Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,2,Mod(191,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("464.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 464.k (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 | 447.10 | ||
Root | of defining polynomial | ||
Character | 464.447 | ||
Dual form | 464.2.k.c.191.10 |
-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 | |||||||||
1.92975 | − | 1.92975i | 1.11414 | − | 1.11414i | 0.121560 | − | 0.992584i | ||
0.992584 | − | 0.121560i | ||||||||
0 | 0 | |||||||||
− | 2.39709i | − | 1.07201i | −0.844214 | − | 0.536006i | ||||
0.844214 | − | 0.536006i | ||||||||
0 | 0 | |||||||||
− | 1.01973i | − | 0.385420i | −0.981256 | − | 0.192710i | ||||
0.981256 | − | 0.192710i | ||||||||
0 | 0 | |||||||||
− | 4.44790i | − | 1.48263i | |||||||
0 | 0 | |||||||||
−2.07012 | + | 2.07012i | −0.624164 | + | 0.624164i | −0.946593 | − | 0.322430i | ||
0.322430 | + | 0.946593i | ||||||||
0 | 0 | |||||||||
− | 1.30477i | − | 0.361878i | −0.983494 | − | 0.180939i | ||||
0.983494 | − | 0.180939i | ||||||||
0 | 0 | |||||||||
−4.62579 | − | 4.62579i | −1.19437 | − | 1.19437i | |||||
0 | 0 | |||||||||
3.78485 | + | 3.78485i | 0.917960 | + | 0.917960i | 0.996881 | − | 0.0789206i | ||
−0.0789206 | + | 0.996881i | ||||||||
0 | 0 | |||||||||
−3.70412 | + | 3.70412i | −0.849783 | + | 0.849783i | −0.990106 | − | 0.140323i | ||
0.140323 | + | 0.990106i | ||||||||
0 | 0 | |||||||||
−1.96782 | − | 1.96782i | −0.429414 | − | 0.429414i | |||||
0 | 0 | |||||||||
− | 4.28773i | − | 0.894053i | −0.894521 | − | 0.447027i | ||||
0.894521 | − | 0.447027i | ||||||||
0 | 0 | |||||||||
−0.746041 | −0.149208 | |||||||||
0 | 0 | |||||||||
−2.79409 | − | 2.79409i | −0.537723 | − | 0.537723i | |||||
0 | 0 | |||||||||
3.15397 | + | 4.36491i | 0.585678 | + | 0.810544i | |||||
0 | 0 | |||||||||
2.93783 | − | 2.93783i | 0.527650 | − | 0.527650i | −0.392221 | − | 0.919871i | ||
0.919871 | + | 0.392221i | ||||||||
0 | 0 | |||||||||
7.98963i | 1.39082i | |||||||||
0 | 0 | |||||||||
−2.44438 | −0.413175 | |||||||||
0 | 0 | |||||||||
−1.63087 | + | 1.63087i | −0.268114 | + | 0.268114i | −0.828340 | − | 0.560226i | ||
0.560226 | + | 0.828340i | ||||||||
0 | 0 | |||||||||
−2.51788 | − | 2.51788i | −0.403184 | − | 0.403184i | |||||
0 | 0 | |||||||||
8.28356 | − | 8.28356i | 1.29367 | − | 1.29367i | 0.361177 | − | 0.932497i | ||
0.932497 | − | 0.361177i | ||||||||
0 | 0 | |||||||||
−8.05370 | + | 8.05370i | −1.22818 | + | 1.22818i | −0.263526 | + | 0.964652i | ||
−0.964652 | + | 0.263526i | ||||||||
0 | 0 | |||||||||
−10.6620 | −1.58940 | |||||||||
0 | 0 | |||||||||
−4.09792 | − | 4.09792i | −0.597743 | − | 0.597743i | 0.341968 | − | 0.939711i | ||
−0.939711 | + | 0.341968i | ||||||||
0 | 0 | |||||||||
5.96016 | 0.851451 | |||||||||
0 | 0 | |||||||||
14.6076 | 2.04548 | |||||||||
0 | 0 | |||||||||
6.32929 | 0.869394 | 0.434697 | − | 0.900577i | ||||||
0.434697 | + | 0.900577i | ||||||||
0 | 0 | |||||||||
4.96226 | + | 4.96226i | 0.669111 | + | 0.669111i | |||||
0 | 0 | |||||||||
14.2961i | 1.89356i | |||||||||
0 | 0 | |||||||||
− | 4.26443i | − | 0.555182i | −0.960699 | − | 0.277591i | ||||
0.960699 | − | 0.277591i | ||||||||
0 | 0 | |||||||||
−8.36809 | − | 8.36809i | −1.07142 | − | 1.07142i | −0.997245 | − | 0.0741794i | ||
−0.0741794 | − | 0.997245i | ||||||||
0 | 0 | |||||||||
−4.53564 | −0.571437 | |||||||||
0 | 0 | |||||||||
−3.12765 | −0.387937 | |||||||||
0 | 0 | |||||||||
9.62370 | 1.17572 | 0.587861 | − | 0.808962i | ||||||
0.587861 | + | 0.808962i | ||||||||
0 | 0 | |||||||||
−8.27426 | − | 8.27426i | −0.996104 | − | 0.996104i | |||||
0 | 0 | |||||||||
11.5718 | 1.37332 | 0.686658 | − | 0.726981i | ||||||
0.686658 | + | 0.726981i | ||||||||
0 | 0 | |||||||||
−2.47075 | + | 2.47075i | −0.289179 | + | 0.289179i | −0.836756 | − | 0.547577i | ||
0.547577 | + | 0.836756i | ||||||||
0 | 0 | |||||||||
−1.43968 | + | 1.43968i | −0.166240 | + | 0.166240i | |||||
0 | 0 | |||||||||
2.11095 | + | 2.11095i | 0.240565 | + | 0.240565i | |||||
0 | 0 | |||||||||
−10.5493 | + | 10.5493i | −1.18689 | + | 1.18689i | −0.208966 | + | 0.977923i | ||
−0.977923 | + | 0.208966i | ||||||||
0 | 0 | |||||||||
2.55989 | 0.284432 | |||||||||
0 | 0 | |||||||||
0.320297i | 0.0351572i | 0.999845 | + | 0.0175786i | ||||||
−0.999845 | + | 0.0175786i | ||||||||
0 | 0 | |||||||||
9.07262 | − | 9.07262i | 0.984064 | − | 0.984064i | |||||
0 | 0 | |||||||||
14.5096 | + | 2.33681i | 1.55559 | + | 0.250532i | |||||
0 | 0 | |||||||||
−8.21575 | − | 8.21575i | −0.870868 | − | 0.870868i | 0.121699 | − | 0.992567i | ||
−0.992567 | + | 0.121699i | ||||||||
0 | 0 | |||||||||
−1.33051 | −0.139475 | |||||||||
0 | 0 | |||||||||
− | 11.3386i | − | 1.17576i | |||||||
0 | 0 | |||||||||
8.87910 | + | 8.87910i | 0.910977 | + | 0.910977i | |||||
0 | 0 | |||||||||
1.53089 | − | 1.53089i | 0.155438 | − | 0.155438i | −0.625104 | − | 0.780542i | ||
0.780542 | + | 0.625104i | ||||||||
0 | 0 | |||||||||
9.20767 | + | 9.20767i | 0.925406 | + | 0.925406i | |||||
0 | 0 | |||||||||
1.65372 | + | 1.65372i | 0.164551 | + | 0.164551i | 0.784579 | − | 0.620028i | ||
−0.620028 | + | 0.784579i | ||||||||
0 | 0 | |||||||||
7.31685i | 0.720951i | 0.932769 | + | 0.360475i | ||||||
−0.932769 | + | 0.360475i | ||||||||
0 | 0 | |||||||||
−4.71704 | + | 4.71704i | −0.460336 | + | 0.460336i | |||||
0 | 0 | |||||||||
2.77845i | 0.268603i | 0.990941 | + | 0.134302i | ||||||
−0.990941 | + | 0.134302i | ||||||||
0 | 0 | |||||||||
7.65884i | 0.733583i | 0.930303 | + | 0.366792i | ||||||
−0.930303 | + | 0.366792i | ||||||||
0 | 0 | |||||||||
6.29437i | 0.597435i | |||||||||
0 | 0 | |||||||||
−13.6620 | + | 13.6620i | −1.28521 | + | 1.28521i | −0.347555 | + | 0.937660i | ||
−0.937660 | + | 0.347555i | ||||||||
0 | 0 | |||||||||
−10.2781 | −0.958435 | |||||||||
0 | 0 | |||||||||
−5.80348 | −0.536532 | |||||||||
0 | 0 | |||||||||
3.85951 | − | 3.85951i | 0.353800 | − | 0.353800i | |||||
0 | 0 | |||||||||
2.42923i | 0.220839i | |||||||||
0 | 0 | |||||||||
− | 31.9704i | − | 2.88268i | |||||||
0 | 0 | |||||||||
− | 10.1971i | − | 0.912058i | |||||||
0 | 0 | |||||||||
−11.7272 | + | 11.7272i | −1.04062 | + | 1.04062i | −0.0414774 | + | 0.999139i | ||
−0.999139 | + | 0.0414774i | ||||||||
0 | 0 | |||||||||
31.0833i | 2.73673i | |||||||||
0 | 0 | |||||||||
3.45621 | + | 3.45621i | 0.301970 | + | 0.301970i | 0.841784 | − | 0.539814i | ||
−0.539814 | + | 0.841784i | ||||||||
0 | 0 | |||||||||
3.77719 | + | 3.77719i | 0.327524 | + | 0.327524i | |||||
0 | 0 | |||||||||
−6.69769 | + | 6.69769i | −0.576445 | + | 0.576445i | |||||
0 | 0 | |||||||||
10.6008 | + | 10.6008i | 0.905691 | + | 0.905691i | 0.995921 | − | 0.0902302i | ||
−0.0902302 | + | 0.995921i | ||||||||
0 | 0 | |||||||||
7.28724i | 0.618096i | 0.951046 | + | 0.309048i | ||||||
−0.951046 | + | 0.309048i | ||||||||
0 | 0 | |||||||||
−15.8160 | −1.33194 | |||||||||
0 | 0 | |||||||||
2.70102 | + | 2.70102i | 0.225871 | + | 0.225871i | |||||
0 | 0 | |||||||||
10.4631 | − | 7.56036i | 0.868912 | − | 0.627854i | |||||
0 | 0 | |||||||||
11.5016 | − | 11.5016i | 0.948639 | − | 0.948639i | |||||
0 | 0 | |||||||||
19.0251i | 1.55860i | 0.626652 | + | 0.779299i | ||||||
−0.626652 | + | 0.779299i | ||||||||
0 | 0 | |||||||||
2.57130 | 0.209249 | 0.104625 | − | 0.994512i | ||||||
0.104625 | + | 0.994512i | ||||||||
0 | 0 | |||||||||
16.8346 | − | 16.8346i | 1.36100 | − | 1.36100i | |||||
0 | 0 | |||||||||
−7.04225 | − | 7.04225i | −0.565647 | − | 0.565647i | |||||
0 | 0 | |||||||||
−12.2269 | + | 12.2269i | −0.975812 | + | 0.975812i | −0.999714 | − | 0.0239018i | ||
0.0239018 | + | 0.999714i | ||||||||
0 | 0 | |||||||||
12.2140 | − | 12.2140i | 0.968630 | − | 0.968630i | |||||
0 | 0 | |||||||||
−4.37231 | −0.344586 | |||||||||
0 | 0 | |||||||||
−10.5052 | − | 10.5052i | −0.822832 | − | 0.822832i | 0.163682 | − | 0.986513i | ||
−0.986513 | + | 0.163682i | ||||||||
0 | 0 | |||||||||
19.1519 | 1.49097 | |||||||||
0 | 0 | |||||||||
0.0200904 | 0.00155464 | 0.000777320 | − | 1.00000i | ||||||
0.000777320 | 1.00000i | |||||||||
0 | 0 | |||||||||
11.2976 | 0.869045 | |||||||||
0 | 0 | |||||||||
16.4755 | + | 16.4755i | 1.25992 | + | 1.25992i | |||||
0 | 0 | |||||||||
5.67975i | 0.431823i | 0.976413 | + | 0.215912i | ||||||
−0.976413 | + | 0.215912i | ||||||||
0 | 0 | |||||||||
0.760758i | 0.0575079i | |||||||||
0 | 0 | |||||||||
−8.22930 | − | 8.22930i | −0.618552 | − | 0.618552i | |||||
0 | 0 | |||||||||
3.66020 | 0.273576 | 0.136788 | − | 0.990600i | ||||||
0.136788 | + | 0.990600i | ||||||||
0 | 0 | |||||||||
−24.3983 | −1.81351 | −0.906755 | − | 0.421657i | ||||||
−0.906755 | + | 0.421657i | ||||||||
0 | 0 | |||||||||
−32.2967 | −2.38744 | |||||||||
0 | 0 | |||||||||
3.90935 | + | 3.90935i | 0.287421 | + | 0.287421i | |||||
0 | 0 | |||||||||
−15.6702 | −1.14591 | |||||||||
0 | 0 | |||||||||
−2.84921 | + | 2.84921i | −0.207249 | + | 0.207249i | |||||
0 | 0 | |||||||||
−5.04414 | + | 5.04414i | −0.364981 | + | 0.364981i | −0.865643 | − | 0.500662i | ||
0.500662 | + | 0.865643i | ||||||||
0 | 0 | |||||||||
−13.3530 | − | 13.3530i | −0.961172 | − | 0.961172i | 0.0381016 | − | 0.999274i | ||
−0.999274 | + | 0.0381016i | ||||||||
0 | 0 | |||||||||
−6.03559 | + | 6.03559i | −0.432217 | + | 0.432217i | |||||
0 | 0 | |||||||||
8.14197 | 0.580091 | 0.290046 | − | 0.957013i | ||||||
0.290046 | + | 0.957013i | ||||||||
0 | 0 | |||||||||
− | 17.8100i | − | 1.26252i | −0.775572 | − | 0.631259i | ||||
0.775572 | − | 0.631259i | ||||||||
0 | 0 | |||||||||
18.5714 | − | 18.5714i | 1.30992 | − | 1.30992i | |||||
0 | 0 | |||||||||
4.45101 | − | 3.21619i | 0.312400 | − | 0.225732i | |||||
0 | 0 | |||||||||
−19.8564 | − | 19.8564i | −1.38683 | − | 1.38683i | |||||
0 | 0 | |||||||||
−19.0714 | −1.32555 | |||||||||
0 | 0 | |||||||||
− | 15.3359i | − | 1.06081i | |||||||
0 | 0 | |||||||||
−11.9689 | − | 11.9689i | −0.823976 | − | 0.823976i | 0.162699 | − | 0.986676i | ||
−0.986676 | + | 0.162699i | ||||||||
0 | 0 | |||||||||
22.3307 | − | 22.3307i | 1.53007 | − | 1.53007i | |||||
0 | 0 | |||||||||
19.3055 | + | 19.3055i | 1.31662 | + | 1.31662i | |||||
0 | 0 | |||||||||
−2.99578 | − | 2.99578i | −0.203367 | − | 0.203367i | |||||
0 | 0 | |||||||||
9.53586i | 0.644374i | |||||||||
0 | 0 | |||||||||
4.93835 | − | 4.93835i | 0.332189 | − | 0.332189i | |||||
0 | 0 | |||||||||
− | 1.58592i | − | 0.106201i | −0.998589 | − | 0.0531007i | ||||
0.998589 | − | 0.0531007i | ||||||||
0 | 0 | |||||||||
3.31832i | 0.221221i | |||||||||
0 | 0 | |||||||||
0.875438i | 0.0581049i | 0.999578 | + | 0.0290524i | ||||||
−0.999578 | + | 0.0290524i | ||||||||
0 | 0 | |||||||||
7.50804 | − | 7.50804i | 0.496145 | − | 0.496145i | −0.414090 | − | 0.910236i | ||
0.910236 | + | 0.414090i | ||||||||
0 | 0 | |||||||||
8.14724 | 0.536049 | |||||||||
0 | 0 | |||||||||
8.17093 | 0.535296 | 0.267648 | − | 0.963517i | ||||||
0.267648 | + | 0.963517i | ||||||||
0 | 0 | |||||||||
−9.82308 | + | 9.82308i | −0.640787 | + | 0.640787i | |||||
0 | 0 | |||||||||
40.7151i | 2.64473i | |||||||||
0 | 0 | |||||||||
− | 27.7911i | − | 1.79766i | −0.438299 | − | 0.898829i | ||||
0.438299 | − | 0.898829i | ||||||||
0 | 0 | |||||||||
− | 17.5034i | − | 1.12749i | −0.825948 | − | 0.563747i | ||||
0.825948 | − | 0.563747i | ||||||||
0 | 0 | |||||||||
13.3222 | − | 13.3222i | 0.854621 | − | 0.854621i | |||||
0 | 0 | |||||||||
− | 14.2870i | − | 0.912765i | |||||||
0 | 0 | |||||||||
4.83301 | + | 4.83301i | 0.307517 | + | 0.307517i | |||||
0 | 0 | |||||||||
0.618095 | + | 0.618095i | 0.0391702 | + | 0.0391702i | |||||
0 | 0 | |||||||||
15.4849 | − | 15.4849i | 0.977396 | − | 0.977396i | −0.0223544 | − | 0.999750i | ||
0.999750 | + | 0.0223544i | ||||||||
0 | 0 | |||||||||
8.87610 | + | 8.87610i | 0.558035 | + | 0.558035i | |||||
0 | 0 | |||||||||
− | 35.0158i | − | 2.19278i | |||||||
0 | 0 | |||||||||
−4.86005 | −0.303162 | −0.151581 | − | 0.988445i | ||||||
−0.151581 | + | 0.988445i | ||||||||
0 | 0 | |||||||||
1.66304 | + | 1.66304i | 0.103336 | + | 0.103336i | |||||
0 | 0 | |||||||||
19.4147 | − | 14.0286i | 1.20174 | − | 0.868346i | |||||
0 | 0 | |||||||||
11.3440 | − | 11.3440i | 0.699503 | − | 0.699503i | −0.264800 | − | 0.964303i | ||
0.964303 | + | 0.264800i | ||||||||
0 | 0 | |||||||||
− | 15.1719i | − | 0.932001i | |||||||
0 | 0 | |||||||||
−31.7088 | −1.94054 | |||||||||
0 | 0 | |||||||||
−6.29276 | + | 6.29276i | −0.383677 | + | 0.383677i | −0.872425 | − | 0.488748i | ||
0.488748 | + | 0.872425i | ||||||||
0 | 0 | |||||||||
18.2544 | + | 18.2544i | 1.10888 | + | 1.10888i | 0.993298 | + | 0.115579i | ||
0.115579 | + | 0.993298i | ||||||||
0 | 0 | |||||||||
−2.56755 | + | 2.56755i | −0.155395 | + | 0.155395i | |||||
0 | 0 | |||||||||
1.54439 | − | 1.54439i | 0.0931304 | − | 0.0931304i | |||||
0 | 0 | |||||||||
−21.9576 | −1.31930 | −0.659651 | − | 0.751572i | ||||||
−0.659651 | + | 0.751572i | ||||||||
0 | 0 | |||||||||
−13.0672 | − | 13.0672i | −0.782312 | − | 0.782312i | |||||
0 | 0 | |||||||||
−14.5131 | −0.865780 | −0.432890 | − | 0.901447i | ||||||
−0.432890 | + | 0.901447i | ||||||||
0 | 0 | |||||||||
8.00022 | 0.475564 | 0.237782 | − | 0.971319i | ||||||
0.237782 | + | 0.971319i | ||||||||
0 | 0 | |||||||||
34.2690 | 2.02992 | |||||||||
0 | 0 | |||||||||
−8.44696 | − | 8.44696i | −0.498608 | − | 0.498608i | |||||
0 | 0 | |||||||||
11.6501i | 0.685302i | |||||||||
0 | 0 | |||||||||
− | 5.90848i | − | 0.346361i | |||||||
0 | 0 | |||||||||
−11.2820 | − | 11.2820i | −0.659102 | − | 0.659102i | 0.296066 | − | 0.955168i | ||
−0.955168 | + | 0.296066i | ||||||||
0 | 0 | |||||||||
−10.2222 | −0.595161 | |||||||||
0 | 0 | |||||||||
11.5682 | 0.671254 | |||||||||
0 | 0 | |||||||||
−5.59449 | −0.323538 | |||||||||
0 | 0 | |||||||||
8.21257 | + | 8.21257i | 0.473365 | + | 0.473365i | |||||
0 | 0 | |||||||||
6.38254 | 0.366667 | |||||||||
0 | 0 | |||||||||
−20.0591 | + | 20.0591i | −1.14858 | + | 1.14858i | |||||
0 | 0 | |||||||||
−11.8614 | + | 11.8614i | −0.676966 | + | 0.676966i | −0.959312 | − | 0.282347i | ||
0.282347 | + | 0.959312i | ||||||||
0 | 0 | |||||||||
14.1197 | + | 14.1197i | 0.803243 | + | 0.803243i | |||||
0 | 0 | |||||||||
−12.8979 | + | 12.8979i | −0.731374 | + | 0.731374i | −0.970892 | − | 0.239518i | ||
0.239518 | + | 0.970892i | ||||||||
0 | 0 | |||||||||
−2.84860 | −0.161012 | −0.0805061 | − | 0.996754i | ||||||
−0.0805061 | + | 0.996754i | ||||||||
0 | 0 | |||||||||
10.8723i | 0.612587i | |||||||||
0 | 0 | |||||||||
8.05244 | − | 8.05244i | 0.452270 | − | 0.452270i | −0.443837 | − | 0.896107i | ||
0.896107 | + | 0.443837i | ||||||||
0 | 0 | |||||||||
−15.5650 | − | 2.50678i | −0.871471 | − | 0.140353i | |||||
0 | 0 | |||||||||
5.36173 | + | 5.36173i | 0.299263 | + | 0.299263i | |||||
0 | 0 | |||||||||
−28.0390 | −1.56013 | |||||||||
0 | 0 | |||||||||
0.973411i | 0.0539951i | |||||||||
0 | 0 | |||||||||
14.7797 | + | 14.7797i | 0.817317 | + | 0.817317i | |||||
0 | 0 | |||||||||
−4.17876 | + | 4.17876i | −0.230382 | + | 0.230382i | |||||
0 | 0 | |||||||||
17.1099 | + | 17.1099i | 0.940446 | + | 0.940446i | 0.998324 | − | 0.0578780i | ||
−0.0578780 | + | 0.998324i | ||||||||
0 | 0 | |||||||||
7.25396 | + | 7.25396i | 0.397514 | + | 0.397514i | |||||
0 | 0 | |||||||||
− | 23.0689i | − | 1.26039i | |||||||
0 | 0 | |||||||||
−19.0347 | + | 19.0347i | −1.03689 | + | 1.03689i | −0.0375939 | + | 0.999293i | ||
−0.999293 | + | 0.0375939i | ||||||||
0 | 0 | |||||||||
52.7287i | 2.86383i | |||||||||
0 | 0 | |||||||||
12.1633i | 0.658680i | |||||||||
0 | 0 | |||||||||
− | 13.2158i | − | 0.713587i | |||||||
0 | 0 | |||||||||
−19.8341 | + | 19.8341i | −1.06783 | + | 1.06783i | |||||
0 | 0 | |||||||||
−5.24183 | −0.281396 | −0.140698 | − | 0.990053i | ||||||
−0.140698 | + | 0.990053i | ||||||||
0 | 0 | |||||||||
3.74531 | 0.200482 | 0.100241 | − | 0.994963i | ||||||
0.100241 | + | 0.994963i | ||||||||
0 | 0 | |||||||||
−3.64564 | + | 3.64564i | −0.194590 | + | 0.194590i | |||||
0 | 0 | |||||||||
3.55110i | 0.189006i | 0.995525 | + | 0.0945030i | ||||||
−0.995525 | + | 0.0945030i | ||||||||
0 | 0 | |||||||||
− | 27.7386i | − | 1.47221i | |||||||
0 | 0 | |||||||||
− | 14.8958i | − | 0.788369i | |||||||
0 | 0 | |||||||||
4.54790 | − | 4.54790i | 0.240029 | − | 0.240029i | −0.576833 | − | 0.816862i | ||
0.816862 | + | 0.576833i | ||||||||
0 | 0 | |||||||||
− | 8.44098i | − | 0.444262i | |||||||
0 | 0 | |||||||||
4.68782 | + | 4.68782i | 0.246047 | + | 0.246047i | |||||
0 | 0 | |||||||||
5.92260 | + | 5.92260i | 0.310003 | + | 0.310003i | |||||
0 | 0 | |||||||||
−16.0417 | + | 16.0417i | −0.837372 | + | 0.837372i | −0.988512 | − | 0.151141i | ||
0.151141 | + | 0.988512i | ||||||||
0 | 0 | |||||||||
−36.8444 | − | 36.8444i | −1.91804 | − | 1.91804i | |||||
0 | 0 | |||||||||
− | 6.45414i | − | 0.335082i | |||||||
0 | 0 | |||||||||
13.3301 | 0.690209 | 0.345104 | − | 0.938564i | ||||||
0.345104 | + | 0.938564i | ||||||||
0 | 0 | |||||||||
−19.6779 | − | 19.6779i | −1.01616 | − | 1.01616i | |||||
0 | 0 | |||||||||
5.69520 | − | 4.11521i | 0.293317 | − | 0.211944i | |||||
0 | 0 | |||||||||
−1.77935 | + | 1.77935i | −0.0913989 | + | 0.0913989i | −0.751328 | − | 0.659929i | ||
0.659929 | + | 0.751328i | ||||||||
0 | 0 | |||||||||
45.2610i | 2.31879i | |||||||||
0 | 0 | |||||||||
3.05809 | 0.156261 | 0.0781304 | − | 0.996943i | ||||||
0.0781304 | + | 0.996943i | ||||||||
0 | 0 | |||||||||
5.06014 | − | 5.06014i | 0.257889 | − | 0.257889i | |||||
0 | 0 | |||||||||
35.8221 | + | 35.8221i | 1.82094 | + | 1.82094i | |||||
0 | 0 | |||||||||
7.57632 | − | 7.57632i | 0.384135 | − | 0.384135i | −0.488455 | − | 0.872589i | ||
0.872589 | + | 0.488455i | ||||||||
0 | 0 | |||||||||
16.2284 | − | 16.2284i | 0.820705 | − | 0.820705i | |||||
0 | 0 | |||||||||
13.3393 | 0.672876 | |||||||||
0 | 0 | |||||||||
25.2876 | + | 25.2876i | 1.27236 | + | 1.27236i | |||||
0 | 0 | |||||||||
−29.7428 | −1.49275 | −0.746374 | − | 0.665526i | ||||||
−0.746374 | + | 0.665526i | ||||||||
0 | 0 | |||||||||
14.5781 | 0.729817 | |||||||||
0 | 0 | |||||||||
−30.4125 | −1.51873 | −0.759365 | − | 0.650665i | ||||||
−0.759365 | + | 0.650665i | ||||||||
0 | 0 | |||||||||
−3.83319 | − | 3.83319i | −0.190945 | − | 0.190945i | |||||
0 | 0 | |||||||||
− | 6.13628i | − | 0.304914i | |||||||
0 | 0 | |||||||||
− | 6.75219i | − | 0.334694i | |||||||
0 | 0 | |||||||||
1.35062 | + | 1.35062i | 0.0667840 | + | 0.0667840i | 0.739710 | − | 0.672926i | ||
−0.672926 | + | 0.739710i | ||||||||
0 | 0 | |||||||||
40.9140 | 2.01814 | |||||||||
0 | 0 | |||||||||
−4.34855 | −0.213978 | |||||||||
0 | 0 | |||||||||
0.767781 | 0.0376889 | |||||||||
0 | 0 | |||||||||
14.0626 | + | 14.0626i | 0.688648 | + | 0.688648i | |||||
0 | 0 | |||||||||
−10.2511 | −0.500798 | −0.250399 | − | 0.968143i | ||||||
−0.250399 | + | 0.968143i | ||||||||
0 | 0 | |||||||||
−15.2038 | + | 15.2038i | −0.740987 | + | 0.740987i | −0.972768 | − | 0.231781i | ||
0.231781 | + | 0.972768i | ||||||||
0 | 0 | |||||||||
−18.2271 | + | 18.2271i | −0.886234 | + | 0.886234i | |||||
0 | 0 | |||||||||
−2.82365 | − | 2.82365i | −0.136967 | − | 0.136967i | |||||
0 | 0 | |||||||||
−8.53316 | + | 8.53316i | −0.412949 | + | 0.412949i | |||||
0 | 0 | |||||||||
10.4246 | 0.503305 | |||||||||
0 | 0 | |||||||||
30.8075i | 1.48395i | 0.670430 | + | 0.741973i | ||||||
−0.670430 | + | 0.741973i | ||||||||
0 | 0 | |||||||||
19.4713 | − | 19.4713i | 0.935729 | − | 0.935729i | −0.0623269 | − | 0.998056i | ||
0.998056 | + | 0.0623269i | ||||||||
0 | 0 | |||||||||
5.60154 | − | 34.7808i | 0.268573 | − | 1.66761i | |||||
0 | 0 | |||||||||
15.8822 | + | 15.8822i | 0.759751 | + | 0.759751i | |||||
0 | 0 | |||||||||
18.0950 | 0.863629 | 0.431815 | − | 0.901962i | ||||||
0.431815 | + | 0.901962i | ||||||||
0 | 0 | |||||||||
− | 26.5102i | − | 1.26239i | |||||||
0 | 0 | |||||||||
−25.8647 | − | 25.8647i | −1.22887 | − | 1.22887i | −0.964391 | − | 0.264479i | ||
−0.264479 | − | 0.964391i | ||||||||
0 | 0 | |||||||||
−19.6939 | + | 19.6939i | −0.933580 | + | 0.933580i | |||||
0 | 0 | |||||||||
36.7138 | + | 36.7138i | 1.73650 | + | 1.73650i | |||||
0 | 0 | |||||||||
9.87295 | + | 9.87295i | 0.465933 | + | 0.465933i | 0.900594 | − | 0.434661i | ||
−0.434661 | + | 0.900594i | ||||||||
0 | 0 | |||||||||
34.2959i | 1.61493i | |||||||||
0 | 0 | |||||||||
4.96197 | − | 4.96197i | 0.233134 | − | 0.233134i | |||||
0 | 0 | |||||||||
3.18934i | 0.149519i | |||||||||
0 | 0 | |||||||||
− | 15.9119i | − | 0.744327i | −0.928167 | − | 0.372163i | ||||
0.928167 | − | 0.372163i | ||||||||
0 | 0 | |||||||||
− | 21.1504i | − | 0.987217i | |||||||
0 | 0 | |||||||||
3.12029 | − | 3.12029i | 0.145326 | − | 0.145326i | −0.630700 | − | 0.776026i | ||
0.776026 | + | 0.630700i | ||||||||
0 | 0 | |||||||||
30.3565 | 1.41078 | 0.705392 | − | 0.708817i | ||||||
0.705392 | + | 0.708817i | ||||||||
0 | 0 | |||||||||
−27.1796 | −1.26042 | |||||||||
0 | 0 | |||||||||
15.6312 | − | 15.6312i | 0.723325 | − | 0.723325i | −0.245956 | − | 0.969281i | ||
0.969281 | + | 0.245956i | ||||||||
0 | 0 | |||||||||
− | 9.81354i | − | 0.453147i | |||||||
0 | 0 | |||||||||
47.1898i | 2.17439i | |||||||||
0 | 0 | |||||||||
− | 33.3442i | − | 1.53317i | |||||||
0 | 0 | |||||||||
2.76343 | − | 2.76343i | 0.126795 | − | 0.126795i | |||||
0 | 0 | |||||||||
− | 28.1520i | − | 1.28899i | |||||||
0 | 0 | |||||||||
10.3990 | + | 10.3990i | 0.475141 | + | 0.475141i | 0.903574 | − | 0.428433i | ||
−0.428433 | + | 0.903574i | ||||||||
0 | 0 | |||||||||
2.12791 | + | 2.12791i | 0.0970244 | + | 0.0970244i | |||||
0 | 0 | |||||||||
−8.43748 | + | 8.43748i | −0.383919 | + | 0.383919i | |||||
0 | 0 | |||||||||
−3.66968 | − | 3.66968i | −0.166632 | − | 0.166632i | |||||
0 | 0 | |||||||||
− | 21.1081i | − | 0.956500i | −0.878224 | − | 0.478250i | ||||
0.878224 | − | 0.478250i | ||||||||
0 | 0 | |||||||||
−40.5449 | −1.83351 | |||||||||
0 | 0 | |||||||||
4.39350 | + | 4.39350i | 0.198276 | + | 0.198276i | 0.799261 | − | 0.600985i | ||
−0.600985 | + | 0.799261i | ||||||||
0 | 0 | |||||||||
−4.58321 | + | 28.4578i | −0.206417 | + | 1.28168i | |||||
0 | 0 | |||||||||
22.0716 | − | 22.0716i | 0.992046 | − | 0.992046i | |||||
0 | 0 | |||||||||
− | 11.8000i | − | 0.529304i | |||||||
0 | 0 | |||||||||
−4.86379 | −0.217733 | −0.108866 | − | 0.994056i | ||||||
−0.108866 | + | 0.994056i | ||||||||
0 | 0 | |||||||||
0.0387695 | − | 0.0387695i | 0.00173209 | − | 0.00173209i | |||||
0 | 0 | |||||||||
−22.7249 | − | 22.7249i | −1.01325 | − | 1.01325i | −0.999911 | − | 0.0133431i | ||
−0.0133431 | − | 0.999911i | ||||||||
0 | 0 | |||||||||
3.96411 | − | 3.96411i | 0.176401 | − | 0.176401i | |||||
0 | 0 | |||||||||
21.8015 | − | 21.8015i | 0.968241 | − | 0.968241i | |||||
0 | 0 | |||||||||
11.3980 | 0.505205 | 0.252603 | − | 0.967570i | ||||||
0.252603 | + | 0.967570i | ||||||||
0 | 0 | |||||||||
2.51948 | + | 2.51948i | 0.111455 | + | 0.111455i | |||||
0 | 0 | |||||||||
20.6993 | 0.913895 | |||||||||
0 | 0 | |||||||||
17.5392 | 0.772868 | |||||||||
0 | 0 | |||||||||
16.9663 | 0.746179 | |||||||||
0 | 0 | |||||||||
10.9605 | + | 10.9605i | 0.481113 | + | 0.481113i | |||||
0 | 0 | |||||||||
20.6772i | 0.905885i | 0.891540 | + | 0.452942i | ||||||
−0.891540 | + | 0.452942i | ||||||||
0 | 0 | |||||||||
− | 10.4479i | − | 0.456856i | −0.973561 | − | 0.228428i | ||||
0.973561 | − | 0.228428i | ||||||||
0 | 0 | |||||||||
1.46808 | + | 1.46808i | 0.0640721 | + | 0.0640721i | |||||
0 | 0 | |||||||||
22.2385 | 0.968724 | |||||||||
0 | 0 | |||||||||
4.61539 | 0.200669 | |||||||||
0 | 0 | |||||||||
−18.9678 | −0.823131 | |||||||||
0 | 0 | |||||||||
−10.8081 | − | 10.8081i | −0.468152 | − | 0.468152i | |||||
0 | 0 | |||||||||
6.66020 | 0.287946 | |||||||||
0 | 0 | |||||||||
7.06329 | − | 7.06329i | 0.304803 | − | 0.304803i | |||||
0 | 0 | |||||||||
−12.3382 | + | 12.3382i | −0.531445 | + | 0.531445i | |||||
0 | 0 | |||||||||
−8.11668 | − | 8.11668i | −0.348963 | − | 0.348963i | 0.510760 | − | 0.859723i | ||
−0.859723 | + | 0.510760i | ||||||||
0 | 0 | |||||||||
−47.0827 | + | 47.0827i | −2.02051 | + | 2.02051i | |||||
0 | 0 | |||||||||
18.3589 | 0.786410 | |||||||||
0 | 0 | |||||||||
25.6172i | 1.09531i | 0.836703 | + | 0.547656i | ||||||
−0.836703 | + | 0.547656i | ||||||||
0 | 0 | |||||||||
−37.2204 | + | 37.2204i | −1.58853 | + | 1.58853i | |||||
0 | 0 | |||||||||
−27.8508 | − | 4.48545i | −1.18649 | − | 0.191087i | |||||
0 | 0 | |||||||||
10.7574 | + | 10.7574i | 0.457451 | + | 0.457451i | |||||
0 | 0 | |||||||||
15.0882 | 0.640457 | |||||||||
0 | 0 | |||||||||
− | 5.26149i | − | 0.222937i | −0.993768 | − | 0.111468i | ||||
0.993768 | − | 0.111468i | ||||||||
0 | 0 | |||||||||
10.5082 | + | 10.5082i | 0.444450 | + | 0.444450i | |||||
0 | 0 | |||||||||
−30.2395 | + | 30.2395i | −1.27671 | + | 1.27671i | |||||
0 | 0 | |||||||||
−18.2037 | − | 18.2037i | −0.767192 | − | 0.767192i | 0.210419 | − | 0.977611i | ||
−0.977611 | + | 0.210419i | ||||||||
0 | 0 | |||||||||
32.7491 | + | 32.7491i | 1.37776 | + | 1.37776i | |||||
0 | 0 | |||||||||
− | 2.61038i | − | 0.109626i | |||||||
0 | 0 | |||||||||
32.9411 | − | 32.9411i | 1.38096 | − | 1.38096i | 0.538049 | − | 0.842914i | ||
0.842914 | − | 0.538049i | ||||||||
0 | 0 | |||||||||
− | 41.7994i | − | 1.74925i | −0.484799 | − | 0.874626i | ||||
0.484799 | − | 0.874626i | ||||||||
0 | 0 | |||||||||
19.4679i | 0.813283i | |||||||||
0 | 0 | |||||||||
3.19882i | 0.133400i | |||||||||
0 | 0 | |||||||||
1.98390 | − | 1.98390i | 0.0825910 | − | 0.0825910i | −0.664604 | − | 0.747195i | ||
0.747195 | + | 0.664604i | ||||||||
0 | 0 | |||||||||
−51.5361 | −2.14177 | |||||||||
0 | 0 | |||||||||
0.326615 | 0.0135503 | |||||||||
0 | 0 | |||||||||
−13.1024 | + | 13.1024i | −0.542644 | + | 0.542644i | |||||
0 | 0 | |||||||||
13.9115i | 0.575168i | |||||||||
0 | 0 | |||||||||
1.01770i | 0.0420051i | 0.999779 | + | 0.0210025i | ||||||
−0.999779 | + | 0.0210025i | ||||||||
0 | 0 | |||||||||
21.7641i | 0.896776i | |||||||||
0 | 0 | |||||||||
15.7120 | − | 15.7120i | 0.646305 | − | 0.646305i | |||||
0 | 0 | |||||||||
17.2975i | 0.710323i | 0.934805 | + | 0.355162i | ||||||
−0.934805 | + | 0.355162i | ||||||||
0 | 0 | |||||||||
−9.25159 | − | 9.25159i | −0.379278 | − | 0.379278i | |||||
0 | 0 | |||||||||
−34.3690 | − | 34.3690i | −1.40663 | − | 1.40663i | |||||
0 | 0 | |||||||||
−18.4376 | + | 18.4376i | −0.753339 | + | 0.753339i | −0.975101 | − | 0.221762i | ||
0.221762 | + | 0.975101i | ||||||||
0 | 0 | |||||||||
−4.48215 | − | 4.48215i | −0.182831 | − | 0.182831i | 0.609757 | − | 0.792588i | ||
−0.792588 | + | 0.609757i | ||||||||
0 | 0 | |||||||||
− | 42.8052i | − | 1.74316i | |||||||
0 | 0 | |||||||||
5.82309 | 0.236742 | |||||||||
0 | 0 | |||||||||
3.31696 | + | 3.31696i | 0.134631 | + | 0.134631i | 0.771211 | − | 0.636580i | ||
−0.636580 | + | 0.771211i | ||||||||
0 | 0 | |||||||||
2.38290 | − | 14.7958i | 0.0965602 | − | 0.599557i | |||||
0 | 0 | |||||||||
−5.34684 | + | 5.34684i | −0.216310 | + | 0.216310i | |||||
0 | 0 | |||||||||
− | 25.9090i | − | 1.04646i | −0.852193 | − | 0.523228i | ||||
0.852193 | − | 0.523228i | ||||||||
0 | 0 | |||||||||
−76.6361 | −3.09026 | |||||||||
0 | 0 | |||||||||
−15.0531 | + | 15.0531i | −0.606014 | + | 0.606014i | −0.941902 | − | 0.335888i | ||
0.335888 | + | 0.941902i | ||||||||
0 | 0 | |||||||||
29.7437 | + | 29.7437i | 1.19550 | + | 1.19550i | 0.975500 | + | 0.220000i | ||
0.220000 | + | 0.975500i | ||||||||
0 | 0 | |||||||||
−11.9803 | + | 11.9803i | −0.480753 | + | 0.480753i | |||||
0 | 0 | |||||||||
−8.37782 | + | 8.37782i | −0.335650 | + | 0.335650i | |||||
0 | 0 | |||||||||
−28.1736 | −1.12695 | |||||||||
0 | 0 | |||||||||
−29.5945 | − | 29.5945i | −1.18189 | − | 1.18189i | |||||
0 | 0 | |||||||||
−12.3452 | −0.492236 | |||||||||
0 | 0 | |||||||||
−46.8743 | −1.86604 | −0.933018 | − | 0.359831i | ||||||
−0.933018 | + | 0.359831i | ||||||||
0 | 0 | |||||||||
−46.1942 | −1.83606 | |||||||||
0 | 0 | |||||||||
28.1111 | + | 28.1111i | 1.11555 | + | 1.11555i | |||||
0 | 0 | |||||||||
− | 7.77662i | − | 0.308121i | |||||||
0 | 0 | |||||||||
− | 51.4701i | − | 2.03612i | |||||||
0 | 0 | |||||||||
22.5210 | + | 22.5210i | 0.889527 | + | 0.889527i | 0.994477 | − | 0.104950i | ||
−0.104950 | + | 0.994477i | ||||||||
0 | 0 | |||||||||
−3.60602 | −0.142208 | −0.0711038 | − | 0.997469i | ||||||
−0.0711038 | + | 0.997469i | ||||||||
0 | 0 | |||||||||
74.5095 | 2.93381 | |||||||||
0 | 0 | |||||||||
8.60945 | 0.338473 | 0.169236 | − | 0.985576i | ||||||
0.169236 | + | 0.985576i | ||||||||
0 | 0 | |||||||||
8.82787 | + | 8.82787i | 0.346524 | + | 0.346524i | |||||
0 | 0 | |||||||||
−11.5622 | −0.453160 | |||||||||
0 | 0 | |||||||||
9.68383 | − | 9.68383i | 0.378957 | − | 0.378957i | −0.491769 | − | 0.870726i | ||
0.870726 | + | 0.491769i | ||||||||
0 | 0 | |||||||||
8.28484 | − | 8.28484i | 0.323715 | − | 0.323715i | |||||
0 | 0 | |||||||||
10.9896 | + | 10.9896i | 0.428746 | + | 0.428746i | |||||
0 | 0 | |||||||||
−1.84113 | + | 1.84113i | −0.0717203 | + | 0.0717203i | −0.742057 | − | 0.670337i | ||
0.670337 | + | 0.742057i | ||||||||
0 | 0 | |||||||||
23.7086 | 0.922157 | 0.461078 | − | 0.887359i | ||||||
0.461078 | + | 0.887359i | ||||||||
0 | 0 | |||||||||
− | 19.0596i | − | 0.740213i | |||||||
0 | 0 | |||||||||
9.05425 | − | 9.05425i | 0.351109 | − | 0.351109i | |||||
0 | 0 | |||||||||
18.7155 | − | 13.5234i | 0.724669 | − | 0.523628i | |||||
0 | 0 | |||||||||
−3.06044 | − | 3.06044i | −0.118324 | − | 0.118324i | |||||
0 | 0 | |||||||||
34.6459 | 1.33749 | |||||||||
0 | 0 | |||||||||
− | 15.8919i | − | 0.612587i | −0.951937 | − | 0.306294i | ||||
0.951937 | − | 0.306294i | ||||||||
0 | 0 | |||||||||
2.08451 | + | 2.08451i | 0.0802327 | + | 0.0802327i | |||||
0 | 0 | |||||||||
3.48507 | − | 3.48507i | 0.133942 | − | 0.133942i | −0.636957 | − | 0.770899i | ||
0.770899 | + | 0.636957i | ||||||||
0 | 0 | |||||||||
−1.56109 | − | 1.56109i | −0.0599090 | − | 0.0599090i | |||||
0 | 0 | |||||||||
1.68938 | + | 1.68938i | 0.0647372 | + | 0.0647372i | |||||
0 | 0 | |||||||||
16.1199i | 0.616809i | 0.951255 | + | 0.308405i | ||||||
−0.951255 | + | 0.308405i | ||||||||
0 | 0 | |||||||||
25.4112 | − | 25.4112i | 0.970911 | − | 0.970911i | |||||
0 | 0 | |||||||||
− | 28.9773i | − | 1.10555i | |||||||
0 | 0 | |||||||||
− | 8.25825i | − | 0.314614i | |||||||
0 | 0 | |||||||||
− | 35.7904i | − | 1.36153i | −0.732502 | − | 0.680765i | ||||
0.732502 | − | 0.680765i | ||||||||
0 | 0 | |||||||||
9.38930 | − | 9.38930i | 0.356670 | − | 0.356670i | |||||
0 | 0 | |||||||||
17.4682 | 0.662606 | |||||||||
0 | 0 | |||||||||
62.7040 | 2.37508 | |||||||||
0 | 0 | |||||||||
15.7679 | − | 15.7679i | 0.596396 | − | 0.596396i | |||||
0 | 0 | |||||||||
− | 2.21227i | − | 0.0835563i | −0.999127 | − | 0.0417782i | ||||
0.999127 | − | 0.0417782i | ||||||||
0 | 0 | |||||||||
− | 12.0819i | − | 0.455677i | |||||||
0 | 0 | |||||||||
37.9123i | 1.42786i | |||||||||
0 | 0 | |||||||||
1.68634 | − | 1.68634i | 0.0634214 | − | 0.0634214i | |||||
0 | 0 | |||||||||
31.0570i | 1.16637i | 0.812340 | + | 0.583184i | ||||||
−0.812340 | + | 0.583184i | ||||||||
0 | 0 | |||||||||
46.9222 | + | 46.9222i | 1.75972 | + | 1.75972i | |||||
0 | 0 | |||||||||
−12.5966 | − | 12.5966i | −0.471747 | − | 0.471747i | |||||
0 | 0 | |||||||||
6.47459 | − | 6.47459i | 0.242136 | − | 0.242136i | |||||
0 | 0 | |||||||||
−53.6300 | − | 53.6300i | −2.00285 | − | 2.00285i | |||||
0 | 0 | |||||||||
36.2112i | 1.35045i | 0.737611 | + | 0.675226i | ||||||
−0.737611 | + | 0.675226i | ||||||||
0 | 0 | |||||||||
7.46119 | 0.277869 | |||||||||
0 | 0 | |||||||||
−33.7773 | − | 33.7773i | −1.25619 | − | 1.25619i | |||||
0 | 0 | |||||||||
−2.35300 | − | 3.25640i | −0.0873881 | − | 0.120940i | |||||
0 | 0 | |||||||||
20.7794 | − | 20.7794i | 0.770667 | − | 0.770667i | −0.207556 | − | 0.978223i | ||
0.978223 | + | 0.207556i | ||||||||
0 | 0 | |||||||||
− | 43.7376i | − | 1.61991i | |||||||
0 | 0 | |||||||||
−60.9641 | −2.25484 | |||||||||
0 | 0 | |||||||||
−8.22927 | + | 8.22927i | −0.303955 | + | 0.303955i | −0.842559 | − | 0.538604i | ||
0.538604 | + | 0.842559i | ||||||||
0 | 0 | |||||||||
−27.5705 | − | 27.5705i | −1.01695 | − | 1.01695i | |||||
0 | 0 | |||||||||
−19.9222 | + | 19.9222i | −0.733843 | + | 0.733843i | |||||
0 | 0 | |||||||||
14.6530 | − | 14.6530i | 0.539017 | − | 0.539017i | −0.384223 | − | 0.923240i | ||
0.923240 | + | 0.384223i | ||||||||
0 | 0 | |||||||||
18.6531 | 0.685237 | |||||||||
0 | 0 | |||||||||
−24.0803 | − | 24.0803i | −0.883419 | − | 0.883419i | 0.110462 | − | 0.993880i | ||
−0.993880 | + | 0.110462i | ||||||||
0 | 0 | |||||||||
45.6049 | 1.67084 | |||||||||
0 | 0 | |||||||||
1.42465 | 0.0521252 | |||||||||
0 | 0 | |||||||||
2.83326 | 0.103525 | |||||||||
0 | 0 | |||||||||
3.36482 | + | 3.36482i | 0.122784 | + | 0.122784i | 0.765829 | − | 0.643045i | ||
−0.643045 | + | 0.765829i | ||||||||
0 | 0 | |||||||||
− | 59.7639i | − | 2.17792i | |||||||
0 | 0 | |||||||||
− | 6.16363i | − | 0.224317i | |||||||
0 | 0 | |||||||||
22.8533 | + | 22.8533i | 0.830619 | + | 0.830619i | 0.987601 | − | 0.156983i | ||
−0.156983 | + | 0.987601i | ||||||||
0 | 0 | |||||||||
34.2574 | 1.24346 | |||||||||
0 | 0 | |||||||||
−24.7027 | −0.895473 | −0.447736 | − | 0.894166i | ||||||
−0.447736 | + | 0.894166i | ||||||||
0 | 0 | |||||||||
7.80991 | 0.282738 | |||||||||
0 | 0 | |||||||||
−40.3541 | − | 40.3541i | −1.45901 | − | 1.45901i | |||||
0 | 0 | |||||||||
−5.56409 | −0.200908 | |||||||||
0 | 0 | |||||||||
25.9480 | − | 25.9480i | 0.935710 | − | 0.935710i | −0.0623451 | − | 0.998055i | ||
0.998055 | + | 0.0623451i | ||||||||
0 | 0 | |||||||||
−9.37870 | + | 9.37870i | −0.337766 | + | 0.337766i | |||||
0 | 0 | |||||||||
−34.1840 | − | 34.1840i | −1.22951 | − | 1.22951i | −0.964147 | − | 0.265367i | ||
−0.265367 | − | 0.964147i | ||||||||
0 | 0 | |||||||||
−2.19174 | + | 2.19174i | −0.0787298 | + | 0.0787298i | |||||
0 | 0 | |||||||||
6.41853 | 0.230263 | |||||||||
0 | 0 | |||||||||
61.3665i | 2.19868i | |||||||||
0 | 0 | |||||||||
−23.9549 | + | 23.9549i | −0.857174 | + | 0.857174i | |||||
0 | 0 | |||||||||
3.38346 | − | 21.0084i | 0.120915 | − | 0.750780i | |||||
0 | 0 | |||||||||
29.3090 | + | 29.3090i | 1.04608 | + | 1.04608i | |||||
0 | 0 | |||||||||
28.0749 | 1.00076 | 0.500381 | − | 0.865805i | ||||||
0.500381 | + | 0.865805i | ||||||||
0 | 0 | |||||||||
− | 43.7824i | − | 1.55869i | |||||||
0 | 0 | |||||||||
13.9315 | + | 13.9315i | 0.495348 | + | 0.495348i | |||||
0 | 0 | |||||||||
−10.9184 | + | 10.9184i | −0.387724 | + | 0.387724i | |||||
0 | 0 | |||||||||
−29.2780 | − | 29.2780i | −1.03838 | − | 1.03838i | |||||
0 | 0 | |||||||||
−10.3597 | − | 10.3597i | −0.366958 | − | 0.366958i | 0.499409 | − | 0.866367i | ||
−0.866367 | + | 0.499409i | ||||||||
0 | 0 | |||||||||
− | 31.0200i | − | 1.09741i | |||||||
0 | 0 | |||||||||
−36.5428 | + | 36.5428i | −1.29118 | + | 1.29118i | |||||
0 | 0 | |||||||||
− | 10.2295i | − | 0.360990i | |||||||
0 | 0 | |||||||||
10.4808i | 0.369400i | |||||||||
0 | 0 | |||||||||
24.2870i | 0.854942i | |||||||||
0 | 0 | |||||||||
−16.1015 | + | 16.1015i | −0.566100 | + | 0.566100i | −0.931033 | − | 0.364934i | ||
0.364934 | + | 0.931033i | ||||||||
0 | 0 | |||||||||
4.16152 | 0.146131 | 0.0730654 | − | 0.997327i | ||||||
0.0730654 | + | 0.997327i | ||||||||
0 | 0 | |||||||||
70.4531 | 2.47090 | |||||||||
0 | 0 | |||||||||
−25.1819 | + | 25.1819i | −0.882085 | + | 0.882085i | |||||
0 | 0 | |||||||||
− | 59.6637i | − | 2.08737i | |||||||
0 | 0 | |||||||||
5.91796i | 0.206790i | |||||||||
0 | 0 | |||||||||
7.38797i | 0.257842i | 0.991655 | + | 0.128921i | ||||||
−0.991655 | + | 0.128921i | ||||||||
0 | 0 | |||||||||
−30.7910 | + | 30.7910i | −1.07331 | + | 1.07331i | −0.0762167 | + | 0.997091i | ||
−0.997091 | + | 0.0762167i | ||||||||
0 | 0 | |||||||||
− | 5.96060i | − | 0.207521i | |||||||
0 | 0 | |||||||||
30.1364 | + | 30.1364i | 1.04794 | + | 1.04794i | 0.998791 | + | 0.0491533i | ||
0.0491533 | + | 0.998791i | ||||||||
0 | 0 | |||||||||
−28.4455 | − | 28.4455i | −0.987954 | − | 0.987954i | 0.0119743 | − | 0.999928i | ||
−0.999928 | + | 0.0119743i | ||||||||
0 | 0 | |||||||||
−42.3727 | + | 42.3727i | −1.46989 | + | 1.46989i | |||||
0 | 0 | |||||||||
22.5583 | + | 22.5583i | 0.781598 | + | 0.781598i | |||||
0 | 0 | |||||||||
− | 0.0481585i | − | 0.00166659i | |||||||
0 | 0 | |||||||||
−16.4171 | −0.567459 | |||||||||
0 | 0 | |||||||||
−35.9098 | − | 35.9098i | −1.23975 | − | 1.23975i | −0.960105 | − | 0.279640i | ||
−0.279640 | − | 0.960105i | ||||||||
0 | 0 | |||||||||
−9.10489 | + | 27.5336i | −0.313962 | + | 0.949436i | |||||
0 | 0 | |||||||||
−28.0068 | + | 28.0068i | −0.964604 | + | 0.964604i | |||||
0 | 0 | |||||||||
− | 27.0813i | − | 0.931626i | |||||||
0 | 0 | |||||||||
2.47715 | 0.0851160 | |||||||||
0 | 0 | |||||||||
15.4385 | − | 15.4385i | 0.529847 | − | 0.529847i | |||||
0 | 0 | |||||||||
6.99274 | + | 6.99274i | 0.239708 | + | 0.239708i | |||||
0 | 0 | |||||||||
−29.1924 | + | 29.1924i | −0.999528 | + | 0.999528i | −1.00000 | 0.000471811i | |||
0.000471811 | 1.00000i | |||||||||
0 | 0 | |||||||||
39.4934 | − | 39.4934i | 1.35064 | − | 1.35064i | |||||
0 | 0 | |||||||||
14.8618 | 0.507669 | 0.253834 | − | 0.967248i | ||||||
0.253834 | + | 0.967248i | ||||||||
0 | 0 | |||||||||
19.8098 | + | 19.8098i | 0.675901 | + | 0.675901i | 0.959070 | − | 0.283169i | ||
−0.283169 | + | 0.959070i | ||||||||
0 | 0 | |||||||||
−32.6011 | −1.11104 | |||||||||
0 | 0 | |||||||||
52.8614 | 1.79942 | 0.899712 | − | 0.436484i | ||||||
0.899712 | + | 0.436484i | ||||||||
0 | 0 | |||||||||
13.6149 | 0.462919 | |||||||||
0 | 0 | |||||||||
22.4819 | + | 22.4819i | 0.763525 | + | 0.763525i | |||||
0 | 0 | |||||||||
− | 43.6766i | − | 1.48163i | |||||||
0 | 0 | |||||||||
− | 12.5567i | − | 0.425467i | |||||||
0 | 0 | |||||||||
−6.80924 | − | 6.80924i | −0.230458 | − | 0.230458i | |||||
0 | 0 | |||||||||
−10.3983 | −0.351526 | |||||||||
0 | 0 | |||||||||
−2.66279 | −0.0899161 | −0.0449580 | − | 0.998989i | ||||||
−0.0449580 | + | 0.998989i | ||||||||
0 | 0 | |||||||||
−43.5430 | −1.46867 | |||||||||
0 | 0 | |||||||||
13.4842 | + | 13.4842i | 0.454293 | + | 0.454293i | 0.896777 | − | 0.442484i | ||
−0.442484 | + | 0.896777i | ||||||||
0 | 0 | |||||||||
36.1788 | 1.21751 | 0.608756 | − | 0.793357i | ||||||
0.608756 | + | 0.793357i | ||||||||
0 | 0 | |||||||||
−19.7264 | + | 19.7264i | −0.663095 | + | 0.663095i | |||||
0 | 0 | |||||||||
0.606597 | − | 0.606597i | 0.0203675 | − | 0.0203675i | −0.696850 | − | 0.717217i | ||
0.717217 | + | 0.696850i | ||||||||
0 | 0 | |||||||||
11.9585 | + | 11.9585i | 0.401075 | + | 0.401075i | |||||
0 | 0 | |||||||||
−5.29927 | + | 5.29927i | −0.177532 | + | 0.177532i | |||||
0 | 0 | |||||||||
30.3584 | 1.01590 | |||||||||
0 | 0 | |||||||||
− | 8.77383i | − | 0.293277i | |||||||
0 | 0 | |||||||||
−10.7960 | + | 10.7960i | −0.360468 | + | 0.360468i | |||||
0 | 0 | |||||||||
22.0892 | + | 3.55753i | 0.736717 | + | 0.118650i | |||||
0 | 0 | |||||||||
23.9554 | + | 23.9554i | 0.798069 | + | 0.798069i | |||||
0 | 0 | |||||||||
31.6965 | 1.05479 | |||||||||
0 | 0 | |||||||||
58.4849i | 1.94410i | |||||||||
0 | 0 | |||||||||
−40.2170 | − | 40.2170i | −1.33538 | − | 1.33538i | −0.900475 | − | 0.434907i | ||
−0.434907 | − | 0.900475i | ||||||||
0 | 0 | |||||||||
7.35558 | − | 7.35558i | 0.243969 | − | 0.243969i | |||||
0 | 0 | |||||||||
−23.3002 | − | 23.3002i | −0.771968 | − | 0.771968i | 0.206482 | − | 0.978450i | ||
−0.978450 | + | 0.206482i | ||||||||
0 | 0 | |||||||||
−0.663052 | − | 0.663052i | −0.0219438 | − | 0.0219438i | |||||
0 | 0 | |||||||||
77.4181i | 2.55936i | |||||||||
0 | 0 | |||||||||
3.52438 | − | 3.52438i | 0.116385 | − | 0.116385i | |||||
0 | 0 | |||||||||
− | 27.0113i | − | 0.891021i | −0.895277 | − | 0.445511i | ||||
0.895277 | − | 0.445511i | ||||||||
0 | 0 | |||||||||
45.7792i | 1.50847i | |||||||||
0 | 0 | |||||||||
− | 15.0985i | − | 0.496972i | |||||||
0 | 0 | |||||||||
1.21670 | − | 1.21670i | 0.0400048 | − | 0.0400048i | |||||
0 | 0 | |||||||||
32.5446 | 1.06891 | |||||||||
0 | 0 | |||||||||
−35.3035 | −1.15827 | −0.579136 | − | 0.815231i | ||||||
−0.579136 | + | 0.815231i | ||||||||
0 | 0 | |||||||||
−22.0771 | + | 22.0771i | −0.723549 | + | 0.723549i | |||||
0 | 0 | |||||||||
49.7796i | 1.62971i | |||||||||
0 | 0 | |||||||||
37.5628i | 1.22843i | |||||||||
0 | 0 | |||||||||
32.2106i | 1.05228i | 0.850399 | + | 0.526138i | ||||||
−0.850399 | + | 0.526138i | ||||||||
0 | 0 | |||||||||
−5.49709 | + | 5.49709i | −0.179391 | + | 0.179391i | |||||
0 | 0 | |||||||||
− | 16.7561i | − | 0.546235i | −0.961981 | − | 0.273117i | ||||
0.961981 | − | 0.273117i | ||||||||
0 | 0 | |||||||||
−35.5176 | − | 35.5176i | −1.15661 | − | 1.15661i | |||||
0 | 0 | |||||||||
6.82981 | + | 6.82981i | 0.222174 | + | 0.222174i | |||||
0 | 0 | |||||||||
19.1359 | − | 19.1359i | 0.621834 | − | 0.621834i | −0.324166 | − | 0.946000i | ||
0.946000 | + | 0.324166i | ||||||||
0 | 0 | |||||||||
3.22375 | + | 3.22375i | 0.104647 | + | 0.104647i | |||||
0 | 0 | |||||||||
− | 31.0785i | − | 1.00779i | |||||||
0 | 0 | |||||||||
−10.6671 | −0.345543 | −0.172771 | − | 0.984962i | ||||||
−0.172771 | + | 0.984962i | ||||||||
0 | 0 | |||||||||
12.0913 | + | 12.0913i | 0.391264 | + | 0.391264i | |||||
0 | 0 | |||||||||
−34.8740 | + | 25.1991i | −1.12732 | + | 0.814571i | |||||
0 | 0 | |||||||||
10.8100 | − | 10.8100i | 0.349072 | − | 0.349072i | |||||
0 | 0 | |||||||||
13.7383i | 0.443171i | |||||||||
0 | 0 | |||||||||
12.3583 | 0.398240 | |||||||||
0 | 0 | |||||||||
−32.0084 | + | 32.0084i | −1.03039 | + | 1.03039i | |||||
0 | 0 | |||||||||
18.6237 | + | 18.6237i | 0.598898 | + | 0.598898i | 0.940019 | − | 0.341121i | ||
−0.341121 | + | 0.940019i | ||||||||
0 | 0 | |||||||||
−54.1084 | + | 54.1084i | −1.73821 | + | 1.73821i | |||||
0 | 0 | |||||||||
14.0949 | − | 14.0949i | 0.452326 | − | 0.452326i | −0.443800 | − | 0.896126i | ||
0.896126 | + | 0.443800i | ||||||||
0 | 0 | |||||||||
7.43099 | 0.238227 | |||||||||
0 | 0 | |||||||||
1.87844 | + | 1.87844i | 0.0601583 | + | 0.0601583i | |||||
0 | 0 | |||||||||
−12.0214 | −0.384598 | −0.192299 | − | 0.981336i | ||||||
−0.192299 | + | 0.981336i | ||||||||
0 | 0 | |||||||||
34.0151 | 1.08713 | |||||||||
0 | 0 | |||||||||
34.0657 | 1.08764 | |||||||||
0 | 0 | |||||||||
18.0750 | + | 18.0750i | 0.576502 | + | 0.576502i | 0.933938 | − | 0.357436i | ||
−0.357436 | + | 0.933938i | ||||||||
0 | 0 | |||||||||
− | 19.5170i | − | 0.621865i | |||||||
0 | 0 | |||||||||
16.1279i | 0.513358i | |||||||||
0 | 0 | |||||||||
34.5321 | + | 34.5321i | 1.09806 | + | 1.09806i | |||||
0 | 0 | |||||||||
48.5529 | 1.54233 | 0.771167 | − | 0.636633i | ||||||
0.771167 | + | 0.636633i | ||||||||
0 | 0 | |||||||||
66.0358 | 2.09558 | |||||||||
0 | 0 | |||||||||
−42.6922 | −1.35343 | |||||||||
0 | 0 | |||||||||
4.56165 | + | 4.56165i | 0.144469 | + | 0.144469i | 0.775642 | − | 0.631173i | ||
−0.631173 | + | 0.775642i | ||||||||
0 | 0 | |||||||||
9.11361 | 0.288342 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 464.2.k.c.447.10 | yes | 20 | |
4.3 | odd | 2 | inner | 464.2.k.c.447.1 | yes | 20 | |
29.17 | odd | 4 | inner | 464.2.k.c.191.1 | ✓ | 20 | |
116.75 | even | 4 | inner | 464.2.k.c.191.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
464.2.k.c.191.1 | ✓ | 20 | 29.17 | odd | 4 | inner | |
464.2.k.c.191.10 | yes | 20 | 116.75 | even | 4 | inner | |
464.2.k.c.447.1 | yes | 20 | 4.3 | odd | 2 | inner | |
464.2.k.c.447.10 | yes | 20 | 1.1 | even | 1 | trivial |