Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,1,Mod(43,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 12, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.43");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1368.dh (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 | 1195.1 | ||
Root | of defining polynomial | ||
Character | 1368.1195 | ||
Dual form | 1368.1.dh.a.427.1 |
-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 .
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | ||
0.173648 | + | 0.984808i | ||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | 0.173648 | − | 0.984808i | ||
0.173648 | − | 0.984808i | ||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | + | 1.85083i | −0.326352 | + | 1.85083i | |||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
1.00000 | 1.00000 | |||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0 | 0 | |||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | |||||
0 | 0 | |||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | −0.500000 | − | 0.866025i | ||
0.766044 | − | 0.642788i | ||||||||
0 | 0 | |||||||||
−0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | ||
−0.939693 | + | 0.342020i | ||||||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
1.00000 | 1.00000 | |||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
−1.87939 | + | 0.684040i | −1.87939 | + | 0.684040i | |||||
0 | 0 | |||||||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | −0.500000 | − | 0.866025i | ||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | |||||
1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | 0.173648 | − | 0.984808i | ||
1.00000 | ||||||||||
2.00000 | 2.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | −0.939693 | − | 0.342020i | ||
−0.500000 | − | 0.866025i | ||||||||
0 | 0 | |||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | |||||
−1.87939 | −1.87939 | −0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | |||||
0 | 0 | |||||||||
−1.87939 | −1.87939 | |||||||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | ||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | 0.766044 | − | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
−1.87939 | −1.87939 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
−1.87939 | − | 0.684040i | −1.87939 | − | 0.684040i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||
−0.500000 | − | 0.866025i | ||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | ||
0.173648 | − | 0.984808i | ||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.26604 | + | 2.19285i | −1.26604 | + | 2.19285i | |||||
0 | 0 | |||||||||
−1.43969 | + | 0.524005i | −1.43969 | + | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | |||||
0 | 0 | |||||||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | −0.500000 | − | 0.866025i | ||
0.173648 | + | 0.984808i | ||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
0 | 0 | |||||||||
1.53209 | 1.53209 | |||||||||
0 | 0 | |||||||||
1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | |||||
1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | 0.173648 | − | 0.984808i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
−0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | 0.173648 | − | 0.984808i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | |||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | ||
0.766044 | + | 0.642788i | ||||||||
1.53209 | 1.53209 | |||||||||
0 | 0 | |||||||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | |||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
0 | 0 | |||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
−1.00000 | −1.00000 | |||||||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | |||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | |||||
−1.00000 | −1.00000 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | ||
0.766044 | − | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.53209 | − | 1.28558i | 3.53209 | − | 1.28558i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
−0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | ||
−0.939693 | + | 0.342020i | ||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
0 | 0 | |||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | |||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
−1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | |||||
0 | 0 | |||||||||
0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | |||||
0 | 0 | |||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | + | 1.85083i | −0.326352 | + | 1.85083i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | |||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | ||
0.766044 | + | 0.642788i | ||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | 0.766044 | − | 0.642788i | ||
1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | −0.500000 | − | 0.866025i | ||
0.173648 | − | 0.984808i | ||||||||
−2.37939 | + | 0.866025i | −2.37939 | + | 0.866025i | |||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
0 | 0 | |||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | 1.00000 | ||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | −0.500000 | + | 0.866025i | ||
−0.939693 | + | 0.342020i | ||||||||
0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | |||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | |||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | |||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0.347296 | + | 1.96962i | 0.347296 | + | 1.96962i | |||||
0 | 0 | |||||||||
1.53209 | 1.53209 | |||||||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | |||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
−0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | −0.500000 | − | 0.866025i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−1.43969 | + | 0.524005i | −1.43969 | + | 0.524005i | −0.939693 | − | 0.342020i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
−2.81908 | − | 1.02606i | −2.81908 | − | 1.02606i | |||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | |||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
0.347296 | + | 1.96962i | 0.347296 | + | 1.96962i | |||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | 0.766044 | − | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | 1.00000 | ||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | |||||
0 | 0 | |||||||||
2.00000 | 2.00000 | |||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | |||||
0 | 0 | |||||||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | ||
0.173648 | − | 0.984808i | ||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | 1.00000 | ||||
0.173648 | + | 0.984808i | ||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
−0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
−0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | 0.766044 | − | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | |||||
−0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | ||
−0.939693 | + | 0.342020i | ||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
0 | 0 | |||||||||
−0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | |||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
2.53209 | 2.53209 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
3.53209 | + | 1.28558i | 3.53209 | + | 1.28558i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | −1.00000 | −0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | |||||
−0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | |||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | |||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | |||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | 0.766044 | − | 0.642788i | ||
1.00000 | ||||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | |||||
0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | −0.500000 | − | 0.866025i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
−1.87939 | −1.87939 | |||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | ||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.00000 | 2.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0.939693 | + | 0.342020i | 0.939693 | + | 0.342020i | 0.766044 | − | 0.642788i | ||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | |||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | 0.766044 | + | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | ||
0.173648 | − | 0.984808i | ||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
2.70574 | − | 0.984808i | 2.70574 | − | 0.984808i | |||||
1.17365 | − | 0.984808i | 1.17365 | − | 0.984808i | |||||
0 | 0 | |||||||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | |||||
0 | 0 | |||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | |||||
0 | 0 | |||||||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
−0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | ||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | |||||
−1.76604 | + | 0.642788i | −1.76604 | + | 0.642788i | |||||
0 | 0 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
0 | 0 | |||||||||
−2.37939 | − | 0.866025i | −2.37939 | − | 0.866025i | |||||
0 | 0 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0.347296 | 0.347296 | |||||||||
0 | 0 | |||||||||
−0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | 0.766044 | + | 0.642788i | ||
−0.939693 | + | 0.342020i | ||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | + | 1.85083i | −0.326352 | + | 1.85083i | |||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | 0.766044 | − | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | 1.00000 | |||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
−1.87939 | −1.87939 | |||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | ||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0.347296 | + | 1.96962i | 0.347296 | + | 1.96962i | 0.173648 | + | 0.984808i | ||
0.173648 | + | 0.984808i | ||||||||
−0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | + | 1.85083i | −0.326352 | + | 1.85083i | |||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | |||||
−1.87939 | −1.87939 | |||||||||
0 | 0 | |||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
0 | 0 | |||||||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | ||
0.173648 | + | 0.984808i | ||||||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | |||||
0 | 0 | |||||||||
−1.87939 | −1.87939 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | |||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.87939 | − | 2.41609i | −2.87939 | − | 2.41609i | |||||
0.347296 | 0.347296 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | ||
0.766044 | − | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | ||
0.173648 | − | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | 1.00000 | |||||||||
−0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | ||
−0.939693 | + | 0.342020i | ||||||||
−1.50000 | − | 2.59808i | −1.50000 | − | 2.59808i | |||||
0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | |||||
0 | 0 | |||||||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | 0.173648 | − | 0.984808i | ||
−0.939693 | + | 0.342020i | ||||||||
0.766044 | − | 0.642788i | 0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | − | 0.524005i | −1.43969 | − | 0.524005i | −0.500000 | − | 0.866025i | ||
−0.939693 | + | 0.342020i | ||||||||
−0.326352 | + | 1.85083i | −0.326352 | + | 1.85083i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0.347296 | 0.347296 | 0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | |||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | −0.500000 | − | 0.866025i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | ||
−0.500000 | − | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
−0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | −0.939693 | − | 0.342020i | ||
1.00000 | ||||||||||
−1.87939 | + | 0.684040i | −1.87939 | + | 0.684040i | |||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | −0.500000 | − | 0.866025i | ||
0.766044 | − | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
1.00000 | 1.00000 | |||||||||
−0.500000 | − | 0.419550i | −0.500000 | − | 0.419550i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | |||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | |||||
0 | 0 | |||||||||
−0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | −0.939693 | − | 0.342020i | ||
0.766044 | − | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | |||||
0 | 0 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | ||||
−0.500000 | + | 0.866025i | ||||||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | |||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−1.43969 | + | 0.524005i | −1.43969 | + | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.347296 | 0.347296 | |||||||||
0 | 0 | |||||||||
−1.00000 | −1.00000 | −0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | −1.00000 | −0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.87939 | − | 1.04801i | −2.87939 | − | 1.04801i | |||||
0 | 0 | |||||||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | |||||
0 | 0 | |||||||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | |||||
0 | 0 | |||||||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | |||||
0 | 0 | −0.173648 | − | 0.984808i | ||||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.93969 | + | 1.62760i | 1.93969 | + | 1.62760i | |||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
1.00000 | 1.00000 | |||||||||
0 | 0 | |||||||||
1.87939 | + | 0.684040i | 1.87939 | + | 0.684040i | |||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.70574 | + | 0.984808i | 2.70574 | + | 0.984808i | |||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | |||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | −0.500000 | − | 0.866025i | ||
0.766044 | − | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
1.87939 | + | 3.25519i | 1.87939 | + | 3.25519i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
−0.766044 | − | 0.642788i | −0.766044 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | ||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | ||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
−1.00000 | −1.00000 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
−0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.53209 | 1.53209 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0 | 0 | |||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
1.53209 | 1.53209 | 0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
−0.173648 | − | 0.984808i | −0.173648 | − | 0.984808i | |||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
0.613341 | − | 3.47843i | 0.613341 | − | 3.47843i | |||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | −0.939693 | − | 0.342020i | ||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | |||||
−1.00000 | −1.00000 | |||||||||
0.347296 | 0.347296 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
−0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | |||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
1.76604 | + | 0.642788i | 1.76604 | + | 0.642788i | |||||
0 | 0 | |||||||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | 0.766044 | + | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.347296 | − | 1.96962i | 0.347296 | − | 1.96962i | |||||
−0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | |||||
0 | 0 | |||||||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | |||||
0 | 0 | |||||||||
−0.173648 | + | 0.984808i | −0.173648 | + | 0.984808i | |||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0.766044 | + | 0.642788i | 0.766044 | + | 0.642788i | |||||
0 | 0 | |||||||||
−0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | |||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | |||||
1.53209 | + | 1.28558i | 1.53209 | + | 1.28558i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.00000 | 2.00000 | |||||||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | 0.766044 | − | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | −0.500000 | − | 0.866025i | ||
0.173648 | − | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | |||||
0.520945 | + | 2.95442i | 0.520945 | + | 2.95442i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.87939 | −1.87939 | |||||||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | ||
0.173648 | + | 0.984808i | ||||||||
−0.939693 | + | 0.342020i | −0.939693 | + | 0.342020i | |||||
0.266044 | + | 1.50881i | 0.266044 | + | 1.50881i | 0.766044 | + | 0.642788i | ||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | |||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | |||||
0 | 0 | |||||||||
0.173648 | − | 0.984808i | 0.173648 | − | 0.984808i | |||||
0 | 0 | |||||||||
2.70574 | + | 0.984808i | 2.70574 | + | 0.984808i | |||||
0 | 0 | |||||||||
1.53209 | 1.53209 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | −0.939693 | − | 0.342020i | ||
1.00000 | ||||||||||
−0.326352 | − | 0.118782i | −0.326352 | − | 0.118782i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | |||||
−1.76604 | − | 3.05888i | −1.76604 | − | 3.05888i | |||||
−0.326352 | + | 0.118782i | −0.326352 | + | 0.118782i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.53209 | − | 1.28558i | 1.53209 | − | 1.28558i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.17365 | + | 0.984808i | 1.17365 | + | 0.984808i | 1.00000 | ||||
0.173648 | + | 0.984808i | ||||||||
0 | 0 | |||||||||
0.173648 | + | 0.984808i | 0.173648 | + | 0.984808i | |||||
0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | |||||
0 | 0 | |||||||||
−1.43969 | + | 0.524005i | −1.43969 | + | 0.524005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | −0.500000 | − | 0.866025i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−0.326352 | − | 1.85083i | −0.326352 | − | 1.85083i | |||||
0 | 0 | |||||||||
0 | 0 | 0.766044 | − | 0.642788i | ||||||
−0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.266044 | − | 0.223238i | 0.266044 | − | 0.223238i | |||||
0 | 0 | |||||||||
−1.76604 | − | 0.642788i | −1.76604 | − | 0.642788i | |||||
0.939693 | − | 0.342020i | 0.939693 | − | 0.342020i | 0.173648 | − | 0.984808i | ||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | − | 1.20805i | −1.43969 | − | 1.20805i | −0.939693 | − | 0.342020i | ||
−0.500000 | − | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
2.00000 | 2.00000 | |||||||||
1.76604 | − | 0.642788i | 1.76604 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
−1.26604 | − | 2.19285i | −1.26604 | − | 2.19285i | |||||
−1.00000 | − | 1.73205i | −1.00000 | − | 1.73205i | |||||
0 | 0 | |||||||||
0.0603074 | − | 0.342020i | 0.0603074 | − | 0.342020i | −0.939693 | − | 0.342020i | ||
1.00000 | ||||||||||
−0.939693 | − | 0.342020i | −0.939693 | − | 0.342020i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.87939 | −1.87939 | −0.939693 | − | 0.342020i | ||||||
−0.939693 | + | 0.342020i | ||||||||
0.266044 | + | 0.223238i | 0.266044 | + | 0.223238i | |||||
−1.76604 | − | 0.642788i | −1.76604 | − | 0.642788i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.766044 | + | 0.642788i | −0.766044 | + | 0.642788i | |||||
0 | 0 | 0.173648 | − | 0.984808i | ||||||
−0.173648 | + | 0.984808i | ||||||||
0.266044 | − | 1.50881i | 0.266044 | − | 1.50881i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.766044 | − | 0.642788i | ||||||
0.766044 | + | 0.642788i | ||||||||
0 | 0 | |||||||||
−0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.43969 | + | 1.20805i | −1.43969 | + | 1.20805i | |||||
0 | 0 | −0.939693 | − | 0.342020i | ||||||
0.939693 | + | 0.342020i | ||||||||
0.0603074 | + | 0.342020i | 0.0603074 | + | 0.342020i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1368.1.dh.a.1195.1 | yes | 6 | |
8.3 | odd | 2 | CM | 1368.1.dh.a.1195.1 | yes | 6 | |
9.4 | even | 3 | 1368.1.en.a.283.1 | yes | 6 | ||
19.9 | even | 9 | 1368.1.en.a.1339.1 | yes | 6 | ||
72.67 | odd | 6 | 1368.1.en.a.283.1 | yes | 6 | ||
152.123 | odd | 18 | 1368.1.en.a.1339.1 | yes | 6 | ||
171.85 | even | 9 | inner | 1368.1.dh.a.427.1 | ✓ | 6 | |
1368.427 | odd | 18 | inner | 1368.1.dh.a.427.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.1.dh.a.427.1 | ✓ | 6 | 171.85 | even | 9 | inner | |
1368.1.dh.a.427.1 | ✓ | 6 | 1368.427 | odd | 18 | inner | |
1368.1.dh.a.1195.1 | yes | 6 | 1.1 | even | 1 | trivial | |
1368.1.dh.a.1195.1 | yes | 6 | 8.3 | odd | 2 | CM | |
1368.1.en.a.283.1 | yes | 6 | 9.4 | even | 3 | ||
1368.1.en.a.283.1 | yes | 6 | 72.67 | odd | 6 | ||
1368.1.en.a.1339.1 | yes | 6 | 19.9 | even | 9 | ||
1368.1.en.a.1339.1 | yes | 6 | 152.123 | odd | 18 |