.150625 | + | 0.988591i | \(0.451872\pi\) | |||||||
\(632\) | −10.9602 | + | 18.9837i | −0.435974 | + | 0.755130i | ||||
\(633\) | 0.240972 | + | 0.417375i | 0.00957776 | + | 0.0165892i | ||||
\(634\) | −10.1179 | − | 17.5247i | −0.401832 | − | 0.695993i | ||||
\(635\) | 14.4017 | − | 24.9445i | 0.571514 | − | 0.989891i | ||||
\(636\) | 8.62823 | 0.342132 | ||||||||
\(637\) | 6.30555 | − | 3.03975i | 0.249835 | − | 0.120439i | ||||
\(638\) | 7.73216 | 0.306119 | ||||||||
\(639\) | 1.13790 | − | 1.97090i | 0.0450147 | − | 0.0779677i | ||||
\(640\) | 7.60439 | + | 13.1712i | 0.300590 | + | 0.520637i | ||||
\(641\) | 2.39047 | + | 4.14041i | 0.0944177 | + | 0.163536i | 0.909365 | − | 0.415998i | \(-0.136568\pi\) |
−0.814948 | + | 0.579534i | \(0.803234\pi\) | |||||||
\(642\) | 2.67549 | − | 4.63409i | 0.105593 | − | 0.182893i | ||||
\(643\) | −20.9917 | −0.827831 | −0.413916 | − | 0.910315i | \(-0.635839\pi\) | ||||
−0.413916 | + | 0.910315i | \(0.635839\pi\) | |||||||
\(644\) | −1.74543 | − | 7.64008i | −0.0687796 | − | 0.301061i | ||||
\(645\) | 20.4782 | 0.806330 | ||||||||
\(646\) | 15.3289 | − | 26.5503i | 0.603106 | − | 1.04461i | ||||
\(647\) | 10.1738 | + | 17.6216i | 0.399974 | + | 0.692775i | 0.993722 | − | 0.111876i | \(-0.0356858\pi\) |
−0.593748 | + | 0.804651i | \(0.702352\pi\) | |||||||
\(648\) | 1.36578 | + | 2.36561i | 0.0536530 | + | 0.0929298i | ||||
\(649\) | −21.5504 | + | 37.3264i | −0.845927 | + | 1.46519i | ||||
\(650\) | 1.38190 | 0.0542025 | ||||||||
\(651\) | −4.37803 | − | 1.34947i | −0.171589 | − | 0.0528899i | ||||
\(652\) | −18.4911 | −0.724166 | ||||||||
\(653\) | −0.816419 | + | 1.41408i | −0.0319489 | + | 0.0553372i | −0.881558 | − | 0.472076i | \(-0.843505\pi\) |
0.849609 | + | 0.527413i | \(0.176838\pi\) | |||||||
\(654\) | −1.47907 | − | 2.56182i | −0.0578361 | − | 0.100175i | ||||
\(655\) | −2.01429 | − | 3.48885i | −0.0787047 | − | 0.136321i | ||||
\(656\) | −1.09210 | + | 1.89158i | −0.0426395 | + | 0.0738537i | ||||
\(657\) | −3.37453 | −0.131653 | ||||||||
\(658\) | 13.0558 | − | 12.1189i | 0.508967 | − | 0.472445i | ||||
\(659\) | 14.5692 | 0.567537 | 0.283768 | − | 0.958893i | \(-0.408415\pi\) | ||||
0.283768 | + | 0.958893i | \(0.408415\pi\) | |||||||
\(660\) | 6.21141 | − | 10.7585i | 0.241779 | − | 0.418773i | ||||
\(661\) | 3.34135 | + | 5.78738i | 0.129963 | + | 0.225103i | 0.923662 | − | 0.383208i | \(-0.125181\pi\) |
−0.793699 | + | 0.608311i | \(0.791847\pi\) | |||||||
\(662\) | 11.3179 | + | 19.6032i | 0.439883 | + | 0.761900i | ||||
\(663\) | −2.43911 | + | 4.22466i | −0.0947271 | + | 0.164072i | ||||
\(664\) | −44.1459 | −1.71319 | ||||||||
\(665\) | 27.0214 | − | 25.0824i | 1.04784 | − | 0.972653i | ||||
\(666\) | −9.09728 | −0.352513 | ||||||||
\(667\) | −2.04397 | + | 3.54026i | −0.0791428 | + | 0.137079i | ||||
\(668\) | −3.74382 | − | 6.48448i | −0.144853 | − | 0.250892i | ||||
\(669\) | 6.10307 | + | 10.5708i | 0.235958 | + | 0.408692i | ||||
\(670\) | −0.371323 | + | 0.643150i | −0.0143454 | + | 0.0248470i | ||||
\(671\) | −12.9756 | −0.500919 | ||||||||
\(672\) | −14.6569 | − | 4.51779i | −0.565402 | − | 0.174278i | ||||
\(673\) | −6.76051 | −0.260598 | −0.130299 | − | 0.991475i | \(-0.541594\pi\) | ||||
−0.130299 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(674\) | 10.3932 | − | 18.0015i | 0.400330 | − | 0.693391i | ||||
\(675\) | 0.841101 | + | 1.45683i | 0.0323740 | + | 0.0560734i | ||||
\(676\) | 0.662583 | + | 1.14763i | 0.0254840 | + | 0.0441395i | ||||
\(677\) | 0.548460 | − | 0.949961i | 0.0210790 | − | 0.0365100i | −0.855293 | − | 0.518144i | \(-0.826623\pi\) |
0.876373 | + | 0.481634i | \(0.159957\pi\) | |||||||
\(678\) | −0.325530 | −0.0125019 | ||||||||
\(679\) | 7.70410 | + | 33.7223i | 0.295656 | + | 1.29414i | ||||
\(680\) | 24.2716 | 0.930772 | ||||||||
\(681\) | 0.503684 | − | 0.872406i | 0.0193012 | − | 0.0334307i | ||||
\(682\) | −3.66043 | − | 6.34005i | −0.140165 | − | 0.242773i | ||||
\(683\) | −9.68245 | − | 16.7705i | −0.370489 | − | 0.641705i | 0.619152 | − | 0.785271i | \(-0.287476\pi\) |
−0.989641 | + | 0.143566i | \(0.954143\pi\) | |||||||
\(684\) | 5.06898 | − | 8.77974i | 0.193817 | − | 0.335702i | ||||
\(685\) | −37.5991 | −1.43659 | ||||||||
\(686\) | 15.0428 | − | 2.27670i | 0.574335 | − | 0.0869249i | ||||
\(687\) | 20.0383 | 0.764508 | ||||||||
\(688\) | −2.28450 | + | 3.95687i | −0.0870956 | + | 0.150854i | ||||
\(689\) | −3.25553 | − | 5.63874i | −0.124026 | − | 0.214819i | ||||
\(690\) | −1.67232 | − | 2.89654i | −0.0636641 | − | 0.110270i | ||||
\(691\) | 10.7499 | − | 18.6194i | 0.408946 | − | 0.708314i | −0.585826 | − | 0.810437i | \(-0.699230\pi\) |
0.994772 | + | 0.102122i | \(0.0325633\pi\) | |||||||
\(692\) | 10.5916 | 0.402631 | ||||||||
\(693\) | 3.03271 | + | 13.2747i | 0.115203 | + | 0.504266i | ||||
\(694\) | −15.0742 | −0.572210 | ||||||||
\(695\) | 9.13006 | − | 15.8137i | 0.346323 | − | 0.599849i | ||||
\(696\) | 2.49781 | + | 4.32634i | 0.0946794 | + | 0.163989i | ||||
\(697\) | 13.1091 | + | 22.7056i | 0.496541 | + | 0.860034i | ||||
\(698\) | −11.5183 | + | 19.9503i | −0.435974 | + | 0.755129i | ||||
\(699\) | −21.7407 | −0.822310 | ||||||||
\(700\) | −5.63623 | − | 1.73729i | −0.213029 | − | 0.0656635i | ||||
\(701\) | −24.7988 | −0.936637 | −0.468319 | − | 0.883560i | \(-0.655140\pi\) | ||||
−0.468319 | + | 0.883560i | \(0.655140\pi\) | |||||||
\(702\) | 0.410741 | − | 0.711425i | 0.0155024 | − | 0.0268510i | ||||
\(703\) | 42.3608 | + | 73.3710i | 1.59767 | + | 2.76724i | ||||
\(704\) | −10.1629 | − | 17.6026i | −0.383028 | − | 0.663424i | ||||
\(705\) | −7.46445 | + | 12.9288i | −0.281127 | + | 0.486927i | ||||
\(706\) | −15.3126 | −0.576297 | ||||||||
\(707\) | −19.8051 | + | 18.3839i | −0.744847 | + | 0.691399i | ||||
\(708\) | −11.0976 | −0.417075 | ||||||||
\(709\) | 10.2389 | − | 17.7342i | 0.384529 | − | 0.666023i | −0.607175 | − | 0.794568i | \(-0.707697\pi\) |
0.991704 | + | 0.128545i | \(0.0410306\pi\) | |||||||
\(710\) | 1.70266 | + | 2.94909i | 0.0638997 | + | 0.110677i | ||||
\(711\) | 4.01243 | + | 6.94974i | 0.150478 | + | 0.260635i | ||||
\(712\) | 17.8226 | − | 30.8696i | 0.667930 | − | 1.15689i | ||||
\(713\) | 3.87048 | 0.144951 | ||||||||
\(714\) | −7.77072 | + | 7.21311i | −0.290812 | + | 0.269944i | ||||
\(715\) | −9.37453 | −0.350588 | ||||||||
\(716\) | −7.21932 | + | 12.5042i | −0.269799 | + | 0.467305i | ||||
\(717\) | −1.71767 | − | 2.97509i | −0.0641475 | − | 0.111107i | ||||
\(718\) | 14.3295 | + | 24.8194i | 0.534772 | + | 0.926252i | ||||
\(719\) | 7.00581 | − | 12.1344i | 0.261272 | − | 0.452537i | −0.705308 | − | 0.708901i | \(-0.749191\pi\) |
0.966580 | + | 0.256364i | \(0.0825246\pi\) | |||||||
\(720\) | 0.740250 | 0.0275875 | ||||||||
\(721\) | 11.4931 | + | 3.54261i | 0.428027 | + | 0.131934i | ||||
\(722\) | 32.4712 | 1.20845 | ||||||||
\(723\) | −2.26041 | + | 3.91514i | −0.0840655 | + | 0.145606i | ||||
\(724\) | −2.52166 | − | 4.36764i | −0.0937166 | − | 0.162322i | ||||
\(725\) | 1.53825 | + | 2.66432i | 0.0571291 | + | 0.0989505i | ||||
\(726\) | −6.36156 | + | 11.0185i | −0.236100 | + | 0.408936i | ||||
\(727\) | −23.9523 | −0.888342 | −0.444171 | − | 0.895942i | \(-0.646502\pi\) | ||||
−0.444171 | + | 0.895942i | \(0.646502\pi\) | |||||||
\(728\) | 1.60960 | + | 7.04552i | 0.0596557 | + | 0.261124i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.52468 | − | 4.37288i | 0.0934427 | − | 0.161847i | ||||
\(731\) | 27.4220 | + | 47.4962i | 1.01424 | + | 1.75671i | ||||
\(732\) | −1.67049 | − | 2.89338i | −0.0617431 | − | 0.106942i | ||||
\(733\) | 6.08419 | − | 10.5381i | 0.224725 | − | 0.389235i | −0.731512 | − | 0.681829i | \(-0.761185\pi\) |
0.956237 | + | 0.292594i | \(0.0945183\pi\) | |||||||
\(734\) | −20.8783 | −0.770634 | ||||||||
\(735\) | −11.4854 | + | 5.53685i | −0.423647 | + | 0.204230i | ||||
\(736\) | 12.9577 | 0.477627 | ||||||||
\(737\) | −1.27718 | + | 2.21214i | −0.0470456 | + | 0.0814854i | ||||
\(738\) | −2.20754 | − | 3.82357i | −0.0812607 | − | 0.140748i | ||||
\(739\) | −11.8531 | − | 20.5301i | −0.436022 | − | 0.755212i | 0.561357 | − | 0.827574i | \(-0.310280\pi\) |
−0.997378 | + | 0.0723622i | \(0.976946\pi\) | |||||||
\(740\) | −13.3653 | + | 23.1494i | −0.491318 | + | 0.850989i | ||||
\(741\) | −7.65033 | −0.281042 | ||||||||
\(742\) | −3.15178 | − | 13.7959i | −0.115705 | − | 0.506464i | ||||
\(743\) | 43.8078 | 1.60715 | 0.803577 | − | 0.595201i | \(-0.202928\pi\) | ||||
0.803577 | + | 0.595201i | \(0.202928\pi\) | |||||||
\(744\) | 2.36494 | − | 4.09620i | 0.0867030 | − | 0.150174i | ||||
\(745\) | −4.05805 | − | 7.02875i | −0.148675 | − | 0.257513i | ||||
\(746\) | −4.35364 | − | 7.54073i | −0.159398 | − | 0.276086i | ||||
\(747\) | −8.08069 | + | 13.9962i | −0.295657 | + | 0.512093i | ||||
\(748\) | 33.2702 | 1.21648 | ||||||||
\(749\) | 16.4693 | + | 5.07645i | 0.601775 | + | 0.185489i | ||||
\(750\) | −9.99868 | −0.365100 | ||||||||
\(751\) | −5.43423 | + | 9.41235i | −0.198298 | + | 0.343462i | −0.947977 | − | 0.318340i | \(-0.896875\pi\) |
0.749679 | + | 0.661802i | \(0.230208\pi\) | |||||||
\(752\) | −1.66543 | − | 2.88461i | −0.0607319 | − | 0.105191i | ||||
\(753\) | 5.66717 | + | 9.81583i | 0.206523 | + | 0.357709i | ||||
\(754\) | 0.751184 | − | 1.30109i | 0.0273565 | − | 0.0473829i | ||||
\(755\) | 29.5276 | 1.07462 | ||||||||
\(756\) | −2.56964 | + | 2.38525i | −0.0934569 | + | 0.0867507i | ||||
\(757\) | −17.6451 | −0.641323 | −0.320662 | − | 0.947194i | \(-0.603905\pi\) | ||||
−0.320662 | + | 0.947194i | \(0.603905\pi\) | |||||||
\(758\) | −11.4080 | + | 19.7593i | −0.414359 | + | 0.717691i | ||||
\(759\) | −5.75202 | − | 9.96280i | −0.208785 | − | 0.361627i | ||||
\(760\) | 19.0321 | + | 32.9646i | 0.690367 | + | 1.19575i | ||||
\(761\) | 5.48919 | − | 9.50756i | 0.198983 | − | 0.344649i | −0.749216 | − | 0.662326i | \(-0.769569\pi\) |
0.948199 | + | 0.317677i | \(0.102903\pi\) | |||||||
\(762\) | −12.9902 | −0.470587 | ||||||||
\(763\) | 6.98267 | − | 6.48161i | 0.252789 | − | 0.234650i | ||||
\(764\) | 19.8890 | 0.719559 | ||||||||
\(765\) | 4.44279 | − | 7.69514i | 0.160629 | − | 0.278218i | ||||
\(766\) | −3.13586 | − | 5.43148i | −0.113303 | − | 0.196247i | ||||
\(767\) | 4.18727 | + | 7.25256i | 0.151193 | + | 0.261875i | ||||
\(768\) | 7.37887 | − | 12.7806i | 0.266262 | − | 0.461180i | ||||
\(769\) | −1.58755 | −0.0572484 | −0.0286242 | − | 0.999590i | \(-0.509113\pi\) | ||||
−0.0286242 | + | 0.999590i | \(0.509113\pi\) | |||||||
\(770\) | −19.4710 | − | 6.00167i | −0.701685 | − | 0.216285i | ||||
\(771\) | −11.1890 | −0.402962 | ||||||||
\(772\) | −14.4108 | + | 24.9602i | −0.518656 | + | 0.898339i | ||||
\(773\) | −22.0386 | − | 38.1720i | −0.792674 | − | 1.37295i | −0.924306 | − | 0.381653i | \(-0.875355\pi\) |
0.131632 | − | 0.991299i | \(-0.457978\pi\) | |||||||
\(774\) | −4.61781 | − | 7.99828i | −0.165984 | − | 0.287492i | ||||
\(775\) | 1.45642 | − | 2.52260i | 0.0523162 | − | 0.0906143i | ||||
\(776\) | −35.7131 | −1.28203 | ||||||||
\(777\) | −6.52559 | − | 28.5637i | −0.234104 | − | 1.02472i | ||||
\(778\) | 2.36332 | 0.0847292 | ||||||||
\(779\) | −20.5585 | + | 35.6083i | −0.736584 | + | 1.27580i | ||||
\(780\) | −1.20688 | − | 2.09038i | −0.0432134 | − | 0.0748478i | ||||
\(781\) | 5.85638 | + | 10.1435i | 0.209558 | + | 0.362965i | ||||
\(782\) | 4.47874 | − | 7.75740i | 0.160159 | − | 0.277404i | ||||
\(783\) | 1.82885 | 0.0653578 | ||||||||
\(784\) | 0.211440 | − | 2.83693i | 0.00755143 | − | 0.101319i | ||||
\(785\) | −3.67483 | −0.131160 | ||||||||
\(786\) | −0.908437 | + | 1.57346i | −0.0324029 | + | 0.0561234i | ||||
\(787\) | −16.5191 | − | 28.6118i | −0.588841 | − | 1.01990i | −0.994385 | − | 0.105827i | \(-0.966251\pi\) |
0.405544 | − | 0.914076i | \(-0.367082\pi\) | |||||||
\(788\) | 1.40706 | + | 2.43709i | 0.0501243 | + | 0.0868179i | ||||
\(789\) | −2.34110 | + | 4.05491i | −0.0833454 | + | 0.144358i | ||||
\(790\) | −12.0077 | −0.427216 | ||||||||
\(791\) | −0.233507 | − | 1.02210i | −0.00830254 | − | 0.0363418i | ||||
\(792\) | −14.0584 | −0.499544 | ||||||||
\(793\) | −1.26059 | + | 2.18341i | −0.0447649 | + | 0.0775350i | ||||
\(794\) | 10.9996 | + | 19.0518i | 0.390361 | + | 0.676125i | ||||
\(795\) | 5.92988 | + | 10.2709i | 0.210311 | + | 0.364270i | ||||
\(796\) | 1.29342 | − | 2.24026i | 0.0458439 | − | 0.0794040i | ||||
\(797\) | −9.81448 | −0.347647 | −0.173823 | − | 0.984777i | \(-0.555612\pi\) | ||||
−0.173823 | + | 0.984777i | \(0.555612\pi\) | |||||||
\(798\) | −15.8898 | − | 4.89782i | −0.562493 | − | 0.173381i | ||||
\(799\) | −39.9819 | −1.41446 | ||||||||
\(800\) | 4.87585 | − | 8.44521i | 0.172387 | − | 0.298583i | ||||
\(801\) | −6.52468 | − | 11.3011i | −0.230538 | − | 0.399304i | ||||
\(802\) | 1.90646 | + | 3.30209i | 0.0673196 | + | 0.116601i | ||||
\(803\) | 8.68376 | − | 15.0407i | 0.306443 | − | 0.530775i | ||||
\(804\) | −0.657701 | −0.0231953 | ||||||||
\(805\) | 7.89502 | − | 7.32849i | 0.278263 | − | 0.258295i | ||||
\(806\) | −1.42245 | −0.0501037 | ||||||||
\(807\) | −9.67942 | + | 16.7652i | −0.340732 | + | 0.590165i | ||||
\(808\) | −13.9494 | − | 24.1611i | −0.490740 | − | 0.849986i | ||||
\(809\) | 23.6464 | + | 40.9567i | 0.831362 | + | 1.43996i | 0.896959 | + | 0.442114i | \(0.145771\pi\) |
−0.0655972 | + | 0.997846i | \(0.520895\pi\) | |||||||
\(810\) | −0.748158 | + | 1.29585i | −0.0262876 | + | 0.0455314i | ||||
\(811\) | 18.8003 | 0.660167 | 0.330083 | − | 0.943952i | \(-0.392923\pi\) | ||||
0.330083 | + | 0.943952i | \(0.392923\pi\) | |||||||
\(812\) | −4.69949 | + | 4.36226i | −0.164920 | + | 0.153085i | ||||
\(813\) | −17.3648 | −0.609009 | ||||||||
\(814\) | 23.4103 | − | 40.5478i | 0.820529 | − | 1.42120i | ||||
\(815\) | −12.7083 | − | 22.0114i | −0.445151 | − | 0.771024i | ||||
\(816\) | 0.991252 | + | 1.71690i | 0.0347008 | + | 0.0601035i | ||||
\(817\) | −43.0049 | + | 74.4866i | −1.50455 | + | 2.60596i | ||||
\(818\) | 4.94784 | 0.172997 | ||||||||
\(819\) | 2.52837 | + | 0.779336i | 0.0883483 | + | 0.0272322i | ||||
\(820\) | −12.9729 | −0.453032 | ||||||||
\(821\) | 10.5865 | − | 18.3363i | 0.369471 | − | 0.639942i | −0.620012 | − | 0.784592i | \(-0.712872\pi\) |
0.989483 | + | 0.144650i | \(0.0462057\pi\) | |||||||
\(822\) | 8.47853 | + | 14.6852i | 0.295723 | + | 0.512206i | ||||
\(823\) | −6.64140 | − | 11.5032i | −0.231505 | − | 0.400978i | 0.726746 | − | 0.686906i | \(-0.241032\pi\) |
−0.958251 | + | 0.285928i | \(0.907698\pi\) | |||||||
\(824\) | −6.20841 | + | 10.7533i | −0.216280 | + | 0.374608i | ||||
\(825\) | −8.65770 | −0.301422 | ||||||||
\(826\) | 4.05382 | + | 17.7444i | 0.141051 | + | 0.617405i | ||||
\(827\) | 14.0291 | 0.487840 | 0.243920 | − | 0.969795i | \(-0.421567\pi\) | ||||
0.243920 | + | 0.969795i | \(0.421567\pi\) | |||||||
\(828\) | 1.48104 | − | 2.56524i | 0.0514697 | − | 0.0891481i | ||||
\(829\) | 5.41786 | + | 9.38401i | 0.188170 | + | 0.325920i | 0.944640 | − | 0.328108i | \(-0.106411\pi\) |
−0.756470 | + | 0.654028i | \(0.773078\pi\) | |||||||
\(830\) | −12.0913 | − | 20.9427i | −0.419694 | − | 0.726931i | ||||
\(831\) | −1.15890 | + | 2.00727i | −0.0402018 | + | 0.0696315i | ||||
\(832\) | −3.94932 | −0.136918 | ||||||||
\(833\) | −28.2218 | − | 19.2245i | −0.977827 | − | 0.666090i | ||||
\(834\) | −8.23525 | −0.285163 | ||||||||
\(835\) | 5.14599 | − | 8.91312i | 0.178084 | − | 0.308451i | ||||
\(836\) | 26.0883 | + | 45.1862i | 0.902282 | + | 1.56280i | ||||
\(837\) | −0.865783 | − | 1.49958i | −0.0299258 | − | 0.0518331i | ||||
\(838\) | −2.86171 | + | 4.95662i | −0.0988561 | + | 0.171224i | ||||
\(839\) | 1.76051 | 0.0607794 | 0.0303897 | − | 0.999538i | \(-0.490325\pi\) | ||||
0.0303897 | + | 0.999538i | \(0.490325\pi\) | |||||||
\(840\) | −2.93186 | − | 12.8333i | −0.101159 | − | 0.442791i | ||||
\(841\) | −25.6553 | −0.884666 | ||||||||
\(842\) | 2.27255 | − | 3.93617i | 0.0783171 | − | 0.135649i | ||||
\(843\) | 13.4036 | + | 23.2156i | 0.461643 | + | 0.799589i | ||||
\(844\) | −0.319328 | − | 0.553092i | −0.0109917 | − | 0.0190382i | ||||
\(845\) | −0.910741 | + | 1.57745i | −0.0313305 | + | 0.0542659i | ||||
\(846\) | 6.73288 | 0.231481 | ||||||||
\(847\) | −39.1593 | − | 12.0703i | −1.34553 | − | 0.414742i | ||||
\(848\) | −2.64609 | −0.0908670 | ||||||||
\(849\) | −7.36090 | + | 12.7495i | −0.252625 | + | 0.437560i | ||||
\(850\) | −3.37060 | − | 5.83805i | −0.115611 | − | 0.200244i | ||||
\(851\) | 12.3768 | + | 21.4373i | 0.424272 | + | 0.734861i | ||||
\(852\) | −1.50791 | + | 2.61177i | −0.0516601 | + | 0.0894779i | ||||
\(853\) | 11.7754 | 0.403181 | 0.201590 | − | 0.979470i | \(-0.435389\pi\) | ||||
0.201590 | + | 0.979470i | \(0.435389\pi\) | |||||||
\(854\) | −4.01610 | + | 3.72791i | −0.137428 | + | 0.127566i | ||||
\(855\) | 13.9349 | 0.476565 | ||||||||
\(856\) | −8.89645 | + | 15.4091i | −0.304075 | + | 0.526673i | ||||
\(857\) | −0.157584 | − | 0.272943i | −0.00538296 | − | 0.00932356i | 0.863321 | − | 0.504655i | \(-0.168380\pi\) |
−0.868704 | + | 0.495331i | \(0.835047\pi\) | |||||||
\(858\) | 2.11394 | + | 3.66145i | 0.0721688 | + | 0.125000i | ||||
\(859\) | −28.0707 | + | 48.6199i | −0.957761 | + | 1.65889i | −0.229841 | + | 0.973228i | \(0.573821\pi\) |
−0.727920 | + | 0.685662i | \(0.759513\pi\) | |||||||
\(860\) | −27.1371 | −0.925366 | ||||||||
\(861\) | 10.4218 | − | 9.67395i | 0.355174 | − | 0.329687i | ||||
\(862\) | −15.6346 | −0.532518 | ||||||||
\(863\) | −26.1297 | + | 45.2579i | −0.889465 | + | 1.54060i | −0.0489551 | + | 0.998801i | \(0.515589\pi\) |
−0.840509 | + | 0.541797i | \(0.817744\pi\) | |||||||
\(864\) | −2.89849 | − | 5.02033i | −0.0986087 | − | 0.170795i | ||||
\(865\) | 7.27922 | + | 12.6080i | 0.247501 | + | 0.428684i | ||||
\(866\) | −9.93596 | + | 17.2096i | −0.337638 | + | 0.584806i | ||||
\(867\) | 6.79698 | 0.230838 | ||||||||
\(868\) | 5.80162 | + | 1.78827i | 0.196920 | + | 0.0606980i | ||||
\(869\) | −41.3012 | −1.40105 | ||||||||
\(870\) | −1.36827 | + | 2.36991i | −0.0463887 | + | 0.0803475i | ||||
\(871\) | 0.248158 | + | 0.429822i | 0.00840851 | + | 0.0145640i | ||||
\(872\) | 4.91814 | + | 8.51847i | 0.166549 | + | 0.288472i | ||||
\(873\) | −6.53711 | + | 11.3226i | −0.221248 | + | 0.383212i | ||||
\(874\) | 14.0477 | 0.475170 | ||||||||
\(875\) | −7.17217 | − | 31.3939i | −0.242464 | − | 1.06131i | ||||
\(876\) | 4.47182 | 0.151089 | ||||||||
\(877\) | 6.22734 | − | 10.7861i | 0.210282 | − | 0.364220i | −0.741520 | − | 0.670930i | \(-0.765895\pi\) |
0.951803 | + | 0.306710i | \(0.0992283\pi\) | |||||||
\(878\) | −5.77730 | − | 10.0066i | −0.194974 | − | 0.337706i | ||||
\(879\) | 5.02993 | + | 8.71209i | 0.169655 | + | 0.293852i | ||||
\(880\) | −1.90490 | + | 3.29939i | −0.0642142 | + | 0.111222i | ||||
\(881\) | 42.2647 | 1.42393 | 0.711967 | − | 0.702213i | \(-0.247804\pi\) | ||||
0.711967 | + | 0.702213i | \(0.247804\pi\) | |||||||
\(882\) | 4.75250 | + | 3.23737i | 0.160025 | + | 0.109008i | ||||
\(883\) | 24.4690 | 0.823448 | 0.411724 | − | 0.911309i | \(-0.364927\pi\) | ||||
0.411724 | + | 0.911309i | \(0.364927\pi\) | |||||||
\(884\) | 3.23222 | − | 5.59838i | 0.108711 | − | 0.188294i | ||||
\(885\) | −7.62703 | − | 13.2104i | −0.256380 | − | 0.444063i | ||||
\(886\) | 4.32262 | + | 7.48699i | 0.145221 | + | 0.251530i | ||||
\(887\) | 6.09057 | − | 10.5492i | 0.204501 | − | 0.354207i | −0.745472 | − | 0.666537i | \(-0.767776\pi\) |
0.949974 | + | 0.312330i | \(0.101109\pi\) | |||||||
\(888\) | 30.2500 | 1.01512 | ||||||||
\(889\) | −9.31804 | − | 40.7868i | −0.312517 | − | 1.36795i | ||||
\(890\) | 19.5260 | 0.654512 | ||||||||
\(891\) | −2.57332 | + | 4.45713i | −0.0862096 | + | 0.149319i | ||||
\(892\) | −8.08759 | − | 14.0081i | −0.270792 | − | 0.469026i | ||||
\(893\) | −31.3511 | − | 54.3017i | −1.04913 | − | 1.81714i | ||||
\(894\) | −1.83017 | + | 3.16994i | −0.0612099 | + | 0.106019i | ||||
\(895\) | −19.8463 | −0.663390 | ||||||||
\(896\) | 21.1110 | + | 6.50719i | 0.705270 | + | 0.217390i | ||||
\(897\) | −2.23525 | −0.0746328 | ||||||||
\(898\) | −5.22294 | + | 9.04639i | −0.174292 | + | 0.301882i | ||||
\(899\) | −1.58339 | − | 2.74251i | −0.0528089 | − | 0.0914678i | ||||
\(900\) | −1.11460 | − | 1.93054i | −0.0371533 | − | 0.0643514i | ||||
\(901\) | −15.8812 | + | 27.5070i | −0.529078 | + | 0.916390i | ||||
\(902\) | 22.7229 | 0.756589 | ||||||||
\(903\) | 21.8006 | − | 20.2363i | 0.725480 | − | 0.673421i | ||||
\(904\) | 1.08244 | 0.0360015 | ||||||||
\(905\) | 3.46609 | − | 6.00345i | 0.115217 | − | 0.199561i | ||||
\(906\) | −6.65842 | − | 11.5327i | −0.221211 | − | 0.383149i | ||||
\(907\) | 2.87537 | + | 4.98029i | 0.0954751 | + | 0.165368i | 0.909807 | − | 0.415032i | \(-0.136230\pi\) |
−0.814332 | + | 0.580400i | \(0.802896\pi\) | |||||||
\(908\) | −0.667465 | + | 1.15608i | −0.0221506 | + | 0.0383660i | ||||
\(909\) | −10.2135 | −0.338761 | ||||||||
\(910\) | −2.90152 | + | 2.69331i | −0.0961844 | + | 0.0892824i | ||||
\(911\) | 47.9209 | 1.58769 | 0.793846 | − | 0.608119i | \(-0.208076\pi\) | ||||
0.793846 | + | 0.608119i | \(0.208076\pi\) | |||||||
\(912\) | −1.55455 | + | 2.69255i | −0.0514762 | + | 0.0891593i | ||||
\(913\) | −41.5885 | − | 72.0334i | −1.37638 | − | 2.38396i | ||||
\(914\) | −0.788710 | − | 1.36609i | −0.0260882 | − | 0.0451861i | ||||
\(915\) | 2.29614 | − | 3.97704i | 0.0759081 | − | 0.131477i | ||||
\(916\) | −26.5541 | −0.877371 | ||||||||
\(917\) | −5.59199 | − | 1.72366i | −0.184664 | − | 0.0569202i | ||||
\(918\) | −4.00737 | −0.132263 | ||||||||
\(919\) | −15.4236 | + | 26.7145i | −0.508778 | + | 0.881229i | 0.491171 | + | 0.871063i | \(0.336569\pi\) |
−0.999948 | + | 0.0101654i | \(0.996764\pi\) | |||||||
\(920\) | 5.56074 | + | 9.63149i | 0.183332 | + | 0.317541i | ||||
\(921\) | −4.66699 | − | 8.08346i | −0.153783 | − | 0.266359i | ||||
\(922\) | −10.1995 | + | 17.6661i | −0.335903 | + | 0.581801i | ||||
\(923\) | 2.27580 | 0.0749089 | ||||||||
\(924\) | −4.01884 | − | 17.5912i | −0.132210 | − | 0.578709i | ||||
\(925\) | 18.6291 | 0.612521 | ||||||||
\(926\) | −3.72111 | + | 6.44515i | −0.122283 | + | 0.211801i | ||||
\(927\) | 2.27284 | + | 3.93667i | 0.0746499 | + | 0.129297i | ||||
\(928\) | −5.30091 | − | 9.18144i | −0.174011 | − | 0.301396i | ||||
\(929\) | −4.85631 | + | 8.41138i | −0.159330 | + | 0.275968i | −0.934627 | − | 0.355628i | \(-0.884267\pi\) |
0.775297 | + | 0.631597i | \(0.217600\pi\) | |||||||
\(930\) | 2.59097 | 0.0849612 | ||||||||
\(931\) | 3.98028 | − | 53.4042i | 0.130449 | − | 1.75025i | ||||
\(932\) | 28.8101 | 0.943706 | ||||||||
\(933\) | 7.67574 | − | 13.2948i | 0.251292 | − | 0.435251i | ||||
\(934\) | 3.31265 | + | 5.73768i | 0.108393 | + | 0.187743i | ||||
\(935\) | 22.8655 | + | 39.6042i | 0.747781 | + | 1.29520i | ||||
\(936\) | −1.36578 | + | 2.36561i | −0.0446420 | + | 0.0773222i | ||||
\(937\) | −55.4352 | −1.81099 | −0.905495 | − | 0.424356i | \(-0.860500\pi\) | ||||
−0.905495 | + | 0.424356i | \(0.860500\pi\) | |||||||
\(938\) | 0.240250 | + | 1.05162i | 0.00784443 | + | 0.0343365i | ||||
\(939\) | −11.2923 | −0.368512 | ||||||||
\(940\) | 9.89164 | − | 17.1328i | 0.322630 | − | 0.558811i | ||||
\(941\) | 12.2114 | + | 21.1508i | 0.398081 | + | 0.689496i | 0.993489 | − | 0.113927i | \(-0.0363431\pi\) |
−0.595409 | + | 0.803423i | \(0.703010\pi\) | |||||||
\(942\) | 0.828669 | + | 1.43530i | 0.0269995 | + | 0.0467645i | ||||
\(943\) | −6.00671 | + | 10.4039i | −0.195605 | + | 0.338799i | ||||
\(944\) | 3.40341 | 0.110771 | ||||||||
\(945\) | −4.60537 | − | 1.41955i | −0.149813 | − | 0.0461778i | ||||
\(946\) | 47.5325 | 1.54541 | ||||||||
\(947\) | −8.32185 | + | 14.4139i | −0.270424 | + | 0.468388i | −0.968970 | − | 0.247177i | \(-0.920497\pi\) |
0.698547 | + | 0.715564i | \(0.253830\pi\) | |||||||
\(948\) | −5.31714 | − | 9.20956i | −0.172693 | − | 0.299113i | ||||
\(949\) | −1.68727 | − | 2.92243i | −0.0547710 | − | 0.0948661i | ||||
\(950\) | 5.28599 | − | 9.15561i | 0.171500 | − | 0.297047i | ||||
\(951\) | 24.6332 | 0.798786 | ||||||||
\(952\) | 25.8389 | − | 23.9848i | 0.837445 | − | 0.777351i | ||||
\(953\) | 44.7918 | 1.45095 | 0.725475 | − | 0.688249i | \(-0.241620\pi\) | ||||
0.725475 | + | 0.688249i | \(0.241620\pi\) | |||||||
\(954\) | 2.67436 | − | 4.63212i | 0.0865855 | − | 0.149971i | ||||
\(955\) | 13.6690 | + | 23.6754i | 0.442319 | + | 0.766120i | ||||
\(956\) | 2.27620 | + | 3.94249i | 0.0736175 | + | 0.127509i | ||||
\(957\) | −4.70623 | + | 8.15142i | −0.152131 | + | 0.263498i | ||||
\(958\) | 7.78668 | 0.251576 | ||||||||
\(959\) | −40.0271 | + | 37.1548i | −1.29254 | + | 1.19979i | ||||
\(960\) | 7.19362 | 0.232173 | ||||||||
\(961\) | 14.0008 | − | 24.2502i | 0.451640 | − | 0.782263i | ||||
\(962\) | −4.54864 | − | 7.87848i | −0.146654 | − | 0.254012i | ||||
\(963\) | 3.25691 | + | 5.64113i | 0.104952 | + | 0.181783i | ||||
\(964\) | 2.99542 | − | 5.18821i | 0.0964759 | − | 0.167101i | ||||
\(965\) | −39.6162 | −1.27529 | ||||||||
\(966\) | −4.64263 | − | 1.43103i | −0.149374 | − | 0.0460427i | ||||
\(967\) | 54.1765 | 1.74220 | 0.871099 | − | 0.491107i | \(-0.163408\pi\) | ||||
0.871099 | + | 0.491107i | \(0.163408\pi\) | |||||||
\(968\) | 21.1532 | − | 36.6385i | 0.679891 | − | 1.17761i | ||||
\(969\) | 18.6600 | + | 32.3200i | 0.599445 | + | 1.03827i | ||||
\(970\) | −9.78159 | − | 16.9422i | −0.314068 | − | 0.543982i | ||||
\(971\) | −16.7999 | + | 29.0984i | −0.539136 | + | 0.933811i | 0.459815 | + | 0.888015i | \(0.347916\pi\) |
−0.998951 | + | 0.0457959i | \(0.985418\pi\) | |||||||
\(972\) | −1.32517 | −0.0425047 | ||||||||
\(973\) | −5.90724 | − | 25.8571i | −0.189377 | − | 0.828941i | ||||
\(974\) | −13.8175 | −0.442740 | ||||||||
\(975\) | −0.841101 | + | 1.45683i | −0.0269368 | + | 0.0466559i | ||||
\(976\) | 0.512303 | + | 0.887335i | 0.0163984 | + | 0.0284029i | ||||
\(977\) | 27.9356 | + | 48.3859i | 0.893739 | + | 1.54800i | 0.835357 | + | 0.549707i | \(0.185261\pi\) |
0.0583819 | + | 0.998294i | \(0.481406\pi\) | |||||||
\(978\) | −5.73138 | + | 9.92705i | −0.183269 | + | 0.317432i | ||||
\(979\) | 67.1605 | 2.14646 | ||||||||
\(980\) | 15.2201 | − | 7.33724i | 0.486189 | − | 0.234380i | ||||
\(981\) | 3.60097 | 0.114970 | ||||||||
\(982\) | 6.08378 | − | 10.5374i | 0.194141 | − | 0.336263i | ||||
\(983\) | −26.0283 | − | 45.0823i | −0.830172 | − | 1.43790i | −0.897901 | − | 0.440197i | \(-0.854909\pi\) |
0.0677289 | − | 0.997704i | \(-0.478425\pi\) | |||||||
\(984\) | 7.34044 | + | 12.7140i | 0.234005 | + | 0.405308i | ||||
\(985\) | −1.93404 | + | 3.34986i | −0.0616238 | + | 0.106735i | ||||
\(986\) | −7.32888 | −0.233399 | ||||||||
\(987\) | 4.82957 | + | 21.1400i | 0.153727 | + | 0.672892i | ||||
\(988\) | 10.1380 | 0.322532 | ||||||||
\(989\) | −12.5650 | + | 21.7633i | −0.399545 | + | 0.692032i | ||||
\(990\) | −3.85051 | − | 6.66927i | −0.122377 | − | 0.211963i | ||||
\(991\) | −7.15402 | − | 12.3911i | −0.227255 | − | 0.393617i | 0.729739 | − | 0.683726i | \(-0.239642\pi\) |
−0.956994 | + | 0.290109i | \(0.906308\pi\) | |||||||
\(992\) | −5.01893 | + | 8.69304i | −0.159351 | + | 0.276004i | ||||
\(993\) | −27.5549 | −0.874427 | ||||||||
\(994\) | 4.72686 | + | 1.45699i | 0.149927 | + | 0.0462130i | ||||
\(995\) | 3.55568 | 0.112723 | ||||||||
\(996\) | 10.7083 | − | 18.5473i | 0.339304 | − | 0.587692i | ||||
\(997\) | −28.3864 | − | 49.1667i | −0.899006 | − | 1.55712i | −0.828766 | − | 0.559595i | \(-0.810957\pi\) |
−0.0702399 | − | 0.997530i | \(-0.522376\pi\) | |||||||
\(998\) | −16.0101 | − | 27.7304i | −0.506792 | − | 0.877789i | ||||
\(999\) | 5.53711 | − | 9.59056i | 0.175187 | − | 0.303432i |
(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 | 273.2.i.d.79.2 | ✓ | 8 | |
3.2 | odd | 2 | 819.2.j.f.352.3 | 8 | |||
7.2 | even | 3 | 1911.2.a.r.1.3 | 4 | |||
7.4 | even | 3 | inner | 273.2.i.d.235.2 | yes | 8 | |
7.5 | odd | 6 | 1911.2.a.q.1.3 | 4 | |||
21.2 | odd | 6 | 5733.2.a.bj.1.2 | 4 | |||
21.5 | even | 6 | 5733.2.a.bk.1.2 | 4 | |||
21.11 | odd | 6 | 819.2.j.f.235.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.i.d.79.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
273.2.i.d.235.2 | yes | 8 | 7.4 | even | 3 | inner | |
819.2.j.f.235.3 | 8 | 21.11 | odd | 6 | |||
819.2.j.f.352.3 | 8 | 3.2 | odd | 2 | |||
1911.2.a.q.1.3 | 4 | 7.5 | odd | 6 | |||
1911.2.a.r.1.3 | 4 | 7.2 | even | 3 | |||
5733.2.a.bj.1.2 | 4 | 21.2 | odd | 6 | |||
5733.2.a.bk.1.2 | 4 | 21.5 | even | 6 |