Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(739,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3330.739");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 3330.e (of order , degree , 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: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 1110) |
Sato-Tate group: |
Embedding invariants
Embedding label | 739.6 | ||
Root | of defining polynomial | ||
Character | 3330.739 | ||
Dual form | 3330.2.e.f.739.5 |
-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 on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
1.00000 | 0.707107 | |||||||||
0 | 0 | |||||||||
1.00000 | 0.500000 | |||||||||
−1.28817 | + | 1.82773i | −0.576089 | + | 0.817387i | |||||
0 | 0 | |||||||||
− | 1.25548i | − | 0.474527i | −0.971445 | − | 0.237263i | ||||
0.971445 | − | 0.237263i | ||||||||
1.00000 | 0.353553 | |||||||||
0 | 0 | |||||||||
−1.28817 | + | 1.82773i | −0.407356 | + | 0.577980i | |||||
5.46829 | 1.64875 | 0.824376 | − | 0.566043i | ||||||
0.824376 | + | 0.566043i | ||||||||
0 | 0 | |||||||||
4.70887 | 1.30601 | 0.653003 | − | 0.757355i | ||||||
0.653003 | + | 0.757355i | ||||||||
− | 1.25548i | − | 0.335541i | |||||||
0 | 0 | |||||||||
1.00000 | 0.250000 | |||||||||
−1.19309 | −0.289367 | −0.144684 | − | 0.989478i | ||||||
−0.144684 | + | 0.989478i | ||||||||
0 | 0 | |||||||||
− | 1.22179i | − | 0.280298i | −0.990130 | − | 0.140149i | ||||
0.990130 | − | 0.140149i | ||||||||
−1.28817 | + | 1.82773i | −0.288044 | + | 0.408694i | |||||
0 | 0 | |||||||||
5.46829 | 1.16584 | |||||||||
−1.91577 | −0.399466 | −0.199733 | − | 0.979850i | ||||||
−0.199733 | + | 0.979850i | ||||||||
0 | 0 | |||||||||
−1.68122 | − | 4.70887i | −0.336244 | − | 0.941775i | |||||
4.70887 | 0.923486 | |||||||||
0 | 0 | |||||||||
− | 1.25548i | − | 0.237263i | |||||||
5.08822i | 0.944858i | 0.881369 | + | 0.472429i | ||||||
−0.881369 | + | 0.472429i | ||||||||
0 | 0 | |||||||||
− | 3.43275i | − | 0.616540i | −0.951299 | − | 0.308270i | ||||
0.951299 | − | 0.308270i | ||||||||
1.00000 | 0.176777 | |||||||||
0 | 0 | |||||||||
−1.19309 | −0.204613 | |||||||||
2.29468 | + | 1.61728i | 0.387872 | + | 0.273370i | |||||
0 | 0 | |||||||||
−4.58473 | − | 3.99753i | −0.753725 | − | 0.657190i | |||||
− | 1.22179i | − | 0.198201i | |||||||
0 | 0 | |||||||||
−1.28817 | + | 1.82773i | −0.203678 | + | 0.288990i | |||||
4.46326 | 0.697043 | 0.348522 | − | 0.937301i | ||||||
0.348522 | + | 0.937301i | ||||||||
0 | 0 | |||||||||
1.34271 | 0.204761 | 0.102380 | − | 0.994745i | ||||||
0.102380 | + | 0.994745i | ||||||||
5.46829 | 0.824376 | |||||||||
0 | 0 | |||||||||
−1.91577 | −0.282465 | |||||||||
− | 1.90301i | − | 0.277583i | −0.990322 | − | 0.138791i | ||||
0.990322 | − | 0.138791i | ||||||||
0 | 0 | |||||||||
5.42377 | 0.774824 | |||||||||
−1.68122 | − | 4.70887i | −0.237760 | − | 0.665935i | |||||
0 | 0 | |||||||||
4.70887 | 0.653003 | |||||||||
1.11671i | 0.153392i | 0.997055 | + | 0.0766959i | ||||||
−0.997055 | + | 0.0766959i | ||||||||
0 | 0 | |||||||||
−7.04410 | + | 9.99458i | −0.949827 | + | 1.34767i | |||||
− | 1.25548i | − | 0.167771i | |||||||
0 | 0 | |||||||||
5.08822i | 0.668116i | |||||||||
8.99577i | 1.17115i | 0.810618 | + | 0.585575i | ||||||
−0.810618 | + | 0.585575i | ||||||||
0 | 0 | |||||||||
− | 6.21190i | − | 0.795352i | −0.917526 | − | 0.397676i | ||||
0.917526 | − | 0.397676i | ||||||||
− | 3.43275i | − | 0.435960i | |||||||
0 | 0 | |||||||||
1.00000 | 0.125000 | |||||||||
−6.06585 | + | 8.60657i | −0.752376 | + | 1.06751i | |||||
0 | 0 | |||||||||
4.21117i | 0.514476i | 0.966348 | + | 0.257238i | ||||||
−0.966348 | + | 0.257238i | ||||||||
−1.19309 | −0.144684 | |||||||||
0 | 0 | |||||||||
2.29468 | + | 1.61728i | 0.274267 | + | 0.193301i | |||||
12.4170 | 1.47363 | 0.736815 | − | 0.676094i | ||||||
0.736815 | + | 0.676094i | ||||||||
0 | 0 | |||||||||
− | 10.2834i | − | 1.20359i | −0.798652 | − | 0.601793i | ||||
0.798652 | − | 0.601793i | ||||||||
−4.58473 | − | 3.99753i | −0.532964 | − | 0.464703i | |||||
0 | 0 | |||||||||
− | 1.22179i | − | 0.140149i | |||||||
− | 6.86533i | − | 0.782377i | |||||||
0 | 0 | |||||||||
1.00691i | 0.113286i | 0.998394 | + | 0.0566431i | ||||||
−0.998394 | + | 0.0566431i | ||||||||
−1.28817 | + | 1.82773i | −0.144022 | + | 0.204347i | |||||
0 | 0 | |||||||||
4.46326 | 0.492884 | |||||||||
0.754493i | 0.0828164i | 0.999142 | + | 0.0414082i | ||||||
−0.999142 | + | 0.0414082i | ||||||||
0 | 0 | |||||||||
1.53691 | − | 2.18065i | 0.166701 | − | 0.236525i | |||||
1.34271 | 0.144788 | |||||||||
0 | 0 | |||||||||
5.46829 | 0.582922 | |||||||||
11.4743i | 1.21627i | 0.793832 | + | 0.608137i | ||||||
−0.793832 | + | 0.608137i | ||||||||
0 | 0 | |||||||||
− | 5.91190i | − | 0.619735i | |||||||
−1.91577 | −0.199733 | |||||||||
0 | 0 | |||||||||
− | 1.90301i | − | 0.196281i | |||||||
2.23311 | + | 1.57388i | 0.229112 | + | 0.161477i | |||||
0 | 0 | |||||||||
16.6814 | 1.69374 | 0.846868 | − | 0.531803i | ||||||
0.846868 | + | 0.531803i | ||||||||
5.42377 | 0.547883 | |||||||||
0 | 0 | |||||||||
−1.68122 | − | 4.70887i | −0.168122 | − | 0.470887i | |||||
−3.26214 | −0.324595 | −0.162298 | − | 0.986742i | ||||||
−0.162298 | + | 0.986742i | ||||||||
0 | 0 | |||||||||
5.19330 | 0.511711 | 0.255856 | − | 0.966715i | ||||||
0.255856 | + | 0.966715i | ||||||||
4.70887 | 0.461743 | |||||||||
0 | 0 | |||||||||
1.11671i | 0.108464i | |||||||||
8.65950i | 0.837146i | 0.908183 | + | 0.418573i | ||||||
−0.908183 | + | 0.418573i | ||||||||
0 | 0 | |||||||||
2.54677i | 0.243936i | 0.992534 | + | 0.121968i | ||||||
−0.992534 | + | 0.121968i | ||||||||
−7.04410 | + | 9.99458i | −0.671629 | + | 0.952945i | |||||
0 | 0 | |||||||||
− | 1.25548i | − | 0.118632i | |||||||
4.72781 | 0.444755 | 0.222378 | − | 0.974961i | ||||||
0.222378 | + | 0.974961i | ||||||||
0 | 0 | |||||||||
2.46784 | − | 3.50152i | 0.230128 | − | 0.326518i | |||||
5.08822i | 0.472429i | |||||||||
0 | 0 | |||||||||
8.99577i | 0.828128i | |||||||||
1.49790i | 0.137312i | |||||||||
0 | 0 | |||||||||
18.9022 | 1.71838 | |||||||||
− | 6.21190i | − | 0.562399i | |||||||
0 | 0 | |||||||||
− | 3.43275i | − | 0.308270i | |||||||
10.7723 | + | 2.99303i | 0.963501 | + | 0.267704i | |||||
0 | 0 | |||||||||
8.05067i | 0.714381i | 0.934031 | + | 0.357191i | ||||||
−0.934031 | + | 0.357191i | ||||||||
1.00000 | 0.0883883 | |||||||||
0 | 0 | |||||||||
−6.06585 | + | 8.60657i | −0.532010 | + | 0.754846i | |||||
12.9999i | 1.13581i | 0.823094 | + | 0.567905i | ||||||
−0.823094 | + | 0.567905i | ||||||||
0 | 0 | |||||||||
−1.53393 | −0.133009 | |||||||||
4.21117i | 0.363790i | |||||||||
0 | 0 | |||||||||
−1.19309 | −0.102307 | |||||||||
− | 13.5487i | − | 1.15754i | −0.815490 | − | 0.578772i | ||||
0.815490 | − | 0.578772i | ||||||||
0 | 0 | |||||||||
15.3257 | 1.29991 | 0.649955 | − | 0.759972i | ||||||
0.649955 | + | 0.759972i | ||||||||
2.29468 | + | 1.61728i | 0.193936 | + | 0.136685i | |||||
0 | 0 | |||||||||
12.4170 | 1.04201 | |||||||||
25.7495 | 2.15328 | |||||||||
0 | 0 | |||||||||
−9.29991 | − | 6.55451i | −0.772315 | − | 0.544322i | |||||
− | 10.2834i | − | 0.851064i | |||||||
0 | 0 | |||||||||
−4.58473 | − | 3.99753i | −0.376863 | − | 0.328595i | |||||
−13.4684 | −1.10337 | −0.551686 | − | 0.834052i | ||||||
−0.551686 | + | 0.834052i | ||||||||
0 | 0 | |||||||||
−10.3930 | −0.845767 | −0.422883 | − | 0.906184i | ||||||
−0.422883 | + | 0.906184i | ||||||||
− | 1.22179i | − | 0.0991003i | |||||||
0 | 0 | |||||||||
− | 6.86533i | − | 0.553224i | |||||||
6.27415 | + | 4.42198i | 0.503952 | + | 0.355182i | |||||
0 | 0 | |||||||||
14.2297i | 1.13565i | 0.823148 | + | 0.567827i | ||||||
−0.823148 | + | 0.567827i | ||||||||
1.00691i | 0.0801054i | |||||||||
0 | 0 | |||||||||
−1.28817 | + | 1.82773i | −0.101839 | + | 0.144495i | |||||
2.40521i | 0.189557i | |||||||||
0 | 0 | |||||||||
0.455364 | 0.0356669 | 0.0178334 | − | 0.999841i | ||||||
0.0178334 | + | 0.999841i | ||||||||
4.46326 | 0.348522 | |||||||||
0 | 0 | |||||||||
0.754493i | 0.0585600i | |||||||||
−0.755752 | −0.0584819 | −0.0292409 | − | 0.999572i | ||||||
−0.0292409 | + | 0.999572i | ||||||||
0 | 0 | |||||||||
9.17350 | 0.705654 | |||||||||
1.53691 | − | 2.18065i | 0.117875 | − | 0.167248i | |||||
0 | 0 | |||||||||
1.34271 | 0.102380 | |||||||||
− | 4.41375i | − | 0.335571i | −0.985823 | − | 0.167786i | ||||
0.985823 | − | 0.167786i | ||||||||
0 | 0 | |||||||||
−5.91190 | + | 2.11074i | −0.446898 | + | 0.159557i | |||||
5.46829 | 0.412188 | |||||||||
0 | 0 | |||||||||
11.4743i | 0.860036i | |||||||||
− | 12.6883i | − | 0.948368i | −0.880426 | − | 0.474184i | ||||
0.880426 | − | 0.474184i | ||||||||
0 | 0 | |||||||||
13.2444 | 0.984445 | 0.492223 | − | 0.870469i | ||||||
0.492223 | + | 0.870469i | ||||||||
− | 5.91190i | − | 0.438219i | |||||||
0 | 0 | |||||||||
−1.91577 | −0.141233 | |||||||||
13.2123 | − | 3.23016i | 0.971391 | − | 0.237486i | |||||
0 | 0 | |||||||||
−6.52417 | −0.477094 | |||||||||
− | 1.90301i | − | 0.138791i | |||||||
0 | 0 | |||||||||
2.23311 | + | 1.57388i | 0.162007 | + | 0.114181i | |||||
7.03990i | 0.509389i | 0.967022 | + | 0.254695i | ||||||
−0.967022 | + | 0.254695i | ||||||||
0 | 0 | |||||||||
−0.635749 | −0.0457622 | −0.0228811 | − | 0.999738i | ||||||
−0.0228811 | + | 0.999738i | ||||||||
16.6814 | 1.19765 | |||||||||
0 | 0 | |||||||||
5.42377 | 0.387412 | |||||||||
− | 5.18937i | − | 0.369727i | −0.982764 | − | 0.184864i | ||||
0.982764 | − | 0.184864i | ||||||||
0 | 0 | |||||||||
23.8852i | 1.69318i | 0.532247 | + | 0.846589i | ||||||
−0.532247 | + | 0.846589i | ||||||||
−1.68122 | − | 4.70887i | −0.118880 | − | 0.332968i | |||||
0 | 0 | |||||||||
−3.26214 | −0.229523 | |||||||||
6.38816 | 0.448361 | |||||||||
0 | 0 | |||||||||
−5.74945 | + | 8.15764i | −0.401559 | + | 0.569754i | |||||
5.19330 | 0.361834 | |||||||||
0 | 0 | |||||||||
4.70887 | 0.326502 | |||||||||
− | 6.68111i | − | 0.462142i | |||||||
0 | 0 | |||||||||
−26.6260 | −1.83301 | −0.916505 | − | 0.400022i | ||||||
−0.916505 | + | 0.400022i | ||||||||
1.11671i | 0.0766959i | |||||||||
0 | 0 | |||||||||
8.65950i | 0.591952i | |||||||||
−1.72964 | + | 2.45411i | −0.117960 | + | 0.167369i | |||||
0 | 0 | |||||||||
−4.30975 | −0.292565 | |||||||||
2.54677i | 0.172489i | |||||||||
0 | 0 | |||||||||
−7.04410 | + | 9.99458i | −0.474913 | + | 0.673834i | |||||
−5.61812 | −0.377915 | |||||||||
0 | 0 | |||||||||
− | 20.0982i | − | 1.34588i | −0.739698 | − | 0.672938i | ||||
0.739698 | − | 0.672938i | ||||||||
− | 1.25548i | − | 0.0838853i | |||||||
0 | 0 | |||||||||
4.72781 | 0.314489 | |||||||||
−15.1621 | −1.00635 | −0.503173 | − | 0.864186i | ||||||
−0.503173 | + | 0.864186i | ||||||||
0 | 0 | |||||||||
−2.54527 | −0.168196 | −0.0840980 | − | 0.996457i | ||||||
−0.0840980 | + | 0.996457i | ||||||||
2.46784 | − | 3.50152i | 0.162725 | − | 0.230883i | |||||
0 | 0 | |||||||||
5.08822i | 0.334058i | |||||||||
13.9212i | 0.912008i | 0.889978 | + | 0.456004i | ||||||
−0.889978 | + | 0.456004i | ||||||||
0 | 0 | |||||||||
3.47820 | + | 2.45141i | 0.226892 | + | 0.159912i | |||||
8.99577i | 0.585575i | |||||||||
0 | 0 | |||||||||
1.49790i | 0.0970945i | |||||||||
− | 28.8753i | − | 1.86779i | −0.357546 | − | 0.933895i | ||||
0.357546 | − | 0.933895i | ||||||||
0 | 0 | |||||||||
− | 6.84853i | − | 0.441152i | −0.975370 | − | 0.220576i | ||||
0.975370 | − | 0.220576i | ||||||||
18.9022 | 1.21508 | |||||||||
0 | 0 | |||||||||
− | 6.21190i | − | 0.397676i | |||||||
−6.98676 | + | 9.91321i | −0.446367 | + | 0.633331i | |||||
0 | 0 | |||||||||
− | 5.75326i | − | 0.366071i | |||||||
− | 3.43275i | − | 0.217980i | |||||||
0 | 0 | |||||||||
10.7723 | + | 2.99303i | 0.681298 | + | 0.189296i | |||||
18.7459i | 1.18323i | 0.806221 | + | 0.591615i | ||||||
−0.806221 | + | 0.591615i | ||||||||
0 | 0 | |||||||||
−10.4760 | −0.658620 | |||||||||
8.05067i | 0.505144i | |||||||||
0 | 0 | |||||||||
1.00000 | 0.0625000 | |||||||||
−17.3509 | −1.08232 | −0.541158 | − | 0.840921i | ||||||
−0.541158 | + | 0.840921i | ||||||||
0 | 0 | |||||||||
−5.01882 | + | 5.75604i | −0.311854 | + | 0.357663i | |||||
−6.06585 | + | 8.60657i | −0.376188 | + | 0.533757i | |||||
0 | 0 | |||||||||
12.9999i | 0.803139i | |||||||||
− | 31.3436i | − | 1.93273i | −0.257176 | − | 0.966364i | ||||
0.257176 | − | 0.966364i | ||||||||
0 | 0 | |||||||||
−2.04105 | − | 1.43851i | −0.125380 | − | 0.0883672i | |||||
−1.53393 | −0.0940516 | |||||||||
0 | 0 | |||||||||
4.21117i | 0.257238i | |||||||||
−20.8503 | −1.27126 | −0.635631 | − | 0.771993i | ||||||
−0.635631 | + | 0.771993i | ||||||||
0 | 0 | |||||||||
−0.977182 | −0.0593596 | −0.0296798 | − | 0.999559i | ||||||
−0.0296798 | + | 0.999559i | ||||||||
−1.19309 | −0.0723418 | |||||||||
0 | 0 | |||||||||
− | 13.5487i | − | 0.818507i | |||||||
−9.19339 | − | 25.7495i | −0.554383 | − | 1.55275i | |||||
0 | 0 | |||||||||
−28.0775 | −1.68701 | −0.843506 | − | 0.537120i | ||||||
−0.843506 | + | 0.537120i | ||||||||
15.3257 | 0.919176 | |||||||||
0 | 0 | |||||||||
2.29468 | + | 1.61728i | 0.137134 | + | 0.0966507i | |||||
− | 20.9112i | − | 1.24746i | −0.781640 | − | 0.623730i | ||||
0.781640 | − | 0.623730i | ||||||||
0 | 0 | |||||||||
−11.7273 | −0.697116 | −0.348558 | − | 0.937287i | ||||||
−0.348558 | + | 0.937287i | ||||||||
12.4170 | 0.736815 | |||||||||
0 | 0 | |||||||||
25.7495 | 1.52260 | |||||||||
− | 5.60353i | − | 0.330766i | |||||||
0 | 0 | |||||||||
−15.5765 | −0.916267 | |||||||||
−9.29991 | − | 6.55451i | −0.546109 | − | 0.384894i | |||||
0 | 0 | |||||||||
− | 10.2834i | − | 0.601793i | |||||||
− | 19.0944i | − | 1.11550i | −0.830007 | − | 0.557752i | ||||
0.830007 | − | 0.557752i | ||||||||
0 | 0 | |||||||||
−16.4419 | − | 11.5881i | −0.957283 | − | 0.674686i | |||||
−4.58473 | − | 3.99753i | −0.266482 | − | 0.232352i | |||||
0 | 0 | |||||||||
−13.4684 | −0.780202 | |||||||||
−9.02113 | −0.521705 | |||||||||
0 | 0 | |||||||||
− | 1.68574i | − | 0.0971645i | |||||||
−10.3930 | −0.598048 | |||||||||
0 | 0 | |||||||||
− | 1.22179i | − | 0.0700745i | |||||||
11.3537 | + | 8.00200i | 0.650111 | + | 0.458193i | |||||
0 | 0 | |||||||||
31.2854i | 1.78555i | 0.450500 | + | 0.892777i | ||||||
−0.450500 | + | 0.892777i | ||||||||
− | 6.86533i | − | 0.391188i | |||||||
0 | 0 | |||||||||
6.27415 | + | 4.42198i | 0.356348 | + | 0.251151i | |||||
7.52409i | 0.426652i | 0.976981 | + | 0.213326i | ||||||
−0.976981 | + | 0.213326i | ||||||||
0 | 0 | |||||||||
−0.0900227 | −0.00508838 | −0.00254419 | − | 0.999997i | ||||||
−0.00254419 | + | 0.999997i | ||||||||
14.2297i | 0.803029i | |||||||||
0 | 0 | |||||||||
1.00691i | 0.0566431i | |||||||||
− | 7.86659i | − | 0.441832i | −0.975293 | − | 0.220916i | ||||
0.975293 | − | 0.220916i | ||||||||
0 | 0 | |||||||||
27.8239i | 1.55784i | |||||||||
−1.28817 | + | 1.82773i | −0.0720111 | + | 0.102173i | |||||
0 | 0 | |||||||||
2.40521i | 0.134037i | |||||||||
1.45771i | 0.0811090i | |||||||||
0 | 0 | |||||||||
−7.91665 | − | 22.1735i | −0.439137 | − | 1.22996i | |||||
0.455364 | 0.0252203 | |||||||||
0 | 0 | |||||||||
4.46326 | 0.246442 | |||||||||
−2.38919 | −0.131720 | |||||||||
0 | 0 | |||||||||
21.5849i | 1.18641i | 0.805051 | + | 0.593205i | ||||||
−0.805051 | + | 0.593205i | ||||||||
0.754493i | 0.0414082i | |||||||||
0 | 0 | |||||||||
−0.755752 | −0.0413529 | |||||||||
−7.69690 | − | 5.42472i | −0.420526 | − | 0.296384i | |||||
0 | 0 | |||||||||
24.3782i | 1.32796i | 0.747748 | + | 0.663982i | ||||||
−0.747748 | + | 0.663982i | ||||||||
9.17350 | 0.498973 | |||||||||
0 | 0 | |||||||||
1.53691 | − | 2.18065i | 0.0833505 | − | 0.118262i | |||||
− | 18.7713i | − | 1.01652i | |||||||
0 | 0 | |||||||||
− | 15.5978i | − | 0.842202i | |||||||
1.34271 | 0.0723939 | |||||||||
0 | 0 | |||||||||
− | 4.41375i | − | 0.237285i | |||||||
−25.4950 | −1.36864 | −0.684321 | − | 0.729181i | ||||||
−0.684321 | + | 0.729181i | ||||||||
0 | 0 | |||||||||
2.69761 | 0.144400 | 0.0721999 | − | 0.997390i | ||||||
0.0721999 | + | 0.997390i | ||||||||
−5.91190 | + | 2.11074i | −0.316004 | + | 0.112824i | |||||
0 | 0 | |||||||||
5.46829 | 0.291461 | |||||||||
21.7179 | 1.15592 | 0.577962 | − | 0.816063i | ||||||
0.577962 | + | 0.816063i | ||||||||
0 | 0 | |||||||||
−15.9953 | + | 22.6950i | −0.848942 | + | 1.20453i | |||||
11.4743i | 0.608137i | |||||||||
0 | 0 | |||||||||
− | 12.6883i | − | 0.670597i | |||||||
20.3716 | 1.07517 | 0.537585 | − | 0.843210i | ||||||
0.537585 | + | 0.843210i | ||||||||
0 | 0 | |||||||||
17.5072 | 0.921433 | |||||||||
13.2444 | 0.696108 | |||||||||
0 | 0 | |||||||||
− | 5.91190i | − | 0.309868i | |||||||
18.7954 | + | 13.2469i | 0.983796 | + | 0.693372i | |||||
0 | 0 | |||||||||
− | 31.0972i | − | 1.62326i | −0.584172 | − | 0.811630i | ||||
0.584172 | − | 0.811630i | ||||||||
−1.91577 | −0.0998665 | |||||||||
0 | 0 | |||||||||
13.2123 | − | 3.23016i | 0.686877 | − | 0.167928i | |||||
1.40201 | 0.0727885 | |||||||||
0 | 0 | |||||||||
− | 33.4131i | − | 1.73006i | −0.501716 | − | 0.865032i | ||||
0.501716 | − | 0.865032i | ||||||||
−6.52417 | −0.337357 | |||||||||
0 | 0 | |||||||||
− | 1.90301i | − | 0.0981403i | |||||||
23.9598i | 1.23399i | |||||||||
0 | 0 | |||||||||
−24.6191 | −1.26460 | −0.632298 | − | 0.774725i | ||||||
−0.632298 | + | 0.774725i | ||||||||
2.23311 | + | 1.57388i | 0.114556 | + | 0.0807383i | |||||
0 | 0 | |||||||||
7.03990i | 0.360192i | |||||||||
−17.5596 | −0.897252 | −0.448626 | − | 0.893720i | ||||||
−0.448626 | + | 0.893720i | ||||||||
0 | 0 | |||||||||
12.5480 | + | 8.84373i | 0.639505 | + | 0.450718i | |||||
−0.635749 | −0.0323587 | |||||||||
0 | 0 | |||||||||
16.6814 | 0.846868 | |||||||||
19.6417i | 0.995875i | 0.867213 | + | 0.497937i | ||||||
−0.867213 | + | 0.497937i | ||||||||
0 | 0 | |||||||||
2.28569 | 0.115592 | |||||||||
5.42377 | 0.273942 | |||||||||
0 | 0 | |||||||||
− | 5.18937i | − | 0.261437i | |||||||
−1.84036 | − | 1.29707i | −0.0925987 | − | 0.0652629i | |||||
0 | 0 | |||||||||
− | 4.31480i | − | 0.216554i | −0.994121 | − | 0.108277i | ||||
0.994121 | − | 0.108277i | ||||||||
23.8852i | 1.19726i | |||||||||
0 | 0 | |||||||||
−1.68122 | − | 4.70887i | −0.0840610 | − | 0.235444i | |||||
− | 9.64980i | − | 0.481888i | −0.970539 | − | 0.240944i | ||||
0.970539 | − | 0.240944i | ||||||||
0 | 0 | |||||||||
− | 16.1644i | − | 0.805206i | |||||||
−3.26214 | −0.162298 | |||||||||
0 | 0 | |||||||||
6.38816 | 0.317039 | |||||||||
−25.0706 | − | 21.8596i | −1.24271 | − | 1.08354i | |||||
0 | 0 | |||||||||
− | 25.5235i | − | 1.26206i | −0.775760 | − | 0.631029i | ||||
0.775760 | − | 0.631029i | ||||||||
−5.74945 | + | 8.15764i | −0.283945 | + | 0.402877i | |||||
0 | 0 | |||||||||
5.19330 | 0.255856 | |||||||||
11.2940 | 0.555742 | |||||||||
0 | 0 | |||||||||
−1.37901 | − | 0.971918i | −0.0676930 | − | 0.0477096i | |||||
4.70887 | 0.230872 | |||||||||
0 | 0 | |||||||||
− | 6.68111i | − | 0.326784i | |||||||
22.0969 | 1.07950 | 0.539751 | − | 0.841824i | ||||||
0.539751 | + | 0.841824i | ||||||||
0 | 0 | |||||||||
− | 8.20101i | − | 0.399693i | −0.979827 | − | 0.199846i | ||||
0.979827 | − | 0.199846i | ||||||||
−26.6260 | −1.29613 | |||||||||
0 | 0 | |||||||||
1.11671i | 0.0542322i | |||||||||
2.00585 | + | 5.61812i | 0.0972979 | + | 0.272519i | |||||
0 | 0 | |||||||||
−7.79891 | −0.377416 | |||||||||
8.65950i | 0.418573i | |||||||||
0 | 0 | |||||||||
−1.72964 | + | 2.45411i | −0.0834106 | + | 0.118348i | |||||
− | 9.83076i | − | 0.473531i | −0.971567 | − | 0.236765i | ||||
0.971567 | − | 0.236765i | ||||||||
0 | 0 | |||||||||
1.61024i | 0.0773832i | 0.999251 | + | 0.0386916i | ||||||
−0.999251 | + | 0.0386916i | ||||||||
−4.30975 | −0.206875 | |||||||||
0 | 0 | |||||||||
2.54677i | 0.121968i | |||||||||
2.34067i | 0.111970i | |||||||||
0 | 0 | |||||||||
32.2443i | 1.53894i | 0.638684 | + | 0.769469i | ||||||
−0.638684 | + | 0.769469i | ||||||||
−7.04410 | + | 9.99458i | −0.335815 | + | 0.476473i | |||||
0 | 0 | |||||||||
−5.61812 | −0.267226 | |||||||||
− | 19.0730i | − | 0.906186i | −0.891463 | − | 0.453093i | ||||
0.891463 | − | 0.453093i | ||||||||
0 | 0 | |||||||||
−20.9720 | − | 14.7809i | −0.994168 | − | 0.700682i | |||||
− | 20.0982i | − | 0.951679i | |||||||
0 | 0 | |||||||||
− | 1.25548i | − | 0.0593159i | |||||||
− | 30.6914i | − | 1.44841i | −0.689582 | − | 0.724207i | ||||
0.689582 | − | 0.724207i | ||||||||
0 | 0 | |||||||||
24.4064 | 1.14925 | |||||||||
4.72781 | 0.222378 | |||||||||
0 | 0 | |||||||||
−15.1621 | −0.711593 | |||||||||
10.8054 | + | 7.61555i | 0.506564 | + | 0.357022i | |||||
0 | 0 | |||||||||
22.4560 | 1.05045 | 0.525223 | − | 0.850965i | ||||||
0.525223 | + | 0.850965i | ||||||||
−2.54527 | −0.118932 | |||||||||
0 | 0 | |||||||||
2.46784 | − | 3.50152i | 0.115064 | − | 0.163259i | |||||
7.37800i | 0.343628i | 0.985129 | + | 0.171814i | ||||||
−0.985129 | + | 0.171814i | ||||||||
0 | 0 | |||||||||
−6.16145 | −0.286347 | −0.143173 | − | 0.989698i | ||||||
−0.143173 | + | 0.989698i | ||||||||
5.08822i | 0.236215i | |||||||||
0 | 0 | |||||||||
13.9212i | 0.644887i | |||||||||
−5.37297 | −0.248631 | −0.124316 | − | 0.992243i | ||||||
−0.124316 | + | 0.992243i | ||||||||
0 | 0 | |||||||||
5.28704 | 0.244133 | |||||||||
3.47820 | + | 2.45141i | 0.160437 | + | 0.113075i | |||||
0 | 0 | |||||||||
8.99577i | 0.414064i | |||||||||
7.34231 | 0.337600 | |||||||||
0 | 0 | |||||||||
−5.75326 | + | 2.05410i | −0.263978 | + | 0.0942485i | |||||
1.49790i | 0.0686562i | |||||||||
0 | 0 | |||||||||
− | 28.8753i | − | 1.32073i | |||||||
21.5810i | 0.986062i | 0.870012 | + | 0.493031i | ||||||
−0.870012 | + | 0.493031i | ||||||||
0 | 0 | |||||||||
−21.5889 | − | 18.8239i | −0.984370 | − | 0.858294i | |||||
− | 6.84853i | − | 0.311942i | |||||||
0 | 0 | |||||||||
18.9022 | 0.859191 | |||||||||
−21.4885 | + | 30.4891i | −0.975742 | + | 1.38444i | |||||
0 | 0 | |||||||||
−0.346315 | −0.0156930 | −0.00784652 | − | 0.999969i | ||||||
−0.00784652 | + | 0.999969i | ||||||||
− | 6.21190i | − | 0.281199i | |||||||
0 | 0 | |||||||||
−6.98676 | + | 9.91321i | −0.315629 | + | 0.447833i | |||||
−10.6278 | −0.479624 | −0.239812 | − | 0.970819i | ||||||
−0.239812 | + | 0.970819i | ||||||||
0 | 0 | |||||||||
− | 6.07071i | − | 0.273411i | |||||||
− | 5.75326i | − | 0.258851i | |||||||
0 | 0 | |||||||||
− | 3.43275i | − | 0.154135i | |||||||
− | 15.5893i | − | 0.699277i | |||||||
0 | 0 | |||||||||
− | 12.0121i | − | 0.537736i | −0.963177 | − | 0.268868i | ||||
0.963177 | − | 0.268868i | ||||||||
10.7723 | + | 2.99303i | 0.481751 | + | 0.133852i | |||||
0 | 0 | |||||||||
18.7459i | 0.836669i | |||||||||
4.15447 | 0.185239 | 0.0926194 | − | 0.995702i | ||||||
0.0926194 | + | 0.995702i | ||||||||
0 | 0 | |||||||||
4.20220 | − | 5.96232i | 0.186996 | − | 0.265320i | |||||
−10.4760 | −0.465715 | |||||||||
0 | 0 | |||||||||
8.05067i | 0.357191i | |||||||||
8.30223 | 0.367990 | 0.183995 | − | 0.982927i | ||||||
0.183995 | + | 0.982927i | ||||||||
0 | 0 | |||||||||
−12.9107 | −0.571134 | |||||||||
1.00000 | 0.0441942 | |||||||||
0 | 0 | |||||||||
−17.3509 | −0.765313 | |||||||||
−6.68987 | + | 9.49197i | −0.294791 | + | 0.418266i | |||||
0 | 0 | |||||||||
− | 10.4062i | − | 0.457665i | |||||||
−5.01882 | + | 5.75604i | −0.220514 | + | 0.252906i | |||||
0 | 0 | |||||||||
−6.06585 | + | 8.60657i | −0.266005 | + | 0.377423i | |||||
−14.0992 | −0.617698 | −0.308849 | − | 0.951111i | ||||||
−0.308849 | + | 0.951111i | ||||||||
0 | 0 | |||||||||
29.0802 | 1.27159 | 0.635794 | − | 0.771858i | ||||||
0.635794 | + | 0.771858i | ||||||||
12.9999i | 0.567905i | |||||||||
0 | 0 | |||||||||
− | 31.3436i | − | 1.36665i | |||||||
4.09558i | 0.178406i | |||||||||
0 | 0 | |||||||||
−19.3298 | −0.840427 | |||||||||
−2.04105 | − | 1.43851i | −0.0886574 | − | 0.0624851i | |||||
0 | 0 | |||||||||
−1.53393 | −0.0665045 | |||||||||
21.0169 | 0.910344 | |||||||||
0 | 0 | |||||||||
−15.8273 | − | 11.1549i | −0.684272 | − | 0.482270i | |||||
4.21117i | 0.181895i | |||||||||
0 | 0 | |||||||||
−20.8503 | −0.898918 | |||||||||
29.6587 | 1.27749 | |||||||||
0 | 0 | |||||||||
10.2446i | 0.440450i | 0.975449 | + | 0.220225i | ||||||
−0.975449 | + | 0.220225i | ||||||||
−0.977182 | −0.0419736 | |||||||||
0 | 0 | |||||||||
−1.19309 | −0.0511533 | |||||||||
−4.65481 | − | 3.28068i | −0.199390 | − | 0.140529i | |||||
0 | 0 | |||||||||
36.6360 | 1.56644 | 0.783220 | − | 0.621744i | ||||||
0.783220 | + | 0.621744i | ||||||||
− | 13.5487i | − | 0.578772i | |||||||
0 | 0 | |||||||||
−9.19339 | − | 25.7495i | −0.392008 | − | 1.09796i | |||||
6.21674 | 0.264842 | |||||||||
0 | 0 | |||||||||
1.26415 | 0.0537573 | |||||||||
−28.0775 | −1.19290 | |||||||||
0 | 0 | |||||||||
15.3257 | 0.649955 | |||||||||
3.19892 | 0.135543 | 0.0677714 | − | 0.997701i | ||||||
0.0677714 | + | 0.997701i | ||||||||
0 | 0 | |||||||||
6.32264 | 0.267419 | |||||||||
2.29468 | + | 1.61728i | 0.0969680 | + | 0.0683424i | |||||
0 | 0 | |||||||||
− | 20.9112i | − | 0.882087i | |||||||
−43.0080 | −1.81257 | −0.906285 | − | 0.422668i | ||||||
−0.906285 | + | 0.422668i | ||||||||
0 | 0 | |||||||||
−6.09024 | + | 8.64118i | −0.256218 | + | 0.363537i | |||||
−11.7273 | −0.492936 | |||||||||
0 | 0 | |||||||||
12.4170 | 0.521007 | |||||||||
− | 19.8692i | − | 0.832960i | −0.909145 | − | 0.416480i | ||||
0.909145 | − | 0.416480i | ||||||||
0 | 0 | |||||||||
−16.6100 | −0.695105 | −0.347553 | − | 0.937660i | ||||||
−0.347553 | + | 0.937660i | ||||||||
25.7495 | 1.07664 | |||||||||
0 | 0 | |||||||||
− | 5.60353i | − | 0.233887i | |||||||
3.22083 | + | 9.02113i | 0.134318 | + | 0.376207i | |||||
0 | 0 | |||||||||
−36.4851 | −1.51890 | −0.759448 | − | 0.650568i | ||||||
−0.759448 | + | 0.650568i | ||||||||
−15.5765 | −0.647898 | |||||||||
0 | 0 | |||||||||
−9.29991 | − | 6.55451i | −0.386158 | − | 0.272161i | |||||
0.947251 | 0.0392986 | |||||||||
0 | 0 | |||||||||
6.10649i | 0.252905i | |||||||||
− | 10.2834i | − | 0.425532i | |||||||
0 | 0 | |||||||||
− | 19.0944i | − | 0.788781i | |||||||
−14.3652 | −0.592917 | −0.296458 | − | 0.955046i | ||||||
−0.296458 | + | 0.955046i | ||||||||
0 | 0 | |||||||||
−4.19411 | −0.172815 | |||||||||
−16.4419 | − | 11.5881i | −0.676901 | − | 0.477075i | |||||
0 | 0 | |||||||||
−4.58473 | − | 3.99753i | −0.188431 | − | 0.164297i | |||||
19.6724i | 0.807850i | 0.914792 | + | 0.403925i | ||||||
−0.914792 | + | 0.403925i | ||||||||
0 | 0 | |||||||||
−2.73777 | − | 1.92956i | −0.112237 | − | 0.0791041i | |||||
−13.4684 | −0.551686 | |||||||||
0 | 0 | |||||||||
−9.02113 | −0.368901 | |||||||||
−32.9039 | −1.34442 | −0.672208 | − | 0.740362i | ||||||
−0.672208 | + | 0.740362i | ||||||||
0 | 0 | |||||||||
43.6508 | 1.78055 | 0.890276 | − | 0.455422i | ||||||
0.890276 | + | 0.455422i | ||||||||
− | 1.68574i | − | 0.0687057i | |||||||
0 | 0 | |||||||||
−10.3930 | −0.422883 | |||||||||
−24.3493 | + | 34.5482i | −0.989940 | + | 1.40458i | |||||
0 | 0 | |||||||||
15.4852 | 0.628523 | 0.314262 | − | 0.949336i | ||||||
0.314262 | + | 0.949336i | ||||||||
− | 1.22179i | − | 0.0495502i | |||||||
0 | 0 | |||||||||
11.3537 | + | 8.00200i | 0.459698 | + | 0.323992i | |||||
− | 8.96104i | − | 0.362525i | |||||||
0 | 0 | |||||||||
47.5322i | 1.91981i | 0.280329 | + | 0.959904i | ||||||
−0.280329 | + | 0.959904i | ||||||||
31.2854i | 1.26258i | |||||||||
0 | 0 | |||||||||
− | 6.86533i | − | 0.276612i | |||||||
31.3888i | 1.26367i | 0.775105 | + | 0.631833i | ||||||
−0.775105 | + | 0.631833i | ||||||||
0 | 0 | |||||||||
8.12905 | 0.326734 | 0.163367 | − | 0.986565i | ||||||
0.163367 | + | 0.986565i | ||||||||
6.27415 | + | 4.42198i | 0.251976 | + | 0.177591i | |||||
0 | 0 | |||||||||
7.52409i | 0.301688i | |||||||||
14.4058 | 0.577155 | |||||||||
0 | 0 | |||||||||
−19.3470 | + | 15.8333i | −0.773880 | + | 0.633332i | |||||
−0.0900227 | −0.00359803 | |||||||||
0 | 0 | |||||||||
14.2297i | 0.567827i | |||||||||
5.47000 | + | 4.76941i | 0.218103 | + | 0.190169i | |||||
0 | 0 | |||||||||
− | 37.9315i | − | 1.51003i | −0.655709 | − | 0.755014i | ||||
0.655709 | − | 0.755014i | ||||||||
1.00691i | 0.0400527i | |||||||||
0 | 0 | |||||||||
− | 7.86659i | − | 0.312422i | |||||||
−14.7145 | − | 10.3707i | −0.583926 | − | 0.411547i | |||||
0 | 0 | |||||||||
25.5399 | 1.01193 | |||||||||
27.8239i | 1.10156i | |||||||||
0 | 0 | |||||||||
−1.28817 | + | 1.82773i | −0.0509195 | + | 0.0722475i | |||||
36.9793 | 1.46059 | 0.730296 | − | 0.683130i | ||||||
0.730296 | + | 0.683130i | ||||||||
0 | 0 | |||||||||
−8.44944 | −0.333213 | −0.166607 | − | 0.986023i | ||||||
−0.166607 | + | 0.986023i | ||||||||
2.40521i | 0.0947786i | |||||||||
0 | 0 | |||||||||
1.45771i | 0.0573527i | |||||||||
−4.22924 | −0.166269 | −0.0831343 | − | 0.996538i | ||||||
−0.0831343 | + | 0.996538i | ||||||||
0 | 0 | |||||||||
49.1915i | 1.93093i | |||||||||
−7.91665 | − | 22.1735i | −0.310517 | − | 0.869716i | |||||
0 | 0 | |||||||||
0.455364 | 0.0178334 | |||||||||
−40.2219 | −1.57400 | −0.787002 | − | 0.616951i | ||||||
−0.787002 | + | 0.616951i | ||||||||
0 | 0 | |||||||||
−23.7604 | − | 16.7462i | −0.928397 | − | 0.654327i | |||||
4.46326 | 0.174261 | |||||||||
0 | 0 | |||||||||
−2.38919 | −0.0931404 | |||||||||
−20.4172 | −0.795341 | −0.397670 | − | 0.917528i | ||||||
−0.397670 | + | 0.917528i | ||||||||
0 | 0 | |||||||||
− | 49.8075i | − | 1.93729i | −0.248454 | − | 0.968644i | ||||
0.248454 | − | 0.968644i | ||||||||
21.5849i | 0.838919i | |||||||||
0 | 0 | |||||||||
0.754493i | 0.0292800i | |||||||||
1.97597 | − | 2.80362i | 0.0766250 | − | 0.108720i | |||||
0 | 0 | |||||||||
− | 9.74786i | − | 0.377439i | |||||||
−0.755752 | −0.0292409 | |||||||||
0 | 0 | |||||||||
−7.69690 | − | 5.42472i | −0.297357 | − | 0.209575i | |||||
− | 33.9685i | − | 1.31134i | |||||||
0 | 0 | |||||||||
30.7799i | 1.18648i | 0.805026 | + | 0.593239i | ||||||
−0.805026 | + | 0.593239i | ||||||||
24.3782i | 0.939013i | |||||||||
0 | 0 | |||||||||
9.17350 | 0.352827 | |||||||||
36.8784i | 1.41735i | 0.705533 | + | 0.708677i | ||||||
−0.705533 | + | 0.708677i | ||||||||
0 | 0 | |||||||||
− | 20.9431i | − | 0.803723i | |||||||
1.53691 | − | 2.18065i | 0.0589377 | − | 0.0836242i | |||||
0 | 0 | |||||||||
− | 18.7713i | − | 0.718789i | |||||||
−22.1763 | −0.848552 | −0.424276 | − | 0.905533i | ||||||
−0.424276 | + | 0.905533i | ||||||||
0 | 0 | |||||||||
24.7634 | + | 17.4531i | 0.946161 | + | 0.666848i | |||||
− | 15.5978i | − | 0.595527i | |||||||
0 | 0 | |||||||||
1.34271 | 0.0511902 | |||||||||
5.25844i | 0.200331i | |||||||||
0 | 0 | |||||||||
15.0935 | 0.574185 | 0.287093 | − | 0.957903i | ||||||
0.287093 | + | 0.957903i | ||||||||
− | 4.41375i | − | 0.167786i | |||||||
0 | 0 | |||||||||
−25.4950 | −0.967776 | |||||||||
−19.7422 | + | 28.0113i | −0.748864 | + | 1.06253i | |||||
0 | 0 | |||||||||
−5.32507 | −0.201701 | |||||||||
2.69761 | 0.102106 | |||||||||
0 | 0 | |||||||||
−5.91190 | + | 2.11074i | −0.223449 | + | 0.0797784i | |||||
− | 31.2390i | − | 1.17988i | −0.807447 | − | 0.589941i | ||||
0.807447 | − | 0.589941i | ||||||||
0 | 0 | |||||||||
−4.88414 | + | 5.60159i | −0.184209 | + | 0.211268i | |||||
5.46829 | 0.206094 | |||||||||
0 | 0 | |||||||||
21.7179 | 0.817362 | |||||||||
4.09555i | 0.154029i | |||||||||
0 | 0 | |||||||||
− | 23.2007i | − | 0.871322i | −0.900111 | − | 0.435661i | ||||
0.900111 | − | 0.435661i | ||||||||
−15.9953 | + | 22.6950i | −0.600293 | + | 0.851729i | |||||
0 | 0 | |||||||||
11.4743i | 0.430018i | |||||||||
6.57636i | 0.246287i | |||||||||
0 | 0 | |||||||||
−33.1698 | + | 47.0632i | −1.24048 | + | 1.76006i | |||||
− | 12.6883i | − | 0.474184i | |||||||
0 | 0 | |||||||||
20.3716 | 0.760260 | |||||||||
−41.3863 | −1.54345 | −0.771724 | − | 0.635958i | ||||||
−0.771724 | + | 0.635958i | ||||||||
0 | 0 | |||||||||
− | 6.52009i | − | 0.242821i | |||||||
17.5072 | 0.651552 | |||||||||
0 | 0 | |||||||||
13.2444 | 0.492223 | |||||||||
23.9598 | − | 8.55441i | 0.889844 | − | 0.317703i | |||||
0 | 0 | |||||||||
−8.02093 | −0.297480 | −0.148740 | − | 0.988876i | ||||||
−0.148740 | + | 0.988876i | ||||||||
− | 5.91190i | − | 0.219110i | |||||||
0 | 0 | |||||||||
18.7954 | + | 13.2469i | 0.695649 | + | 0.490288i | |||||
−1.60197 | −0.0592510 | |||||||||
0 | 0 | |||||||||
43.5044i | 1.60687i | 0.595391 | + | 0.803436i | ||||||
−0.595391 | + | 0.803436i | ||||||||
− | 31.0972i | − | 1.14782i | |||||||
0 | 0 | |||||||||
−1.91577 | −0.0706163 | |||||||||
23.0279i | 0.848244i | |||||||||
0 | 0 | |||||||||
−40.4960 | −1.48967 | −0.744834 | − | 0.667249i | ||||||
−0.744834 | + | 0.667249i | ||||||||
13.2123 | − | 3.23016i | 0.485695 | − | 0.118743i | |||||
0 | 0 | |||||||||
1.40201 | 0.0514692 | |||||||||
33.7617i | 1.23860i | 0.785156 | + | 0.619298i | ||||||
−0.785156 | + | 0.619298i | ||||||||
0 | 0 | |||||||||
17.3496 | − | 24.6166i | 0.635640 | − | 0.901882i | |||||
− | 33.4131i | − | 1.22334i | |||||||
0 | 0 | |||||||||
−6.52417 | −0.238547 | |||||||||
10.8718 | 0.397248 | |||||||||
0 | 0 | |||||||||
−16.9597 | −0.618867 | −0.309434 | − | 0.950921i | ||||||
−0.309434 | + | 0.950921i | ||||||||
− | 1.90301i | − | 0.0693956i | |||||||
0 | 0 | |||||||||
23.9598i | 0.872564i | |||||||||
13.3879 | − | 18.9956i | 0.487237 | − | 0.691319i | |||||
0 | 0 | |||||||||
10.2892 | 0.373969 | 0.186984 | − | 0.982363i | ||||||
0.186984 | + | 0.982363i | ||||||||
−24.6191 | −0.894204 | |||||||||
0 | 0 | |||||||||
2.23311 | + | 1.57388i | 0.0810034 | + | 0.0570906i | |||||
30.3977 | 1.10192 | 0.550959 | − | 0.834533i | ||||||
0.550959 | + | 0.834533i | ||||||||
0 | 0 | |||||||||
3.19741 | 0.115754 | |||||||||
7.03990i | 0.254695i | |||||||||
0 | 0 | |||||||||
−17.5596 | −0.634453 | |||||||||
42.3600i | 1.52953i | |||||||||
0 | 0 | |||||||||
46.4643i | 1.67554i | 0.546019 | + | 0.837772i | ||||||
−0.546019 | + | 0.837772i | ||||||||
12.5480 | + | 8.84373i | 0.452198 | + | 0.318706i | |||||
0 | 0 | |||||||||
−0.635749 | −0.0228811 | |||||||||
30.6420i | 1.10212i | 0.834467 | + | 0.551058i | ||||||
−0.834467 | + | 0.551058i | ||||||||
0 | 0 | |||||||||
−16.1644 | + | 5.77121i | −0.580642 | + | 0.207308i | |||||
16.6814 | 0.598826 | |||||||||
0 | 0 | |||||||||
19.6417i | 0.704190i | |||||||||
− | 5.45317i | − | 0.195380i | |||||||
0 | 0 | |||||||||
67.8999 | 2.42965 | |||||||||
2.28569 | 0.0817361 | |||||||||
0 | 0 | |||||||||
5.42377 | 0.193706 | |||||||||
−26.0081 | − | 18.3303i | −0.928270 | − | 0.654238i | |||||
0 | 0 | |||||||||
8.65409i | 0.308485i | 0.988033 | + | 0.154243i | ||||||
−0.988033 | + | 0.154243i | ||||||||
− | 5.18937i | − | 0.184864i | |||||||
0 | 0 | |||||||||
−1.84036 | − | 1.29707i | −0.0654772 | − | 0.0461478i | |||||
− | 5.93567i | − | 0.211048i | |||||||
0 | 0 | |||||||||
− | 29.2511i | − | 1.03874i | |||||||
− | 4.31480i | − | 0.153127i | |||||||
0 | 0 | |||||||||
23.8852i | 0.846589i | |||||||||
25.1436 | 0.890634 | 0.445317 | − | 0.895373i | ||||||
0.445317 | + | 0.895373i | ||||||||
0 | 0 | |||||||||
2.27046i | 0.0803232i | |||||||||
−1.68122 | − | 4.70887i | −0.0594401 | − | 0.166484i | |||||
0 | 0 | |||||||||
− | 9.64980i | − | 0.340746i | |||||||
− | 56.2328i | − | 1.98441i | |||||||
0 | 0 | |||||||||
−4.39609 | − | 3.09833i | −0.154942 | − | 0.109202i | |||||
− | 16.1644i | − | 0.569367i | |||||||
0 | 0 | |||||||||
−3.26214 | −0.114762 | |||||||||
− | 54.4206i | − | 1.91333i | −0.291199 | − | 0.956663i | ||||
0.291199 | − | 0.956663i | ||||||||
0 | 0 | |||||||||
32.8378 | 1.15309 | 0.576546 | − | 0.817065i | ||||||
0.576546 | + | 0.817065i | ||||||||
6.38816 | 0.224180 | |||||||||
0 | 0 | |||||||||
−25.0706 | − | 21.8596i | −0.878726 | − | 0.766180i | |||||
−0.586588 | + | 0.832284i | −0.0205473 | + | 0.0291536i | |||||
0 | 0 | |||||||||
− | 1.64051i | − | 0.0573941i | |||||||
− | 25.5235i | − | 0.892409i | |||||||
0 | 0 | |||||||||
−5.74945 | + | 8.15764i | −0.200779 | + | 0.284877i | |||||
−25.1041 | −0.876138 | −0.438069 | − | 0.898941i | ||||||
−0.438069 | + | 0.898941i | ||||||||
0 | 0 | |||||||||
11.1202i | 0.387627i | 0.981038 | + | 0.193814i | ||||||
−0.981038 | + | 0.193814i | ||||||||
5.19330 | 0.180917 | |||||||||
0 | 0 | |||||||||
11.2940 | 0.392969 | |||||||||
−7.01483 | −0.243930 | −0.121965 | − | 0.992534i | ||||||
−0.121965 | + | 0.992534i | ||||||||
0 | 0 | |||||||||
− | 12.5028i | − | 0.434240i | −0.976145 | − | 0.217120i | ||||
0.976145 | − | 0.217120i | ||||||||
−1.37901 | − | 0.971918i | −0.0478662 | − | 0.0337358i | |||||
0 | 0 | |||||||||
4.70887 | 0.163251 | |||||||||
−6.47105 | −0.224209 | |||||||||
0 | 0 | |||||||||
0.973540 | − | 1.38131i | 0.0336907 | − | 0.0478023i | |||||
− | 6.68111i | − | 0.231071i | |||||||
0 | 0 | |||||||||
22.0969 | 0.763324 | |||||||||
−44.6267 | −1.54069 | −0.770343 | − | 0.637630i | ||||||
−0.770343 | + | 0.637630i | ||||||||
0 | 0 | |||||||||
3.11004 | 0.107243 | |||||||||
− | 8.20101i | − | 0.282626i | |||||||
0 | 0 | |||||||||
−26.6260 | −0.916505 | |||||||||
−11.8171 | + | 16.7667i | −0.406519 | + | 0.576793i | |||||
0 | 0 | |||||||||
− | 23.7313i | − | 0.815418i | |||||||
1.11671i | 0.0383479i | |||||||||
0 | 0 | |||||||||
2.00585 | + | 5.61812i | 0.0688000 | + | 0.192700i | |||||
8.78330 | + | 7.65835i | 0.301088 | + | 0.262525i | |||||
0 | 0 | |||||||||
3.59757 | 0.123178 | 0.0615892 | − | 0.998102i | ||||||
0.0615892 | + | 0.998102i | ||||||||
−7.79891 | −0.266873 | |||||||||
0 | 0 | |||||||||
8.65950i | 0.295976i | |||||||||
−7.66263 | −0.261750 | −0.130875 | − | 0.991399i | ||||||
−0.130875 | + | 0.991399i | ||||||||
0 | 0 | |||||||||
− | 56.3900i | − | 1.92400i | −0.273046 | − | 0.962001i | ||||
0.273046 | − | 0.962001i | ||||||||
−1.72964 | + | 2.45411i | −0.0589802 | + | 0.0836844i | |||||
0 | 0 | |||||||||
− | 9.83076i | − | 0.334837i | |||||||
− | 12.7800i | − | 0.435037i | −0.976056 | − | 0.217518i | ||||
0.976056 | − | 0.217518i | ||||||||
0 | 0 | |||||||||
8.06716 | + | 5.68568i | 0.274292 | + | 0.193319i | |||||
1.61024i | 0.0547182i | |||||||||
0 | 0 | |||||||||
−4.30975 | −0.146282 | |||||||||
5.50607i | 0.186781i | |||||||||
0 | 0 | |||||||||
19.8299i | 0.671910i | |||||||||
2.54677i | 0.0862444i | |||||||||
0 | 0 | |||||||||
2.34067i | 0.0791744i | |||||||||
3.75768 | − | 13.5244i | 0.127033 | − | 0.457207i | |||||
0 | 0 | |||||||||
− | 40.4607i | − | 1.36626i | −0.730297 | − | 0.683130i | ||||
0.730297 | − | 0.683130i | ||||||||
32.2443i | 1.08819i | |||||||||
0 | 0 | |||||||||
−7.04410 | + | 9.99458i | −0.237457 | + | 0.336917i | |||||
48.2664 | 1.62614 | 0.813069 | − | 0.582168i | ||||||
0.813069 | + | 0.582168i | ||||||||
0 | 0 | |||||||||
−7.33442 | −0.246823 | −0.123411 | − | 0.992356i | ||||||
−0.123411 | + | 0.992356i | ||||||||
−5.61812 | −0.188958 | |||||||||
0 | 0 | |||||||||
− | 19.0730i | − | 0.640770i | |||||||
− | 28.5353i | − | 0.958120i | −0.877782 | − | 0.479060i | ||||
0.877782 | − | 0.479060i | ||||||||
0 | 0 | |||||||||
10.1075 | 0.338993 | |||||||||
−20.9720 | − | 14.7809i | −0.702983 | − | 0.495457i | |||||
0 | 0 | |||||||||
− | 20.0982i | − | 0.672938i | |||||||
−2.32508 | −0.0778059 | |||||||||
0 | 0 | |||||||||
23.1908 | + | 16.3447i | 0.775184 | + | 0.546344i | |||||
− | 1.25548i | − | 0.0419426i | |||||||
0 | 0 | |||||||||
− | 30.6914i | − | 1.02418i | |||||||
17.4666 | 0.582543 | |||||||||
0 | 0 | |||||||||
− | 1.33233i | − | 0.0443865i | |||||||
24.4064 | 0.812643 | |||||||||
0 | 0 | |||||||||
4.72781 | 0.157245 | |||||||||
−17.0610 | + | 24.2072i | −0.567128 | + | 0.804673i | |||||
0 | 0 | |||||||||
−31.6207 | −1.04995 | −0.524974 | − | 0.851118i | ||||||
−0.524974 | + | 0.851118i | ||||||||
−15.1621 | −0.503173 | |||||||||
0 | 0 | |||||||||
10.8054 | + | 7.61555i | 0.358195 | + | 0.252453i | |||||
2.67057i | 0.0884800i | 0.999021 | + | 0.0442400i | ||||||
−0.999021 | + | 0.0442400i | ||||||||
0 | 0 | |||||||||
4.12579i | 0.136544i | |||||||||
22.4560 | 0.742777 | |||||||||
0 | 0 | |||||||||
−2.54527 | −0.0840980 | |||||||||
16.3212 | 0.538972 | |||||||||
0 | 0 | |||||||||
40.0514i | 1.32117i | 0.750750 | + | 0.660587i | ||||||
−0.750750 | + | 0.660587i | ||||||||
2.46784 | − | 3.50152i | 0.0813624 | − | 0.115442i | |||||
0 | 0 | |||||||||
7.37800i | 0.242981i | |||||||||
58.4703 | 1.92457 | |||||||||
0 | 0 | |||||||||
−11.1159 | + | 28.3097i | −0.365489 | + | 0.930816i | |||||
−6.16145 | −0.202478 | |||||||||
0 | 0 | |||||||||
5.08822i | 0.167029i | |||||||||
−47.8279 | −1.56918 | −0.784592 | − | 0.620013i | ||||||
−0.784592 | + | 0.620013i | ||||||||
0 | 0 | |||||||||
− | 6.62671i | − | 0.217182i | |||||||
13.9212i | 0.456004i | |||||||||
0 | 0 | |||||||||
−5.37297 | −0.175809 | |||||||||
8.40426 | − | 11.9244i | 0.274849 | − | 0.389971i | |||||
0 | 0 | |||||||||
44.7707i | 1.46260i | 0.682058 | + | 0.731298i | ||||||
−0.682058 | + | 0.731298i | ||||||||
5.28704 | 0.172628 | |||||||||
0 | 0 | |||||||||
3.47820 | + | 2.45141i | 0.113446 | + | 0.0799561i | |||||
−38.1052 | −1.24219 | −0.621097 | − | 0.783734i | ||||||
−0.621097 | + | 0.783734i | ||||||||
0 | 0 | |||||||||
−8.55058 | −0.278445 | |||||||||
8.99577i | 0.292787i | |||||||||
0 | 0 | |||||||||
7.34231 | 0.238719 | |||||||||
−53.7661 | −1.74716 | −0.873582 | − | 0.486678i | ||||||
−0.873582 | + | 0.486678i | ||||||||
0 | 0 | |||||||||
− | 48.4234i | − | 1.57189i | |||||||
−5.75326 | + | 2.05410i | −0.186660 | + | 0.0666438i | |||||
0 | 0 | |||||||||
1.49790i | 0.0485473i | |||||||||
− | 12.7882i | − | 0.414252i | −0.978314 | − | 0.207126i | ||||
0.978314 | − | 0.207126i | ||||||||
0 | 0 | |||||||||
−12.8671 | − | 9.06861i | −0.416368 | − | 0.293453i | |||||
− | 28.8753i | − | 0.933895i | |||||||
0 | 0 | |||||||||
21.5810i | 0.697251i | |||||||||
−17.0101 | −0.549286 | |||||||||
0 | 0 | |||||||||
19.2162 | 0.619878 | |||||||||
−21.5889 | − | 18.8239i | −0.696055 | − | 0.606906i | |||||
0 | 0 | |||||||||
− | 6.84853i | − | 0.220576i | |||||||
0.818954 | − | 1.16198i | 0.0263631 | − | 0.0374054i | |||||
0 | 0 | |||||||||
−49.4979 | −1.59175 | −0.795873 | − | 0.605463i | ||||||
−0.795873 | + | 0.605463i | ||||||||
18.9022 | 0.607540 | |||||||||
0 | 0 | |||||||||
−21.4885 | + | 30.4891i | −0.689954 | + | 0.978946i | |||||
22.7751 | 0.730887 | 0.365444 | − | 0.930834i | ||||||
0.365444 | + | 0.930834i | ||||||||
0 | 0 | |||||||||
− | 19.2411i | − | 0.616843i | |||||||
−0.346315 | −0.0110967 | |||||||||
0 | 0 | |||||||||
− | 6.21190i | − | 0.198838i | |||||||
−7.08386 | −0.226633 | −0.113316 | − | 0.993559i | ||||||
−0.113316 | + | 0.993559i | ||||||||
0 | 0 | |||||||||
62.7449i | 2.00534i | |||||||||
−6.98676 | + | 9.91321i | −0.223184 | + | 0.316666i | |||||
0 | 0 | |||||||||
−10.6278 | −0.339146 | |||||||||
− | 50.8277i | − | 1.62115i | −0.585634 | − | 0.810576i | ||||
0.585634 | − | 0.810576i | ||||||||
0 | 0 | |||||||||
9.48478 | + | 6.68481i | 0.302210 | + | 0.212996i | |||||
− | 6.07071i | − | 0.193331i | |||||||
0 | 0 | |||||||||
− | 5.75326i | − | 0.183036i | |||||||
−2.57232 | −0.0817949 | |||||||||
0 | 0 | |||||||||
− | 42.8852i | − | 1.36229i | −0.732146 | − | 0.681147i | ||||
0.732146 | − | 0.681147i | ||||||||
− | 3.43275i | − | 0.108990i | |||||||
0 | 0 | |||||||||
− | 15.5893i | − | 0.494464i | |||||||
−43.6558 | − | 30.7683i | −1.38398 | − | 0.975421i | |||||
0 | 0 | |||||||||
6.15244 | 0.194850 | 0.0974248 | − | 0.995243i | ||||||
0.0974248 | + | 0.995243i | ||||||||
− | 12.0121i | − | 0.380237i | |||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3330.2.e.f.739.6 | 16 | ||
3.2 | odd | 2 | 1110.2.e.c.739.14 | yes | 16 | ||
5.4 | even | 2 | 3330.2.e.e.739.12 | 16 | |||
15.14 | odd | 2 | 1110.2.e.d.739.3 | yes | 16 | ||
37.36 | even | 2 | 3330.2.e.e.739.11 | 16 | |||
111.110 | odd | 2 | 1110.2.e.d.739.11 | yes | 16 | ||
185.184 | even | 2 | inner | 3330.2.e.f.739.5 | 16 | ||
555.554 | odd | 2 | 1110.2.e.c.739.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.e.c.739.6 | ✓ | 16 | 555.554 | odd | 2 | ||
1110.2.e.c.739.14 | yes | 16 | 3.2 | odd | 2 | ||
1110.2.e.d.739.3 | yes | 16 | 15.14 | odd | 2 | ||
1110.2.e.d.739.11 | yes | 16 | 111.110 | odd | 2 | ||
3330.2.e.e.739.11 | 16 | 37.36 | even | 2 | |||
3330.2.e.e.739.12 | 16 | 5.4 | even | 2 | |||
3330.2.e.f.739.5 | 16 | 185.184 | even | 2 | inner | ||
3330.2.e.f.739.6 | 16 | 1.1 | even | 1 | trivial |