Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1156,1,Mod(47,1156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1156, base_ring=CyclotomicField(68))
chi = DirichletCharacter(H, H._module([34, 25]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1156.47");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1156.o (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: | yes |
Projective image: | |
Projective field: | Galois closure of |
Embedding invariants
Embedding label | 191.1 | ||
Root | of defining polynomial | ||
Character | 1156.191 | ||
Dual form | 1156.1.o.a.115.1 |
-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 .
−0.673696 | − | 0.739009i | −0.673696 | − | 0.739009i | |||||
0 | 0 | −0.486604 | − | 0.873622i | ||||||
0.486604 | + | 0.873622i | ||||||||
−0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | |||||
0.273663 | + | 1.96183i | 0.273663 | + | 1.96183i | 0.273663 | + | 0.961826i | ||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | −0.228951 | − | 0.973438i | ||||||
0.228951 | + | 0.973438i | ||||||||
0.798017 | − | 0.602635i | 0.798017 | − | 0.602635i | |||||
−0.526432 | + | 0.850217i | −0.526432 | + | 0.850217i | |||||
1.26544 | − | 1.52391i | 1.26544 | − | 1.52391i | |||||
0 | 0 | 0.769334 | − | 0.638847i | ||||||
−0.769334 | + | 0.638847i | ||||||||
0 | 0 | |||||||||
−0.634493 | − | 0.840204i | −0.634493 | − | 0.840204i | 0.361242 | − | 0.932472i | ||
−0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.982973 | − | 0.183750i | −0.982973 | − | 0.183750i | |||||
0.982973 | + | 0.183750i | 0.982973 | + | 0.183750i | |||||
0.982973 | − | 0.183750i | 0.982973 | − | 0.183750i | |||||
0 | 0 | 0.673696 | − | 0.739009i | ||||||
−0.673696 | + | 0.739009i | ||||||||
−1.97871 | + | 0.0914812i | −1.97871 | + | 0.0914812i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.228951 | − | 0.973438i | ||||||
0.228951 | + | 0.973438i | ||||||||
0 | 0 | |||||||||
−2.81204 | + | 0.800095i | −2.81204 | + | 0.800095i | |||||
−0.193463 | + | 1.03494i | −0.193463 | + | 1.03494i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.292529 | + | 0.352279i | 0.292529 | + | 0.352279i | 0.895163 | − | 0.445738i | ||
−0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.990410 | − | 0.138156i | ||||||
0.990410 | + | 0.138156i | ||||||||
0.526432 | + | 0.850217i | 0.526432 | + | 0.850217i | |||||
0 | 0 | |||||||||
−0.526432 | − | 0.850217i | −0.526432 | − | 0.850217i | |||||
0 | 0 | |||||||||
−0.798017 | − | 0.602635i | −0.798017 | − | 0.602635i | |||||
−0.806980 | + | 1.82764i | −0.806980 | + | 1.82764i | −0.361242 | + | 0.932472i | ||
−0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.40065 | + | 1.40065i | 1.40065 | + | 1.40065i | |||||
−0.241393 | + | 0.134455i | −0.241393 | + | 0.134455i | −0.602635 | − | 0.798017i | ||
0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.183750 | − | 0.982973i | ||||||
0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
−1.81204 | − | 0.800095i | −1.81204 | − | 0.800095i | |||||
0 | 0 | |||||||||
0 | 0 | 0.850217 | − | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
−0.895163 | + | 0.445738i | −0.895163 | + | 0.445738i | |||||
2.48574 | + | 1.53910i | 2.48574 | + | 1.53910i | |||||
0 | 0 | |||||||||
0.895163 | − | 0.554262i | 0.895163 | − | 0.554262i | |||||
0.942485 | − | 1.52217i | 0.942485 | − | 1.52217i | 0.0922684 | − | 0.995734i | ||
0.850217 | − | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0632619 | − | 0.453510i | 0.0632619 | − | 0.453510i | |||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
−0.555259 | + | 1.65667i | −0.555259 | + | 1.65667i | 0.183750 | + | 0.982973i | ||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | |||||
1.47470 | − | 1.47470i | 1.47470 | − | 1.47470i | |||||
0 | 0 | |||||||||
0 | 0 | −0.739009 | − | 0.673696i | ||||||
0.739009 | + | 0.673696i | ||||||||
−0.273663 | + | 0.961826i | −0.273663 | + | 0.961826i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.973438 | − | 0.228951i | ||||||
−0.973438 | + | 0.228951i | ||||||||
0.0922684 | + | 0.995734i | 0.0922684 | + | 0.995734i | |||||
1.60617 | − | 1.10025i | 1.60617 | − | 1.10025i | 0.673696 | − | 0.739009i | ||
0.932472 | − | 0.361242i | ||||||||
1.89430 | − | 0.634905i | 1.89430 | − | 0.634905i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.0461835 | − | 0.998933i | ||||||
0.0461835 | + | 0.998933i | ||||||||
0.0914812 | − | 1.97871i | 0.0914812 | − | 1.97871i | |||||
−0.445738 | − | 0.895163i | −0.445738 | − | 0.895163i | |||||
0.261989 | + | 0.0878098i | 0.261989 | + | 0.0878098i | |||||
0 | 0 | 0.961826 | − | 0.273663i | ||||||
−0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
−0.0914812 | + | 1.97871i | −0.0914812 | + | 1.97871i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.811985 | − | 1.07524i | 0.811985 | − | 1.07524i | −0.183750 | − | 0.982973i | ||
0.995734 | − | 0.0922684i | ||||||||
0.629488 | + | 1.87814i | 0.629488 | + | 1.87814i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.49780 | − | 0.352279i | 1.49780 | − | 0.352279i | 0.602635 | − | 0.798017i | ||
0.895163 | + | 0.445738i | ||||||||
0.932472 | + | 0.361242i | 0.932472 | + | 0.361242i | |||||
0 | 0 | |||||||||
−0.537220 | − | 2.87387i | −0.537220 | − | 2.87387i | |||||
0.163808 | + | 0.328972i | 0.163808 | + | 0.328972i | 0.961826 | − | 0.273663i | ||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.445738 | − | 0.895163i | ||||||
−0.445738 | + | 0.895163i | ||||||||
−1.01267 | − | 0.288130i | −1.01267 | − | 0.288130i | |||||
0 | 0 | |||||||||
−1.75984 | + | 0.328972i | −1.75984 | + | 0.328972i | |||||
0 | 0 | 0.998933 | − | 0.0461835i | ||||||
−0.998933 | + | 0.0461835i | ||||||||
0 | 0 | |||||||||
−0.0449462 | + | 0.0806938i | −0.0449462 | + | 0.0806938i | −0.895163 | − | 0.445738i | ||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.23549 | − | 0.688163i | 1.23549 | − | 0.688163i | 0.273663 | − | 0.961826i | ||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.377767 | + | 0.258777i | −0.377767 | + | 0.258777i | |||||
1.04837 | − | 0.0971461i | 1.04837 | − | 0.0971461i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.183750 | − | 0.982973i | 0.183750 | − | 0.982973i | |||||
1.59837 | − | 0.705749i | 1.59837 | − | 0.705749i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.53910 | − | 3.48574i | −1.53910 | − | 3.48574i | |||||
0 | 0 | |||||||||
0 | 0 | 0.361242 | − | 0.932472i | ||||||
−0.361242 | + | 0.932472i | ||||||||
−0.895163 | + | 0.445738i | −0.895163 | + | 0.445738i | |||||
0 | 0 | |||||||||
−2.08331 | − | 0.0963172i | −2.08331 | − | 0.0963172i | |||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.895163 | − | 0.445738i | 0.895163 | − | 0.445738i | |||||
−0.147263 | + | 1.58923i | −0.147263 | + | 1.58923i | 0.526432 | + | 0.850217i | ||
−0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.0461835 | − | 0.998933i | ||||||
−0.0461835 | + | 0.998933i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.673696 | − | 0.739009i | 0.673696 | − | 0.739009i | |||||
−0.611055 | + | 0.670296i | −0.611055 | + | 0.670296i | |||||
−1.89516 | − | 0.445738i | −1.89516 | − | 0.445738i | |||||
0 | 0 | |||||||||
−1.74538 | − | 0.972171i | −1.74538 | − | 0.972171i | |||||
0.465346 | + | 1.63552i | 0.465346 | + | 1.63552i | 0.739009 | + | 0.673696i | ||
−0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.995734 | − | 0.0922684i | ||||||
0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
−0.673696 | + | 0.739009i | −0.673696 | + | 0.739009i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.537235 | + | 1.07891i | −0.537235 | + | 1.07891i | 0.445738 | + | 0.895163i | ||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.52391 | + | 1.26544i | −1.52391 | + | 1.26544i | |||||
0 | 0 | |||||||||
−0.361242 | + | 0.932472i | −0.361242 | + | 0.932472i | |||||
0 | 0 | −0.403921 | − | 0.914794i | ||||||
0.403921 | + | 0.914794i | ||||||||
−0.111609 | − | 0.252769i | −0.111609 | − | 0.252769i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.914794 | − | 0.403921i | ||||||
−0.914794 | + | 0.403921i | ||||||||
0 | 0 | |||||||||
−0.0296988 | + | 0.104380i | −0.0296988 | + | 0.104380i | |||||
1.52391 | − | 1.26544i | 1.52391 | − | 1.26544i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.524354 | − | 0.359191i | 0.524354 | − | 0.359191i | −0.273663 | − | 0.961826i | ||
0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.34164 | + | 0.124322i | −1.34164 | + | 0.124322i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0.963876 | − | 1.73049i | 0.963876 | − | 1.73049i | |||||
−0.134455 | + | 0.963876i | −0.134455 | + | 0.963876i | 0.798017 | + | 0.602635i | ||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.80634 | − | 1.08300i | −3.80634 | − | 1.08300i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.932472 | − | 0.361242i | ||||||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0.922758 | − | 1.65667i | 0.922758 | − | 1.65667i | 0.183750 | − | 0.982973i | ||
0.739009 | − | 0.673696i | ||||||||
−1.26940 | − | 0.869557i | −1.26940 | − | 0.869557i | |||||
0 | 0 | |||||||||
−0.361242 | − | 0.932472i | −0.361242 | − | 0.932472i | |||||
1.11943 | − | 0.156154i | 1.11943 | − | 0.156154i | 0.445738 | − | 0.895163i | ||
0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.317791 | − | 0.948161i | ||||||
0.317791 | + | 0.948161i | ||||||||
−1.76189 | + | 2.33312i | −1.76189 | + | 2.33312i | |||||
0 | 0 | |||||||||
0.132756 | − | 0.342683i | 0.132756 | − | 0.342683i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.329838 | − | 0.436776i | −0.329838 | − | 0.436776i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.469302 | + | 0.942485i | 0.469302 | + | 0.942485i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.948161 | − | 0.317791i | ||||||
−0.948161 | + | 0.317791i | ||||||||
1.42871 | + | 1.07891i | 1.42871 | + | 1.07891i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0899135 | − | 0.0211475i | 0.0899135 | − | 0.0211475i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.469302 | − | 0.942485i | −0.469302 | − | 0.942485i | |||||
0 | 0 | |||||||||
0 | 0 | −0.361242 | − | 0.932472i | ||||||
0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0.800095 | − | 2.81204i | 0.800095 | − | 2.81204i | |||||
−1.34090 | − | 0.449425i | −1.34090 | − | 0.449425i | |||||
0 | 0 | −0.565136 | − | 0.824997i | ||||||
0.565136 | + | 0.824997i | ||||||||
0 | 0 | |||||||||
−0.981767 | − | 1.58561i | −0.981767 | − | 1.58561i | −0.798017 | − | 0.602635i | ||
−0.183750 | − | 0.982973i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.445738 | + | 0.104837i | 0.445738 | + | 0.104837i | |||||
0.869557 | + | 0.722071i | 0.869557 | + | 0.722071i | 0.961826 | − | 0.273663i | ||
−0.0922684 | + | 0.995734i | ||||||||
−0.778076 | − | 0.709310i | −0.778076 | − | 0.709310i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.850217 | − | 0.526432i | ||||||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
−0.309277 | − | 0.922758i | −0.309277 | − | 0.922758i | −0.982973 | − | 0.183750i | ||
0.673696 | − | 0.739009i | ||||||||
−0.850217 | + | 0.526432i | −0.850217 | + | 0.526432i | |||||
0 | 0 | |||||||||
−1.59837 | − | 0.705749i | −1.59837 | − | 0.705749i | |||||
−1.11943 | − | 1.63417i | −1.11943 | − | 1.63417i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.53910 | + | 3.48574i | −1.53910 | + | 3.48574i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.932472 | + | 0.361242i | 0.932472 | + | 0.361242i | |||||
0.778076 | + | 1.25664i | 0.778076 | + | 1.25664i | 0.961826 | + | 0.273663i | ||
−0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.33234 | + | 1.60447i | 1.33234 | + | 1.60447i | |||||
−0.453510 | + | 0.0632619i | −0.453510 | + | 0.0632619i | |||||
0 | 0 | |||||||||
0 | 0 | 0.183750 | − | 0.982973i | ||||||
−0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
3.24415 | + | 1.43243i | 3.24415 | + | 1.43243i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.64823 | − | 0.0762025i | 1.64823 | − | 0.0762025i | 0.798017 | − | 0.602635i | ||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.982973 | − | 0.183750i | ||||||
−0.982973 | + | 0.183750i | ||||||||
−0.932472 | − | 0.361242i | −0.932472 | − | 0.361242i | |||||
0 | 0 | |||||||||
1.27366 | − | 0.961826i | 1.27366 | − | 0.961826i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.581427 | + | 0.256725i | −0.581427 | + | 0.256725i | −0.673696 | − | 0.739009i | ||
0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.58923 | − | 1.20013i | 1.58923 | − | 1.20013i | 0.739009 | − | 0.673696i | ||
0.850217 | − | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.317791 | − | 0.948161i | ||||||
−0.317791 | + | 0.948161i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | −1.00000 | |||||||||
0.932472 | + | 0.361242i | 0.932472 | + | 0.361242i | |||||
0.907020 | 0.907020 | |||||||||
0 | 0 | |||||||||
0.947359 | + | 1.70083i | 0.947359 | + | 1.70083i | |||||
−0.136374 | + | 1.47171i | −0.136374 | + | 1.47171i | 0.602635 | + | 0.798017i | ||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.457413 | + | 1.94480i | 0.457413 | + | 1.94480i | |||||
0 | 0 | |||||||||
0.895163 | − | 1.44574i | 0.895163 | − | 1.44574i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.40205 | − | 0.635953i | −3.40205 | − | 0.635953i | |||||
1.00000 | 1.00000 | |||||||||
0 | 0 | 0.982973 | − | 0.183750i | ||||||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.990410 | − | 0.138156i | ||||||
0.990410 | + | 0.138156i | ||||||||
0 | 0 | |||||||||
−1.50941 | − | 0.666468i | −1.50941 | − | 0.666468i | −0.526432 | − | 0.850217i | ||
−0.982973 | + | 0.183750i | ||||||||
1.15926 | − | 0.329838i | 1.15926 | − | 0.329838i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.63417 | − | 0.227957i | 1.63417 | − | 0.227957i | 0.739009 | − | 0.673696i | ||
0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.96183 | + | 0.273663i | 1.96183 | + | 0.273663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.932472 | − | 0.361242i | 0.932472 | − | 0.361242i | |||||
2.45646 | + | 1.85503i | 2.45646 | + | 1.85503i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.111609 | + | 0.252769i | −0.111609 | + | 0.252769i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.995734 | − | 0.0922684i | ||||||
0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
−1.12907 | − | 1.64823i | −1.12907 | − | 1.64823i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.581427 | − | 1.73474i | −0.581427 | − | 1.73474i | −0.673696 | − | 0.739009i | ||
0.0922684 | − | 0.995734i | ||||||||
0.0971461 | − | 0.0483730i | 0.0971461 | − | 0.0483730i | |||||
0 | 0 | |||||||||
−1.96183 | − | 0.273663i | −1.96183 | − | 0.273663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.618701 | − | 0.145517i | −0.618701 | − | 0.145517i | |||||
0 | 0 | 0.138156 | − | 0.990410i | ||||||
−0.138156 | + | 0.990410i | ||||||||
0 | 0 | |||||||||
0.380338 | + | 0.614268i | 0.380338 | + | 0.614268i | 0.982973 | − | 0.183750i | ||
−0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.538007 | + | 1.89090i | −0.538007 | + | 1.89090i | −0.0922684 | + | 0.995734i | ||
−0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.995734 | + | 0.907732i | 0.995734 | + | 0.907732i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
−1.92821 | + | 0.453510i | −1.92821 | + | 0.453510i | |||||
−0.0922684 | − | 0.995734i | −0.0922684 | − | 0.995734i | |||||
0.802895 | − | 0.549996i | 0.802895 | − | 0.549996i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.59805 | + | 2.84992i | 2.59805 | + | 2.84992i | |||||
0 | 0 | |||||||||
0 | 0 | 0.948161 | − | 0.317791i | ||||||
−0.948161 | + | 0.317791i | ||||||||
0 | 0 | |||||||||
0.0127611 | − | 0.276018i | 0.0127611 | − | 0.276018i | |||||
1.76397 | + | 3.54253i | 1.76397 | + | 3.54253i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.435393 | − | 0.576554i | −0.435393 | − | 0.576554i | 0.526432 | − | 0.850217i | ||
−0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.110379 | − | 0.469302i | 0.110379 | − | 0.469302i | |||||
0 | 0 | |||||||||
0 | 0 | −0.317791 | − | 0.948161i | ||||||
0.317791 | + | 0.948161i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.84595 | + | 0.434164i | −1.84595 | + | 0.434164i | |||||
0 | 0 | |||||||||
0.212577 | + | 1.52391i | 0.212577 | + | 1.52391i | |||||
−0.163808 | − | 0.876298i | −0.163808 | − | 0.876298i | −0.961826 | − | 0.273663i | ||
0.798017 | − | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | |||||
0 | 0 | |||||||||
−0.869557 | − | 0.722071i | −0.869557 | − | 0.722071i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0127611 | + | 0.0914812i | −0.0127611 | + | 0.0914812i | −0.995734 | − | 0.0922684i | ||
0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.91118 | − | 0.269761i | 2.91118 | − | 0.269761i | |||||
−0.0293534 | − | 0.634905i | −0.0293534 | − | 0.634905i | −0.961826 | − | 0.273663i | ||
0.932472 | − | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.342683 | + | 0.132756i | −0.342683 | + | 0.132756i | |||||
1.63417 | − | 1.11943i | 1.63417 | − | 1.11943i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.149783 | + | 0.526432i | −0.149783 | + | 0.526432i | 0.850217 | + | 0.526432i | ||
−1.00000 | ||||||||||
−0.100571 | + | 0.538007i | −0.100571 | + | 0.538007i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.380338 | − | 0.981767i | 0.380338 | − | 0.981767i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.998933 | − | 0.0461835i | ||||||
0.998933 | + | 0.0461835i | ||||||||
0 | 0 | |||||||||
0.163808 | − | 0.328972i | 0.163808 | − | 0.328972i | −0.798017 | − | 0.602635i | ||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.165190 | − | 1.78269i | −0.165190 | − | 1.78269i | |||||
−2.91118 | + | 0.269761i | −2.91118 | + | 0.269761i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.824997 | − | 0.565136i | ||||||
0.824997 | + | 0.565136i | ||||||||
0 | 0 | |||||||||
−0.811985 | + | 0.890705i | −0.811985 | + | 0.890705i | −0.995734 | − | 0.0922684i | ||
0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0762025 | − | 0.0521999i | −0.0762025 | − | 0.0521999i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.0461835 | − | 0.998933i | ||||||
−0.0461835 | + | 0.998933i | ||||||||
0 | 0 | |||||||||
0.0922684 | − | 0.995734i | 0.0922684 | − | 0.995734i | |||||
−0.380338 | + | 0.981767i | −0.380338 | + | 0.981767i | |||||
0 | 0 | −0.0922684 | − | 0.995734i | ||||||
0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
2.33165 | + | 1.29872i | 2.33165 | + | 1.29872i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.45890 | + | 1.21146i | −1.45890 | + | 1.21146i | −0.526432 | + | 0.850217i | ||
−0.932472 | + | 0.361242i | ||||||||
−2.61715 | + | 1.30318i | −2.61715 | + | 1.30318i | |||||
0 | 0 | |||||||||
0.571231 | + | 1.29371i | 0.571231 | + | 1.29371i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.361242 | − | 1.93247i | 0.361242 | − | 1.93247i | − | 1.00000i | |||
0.361242 | − | 0.932472i | ||||||||
−0.510366 | + | 1.79375i | −0.510366 | + | 1.79375i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.98297 | + | 0.183750i | −1.98297 | + | 0.183750i | −0.982973 | + | 0.183750i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | 0.932472 | − | 0.361242i | ||||||
−0.932472 | + | 0.361242i | ||||||||
−0.222817 | − | 0.400033i | −0.222817 | − | 0.400033i | |||||
0 | 0 | |||||||||
−0.0521999 | − | 1.12907i | −0.0521999 | − | 1.12907i | |||||
0 | 0 | 0.995734 | − | 0.0922684i | ||||||
−0.995734 | + | 0.0922684i | ||||||||
1.05286i | 1.05286i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.798017 | + | 1.60263i | 0.798017 | + | 1.60263i | |||||
0 | 0 | |||||||||
0 | 0 | −0.138156 | − | 0.990410i | ||||||
0.138156 | + | 0.990410i | ||||||||
0 | 0 | |||||||||
2.04761 | − | 0.481593i | 2.04761 | − | 0.481593i | |||||
−0.473568 | + | 0.850217i | −0.473568 | + | 0.850217i | |||||
0 | 0 | |||||||||
0.961826 | + | 0.273663i | 0.961826 | + | 0.273663i | |||||
1.10100 | + | 2.84201i | 1.10100 | + | 2.84201i | |||||
0 | 0 | |||||||||
0 | 0 | 0.638847 | − | 0.769334i | ||||||
−0.638847 | + | 0.769334i | ||||||||
0.555259 | + | 1.65667i | 0.555259 | + | 1.65667i | |||||
0 | 0 | |||||||||
−0.453510 | + | 1.92821i | −0.453510 | + | 1.92821i | |||||
0 | 0 | 0.361242 | − | 0.932472i | ||||||
−0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0.222817 | + | 0.400033i | 0.222817 | + | 0.400033i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.0461835 | − | 0.998933i | ||||||
0.0461835 | + | 0.998933i | ||||||||
3.61288 | − | 1.21092i | 3.61288 | − | 1.21092i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
−0.600557 | + | 0.411391i | −0.600557 | + | 0.411391i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.658809 | + | 0.600584i | −0.658809 | + | 0.600584i | −0.932472 | − | 0.361242i | ||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.361242 | − | 0.932472i | −0.361242 | − | 0.932472i | |||||
0 | 0 | |||||||||
0.404479 | − | 1.42160i | 0.404479 | − | 1.42160i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.288130 | − | 2.06554i | 0.288130 | − | 2.06554i | |||||
−1.37665 | − | 0.323785i | −1.37665 | − | 0.323785i | −0.526432 | − | 0.850217i | ||
−0.850217 | + | 0.526432i | ||||||||
0.352279 | + | 0.292529i | 0.352279 | + | 0.292529i | |||||
0 | 0 | −0.739009 | − | 0.673696i | ||||||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.895163 | + | 0.445738i | −0.895163 | + | 0.445738i | |||||
−1.12699 | − | 3.36248i | −1.12699 | − | 3.36248i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266132 | + | 0.117509i | 0.266132 | + | 0.117509i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.16672 | − | 1.16672i | −1.16672 | − | 1.16672i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.393100 | + | 0.890286i | −0.393100 | + | 0.890286i | 0.602635 | + | 0.798017i | ||
−0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.361242 | + | 0.932472i | 0.361242 | + | 0.932472i | |||||
−0.170607 | − | 0.0660936i | −0.170607 | − | 0.0660936i | |||||
0 | 0 | |||||||||
0 | 0 | −0.990410 | − | 0.138156i | ||||||
0.990410 | + | 0.138156i | ||||||||
−1.56886 | − | 0.293271i | −1.56886 | − | 0.293271i | |||||
−1.11622 | − | 1.34421i | −1.11622 | − | 1.34421i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.581427 | + | 0.256725i | 0.581427 | + | 0.256725i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.995734 | − | 0.907732i | 0.995734 | − | 0.907732i | − | 1.00000i | |||
0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.95756 | − | 0.365931i | −1.95756 | − | 0.365931i | |||||
0 | 0 | 0.798017 | − | 0.602635i | ||||||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
1.68816 | + | 2.23549i | 1.68816 | + | 2.23549i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.850217 | − | 0.526432i | ||||||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.228951 | − | 0.973438i | ||||||
0.228951 | + | 0.973438i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.673696 | + | 0.739009i | 0.673696 | + | 0.739009i | |||||
−0.722483 | −0.722483 | −0.361242 | − | 0.932472i | ||||||
−0.361242 | + | 0.932472i | ||||||||
−0.361242 | − | 0.932472i | −0.361242 | − | 0.932472i | |||||
0 | 0 | |||||||||
−0.611055 | − | 0.670296i | −0.611055 | − | 0.670296i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.618701 | − | 1.84595i | 0.618701 | − | 1.84595i | |||||
0.477485 | + | 2.03014i | 0.477485 | + | 2.03014i | |||||
1.17948 | − | 0.890705i | 1.17948 | − | 0.890705i | |||||
0 | 0 | 0.526432 | − | 0.850217i | ||||||
−0.526432 | + | 0.850217i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.12907 | − | 1.64823i | 1.12907 | − | 1.64823i | |||||
1.27366 | − | 0.961826i | 1.27366 | − | 0.961826i | 0.273663 | − | 0.961826i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.67148 | + | 0.312454i | −1.67148 | + | 0.312454i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.739009 | − | 0.673696i | ||||||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0.445738 | + | 1.89516i | 0.445738 | + | 1.89516i | 0.445738 | + | 0.895163i | ||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.97871 | + | 0.0914812i | 1.97871 | + | 0.0914812i | |||||
0 | 0 | |||||||||
0 | 0 | −0.638847 | − | 0.769334i | ||||||
0.638847 | + | 0.769334i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.82197 | + | 2.94258i | 1.82197 | + | 2.94258i | |||||
0 | 0 | |||||||||
−0.673696 | − | 0.739009i | −0.673696 | − | 0.739009i | |||||
0.172075 | − | 0.0666624i | 0.172075 | − | 0.0666624i | −0.273663 | − | 0.961826i | ||
0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.786384 | − | 1.78099i | 0.786384 | − | 1.78099i | 0.183750 | − | 0.982973i | ||
0.602635 | − | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.873622 | − | 0.486604i | ||||||
−0.873622 | + | 0.486604i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.93148 | − | 2.43427i | 3.93148 | − | 2.43427i | |||||
0.524354 | + | 1.56446i | 0.524354 | + | 1.56446i | |||||
0 | 0 | |||||||||
−1.02474 | − | 0.634493i | −1.02474 | − | 0.634493i | |||||
−1.12907 | + | 1.64823i | −1.12907 | + | 1.64823i | |||||
0 | 0 | |||||||||
0 | 0 | 0.526432 | − | 0.850217i | ||||||
−0.526432 | + | 0.850217i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.26940 | − | 1.05409i | −1.26940 | − | 1.05409i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.942485 | + | 0.469302i | 0.942485 | + | 0.469302i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.11943 | − | 1.63417i | −1.11943 | − | 1.63417i | |||||
−1.73474 | − | 0.581427i | −1.73474 | − | 0.581427i | −0.739009 | − | 0.673696i | ||
−0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.739009 | − | 0.673696i | ||||||
−0.739009 | + | 0.673696i | ||||||||
−0.895163 | − | 0.445738i | −0.895163 | − | 0.445738i | |||||
0 | 0 | |||||||||
−0.284021 | − | 3.06508i | −0.284021 | − | 3.06508i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.571231 | + | 0.571231i | 0.571231 | + | 0.571231i | 0.932472 | − | 0.361242i | ||
−0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.261989 | − | 0.0878098i | 0.261989 | − | 0.0878098i | |||||
0.0899135 | + | 1.94480i | 0.0899135 | + | 1.94480i | |||||
0 | 0 | |||||||||
0 | 0 | −0.445738 | − | 0.895163i | ||||||
0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.273663 | − | 0.961826i | ||||||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.457413 | + | 1.94480i | −0.457413 | + | 1.94480i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.05409 | − | 0.722071i | −1.05409 | − | 0.722071i | −0.0922684 | − | 0.995734i | ||
−0.961826 | + | 0.273663i | ||||||||
−0.890286 | + | 1.59837i | −0.890286 | + | 1.59837i | |||||
0 | 0 | |||||||||
−0.101195 | − | 0.0392031i | −0.101195 | − | 0.0392031i | |||||
−0.176521 | − | 1.26544i | −0.176521 | − | 1.26544i | −0.850217 | − | 0.526432i | ||
0.673696 | − | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.11943 | + | 1.63417i | 1.11943 | + | 1.63417i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.769334 | − | 0.638847i | ||||||
0.769334 | + | 0.638847i | ||||||||
0 | 0 | |||||||||
−3.15808 | + | 0.146007i | −3.15808 | + | 0.146007i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.87693 | + | 0.173923i | −1.87693 | + | 0.173923i | |||||
0 | 0 | |||||||||
0 | 0 | 0.873622 | − | 0.486604i | ||||||
−0.873622 | + | 0.486604i | ||||||||
0.309277 | + | 0.555259i | 0.309277 | + | 0.555259i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.261989 | + | 0.0878098i | −0.261989 | + | 0.0878098i | |||||
0.197717 | − | 0.694903i | 0.197717 | − | 0.694903i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.312454 | − | 0.193463i | −0.312454 | − | 0.193463i | 0.361242 | − | 0.932472i | ||
−0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.75984 | − | 0.876298i | 1.75984 | − | 0.876298i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.571231 | − | 0.571231i | 0.571231 | − | 0.571231i | −0.361242 | − | 0.932472i | ||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.34739i | − | 1.34739i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.873622 | − | 0.486604i | ||||||
0.873622 | + | 0.486604i | ||||||||
1.63417 | + | 1.11943i | 1.63417 | + | 1.11943i | |||||
0 | 0 | |||||||||
−0.673696 | + | 0.739009i | −0.673696 | + | 0.739009i | |||||
0 | 0 | |||||||||
−0.947359 | − | 0.222817i | −0.947359 | − | 0.222817i | |||||
−1.10446 | − | 0.756572i | −1.10446 | − | 0.756572i | |||||
0 | 0 | |||||||||
0 | 0 | −0.273663 | − | 0.961826i | ||||||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0.995734 | + | 0.0922684i | 0.995734 | + | 0.0922684i | |||||
0.355825 | − | 3.83996i | 0.355825 | − | 3.83996i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.59603i | − | 1.59603i | −0.602635 | − | 0.798017i | ||||
0.602635 | − | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.212577 | + | 0.176521i | −0.212577 | + | 0.176521i | |||||
0 | 0 | 0.895163 | − | 0.445738i | ||||||
−0.895163 | + | 0.445738i | ||||||||
1.42958 | − | 3.69018i | 1.42958 | − | 3.69018i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.228951 | − | 0.973438i | ||||||
−0.228951 | + | 0.973438i | ||||||||
0 | 0 | |||||||||
−3.08126 | + | 1.36051i | −3.08126 | + | 1.36051i | |||||
−0.132756 | + | 0.710182i | −0.132756 | + | 0.710182i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.824997 | − | 0.565136i | ||||||
−0.824997 | + | 0.565136i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.421180 | + | 0.234596i | −0.421180 | + | 0.234596i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.184537i | 0.184537i | 0.995734 | + | 0.0922684i | ||||||
−0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.56886 | + | 0.293271i | −1.56886 | + | 0.293271i | −0.895163 | − | 0.445738i | ||
−0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.63417 | − | 1.11943i | −1.63417 | − | 1.11943i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.25640 | + | 0.486734i | 1.25640 | + | 0.486734i | 0.895163 | − | 0.445738i | ||
0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.56446 | + | 1.07168i | 1.56446 | + | 1.07168i | |||||
−1.15926 | − | 0.329838i | −1.15926 | − | 0.329838i | −0.361242 | − | 0.932472i | ||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.982973 | − | 1.18375i | 0.982973 | − | 1.18375i | |||||
0 | 0 | |||||||||
−0.537235 | + | 0.711414i | −0.537235 | + | 0.711414i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.961826 | − | 0.273663i | 0.961826 | − | 0.273663i | |||||
−2.26366 | − | 0.758702i | −2.26366 | − | 0.758702i | |||||
0 | 0 | |||||||||
0 | 0 | 0.0461835 | − | 0.998933i | ||||||
−0.0461835 | + | 0.998933i | ||||||||
0.0521999 | + | 1.12907i | 0.0521999 | + | 1.12907i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.74425 | − | 0.584613i | 1.74425 | − | 0.584613i | |||||
0.0762025 | − | 0.0521999i | 0.0762025 | − | 0.0521999i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.60263 | − | 0.798017i | −1.60263 | − | 0.798017i | −0.602635 | − | 0.798017i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.16060 | − | 1.96965i | −2.16060 | − | 1.96965i | |||||
0.486734 | + | 1.25640i | 0.486734 | + | 1.25640i | |||||
−0.449425 | + | 0.449425i | −0.449425 | + | 0.449425i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.328972 | + | 0.163808i | 0.328972 | + | 0.163808i | |||||
0.156154 | − | 1.11943i | 0.156154 | − | 1.11943i | −0.739009 | − | 0.673696i | ||
0.895163 | − | 0.445738i | ||||||||
−1.92821 | − | 0.453510i | −1.92821 | − | 0.453510i | |||||
0 | 0 | −0.769334 | − | 0.638847i | ||||||
0.769334 | + | 0.638847i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.489946 | − | 0.243964i | 0.489946 | − | 0.243964i | |||||
0 | 0 | |||||||||
0.465346 | − | 0.288130i | 0.465346 | − | 0.288130i | |||||
0.987432 | − | 1.44147i | 0.987432 | − | 1.44147i | 0.0922684 | − | 0.995734i | ||
0.895163 | − | 0.445738i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.565136 | − | 0.824997i | ||||||
0.565136 | + | 0.824997i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
−1.70043 | −1.70043 | −0.850217 | − | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.981767 | + | 0.380338i | −0.981767 | + | 0.380338i | |||||
−0.961826 | + | 0.273663i | −0.961826 | + | 0.273663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.990410 | − | 0.138156i | ||||||
−0.990410 | + | 0.138156i | ||||||||
0 | 0 | |||||||||
0.145222 | − | 0.776870i | 0.145222 | − | 0.776870i | |||||
−0.353470 | + | 0.100571i | −0.353470 | + | 0.100571i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.212904 | − | 0.0296988i | −0.212904 | − | 0.0296988i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.20614 | + | 1.32307i | −1.20614 | + | 1.32307i | |||||
0 | 0 | |||||||||
2.16060 | + | 1.96965i | 2.16060 | + | 1.96965i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.03397 | − | 1.50941i | 1.03397 | − | 1.50941i | 0.183750 | − | 0.982973i | ||
0.850217 | − | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.516087 | + | 0.621500i | −0.516087 | + | 0.621500i | −0.961826 | − | 0.273663i | ||
0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.798017 | − | 0.602635i | ||||||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.0922684 | − | 0.995734i | ||||||
−0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0.848166 | + | 0.930394i | 0.848166 | + | 0.930394i | |||||
1.20527 | 1.20527 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0127611 | + | 0.0914812i | 0.0127611 | + | 0.0914812i | |||||
−0.488975 | + | 1.45890i | −0.488975 | + | 1.45890i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.24376 | + | 1.49780i | −1.24376 | + | 1.49780i | −0.445738 | + | 0.895163i | ||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.869557 | + | 1.26940i | −0.869557 | + | 1.26940i | 0.0922684 | + | 0.995734i | ||
−0.961826 | + | 0.273663i | ||||||||
−0.798017 | + | 0.602635i | −0.798017 | + | 0.602635i | |||||
0 | 0 | −0.982973 | − | 0.183750i | ||||||
0.982973 | + | 0.183750i | ||||||||
0.981767 | − | 0.380338i | 0.981767 | − | 0.380338i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.998933 | − | 0.0461835i | ||||||
−0.998933 | + | 0.0461835i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.611055 | − | 2.59805i | −0.611055 | − | 2.59805i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.87814 | + | 0.261989i | 1.87814 | + | 0.261989i | |||||
0 | 0 | |||||||||
2.72622 | + | 1.05614i | 2.72622 | + | 1.05614i | |||||
1.20614 | − | 1.32307i | 1.20614 | − | 1.32307i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.571231 | − | 1.29371i | 0.571231 | − | 1.29371i | |||||
−1.92775 | −1.92775 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
−0.365931 | − | 0.0339085i | −0.365931 | − | 0.0339085i | |||||
0 | 0 | |||||||||
0 | 0 | −0.565136 | − | 0.824997i | ||||||
0.565136 | + | 0.824997i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.67148 | + | 1.03494i | −1.67148 | + | 1.03494i | |||||
0 | 0 | |||||||||
1.66943 | − | 0.831277i | 1.66943 | − | 0.831277i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.850217 | − | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.47171 | + | 1.34164i | 1.47171 | + | 1.34164i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.806980 | − | 5.78505i | 0.806980 | − | 5.78505i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.145517 | + | 0.434164i | −0.145517 | + | 0.434164i | |||||
0.722071 | + | 1.05409i | 0.722071 | + | 1.05409i | 0.995734 | + | 0.0922684i | ||
−0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.799224 | + | 0.799224i | −0.799224 | + | 0.799224i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.778076 | − | 0.709310i | 0.778076 | − | 0.709310i | |||||
−1.78269 | − | 0.887674i | −1.78269 | − | 0.887674i | −0.932472 | − | 0.361242i | ||
−0.850217 | − | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.21146 | + | 0.406040i | −1.21146 | + | 0.406040i | −0.850217 | − | 0.526432i | ||
−0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.0461835 | − | 0.998933i | ||||||
−0.0461835 | + | 0.998933i | ||||||||
0 | 0 | |||||||||
−1.94354 | − | 0.651408i | −1.94354 | − | 0.651408i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.811985 | + | 1.07524i | −0.811985 | + | 1.07524i | 0.183750 | + | 0.982973i | ||
−0.995734 | + | 0.0922684i | ||||||||
0.646741 | − | 1.66943i | 0.646741 | − | 1.66943i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.961826 | + | 0.273663i | 0.961826 | + | 0.273663i | |||||
−1.73537 | − | 1.18875i | −1.73537 | − | 1.18875i | |||||
0 | 0 | |||||||||
0.947359 | − | 0.222817i | 0.947359 | − | 0.222817i | |||||
3.50262 | + | 1.35692i | 3.50262 | + | 1.35692i | |||||
0 | 0 | |||||||||
0 | 0 | −0.183750 | − | 0.982973i | ||||||
0.183750 | + | 0.982973i | ||||||||
−0.445738 | − | 0.895163i | −0.445738 | − | 0.895163i | |||||
0 | 0 | |||||||||
1.35853 | − | 2.72830i | 1.35853 | − | 2.72830i | |||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.850217 | − | 1.52643i | 0.850217 | − | 1.52643i | |||||
− | 0.722483i | − | 0.722483i | −0.932472 | − | 0.361242i | ||||
0.932472 | − | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.73049 | − | 0.963876i | 1.73049 | − | 0.963876i | |||||
−0.0449462 | − | 0.0806938i | −0.0449462 | − | 0.0806938i | |||||
0 | 0 | |||||||||
0 | 0 | 0.824997 | − | 0.565136i | ||||||
−0.824997 | + | 0.565136i | ||||||||
0 | 0 | |||||||||
0.612695 | + | 2.15340i | 0.612695 | + | 2.15340i | |||||
0.145517 | − | 0.434164i | 0.145517 | − | 0.434164i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.228951 | − | 0.973438i | ||||||
−0.228951 | + | 0.973438i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.89430 | + | 0.0875787i | 1.89430 | + | 0.0875787i | 0.961826 | − | 0.273663i | ||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1156.1.o.a.191.1 | yes | 32 | |
4.3 | odd | 2 | CM | 1156.1.o.a.191.1 | yes | 32 | |
289.115 | even | 68 | inner | 1156.1.o.a.115.1 | ✓ | 32 | |
1156.115 | odd | 68 | inner | 1156.1.o.a.115.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1156.1.o.a.115.1 | ✓ | 32 | 289.115 | even | 68 | inner | |
1156.1.o.a.115.1 | ✓ | 32 | 1156.115 | odd | 68 | inner | |
1156.1.o.a.191.1 | yes | 32 | 1.1 | even | 1 | trivial | |
1156.1.o.a.191.1 | yes | 32 | 4.3 | odd | 2 | CM |