Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3840,1,Mod(29,3840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3840, base_ring=CyclotomicField(64))
chi = DirichletCharacter(H, H._module([0, 59, 32, 32]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3840.29");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 3840.dy (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: | |
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: | yes |
Projective image: | |
Projective field: | Galois closure of |
Embedding invariants
Embedding label | 149.1 | ||
Root | of defining polynomial | ||
Character | 3840.149 | ||
Dual form | 3840.1.dy.a.1469.1 |
-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 .
−0.857729 | − | 0.514103i | −0.857729 | − | 0.514103i | |||||
0.941544 | + | 0.336890i | 0.941544 | + | 0.336890i | |||||
0.471397 | + | 0.881921i | 0.471397 | + | 0.881921i | |||||
−0.803208 | − | 0.595699i | −0.803208 | − | 0.595699i | |||||
−0.634393 | − | 0.773010i | −0.634393 | − | 0.773010i | |||||
0 | 0 | −0.995185 | − | 0.0980171i | ||||||
0.995185 | + | 0.0980171i | ||||||||
0.0490677 | − | 0.998795i | 0.0490677 | − | 0.998795i | |||||
0.773010 | + | 0.634393i | 0.773010 | + | 0.634393i | |||||
0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | |||||
0 | 0 | −0.671559 | − | 0.740951i | ||||||
0.671559 | + | 0.740951i | ||||||||
0.146730 | + | 0.989177i | 0.146730 | + | 0.989177i | |||||
0 | 0 | 0.146730 | − | 0.989177i | ||||||
−0.146730 | + | 0.989177i | ||||||||
0 | 0 | |||||||||
−0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | |||||
−0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | |||||
−1.09911 | + | 1.64494i | −1.09911 | + | 1.64494i | −0.427555 | + | 0.903989i | ||
−0.671559 | + | 0.740951i | ||||||||
−0.336890 | − | 0.941544i | −0.336890 | − | 0.941544i | |||||
0.0504517 | − | 0.0841735i | 0.0504517 | − | 0.0841735i | −0.831470 | − | 0.555570i | ||
0.881921 | + | 0.471397i | ||||||||
0.146730 | − | 0.989177i | 0.146730 | − | 0.989177i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.71098 | + | 0.914539i | −1.71098 | + | 0.914539i | −0.740951 | + | 0.671559i | ||
−0.970031 | + | 0.242980i | ||||||||
0.382683 | − | 0.923880i | 0.382683 | − | 0.923880i | |||||
0.290285 | + | 0.956940i | 0.290285 | + | 0.956940i | |||||
0 | 0 | |||||||||
0.514103 | + | 0.857729i | 0.514103 | + | 0.857729i | |||||
0 | 0 | |||||||||
0 | 0 | 0.998795 | − | 0.0490677i | ||||||
−0.998795 | + | 0.0490677i | ||||||||
0.0490677 | + | 0.998795i | 0.0490677 | + | 0.998795i | |||||
−0.674993 | + | 1.62958i | −0.674993 | + | 1.62958i | 0.0980171 | + | 0.995185i | ||
−0.773010 | + | 0.634393i | ||||||||
0.903989 | − | 0.427555i | 0.903989 | − | 0.427555i | |||||
0 | 0 | |||||||||
1.78841 | − | 0.845855i | 1.78841 | − | 0.845855i | |||||
0 | 0 | |||||||||
−0.195090 | + | 0.980785i | −0.195090 | + | 0.980785i | |||||
0 | 0 | −0.970031 | − | 0.242980i | ||||||
0.970031 | + | 0.242980i | ||||||||
−0.0865477 | + | 0.0462607i | −0.0865477 | + | 0.0462607i | |||||
0 | 0 | |||||||||
−0.634393 | + | 0.773010i | −0.634393 | + | 0.773010i | |||||
0 | 0 | 0.290285 | − | 0.956940i | ||||||
−0.290285 | + | 0.956940i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.336890 | − | 0.941544i | ||||||
0.336890 | + | 0.941544i | ||||||||
0 | 0 | |||||||||
−0.242980 | − | 0.970031i | −0.242980 | − | 0.970031i | |||||
1.93773 | + | 0.0951944i | 1.93773 | + | 0.0951944i | |||||
1.77324 | − | 0.352719i | 1.77324 | − | 0.352719i | 0.803208 | − | 0.595699i | ||
0.970031 | + | 0.242980i | ||||||||
−0.803208 | + | 0.595699i | −0.803208 | + | 0.595699i | |||||
0.980785 | + | 0.195090i | 0.980785 | + | 0.195090i | |||||
0.242980 | − | 0.970031i | 0.242980 | − | 0.970031i | |||||
−1.58903 | + | 1.17850i | −1.58903 | + | 1.17850i | |||||
0 | 0 | |||||||||
−0.195798 | − | 0.00961895i | −0.195798 | − | 0.00961895i | −0.0490677 | − | 0.998795i | ||
−0.146730 | + | 0.989177i | ||||||||
− | 1.00000i | − | 1.00000i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0758597 | − | 0.0622564i | 0.0758597 | − | 0.0622564i | |||||
0 | 0 | |||||||||
0 | 0 | −0.146730 | − | 0.989177i | ||||||
0.146730 | + | 0.989177i | ||||||||
0.471397 | − | 0.881921i | 0.471397 | − | 0.881921i | |||||
−1.21416 | + | 0.574257i | −1.21416 | + | 0.574257i | −0.923880 | − | 0.382683i | ||
−0.290285 | + | 0.956940i | ||||||||
1.41673 | − | 1.05072i | 1.41673 | − | 1.05072i | |||||
0 | 0 | |||||||||
−0.995185 | − | 0.0980171i | −0.995185 | − | 0.0980171i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.427555 | − | 0.903989i | ||||||
0.427555 | + | 0.903989i | ||||||||
−1.96883 | − | 0.193913i | −1.96883 | − | 0.193913i | |||||
−1.91906 | + | 0.284666i | −1.91906 | + | 0.284666i | |||||
0 | 0 | |||||||||
0 | 0 | −0.634393 | − | 0.773010i | ||||||
0.634393 | + | 0.773010i | ||||||||
0.671559 | − | 0.740951i | 0.671559 | − | 0.740951i | |||||
0 | 0 | 0.995185 | − | 0.0980171i | ||||||
−0.995185 | + | 0.0980171i | ||||||||
0 | 0 | |||||||||
−0.0490677 | + | 0.998795i | −0.0490677 | + | 0.998795i | |||||
0.0980171 | + | 0.00481527i | 0.0980171 | + | 0.00481527i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.216773 | − | 1.08979i | 0.216773 | − | 1.08979i | −0.707107 | − | 0.707107i | ||
0.923880 | − | 0.382683i | ||||||||
0.941544 | − | 0.336890i | 0.941544 | − | 0.336890i | |||||
0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | |||||
0 | 0 | |||||||||
1.49969 | − | 0.375652i | 1.49969 | − | 0.375652i | 0.595699 | − | 0.803208i | ||
0.903989 | + | 0.427555i | ||||||||
0 | 0 | |||||||||
1.86271 | − | 0.666487i | 1.86271 | − | 0.666487i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.881921 | − | 0.471397i | ||||||
0.881921 | + | 0.471397i | ||||||||
−0.290285 | + | 0.956940i | −0.290285 | + | 0.956940i | |||||
0 | 0 | |||||||||
−1.61310 | − | 1.07784i | −1.61310 | − | 1.07784i | |||||
−1.18452 | + | 1.30692i | −1.18452 | + | 1.30692i | |||||
−1.70229 | − | 0.609090i | −1.70229 | − | 0.609090i | |||||
−0.0906652 | + | 0.0375548i | −0.0906652 | + | 0.0375548i | |||||
0.995185 | − | 0.0980171i | 0.995185 | − | 0.0980171i | |||||
0 | 0 | −0.923880 | − | 0.382683i | ||||||
0.923880 | + | 0.382683i | ||||||||
−0.740951 | − | 0.671559i | −0.740951 | − | 0.671559i | |||||
0 | 0 | |||||||||
−0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | |||||
0 | 0 | 0.857729 | − | 0.514103i | ||||||
−0.857729 | + | 0.514103i | ||||||||
1.96883 | − | 0.193913i | 1.96883 | − | 0.193913i | |||||
0 | 0 | 0.956940 | − | 0.290285i | ||||||
−0.956940 | + | 0.290285i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.162997 | + | 0.108911i | 0.162997 | + | 0.108911i | |||||
−0.248225 | + | 0.524828i | −0.248225 | + | 0.524828i | −0.989177 | − | 0.146730i | ||
0.740951 | + | 0.671559i | ||||||||
−0.514103 | + | 0.857729i | −0.514103 | + | 0.857729i | |||||
0.577920 | + | 0.346392i | 0.577920 | + | 0.346392i | 0.773010 | − | 0.634393i | ||
−0.195090 | + | 0.980785i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.710998 | − | 0.475074i | 0.710998 | − | 0.475074i | −0.146730 | − | 0.989177i | ||
0.857729 | + | 0.514103i | ||||||||
−0.0970732 | + | 0.0143994i | −0.0970732 | + | 0.0143994i | |||||
1.91906 | + | 0.284666i | 1.91906 | + | 0.284666i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.857729 | + | 0.514103i | −0.857729 | + | 0.514103i | |||||
−0.0980171 | + | 0.995185i | −0.0980171 | + | 0.995185i | |||||
1.33665 | + | 0.131649i | 1.33665 | + | 0.131649i | |||||
0 | 0 | |||||||||
−1.75535 | + | 0.172887i | −1.75535 | + | 0.172887i | |||||
0.336890 | − | 0.941544i | 0.336890 | − | 0.941544i | |||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0.803208 | + | 0.595699i | 0.803208 | + | 0.595699i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.336890 | − | 0.941544i | ||||||
−0.336890 | + | 0.941544i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0980171 | − | 0.995185i | 0.0980171 | − | 0.995185i | |||||
1.58903 | + | 1.17850i | 1.58903 | + | 1.17850i | |||||
−1.19462 | + | 1.45565i | −1.19462 | + | 1.45565i | −0.336890 | + | 0.941544i | ||
−0.857729 | + | 0.514103i | ||||||||
1.79238 | + | 0.742430i | 1.79238 | + | 0.742430i | |||||
0.761850 | − | 0.690501i | 0.761850 | − | 0.690501i | −0.195090 | − | 0.980785i | ||
0.956940 | + | 0.290285i | ||||||||
0 | 0 | |||||||||
1.78841 | + | 0.265286i | 1.78841 | + | 0.265286i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.956940 | + | 0.290285i | −0.956940 | + | 0.290285i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.857729 | + | 0.514103i | 0.857729 | + | 0.514103i | |||||
0 | 0 | |||||||||
0 | 0 | 0.427555 | − | 0.903989i | ||||||
−0.427555 | + | 0.903989i | ||||||||
0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | |||||
−0.598102 | − | 1.11897i | −0.598102 | − | 1.11897i | −0.980785 | − | 0.195090i | ||
0.382683 | − | 0.923880i | ||||||||
−0.0815966 | − | 0.0545211i | −0.0815966 | − | 0.0545211i | |||||
−1.89317 | + | 0.574286i | −1.89317 | + | 0.574286i | |||||
0 | 0 | |||||||||
1.51290 | − | 0.906796i | 1.51290 | − | 0.906796i | |||||
0 | 0 | |||||||||
0 | 0 | −0.0490677 | − | 0.998795i | ||||||
0.0490677 | + | 0.998795i | ||||||||
−0.746196 | + | 0.823301i | −0.746196 | + | 0.823301i | |||||
−0.181112 | − | 0.0750191i | −0.181112 | − | 0.0750191i | |||||
−0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | |||||
0 | 0 | |||||||||
0.336890 | − | 0.941544i | 0.336890 | − | 0.941544i | |||||
0 | 0 | 0.671559 | − | 0.740951i | ||||||
−0.671559 | + | 0.740951i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.47945 | − | 0.448786i | −1.47945 | − | 0.448786i | |||||
−1.05072 | − | 0.561621i | −1.05072 | − | 0.561621i | −0.146730 | − | 0.989177i | ||
−0.903989 | + | 0.427555i | ||||||||
0 | 0 | |||||||||
−0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | |||||
−1.94034 | − | 0.385958i | −1.94034 | − | 0.385958i | |||||
0.0923988 | − | 0.0330608i | 0.0923988 | − | 0.0330608i | |||||
0 | 0 | |||||||||
1.85652 | − | 0.465035i | 1.85652 | − | 0.465035i | 0.857729 | − | 0.514103i | ||
0.998795 | + | 0.0490677i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.595699 | − | 0.803208i | ||||||
0.595699 | + | 0.803208i | ||||||||
0.740951 | − | 0.671559i | 0.740951 | − | 0.671559i | |||||
−0.0788231 | + | 1.60448i | −0.0788231 | + | 1.60448i | 0.555570 | + | 0.831470i | ||
−0.634393 | + | 0.773010i | ||||||||
0 | 0 | |||||||||
−1.33665 | + | 0.131649i | −1.33665 | + | 0.131649i | |||||
0.829484 | + | 1.75380i | 0.829484 | + | 1.75380i | |||||
0 | 0 | |||||||||
1.68789 | − | 0.512016i | 1.68789 | − | 0.512016i | |||||
0 | 0 | |||||||||
1.14697 | + | 1.39759i | 1.14697 | + | 1.39759i | |||||
0 | 0 | |||||||||
0.0970732 | + | 0.0143994i | 0.0970732 | + | 0.0143994i | |||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
−0.903989 | − | 0.427555i | −0.903989 | − | 0.427555i | |||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.290285 | + | 0.956940i | 0.290285 | + | 0.956940i | |||||
0.287822 | + | 1.94034i | 0.287822 | + | 1.94034i | 0.336890 | + | 0.941544i | ||
−0.0490677 | + | 0.998795i | ||||||||
0 | 0 | |||||||||
−0.301614 | + | 0.247528i | −0.301614 | + | 0.247528i | −0.773010 | − | 0.634393i | ||
0.471397 | + | 0.881921i | ||||||||
0.970031 | − | 0.242980i | 0.970031 | − | 0.242980i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.78841 | − | 0.845855i | −1.78841 | − | 0.845855i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.90278 | − | 0.378487i | −1.90278 | − | 0.378487i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.163715 | + | 0.653587i | 0.163715 | + | 0.653587i | 0.995185 | + | 0.0980171i | ||
−0.831470 | + | 0.555570i | ||||||||
−0.0838155 | − | 0.177213i | −0.0838155 | − | 0.177213i | |||||
0 | 0 | |||||||||
0.482726 | − | 0.322547i | 0.482726 | − | 0.322547i | |||||
0 | 0 | |||||||||
0.881921 | − | 0.471397i | 0.881921 | − | 0.471397i | |||||
0 | 0 | |||||||||
−0.317618 | − | 0.594221i | −0.317618 | − | 0.594221i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
0 | 0 | |||||||||
−0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | |||||
−0.854080 | + | 0.0419583i | −0.854080 | + | 0.0419583i | |||||
−1.98797 | + | 0.0976628i | −1.98797 | + | 0.0976628i | −0.998795 | − | 0.0490677i | ||
−0.989177 | + | 0.146730i | ||||||||
0.0906652 | + | 0.0375548i | 0.0906652 | + | 0.0375548i | |||||
−0.881921 | − | 1.47140i | −0.881921 | − | 1.47140i | −0.881921 | − | 0.471397i | ||
− | 1.00000i | |||||||||
−1.49969 | − | 1.23076i | −1.49969 | − | 1.23076i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.51290 | + | 0.808661i | −1.51290 | + | 0.808661i | −0.998795 | − | 0.0490677i | ||
−0.514103 | + | 0.857729i | ||||||||
0 | 0 | |||||||||
−1.63439 | − | 0.773010i | −1.63439 | − | 0.773010i | |||||
0 | 0 | |||||||||
0.571240 | − | 0.953057i | 0.571240 | − | 0.953057i | |||||
0 | 0 | |||||||||
0 | 0 | 0.555570 | − | 0.831470i | ||||||
−0.555570 | + | 0.831470i | ||||||||
1.00000 | 1.00000 | |||||||||
−0.523788 | − | 0.783904i | −0.523788 | − | 0.783904i | 0.471397 | − | 0.881921i | ||
−0.995185 | + | 0.0980171i | ||||||||
0.595699 | − | 0.803208i | 0.595699 | − | 0.803208i | |||||
−0.146730 | + | 0.989177i | −0.146730 | + | 0.989177i | |||||
−1.07880 | − | 0.800094i | −1.07880 | − | 0.800094i | |||||
−0.671559 | − | 0.740951i | −0.671559 | − | 0.740951i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.59449 | + | 0.754140i | 1.59449 | + | 0.754140i | |||||
1.53858 | + | 0.151537i | 1.53858 | + | 0.151537i | |||||
−0.773010 | + | 0.634393i | −0.773010 | + | 0.634393i | |||||
0 | 0 | −0.803208 | − | 0.595699i | ||||||
0.803208 | + | 0.595699i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.97835 | 1.97835 | |||||||||
−0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | |||||
0.485960 | 0.485960 | 0.242980 | − | 0.970031i | ||||||
0.242980 | + | 0.970031i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.292048 | − | 0.0287642i | −0.292048 | − | 0.0287642i | −0.0490677 | − | 0.998795i | ||
−0.242980 | + | 0.970031i | ||||||||
0 | 0 | |||||||||
0.151537 | + | 0.124363i | 0.151537 | + | 0.124363i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.146730 | − | 0.989177i | ||||||
−0.146730 | + | 0.989177i | ||||||||
−0.595699 | + | 0.803208i | −0.595699 | + | 0.803208i | |||||
−0.425215 | − | 0.636379i | −0.425215 | − | 0.636379i | 0.555570 | − | 0.831470i | ||
−0.980785 | + | 0.195090i | ||||||||
−0.757083 | − | 1.82776i | −0.757083 | − | 1.82776i | |||||
0 | 0 | |||||||||
1.77301 | − | 0.634393i | 1.77301 | − | 0.634393i | |||||
0 | 0 | |||||||||
−1.15569 | − | 1.55827i | −1.15569 | − | 1.55827i | |||||
0 | 0 | −0.903989 | − | 0.427555i | ||||||
0.903989 | + | 0.427555i | ||||||||
−1.00845 | + | 0.200593i | −1.00845 | + | 0.200593i | |||||
−1.55557 | + | 0.831470i | −1.55557 | + | 0.831470i | |||||
0 | 0 | |||||||||
0 | 0 | −0.290285 | − | 0.956940i | ||||||
0.290285 | + | 0.956940i | ||||||||
−1.39759 | − | 1.14697i | −1.39759 | − | 1.14697i | |||||
0 | 0 | −0.514103 | − | 0.857729i | ||||||
0.514103 | + | 0.857729i | ||||||||
0 | 0 | |||||||||
−0.0980171 | + | 0.00481527i | −0.0980171 | + | 0.00481527i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.970031 | + | 0.242980i | 0.970031 | + | 0.242980i | |||||
−1.11509 | − | 2.69207i | −1.11509 | − | 2.69207i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.49969 | + | 0.375652i | 1.49969 | + | 0.375652i | 0.903989 | − | 0.427555i | ||
0.595699 | + | 0.803208i | ||||||||
−0.471397 | − | 0.881921i | −0.471397 | − | 0.881921i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.903989 | + | 0.427555i | −0.903989 | + | 0.427555i | |||||
0 | 0 | |||||||||
−0.0622564 | + | 1.26726i | −0.0622564 | + | 1.26726i | |||||
0 | 0 | |||||||||
0.0419583 | + | 0.0887133i | 0.0419583 | + | 0.0887133i | |||||
1.31731 | + | 0.262029i | 1.31731 | + | 0.262029i | |||||
1.91906 | + | 0.480701i | 1.91906 | + | 0.480701i | |||||
0 | 0 | 0.803208 | − | 0.595699i | ||||||
−0.803208 | + | 0.595699i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.76384 | −1.76384 | |||||||||
0 | 0 | −0.0980171 | − | 0.995185i | ||||||
0.0980171 | + | 0.995185i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.773010 | − | 0.634393i | ||||||
−0.773010 | + | 0.634393i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.06330 | − | 0.322547i | 1.06330 | − | 0.322547i | |||||
1.50328 | − | 0.710998i | 1.50328 | − | 0.710998i | 0.514103 | − | 0.857729i | ||
0.989177 | + | 0.146730i | ||||||||
0.116777 | + | 0.157456i | 0.116777 | + | 0.157456i | |||||
0 | 0 | |||||||||
0.740951 | + | 0.671559i | 0.740951 | + | 0.671559i | |||||
−0.410525 | + | 0.410525i | −0.410525 | + | 0.410525i | |||||
0 | 0 | |||||||||
0.0830083 | + | 0.175506i | 0.0830083 | + | 0.175506i | |||||
−0.773010 | + | 0.634393i | −0.773010 | + | 0.634393i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.427441 | + | 0.520839i | 0.427441 | + | 0.520839i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0584592 | − | 1.18996i | 0.0584592 | − | 1.18996i | −0.773010 | − | 0.634393i | ||
0.831470 | − | 0.555570i | ||||||||
1.03824 | + | 1.14553i | 1.03824 | + | 1.14553i | |||||
0 | 0 | |||||||||
0.612501 | + | 1.02190i | 0.612501 | + | 1.02190i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.195090 | − | 0.980785i | ||||||
0.195090 | + | 0.980785i | ||||||||
0.671559 | + | 0.740951i | 0.671559 | + | 0.740951i | |||||
0.829484 | − | 0.207775i | 0.829484 | − | 0.207775i | |||||
1.46586 | + | 1.32858i | 1.46586 | + | 1.32858i | |||||
0 | 0 | |||||||||
−0.0962497 | − | 0.0191453i | −0.0962497 | − | 0.0191453i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.71098 | + | 0.914539i | 1.71098 | + | 0.914539i | |||||
−1.83147 | − | 0.555570i | −1.83147 | − | 0.555570i | |||||
0.404061 | − | 1.61310i | 0.404061 | − | 1.61310i | −0.336890 | − | 0.941544i | ||
0.740951 | − | 0.671559i | ||||||||
0 | 0 | |||||||||
1.34150 | − | 1.48012i | 1.34150 | − | 1.48012i | 0.634393 | − | 0.773010i | ||
0.707107 | − | 0.707107i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.36910 | + | 0.567099i | 1.36910 | + | 0.567099i | 0.941544 | − | 0.336890i | ||
0.427555 | + | 0.903989i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.956940 | − | 0.290285i | ||||||
−0.956940 | + | 0.290285i | ||||||||
−0.980785 | + | 0.195090i | −0.980785 | + | 0.195090i | |||||
0.466857 | + | 0.873428i | 0.466857 | + | 0.873428i | |||||
0.892476 | − | 1.33569i | 0.892476 | − | 1.33569i | |||||
−0.427555 | + | 0.903989i | −0.427555 | + | 0.903989i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.21416 | + | 0.574257i | 1.21416 | + | 0.574257i | |||||
0 | 0 | −0.831470 | − | 0.555570i | ||||||
0.831470 | + | 0.555570i | ||||||||
0.190159 | − | 1.93072i | 0.190159 | − | 1.93072i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.71098 | − | 0.428579i | −1.71098 | − | 0.428579i | |||||
0 | 0 | 0.740951 | − | 0.671559i | ||||||
−0.740951 | + | 0.671559i | ||||||||
0 | 0 | |||||||||
0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | |||||
−0.265286 | − | 1.78841i | −0.265286 | − | 1.78841i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.956940 | + | 1.29028i | −0.956940 | + | 1.29028i | 1.00000i | ||||
−0.956940 | + | 0.290285i | ||||||||
−0.0758597 | − | 0.0622564i | −0.0758597 | − | 0.0622564i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.48190i | 1.48190i | 0.671559 | + | 0.740951i | ||||||
−0.671559 | + | 0.740951i | ||||||||
0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.595699 | − | 0.803208i | ||||||
−0.595699 | + | 0.803208i | ||||||||
0 | 0 | |||||||||
0.376202 | − | 3.81965i | 0.376202 | − | 3.81965i | |||||
0.242980 | − | 0.970031i | 0.242980 | − | 0.970031i | |||||
0 | 0 | |||||||||
0.750661 | − | 1.81225i | 0.750661 | − | 1.81225i | |||||
−0.823301 | + | 0.746196i | −0.823301 | + | 0.746196i | |||||
0 | 0 | |||||||||
0 | 0 | −0.989177 | − | 0.146730i | ||||||
0.989177 | + | 0.146730i | ||||||||
0.385958 | − | 0.0572514i | 0.385958 | − | 0.0572514i | |||||
0 | 0 | |||||||||
−0.956940 | − | 0.290285i | −0.956940 | − | 0.290285i | |||||
0 | 0 | −0.831470 | − | 0.555570i | ||||||
0.831470 | + | 0.555570i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.427555 | − | 0.903989i | 0.427555 | − | 0.903989i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.09911 | + | 1.64494i | 1.09911 | + | 1.64494i | |||||
1.21415 | − | 0.368309i | 1.21415 | − | 0.368309i | 0.382683 | − | 0.923880i | ||
0.831470 | + | 0.555570i | ||||||||
0 | 0 | |||||||||
−1.61518 | + | 0.968101i | −1.61518 | + | 0.968101i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.43749 | + | 1.30287i | 1.43749 | + | 1.30287i | |||||
−1.42834 | − | 0.591637i | −1.42834 | − | 0.591637i | |||||
0 | 0 | |||||||||
0.949938 | − | 0.393477i | 0.949938 | − | 0.393477i | |||||
0 | 0 | |||||||||
0 | 0 | 0.671559 | − | 0.740951i | ||||||
−0.671559 | + | 0.740951i | ||||||||
0 | 0 | |||||||||
−0.249834 | + | 0.997391i | −0.249834 | + | 0.997391i | 0.707107 | + | 0.707107i | ||
−0.956940 | + | 0.290285i | ||||||||
0.195588 | − | 0.644767i | 0.195588 | − | 0.644767i | |||||
1.59449 | + | 0.852275i | 1.59449 | + | 0.852275i | |||||
−0.0192147 | + | 0.195090i | −0.0192147 | + | 0.195090i | |||||
−1.89317 | − | 0.574286i | −1.89317 | − | 0.574286i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.579870 | + | 0.0284872i | −0.579870 | + | 0.0284872i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.195090 | − | 0.980785i | ||||||
0.195090 | + | 0.980785i | ||||||||
−0.998795 | − | 0.0490677i | −0.998795 | − | 0.0490677i | |||||
0 | 0 | 0.195090 | − | 0.980785i | ||||||
−0.195090 | + | 0.980785i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0330608 | + | 0.672968i | −0.0330608 | + | 0.672968i | |||||
−0.00934193 | + | 0.190159i | −0.00934193 | + | 0.190159i | |||||
0 | 0 | |||||||||
1.95213 | − | 0.192268i | 1.95213 | − | 0.192268i | 0.956940 | − | 0.290285i | ||
0.995185 | + | 0.0980171i | ||||||||
0 | 0 | |||||||||
0.634393 | + | 0.773010i | 0.634393 | + | 0.773010i | |||||
0 | 0 | |||||||||
−0.932589 | + | 0.138337i | −0.932589 | + | 0.138337i | −0.595699 | − | 0.803208i | ||
−0.336890 | + | 0.941544i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0.803208 | − | 0.595699i | 0.803208 | − | 0.595699i | |||||
0 | 0 | |||||||||
0.754140 | + | 0.403096i | 0.754140 | + | 0.403096i | |||||
−0.186170 | − | 1.25505i | −0.186170 | − | 1.25505i | |||||
1.75535 | + | 0.938254i | 1.75535 | + | 0.938254i | |||||
0 | 0 | |||||||||
−0.0584592 | − | 0.0788231i | −0.0584592 | − | 0.0788231i | |||||
0 | 0 | −0.0980171 | − | 0.995185i | ||||||
0.0980171 | + | 0.995185i | ||||||||
1.71546i | 1.71546i | |||||||||
−1.97597 | − | 0.0970732i | −1.97597 | − | 0.0970732i | |||||
0.653587 | + | 1.82665i | 0.653587 | + | 1.82665i | |||||
0 | 0 | 0.803208 | − | 0.595699i | ||||||
−0.803208 | + | 0.595699i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.980785 | − | 0.195090i | ||||||
0.980785 | + | 0.195090i | ||||||||
0 | 0 | |||||||||
1.72995 | − | 0.344109i | 1.72995 | − | 0.344109i | |||||
1.71339 | + | 0.0841735i | 1.71339 | + | 0.0841735i | |||||
0.476623 | + | 1.90278i | 0.476623 | + | 1.90278i | 0.427555 | + | 0.903989i | ||
0.0490677 | + | 0.998795i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00446 | + | 1.50328i | 1.00446 | + | 1.50328i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.979938 | + | 0.523788i | −0.979938 | + | 0.523788i | |||||
0.0951944 | + | 0.0238449i | 0.0951944 | + | 0.0238449i | |||||
0 | 0 | |||||||||
−0.145252 | − | 0.131649i | −0.145252 | − | 0.131649i | |||||
0 | 0 | |||||||||
0 | 0 | −0.382683 | − | 0.923880i | ||||||
0.382683 | + | 0.923880i | ||||||||
−0.857729 | − | 0.514103i | −0.857729 | − | 0.514103i | |||||
0 | 0 | |||||||||
0.0462607 | + | 0.941658i | 0.0462607 | + | 0.941658i | |||||
0 | 0 | |||||||||
−0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | |||||
0 | 0 | |||||||||
0.634393 | − | 0.773010i | 0.634393 | − | 0.773010i | |||||
0 | 0 | −0.290285 | − | 0.956940i | ||||||
0.290285 | + | 0.956940i | ||||||||
0.513989 | + | 1.24088i | 0.513989 | + | 1.24088i | |||||
0 | 0 | |||||||||
0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | |||||
0 | 0 | −0.903989 | − | 0.427555i | ||||||
0.903989 | + | 0.427555i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.979938 | − | 1.46658i | −0.979938 | − | 1.46658i | |||||
0 | 0 | |||||||||
−1.24178 | − | 0.920964i | −1.24178 | − | 0.920964i | |||||
0.251710 | − | 1.69689i | 0.251710 | − | 1.69689i | −0.382683 | − | 0.923880i | ||
0.634393 | − | 0.773010i | ||||||||
0.989177 | − | 0.146730i | 0.989177 | − | 0.146730i | |||||
−0.800094 | − | 0.882768i | −0.800094 | − | 0.882768i | |||||
0 | 0 | |||||||||
−1.45565 | − | 1.19462i | −1.45565 | − | 1.19462i | −0.941544 | − | 0.336890i | ||
−0.514103 | − | 0.857729i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.803208 | − | 0.595699i | −0.803208 | − | 0.595699i | |||||
0 | 0 | |||||||||
0 | 0 | −0.941544 | − | 0.336890i | ||||||
0.941544 | + | 0.336890i | ||||||||
−1.69689 | − | 1.01708i | −1.69689 | − | 1.01708i | |||||
0 | 0 | |||||||||
−0.146730 | + | 0.989177i | −0.146730 | + | 0.989177i | |||||
0.0981353 | 0.0981353 | |||||||||
−0.416822 | − | 0.249834i | −0.416822 | − | 0.249834i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.90466 | + | 0.187593i | 1.90466 | + | 0.187593i | |||||
0 | 0 | |||||||||
0 | 0 | −0.773010 | − | 0.634393i | ||||||
0.773010 | + | 0.634393i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.671559 | − | 0.740951i | ||||||
0.671559 | + | 0.740951i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.235710 | + | 0.174814i | 0.235710 | + | 0.174814i | |||||
−1.93866 | − | 2.90142i | −1.93866 | − | 2.90142i | |||||
0 | 0 | |||||||||
1.53551 | − | 2.29805i | 1.53551 | − | 2.29805i | |||||
−0.0660420 | − | 0.184575i | −0.0660420 | − | 0.184575i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.512016 | − | 0.273678i | 0.512016 | − | 0.273678i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | |||||
1.18996 | − | 0.0584592i | 1.18996 | − | 0.0584592i | 0.555570 | − | 0.831470i | ||
0.634393 | + | 0.773010i | ||||||||
0.0375548 | + | 0.764445i | 0.0375548 | + | 0.764445i | |||||
−0.614748 | + | 1.48413i | −0.614748 | + | 1.48413i | |||||
−0.290285 | + | 1.95694i | −0.290285 | + | 1.95694i | |||||
−0.257844 | − | 0.622491i | −0.257844 | − | 0.622491i | |||||
0 | 0 | |||||||||
0 | 0 | −0.740951 | − | 0.671559i | ||||||
0.740951 | + | 0.671559i | ||||||||
−1.84691 | − | 0.367372i | −1.84691 | − | 0.367372i | |||||
−1.30287 | − | 0.326351i | −1.30287 | − | 0.326351i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.190159 | + | 1.93072i | 0.190159 | + | 1.93072i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.968101 | + | 0.346392i | 0.968101 | + | 0.346392i | |||||
0.308290 | + | 1.23076i | 0.308290 | + | 1.23076i | 0.903989 | + | 0.427555i | ||
−0.595699 | + | 0.803208i | ||||||||
1.76172 | + | 0.0865477i | 1.76172 | + | 0.0865477i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.57555 | − | 1.16851i | 1.57555 | − | 1.16851i | 0.671559 | − | 0.740951i | ||
0.903989 | − | 0.427555i | ||||||||
0.609090 | + | 1.70229i | 0.609090 | + | 1.70229i | |||||
−0.854080 | − | 0.0419583i | −0.854080 | − | 0.0419583i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.773010 | − | 0.634393i | ||||||
−0.773010 | + | 0.634393i | ||||||||
0.0865477 | + | 0.0462607i | 0.0865477 | + | 0.0462607i | |||||
−0.0713052 | − | 0.480701i | −0.0713052 | − | 0.480701i | −0.995185 | − | 0.0980171i | ||
0.923880 | − | 0.382683i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.37183 | − | 1.37183i | −1.37183 | − | 1.37183i | |||||
−0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | |||||
0 | 0 | 0.707107 | − | 0.707107i | ||||||
−0.707107 | + | 0.707107i | ||||||||
−0.427555 | + | 2.88234i | −0.427555 | + | 2.88234i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.09320 | − | 1.09320i | −1.09320 | − | 1.09320i | |||||
0.0939097 | − | 1.91158i | 0.0939097 | − | 1.91158i | −0.242980 | − | 0.970031i | ||
0.336890 | − | 0.941544i | ||||||||
−0.0490677 | + | 0.998795i | −0.0490677 | + | 0.998795i | |||||
0.103113 | + | 0.139031i | 0.103113 | + | 0.139031i | |||||
0 | 0 | |||||||||
−0.382683 | + | 1.92388i | −0.382683 | + | 1.92388i | |||||
0 | 0 | |||||||||
0.200593 | + | 1.00845i | 0.200593 | + | 1.00845i | 0.941544 | + | 0.336890i | ||
−0.740951 | + | 0.671559i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.367372 | + | 0.131448i | −0.367372 | + | 0.131448i | |||||
0 | 0 | |||||||||
0 | 0 | −0.956940 | − | 0.290285i | ||||||
0.956940 | + | 0.290285i | ||||||||
0.995185 | + | 0.0980171i | 0.995185 | + | 0.0980171i | |||||
−1.11897 | − | 0.598102i | −1.11897 | − | 0.598102i | −0.195090 | − | 0.980785i | ||
−0.923880 | + | 0.382683i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.704900 | − | 1.05496i | 0.704900 | − | 1.05496i | |||||
0.671559 | − | 0.740951i | 0.671559 | − | 0.740951i | |||||
0 | 0 | |||||||||
0 | 0 | 0.923880 | − | 0.382683i | ||||||
−0.923880 | + | 0.382683i | ||||||||
0.00961895 | − | 0.0976628i | 0.00961895 | − | 0.0976628i | |||||
0 | 0 | |||||||||
−0.995185 | − | 0.901983i | −0.995185 | − | 0.901983i | |||||
0 | 0 | |||||||||
−1.39891 | − | 1.39891i | −1.39891 | − | 1.39891i | |||||
0 | 0 | 0.857729 | − | 0.514103i | ||||||
−0.857729 | + | 0.514103i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.852275 | + | 1.59449i | 0.852275 | + | 1.59449i | 0.803208 | + | 0.595699i | ||
0.0490677 | + | 0.998795i | ||||||||
0 | 0 | |||||||||
0.805124 | − | 1.70229i | 0.805124 | − | 1.70229i | 0.0980171 | − | 0.995185i | ||
0.707107 | − | 0.707107i | ||||||||
1.51290 | + | 0.906796i | 1.51290 | + | 0.906796i | |||||
−1.66405 | − | 0.997391i | −1.66405 | − | 0.997391i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.17221 | + | 1.42834i | −1.17221 | + | 1.42834i | −0.290285 | + | 0.956940i | ||
−0.881921 | + | 0.471397i | ||||||||
−1.07784 | − | 0.269985i | −1.07784 | − | 0.269985i | |||||
−0.0660420 | + | 0.670535i | −0.0660420 | + | 0.670535i | |||||
−1.65493 | − | 0.162997i | −1.65493 | − | 0.162997i | |||||
0 | 0 | |||||||||
−0.0192147 | − | 0.195090i | −0.0192147 | − | 0.195090i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.290285 | − | 0.956940i | −0.290285 | − | 0.956940i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0.563170 | − | 0.141067i | 0.563170 | − | 0.141067i | |||||
0 | 0 | 0.336890 | − | 0.941544i | ||||||
−0.336890 | + | 0.941544i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0190297 | − | 0.193211i | 0.0190297 | − | 0.193211i | |||||
0.195798 | − | 1.98797i | 0.195798 | − | 1.98797i | 0.0490677 | − | 0.998795i | ||
0.146730 | − | 0.989177i | ||||||||
0.989177 | − | 0.146730i | 0.989177 | − | 0.146730i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.574286 | + | 0.0851872i | 0.574286 | + | 0.0851872i | 0.427555 | − | 0.903989i | ||
0.146730 | + | 0.989177i | ||||||||
−0.0988640 | − | 0.666487i | −0.0988640 | − | 0.666487i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.857729 | − | 0.514103i | ||||||
0.857729 | + | 0.514103i | ||||||||
0 | 0 | |||||||||
−0.805124 | + | 1.70229i | −0.805124 | + | 1.70229i | −0.0980171 | + | 0.995185i | ||
−0.707107 | + | 0.707107i | ||||||||
−0.661906 | + | 0.990612i | −0.661906 | + | 0.990612i | |||||
0 | 0 | |||||||||
−0.301614 | − | 1.51631i | −0.301614 | − | 1.51631i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.19140i | − | 1.19140i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.923880 | − | 0.382683i | ||||||
−0.923880 | + | 0.382683i | ||||||||
0 | 0 | |||||||||
−0.671559 | + | 0.740951i | −0.671559 | + | 0.740951i | |||||
−0.195090 | − | 0.980785i | −0.195090 | − | 0.980785i | |||||
0.229080 | − | 0.914539i | 0.229080 | − | 0.914539i | −0.740951 | − | 0.671559i | ||
0.970031 | − | 0.242980i | ||||||||
−0.818289 | − | 0.248225i | −0.818289 | − | 0.248225i | |||||
0 | 0 | |||||||||
−0.574286 | − | 1.89317i | −0.574286 | − | 1.89317i | |||||
−1.90466 | − | 0.577774i | −1.90466 | − | 0.577774i | |||||
0 | 0 | |||||||||
1.04619 | − | 0.374332i | 1.04619 | − | 0.374332i | 0.242980 | − | 0.970031i | ||
0.803208 | + | 0.595699i | ||||||||
0.0727135 | + | 0.0659037i | 0.0727135 | + | 0.0659037i | |||||
1.82665 | − | 0.457553i | 1.82665 | − | 0.457553i | |||||
0 | 0 | |||||||||
−0.334669 | − | 1.68250i | −0.334669 | − | 1.68250i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.997391 | − | 1.66405i | −0.997391 | − | 1.66405i | |||||
−0.956940 | − | 1.29028i | −0.956940 | − | 1.29028i | −0.956940 | − | 0.290285i | ||
− | 1.00000i | |||||||||
1.28528 | + | 1.41809i | 1.28528 | + | 1.41809i | |||||
0 | 0 | |||||||||
−1.17588 | + | 1.17588i | −1.17588 | + | 1.17588i | |||||
−1.02325 | + | 0.100782i | −1.02325 | + | 0.100782i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.91158 | + | 0.579870i | −1.91158 | + | 0.579870i | |||||
−1.69689 | + | 0.251710i | −1.69689 | + | 0.251710i | |||||
0 | 0 | |||||||||
0 | 0 | −0.427555 | − | 0.903989i | ||||||
0.427555 | + | 0.903989i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.27843 | − | 1.27843i | −1.27843 | − | 1.27843i | |||||
−0.882768 | − | 1.19028i | −0.882768 | − | 1.19028i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.293107 | + | 1.97597i | 0.293107 | + | 1.97597i | 0.195090 | + | 0.980785i | ||
0.0980171 | + | 0.995185i | ||||||||
0 | 0 | |||||||||
0.858923 | − | 0.704900i | 0.858923 | − | 0.704900i | |||||
0 | 0 | |||||||||
−0.335411 | − | 3.40549i | −0.335411 | − | 3.40549i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.980785 | − | 0.195090i | ||||||
0.980785 | + | 0.195090i | ||||||||
0.941544 | + | 0.336890i | 0.941544 | + | 0.336890i | |||||
0 | 0 | |||||||||
0.0485951 | − | 0.989177i | 0.0485951 | − | 0.989177i | |||||
−0.229080 | − | 0.914539i | −0.229080 | − | 0.914539i | |||||
−1.45218 | + | 0.686831i | −1.45218 | + | 0.686831i | |||||
0 | 0 | |||||||||
0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | |||||
0 | 0 | 0.290285 | − | 0.956940i | ||||||
−0.290285 | + | 0.956940i | ||||||||
0 | 0 | |||||||||
−0.471397 | + | 0.881921i | −0.471397 | + | 0.881921i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.746196 | − | 1.11676i | −0.746196 | − | 1.11676i | |||||
0 | 0 | −0.740951 | − | 0.671559i | ||||||
0.740951 | + | 0.671559i | ||||||||
0 | 0 | |||||||||
−0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | |||||
−1.15569 | + | 1.55827i | −1.15569 | + | 1.55827i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.854080 | + | 0.0419583i | −0.854080 | + | 0.0419583i | −0.471397 | − | 0.881921i | ||
−0.382683 | + | 0.923880i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.430174 | − | 1.41809i | −0.430174 | − | 1.41809i | −0.857729 | − | 0.514103i | ||
0.427555 | − | 0.903989i | ||||||||
1.24723 | + | 1.24723i | 1.24723 | + | 1.24723i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.39759 | + | 0.661009i | 1.39759 | + | 0.661009i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.941544 | + | 0.336890i | −0.941544 | + | 0.336890i | |||||
−0.322547 | + | 0.482726i | −0.322547 | + | 0.482726i | −0.956940 | − | 0.290285i | ||
0.634393 | + | 0.773010i | ||||||||
−0.691883 | + | 1.67035i | −0.691883 | + | 1.67035i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.186170 | + | 1.25505i | −0.186170 | + | 1.25505i | |||||
0 | 0 | |||||||||
0 | 0 | −0.671559 | − | 0.740951i | ||||||
0.671559 | + | 0.740951i | ||||||||
1.48413 | − | 0.614748i | 1.48413 | − | 0.614748i | |||||
0 | 0 | |||||||||
0.0330608 | + | 0.0923988i | 0.0330608 | + | 0.0923988i | |||||
0 | 0 | −0.995185 | − | 0.0980171i | ||||||
0.995185 | + | 0.0980171i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.86271 | + | 0.666487i | 1.86271 | + | 0.666487i | |||||
0.761850 | − | 1.27107i | 0.761850 | − | 1.27107i | |||||
0 | 0 | |||||||||
−0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | |||||
−0.580569 | −0.580569 | −0.290285 | − | 0.956940i | ||||||
−0.290285 | + | 0.956940i | ||||||||
0 | 0 | |||||||||
0.457553 | + | 0.163715i | 0.457553 | + | 0.163715i | |||||
0 | 0 | |||||||||
1.48413 | + | 1.10071i | 1.48413 | + | 1.10071i | 0.970031 | + | 0.242980i | ||
0.514103 | + | 0.857729i | ||||||||
0 | 0 | |||||||||
−1.75535 | − | 0.172887i | −1.75535 | − | 0.172887i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.28637 | + | 3.08281i | −2.28637 | + | 3.08281i | |||||
0 | 0 | |||||||||
−0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.514103 | − | 0.857729i | ||||||
−0.514103 | + | 0.857729i | ||||||||
−1.57555 | + | 1.16851i | −1.57555 | + | 1.16851i | |||||
−0.265286 | − | 0.125471i | −0.265286 | − | 0.125471i | |||||
1.08979 | − | 0.216773i | 1.08979 | − | 0.216773i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.100782 | + | 0.168144i | 0.100782 | + | 0.168144i | |||||
−0.360480 | − | 0.149316i | −0.360480 | − | 0.149316i | |||||
−1.66094 | + | 0.0815966i | −1.66094 | + | 0.0815966i | −0.857729 | − | 0.514103i | ||
−0.803208 | + | 0.595699i | ||||||||
0 | 0 | |||||||||
−1.36879 | + | 3.30455i | −1.36879 | + | 3.30455i | |||||
0.671559 | + | 0.740951i | 0.671559 | + | 0.740951i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.290285 | − | 0.956940i | ||||||
−0.290285 | + | 0.956940i | ||||||||
−0.831470 | + | 0.555570i | −0.831470 | + | 0.555570i | |||||
−0.499238 | − | 1.39528i | −0.499238 | − | 1.39528i | −0.881921 | − | 0.471397i | ||
0.382683 | − | 0.923880i | ||||||||
0 | 0 | |||||||||
−0.185969 | − | 0.742430i | −0.185969 | − | 0.742430i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0970732 | − | 1.97597i | −0.0970732 | − | 1.97597i | |||||
0 | 0 | |||||||||
−1.23076 | − | 0.308290i | −1.23076 | − | 0.308290i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.998795 | − | 0.0490677i | ||||||
0.998795 | + | 0.0490677i | ||||||||
1.88309 | 1.88309 | |||||||||
0 | 0 | −0.0980171 | − | 0.995185i | ||||||
0.0980171 | + | 0.995185i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.244004 | − | 1.64494i | −0.244004 | − | 1.64494i | −0.671559 | − | 0.740951i | ||
0.427555 | − | 0.903989i | ||||||||
−0.563170 | − | 1.85652i | −0.563170 | − | 1.85652i | |||||
−0.265286 | + | 0.125471i | −0.265286 | + | 0.125471i | −0.555570 | − | 0.831470i | ||
0.290285 | + | 0.956940i | ||||||||
0.920964 | + | 1.24178i | 0.920964 | + | 1.24178i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.39891 | + | 1.39891i | −1.39891 | + | 1.39891i | |||||
−1.01708 | − | 0.150869i | −1.01708 | − | 0.150869i | |||||
0.509389 | + | 1.07701i | 0.509389 | + | 1.07701i | |||||
0 | 0 | |||||||||
−1.74475 | + | 0.258809i | −1.74475 | + | 0.258809i | |||||
0 | 0 | |||||||||
0 | 0 | −0.634393 | − | 0.773010i | ||||||
0.634393 | + | 0.773010i | ||||||||
0 | 0 | |||||||||
0.995185 | − | 0.0980171i | 0.995185 | − | 0.0980171i | |||||
0.727051 | − | 0.727051i | 0.727051 | − | 0.727051i | |||||
0 | 0 | |||||||||
−0.499238 | + | 0.452483i | −0.499238 | + | 0.452483i | |||||
0.595699 | + | 0.803208i | 0.595699 | + | 0.803208i | |||||
−0.929487 | − | 1.55075i | −0.929487 | − | 1.55075i | |||||
0 | 0 | |||||||||
0.116777 | − | 0.157456i | 0.116777 | − | 0.157456i | |||||
0 | 0 | |||||||||
1.32858 | + | 1.46586i | 1.32858 | + | 1.46586i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.941544 | − | 0.336890i | ||||||
−0.941544 | + | 0.336890i | ||||||||
0 | 0 | |||||||||
−0.0939097 | − | 0.0284872i | −0.0939097 | − | 0.0284872i | |||||
0.512016 | + | 0.273678i | 0.512016 | + | 0.273678i | |||||
1.18452 | + | 0.633141i | 1.18452 | + | 0.633141i | 0.941544 | − | 0.336890i | ||
0.242980 | + | 0.970031i | ||||||||
0 | 0 | |||||||||
0.326351 | − | 1.30287i | 0.326351 | − | 1.30287i | −0.555570 | − | 0.831470i | ||
0.881921 | − | 0.471397i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.949938 | − | 0.393477i | 0.949938 | − | 0.393477i | 0.146730 | − | 0.989177i | ||
0.803208 | + | 0.595699i | ||||||||
0.831470 | + | 0.555570i | 0.831470 | + | 0.555570i | |||||
−1.76820 | − | 0.732410i | −1.76820 | − | 0.732410i | |||||
0 | 0 | |||||||||
−0.142977 | − | 2.91037i | −0.142977 | − | 2.91037i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.374332 | − | 0.560227i | 0.374332 | − | 0.560227i | |||||
0 | 0 | |||||||||
0.105774 | − | 0.158302i | 0.105774 | − | 0.158302i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.857729 | − | 0.514103i | ||||||
0.857729 | + | 0.514103i | ||||||||
−1.77324 | − | 0.838679i | −1.77324 | − | 0.838679i | |||||
1.28547 | + | 0.858923i | 1.28547 | + | 0.858923i | |||||
0 | 0 | |||||||||
0 | 0 | 0.831470 | − | 0.555570i | ||||||
−0.831470 | + | 0.555570i | ||||||||
−0.146730 | − | 0.989177i | −0.146730 | − | 0.989177i | |||||
0 | 0 | −0.989177 | − | 0.146730i | ||||||
0.989177 | + | 0.146730i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.871028 | + | 0.360791i | 0.871028 | + | 0.360791i | |||||
−1.08827 | + | 1.32607i | −1.08827 | + | 1.32607i | −0.146730 | + | 0.989177i | ||
−0.941544 | + | 0.336890i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0597732 | − | 0.167055i | 0.0597732 | − | 0.167055i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.995185 | + | 0.0980171i | −0.995185 | + | 0.0980171i | |||||
0.231027 | − | 0.311504i | 0.231027 | − | 0.311504i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.439614 | − | 0.733452i | −0.439614 | − | 0.733452i | |||||
1.01910 | − | 1.24178i | 1.01910 | − | 1.24178i | |||||
−0.485544 | + | 1.17221i | −0.485544 | + | 1.17221i | |||||
0 | 0 | 0.740951 | − | 0.671559i | ||||||
−0.740951 | + | 0.671559i | ||||||||
−1.02325 | − | 1.70720i | −1.02325 | − | 1.70720i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.831470 | − | 0.555570i | ||||||
−0.831470 | + | 0.555570i | ||||||||
0.00961895 | + | 0.0976628i | 0.00961895 | + | 0.0976628i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.15203 | + | 0.690501i | 1.15203 | + | 0.690501i | |||||
0.881921 | − | 1.47140i | 0.881921 | − | 1.47140i | |||||
0 | 0 | |||||||||
1.64494 | + | 1.09911i | 1.64494 | + | 1.09911i | |||||
0.938254 | + | 1.75535i | 0.938254 | + | 1.75535i | 0.555570 | + | 0.831470i | ||
0.382683 | + | 0.923880i | ||||||||
0.378487 | − | 1.90278i | 0.378487 | − | 1.90278i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.923880 | − | 0.382683i | ||||||
−0.923880 | + | 0.382683i | ||||||||
−1.66074 | − | 0.594221i | −1.66074 | − | 0.594221i | |||||
0.0659037 | − | 0.0727135i | 0.0659037 | − | 0.0727135i | |||||
−1.42635 | − | 0.953057i | −1.42635 | − | 0.953057i | |||||
0 | 0 | |||||||||
0.569414 | − | 1.87711i | 0.569414 | − | 1.87711i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.956940 | − | 0.290285i | ||||||
0.956940 | + | 0.290285i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.0887133 | − | 1.80580i | −0.0887133 | − | 1.80580i | |||||
0 | 0 | 0.970031 | − | 0.242980i | ||||||
−0.970031 | + | 0.242980i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.755815 | + | 1.01910i | 0.755815 | + | 1.01910i | 0.998795 | + | 0.0490677i | ||
−0.242980 | + | 0.970031i | ||||||||
1.10980 | + | 0.0545211i | 1.10980 | + | 0.0545211i | |||||
0 | 0 | |||||||||
−0.0693922 | − | 0.0693922i | −0.0693922 | − | 0.0693922i | |||||
1.65493 | − | 0.162997i | 1.65493 | − | 0.162997i | |||||
0 | 0 | |||||||||
−0.755815 | − | 0.920964i | −0.755815 | − | 0.920964i | 0.242980 | − | 0.970031i | ||
−0.998795 | + | 0.0490677i | ||||||||
0.0569057 | + | 0.187593i | 0.0569057 | + | 0.187593i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.471397 | + | 0.881921i | 0.471397 | + | 0.881921i | |||||
−1.49280 | − | 1.49280i | −1.49280 | − | 1.49280i | |||||
0 | 0 | |||||||||
−0.524828 | + | 0.248225i | −0.524828 | + | 0.248225i | |||||
0.444430 | − | 0.831470i | 0.444430 | − | 0.831470i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.773010 | − | 0.634393i | ||||||
−0.773010 | + | 0.634393i | ||||||||
0.989177 | + | 0.146730i | 0.989177 | + | 0.146730i | |||||
0.0190297 | + | 0.193211i | 0.0190297 | + | 0.193211i | |||||
0 | 0 | |||||||||
0 | 0 | −0.998795 | − | 0.0490677i | ||||||
0.998795 | + | 0.0490677i | ||||||||
−0.941544 | + | 0.336890i | −0.941544 | + | 0.336890i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.197076 | − | 1.32858i | 0.197076 | − | 1.32858i | |||||
−0.476623 | + | 0.0948062i | −0.476623 | + | 0.0948062i | −0.427555 | − | 0.903989i | ||
−0.0490677 | + | 0.998795i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.336890 | − | 0.941544i | 0.336890 | − | 0.941544i | |||||
0.226990 | + | 0.634393i | 0.226990 | + | 0.634393i | |||||
0 | 0 | |||||||||
0.0851872 | − | 0.280825i | 0.0851872 | − | 0.280825i | −0.903989 | − | 0.427555i | ||
0.989177 | + | 0.146730i | ||||||||
0 | 0 | |||||||||
0.924678 | − | 1.72995i | 0.924678 | − | 1.72995i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.292893 | + | 0.707107i | 0.292893 | + | 0.707107i | 1.00000 | ||||
−0.707107 | + | 0.707107i | ||||||||
0.0865477 | + | 1.76172i | 0.0865477 | + | 1.76172i | |||||
0.455929 | − | 1.10071i | 0.455929 | − | 1.10071i | |||||
0 | 0 | |||||||||
0.389711 | − | 0.0191453i | 0.389711 | − | 0.0191453i | |||||
0.591637 | + | 1.42834i | 0.591637 | + | 1.42834i | |||||
0 | 0 | −0.514103 | − | 0.857729i | ||||||
0.514103 | + | 0.857729i | ||||||||
−1.08827 | + | 1.32607i | −1.08827 | + | 1.32607i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3840.1.dy.a.149.1 | ✓ | 64 | |
3.2 | odd | 2 | inner | 3840.1.dy.a.149.2 | yes | 64 | |
5.4 | even | 2 | inner | 3840.1.dy.a.149.2 | yes | 64 | |
15.14 | odd | 2 | CM | 3840.1.dy.a.149.1 | ✓ | 64 | |
256.189 | even | 64 | inner | 3840.1.dy.a.1469.1 | yes | 64 | |
768.701 | odd | 64 | inner | 3840.1.dy.a.1469.2 | yes | 64 | |
1280.189 | even | 64 | inner | 3840.1.dy.a.1469.2 | yes | 64 | |
3840.1469 | odd | 64 | inner | 3840.1.dy.a.1469.1 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3840.1.dy.a.149.1 | ✓ | 64 | 1.1 | even | 1 | trivial | |
3840.1.dy.a.149.1 | ✓ | 64 | 15.14 | odd | 2 | CM | |
3840.1.dy.a.149.2 | yes | 64 | 3.2 | odd | 2 | inner | |
3840.1.dy.a.149.2 | yes | 64 | 5.4 | even | 2 | inner | |
3840.1.dy.a.1469.1 | yes | 64 | 256.189 | even | 64 | inner | |
3840.1.dy.a.1469.1 | yes | 64 | 3840.1469 | odd | 64 | inner | |
3840.1.dy.a.1469.2 | yes | 64 | 768.701 | odd | 64 | inner | |
3840.1.dy.a.1469.2 | yes | 64 | 1280.189 | even | 64 | inner |