Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [832,2,Mod(321,832)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(832, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("832.321");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 832.i (of order , degree , 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: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
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 416) |
Sato-Tate group: |
Embedding invariants
Embedding label | 705.1 | ||
Root | of defining polynomial | ||
Character | 832.705 | ||
Dual form | 832.2.i.k.321.1 |
-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 .
0 | 0 | |||||||||
−1.20711 | − | 2.09077i | −0.696923 | − | 1.20711i | −0.969528 | − | 0.244981i | ||
0.272605 | − | 0.962126i | ||||||||
0 | 0 | |||||||||
−2.82843 | −1.26491 | −0.632456 | − | 0.774597i | ||||||
−0.632456 | + | 0.774597i | ||||||||
0 | 0 | |||||||||
−2.20711 | + | 3.82282i | −0.834208 | + | 1.44489i | 0.0604657 | + | 0.998170i | ||
−0.894674 | + | 0.446720i | ||||||||
0 | 0 | |||||||||
−1.41421 | + | 2.44949i | −0.471405 | + | 0.816497i | |||||
0 | 0 | |||||||||
1.62132 | + | 2.80821i | 0.488846 | + | 0.846707i | 0.999918 | − | 0.0128314i | ||
−0.511071 | + | 0.859538i | ||||||||
0 | 0 | |||||||||
1.00000 | − | 3.46410i | 0.277350 | − | 0.960769i | |||||
0 | 0 | |||||||||
3.41421 | + | 5.91359i | 0.881546 | + | 1.52688i | |||||
0 | 0 | |||||||||
2.91421 | − | 5.04757i | 0.706801 | − | 1.22421i | −0.259237 | − | 0.965814i | ||
0.966038 | − | 0.258401i | ||||||||
0 | 0 | |||||||||
−0.621320 | + | 1.07616i | −0.142541 | + | 0.246888i | −0.928453 | − | 0.371451i | ||
0.785912 | + | 0.618338i | ||||||||
0 | 0 | |||||||||
10.6569 | 2.32552 | |||||||||
0 | 0 | |||||||||
−0.621320 | − | 1.07616i | −0.129554 | − | 0.224395i | 0.793950 | − | 0.607983i | ||
−0.923504 | + | 0.383589i | ||||||||
0 | 0 | |||||||||
3.00000 | 0.600000 | |||||||||
0 | 0 | |||||||||
−0.414214 | −0.0797154 | |||||||||
0 | 0 | |||||||||
4.32843 | + | 7.49706i | 0.803769 | + | 1.39217i | 0.917119 | + | 0.398613i | ||
−0.113350 | + | 0.993555i | ||||||||
0 | 0 | |||||||||
5.65685 | 1.01600 | 0.508001 | − | 0.861357i | ||||||
0.508001 | + | 0.861357i | ||||||||
0 | 0 | |||||||||
3.91421 | − | 6.77962i | 0.681377 | − | 1.18018i | |||||
0 | 0 | |||||||||
6.24264 | − | 10.8126i | 1.05520 | − | 1.82766i | |||||
0 | 0 | |||||||||
−3.74264 | − | 6.48244i | −0.615286 | − | 1.06571i | −0.990334 | − | 0.138702i | ||
0.375048 | − | 0.927005i | ||||||||
0 | 0 | |||||||||
−8.44975 | + | 2.09077i | −1.35304 | + | 0.334791i | |||||
0 | 0 | |||||||||
2.91421 | + | 5.04757i | 0.455124 | + | 0.788297i | 0.998695 | − | 0.0510654i | ||
−0.543572 | + | 0.839363i | ||||||||
0 | 0 | |||||||||
2.03553 | − | 3.52565i | 0.310416 | − | 0.537656i | −0.668036 | − | 0.744129i | ||
0.978452 | + | 0.206472i | ||||||||
0 | 0 | |||||||||
4.00000 | − | 6.92820i | 0.596285 | − | 1.03280i | |||||
0 | 0 | |||||||||
6.00000 | 0.875190 | 0.437595 | − | 0.899172i | ||||||
0.437595 | + | 0.899172i | ||||||||
0 | 0 | |||||||||
−6.24264 | − | 10.8126i | −0.891806 | − | 1.54465i | |||||
0 | 0 | |||||||||
−14.0711 | −1.97034 | |||||||||
0 | 0 | |||||||||
2.82843 | 0.388514 | 0.194257 | − | 0.980951i | ||||||
0.194257 | + | 0.980951i | ||||||||
0 | 0 | |||||||||
−4.58579 | − | 7.94282i | −0.618347 | − | 1.07101i | |||||
0 | 0 | |||||||||
3.00000 | 0.397360 | |||||||||
0 | 0 | |||||||||
−0.621320 | + | 1.07616i | −0.0808890 | + | 0.140104i | −0.903632 | − | 0.428310i | ||
0.822743 | + | 0.568414i | ||||||||
0 | 0 | |||||||||
3.50000 | − | 6.06218i | 0.448129 | − | 0.776182i | −0.550135 | − | 0.835076i | ||
0.998264 | + | 0.0588933i | ||||||||
0 | 0 | |||||||||
−6.24264 | − | 10.8126i | −0.786499 | − | 1.36226i | |||||
0 | 0 | |||||||||
−2.82843 | + | 9.79796i | −0.350823 | + | 1.21529i | |||||
0 | 0 | |||||||||
6.62132 | + | 11.4685i | 0.808923 | + | 1.40110i | 0.913610 | + | 0.406591i | ||
−0.104687 | + | 0.994505i | ||||||||
0 | 0 | |||||||||
−1.50000 | + | 2.59808i | −0.180579 | + | 0.312772i | |||||
0 | 0 | |||||||||
3.62132 | − | 6.27231i | 0.429772 | − | 0.744386i | −0.567081 | − | 0.823662i | ||
0.996853 | + | 0.0792756i | ||||||||
0 | 0 | |||||||||
12.4853 | 1.46129 | 0.730646 | − | 0.682757i | ||||||
0.730646 | + | 0.682757i | ||||||||
0 | 0 | |||||||||
−3.62132 | − | 6.27231i | −0.418154 | − | 0.724264i | |||||
0 | 0 | |||||||||
−14.3137 | −1.63120 | |||||||||
0 | 0 | |||||||||
−6.00000 | −0.675053 | −0.337526 | − | 0.941316i | ||||||
−0.337526 | + | 0.941316i | ||||||||
0 | 0 | |||||||||
4.74264 | + | 8.21449i | 0.526960 | + | 0.912722i | |||||
0 | 0 | |||||||||
−4.00000 | −0.439057 | −0.219529 | − | 0.975606i | ||||||
−0.219529 | + | 0.975606i | ||||||||
0 | 0 | |||||||||
−8.24264 | + | 14.2767i | −0.894040 | + | 1.54852i | |||||
0 | 0 | |||||||||
10.4497 | − | 18.0995i | 1.12033 | − | 1.94047i | |||||
0 | 0 | |||||||||
1.67157 | + | 2.89525i | 0.177186 | + | 0.306896i | 0.940916 | − | 0.338641i | ||
−0.763729 | + | 0.645537i | ||||||||
0 | 0 | |||||||||
11.0355 | + | 11.4685i | 1.15684 | + | 1.20222i | |||||
0 | 0 | |||||||||
−6.82843 | − | 11.8272i | −0.708075 | − | 1.22642i | |||||
0 | 0 | |||||||||
1.75736 | − | 3.04384i | 0.180301 | − | 0.312291i | |||||
0 | 0 | |||||||||
4.50000 | − | 7.79423i | 0.456906 | − | 0.791384i | −0.541890 | − | 0.840450i | ||
0.998796 | + | 0.0490655i | ||||||||
0 | 0 | |||||||||
−9.17157 | −0.921778 | |||||||||
0 | 0 | |||||||||
5.91421 | + | 10.2437i | 0.588486 | + | 1.01929i | 0.994431 | + | 0.105390i | ||
−0.405945 | + | 0.913898i | ||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
−30.1421 | −2.94157 | |||||||||
0 | 0 | |||||||||
9.62132 | + | 16.6646i | 0.930128 | + | 1.61103i | 0.783099 | + | 0.621897i | ||
0.147029 | + | 0.989132i | ||||||||
0 | 0 | |||||||||
8.48528 | 0.812743 | 0.406371 | − | 0.913708i | ||||||
0.406371 | + | 0.913708i | ||||||||
0 | 0 | |||||||||
−9.03553 | + | 15.6500i | −0.857615 | + | 1.48543i | |||||
0 | 0 | |||||||||
0.0857864 | − | 0.148586i | 0.00807011 | − | 0.0139778i | −0.861962 | − | 0.506973i | ||
0.870032 | + | 0.492995i | ||||||||
0 | 0 | |||||||||
1.75736 | + | 3.04384i | 0.163875 | + | 0.283839i | |||||
0 | 0 | |||||||||
7.07107 | + | 7.34847i | 0.653720 | + | 0.679366i | |||||
0 | 0 | |||||||||
12.8640 | + | 22.2810i | 1.17924 | + | 2.04250i | |||||
0 | 0 | |||||||||
0.242641 | − | 0.420266i | 0.0220582 | − | 0.0382060i | |||||
0 | 0 | |||||||||
7.03553 | − | 12.1859i | 0.634373 | − | 1.09877i | |||||
0 | 0 | |||||||||
5.65685 | 0.505964 | |||||||||
0 | 0 | |||||||||
−0.792893 | − | 1.37333i | −0.0703579 | − | 0.121863i | 0.828700 | − | 0.559693i | ||
−0.899058 | + | 0.437829i | ||||||||
0 | 0 | |||||||||
−9.82843 | −0.865345 | |||||||||
0 | 0 | |||||||||
4.00000 | 0.349482 | 0.174741 | − | 0.984614i | ||||||
0.174741 | + | 0.984614i | ||||||||
0 | 0 | |||||||||
−2.74264 | − | 4.75039i | −0.237817 | − | 0.411911i | |||||
0 | 0 | |||||||||
1.17157 | 0.100833 | |||||||||
0 | 0 | |||||||||
−4.67157 | + | 8.09140i | −0.399119 | + | 0.691295i | −0.993617 | − | 0.112802i | ||
0.594498 | + | 0.804097i | ||||||||
0 | 0 | |||||||||
−0.621320 | + | 1.07616i | −0.0526997 | + | 0.0912786i | −0.891172 | − | 0.453666i | ||
0.838472 | + | 0.544944i | ||||||||
0 | 0 | |||||||||
−7.24264 | − | 12.5446i | −0.609940 | − | 1.05645i | |||||
0 | 0 | |||||||||
11.3492 | − | 2.80821i | 0.949071 | − | 0.234834i | |||||
0 | 0 | |||||||||
−12.2426 | − | 21.2049i | −1.01670 | − | 1.76097i | |||||
0 | 0 | |||||||||
−15.0711 | + | 26.1039i | −1.24304 | + | 2.15301i | |||||
0 | 0 | |||||||||
−1.67157 | + | 2.89525i | −0.136941 | + | 0.237188i | −0.926337 | − | 0.376696i | ||
0.789397 | + | 0.613884i | ||||||||
0 | 0 | |||||||||
−16.9706 | −1.38104 | −0.690522 | − | 0.723311i | ||||||
−0.690522 | + | 0.723311i | ||||||||
0 | 0 | |||||||||
8.24264 | + | 14.2767i | 0.666378 | + | 1.15420i | |||||
0 | 0 | |||||||||
−16.0000 | −1.28515 | |||||||||
0 | 0 | |||||||||
0.485281 | 0.0387297 | 0.0193648 | − | 0.999812i | ||||||
0.0193648 | + | 0.999812i | ||||||||
0 | 0 | |||||||||
−3.41421 | − | 5.91359i | −0.270765 | − | 0.468978i | |||||
0 | 0 | |||||||||
5.48528 | 0.432301 | |||||||||
0 | 0 | |||||||||
8.37868 | − | 14.5123i | 0.656269 | − | 1.13669i | −0.325305 | − | 0.945609i | ||
0.981574 | − | 0.191082i | ||||||||
0 | 0 | |||||||||
−11.0711 | + | 19.1757i | −0.861881 | + | 1.49282i | |||||
0 | 0 | |||||||||
7.86396 | + | 13.6208i | 0.608532 | + | 1.05401i | 0.991483 | + | 0.130239i | ||
−0.382951 | + | 0.923769i | ||||||||
0 | 0 | |||||||||
−11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | |||||
0 | 0 | |||||||||
−1.75736 | − | 3.04384i | −0.134389 | − | 0.232768i | |||||
0 | 0 | |||||||||
−4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | ||
0.642699 | + | 0.766119i | ||||||||
0 | 0 | |||||||||
−6.62132 | + | 11.4685i | −0.500525 | + | 0.866934i | |||||
0 | 0 | |||||||||
3.00000 | 0.225494 | |||||||||
0 | 0 | |||||||||
−6.37868 | − | 11.0482i | −0.476765 | − | 0.825781i | 0.522881 | − | 0.852406i | ||
−0.999645 | + | 0.0266249i | ||||||||
0 | 0 | |||||||||
0.485281 | 0.0360707 | 0.0180353 | − | 0.999837i | ||||||
0.0180353 | + | 0.999837i | ||||||||
0 | 0 | |||||||||
−16.8995 | −1.24925 | |||||||||
0 | 0 | |||||||||
10.5858 | + | 18.3351i | 0.778282 | + | 1.34802i | |||||
0 | 0 | |||||||||
18.8995 | 1.38207 | |||||||||
0 | 0 | |||||||||
0.914214 | − | 1.58346i | 0.0664993 | − | 0.115180i | |||||
0 | 0 | |||||||||
−3.37868 | + | 5.85204i | −0.244473 | + | 0.423439i | −0.961983 | − | 0.273109i | ||
0.717511 | + | 0.696548i | ||||||||
0 | 0 | |||||||||
9.74264 | + | 16.8747i | 0.701291 | + | 1.21467i | 0.968014 | + | 0.250898i | ||
−0.266723 | + | 0.963773i | ||||||||
0 | 0 | |||||||||
23.8995 | − | 5.91359i | 1.71148 | − | 0.423481i | |||||
0 | 0 | |||||||||
1.50000 | + | 2.59808i | 0.106871 | + | 0.185105i | 0.914501 | − | 0.404584i | ||
−0.807630 | + | 0.589689i | ||||||||
0 | 0 | |||||||||
12.1066 | − | 20.9692i | 0.858214 | − | 1.48647i | −0.0154165 | − | 0.999881i | ||
0.873631 | − | 0.486590i | ||||||||
0 | 0 | |||||||||
15.9853 | − | 27.6873i | 1.12751 | − | 1.95291i | |||||
0 | 0 | |||||||||
−38.2132 | −2.68204 | |||||||||
0 | 0 | |||||||||
−8.24264 | − | 14.2767i | −0.575691 | − | 0.997126i | |||||
0 | 0 | |||||||||
3.51472 | 0.244290 | |||||||||
0 | 0 | |||||||||
−4.02944 | −0.278722 | |||||||||
0 | 0 | |||||||||
6.79289 | + | 11.7656i | 0.467642 | + | 0.809980i | 0.999316 | − | 0.0369691i | ||
−0.531674 | + | 0.846949i | ||||||||
0 | 0 | |||||||||
−17.4853 | −1.19807 | |||||||||
0 | 0 | |||||||||
−5.75736 | + | 9.97204i | −0.392649 | + | 0.680087i | |||||
0 | 0 | |||||||||
−12.4853 | + | 21.6251i | −0.847556 | + | 1.46801i | |||||
0 | 0 | |||||||||
−15.0711 | − | 26.1039i | −1.01841 | − | 1.76394i | |||||
0 | 0 | |||||||||
−14.5711 | − | 15.1427i | −0.980156 | − | 1.01861i | |||||
0 | 0 | |||||||||
−3.44975 | − | 5.97514i | −0.231012 | − | 0.400125i | 0.727094 | − | 0.686538i | ||
−0.958106 | + | 0.286413i | ||||||||
0 | 0 | |||||||||
−4.24264 | + | 7.34847i | −0.282843 | + | 0.489898i | |||||
0 | 0 | |||||||||
7.86396 | − | 13.6208i | 0.521949 | − | 0.904043i | −0.477725 | − | 0.878510i | ||
0.999674 | − | 0.0255332i | ||||||||
0 | 0 | |||||||||
−8.48528 | −0.560723 | −0.280362 | − | 0.959894i | ||||||
−0.280362 | + | 0.959894i | ||||||||
0 | 0 | |||||||||
17.2782 | + | 29.9267i | 1.13682 | + | 1.96903i | |||||
0 | 0 | |||||||||
−20.4853 | −1.34204 | −0.671018 | − | 0.741441i | ||||||
−0.671018 | + | 0.741441i | ||||||||
0 | 0 | |||||||||
−16.9706 | −1.10704 | |||||||||
0 | 0 | |||||||||
7.24264 | + | 12.5446i | 0.470460 | + | 0.814861i | |||||
0 | 0 | |||||||||
−8.97056 | −0.580257 | −0.290129 | − | 0.956988i | ||||||
−0.290129 | + | 0.956988i | ||||||||
0 | 0 | |||||||||
−15.2279 | + | 26.3755i | −0.980917 | + | 1.69900i | −0.322078 | + | 0.946713i | ||
−0.658838 | + | 0.752285i | ||||||||
0 | 0 | |||||||||
10.8284 | − | 18.7554i | 0.694644 | − | 1.20316i | |||||
0 | 0 | |||||||||
17.6569 | + | 30.5826i | 1.12806 | + | 1.95385i | |||||
0 | 0 | |||||||||
3.10660 | + | 3.22848i | 0.197668 | + | 0.205423i | |||||
0 | 0 | |||||||||
4.82843 | + | 8.36308i | 0.305989 | + | 0.529989i | |||||
0 | 0 | |||||||||
8.86396 | − | 15.3528i | 0.559488 | − | 0.969062i | −0.438051 | − | 0.898950i | ||
0.997539 | − | 0.0701119i | ||||||||
0 | 0 | |||||||||
2.01472 | − | 3.48960i | 0.126664 | − | 0.219389i | |||||
0 | 0 | |||||||||
39.7990 | 2.49231 | |||||||||
0 | 0 | |||||||||
−8.39949 | − | 14.5484i | −0.523946 | − | 0.907501i | −0.999611 | − | 0.0278749i | ||
0.475665 | − | 0.879626i | ||||||||
0 | 0 | |||||||||
33.0416 | 2.05311 | |||||||||
0 | 0 | |||||||||
−24.4853 | −1.51560 | |||||||||
0 | 0 | |||||||||
−4.62132 | − | 8.00436i | −0.284963 | − | 0.493570i | 0.687637 | − | 0.726054i | ||
−0.972600 | + | 0.232484i | ||||||||
0 | 0 | |||||||||
−8.00000 | −0.491436 | |||||||||
0 | 0 | |||||||||
4.03553 | − | 6.98975i | 0.246971 | − | 0.427766i | |||||
0 | 0 | |||||||||
2.74264 | − | 4.75039i | 0.167222 | − | 0.289637i | −0.770220 | − | 0.637778i | ||
0.937442 | + | 0.348141i | ||||||||
0 | 0 | |||||||||
−12.6213 | − | 21.8608i | −0.766691 | − | 1.32795i | −0.939348 | − | 0.342965i | ||
0.172658 | − | 0.984982i | ||||||||
0 | 0 | |||||||||
10.6569 | − | 36.9164i | 0.644982 | − | 2.23428i | |||||
0 | 0 | |||||||||
4.86396 | + | 8.42463i | 0.293308 | + | 0.508024i | |||||
0 | 0 | |||||||||
6.74264 | − | 11.6786i | 0.405126 | − | 0.701699i | −0.589210 | − | 0.807980i | ||
0.994336 | + | 0.106281i | ||||||||
0 | 0 | |||||||||
−8.00000 | + | 13.8564i | −0.478947 | + | 0.829561i | |||||
0 | 0 | |||||||||
−2.14214 | −0.127789 | −0.0638945 | − | 0.997957i | ||||||
−0.0638945 | + | 0.997957i | ||||||||
0 | 0 | |||||||||
−5.20711 | − | 9.01897i | −0.309530 | − | 0.536122i | 0.668729 | − | 0.743506i | ||
−0.978260 | + | 0.207384i | ||||||||
0 | 0 | |||||||||
−8.48528 | −0.502625 | |||||||||
0 | 0 | |||||||||
−25.7279 | −1.51867 | |||||||||
0 | 0 | |||||||||
−8.48528 | − | 14.6969i | −0.499134 | − | 0.864526i | |||||
0 | 0 | |||||||||
−21.7279 | −1.27371 | |||||||||
0 | 0 | |||||||||
1.15685 | − | 2.00373i | 0.0675841 | − | 0.117059i | −0.830253 | − | 0.557386i | ||
0.897837 | + | 0.440327i | ||||||||
0 | 0 | |||||||||
1.75736 | − | 3.04384i | 0.102317 | − | 0.177219i | |||||
0 | 0 | |||||||||
−0.671573 | − | 1.16320i | −0.0389686 | − | 0.0674956i | |||||
0 | 0 | |||||||||
−4.34924 | + | 1.07616i | −0.251523 | + | 0.0622358i | |||||
0 | 0 | |||||||||
8.98528 | + | 15.5630i | 0.517903 | + | 0.897034i | |||||
0 | 0 | |||||||||
14.2782 | − | 24.7305i | 0.820260 | − | 1.42073i | |||||
0 | 0 | |||||||||
−9.89949 | + | 17.1464i | −0.566843 | + | 0.981802i | |||||
0 | 0 | |||||||||
−12.0000 | −0.684876 | −0.342438 | − | 0.939540i | ||||||
−0.342438 | + | 0.939540i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
24.0000 | 1.36092 | 0.680458 | − | 0.732787i | ||||||
0.680458 | + | 0.732787i | ||||||||
0 | 0 | |||||||||
20.4853 | 1.15790 | 0.578948 | − | 0.815364i | ||||||
0.578948 | + | 0.815364i | ||||||||
0 | 0 | |||||||||
17.6569 | + | 30.5826i | 0.994851 | + | 1.72313i | |||||
0 | 0 | |||||||||
17.3137 | 0.972435 | 0.486217 | − | 0.873838i | ||||||
0.486217 | + | 0.873838i | ||||||||
0 | 0 | |||||||||
−14.0355 | + | 24.3103i | −0.785839 | + | 1.36111i | |||||
0 | 0 | |||||||||
23.2279 | − | 40.2319i | 1.29646 | − | 2.24553i | |||||
0 | 0 | |||||||||
3.62132 | + | 6.27231i | 0.201496 | + | 0.349001i | |||||
0 | 0 | |||||||||
3.00000 | − | 10.3923i | 0.166410 | − | 0.576461i | |||||
0 | 0 | |||||||||
−10.2426 | − | 17.7408i | −0.566419 | − | 0.981067i | |||||
0 | 0 | |||||||||
−13.2426 | + | 22.9369i | −0.730090 | + | 1.26455i | |||||
0 | 0 | |||||||||
−3.62132 | + | 6.27231i | −0.199046 | + | 0.344757i | −0.948219 | − | 0.317616i | ||
0.749174 | + | 0.662374i | ||||||||
0 | 0 | |||||||||
21.1716 | 1.16020 | |||||||||
0 | 0 | |||||||||
−18.7279 | − | 32.4377i | −1.02322 | − | 1.77226i | |||||
0 | 0 | |||||||||
4.48528 | 0.244329 | 0.122164 | − | 0.992510i | ||||||
0.122164 | + | 0.992510i | ||||||||
0 | 0 | |||||||||
−0.414214 | −0.0224970 | |||||||||
0 | 0 | |||||||||
9.17157 | + | 15.8856i | 0.496669 | + | 0.860255i | |||||
0 | 0 | |||||||||
24.2132 | 1.30739 | |||||||||
0 | 0 | |||||||||
4.24264 | − | 7.34847i | 0.228416 | − | 0.395628i | |||||
0 | 0 | |||||||||
−15.6213 | + | 27.0569i | −0.838596 | + | 1.45249i | 0.0524719 | + | 0.998622i | ||
−0.891068 | + | 0.453869i | ||||||||
0 | 0 | |||||||||
17.2279 | + | 29.8396i | 0.922190 | + | 1.59728i | 0.796020 | + | 0.605270i | ||
0.126170 | + | 0.992009i | ||||||||
0 | 0 | |||||||||
−0.414214 | + | 1.43488i | −0.0221091 | + | 0.0765881i | |||||
0 | 0 | |||||||||
7.32843 | + | 12.6932i | 0.390053 | + | 0.675591i | 0.992456 | − | 0.122601i | ||
−0.602403 | + | 0.798192i | ||||||||
0 | 0 | |||||||||
−10.2426 | + | 17.7408i | −0.543623 | + | 0.941583i | |||||
0 | 0 | |||||||||
31.0563 | − | 53.7912i | 1.64368 | − | 2.84693i | |||||
0 | 0 | |||||||||
−8.00000 | −0.422224 | −0.211112 | − | 0.977462i | ||||||
−0.211112 | + | 0.977462i | ||||||||
0 | 0 | |||||||||
8.72792 | + | 15.1172i | 0.459364 | + | 0.795642i | |||||
0 | 0 | |||||||||
−1.17157 | −0.0614916 | |||||||||
0 | 0 | |||||||||
−35.3137 | −1.84840 | |||||||||
0 | 0 | |||||||||
−4.13604 | − | 7.16383i | −0.215899 | − | 0.373949i | 0.737651 | − | 0.675182i | ||
−0.953550 | + | 0.301233i | ||||||||
0 | 0 | |||||||||
−16.4853 | −0.858189 | |||||||||
0 | 0 | |||||||||
−6.24264 | + | 10.8126i | −0.324102 | + | 0.561361i | |||||
0 | 0 | |||||||||
18.7426 | − | 32.4632i | 0.970457 | − | 1.68088i | 0.276280 | − | 0.961077i | ||
0.694178 | − | 0.719804i | ||||||||
0 | 0 | |||||||||
−6.82843 | − | 11.8272i | −0.352618 | − | 0.610753i | |||||
0 | 0 | |||||||||
30.2990 | − | 7.49706i | 1.56048 | − | 0.386118i | |||||
0 | 0 | |||||||||
−13.6924 | − | 23.7159i | −0.703331 | − | 1.21820i | −0.967291 | − | 0.253671i | ||
0.263960 | − | 0.964534i | ||||||||
0 | 0 | |||||||||
−1.91421 | + | 3.31552i | −0.0980681 | + | 0.169859i | |||||
0 | 0 | |||||||||
−7.86396 | + | 13.6208i | −0.401830 | + | 0.695989i | −0.993947 | − | 0.109863i | ||
0.592117 | + | 0.805852i | ||||||||
0 | 0 | |||||||||
40.4853 | 2.06332 | |||||||||
0 | 0 | |||||||||
5.75736 | + | 9.97204i | 0.292663 | + | 0.506907i | |||||
0 | 0 | |||||||||
16.6274 | 0.843044 | 0.421522 | − | 0.906818i | ||||||
0.421522 | + | 0.906818i | ||||||||
0 | 0 | |||||||||
−7.24264 | −0.366276 | |||||||||
0 | 0 | |||||||||
−4.82843 | − | 8.36308i | −0.243562 | − | 0.421862i | |||||
0 | 0 | |||||||||
16.9706 | 0.853882 | |||||||||
0 | 0 | |||||||||
−5.74264 | + | 9.94655i | −0.288215 | + | 0.499203i | −0.973384 | − | 0.229181i | ||
0.685169 | + | 0.728384i | ||||||||
0 | 0 | |||||||||
−6.62132 | + | 11.4685i | −0.331481 | + | 0.574141i | |||||
0 | 0 | |||||||||
−5.57107 | − | 9.64937i | −0.278206 | − | 0.481867i | 0.692733 | − | 0.721194i | ||
−0.970939 | + | 0.239327i | ||||||||
0 | 0 | |||||||||
5.65685 | − | 19.5959i | 0.281788 | − | 0.976142i | |||||
0 | 0 | |||||||||
−13.4142 | − | 23.2341i | −0.666558 | − | 1.15451i | |||||
0 | 0 | |||||||||
12.1360 | − | 21.0202i | 0.601561 | − | 1.04193i | |||||
0 | 0 | |||||||||
5.25736 | − | 9.10601i | 0.259960 | − | 0.450263i | −0.706271 | − | 0.707941i | ||
0.966231 | + | 0.257678i | ||||||||
0 | 0 | |||||||||
22.5563 | 1.11262 | |||||||||
0 | 0 | |||||||||
−2.74264 | − | 4.75039i | −0.134957 | − | 0.233752i | |||||
0 | 0 | |||||||||
11.3137 | 0.555368 | |||||||||
0 | 0 | |||||||||
3.00000 | 0.146911 | |||||||||
0 | 0 | |||||||||
−5.86396 | − | 10.1567i | −0.286473 | − | 0.496186i | 0.686492 | − | 0.727137i | ||
−0.972965 | + | 0.230951i | ||||||||
0 | 0 | |||||||||
−0.485281 | −0.0236512 | −0.0118256 | − | 0.999930i | ||||||
−0.0118256 | + | 0.999930i | ||||||||
0 | 0 | |||||||||
−8.48528 | + | 14.6969i | −0.412568 | + | 0.714590i | |||||
0 | 0 | |||||||||
8.74264 | − | 15.1427i | 0.424080 | − | 0.734529i | |||||
0 | 0 | |||||||||
15.4497 | + | 26.7597i | 0.747666 | + | 1.29499i | |||||
0 | 0 | |||||||||
−19.5711 | − | 20.3389i | −0.944900 | − | 0.981969i | |||||
0 | 0 | |||||||||
17.3492 | + | 30.0498i | 0.835684 | + | 1.44745i | 0.893473 | + | 0.449118i | ||
−0.0577890 | + | 0.998329i | ||||||||
0 | 0 | |||||||||
1.25736 | − | 2.17781i | 0.0604248 | − | 0.104659i | −0.834231 | − | 0.551416i | ||
0.894655 | + | 0.446757i | ||||||||
0 | 0 | |||||||||
−29.5563 | + | 51.1931i | −1.41712 | + | 2.45452i | |||||
0 | 0 | |||||||||
1.54416 | 0.0738670 | |||||||||
0 | 0 | |||||||||
14.0355 | + | 24.3103i | 0.669879 | + | 1.16027i | 0.977937 | + | 0.208898i | ||
−0.308058 | + | 0.951368i | ||||||||
0 | 0 | |||||||||
35.3137 | 1.68161 | |||||||||
0 | 0 | |||||||||
28.9706 | 1.37643 | 0.688216 | − | 0.725505i | ||||||
0.688216 | + | 0.725505i | ||||||||
0 | 0 | |||||||||
−4.72792 | − | 8.18900i | −0.224125 | − | 0.388196i | |||||
0 | 0 | |||||||||
8.07107 | 0.381748 | |||||||||
0 | 0 | |||||||||
−6.25736 | + | 10.8381i | −0.295303 | + | 0.511480i | −0.975055 | − | 0.221962i | ||
0.679752 | + | 0.733442i | ||||||||
0 | 0 | |||||||||
−9.44975 | + | 16.3674i | −0.444971 | + | 0.770713i | |||||
0 | 0 | |||||||||
20.4853 | + | 35.4815i | 0.962482 | + | 1.66707i | |||||
0 | 0 | |||||||||
−31.2132 | − | 32.4377i | −1.46330 | − | 1.52070i | |||||
0 | 0 | |||||||||
−15.5000 | − | 26.8468i | −0.725059 | − | 1.25584i | −0.958950 | − | 0.283577i | ||
0.233890 | − | 0.972263i | ||||||||
0 | 0 | |||||||||
−1.20711 | + | 2.09077i | −0.0563429 | + | 0.0975888i | |||||
0 | 0 | |||||||||
0.600505 | − | 1.04011i | 0.0279683 | − | 0.0484425i | −0.851702 | − | 0.524026i | ||
0.879671 | + | 0.475583i | ||||||||
0 | 0 | |||||||||
18.3431 | 0.852478 | 0.426239 | − | 0.904611i | ||||||
0.426239 | + | 0.904611i | ||||||||
0 | 0 | |||||||||
19.3137 | + | 33.4523i | 0.895652 | + | 1.55131i | |||||
0 | 0 | |||||||||
−6.97056 | −0.322559 | −0.161280 | − | 0.986909i | ||||||
−0.161280 | + | 0.986909i | ||||||||
0 | 0 | |||||||||
−58.4558 | −2.69924 | |||||||||
0 | 0 | |||||||||
−0.585786 | − | 1.01461i | −0.0269916 | − | 0.0467508i | |||||
0 | 0 | |||||||||
13.2010 | 0.606983 | |||||||||
0 | 0 | |||||||||
−1.86396 | + | 3.22848i | −0.0855244 | + | 0.148133i | |||||
0 | 0 | |||||||||
−4.00000 | + | 6.92820i | −0.183147 | + | 0.317221i | |||||
0 | 0 | |||||||||
4.37868 | + | 7.58410i | 0.200067 | + | 0.346526i | 0.948550 | − | 0.316628i | ||
−0.748483 | + | 0.663154i | ||||||||
0 | 0 | |||||||||
−26.1985 | + | 6.48244i | −1.19455 | + | 0.295574i | |||||
0 | 0 | |||||||||
−6.62132 | − | 11.4685i | −0.301281 | − | 0.521833i | |||||
0 | 0 | |||||||||
−12.7279 | + | 22.0454i | −0.577945 | + | 1.00103i | |||||
0 | 0 | |||||||||
6.44975 | − | 11.1713i | 0.292266 | − | 0.506219i | −0.682079 | − | 0.731278i | ||
0.974345 | + | 0.225059i | ||||||||
0 | 0 | |||||||||
−40.4558 | −1.82948 | |||||||||
0 | 0 | |||||||||
11.1066 | + | 19.2372i | 0.501234 | + | 0.868163i | 0.999999 | + | 0.00142539i | ||
−0.498765 | + | 0.866737i | ||||||||
0 | 0 | |||||||||
50.4558 | 2.27242 | |||||||||
0 | 0 | |||||||||
25.9411 | 1.16597 | |||||||||
0 | 0 | |||||||||
15.9853 | + | 27.6873i | 0.717038 | + | 1.24195i | |||||
0 | 0 | |||||||||
17.6569 | 0.790429 | 0.395215 | − | 0.918589i | ||||||
0.395215 | + | 0.918589i | ||||||||
0 | 0 | |||||||||
18.9853 | − | 32.8835i | 0.848200 | − | 1.46913i | |||||
0 | 0 | |||||||||
−7.37868 | + | 12.7802i | −0.328999 | + | 0.569843i | −0.982314 | − | 0.187244i | ||
0.653314 | + | 0.757087i | ||||||||
0 | 0 | |||||||||
−16.7279 | − | 28.9736i | −0.744383 | − | 1.28931i | |||||
0 | 0 | |||||||||
−1.20711 | + | 31.3616i | −0.0536095 | + | 1.39282i | |||||
0 | 0 | |||||||||
−2.57107 | − | 4.45322i | −0.113961 | − | 0.197386i | 0.803403 | − | 0.595435i | ||
−0.917364 | + | 0.398050i | ||||||||
0 | 0 | |||||||||
−27.5563 | + | 47.7290i | −1.21902 | + | 2.11141i | |||||
0 | 0 | |||||||||
0.257359 | − | 0.445759i | 0.0113627 | − | 0.0196808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.72792 | + | 16.8493i | 0.427834 | + | 0.741029i | |||||
0 | 0 | |||||||||
21.7279 | 0.953750 | |||||||||
0 | 0 | |||||||||
−9.17157 | −0.401814 | −0.200907 | − | 0.979610i | ||||||
−0.200907 | + | 0.979610i | ||||||||
0 | 0 | |||||||||
−8.20711 | − | 14.2151i | −0.358872 | − | 0.621584i | 0.628901 | − | 0.777485i | ||
−0.987773 | + | 0.155901i | ||||||||
0 | 0 | |||||||||
31.9706 | 1.39531 | |||||||||
0 | 0 | |||||||||
16.4853 | − | 28.5533i | 0.718110 | − | 1.24380i | |||||
0 | 0 | |||||||||
10.7279 | − | 18.5813i | 0.466431 | − | 0.807883i | |||||
0 | 0 | |||||||||
−1.75736 | − | 3.04384i | −0.0762629 | − | 0.132091i | |||||
0 | 0 | |||||||||
20.3995 | − | 5.04757i | 0.883600 | − | 0.218634i | |||||
0 | 0 | |||||||||
−27.2132 | − | 47.1347i | −1.17653 | − | 2.03781i | |||||
0 | 0 | |||||||||
−15.3995 | + | 26.6727i | −0.664537 | + | 1.15101i | |||||
0 | 0 | |||||||||
20.2426 | − | 35.0613i | 0.871912 | − | 1.51020i | |||||
0 | 0 | |||||||||
2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | ||||||
0.0429934 | + | 0.999075i | ||||||||
0 | 0 | |||||||||
−0.585786 | − | 1.01461i | −0.0251385 | − | 0.0435412i | |||||
0 | 0 | |||||||||
−24.0000 | −1.02805 | |||||||||
0 | 0 | |||||||||
−36.0000 | −1.53925 | −0.769624 | − | 0.638497i | ||||||
−0.769624 | + | 0.638497i | ||||||||
0 | 0 | |||||||||
9.89949 | + | 17.1464i | 0.422500 | + | 0.731792i | |||||
0 | 0 | |||||||||
−10.7574 | −0.458279 | |||||||||
0 | 0 | |||||||||
13.2426 | − | 22.9369i | 0.563134 | − | 0.975377i | |||||
0 | 0 | |||||||||
25.5563 | − | 44.2649i | 1.08481 | − | 1.87894i | |||||
0 | 0 | |||||||||
4.32843 | + | 7.49706i | 0.183401 | + | 0.317660i | 0.943037 | − | 0.332689i | ||
−0.759635 | + | 0.650349i | ||||||||
0 | 0 | |||||||||
−10.1777 | − | 10.5769i | −0.430470 | − | 0.447357i | |||||
0 | 0 | |||||||||
−22.8137 | − | 39.5145i | −0.963196 | − | 1.66830i | |||||
0 | 0 | |||||||||
16.3492 | − | 28.3177i | 0.689038 | − | 1.19345i | −0.283111 | − | 0.959087i | ||
0.972149 | − | 0.234362i | ||||||||
0 | 0 | |||||||||
−0.242641 | + | 0.420266i | −0.0102080 | + | 0.0176807i | |||||
0 | 0 | |||||||||
−41.8701 | −1.75838 | |||||||||
0 | 0 | |||||||||
12.9853 | + | 22.4912i | 0.544371 | + | 0.942879i | 0.998646 | + | 0.0520172i | ||
−0.454275 | + | 0.890862i | ||||||||
0 | 0 | |||||||||
−40.2843 | −1.68584 | −0.842922 | − | 0.538036i | ||||||
−0.842922 | + | 0.538036i | ||||||||
0 | 0 | |||||||||
16.3137 | 0.681515 | |||||||||
0 | 0 | |||||||||
−1.86396 | − | 3.22848i | −0.0777325 | − | 0.134637i | |||||
0 | 0 | |||||||||
4.48528 | 0.186725 | 0.0933624 | − | 0.995632i | ||||||
0.0933624 | + | 0.995632i | ||||||||
0 | 0 | |||||||||
23.5208 | − | 40.7392i | 0.977492 | − | 1.69307i | |||||
0 | 0 | |||||||||
8.82843 | − | 15.2913i | 0.366265 | − | 0.634389i | |||||
0 | 0 | |||||||||
4.58579 | + | 7.94282i | 0.189924 | + | 0.328958i | |||||
0 | 0 | |||||||||
−20.0000 | − | 20.7846i | −0.826898 | − | 0.859338i | |||||
0 | 0 | |||||||||
−10.3492 | − | 17.9254i | −0.427159 | − | 0.739861i | 0.569460 | − | 0.822019i | ||
−0.996619 | + | 0.0821578i | ||||||||
0 | 0 | |||||||||
−3.51472 | + | 6.08767i | −0.144821 | + | 0.250838i | |||||
0 | 0 | |||||||||
3.62132 | − | 6.27231i | 0.148961 | − | 0.258008i | |||||
0 | 0 | |||||||||
14.8284 | 0.608931 | 0.304465 | − | 0.952523i | ||||||
0.304465 | + | 0.952523i | ||||||||
0 | 0 | |||||||||
−36.3848 | − | 63.0203i | −1.49163 | − | 2.58358i | |||||
0 | 0 | |||||||||
−58.4558 | −2.39244 | |||||||||
0 | 0 | |||||||||
47.9411 | 1.95882 | 0.979411 | − | 0.201878i | ||||||
0.979411 | + | 0.201878i | ||||||||
0 | 0 | |||||||||
5.25736 | + | 9.10601i | 0.214452 | + | 0.371442i | 0.953103 | − | 0.302646i | ||
−0.738651 | + | 0.674088i | ||||||||
0 | 0 | |||||||||
−37.4558 | −1.52532 | |||||||||
0 | 0 | |||||||||
−0.686292 | + | 1.18869i | −0.0279017 | + | 0.0483272i | |||||
0 | 0 | |||||||||
0.792893 | − | 1.37333i | 0.0321825 | − | 0.0557418i | −0.849486 | − | 0.527612i | ||
0.881668 | + | 0.471870i | ||||||||
0 | 0 | |||||||||
46.1274 | + | 79.8950i | 1.86918 | + | 3.23751i | |||||
0 | 0 | |||||||||
6.00000 | − | 20.7846i | 0.242734 | − | 0.840855i | |||||
0 | 0 | |||||||||
−7.25736 | − | 12.5701i | −0.293122 | − | 0.507702i | 0.681424 | − | 0.731889i | ||
−0.974546 | + | 0.224186i | ||||||||
0 | 0 | |||||||||
−19.8995 | + | 34.4669i | −0.802425 | + | 1.38984i | |||||
0 | 0 | |||||||||
22.1569 | − | 38.3768i | 0.892001 | − | 1.54499i | 0.0545289 | − | 0.998512i | ||
0.837472 | − | 0.546479i | ||||||||
0 | 0 | |||||||||
4.97056 | 0.199784 | 0.0998919 | − | 0.994998i | ||||||
0.0998919 | + | 0.994998i | ||||||||
0 | 0 | |||||||||
0.257359 | + | 0.445759i | 0.0103275 | + | 0.0178877i | |||||
0 | 0 | |||||||||
−14.7574 | −0.591241 | |||||||||
0 | 0 | |||||||||
−31.0000 | −1.24000 | |||||||||
0 | 0 | |||||||||
4.86396 | + | 8.42463i | 0.194248 | + | 0.336447i | |||||
0 | 0 | |||||||||
−43.6274 | −1.73954 | |||||||||
0 | 0 | |||||||||
3.62132 | − | 6.27231i | 0.144162 | − | 0.249697i | −0.784898 | − | 0.619625i | ||
0.929060 | + | 0.369929i | ||||||||
0 | 0 | |||||||||
16.3995 | − | 28.4048i | 0.651821 | − | 1.12899i | |||||
0 | 0 | |||||||||
2.24264 | + | 3.88437i | 0.0889965 | + | 0.154146i | |||||
0 | 0 | |||||||||
−43.6985 | + | 10.8126i | −1.73140 | + | 0.428410i | |||||
0 | 0 | |||||||||
10.2426 | + | 17.7408i | 0.405193 | + | 0.701814i | |||||
0 | 0 | |||||||||
11.3995 | − | 19.7445i | 0.450253 | − | 0.779861i | −0.548148 | − | 0.836381i | ||
0.998401 | + | 0.0565200i | ||||||||
0 | 0 | |||||||||
−0.106602 | + | 0.184640i | −0.00420396 | + | 0.00728147i | −0.868120 | − | 0.496355i | ||
0.863916 | + | 0.503636i | ||||||||
0 | 0 | |||||||||
27.7990 | 1.09458 | |||||||||
0 | 0 | |||||||||
−11.6213 | − | 20.1287i | −0.456881 | − | 0.791342i | 0.541913 | − | 0.840435i | ||
−0.998794 | + | 0.0490931i | ||||||||
0 | 0 | |||||||||
−4.02944 | −0.158169 | |||||||||
0 | 0 | |||||||||
60.2843 | 2.36273 | |||||||||
0 | 0 | |||||||||
11.5711 | + | 20.0417i | 0.452811 | + | 0.784291i | 0.998559 | − | 0.0536576i | ||
−0.545749 | + | 0.837949i | ||||||||
0 | 0 | |||||||||
−11.3137 | −0.442063 | |||||||||
0 | 0 | |||||||||
−17.6569 | + | 30.5826i | −0.688859 | + | 1.19314i | |||||
0 | 0 | |||||||||
−12.1066 | + | 20.9692i | −0.471606 | + | 0.816846i | −0.999472 | − | 0.0324816i | ||
0.527866 | + | 0.849328i | ||||||||
0 | 0 | |||||||||
−12.2279 | − | 21.1794i | −0.475611 | − | 0.823782i | 0.523999 | − | 0.851719i | ||
−0.999610 | + | 0.0279366i | ||||||||
0 | 0 | |||||||||
−14.0711 | + | 48.7436i | −0.546475 | + | 1.89304i | |||||
0 | 0 | |||||||||
7.75736 | + | 13.4361i | 0.300817 | + | 0.521031i | |||||
0 | 0 | |||||||||
5.37868 | − | 9.31615i | 0.208263 | − | 0.360723i | |||||
0 | 0 | |||||||||
−8.32843 | + | 14.4253i | −0.321996 | + | 0.557713i | |||||
0 | 0 | |||||||||
22.6985 | 0.876265 | |||||||||
0 | 0 | |||||||||
4.01472 | + | 6.95370i | 0.154756 | + | 0.268045i | 0.932970 | − | 0.359954i | ||
−0.778214 | + | 0.627999i | ||||||||
0 | 0 | |||||||||
−1.24264 | −0.0478293 | |||||||||
0 | 0 | |||||||||
25.4558 | 0.978348 | 0.489174 | − | 0.872186i | ||||||
0.489174 | + | 0.872186i | ||||||||
0 | 0 | |||||||||
19.8640 | + | 34.4054i | 0.762309 | + | 1.32036i | |||||
0 | 0 | |||||||||
−37.9706 | −1.45504 | |||||||||
0 | 0 | |||||||||
−4.62132 | + | 8.00436i | −0.176830 | + | 0.306278i | −0.940793 | − | 0.338982i | ||
0.763963 | + | 0.645260i | ||||||||
0 | 0 | |||||||||
13.2132 | − | 22.8859i | 0.504851 | − | 0.874427i | |||||
0 | 0 | |||||||||
10.2426 | + | 17.7408i | 0.390781 | + | 0.676853i | |||||
0 | 0 | |||||||||
2.82843 | − | 9.79796i | 0.107754 | − | 0.373273i | |||||
0 | 0 | |||||||||
−8.03553 | − | 13.9180i | −0.305686 | − | 0.529464i | 0.671728 | − | 0.740798i | ||
−0.977414 | + | 0.211334i | ||||||||
0 | 0 | |||||||||
20.2426 | − | 35.0613i | 0.768954 | − | 1.33187i | |||||
0 | 0 | |||||||||
1.75736 | − | 3.04384i | 0.0666604 | − | 0.115459i | |||||
0 | 0 | |||||||||
33.9706 | 1.28673 | |||||||||
0 | 0 | |||||||||
24.7279 | + | 42.8300i | 0.935296 | + | 1.61998i | |||||
0 | 0 | |||||||||
8.48528 | 0.320485 | 0.160242 | − | 0.987078i | ||||||
0.160242 | + | 0.987078i | ||||||||
0 | 0 | |||||||||
9.30152 | 0.350813 | |||||||||
0 | 0 | |||||||||
20.4853 | + | 35.4815i | 0.771520 | + | 1.33631i | |||||
0 | 0 | |||||||||
−52.2132 | −1.96368 | |||||||||
0 | 0 | |||||||||
−9.74264 | + | 16.8747i | −0.365893 | + | 0.633744i | −0.988919 | − | 0.148456i | ||
0.623026 | + | 0.782201i | ||||||||
0 | 0 | |||||||||
8.48528 | − | 14.6969i | 0.318223 | − | 0.551178i | |||||
0 | 0 | |||||||||
−3.51472 | − | 6.08767i | −0.131627 | − | 0.227985i | |||||
0 | 0 | |||||||||
−32.1005 | + | 7.94282i | −1.20049 | + | 0.297044i | |||||
0 | 0 | |||||||||
10.8284 | + | 18.7554i | 0.404395 | + | 0.700433i | |||||
0 | 0 | |||||||||
−11.3787 | + | 19.7085i | −0.424353 | + | 0.735001i | −0.996360 | − | 0.0852478i | ||
0.572007 | + | 0.820249i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
73.5269 | 2.73450 | |||||||||
0 | 0 | |||||||||
12.9853 | + | 22.4912i | 0.482261 | + | 0.835301i | |||||
0 | 0 | |||||||||
−35.3137 | −1.30971 | −0.654856 | − | 0.755753i | ||||||
−0.654856 | + | 0.755753i | ||||||||
0 | 0 | |||||||||
−23.8284 | −0.882534 | |||||||||
0 | 0 | |||||||||
−11.8640 | − | 20.5490i | −0.438804 | − | 0.760032i | |||||
0 | 0 | |||||||||
−43.9411 | −1.62300 | −0.811501 | − | 0.584351i | ||||||
−0.811501 | + | 0.584351i | ||||||||
0 | 0 | |||||||||
42.6274 | − | 73.8329i | 1.57234 | − | 2.72337i | |||||
0 | 0 | |||||||||
−21.4706 | + | 37.1881i | −0.790878 | + | 1.36984i | |||||
0 | 0 | |||||||||
15.1066 | + | 26.1654i | 0.555705 | + | 0.962510i | 0.997848 | + | 0.0655653i | ||
−0.442143 | + | 0.896945i | ||||||||
0 | 0 | |||||||||
3.00000 | − | 10.3923i | 0.110208 | − | 0.381771i | |||||
0 | 0 | |||||||||
−3.62132 | − | 6.27231i | −0.132853 | − | 0.230109i | 0.791922 | − | 0.610622i | ||
−0.924775 | + | 0.380513i | ||||||||
0 | 0 | |||||||||
4.72792 | − | 8.18900i | 0.173218 | − | 0.300022i | |||||
0 | 0 | |||||||||
5.65685 | − | 9.79796i | 0.206973 | − | 0.358489i | |||||
0 | 0 | |||||||||
−84.9411 | −3.10368 | |||||||||
0 | 0 | |||||||||
8.55025 | + | 14.8095i | 0.312003 | + | 0.540405i | 0.978796 | − | 0.204838i | ||
−0.666793 | + | 0.745243i | ||||||||
0 | 0 | |||||||||
−42.7990 | −1.55968 | |||||||||
0 | 0 | |||||||||
48.0000 | 1.74690 | |||||||||
0 | 0 | |||||||||
−11.7426 | − | 20.3389i | −0.426794 | − | 0.739228i | 0.569793 | − | 0.821789i | ||
−0.996586 | + | 0.0825605i | ||||||||
0 | 0 | |||||||||
−9.72792 | −0.353101 | |||||||||
0 | 0 | |||||||||
−14.7426 | + | 25.5350i | −0.534420 | + | 0.925643i | 0.464771 | + | 0.885431i | ||
−0.999191 | + | 0.0402121i | ||||||||
0 | 0 | |||||||||
−18.7279 | + | 32.4377i | −0.677996 | + | 1.17432i | |||||
0 | 0 | |||||||||
−23.3137 | − | 40.3805i | −0.842909 | − | 1.45996i | |||||
0 | 0 | |||||||||
3.10660 | + | 3.22848i | 0.112173 | + | 0.116573i | |||||
0 | 0 | |||||||||
22.7132 | + | 39.3404i | 0.819059 | + | 1.41865i | 0.906376 | + | 0.422471i | ||
−0.0873172 | + | 0.996181i | ||||||||
0 | 0 | |||||||||
−20.2782 | + | 35.1228i | −0.730301 | + | 1.26492i | |||||
0 | 0 | |||||||||
−5.74264 | + | 9.94655i | −0.206548 | + | 0.357752i | −0.950625 | − | 0.310342i | ||
0.744077 | + | 0.668094i | ||||||||
0 | 0 | |||||||||
16.9706 | 0.609601 | |||||||||
0 | 0 | |||||||||
−39.8848 | − | 69.0825i | −1.43086 | − | 2.47832i | |||||
0 | 0 | |||||||||
−7.24264 | −0.259495 | |||||||||
0 | 0 | |||||||||
23.4853 | 0.840369 | |||||||||
0 | 0 | |||||||||
−1.79289 | − | 3.10538i | −0.0640728 | − | 0.110977i | |||||
0 | 0 | |||||||||
−1.37258 | −0.0489896 | |||||||||
0 | 0 | |||||||||
19.0061 | − | 32.9195i | 0.677494 | − | 1.17345i | −0.298239 | − | 0.954491i | ||
0.975733 | − | 0.218963i | ||||||||
0 | 0 | |||||||||
−11.1569 | + | 19.3242i | −0.397195 | + | 0.687961i | |||||
0 | 0 | |||||||||
0.378680 | + | 0.655892i | 0.0134643 | + | 0.0233208i | |||||
0 | 0 | |||||||||
−17.5000 | − | 18.1865i | −0.621443 | − | 0.645823i | |||||
0 | 0 | |||||||||
9.65685 | + | 16.7262i | 0.342493 | + | 0.593216i | |||||
0 | 0 | |||||||||
−16.5000 | + | 28.5788i | −0.584460 | + | 1.01231i | 0.410483 | + | 0.911868i | ||
−0.994943 | + | 0.100446i | ||||||||
0 | 0 | |||||||||
17.4853 | − | 30.2854i | 0.618585 | − | 1.07142i | |||||
0 | 0 | |||||||||
−9.45584 | −0.334106 | |||||||||
0 | 0 | |||||||||
20.2426 | + | 35.0613i | 0.714347 | + | 1.23729i | |||||
0 | 0 | |||||||||
−15.5147 | −0.546822 | |||||||||
0 | 0 | |||||||||
−13.2426 | −0.466163 | |||||||||
0 | 0 | |||||||||
2.91421 | + | 5.04757i | 0.102458 | + | 0.177463i | 0.912697 | − | 0.408637i | ||
−0.810239 | + | 0.586100i | ||||||||
0 | 0 | |||||||||
12.3431 | 0.433426 | 0.216713 | − | 0.976235i | ||||||
0.216713 | + | 0.976235i | ||||||||
0 | 0 | |||||||||
−30.4706 | + | 52.7766i | −1.06865 | + | 1.85095i | |||||
0 | 0 | |||||||||
−23.6985 | + | 41.0470i | −0.830122 | + | 1.43781i | |||||
0 | 0 | |||||||||
2.52944 | + | 4.38111i | 0.0884938 | + | 0.153276i | |||||
0 | 0 | |||||||||
−43.6985 | + | 10.8126i | −1.52695 | + | 0.377822i | |||||
0 | 0 | |||||||||
9.98528 | + | 17.2950i | 0.348489 | + | 0.603600i | 0.985981 | − | 0.166856i | ||
−0.637492 | + | 0.770457i | ||||||||
0 | 0 | |||||||||
0.106602 | − | 0.184640i | 0.00371590 | − | 0.00643613i | −0.864161 | − | 0.503215i | ||
0.867877 | + | 0.496778i | ||||||||
0 | 0 | |||||||||
11.7426 | − | 20.3389i | 0.408826 | − | 0.708108i | |||||
0 | 0 | |||||||||
−21.9411 | −0.762968 | −0.381484 | − | 0.924376i | ||||||
−0.381484 | + | 0.924376i | ||||||||
0 | 0 | |||||||||
17.9853 | + | 31.1514i | 0.624655 | + | 1.08193i | 0.988608 | + | 0.150516i | ||
−0.363953 | + | 0.931417i | ||||||||
0 | 0 | |||||||||
−32.5563 | −1.12937 | |||||||||
0 | 0 | |||||||||
−72.7696 | −2.52132 | |||||||||
0 | 0 | |||||||||
−22.2426 | − | 38.5254i | −0.769738 | − | 1.33323i | |||||
0 | 0 | |||||||||
−2.34315 | −0.0809910 | |||||||||
0 | 0 | |||||||||
−5.34924 | + | 9.26516i | −0.184676 | + | 0.319869i | −0.943467 | − | 0.331465i | ||
0.758791 | + | 0.651334i | ||||||||
0 | 0 | |||||||||
−22.9706 | + | 39.7862i | −0.792088 | + | 1.37194i | |||||
0 | 0 | |||||||||
2.58579 | + | 4.47871i | 0.0890592 | + | 0.154255i | |||||
0 | 0 | |||||||||
31.1127 | + | 19.5959i | 1.07031 | + | 0.674120i | |||||
0 | 0 | |||||||||
1.07107 | + | 1.85514i | 0.0368023 | + | 0.0637435i | |||||
0 | 0 | |||||||||
−12.5711 | + | 21.7737i | −0.431438 | + | 0.747272i | |||||
0 | 0 | |||||||||
−4.65076 | + | 8.05535i | −0.159426 | + | 0.276134i | |||||
0 | 0 | |||||||||
41.4558 | 1.41942 | 0.709711 | − | 0.704493i | ||||||
0.709711 | + | 0.704493i | ||||||||
0 | 0 | |||||||||
4.97056 | + | 8.60927i | 0.169990 | + | 0.294431i | |||||
0 | 0 | |||||||||
33.1716 | 1.13312 | 0.566560 | − | 0.824021i | ||||||
0.566560 | + | 0.824021i | ||||||||
0 | 0 | |||||||||
−36.0000 | −1.22830 | −0.614152 | − | 0.789188i | ||||||
−0.614152 | + | 0.789188i | ||||||||
0 | 0 | |||||||||
31.0563 | + | 53.7912i | 1.05840 | + | 1.83320i | |||||
0 | 0 | |||||||||
−32.0000 | −1.08929 | −0.544646 | − | 0.838666i | ||||||
−0.544646 | + | 0.838666i | ||||||||
0 | 0 | |||||||||
12.7279 | − | 22.0454i | 0.432762 | − | 0.749566i | |||||
0 | 0 | |||||||||
−20.4853 | + | 35.4815i | −0.695717 | + | 1.20502i | |||||
0 | 0 | |||||||||
−9.72792 | − | 16.8493i | −0.329997 | − | 0.571572i | |||||
0 | 0 | |||||||||
46.3492 | − | 11.4685i | 1.57048 | − | 0.388594i | |||||
0 | 0 | |||||||||
12.7279 | + | 22.0454i | 0.430775 | + | 0.746124i | |||||
0 | 0 | |||||||||
−12.4853 | + | 21.6251i | −0.422080 | + | 0.731063i | |||||
0 | 0 | |||||||||
11.9853 | − | 20.7591i | 0.404714 | − | 0.700986i | −0.589574 | − | 0.807714i | ||
0.994288 | + | 0.106729i | ||||||||
0 | 0 | |||||||||
−5.58579 | −0.188404 | |||||||||
0 | 0 | |||||||||
−9.08579 | − | 15.7370i | −0.306108 | − | 0.530194i | 0.671399 | − | 0.741096i | ||
−0.977507 | + | 0.210901i | ||||||||
0 | 0 | |||||||||
27.5980 | 0.928746 | 0.464373 | − | 0.885640i | ||||||
0.464373 | + | 0.885640i | ||||||||
0 | 0 | |||||||||
−8.48528 | −0.285230 | |||||||||
0 | 0 | |||||||||
−12.1066 | − | 20.9692i | −0.406500 | − | 0.704078i | 0.587995 | − | 0.808865i | ||
−0.994495 | + | 0.104786i | ||||||||
0 | 0 | |||||||||
7.00000 | 0.234772 | |||||||||
0 | 0 | |||||||||
−15.3787 | + | 26.6367i | −0.515205 | + | 0.892362i | |||||
0 | 0 | |||||||||
−3.72792 | + | 6.45695i | −0.124750 | + | 0.216074i | |||||
0 | 0 | |||||||||
18.0416 | + | 31.2490i | 0.603065 | + | 1.04454i | |||||
0 | 0 | |||||||||
7.50000 | + | 7.79423i | 0.250418 | + | 0.260242i | |||||
0 | 0 | |||||||||
24.4853 | + | 42.4098i | 0.816630 | + | 1.41444i | |||||
0 | 0 | |||||||||
8.24264 | − | 14.2767i | 0.274602 | − | 0.475625i | |||||
0 | 0 | |||||||||
21.6924 | − | 37.5723i | 0.721877 | − | 1.25033i | |||||
0 | 0 | |||||||||
−1.37258 | −0.0456262 | |||||||||
0 | 0 | |||||||||
18.1066 | + | 31.3616i | 0.601220 | + | 1.04134i | 0.992637 | + | 0.121130i | ||
−0.391417 | + | 0.920213i | ||||||||
0 | 0 | |||||||||
−33.4558 | −1.10966 | |||||||||
0 | 0 | |||||||||
24.0000 | 0.795155 | 0.397578 | − | 0.917568i | ||||||
0.397578 | + | 0.917568i | ||||||||
0 | 0 | |||||||||
−6.48528 | − | 11.2328i | −0.214631 | − | 0.371753i | |||||
0 | 0 | |||||||||
47.7990 | 1.58019 | |||||||||
0 | 0 | |||||||||
−8.82843 | + | 15.2913i | −0.291540 | + | 0.504963i | |||||
0 | 0 | |||||||||
−19.1777 | + | 33.2167i | −0.632613 | + | 1.09572i | 0.354403 | + | 0.935093i | ||
−0.987016 | + | 0.160625i | ||||||||
0 | 0 | |||||||||
14.4853 | + | 25.0892i | 0.477306 | + | 0.826719i | |||||
0 | 0 | |||||||||
−18.1066 | − | 18.8169i | −0.595986 | − | 0.619367i | |||||
0 | 0 | |||||||||
−11.2279 | − | 19.4473i | −0.369172 | − | 0.639424i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.05635 | − | 8.75785i | 0.165893 | − | 0.287336i | −0.771079 | − | 0.636740i | ||
0.936972 | + | 0.349404i | ||||||||
0 | 0 | |||||||||
15.5147 | 0.508474 | |||||||||
0 | 0 | |||||||||
−28.9706 | − | 50.1785i | −0.948454 | − | 1.64277i | |||||
0 | 0 | |||||||||
−53.4558 | −1.74819 | |||||||||
0 | 0 | |||||||||
−45.4558 | −1.48498 | −0.742489 | − | 0.669858i | ||||||
−0.742489 | + | 0.669858i | ||||||||
0 | 0 | |||||||||
−24.7279 | − | 42.8300i | −0.806965 | − | 1.39770i | |||||
0 | 0 | |||||||||
18.0000 | 0.586783 | 0.293392 | − | 0.955992i | ||||||
0.293392 | + | 0.955992i | ||||||||
0 | 0 | |||||||||
3.62132 | − | 6.27231i | 0.117926 | − | 0.204255i | |||||
0 | 0 | |||||||||
−2.58579 | + | 4.47871i | −0.0841156 | + | 0.145693i | |||||
0 | 0 | |||||||||
1.62132 | + | 2.80821i | 0.0526858 | + | 0.0912545i | 0.891166 | − | 0.453678i | ||
−0.838480 | + | 0.544933i | ||||||||
0 | 0 | |||||||||
12.4853 | − | 43.2503i | 0.405289 | − | 1.40396i | |||||
0 | 0 | |||||||||
−20.8995 | − | 36.1990i | −0.677713 | − | 1.17383i | |||||
0 | 0 | |||||||||
1.67157 | − | 2.89525i | 0.0541476 | − | 0.0937863i | −0.837681 | − | 0.546160i | ||
0.891829 | + | 0.452373i | ||||||||
0 | 0 | |||||||||
9.55635 | − | 16.5521i | 0.309236 | − | 0.535613i | |||||
0 | 0 | |||||||||
67.7696 | 2.19068 | |||||||||
0 | 0 | |||||||||
−20.6213 | − | 35.7172i | −0.665897 | − | 1.15337i | |||||
0 | 0 | |||||||||
1.00000 | 0.0322581 | |||||||||
0 | 0 | |||||||||
−54.4264 | −1.75387 | |||||||||
0 | 0 | |||||||||
−27.5563 | − | 47.7290i | −0.887070 | − | 1.53645i | |||||
0 | 0 | |||||||||
7.02944 | 0.226051 | 0.113026 | − | 0.993592i | ||||||
0.113026 | + | 0.993592i | ||||||||
0 | 0 | |||||||||
8.74264 | − | 15.1427i | 0.280854 | − | 0.486454i | |||||
0 | 0 | |||||||||
16.3787 | − | 28.3687i | 0.525617 | − | 0.910395i | −0.473938 | − | 0.880558i | ||
0.999555 | − | 0.0298368i | ||||||||
0 | 0 | |||||||||
−2.74264 | − | 4.75039i | −0.0879250 | − | 0.152291i | |||||
0 | 0 | |||||||||
−25.3492 | + | 6.27231i | −0.811825 | + | 0.200875i | |||||
0 | 0 | |||||||||
−21.6421 | − | 37.4853i | −0.692393 | − | 1.19926i | −0.971052 | − | 0.238870i | ||
0.278658 | − | 0.960390i | ||||||||
0 | 0 | |||||||||
−5.42031 | + | 9.38825i | −0.173234 | + | 0.300050i | |||||
0 | 0 | |||||||||
−12.0000 | + | 20.7846i | −0.383131 | + | 0.663602i | |||||
0 | 0 | |||||||||
0.970563 | 0.0309561 | 0.0154781 | − | 0.999880i | ||||||
0.0154781 | + | 0.999880i | ||||||||
0 | 0 | |||||||||
−4.24264 | − | 7.34847i | −0.135182 | − | 0.234142i | |||||
0 | 0 | |||||||||
63.9411 | 2.03527 | |||||||||
0 | 0 | |||||||||
−5.05887 | −0.160863 | |||||||||
0 | 0 | |||||||||
−29.0772 | − | 50.3631i | −0.923667 | − | 1.59984i | −0.793692 | − | 0.608320i | ||
−0.129975 | − | 0.991517i | ||||||||
0 | 0 | |||||||||
17.4853 | 0.554879 | |||||||||
0 | 0 | |||||||||
−34.2426 | + | 59.3100i | −1.08556 | + | 1.88025i | |||||
0 | 0 | |||||||||
−17.4706 | + | 30.2599i | −0.553298 | + | 0.958341i | 0.444735 | + | 0.895662i | ||
−0.998034 | + | 0.0626788i | ||||||||
0 | 0 | |||||||||
1.55025 | + | 2.68512i | 0.0490478 | + | 0.0849533i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 832.2.i.k.705.1 | 4 | ||
4.3 | odd | 2 | 832.2.i.p.705.2 | 4 | |||
8.3 | odd | 2 | 416.2.i.c.289.1 | ✓ | 4 | ||
8.5 | even | 2 | 416.2.i.f.289.2 | yes | 4 | ||
13.9 | even | 3 | inner | 832.2.i.k.321.1 | 4 | ||
52.35 | odd | 6 | 832.2.i.p.321.2 | 4 | |||
104.3 | odd | 6 | 5408.2.a.be.1.2 | 2 | |||
104.29 | even | 6 | 5408.2.a.o.1.1 | 2 | |||
104.35 | odd | 6 | 416.2.i.c.321.1 | yes | 4 | ||
104.61 | even | 6 | 416.2.i.f.321.2 | yes | 4 | ||
104.75 | odd | 6 | 5408.2.a.bf.1.2 | 2 | |||
104.101 | even | 6 | 5408.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
416.2.i.c.289.1 | ✓ | 4 | 8.3 | odd | 2 | ||
416.2.i.c.321.1 | yes | 4 | 104.35 | odd | 6 | ||
416.2.i.f.289.2 | yes | 4 | 8.5 | even | 2 | ||
416.2.i.f.321.2 | yes | 4 | 104.61 | even | 6 | ||
832.2.i.k.321.1 | 4 | 13.9 | even | 3 | inner | ||
832.2.i.k.705.1 | 4 | 1.1 | even | 1 | trivial | ||
832.2.i.p.321.2 | 4 | 52.35 | odd | 6 | |||
832.2.i.p.705.2 | 4 | 4.3 | odd | 2 | |||
5408.2.a.n.1.1 | 2 | 104.101 | even | 6 | |||
5408.2.a.o.1.1 | 2 | 104.29 | even | 6 | |||
5408.2.a.be.1.2 | 2 | 104.3 | odd | 6 | |||
5408.2.a.bf.1.2 | 2 | 104.75 | odd | 6 |