Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(647,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 855.n (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 818.4 | ||
Root | of defining polynomial | ||
Character | 855.818 | ||
Dual form | 855.2.n.c.647.4 |
-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 .
1.41421 | + | 1.41421i | 1.00000 | + | 1.00000i | 1.00000 | ||||
1.00000i | ||||||||||
0 | 0 | |||||||||
2.00000i | 1.00000i | |||||||||
−0.448288 | + | 2.19067i | −0.200480 | + | 0.979698i | |||||
0 | 0 | |||||||||
2.36603 | − | 2.36603i | 0.894274 | − | 0.894274i | −0.100649 | − | 0.994922i | ||
0.994922 | + | 0.100649i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.73205 | + | 2.46410i | −1.18018 | + | 0.779217i | |||||
1.55291i | 0.468221i | 0.972210 | + | 0.234111i | ||||||
−0.972210 | + | 0.234111i | ||||||||
0 | 0 | |||||||||
0.732051 | + | 0.732051i | 0.203034 | + | 0.203034i | 0.801299 | − | 0.598264i | ||
−0.598264 | + | 0.801299i | ||||||||
6.69213 | 1.78855 | |||||||||
0 | 0 | |||||||||
4.00000 | 1.00000 | |||||||||
4.57081 | + | 4.57081i | 1.10858 | + | 1.10858i | 0.993337 | + | 0.115247i | ||
0.115247 | + | 0.993337i | ||||||||
0 | 0 | |||||||||
1.00000i | 0.229416i | |||||||||
−4.38134 | − | 0.896575i | −0.979698 | − | 0.200480i | |||||
0 | 0 | |||||||||
−2.19615 | + | 2.19615i | −0.468221 | + | 0.468221i | |||||
−2.44949 | + | 2.44949i | −0.510754 | + | 0.510754i | −0.914757 | − | 0.404004i | ||
0.404004 | + | 0.914757i | ||||||||
0 | 0 | |||||||||
−4.59808 | − | 1.96410i | −0.919615 | − | 0.392820i | |||||
2.07055i | 0.406069i | |||||||||
0 | 0 | |||||||||
4.73205 | + | 4.73205i | 0.894274 | + | 0.894274i | |||||
−8.76268 | −1.62719 | −0.813595 | − | 0.581432i | ||||||
−0.813595 | + | 0.581432i | ||||||||
0 | 0 | |||||||||
−0.535898 | −0.0962502 | −0.0481251 | − | 0.998841i | ||||||
−0.0481251 | + | 0.998841i | ||||||||
5.65685 | + | 5.65685i | 1.00000 | + | 1.00000i | |||||
0 | 0 | |||||||||
12.9282i | 2.21717i | |||||||||
4.12252 | + | 6.24384i | 0.696833 | + | 1.05540i | |||||
0 | 0 | |||||||||
3.46410 | − | 3.46410i | 0.569495 | − | 0.569495i | −0.362492 | − | 0.931987i | ||
0.931987 | + | 0.362492i | ||||||||
−1.41421 | + | 1.41421i | −0.229416 | + | 0.229416i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 2.82843i | − | 0.441726i | −0.975305 | − | 0.220863i | ||||
0.975305 | − | 0.220863i | ||||||||
0 | 0 | |||||||||
−3.09808 | − | 3.09808i | −0.472452 | − | 0.472452i | 0.430255 | − | 0.902707i | ||
−0.902707 | + | 0.430255i | ||||||||
−3.10583 | −0.468221 | |||||||||
0 | 0 | |||||||||
−6.92820 | −1.02151 | |||||||||
−2.63896 | − | 2.63896i | −0.384932 | − | 0.384932i | 0.487944 | − | 0.872875i | ||
−0.872875 | + | 0.487944i | ||||||||
0 | 0 | |||||||||
− | 4.19615i | − | 0.599450i | |||||||
−3.72500 | − | 9.28032i | −0.526795 | − | 1.31244i | |||||
0 | 0 | |||||||||
−1.46410 | + | 1.46410i | −0.203034 | + | 0.203034i | |||||
4.24264 | − | 4.24264i | 0.582772 | − | 0.582772i | −0.352892 | − | 0.935664i | ||
0.935664 | + | 0.352892i | ||||||||
0 | 0 | |||||||||
−3.40192 | − | 0.696152i | −0.458715 | − | 0.0938692i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.3923 | − | 12.3923i | −1.62719 | − | 1.62719i | |||||
13.3843 | 1.74248 | 0.871241 | − | 0.490855i | ||||||
0.871241 | + | 0.490855i | ||||||||
0 | 0 | |||||||||
−12.8564 | −1.64609 | −0.823047 | − | 0.567973i | ||||||
−0.823047 | + | 0.567973i | ||||||||
−0.757875 | − | 0.757875i | −0.0962502 | − | 0.0962502i | |||||
0 | 0 | |||||||||
8.00000i | 1.00000i | |||||||||
−1.93185 | + | 1.27551i | −0.239617 | + | 0.158208i | |||||
0 | 0 | |||||||||
9.46410 | − | 9.46410i | 1.15622 | − | 1.15622i | 0.170943 | − | 0.985281i | ||
0.985281 | − | 0.170943i | ||||||||
−9.14162 | + | 9.14162i | −1.10858 | + | 1.10858i | |||||
0 | 0 | |||||||||
−3.00000 | + | 14.6603i | −0.358569 | + | 1.75224i | |||||
− | 0.757875i | − | 0.0899432i | −0.998988 | − | 0.0449716i | ||||
0.998988 | − | 0.0449716i | ||||||||
0 | 0 | |||||||||
−3.90192 | − | 3.90192i | −0.456686 | − | 0.456686i | 0.440880 | − | 0.897566i | ||
−0.897566 | + | 0.440880i | ||||||||
9.79796 | 1.13899 | |||||||||
0 | 0 | |||||||||
−2.00000 | −0.229416 | |||||||||
3.67423 | + | 3.67423i | 0.418718 | + | 0.418718i | |||||
0 | 0 | |||||||||
13.4641i | 1.51483i | 0.652934 | + | 0.757415i | ||||||
−0.652934 | + | 0.757415i | ||||||||
−1.79315 | + | 8.76268i | −0.200480 | + | 0.979698i | |||||
0 | 0 | |||||||||
4.00000 | − | 4.00000i | 0.441726 | − | 0.441726i | |||||
−0.757875 | + | 0.757875i | −0.0831876 | + | 0.0831876i | −0.747476 | − | 0.664289i | ||
0.664289 | + | 0.747476i | ||||||||
0 | 0 | |||||||||
−12.0622 | + | 7.96410i | −1.30833 | + | 0.863828i | |||||
− | 8.76268i | − | 0.944904i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.76268 | 0.928843 | 0.464421 | − | 0.885614i | ||||||
0.464421 | + | 0.885614i | ||||||||
0 | 0 | |||||||||
3.46410 | 0.363137 | |||||||||
−4.89898 | − | 4.89898i | −0.510754 | − | 0.510754i | |||||
0 | 0 | |||||||||
− | 7.46410i | − | 0.769863i | |||||||
−2.19067 | − | 0.448288i | −0.224758 | − | 0.0459934i | |||||
0 | 0 | |||||||||
−5.66025 | + | 5.66025i | −0.574712 | + | 0.574712i | −0.933441 | − | 0.358730i | ||
0.358730 | + | 0.933441i | ||||||||
5.93426 | − | 5.93426i | 0.599450 | − | 0.599450i | |||||
0 | 0 | |||||||||
3.92820 | − | 9.19615i | 0.392820 | − | 0.919615i | |||||
− | 18.9396i | − | 1.88456i | −0.334828 | − | 0.942279i | ||||
0.334828 | − | 0.942279i | ||||||||
0 | 0 | |||||||||
1.80385 | + | 1.80385i | 0.177738 | + | 0.177738i | 0.790369 | − | 0.612631i | ||
−0.612631 | + | 0.790369i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12.0000 | 1.16554 | |||||||||
−0.378937 | − | 0.378937i | −0.0366333 | − | 0.0366333i | 0.688553 | − | 0.725186i | ||
−0.725186 | + | 0.688553i | ||||||||
0 | 0 | |||||||||
− | 8.39230i | − | 0.803837i | −0.915675 | − | 0.401919i | ||||
0.915675 | − | 0.401919i | ||||||||
−3.82654 | − | 5.79555i | −0.364846 | − | 0.552584i | |||||
0 | 0 | |||||||||
9.46410 | − | 9.46410i | 0.894274 | − | 0.894274i | |||||
−10.9348 | + | 10.9348i | −1.02866 | + | 1.02866i | −0.0290796 | + | 0.999577i | ||
−0.999577 | + | 0.0290796i | ||||||||
0 | 0 | |||||||||
−4.26795 | − | 6.46410i | −0.397988 | − | 0.602781i | |||||
− | 17.5254i | − | 1.62719i | |||||||
0 | 0 | |||||||||
18.9282 | + | 18.9282i | 1.74248 | + | 1.74248i | |||||
21.6293 | 1.98276 | |||||||||
0 | 0 | |||||||||
8.58846 | 0.780769 | |||||||||
−18.1817 | − | 18.1817i | −1.64609 | − | 1.64609i | |||||
0 | 0 | |||||||||
− | 1.07180i | − | 0.0962502i | |||||||
6.36396 | − | 9.19239i | 0.569210 | − | 0.822192i | |||||
0 | 0 | |||||||||
−1.26795 | + | 1.26795i | −0.112512 | + | 0.112512i | −0.761122 | − | 0.648609i | ||
0.648609 | + | 0.761122i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.53590 | − | 0.928203i | −0.397825 | − | 0.0814088i | |||||
− | 12.8666i | − | 1.12416i | −0.827082 | − | 0.562081i | ||||
0.827082 | − | 0.562081i | ||||||||
0 | 0 | |||||||||
2.36603 | + | 2.36603i | 0.205160 | + | 0.205160i | |||||
26.7685 | 2.31245 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.08604 | − | 1.08604i | −0.0927870 | − | 0.0927870i | 0.659190 | − | 0.751977i | ||
−0.751977 | + | 0.659190i | ||||||||
0 | 0 | |||||||||
− | 9.73205i | − | 0.825462i | −0.910853 | − | 0.412731i | ||||
0.910853 | − | 0.412731i | ||||||||
−12.4877 | + | 8.24504i | −1.05540 | + | 0.696833i | |||||
0 | 0 | |||||||||
1.07180 | − | 1.07180i | 0.0899432 | − | 0.0899432i | |||||
−1.13681 | + | 1.13681i | −0.0950650 | + | 0.0950650i | |||||
0 | 0 | |||||||||
3.92820 | − | 19.1962i | 0.326220 | − | 1.59415i | |||||
− | 11.0363i | − | 0.913371i | |||||||
0 | 0 | |||||||||
6.92820 | + | 6.92820i | 0.569495 | + | 0.569495i | |||||
−24.3562 | −1.99534 | −0.997669 | − | 0.0682436i | ||||||
−0.997669 | + | 0.0682436i | ||||||||
0 | 0 | |||||||||
1.07180 | 0.0872216 | 0.0436108 | − | 0.999049i | ||||||
0.0436108 | + | 0.999049i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
10.3923i | 0.837436i | |||||||||
0.240237 | − | 1.17398i | 0.0192963 | − | 0.0942961i | |||||
0 | 0 | |||||||||
−0.0717968 | + | 0.0717968i | −0.00573001 | + | 0.00573001i | −0.709966 | − | 0.704236i | ||
0.704236 | + | 0.709966i | ||||||||
−19.0411 | + | 19.0411i | −1.51483 | + | 1.51483i | |||||
0 | 0 | |||||||||
−14.9282 | + | 9.85641i | −1.18018 | + | 0.779217i | |||||
11.5911i | 0.913507i | |||||||||
0 | 0 | |||||||||
−9.19615 | − | 9.19615i | −0.720298 | − | 0.720298i | 0.248368 | − | 0.968666i | ||
−0.968666 | + | 0.248368i | ||||||||
5.65685 | 0.441726 | |||||||||
0 | 0 | |||||||||
−2.14359 | −0.166375 | |||||||||
14.0406 | + | 14.0406i | 1.08649 | + | 1.08649i | 0.995887 | + | 0.0906075i | ||
0.0906075 | + | 0.995887i | ||||||||
0 | 0 | |||||||||
− | 11.9282i | − | 0.917554i | |||||||
−28.3214 | − | 5.79555i | −2.17215 | − | 0.444499i | |||||
0 | 0 | |||||||||
6.19615 | − | 6.19615i | 0.472452 | − | 0.472452i | |||||
−8.10634 | + | 8.10634i | −0.616314 | + | 0.616314i | −0.944584 | − | 0.328270i | ||
0.328270 | + | 0.944584i | ||||||||
0 | 0 | |||||||||
−15.5263 | + | 6.23205i | −1.17368 | + | 0.471099i | |||||
6.21166i | 0.468221i | |||||||||
0 | 0 | |||||||||
12.3923 | + | 12.3923i | 0.928843 | + | 0.928843i | |||||
−5.17638 | −0.386901 | −0.193450 | − | 0.981110i | ||||||
−0.193450 | + | 0.981110i | ||||||||
0 | 0 | |||||||||
18.3923 | 1.36709 | 0.683545 | − | 0.729909i | ||||||
0.683545 | + | 0.729909i | ||||||||
4.89898 | + | 4.89898i | 0.363137 | + | 0.363137i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.03579 | + | 9.14162i | 0.443760 | + | 0.672105i | |||||
0 | 0 | |||||||||
−7.09808 | + | 7.09808i | −0.519063 | + | 0.519063i | |||||
5.27792 | − | 5.27792i | 0.384932 | − | 0.384932i | |||||
0 | 0 | |||||||||
−2.46410 | − | 3.73205i | −0.178765 | − | 0.270751i | |||||
2.58819i | 0.187275i | 0.995606 | + | 0.0936374i | ||||||
−0.995606 | + | 0.0936374i | ||||||||
0 | 0 | |||||||||
−11.4641 | − | 11.4641i | −0.825204 | − | 0.825204i | 0.161645 | − | 0.986849i | ||
−0.986849 | + | 0.161645i | ||||||||
−16.0096 | −1.14942 | |||||||||
0 | 0 | |||||||||
8.39230 | 0.599450 | |||||||||
−9.79796 | − | 9.79796i | −0.698076 | − | 0.698076i | 0.265920 | − | 0.963995i | ||
−0.963995 | + | 0.265920i | ||||||||
0 | 0 | |||||||||
− | 9.73205i | − | 0.689887i | −0.938623 | − | 0.344943i | ||||
0.938623 | − | 0.344943i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
26.7846 | − | 26.7846i | 1.88456 | − | 1.88456i | |||||
−20.7327 | + | 20.7327i | −1.45515 | + | 1.45515i | |||||
0 | 0 | |||||||||
6.19615 | + | 1.26795i | 0.432758 | + | 0.0885574i | |||||
5.10205i | 0.355477i | |||||||||
0 | 0 | |||||||||
2.92820 | + | 2.92820i | 0.203034 | + | 0.203034i | |||||
−1.55291 | −0.107417 | |||||||||
0 | 0 | |||||||||
−5.85641 | −0.403172 | −0.201586 | − | 0.979471i | ||||||
−0.201586 | + | 0.979471i | ||||||||
8.48528 | + | 8.48528i | 0.582772 | + | 0.582772i | |||||
0 | 0 | |||||||||
− | 1.07180i | − | 0.0732665i | |||||||
8.17569 | − | 5.39804i | 0.557578 | − | 0.368143i | |||||
0 | 0 | |||||||||
−1.26795 | + | 1.26795i | −0.0860740 | + | 0.0860740i | |||||
11.8685 | − | 11.8685i | 0.803837 | − | 0.803837i | |||||
0 | 0 | |||||||||
1.39230 | − | 6.80385i | 0.0938692 | − | 0.458715i | |||||
6.69213i | 0.450161i | |||||||||
0 | 0 | |||||||||
−4.92820 | − | 4.92820i | −0.330017 | − | 0.330017i | 0.522576 | − | 0.852593i | ||
−0.852593 | + | 0.522576i | ||||||||
26.7685 | 1.78855 | |||||||||
0 | 0 | |||||||||
−30.9282 | −2.05731 | |||||||||
−17.1464 | − | 17.1464i | −1.13805 | − | 1.13805i | −0.988800 | − | 0.149249i | ||
−0.149249 | − | 0.988800i | ||||||||
0 | 0 | |||||||||
− | 12.6603i | − | 0.836613i | −0.908306 | − | 0.418307i | ||||
0.908306 | − | 0.418307i | ||||||||
3.10583 | − | 15.1774i | 0.204792 | − | 1.00077i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.46739 | + | 5.46739i | −0.358180 | + | 0.358180i | −0.863142 | − | 0.504962i | ||
0.504962 | + | 0.863142i | ||||||||
0 | 0 | |||||||||
6.96410 | − | 4.59808i | 0.454288 | − | 0.299945i | |||||
26.7685i | 1.74248i | |||||||||
0 | 0 | |||||||||
30.5885 | + | 30.5885i | 1.98276 | + | 1.98276i | |||||
8.14351 | 0.526760 | 0.263380 | − | 0.964692i | ||||||
0.263380 | + | 0.964692i | ||||||||
0 | 0 | |||||||||
28.3923 | 1.82891 | 0.914455 | − | 0.404689i | ||||||
0.914455 | + | 0.404689i | ||||||||
12.1459 | + | 12.1459i | 0.780769 | + | 0.780769i | |||||
0 | 0 | |||||||||
− | 25.7128i | − | 1.64609i | |||||||
9.19239 | + | 1.88108i | 0.587280 | + | 0.120178i | |||||
0 | 0 | |||||||||
−0.732051 | + | 0.732051i | −0.0465793 | + | 0.0465793i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
22.0000 | − | 4.00000i | 1.39140 | − | 0.252982i | |||||
15.0387i | 0.949235i | 0.880192 | + | 0.474618i | ||||||
−0.880192 | + | 0.474618i | ||||||||
0 | 0 | |||||||||
−3.80385 | − | 3.80385i | −0.239146 | − | 0.239146i | |||||
−3.58630 | −0.225025 | |||||||||
0 | 0 | |||||||||
16.0000 | 1.00000 | |||||||||
−18.5606 | − | 18.5606i | −1.15778 | − | 1.15778i | −0.984952 | − | 0.172829i | ||
−0.172829 | − | 0.984952i | ||||||||
0 | 0 | |||||||||
− | 16.3923i | − | 1.01857i | |||||||
−2.55103 | − | 3.86370i | −0.158208 | − | 0.239617i | |||||
0 | 0 | |||||||||
18.1962 | − | 18.1962i | 1.12416 | − | 1.12416i | |||||
−12.9546 | + | 12.9546i | −0.798812 | + | 0.798812i | −0.982908 | − | 0.184096i | ||
0.184096 | + | 0.982908i | ||||||||
0 | 0 | |||||||||
7.39230 | + | 11.1962i | 0.454106 | + | 0.687774i | |||||
6.69213i | 0.410321i | |||||||||
0 | 0 | |||||||||
18.9282 | + | 18.9282i | 1.15622 | + | 1.15622i | |||||
−16.4901 | −1.00542 | −0.502709 | − | 0.864456i | ||||||
−0.502709 | + | 0.864456i | ||||||||
0 | 0 | |||||||||
19.4641 | 1.18236 | 0.591180 | − | 0.806540i | ||||||
0.591180 | + | 0.806540i | ||||||||
18.2832 | + | 18.2832i | 1.10858 | + | 1.10858i | |||||
0 | 0 | |||||||||
− | 3.07180i | − | 0.185574i | |||||||
3.05008 | − | 7.14042i | 0.183927 | − | 0.430583i | |||||
0 | 0 | |||||||||
−9.16987 | + | 9.16987i | −0.550964 | + | 0.550964i | −0.926719 | − | 0.375755i | ||
0.375755 | + | 0.926719i | ||||||||
13.7632 | − | 13.7632i | 0.825462 | − | 0.825462i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.10583i | 0.185278i | 0.995700 | + | 0.0926391i | ||||||
−0.995700 | + | 0.0926391i | ||||||||
0 | 0 | |||||||||
0.633975 | + | 0.633975i | 0.0376859 | + | 0.0376859i | 0.725699 | − | 0.688013i | ||
−0.688013 | + | 0.725699i | ||||||||
1.51575 | 0.0899432 | |||||||||
0 | 0 | |||||||||
−3.21539 | −0.190130 | |||||||||
−6.69213 | − | 6.69213i | −0.395024 | − | 0.395024i | |||||
0 | 0 | |||||||||
24.7846i | 1.45792i | |||||||||
32.7028 | − | 21.5921i | 1.92037 | − | 1.26793i | |||||
0 | 0 | |||||||||
7.80385 | − | 7.80385i | 0.456686 | − | 0.456686i | |||||
−10.2784 | + | 10.2784i | −0.600472 | + | 0.600472i | −0.940438 | − | 0.339965i | ||
0.339965 | + | 0.940438i | ||||||||
0 | 0 | |||||||||
−6.00000 | + | 29.3205i | −0.349334 | + | 1.70711i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−34.4449 | − | 34.4449i | −1.99534 | − | 1.99534i | |||||
−3.58630 | −0.207401 | |||||||||
0 | 0 | |||||||||
−14.6603 | −0.845003 | |||||||||
1.51575 | + | 1.51575i | 0.0872216 | + | 0.0872216i | |||||
0 | 0 | |||||||||
4.00000i | 0.229416i | |||||||||
5.76337 | − | 28.1642i | 0.330010 | − | 1.61267i | |||||
0 | 0 | |||||||||
−18.3923 | + | 18.3923i | −1.04970 | + | 1.04970i | −0.0510059 | + | 0.998698i | ||
−0.998698 | + | 0.0510059i | ||||||||
−7.34847 | + | 7.34847i | −0.418718 | + | 0.418718i | |||||
0 | 0 | |||||||||
2.00000 | − | 1.32051i | 0.113592 | − | 0.0749998i | |||||
− | 9.65926i | − | 0.547726i | −0.961769 | − | 0.273863i | ||||
0.961769 | − | 0.273863i | ||||||||
0 | 0 | |||||||||
22.3205 | + | 22.3205i | 1.26163 | + | 1.26163i | 0.950303 | + | 0.311327i | ||
0.311327 | + | 0.950303i | ||||||||
−0.203072 | −0.0114600 | |||||||||
0 | 0 | |||||||||
−26.9282 | −1.51483 | |||||||||
7.45001 | + | 7.45001i | 0.418434 | + | 0.418434i | 0.884664 | − | 0.466230i | ||
−0.466230 | + | 0.884664i | ||||||||
0 | 0 | |||||||||
− | 13.6077i | − | 0.761885i | |||||||
−17.5254 | − | 3.58630i | −0.979698 | − | 0.200480i | |||||
0 | 0 | |||||||||
−16.3923 | + | 16.3923i | −0.913507 | + | 0.913507i | |||||
−4.57081 | + | 4.57081i | −0.254327 | + | 0.254327i | |||||
0 | 0 | |||||||||
−1.92820 | − | 4.80385i | −0.106957 | − | 0.266470i | |||||
− | 26.0106i | − | 1.44060i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.4877 | −0.688468 | |||||||||
0 | 0 | |||||||||
2.14359 | 0.117823 | 0.0589113 | − | 0.998263i | ||||||
0.0589113 | + | 0.998263i | ||||||||
−1.51575 | − | 1.51575i | −0.0831876 | − | 0.0831876i | |||||
0 | 0 | |||||||||
39.7128i | 2.17299i | |||||||||
16.4901 | + | 24.9754i | 0.900950 | + | 1.36455i | |||||
0 | 0 | |||||||||
3.66025 | − | 3.66025i | 0.199387 | − | 0.199387i | −0.600350 | − | 0.799737i | ||
0.799737 | + | 0.600350i | ||||||||
16.8690 | − | 16.8690i | 0.917554 | − | 0.917554i | |||||
0 | 0 | |||||||||
−15.9282 | − | 24.1244i | −0.863828 | − | 1.30833i | |||||
− | 0.832204i | − | 0.0450664i | |||||||
0 | 0 | |||||||||
6.63397 | + | 6.63397i | 0.358201 | + | 0.358201i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−22.9282 | −1.23263 | |||||||||
24.1667 | + | 24.1667i | 1.29734 | + | 1.29734i | 0.930145 | + | 0.367193i | ||
0.367193 | + | 0.930145i | ||||||||
0 | 0 | |||||||||
− | 11.3397i | − | 0.607003i | −0.952831 | − | 0.303501i | ||||
0.952831 | − | 0.303501i | ||||||||
−30.7709 | − | 13.1440i | −1.64478 | − | 0.702578i | |||||
0 | 0 | |||||||||
−8.78461 | + | 8.78461i | −0.468221 | + | 0.468221i | |||||
12.6264 | − | 12.6264i | 0.672035 | − | 0.672035i | −0.286150 | − | 0.958185i | ||
0.958185 | + | 0.286150i | ||||||||
0 | 0 | |||||||||
1.66025 | + | 0.339746i | 0.0881171 | + | 0.0180318i | |||||
17.5254i | 0.928843i | |||||||||
0 | 0 | |||||||||
−7.32051 | − | 7.32051i | −0.386901 | − | 0.386901i | |||||
0.517638 | 0.0273199 | 0.0136599 | − | 0.999907i | ||||||
0.0136599 | + | 0.999907i | ||||||||
0 | 0 | |||||||||
−1.00000 | −0.0526316 | |||||||||
26.0106 | + | 26.0106i | 1.36709 | + | 1.36709i | |||||
0 | 0 | |||||||||
6.92820i | 0.363137i | |||||||||
10.2970 | − | 6.79865i | 0.538970 | − | 0.355857i | |||||
0 | 0 | |||||||||
−13.7321 | + | 13.7321i | −0.716807 | + | 0.716807i | −0.967950 | − | 0.251143i | ||
0.251143 | + | 0.967950i | ||||||||
−9.79796 | + | 9.79796i | −0.510754 | + | 0.510754i | |||||
0 | 0 | |||||||||
−4.39230 | + | 21.4641i | −0.228345 | + | 1.11587i | |||||
− | 20.0764i | − | 1.04231i | |||||||
0 | 0 | |||||||||
−3.46410 | − | 3.46410i | −0.179364 | − | 0.179364i | 0.611714 | − | 0.791079i | ||
−0.791079 | + | 0.611714i | ||||||||
−20.0764 | −1.03813 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.41473 | − | 6.41473i | −0.330375 | − | 0.330375i | |||||
0 | 0 | |||||||||
20.9282i | 1.07501i | 0.843261 | + | 0.537505i | ||||||
−0.843261 | + | 0.537505i | ||||||||
0.896575 | − | 4.38134i | 0.0459934 | − | 0.224758i | |||||
0 | 0 | |||||||||
−3.66025 | + | 3.66025i | −0.187275 | + | 0.187275i | |||||
−14.0406 | + | 14.0406i | −0.717441 | + | 0.717441i | −0.968081 | − | 0.250639i | ||
0.250639 | + | 0.968081i | ||||||||
0 | 0 | |||||||||
−9.69615 | + | 6.40192i | −0.494162 | + | 0.326272i | |||||
− | 32.4254i | − | 1.65041i | |||||||
0 | 0 | |||||||||
−11.3205 | − | 11.3205i | −0.574712 | − | 0.574712i | |||||
−11.0735 | −0.561447 | −0.280724 | − | 0.959789i | ||||||
−0.280724 | + | 0.959789i | ||||||||
0 | 0 | |||||||||
−22.3923 | −1.13243 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 27.7128i | − | 1.39615i | |||||||
−29.4954 | − | 6.03579i | −1.48408 | − | 0.303694i | |||||
0 | 0 | |||||||||
23.2224 | − | 23.2224i | 1.16550 | − | 1.16550i | 0.182248 | − | 0.983253i | ||
0.983253 | − | 0.182248i | ||||||||
13.7632 | − | 13.7632i | 0.689887 | − | 0.689887i | |||||
0 | 0 | |||||||||
−18.3923 | − | 7.85641i | −0.919615 | − | 0.392820i | |||||
19.0411i | 0.950868i | 0.879751 | + | 0.475434i | ||||||
−0.879751 | + | 0.475434i | ||||||||
0 | 0 | |||||||||
−0.392305 | − | 0.392305i | −0.0195421 | − | 0.0195421i | |||||
37.8792 | 1.88456 | |||||||||
0 | 0 | |||||||||
−58.6410 | −2.91030 | |||||||||
5.37945 | + | 5.37945i | 0.266650 | + | 0.266650i | |||||
0 | 0 | |||||||||
11.8564i | 0.586262i | 0.956072 | + | 0.293131i | ||||||
−0.956072 | + | 0.293131i | ||||||||
6.96953 | + | 10.5558i | 0.344201 | + | 0.521315i | |||||
0 | 0 | |||||||||
−3.60770 | + | 3.60770i | −0.177738 | + | 0.177738i | |||||
31.6675 | − | 31.6675i | 1.55826 | − | 1.55826i | |||||
0 | 0 | |||||||||
−1.32051 | − | 2.00000i | −0.0648212 | − | 0.0981761i | |||||
8.28221i | 0.406069i | |||||||||
0 | 0 | |||||||||
−2.19615 | − | 2.19615i | −0.107417 | − | 0.107417i | |||||
29.9759 | 1.46442 | 0.732209 | − | 0.681080i | ||||||
0.732209 | + | 0.681080i | ||||||||
0 | 0 | |||||||||
9.60770 | 0.468250 | 0.234125 | − | 0.972206i | ||||||
0.234125 | + | 0.972206i | ||||||||
−8.28221 | − | 8.28221i | −0.403172 | − | 0.403172i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.0394 | − | 29.9945i | −0.583997 | − | 1.45495i | |||||
0 | 0 | |||||||||
−30.4186 | + | 30.4186i | −1.47206 | + | 1.47206i | |||||
0.757875 | − | 0.757875i | 0.0366333 | − | 0.0366333i | |||||
0 | 0 | |||||||||
19.1962 | + | 3.92820i | 0.925721 | + | 0.189435i | |||||
8.76268i | 0.422084i | 0.977477 | + | 0.211042i | ||||||
−0.977477 | + | 0.211042i | ||||||||
0 | 0 | |||||||||
−4.73205 | − | 4.73205i | −0.227408 | − | 0.227408i | 0.584201 | − | 0.811609i | ||
−0.811609 | + | 0.584201i | ||||||||
−3.58630 | −0.172148 | |||||||||
0 | 0 | |||||||||
16.7846 | 0.803837 | |||||||||
−2.44949 | − | 2.44949i | −0.117175 | − | 0.117175i | |||||
0 | 0 | |||||||||
31.8564i | 1.52042i | 0.649675 | + | 0.760212i | ||||||
−0.649675 | + | 0.760212i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.46410 | + | 9.46410i | −0.450161 | + | 0.450161i | |||||
−22.4379 | + | 22.4379i | −1.06606 | + | 1.06606i | −0.0684012 | + | 0.997658i | ||
−0.997658 | + | 0.0684012i | ||||||||
0 | 0 | |||||||||
−3.92820 | + | 19.1962i | −0.186215 | + | 0.909985i | |||||
− | 13.9391i | − | 0.660034i | |||||||
0 | 0 | |||||||||
18.9282 | + | 18.9282i | 0.894274 | + | 0.894274i | |||||
−6.41473 | −0.302730 | −0.151365 | − | 0.988478i | ||||||
−0.151365 | + | 0.988478i | ||||||||
0 | 0 | |||||||||
4.39230 | 0.206826 | |||||||||
−21.8695 | − | 21.8695i | −1.02866 | − | 1.02866i | |||||
0 | 0 | |||||||||
− | 48.4974i | − | 2.27610i | |||||||
−1.55291 | + | 7.58871i | −0.0728017 | + | 0.355764i | |||||
0 | 0 | |||||||||
0.0262794 | − | 0.0262794i | 0.00122930 | − | 0.00122930i | −0.706492 | − | 0.707721i | ||
0.707721 | + | 0.706492i | ||||||||
17.9043 | − | 17.9043i | 0.836613 | − | 0.836613i | |||||
0 | 0 | |||||||||
12.9282 | − | 8.53590i | 0.602781 | − | 0.397988i | |||||
− | 17.5897i | − | 0.819236i | −0.912257 | − | 0.409618i | ||||
0.912257 | − | 0.409618i | ||||||||
0 | 0 | |||||||||
9.97372 | + | 9.97372i | 0.463518 | + | 0.463518i | 0.899807 | − | 0.436289i | ||
−0.436289 | + | 0.899807i | ||||||||
−35.0507 | −1.62719 | |||||||||
0 | 0 | |||||||||
−15.4641 | −0.716361 | |||||||||
−7.91688 | − | 7.91688i | −0.366349 | − | 0.366349i | 0.499795 | − | 0.866144i | ||
−0.866144 | + | 0.499795i | ||||||||
0 | 0 | |||||||||
− | 44.7846i | − | 2.06796i | |||||||
16.3514 | + | 3.34607i | 0.754233 | + | 0.154342i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.81105 | − | 4.81105i | 0.221212 | − | 0.221212i | |||||
0 | 0 | |||||||||
1.96410 | − | 4.59808i | 0.0901192 | − | 0.210974i | |||||
43.2586i | 1.98276i | |||||||||
0 | 0 | |||||||||
11.5167 | + | 11.5167i | 0.526760 | + | 0.526760i | |||||
−23.7642 | −1.08582 | −0.542908 | − | 0.839792i | ||||||
−0.542908 | + | 0.839792i | ||||||||
0 | 0 | |||||||||
5.07180 | 0.231254 | |||||||||
40.1528 | + | 40.1528i | 1.82891 | + | 1.82891i | |||||
0 | 0 | |||||||||
17.1769i | 0.780769i | |||||||||
−9.86233 | − | 14.9372i | −0.447825 | − | 0.678262i | |||||
0 | 0 | |||||||||
−26.9282 | + | 26.9282i | −1.22023 | + | 1.22023i | −0.252685 | + | 0.967549i | ||
−0.967549 | + | 0.252685i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
10.3397 | + | 15.6603i | 0.467102 | + | 0.707458i | |||||
37.7033i | 1.70153i | 0.525550 | + | 0.850763i | ||||||
−0.525550 | + | 0.850763i | ||||||||
0 | 0 | |||||||||
−40.0526 | − | 40.0526i | −1.80388 | − | 1.80388i | |||||
−2.07055 | −0.0931586 | |||||||||
0 | 0 | |||||||||
−2.14359 | −0.0962502 | |||||||||
−1.79315 | − | 1.79315i | −0.0804338 | − | 0.0804338i | |||||
0 | 0 | |||||||||
− | 41.7321i | − | 1.86818i | −0.357033 | − | 0.934092i | ||||
0.357033 | − | 0.934092i | ||||||||
18.3848 | + | 12.7279i | 0.822192 | + | 0.569210i | |||||
0 | 0 | |||||||||
−21.2679 | + | 21.2679i | −0.949235 | + | 0.949235i | |||||
−2.07055 | + | 2.07055i | −0.0923214 | + | 0.0923214i | −0.751759 | − | 0.659438i | ||
0.659438 | + | 0.751759i | ||||||||
0 | 0 | |||||||||
41.4904 | + | 8.49038i | 1.84630 | + | 0.377817i | |||||
− | 10.7589i | − | 0.478292i | |||||||
0 | 0 | |||||||||
−2.53590 | − | 2.53590i | −0.112512 | − | 0.112512i | |||||
−11.0363 | −0.489176 | −0.244588 | − | 0.969627i | ||||||
−0.244588 | + | 0.969627i | ||||||||
0 | 0 | |||||||||
−18.4641 | −0.816804 | |||||||||
22.6274 | + | 22.6274i | 1.00000 | + | 1.00000i | |||||
0 | 0 | |||||||||
− | 52.4974i | − | 2.31556i | |||||||
−4.76028 | + | 3.14299i | −0.209763 | + | 0.138497i | |||||
0 | 0 | |||||||||
4.09808 | − | 4.09808i | 0.180233 | − | 0.180233i | |||||
23.1822 | − | 23.1822i | 1.01857 | − | 1.01857i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.65685i | 0.247831i | 0.992293 | + | 0.123916i | ||||||
−0.992293 | + | 0.123916i | ||||||||
0 | 0 | |||||||||
25.6603 | + | 25.6603i | 1.12204 | + | 1.12204i | 0.991434 | + | 0.130611i | ||
0.130611 | + | 0.991434i | ||||||||
25.7332 | 1.12416 | |||||||||
0 | 0 | |||||||||
−36.6410 | −1.59762 | |||||||||
−2.44949 | − | 2.44949i | −0.106701 | − | 0.106701i | |||||
0 | 0 | |||||||||
11.0000i | 0.478261i | |||||||||
−5.37945 | + | 26.2880i | −0.233668 | + | 1.14188i | |||||
0 | 0 | |||||||||
−4.73205 | + | 4.73205i | −0.205160 | + | 0.205160i | |||||
2.07055 | − | 2.07055i | 0.0896856 | − | 0.0896856i | |||||
0 | 0 | |||||||||
1.00000 | − | 0.660254i | 0.0432338 | − | 0.0285453i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−23.3205 | − | 23.3205i | −1.00542 | − | 1.00542i | |||||
6.51626 | 0.280675 | |||||||||
0 | 0 | |||||||||
29.1962 | 1.25524 | 0.627620 | − | 0.778520i | ||||||
0.627620 | + | 0.778520i | ||||||||
27.5264 | + | 27.5264i | 1.18236 | + | 1.18236i | |||||
0 | 0 | |||||||||
51.7128i | 2.21717i | |||||||||
18.3848 | + | 3.76217i | 0.787517 | + | 0.161154i | |||||
0 | 0 | |||||||||
−22.0526 | + | 22.0526i | −0.942899 | + | 0.942899i | −0.998456 | − | 0.0555562i | ||
0.0555562 | + | 0.998456i | ||||||||
2.17209 | − | 2.17209i | 0.0927870 | − | 0.0927870i | |||||
0 | 0 | |||||||||
14.4115 | − | 5.78461i | 0.614510 | − | 0.246657i | |||||
− | 8.76268i | − | 0.373303i | |||||||
0 | 0 | |||||||||
31.8564 | + | 31.8564i | 1.35467 | + | 1.35467i | |||||
−25.9363 | −1.10193 | |||||||||
0 | 0 | |||||||||
19.4641 | 0.825462 | |||||||||
15.0895 | + | 15.0895i | 0.639362 | + | 0.639362i | 0.950398 | − | 0.311036i | ||
−0.311036 | + | 0.950398i | ||||||||
0 | 0 | |||||||||
− | 4.53590i | − | 0.191848i | |||||||
16.4901 | + | 24.9754i | 0.696833 | + | 1.05540i | |||||
0 | 0 | |||||||||
−4.39230 | + | 4.39230i | −0.185278 | + | 0.185278i | |||||
28.2843 | − | 28.2843i | 1.19204 | − | 1.19204i | 0.215546 | − | 0.976494i | ||
0.976494 | − | 0.215546i | ||||||||
0 | 0 | |||||||||
−19.0526 | − | 28.8564i | −0.801547 | − | 1.21400i | |||||
1.79315i | 0.0753718i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−17.4510 | −0.731585 | −0.365793 | − | 0.930696i | ||||||
−0.365793 | + | 0.930696i | ||||||||
0 | 0 | |||||||||
−42.3923 | −1.77406 | −0.887031 | − | 0.461709i | ||||||
−0.887031 | + | 0.461709i | ||||||||
−2.27362 | − | 2.27362i | −0.0950650 | − | 0.0950650i | |||||
0 | 0 | |||||||||
− | 18.9282i | − | 0.790048i | |||||||
16.0740 | − | 6.45189i | 0.670332 | − | 0.269063i | |||||
0 | 0 | |||||||||
14.8301 | − | 14.8301i | 0.617386 | − | 0.617386i | −0.327474 | − | 0.944860i | ||
0.944860 | + | 0.327474i | ||||||||
−35.0507 | + | 35.0507i | −1.45792 | + | 1.45792i | |||||
0 | 0 | |||||||||
38.3923 | + | 7.85641i | 1.59415 | + | 0.326220i | |||||
3.58630i | 0.148785i | |||||||||
0 | 0 | |||||||||
6.58846 | + | 6.58846i | 0.272866 | + | 0.272866i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−29.0718 | −1.20094 | |||||||||
24.6844 | + | 24.6844i | 1.01883 | + | 1.01883i | 0.999819 | + | 0.0190136i | ||
0.0190136 | + | 0.999819i | ||||||||
0 | 0 | |||||||||
− | 0.535898i | − | 0.0220813i | |||||||
−49.9507 | + | 32.9802i | −2.05644 | + | 1.35777i | |||||
0 | 0 | |||||||||
13.8564 | − | 13.8564i | 0.569495 | − | 0.569495i | |||||
−5.00052 | + | 5.00052i | −0.205347 | + | 0.205347i | −0.802286 | − | 0.596940i | ||
0.596940 | + | 0.802286i | ||||||||
0 | 0 | |||||||||
−9.69615 | + | 47.3827i | −0.397503 | + | 1.94250i | |||||
− | 48.7124i | − | 1.99534i | |||||||
0 | 0 | |||||||||
−5.07180 | − | 5.07180i | −0.207401 | − | 0.207401i | |||||
23.3853 | 0.955497 | 0.477749 | − | 0.878497i | ||||||
0.477749 | + | 0.878497i | ||||||||
0 | 0 | |||||||||
16.0000 | 0.652654 | 0.326327 | − | 0.945257i | ||||||
0.326327 | + | 0.945257i | ||||||||
−20.7327 | − | 20.7327i | −0.845003 | − | 0.845003i | |||||
0 | 0 | |||||||||
2.14359i | 0.0872216i | |||||||||
−3.85010 | + | 18.8145i | −0.156529 | + | 0.764917i | |||||
0 | 0 | |||||||||
−11.5167 | + | 11.5167i | −0.467447 | + | 0.467447i | −0.901086 | − | 0.433640i | ||
0.433640 | + | 0.901086i | ||||||||
−5.65685 | + | 5.65685i | −0.229416 | + | 0.229416i | |||||
0 | 0 | |||||||||
47.9808 | − | 31.6795i | 1.94268 | − | 1.28267i | |||||
− | 3.86370i | − | 0.156309i | |||||||
0 | 0 | |||||||||
13.1506 | + | 13.1506i | 0.531149 | + | 0.531149i | 0.920914 | − | 0.389765i | ||
−0.389765 | + | 0.920914i | ||||||||
−52.0213 | −2.09941 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−28.5109 | − | 28.5109i | −1.14781 | − | 1.14781i | −0.986983 | − | 0.160822i | ||
−0.160822 | − | 0.986983i | ||||||||
0 | 0 | |||||||||
− | 36.2487i | − | 1.45696i | −0.685068 | − | 0.728479i | ||||
0.685068 | − | 0.728479i | ||||||||
2.34795 | + | 0.480473i | 0.0942961 | + | 0.0192963i | |||||
0 | 0 | |||||||||
13.6603 | − | 13.6603i | 0.547726 | − | 0.547726i | |||||
20.7327 | − | 20.7327i | 0.830639 | − | 0.830639i | |||||
0 | 0 | |||||||||
17.2846 | + | 18.0622i | 0.691384 | + | 0.722487i | |||||
63.1319i | 2.52326i | |||||||||
0 | 0 | |||||||||
−0.143594 | − | 0.143594i | −0.00573001 | − | 0.00573001i | |||||
31.6675 | 1.26267 | |||||||||
0 | 0 | |||||||||
7.00000 | 0.278666 | 0.139333 | − | 0.990246i | ||||||
0.139333 | + | 0.990246i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
21.0718i | 0.836868i | |||||||||
−2.20925 | − | 3.34607i | −0.0876715 | − | 0.132785i | |||||
0 | 0 | |||||||||
3.07180 | − | 3.07180i | 0.121709 | − | 0.121709i | |||||
19.2442 | − | 19.2442i | 0.761885 | − | 0.761885i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12.5521i | 0.495776i | 0.968789 | + | 0.247888i | ||||||
−0.968789 | + | 0.247888i | ||||||||
0 | 0 | |||||||||
−8.24167 | − | 8.24167i | −0.325020 | − | 0.325020i | 0.525669 | − | 0.850689i | ||
−0.850689 | + | 0.525669i | ||||||||
−23.1822 | −0.913507 | |||||||||
0 | 0 | |||||||||
−12.9282 | −0.508653 | |||||||||
−22.1977 | − | 22.1977i | −0.872682 | − | 0.872682i | 0.120082 | − | 0.992764i | ||
−0.992764 | + | 0.120082i | ||||||||
0 | 0 | |||||||||
20.7846i | 0.815867i | |||||||||
4.06678 | − | 9.52056i | 0.159512 | − | 0.373427i | |||||
0 | 0 | |||||||||
18.3923 | − | 18.3923i | 0.720298 | − | 0.720298i | |||||
−13.7124 | + | 13.7124i | −0.536609 | + | 0.536609i | −0.922531 | − | 0.385922i | ||
0.385922 | + | 0.922531i | ||||||||
0 | 0 | |||||||||
28.1865 | + | 5.76795i | 1.10134 | + | 0.225372i | |||||
− | 11.3137i | − | 0.441726i | |||||||
0 | 0 | |||||||||
−17.6603 | − | 17.6603i | −0.688468 | − | 0.688468i | |||||
−12.9038 | −0.502660 | −0.251330 | − | 0.967901i | ||||||
−0.251330 | + | 0.967901i | ||||||||
0 | 0 | |||||||||
37.5692 | 1.46127 | 0.730637 | − | 0.682767i | ||||||
0.730637 | + | 0.682767i | ||||||||
3.03150 | + | 3.03150i | 0.117823 | + | 0.117823i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.24384 | + | 4.12252i | −0.242126 | + | 0.159865i | |||||
0 | 0 | |||||||||
21.4641 | − | 21.4641i | 0.831093 | − | 0.831093i | |||||
−28.0812 | + | 28.0812i | −1.08649 | + | 1.08649i | |||||
0 | 0 | |||||||||
−12.0000 | + | 58.6410i | −0.463600 | + | 2.26550i | |||||
− | 19.9649i | − | 0.770736i | |||||||
0 | 0 | |||||||||
6.92820 | + | 6.92820i | 0.267063 | + | 0.267063i | 0.827915 | − | 0.560853i | ||
−0.560853 | + | 0.827915i | ||||||||
10.3528 | 0.398773 | |||||||||
0 | 0 | |||||||||
23.8564 | 0.917554 | |||||||||
12.2474 | + | 12.2474i | 0.470708 | + | 0.470708i | 0.902144 | − | 0.431436i | ||
−0.431436 | + | 0.902144i | ||||||||
0 | 0 | |||||||||
26.7846i | 1.02790i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.17691 | − | 1.17691i | 0.0450664 | − | 0.0450664i | |||||
21.2132 | − | 21.2132i | 0.811701 | − | 0.811701i | −0.173188 | − | 0.984889i | ||
0.984889 | + | 0.173188i | ||||||||
0 | 0 | |||||||||
2.86603 | − | 1.89230i | 0.109505 | − | 0.0723013i | |||||
18.7637i | 0.716402i | |||||||||
0 | 0 | |||||||||
−12.3923 | − | 12.3923i | −0.472452 | − | 0.472452i | |||||
6.21166 | 0.236645 | |||||||||
0 | 0 | |||||||||
30.5167 | 1.16091 | 0.580454 | − | 0.814293i | ||||||
0.580454 | + | 0.814293i | ||||||||
−16.2127 | − | 16.2127i | −0.616314 | − | 0.616314i | |||||
0 | 0 | |||||||||
68.3538i | 2.59468i | |||||||||
21.3197 | + | 4.36276i | 0.808703 | + | 0.165489i | |||||
0 | 0 | |||||||||
12.9282 | − | 12.9282i | 0.489691 | − | 0.489691i | |||||
16.0368 | − | 16.0368i | 0.607003 | − | 0.607003i | |||||
0 | 0 | |||||||||
−12.4641 | − | 31.0526i | −0.471099 | − | 1.17368i | |||||
42.8797i | 1.61954i | 0.586745 | + | 0.809771i | ||||||
−0.586745 | + | 0.809771i | ||||||||
0 | 0 | |||||||||
3.46410 | + | 3.46410i | 0.130651 | + | 0.130651i | |||||
−12.4233 | −0.468221 | |||||||||
0 | 0 | |||||||||
35.7128 | 1.34407 | |||||||||
−44.8115 | − | 44.8115i | −1.68531 | − | 1.68531i | |||||
0 | 0 | |||||||||
− | 29.8564i | − | 1.12128i | −0.828059 | − | 0.560640i | ||||
0.828059 | − | 0.560640i | ||||||||
1.86748 | + | 2.82843i | 0.0700853 | + | 0.106149i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.31268 | − | 1.31268i | 0.0491602 | − | 0.0491602i | |||||
0 | 0 | |||||||||
−1.98076 | − | 3.00000i | −0.0740763 | − | 0.112194i | |||||
− | 10.3528i | − | 0.386901i | |||||||
0 | 0 | |||||||||
0.732051 | + | 0.732051i | 0.0273199 | + | 0.0273199i | |||||
20.4182 | 0.761469 | 0.380735 | − | 0.924684i | ||||||
0.380735 | + | 0.924684i | ||||||||
0 | 0 | |||||||||
8.53590 | 0.317893 | |||||||||
−1.41421 | − | 1.41421i | −0.0526316 | − | 0.0526316i | |||||
0 | 0 | |||||||||
36.7846i | 1.36709i | |||||||||
40.2915 | + | 17.2108i | 1.49639 | + | 0.639193i | |||||
0 | 0 | |||||||||
8.95448 | − | 8.95448i | 0.332103 | − | 0.332103i | −0.521281 | − | 0.853385i | ||
0.853385 | + | 0.521281i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
24.1769 | + | 4.94744i | 0.894828 | + | 0.183113i | |||||
− | 28.3214i | − | 1.04751i | |||||||
0 | 0 | |||||||||
−3.00000 | − | 3.00000i | −0.110808 | − | 0.110808i | 0.649529 | − | 0.760337i | ||
−0.760337 | + | 0.649529i | ||||||||
−38.8401 | −1.43361 | |||||||||
0 | 0 | |||||||||
−27.7128 | −1.02151 | |||||||||
14.6969 | + | 14.6969i | 0.541369 | + | 0.541369i | |||||
0 | 0 | |||||||||
3.78461i | 0.139219i | 0.997574 | + | 0.0696096i | ||||||
−0.997574 | + | 0.0696096i | ||||||||
−18.2832 | + | 12.0716i | −0.672105 | + | 0.443760i | |||||
0 | 0 | |||||||||
28.3923 | − | 28.3923i | 1.04231 | − | 1.04231i | |||||
−8.76268 | + | 8.76268i | −0.321472 | + | 0.321472i | −0.849331 | − | 0.527860i | ||
0.527860 | + | 0.849331i | ||||||||
0 | 0 | |||||||||
10.9186 | − | 53.3564i | 0.400026 | − | 1.95483i | |||||
− | 9.79796i | − | 0.358729i | |||||||
0 | 0 | |||||||||
−14.1962 | − | 14.1962i | −0.519063 | − | 0.519063i | |||||
−1.79315 | −0.0655203 | |||||||||
0 | 0 | |||||||||
−40.1051 | −1.46346 | −0.731728 | − | 0.681596i | ||||||
−0.731728 | + | 0.681596i | ||||||||
−10.5558 | − | 10.5558i | −0.384932 | − | 0.384932i | |||||
0 | 0 | |||||||||
− | 18.1436i | − | 0.660751i | |||||||
−0.480473 | + | 2.34795i | −0.0174862 | + | 0.0854508i | |||||
0 | 0 | |||||||||
−5.43782 | + | 5.43782i | −0.197641 | + | 0.197641i | −0.798988 | − | 0.601347i | ||
0.601347 | + | 0.798988i | ||||||||
−29.5969 | + | 29.5969i | −1.07501 | + | 1.07501i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 17.7656i | − | 0.644003i | −0.946739 | − | 0.322001i | ||||
0.946739 | − | 0.322001i | ||||||||
0 | 0 | |||||||||
−19.8564 | − | 19.8564i | −0.718850 | − | 0.718850i | |||||
−5.17638 | −0.187275 | |||||||||
0 | 0 | |||||||||
−39.7128 | −1.43488 | |||||||||
9.79796 | + | 9.79796i | 0.353784 | + | 0.353784i | |||||
0 | 0 | |||||||||
− | 10.8038i | − | 0.389597i | −0.980843 | − | 0.194798i | ||||
0.980843 | − | 0.194798i | ||||||||
−22.7661 | − | 4.65874i | −0.820434 | − | 0.167889i | |||||
0 | 0 | |||||||||
22.9282 | − | 22.9282i | 0.825204 | − | 0.825204i | |||||
21.6665 | − | 21.6665i | 0.779289 | − | 0.779289i | −0.200421 | − | 0.979710i | ||
0.979710 | + | 0.200421i | ||||||||
0 | 0 | |||||||||
2.46410 | + | 1.05256i | 0.0885131 | + | 0.0378090i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−15.6603 | − | 15.6603i | −0.561447 | − | 0.561447i | |||||
2.82843 | 0.101339 | |||||||||
0 | 0 | |||||||||
1.17691 | 0.0421133 | |||||||||
−31.6675 | − | 31.6675i | −1.13243 | − | 1.13243i | |||||
0 | 0 | |||||||||
− | 16.7846i | − | 0.599450i | |||||||
−0.125097 | − | 0.189469i | −0.00446492 | − | 0.00676243i | |||||
0 | 0 | |||||||||
−9.46410 | + | 9.46410i | −0.337359 | + | 0.337359i | −0.855372 | − | 0.518014i | ||
0.518014 | + | 0.855372i | ||||||||
19.5959 | − | 19.5959i | 0.698076 | − | 0.698076i | |||||
0 | 0 | |||||||||
−33.1769 | − | 50.2487i | −1.18038 | − | 1.78777i | |||||
51.7439i | 1.83980i | |||||||||
0 | 0 | |||||||||
−9.41154 | − | 9.41154i | −0.334214 | − | 0.334214i | |||||
65.6830 | 2.33100 | |||||||||
0 | 0 | |||||||||
19.4641 | 0.689887 | |||||||||
−15.6579 | − | 15.6579i | −0.554631 | − | 0.554631i | 0.373143 | − | 0.927774i | ||
−0.927774 | + | 0.373143i | ||||||||
0 | 0 | |||||||||
− | 24.1244i | − | 0.853458i | |||||||
−14.9000 | − | 37.1213i | −0.526795 | − | 1.31244i | |||||
0 | 0 | |||||||||
−26.9282 | + | 26.9282i | −0.950868 | + | 0.950868i | |||||
6.05935 | − | 6.05935i | 0.213830 | − | 0.213830i | |||||
0 | 0 | |||||||||
−25.3923 | − | 5.19615i | −0.894961 | − | 0.183140i | |||||
− | 1.10961i | − | 0.0390842i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.314566 | 0.0110596 | 0.00552978 | − | 0.999985i | ||||||
0.00552978 | + | 0.999985i | ||||||||
0 | 0 | |||||||||
39.8564 | 1.39955 | 0.699774 | − | 0.714364i | ||||||
0.699774 | + | 0.714364i | ||||||||
−41.4655 | − | 41.4655i | −1.45515 | − | 1.45515i | |||||
0 | 0 | |||||||||
15.2154i | 0.533299i | |||||||||
24.2683 | − | 16.0232i | 0.850080 | − | 0.561269i | |||||
0 | 0 | |||||||||
3.09808 | − | 3.09808i | 0.108388 | − | 0.108388i | |||||
−16.7675 | + | 16.7675i | −0.586262 | + | 0.586262i | |||||
0 | 0 | |||||||||
−2.53590 | + | 12.3923i | −0.0885574 | + | 0.432758i | |||||
− | 33.7752i | − | 1.17876i | −0.807855 | − | 0.589382i | ||||
0.807855 | − | 0.589382i | ||||||||
0 | 0 | |||||||||
12.6340 | + | 12.6340i | 0.440393 | + | 0.440393i | 0.892144 | − | 0.451751i | ||
−0.451751 | + | 0.892144i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
89.5692 | 3.11651 | |||||||||
39.1918 | + | 39.1918i | 1.36283 | + | 1.36283i | 0.870285 | + | 0.492549i | ||
0.492549 | + | 0.870285i | ||||||||
0 | 0 | |||||||||
16.6795i | 0.579303i | 0.957132 | + | 0.289651i | ||||||
−0.957132 | + | 0.289651i | ||||||||
0.960947 | − | 4.69591i | 0.0333549 | − | 0.162997i | |||||
0 | 0 | |||||||||
−5.85641 | + | 5.85641i | −0.203034 | + | 0.203034i | |||||
19.1798 | − | 19.1798i | 0.664541 | − | 0.664541i | |||||
0 | 0 | |||||||||
−37.0526 | + | 24.4641i | −1.28226 | + | 0.846615i | |||||
− | 3.10583i | − | 0.107417i | |||||||
0 | 0 | |||||||||
42.3923 | + | 42.3923i | 1.46442 | + | 1.46442i | |||||
−21.5921 | −0.745443 | −0.372722 | − | 0.927943i | ||||||
−0.372722 | + | 0.927943i | ||||||||
0 | 0 | |||||||||
47.7846 | 1.64775 | |||||||||
13.5873 | + | 13.5873i | 0.468250 | + | 0.468250i | |||||
0 | 0 | |||||||||
− | 11.7128i | − | 0.403172i | |||||||
26.1308 | + | 5.34727i | 0.898926 | + | 0.183952i | |||||
0 | 0 | |||||||||
20.3205 | − | 20.3205i | 0.698221 | − | 0.698221i | |||||
16.9706 | − | 16.9706i | 0.582772 | − | 0.582772i | |||||
0 | 0 | |||||||||
25.3923 | − | 59.4449i | 0.870949 | − | 2.03894i | |||||
16.9706i | 0.581743i | |||||||||
0 | 0 | |||||||||
−24.7128 | − | 24.7128i | −0.846151 | − | 0.846151i | 0.143500 | − | 0.989650i | ||
−0.989650 | + | 0.143500i | ||||||||
−86.0367 | −2.94412 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.62158 | − | 4.62158i | −0.157870 | − | 0.157870i | 0.623752 | − | 0.781622i | ||
−0.781622 | + | 0.623752i | ||||||||
0 | 0 | |||||||||
− | 28.5692i | − | 0.974769i | −0.873187 | − | 0.487385i | ||||
0.873187 | − | 0.487385i | ||||||||
10.7961 | + | 16.3514i | 0.368143 | + | 0.557578i | |||||
0 | 0 | |||||||||
−12.3923 | + | 12.3923i | −0.422084 | + | 0.422084i | |||||
−11.5911 | + | 11.5911i | −0.394566 | + | 0.394566i | −0.876311 | − | 0.481745i | ||
0.481745 | + | 0.876311i | ||||||||
0 | 0 | |||||||||
−14.1244 | − | 21.3923i | −0.480242 | − | 0.727360i | |||||
− | 13.3843i | − | 0.454816i | |||||||
0 | 0 | |||||||||
−2.53590 | − | 2.53590i | −0.0860740 | − | 0.0860740i | |||||
−20.9086 | −0.709276 | |||||||||
0 | 0 | |||||||||
13.8564 | 0.469506 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 6.92820i | − | 0.234350i | |||||||
−6.69213 | − | 36.8067i | −0.226235 | − | 1.24429i | |||||
0 | 0 | |||||||||
−17.2679 | + | 17.2679i | −0.583097 | + | 0.583097i | −0.935753 | − | 0.352656i | ||
0.352656 | + | 0.935753i | ||||||||
−45.0518 | + | 45.0518i | −1.52042 | + | 1.52042i | |||||
0 | 0 | |||||||||
−13.6077 | − | 2.78461i | −0.458715 | − | 0.0938692i | |||||
30.0131i | 1.01117i | 0.862778 | + | 0.505583i | ||||||
−0.862778 | + | 0.505583i | ||||||||
0 | 0 | |||||||||
−24.6340 | − | 24.6340i | −0.828999 | − | 0.828999i | 0.158379 | − | 0.987378i | ||
−0.987378 | + | 0.158379i | ||||||||
−13.3843 | −0.450161 | |||||||||
0 | 0 | |||||||||
−63.4641 | −2.13212 | |||||||||
16.2127 | + | 16.2127i | 0.544369 | + | 0.544369i | 0.924807 | − | 0.380438i | ||
−0.380438 | + | 0.924807i | ||||||||
0 | 0 | |||||||||
6.00000i | 0.201234i | |||||||||
−32.7028 | + | 21.5921i | −1.09620 | + | 0.723770i | |||||
0 | 0 | |||||||||
9.85641 | − | 9.85641i | 0.330017 | − | 0.330017i | |||||
2.63896 | − | 2.63896i | 0.0883094 | − | 0.0883094i | |||||
0 | 0 | |||||||||
2.32051 | − | 11.3397i | 0.0775660 | − | 0.379046i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.07180 | − | 9.07180i | −0.302730 | − | 0.302730i | |||||
4.69591 | 0.156617 | |||||||||
0 | 0 | |||||||||
38.7846 | 1.29210 | |||||||||
6.21166 | + | 6.21166i | 0.206826 | + | 0.206826i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8.24504 | + | 40.2915i | −0.274075 | + | 1.33933i | |||||
0 | 0 | |||||||||
−6.33975 | + | 6.33975i | −0.210508 | + | 0.210508i | −0.804483 | − | 0.593975i | ||
0.593975 | + | 0.804483i | ||||||||
34.2929 | − | 34.2929i | 1.13805 | − | 1.13805i | |||||
0 | 0 | |||||||||
−12.9282 | + | 8.53590i | −0.428566 | + | 0.282962i | |||||
− | 57.4007i | − | 1.90177i | −0.309542 | − | 0.950886i | ||||
0.309542 | − | 0.950886i | ||||||||
0 | 0 | |||||||||
−1.17691 | − | 1.17691i | −0.0389502 | − | 0.0389502i | |||||
0.0743295 | 0.00245860 | |||||||||
0 | 0 | |||||||||
25.3205 | 0.836613 | |||||||||
−30.4428 | − | 30.4428i | −1.00531 | − | 1.00531i | |||||
0 | 0 | |||||||||
43.7128i | 1.44195i | 0.692960 | + | 0.720976i | ||||||
−0.692960 | + | 0.720976i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
24.8756 | − | 24.8756i | 0.819236 | − | 0.819236i | |||||
0.554803 | − | 0.554803i | 0.0182616 | − | 0.0182616i | |||||
0 | 0 | |||||||||
−22.7321 | + | 9.12436i | −0.747425 | + | 0.300007i | |||||
28.2099i | 0.927036i | |||||||||
0 | 0 | |||||||||
−49.5692 | − | 49.5692i | −1.62719 | − | 1.62719i | |||||
−5.00052 | −0.164062 | −0.0820308 | − | 0.996630i | ||||||
−0.0820308 | + | 0.996630i | ||||||||
0 | 0 | |||||||||
4.19615 | 0.137523 | |||||||||
−10.9348 | − | 10.9348i | −0.358180 | − | 0.358180i | |||||
0 | 0 | |||||||||
− | 22.3923i | − | 0.732699i | |||||||
−12.3676 | − | 18.7315i | −0.404463 | − | 0.612586i | |||||
0 | 0 | |||||||||
−13.7583 | + | 13.7583i | −0.449465 | + | 0.449465i | −0.895177 | − | 0.445712i | ||
0.445712 | + | 0.895177i | ||||||||
63.3350 | − | 63.3350i | 2.06796 | − | 2.06796i | |||||
0 | 0 | |||||||||
9.19615 | + | 13.9282i | 0.299945 | + | 0.454288i | |||||
− | 37.6018i | − | 1.22578i | −0.790167 | − | 0.612891i | ||||
0.790167 | − | 0.612891i | ||||||||
0 | 0 | |||||||||
6.92820 | + | 6.92820i | 0.225613 | + | 0.225613i | |||||
53.5370 | 1.74248 | |||||||||
0 | 0 | |||||||||
13.6077 | 0.442424 | |||||||||
−31.6675 | − | 31.6675i | −1.02906 | − | 1.02906i | −0.999565 | − | 0.0294905i | ||
−0.0294905 | − | 0.999565i | ||||||||
0 | 0 | |||||||||
− | 5.71281i | − | 0.185446i | |||||||
9.28032 | − | 3.72500i | 0.301093 | − | 0.120855i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
34.9764 | − | 34.9764i | 1.13300 | − | 1.13300i | 0.143320 | − | 0.989676i | ||
0.989676 | − | 0.143320i | ||||||||
0 | 0 | |||||||||
−5.66987 | − | 1.16025i | −0.183473 | − | 0.0375449i | |||||
16.2870i | 0.526760i | |||||||||
0 | 0 | |||||||||
−33.6077 | − | 33.6077i | −1.08582 | − | 1.08582i | |||||
−5.13922 | −0.165954 | |||||||||
0 | 0 | |||||||||
−30.7128 | −0.990736 | |||||||||
7.17260 | + | 7.17260i | 0.231254 | + | 0.231254i | |||||
0 | 0 | |||||||||
56.7846i | 1.82891i | |||||||||
30.2533 | − | 19.9749i | 0.973888 | − | 0.643013i | |||||
0 | 0 | |||||||||
−25.9808 | + | 25.9808i | −0.835485 | + | 0.835485i | −0.988261 | − | 0.152776i | ||
0.152776 | + | 0.988261i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.17691 | − | 35.0718i | 0.230437 | − | 1.12609i | |||||
26.0106i | 0.834721i | 0.908741 | + | 0.417361i | ||||||
−0.908741 | + | 0.417361i | ||||||||
0 | 0 | |||||||||
−23.0263 | − | 23.0263i | −0.738189 | − | 0.738189i | |||||
−76.1645 | −2.44047 | |||||||||
0 | 0 | |||||||||
−51.4256 | −1.64609 | |||||||||
2.24642 | + | 2.24642i | 0.0718693 | + | 0.0718693i | 0.742128 | − | 0.670258i | ||
−0.670258 | + | 0.742128i | ||||||||
0 | 0 | |||||||||
13.6077i | 0.434904i | |||||||||
−3.76217 | + | 18.3848i | −0.120178 | + | 0.587280i | |||||
0 | 0 | |||||||||
−53.3205 | + | 53.3205i | −1.70153 | + | 1.70153i | |||||
−13.9391 | + | 13.9391i | −0.444587 | + | 0.444587i | −0.893550 | − | 0.448963i | ||
0.448963 | + | 0.893550i | ||||||||
0 | 0 | |||||||||
25.8564 | − | 17.0718i | 0.823854 | − | 0.543953i | |||||
− | 113.286i | − | 3.60775i | |||||||
0 | 0 | |||||||||
−1.46410 | − | 1.46410i | −0.0465793 | − | 0.0465793i | |||||
15.1774 | 0.482614 | |||||||||
0 | 0 | |||||||||
26.1436 | 0.830479 | 0.415239 | − | 0.909712i | ||||||
0.415239 | + | 0.909712i | ||||||||
−3.03150 | − | 3.03150i | −0.0962502 | − | 0.0962502i | |||||
0 | 0 | |||||||||
− | 5.07180i | − | 0.160868i | |||||||
21.3197 | + | 4.36276i | 0.675881 | + | 0.138309i | |||||
0 | 0 | |||||||||
−16.3660 | + | 16.3660i | −0.518317 | + | 0.518317i | −0.917062 | − | 0.398745i | ||
0.398745 | + | 0.917062i | ||||||||
59.0180 | − | 59.0180i | 1.86818 | − | 1.86818i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 855.2.n.c.818.4 | yes | 8 | |
3.2 | odd | 2 | inner | 855.2.n.c.818.1 | yes | 8 | |
5.2 | odd | 4 | inner | 855.2.n.c.647.1 | ✓ | 8 | |
15.2 | even | 4 | inner | 855.2.n.c.647.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
855.2.n.c.647.1 | ✓ | 8 | 5.2 | odd | 4 | inner | |
855.2.n.c.647.4 | yes | 8 | 15.2 | even | 4 | inner | |
855.2.n.c.818.1 | yes | 8 | 3.2 | odd | 2 | inner | |
855.2.n.c.818.4 | yes | 8 | 1.1 | even | 1 | trivial |