Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [304,2,Mod(77,304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("304.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 304.k (of order \(4\), 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: | \(2.42745222145\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.8 | ||
Character | \(\chi\) | \(=\) | 304.77 |
Dual form | 304.2.k.b.229.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(191\) | \(229\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18841 | − | 0.766601i | −0.840334 | − | 0.542069i | ||||
\(3\) | 0.982629 | + | 0.982629i | 0.567321 | + | 0.567321i | 0.931377 | − | 0.364056i | \(-0.118608\pi\) |
−0.364056 | + | 0.931377i | \(0.618608\pi\) | |||||||
\(4\) | 0.824645 | + | 1.82208i | 0.412322 | + | 0.911038i | ||||
\(5\) | −2.22243 | + | 2.22243i | −0.993901 | + | 0.993901i | −0.999982 | − | 0.00608049i | \(-0.998065\pi\) |
0.00608049 | + | 0.999982i | \(0.498065\pi\) | |||||||
\(6\) | −0.414483 | − | 1.92105i | −0.169212 | − | 0.784267i | ||||
\(7\) | 0.518576i | 0.196003i | 0.995186 | + | 0.0980016i | \(0.0312450\pi\) | ||||
−0.995186 | + | 0.0980016i | \(0.968755\pi\) | |||||||
\(8\) | 0.416789 | − | 2.79755i | 0.147357 | − | 0.989083i | ||||
\(9\) | − | 1.06888i | − | 0.356293i | ||||||
\(10\) | 4.34488 | − | 0.937444i | 1.37397 | − | 0.296446i | ||||
\(11\) | −2.50778 | + | 2.50778i | −0.756125 | + | 0.756125i | −0.975615 | − | 0.219489i | \(-0.929561\pi\) |
0.219489 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(12\) | −0.980105 | + | 2.60075i | −0.282932 | + | 0.750770i | ||||
\(13\) | 2.14144 | + | 2.14144i | 0.593930 | + | 0.593930i | 0.938691 | − | 0.344761i | \(-0.112040\pi\) |
−0.344761 | + | 0.938691i | \(0.612040\pi\) | |||||||
\(14\) | 0.397541 | − | 0.616281i | 0.106247 | − | 0.164708i | ||||
\(15\) | −4.36765 | −1.12772 | ||||||||
\(16\) | −2.63992 | + | 3.00513i | −0.659981 | + | 0.751283i | ||||
\(17\) | −8.17716 | −1.98325 | −0.991626 | − | 0.129144i | \(-0.958777\pi\) | ||||
−0.991626 | + | 0.129144i | \(0.958777\pi\) | |||||||
\(18\) | −0.819405 | + | 1.27027i | −0.193136 | + | 0.299405i | ||||
\(19\) | −0.707107 | − | 0.707107i | −0.162221 | − | 0.162221i | ||||
\(20\) | −5.88215 | − | 2.21672i | −1.31529 | − | 0.495674i | ||||
\(21\) | −0.509568 | + | 0.509568i | −0.111197 | + | 0.111197i | ||||
\(22\) | 4.90275 | − | 1.05781i | 1.04527 | − | 0.225526i | ||||
\(23\) | 3.67724i | 0.766758i | 0.923591 | + | 0.383379i | \(0.125240\pi\) | ||||
−0.923591 | + | 0.383379i | \(0.874760\pi\) | |||||||
\(24\) | 3.15850 | − | 2.33941i | 0.644727 | − | 0.477529i | ||||
\(25\) | − | 4.87839i | − | 0.975678i | ||||||
\(26\) | −0.903283 | − | 4.18655i | −0.177148 | − | 0.821050i | ||||
\(27\) | 3.99820 | − | 3.99820i | 0.769454 | − | 0.769454i | ||||
\(28\) | −0.944884 | + | 0.427641i | −0.178566 | + | 0.0808165i | ||||
\(29\) | 5.60762 | + | 5.60762i | 1.04131 | + | 1.04131i | 0.999109 | + | 0.0422006i | \(0.0134369\pi\) |
0.0422006 | + | 0.999109i | \(0.486563\pi\) | |||||||
\(30\) | 5.19057 | + | 3.34825i | 0.947663 | + | 0.611303i | ||||
\(31\) | −5.48577 | −0.985273 | −0.492636 | − | 0.870235i | \(-0.663967\pi\) | ||||
−0.492636 | + | 0.870235i | \(0.663967\pi\) | |||||||
\(32\) | 5.44105 | − | 1.54756i | 0.961851 | − | 0.273573i | ||||
\(33\) | −4.92844 | −0.857932 | ||||||||
\(34\) | 9.71783 | + | 6.26862i | 1.66659 | + | 1.07506i | ||||
\(35\) | −1.15250 | − | 1.15250i | −0.194808 | − | 0.194808i | ||||
\(36\) | 1.94758 | − | 0.881446i | 0.324597 | − | 0.146908i | ||||
\(37\) | −5.30795 | + | 5.30795i | −0.872621 | + | 0.872621i | −0.992757 | − | 0.120136i | \(-0.961667\pi\) |
0.120136 | + | 0.992757i | \(0.461667\pi\) | |||||||
\(38\) | 0.298265 | + | 1.38240i | 0.0483850 | + | 0.224255i | ||||
\(39\) | 4.20849i | 0.673898i | ||||||||
\(40\) | 5.29108 | + | 7.14364i | 0.836593 | + | 1.12951i | ||||
\(41\) | 4.28518i | 0.669233i | 0.942354 | + | 0.334616i | \(0.108607\pi\) | ||||
−0.942354 | + | 0.334616i | \(0.891393\pi\) | |||||||
\(42\) | 0.996211 | − | 0.214941i | 0.153719 | − | 0.0331661i | ||||
\(43\) | 5.38822 | − | 5.38822i | 0.821696 | − | 0.821696i | −0.164655 | − | 0.986351i | \(-0.552651\pi\) |
0.986351 | + | 0.164655i | \(0.0526512\pi\) | |||||||
\(44\) | −6.63740 | − | 2.50134i | −1.00063 | − | 0.377092i | ||||
\(45\) | 2.37551 | + | 2.37551i | 0.354120 | + | 0.354120i | ||||
\(46\) | 2.81898 | − | 4.37007i | 0.415636 | − | 0.644332i | ||||
\(47\) | 7.68662 | 1.12121 | 0.560604 | − | 0.828084i | \(-0.310569\pi\) | ||||
0.560604 | + | 0.828084i | \(0.310569\pi\) | |||||||
\(48\) | −5.54699 | + | 0.358864i | −0.800640 | + | 0.0517975i | ||||
\(49\) | 6.73108 | 0.961583 | ||||||||
\(50\) | −3.73978 | + | 5.79754i | −0.528885 | + | 0.819896i | ||||
\(51\) | −8.03511 | − | 8.03511i | −1.12514 | − | 1.12514i | ||||
\(52\) | −2.13594 | + | 5.66781i | −0.296202 | + | 0.785983i | ||||
\(53\) | −2.40234 | + | 2.40234i | −0.329987 | + | 0.329987i | −0.852581 | − | 0.522594i | \(-0.824964\pi\) |
0.522594 | + | 0.852581i | \(0.324964\pi\) | |||||||
\(54\) | −7.81653 | + | 1.68648i | −1.06370 | + | 0.229501i | ||||
\(55\) | − | 11.1468i | − | 1.50303i | ||||||
\(56\) | 1.45074 | + | 0.216137i | 0.193863 | + | 0.0288825i | ||||
\(57\) | − | 1.38965i | − | 0.184063i | ||||||
\(58\) | −2.36535 | − | 10.9630i | −0.310586 | − | 1.43951i | ||||
\(59\) | 5.28583 | − | 5.28583i | 0.688156 | − | 0.688156i | −0.273668 | − | 0.961824i | \(-0.588237\pi\) |
0.961824 | + | 0.273668i | \(0.0882370\pi\) | |||||||
\(60\) | −3.60176 | − | 7.95819i | −0.464985 | − | 1.02740i | ||||
\(61\) | 5.16376 | + | 5.16376i | 0.661151 | + | 0.661151i | 0.955651 | − | 0.294500i | \(-0.0951532\pi\) |
−0.294500 | + | 0.955651i | \(0.595153\pi\) | |||||||
\(62\) | 6.51935 | + | 4.20540i | 0.827958 | + | 0.534086i | ||||
\(63\) | 0.554295 | 0.0698346 | ||||||||
\(64\) | −7.65257 | − | 2.33198i | −0.956572 | − | 0.291497i | ||||
\(65\) | −9.51842 | −1.18061 | ||||||||
\(66\) | 5.85702 | + | 3.77815i | 0.720949 | + | 0.465058i | ||||
\(67\) | 0.328680 | + | 0.328680i | 0.0401547 | + | 0.0401547i | 0.726899 | − | 0.686744i | \(-0.240961\pi\) |
−0.686744 | + | 0.726899i | \(0.740961\pi\) | |||||||
\(68\) | −6.74325 | − | 14.8994i | −0.817739 | − | 1.80682i | ||||
\(69\) | −3.61336 | + | 3.61336i | −0.434998 | + | 0.434998i | ||||
\(70\) | 0.486136 | + | 2.25315i | 0.0581043 | + | 0.269303i | ||||
\(71\) | − | 8.49376i | − | 1.00802i | −0.863697 | − | 0.504012i | \(-0.831857\pi\) | ||
0.863697 | − | 0.504012i | \(-0.168143\pi\) | |||||||
\(72\) | −2.99024 | − | 0.445497i | −0.352404 | − | 0.0525024i | ||||
\(73\) | 10.7641i | 1.25984i | 0.776661 | + | 0.629919i | \(0.216912\pi\) | ||||
−0.776661 | + | 0.629919i | \(0.783088\pi\) | |||||||
\(74\) | 10.3771 | − | 2.23895i | 1.20631 | − | 0.260272i | ||||
\(75\) | 4.79365 | − | 4.79365i | 0.553523 | − | 0.553523i | ||||
\(76\) | 0.705291 | − | 1.87151i | 0.0809024 | − | 0.214677i | ||||
\(77\) | −1.30048 | − | 1.30048i | −0.148203 | − | 0.148203i | ||||
\(78\) | 3.22624 | − | 5.00142i | 0.365299 | − | 0.566299i | ||||
\(79\) | 7.35306 | 0.827284 | 0.413642 | − | 0.910440i | \(-0.364256\pi\) | ||||
0.413642 | + | 0.910440i | \(0.364256\pi\) | |||||||
\(80\) | −0.811648 | − | 12.5457i | −0.0907450 | − | 1.40266i | ||||
\(81\) | 4.65086 | 0.516762 | ||||||||
\(82\) | 3.28502 | − | 5.09256i | 0.362770 | − | 0.562379i | ||||
\(83\) | −6.00404 | − | 6.00404i | −0.659029 | − | 0.659029i | 0.296121 | − | 0.955150i | \(-0.404307\pi\) |
−0.955150 | + | 0.296121i | \(0.904307\pi\) | |||||||
\(84\) | −1.34868 | − | 0.508259i | −0.147153 | − | 0.0554556i | ||||
\(85\) | 18.1732 | − | 18.1732i | 1.97116 | − | 1.97116i | ||||
\(86\) | −10.5340 | + | 2.27281i | −1.13591 | + | 0.245083i | ||||
\(87\) | 11.0204i | 1.18151i | ||||||||
\(88\) | 5.97044 | + | 8.06087i | 0.636451 | + | 0.859292i | ||||
\(89\) | − | 9.35796i | − | 0.991941i | −0.868339 | − | 0.495971i | \(-0.834812\pi\) | ||
0.868339 | − | 0.495971i | \(-0.165188\pi\) | |||||||
\(90\) | −1.00201 | − | 4.64415i | −0.105622 | − | 0.489537i | ||||
\(91\) | −1.11050 | + | 1.11050i | −0.116412 | + | 0.116412i | ||||
\(92\) | −6.70021 | + | 3.03242i | −0.698545 | + | 0.316151i | ||||
\(93\) | −5.39047 | − | 5.39047i | −0.558966 | − | 0.558966i | ||||
\(94\) | −9.13486 | − | 5.89257i | −0.942189 | − | 0.607772i | ||||
\(95\) | 3.14299 | 0.322464 | ||||||||
\(96\) | 6.86722 | + | 3.82586i | 0.700882 | + | 0.390475i | ||||
\(97\) | −4.65969 | −0.473120 | −0.236560 | − | 0.971617i | \(-0.576020\pi\) | ||||
−0.236560 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(98\) | −7.99929 | − | 5.16005i | −0.808051 | − | 0.521244i | ||||
\(99\) | 2.68052 | + | 2.68052i | 0.269402 | + | 0.269402i | ||||
\(100\) | 8.88880 | − | 4.02294i | 0.888880 | − | 0.402294i | ||||
\(101\) | −3.60362 | + | 3.60362i | −0.358574 | + | 0.358574i | −0.863287 | − | 0.504713i | \(-0.831598\pi\) |
0.504713 | + | 0.863287i | \(0.331598\pi\) | |||||||
\(102\) | 3.38929 | + | 15.7088i | 0.335590 | + | 1.55540i | ||||
\(103\) | − | 7.32138i | − | 0.721397i | −0.932682 | − | 0.360699i | \(-0.882538\pi\) | ||
0.932682 | − | 0.360699i | \(-0.117462\pi\) | |||||||
\(104\) | 6.88333 | − | 5.09827i | 0.674966 | − | 0.499926i | ||||
\(105\) | − | 2.26496i | − | 0.221037i | ||||||
\(106\) | 4.69661 | − | 1.01333i | 0.456175 | − | 0.0984236i | ||||
\(107\) | −8.23856 | + | 8.23856i | −0.796451 | + | 0.796451i | −0.982534 | − | 0.186083i | \(-0.940421\pi\) |
0.186083 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(108\) | 10.5821 | + | 3.98793i | 1.01826 | + | 0.383739i | ||||
\(109\) | 12.9093 | + | 12.9093i | 1.23648 | + | 1.23648i | 0.961429 | + | 0.275055i | \(0.0886960\pi\) |
0.275055 | + | 0.961429i | \(0.411304\pi\) | |||||||
\(110\) | −8.54512 | + | 13.2469i | −0.814745 | + | 1.26305i | ||||
\(111\) | −10.4315 | −0.990113 | ||||||||
\(112\) | −1.55839 | − | 1.36900i | −0.147254 | − | 0.129358i | ||||
\(113\) | 7.27746 | 0.684606 | 0.342303 | − | 0.939590i | \(-0.388793\pi\) | ||||
0.342303 | + | 0.939590i | \(0.388793\pi\) | |||||||
\(114\) | −1.06531 | + | 1.65147i | −0.0997750 | + | 0.154675i | ||||
\(115\) | −8.17241 | − | 8.17241i | −0.762081 | − | 0.762081i | ||||
\(116\) | −5.59322 | + | 14.8418i | −0.519318 | + | 1.37803i | ||||
\(117\) | 2.28895 | − | 2.28895i | 0.211613 | − | 0.211613i | ||||
\(118\) | −10.3339 | + | 2.22962i | −0.951309 | + | 0.205253i | ||||
\(119\) | − | 4.24047i | − | 0.388724i | ||||||
\(120\) | −1.82039 | + | 12.2187i | −0.166178 | + | 1.11541i | ||||
\(121\) | − | 1.57797i | − | 0.143451i | ||||||
\(122\) | −2.17812 | − | 10.0952i | −0.197198 | − | 0.913977i | ||||
\(123\) | −4.21074 | + | 4.21074i | −0.379670 | + | 0.379670i | ||||
\(124\) | −4.52381 | − | 9.99548i | −0.406250 | − | 0.897621i | ||||
\(125\) | −0.270264 | − | 0.270264i | −0.0241732 | − | 0.0241732i | ||||
\(126\) | −0.658731 | − | 0.424923i | −0.0586844 | − | 0.0378552i | ||||
\(127\) | −8.85350 | −0.785621 | −0.392810 | − | 0.919619i | \(-0.628497\pi\) | ||||
−0.392810 | + | 0.919619i | \(0.628497\pi\) | |||||||
\(128\) | 7.30671 | + | 8.63782i | 0.645828 | + | 0.763483i | ||||
\(129\) | 10.5892 | 0.932331 | ||||||||
\(130\) | 11.3118 | + | 7.29684i | 0.992111 | + | 0.639975i | ||||
\(131\) | 10.9432 | + | 10.9432i | 0.956116 | + | 0.956116i | 0.999077 | − | 0.0429611i | \(-0.0136791\pi\) |
−0.0429611 | + | 0.999077i | \(0.513679\pi\) | |||||||
\(132\) | −4.06421 | − | 8.98000i | −0.353745 | − | 0.781609i | ||||
\(133\) | 0.366688 | − | 0.366688i | 0.0317959 | − | 0.0317959i | ||||
\(134\) | −0.138641 | − | 0.642574i | −0.0119767 | − | 0.0555099i | ||||
\(135\) | 17.7714i | 1.52952i | ||||||||
\(136\) | −3.40815 | + | 22.8760i | −0.292246 | + | 1.96160i | ||||
\(137\) | 12.6102i | 1.07737i | 0.842509 | + | 0.538683i | \(0.181078\pi\) | ||||
−0.842509 | + | 0.538683i | \(0.818922\pi\) | |||||||
\(138\) | 7.06417 | − | 1.52415i | 0.601342 | − | 0.129745i | ||||
\(139\) | 10.0742 | − | 10.0742i | 0.854479 | − | 0.854479i | −0.136202 | − | 0.990681i | \(-0.543490\pi\) |
0.990681 | + | 0.136202i | \(0.0434896\pi\) | |||||||
\(140\) | 1.14954 | − | 3.05034i | 0.0971537 | − | 0.257801i | ||||
\(141\) | 7.55309 | + | 7.55309i | 0.636085 | + | 0.636085i | ||||
\(142\) | −6.51133 | + | 10.0941i | −0.546419 | + | 0.847077i | ||||
\(143\) | −10.7406 | −0.898171 | ||||||||
\(144\) | 3.21212 | + | 2.82176i | 0.267677 | + | 0.235147i | ||||
\(145\) | −24.9251 | −2.06992 | ||||||||
\(146\) | 8.25174 | − | 12.7921i | 0.682919 | − | 1.05868i | ||||
\(147\) | 6.61416 | + | 6.61416i | 0.545526 | + | 0.545526i | ||||
\(148\) | −14.0487 | − | 5.29432i | −1.15479 | − | 0.435190i | ||||
\(149\) | 2.60931 | − | 2.60931i | 0.213763 | − | 0.213763i | −0.592101 | − | 0.805864i | \(-0.701701\pi\) |
0.805864 | + | 0.592101i | \(0.201701\pi\) | |||||||
\(150\) | −9.37165 | + | 2.02201i | −0.765192 | + | 0.165097i | ||||
\(151\) | 15.7722i | 1.28352i | 0.766905 | + | 0.641761i | \(0.221796\pi\) | ||||
−0.766905 | + | 0.641761i | \(0.778204\pi\) | |||||||
\(152\) | −2.27288 | + | 1.68345i | −0.184355 | + | 0.136546i | ||||
\(153\) | 8.74040i | 0.706619i | ||||||||
\(154\) | 0.548554 | + | 2.54245i | 0.0442037 | + | 0.204876i | ||||
\(155\) | 12.1917 | − | 12.1917i | 0.979263 | − | 0.979263i | ||||
\(156\) | −7.66819 | + | 3.47051i | −0.613947 | + | 0.277863i | ||||
\(157\) | −1.91124 | − | 1.91124i | −0.152533 | − | 0.152533i | 0.626715 | − | 0.779248i | \(-0.284399\pi\) |
−0.779248 | + | 0.626715i | \(0.784399\pi\) | |||||||
\(158\) | −8.73847 | − | 5.63687i | −0.695195 | − | 0.448445i | ||||
\(159\) | −4.72122 | −0.374417 | ||||||||
\(160\) | −8.65301 | + | 15.5317i | −0.684080 | + | 1.22789i | ||||
\(161\) | −1.90693 | −0.150287 | ||||||||
\(162\) | −5.52713 | − | 3.56535i | −0.434253 | − | 0.280121i | ||||
\(163\) | −2.74842 | − | 2.74842i | −0.215273 | − | 0.215273i | 0.591230 | − | 0.806503i | \(-0.298643\pi\) |
−0.806503 | + | 0.591230i | \(0.798643\pi\) | |||||||
\(164\) | −7.80792 | + | 3.53375i | −0.609696 | + | 0.275939i | ||||
\(165\) | 10.9531 | − | 10.9531i | 0.852700 | − | 0.852700i | ||||
\(166\) | 2.53257 | + | 11.7380i | 0.196565 | + | 0.911044i | ||||
\(167\) | 2.00369i | 0.155050i | 0.996990 | + | 0.0775252i | \(0.0247018\pi\) | ||||
−0.996990 | + | 0.0775252i | \(0.975298\pi\) | |||||||
\(168\) | 1.21316 | + | 1.63792i | 0.0935972 | + | 0.126369i | ||||
\(169\) | − | 3.82843i | − | 0.294495i | ||||||
\(170\) | −35.5288 | + | 7.66562i | −2.72493 | + | 0.587927i | ||||
\(171\) | −0.755812 | + | 0.755812i | −0.0577984 | + | 0.0577984i | ||||
\(172\) | 14.2611 | + | 5.37438i | 1.08740 | + | 0.409793i | ||||
\(173\) | −6.45544 | − | 6.45544i | −0.490798 | − | 0.490798i | 0.417759 | − | 0.908558i | \(-0.362816\pi\) |
−0.908558 | + | 0.417759i | \(0.862816\pi\) | |||||||
\(174\) | 8.44828 | − | 13.0968i | 0.640462 | − | 0.992867i | ||||
\(175\) | 2.52982 | 0.191236 | ||||||||
\(176\) | −0.915862 | − | 14.1566i | −0.0690357 | − | 1.06709i | ||||
\(177\) | 10.3880 | 0.780811 | ||||||||
\(178\) | −7.17382 | + | 11.1211i | −0.537701 | + | 0.833562i | ||||
\(179\) | 13.5884 | + | 13.5884i | 1.01565 | + | 1.01565i | 0.999876 | + | 0.0157707i | \(0.00502019\pi\) |
0.0157707 | + | 0.999876i | \(0.494980\pi\) | |||||||
\(180\) | −2.36941 | + | 6.28731i | −0.176605 | + | 0.468629i | ||||
\(181\) | −0.0664873 | + | 0.0664873i | −0.00494196 | + | 0.00494196i | −0.709573 | − | 0.704631i | \(-0.751112\pi\) |
0.704631 | + | 0.709573i | \(0.251112\pi\) | |||||||
\(182\) | 2.17104 | − | 0.468421i | 0.160928 | − | 0.0347217i | ||||
\(183\) | 10.1481i | 0.750170i | ||||||||
\(184\) | 10.2873 | + | 1.53263i | 0.758387 | + | 0.112987i | ||||
\(185\) | − | 23.5931i | − | 1.73460i | ||||||
\(186\) | 2.27376 | + | 10.5384i | 0.166720 | + | 0.772716i | ||||
\(187\) | 20.5065 | − | 20.5065i | 1.49959 | − | 1.49959i | ||||
\(188\) | 6.33873 | + | 14.0056i | 0.462299 | + | 1.02146i | ||||
\(189\) | 2.07337 | + | 2.07337i | 0.150815 | + | 0.150815i | ||||
\(190\) | −3.73517 | − | 2.40942i | −0.270978 | − | 0.174798i | ||||
\(191\) | 18.9056 | 1.36796 | 0.683982 | − | 0.729499i | \(-0.260246\pi\) | ||||
0.683982 | + | 0.729499i | \(0.260246\pi\) | |||||||
\(192\) | −5.22817 | − | 9.81111i | −0.377311 | − | 0.708056i | ||||
\(193\) | −2.20445 | −0.158680 | −0.0793398 | − | 0.996848i | \(-0.525281\pi\) | ||||
−0.0793398 | + | 0.996848i | \(0.525281\pi\) | |||||||
\(194\) | 5.53763 | + | 3.57212i | 0.397579 | + | 0.256464i | ||||
\(195\) | −9.35308 | − | 9.35308i | −0.669788 | − | 0.669788i | ||||
\(196\) | 5.55075 | + | 12.2645i | 0.396482 | + | 0.876038i | ||||
\(197\) | 3.12323 | − | 3.12323i | 0.222521 | − | 0.222521i | −0.587038 | − | 0.809559i | \(-0.699706\pi\) |
0.809559 | + | 0.587038i | \(0.199706\pi\) | |||||||
\(198\) | −1.13067 | − | 5.24045i | −0.0803533 | − | 0.372423i | ||||
\(199\) | − | 12.4844i | − | 0.884997i | −0.896769 | − | 0.442499i | \(-0.854092\pi\) | ||
0.896769 | − | 0.442499i | \(-0.145908\pi\) | |||||||
\(200\) | −13.6475 | − | 2.03326i | −0.965027 | − | 0.143773i | ||||
\(201\) | 0.645941i | 0.0455612i | ||||||||
\(202\) | 7.04513 | − | 1.52005i | 0.495694 | − | 0.106950i | ||||
\(203\) | −2.90798 | + | 2.90798i | −0.204100 | + | 0.204100i | ||||
\(204\) | 8.01448 | − | 21.2667i | 0.561126 | − | 1.48897i | ||||
\(205\) | −9.52351 | − | 9.52351i | −0.665151 | − | 0.665151i | ||||
\(206\) | −5.61258 | + | 8.70081i | −0.391047 | + | 0.606214i | ||||
\(207\) | 3.93053 | 0.273190 | ||||||||
\(208\) | −12.0886 | + | 0.782071i | −0.838191 | + | 0.0542269i | ||||
\(209\) | 3.54654 | 0.245319 | ||||||||
\(210\) | −1.73632 | + | 2.69170i | −0.119817 | + | 0.185745i | ||||
\(211\) | 8.02018 | + | 8.02018i | 0.552132 | + | 0.552132i | 0.927056 | − | 0.374924i | \(-0.122331\pi\) |
−0.374924 | + | 0.927056i | \(0.622331\pi\) | |||||||
\(212\) | −6.35833 | − | 2.39617i | −0.436692 | − | 0.164570i | ||||
\(213\) | 8.34622 | − | 8.34622i | 0.571874 | − | 0.571874i | ||||
\(214\) | 16.1065 | − | 3.47511i | 1.10102 | − | 0.237553i | ||||
\(215\) | 23.9499i | 1.63337i | ||||||||
\(216\) | −9.51876 | − | 12.8516i | −0.647670 | − | 0.874439i | ||||
\(217\) | − | 2.84478i | − | 0.193117i | ||||||
\(218\) | −5.44526 | − | 25.2378i | −0.368800 | − | 1.70932i | ||||
\(219\) | −10.5771 | + | 10.5771i | −0.714733 | + | 0.714733i | ||||
\(220\) | 20.3102 | − | 9.19211i | 1.36932 | − | 0.619732i | ||||
\(221\) | −17.5109 | − | 17.5109i | −1.17791 | − | 1.17791i | ||||
\(222\) | 12.3969 | + | 7.99680i | 0.832026 | + | 0.536710i | ||||
\(223\) | −23.2799 | −1.55893 | −0.779467 | − | 0.626443i | \(-0.784510\pi\) | ||||
−0.779467 | + | 0.626443i | \(0.784510\pi\) | |||||||
\(224\) | 0.802529 | + | 2.82160i | 0.0536212 | + | 0.188526i | ||||
\(225\) | −5.21441 | −0.347628 | ||||||||
\(226\) | −8.64862 | − | 5.57891i | −0.575298 | − | 0.371104i | ||||
\(227\) | 5.82988 | + | 5.82988i | 0.386943 | + | 0.386943i | 0.873595 | − | 0.486653i | \(-0.161782\pi\) |
−0.486653 | + | 0.873595i | \(0.661782\pi\) | |||||||
\(228\) | 2.53204 | − | 1.14597i | 0.167689 | − | 0.0758934i | ||||
\(229\) | −16.9493 | + | 16.9493i | −1.12004 | + | 1.12004i | −0.128307 | + | 0.991734i | \(0.540954\pi\) |
−0.991734 | + | 0.128307i | \(0.959046\pi\) | |||||||
\(230\) | 3.44721 | + | 15.9772i | 0.227302 | + | 1.05350i | ||||
\(231\) | − | 2.55577i | − | 0.168157i | ||||||
\(232\) | 18.0248 | − | 13.3504i | 1.18339 | − | 0.876498i | ||||
\(233\) | − | 12.5017i | − | 0.819016i | −0.912306 | − | 0.409508i | \(-0.865700\pi\) | ||
0.912306 | − | 0.409508i | \(-0.134300\pi\) | |||||||
\(234\) | −4.47492 | + | 0.965501i | −0.292535 | + | 0.0631168i | ||||
\(235\) | −17.0830 | + | 17.0830i | −1.11437 | + | 1.11437i | ||||
\(236\) | 13.9901 | + | 5.27225i | 0.910679 | + | 0.343194i | ||||
\(237\) | 7.22534 | + | 7.22534i | 0.469336 | + | 0.469336i | ||||
\(238\) | −3.25075 | + | 5.03943i | −0.210715 | + | 0.326658i | ||||
\(239\) | −10.1018 | −0.653432 | −0.326716 | − | 0.945123i | \(-0.605942\pi\) | ||||
−0.326716 | + | 0.945123i | \(0.605942\pi\) | |||||||
\(240\) | 11.5303 | − | 13.1254i | 0.744275 | − | 0.847238i | ||||
\(241\) | −12.0760 | −0.777885 | −0.388942 | − | 0.921262i | \(-0.627160\pi\) | ||||
−0.388942 | + | 0.921262i | \(0.627160\pi\) | |||||||
\(242\) | −1.20967 | + | 1.87527i | −0.0777606 | + | 0.120547i | ||||
\(243\) | −7.42453 | − | 7.42453i | −0.476284 | − | 0.476284i | ||||
\(244\) | −5.15049 | + | 13.6670i | −0.329727 | + | 0.874941i | ||||
\(245\) | −14.9594 | + | 14.9594i | −0.955718 | + | 0.955718i | ||||
\(246\) | 8.23206 | − | 1.77613i | 0.524857 | − | 0.113242i | ||||
\(247\) | − | 3.02846i | − | 0.192696i | ||||||
\(248\) | −2.28641 | + | 15.3467i | −0.145187 | + | 0.974517i | ||||
\(249\) | − | 11.7995i | − | 0.747763i | ||||||
\(250\) | 0.114000 | + | 0.528370i | 0.00721001 | + | 0.0334171i | ||||
\(251\) | 16.1217 | − | 16.1217i | 1.01759 | − | 1.01759i | 0.0177490 | − | 0.999842i | \(-0.494350\pi\) |
0.999842 | − | 0.0177490i | \(-0.00564999\pi\) | |||||||
\(252\) | 0.457096 | + | 1.00997i | 0.0287944 | + | 0.0636220i | ||||
\(253\) | −9.22173 | − | 9.22173i | −0.579765 | − | 0.579765i | ||||
\(254\) | 10.5216 | + | 6.78710i | 0.660184 | + | 0.425861i | ||||
\(255\) | 35.7150 | 2.23656 | ||||||||
\(256\) | −2.06162 | − | 15.8666i | −0.128851 | − | 0.991664i | ||||
\(257\) | −8.63368 | −0.538554 | −0.269277 | − | 0.963063i | \(-0.586785\pi\) | ||||
−0.269277 | + | 0.963063i | \(0.586785\pi\) | |||||||
\(258\) | −12.5844 | − | 8.11773i | −0.783469 | − | 0.505388i | ||||
\(259\) | −2.75257 | − | 2.75257i | −0.171037 | − | 0.171037i | ||||
\(260\) | −7.84931 | − | 17.3433i | −0.486794 | − | 1.07559i | ||||
\(261\) | 5.99388 | − | 5.99388i | 0.371012 | − | 0.371012i | ||||
\(262\) | −4.61597 | − | 21.3942i | −0.285176 | − | 1.32174i | ||||
\(263\) | − | 12.5077i | − | 0.771258i | −0.922654 | − | 0.385629i | \(-0.873985\pi\) | ||
0.922654 | − | 0.385629i | \(-0.126015\pi\) | |||||||
\(264\) | −2.05412 | + | 13.7876i | −0.126422 | + | 0.848566i | ||||
\(265\) | − | 10.6781i | − | 0.655949i | ||||||
\(266\) | −0.716881 | + | 0.154673i | −0.0439548 | + | 0.00948360i | ||||
\(267\) | 9.19540 | − | 9.19540i | 0.562749 | − | 0.562749i | ||||
\(268\) | −0.327836 | + | 0.869924i | −0.0200258 | + | 0.0531391i | ||||
\(269\) | 2.84573 | + | 2.84573i | 0.173507 | + | 0.173507i | 0.788518 | − | 0.615011i | \(-0.210849\pi\) |
−0.615011 | + | 0.788518i | \(0.710849\pi\) | |||||||
\(270\) | 13.6236 | − | 21.1198i | 0.829107 | − | 1.28531i | ||||
\(271\) | −26.1363 | −1.58767 | −0.793834 | − | 0.608134i | \(-0.791918\pi\) | ||||
−0.793834 | + | 0.608134i | \(0.791918\pi\) | |||||||
\(272\) | 21.5871 | − | 24.5734i | 1.30891 | − | 1.48998i | ||||
\(273\) | −2.18242 | −0.132086 | ||||||||
\(274\) | 9.66703 | − | 14.9862i | 0.584007 | − | 0.905347i | ||||
\(275\) | 12.2340 | + | 12.2340i | 0.737735 | + | 0.737735i | ||||
\(276\) | −9.56356 | − | 3.60408i | −0.575659 | − | 0.216940i | ||||
\(277\) | 1.11397 | − | 1.11397i | 0.0669318 | − | 0.0669318i | −0.672848 | − | 0.739780i | \(-0.734929\pi\) |
0.739780 | + | 0.672848i | \(0.234929\pi\) | |||||||
\(278\) | −19.6951 | + | 4.24938i | −1.18123 | + | 0.254861i | ||||
\(279\) | 5.86362i | 0.351046i | ||||||||
\(280\) | −3.70452 | + | 2.74382i | −0.221387 | + | 0.163975i | ||||
\(281\) | − | 3.69892i | − | 0.220659i | −0.993895 | − | 0.110330i | \(-0.964809\pi\) | ||
0.993895 | − | 0.110330i | \(-0.0351906\pi\) | |||||||
\(282\) | −3.18597 | − | 14.7664i | −0.189722 | − | 0.879326i | ||||
\(283\) | −10.2024 | + | 10.2024i | −0.606471 | + | 0.606471i | −0.942022 | − | 0.335551i | \(-0.891077\pi\) |
0.335551 | + | 0.942022i | \(0.391077\pi\) | |||||||
\(284\) | 15.4763 | − | 7.00434i | 0.918348 | − | 0.415631i | ||||
\(285\) | 3.08839 | + | 3.08839i | 0.182941 | + | 0.182941i | ||||
\(286\) | 12.7642 | + | 8.23373i | 0.754764 | + | 0.486871i | ||||
\(287\) | −2.22219 | −0.131172 | ||||||||
\(288\) | −1.65416 | − | 5.81583i | −0.0974722 | − | 0.342701i | ||||
\(289\) | 49.8659 | 2.93329 | ||||||||
\(290\) | 29.6213 | + | 19.1076i | 1.73942 | + | 1.12204i | ||||
\(291\) | −4.57875 | − | 4.57875i | −0.268411 | − | 0.268411i | ||||
\(292\) | −19.6129 | + | 8.87652i | −1.14776 | + | 0.519459i | ||||
\(293\) | −16.9050 | + | 16.9050i | −0.987603 | + | 0.987603i | −0.999924 | − | 0.0123212i | \(-0.996078\pi\) |
0.0123212 | + | 0.999924i | \(0.496078\pi\) | |||||||
\(294\) | −2.78992 | − | 12.9308i | −0.162711 | − | 0.754137i | ||||
\(295\) | 23.4948i | 1.36792i | ||||||||
\(296\) | 12.6370 | + | 17.0615i | 0.734508 | + | 0.991682i | ||||
\(297\) | 20.0532i | 1.16361i | ||||||||
\(298\) | −5.10123 | + | 1.10063i | −0.295506 | + | 0.0637579i | ||||
\(299\) | −7.87461 | + | 7.87461i | −0.455400 | + | 0.455400i | ||||
\(300\) | 12.6875 | + | 4.78134i | 0.732511 | + | 0.276051i | ||||
\(301\) | 2.79420 | + | 2.79420i | 0.161055 | + | 0.161055i | ||||
\(302\) | 12.0910 | − | 18.7438i | 0.695757 | − | 1.07859i | ||||
\(303\) | −7.08205 | −0.406853 | ||||||||
\(304\) | 3.99166 | − | 0.258241i | 0.228937 | − | 0.0148111i | ||||
\(305\) | −22.9522 | −1.31424 | ||||||||
\(306\) | 6.70040 | − | 10.3872i | 0.383036 | − | 0.593796i | ||||
\(307\) | −2.84284 | − | 2.84284i | −0.162250 | − | 0.162250i | 0.621313 | − | 0.783563i | \(-0.286600\pi\) |
−0.783563 | + | 0.621313i | \(0.786600\pi\) | |||||||
\(308\) | 1.29714 | − | 3.44200i | 0.0739112 | − | 0.196126i | ||||
\(309\) | 7.19420 | − | 7.19420i | 0.409264 | − | 0.409264i | ||||
\(310\) | −23.8350 | + | 5.14260i | −1.35374 | + | 0.292080i | ||||
\(311\) | − | 25.9320i | − | 1.47047i | −0.677812 | − | 0.735235i | \(-0.737072\pi\) | ||
0.677812 | − | 0.735235i | \(-0.262928\pi\) | |||||||
\(312\) | 11.7735 | + | 1.75405i | 0.666541 | + | 0.0993037i | ||||
\(313\) | − | 11.4082i | − | 0.644828i | −0.946599 | − | 0.322414i | \(-0.895506\pi\) | ||
0.946599 | − | 0.322414i | \(-0.104494\pi\) | |||||||
\(314\) | 0.806180 | + | 3.73649i | 0.0454953 | + | 0.210863i | ||||
\(315\) | −1.23188 | + | 1.23188i | −0.0694087 | + | 0.0694087i | ||||
\(316\) | 6.06366 | + | 13.3978i | 0.341108 | + | 0.753688i | ||||
\(317\) | 11.2287 | + | 11.2287i | 0.630669 | + | 0.630669i | 0.948236 | − | 0.317567i | \(-0.102866\pi\) |
−0.317567 | + | 0.948236i | \(0.602866\pi\) | |||||||
\(318\) | 5.61076 | + | 3.61930i | 0.314636 | + | 0.202960i | ||||
\(319\) | −28.1254 | −1.57472 | ||||||||
\(320\) | 22.1900 | − | 11.8247i | 1.24046 | − | 0.661018i | ||||
\(321\) | −16.1909 | −0.903688 | ||||||||
\(322\) | 2.26621 | + | 1.46185i | 0.126291 | + | 0.0814659i | ||||
\(323\) | 5.78212 | + | 5.78212i | 0.321726 | + | 0.321726i | ||||
\(324\) | 3.83530 | + | 8.47422i | 0.213072 | + | 0.470790i | ||||
\(325\) | 10.4468 | − | 10.4468i | 0.579485 | − | 0.579485i | ||||
\(326\) | 1.15931 | + | 5.37320i | 0.0642084 | + | 0.297594i | ||||
\(327\) | 25.3700i | 1.40297i | ||||||||
\(328\) | 11.9880 | + | 1.78602i | 0.661927 | + | 0.0986162i | ||||
\(329\) | 3.98609i | 0.219760i | ||||||||
\(330\) | −21.4135 | + | 4.62014i | −1.17877 | + | 0.254330i | ||||
\(331\) | −7.05044 | + | 7.05044i | −0.387527 | + | 0.387527i | −0.873804 | − | 0.486277i | \(-0.838354\pi\) |
0.486277 | + | 0.873804i | \(0.338354\pi\) | |||||||
\(332\) | 5.98862 | − | 15.8910i | 0.328668 | − | 0.872133i | ||||
\(333\) | 5.67356 | + | 5.67356i | 0.310909 | + | 0.310909i | ||||
\(334\) | 1.53603 | − | 2.38121i | 0.0840480 | − | 0.130294i | ||||
\(335\) | −1.46094 | −0.0798195 | ||||||||
\(336\) | −0.186098 | − | 2.87654i | −0.0101525 | − | 0.156928i | ||||
\(337\) | −22.3426 | −1.21708 | −0.608539 | − | 0.793524i | \(-0.708244\pi\) | ||||
−0.608539 | + | 0.793524i | \(0.708244\pi\) | |||||||
\(338\) | −2.93488 | + | 4.54975i | −0.159636 | + | 0.247474i | ||||
\(339\) | 7.15105 | + | 7.15105i | 0.388392 | + | 0.388392i | ||||
\(340\) | 48.0993 | + | 18.1265i | 2.60855 | + | 0.983047i | ||||
\(341\) | 13.7571 | − | 13.7571i | 0.744990 | − | 0.744990i | ||||
\(342\) | 1.47762 | − | 0.318809i | 0.0799007 | − | 0.0172392i | ||||
\(343\) | 7.12060i | 0.384476i | ||||||||
\(344\) | −12.8281 | − | 17.3196i | −0.691643 | − | 0.933808i | ||||
\(345\) | − | 16.0609i | − | 0.864690i | ||||||
\(346\) | 2.72297 | + | 12.6205i | 0.146388 | + | 0.678481i | ||||
\(347\) | −23.3395 | + | 23.3395i | −1.25293 | + | 1.25293i | −0.298527 | + | 0.954401i | \(0.596495\pi\) |
−0.954401 | + | 0.298527i | \(0.903505\pi\) | |||||||
\(348\) | −20.0801 | + | 9.08794i | −1.07640 | + | 0.487165i | ||||
\(349\) | 17.6030 | + | 17.6030i | 0.942267 | + | 0.942267i | 0.998422 | − | 0.0561552i | \(-0.0178842\pi\) |
−0.0561552 | + | 0.998422i | \(0.517884\pi\) | |||||||
\(350\) | −3.00646 | − | 1.93936i | −0.160702 | − | 0.103663i | ||||
\(351\) | 17.1238 | 0.914003 | ||||||||
\(352\) | −9.76403 | + | 17.5259i | −0.520425 | + | 0.934136i | ||||
\(353\) | 0.192537 | 0.0102477 | 0.00512387 | − | 0.999987i | \(-0.498369\pi\) | ||||
0.00512387 | + | 0.999987i | \(0.498369\pi\) | |||||||
\(354\) | −12.3452 | − | 7.96347i | −0.656142 | − | 0.423254i | ||||
\(355\) | 18.8768 | + | 18.8768i | 1.00188 | + | 1.00188i | ||||
\(356\) | 17.0509 | − | 7.71699i | 0.903696 | − | 0.409000i | ||||
\(357\) | 4.16681 | − | 4.16681i | 0.220531 | − | 0.220531i | ||||
\(358\) | −5.73174 | − | 26.5655i | −0.302932 | − | 1.40403i | ||||
\(359\) | − | 0.665573i | − | 0.0351276i | −0.999846 | − | 0.0175638i | \(-0.994409\pi\) | ||
0.999846 | − | 0.0175638i | \(-0.00559102\pi\) | |||||||
\(360\) | 7.63570 | − | 5.65552i | 0.402437 | − | 0.298072i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 0.129984 | − | 0.0280450i | 0.00683178 | − | 0.00147401i | ||||
\(363\) | 1.55056 | − | 1.55056i | 0.0813830 | − | 0.0813830i | ||||
\(364\) | −2.93919 | − | 1.10765i | −0.154055 | − | 0.0580566i | ||||
\(365\) | −23.9224 | − | 23.9224i | −1.25215 | − | 1.25215i | ||||
\(366\) | 7.77956 | − | 12.0601i | 0.406644 | − | 0.630393i | ||||
\(367\) | −4.73699 | −0.247269 | −0.123634 | − | 0.992328i | \(-0.539455\pi\) | ||||
−0.123634 | + | 0.992328i | \(0.539455\pi\) | |||||||
\(368\) | −11.0506 | − | 9.70763i | −0.576052 | − | 0.506045i | ||||
\(369\) | 4.58034 | 0.238443 | ||||||||
\(370\) | −18.0865 | + | 28.0383i | −0.940272 | + | 1.45764i | ||||
\(371\) | −1.24580 | − | 1.24580i | −0.0646785 | − | 0.0646785i | ||||
\(372\) | 5.37663 | − | 14.2671i | 0.278765 | − | 0.739714i | ||||
\(373\) | 6.02933 | − | 6.02933i | 0.312187 | − | 0.312187i | −0.533569 | − | 0.845756i | \(-0.679150\pi\) |
0.845756 | + | 0.533569i | \(0.179150\pi\) | |||||||
\(374\) | −40.0906 | + | 8.64987i | −2.07303 | + | 0.447274i | ||||
\(375\) | − | 0.531139i | − | 0.0274279i | ||||||
\(376\) | 3.20370 | − | 21.5037i | 0.165218 | − | 1.10897i | ||||
\(377\) | 24.0168i | 1.23693i | ||||||||
\(378\) | −0.874568 | − | 4.05346i | −0.0449829 | − | 0.208488i | ||||
\(379\) | −19.2425 | + | 19.2425i | −0.988420 | + | 0.988420i | −0.999934 | − | 0.0115132i | \(-0.996335\pi\) |
0.0115132 | + | 0.999934i | \(0.496335\pi\) | |||||||
\(380\) | 2.59185 | + | 5.72677i | 0.132959 | + | 0.293777i | ||||
\(381\) | −8.69970 | − | 8.69970i | −0.445699 | − | 0.445699i | ||||
\(382\) | −22.4677 | − | 14.4931i | −1.14955 | − | 0.741531i | ||||
\(383\) | 27.5509 | 1.40778 | 0.703892 | − | 0.710307i | \(-0.251444\pi\) | ||||
0.703892 | + | 0.710307i | \(0.251444\pi\) | |||||||
\(384\) | −1.30799 | + | 15.6676i | −0.0667479 | + | 0.799532i | ||||
\(385\) | 5.78043 | 0.294598 | ||||||||
\(386\) | 2.61979 | + | 1.68993i | 0.133344 | + | 0.0860153i | ||||
\(387\) | −5.75936 | − | 5.75936i | −0.292765 | − | 0.292765i | ||||
\(388\) | −3.84259 | − | 8.49031i | −0.195078 | − | 0.431030i | ||||
\(389\) | −1.99617 | + | 1.99617i | −0.101210 | + | 0.101210i | −0.755899 | − | 0.654689i | \(-0.772800\pi\) |
0.654689 | + | 0.755899i | \(0.272800\pi\) | |||||||
\(390\) | 3.94522 | + | 18.2854i | 0.199774 | + | 0.925917i | ||||
\(391\) | − | 30.0694i | − | 1.52067i | ||||||
\(392\) | 2.80544 | − | 18.8305i | 0.141696 | − | 0.951085i | ||||
\(393\) | 21.5063i | 1.08485i | ||||||||
\(394\) | −6.10596 | + | 1.31741i | −0.307614 | + | 0.0663702i | ||||
\(395\) | −16.3417 | + | 16.3417i | −0.822239 | + | 0.822239i | ||||
\(396\) | −2.67363 | + | 7.09459i | −0.134355 | + | 0.356516i | ||||
\(397\) | −18.2874 | − | 18.2874i | −0.917820 | − | 0.917820i | 0.0790506 | − | 0.996871i | \(-0.474811\pi\) |
−0.996871 | + | 0.0790506i | \(0.974811\pi\) | |||||||
\(398\) | −9.57058 | + | 14.8366i | −0.479730 | + | 0.743693i | ||||
\(399\) | 0.720637 | 0.0360770 | ||||||||
\(400\) | 14.6602 | + | 12.8786i | 0.733010 | + | 0.643929i | ||||
\(401\) | 36.9382 | 1.84461 | 0.922304 | − | 0.386466i | \(-0.126304\pi\) | ||||
0.922304 | + | 0.386466i | \(0.126304\pi\) | |||||||
\(402\) | 0.495180 | − | 0.767644i | 0.0246973 | − | 0.0382866i | ||||
\(403\) | −11.7475 | − | 11.7475i | −0.585183 | − | 0.585183i | ||||
\(404\) | −9.53778 | − | 3.59437i | −0.474522 | − | 0.178826i | ||||
\(405\) | −10.3362 | + | 10.3362i | −0.513610 | + | 0.513610i | ||||
\(406\) | 5.68513 | − | 1.22661i | 0.282148 | − | 0.0608759i | ||||
\(407\) | − | 26.6224i | − | 1.31962i | ||||||
\(408\) | −25.8276 | + | 19.1297i | −1.27866 | + | 0.947061i | ||||
\(409\) | − | 20.8320i | − | 1.03007i | −0.857168 | − | 0.515037i | \(-0.827778\pi\) | ||
0.857168 | − | 0.515037i | \(-0.172222\pi\) | |||||||
\(410\) | 4.01712 | + | 18.6186i | 0.198391 | + | 0.919507i | ||||
\(411\) | −12.3912 | + | 12.3912i | −0.611212 | + | 0.611212i | ||||
\(412\) | 13.3401 | − | 6.03754i | 0.657220 | − | 0.297448i | ||||
\(413\) | 2.74110 | + | 2.74110i | 0.134881 | + | 0.134881i | ||||
\(414\) | −4.67108 | − | 3.01315i | −0.229571 | − | 0.148088i | ||||
\(415\) | 26.6871 | 1.31002 | ||||||||
\(416\) | 14.9657 | + | 8.33769i | 0.733755 | + | 0.408789i | ||||
\(417\) | 19.7983 | 0.969528 | ||||||||
\(418\) | −4.21475 | − | 2.71878i | −0.206150 | − | 0.132980i | ||||
\(419\) | −16.7006 | − | 16.7006i | −0.815877 | − | 0.815877i | 0.169631 | − | 0.985508i | \(-0.445743\pi\) |
−0.985508 | + | 0.169631i | \(0.945743\pi\) | |||||||
\(420\) | 4.12692 | − | 1.86778i | 0.201373 | − | 0.0911385i | ||||
\(421\) | −12.7537 | + | 12.7537i | −0.621577 | + | 0.621577i | −0.945935 | − | 0.324357i | \(-0.894852\pi\) |
0.324357 | + | 0.945935i | \(0.394852\pi\) | |||||||
\(422\) | −3.38299 | − | 15.6796i | −0.164682 | − | 0.763269i | ||||
\(423\) | − | 8.21607i | − | 0.399479i | ||||||
\(424\) | 5.71940 | + | 7.72194i | 0.277759 | + | 0.375011i | ||||
\(425\) | 39.8914i | 1.93502i | ||||||||
\(426\) | −16.3170 | + | 3.52052i | −0.790560 | + | 0.170570i | ||||
\(427\) | −2.67780 | + | 2.67780i | −0.129588 | + | 0.129588i | ||||
\(428\) | −21.8052 | − | 8.21740i | −1.05399 | − | 0.397203i | ||||
\(429\) | −10.5540 | − | 10.5540i | −0.509551 | − | 0.509551i | ||||
\(430\) | 18.3600 | − | 28.4623i | 0.885398 | − | 1.37257i | ||||
\(431\) | 12.5666 | 0.605311 | 0.302656 | − | 0.953100i | \(-0.402127\pi\) | ||||
0.302656 | + | 0.953100i | \(0.402127\pi\) | |||||||
\(432\) | 1.46017 | + | 22.5701i | 0.0702526 | + | 1.08590i | ||||
\(433\) | 13.0595 | 0.627601 | 0.313801 | − | 0.949489i | \(-0.398398\pi\) | ||||
0.313801 | + | 0.949489i | \(0.398398\pi\) | |||||||
\(434\) | −2.18082 | + | 3.38078i | −0.104683 | + | 0.162282i | ||||
\(435\) | −24.4921 | − | 24.4921i | −1.17431 | − | 1.17431i | ||||
\(436\) | −12.8761 | + | 34.1672i | −0.616654 | + | 1.63631i | ||||
\(437\) | 2.60020 | − | 2.60020i | 0.124385 | − | 0.124385i | ||||
\(438\) | 20.6783 | − | 4.46152i | 0.988049 | − | 0.213180i | ||||
\(439\) | − | 3.55838i | − | 0.169832i | −0.996388 | − | 0.0849161i | \(-0.972938\pi\) | ||
0.996388 | − | 0.0849161i | \(-0.0270622\pi\) | |||||||
\(440\) | −31.1836 | − | 4.64584i | −1.48662 | − | 0.221482i | ||||
\(441\) | − | 7.19471i | − | 0.342605i | ||||||
\(442\) | 7.38629 | + | 34.2341i | 0.351330 | + | 1.62835i | ||||
\(443\) | 19.9992 | − | 19.9992i | 0.950190 | − | 0.950190i | −0.0486271 | − | 0.998817i | \(-0.515485\pi\) |
0.998817 | + | 0.0486271i | \(0.0154846\pi\) | |||||||
\(444\) | −8.60227 | − | 19.0070i | −0.408246 | − | 0.902031i | ||||
\(445\) | 20.7974 | + | 20.7974i | 0.985892 | + | 0.985892i | ||||
\(446\) | 27.6660 | + | 17.8464i | 1.31003 | + | 0.845050i | ||||
\(447\) | 5.12796 | 0.242544 | ||||||||
\(448\) | 1.20931 | − | 3.96844i | 0.0571343 | − | 0.187491i | ||||
\(449\) | 5.72617 | 0.270235 | 0.135117 | − | 0.990830i | \(-0.456859\pi\) | ||||
0.135117 | + | 0.990830i | \(0.456859\pi\) | |||||||
\(450\) | 6.19687 | + | 3.99738i | 0.292123 | + | 0.188438i | ||||
\(451\) | −10.7463 | − | 10.7463i | −0.506024 | − | 0.506024i | ||||
\(452\) | 6.00132 | + | 13.2601i | 0.282278 | + | 0.623702i | ||||
\(453\) | −15.4982 | + | 15.4982i | −0.728169 | + | 0.728169i | ||||
\(454\) | −2.45910 | − | 11.3975i | −0.115411 | − | 0.534911i | ||||
\(455\) | − | 4.93602i | − | 0.231404i | ||||||
\(456\) | −3.88761 | − | 0.579190i | −0.182054 | − | 0.0271230i | ||||
\(457\) | − | 23.3540i | − | 1.09246i | −0.837637 | − | 0.546228i | \(-0.816063\pi\) | ||
0.837637 | − | 0.546228i | \(-0.183937\pi\) | |||||||
\(458\) | 33.1361 | − | 7.14939i | 1.54835 | − | 0.334069i | ||||
\(459\) | −32.6939 | + | 32.6939i | −1.52602 | + | 1.52602i | ||||
\(460\) | 8.15142 | − | 21.6301i | 0.380062 | − | 1.00851i | ||||
\(461\) | −7.15231 | − | 7.15231i | −0.333116 | − | 0.333116i | 0.520653 | − | 0.853769i | \(-0.325689\pi\) |
−0.853769 | + | 0.520653i | \(0.825689\pi\) | |||||||
\(462\) | −1.95926 | + | 3.03731i | −0.0911529 | + | 0.141308i | ||||
\(463\) | 13.8558 | 0.643932 | 0.321966 | − | 0.946751i | \(-0.395656\pi\) | ||||
0.321966 | + | 0.946751i | \(0.395656\pi\) | |||||||
\(464\) | −31.6553 | + | 2.04795i | −1.46956 | + | 0.0950735i | ||||
\(465\) | 23.9599 | 1.11111 | ||||||||
\(466\) | −9.58385 | + | 14.8572i | −0.443963 | + | 0.688247i | ||||
\(467\) | −2.57565 | − | 2.57565i | −0.119187 | − | 0.119187i | 0.644998 | − | 0.764185i | \(-0.276858\pi\) |
−0.764185 | + | 0.644998i | \(0.776858\pi\) | |||||||
\(468\) | 6.05820 | + | 2.28307i | 0.280040 | + | 0.105535i | ||||
\(469\) | −0.170445 | + | 0.170445i | −0.00787044 | + | 0.00787044i | ||||
\(470\) | 33.3974 | − | 7.20577i | 1.54051 | − | 0.332377i | ||||
\(471\) | − | 3.75608i | − | 0.173071i | ||||||
\(472\) | −12.5843 | − | 16.9904i | −0.579239 | − | 0.782049i | ||||
\(473\) | 27.0250i | 1.24261i | ||||||||
\(474\) | −3.04772 | − | 14.1256i | −0.139986 | − | 0.648812i | ||||
\(475\) | −3.44954 | + | 3.44954i | −0.158276 | + | 0.158276i | ||||
\(476\) | 7.72647 | − | 3.49688i | 0.354142 | − | 0.160279i | ||||
\(477\) | 2.56782 | + | 2.56782i | 0.117572 | + | 0.117572i | ||||
\(478\) | 12.0051 | + | 7.74406i | 0.549101 | + | 0.354205i | ||||
\(479\) | 1.05236 | 0.0480835 | 0.0240418 | − | 0.999711i | \(-0.492347\pi\) | ||||
0.0240418 | + | 0.999711i | \(0.492347\pi\) | |||||||
\(480\) | −23.7646 | + | 6.75921i | −1.08470 | + | 0.308515i | ||||
\(481\) | −22.7334 | −1.03655 | ||||||||
\(482\) | 14.3513 | + | 9.25750i | 0.653683 | + | 0.421667i | ||||
\(483\) | −1.87380 | − | 1.87380i | −0.0852610 | − | 0.0852610i | ||||
\(484\) | 2.87517 | − | 1.30126i | 0.130690 | − | 0.0591482i | ||||
\(485\) | 10.3558 | − | 10.3558i | 0.470234 | − | 0.470234i | ||||
\(486\) | 3.13174 | + | 14.5151i | 0.142059 | + | 0.658416i | ||||
\(487\) | − | 18.1274i | − | 0.821432i | −0.911763 | − | 0.410716i | \(-0.865279\pi\) | ||
0.911763 | − | 0.410716i | \(-0.134721\pi\) | |||||||
\(488\) | 16.5981 | − | 12.2937i | 0.751359 | − | 0.556508i | ||||
\(489\) | − | 5.40136i | − | 0.244258i | ||||||
\(490\) | 29.2457 | − | 6.31001i | 1.32119 | − | 0.285057i | ||||
\(491\) | 24.7876 | − | 24.7876i | 1.11865 | − | 1.11865i | 0.126709 | − | 0.991940i | \(-0.459558\pi\) |
0.991940 | − | 0.126709i | \(-0.0404416\pi\) | |||||||
\(492\) | −11.1447 | − | 4.19993i | −0.502440 | − | 0.189347i | ||||
\(493\) | −45.8544 | − | 45.8544i | −2.06518 | − | 2.06518i | ||||
\(494\) | −2.32162 | + | 3.59906i | −0.104455 | + | 0.161929i | ||||
\(495\) | −11.9145 | −0.535519 | ||||||||
\(496\) | 14.4820 | − | 16.4854i | 0.650261 | − | 0.740218i | ||||
\(497\) | 4.40466 | 0.197576 | ||||||||
\(498\) | −9.04551 | + | 14.0227i | −0.405339 | + | 0.628370i | ||||
\(499\) | 0.386258 | + | 0.386258i | 0.0172913 | + | 0.0172913i | 0.715700 | − | 0.698408i | \(-0.246108\pi\) |
−0.698408 | + | 0.715700i | \(0.746108\pi\) | |||||||
\(500\) | 0.269570 | − | 0.715314i | 0.0120555 | − | 0.0319898i | ||||
\(501\) | −1.96889 | + | 1.96889i | −0.0879634 | + | 0.0879634i | ||||
\(502\) | −31.5181 | + | 6.80029i | −1.40672 | + | 0.303512i | ||||
\(503\) | 38.3162i | 1.70843i | 0.519917 | + | 0.854217i | \(0.325963\pi\) | ||||
−0.519917 | + | 0.854217i | \(0.674037\pi\) | |||||||
\(504\) | 0.231024 | − | 1.55067i | 0.0102906 | − | 0.0690722i | ||||
\(505\) | − | 16.0176i | − | 0.712774i | ||||||
\(506\) | 3.88982 | + | 18.0286i | 0.172924 | + | 0.801469i | ||||
\(507\) | 3.76193 | − | 3.76193i | 0.167073 | − | 0.167073i | ||||
\(508\) | −7.30099 | − | 16.1317i | −0.323929 | − | 0.715730i | ||||
\(509\) | 7.78865 | + | 7.78865i | 0.345226 | + | 0.345226i | 0.858328 | − | 0.513102i | \(-0.171504\pi\) |
−0.513102 | + | 0.858328i | \(0.671504\pi\) | |||||||
\(510\) | −42.4441 | − | 27.3791i | −1.87945 | − | 1.21237i | ||||
\(511\) | −5.58198 | −0.246932 | ||||||||
\(512\) | −9.71333 | + | 20.4365i | −0.429273 | + | 0.903175i | ||||
\(513\) | −5.65431 | −0.249644 | ||||||||
\(514\) | 10.2604 | + | 6.61859i | 0.452565 | + | 0.291934i | ||||
\(515\) | 16.2713 | + | 16.2713i | 0.716997 | + | 0.716997i | ||||
\(516\) | 8.73236 | + | 19.2944i | 0.384421 | + | 0.849389i | ||||
\(517\) | −19.2764 | + | 19.2764i | −0.847774 | + | 0.847774i | ||||
\(518\) | 1.16106 | + | 5.38132i | 0.0510142 | + | 0.236441i | ||||
\(519\) | − | 12.6866i | − | 0.556881i | ||||||
\(520\) | −3.96717 | + | 26.6283i | −0.173972 | + | 1.16773i | ||||
\(521\) | 22.2075i | 0.972930i | 0.873700 | + | 0.486465i | \(0.161714\pi\) | ||||
−0.873700 | + | 0.486465i | \(0.838286\pi\) | |||||||
\(522\) | −11.7181 | + | 2.52828i | −0.512888 | + | 0.110660i | ||||
\(523\) | 0.541177 | − | 0.541177i | 0.0236640 | − | 0.0236640i | −0.695176 | − | 0.718840i | \(-0.744673\pi\) |
0.718840 | + | 0.695176i | \(0.244673\pi\) | |||||||
\(524\) | −10.9151 | + | 28.9637i | −0.476830 | + | 1.26529i | ||||
\(525\) | 2.48587 | + | 2.48587i | 0.108492 | + | 0.108492i | ||||
\(526\) | −9.58842 | + | 14.8643i | −0.418075 | + | 0.648114i | ||||
\(527\) | 44.8580 | 1.95404 | ||||||||
\(528\) | 13.0107 | − | 14.8106i | 0.566219 | − | 0.644549i | ||||
\(529\) | 9.47791 | 0.412083 | ||||||||
\(530\) | −8.18583 | + | 12.6900i | −0.355570 | + | 0.551216i | ||||
\(531\) | −5.64991 | − | 5.64991i | −0.245185 | − | 0.245185i | ||||
\(532\) | 0.970522 | + | 0.365747i | 0.0420775 | + | 0.0158571i | ||||
\(533\) | −9.17647 | + | 9.17647i | −0.397477 | + | 0.397477i | ||||
\(534\) | −17.9771 | + | 3.87871i | −0.777947 | + | 0.167848i | ||||
\(535\) | − | 36.6192i | − | 1.58319i | ||||||
\(536\) | 1.05649 | − | 0.782509i | 0.0456334 | − | 0.0337992i | ||||
\(537\) | 26.7048i | 1.15240i | ||||||||
\(538\) | −1.20036 | − | 5.56343i | −0.0517510 | − | 0.239857i | ||||
\(539\) | −16.8801 | + | 16.8801i | −0.727077 | + | 0.727077i | ||||
\(540\) | −32.3809 | + | 14.6551i | −1.39345 | + | 0.630656i | ||||
\(541\) | −10.6946 | − | 10.6946i | −0.459797 | − | 0.459797i | 0.438792 | − | 0.898589i | \(-0.355406\pi\) |
−0.898589 | + | 0.438792i | \(0.855406\pi\) | |||||||
\(542\) | 31.0607 | + | 20.0361i | 1.33417 | + | 0.860626i | ||||
\(543\) | −0.130665 | −0.00560736 | ||||||||
\(544\) | −44.4923 | + | 12.6547i | −1.90759 | + | 0.542564i | ||||
\(545\) | −57.3799 | −2.45788 | ||||||||
\(546\) | 2.59362 | + | 1.67305i | 0.110996 | + | 0.0715998i | ||||
\(547\) | 27.7156 | + | 27.7156i | 1.18503 | + | 1.18503i | 0.978423 | + | 0.206611i | \(0.0662434\pi\) |
0.206611 | + | 0.978423i | \(0.433757\pi\) | |||||||
\(548\) | −22.9768 | + | 10.3990i | −0.981521 | + | 0.444222i | ||||
\(549\) | 5.51943 | − | 5.51943i | 0.235564 | − | 0.235564i | ||||
\(550\) | −5.16041 | − | 23.9175i | −0.220041 | − | 1.01985i | ||||
\(551\) | − | 7.93038i | − | 0.337845i | ||||||
\(552\) | 8.60256 | + | 11.6146i | 0.366149 | + | 0.494349i | ||||
\(553\) | 3.81312i | 0.162150i | ||||||||
\(554\) | −2.17782 | + | 0.469883i | −0.0925268 | + | 0.0199634i | ||||
\(555\) | 23.1833 | − | 23.1833i | 0.984075 | − | 0.984075i | ||||
\(556\) | 26.6635 | + | 10.0483i | 1.13078 | + | 0.426142i | ||||
\(557\) | −0.803237 | − | 0.803237i | −0.0340343 | − | 0.0340343i | 0.689885 | − | 0.723919i | \(-0.257661\pi\) |
−0.723919 | + | 0.689885i | \(0.757661\pi\) | |||||||
\(558\) | 4.49506 | − | 6.96840i | 0.190291 | − | 0.294996i | ||||
\(559\) | 23.0771 | 0.976059 | ||||||||
\(560\) | 6.50591 | − | 0.420901i | 0.274925 | − | 0.0177863i | ||||
\(561\) | 40.3007 | 1.70150 | ||||||||
\(562\) | −2.83560 | + | 4.39584i | −0.119612 | + | 0.185427i | ||||
\(563\) | −16.8339 | − | 16.8339i | −0.709466 | − | 0.709466i | 0.256957 | − | 0.966423i | \(-0.417280\pi\) |
−0.966423 | + | 0.256957i | \(0.917280\pi\) | |||||||
\(564\) | −7.53369 | + | 19.9909i | −0.317226 | + | 0.841770i | ||||
\(565\) | −16.1737 | + | 16.1737i | −0.680431 | + | 0.680431i | ||||
\(566\) | 19.9459 | − | 4.30348i | 0.838387 | − | 0.180889i | ||||
\(567\) | 2.41182i | 0.101287i | ||||||||
\(568\) | −23.7617 | − | 3.54011i | −0.997020 | − | 0.148540i | ||||
\(569\) | 37.6346i | 1.57772i | 0.614570 | + | 0.788862i | \(0.289330\pi\) | ||||
−0.614570 | + | 0.788862i | \(0.710670\pi\) | |||||||
\(570\) | −1.30272 | − | 6.03785i | −0.0545648 | − | 0.252898i | ||||
\(571\) | 20.2923 | − | 20.2923i | 0.849205 | − | 0.849205i | −0.140829 | − | 0.990034i | \(-0.544977\pi\) |
0.990034 | + | 0.140829i | \(0.0449767\pi\) | |||||||
\(572\) | −8.85715 | − | 19.5701i | −0.370336 | − | 0.818268i | ||||
\(573\) | 18.5772 | + | 18.5772i | 0.776075 | + | 0.776075i | ||||
\(574\) | 2.64088 | + | 1.70353i | 0.110228 | + | 0.0711041i | ||||
\(575\) | 17.9390 | 0.748109 | ||||||||
\(576\) | −2.49260 | + | 8.17968i | −0.103858 | + | 0.340820i | ||||
\(577\) | 1.24449 | 0.0518090 | 0.0259045 | − | 0.999664i | \(-0.491753\pi\) | ||||
0.0259045 | + | 0.999664i | \(0.491753\pi\) | |||||||
\(578\) | −59.2612 | − | 38.2273i | −2.46494 | − | 1.59004i | ||||
\(579\) | −2.16615 | − | 2.16615i | −0.0900223 | − | 0.0900223i | ||||
\(580\) | −20.5544 | − | 45.4154i | −0.853473 | − | 1.88577i | ||||
\(581\) | 3.11355 | − | 3.11355i | 0.129172 | − | 0.129172i | ||||
\(582\) | 1.93136 | + | 8.95151i | 0.0800575 | + | 0.371052i | ||||
\(583\) | − | 12.0491i | − | 0.499023i | ||||||
\(584\) | 30.1130 | + | 4.48634i | 1.24608 | + | 0.185646i | ||||
\(585\) | 10.1740i | 0.420645i | ||||||||
\(586\) | 33.0496 | − | 7.13072i | 1.36527 | − | 0.294567i | ||||
\(587\) | −8.89264 | + | 8.89264i | −0.367038 | + | 0.367038i | −0.866396 | − | 0.499358i | \(-0.833569\pi\) |
0.499358 | + | 0.866396i | \(0.333569\pi\) | |||||||
\(588\) | −6.59717 | + | 17.5058i | −0.272063 | + | 0.721928i | ||||
\(589\) | 3.87902 | + | 3.87902i | 0.159832 | + | 0.159832i | ||||
\(590\) | 18.0111 | − | 27.9215i | 0.741506 | − | 1.14951i | ||||
\(591\) | 6.13796 | 0.252482 | ||||||||
\(592\) | −1.93850 | − | 29.9636i | −0.0796719 | − | 1.23150i | ||||
\(593\) | 47.5658 | 1.95330 | 0.976648 | − | 0.214848i | \(-0.0689255\pi\) | ||||
0.976648 | + | 0.214848i | \(0.0689255\pi\) | |||||||
\(594\) | 15.3728 | − | 23.8315i | 0.630756 | − | 0.977819i | ||||
\(595\) | 9.42416 | + | 9.42416i | 0.386353 | + | 0.386353i | ||||
\(596\) | 6.90611 | + | 2.60260i | 0.282885 | + | 0.106607i | ||||
\(597\) | 12.2676 | − | 12.2676i | 0.502078 | − | 0.502078i | ||||
\(598\) | 15.3950 | − | 3.32159i | 0.629547 | − | 0.135830i | ||||
\(599\) | 24.1212i | 0.985564i | 0.870153 | + | 0.492782i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492782i | \(0.835980\pi\) | |||||||
\(600\) | −11.4125 | − | 15.4084i | −0.465915 | − | 0.629046i | ||||
\(601\) | − | 31.2134i | − | 1.27322i | −0.771185 | − | 0.636611i | \(-0.780336\pi\) | ||
0.771185 | − | 0.636611i | \(-0.219664\pi\) | |||||||
\(602\) | −1.17862 | − | 5.46270i | −0.0480370 | − | 0.222643i | ||||
\(603\) | 0.351319 | − | 0.351319i | 0.0143068 | − | 0.0143068i | ||||
\(604\) | −28.7381 | + | 13.0064i | −1.16934 | + | 0.529224i | ||||
\(605\) | 3.50692 | + | 3.50692i | 0.142577 | + | 0.142577i | ||||
\(606\) | 8.41639 | + | 5.42911i | 0.341893 | + | 0.220543i | ||||
\(607\) | 32.2613 | 1.30945 | 0.654723 | − | 0.755869i | \(-0.272785\pi\) | ||||
0.654723 | + | 0.755869i | \(0.272785\pi\) | |||||||
\(608\) | −4.94170 | − | 2.75311i | −0.200412 | − | 0.111653i | ||||
\(609\) | −5.71493 | −0.231581 | ||||||||
\(610\) | 27.2766 | + | 17.5952i | 1.10440 | + | 0.712408i | ||||
\(611\) | 16.4605 | + | 16.4605i | 0.665919 | + | 0.665919i | ||||
\(612\) | −15.9257 | + | 7.20772i | −0.643757 | + | 0.291355i | ||||
\(613\) | −6.65388 | + | 6.65388i | −0.268748 | + | 0.268748i | −0.828595 | − | 0.559848i | \(-0.810860\pi\) |
0.559848 | + | 0.828595i | \(0.310860\pi\) | |||||||
\(614\) | 1.19914 | + | 5.55779i | 0.0483934 | + | 0.224294i | ||||
\(615\) | − | 18.7162i | − | 0.754709i | ||||||
\(616\) | −4.18017 | + | 3.09612i | −0.168424 | + | 0.124746i | ||||
\(617\) | − | 9.85131i | − | 0.396599i | −0.980141 | − | 0.198299i | \(-0.936458\pi\) | ||
0.980141 | − | 0.198299i | \(-0.0635419\pi\) | |||||||
\(618\) | −14.0648 | + | 3.03459i | −0.565768 | + | 0.122069i | ||||
\(619\) | −6.57288 | + | 6.57288i | −0.264186 | + | 0.264186i | −0.826752 | − | 0.562566i | \(-0.809814\pi\) |
0.562566 | + | 0.826752i | \(0.309814\pi\) | |||||||
\(620\) | 32.2681 | + | 12.1604i | 1.29592 | + | 0.488374i | ||||
\(621\) | 14.7023 | + | 14.7023i | 0.589985 | + | 0.589985i | ||||
\(622\) | −19.8795 | + | 30.8179i | −0.797096 | + | 1.23569i | ||||
\(623\) | 4.85281 | 0.194424 | ||||||||
\(624\) | −12.6471 | − | 11.1101i | −0.506288 | − | 0.444760i | ||||
\(625\) | 25.5932 | 1.02373 | ||||||||
\(626\) | −8.74552 | + | 13.5576i | −0.349541 | + | 0.541871i | ||||
\(627\) | 3.48494 | + | 3.48494i | 0.139175 | + | 0.139175i | ||||
\(628\) | 1.90633 | − | 5.05851i | 0.0760708 | − | 0.201857i | ||||
\(629\) | 43.4039 | − | 43.4039i | 1.73063 | − | 1.73063i | ||||
\(630\) | 2.40835 | − | 0.519620i | 0.0959508 | − | 0.0207022i | ||||
\(631\) | − | 27.2487i | − | 1.08475i | −0.840136 | − | 0.542376i | \(-0.817525\pi\) | ||
0.840136 | − | 0.542376i | \(-0.182475\pi\) | |||||||
\(632\) | 3.06468 | − | 20.5706i | 0.121906 | − | 0.818253i | ||||
\(633\) | 15.7617i | 0.626473i | ||||||||
\(634\) | −4.73640 | − | 21.9523i | −0.188106 | − | 0.871838i | ||||
\(635\) | 19.6763 | − | 19.6763i | 0.780829 | − | 0.780829i | ||||
\(636\) | −3.89333 | − | 8.60243i | −0.154381 | − | 0.341109i | ||||
\(637\) | 14.4142 | + | 14.4142i | 0.571113 | + | 0.571113i | ||||
\(638\) | 33.4246 | + | 21.5610i | 1.32329 | + | 0.853608i | ||||
\(639\) | −9.07881 | −0.359152 | ||||||||
\(640\) | −35.4356 | − | 2.95830i | −1.40072 | − | 0.116937i | ||||
\(641\) | −36.8300 | −1.45470 | −0.727349 | − | 0.686268i | \(-0.759248\pi\) | ||||
−0.727349 | + | 0.686268i | \(0.759248\pi\) | |||||||
\(642\) | 19.2414 | + | 12.4120i | 0.759399 | + | 0.489861i | ||||
\(643\) | −9.87365 | − | 9.87365i | −0.389379 | − | 0.389379i | 0.485087 | − | 0.874466i | \(-0.338788\pi\) |
−0.874466 | + | 0.485087i | \(0.838788\pi\) | |||||||
\(644\) | −1.57254 | − | 3.47457i | −0.0619666 | − | 0.136917i | ||||
\(645\) | −23.5339 | + | 23.5339i | −0.926645 | + | 0.926645i | ||||
\(646\) | −2.43896 | − | 11.3041i | −0.0959595 | − | 0.444755i | ||||
\(647\) | − | 31.5428i | − | 1.24007i | −0.784572 | − | 0.620037i | \(-0.787117\pi\) | ||
0.784572 | − | 0.620037i | \(-0.212883\pi\) | |||||||
\(648\) | 1.93843 | − | 13.0110i | 0.0761486 | − | 0.511121i | ||||
\(649\) | 26.5114i | 1.04066i | ||||||||
\(650\) | −20.4236 | + | 4.40657i | −0.801081 | + | 0.172840i | ||||
\(651\) | 2.79537 | − | 2.79537i | 0.109559 | − | 0.109559i | ||||
\(652\) | 2.74136 | − | 7.27430i | 0.107360 | − | 0.284884i | ||||
\(653\) | −4.98004 | − | 4.98004i | −0.194884 | − | 0.194884i | 0.602919 | − | 0.797803i | \(-0.294004\pi\) |
−0.797803 | + | 0.602919i | \(0.794004\pi\) | |||||||
\(654\) | 19.4487 | − | 30.1501i | 0.760505 | − | 1.17896i | ||||
\(655\) | −48.6412 | −1.90057 | ||||||||
\(656\) | −12.8775 | − | 11.3125i | −0.502783 | − | 0.441681i | ||||
\(657\) | 11.5055 | 0.448872 | ||||||||
\(658\) | 3.05574 | − | 4.73712i | 0.119125 | − | 0.184672i | ||||
\(659\) | 21.6158 | + | 21.6158i | 0.842033 | + | 0.842033i | 0.989123 | − | 0.147090i | \(-0.0469906\pi\) |
−0.147090 | + | 0.989123i | \(0.546991\pi\) | |||||||
\(660\) | 28.9899 | + | 10.9250i | 1.12843 | + | 0.425255i | ||||
\(661\) | 31.1470 | − | 31.1470i | 1.21148 | − | 1.21148i | 0.240935 | − | 0.970541i | \(-0.422546\pi\) |
0.970541 | − | 0.240935i | \(-0.0774540\pi\) | |||||||
\(662\) | 13.7837 | − | 2.97395i | 0.535719 | − | 0.115586i | ||||
\(663\) | − | 34.4135i | − | 1.33651i | ||||||
\(664\) | −19.2990 | + | 14.2942i | −0.748948 | + | 0.554722i | ||||
\(665\) | 1.62988i | 0.0632040i | ||||||||
\(666\) | −2.39316 | − | 11.0919i | −0.0927332 | − | 0.429802i | ||||
\(667\) | −20.6206 | + | 20.6206i | −0.798432 | + | 0.798432i | ||||
\(668\) | −3.65088 | + | 1.65233i | −0.141257 | + | 0.0639307i | ||||
\(669\) | −22.8755 | − | 22.8755i | −0.884416 | − | 0.884416i | ||||
\(670\) | 1.73619 | + | 1.11996i | 0.0670750 | + | 0.0432677i | ||||
\(671\) | −25.8992 | −0.999826 | ||||||||
\(672\) | −1.98400 | + | 3.56117i | −0.0765343 | + | 0.137375i | ||||
\(673\) | 10.9006 | 0.420187 | 0.210093 | − | 0.977681i | \(-0.432623\pi\) | ||||
0.210093 | + | 0.977681i | \(0.432623\pi\) | |||||||
\(674\) | 26.5522 | + | 17.1279i | 1.02275 | + | 0.659741i | ||||
\(675\) | −19.5048 | − | 19.5048i | −0.750740 | − | 0.750740i | ||||
\(676\) | 6.97569 | − | 3.15709i | 0.268296 | − | 0.121427i | ||||
\(677\) | −14.9245 | + | 14.9245i | −0.573594 | + | 0.573594i | −0.933131 | − | 0.359537i | \(-0.882935\pi\) |
0.359537 | + | 0.933131i | \(0.382935\pi\) | |||||||
\(678\) | −3.01638 | − | 13.9804i | −0.115844 | − | 0.536914i | ||||
\(679\) | − | 2.41640i | − | 0.0927330i | ||||||
\(680\) | −43.2660 | − | 58.4147i | −1.65917 | − | 2.24010i | ||||
\(681\) | 11.4572i | 0.439041i | ||||||||
\(682\) | −26.8953 | + | 5.80289i | −1.02988 | + | 0.222204i | ||||
\(683\) | 22.8976 | − | 22.8976i | 0.876154 | − | 0.876154i | −0.116980 | − | 0.993134i | \(-0.537321\pi\) |
0.993134 | + | 0.116980i | \(0.0373215\pi\) | |||||||
\(684\) | −2.00042 | − | 0.753871i | −0.0764881 | − | 0.0288250i | ||||
\(685\) | −28.0254 | − | 28.0254i | −1.07079 | − | 1.07079i | ||||
\(686\) | 5.45866 | − | 8.46221i | 0.208413 | − | 0.323089i | ||||
\(687\) | −33.3098 | −1.27085 | ||||||||
\(688\) | 1.96782 | + | 30.4168i | 0.0750223 | + | 1.15963i | ||||
\(689\) | −10.2890 | −0.391978 | ||||||||
\(690\) | −12.3123 | + | 19.0870i | −0.468721 | + | 0.726628i | ||||
\(691\) | 28.7834 | + | 28.7834i | 1.09497 | + | 1.09497i | 0.994989 | + | 0.0999813i | \(0.0318783\pi\) |
0.0999813 | + | 0.994989i | \(0.468122\pi\) | |||||||
\(692\) | 6.43886 | − | 17.0858i | 0.244769 | − | 0.649503i | ||||
\(693\) | −1.39005 | + | 1.39005i | −0.0528037 | + | 0.0528037i | ||||
\(694\) | 45.6290 | − | 9.84483i | 1.73205 | − | 0.373705i | ||||
\(695\) | 44.7782i | 1.69854i | ||||||||
\(696\) | 30.8302 | + | 4.59319i | 1.16862 | + | 0.174105i | ||||
\(697\) | − | 35.0406i | − | 1.32726i | ||||||
\(698\) | −7.42512 | − | 34.4141i | −0.281045 | − | 1.30259i | ||||
\(699\) | 12.2846 | − | 12.2846i | 0.464645 | − | 0.464645i | ||||
\(700\) | 2.08620 | + | 4.60952i | 0.0788509 | + | 0.174223i | ||||
\(701\) | −0.585300 | − | 0.585300i | −0.0221065 | − | 0.0221065i | 0.695967 | − | 0.718074i | \(-0.254976\pi\) |
−0.718074 | + | 0.695967i | \(0.754976\pi\) | |||||||
\(702\) | −20.3502 | − | 13.1272i | −0.768068 | − | 0.495453i | ||||
\(703\) | 7.50657 | 0.283116 | ||||||||
\(704\) | 25.0391 | − | 13.3429i | 0.943697 | − | 0.502880i | ||||
\(705\) | −33.5724 | −1.26441 | ||||||||
\(706\) | −0.228814 | − | 0.147599i | −0.00861152 | − | 0.00555498i | ||||
\(707\) | −1.86875 | − | 1.86875i | −0.0702816 | − | 0.0702816i | ||||
\(708\) | 8.56642 | + | 18.9278i | 0.321946 | + | 0.711349i | ||||
\(709\) | −9.30375 | + | 9.30375i | −0.349410 | + | 0.349410i | −0.859890 | − | 0.510480i | \(-0.829468\pi\) |
0.510480 | + | 0.859890i | \(0.329468\pi\) | |||||||
\(710\) | −7.96243 | − | 36.9044i | −0.298825 | − | 1.38500i | ||||
\(711\) | − | 7.85954i | − | 0.294756i | ||||||
\(712\) | −26.1794 | − | 3.90029i | −0.981113 | − | 0.146170i | ||||
\(713\) | − | 20.1725i | − | 0.755465i | ||||||
\(714\) | −8.14618 | + | 1.75760i | −0.304863 | + | 0.0657767i | ||||
\(715\) | 23.8702 | − | 23.8702i | 0.892693 | − | 0.892693i | ||||
\(716\) | −13.5535 | + | 35.9648i | −0.506519 | + | 1.34407i | ||||
\(717\) | −9.92633 | − | 9.92633i | −0.370706 | − | 0.370706i | ||||
\(718\) | −0.510229 | + | 0.790975i | −0.0190416 | + | 0.0295189i | ||||
\(719\) | −19.6784 | −0.733880 | −0.366940 | − | 0.930245i | \(-0.619594\pi\) | ||||
−0.366940 | + | 0.930245i | \(0.619594\pi\) | |||||||
\(720\) | −13.4099 | + | 0.867554i | −0.499757 | + | 0.0323318i | ||||
\(721\) | 3.79669 | 0.141396 | ||||||||
\(722\) | 0.766601 | − | 1.18841i | 0.0285300 | − | 0.0442281i | ||||
\(723\) | −11.8663 | − | 11.8663i | −0.441311 | − | 0.441311i | ||||
\(724\) | −0.175973 | − | 0.0663165i | −0.00654000 | − | 0.00246463i | ||||
\(725\) | 27.3562 | − | 27.3562i | 1.01598 | − | 1.01598i | ||||
\(726\) | −3.03136 | + | 0.654040i | −0.112504 | + | 0.0242737i | ||||
\(727\) | 2.04226i | 0.0757432i | 0.999283 | + | 0.0378716i | \(0.0120578\pi\) | ||||
−0.999283 | + | 0.0378716i | \(0.987942\pi\) | |||||||
\(728\) | 2.64384 | + | 3.56953i | 0.0979871 | + | 0.132295i | ||||
\(729\) | − | 28.5437i | − | 1.05717i | ||||||
\(730\) | 10.0907 | + | 46.7685i | 0.373474 | + | 1.73098i | ||||
\(731\) | −44.0603 | + | 44.0603i | −1.62963 | + | 1.62963i | ||||
\(732\) | −18.4906 | + | 8.36859i | −0.683434 | + | 0.309312i | ||||
\(733\) | 28.0186 | + | 28.0186i | 1.03489 | + | 1.03489i | 0.999369 | + | 0.0355234i | \(0.0113098\pi\) |
0.0355234 | + | 0.999369i | \(0.488690\pi\) | |||||||
\(734\) | 5.62949 | + | 3.63138i | 0.207788 | + | 0.134037i | ||||
\(735\) | −29.3990 | −1.08440 | ||||||||
\(736\) | 5.69076 | + | 20.0081i | 0.209764 | + | 0.737507i | ||||
\(737\) | −1.64852 | −0.0607239 | ||||||||
\(738\) | −5.44333 | − | 3.51130i | −0.200372 | − | 0.129253i | ||||
\(739\) | 12.9329 | + | 12.9329i | 0.475746 | + | 0.475746i | 0.903768 | − | 0.428022i | \(-0.140789\pi\) |
−0.428022 | + | 0.903768i | \(0.640789\pi\) | |||||||
\(740\) | 42.9884 | − | 19.4559i | 1.58029 | − | 0.715214i | ||||
\(741\) | 2.97585 | − | 2.97585i | 0.109321 | − | 0.109321i | ||||
\(742\) | 0.525490 | + | 2.43555i | 0.0192913 | + | 0.0894118i | ||||
\(743\) | − | 24.3241i | − | 0.892363i | −0.894943 | − | 0.446181i | \(-0.852784\pi\) | ||
0.894943 | − | 0.446181i | \(-0.147216\pi\) | |||||||
\(744\) | −17.3268 | + | 12.8334i | −0.635232 | + | 0.470496i | ||||
\(745\) | 11.5980i | 0.424918i | ||||||||
\(746\) | −11.7874 | + | 2.54323i | −0.431568 | + | 0.0931144i | ||||
\(747\) | −6.41760 | + | 6.41760i | −0.234808 | + | 0.234808i | ||||
\(748\) | 54.2751 | + | 20.4539i | 1.98449 | + | 0.747868i | ||||
\(749\) | −4.27232 | − | 4.27232i | −0.156107 | − | 0.156107i | ||||
\(750\) | −0.407172 | + | 0.631212i | −0.0148678 | + | 0.0230486i | ||||
\(751\) | −1.33891 | −0.0488575 | −0.0244288 | − | 0.999702i | \(-0.507777\pi\) | ||||
−0.0244288 | + | 0.999702i | \(0.507777\pi\) | |||||||
\(752\) | −20.2921 | + | 23.0993i | −0.739976 | + | 0.842344i | ||||
\(753\) | 31.6833 | 1.15460 | ||||||||
\(754\) | 18.4113 | − | 28.5419i | 0.670501 | − | 1.03943i | ||||
\(755\) | −35.0526 | − | 35.0526i | −1.27569 | − | 1.27569i | ||||
\(756\) | −2.06804 | + | 5.48763i | −0.0752140 | + | 0.199583i | ||||
\(757\) | −31.7159 | + | 31.7159i | −1.15273 | + | 1.15273i | −0.166731 | + | 0.986002i | \(0.553321\pi\) |
−0.986002 | + | 0.166731i | \(0.946679\pi\) | |||||||
\(758\) | 37.6193 | − | 8.11668i | 1.36640 | − | 0.294811i | ||||
\(759\) | − | 18.1231i | − | 0.657826i | ||||||
\(760\) | 1.30996 | − | 8.79268i | 0.0475174 | − | 0.318944i | ||||
\(761\) | 2.84907i | 0.103279i | 0.998666 | + | 0.0516394i | \(0.0164446\pi\) | ||||
−0.998666 | + | 0.0516394i | \(0.983555\pi\) | |||||||
\(762\) | 3.66962 | + | 17.0080i | 0.132936 | + | 0.616136i | ||||
\(763\) | −6.69443 | + | 6.69443i | −0.242355 | + | 0.242355i | ||||
\(764\) | 15.5904 | + | 34.4475i | 0.564042 | + | 1.24627i | ||||
\(765\) | −19.4249 | − | 19.4249i | −0.702309 | − | 0.702309i | ||||
\(766\) | −32.7418 | − | 21.1205i | −1.18301 | − | 0.763116i | ||||
\(767\) | 22.6386 | 0.817433 | ||||||||
\(768\) | 13.5652 | − | 17.6168i | 0.489492 | − | 0.635692i | ||||
\(769\) | 42.0931 | 1.51792 | 0.758958 | − | 0.651139i | \(-0.225709\pi\) | ||||
0.758958 | + | 0.651139i | \(0.225709\pi\) | |||||||
\(770\) | −6.86954 | − | 4.43129i | −0.247561 | − | 0.159693i | ||||
\(771\) | −8.48371 | − | 8.48371i | −0.305533 | − | 0.305533i | ||||
\(772\) | −1.81789 | − | 4.01667i | −0.0654271 | − | 0.144563i | ||||
\(773\) | 13.6204 | − | 13.6204i | 0.489891 | − | 0.489891i | −0.418381 | − | 0.908272i | \(-0.637402\pi\) |
0.908272 | + | 0.418381i | \(0.137402\pi\) | |||||||
\(774\) | 2.42936 | + | 11.2596i | 0.0873214 | + | 0.404719i | ||||
\(775\) | 26.7617i | 0.961309i | ||||||||
\(776\) | −1.94211 | + | 13.0357i | −0.0697176 | + | 0.467955i | ||||
\(777\) | − | 5.40952i | − | 0.194065i | ||||||
\(778\) | 3.90254 | − | 0.842006i | 0.139913 | − | 0.0301874i | ||||
\(779\) | 3.03008 | − | 3.03008i | 0.108564 | − | 0.108564i | ||||
\(780\) | 9.32906 | − | 24.7550i | 0.334034 | − | 0.886371i | ||||
\(781\) | 21.3005 | + | 21.3005i | 0.762193 | + | 0.762193i | ||||
\(782\) | −23.0512 | + | 35.7348i | −0.824310 | + | 1.27787i | ||||
\(783\) | 44.8408 | 1.60248 | ||||||||
\(784\) | −17.7695 | + | 20.2278i | −0.634626 | + | 0.722420i | ||||
\(785\) | 8.49518 | 0.303206 | ||||||||
\(786\) | 16.4868 | − | 25.5583i | 0.588063 | − | 0.911636i | ||||
\(787\) | 27.0243 | + | 27.0243i | 0.963312 | + | 0.963312i | 0.999350 | − | 0.0360382i | \(-0.0114738\pi\) |
−0.0360382 | + | 0.999350i | \(0.511474\pi\) | |||||||
\(788\) | 8.26633 | + | 3.11521i | 0.294476 | + | 0.110975i | ||||
\(789\) | 12.2904 | − | 12.2904i | 0.437551 | − | 0.437551i | ||||
\(790\) | 31.9482 | − | 6.89309i | 1.13667 | − | 0.245245i | ||||
\(791\) | 3.77391i | 0.134185i | ||||||||
\(792\) | 8.61610 | − | 6.38168i | 0.306160 | − | 0.226763i | ||||
\(793\) | 22.1158i | 0.785355i | ||||||||
\(794\) | 7.71383 | + | 35.7522i | 0.273753 | + | 1.26880i | ||||
\(795\) | 10.4926 | − | 10.4926i | 0.372134 | − | 0.372134i | ||||
\(796\) | 22.7476 | − | 10.2952i | 0.806266 | − | 0.364904i | ||||
\(797\) | 28.7589 | + | 28.7589i | 1.01869 | + | 1.01869i | 0.999822 | + | 0.0188715i | \(0.00600735\pi\) |
0.0188715 | + | 0.999822i | \(0.493993\pi\) | |||||||
\(798\) | −0.856414 | − | 0.552442i | −0.0303167 | − | 0.0195562i | ||||
\(799\) | −62.8547 | −2.22364 | ||||||||
\(800\) | −7.54962 | − | 26.5436i | −0.266919 | − | 0.938458i | ||||
\(801\) | −10.0025 | −0.353422 | ||||||||
\(802\) | −43.8978 | − | 28.3169i | −1.55009 | − | 0.999905i | ||||
\(803\) | −26.9939 | − | 26.9939i | −0.952595 | − | 0.952595i | ||||
\(804\) | −1.17695 | + | 0.532672i | −0.0415080 | + | 0.0187859i | ||||
\(805\) | 4.23801 | − | 4.23801i | 0.149370 | − | 0.149370i | ||||
\(806\) | 4.95520 | + | 22.9664i | 0.174539 | + | 0.808958i | ||||
\(807\) | 5.59259i | 0.196868i | ||||||||
\(808\) | 8.57937 | + | 11.5833i | 0.301821 | + | 0.407498i | ||||
\(809\) | − | 40.9557i | − | 1.43993i | −0.694012 | − | 0.719964i | \(-0.744158\pi\) | ||
0.694012 | − | 0.719964i | \(-0.255842\pi\) | |||||||
\(810\) | 20.2074 | − | 4.35992i | 0.710016 | − | 0.153192i | ||||
\(811\) | −10.7575 | + | 10.7575i | −0.377746 | + | 0.377746i | −0.870288 | − | 0.492543i | \(-0.836068\pi\) |
0.492543 | + | 0.870288i | \(0.336068\pi\) | |||||||
\(812\) | −7.69660 | − | 2.90051i | −0.270098 | − | 0.101788i | ||||
\(813\) | −25.6823 | − | 25.6823i | −0.900718 | − | 0.900718i | ||||
\(814\) | −20.4088 | + | 31.6383i | −0.715326 | + | 1.10892i | ||||
\(815\) | 12.2163 | 0.427920 | ||||||||
\(816\) | 45.3586 | − | 2.93448i | 1.58787 | − | 0.102727i | ||||
\(817\) | −7.62009 | −0.266593 | ||||||||
\(818\) | −15.9698 | + | 24.7569i | −0.558371 | + | 0.865606i | ||||
\(819\) | 1.18699 | + | 1.18699i | 0.0414769 | + | 0.0414769i | ||||
\(820\) | 9.49905 | − | 25.2061i | 0.331721 | − | 0.880234i | ||||
\(821\) | −29.4421 | + | 29.4421i | −1.02753 | + | 1.02753i | −0.0279247 | + | 0.999610i | \(0.508890\pi\) |
−0.999610 | + | 0.0279247i | \(0.991110\pi\) | |||||||
\(822\) | 24.2249 | − | 5.22673i | 0.844942 | − | 0.182303i | ||||
\(823\) | 22.2738i | 0.776416i | 0.921572 | + | 0.388208i | \(0.126906\pi\) | ||||
−0.921572 | + | 0.388208i | \(0.873094\pi\) | |||||||
\(824\) | −20.4819 | − | 3.05147i | −0.713522 | − | 0.106303i | ||||
\(825\) | 24.0429i | 0.837066i | ||||||||
\(826\) | −1.15622 | − | 5.35889i | −0.0402302 | − | 0.186460i | ||||
\(827\) | 31.3520 | − | 31.3520i | 1.09022 | − | 1.09022i | 0.0947117 | − | 0.995505i | \(-0.469807\pi\) |
0.995505 | − | 0.0947117i | \(-0.0301929\pi\) | |||||||
\(828\) | 3.24129 | + | 7.16172i | 0.112643 | + | 0.248887i | ||||
\(829\) | 1.27686 | + | 1.27686i | 0.0443473 | + | 0.0443473i | 0.728933 | − | 0.684585i | \(-0.240017\pi\) |
−0.684585 | + | 0.728933i | \(0.740017\pi\) | |||||||
\(830\) | −31.7153 | − | 20.4584i | −1.10085 | − | 0.710121i | ||||
\(831\) | 2.18923 | 0.0759437 | ||||||||
\(832\) | −11.3938 | − | 21.3814i | −0.395008 | − | 0.741265i | ||||
\(833\) | −55.0411 | −1.90706 | ||||||||
\(834\) | −23.5286 | − | 15.1774i | −0.814728 | − | 0.525551i | ||||
\(835\) | −4.45307 | − | 4.45307i | −0.154105 | − | 0.154105i | ||||
\(836\) | 2.92464 | + | 6.46207i | 0.101151 | + | 0.223495i | ||||
\(837\) | −21.9332 | + | 21.9332i | −0.758122 | + | 0.758122i | ||||
\(838\) | 7.04448 | + | 32.6499i | 0.243347 | + | 1.12787i | ||||
\(839\) | 45.4357i | 1.56861i | 0.620372 | + | 0.784307i | \(0.286981\pi\) | ||||
−0.620372 | + | 0.784307i | \(0.713019\pi\) | |||||||
\(840\) | −6.33633 | − | 0.944009i | −0.218624 | − | 0.0325714i | ||||
\(841\) | 33.8909i | 1.16865i | ||||||||
\(842\) | 24.9336 | − | 5.37964i | 0.859270 | − | 0.185395i | ||||
\(843\) | 3.63467 | − | 3.63467i | 0.125185 | − | 0.125185i | ||||
\(844\) | −7.99958 | + | 21.2272i | −0.275357 | + | 0.730670i | ||||
\(845\) | 8.50842 | + | 8.50842i | 0.292699 | + | 0.292699i | ||||
\(846\) | −6.29845 | + | 9.76407i | −0.216545 | + | 0.335696i | ||||
\(847\) | 0.818295 | 0.0281169 | ||||||||
\(848\) | −0.877353 | − | 13.5614i | −0.0301284 | − | 0.465699i | ||||
\(849\) | −20.0504 | −0.688128 | ||||||||
\(850\) | 30.5808 | − | 47.4074i | 1.04891 | − | 1.62606i | ||||
\(851\) | −19.5186 | − | 19.5186i | −0.669089 | − | 0.669089i | ||||
\(852\) | 22.0901 | + | 8.32478i | 0.756795 | + | 0.285202i | ||||
\(853\) | −19.3036 | + | 19.3036i | −0.660943 | + | 0.660943i | −0.955602 | − | 0.294660i | \(-0.904794\pi\) |
0.294660 | + | 0.955602i | \(0.404794\pi\) | |||||||
\(854\) | 5.23513 | − | 1.12952i | 0.179142 | − | 0.0386515i | ||||
\(855\) | − | 3.35948i | − | 0.114892i | ||||||
\(856\) | 19.6140 | + | 26.4815i | 0.670394 | + | 0.905120i | ||||
\(857\) | 19.2716i | 0.658305i | 0.944277 | + | 0.329152i | \(0.106763\pi\) | ||||
−0.944277 | + | 0.329152i | \(0.893237\pi\) | |||||||
\(858\) | 4.45178 | + | 20.6332i | 0.151981 | + | 0.704405i | ||||
\(859\) | 24.6106 | − | 24.6106i | 0.839702 | − | 0.839702i | −0.149118 | − | 0.988819i | \(-0.547643\pi\) |
0.988819 | + | 0.149118i | \(0.0476434\pi\) | |||||||
\(860\) | −43.6385 | + | 19.7501i | −1.48806 | + | 0.673474i | ||||
\(861\) | −2.18359 | − | 2.18359i | −0.0744165 | − | 0.0744165i | ||||
\(862\) | −14.9343 | − | 9.63356i | −0.508664 | − | 0.328120i | ||||
\(863\) | −6.90091 | −0.234910 | −0.117455 | − | 0.993078i | \(-0.537474\pi\) | ||||
−0.117455 | + | 0.993078i | \(0.537474\pi\) | |||||||
\(864\) | 15.5669 | − | 27.9419i | 0.529598 | − | 0.950602i | ||||
\(865\) | 28.6935 | 0.975610 | ||||||||
\(866\) | −15.5201 | − | 10.0115i | −0.527395 | − | 0.340203i | ||||
\(867\) | 48.9997 | + | 48.9997i | 1.66412 | + | 1.66412i | ||||
\(868\) | 5.18341 | − | 2.34594i | 0.175937 | − | 0.0796263i | ||||
\(869\) | −18.4399 | + | 18.4399i | −0.625531 | + | 0.625531i | ||||
\(870\) | 10.3310 | + | 47.8825i | 0.350255 | + | 1.62337i | ||||
\(871\) | 1.40770i | 0.0476981i | ||||||||
\(872\) | 41.4948 | − | 30.7339i | 1.40519 | − | 1.04078i | ||||
\(873\) | 4.98065i | 0.168569i | ||||||||
\(874\) | −5.08343 | + | 1.09679i | −0.171950 | + | 0.0370995i | ||||
\(875\) | 0.140152 | − | 0.140152i | 0.00473802 | − | 0.00473802i | ||||
\(876\) | −27.9946 | − | 10.5499i | −0.945849 | − | 0.356448i | ||||
\(877\) | 18.6196 | + | 18.6196i | 0.628740 | + | 0.628740i | 0.947751 | − | 0.319011i | \(-0.103351\pi\) |
−0.319011 | + | 0.947751i | \(0.603351\pi\) | |||||||
\(878\) | −2.72786 | + | 4.22882i | −0.0920608 | + | 0.142716i | ||||
\(879\) | −33.2228 | −1.12058 | ||||||||
\(880\) | 33.4974 | + | 29.4266i | 1.12920 | + | 0.991969i | ||||
\(881\) | 5.78877 | 0.195029 | 0.0975143 | − | 0.995234i | \(-0.468911\pi\) | ||||
0.0975143 | + | 0.995234i | \(0.468911\pi\) | |||||||
\(882\) | −5.51548 | + | 8.55028i | −0.185716 | + | 0.287903i | ||||
\(883\) | 0.739375 | + | 0.739375i | 0.0248819 | + | 0.0248819i | 0.719438 | − | 0.694556i | \(-0.244399\pi\) |
−0.694556 | + | 0.719438i | \(0.744399\pi\) | |||||||
\(884\) | 17.4660 | − | 46.3465i | 0.587444 | − | 1.55880i | ||||
\(885\) | −23.0866 | + | 23.0866i | −0.776049 | + | 0.776049i | ||||
\(886\) | −39.0987 | + | 8.43586i | −1.31355 | + | 0.283408i | ||||
\(887\) | − | 34.9584i | − | 1.17379i | −0.809663 | − | 0.586895i | \(-0.800350\pi\) | ||
0.809663 | − | 0.586895i | \(-0.199650\pi\) | |||||||
\(888\) | −4.34773 | + | 29.1826i | −0.145900 | + | 0.979305i | ||||
\(889\) | − | 4.59121i | − | 0.153984i | ||||||
\(890\) | −8.77256 | − | 40.6592i | −0.294057 | − | 1.36290i | ||||
\(891\) | −11.6633 | + | 11.6633i | −0.390737 | + | 0.390737i | ||||
\(892\) | −19.1976 | − | 42.4177i | −0.642783 | − | 1.42025i | ||||
\(893\) | −5.43526 | − | 5.43526i | −0.181884 | − | 0.181884i | ||||
\(894\) | −6.09413 | − | 3.93110i | −0.203818 | − | 0.131476i | ||||
\(895\) | −60.3986 | −2.01890 | ||||||||
\(896\) | −4.47936 | + | 3.78908i | −0.149645 | + | 0.126584i | ||||
\(897\) | −15.4756 | −0.516716 | ||||||||
\(898\) | −6.80505 | − | 4.38969i | −0.227087 | − | 0.146486i | ||||
\(899\) | −30.7621 | − | 30.7621i | −1.02597 | − | 1.02597i | ||||
\(900\) | −4.30004 | − | 9.50106i | −0.143335 | − | 0.316702i | ||||
\(901\) | 19.6443 | − | 19.6443i | 0.654448 | − | 0.654448i | ||||
\(902\) | 4.53290 | + | 21.0092i | 0.150929 | + | 0.699529i | ||||
\(903\) | 5.49132i | 0.182740i | ||||||||
\(904\) | 3.03317 | − | 20.3591i | 0.100882 | − | 0.677132i | ||||
\(905\) | − | 0.295527i | − | 0.00982364i | ||||||
\(906\) | 30.2992 | − | 6.53730i | 1.00662 | − | 0.217187i | ||||
\(907\) | 10.2520 | − | 10.2520i | 0.340411 | − | 0.340411i | −0.516111 | − | 0.856522i | \(-0.672621\pi\) |
0.856522 | + | 0.516111i | \(0.172621\pi\) | |||||||
\(908\) | −5.81490 | + | 15.4301i | −0.192974 | + | 0.512064i | ||||
\(909\) | 3.85184 | + | 3.85184i | 0.127757 | + | 0.127757i | ||||
\(910\) | −3.78396 | + | 5.86603i | −0.125437 | + | 0.194457i | ||||
\(911\) | 48.1075 | 1.59387 | 0.796935 | − | 0.604064i | \(-0.206453\pi\) | ||||
0.796935 | + | 0.604064i | \(0.206453\pi\) | |||||||
\(912\) | 4.17607 | + | 3.66856i | 0.138284 | + | 0.121478i | ||||
\(913\) | 30.1137 | 0.996618 | ||||||||
\(914\) | −17.9032 | + | 27.7542i | −0.592186 | + | 0.918028i | ||||
\(915\) | −22.5535 | − | 22.5535i | −0.745595 | − | 0.745595i | ||||
\(916\) | −44.8601 | − | 16.9058i | −1.48222 | − | 0.558582i | ||||
\(917\) | −5.67490 | + | 5.67490i | −0.187402 | + | 0.187402i | ||||
\(918\) | 63.9170 | − | 13.7906i | 2.10958 | − | 0.455158i | ||||
\(919\) | − | 45.3411i | − | 1.49567i | −0.663887 | − | 0.747833i | \(-0.731094\pi\) | ||
0.663887 | − | 0.747833i | \(-0.268906\pi\) | |||||||
\(920\) | −26.2689 | + | 19.4566i | −0.866060 | + | 0.641464i | ||||
\(921\) | − | 5.58692i | − | 0.184095i | ||||||
\(922\) | 3.01692 | + | 13.9829i | 0.0993568 | + | 0.460501i | ||||
\(923\) | 18.1889 | − | 18.1889i | 0.598696 | − | 0.598696i | ||||
\(924\) | 4.65681 | − | 2.10760i | 0.153198 | − | 0.0693350i | ||||
\(925\) | 25.8943 | + | 25.8943i | 0.851398 | + | 0.851398i | ||||
\(926\) | −16.4663 | − | 10.6218i | −0.541118 | − | 0.349056i | ||||
\(927\) | −7.82567 | −0.257029 | ||||||||
\(928\) | 39.1895 | + | 21.8332i | 1.28646 | + | 0.716711i | ||||
\(929\) | −48.8327 | −1.60215 | −0.801075 | − | 0.598565i | \(-0.795738\pi\) | ||||
−0.801075 | + | 0.598565i | \(0.795738\pi\) | |||||||
\(930\) | −28.4742 | − | 18.3677i | −0.933707 | − | 0.602300i | ||||
\(931\) | −4.75959 | − | 4.75959i | −0.155989 | − | 0.155989i | ||||
\(932\) | 22.7791 | − | 10.3095i | 0.746155 | − | 0.337699i | ||||
\(933\) | 25.4816 | − | 25.4816i | 0.834229 | − | 0.834229i | ||||
\(934\) | 1.08644 | + | 5.03543i | 0.0355493 | + | 0.164764i | ||||
\(935\) | 91.1487i | 2.98088i | ||||||||
\(936\) | −5.44943 | − | 7.35745i | −0.178120 | − | 0.240486i | ||||
\(937\) | 43.1736i | 1.41042i | 0.708998 | + | 0.705211i | \(0.249148\pi\) | ||||
−0.708998 | + | 0.705211i | \(0.750852\pi\) | |||||||
\(938\) | 0.333223 | − | 0.0718957i | 0.0108801 | − | 0.00234748i | ||||
\(939\) | 11.2100 | − | 11.2100i | 0.365825 | − | 0.365825i | ||||
\(940\) | −45.2138 | − | 17.0391i | −1.47471 | − | 0.555754i | ||||
\(941\) | −11.9634 | − | 11.9634i | −0.389995 | − | 0.389995i | 0.484691 | − | 0.874686i | \(-0.338932\pi\) |
−0.874686 | + | 0.484691i | \(0.838932\pi\) | |||||||
\(942\) | −2.87941 | + | 4.46376i | −0.0938163 | + | 0.145437i | ||||
\(943\) | −15.7576 | −0.513139 | ||||||||
\(944\) | 1.93042 | + | 29.8388i | 0.0628299 | + | 0.971169i | ||||
\(945\) | −9.21584 | −0.299791 | ||||||||
\(946\) | 20.7174 | − | 32.1168i | 0.673580 | − | 1.04421i | ||||
\(947\) | 24.5656 | + | 24.5656i | 0.798274 | + | 0.798274i | 0.982823 | − | 0.184549i | \(-0.0590824\pi\) |
−0.184549 | + | 0.982823i | \(0.559082\pi\) | |||||||
\(948\) | −7.20678 | + | 19.1234i | −0.234065 | + | 0.621101i | ||||
\(949\) | −23.0506 | + | 23.0506i | −0.748255 | + | 0.748255i | ||||
\(950\) | 6.74390 | − | 1.45505i | 0.218801 | − | 0.0472082i | ||||
\(951\) | 22.0674i | 0.715583i | ||||||||
\(952\) | −11.8629 | − | 1.76738i | −0.384480 | − | 0.0572812i | ||||
\(953\) | − | 16.8701i | − | 0.546476i | −0.961946 | − | 0.273238i | \(-0.911905\pi\) | ||
0.961946 | − | 0.273238i | \(-0.0880947\pi\) | |||||||
\(954\) | −1.08313 | − | 5.02011i | −0.0350677 | − | 0.162532i | ||||
\(955\) | −42.0165 | + | 42.0165i | −1.35962 | + | 1.35962i | ||||
\(956\) | −8.33040 | − | 18.4063i | −0.269424 | − | 0.595301i | ||||
\(957\) | −27.6369 | − | 27.6369i | −0.893373 | − | 0.893373i | ||||
\(958\) | −1.25064 | − | 0.806740i | −0.0404062 | − | 0.0260646i | ||||
\(959\) | −6.53937 | −0.211167 | ||||||||
\(960\) | 33.4238 | + | 10.1853i | 1.07875 | + | 0.328728i | ||||
\(961\) | −0.906376 | −0.0292379 | ||||||||
\(962\) | 27.0166 | + | 17.4274i | 0.871050 | + | 0.561883i | ||||
\(963\) | 8.80603 | + | 8.80603i | 0.283770 | + | 0.283770i | ||||
\(964\) | −9.95843 | − | 22.0034i | −0.320739 | − | 0.708683i | ||||
\(965\) | 4.89923 | − | 4.89923i | 0.157712 | − | 0.157712i | ||||
\(966\) | 0.790389 | + | 3.66331i | 0.0254304 | + | 0.117865i | ||||
\(967\) | − | 28.5983i | − | 0.919660i | −0.888007 | − | 0.459830i | \(-0.847910\pi\) | ||
0.888007 | − | 0.459830i | \(-0.152090\pi\) | |||||||
\(968\) | −4.41444 | − | 0.657679i | −0.141885 | − | 0.0211386i | ||||
\(969\) | 11.3634i | 0.365044i | ||||||||
\(970\) | −20.2458 | + | 4.36820i | −0.650053 | + | 0.140254i | ||||
\(971\) | −32.7772 | + | 32.7772i | −1.05187 | + | 1.05187i | −0.0532921 | + | 0.998579i | \(0.516971\pi\) |
−0.998579 | + | 0.0532921i | \(0.983029\pi\) | |||||||
\(972\) | 7.40546 | − | 19.6507i | 0.237530 | − | 0.630295i | ||||
\(973\) | 5.22421 | + | 5.22421i | 0.167481 | + | 0.167481i | ||||
\(974\) | −13.8965 | + | 21.5428i | −0.445273 | + | 0.690277i | ||||
\(975\) | 20.5307 | 0.657508 | ||||||||
\(976\) | −29.1497 | + | 1.88584i | −0.933058 | + | 0.0603643i | ||||
\(977\) | −15.8114 | −0.505851 | −0.252926 | − | 0.967486i | \(-0.581393\pi\) | ||||
−0.252926 | + | 0.967486i | \(0.581393\pi\) | |||||||
\(978\) | −4.14069 | + | 6.41904i | −0.132405 | + | 0.205258i | ||||
\(979\) | 23.4677 | + | 23.4677i | 0.750032 | + | 0.750032i | ||||
\(980\) | −39.5932 | − | 14.9209i | −1.26476 | − | 0.476632i | ||||
\(981\) | 13.7984 | − | 13.7984i | 0.440551 | − | 0.440551i | ||||
\(982\) | −48.4601 | + | 10.4557i | −1.54642 | + | 0.333654i | ||||
\(983\) | 22.0397i | 0.702958i | 0.936196 | + | 0.351479i | \(0.114321\pi\) | ||||
−0.936196 | + | 0.351479i | \(0.885679\pi\) | |||||||
\(984\) | 10.0248 | + | 13.5348i | 0.319578 | + | 0.431472i | ||||
\(985\) | 13.8823i | 0.442328i | ||||||||
\(986\) | 19.3419 | + | 89.6460i | 0.615970 | + | 2.85491i | ||||
\(987\) | −3.91685 | + | 3.91685i | −0.124675 | + | 0.124675i | ||||
\(988\) | 5.51808 | − | 2.49740i | 0.175554 | − | 0.0794530i | ||||
\(989\) | 19.8138 | + | 19.8138i | 0.630041 | + | 0.630041i | ||||
\(990\) | 14.1594 | + | 9.13370i | 0.450014 | + | 0.290288i | ||||
\(991\) | −13.5824 | −0.431458 | −0.215729 | − | 0.976453i | \(-0.569213\pi\) | ||||
−0.215729 | + | 0.976453i | \(0.569213\pi\) | |||||||
\(992\) | −29.8483 | + | 8.48957i | −0.947686 | + | 0.269544i | ||||
\(993\) | −13.8559 | −0.439705 | ||||||||
\(994\) | −5.23455 | − | 3.37662i | −0.166030 | − | 0.107100i | ||||
\(995\) | 27.7458 | + | 27.7458i | 0.879600 | + | 0.879600i | ||||
\(996\) | 21.4996 | − | 9.73039i | 0.681240 | − | 0.308319i | ||||
\(997\) | 3.18735 | − | 3.18735i | 0.100945 | − | 0.100945i | −0.654831 | − | 0.755775i | \(-0.727260\pi\) |
0.755775 | + | 0.654831i | \(0.227260\pi\) | |||||||
\(998\) | −0.162928 | − | 0.755139i | −0.00515738 | − | 0.0239035i | ||||
\(999\) | 42.4445i | 1.34288i |
(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 | 304.2.k.b.77.8 | ✓ | 68 | |
4.3 | odd | 2 | 1216.2.k.b.913.12 | 68 | |||
16.5 | even | 4 | inner | 304.2.k.b.229.8 | yes | 68 | |
16.11 | odd | 4 | 1216.2.k.b.305.12 | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.k.b.77.8 | ✓ | 68 | 1.1 | even | 1 | trivial | |
304.2.k.b.229.8 | yes | 68 | 16.5 | even | 4 | inner | |
1216.2.k.b.305.12 | 68 | 16.11 | odd | 4 | |||
1216.2.k.b.913.12 | 68 | 4.3 | odd | 2 |