Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [361,2,Mod(28,361)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(361, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("361.28");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 361 = 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 361.e (of order \(9\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.88259951297\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | 12.0.6053445140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 54.2 | ||
Root | \(-1.23949 - 1.04005i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 361.54 |
Dual form | 361.2.e.j.234.2 |
$q$-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 \(\left(\mathbb{Z}/361\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23949 | + | 1.04005i | 0.876449 | + | 0.735428i | 0.965446 | − | 0.260604i | \(-0.0839217\pi\) |
−0.0889969 | + | 0.996032i | \(0.528366\pi\) | |||||||
\(3\) | −0.358931 | + | 0.130640i | −0.207229 | + | 0.0754251i | −0.443549 | − | 0.896250i | \(-0.646281\pi\) |
0.236320 | + | 0.971675i | \(0.424059\pi\) | |||||||
\(4\) | 0.107320 | + | 0.608645i | 0.0536602 | + | 0.304322i | ||||
\(5\) | 0.561937 | − | 3.18690i | 0.251306 | − | 1.42523i | −0.554074 | − | 0.832468i | \(-0.686927\pi\) |
0.805380 | − | 0.592759i | \(-0.201962\pi\) | |||||||
\(6\) | −0.580762 | − | 0.211380i | −0.237095 | − | 0.0862956i | ||||
\(7\) | −1.50000 | − | 2.59808i | −0.566947 | − | 0.981981i | −0.996866 | − | 0.0791130i | \(-0.974791\pi\) |
0.429919 | − | 0.902867i | \(-0.358542\pi\) | |||||||
\(8\) | 1.11803 | − | 1.93649i | 0.395285 | − | 0.684653i | ||||
\(9\) | −2.18637 | + | 1.83458i | −0.728790 | + | 0.611527i | ||||
\(10\) | 4.01106 | − | 3.36568i | 1.26841 | − | 1.06432i | ||||
\(11\) | 0.809017 | − | 1.40126i | 0.243928 | − | 0.422495i | −0.717902 | − | 0.696144i | \(-0.754897\pi\) |
0.961830 | + | 0.273649i | \(0.0882307\pi\) | |||||||
\(12\) | −0.118034 | − | 0.204441i | −0.0340735 | − | 0.0590170i | ||||
\(13\) | 0.939693 | + | 0.342020i | 0.260624 | + | 0.0948593i | 0.469027 | − | 0.883184i | \(-0.344605\pi\) |
−0.208404 | + | 0.978043i | \(0.566827\pi\) | |||||||
\(14\) | 0.842906 | − | 4.78036i | 0.225276 | − | 1.27760i | ||||
\(15\) | 0.214641 | + | 1.21729i | 0.0554201 | + | 0.314303i | ||||
\(16\) | 4.56136 | − | 1.66020i | 1.14034 | − | 0.415050i | ||||
\(17\) | 0.585206 | + | 0.491046i | 0.141933 | + | 0.119096i | 0.710990 | − | 0.703202i | \(-0.248247\pi\) |
−0.569057 | + | 0.822298i | \(0.692692\pi\) | |||||||
\(18\) | −4.61803 | −1.08848 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 0.877809 | + | 0.736569i | 0.191554 | + | 0.160733i | ||||
\(22\) | 2.46015 | − | 0.895420i | 0.524505 | − | 0.190904i | ||||
\(23\) | 0.934569 | + | 5.30020i | 0.194871 | + | 1.10517i | 0.912602 | + | 0.408848i | \(0.134069\pi\) |
−0.717731 | + | 0.696320i | \(0.754819\pi\) | |||||||
\(24\) | −0.148313 | + | 0.841126i | −0.0302743 | + | 0.171694i | ||||
\(25\) | −5.14213 | − | 1.87158i | −1.02843 | − | 0.374316i | ||||
\(26\) | 0.809017 | + | 1.40126i | 0.158661 | + | 0.274809i | ||||
\(27\) | 1.11803 | − | 1.93649i | 0.215166 | − | 0.372678i | ||||
\(28\) | 1.42032 | − | 1.19179i | 0.268416 | − | 0.225228i | ||||
\(29\) | −2.77157 | + | 2.32563i | −0.514669 | + | 0.431858i | −0.862768 | − | 0.505599i | \(-0.831271\pi\) |
0.348100 | + | 0.937457i | \(0.386827\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | 4.42705 | + | 7.66788i | 0.795122 | + | 1.37719i | 0.922762 | + | 0.385371i | \(0.125926\pi\) |
−0.127640 | + | 0.991821i | \(0.540740\pi\) | |||||||
\(32\) | 3.17801 | + | 1.15670i | 0.561798 | + | 0.204478i | ||||
\(33\) | −0.107320 | + | 0.608645i | −0.0186821 | + | 0.105951i | ||||
\(34\) | 0.214641 | + | 1.21729i | 0.0368106 | + | 0.208763i | ||||
\(35\) | −9.12273 | + | 3.32040i | −1.54202 | + | 0.561250i | ||||
\(36\) | −1.35125 | − | 1.13383i | −0.225208 | − | 0.188972i | ||||
\(37\) | 8.85410 | 1.45561 | 0.727803 | − | 0.685787i | \(-0.240542\pi\) | ||||
0.727803 | + | 0.685787i | \(0.240542\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.381966 | −0.0611635 | ||||||||
\(40\) | −5.54315 | − | 4.65125i | −0.876449 | − | 0.735428i | ||||
\(41\) | 2.81908 | − | 1.02606i | 0.440266 | − | 0.160244i | −0.112370 | − | 0.993666i | \(-0.535844\pi\) |
0.552636 | + | 0.833423i | \(0.313622\pi\) | |||||||
\(42\) | 0.321961 | + | 1.82593i | 0.0496797 | + | 0.281748i | ||||
\(43\) | −0.0253349 | + | 0.143682i | −0.00386354 | + | 0.0219112i | −0.986679 | − | 0.162682i | \(-0.947986\pi\) |
0.982815 | + | 0.184593i | \(0.0590967\pi\) | |||||||
\(44\) | 0.939693 | + | 0.342020i | 0.141664 | + | 0.0515615i | ||||
\(45\) | 4.61803 | + | 7.99867i | 0.688416 | + | 1.19237i | ||||
\(46\) | −4.35410 | + | 7.54153i | −0.641977 | + | 1.11194i | ||||
\(47\) | 2.29813 | − | 1.92836i | 0.335217 | − | 0.281281i | −0.459604 | − | 0.888124i | \(-0.652009\pi\) |
0.794822 | + | 0.606843i | \(0.207564\pi\) | |||||||
\(48\) | −1.42032 | + | 1.19179i | −0.205006 | + | 0.172021i | ||||
\(49\) | −1.00000 | + | 1.73205i | −0.142857 | + | 0.247436i | ||||
\(50\) | −4.42705 | − | 7.66788i | −0.626080 | − | 1.08440i | ||||
\(51\) | −0.274199 | − | 0.0998001i | −0.0383955 | − | 0.0139748i | ||||
\(52\) | −0.107320 | + | 0.608645i | −0.0148827 | + | 0.0844038i | ||||
\(53\) | −1.09854 | − | 6.23013i | −0.150896 | − | 0.855774i | −0.962442 | − | 0.271486i | \(-0.912485\pi\) |
0.811546 | − | 0.584288i | \(-0.198626\pi\) | |||||||
\(54\) | 3.39984 | − | 1.23744i | 0.462660 | − | 0.168394i | ||||
\(55\) | −4.01106 | − | 3.36568i | −0.540851 | − | 0.453828i | ||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.85410 | −0.768681 | ||||||||
\(59\) | 0.249913 | + | 0.209702i | 0.0325359 | + | 0.0273008i | 0.658911 | − | 0.752221i | \(-0.271018\pi\) |
−0.626375 | + | 0.779522i | \(0.715462\pi\) | |||||||
\(60\) | −0.717861 | + | 0.261280i | −0.0926755 | + | 0.0337311i | ||||
\(61\) | −1.77747 | − | 10.0806i | −0.227582 | − | 1.29068i | −0.857687 | − | 0.514173i | \(-0.828099\pi\) |
0.630104 | − | 0.776511i | \(-0.283012\pi\) | |||||||
\(62\) | −2.48773 | + | 14.1086i | −0.315941 | + | 1.79179i | ||||
\(63\) | 8.04594 | + | 2.92848i | 1.01369 | + | 0.368954i | ||||
\(64\) | −2.11803 | − | 3.66854i | −0.264754 | − | 0.458568i | ||||
\(65\) | 1.61803 | − | 2.80252i | 0.200692 | − | 0.347609i | ||||
\(66\) | −0.766044 | + | 0.642788i | −0.0942936 | + | 0.0791217i | ||||
\(67\) | −5.36231 | + | 4.49951i | −0.655111 | + | 0.549703i | −0.908617 | − | 0.417631i | \(-0.862861\pi\) |
0.253506 | + | 0.967334i | \(0.418416\pi\) | |||||||
\(68\) | −0.236068 | + | 0.408882i | −0.0286274 | + | 0.0495842i | ||||
\(69\) | −1.02786 | − | 1.78031i | −0.123740 | − | 0.214324i | ||||
\(70\) | −14.7609 | − | 5.37252i | −1.76426 | − | 0.642139i | ||||
\(71\) | −1.29752 | + | 7.35862i | −0.153988 | + | 0.873307i | 0.805718 | + | 0.592299i | \(0.201780\pi\) |
−0.959706 | + | 0.281008i | \(0.909331\pi\) | |||||||
\(72\) | 1.10822 | + | 6.28501i | 0.130605 | + | 0.740695i | ||||
\(73\) | 2.54488 | − | 0.926260i | 0.297856 | − | 0.108411i | −0.188770 | − | 0.982021i | \(-0.560450\pi\) |
0.486625 | + | 0.873611i | \(0.338228\pi\) | |||||||
\(74\) | 10.9745 | + | 9.20873i | 1.27576 | + | 1.07049i | ||||
\(75\) | 2.09017 | 0.241352 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.85410 | −0.553176 | ||||||||
\(78\) | −0.473442 | − | 0.397265i | −0.0536067 | − | 0.0449814i | ||||
\(79\) | −12.6073 | + | 4.58868i | −1.41843 | + | 0.516267i | −0.933593 | − | 0.358336i | \(-0.883344\pi\) |
−0.484839 | + | 0.874603i | \(0.661122\pi\) | |||||||
\(80\) | −2.72770 | − | 15.4696i | −0.304966 | − | 1.72955i | ||||
\(81\) | 1.33852 | − | 7.59110i | 0.148724 | − | 0.843455i | ||||
\(82\) | 4.56136 | + | 1.66020i | 0.503718 | + | 0.183338i | ||||
\(83\) | −4.23607 | − | 7.33708i | −0.464969 | − | 0.805350i | 0.534231 | − | 0.845338i | \(-0.320601\pi\) |
−0.999200 | + | 0.0399887i | \(0.987268\pi\) | |||||||
\(84\) | −0.354102 | + | 0.613323i | −0.0386357 | + | 0.0669190i | ||||
\(85\) | 1.89377 | − | 1.58906i | 0.205408 | − | 0.172358i | ||||
\(86\) | −0.180839 | + | 0.151742i | −0.0195003 | + | 0.0163627i | ||||
\(87\) | 0.690983 | − | 1.19682i | 0.0740812 | − | 0.128312i | ||||
\(88\) | −1.80902 | − | 3.13331i | −0.192842 | − | 0.334012i | ||||
\(89\) | 7.29571 | + | 2.65542i | 0.773344 | + | 0.281474i | 0.698394 | − | 0.715713i | \(-0.253898\pi\) |
0.0749494 | + | 0.997187i | \(0.476120\pi\) | |||||||
\(90\) | −2.59505 | + | 14.7172i | −0.273542 | + | 1.55133i | ||||
\(91\) | −0.520945 | − | 2.95442i | −0.0546098 | − | 0.309708i | ||||
\(92\) | −3.12564 | + | 1.13764i | −0.325871 | + | 0.118607i | ||||
\(93\) | −2.59074 | − | 2.17389i | −0.268647 | − | 0.225421i | ||||
\(94\) | 4.85410 | 0.500662 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.29180 | −0.131843 | ||||||||
\(97\) | 10.6129 | + | 8.90525i | 1.07757 | + | 0.904191i | 0.995717 | − | 0.0924536i | \(-0.0294710\pi\) |
0.0818555 | + | 0.996644i | \(0.473915\pi\) | |||||||
\(98\) | −3.04091 | + | 1.10680i | −0.307178 | + | 0.111804i | ||||
\(99\) | 0.801913 | + | 4.54788i | 0.0805953 | + | 0.457079i | ||||
\(100\) | 0.587272 | − | 3.33059i | 0.0587272 | − | 0.333059i | ||||
\(101\) | 8.62670 | + | 3.13986i | 0.858388 | + | 0.312428i | 0.733456 | − | 0.679737i | \(-0.237906\pi\) |
0.124933 | + | 0.992165i | \(0.460128\pi\) | |||||||
\(102\) | −0.236068 | − | 0.408882i | −0.0233742 | − | 0.0404853i | ||||
\(103\) | −7.16312 | + | 12.4069i | −0.705803 | + | 1.22249i | 0.260598 | + | 0.965447i | \(0.416080\pi\) |
−0.966401 | + | 0.257039i | \(0.917253\pi\) | |||||||
\(104\) | 1.71293 | − | 1.43732i | 0.167966 | − | 0.140941i | ||||
\(105\) | 2.84065 | − | 2.38359i | 0.277219 | − | 0.232614i | ||||
\(106\) | 5.11803 | − | 8.86469i | 0.497107 | − | 0.861015i | ||||
\(107\) | −8.20820 | − | 14.2170i | −0.793517 | − | 1.37441i | −0.923777 | − | 0.382932i | \(-0.874914\pi\) |
0.130260 | − | 0.991480i | \(-0.458419\pi\) | |||||||
\(108\) | 1.29862 | + | 0.472660i | 0.124960 | + | 0.0454818i | ||||
\(109\) | −0.571614 | + | 3.24179i | −0.0547507 | + | 0.310507i | −0.999868 | − | 0.0162234i | \(-0.994836\pi\) |
0.945118 | + | 0.326730i | \(0.105947\pi\) | |||||||
\(110\) | −1.47117 | − | 8.34343i | −0.140271 | − | 0.795514i | ||||
\(111\) | −3.17801 | + | 1.15670i | −0.301643 | + | 0.109789i | ||||
\(112\) | −11.1554 | − | 9.36047i | −1.05408 | − | 0.884481i | ||||
\(113\) | 6.76393 | 0.636297 | 0.318149 | − | 0.948041i | \(-0.396939\pi\) | ||||
0.318149 | + | 0.948041i | \(0.396939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.4164 | 1.62409 | ||||||||
\(116\) | −1.71293 | − | 1.43732i | −0.159041 | − | 0.133452i | ||||
\(117\) | −2.68198 | + | 0.976160i | −0.247949 | + | 0.0902461i | ||||
\(118\) | 0.0916626 | + | 0.519845i | 0.00843823 | + | 0.0478556i | ||||
\(119\) | 0.397966 | − | 2.25698i | 0.0364815 | − | 0.206897i | ||||
\(120\) | 2.59725 | + | 0.945320i | 0.237095 | + | 0.0862956i | ||||
\(121\) | 4.19098 | + | 7.25900i | 0.380998 | + | 0.659909i | ||||
\(122\) | 8.28115 | − | 14.3434i | 0.749740 | − | 1.29859i | ||||
\(123\) | −0.877809 | + | 0.736569i | −0.0791494 | + | 0.0664142i | ||||
\(124\) | −4.19190 | + | 3.51742i | −0.376444 | + | 0.315874i | ||||
\(125\) | −0.763932 | + | 1.32317i | −0.0683282 | + | 0.118348i | ||||
\(126\) | 6.92705 | + | 11.9980i | 0.617111 | + | 1.06887i | ||||
\(127\) | −5.41632 | − | 1.97138i | −0.480621 | − | 0.174932i | 0.0903366 | − | 0.995911i | \(-0.471206\pi\) |
−0.570958 | + | 0.820980i | \(0.693428\pi\) | |||||||
\(128\) | 2.36475 | − | 13.4111i | 0.209016 | − | 1.18539i | ||||
\(129\) | −0.00967708 | − | 0.0548815i | −0.000852019 | − | 0.00483204i | ||||
\(130\) | 4.92029 | − | 1.79084i | 0.431538 | − | 0.157067i | ||||
\(131\) | 11.5597 | + | 9.69977i | 1.00998 | + | 0.847473i | 0.988335 | − | 0.152293i | \(-0.0486656\pi\) |
0.0216438 | + | 0.999766i | \(0.493110\pi\) | |||||||
\(132\) | −0.381966 | −0.0332459 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.3262 | −0.978438 | ||||||||
\(135\) | −5.54315 | − | 4.65125i | −0.477078 | − | 0.400316i | ||||
\(136\) | 1.60519 | − | 0.584240i | 0.137644 | − | 0.0500982i | ||||
\(137\) | 1.29752 | + | 7.35862i | 0.110855 | + | 0.628689i | 0.988719 | + | 0.149780i | \(0.0478565\pi\) |
−0.877864 | + | 0.478909i | \(0.841032\pi\) | |||||||
\(138\) | 0.577595 | − | 3.27570i | 0.0491682 | − | 0.278847i | ||||
\(139\) | −13.9059 | − | 5.06134i | −1.17948 | − | 0.429297i | −0.323465 | − | 0.946240i | \(-0.604848\pi\) |
−0.856020 | + | 0.516943i | \(0.827070\pi\) | |||||||
\(140\) | −3.00000 | − | 5.19615i | −0.253546 | − | 0.439155i | ||||
\(141\) | −0.572949 | + | 0.992377i | −0.0482510 | + | 0.0835732i | ||||
\(142\) | −9.26161 | + | 7.77141i | −0.777217 | + | 0.652162i | ||||
\(143\) | 1.23949 | − | 1.04005i | 0.103651 | − | 0.0869735i | ||||
\(144\) | −6.92705 | + | 11.9980i | −0.577254 | + | 0.999834i | ||||
\(145\) | 5.85410 | + | 10.1396i | 0.486157 | + | 0.842048i | ||||
\(146\) | 4.11770 | + | 1.49872i | 0.340783 | + | 0.124035i | ||||
\(147\) | 0.132655 | − | 0.752326i | 0.0109412 | − | 0.0620508i | ||||
\(148\) | 0.950226 | + | 5.38900i | 0.0781081 | + | 0.442973i | ||||
\(149\) | 1.79465 | − | 0.653200i | 0.147024 | − | 0.0535123i | −0.267460 | − | 0.963569i | \(-0.586184\pi\) |
0.414484 | + | 0.910057i | \(0.363962\pi\) | |||||||
\(150\) | 2.59074 | + | 2.17389i | 0.211533 | + | 0.177497i | ||||
\(151\) | −21.0902 | −1.71629 | −0.858147 | − | 0.513404i | \(-0.828384\pi\) | ||||
−0.858147 | + | 0.513404i | \(0.828384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.18034 | −0.176270 | ||||||||
\(154\) | −6.01659 | − | 5.04852i | −0.484831 | − | 0.406821i | ||||
\(155\) | 26.9245 | − | 9.79972i | 2.16263 | − | 0.787133i | ||||
\(156\) | −0.0409928 | − | 0.232482i | −0.00328205 | − | 0.0186134i | ||||
\(157\) | −3.10033 | + | 17.5829i | −0.247433 | + | 1.40326i | 0.567339 | + | 0.823484i | \(0.307973\pi\) |
−0.814773 | + | 0.579781i | \(0.803138\pi\) | |||||||
\(158\) | −20.3990 | − | 7.42464i | −1.62286 | − | 0.590673i | ||||
\(159\) | 1.20820 | + | 2.09267i | 0.0958168 | + | 0.165960i | ||||
\(160\) | 5.47214 | − | 9.47802i | 0.432610 | − | 0.749303i | ||||
\(161\) | 12.3685 | − | 10.3784i | 0.974772 | − | 0.817931i | ||||
\(162\) | 9.55421 | − | 8.01693i | 0.750650 | − | 0.629870i | ||||
\(163\) | −0.881966 | + | 1.52761i | −0.0690809 | + | 0.119652i | −0.898497 | − | 0.438980i | \(-0.855340\pi\) |
0.829416 | + | 0.558631i | \(0.188673\pi\) | |||||||
\(164\) | 0.927051 | + | 1.60570i | 0.0723905 | + | 0.125384i | ||||
\(165\) | 1.87939 | + | 0.684040i | 0.146310 | + | 0.0532525i | ||||
\(166\) | 2.38040 | − | 13.4999i | 0.184755 | − | 1.04780i | ||||
\(167\) | 3.51396 | + | 19.9286i | 0.271918 | + | 1.54212i | 0.748584 | + | 0.663040i | \(0.230734\pi\) |
−0.476666 | + | 0.879084i | \(0.658155\pi\) | |||||||
\(168\) | 2.40778 | − | 0.876360i | 0.185764 | − | 0.0676127i | ||||
\(169\) | −9.19253 | − | 7.71345i | −0.707118 | − | 0.593342i | ||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0901699 | −0.00687539 | ||||||||
\(173\) | −0.361677 | − | 0.303483i | −0.0274978 | − | 0.0230734i | 0.628935 | − | 0.777458i | \(-0.283491\pi\) |
−0.656433 | + | 0.754384i | \(0.727936\pi\) | |||||||
\(174\) | 2.10122 | − | 0.764780i | 0.159293 | − | 0.0579778i | ||||
\(175\) | 2.85068 | + | 16.1670i | 0.215491 | + | 1.22211i | ||||
\(176\) | 1.36385 | − | 7.73478i | 0.102804 | − | 0.583031i | ||||
\(177\) | −0.117097 | − | 0.0426197i | −0.00880153 | − | 0.00320350i | ||||
\(178\) | 6.28115 | + | 10.8793i | 0.470792 | + | 0.815436i | ||||
\(179\) | −6.11803 | + | 10.5967i | −0.457283 | + | 0.792038i | −0.998816 | − | 0.0486416i | \(-0.984511\pi\) |
0.541533 | + | 0.840680i | \(0.317844\pi\) | |||||||
\(180\) | −4.37274 | + | 3.66916i | −0.325925 | + | 0.273483i | ||||
\(181\) | 9.19253 | − | 7.71345i | 0.683276 | − | 0.573336i | −0.233686 | − | 0.972312i | \(-0.575079\pi\) |
0.916961 | + | 0.398976i | \(0.130634\pi\) | |||||||
\(182\) | 2.42705 | − | 4.20378i | 0.179905 | − | 0.311605i | ||||
\(183\) | 1.95492 | + | 3.38601i | 0.144511 | + | 0.250301i | ||||
\(184\) | 11.3087 | + | 4.11602i | 0.833687 | + | 0.303437i | ||||
\(185\) | 4.97545 | − | 28.2172i | 0.365802 | − | 2.07457i | ||||
\(186\) | −0.950226 | − | 5.38900i | −0.0696740 | − | 0.395141i | ||||
\(187\) | 1.16152 | − | 0.422760i | 0.0849390 | − | 0.0309153i | ||||
\(188\) | 1.42032 | + | 1.19179i | 0.103588 | + | 0.0869205i | ||||
\(189\) | −6.70820 | −0.487950 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.2361 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(192\) | 1.23949 | + | 1.04005i | 0.0894522 | + | 0.0750593i | ||||
\(193\) | −4.75083 | + | 1.72916i | −0.341972 | + | 0.124468i | −0.507297 | − | 0.861772i | \(-0.669355\pi\) |
0.165324 | + | 0.986239i | \(0.447133\pi\) | |||||||
\(194\) | 3.89257 | + | 22.0759i | 0.279470 | + | 1.58495i | ||||
\(195\) | −0.214641 | + | 1.21729i | −0.0153708 | + | 0.0871719i | ||||
\(196\) | −1.16152 | − | 0.422760i | −0.0829660 | − | 0.0301972i | ||||
\(197\) | −1.50000 | − | 2.59808i | −0.106871 | − | 0.185105i | 0.807630 | − | 0.589689i | \(-0.200750\pi\) |
−0.914501 | + | 0.404584i | \(0.867416\pi\) | |||||||
\(198\) | −3.73607 | + | 6.47106i | −0.265511 | + | 0.459878i | ||||
\(199\) | −10.2776 | + | 8.62390i | −0.728557 | + | 0.611332i | −0.929738 | − | 0.368222i | \(-0.879967\pi\) |
0.201181 | + | 0.979554i | \(0.435522\pi\) | |||||||
\(200\) | −9.37337 | + | 7.86519i | −0.662797 | + | 0.556153i | ||||
\(201\) | 1.33688 | − | 2.31555i | 0.0942963 | − | 0.163326i | ||||
\(202\) | 7.42705 | + | 12.8640i | 0.522565 | + | 0.905110i | ||||
\(203\) | 10.1995 | + | 3.71232i | 0.715866 | + | 0.260554i | ||||
\(204\) | 0.0313157 | − | 0.177600i | 0.00219254 | − | 0.0124345i | ||||
\(205\) | −1.68581 | − | 9.56071i | −0.117742 | − | 0.667749i | ||||
\(206\) | −21.7824 | + | 7.92814i | −1.51765 | + | 0.552380i | ||||
\(207\) | −11.7670 | − | 9.87365i | −0.817860 | − | 0.686266i | ||||
\(208\) | 4.85410 | 0.336571 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 6.00000 | 0.414039 | ||||||||
\(211\) | −2.95241 | − | 2.47737i | −0.203253 | − | 0.170549i | 0.535480 | − | 0.844548i | \(-0.320131\pi\) |
−0.738732 | + | 0.673999i | \(0.764575\pi\) | |||||||
\(212\) | 3.67404 | − | 1.33724i | 0.252334 | − | 0.0918421i | ||||
\(213\) | −0.495610 | − | 2.81074i | −0.0339586 | − | 0.192589i | ||||
\(214\) | 4.61250 | − | 26.1588i | 0.315304 | − | 1.78818i | ||||
\(215\) | 0.443663 | + | 0.161480i | 0.0302575 | + | 0.0110128i | ||||
\(216\) | −2.50000 | − | 4.33013i | −0.170103 | − | 0.294628i | ||||
\(217\) | 13.2812 | − | 23.0036i | 0.901583 | − | 1.56159i | ||||
\(218\) | −4.08013 | + | 3.42364i | −0.276342 | + | 0.231878i | ||||
\(219\) | −0.792428 | + | 0.664926i | −0.0535474 | + | 0.0449316i | ||||
\(220\) | 1.61803 | − | 2.80252i | 0.109088 | − | 0.188946i | ||||
\(221\) | 0.381966 | + | 0.661585i | 0.0256938 | + | 0.0445030i | ||||
\(222\) | −5.14213 | − | 1.87158i | −0.345117 | − | 0.125612i | ||||
\(223\) | −2.02343 | + | 11.4754i | −0.135499 | + | 0.768453i | 0.839012 | + | 0.544113i | \(0.183134\pi\) |
−0.974511 | + | 0.224340i | \(0.927977\pi\) | |||||||
\(224\) | −1.76182 | − | 9.99176i | −0.117716 | − | 0.667602i | ||||
\(225\) | 14.6762 | − | 5.34168i | 0.978410 | − | 0.356112i | ||||
\(226\) | 8.38380 | + | 7.03484i | 0.557682 | + | 0.467951i | ||||
\(227\) | 16.4164 | 1.08960 | 0.544798 | − | 0.838568i | \(-0.316606\pi\) | ||||
0.544798 | + | 0.838568i | \(0.316606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6180 | −0.899905 | −0.449953 | − | 0.893052i | \(-0.648559\pi\) | ||||
−0.449953 | + | 0.893052i | \(0.648559\pi\) | |||||||
\(230\) | 21.5874 | + | 18.1140i | 1.42343 | + | 1.19440i | ||||
\(231\) | 1.74229 | − | 0.634140i | 0.114634 | − | 0.0417234i | ||||
\(232\) | 1.40484 | + | 7.96726i | 0.0922325 | + | 0.523076i | ||||
\(233\) | 0.786255 | − | 4.45908i | 0.0515093 | − | 0.292124i | −0.948161 | − | 0.317790i | \(-0.897059\pi\) |
0.999671 | + | 0.0256658i | \(0.00817057\pi\) | |||||||
\(234\) | −4.33953 | − | 1.57946i | −0.283684 | − | 0.103253i | ||||
\(235\) | −4.85410 | − | 8.40755i | −0.316647 | − | 0.548448i | ||||
\(236\) | −0.100813 | + | 0.174613i | −0.00656237 | + | 0.0113664i | ||||
\(237\) | 3.92568 | − | 3.29404i | 0.255000 | − | 0.213971i | ||||
\(238\) | 2.84065 | − | 2.38359i | 0.184132 | − | 0.154505i | ||||
\(239\) | 0.163119 | − | 0.282530i | 0.0105513 | − | 0.0182754i | −0.860702 | − | 0.509110i | \(-0.829975\pi\) |
0.871253 | + | 0.490834i | \(0.163308\pi\) | |||||||
\(240\) | 3.00000 | + | 5.19615i | 0.193649 | + | 0.335410i | ||||
\(241\) | −2.98854 | − | 1.08774i | −0.192509 | − | 0.0700675i | 0.243967 | − | 0.969784i | \(-0.421551\pi\) |
−0.436476 | + | 0.899716i | \(0.643773\pi\) | |||||||
\(242\) | −2.35507 | + | 13.3563i | −0.151390 | + | 0.858573i | ||||
\(243\) | 1.67613 | + | 9.50583i | 0.107524 | + | 0.609799i | ||||
\(244\) | 5.94472 | − | 2.16370i | 0.380572 | − | 0.138517i | ||||
\(245\) | 4.95794 | + | 4.16021i | 0.316751 | + | 0.265786i | ||||
\(246\) | −1.85410 | −0.118213 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 19.7984 | 1.25720 | ||||||||
\(249\) | 2.47897 | + | 2.08010i | 0.157098 | + | 0.131821i | ||||
\(250\) | −2.32305 | + | 0.845520i | −0.146922 | + | 0.0534754i | ||||
\(251\) | −4.40384 | − | 24.9754i | −0.277968 | − | 1.57643i | −0.729374 | − | 0.684115i | \(-0.760189\pi\) |
0.451407 | − | 0.892318i | \(-0.350922\pi\) | |||||||
\(252\) | −0.918911 | + | 5.21140i | −0.0578859 | + | 0.328287i | ||||
\(253\) | 8.18303 | + | 2.97838i | 0.514463 | + | 0.187249i | ||||
\(254\) | −4.66312 | − | 8.07676i | −0.292590 | − | 0.506781i | ||||
\(255\) | −0.472136 | + | 0.817763i | −0.0295663 | + | 0.0512103i | ||||
\(256\) | 10.3893 | − | 8.71768i | 0.649333 | − | 0.544855i | ||||
\(257\) | 15.5972 | − | 13.0876i | 0.972926 | − | 0.816382i | −0.0100814 | − | 0.999949i | \(-0.503209\pi\) |
0.983007 | + | 0.183568i | \(0.0587646\pi\) | |||||||
\(258\) | 0.0450850 | − | 0.0780895i | 0.00280687 | − | 0.00486164i | ||||
\(259\) | −13.2812 | − | 23.0036i | −0.825251 | − | 1.42938i | ||||
\(260\) | 1.87939 | + | 0.684040i | 0.116555 | + | 0.0424224i | ||||
\(261\) | 1.79313 | − | 10.1694i | 0.110992 | − | 0.629468i | ||||
\(262\) | 4.23986 | + | 24.0455i | 0.261940 | + | 1.48553i | ||||
\(263\) | 14.0430 | − | 5.11124i | 0.865930 | − | 0.315173i | 0.129412 | − | 0.991591i | \(-0.458691\pi\) |
0.736518 | + | 0.676418i | \(0.236469\pi\) | |||||||
\(264\) | 1.05865 | + | 0.888311i | 0.0651552 | + | 0.0546717i | ||||
\(265\) | −20.4721 | −1.25759 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.96556 | −0.181489 | ||||||||
\(268\) | −3.31409 | − | 2.78085i | −0.202440 | − | 0.169868i | ||||
\(269\) | −28.4973 | + | 10.3722i | −1.73751 | + | 0.632403i | −0.999119 | − | 0.0419657i | \(-0.986638\pi\) |
−0.738395 | + | 0.674369i | \(0.764416\pi\) | |||||||
\(270\) | −2.03311 | − | 11.5303i | −0.123731 | − | 0.701714i | ||||
\(271\) | 0.198983 | − | 1.12849i | 0.0120874 | − | 0.0685508i | −0.978167 | − | 0.207818i | \(-0.933364\pi\) |
0.990255 | + | 0.139268i | \(0.0444748\pi\) | |||||||
\(272\) | 3.48457 | + | 1.26828i | 0.211283 | + | 0.0769008i | ||||
\(273\) | 0.572949 | + | 0.992377i | 0.0346765 | + | 0.0600614i | ||||
\(274\) | −6.04508 | + | 10.4704i | −0.365197 | + | 0.632540i | ||||
\(275\) | −6.78264 | + | 5.69131i | −0.409008 | + | 0.343199i | ||||
\(276\) | 0.973267 | − | 0.816668i | 0.0585838 | − | 0.0491576i | ||||
\(277\) | −5.70820 | + | 9.88690i | −0.342973 | + | 0.594046i | −0.984983 | − | 0.172650i | \(-0.944767\pi\) |
0.642011 | + | 0.766696i | \(0.278101\pi\) | |||||||
\(278\) | −11.9721 | − | 20.7363i | −0.718041 | − | 1.24368i | ||||
\(279\) | −23.7465 | − | 8.64302i | −1.42167 | − | 0.517444i | ||||
\(280\) | −3.76959 | + | 21.3784i | −0.225276 | + | 1.27760i | ||||
\(281\) | −5.12376 | − | 29.0583i | −0.305658 | − | 1.73347i | −0.620391 | − | 0.784293i | \(-0.713026\pi\) |
0.314733 | − | 0.949180i | \(-0.398085\pi\) | |||||||
\(282\) | −1.74229 | + | 0.634140i | −0.103752 | + | 0.0377625i | ||||
\(283\) | 19.9435 | + | 16.7346i | 1.18552 | + | 0.994770i | 0.999926 | + | 0.0121432i | \(0.00386540\pi\) |
0.185594 | + | 0.982626i | \(0.440579\pi\) | |||||||
\(284\) | −4.61803 | −0.274030 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.61803 | 0.154808 | ||||||||
\(287\) | −6.89440 | − | 5.78509i | −0.406964 | − | 0.341483i | ||||
\(288\) | −9.07036 | + | 3.30134i | −0.534476 | + | 0.194533i | ||||
\(289\) | −2.85068 | − | 16.1670i | −0.167687 | − | 0.951000i | ||||
\(290\) | −3.28964 | + | 18.6565i | −0.193174 | + | 1.09555i | ||||
\(291\) | −4.97266 | − | 1.80990i | −0.291503 | − | 0.106098i | ||||
\(292\) | 0.836881 | + | 1.44952i | 0.0489748 | + | 0.0848268i | ||||
\(293\) | 5.07295 | − | 8.78661i | 0.296365 | − | 0.513319i | −0.678937 | − | 0.734197i | \(-0.737559\pi\) |
0.975301 | + | 0.220878i | \(0.0708922\pi\) | |||||||
\(294\) | 0.946883 | − | 0.794529i | 0.0552233 | − | 0.0463379i | ||||
\(295\) | 0.808735 | − | 0.678609i | 0.0470864 | − | 0.0395101i | ||||
\(296\) | 9.89919 | − | 17.1459i | 0.575379 | − | 0.996585i | ||||
\(297\) | −1.80902 | − | 3.13331i | −0.104970 | − | 0.181813i | ||||
\(298\) | 2.90381 | + | 1.05690i | 0.168213 | + | 0.0612246i | ||||
\(299\) | −0.934569 | + | 5.30020i | −0.0540475 | + | 0.306519i | ||||
\(300\) | 0.224318 | + | 1.27217i | 0.0129510 | + | 0.0734488i | ||||
\(301\) | 0.411298 | − | 0.149700i | 0.0237068 | − | 0.00862858i | ||||
\(302\) | −26.1410 | − | 21.9349i | −1.50424 | − | 1.26221i | ||||
\(303\) | −3.50658 | −0.201448 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.1246 | −1.89671 | ||||||||
\(306\) | −2.70250 | − | 2.26767i | −0.154492 | − | 0.129634i | ||||
\(307\) | 16.2813 | − | 5.92592i | 0.929225 | − | 0.338210i | 0.167323 | − | 0.985902i | \(-0.446488\pi\) |
0.761902 | + | 0.647692i | \(0.224266\pi\) | |||||||
\(308\) | −0.520945 | − | 2.95442i | −0.0296836 | − | 0.168344i | ||||
\(309\) | 0.950226 | − | 5.38900i | 0.0540565 | − | 0.306570i | ||||
\(310\) | 43.5648 | + | 15.8563i | 2.47431 | + | 0.900577i | ||||
\(311\) | −6.32624 | − | 10.9574i | −0.358728 | − | 0.621335i | 0.629021 | − | 0.777389i | \(-0.283456\pi\) |
−0.987749 | + | 0.156053i | \(0.950123\pi\) | |||||||
\(312\) | −0.427051 | + | 0.739674i | −0.0241770 | + | 0.0418758i | ||||
\(313\) | −8.67640 | + | 7.28037i | −0.490419 | + | 0.411511i | −0.854176 | − | 0.519983i | \(-0.825938\pi\) |
0.363757 | + | 0.931494i | \(0.381494\pi\) | |||||||
\(314\) | −22.1299 | + | 18.5692i | −1.24886 | + | 1.04792i | ||||
\(315\) | 13.8541 | − | 23.9960i | 0.780590 | − | 1.35202i | ||||
\(316\) | −4.14590 | − | 7.18091i | −0.233225 | − | 0.403958i | ||||
\(317\) | −16.9145 | − | 6.15636i | −0.950011 | − | 0.345776i | −0.179900 | − | 0.983685i | \(-0.557577\pi\) |
−0.770112 | + | 0.637909i | \(0.779799\pi\) | |||||||
\(318\) | −0.678935 | + | 3.85043i | −0.0380728 | + | 0.215921i | ||||
\(319\) | 1.01655 | + | 5.76517i | 0.0569161 | + | 0.322787i | ||||
\(320\) | −12.8815 | + | 4.68848i | −0.720098 | + | 0.262094i | ||||
\(321\) | 4.80349 | + | 4.03061i | 0.268105 | + | 0.224966i | ||||
\(322\) | 26.1246 | 1.45587 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.76393 | 0.264663 | ||||||||
\(325\) | −4.19190 | − | 3.51742i | −0.232525 | − | 0.195111i | ||||
\(326\) | −2.68198 | + | 0.976160i | −0.148541 | + | 0.0540645i | ||||
\(327\) | −0.218337 | − | 1.23825i | −0.0120741 | − | 0.0684755i | ||||
\(328\) | 1.16487 | − | 6.60629i | 0.0643190 | − | 0.364771i | ||||
\(329\) | −8.45723 | − | 3.07818i | −0.466262 | − | 0.169706i | ||||
\(330\) | 1.61803 | + | 2.80252i | 0.0890698 | + | 0.154273i | ||||
\(331\) | −5.47214 | + | 9.47802i | −0.300776 | + | 0.520959i | −0.976312 | − | 0.216368i | \(-0.930579\pi\) |
0.675536 | + | 0.737327i | \(0.263912\pi\) | |||||||
\(332\) | 4.01106 | − | 3.36568i | 0.220136 | − | 0.184716i | ||||
\(333\) | −19.3583 | + | 16.2436i | −1.06083 | + | 0.890142i | ||||
\(334\) | −16.3713 | + | 28.3560i | −0.895799 | + | 1.55157i | ||||
\(335\) | 11.3262 | + | 19.6176i | 0.618818 | + | 1.07183i | ||||
\(336\) | 5.22686 | + | 1.90242i | 0.285148 | + | 0.103786i | ||||
\(337\) | −2.97366 | + | 16.8645i | −0.161985 | + | 0.918665i | 0.790133 | + | 0.612936i | \(0.210011\pi\) |
−0.952118 | + | 0.305730i | \(0.901100\pi\) | |||||||
\(338\) | −3.37162 | − | 19.1214i | −0.183392 | − | 1.04007i | ||||
\(339\) | −2.42778 | + | 0.883641i | −0.131859 | + | 0.0479928i | ||||
\(340\) | 1.17041 | + | 0.982092i | 0.0634745 | + | 0.0532614i | ||||
\(341\) | 14.3262 | 0.775809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0.249913 | + | 0.209702i | 0.0134744 | + | 0.0113064i | ||||
\(345\) | −6.25128 | + | 2.27528i | −0.336558 | + | 0.122497i | ||||
\(346\) | −0.132655 | − | 0.752326i | −0.00713160 | − | 0.0404453i | ||||
\(347\) | −4.41351 | + | 25.0303i | −0.236930 | + | 1.34370i | 0.601582 | + | 0.798811i | \(0.294537\pi\) |
−0.838511 | + | 0.544884i | \(0.816574\pi\) | |||||||
\(348\) | 0.802593 | + | 0.292120i | 0.0430235 | + | 0.0156593i | ||||
\(349\) | 10.4894 | + | 18.1681i | 0.561482 | + | 0.972516i | 0.997367 | + | 0.0725137i | \(0.0231021\pi\) |
−0.435885 | + | 0.900002i | \(0.643565\pi\) | |||||||
\(350\) | −13.2812 | + | 23.0036i | −0.709907 | + | 1.22960i | ||||
\(351\) | 1.71293 | − | 1.43732i | 0.0914293 | − | 0.0767183i | ||||
\(352\) | 4.19190 | − | 3.51742i | 0.223429 | − | 0.187479i | ||||
\(353\) | −12.2254 | + | 21.1751i | −0.650694 | + | 1.12703i | 0.332261 | + | 0.943187i | \(0.392188\pi\) |
−0.982955 | + | 0.183847i | \(0.941145\pi\) | |||||||
\(354\) | −0.100813 | − | 0.174613i | −0.00535815 | − | 0.00928059i | ||||
\(355\) | 22.7221 | + | 8.27016i | 1.20596 | + | 0.438935i | ||||
\(356\) | −0.833229 | + | 4.72548i | −0.0441610 | + | 0.250450i | ||||
\(357\) | 0.152010 | + | 0.862089i | 0.00804520 | + | 0.0456266i | ||||
\(358\) | −18.6044 | + | 6.77144i | −0.983272 | + | 0.357882i | ||||
\(359\) | 5.38870 | + | 4.52165i | 0.284404 | + | 0.238644i | 0.773818 | − | 0.633408i | \(-0.218345\pi\) |
−0.489413 | + | 0.872052i | \(0.662789\pi\) | |||||||
\(360\) | 20.6525 | 1.08848 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 19.4164 | 1.02050 | ||||||||
\(363\) | −2.45259 | − | 2.05797i | −0.128727 | − | 0.108015i | ||||
\(364\) | 1.74229 | − | 0.634140i | 0.0913206 | − | 0.0332380i | ||||
\(365\) | −1.52184 | − | 8.63079i | −0.0796568 | − | 0.451756i | ||||
\(366\) | −1.09854 | + | 6.23013i | −0.0574216 | + | 0.325654i | ||||
\(367\) | 14.9827 | + | 5.45326i | 0.782091 | + | 0.284658i | 0.702044 | − | 0.712133i | \(-0.252271\pi\) |
0.0800469 | + | 0.996791i | \(0.474493\pi\) | |||||||
\(368\) | 13.0623 | + | 22.6246i | 0.680920 | + | 1.17939i | ||||
\(369\) | −4.28115 | + | 7.41517i | −0.222868 | + | 0.386019i | ||||
\(370\) | 35.5143 | − | 29.8001i | 1.84630 | − | 1.54923i | ||||
\(371\) | −14.5385 | + | 12.1993i | −0.754803 | + | 0.633355i | ||||
\(372\) | 1.04508 | − | 1.81014i | 0.0541851 | − | 0.0938514i | ||||
\(373\) | 2.73607 | + | 4.73901i | 0.141668 | + | 0.245377i | 0.928125 | − | 0.372269i | \(-0.121420\pi\) |
−0.786457 | + | 0.617645i | \(0.788087\pi\) | |||||||
\(374\) | 1.87939 | + | 0.684040i | 0.0971807 | + | 0.0353709i | ||||
\(375\) | 0.101340 | − | 0.574726i | 0.00523316 | − | 0.0296787i | ||||
\(376\) | −1.16487 | − | 6.60629i | −0.0600734 | − | 0.340693i | ||||
\(377\) | −3.39984 | + | 1.23744i | −0.175101 | + | 0.0637314i | ||||
\(378\) | −8.31472 | − | 6.97688i | −0.427663 | − | 0.358852i | ||||
\(379\) | −15.1246 | −0.776899 | −0.388450 | − | 0.921470i | \(-0.626989\pi\) | ||||
−0.388450 | + | 0.921470i | \(0.626989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.20163 | 0.112793 | ||||||||
\(382\) | 17.6454 | + | 14.8063i | 0.902818 | + | 0.757554i | ||||
\(383\) | −0.358931 | + | 0.130640i | −0.0183405 | + | 0.00667540i | −0.351174 | − | 0.936310i | \(-0.614217\pi\) |
0.332834 | + | 0.942986i | \(0.391995\pi\) | |||||||
\(384\) | 0.903253 | + | 5.12260i | 0.0460939 | + | 0.261412i | ||||
\(385\) | −2.72770 | + | 15.4696i | −0.139017 | + | 0.788402i | ||||
\(386\) | −7.68701 | − | 2.79784i | −0.391258 | − | 0.142406i | ||||
\(387\) | −0.208204 | − | 0.360620i | −0.0105836 | − | 0.0183313i | ||||
\(388\) | −4.28115 | + | 7.41517i | −0.217343 | + | 0.376448i | ||||
\(389\) | 7.10162 | − | 5.95897i | 0.360067 | − | 0.302132i | −0.444751 | − | 0.895654i | \(-0.646708\pi\) |
0.804817 | + | 0.593523i | \(0.202263\pi\) | |||||||
\(390\) | −1.53209 | + | 1.28558i | −0.0775803 | + | 0.0650976i | ||||
\(391\) | −2.05573 | + | 3.56063i | −0.103963 | + | 0.180069i | ||||
\(392\) | 2.23607 | + | 3.87298i | 0.112938 | + | 0.195615i | ||||
\(393\) | −5.41632 | − | 1.97138i | −0.273217 | − | 0.0994430i | ||||
\(394\) | 0.842906 | − | 4.78036i | 0.0424650 | − | 0.240831i | ||||
\(395\) | 7.53918 | + | 42.7568i | 0.379337 | + | 2.15133i | ||||
\(396\) | −2.68198 | + | 0.976160i | −0.134774 | + | 0.0490539i | ||||
\(397\) | −8.78817 | − | 7.37415i | −0.441065 | − | 0.370098i | 0.395042 | − | 0.918663i | \(-0.370730\pi\) |
−0.836108 | + | 0.548565i | \(0.815174\pi\) | |||||||
\(398\) | −21.7082 | −1.08813 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.5623 | −1.32812 | ||||||||
\(401\) | −27.4922 | − | 23.0687i | −1.37290 | − | 1.15200i | −0.971758 | − | 0.235979i | \(-0.924170\pi\) |
−0.401138 | − | 0.916018i | \(-0.631385\pi\) | |||||||
\(402\) | 4.06533 | − | 1.47966i | 0.202760 | − | 0.0737988i | ||||
\(403\) | 1.53750 | + | 8.71959i | 0.0765883 | + | 0.434354i | ||||
\(404\) | −0.985238 | + | 5.58756i | −0.0490174 | + | 0.277992i | ||||
\(405\) | −23.4399 | − | 8.53144i | −1.16474 | − | 0.423931i | ||||
\(406\) | 8.78115 | + | 15.2094i | 0.435801 | + | 0.754830i | ||||
\(407\) | 7.16312 | − | 12.4069i | 0.355063 | − | 0.614987i | ||||
\(408\) | −0.499825 | + | 0.419403i | −0.0247450 | + | 0.0207636i | ||||
\(409\) | −6.35188 | + | 5.32986i | −0.314080 | + | 0.263545i | −0.786176 | − | 0.618003i | \(-0.787942\pi\) |
0.472096 | + | 0.881547i | \(0.343498\pi\) | |||||||
\(410\) | 7.85410 | − | 13.6037i | 0.387886 | − | 0.671839i | ||||
\(411\) | −1.42705 | − | 2.47172i | −0.0703912 | − | 0.121921i | ||||
\(412\) | −8.32013 | − | 3.02828i | −0.409904 | − | 0.149193i | ||||
\(413\) | 0.169952 | − | 0.963845i | 0.00836278 | − | 0.0474277i | ||||
\(414\) | −4.31587 | − | 24.4765i | −0.212113 | − | 1.20295i | ||||
\(415\) | −25.7630 | + | 9.37696i | −1.26466 | + | 0.460297i | ||||
\(416\) | 2.59074 | + | 2.17389i | 0.127021 | + | 0.106584i | ||||
\(417\) | 5.65248 | 0.276803 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.94427 | −0.436956 | −0.218478 | − | 0.975842i | \(-0.570109\pi\) | ||||
−0.218478 | + | 0.975842i | \(0.570109\pi\) | |||||||
\(420\) | 1.75562 | + | 1.47314i | 0.0856654 | + | 0.0718818i | ||||
\(421\) | 25.8154 | − | 9.39602i | 1.25816 | − | 0.457934i | 0.375011 | − | 0.927020i | \(-0.377639\pi\) |
0.883152 | + | 0.469086i | \(0.155417\pi\) | |||||||
\(422\) | −1.08288 | − | 6.14133i | −0.0527139 | − | 0.298955i | ||||
\(423\) | −1.48683 | + | 8.43223i | −0.0722921 | + | 0.409989i | ||||
\(424\) | −13.2928 | − | 4.83818i | −0.645555 | − | 0.234963i | ||||
\(425\) | −2.09017 | − | 3.62028i | −0.101388 | − | 0.175609i | ||||
\(426\) | 2.30902 | − | 3.99933i | 0.111872 | − | 0.193768i | ||||
\(427\) | −23.5238 | + | 19.7389i | −1.13840 | + | 0.955230i | ||||
\(428\) | 7.77221 | − | 6.52166i | 0.375684 | − | 0.315236i | ||||
\(429\) | −0.309017 | + | 0.535233i | −0.0149195 | + | 0.0258413i | ||||
\(430\) | 0.381966 | + | 0.661585i | 0.0184200 | + | 0.0319044i | ||||
\(431\) | −25.9848 | − | 9.45770i | −1.25165 | − | 0.455562i | −0.370688 | − | 0.928757i | \(-0.620878\pi\) |
−0.880957 | + | 0.473196i | \(0.843100\pi\) | |||||||
\(432\) | 1.88480 | − | 10.6892i | 0.0906822 | − | 0.514285i | ||||
\(433\) | −0.596949 | − | 3.38547i | −0.0286876 | − | 0.162695i | 0.967098 | − | 0.254402i | \(-0.0818787\pi\) |
−0.995786 | + | 0.0917071i | \(0.970768\pi\) | |||||||
\(434\) | 40.3868 | − | 14.6996i | 1.93863 | − | 0.705603i | ||||
\(435\) | −3.42585 | − | 2.87463i | −0.164257 | − | 0.137828i | ||||
\(436\) | −2.03444 | −0.0974321 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.67376 | −0.0799754 | ||||||||
\(439\) | −26.5026 | − | 22.2384i | −1.26490 | − | 1.06138i | −0.995142 | − | 0.0984516i | \(-0.968611\pi\) |
−0.269760 | − | 0.962927i | \(-0.586945\pi\) | |||||||
\(440\) | −11.0021 | + | 4.00444i | −0.524505 | + | 0.190904i | ||||
\(441\) | −0.991219 | − | 5.62148i | −0.0472009 | − | 0.267690i | ||||
\(442\) | −0.214641 | + | 1.21729i | −0.0102094 | + | 0.0579005i | ||||
\(443\) | 7.12625 | + | 2.59374i | 0.338578 | + | 0.123232i | 0.505713 | − | 0.862702i | \(-0.331229\pi\) |
−0.167135 | + | 0.985934i | \(0.553452\pi\) | |||||||
\(444\) | −1.04508 | − | 1.81014i | −0.0495975 | − | 0.0859055i | ||||
\(445\) | 12.5623 | − | 21.7586i | 0.595510 | − | 1.03145i | ||||
\(446\) | −14.4431 | + | 12.1192i | −0.683900 | + | 0.573860i | ||||
\(447\) | −0.558822 | + | 0.468907i | −0.0264314 | + | 0.0221786i | ||||
\(448\) | −6.35410 | + | 11.0056i | −0.300203 | + | 0.519967i | ||||
\(449\) | −1.44427 | − | 2.50155i | −0.0681594 | − | 0.118056i | 0.829932 | − | 0.557865i | \(-0.188379\pi\) |
−0.898091 | + | 0.439809i | \(0.855046\pi\) | |||||||
\(450\) | 23.7465 | + | 8.64302i | 1.11942 | + | 0.407436i | ||||
\(451\) | 0.842906 | − | 4.78036i | 0.0396909 | − | 0.225098i | ||||
\(452\) | 0.725908 | + | 4.11683i | 0.0341439 | + | 0.193639i | ||||
\(453\) | 7.56991 | − | 2.75522i | 0.355665 | − | 0.129452i | ||||
\(454\) | 20.3479 | + | 17.0739i | 0.954975 | + | 0.801319i | ||||
\(455\) | −9.70820 | −0.455128 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.7082 | 0.921911 | 0.460955 | − | 0.887423i | \(-0.347507\pi\) | ||||
0.460955 | + | 0.887423i | \(0.347507\pi\) | |||||||
\(458\) | −16.8794 | − | 14.1635i | −0.788721 | − | 0.661815i | ||||
\(459\) | 1.60519 | − | 0.584240i | 0.0749237 | − | 0.0272700i | ||||
\(460\) | 1.86914 | + | 10.6004i | 0.0871490 | + | 0.494246i | ||||
\(461\) | 3.63693 | − | 20.6261i | 0.169389 | − | 0.960652i | −0.775034 | − | 0.631920i | \(-0.782267\pi\) |
0.944423 | − | 0.328733i | \(-0.106622\pi\) | |||||||
\(462\) | 2.81908 | + | 1.02606i | 0.131155 | + | 0.0477367i | ||||
\(463\) | −14.1353 | − | 24.4830i | −0.656921 | − | 1.13782i | −0.981409 | − | 0.191931i | \(-0.938525\pi\) |
0.324487 | − | 0.945890i | \(-0.394808\pi\) | |||||||
\(464\) | −8.78115 | + | 15.2094i | −0.407655 | + | 0.706079i | ||||
\(465\) | −8.38380 | + | 7.03484i | −0.388789 | + | 0.326233i | ||||
\(466\) | 5.61222 | − | 4.70921i | 0.259981 | − | 0.218150i | ||||
\(467\) | 7.97214 | − | 13.8081i | 0.368906 | − | 0.638965i | −0.620488 | − | 0.784216i | \(-0.713066\pi\) |
0.989395 | + | 0.145251i | \(0.0463989\pi\) | |||||||
\(468\) | −0.881966 | − | 1.52761i | −0.0407689 | − | 0.0706138i | ||||
\(469\) | 19.7335 | + | 7.18242i | 0.911210 | + | 0.331653i | ||||
\(470\) | 2.72770 | − | 15.4696i | 0.125819 | − | 0.713558i | ||||
\(471\) | −1.18422 | − | 6.71605i | −0.0545660 | − | 0.309459i | ||||
\(472\) | 0.685497 | − | 0.249500i | 0.0315525 | − | 0.0114842i | ||||
\(473\) | 0.180839 | + | 0.151742i | 0.00831497 | + | 0.00697708i | ||||
\(474\) | 8.29180 | 0.380855 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.41641 | 0.0649209 | ||||||||
\(477\) | 13.8315 | + | 11.6060i | 0.633300 | + | 0.531402i | ||||
\(478\) | 0.496030 | − | 0.180540i | 0.0226879 | − | 0.00825771i | ||||
\(479\) | 4.00957 | + | 22.7394i | 0.183202 | + | 1.03899i | 0.928244 | + | 0.371972i | \(0.121318\pi\) |
−0.745042 | + | 0.667017i | \(0.767571\pi\) | |||||||
\(480\) | −0.725908 | + | 4.11683i | −0.0331330 | + | 0.187907i | ||||
\(481\) | 8.32013 | + | 3.02828i | 0.379365 | + | 0.138078i | ||||
\(482\) | −2.57295 | − | 4.45648i | −0.117195 | − | 0.202987i | ||||
\(483\) | −3.08359 | + | 5.34094i | −0.140308 | + | 0.243021i | ||||
\(484\) | −3.96837 | + | 3.32986i | −0.180380 | + | 0.151357i | ||||
\(485\) | 34.3439 | − | 28.8180i | 1.55948 | − | 1.30856i | ||||
\(486\) | −7.80902 | + | 13.5256i | −0.354224 | + | 0.613534i | ||||
\(487\) | −2.09017 | − | 3.62028i | −0.0947146 | − | 0.164051i | 0.814775 | − | 0.579778i | \(-0.196861\pi\) |
−0.909489 | + | 0.415727i | \(0.863527\pi\) | |||||||
\(488\) | −21.5082 | − | 7.82834i | −0.973630 | − | 0.354372i | ||||
\(489\) | 0.116998 | − | 0.663526i | 0.00529081 | − | 0.0300057i | ||||
\(490\) | 1.81847 | + | 10.3130i | 0.0821500 | + | 0.465896i | ||||
\(491\) | 19.9354 | − | 7.25588i | 0.899671 | − | 0.327453i | 0.149550 | − | 0.988754i | \(-0.452218\pi\) |
0.750121 | + | 0.661301i | \(0.229995\pi\) | |||||||
\(492\) | −0.542516 | − | 0.455225i | −0.0244585 | − | 0.0205231i | ||||
\(493\) | −2.76393 | −0.124481 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.9443 | 0.671695 | ||||||||
\(496\) | 32.9236 | + | 27.6262i | 1.47831 | + | 1.24045i | ||||
\(497\) | 21.0645 | − | 7.66686i | 0.944873 | − | 0.343906i | ||||
\(498\) | 0.909234 | + | 5.15652i | 0.0407437 | + | 0.231069i | ||||
\(499\) | 4.36284 | − | 24.7429i | 0.195308 | − | 1.10764i | −0.716672 | − | 0.697410i | \(-0.754336\pi\) |
0.911980 | − | 0.410235i | \(-0.134553\pi\) | |||||||
\(500\) | −0.887325 | − | 0.322960i | −0.0396824 | − | 0.0144432i | ||||
\(501\) | −3.86475 | − | 6.69393i | −0.172664 | − | 0.299063i | ||||
\(502\) | 20.5172 | − | 35.5369i | 0.915728 | − | 1.58609i | ||||
\(503\) | 27.4495 | − | 23.0329i | 1.22391 | − | 1.02699i | 0.225303 | − | 0.974289i | \(-0.427663\pi\) |
0.998611 | − | 0.0526972i | \(-0.0167818\pi\) | |||||||
\(504\) | 14.6666 | − | 12.3067i | 0.653303 | − | 0.548186i | ||||
\(505\) | 14.8541 | − | 25.7281i | 0.660999 | − | 1.14488i | ||||
\(506\) | 7.04508 | + | 12.2024i | 0.313192 | + | 0.542465i | ||||
\(507\) | 4.30717 | + | 1.56768i | 0.191288 | + | 0.0696232i | ||||
\(508\) | 0.618588 | − | 3.50819i | 0.0274454 | − | 0.155651i | ||||
\(509\) | 0.353277 | + | 2.00353i | 0.0156587 | + | 0.0888051i | 0.991636 | − | 0.129069i | \(-0.0411989\pi\) |
−0.975977 | + | 0.217874i | \(0.930088\pi\) | |||||||
\(510\) | −1.43572 | + | 0.522560i | −0.0635749 | + | 0.0231394i | ||||
\(511\) | −6.22381 | − | 5.22240i | −0.275325 | − | 0.231025i | ||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.9443 | 1.45311 | ||||||||
\(515\) | 35.5143 | + | 29.8001i | 1.56495 | + | 1.31315i | ||||
\(516\) | 0.0323648 | − | 0.0117798i | 0.00142478 | − | 0.000518577i | ||||
\(517\) | −0.842906 | − | 4.78036i | −0.0370710 | − | 0.210240i | ||||
\(518\) | 7.46318 | − | 42.3258i | 0.327913 | − | 1.85969i | ||||
\(519\) | 0.169464 | + | 0.0616799i | 0.00743865 | + | 0.00270745i | ||||
\(520\) | −3.61803 | − | 6.26662i | −0.158661 | − | 0.274809i | ||||
\(521\) | −3.13525 | + | 5.43042i | −0.137358 | + | 0.237911i | −0.926496 | − | 0.376305i | \(-0.877194\pi\) |
0.789138 | + | 0.614216i | \(0.210528\pi\) | |||||||
\(522\) | 12.7992 | − | 10.7398i | 0.560207 | − | 0.470069i | ||||
\(523\) | −3.38316 | + | 2.83881i | −0.147935 | + | 0.124133i | −0.713752 | − | 0.700399i | \(-0.753006\pi\) |
0.565816 | + | 0.824531i | \(0.308561\pi\) | |||||||
\(524\) | −4.66312 | + | 8.07676i | −0.203709 | + | 0.352835i | ||||
\(525\) | −3.13525 | − | 5.43042i | −0.136834 | − | 0.237003i | ||||
\(526\) | 22.7221 | + | 8.27016i | 0.990730 | + | 0.360596i | ||||
\(527\) | −1.17454 | + | 6.66117i | −0.0511640 | + | 0.290165i | ||||
\(528\) | 0.520945 | + | 2.95442i | 0.0226712 | + | 0.128575i | ||||
\(529\) | −5.60579 | + | 2.04034i | −0.243730 | + | 0.0887105i | ||||
\(530\) | −25.3749 | − | 21.2921i | −1.10222 | − | 0.924869i | ||||
\(531\) | −0.931116 | −0.0404070 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | −3.67577 | − | 3.08434i | −0.159066 | − | 0.133472i | ||||
\(535\) | −49.9208 | + | 18.1697i | −2.15826 | + | 0.785544i | ||||
\(536\) | 2.71802 | + | 15.4147i | 0.117401 | + | 0.665813i | ||||
\(537\) | 0.811590 | − | 4.60276i | 0.0350227 | − | 0.198624i | ||||
\(538\) | −46.1097 | − | 16.7825i | −1.98793 | − | 0.723547i | ||||
\(539\) | 1.61803 | + | 2.80252i | 0.0696937 | + | 0.120713i | ||||
\(540\) | 2.23607 | − | 3.87298i | 0.0962250 | − | 0.166667i | ||||
\(541\) | −22.8533 | + | 19.1762i | −0.982539 | + | 0.824448i | −0.984470 | − | 0.175550i | \(-0.943829\pi\) |
0.00193193 | + | 0.999998i | \(0.499385\pi\) | |||||||
\(542\) | 1.42032 | − | 1.19179i | 0.0610082 | − | 0.0511919i | ||||
\(543\) | −2.29180 | + | 3.96951i | −0.0983504 | + | 0.170348i | ||||
\(544\) | 1.29180 | + | 2.23746i | 0.0553853 | + | 0.0959302i | ||||
\(545\) | 10.0101 | + | 3.64336i | 0.428784 | + | 0.156064i | ||||
\(546\) | −0.321961 | + | 1.82593i | −0.0137787 | + | 0.0781428i | ||||
\(547\) | −4.67513 | − | 26.5140i | −0.199894 | − | 1.13366i | −0.905275 | − | 0.424827i | \(-0.860335\pi\) |
0.705381 | − | 0.708829i | \(-0.250776\pi\) | |||||||
\(548\) | −4.33953 | + | 1.57946i | −0.185376 | + | 0.0674712i | ||||
\(549\) | 22.3798 | + | 18.7789i | 0.955147 | + | 0.801464i | ||||
\(550\) | −14.3262 | −0.610873 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −4.59675 | −0.195651 | ||||||||
\(553\) | 30.8327 | + | 25.8717i | 1.31114 | + | 1.10018i | ||||
\(554\) | −17.3581 | + | 6.31784i | −0.737476 | + | 0.268419i | ||||
\(555\) | 1.90045 | + | 10.7780i | 0.0806697 | + | 0.457501i | ||||
\(556\) | 1.58817 | − | 9.00695i | 0.0673533 | − | 0.381980i | ||||
\(557\) | 0.770229 | + | 0.280340i | 0.0326356 | + | 0.0118784i | 0.358286 | − | 0.933612i | \(-0.383361\pi\) |
−0.325651 | + | 0.945490i | \(0.605583\pi\) | |||||||
\(558\) | −20.4443 | − | 35.4105i | −0.865475 | − | 1.49905i | ||||
\(559\) | −0.0729490 | + | 0.126351i | −0.00308541 | + | 0.00534409i | ||||
\(560\) | −36.0995 | + | 30.2911i | −1.52548 | + | 1.28003i | ||||
\(561\) | −0.361677 | + | 0.303483i | −0.0152700 | + | 0.0128131i | ||||
\(562\) | 23.8713 | − | 41.3463i | 1.00695 | − | 1.74409i | ||||
\(563\) | 16.4164 | + | 28.4341i | 0.691869 | + | 1.19835i | 0.971225 | + | 0.238165i | \(0.0765458\pi\) |
−0.279356 | + | 0.960188i | \(0.590121\pi\) | |||||||
\(564\) | −0.665494 | − | 0.242220i | −0.0280224 | − | 0.0101993i | ||||
\(565\) | 3.80091 | − | 21.5560i | 0.159905 | − | 0.906868i | ||||
\(566\) | 7.31486 | + | 41.4846i | 0.307467 | + | 1.74373i | ||||
\(567\) | −21.7300 | + | 7.90908i | −0.912575 | + | 0.332150i | ||||
\(568\) | 12.7992 | + | 10.7398i | 0.537044 | + | 0.450633i | ||||
\(569\) | 16.9098 | 0.708897 | 0.354448 | − | 0.935076i | \(-0.384669\pi\) | ||||
0.354448 | + | 0.935076i | \(0.384669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.67376 | 0.279288 | 0.139644 | − | 0.990202i | \(-0.455404\pi\) | ||||
0.139644 | + | 0.990202i | \(0.455404\pi\) | |||||||
\(572\) | 0.766044 | + | 0.642788i | 0.0320299 | + | 0.0268763i | ||||
\(573\) | −5.10976 | + | 1.85980i | −0.213463 | + | 0.0776943i | ||||
\(574\) | −2.52872 | − | 14.3411i | −0.105547 | − | 0.598585i | ||||
\(575\) | 5.11409 | − | 29.0034i | 0.213272 | − | 1.20953i | ||||
\(576\) | 11.3610 | + | 4.13508i | 0.473377 | + | 0.172295i | ||||
\(577\) | 6.06231 | + | 10.5002i | 0.252377 | + | 0.437130i | 0.964180 | − | 0.265250i | \(-0.0854543\pi\) |
−0.711803 | + | 0.702379i | \(0.752121\pi\) | |||||||
\(578\) | 13.2812 | − | 23.0036i | 0.552423 | − | 0.956825i | ||||
\(579\) | 1.47932 | − | 1.24130i | 0.0614785 | − | 0.0515866i | ||||
\(580\) | −5.54315 | + | 4.65125i | −0.230167 | + | 0.193133i | ||||
\(581\) | −12.7082 | + | 22.0113i | −0.527225 | + | 0.913181i | ||||
\(582\) | −4.28115 | − | 7.41517i | −0.177459 | − | 0.307369i | ||||
\(583\) | −9.61876 | − | 3.50094i | −0.398368 | − | 0.144994i | ||||
\(584\) | 1.05157 | − | 5.96373i | 0.0435141 | − | 0.246781i | ||||
\(585\) | 1.60383 | + | 9.09575i | 0.0663101 | + | 0.376063i | ||||
\(586\) | 15.4264 | − | 5.61474i | 0.637258 | − | 0.231943i | ||||
\(587\) | −1.62755 | − | 1.36567i | −0.0671761 | − | 0.0563674i | 0.608581 | − | 0.793491i | \(-0.291739\pi\) |
−0.675757 | + | 0.737124i | \(0.736183\pi\) | |||||||
\(588\) | 0.472136 | 0.0194706 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.70820 | 0.0703256 | ||||||||
\(591\) | 0.877809 | + | 0.736569i | 0.0361082 | + | 0.0302984i | ||||
\(592\) | 40.3868 | − | 14.6996i | 1.65989 | − | 0.604149i | ||||
\(593\) | 0.122978 | + | 0.697445i | 0.00505011 | + | 0.0286406i | 0.987229 | − | 0.159310i | \(-0.0509268\pi\) |
−0.982179 | + | 0.187950i | \(0.939816\pi\) | |||||||
\(594\) | 1.01655 | − | 5.76517i | 0.0417097 | − | 0.236548i | ||||
\(595\) | −6.96914 | − | 2.53656i | −0.285707 | − | 0.103989i | ||||
\(596\) | 0.590170 | + | 1.02220i | 0.0241743 | + | 0.0418711i | ||||
\(597\) | 2.56231 | − | 4.43804i | 0.104868 | − | 0.181637i | ||||
\(598\) | −6.67087 | + | 5.59753i | −0.272792 | + | 0.228900i | ||||
\(599\) | 21.7682 | − | 18.2657i | 0.889426 | − | 0.746317i | −0.0786691 | − | 0.996901i | \(-0.525067\pi\) |
0.968095 | + | 0.250584i | \(0.0806226\pi\) | |||||||
\(600\) | 2.33688 | − | 4.04760i | 0.0954028 | − | 0.165242i | ||||
\(601\) | −10.1459 | − | 17.5732i | −0.413860 | − | 0.716826i | 0.581448 | − | 0.813583i | \(-0.302486\pi\) |
−0.995308 | + | 0.0967572i | \(0.969153\pi\) | |||||||
\(602\) | 0.665494 | + | 0.242220i | 0.0271235 | + | 0.00987215i | ||||
\(603\) | 3.46927 | − | 19.6752i | 0.141279 | − | 0.801236i | ||||
\(604\) | −2.26341 | − | 12.8364i | −0.0920967 | − | 0.522306i | ||||
\(605\) | 25.4888 | − | 9.27716i | 1.03627 | − | 0.377170i | ||||
\(606\) | −4.34635 | − | 3.64702i | −0.176559 | − | 0.148150i | ||||
\(607\) | −6.27051 | −0.254512 | −0.127256 | − | 0.991870i | \(-0.540617\pi\) | ||||
−0.127256 | + | 0.991870i | \(0.540617\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.14590 | −0.168000 | ||||||||
\(610\) | −41.0575 | − | 34.4513i | −1.66237 | − | 1.39489i | ||||
\(611\) | 2.81908 | − | 1.02606i | 0.114048 | − | 0.0415100i | ||||
\(612\) | −0.233995 | − | 1.32705i | −0.00945869 | − | 0.0536429i | ||||
\(613\) | −3.46329 | + | 19.6413i | −0.139881 | + | 0.793304i | 0.831455 | + | 0.555592i | \(0.187508\pi\) |
−0.971336 | + | 0.237711i | \(0.923603\pi\) | |||||||
\(614\) | 26.3438 | + | 9.58834i | 1.06315 | + | 0.386954i | ||||
\(615\) | 1.85410 | + | 3.21140i | 0.0747646 | + | 0.129496i | ||||
\(616\) | −5.42705 | + | 9.39993i | −0.218662 | + | 0.378734i | ||||
\(617\) | 5.87844 | − | 4.93260i | 0.236657 | − | 0.198579i | −0.516744 | − | 0.856140i | \(-0.672856\pi\) |
0.753401 | + | 0.657561i | \(0.228412\pi\) | |||||||
\(618\) | 6.78264 | − | 5.69131i | 0.272838 | − | 0.228938i | ||||
\(619\) | −5.06231 | + | 8.76817i | −0.203471 | + | 0.352423i | −0.949645 | − | 0.313329i | \(-0.898556\pi\) |
0.746173 | + | 0.665752i | \(0.231889\pi\) | |||||||
\(620\) | 8.85410 | + | 15.3358i | 0.355589 | + | 0.615899i | ||||
\(621\) | 11.3087 | + | 4.11602i | 0.453802 | + | 0.165170i | ||||
\(622\) | 3.55495 | − | 20.1611i | 0.142540 | − | 0.808387i | ||||
\(623\) | −4.04458 | − | 22.9379i | −0.162043 | − | 0.918989i | ||||
\(624\) | −1.74229 | + | 0.634140i | −0.0697473 | + | 0.0253859i | ||||
\(625\) | −17.1720 | − | 14.4090i | −0.686879 | − | 0.576360i | ||||
\(626\) | −18.3262 | −0.732464 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0344 | −0.440322 | ||||||||
\(629\) | 5.18147 | + | 4.34777i | 0.206599 | + | 0.173357i | ||||
\(630\) | 42.1291 | − | 15.3337i | 1.67846 | − | 0.610910i | ||||
\(631\) | 5.09843 | + | 28.9146i | 0.202965 | + | 1.15107i | 0.900610 | + | 0.434629i | \(0.143120\pi\) |
−0.697644 | + | 0.716444i | \(0.745768\pi\) | |||||||
\(632\) | −5.20945 | + | 29.5442i | −0.207221 | + | 1.17521i | ||||
\(633\) | 1.38336 | + | 0.503500i | 0.0549834 | + | 0.0200123i | ||||
\(634\) | −14.5623 | − | 25.2227i | −0.578343 | − | 1.00172i | ||||
\(635\) | −9.32624 | + | 16.1535i | −0.370100 | + | 0.641033i | ||||
\(636\) | −1.14403 | + | 0.959953i | −0.0453637 | + | 0.0380646i | ||||
\(637\) | −1.53209 | + | 1.28558i | −0.0607036 | + | 0.0509363i | ||||
\(638\) | −4.73607 | + | 8.20311i | −0.187503 | + | 0.324764i | ||||
\(639\) | −10.6631 | − | 18.4691i | −0.421826 | − | 0.730625i | ||||
\(640\) | −41.4112 | − | 15.0724i | −1.63692 | − | 0.595791i | ||||
\(641\) | −6.86025 | + | 38.9064i | −0.270963 | + | 1.53671i | 0.480535 | + | 0.876975i | \(0.340442\pi\) |
−0.751499 | + | 0.659734i | \(0.770669\pi\) | |||||||
\(642\) | 1.76182 | + | 9.99176i | 0.0695334 | + | 0.394343i | ||||
\(643\) | 22.8268 | − | 8.30828i | 0.900202 | − | 0.327647i | 0.149868 | − | 0.988706i | \(-0.452115\pi\) |
0.750334 | + | 0.661059i | \(0.229893\pi\) | |||||||
\(644\) | 7.64414 | + | 6.41419i | 0.301221 | + | 0.252755i | ||||
\(645\) | −0.180340 | −0.00710088 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.47214 | 0.293760 | 0.146880 | − | 0.989154i | \(-0.453077\pi\) | ||||
0.146880 | + | 0.989154i | \(0.453077\pi\) | |||||||
\(648\) | −13.2036 | − | 11.0791i | −0.518686 | − | 0.435229i | ||||
\(649\) | 0.496030 | − | 0.180540i | 0.0194709 | − | 0.00708682i | ||||
\(650\) | −1.53750 | − | 8.71959i | −0.0603057 | − | 0.342010i | ||||
\(651\) | −1.76182 | + | 9.99176i | −0.0690510 | + | 0.391608i | ||||
\(652\) | −1.02442 | − | 0.372860i | −0.0401196 | − | 0.0146023i | ||||
\(653\) | 11.7812 | + | 20.4056i | 0.461032 | + | 0.798531i | 0.999013 | − | 0.0444262i | \(-0.0141459\pi\) |
−0.537981 | + | 0.842957i | \(0.680813\pi\) | |||||||
\(654\) | 1.01722 | − | 1.76188i | 0.0397765 | − | 0.0688949i | ||||
\(655\) | 37.4081 | − | 31.3891i | 1.46166 | − | 1.22647i | ||||
\(656\) | 11.1554 | − | 9.36047i | 0.435544 | − | 0.365465i | ||||
\(657\) | −3.86475 | + | 6.69393i | −0.150778 | + | 0.261155i | ||||
\(658\) | −7.28115 | − | 12.6113i | −0.283849 | − | 0.491641i | ||||
\(659\) | 24.2225 | + | 8.81628i | 0.943576 | + | 0.343434i | 0.767577 | − | 0.640957i | \(-0.221462\pi\) |
0.175999 | + | 0.984390i | \(0.443684\pi\) | |||||||
\(660\) | −0.214641 | + | 1.21729i | −0.00835489 | + | 0.0473829i | ||||
\(661\) | 0.940549 | + | 5.33412i | 0.0365831 | + | 0.207473i | 0.997620 | − | 0.0689455i | \(-0.0219635\pi\) |
−0.961037 | + | 0.276419i | \(0.910852\pi\) | |||||||
\(662\) | −16.6403 | + | 6.05656i | −0.646742 | + | 0.235395i | ||||
\(663\) | −0.223529 | − | 0.187563i | −0.00868114 | − | 0.00728434i | ||||
\(664\) | −18.9443 | −0.735180 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −40.8885 | −1.58440 | ||||||||
\(667\) | −14.9165 | − | 12.5164i | −0.577570 | − | 0.484639i | ||||
\(668\) | −11.7523 | + | 4.27750i | −0.454712 | + | 0.165502i | ||||
\(669\) | −0.772882 | − | 4.38323i | −0.0298813 | − | 0.169466i | ||||
\(670\) | −6.36464 | + | 36.0956i | −0.245887 | + | 1.39450i | ||||
\(671\) | −15.5635 | − | 5.66464i | −0.600821 | − | 0.218681i | ||||
\(672\) | 1.93769 | + | 3.35618i | 0.0747482 | + | 0.129468i | ||||
\(673\) | −17.0623 | + | 29.5528i | −0.657704 | + | 1.13918i | 0.323505 | + | 0.946226i | \(0.395139\pi\) |
−0.981209 | + | 0.192950i | \(0.938195\pi\) | |||||||
\(674\) | −21.2257 | + | 17.8105i | −0.817584 | + | 0.686034i | ||||
\(675\) | −9.37337 | + | 7.86519i | −0.360781 | + | 0.302731i | ||||
\(676\) | 3.70820 | − | 6.42280i | 0.142623 | − | 0.247031i | ||||
\(677\) | 15.3713 | + | 26.6239i | 0.590768 | + | 1.02324i | 0.994129 | + | 0.108199i | \(0.0345085\pi\) |
−0.403361 | + | 0.915041i | \(0.632158\pi\) | |||||||
\(678\) | −3.92823 | − | 1.42976i | −0.150863 | − | 0.0549096i | ||||
\(679\) | 7.21722 | − | 40.9309i | 0.276971 | − | 1.57078i | ||||
\(680\) | −0.959904 | − | 5.44388i | −0.0368106 | − | 0.208763i | ||||
\(681\) | −5.89235 | + | 2.14464i | −0.225795 | + | 0.0821828i | ||||
\(682\) | 17.7572 | + | 14.9000i | 0.679957 | + | 0.570552i | ||||
\(683\) | 9.65248 | 0.369342 | 0.184671 | − | 0.982800i | \(-0.440878\pi\) | ||||
0.184671 | + | 0.982800i | \(0.440878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.1803 | 0.923883 | ||||||||
\(686\) | −18.5923 | − | 15.6008i | −0.709857 | − | 0.595641i | ||||
\(687\) | 4.88793 | − | 1.77906i | 0.186486 | − | 0.0678754i | ||||
\(688\) | 0.122978 | + | 0.697445i | 0.00468850 | + | 0.0265898i | ||||
\(689\) | 1.09854 | − | 6.23013i | 0.0418510 | − | 0.237349i | ||||
\(690\) | −10.1148 | − | 3.68148i | −0.385063 | − | 0.140152i | ||||
\(691\) | 19.5902 | + | 33.9312i | 0.745245 | + | 1.29080i | 0.950080 | + | 0.312006i | \(0.101001\pi\) |
−0.204835 | + | 0.978797i | \(0.565666\pi\) | |||||||
\(692\) | 0.145898 | − | 0.252703i | 0.00554621 | − | 0.00960632i | ||||
\(693\) | 10.6129 | − | 8.90525i | 0.403149 | − | 0.338282i | ||||
\(694\) | −31.5033 | + | 26.4344i | −1.19585 | + | 1.00344i | ||||
\(695\) | −23.9443 | + | 41.4727i | −0.908258 | + | 1.57315i | ||||
\(696\) | −1.54508 | − | 2.67617i | −0.0585663 | − | 0.101440i | ||||
\(697\) | 2.15358 | + | 0.783840i | 0.0815728 | + | 0.0296901i | ||||
\(698\) | −5.89436 | + | 33.4286i | −0.223105 | + | 1.26529i | ||||
\(699\) | 0.300323 | + | 1.70322i | 0.0113593 | + | 0.0644215i | ||||
\(700\) | −9.53403 | + | 3.47010i | −0.360352 | + | 0.131158i | ||||
\(701\) | −30.3593 | − | 25.4744i | −1.14665 | − | 0.962156i | −0.147017 | − | 0.989134i | \(-0.546967\pi\) |
−0.999636 | + | 0.0269777i | \(0.991412\pi\) | |||||||
\(702\) | 3.61803 | 0.136554 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −6.85410 | −0.258324 | ||||||||
\(705\) | 2.84065 | + | 2.38359i | 0.106985 | + | 0.0897711i | ||||
\(706\) | −37.1764 | + | 13.5311i | −1.39915 | + | 0.509250i | ||||
\(707\) | −4.78245 | − | 27.1226i | −0.179862 | − | 1.02005i | ||||
\(708\) | 0.0133734 | − | 0.0758443i | 0.000502603 | − | 0.00285040i | ||||
\(709\) | −15.5835 | − | 5.67192i | −0.585250 | − | 0.213014i | 0.0323891 | − | 0.999475i | \(-0.489688\pi\) |
−0.617639 | + | 0.786462i | \(0.711911\pi\) | |||||||
\(710\) | 19.5623 | + | 33.8829i | 0.734160 | + | 1.27160i | ||||
\(711\) | 19.1459 | − | 33.1617i | 0.718027 | − | 1.24366i | ||||
\(712\) | 13.2991 | − | 11.1592i | 0.498403 | − | 0.418210i | ||||
\(713\) | −36.5039 | + | 30.6304i | −1.36708 | + | 1.14712i | ||||
\(714\) | −0.708204 | + | 1.22665i | −0.0265039 | + | 0.0459060i | ||||
\(715\) | −2.61803 | − | 4.53457i | −0.0979089 | − | 0.169583i | ||||
\(716\) | −7.10624 | − | 2.58646i | −0.265573 | − | 0.0966606i | ||||
\(717\) | −0.0216386 | + | 0.122719i | −0.000808109 | + | 0.00458301i | ||||
\(718\) | 1.97646 | + | 11.2090i | 0.0737607 | + | 0.418318i | ||||
\(719\) | −44.1979 | + | 16.0867i | −1.64830 | + | 0.599934i | −0.988462 | − | 0.151470i | \(-0.951599\pi\) |
−0.659842 | + | 0.751404i | \(0.729377\pi\) | |||||||
\(720\) | 34.3439 | + | 28.8180i | 1.27992 | + | 1.07398i | ||||
\(721\) | 42.9787 | 1.60061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.21478 | 0.0451782 | ||||||||
\(724\) | 5.68130 | + | 4.76718i | 0.211144 | + | 0.177171i | ||||
\(725\) | 18.6044 | − | 6.77144i | 0.690950 | − | 0.251485i | ||||
\(726\) | −0.899557 | − | 5.10164i | −0.0333857 | − | 0.189340i | ||||
\(727\) | −2.79033 | + | 15.8248i | −0.103488 | + | 0.586908i | 0.888326 | + | 0.459214i | \(0.151869\pi\) |
−0.991814 | + | 0.127694i | \(0.959242\pi\) | |||||||
\(728\) | −6.30365 | − | 2.29434i | −0.233629 | − | 0.0850339i | ||||
\(729\) | 9.71885 | + | 16.8335i | 0.359957 | + | 0.623464i | ||||
\(730\) | 7.09017 | − | 12.2805i | 0.262419 | − | 0.454523i | ||||
\(731\) | −0.0853804 | + | 0.0716427i | −0.00315791 | + | 0.00264980i | ||||
\(732\) | −1.85108 | + | 1.55324i | −0.0684177 | + | 0.0574093i | ||||
\(733\) | 26.4787 | − | 45.8625i | 0.978014 | − | 1.69397i | 0.308405 | − | 0.951255i | \(-0.400205\pi\) |
0.669609 | − | 0.742714i | \(-0.266462\pi\) | |||||||
\(734\) | 12.8992 | + | 22.3420i | 0.476118 | + | 0.824660i | ||||
\(735\) | −2.32305 | − | 0.845520i | −0.0856869 | − | 0.0311875i | ||||
\(736\) | −3.16068 | + | 17.9251i | −0.116504 | + | 0.660728i | ||||
\(737\) | 1.96678 | + | 11.1542i | 0.0724473 | + | 0.410869i | ||||
\(738\) | −13.0186 | + | 4.73838i | −0.479221 | + | 0.174422i | ||||
\(739\) | −19.1511 | − | 16.0697i | −0.704485 | − | 0.591133i | 0.218561 | − | 0.975823i | \(-0.429864\pi\) |
−0.923046 | + | 0.384690i | \(0.874308\pi\) | |||||||
\(740\) | 17.7082 | 0.650967 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.7082 | −1.12733 | ||||||||
\(743\) | −2.57443 | − | 2.16020i | −0.0944467 | − | 0.0792502i | 0.594342 | − | 0.804213i | \(-0.297413\pi\) |
−0.688788 | + | 0.724962i | \(0.741857\pi\) | |||||||
\(744\) | −7.10624 | + | 2.58646i | −0.260528 | + | 0.0948243i | ||||
\(745\) | −1.07320 | − | 6.08645i | −0.0393192 | − | 0.222990i | ||||
\(746\) | −1.53750 | + | 8.71959i | −0.0562918 | + | 0.319247i | ||||
\(747\) | 22.7221 | + | 8.27016i | 0.831358 | + | 0.302589i | ||||
\(748\) | 0.381966 | + | 0.661585i | 0.0139661 | + | 0.0241899i | ||||
\(749\) | −24.6246 | + | 42.6511i | −0.899764 | + | 1.55844i | ||||
\(750\) | 0.723354 | − | 0.606966i | 0.0264132 | − | 0.0221633i | ||||
\(751\) | −13.1345 | + | 11.0212i | −0.479285 | + | 0.402168i | −0.850168 | − | 0.526512i | \(-0.823500\pi\) |
0.370883 | + | 0.928680i | \(0.379055\pi\) | |||||||
\(752\) | 7.28115 | − | 12.6113i | 0.265516 | − | 0.459888i | ||||
\(753\) | 4.84346 | + | 8.38912i | 0.176505 | + | 0.305716i | ||||
\(754\) | −5.50106 | − | 2.00222i | −0.200337 | − | 0.0729166i | ||||
\(755\) | −11.8514 | + | 67.2124i | −0.431315 | + | 2.44611i | ||||
\(756\) | −0.719928 | − | 4.08291i | −0.0261835 | − | 0.148494i | ||||
\(757\) | −25.1299 | + | 9.14652i | −0.913361 | + | 0.332436i | −0.755594 | − | 0.655040i | \(-0.772652\pi\) |
−0.157767 | + | 0.987476i | \(0.550429\pi\) | |||||||
\(758\) | −18.7467 | − | 15.7304i | −0.680912 | − | 0.571353i | ||||
\(759\) | −3.32624 | −0.120735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.88854 | 0.177210 | 0.0886048 | − | 0.996067i | \(-0.471759\pi\) | ||||
0.0886048 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(762\) | 2.72888 | + | 2.28981i | 0.0988571 | + | 0.0829509i | ||||
\(763\) | 9.27983 | − | 3.37758i | 0.335952 | − | 0.122277i | ||||
\(764\) | 1.52782 | + | 8.66471i | 0.0552746 | + | 0.313478i | ||||
\(765\) | −1.22521 | + | 6.94854i | −0.0442977 | + | 0.251225i | ||||
\(766\) | −0.580762 | − | 0.211380i | −0.0209838 | − | 0.00763747i | ||||
\(767\) | 0.163119 | + | 0.282530i | 0.00588988 | + | 0.0102016i | ||||
\(768\) | −2.59017 | + | 4.48631i | −0.0934647 | + | 0.161886i | ||||
\(769\) | 28.0611 | − | 23.5461i | 1.01191 | − | 0.849093i | 0.0233204 | − | 0.999728i | \(-0.492576\pi\) |
0.988589 | + | 0.150635i | \(0.0481318\pi\) | |||||||
\(770\) | −19.4701 | + | 16.3374i | −0.701654 | + | 0.588757i | ||||
\(771\) | −3.88854 | + | 6.73516i | −0.140042 | + | 0.242561i | ||||
\(772\) | −1.56231 | − | 2.70599i | −0.0562286 | − | 0.0973908i | ||||
\(773\) | 33.7566 | + | 12.2864i | 1.21414 | + | 0.441911i | 0.868138 | − | 0.496323i | \(-0.165317\pi\) |
0.346002 | + | 0.938234i | \(0.387539\pi\) | |||||||
\(774\) | 0.116998 | − | 0.663526i | 0.00420539 | − | 0.0238500i | ||||
\(775\) | −8.41340 | − | 47.7148i | −0.302218 | − | 1.71397i | ||||
\(776\) | 29.1105 | − | 10.5953i | 1.04500 | − | 0.380351i | ||||
\(777\) | 7.77221 | + | 6.52166i | 0.278826 | + | 0.233963i | ||||
\(778\) | 15.0000 | 0.537776 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.763932 | −0.0273532 | ||||||||
\(781\) | 9.26161 | + | 7.77141i | 0.331406 | + | 0.278083i | ||||
\(782\) | −6.25128 | + | 2.27528i | −0.223545 | + | 0.0813639i | ||||
\(783\) | 1.40484 | + | 7.96726i | 0.0502050 | + | 0.284727i | ||||
\(784\) | −1.68581 | + | 9.56071i | −0.0602076 | + | 0.341454i | ||||
\(785\) | 54.2927 | + | 19.7609i | 1.93779 | + | 0.705298i | ||||
\(786\) | −4.66312 | − | 8.07676i | −0.166328 | − | 0.288088i | ||||
\(787\) | −19.0000 | + | 32.9090i | −0.677277 | + | 1.17308i | 0.298521 | + | 0.954403i | \(0.403507\pi\) |
−0.975798 | + | 0.218675i | \(0.929827\pi\) | |||||||
\(788\) | 1.42032 | − | 1.19179i | 0.0505970 | − | 0.0424559i | ||||
\(789\) | −4.37274 | + | 3.66916i | −0.155674 | + | 0.130626i | ||||
\(790\) | −35.1246 | + | 60.8376i | −1.24968 | + | 2.16451i | ||||
\(791\) | −10.1459 | − | 17.5732i | −0.360747 | − | 0.624831i | ||||
\(792\) | 9.70349 | + | 3.53178i | 0.344798 | + | 0.125496i | ||||
\(793\) | 1.77747 | − | 10.0806i | 0.0631200 | − | 0.357971i | ||||
\(794\) | −3.22331 | − | 18.2803i | −0.114391 | − | 0.648744i | ||||
\(795\) | 7.34808 | − | 2.67448i | 0.260609 | − | 0.0948541i | ||||
\(796\) | −6.35188 | − | 5.32986i | −0.225137 | − | 0.188912i | ||||
\(797\) | −20.2918 | −0.718772 | −0.359386 | − | 0.933189i | \(-0.617014\pi\) | ||||
−0.359386 | + | 0.933189i | \(0.617014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.29180 | 0.0810779 | ||||||||
\(800\) | −14.1769 | − | 11.8958i | −0.501228 | − | 0.420580i | ||||
\(801\) | −20.8227 | + | 7.57884i | −0.735734 | + | 0.267785i | ||||
\(802\) | −10.0836 | − | 57.1867i | −0.356063 | − | 2.01933i | ||||
\(803\) | 0.760920 | − | 4.31539i | 0.0268523 | − | 0.152287i | ||||
\(804\) | 1.55282 | + | 0.565180i | 0.0547637 | + | 0.0199324i | ||||
\(805\) | −26.1246 | − | 45.2492i | −0.920772 | − | 1.59482i | ||||
\(806\) | −7.16312 | + | 12.4069i | −0.252310 | + | 0.437014i | ||||
\(807\) | 8.87355 | − | 7.44579i | 0.312364 | − | 0.262104i | ||||
\(808\) | 15.7253 | − | 13.1951i | 0.553213 | − | 0.464200i | ||||
\(809\) | 12.3992 | − | 21.4760i | 0.435932 | − | 0.755057i | −0.561439 | − | 0.827518i | \(-0.689752\pi\) |
0.997371 | + | 0.0724614i | \(0.0230854\pi\) | |||||||
\(810\) | −20.1803 | − | 34.9534i | −0.709065 | − | 1.22814i | ||||
\(811\) | −21.5929 | − | 7.85918i | −0.758230 | − | 0.275973i | −0.0661655 | − | 0.997809i | \(-0.521077\pi\) |
−0.692065 | + | 0.721835i | \(0.743299\pi\) | |||||||
\(812\) | −1.16487 | + | 6.60629i | −0.0408788 | + | 0.231835i | ||||
\(813\) | 0.0760048 | + | 0.431045i | 0.00266560 | + | 0.0151174i | ||||
\(814\) | 21.7824 | − | 7.92814i | 0.763473 | − | 0.277881i | ||||
\(815\) | 4.37274 | + | 3.66916i | 0.153170 | + | 0.128525i | ||||
\(816\) | −1.41641 | −0.0495842 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −13.4164 | −0.469094 | ||||||||
\(819\) | 6.55911 | + | 5.50374i | 0.229194 | + | 0.192316i | ||||
\(820\) | 5.63816 | − | 2.05212i | 0.196893 | − | 0.0716632i | ||||
\(821\) | 9.03797 | + | 51.2569i | 0.315427 | + | 1.78888i | 0.569813 | + | 0.821774i | \(0.307016\pi\) |
−0.254386 | + | 0.967103i | \(0.581873\pi\) | |||||||
\(822\) | 0.801913 | − | 4.54788i | 0.0279699 | − | 0.158625i | ||||
\(823\) | 24.0531 | + | 8.75460i | 0.838437 | + | 0.305166i | 0.725317 | − | 0.688415i | \(-0.241693\pi\) |
0.113120 | + | 0.993581i | \(0.463915\pi\) | |||||||
\(824\) | 16.0172 | + | 27.7426i | 0.557986 | + | 0.966461i | ||||
\(825\) | 1.69098 | − | 2.92887i | 0.0588725 | − | 0.101970i | ||||
\(826\) | 1.21310 | − | 1.01791i | 0.0422092 | − | 0.0354177i | ||||
\(827\) | 24.9706 | − | 20.9528i | 0.868311 | − | 0.728600i | −0.0954305 | − | 0.995436i | \(-0.530423\pi\) |
0.963742 | + | 0.266836i | \(0.0859783\pi\) | |||||||
\(828\) | 4.74671 | − | 8.22154i | 0.164960 | − | 0.285718i | ||||
\(829\) | −2.33688 | − | 4.04760i | −0.0811632 | − | 0.140579i | 0.822587 | − | 0.568640i | \(-0.192530\pi\) |
−0.903750 | + | 0.428061i | \(0.859197\pi\) | |||||||
\(830\) | −41.6854 | − | 15.1722i | −1.44692 | − | 0.526636i | ||||
\(831\) | 0.757224 | − | 4.29443i | 0.0262678 | − | 0.148972i | ||||
\(832\) | −0.735585 | − | 4.17171i | −0.0255018 | − | 0.144628i | ||||
\(833\) | −1.43572 | + | 0.522560i | −0.0497448 | + | 0.0181056i | ||||
\(834\) | 7.00616 | + | 5.87887i | 0.242604 | + | 0.203569i | ||||
\(835\) | 65.4853 | 2.26621 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7984 | 0.684332 | ||||||||
\(838\) | −11.0863 | − | 9.30251i | −0.382970 | − | 0.321350i | ||||
\(839\) | −14.2849 | + | 5.19926i | −0.493168 | + | 0.179498i | −0.576619 | − | 0.817013i | \(-0.695628\pi\) |
0.0834506 | + | 0.996512i | \(0.473406\pi\) | |||||||
\(840\) | −1.43986 | − | 8.16583i | −0.0496797 | − | 0.281748i | ||||
\(841\) | −2.76271 | + | 15.6681i | −0.0952660 | + | 0.540280i | ||||
\(842\) | 41.7701 | + | 15.2031i | 1.43949 | + | 0.523933i | ||||
\(843\) | 5.63525 | + | 9.76055i | 0.194088 | + | 0.336171i | ||||
\(844\) | 1.19098 | − | 2.06284i | 0.0409953 | − | 0.0710060i | ||||
\(845\) | −29.7477 | + | 24.9613i | −1.02335 | + | 0.858693i | ||||
\(846\) | −10.6129 | + | 8.90525i | −0.364878 | + | 0.306169i | ||||
\(847\) | 12.5729 | − | 21.7770i | 0.432012 | − | 0.748266i | ||||
\(848\) | −15.3541 | − | 26.5941i | −0.527262 | − | 0.913245i | ||||
\(849\) | −9.34456 | − | 3.40114i | −0.320704 | − | 0.116727i | ||||
\(850\) | 1.17454 | − | 6.66117i | 0.0402865 | − | 0.228476i | ||||
\(851\) | 8.27477 | + | 46.9285i | 0.283655 | + | 1.60869i | ||||
\(852\) | 1.65755 | − | 0.603300i | 0.0567869 | − | 0.0206687i | ||||
\(853\) | 23.5238 | + | 19.7389i | 0.805441 | + | 0.675845i | 0.949515 | − | 0.313721i | \(-0.101576\pi\) |
−0.144074 | + | 0.989567i | \(0.546020\pi\) | |||||||
\(854\) | −49.6869 | −1.70025 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.7082 | −1.25466 | ||||||||
\(857\) | −8.13389 | − | 6.82514i | −0.277848 | − | 0.233142i | 0.493205 | − | 0.869913i | \(-0.335825\pi\) |
−0.771053 | + | 0.636771i | \(0.780270\pi\) | |||||||
\(858\) | −0.939693 | + | 0.342020i | −0.0320806 | + | 0.0116764i | ||||
\(859\) | −8.42906 | − | 47.8036i | −0.287596 | − | 1.63104i | −0.695863 | − | 0.718174i | \(-0.744978\pi\) |
0.408267 | − | 0.912862i | \(-0.366133\pi\) | |||||||
\(860\) | −0.0506699 | + | 0.287363i | −0.00172783 | + | 0.00979900i | ||||
\(861\) | 3.23038 | + | 1.17576i | 0.110091 | + | 0.0400698i | ||||
\(862\) | −22.3713 | − | 38.7483i | −0.761970 | − | 1.31977i | ||||
\(863\) | 13.5279 | − | 23.4309i | 0.460494 | − | 0.797599i | −0.538492 | − | 0.842631i | \(-0.681006\pi\) |
0.998986 | + | 0.0450321i | \(0.0143390\pi\) | |||||||
\(864\) | 5.79306 | − | 4.86096i | 0.197084 | − | 0.165373i | ||||
\(865\) | −1.17041 | + | 0.982092i | −0.0397952 | + | 0.0333921i | ||||
\(866\) | 2.78115 | − | 4.81710i | 0.0945074 | − | 0.163692i | ||||
\(867\) | 3.13525 | + | 5.43042i | 0.106479 | + | 0.184427i | ||||
\(868\) | 15.4264 | + | 5.61474i | 0.523605 | + | 0.190577i | ||||
\(869\) | −3.76959 | + | 21.3784i | −0.127875 | + | 0.725213i | ||||
\(870\) | −1.25653 | − | 7.12614i | −0.0426004 | − | 0.241599i | ||||
\(871\) | −6.57785 | + | 2.39414i | −0.222882 | + | 0.0811224i | ||||
\(872\) | 5.63861 | + | 4.73135i | 0.190947 | + | 0.160224i | ||||
\(873\) | −39.5410 | −1.33826 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.58359 | 0.154954 | ||||||||
\(876\) | −0.489748 | − | 0.410947i | −0.0165470 | − | 0.0138846i | ||||
\(877\) | −11.1068 | + | 4.04256i | −0.375052 | + | 0.136508i | −0.522666 | − | 0.852537i | \(-0.675063\pi\) |
0.147615 | + | 0.989045i | \(0.452840\pi\) | |||||||
\(878\) | −9.72060 | − | 55.1283i | −0.328054 | − | 1.86049i | ||||
\(879\) | −0.672954 | + | 3.81651i | −0.0226982 | + | 0.128728i | ||||
\(880\) | −23.8836 | − | 8.69292i | −0.805116 | − | 0.293038i | ||||
\(881\) | −16.2254 | − | 28.1033i | −0.546648 | − | 0.946823i | −0.998501 | − | 0.0547303i | \(-0.982570\pi\) |
0.451853 | − | 0.892093i | \(-0.350763\pi\) | |||||||
\(882\) | 4.61803 | − | 7.99867i | 0.155497 | − | 0.269329i | ||||
\(883\) | −39.0093 | + | 32.7327i | −1.31277 | + | 1.10154i | −0.324981 | + | 0.945720i | \(0.605358\pi\) |
−0.987785 | + | 0.155821i | \(0.950198\pi\) | |||||||
\(884\) | −0.361677 | + | 0.303483i | −0.0121645 | + | 0.0102072i | ||||
\(885\) | −0.201626 | + | 0.349227i | −0.00677759 | + | 0.0117391i | ||||
\(886\) | 6.13525 | + | 10.6266i | 0.206118 | + | 0.357007i | ||||
\(887\) | −25.6983 | − | 9.35340i | −0.862863 | − | 0.314057i | −0.127590 | − | 0.991827i | \(-0.540724\pi\) |
−0.735274 | + | 0.677770i | \(0.762946\pi\) | |||||||
\(888\) | −1.31318 | + | 7.44742i | −0.0440675 | + | 0.249919i | ||||
\(889\) | 3.00269 | + | 17.0291i | 0.100707 | + | 0.571138i | ||||
\(890\) | 38.2008 | − | 13.9040i | 1.28049 | − | 0.466062i | ||||
\(891\) | −9.55421 | − | 8.01693i | −0.320078 | − | 0.268577i | ||||
\(892\) | −7.20163 | −0.241128 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.18034 | −0.0394765 | ||||||||
\(895\) | 30.3329 | + | 25.4523i | 1.01392 | + | 0.850777i | ||||
\(896\) | −38.3903 | + | 13.9729i | −1.28253 | + | 0.466803i | ||||
\(897\) | −0.356973 | − | 2.02450i | −0.0119190 | − | 0.0675960i | ||||
\(898\) | 0.811590 | − | 4.60276i | 0.0270831 | − | 0.153596i | ||||
\(899\) | −30.1025 | − | 10.9564i | −1.00398 | − | 0.365417i | ||||
\(900\) | 4.82624 | + | 8.35929i | 0.160875 | + | 0.278643i | ||||
\(901\) | 2.41641 | − | 4.18534i | 0.0805022 | − | 0.139434i | ||||
\(902\) | 6.01659 | − | 5.04852i | 0.200331 | − | 0.168097i | ||||
\(903\) | −0.128071 | + | 0.107464i | −0.00426192 | + | 0.00357618i | ||||
\(904\) | 7.56231 | − | 13.0983i | 0.251519 | − | 0.435643i | ||||
\(905\) | −19.4164 | − | 33.6302i | −0.645423 | − | 1.11791i | ||||
\(906\) | 12.2484 | + | 4.45804i | 0.406925 | + | 0.148109i | ||||
\(907\) | −4.59684 | + | 26.0700i | −0.152636 | + | 0.865639i | 0.808280 | + | 0.588798i | \(0.200399\pi\) |
−0.960916 | + | 0.276841i | \(0.910712\pi\) | |||||||
\(908\) | 1.76182 | + | 9.99176i | 0.0584679 | + | 0.331588i | ||||
\(909\) | −24.6215 | + | 8.96148i | −0.816643 | + | 0.297234i | ||||
\(910\) | −12.0332 | − | 10.0970i | −0.398896 | − | 0.334714i | ||||
\(911\) | 3.38197 | 0.112050 | 0.0560248 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560248 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7082 | −0.453675 | ||||||||
\(914\) | 24.4280 | + | 20.4976i | 0.808008 | + | 0.677999i | ||||
\(915\) | 11.8894 | − | 4.32740i | 0.393053 | − | 0.143059i | ||||
\(916\) | −1.46149 | − | 8.28854i | −0.0482891 | − | 0.273861i | ||||
\(917\) | 7.86114 | − | 44.5827i | 0.259598 | − | 1.47225i | ||||
\(918\) | 2.59725 | + | 0.945320i | 0.0857219 | + | 0.0312002i | ||||
\(919\) | −11.6459 | − | 20.1713i | −0.384163 | − | 0.665389i | 0.607490 | − | 0.794327i | \(-0.292177\pi\) |
−0.991653 | + | 0.128938i | \(0.958843\pi\) | |||||||
\(920\) | 19.4721 | − | 33.7267i | 0.641977 | − | 1.11194i | ||||
\(921\) | −5.06971 | + | 4.25399i | −0.167053 | + | 0.140174i | ||||
\(922\) | 25.9601 | − | 21.7831i | 0.854951 | − | 0.717389i | ||||
\(923\) | −3.73607 | + | 6.47106i | −0.122974 | + | 0.212998i | ||||
\(924\) | 0.572949 | + | 0.992377i | 0.0188486 | + | 0.0326468i | ||||
\(925\) | −45.5289 | − | 16.5712i | −1.49698 | − | 0.544857i | ||||
\(926\) | 7.94313 | − | 45.0477i | 0.261027 | − | 1.48036i | ||||
\(927\) | −7.10022 | − | 40.2674i | −0.233202 | − | 1.32255i | ||||
\(928\) | −11.4981 | + | 4.18498i | −0.377445 | + | 0.137379i | ||||
\(929\) | 12.5493 | + | 10.5301i | 0.411730 | + | 0.345482i | 0.825007 | − | 0.565123i | \(-0.191171\pi\) |
−0.413277 | + | 0.910605i | \(0.635616\pi\) | |||||||
\(930\) | −17.7082 | −0.580675 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.79837 | 0.0916638 | ||||||||
\(933\) | 3.70215 | + | 3.10647i | 0.121203 | + | 0.101701i | ||||
\(934\) | 24.2425 | − | 8.82356i | 0.793240 | − | 0.288716i | ||||
\(935\) | −0.694593 | − | 3.93923i | −0.0227156 | − | 0.128827i | ||||
\(936\) | −1.10822 | + | 6.28501i | −0.0362232 | + | 0.205432i | ||||
\(937\) | −38.1161 | − | 13.8731i | −1.24520 | − | 0.453215i | −0.366422 | − | 0.930449i | \(-0.619417\pi\) |
−0.878777 | + | 0.477233i | \(0.841640\pi\) | |||||||
\(938\) | 16.9894 | + | 29.4264i | 0.554722 | + | 0.960807i | ||||
\(939\) | 2.16312 | − | 3.74663i | 0.0705907 | − | 0.122267i | ||||
\(940\) | 4.59627 | − | 3.85673i | 0.149914 | − | 0.125793i | ||||
\(941\) | −8.18665 | + | 6.86942i | −0.266877 | + | 0.223937i | −0.766399 | − | 0.642365i | \(-0.777953\pi\) |
0.499522 | + | 0.866301i | \(0.333509\pi\) | |||||||
\(942\) | 5.51722 | − | 9.55611i | 0.179761 | − | 0.311355i | ||||
\(943\) | 8.07295 | + | 13.9828i | 0.262891 | + | 0.455341i | ||||
\(944\) | 1.48809 | + | 0.541620i | 0.0484332 | + | 0.0176282i | ||||
\(945\) | −3.76959 | + | 21.3784i | −0.122625 | + | 0.695440i | ||||
\(946\) | 0.0663277 | + | 0.376163i | 0.00215650 | + | 0.0122301i | ||||
\(947\) | 30.6833 | − | 11.1678i | 0.997073 | − | 0.362905i | 0.208618 | − | 0.977997i | \(-0.433104\pi\) |
0.788455 | + | 0.615092i | \(0.210881\pi\) | |||||||
\(948\) | 2.42620 | + | 2.03583i | 0.0787994 | + | 0.0661206i | ||||
\(949\) | 2.70820 | 0.0879120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.87539 | 0.222950 | ||||||||
\(952\) | −3.92568 | − | 3.29404i | −0.127232 | − | 0.106760i | ||||
\(953\) | −16.2490 | + | 5.91414i | −0.526356 | + | 0.191578i | −0.591510 | − | 0.806297i | \(-0.701468\pi\) |
0.0651546 | + | 0.997875i | \(0.479246\pi\) | |||||||
\(954\) | 5.07309 | + | 28.7709i | 0.164247 | + | 0.931494i | ||||
\(955\) | 7.99978 | − | 45.3690i | 0.258867 | − | 1.46811i | ||||
\(956\) | 0.189467 | + | 0.0689602i | 0.00612779 | + | 0.00223033i | ||||
\(957\) | −1.11803 | − | 1.93649i | −0.0361409 | − | 0.0625979i | ||||
\(958\) | −18.6803 | + | 32.3553i | −0.603534 | + | 1.04535i | ||||
\(959\) | 17.1720 | − | 14.4090i | 0.554512 | − | 0.465291i | ||||
\(960\) | 4.01106 | − | 3.36568i | 0.129456 | − | 0.108627i | ||||
\(961\) | −23.6976 | + | 41.0454i | −0.764437 | + | 1.32404i | ||||
\(962\) | 7.16312 | + | 12.4069i | 0.230948 | + | 0.400014i | ||||
\(963\) | 44.0285 | + | 16.0250i | 1.41880 | + | 0.516400i | ||||
\(964\) | 0.341316 | − | 1.93570i | 0.0109930 | − | 0.0623446i | ||||
\(965\) | 2.84100 | + | 16.1121i | 0.0914551 | + | 0.518668i | ||||
\(966\) | −9.37692 | + | 3.41292i | −0.301698 | + | 0.109809i | ||||
\(967\) | 5.01071 | + | 4.20449i | 0.161134 | + | 0.135207i | 0.719790 | − | 0.694192i | \(-0.244238\pi\) |
−0.558656 | + | 0.829400i | \(0.688683\pi\) | |||||||
\(968\) | 18.7426 | 0.602411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.5410 | 2.32915 | ||||||||
\(971\) | 18.0071 | + | 15.1097i | 0.577875 | + | 0.484895i | 0.884248 | − | 0.467017i | \(-0.154671\pi\) |
−0.306374 | + | 0.951911i | \(0.599116\pi\) | |||||||
\(972\) | −5.60579 | + | 2.04034i | −0.179806 | + | 0.0654440i | ||||
\(973\) | 7.70913 | + | 43.7207i | 0.247143 | + | 1.40162i | ||||
\(974\) | 1.17454 | − | 6.66117i | 0.0376348 | − | 0.213438i | ||||
\(975\) | 1.96412 | + | 0.714880i | 0.0629021 | + | 0.0228945i | ||||
\(976\) | −24.8435 | − | 43.0301i | −0.795220 | − | 1.37736i | ||||
\(977\) | −5.31966 | + | 9.21392i | −0.170191 | + | 0.294779i | −0.938487 | − | 0.345316i | \(-0.887772\pi\) |
0.768296 | + | 0.640095i | \(0.221105\pi\) | |||||||
\(978\) | 0.835119 | − | 0.700748i | 0.0267041 | − | 0.0224074i | ||||
\(979\) | 9.62328 | − | 8.07489i | 0.307562 | − | 0.258075i | ||||
\(980\) | −2.00000 | + | 3.46410i | −0.0638877 | + | 0.110657i | ||||
\(981\) | −4.69756 | − | 8.13641i | −0.149982 | − | 0.259776i | ||||
\(982\) | 32.2561 | + | 11.7403i | 1.02933 | + | 0.374647i | ||||
\(983\) | 5.66406 | − | 32.1225i | 0.180656 | − | 1.02455i | −0.750756 | − | 0.660580i | \(-0.770310\pi\) |
0.931411 | − | 0.363968i | \(-0.118578\pi\) | |||||||
\(984\) | 0.444940 | + | 2.52338i | 0.0141842 | + | 0.0804424i | ||||
\(985\) | −9.12273 | + | 3.32040i | −0.290674 | + | 0.105797i | ||||
\(986\) | −3.42585 | − | 2.87463i | −0.109101 | − | 0.0915470i | ||||
\(987\) | 3.43769 | 0.109423 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.785218 | −0.0249685 | ||||||||
\(990\) | 18.5232 | + | 15.5428i | 0.588706 | + | 0.493983i | ||||
\(991\) | −7.00151 | + | 2.54834i | −0.222410 | + | 0.0809507i | −0.450822 | − | 0.892614i | \(-0.648869\pi\) |
0.228412 | + | 0.973565i | \(0.426647\pi\) | |||||||
\(992\) | 5.19977 | + | 29.4894i | 0.165093 | + | 0.936288i | ||||
\(993\) | 0.725908 | − | 4.11683i | 0.0230360 | − | 0.130644i | ||||
\(994\) | 34.0831 | + | 12.4052i | 1.08105 | + | 0.393470i | ||||
\(995\) | 21.7082 | + | 37.5997i | 0.688196 | + | 1.19199i | ||||
\(996\) | −1.00000 | + | 1.73205i | −0.0316862 | + | 0.0548821i | ||||
\(997\) | 30.4182 | − | 25.5239i | 0.963356 | − | 0.808351i | −0.0181401 | − | 0.999835i | \(-0.505774\pi\) |
0.981496 | + | 0.191484i | \(0.0613300\pi\) | |||||||
\(998\) | 31.1416 | − | 26.1309i | 0.985770 | − | 0.827159i | ||||
\(999\) | 9.89919 | − | 17.1459i | 0.313196 | − | 0.542472i |
(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 | 361.2.e.j.54.2 | 12 | ||
19.2 | odd | 18 | 361.2.c.g.292.2 | 4 | |||
19.3 | odd | 18 | 361.2.c.g.68.2 | 4 | |||
19.4 | even | 9 | inner | 361.2.e.j.28.2 | 12 | ||
19.5 | even | 9 | 361.2.a.f.1.2 | yes | 2 | ||
19.6 | even | 9 | inner | 361.2.e.j.234.2 | 12 | ||
19.7 | even | 3 | inner | 361.2.e.j.62.1 | 12 | ||
19.8 | odd | 6 | 361.2.e.i.245.1 | 12 | |||
19.9 | even | 9 | inner | 361.2.e.j.99.1 | 12 | ||
19.10 | odd | 18 | 361.2.e.i.99.2 | 12 | |||
19.11 | even | 3 | inner | 361.2.e.j.245.2 | 12 | ||
19.12 | odd | 6 | 361.2.e.i.62.2 | 12 | |||
19.13 | odd | 18 | 361.2.e.i.234.1 | 12 | |||
19.14 | odd | 18 | 361.2.a.c.1.1 | ✓ | 2 | ||
19.15 | odd | 18 | 361.2.e.i.28.1 | 12 | |||
19.16 | even | 9 | 361.2.c.d.68.1 | 4 | |||
19.17 | even | 9 | 361.2.c.d.292.1 | 4 | |||
19.18 | odd | 2 | 361.2.e.i.54.1 | 12 | |||
57.5 | odd | 18 | 3249.2.a.i.1.1 | 2 | |||
57.14 | even | 18 | 3249.2.a.o.1.2 | 2 | |||
76.43 | odd | 18 | 5776.2.a.s.1.2 | 2 | |||
76.71 | even | 18 | 5776.2.a.bg.1.1 | 2 | |||
95.14 | odd | 18 | 9025.2.a.s.1.2 | 2 | |||
95.24 | even | 18 | 9025.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
361.2.a.c.1.1 | ✓ | 2 | 19.14 | odd | 18 | ||
361.2.a.f.1.2 | yes | 2 | 19.5 | even | 9 | ||
361.2.c.d.68.1 | 4 | 19.16 | even | 9 | |||
361.2.c.d.292.1 | 4 | 19.17 | even | 9 | |||
361.2.c.g.68.2 | 4 | 19.3 | odd | 18 | |||
361.2.c.g.292.2 | 4 | 19.2 | odd | 18 | |||
361.2.e.i.28.1 | 12 | 19.15 | odd | 18 | |||
361.2.e.i.54.1 | 12 | 19.18 | odd | 2 | |||
361.2.e.i.62.2 | 12 | 19.12 | odd | 6 | |||
361.2.e.i.99.2 | 12 | 19.10 | odd | 18 | |||
361.2.e.i.234.1 | 12 | 19.13 | odd | 18 | |||
361.2.e.i.245.1 | 12 | 19.8 | odd | 6 | |||
361.2.e.j.28.2 | 12 | 19.4 | even | 9 | inner | ||
361.2.e.j.54.2 | 12 | 1.1 | even | 1 | trivial | ||
361.2.e.j.62.1 | 12 | 19.7 | even | 3 | inner | ||
361.2.e.j.99.1 | 12 | 19.9 | even | 9 | inner | ||
361.2.e.j.234.2 | 12 | 19.6 | even | 9 | inner | ||
361.2.e.j.245.2 | 12 | 19.11 | even | 3 | inner | ||
3249.2.a.i.1.1 | 2 | 57.5 | odd | 18 | |||
3249.2.a.o.1.2 | 2 | 57.14 | even | 18 | |||
5776.2.a.s.1.2 | 2 | 76.43 | odd | 18 | |||
5776.2.a.bg.1.1 | 2 | 76.71 | even | 18 | |||
9025.2.a.n.1.1 | 2 | 95.24 | even | 18 | |||
9025.2.a.s.1.2 | 2 | 95.14 | odd | 18 |