Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,2,Mod(4,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 39.j (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 |
Sato-Tate group: |
Embedding invariants
Embedding label | 4.1 | ||
Root | of defining polynomial | ||
Character | 39.4 | ||
Dual form | 39.2.j.a.10.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | |||||
−1.00000 | − | 1.73205i | −0.500000 | − | 0.866025i | |||||
3.46410i | 1.54919i | 0.632456 | + | 0.774597i | ||||||
−0.632456 | + | 0.774597i | ||||||||
0 | 0 | |||||||||
−1.50000 | + | 0.866025i | −0.566947 | + | 0.327327i | −0.755929 | − | 0.654654i | ||
0.188982 | + | 0.981981i | ||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | |||||
0 | 0 | |||||||||
−3.00000 | − | 1.73205i | −0.904534 | − | 0.522233i | −0.0258656 | − | 0.999665i | ||
−0.878668 | + | 0.477432i | ||||||||
−2.00000 | −0.577350 | |||||||||
3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | |||||
0 | 0 | |||||||||
3.00000 | + | 1.73205i | 0.774597 | + | 0.447214i | |||||
−2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | |||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
3.00000 | − | 1.73205i | 0.688247 | − | 0.397360i | −0.114708 | − | 0.993399i | ||
0.802955 | + | 0.596040i | ||||||||
6.00000 | − | 3.46410i | 1.34164 | − | 0.774597i | |||||
1.73205i | 0.377964i | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.625543 | − | 1.08347i | −0.362892 | − | 0.931831i | ||
0.988436 | − | 0.151642i | ||||||||
0 | 0 | |||||||||
−7.00000 | −1.40000 | |||||||||
0 | 0 | |||||||||
−1.00000 | −0.192450 | |||||||||
3.00000 | + | 1.73205i | 0.566947 | + | 0.327327i | |||||
−3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | ||
−0.997738 | + | 0.0672232i | ||||||||
0 | 0 | |||||||||
1.73205i | 0.311086i | 0.987829 | + | 0.155543i | ||||||
−0.987829 | + | 0.155543i | ||||||||
0 | 0 | |||||||||
−3.00000 | + | 1.73205i | −0.522233 | + | 0.301511i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.507093 | − | 0.878310i | |||||
−1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
1.00000 | − | 3.46410i | 0.160128 | − | 0.554700i | |||||
0 | 0 | |||||||||
−6.00000 | − | 3.46410i | −0.937043 | − | 0.541002i | −0.0480106 | − | 0.998847i | ||
−0.889032 | + | 0.457845i | ||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | ||
−0.825380 | + | 0.564578i | ||||||||
6.92820i | 1.04447i | |||||||||
3.00000 | − | 1.73205i | 0.447214 | − | 0.258199i | |||||
0 | 0 | |||||||||
3.46410i | 0.505291i | 0.967559 | + | 0.252646i | ||||||
−0.967559 | + | 0.252646i | ||||||||
2.00000 | + | 3.46410i | 0.288675 | + | 0.500000i | |||||
−2.00000 | + | 3.46410i | −0.285714 | + | 0.494872i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.00000 | − | 5.19615i | −0.693375 | − | 0.720577i | |||||
12.0000 | 1.64833 | 0.824163 | − | 0.566352i | ||||||
0.824163 | + | 0.566352i | ||||||||
0 | 0 | |||||||||
6.00000 | − | 10.3923i | 0.809040 | − | 1.40130i | |||||
0 | 0 | |||||||||
− | 3.46410i | − | 0.458831i | |||||||
0 | 0 | |||||||||
−3.00000 | + | 1.73205i | −0.390567 | + | 0.225494i | −0.682406 | − | 0.730974i | ||
0.291839 | + | 0.956467i | ||||||||
− | 6.92820i | − | 0.894427i | |||||||
−0.500000 | − | 0.866025i | −0.0640184 | − | 0.110883i | 0.832240 | − | 0.554416i | ||
−0.896258 | + | 0.443533i | ||||||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 0.188982 | + | 0.109109i | |||||
8.00000 | 1.00000 | |||||||||
3.00000 | + | 12.1244i | 0.372104 | + | 1.50384i | |||||
0 | 0 | |||||||||
7.50000 | + | 4.33013i | 0.916271 | + | 0.529009i | 0.882443 | − | 0.470418i | ||
0.0338274 | + | 0.999428i | ||||||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.361158 | − | 0.625543i | |||||
0 | 0 | |||||||||
−9.00000 | + | 5.19615i | −1.06810 | + | 0.616670i | −0.927663 | − | 0.373419i | ||
−0.140441 | + | 0.990089i | ||||||||
0 | 0 | |||||||||
1.73205i | 0.202721i | 0.994850 | + | 0.101361i | ||||||
−0.994850 | + | 0.101361i | ||||||||
0 | 0 | |||||||||
−3.50000 | + | 6.06218i | −0.404145 | + | 0.700000i | |||||
−6.00000 | − | 3.46410i | −0.688247 | − | 0.397360i | |||||
6.00000 | 0.683763 | |||||||||
0 | 0 | |||||||||
−11.0000 | −1.23760 | −0.618798 | − | 0.785550i | ||||||
−0.618798 | + | 0.785550i | ||||||||
−12.0000 | − | 6.92820i | −1.34164 | − | 0.774597i | |||||
−0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | |||||
0 | 0 | |||||||||
− | 13.8564i | − | 1.52094i | −0.649374 | − | 0.760469i | ||||
0.649374 | − | 0.760469i | ||||||||
3.00000 | − | 1.73205i | 0.327327 | − | 0.188982i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.321634 | + | 0.557086i | |||||
0 | 0 | |||||||||
6.00000 | + | 3.46410i | 0.635999 | + | 0.367194i | 0.783072 | − | 0.621932i | ||
−0.147073 | + | 0.989126i | ||||||||
0 | 0 | |||||||||
−4.50000 | + | 4.33013i | −0.471728 | + | 0.453921i | |||||
−12.0000 | −1.25109 | |||||||||
1.50000 | + | 0.866025i | 0.155543 | + | 0.0898027i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.615587 | + | 1.06623i | |||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.456906 | + | 0.263795i | −0.710742 | − | 0.703452i | ||
0.253837 | + | 0.967247i | ||||||||
0 | 0 | |||||||||
3.46410i | 0.348155i | |||||||||
7.00000 | + | 12.1244i | 0.700000 | + | 1.21244i | |||||
9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | ||
0.833143 | − | 0.553058i | ||||||||
0 | 0 | |||||||||
−1.00000 | −0.0985329 | −0.0492665 | − | 0.998786i | ||||||
−0.0492665 | + | 0.998786i | ||||||||
0 | 0 | |||||||||
−6.00000 | −0.585540 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.290021 | − | 0.502331i | −0.683793 | − | 0.729676i | ||
0.973814 | + | 0.227345i | ||||||||
1.00000 | + | 1.73205i | 0.0962250 | + | 0.166667i | |||||
− | 15.5885i | − | 1.49310i | −0.665327 | − | 0.746552i | ||||
0.665327 | − | 0.746552i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 6.92820i | − | 0.654654i | |||||||
−3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | ||
−0.971930 | + | 0.235269i | ||||||||
0 | 0 | |||||||||
18.0000 | + | 10.3923i | 1.67851 | + | 0.969087i | |||||
12.0000 | 1.11417 | |||||||||
−2.50000 | − | 2.59808i | −0.231125 | − | 0.240192i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | |||||
0 | 0 | |||||||||
−6.00000 | + | 3.46410i | −0.541002 | + | 0.312348i | |||||
3.00000 | − | 1.73205i | 0.269408 | − | 0.155543i | |||||
− | 6.92820i | − | 0.619677i | |||||||
0 | 0 | |||||||||
−6.50000 | + | 11.2583i | −0.576782 | + | 0.999015i | 0.419064 | + | 0.907957i | ||
−0.995846 | + | 0.0910585i | ||||||||
0 | 0 | |||||||||
1.00000 | 0.0880451 | |||||||||
0 | 0 | |||||||||
6.00000 | 0.524222 | 0.262111 | − | 0.965038i | ||||||
0.262111 | + | 0.965038i | ||||||||
6.00000 | + | 3.46410i | 0.522233 | + | 0.301511i | |||||
−3.00000 | + | 5.19615i | −0.260133 | + | 0.450564i | |||||
0 | 0 | |||||||||
− | 3.46410i | − | 0.298142i | |||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−2.50000 | − | 4.33013i | −0.212047 | − | 0.367277i | 0.740308 | − | 0.672268i | ||
−0.952355 | + | 0.304991i | ||||||||
−6.00000 | + | 10.3923i | −0.507093 | + | 0.878310i | |||||
3.00000 | + | 1.73205i | 0.252646 | + | 0.145865i | |||||
0 | 0 | |||||||||
−12.0000 | − | 3.46410i | −1.00349 | − | 0.289683i | |||||
4.00000 | 0.333333 | |||||||||
−18.0000 | − | 10.3923i | −1.49482 | − | 0.863034i | |||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.164957 | + | 0.285714i | |||||
0 | 0 | |||||||||
−6.00000 | + | 3.46410i | −0.491539 | + | 0.283790i | −0.725213 | − | 0.688525i | ||
0.233674 | + | 0.972315i | ||||||||
0 | 0 | |||||||||
− | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | ||||
0.990016 | − | 0.140952i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.00000 | −0.481932 | |||||||||
−7.00000 | + | 1.73205i | −0.560449 | + | 0.138675i | |||||
11.0000 | 0.877896 | 0.438948 | − | 0.898513i | ||||||
0.438948 | + | 0.898513i | ||||||||
0 | 0 | |||||||||
6.00000 | − | 10.3923i | 0.475831 | − | 0.824163i | |||||
0 | 0 | |||||||||
10.3923i | 0.819028i | |||||||||
0 | 0 | |||||||||
−16.5000 | + | 9.52628i | −1.29238 | + | 0.746156i | −0.979076 | − | 0.203497i | ||
−0.313304 | + | 0.949653i | ||||||||
13.8564i | 1.08200i | |||||||||
−6.00000 | − | 10.3923i | −0.467099 | − | 0.809040i | |||||
0 | 0 | |||||||||
−6.00000 | − | 3.46410i | −0.464294 | − | 0.268060i | 0.249554 | − | 0.968361i | ||
−0.713848 | + | 0.700301i | ||||||||
0 | 0 | |||||||||
11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | |||||
0 | 0 | |||||||||
−3.00000 | − | 1.73205i | −0.229416 | − | 0.132453i | |||||
1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | |||||
3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | ||
−0.729155 | + | 0.684349i | ||||||||
0 | 0 | |||||||||
10.5000 | − | 6.06218i | 0.793725 | − | 0.458258i | |||||
12.0000 | − | 6.92820i | 0.904534 | − | 0.522233i | |||||
3.46410i | 0.260378i | |||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | ||
0.549825 | + | 0.835280i | ||||||||
−6.00000 | − | 3.46410i | −0.447214 | − | 0.258199i | |||||
14.0000 | 1.04061 | 0.520306 | − | 0.853980i | ||||||
0.520306 | + | 0.853980i | ||||||||
0 | 0 | |||||||||
−1.00000 | −0.0739221 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.00000 | − | 3.46410i | 0.437595 | − | 0.252646i | |||||
1.50000 | − | 0.866025i | 0.109109 | − | 0.0629941i | |||||
0 | 0 | |||||||||
9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | ||
−0.331611 | + | 0.943416i | ||||||||
4.00000 | − | 6.92820i | 0.288675 | − | 0.500000i | |||||
−13.5000 | − | 7.79423i | −0.971751 | − | 0.561041i | −0.0719816 | − | 0.997406i | ||
−0.899770 | + | 0.436365i | ||||||||
0 | 0 | |||||||||
12.0000 | + | 3.46410i | 0.859338 | + | 0.248069i | |||||
8.00000 | 0.571429 | |||||||||
12.0000 | + | 6.92820i | 0.854965 | + | 0.493614i | 0.862323 | − | 0.506359i | ||
−0.00735824 | + | 0.999973i | ||||||||
0 | 0 | |||||||||
−3.50000 | − | 6.06218i | −0.248108 | − | 0.429736i | 0.714893 | − | 0.699234i | ||
−0.963001 | + | 0.269498i | ||||||||
0 | 0 | |||||||||
7.50000 | − | 4.33013i | 0.529009 | − | 0.305424i | |||||
0 | 0 | |||||||||
− | 10.3923i | − | 0.729397i | |||||||
0 | 0 | |||||||||
12.0000 | − | 20.7846i | 0.838116 | − | 1.45166i | |||||
0 | 0 | |||||||||
−6.00000 | −0.417029 | |||||||||
−4.00000 | + | 13.8564i | −0.277350 | + | 0.960769i | |||||
−12.0000 | −0.830057 | |||||||||
0 | 0 | |||||||||
−6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | ||
0.550743 | + | 0.834675i | ||||||||
−12.0000 | − | 20.7846i | −0.824163 | − | 1.42749i | |||||
10.3923i | 0.712069i | |||||||||
0 | 0 | |||||||||
−3.00000 | + | 1.73205i | −0.204598 | + | 0.118125i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.101827 | − | 0.176369i | |||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 0.101361 | + | 0.0585206i | |||||
−24.0000 | −1.61808 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
15.0000 | + | 8.66025i | 1.00447 | + | 0.579934i | 0.909569 | − | 0.415553i | ||
0.0949052 | + | 0.995486i | ||||||||
0 | 0 | |||||||||
3.50000 | + | 6.06218i | 0.233333 | + | 0.404145i | |||||
0 | 0 | |||||||||
18.0000 | − | 10.3923i | 1.19470 | − | 0.689761i | 0.235333 | − | 0.971915i | ||
0.959369 | + | 0.282153i | ||||||||
−6.00000 | + | 3.46410i | −0.397360 | + | 0.229416i | |||||
27.7128i | 1.83131i | 0.401960 | + | 0.915657i | ||||||
−0.401960 | + | 0.915657i | ||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.197386 | − | 0.341882i | |||||
0 | 0 | |||||||||
−18.0000 | −1.17922 | −0.589610 | − | 0.807688i | ||||||
−0.589610 | + | 0.807688i | ||||||||
0 | 0 | |||||||||
−12.0000 | −0.782794 | |||||||||
6.00000 | + | 3.46410i | 0.390567 | + | 0.225494i | |||||
−5.50000 | + | 9.52628i | −0.357263 | + | 0.618798i | |||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−12.0000 | + | 6.92820i | −0.774597 | + | 0.447214i | |||||
18.0000 | − | 10.3923i | 1.15948 | − | 0.669427i | 0.208302 | − | 0.978065i | ||
0.951180 | + | 0.308637i | ||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | |||||
−1.00000 | + | 1.73205i | −0.0640184 | + | 0.110883i | |||||
−12.0000 | − | 6.92820i | −0.766652 | − | 0.442627i | |||||
0 | 0 | |||||||||
9.00000 | − | 8.66025i | 0.572656 | − | 0.551039i | |||||
0 | 0 | |||||||||
−12.0000 | − | 6.92820i | −0.760469 | − | 0.439057i | |||||
0 | 0 | |||||||||
−6.00000 | − | 10.3923i | −0.378717 | − | 0.655956i | 0.612159 | − | 0.790735i | ||
−0.990876 | + | 0.134778i | ||||||||
− | 3.46410i | − | 0.218218i | |||||||
−18.0000 | + | 10.3923i | −1.13165 | + | 0.653359i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
18.0000 | − | 17.3205i | 1.11631 | − | 1.07417i | |||||
6.00000 | 0.371391 | |||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.369976 | + | 0.640817i | −0.989561 | − | 0.144112i | ||
0.619586 | + | 0.784929i | ||||||||
0 | 0 | |||||||||
41.5692i | 2.55358i | |||||||||
0 | 0 | |||||||||
6.00000 | − | 3.46410i | 0.367194 | − | 0.212000i | |||||
− | 17.3205i | − | 1.05802i | |||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
−4.50000 | − | 2.59808i | −0.273356 | − | 0.157822i | 0.357056 | − | 0.934083i | ||
−0.630412 | + | 0.776261i | ||||||||
0 | 0 | |||||||||
1.50000 | + | 6.06218i | 0.0907841 | + | 0.366900i | |||||
0 | 0 | |||||||||
21.0000 | + | 12.1244i | 1.26635 | + | 0.731126i | |||||
−6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | |||||
5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | ||
−0.675810 | + | 0.737075i | ||||||||
0 | 0 | |||||||||
1.50000 | − | 0.866025i | 0.0898027 | − | 0.0518476i | |||||
0 | 0 | |||||||||
− | 24.2487i | − | 1.44656i | −0.690557 | − | 0.723278i | ||||
0.690557 | − | 0.723278i | ||||||||
0 | 0 | |||||||||
5.50000 | − | 9.52628i | 0.326941 | − | 0.566279i | −0.654962 | − | 0.755662i | ||
0.981903 | + | 0.189383i | ||||||||
18.0000 | + | 10.3923i | 1.06810 | + | 0.616670i | |||||
12.0000 | 0.710819 | |||||||||
0 | 0 | |||||||||
12.0000 | 0.708338 | |||||||||
0 | 0 | |||||||||
8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
5.19615i | 0.304604i | |||||||||
3.00000 | − | 1.73205i | 0.175562 | − | 0.101361i | |||||
−15.0000 | + | 8.66025i | −0.876309 | + | 0.505937i | −0.869440 | − | 0.494039i | ||
−0.00686959 | + | 0.999976i | ||||||||
0 | 0 | |||||||||
−6.00000 | − | 10.3923i | −0.349334 | − | 0.605063i | |||||
0 | 0 | |||||||||
3.00000 | + | 1.73205i | 0.174078 | + | 0.100504i | |||||
0 | 0 | |||||||||
6.00000 | − | 20.7846i | 0.346989 | − | 1.20201i | |||||
14.0000 | 0.808290 | |||||||||
−1.50000 | − | 0.866025i | −0.0864586 | − | 0.0499169i | |||||
0 | 0 | |||||||||
−9.00000 | − | 15.5885i | −0.517036 | − | 0.895533i | |||||
13.8564i | 0.794719i | |||||||||
3.00000 | − | 1.73205i | 0.171780 | − | 0.0991769i | |||||
0 | 0 | |||||||||
− | 1.73205i | − | 0.0988534i | −0.998778 | − | 0.0494267i | ||||
0.998778 | − | 0.0494267i | ||||||||
−6.00000 | − | 10.3923i | −0.341882 | − | 0.592157i | |||||
−0.500000 | + | 0.866025i | −0.0284440 | + | 0.0492665i | |||||
0 | 0 | |||||||||
−24.0000 | −1.36092 | −0.680458 | − | 0.732787i | ||||||
−0.680458 | + | 0.732787i | ||||||||
0 | 0 | |||||||||
13.0000 | 0.734803 | 0.367402 | − | 0.930062i | ||||||
0.367402 | + | 0.930062i | ||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.169031 | + | 0.292770i | |||||
11.0000 | + | 19.0526i | 0.618798 | + | 1.07179i | |||||
6.92820i | 0.389127i | 0.980890 | + | 0.194563i | ||||||
−0.980890 | + | 0.194563i | ||||||||
0 | 0 | |||||||||
18.0000 | − | 10.3923i | 1.00781 | − | 0.581857i | |||||
27.7128i | 1.54919i | |||||||||
−3.00000 | − | 5.19615i | −0.167444 | − | 0.290021i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.00000 | 0.111111 | |||||||||
−24.5000 | + | 6.06218i | −1.35902 | + | 0.336269i | |||||
0 | 0 | |||||||||
−13.5000 | − | 7.79423i | −0.746552 | − | 0.431022i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | |||||
0 | 0 | |||||||||
4.50000 | − | 2.59808i | 0.247342 | − | 0.142803i | −0.371204 | − | 0.928551i | ||
0.618547 | + | 0.785748i | ||||||||
−24.0000 | + | 13.8564i | −1.31717 | + | 0.760469i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−15.0000 | + | 25.9808i | −0.819538 | + | 1.41948i | |||||
−6.00000 | − | 3.46410i | −0.327327 | − | 0.188982i | |||||
−5.00000 | −0.272367 | −0.136184 | − | 0.990684i | ||||||
−0.136184 | + | 0.990684i | ||||||||
0 | 0 | |||||||||
−6.00000 | −0.325875 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | |||||
0 | 0 | |||||||||
− | 19.0526i | − | 1.02874i | |||||||
0 | 0 | |||||||||
18.0000 | − | 10.3923i | 0.969087 | − | 0.559503i | |||||
0 | 0 | |||||||||
12.0000 | + | 20.7846i | 0.644194 | + | 1.11578i | 0.984487 | + | 0.175457i | ||
−0.340293 | + | 0.940319i | ||||||||
6.00000 | − | 10.3923i | 0.321634 | − | 0.557086i | |||||
−16.5000 | − | 9.52628i | −0.883225 | − | 0.509930i | −0.0115044 | − | 0.999934i | ||
−0.871720 | + | 0.490004i | ||||||||
0 | 0 | |||||||||
−3.50000 | + | 0.866025i | −0.186816 | + | 0.0462250i | |||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.479022 | + | 0.276563i | 0.720009 | − | 0.693965i | ||
−0.240987 | + | 0.970528i | ||||||||
0 | 0 | |||||||||
−18.0000 | − | 31.1769i | −0.955341 | − | 1.65470i | |||||
− | 13.8564i | − | 0.734388i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.92820i | 0.365657i | 0.983145 | + | 0.182828i | ||||||
−0.983145 | + | 0.182828i | ||||||||
0 | 0 | |||||||||
−3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | |||||
0 | 0 | |||||||||
1.00000 | 0.0524864 | |||||||||
12.0000 | + | 3.46410i | 0.628971 | + | 0.181568i | |||||
−6.00000 | −0.314054 | |||||||||
0 | 0 | |||||||||
−8.50000 | + | 14.7224i | −0.443696 | + | 0.768505i | −0.997960 | − | 0.0638362i | ||
0.554264 | + | 0.832341i | ||||||||
12.0000 | + | 20.7846i | 0.625543 | + | 1.08347i | |||||
6.92820i | 0.360668i | |||||||||
0 | 0 | |||||||||
−18.0000 | + | 10.3923i | −0.934513 | + | 0.539542i | |||||
− | 3.46410i | − | 0.179605i | |||||||
5.50000 | + | 9.52628i | 0.284779 | + | 0.493252i | 0.972556 | − | 0.232671i | ||
−0.687776 | + | 0.725923i | ||||||||
0 | 0 | |||||||||
−6.00000 | − | 3.46410i | −0.309839 | − | 0.178885i | |||||
0 | 0 | |||||||||
−6.00000 | + | 20.7846i | −0.309016 | + | 1.07046i | |||||
0 | 0 | |||||||||
−19.5000 | − | 11.2583i | −1.00165 | − | 0.578302i | −0.0929123 | − | 0.995674i | ||
−0.908735 | + | 0.417373i | ||||||||
12.0000 | − | 20.7846i | 0.615587 | − | 1.06623i | |||||
6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | |||||
0 | 0 | |||||||||
24.0000 | − | 13.8564i | 1.22634 | − | 0.708029i | 0.260080 | − | 0.965587i | ||
0.966263 | + | 0.257558i | ||||||||
0 | 0 | |||||||||
20.7846i | 1.05928i | |||||||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.0254164 | − | 0.0440225i | |||||
9.00000 | + | 5.19615i | 0.456906 | + | 0.263795i | |||||
12.0000 | 0.608424 | 0.304212 | − | 0.952604i | ||||||
0.304212 | + | 0.952604i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.151330 | − | 0.262111i | |||||
0 | 0 | |||||||||
− | 38.1051i | − | 1.91728i | |||||||
6.00000 | − | 3.46410i | 0.301511 | − | 0.174078i | |||||
13.5000 | − | 7.79423i | 0.677546 | − | 0.391181i | −0.121384 | − | 0.992606i | ||
0.798930 | + | 0.601424i | ||||||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.150188 | + | 0.260133i | |||||
14.0000 | − | 24.2487i | 0.700000 | − | 1.21244i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
1.50000 | + | 6.06218i | 0.0747203 | + | 0.301979i | |||||
−36.0000 | −1.79107 | |||||||||
−3.00000 | − | 1.73205i | −0.149071 | − | 0.0860663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.50000 | − | 4.33013i | 0.370851 | − | 0.214111i | −0.302979 | − | 0.952997i | ||
0.673830 | + | 0.738886i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | + | 1.73205i | 0.0492665 | + | 0.0853320i | |||||
3.00000 | − | 5.19615i | 0.147620 | − | 0.255686i | |||||
0 | 0 | |||||||||
48.0000 | 2.35623 | |||||||||
0 | 0 | |||||||||
−5.00000 | −0.244851 | |||||||||
0 | 0 | |||||||||
6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | ||
0.974546 | + | 0.224189i | ||||||||
6.00000 | + | 10.3923i | 0.292770 | + | 0.507093i | |||||
− | 12.1244i | − | 0.590905i | −0.955357 | − | 0.295452i | ||||
0.955357 | − | 0.295452i | ||||||||
0 | 0 | |||||||||
3.00000 | − | 1.73205i | 0.145865 | − | 0.0842152i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 0.0725901 | + | 0.0419099i | |||||
−12.0000 | −0.580042 | |||||||||
−9.00000 | + | 8.66025i | −0.434524 | + | 0.418121i | |||||
0 | 0 | |||||||||
18.0000 | + | 10.3923i | 0.867029 | + | 0.500580i | 0.866360 | − | 0.499420i | ||
0.000669521 | 1.00000i | |||||||||
2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | |||||
11.5000 | + | 19.9186i | 0.552655 | + | 0.957226i | 0.998082 | + | 0.0619079i | ||
−0.445427 | + | 0.895318i | ||||||||
0 | 0 | |||||||||
−18.0000 | + | 10.3923i | −0.863034 | + | 0.498273i | |||||
−27.0000 | + | 15.5885i | −1.29307 | + | 0.746552i | |||||
− | 20.7846i | − | 0.994263i | |||||||
0 | 0 | |||||||||
−17.5000 | + | 30.3109i | −0.835229 | + | 1.44666i | 0.0586141 | + | 0.998281i | ||
−0.893843 | + | 0.448379i | ||||||||
0 | 0 | |||||||||
4.00000 | 0.190476 | |||||||||
0 | 0 | |||||||||
24.0000 | 1.14027 | 0.570137 | − | 0.821549i | ||||||
0.570137 | + | 0.821549i | ||||||||
0 | 0 | |||||||||
−12.0000 | + | 20.7846i | −0.568855 | + | 0.985285i | |||||
0 | 0 | |||||||||
6.92820i | 0.327693i | |||||||||
−12.0000 | + | 6.92820i | −0.566947 | + | 0.327327i | |||||
33.0000 | − | 19.0526i | 1.55737 | − | 0.899146i | 0.559859 | − | 0.828588i | ||
0.997508 | − | 0.0705577i | ||||||||
0 | 0 | |||||||||
12.0000 | + | 20.7846i | 0.565058 | + | 0.978709i | |||||
−6.00000 | + | 10.3923i | −0.282216 | + | 0.488813i | |||||
−3.00000 | − | 1.73205i | −0.140952 | − | 0.0813788i | |||||
0 | 0 | |||||||||
−15.0000 | − | 15.5885i | −0.703211 | − | 0.730798i | |||||
0 | 0 | |||||||||
−31.5000 | − | 18.1865i | −1.47351 | − | 0.850730i | −0.473953 | − | 0.880550i | ||
−0.999555 | + | 0.0298202i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 41.5692i | − | 1.93817i | |||||||
−36.0000 | + | 20.7846i | −1.67669 | + | 0.968036i | −0.712938 | + | 0.701228i | ||
−0.963750 | + | 0.266808i | ||||||||
0 | 0 | |||||||||
− | 36.3731i | − | 1.69040i | −0.534450 | − | 0.845200i | ||||
0.534450 | − | 0.845200i | ||||||||
−12.0000 | − | 20.7846i | −0.557086 | − | 0.964901i | |||||
−3.00000 | + | 5.19615i | −0.139122 | + | 0.240966i | |||||
0 | 0 | |||||||||
6.00000 | 0.277647 | 0.138823 | − | 0.990317i | ||||||
0.138823 | + | 0.990317i | ||||||||
−2.00000 | + | 6.92820i | −0.0924500 | + | 0.320256i | |||||
−15.0000 | −0.692636 | |||||||||
0 | 0 | |||||||||
5.50000 | − | 9.52628i | 0.253427 | − | 0.438948i | |||||
0 | 0 | |||||||||
− | 3.46410i | − | 0.159280i | |||||||
0 | 0 | |||||||||
−21.0000 | + | 12.1244i | −0.963546 | + | 0.556304i | |||||
0 | 0 | |||||||||
−6.00000 | − | 10.3923i | −0.274721 | − | 0.475831i | |||||
0 | 0 | |||||||||
30.0000 | + | 17.3205i | 1.37073 | + | 0.791394i | 0.991021 | − | 0.133710i | ||
0.379714 | + | 0.925104i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.409514 | + | 0.236433i | |||||
1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | |||||
−9.00000 | − | 15.5885i | −0.408669 | − | 0.707835i | |||||
0 | 0 | |||||||||
−21.0000 | + | 12.1244i | −0.951601 | + | 0.549407i | −0.893578 | − | 0.448908i | ||
−0.0580230 | + | 0.998315i | ||||||||
0 | 0 | |||||||||
19.0526i | 0.861586i | |||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.135388 | + | 0.234499i | −0.925746 | − | 0.378147i | ||
0.790358 | + | 0.612646i | ||||||||
12.0000 | + | 6.92820i | 0.541002 | + | 0.312348i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.0000 | −0.539360 | |||||||||
−6.00000 | − | 3.46410i | −0.269408 | − | 0.155543i | |||||
9.00000 | − | 15.5885i | 0.403705 | − | 0.699238i | |||||
0 | 0 | |||||||||
31.1769i | 1.39567i | 0.716258 | + | 0.697835i | ||||||
−0.716258 | + | 0.697835i | ||||||||
−12.0000 | + | 6.92820i | −0.536656 | + | 0.309839i | |||||
−6.00000 | + | 3.46410i | −0.268060 | + | 0.154765i | |||||
0 | 0 | |||||||||
15.0000 | + | 25.9808i | 0.668817 | + | 1.15842i | 0.978235 | + | 0.207499i | ||
−0.309418 | + | 0.950926i | ||||||||
0 | 0 | |||||||||
54.0000 | + | 31.1769i | 2.40297 | + | 1.38735i | |||||
0 | 0 | |||||||||
0.500000 | − | 12.9904i | 0.0222058 | − | 0.576923i | |||||
26.0000 | 1.15356 | |||||||||
−15.0000 | − | 8.66025i | −0.664863 | − | 0.383859i | 0.129264 | − | 0.991610i | ||
−0.794128 | + | 0.607751i | ||||||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.0663561 | − | 0.114932i | |||||
0 | 0 | |||||||||
−3.00000 | + | 1.73205i | −0.132453 | + | 0.0764719i | |||||
0 | 0 | |||||||||
− | 3.46410i | − | 0.152647i | |||||||
−1.00000 | − | 1.73205i | −0.0440225 | − | 0.0762493i | |||||
6.00000 | − | 10.3923i | 0.263880 | − | 0.457053i | |||||
0 | 0 | |||||||||
6.00000 | 0.263371 | |||||||||
0 | 0 | |||||||||
−24.0000 | −1.05146 | −0.525730 | − | 0.850652i | ||||||
−0.525730 | + | 0.850652i | ||||||||
0 | 0 | |||||||||
14.0000 | − | 24.2487i | 0.612177 | − | 1.06032i | −0.378695 | − | 0.925521i | ||
0.990873 | − | 0.134801i | ||||||||
−6.00000 | − | 10.3923i | −0.262111 | − | 0.453990i | |||||
− | 12.1244i | − | 0.529150i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 13.8564i | − | 0.603023i | |||||||
−6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | |||||
0 | 0 | |||||||||
3.00000 | + | 1.73205i | 0.130189 | + | 0.0751646i | |||||
12.0000 | 0.520266 | |||||||||
−24.0000 | − | 6.92820i | −1.03956 | − | 0.300094i | |||||
0 | 0 | |||||||||
18.0000 | + | 10.3923i | 0.778208 | + | 0.449299i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.258919 | + | 0.448461i | |||||
0 | 0 | |||||||||
12.0000 | − | 6.92820i | 0.516877 | − | 0.298419i | |||||
−6.00000 | + | 3.46410i | −0.258199 | + | 0.149071i | |||||
− | 29.4449i | − | 1.26593i | −0.774179 | − | 0.632967i | ||||
0.774179 | − | 0.632967i | ||||||||
0 | 0 | |||||||||
7.00000 | − | 12.1244i | 0.300399 | − | 0.520306i | |||||
0 | 0 | |||||||||
54.0000 | 2.31311 | |||||||||
0 | 0 | |||||||||
−19.0000 | −0.812381 | −0.406191 | − | 0.913788i | ||||||
−0.406191 | + | 0.913788i | ||||||||
0 | 0 | |||||||||
−0.500000 | + | 0.866025i | −0.0213395 | + | 0.0369611i | |||||
0 | 0 | |||||||||
20.7846i | 0.885454i | |||||||||
0 | 0 | |||||||||
16.5000 | − | 9.52628i | 0.701651 | − | 0.405099i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.00000 | + | 8.66025i | −0.212047 | + | 0.367277i | |||||
−24.0000 | − | 13.8564i | −1.01691 | − | 0.587115i | −0.103704 | − | 0.994608i | ||
−0.913208 | + | 0.407493i | ||||||||
0 | 0 | |||||||||
2.50000 | + | 2.59808i | 0.105739 | + | 0.109887i | |||||
24.0000 | 1.01419 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
21.0000 | + | 36.3731i | 0.885044 | + | 1.53294i | 0.845663 | + | 0.533718i | ||
0.0393818 | + | 0.999224i | ||||||||
− | 6.92820i | − | 0.291730i | |||||||
18.0000 | − | 10.3923i | 0.757266 | − | 0.437208i | |||||
0 | 0 | |||||||||
− | 1.73205i | − | 0.0727393i | |||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | ||
0.922032 | + | 0.387113i | ||||||||
0 | 0 | |||||||||
−44.0000 | −1.84134 | −0.920671 | − | 0.390339i | ||||||
−0.920671 | + | 0.390339i | ||||||||
6.00000 | + | 24.2487i | 0.250873 | + | 1.01389i | |||||
18.0000 | 0.751961 | |||||||||
0 | 0 | |||||||||
−21.0000 | + | 36.3731i | −0.875761 | + | 1.51686i | |||||
−4.00000 | − | 6.92820i | −0.166667 | − | 0.288675i | |||||
− | 34.6410i | − | 1.44212i | −0.692870 | − | 0.721062i | ||||
0.692870 | − | 0.721062i | ||||||||
0 | 0 | |||||||||
−13.5000 | + | 7.79423i | −0.561041 | + | 0.323917i | |||||
41.5692i | 1.72607i | |||||||||
12.0000 | + | 20.7846i | 0.497844 | + | 0.862291i | |||||
0 | 0 | |||||||||
−36.0000 | − | 20.7846i | −1.49097 | − | 0.860811i | |||||
0 | 0 | |||||||||
9.00000 | − | 8.66025i | 0.372104 | − | 0.358057i | |||||
0 | 0 | |||||||||
−27.0000 | − | 15.5885i | −1.11441 | − | 0.643404i | −0.174441 | − | 0.984668i | ||
−0.939968 | + | 0.341263i | ||||||||
4.00000 | − | 6.92820i | 0.164957 | − | 0.285714i | |||||
3.00000 | + | 5.19615i | 0.123613 | + | 0.214104i | |||||
0 | 0 | |||||||||
12.0000 | − | 6.92820i | 0.493614 | − | 0.284988i | |||||
0 | 0 | |||||||||
3.46410i | 0.142254i | 0.997467 | + | 0.0711268i | ||||||
−0.997467 | + | 0.0711268i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12.0000 | + | 6.92820i | 0.491539 | + | 0.283790i | |||||
−7.00000 | −0.286491 | |||||||||
0 | 0 | |||||||||
−30.0000 | −1.22577 | −0.612883 | − | 0.790173i | ||||||
−0.612883 | + | 0.790173i | ||||||||
0 | 0 | |||||||||
13.0000 | − | 22.5167i | 0.530281 | − | 0.918474i | −0.469095 | − | 0.883148i | ||
0.999376 | − | 0.0353259i | ||||||||
0 | 0 | |||||||||
− | 8.66025i | − | 0.352673i | |||||||
−6.00000 | + | 3.46410i | −0.244137 | + | 0.140952i | |||||
−3.00000 | + | 1.73205i | −0.121967 | + | 0.0704179i | |||||
0 | 0 | |||||||||
−4.00000 | − | 6.92820i | −0.162355 | − | 0.281207i | 0.773358 | − | 0.633970i | ||
−0.935713 | + | 0.352763i | ||||||||
0 | 0 | |||||||||
−9.00000 | − | 5.19615i | −0.364698 | − | 0.210559i | |||||
0 | 0 | |||||||||
3.00000 | + | 12.1244i | 0.121367 | + | 0.490499i | |||||
0 | 0 | |||||||||
7.50000 | + | 4.33013i | 0.302922 | + | 0.174892i | 0.643755 | − | 0.765232i | ||
−0.340833 | + | 0.940124i | ||||||||
0 | 0 | |||||||||
−12.0000 | − | 20.7846i | −0.483887 | − | 0.838116i | |||||
0 | 0 | |||||||||
−9.00000 | + | 5.19615i | −0.362326 | + | 0.209189i | −0.670101 | − | 0.742270i | ||
0.307774 | + | 0.951459i | ||||||||
0 | 0 | |||||||||
25.9808i | 1.04425i | 0.852867 | + | 0.522127i | ||||||
−0.852867 | + | 0.522127i | ||||||||
6.00000 | + | 10.3923i | 0.240966 | + | 0.417365i | |||||
−3.00000 | + | 5.19615i | −0.120386 | + | 0.208514i | |||||
0 | 0 | |||||||||
−12.0000 | −0.480770 | |||||||||
10.0000 | + | 10.3923i | 0.400320 | + | 0.416025i | |||||
−11.0000 | −0.440000 | |||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.239617 | + | 0.415029i | |||||
−11.0000 | − | 19.0526i | −0.438948 | − | 0.760280i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.50000 | − | 0.866025i | 0.0597141 | − | 0.0344759i | −0.469846 | − | 0.882749i | ||
0.529560 | + | 0.848273i | ||||||||
0 | 0 | |||||||||
6.50000 | + | 11.2583i | 0.258352 | + | 0.447478i | |||||
0 | 0 | |||||||||
−39.0000 | − | 22.5167i | −1.54767 | − | 0.893546i | |||||
−24.0000 | −0.951662 | |||||||||
−4.00000 | + | 13.8564i | −0.158486 | + | 0.549011i | |||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.356034 | + | 0.205557i | |||||
0 | 0 | |||||||||
−9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | ||
−0.987200 | + | 0.159489i | ||||||||
0 | 0 | |||||||||
16.5000 | − | 9.52628i | 0.650696 | − | 0.375680i | −0.138027 | − | 0.990429i | ||
0.788723 | + | 0.614749i | ||||||||
18.0000 | − | 10.3923i | 0.709299 | − | 0.409514i | |||||
3.46410i | 0.136399i | |||||||||
0 | 0 | |||||||||
9.00000 | − | 15.5885i | 0.353827 | − | 0.612845i | −0.633090 | − | 0.774078i | ||
0.986916 | + | 0.161233i | ||||||||
0 | 0 | |||||||||
12.0000 | 0.471041 | |||||||||
0 | 0 | |||||||||
−3.00000 | −0.117579 | |||||||||
33.0000 | + | 19.0526i | 1.29238 | + | 0.746156i | |||||
−18.0000 | + | 31.1769i | −0.704394 | + | 1.22005i | 0.262515 | + | 0.964928i | ||
−0.966910 | + | 0.255119i | ||||||||
0 | 0 | |||||||||
20.7846i | 0.812122i | |||||||||
24.0000 | − | 13.8564i | 0.937043 | − | 0.541002i | |||||
1.50000 | − | 0.866025i | 0.0585206 | − | 0.0337869i | |||||
0 | 0 | |||||||||
−24.0000 | − | 41.5692i | −0.934907 | − | 1.61931i | −0.774799 | − | 0.632207i | ||
−0.160108 | − | 0.987099i | ||||||||
−12.0000 | + | 20.7846i | −0.467099 | + | 0.809040i | |||||
−22.5000 | − | 12.9904i | −0.875149 | − | 0.505267i | −0.00609283 | − | 0.999981i | ||
−0.869056 | + | 0.494714i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−18.0000 | − | 10.3923i | −0.698010 | − | 0.402996i | |||||
0 | 0 | |||||||||
18.0000 | + | 31.1769i | 0.696963 | + | 1.20717i | |||||
13.8564i | 0.536120i | |||||||||
15.0000 | − | 8.66025i | 0.579934 | − | 0.334825i | |||||
0 | 0 | |||||||||
3.46410i | 0.133730i | |||||||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | ||
0.875501 | + | 0.483216i | ||||||||
0 | 0 | |||||||||
7.00000 | 0.269430 | |||||||||
−22.0000 | − | 13.8564i | −0.846154 | − | 0.532939i | |||||
48.0000 | 1.84479 | 0.922395 | − | 0.386248i | ||||||
0.922395 | + | 0.386248i | ||||||||
0 | 0 | |||||||||
4.50000 | − | 7.79423i | 0.172694 | − | 0.299115i | |||||
0 | 0 | |||||||||
− | 20.7846i | − | 0.796468i | |||||||
0 | 0 | |||||||||
21.0000 | − | 12.1244i | 0.803543 | − | 0.463926i | −0.0411658 | − | 0.999152i | ||
0.844708 | + | 0.535227i | ||||||||
6.92820i | 0.264906i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
24.0000 | + | 13.8564i | 0.915657 | + | 0.528655i | |||||
−4.00000 | −0.152499 | |||||||||
42.0000 | − | 10.3923i | 1.60007 | − | 0.395915i | |||||
0 | 0 | |||||||||
37.5000 | + | 21.6506i | 1.42657 | + | 0.823629i | 0.996848 | − | 0.0793336i | ||
0.429719 | + | 0.902963i | ||||||||
6.00000 | − | 10.3923i | 0.228086 | − | 0.395056i | |||||
−3.00000 | − | 5.19615i | −0.113961 | − | 0.197386i | |||||
0 | 0 | |||||||||
15.0000 | − | 8.66025i | 0.568982 | − | 0.328502i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.00000 | + | 15.5885i | −0.340411 | + | 0.589610i | |||||
−21.0000 | − | 12.1244i | −0.793725 | − | 0.458258i | |||||
−12.0000 | −0.453234 | −0.226617 | − | 0.973984i | ||||||
−0.226617 | + | 0.973984i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.0000 | − | 13.8564i | −0.904534 | − | 0.522233i | |||||
−6.00000 | + | 10.3923i | −0.225973 | + | 0.391397i | |||||
0 | 0 | |||||||||
31.1769i | 1.17253i | |||||||||
6.00000 | − | 3.46410i | 0.225494 | − | 0.130189i | |||||
−16.5000 | + | 9.52628i | −0.619671 | + | 0.357767i | −0.776741 | − | 0.629821i | ||
0.157070 | + | 0.987587i | ||||||||
0 | 0 | |||||||||
5.50000 | + | 9.52628i | 0.206266 | + | 0.357263i | |||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.337053 | + | 0.194597i | |||||
0 | 0 | |||||||||
12.0000 | − | 41.5692i | 0.448775 | − | 1.55460i | |||||
24.0000 | 0.896922 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | ||
−0.804648 | + | 0.593753i | ||||||||
13.8564i | 0.516398i | |||||||||
1.50000 | − | 0.866025i | 0.0558629 | − | 0.0322525i | |||||
0 | 0 | |||||||||
− | 20.7846i | − | 0.772988i | |||||||
−14.0000 | − | 24.2487i | −0.520306 | − | 0.901196i | |||||
21.0000 | − | 36.3731i | 0.779920 | − | 1.35086i | |||||
0 | 0 | |||||||||
−35.0000 | −1.29808 | −0.649039 | − | 0.760755i | ||||||
−0.649039 | + | 0.760755i | ||||||||
0 | 0 | |||||||||
1.00000 | 0.0370370 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00000 | + | 1.73205i | 0.0369611 | + | 0.0640184i | |||||
39.8372i | 1.47142i | 0.677297 | + | 0.735710i | ||||||
−0.677297 | + | 0.735710i | ||||||||
0 | 0 | |||||||||
−12.0000 | + | 6.92820i | −0.442627 | + | 0.255551i | |||||
0 | 0 | |||||||||
−15.0000 | − | 25.9808i | −0.552532 | − | 0.957014i | |||||
0 | 0 | |||||||||
39.0000 | + | 22.5167i | 1.43464 | + | 0.828289i | 0.997470 | − | 0.0710909i | ||
0.437168 | + | 0.899380i | ||||||||
0 | 0 | |||||||||
−3.00000 | − | 12.1244i | −0.110208 | − | 0.445399i | |||||
0 | 0 | |||||||||
−9.00000 | − | 5.19615i | −0.330178 | − | 0.190628i | 0.325742 | − | 0.945459i | ||
−0.655920 | + | 0.754830i | ||||||||
0 | 0 | |||||||||
−12.0000 | − | 20.7846i | −0.439646 | − | 0.761489i | |||||
0 | 0 | |||||||||
−12.0000 | + | 6.92820i | −0.439057 | + | 0.253490i | |||||
0 | 0 | |||||||||
10.3923i | 0.379727i | |||||||||
0 | 0 | |||||||||
−4.00000 | + | 6.92820i | −0.145962 | + | 0.252814i | −0.929731 | − | 0.368238i | ||
0.783769 | + | 0.621052i | ||||||||
−12.0000 | − | 6.92820i | −0.437595 | − | 0.252646i | |||||
−12.0000 | −0.437304 | |||||||||
0 | 0 | |||||||||
12.0000 | 0.436725 | |||||||||
−3.00000 | − | 1.73205i | −0.109109 | − | 0.0629941i | |||||
−17.0000 | + | 29.4449i | −0.617876 | + | 1.07019i | 0.371997 | + | 0.928234i | ||
−0.989873 | + | 0.141958i | ||||||||
0 | 0 | |||||||||
20.7846i | 0.754434i | |||||||||
0 | 0 | |||||||||
−18.0000 | + | 10.3923i | −0.652499 | + | 0.376721i | −0.789413 | − | 0.613862i | ||
0.136914 | + | 0.990583i | ||||||||
0 | 0 | |||||||||
13.5000 | + | 23.3827i | 0.488733 | + | 0.846510i | |||||
18.0000 | − | 31.1769i | 0.651217 | − | 1.12794i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.00000 | + | 8.66025i | −0.324971 | + | 0.312704i | |||||
−16.0000 | −0.577350 | |||||||||
−6.00000 | − | 3.46410i | −0.216366 | − | 0.124919i | 0.387901 | − | 0.921701i | ||
−0.604266 | + | 0.796782i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
31.1769i | 1.12208i | |||||||||
−45.0000 | + | 25.9808i | −1.61854 | + | 0.934463i | −0.631239 | + | 0.775589i | ||
−0.987299 | + | 0.158874i | ||||||||
0 | 0 | |||||||||
− | 12.1244i | − | 0.435520i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.0000 | −0.859889 | |||||||||
−6.00000 | − | 24.2487i | −0.214834 | − | 0.868243i | |||||
36.0000 | 1.28818 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.107211 | − | 0.185695i | |||||
−8.00000 | − | 13.8564i | −0.285714 | − | 0.494872i | |||||
38.1051i | 1.36003i | |||||||||
0 | 0 | |||||||||
28.5000 | − | 16.4545i | 1.01592 | − | 0.586539i | 0.102997 | − | 0.994682i | ||
0.912918 | + | 0.408143i | ||||||||
− | 27.7128i | − | 0.987228i | |||||||
6.00000 | + | 10.3923i | 0.213606 | + | 0.369976i | |||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.320003 | + | 0.184754i | |||||
0 | 0 | |||||||||
−2.50000 | − | 2.59808i | −0.0887776 | − | 0.0922604i | |||||
0 | 0 | |||||||||
36.0000 | + | 20.7846i | 1.27679 | + | 0.737154i | |||||
−7.00000 | + | 12.1244i | −0.248108 | + | 0.429736i | |||||
−6.00000 | − | 10.3923i | −0.212531 | − | 0.368114i | 0.739975 | − | 0.672634i | ||
−0.952506 | + | 0.304520i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 6.92820i | − | 0.244796i | |||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.105868 | − | 0.183368i | |||||
−15.0000 | − | 8.66025i | −0.529009 | − | 0.305424i | |||||
−36.0000 | −1.26883 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.210949 | + | 0.365374i | −0.952012 | − | 0.306062i | ||
0.741063 | + | 0.671436i | ||||||||
0 | 0 | |||||||||
− | 25.9808i | − | 0.912308i | −0.889901 | − | 0.456154i | ||||
0.889901 | − | 0.456154i | ||||||||
−18.0000 | + | 10.3923i | −0.631676 | + | 0.364698i | |||||
−4.50000 | + | 2.59808i | −0.157822 | + | 0.0911185i | |||||
0 | 0 | |||||||||
−33.0000 | − | 57.1577i | −1.15594 | − | 2.00215i | |||||
0 | 0 | |||||||||
3.00000 | + | 1.73205i | 0.104957 | + | 0.0605968i | |||||
0 | 0 | |||||||||
6.00000 | + | 1.73205i | 0.209657 | + | 0.0605228i | |||||
−48.0000 | −1.67623 | |||||||||
21.0000 | + | 12.1244i | 0.732905 | + | 0.423143i | 0.819484 | − | 0.573102i | ||
−0.0865789 | + | 0.996245i | ||||||||
0 | 0 | |||||||||
−16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | ||
0.439961 | − | 0.898017i | ||||||||
0 | 0 | |||||||||
21.0000 | − | 12.1244i | 0.731126 | − | 0.422116i | |||||
0 | 0 | |||||||||
48.4974i | 1.68642i | 0.537584 | + | 0.843210i | ||||||
−0.537584 | + | 0.843210i | ||||||||
6.00000 | + | 10.3923i | 0.208514 | + | 0.361158i | |||||
−15.5000 | + | 26.8468i | −0.538337 | + | 0.932427i | 0.460657 | + | 0.887578i | ||
−0.998994 | + | 0.0448490i | ||||||||
0 | 0 | |||||||||
10.0000 | 0.346896 | |||||||||
28.0000 | − | 6.92820i | 0.970725 | − | 0.240192i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12.0000 | − | 20.7846i | 0.415277 | − | 0.719281i | |||||
12.0000 | + | 20.7846i | 0.415029 | + | 0.718851i | |||||
− | 1.73205i | − | 0.0598684i | |||||||
0 | 0 | |||||||||
27.0000 | − | 15.5885i | 0.932144 | − | 0.538173i | 0.0446547 | − | 0.999002i | ||
0.887489 | + | 0.460829i | ||||||||
0 | 0 | |||||||||
−3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | |||||
0 | 0 | |||||||||
−21.0000 | − | 12.1244i | −0.723278 | − | 0.417585i | |||||
26.0000 | 0.894957 | |||||||||
21.0000 | + | 39.8372i | 0.722422 | + | 1.37044i | |||||
0 | 0 | |||||||||
−1.50000 | − | 0.866025i | −0.0515406 | − | 0.0297570i | |||||
−24.0000 | + | 41.5692i | −0.824163 | + | 1.42749i | |||||
−5.50000 | − | 9.52628i | −0.188760 | − | 0.326941i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
18.0000 | − | 10.3923i | 0.616670 | − | 0.356034i | |||||
− | 25.9808i | − | 0.889564i | −0.895639 | − | 0.444782i | ||||
0.895639 | − | 0.444782i | ||||||||
0 | 0 | |||||||||
6.00000 | − | 10.3923i | 0.205196 | − | 0.355409i | |||||
0 | 0 | |||||||||
18.0000 | 0.614868 | 0.307434 | − | 0.951569i | ||||||
0.307434 | + | 0.951569i | ||||||||
0 | 0 | |||||||||
13.0000 | 0.443554 | 0.221777 | − | 0.975097i | ||||||
0.221777 | + | 0.975097i | ||||||||
6.00000 | + | 3.46410i | 0.204598 | + | 0.118125i | |||||
6.00000 | − | 10.3923i | 0.204479 | − | 0.354169i | |||||
0 | 0 | |||||||||
− | 17.3205i | − | 0.589597i | −0.955559 | − | 0.294798i | ||||
0.955559 | − | 0.294798i | ||||||||
0 | 0 | |||||||||
−18.0000 | + | 10.3923i | −0.612018 | + | 0.353349i | |||||
0 | 0 | |||||||||
−8.50000 | − | 14.7224i | −0.288675 | − | 0.500000i | |||||
−3.00000 | + | 5.19615i | −0.101827 | + | 0.176369i | |||||
33.0000 | + | 19.0526i | 1.11945 | + | 0.646314i | |||||
0 | 0 | |||||||||
30.0000 | + | 8.66025i | 1.01651 | + | 0.293442i | |||||
0 | 0 | |||||||||
4.50000 | + | 2.59808i | 0.152302 | + | 0.0879316i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.202837 | + | 0.351324i | |||||
− | 3.46410i | − | 0.117041i | |||||||
36.0000 | − | 20.7846i | 1.21563 | − | 0.701846i | 0.251653 | − | 0.967818i | ||
0.963981 | + | 0.265971i | ||||||||
0 | 0 | |||||||||
17.3205i | 0.584206i | |||||||||
24.0000 | + | 41.5692i | 0.809040 | + | 1.40130i | |||||
6.00000 | − | 10.3923i | 0.202145 | − | 0.350126i | −0.747074 | − | 0.664741i | ||
0.949219 | + | 0.314615i | ||||||||
0 | 0 | |||||||||
−5.00000 | −0.168263 | −0.0841317 | − | 0.996455i | ||||||
−0.0841317 | + | 0.996455i | ||||||||
0 | 0 | |||||||||
−12.0000 | −0.403376 | |||||||||
0 | 0 | |||||||||
21.0000 | − | 36.3731i | 0.705111 | − | 1.22129i | −0.261540 | − | 0.965193i | ||
0.966651 | − | 0.256096i | ||||||||
0 | 0 | |||||||||
− | 22.5167i | − | 0.755185i | |||||||
0 | 0 | |||||||||
3.00000 | − | 1.73205i | 0.100504 | − | 0.0580259i | |||||
− | 34.6410i | − | 1.15987i | |||||||
6.00000 | + | 10.3923i | 0.200782 | + | 0.347765i | |||||
0 | 0 | |||||||||
−36.0000 | − | 20.7846i | −1.20335 | − | 0.694753i | |||||
0 | 0 | |||||||||
−15.0000 | − | 15.5885i | −0.500835 | − | 0.520483i | |||||
0 | 0 | |||||||||
−9.00000 | − | 5.19615i | −0.300167 | − | 0.173301i | |||||
7.00000 | − | 12.1244i | 0.233333 | − | 0.404145i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.50000 | + | 0.866025i | −0.0499169 | + | 0.0288195i | |||||
0 | 0 | |||||||||
48.4974i | 1.61211i | |||||||||
0 | 0 | |||||||||
22.0000 | − | 38.1051i | 0.730498 | − | 1.26526i | −0.226173 | − | 0.974087i | ||
0.956671 | − | 0.291172i | ||||||||
−36.0000 | − | 20.7846i | −1.19470 | − | 0.689761i | |||||
−18.0000 | −0.597022 | |||||||||
0 | 0 | |||||||||
−12.0000 | −0.397578 | −0.198789 | − | 0.980042i | ||||||
−0.198789 | + | 0.980042i | ||||||||
12.0000 | + | 6.92820i | 0.397360 | + | 0.229416i | |||||
−24.0000 | + | 41.5692i | −0.794284 | + | 1.37574i | |||||
0 | 0 | |||||||||
− | 3.46410i | − | 0.114520i | |||||||
48.0000 | − | 27.7128i | 1.58596 | − | 0.915657i | |||||
−9.00000 | + | 5.19615i | −0.297206 | + | 0.171592i | |||||
0 | 0 | |||||||||
16.0000 | + | 27.7128i | 0.527791 | + | 0.914161i | 0.999475 | + | 0.0323936i | ||
−0.471684 | + | 0.881768i | ||||||||
0 | 0 | |||||||||
−1.50000 | − | 0.866025i | −0.0494267 | − | 0.0285365i | |||||
0 | 0 | |||||||||
−27.0000 | + | 25.9808i | −0.888716 | + | 0.855167i | |||||
−12.0000 | −0.394771 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.0164222 | + | 0.0284440i | |||||
0 | 0 | |||||||||
−18.0000 | + | 10.3923i | −0.590561 | + | 0.340960i | −0.765319 | − | 0.643651i | ||
0.174758 | + | 0.984611i | ||||||||
0 | 0 | |||||||||
13.8564i | 0.454125i | |||||||||
18.0000 | + | 31.1769i | 0.589610 | + | 1.02123i | |||||
−12.0000 | + | 20.7846i | −0.392862 | + | 0.680458i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−14.0000 | −0.457360 | −0.228680 | − | 0.973502i | ||||||
−0.228680 | + | 0.973502i | ||||||||
0 | 0 | |||||||||
6.50000 | − | 11.2583i | 0.212119 | − | 0.367402i | |||||
12.0000 | + | 20.7846i | 0.391397 | + | 0.677919i | |||||
− | 10.3923i | − | 0.338779i | −0.985549 | − | 0.169390i | ||||
0.985549 | − | 0.169390i | ||||||||
0 | 0 | |||||||||
−36.0000 | + | 20.7846i | −1.17232 | + | 0.676840i | |||||
− | 13.8564i | − | 0.450988i | |||||||
3.00000 | + | 5.19615i | 0.0975900 | + | 0.169031i | |||||
0 | 0 | |||||||||
−42.0000 | − | 24.2487i | −1.36482 | − | 0.787977i | −0.374556 | − | 0.927204i | ||
−0.990260 | + | 0.139227i | ||||||||
22.0000 | 0.714527 | |||||||||
1.50000 | + | 6.06218i | 0.0486921 | + | 0.196787i | |||||
0 | 0 | |||||||||
6.00000 | + | 3.46410i | 0.194563 | + | 0.112331i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.0971795 | − | 0.168320i | 0.813337 | − | 0.581793i | ||
−0.910516 | + | 0.413473i | ||||||||
0 | 0 | |||||||||
−54.0000 | + | 31.1769i | −1.74740 | + | 1.00886i | |||||
0 | 0 | |||||||||
− | 20.7846i | − | 0.671871i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
24.0000 | + | 13.8564i | 0.774597 | + | 0.447214i | |||||
28.0000 | 0.903226 | |||||||||
0 | 0 | |||||||||
−6.00000 | −0.193347 | |||||||||
−36.0000 | − | 20.7846i | −1.15948 | − | 0.669427i | |||||
27.0000 | − | 46.7654i | 0.869161 | − | 1.50543i | |||||
0 | 0 | |||||||||
− | 24.2487i | − | 0.779786i | −0.920860 | − | 0.389893i | ||||
0.920860 | − | 0.389893i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−18.0000 | − | 31.1769i | −0.577647 | − | 1.00051i | −0.995748 | − | 0.0921142i | ||
0.418101 | − | 0.908401i | ||||||||
1.00000 | − | 1.73205i | 0.0320750 | − | 0.0555556i | |||||
7.50000 | + | 4.33013i | 0.240439 | + | 0.138817i | |||||
0 | 0 | |||||||||
−7.00000 | + | 24.2487i | −0.224179 | + | 0.776580i | |||||
4.00000 | 0.128037 | |||||||||
−24.0000 | − | 13.8564i | −0.767828 | − | 0.443306i | 0.0642712 | − | 0.997932i | ||
−0.832099 | + | 0.554627i | ||||||||
0 | 0 | |||||||||
−12.0000 | − | 20.7846i | −0.383522 | − | 0.664279i | |||||
27.7128i | 0.885253i | |||||||||
−13.5000 | + | 7.79423i | −0.431022 | + | 0.248851i | |||||
0 | 0 | |||||||||
− | 10.3923i | − | 0.331463i | −0.986171 | − | 0.165732i | ||||
0.986171 | − | 0.165732i | ||||||||
0 | 0 | |||||||||
−24.0000 | + | 41.5692i | −0.764704 | + | 1.32451i | |||||
0 | 0 | |||||||||
−6.00000 | −0.190982 | |||||||||
−24.0000 | − | 6.92820i | −0.763542 | − | 0.220416i | |||||
6.00000 | 0.190789 | |||||||||
0 | 0 | |||||||||
8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | ||
0.964658 | + | 0.263504i | ||||||||
0 | 0 | |||||||||
− | 5.19615i | − | 0.164895i | |||||||
0 | 0 | |||||||||
21.0000 | − | 12.1244i | 0.665745 | − | 0.384368i | |||||
27.7128i | 0.878114i | |||||||||
−17.5000 | − | 30.3109i | −0.554231 | − | 0.959955i | −0.997963 | − | 0.0637961i | ||
0.443732 | − | 0.896159i | ||||||||
0 | 0 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 39.2.j.a.4.1 | ✓ | 2 | |
3.2 | odd | 2 | 117.2.q.a.82.1 | 2 | |||
4.3 | odd | 2 | 624.2.bv.b.433.1 | 2 | |||
5.2 | odd | 4 | 975.2.w.d.199.1 | 4 | |||
5.3 | odd | 4 | 975.2.w.d.199.2 | 4 | |||
5.4 | even | 2 | 975.2.bc.c.901.1 | 2 | |||
12.11 | even | 2 | 1872.2.by.f.433.1 | 2 | |||
13.2 | odd | 12 | 507.2.e.f.484.2 | 4 | |||
13.3 | even | 3 | 507.2.j.b.361.1 | 2 | |||
13.4 | even | 6 | 507.2.b.c.337.1 | 2 | |||
13.5 | odd | 4 | 507.2.e.f.22.2 | 4 | |||
13.6 | odd | 12 | 507.2.a.e.1.2 | 2 | |||
13.7 | odd | 12 | 507.2.a.e.1.1 | 2 | |||
13.8 | odd | 4 | 507.2.e.f.22.1 | 4 | |||
13.9 | even | 3 | 507.2.b.c.337.2 | 2 | |||
13.10 | even | 6 | inner | 39.2.j.a.10.1 | yes | 2 | |
13.11 | odd | 12 | 507.2.e.f.484.1 | 4 | |||
13.12 | even | 2 | 507.2.j.b.316.1 | 2 | |||
39.17 | odd | 6 | 1521.2.b.f.1351.2 | 2 | |||
39.20 | even | 12 | 1521.2.a.h.1.2 | 2 | |||
39.23 | odd | 6 | 117.2.q.a.10.1 | 2 | |||
39.32 | even | 12 | 1521.2.a.h.1.1 | 2 | |||
39.35 | odd | 6 | 1521.2.b.f.1351.1 | 2 | |||
52.7 | even | 12 | 8112.2.a.bu.1.1 | 2 | |||
52.19 | even | 12 | 8112.2.a.bu.1.2 | 2 | |||
52.23 | odd | 6 | 624.2.bv.b.49.1 | 2 | |||
65.23 | odd | 12 | 975.2.w.d.49.1 | 4 | |||
65.49 | even | 6 | 975.2.bc.c.751.1 | 2 | |||
65.62 | odd | 12 | 975.2.w.d.49.2 | 4 | |||
156.23 | even | 6 | 1872.2.by.f.1297.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.2.j.a.4.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
39.2.j.a.10.1 | yes | 2 | 13.10 | even | 6 | inner | |
117.2.q.a.10.1 | 2 | 39.23 | odd | 6 | |||
117.2.q.a.82.1 | 2 | 3.2 | odd | 2 | |||
507.2.a.e.1.1 | 2 | 13.7 | odd | 12 | |||
507.2.a.e.1.2 | 2 | 13.6 | odd | 12 | |||
507.2.b.c.337.1 | 2 | 13.4 | even | 6 | |||
507.2.b.c.337.2 | 2 | 13.9 | even | 3 | |||
507.2.e.f.22.1 | 4 | 13.8 | odd | 4 | |||
507.2.e.f.22.2 | 4 | 13.5 | odd | 4 | |||
507.2.e.f.484.1 | 4 | 13.11 | odd | 12 | |||
507.2.e.f.484.2 | 4 | 13.2 | odd | 12 | |||
507.2.j.b.316.1 | 2 | 13.12 | even | 2 | |||
507.2.j.b.361.1 | 2 | 13.3 | even | 3 | |||
624.2.bv.b.49.1 | 2 | 52.23 | odd | 6 | |||
624.2.bv.b.433.1 | 2 | 4.3 | odd | 2 | |||
975.2.w.d.49.1 | 4 | 65.23 | odd | 12 | |||
975.2.w.d.49.2 | 4 | 65.62 | odd | 12 | |||
975.2.w.d.199.1 | 4 | 5.2 | odd | 4 | |||
975.2.w.d.199.2 | 4 | 5.3 | odd | 4 | |||
975.2.bc.c.751.1 | 2 | 65.49 | even | 6 | |||
975.2.bc.c.901.1 | 2 | 5.4 | even | 2 | |||
1521.2.a.h.1.1 | 2 | 39.32 | even | 12 | |||
1521.2.a.h.1.2 | 2 | 39.20 | even | 12 | |||
1521.2.b.f.1351.1 | 2 | 39.35 | odd | 6 | |||
1521.2.b.f.1351.2 | 2 | 39.17 | odd | 6 | |||
1872.2.by.f.433.1 | 2 | 12.11 | even | 2 | |||
1872.2.by.f.1297.1 | 2 | 156.23 | even | 6 | |||
8112.2.a.bu.1.1 | 2 | 52.7 | even | 12 | |||
8112.2.a.bu.1.2 | 2 | 52.19 | even | 12 |