Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1156,1,Mod(67,1156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1156, base_ring=CyclotomicField(34))
chi = DirichletCharacter(H, H._module([17, 23]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1156.67");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1156.l (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 | 339.1 | ||
Root | of defining polynomial | ||
Character | 1156.339 | ||
Dual form | 1156.1.l.a.815.1 |
-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 .
−0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | |||||
0 | 0 | −0.361242 | − | 0.932472i | ||||||
0.361242 | + | 0.932472i | ||||||||
−0.602635 | − | 0.798017i | −0.602635 | − | 0.798017i | |||||
−0.0675278 | + | 0.361242i | −0.0675278 | + | 0.361242i | 0.932472 | + | 0.361242i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | −0.673696 | − | 0.739009i | ||||||
0.673696 | + | 0.739009i | ||||||||
0.982973 | − | 0.183750i | 0.982973 | − | 0.183750i | |||||
−0.739009 | + | 0.673696i | −0.739009 | + | 0.673696i | |||||
−0.293271 | − | 0.221468i | −0.293271 | − | 0.221468i | |||||
0 | 0 | 0.798017 | − | 0.602635i | ||||||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
1.45285 | − | 0.271585i | 1.45285 | − | 0.271585i | 0.602635 | − | 0.798017i | ||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.273663 | + | 0.961826i | −0.273663 | + | 0.961826i | |||||
−0.273663 | + | 0.961826i | −0.273663 | + | 0.961826i | |||||
−0.273663 | − | 0.961826i | −0.273663 | − | 0.961826i | |||||
0 | 0 | −0.445738 | − | 0.895163i | ||||||
0.445738 | + | 0.895163i | ||||||||
0.328972 | − | 0.163808i | 0.328972 | − | 0.163808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.673696 | − | 0.739009i | ||||||
0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0.806537 | + | 0.312454i | 0.806537 | + | 0.312454i | |||||
−0.404479 | + | 1.42160i | −0.404479 | + | 1.42160i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.07524 | + | 0.811985i | −1.07524 | + | 0.811985i | −0.982973 | − | 0.183750i | ||
−0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.183750 | − | 0.982973i | ||||||
0.183750 | + | 0.982973i | ||||||||
−0.739009 | − | 0.673696i | −0.739009 | − | 0.673696i | |||||
0 | 0 | |||||||||
−0.739009 | − | 0.673696i | −0.739009 | − | 0.673696i | |||||
0 | 0 | |||||||||
0.982973 | + | 0.183750i | 0.982973 | + | 0.183750i | |||||
0.942485 | + | 1.52217i | 0.942485 | + | 1.52217i | 0.850217 | + | 0.526432i | ||
0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.367499i | 0.367499i | |||||||||
−0.132756 | − | 0.342683i | −0.132756 | − | 0.342683i | 0.850217 | − | 0.526432i | ||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.273663 | − | 0.961826i | ||||||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
−0.193463 | − | 0.312454i | −0.193463 | − | 0.312454i | |||||
0 | 0 | |||||||||
0 | 0 | −0.739009 | − | 0.673696i | ||||||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
−0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | |||||
−0.639202 | + | 0.582709i | −0.639202 | + | 0.582709i | |||||
0 | 0 | |||||||||
−1.09227 | − | 0.995734i | −1.09227 | − | 0.995734i | |||||
0.136374 | − | 0.124322i | 0.136374 | − | 0.124322i | −0.602635 | − | 0.798017i | ||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.247582 | − | 1.32445i | −0.247582 | − | 1.32445i | |||||
0 | 0 | −0.0922684 | − | 0.995734i | ||||||
0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0.719401 | + | 0.0666624i | 0.719401 | + | 0.0666624i | 0.445738 | − | 0.895163i | ||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.932472 | − | 0.361242i | 0.932472 | − | 0.361242i | |||||
0.543170i | 0.543170i | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.445738 | − | 0.895163i | ||||||
0.445738 | + | 0.895163i | ||||||||
0.932472 | − | 0.361242i | 0.932472 | − | 0.361242i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.673696 | − | 0.739009i | ||||||
0.673696 | + | 0.739009i | ||||||||
−0.602635 | + | 0.798017i | −0.602635 | + | 0.798017i | |||||
−1.29596 | − | 0.368731i | −1.29596 | − | 0.368731i | −0.445738 | − | 0.895163i | ||
−0.850217 | + | 0.526432i | ||||||||
−1.78269 | + | 0.165190i | −1.78269 | + | 0.165190i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.895163 | − | 0.445738i | ||||||
−0.895163 | + | 0.445738i | ||||||||
−0.328972 | − | 0.163808i | −0.328972 | − | 0.163808i | |||||
0.0922684 | − | 0.995734i | 0.0922684 | − | 0.995734i | |||||
0.365931 | + | 0.0339085i | 0.365931 | + | 0.0339085i | |||||
0 | 0 | −0.932472 | − | 0.361242i | ||||||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
−0.328972 | − | 0.163808i | −0.328972 | − | 0.163808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.876298 | + | 0.163808i | 0.876298 | + | 0.163808i | 0.602635 | − | 0.798017i | ||
0.273663 | + | 0.961826i | ||||||||
0.365931 | − | 0.0339085i | 0.365931 | − | 0.0339085i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.07524 | − | 1.17948i | −1.07524 | − | 1.17948i | −0.982973 | − | 0.183750i | ||
−0.0922684 | − | 0.995734i | ||||||||
−0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | |||||
0 | 0 | |||||||||
−0.236703 | − | 0.831926i | −0.236703 | − | 0.831926i | |||||
0.0505009 | − | 0.544991i | 0.0505009 | − | 0.544991i | −0.932472 | − | 0.361242i | ||
0.982973 | − | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.0922684 | − | 0.995734i | ||||||
0.0922684 | + | 0.995734i | ||||||||
1.37821 | − | 0.533922i | 1.37821 | − | 0.533922i | |||||
0 | 0 | |||||||||
0.0505009 | + | 0.177492i | 0.0505009 | + | 0.177492i | |||||
0 | 0 | 0.895163 | − | 0.445738i | ||||||
−0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
0.646741 | − | 1.66943i | 0.646741 | − | 1.66943i | −0.0922684 | − | 0.995734i | ||
0.739009 | − | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.932472 | − | 0.361242i | ||||||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.29596 | + | 0.368731i | 1.29596 | + | 0.368731i | |||||
−0.890705 | + | 1.17948i | −0.890705 | + | 1.17948i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.273663 | − | 0.961826i | 0.273663 | − | 0.961826i | |||||
−0.380338 | + | 0.614268i | −0.380338 | + | 0.614268i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.360798 | + | 0.582709i | −0.360798 | + | 0.582709i | |||||
0 | 0 | |||||||||
0 | 0 | −0.850217 | − | 0.526432i | ||||||
0.850217 | + | 0.526432i | ||||||||
−0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | |||||
0 | 0 | |||||||||
−0.486226 | − | 0.242112i | −0.486226 | − | 0.242112i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | |||||
−1.18475 | − | 1.56886i | −1.18475 | − | 1.56886i | −0.739009 | − | 0.673696i | ||
−0.445738 | − | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.445738 | − | 0.895163i | −0.445738 | − | 0.895163i | |||||
−0.220714 | − | 0.443254i | −0.220714 | − | 0.443254i | |||||
0.907732 | − | 0.995734i | 0.907732 | − | 0.995734i | |||||
0 | 0 | |||||||||
0.646741 | − | 1.66943i | 0.646741 | − | 1.66943i | |||||
1.37821 | + | 0.533922i | 1.37821 | + | 0.533922i | 0.932472 | − | 0.361242i | ||
0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.602635 | − | 0.798017i | ||||||
0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
−0.445738 | − | 0.895163i | −0.445738 | − | 0.895163i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.181395 | − | 1.95756i | −0.181395 | − | 1.95756i | −0.273663 | − | 0.961826i | ||
0.0922684 | − | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.293271 | − | 0.221468i | 0.293271 | − | 0.221468i | |||||
0 | 0 | |||||||||
0.850217 | + | 0.526432i | 0.850217 | + | 0.526432i | |||||
0 | 0 | 0.526432 | − | 0.850217i | ||||||
−0.526432 | + | 0.850217i | ||||||||
−0.193463 | + | 0.312454i | −0.193463 | + | 0.312454i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.526432 | − | 0.850217i | ||||||
−0.526432 | + | 0.850217i | ||||||||
0 | 0 | |||||||||
1.10455 | − | 0.427904i | 1.10455 | − | 0.427904i | |||||
0.293271 | − | 0.221468i | 0.293271 | − | 0.221468i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.91545 | + | 0.544991i | 1.91545 | + | 0.544991i | 0.982973 | + | 0.183750i | ||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.537235 | + | 0.711414i | −0.537235 | + | 0.711414i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−0.132756 | + | 0.342683i | −0.132756 | + | 0.342683i | |||||
0.132756 | + | 0.710182i | 0.132756 | + | 0.710182i | 0.982973 | + | 0.183750i | ||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.613514 | + | 0.237677i | −0.613514 | + | 0.237677i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.850217 | − | 0.526432i | ||||||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0.719401 | − | 1.85699i | 0.719401 | − | 1.85699i | 0.273663 | − | 0.961826i | ||
0.445738 | − | 0.895163i | ||||||||
1.53511 | − | 0.436776i | 1.53511 | − | 0.436776i | |||||
0 | 0 | |||||||||
0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | |||||
−0.353470 | + | 1.89090i | −0.353470 | + | 1.89090i | 0.0922684 | + | 0.995734i | ||
−0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.995734 | − | 0.0922684i | ||||||
−0.995734 | + | 0.0922684i | ||||||||
0.850217 | + | 0.158933i | 0.850217 | + | 0.158933i | |||||
0 | 0 | |||||||||
0.465346 | + | 0.288130i | 0.465346 | + | 0.288130i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.132756 | − | 0.0248164i | 0.132756 | − | 0.0248164i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.136374 | + | 1.47171i | −0.136374 | + | 1.47171i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.995734 | − | 0.0922684i | ||||||
−0.995734 | + | 0.0922684i | ||||||||
−0.181395 | − | 0.0339085i | −0.181395 | − | 0.0339085i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.20614 | + | 1.32307i | 1.20614 | + | 1.32307i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.136374 | + | 1.47171i | −0.136374 | + | 1.47171i | |||||
0 | 0 | |||||||||
0 | 0 | 0.850217 | − | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
−0.806537 | + | 0.312454i | −0.806537 | + | 0.312454i | |||||
0 | 0 | |||||||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
1.25664 | + | 1.14558i | 1.25664 | + | 1.14558i | 0.982973 | + | 0.183750i | ||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.907732 | + | 0.995734i | −0.907732 | + | 0.995734i | |||||
−1.53511 | − | 1.15926i | −1.53511 | − | 1.15926i | −0.932472 | − | 0.361242i | ||
−0.602635 | − | 0.798017i | ||||||||
−0.658809 | − | 1.32307i | −0.658809 | − | 1.32307i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.739009 | − | 0.673696i | ||||||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
−0.719401 | + | 0.0666624i | −0.719401 | + | 0.0666624i | −0.445738 | − | 0.895163i | ||
−0.273663 | + | 0.961826i | ||||||||
0.739009 | + | 0.673696i | 0.739009 | + | 0.673696i | |||||
0 | 0 | |||||||||
−0.380338 | − | 0.614268i | −0.380338 | − | 0.614268i | |||||
−0.353470 | − | 0.100571i | −0.353470 | − | 0.100571i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.360798 | − | 0.582709i | −0.360798 | − | 0.582709i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | |||||
−0.658809 | − | 0.600584i | −0.658809 | − | 0.600584i | 0.273663 | − | 0.961826i | ||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.433459 | − | 0.327333i | 0.433459 | − | 0.327333i | |||||
0.247582 | − | 1.32445i | 0.247582 | − | 1.32445i | |||||
0 | 0 | |||||||||
0 | 0 | 0.273663 | − | 0.961826i | ||||||
−0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0.0357011 | + | 0.0576592i | 0.0357011 | + | 0.0576592i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.72198 | − | 0.857445i | 1.72198 | − | 0.857445i | 0.739009 | − | 0.673696i | ||
0.982973 | − | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.273663 | − | 0.961826i | ||||||
0.273663 | + | 0.961826i | ||||||||
−0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | |||||
0 | 0 | |||||||||
1.93247 | − | 0.361242i | 1.93247 | − | 0.361242i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.04837 | + | 1.69318i | −1.04837 | + | 1.69318i | −0.445738 | + | 0.895163i | ||
−0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.18475 | − | 0.221468i | 1.18475 | − | 0.221468i | 0.445738 | − | 0.895163i | ||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.995734 | − | 0.0922684i | ||||||
0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | 1.00000 | |||||||||
−0.850217 | − | 0.526432i | −0.850217 | − | 0.526432i | |||||
0.495165 | 0.495165 | |||||||||
0 | 0 | |||||||||
0.486734 | + | 1.25640i | 0.486734 | + | 1.25640i | |||||
−0.537235 | − | 0.711414i | −0.537235 | − | 0.711414i | 0.445738 | − | 0.895163i | ||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.20614 | + | 1.32307i | 1.20614 | + | 1.32307i | |||||
0 | 0 | |||||||||
−1.09227 | + | 0.995734i | −1.09227 | + | 0.995734i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0726608 | + | 0.255376i | −0.0726608 | + | 0.255376i | |||||
1.00000 | 1.00000 | |||||||||
0 | 0 | −0.273663 | − | 0.961826i | ||||||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.183750 | − | 0.982973i | ||||||
0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
−1.01267 | − | 1.63552i | −1.01267 | − | 1.63552i | −0.739009 | − | 0.673696i | ||
−0.273663 | − | 0.961826i | ||||||||
1.83319 | + | 0.710182i | 1.83319 | + | 0.710182i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.353470 | − | 1.89090i | 0.353470 | − | 1.89090i | −0.0922684 | − | 0.995734i | ||
0.445738 | − | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0675278 | + | 0.361242i | 0.0675278 | + | 0.361242i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.850217 | + | 0.526432i | −0.850217 | + | 0.526432i | |||||
1.25664 | + | 0.234906i | 1.25664 | + | 0.234906i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.193463 | − | 0.312454i | −0.193463 | − | 0.312454i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.602635 | − | 0.798017i | ||||||
0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
−1.72198 | − | 0.489946i | −1.72198 | − | 0.489946i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.04837 | + | 0.0971461i | −1.04837 | + | 0.0971461i | −0.602635 | − | 0.798017i | ||
−0.445738 | + | 0.895163i | ||||||||
−0.109295 | + | 1.17948i | −0.109295 | + | 1.17948i | |||||
0 | 0 | |||||||||
0.0675278 | + | 0.361242i | 0.0675278 | + | 0.361242i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.34164 | + | 1.47171i | −1.34164 | + | 1.47171i | |||||
0 | 0 | −0.183750 | − | 0.982973i | ||||||
0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
−1.25664 | − | 1.14558i | −1.25664 | − | 1.14558i | −0.982973 | − | 0.183750i | ||
−0.273663 | − | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.510366 | + | 0.197717i | −0.510366 | + | 0.197717i | −0.602635 | − | 0.798017i | ||
0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.397365 | − | 0.798017i | −0.397365 | − | 0.798017i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.0922684 | − | 0.995734i | ||||||
0.0922684 | + | 0.995734i | ||||||||
−0.247582 | − | 0.271585i | −0.247582 | − | 0.271585i | |||||
−0.602635 | + | 0.798017i | −0.602635 | + | 0.798017i | |||||
−0.694903 | − | 0.197717i | −0.694903 | − | 0.197717i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.220714 | − | 0.443254i | 0.220714 | − | 0.443254i | |||||
0 | 0 | |||||||||
0 | 0 | 0.995734 | − | 0.0922684i | ||||||
−0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0.328972 | + | 0.163808i | 0.328972 | + | 0.163808i | |||||
0.0607073 | − | 0.655137i | 0.0607073 | − | 0.655137i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.67148 | + | 0.312454i | −1.67148 | + | 0.312454i | −0.932472 | − | 0.361242i | ||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.34164 | + | 1.47171i | −1.34164 | + | 1.47171i | |||||
0 | 0 | |||||||||
0 | 0 | 0.995734 | − | 0.0922684i | ||||||
−0.995734 | + | 0.0922684i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.932472 | − | 0.361242i | ||||||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.34164 | + | 1.47171i | 1.34164 | + | 1.47171i | |||||
0 | 0 | |||||||||
−0.293271 | + | 1.56886i | −0.293271 | + | 1.56886i | |||||
0.0505009 | + | 0.177492i | 0.0505009 | + | 0.177492i | 0.982973 | − | 0.183750i | ||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0922684 | + | 0.995734i | 0.0922684 | + | 0.995734i | |||||
0 | 0 | |||||||||
−1.53511 | − | 1.15926i | −1.53511 | − | 1.15926i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.328972 | + | 1.75984i | 0.328972 | + | 1.75984i | 0.602635 | + | 0.798017i | ||
−0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.521245 | + | 0.690241i | −0.521245 | + | 0.690241i | |||||
−1.78269 | + | 0.887674i | −1.78269 | + | 0.887674i | −0.850217 | + | 0.526432i | ||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.465346 | + | 0.288130i | −0.465346 | + | 0.288130i | |||||
0.353470 | + | 0.100571i | 0.353470 | + | 0.100571i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.73901 | − | 0.673696i | 1.73901 | − | 0.673696i | 0.739009 | − | 0.673696i | ||
1.00000 | ||||||||||
−0.0369597 | + | 0.129900i | −0.0369597 | + | 0.129900i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.25664 | − | 0.778076i | −1.25664 | − | 0.778076i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
0.0505009 | + | 0.544991i | 0.0505009 | + | 0.544991i | 0.982973 | + | 0.183750i | ||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.111208 | − | 0.147263i | 0.111208 | − | 0.147263i | |||||
−0.521245 | + | 0.690241i | −0.521245 | + | 0.690241i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.961826 | − | 0.273663i | ||||||
−0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0.876298 | + | 1.75984i | 0.876298 | + | 1.75984i | 0.602635 | + | 0.798017i | ||
0.273663 | + | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.72198 | + | 0.489946i | −1.72198 | + | 0.489946i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
−0.602635 | − | 0.798017i | −0.602635 | − | 0.798017i | |||||
−1.25664 | − | 0.778076i | −1.25664 | − | 0.778076i | |||||
0 | 0 | 0.602635 | − | 0.798017i | ||||||
−0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
−0.118349 | + | 0.305494i | −0.118349 | + | 0.305494i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.58923 | + | 1.20013i | −1.58923 | + | 1.20013i | −0.739009 | + | 0.673696i | ||
−0.850217 | + | 0.526432i | ||||||||
0.0798070 | − | 0.861255i | 0.0798070 | − | 0.861255i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.149783 | + | 0.526432i | −0.149783 | + | 0.526432i | 0.850217 | + | 0.526432i | ||
−1.00000 | ||||||||||
−1.58561 | + | 0.614268i | −1.58561 | + | 0.614268i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.726337 | − | 0.961826i | 0.726337 | − | 0.961826i | −0.273663 | − | 0.961826i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | 0.850217 | − | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
−0.486734 | − | 1.25640i | −0.486734 | − | 1.25640i | |||||
0 | 0 | |||||||||
1.72198 | − | 0.857445i | 1.72198 | − | 0.857445i | |||||
0 | 0 | 0.602635 | − | 0.798017i | ||||||
−0.602635 | + | 0.798017i | ||||||||
1.47802 | 1.47802 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0170269 | + | 0.183750i | −0.0170269 | + | 0.183750i | |||||
0 | 0 | |||||||||
0 | 0 | 0.183750 | − | 0.982973i | ||||||
−0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
1.78269 | + | 1.95552i | 1.78269 | + | 1.95552i | |||||
0.260991 | − | 0.673696i | 0.260991 | − | 0.673696i | |||||
0 | 0 | |||||||||
−0.932472 | + | 0.361242i | −0.932472 | + | 0.361242i | |||||
0.498687 | − | 0.308774i | 0.498687 | − | 0.308774i | |||||
0 | 0 | |||||||||
0 | 0 | −0.798017 | − | 0.602635i | ||||||
0.798017 | + | 0.602635i | ||||||||
0.719401 | − | 0.0666624i | 0.719401 | − | 0.0666624i | |||||
0 | 0 | |||||||||
0.247582 | − | 0.271585i | 0.247582 | − | 0.271585i | |||||
0 | 0 | −0.850217 | − | 0.526432i | ||||||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
−0.486734 | − | 1.25640i | −0.486734 | − | 1.25640i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.895163 | − | 0.445738i | ||||||
−0.895163 | + | 0.445738i | ||||||||
0.682442 | − | 0.0632375i | 0.682442 | − | 0.0632375i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0.193463 | + | 0.0550451i | 0.193463 | + | 0.0550451i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0822551 | − | 0.165190i | 0.0822551 | − | 0.165190i | −0.850217 | − | 0.526432i | ||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | |||||
0 | 0 | |||||||||
0.831277 | − | 0.322039i | 0.831277 | − | 0.322039i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0998072 | + | 0.533922i | 0.0998072 | + | 0.533922i | |||||
0 | 0 | −0.739009 | − | 0.673696i | ||||||
0.739009 | + | 0.673696i | ||||||||
1.07524 | + | 0.811985i | 1.07524 | + | 0.811985i | |||||
0 | 0 | −0.445738 | − | 0.895163i | ||||||
0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0922684 | + | 0.995734i | −0.0922684 | + | 0.995734i | |||||
−0.0675278 | + | 0.00625737i | −0.0675278 | + | 0.00625737i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.285942 | − | 0.461813i | −0.285942 | − | 0.461813i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.92365i | 1.92365i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.380338 | − | 0.614268i | −0.380338 | − | 0.614268i | 0.602635 | − | 0.798017i | ||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | |||||
0.559395 | + | 0.346363i | 0.559395 | + | 0.346363i | |||||
0 | 0 | |||||||||
0 | 0 | −0.183750 | − | 0.982973i | ||||||
0.183750 | + | 0.982973i | ||||||||
−0.538007 | + | 1.89090i | −0.538007 | + | 1.89090i | |||||
−0.576554 | + | 0.435393i | −0.576554 | + | 0.435393i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.04837 | − | 1.69318i | −1.04837 | − | 1.69318i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.397365 | + | 0.798017i | −0.397365 | + | 0.798017i | 0.602635 | + | 0.798017i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.329838 | + | 1.15926i | −0.329838 | + | 1.15926i | |||||
0 | 0 | 0.982973 | − | 0.183750i | ||||||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.47802 | − | 1.34739i | 1.47802 | − | 1.34739i | 0.739009 | − | 0.673696i | ||
0.739009 | − | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.673696 | − | 0.739009i | ||||||
0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | |||||
1.70043 | 1.70043 | 0.850217 | − | 0.526432i | ||||||
0.850217 | + | 0.526432i | ||||||||
0.850217 | − | 0.526432i | 0.850217 | − | 0.526432i | |||||
0 | 0 | |||||||||
−0.220714 | + | 0.443254i | −0.220714 | + | 0.443254i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.34164 | − | 0.124322i | −1.34164 | − | 0.124322i | |||||
−0.365931 | − | 0.401408i | −0.365931 | − | 0.401408i | |||||
0.876298 | − | 0.163808i | 0.876298 | − | 0.163808i | |||||
0 | 0 | 0.739009 | − | 0.673696i | ||||||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.72198 | + | 0.489946i | −1.72198 | + | 0.489946i | |||||
1.93247 | − | 0.361242i | 1.93247 | − | 0.361242i | 0.932472 | − | 0.361242i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.404479 | − | 1.42160i | −0.404479 | − | 1.42160i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.445738 | − | 0.895163i | ||||||
−0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
−0.907732 | − | 0.995734i | −0.907732 | − | 0.995734i | 0.0922684 | − | 0.995734i | ||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.328972 | + | 0.163808i | 0.328972 | + | 0.163808i | |||||
0 | 0 | |||||||||
0 | 0 | 0.798017 | − | 0.602635i | ||||||
−0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.196216 | − | 0.178874i | −0.196216 | − | 0.178874i | |||||
0 | 0 | |||||||||
−0.445738 | + | 0.895163i | −0.445738 | + | 0.895163i | |||||
1.02474 | − | 0.634493i | 1.02474 | − | 0.634493i | 0.0922684 | − | 0.995734i | ||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.709310 | − | 1.14558i | −0.709310 | − | 1.14558i | −0.982973 | − | 0.183750i | ||
0.273663 | − | 0.961826i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.361242 | − | 0.932472i | ||||||
0.361242 | + | 0.932472i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.453067 | + | 0.413025i | 0.453067 | + | 0.413025i | |||||
1.91545 | − | 0.177492i | 1.91545 | − | 0.177492i | |||||
0 | 0 | |||||||||
−1.45285 | + | 1.32445i | −1.45285 | + | 1.32445i | |||||
−1.72198 | + | 0.489946i | −1.72198 | + | 0.489946i | |||||
0 | 0 | |||||||||
0 | 0 | 0.739009 | − | 0.673696i | ||||||
−0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.53511 | + | 1.15926i | 1.53511 | + | 1.15926i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.136374 | + | 1.47171i | 0.136374 | + | 1.47171i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.353470 | − | 0.100571i | −0.353470 | − | 0.100571i | |||||
1.04837 | + | 0.0971461i | 1.04837 | + | 0.0971461i | 0.602635 | − | 0.798017i | ||
0.445738 | + | 0.895163i | ||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.445738 | − | 0.895163i | ||||||
−0.445738 | + | 0.895163i | ||||||||
−0.0922684 | − | 0.995734i | −0.0922684 | − | 0.995734i | |||||
0 | 0 | |||||||||
−0.770410 | + | 1.02019i | −0.770410 | + | 1.02019i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.05286i | 1.05286i | 0.850217 | + | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.365931 | − | 0.0339085i | 0.365931 | − | 0.0339085i | |||||
1.20614 | − | 0.600584i | 1.20614 | − | 0.600584i | |||||
0 | 0 | |||||||||
0 | 0 | 0.0922684 | − | 0.995734i | ||||||
−0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
1.86494 | + | 0.722483i | 1.86494 | + | 0.722483i | 0.932472 | + | 0.361242i | ||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.20614 | − | 1.32307i | 1.20614 | − | 1.32307i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.53511 | + | 0.436776i | −1.53511 | + | 0.436776i | −0.932472 | − | 0.361242i | ||
−0.602635 | + | 0.798017i | ||||||||
0.380338 | − | 0.981767i | 0.380338 | − | 0.981767i | |||||
0 | 0 | |||||||||
−1.00711 | − | 0.623578i | −1.00711 | − | 0.623578i | |||||
0.293271 | − | 1.56886i | 0.293271 | − | 1.56886i | −0.445738 | − | 0.895163i | ||
0.739009 | − | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.353470 | − | 0.100571i | −0.353470 | − | 0.100571i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.798017 | − | 0.602635i | ||||||
0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0.646741 | − | 0.322039i | 0.646741 | − | 0.322039i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.164368 | − | 0.217658i | 0.164368 | − | 0.217658i | |||||
0 | 0 | |||||||||
0 | 0 | −0.361242 | − | 0.932472i | ||||||
0.361242 | + | 0.932472i | ||||||||
−0.719401 | − | 1.85699i | −0.719401 | − | 1.85699i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.365931 | − | 0.0339085i | 0.365931 | − | 0.0339085i | |||||
1.58561 | − | 0.614268i | 1.58561 | − | 0.614268i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.404479 | − | 0.368731i | 0.404479 | − | 0.368731i | −0.445738 | − | 0.895163i | ||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0505009 | − | 0.544991i | 0.0505009 | − | 0.544991i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.05286i | − | 1.05286i | −0.850217 | − | 0.526432i | ||||
0.850217 | − | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.891477 | 0.891477 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.361242 | − | 0.932472i | ||||||
−0.361242 | + | 0.932472i | ||||||||
0.353470 | − | 0.100571i | 0.353470 | − | 0.100571i | |||||
0 | 0 | |||||||||
−0.445738 | − | 0.895163i | −0.445738 | − | 0.895163i | |||||
0 | 0 | |||||||||
0.486734 | − | 0.533922i | 0.486734 | − | 0.533922i | |||||
−1.12093 | + | 0.318932i | −1.12093 | + | 0.318932i | |||||
0 | 0 | |||||||||
0 | 0 | −0.932472 | − | 0.361242i | ||||||
0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0.602635 | + | 0.798017i | 0.602635 | + | 0.798017i | |||||
0.298404 | + | 0.395150i | 0.298404 | + | 0.395150i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.96595 | −1.96595 | −0.982973 | − | 0.183750i | ||||||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.293271 | + | 0.221468i | −0.293271 | + | 0.221468i | |||||
0 | 0 | 0.0922684 | − | 0.995734i | ||||||
−0.0922684 | + | 0.995734i | ||||||||
0.559395 | + | 0.346363i | 0.559395 | + | 0.346363i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.673696 | − | 0.739009i | ||||||
−0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
−0.285942 | + | 0.461813i | −0.285942 | + | 0.461813i | |||||
0.465346 | − | 1.63552i | 0.465346 | − | 1.63552i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.719401 | − | 1.85699i | −0.719401 | − | 1.85699i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.20527 | 1.20527 | 0.602635 | − | 0.798017i | ||||||
0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.538007 | − | 1.89090i | −0.538007 | − | 1.89090i | −0.445738 | − | 0.895163i | ||
−0.0922684 | − | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.353470 | − | 0.100571i | 0.353470 | − | 0.100571i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.757949 | + | 0.469302i | 0.757949 | + | 0.469302i | 0.850217 | − | 0.526432i | ||
−0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.91545 | + | 0.544991i | −1.91545 | + | 0.544991i | |||||
1.83319 | − | 0.710182i | 1.83319 | − | 0.710182i | 0.850217 | − | 0.526432i | ||
0.982973 | − | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.27366 | − | 0.961826i | −1.27366 | − | 0.961826i | |||||
0 | 0 | |||||||||
−0.181395 | − | 0.0339085i | −0.181395 | − | 0.0339085i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.932472 | − | 0.361242i | −0.932472 | − | 0.361242i | |||||
0.719401 | + | 0.0666624i | 0.719401 | + | 0.0666624i | |||||
0 | 0 | |||||||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
1.72198 | − | 0.857445i | 1.72198 | − | 0.857445i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.06329 | − | 0.0985281i | 1.06329 | − | 0.0985281i | |||||
−1.72198 | − | 0.489946i | −1.72198 | − | 0.489946i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0170269 | + | 0.183750i | 0.0170269 | + | 0.183750i | 1.00000 | ||||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.385539 | − | 0.774267i | −0.385539 | − | 0.774267i | |||||
−0.757949 | + | 0.469302i | −0.757949 | + | 0.469302i | |||||
− | 1.99147i | − | 1.99147i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0505009 | − | 0.544991i | −0.0505009 | − | 0.544991i | |||||
0.353470 | + | 1.89090i | 0.353470 | + | 1.89090i | 0.445738 | + | 0.895163i | ||
−0.0922684 | + | 0.995734i | ||||||||
−0.247582 | + | 0.271585i | −0.247582 | + | 0.271585i | |||||
0 | 0 | −0.798017 | − | 0.602635i | ||||||
0.798017 | + | 0.602635i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.172075 | + | 1.85699i | −0.172075 | + | 1.85699i | |||||
0 | 0 | |||||||||
−0.0998072 | − | 0.0909863i | −0.0998072 | − | 0.0909863i | |||||
−0.694903 | + | 0.197717i | −0.694903 | + | 0.197717i | −0.602635 | − | 0.798017i | ||
−0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
1.47802 | 1.47802 | 0.739009 | − | 0.673696i | ||||||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.25664 | − | 0.778076i | 1.25664 | − | 0.778076i | |||||
−0.932472 | − | 0.361242i | −0.932472 | − | 0.361242i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.183750 | − | 0.982973i | ||||||
−0.183750 | + | 0.982973i | ||||||||
0 | 0 | |||||||||
0.223162 | − | 0.784333i | 0.223162 | − | 0.784333i | |||||
−0.510366 | − | 0.197717i | −0.510366 | − | 0.197717i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0799891 | + | 0.427904i | 0.0799891 | + | 0.427904i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0822551 | + | 0.165190i | 0.0822551 | + | 0.165190i | |||||
0 | 0 | |||||||||
−0.385539 | − | 0.774267i | −0.385539 | − | 0.774267i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.01267 | − | 0.288130i | 1.01267 | − | 0.288130i | 0.273663 | − | 0.961826i | ||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.840204 | − | 0.634493i | −0.840204 | − | 0.634493i | 0.0922684 | − | 0.995734i | ||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.982973 | − | 0.183750i | ||||||
−0.982973 | + | 0.183750i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.602635 | − | 0.798017i | ||||||
0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
−0.326219 | + | 0.655137i | −0.326219 | + | 0.655137i | |||||
−1.96595 | −1.96595 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.328972 | − | 1.75984i | 0.328972 | − | 1.75984i | |||||
1.58923 | + | 0.147263i | 1.58923 | + | 0.147263i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.07524 | + | 0.811985i | 1.07524 | + | 0.811985i | 0.982973 | − | 0.183750i | ||
0.0922684 | + | 0.995734i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.53511 | + | 0.436776i | −1.53511 | + | 0.436776i | −0.932472 | − | 0.361242i | ||
−0.602635 | + | 0.798017i | ||||||||
0.982973 | − | 0.183750i | 0.982973 | − | 0.183750i | |||||
0 | 0 | 0.273663 | − | 0.961826i | ||||||
−0.273663 | + | 0.961826i | ||||||||
1.25664 | − | 0.778076i | 1.25664 | − | 0.778076i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.895163 | − | 0.445738i | ||||||
−0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.220714 | − | 0.242112i | −0.220714 | − | 0.242112i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.365931 | − | 1.95756i | −0.365931 | − | 1.95756i | |||||
0 | 0 | |||||||||
0.735391 | + | 0.455335i | 0.735391 | + | 0.455335i | |||||
0.0822551 | + | 0.165190i | 0.0822551 | + | 0.165190i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.265512 | −0.265512 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0.329838 | + | 0.436776i | 0.329838 | + | 0.436776i | |||||
0 | 0 | |||||||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.404479 | − | 0.368731i | −0.404479 | − | 0.368731i | |||||
0 | 0 | |||||||||
0.156896 | − | 1.69318i | 0.156896 | − | 1.69318i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.739009 | − | 0.673696i | ||||||
0.739009 | + | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.537235 | + | 1.07891i | 0.537235 | + | 1.07891i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.284542 | + | 1.52217i | 0.284542 | + | 1.52217i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.34164 | + | 0.124322i | 1.34164 | + | 0.124322i | |||||
1.53511 | + | 0.436776i | 1.53511 | + | 0.436776i | 0.932472 | − | 0.361242i | ||
0.602635 | + | 0.798017i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.92365i | 1.92365i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.658809 | + | 1.32307i | −0.658809 | + | 1.32307i | |||||
−0.111208 | − | 1.20013i | −0.111208 | − | 1.20013i | −0.850217 | − | 0.526432i | ||
0.739009 | − | 0.673696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.58923 | − | 0.147263i | 1.58923 | − | 0.147263i | 0.739009 | − | 0.673696i | ||
0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.895163 | − | 0.445738i | ||||||
0.895163 | + | 0.445738i | ||||||||
0 | 0 | |||||||||
−1.98297 | − | 0.183750i | −1.98297 | − | 0.183750i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.876298 | + | 0.163808i | 0.876298 | + | 0.163808i | 0.602635 | − | 0.798017i | ||
0.273663 | + | 0.961826i | ||||||||
−0.156896 | − | 0.0971461i | −0.156896 | − | 0.0971461i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.932472 | + | 0.361242i | −0.932472 | + | 0.361242i | |||||
−2.54512 | + | 0.724149i | −2.54512 | + | 0.724149i | |||||
0 | 0 | |||||||||
0.486734 | + | 0.533922i | 0.486734 | + | 0.533922i | |||||
0.622242 | + | 0.385276i | 0.622242 | + | 0.385276i | |||||
0 | 0 | |||||||||
0 | 0 | −0.273663 | − | 0.961826i | ||||||
0.273663 | + | 0.961826i | ||||||||
0.0922684 | − | 0.995734i | 0.0922684 | − | 0.995734i | |||||
0 | 0 | |||||||||
0.0541192 | + | 0.584039i | 0.0541192 | + | 0.584039i | |||||
0 | 0 | 0.932472 | − | 0.361242i | ||||||
−0.932472 | + | 0.361242i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.260991 | + | 0.673696i | −0.260991 | + | 0.673696i | |||||
−1.70043 | −1.70043 | −0.850217 | − | 0.526432i | ||||||
−0.850217 | + | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.132756 | + | 0.342683i | 0.132756 | + | 0.342683i | |||||
0.646741 | + | 1.66943i | 0.646741 | + | 1.66943i | |||||
0 | 0 | |||||||||
0 | 0 | −0.961826 | − | 0.273663i | ||||||
0.961826 | + | 0.273663i | ||||||||
0 | 0 | |||||||||
−0.659202 | − | 0.255376i | −0.659202 | − | 0.255376i | |||||
1.34164 | + | 0.124322i | 1.34164 | + | 0.124322i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.673696 | − | 0.739009i | ||||||
−0.673696 | + | 0.739009i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.78269 | − | 0.887674i | −1.78269 | − | 0.887674i | −0.932472 | − | 0.361242i | ||
−0.850217 | − | 0.526432i | ||||||||
0 | 0 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1156.1.l.a.339.1 | ✓ | 16 | |
4.3 | odd | 2 | CM | 1156.1.l.a.339.1 | ✓ | 16 | |
289.237 | even | 34 | inner | 1156.1.l.a.815.1 | yes | 16 | |
1156.815 | odd | 34 | inner | 1156.1.l.a.815.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1156.1.l.a.339.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1156.1.l.a.339.1 | ✓ | 16 | 4.3 | odd | 2 | CM | |
1156.1.l.a.815.1 | yes | 16 | 289.237 | even | 34 | inner | |
1156.1.l.a.815.1 | yes | 16 | 1156.815 | odd | 34 | inner |