Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(47,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 448.z (of order , degree , not 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 |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: |
Embedding invariants
Embedding label | 47.10 | ||
Character | 448.47 | ||
Dual form | 448.2.z.a.143.10 |
-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 | |||||||||
0.282507 | − | 1.05433i | 0.163106 | − | 0.608719i | −0.835169 | − | 0.549994i | ||
0.998274 | − | 0.0587246i | ||||||||
0 | 0 | |||||||||
−1.39922 | + | 0.374919i | −0.625749 | + | 0.167669i | −0.557740 | − | 0.830016i | ||
−0.0680093 | + | 0.997685i | ||||||||
0 | 0 | |||||||||
0.298614 | + | 2.62885i | 0.112866 | + | 0.993610i | |||||
0 | 0 | |||||||||
1.56627 | + | 0.904287i | 0.522090 | + | 0.301429i | |||||
0 | 0 | |||||||||
−1.42219 | + | 5.30770i | −0.428807 | + | 1.60033i | 0.326658 | + | 0.945143i | ||
−0.755465 | + | 0.655189i | ||||||||
0 | 0 | |||||||||
−1.84531 | + | 1.84531i | −0.511798 | + | 0.511798i | −0.915077 | − | 0.403279i | ||
0.403279 | + | 0.915077i | ||||||||
0 | 0 | |||||||||
1.58116i | 0.408253i | |||||||||
0 | 0 | |||||||||
5.69424 | − | 3.28757i | 1.38106 | − | 0.797353i | 0.388771 | − | 0.921334i | ||
0.992285 | + | 0.123982i | ||||||||
0 | 0 | |||||||||
3.24453 | − | 0.869370i | 0.744347 | − | 0.199447i | 0.133338 | − | 0.991071i | ||
0.611009 | + | 0.791624i | ||||||||
0 | 0 | |||||||||
2.85604 | + | 0.427830i | 0.623238 | + | 0.0933601i | |||||
0 | 0 | |||||||||
0.256173 | − | 0.443704i | 0.0534157 | − | 0.0925187i | −0.838081 | − | 0.545546i | ||
0.891497 | + | 0.453027i | ||||||||
0 | 0 | |||||||||
−2.51288 | + | 1.45081i | −0.502576 | + | 0.290162i | |||||
0 | 0 | |||||||||
3.71137 | − | 3.71137i | 0.714254 | − | 0.714254i | |||||
0 | 0 | |||||||||
−2.30263 | − | 2.30263i | −0.427587 | − | 0.427587i | 0.460219 | − | 0.887806i | ||
−0.887806 | + | 0.460219i | ||||||||
0 | 0 | |||||||||
3.79637 | + | 6.57551i | 0.681848 | + | 1.18100i | 0.974416 | + | 0.224751i | ||
−0.292568 | + | 0.956245i | ||||||||
0 | 0 | |||||||||
5.19429 | + | 2.99893i | 0.904211 | + | 0.522046i | |||||
0 | 0 | |||||||||
−1.40343 | − | 3.56637i | −0.237223 | − | 0.602827i | |||||
0 | 0 | |||||||||
1.07603 | + | 4.01582i | 0.176899 | + | 0.660196i | 0.996220 | + | 0.0868615i | ||
−0.819321 | + | 0.573334i | ||||||||
0 | 0 | |||||||||
1.42426 | + | 2.46689i | 0.228064 | + | 0.395018i | |||||
0 | 0 | |||||||||
−0.453189 | −0.0707762 | −0.0353881 | − | 0.999374i | ||||||
−0.0353881 | + | 0.999374i | ||||||||
0 | 0 | |||||||||
−3.40842 | − | 3.40842i | −0.519779 | − | 0.519779i | 0.397726 | − | 0.917504i | ||
−0.917504 | + | 0.397726i | ||||||||
0 | 0 | |||||||||
−2.53059 | − | 0.678070i | −0.377238 | − | 0.101081i | |||||
0 | 0 | |||||||||
1.71468 | − | 2.96992i | 0.250112 | − | 0.433207i | −0.713444 | − | 0.700712i | ||
0.963556 | + | 0.267505i | ||||||||
0 | 0 | |||||||||
−6.82166 | + | 1.57002i | −0.974523 | + | 0.224289i | |||||
0 | 0 | |||||||||
−1.85753 | − | 6.93238i | −0.260106 | − | 0.970727i | |||||
0 | 0 | |||||||||
−1.37226 | − | 0.367696i | −0.188495 | − | 0.0505070i | 0.163337 | − | 0.986570i | ||
−0.351831 | + | 0.936063i | ||||||||
0 | 0 | |||||||||
− | 7.95984i | − | 1.07330i | |||||||
0 | 0 | |||||||||
− | 3.66642i | − | 0.485629i | |||||||
0 | 0 | |||||||||
−6.57560 | − | 1.76193i | −0.856070 | − | 0.229383i | −0.196015 | − | 0.980601i | ||
−0.660055 | + | 0.751218i | ||||||||
0 | 0 | |||||||||
1.30846 | + | 4.88324i | 0.167531 | + | 0.625235i | 0.997704 | + | 0.0677284i | ||
−0.830173 | + | 0.557506i | ||||||||
0 | 0 | |||||||||
−1.90952 | + | 4.38752i | −0.240577 | + | 0.552775i | |||||
0 | 0 | |||||||||
1.89015 | − | 3.27384i | 0.234445 | − | 0.406070i | |||||
0 | 0 | |||||||||
6.19818 | + | 1.66080i | 0.757229 | + | 0.202899i | 0.616722 | − | 0.787181i | ||
0.140507 | + | 0.990080i | ||||||||
0 | 0 | |||||||||
−0.395441 | − | 0.395441i | −0.0476055 | − | 0.0476055i | |||||
0 | 0 | |||||||||
−6.44865 | −0.765314 | −0.382657 | − | 0.923890i | ||||||
−0.382657 | + | 0.923890i | ||||||||
0 | 0 | |||||||||
7.43995 | + | 12.8864i | 0.870780 | + | 1.50823i | 0.861191 | + | 0.508281i | ||
0.00958835 | + | 0.999954i | ||||||||
0 | 0 | |||||||||
0.819730 | + | 3.05927i | 0.0946543 | + | 0.353255i | |||||
0 | 0 | |||||||||
−14.3778 | − | 2.15377i | −1.63850 | − | 0.245445i | |||||
0 | 0 | |||||||||
3.33780 | + | 1.92708i | 0.375532 | + | 0.216813i | 0.675873 | − | 0.737019i | ||
−0.300341 | + | 0.953832i | ||||||||
0 | 0 | |||||||||
−0.151668 | − | 0.262697i | −0.0168520 | − | 0.0291886i | |||||
0 | 0 | |||||||||
−2.44051 | − | 2.44051i | −0.267881 | − | 0.267881i | 0.560365 | − | 0.828246i | ||
−0.828246 | + | 0.560365i | ||||||||
0 | 0 | |||||||||
−6.73491 | + | 6.73491i | −0.730503 | + | 0.730503i | |||||
0 | 0 | |||||||||
−3.07824 | + | 1.77722i | −0.330022 | + | 0.190538i | |||||
0 | 0 | |||||||||
3.81344 | − | 6.60506i | 0.404223 | − | 0.700135i | −0.590007 | − | 0.807398i | ||
0.994231 | + | 0.107262i | ||||||||
0 | 0 | |||||||||
−5.40208 | − | 4.30001i | −0.566292 | − | 0.450763i | |||||
0 | 0 | |||||||||
8.00527 | − | 2.14500i | 0.830107 | − | 0.222427i | |||||
0 | 0 | |||||||||
−4.21387 | + | 2.43288i | −0.432334 | + | 0.249608i | |||||
0 | 0 | |||||||||
− | 11.2152i | − | 1.13873i | −0.822085 | − | 0.569365i | ||||
0.822085 | − | 0.569365i | ||||||||
0 | 0 | |||||||||
−7.02722 | + | 7.02722i | −0.706263 | + | 0.706263i | |||||
0 | 0 | |||||||||
5.03457 | − | 18.7893i | 0.500959 | − | 1.86960i | 0.00725520 | − | 0.999974i | ||
0.493704 | − | 0.869630i | ||||||||
0 | 0 | |||||||||
−6.15035 | − | 3.55091i | −0.606012 | − | 0.349881i | 0.165391 | − | 0.986228i | ||
−0.771403 | + | 0.636347i | ||||||||
0 | 0 | |||||||||
−4.15662 | + | 0.472156i | −0.405645 | + | 0.0460777i | |||||
0 | 0 | |||||||||
11.5830 | − | 3.10366i | 1.11977 | − | 0.300042i | 0.348981 | − | 0.937130i | ||
0.770791 | + | 0.637088i | ||||||||
0 | 0 | |||||||||
2.68591 | − | 10.0240i | 0.257264 | − | 0.960122i | −0.709553 | − | 0.704652i | ||
0.966817 | − | 0.255470i | ||||||||
0 | 0 | |||||||||
4.53799 | 0.430727 | |||||||||
0 | 0 | |||||||||
−13.4601 | −1.26622 | −0.633109 | − | 0.774062i | ||||||
−0.633109 | + | 0.774062i | ||||||||
0 | 0 | |||||||||
−0.192088 | + | 0.716883i | −0.0179123 | + | 0.0668497i | |||||
0 | 0 | |||||||||
−4.55896 | + | 1.22157i | −0.421476 | + | 0.112934i | |||||
0 | 0 | |||||||||
10.3429 | + | 13.9876i | 0.948132 | + | 1.28224i | |||||
0 | 0 | |||||||||
−16.6227 | − | 9.59715i | −1.51116 | − | 0.872468i | |||||
0 | 0 | |||||||||
−0.128029 | + | 0.477811i | −0.0115440 | + | 0.0430828i | |||||
0 | 0 | |||||||||
8.09362 | − | 8.09362i | 0.723916 | − | 0.723916i | |||||
0 | 0 | |||||||||
− | 13.7356i | − | 1.21884i | −0.792849 | − | 0.609418i | ||||
0.792849 | − | 0.609418i | ||||||||
0 | 0 | |||||||||
−4.55651 | + | 2.63070i | −0.401178 | + | 0.231620i | |||||
0 | 0 | |||||||||
−2.81460 | + | 0.754169i | −0.245912 | + | 0.0658920i | −0.379670 | − | 0.925122i | ||
0.133757 | + | 0.991014i | ||||||||
0 | 0 | |||||||||
3.25430 | + | 8.26977i | 0.282184 | + | 0.717080i | |||||
0 | 0 | |||||||||
−3.80156 | + | 6.58449i | −0.327186 | + | 0.566703i | |||||
0 | 0 | |||||||||
6.25695 | − | 3.61245i | 0.534568 | − | 0.308633i | −0.208307 | − | 0.978064i | ||
0.742874 | + | 0.669431i | ||||||||
0 | 0 | |||||||||
−0.708981 | + | 0.708981i | −0.0601350 | + | 0.0601350i | −0.736535 | − | 0.676400i | ||
0.676400 | + | 0.736535i | ||||||||
0 | 0 | |||||||||
−2.64687 | − | 2.64687i | −0.222906 | − | 0.222906i | |||||
0 | 0 | |||||||||
−7.16997 | − | 12.4188i | −0.599583 | − | 1.03851i | |||||
0 | 0 | |||||||||
4.08518 | + | 2.35858i | 0.339255 | + | 0.195869i | |||||
0 | 0 | |||||||||
−0.271845 | + | 7.63583i | −0.0224214 | + | 0.629793i | |||||
0 | 0 | |||||||||
2.46397 | + | 9.19566i | 0.201856 | + | 0.753338i | 0.990385 | + | 0.138340i | ||
−0.788529 | + | 0.614998i | ||||||||
0 | 0 | |||||||||
−3.55073 | − | 6.15004i | −0.288954 | − | 0.500483i | 0.684606 | − | 0.728913i | ||
−0.973560 | + | 0.228430i | ||||||||
0 | 0 | |||||||||
11.8916 | 0.961381 | |||||||||
0 | 0 | |||||||||
−7.77723 | − | 7.77723i | −0.624683 | − | 0.624683i | |||||
0 | 0 | |||||||||
8.47741 | + | 2.27152i | 0.676571 | + | 0.181287i | 0.580713 | − | 0.814108i | ||
0.0958582 | + | 0.995395i | ||||||||
0 | 0 | |||||||||
−0.775348 | + | 1.34294i | −0.0614891 | + | 0.106502i | |||||
0 | 0 | |||||||||
1.24293 | + | 0.540942i | 0.0979563 | + | 0.0426322i | |||||
0 | 0 | |||||||||
3.28686 | + | 12.2667i | 0.257447 | + | 0.960805i | 0.966713 | + | 0.255864i | ||
−0.709266 | + | 0.704941i | ||||||||
0 | 0 | |||||||||
−8.39231 | − | 2.24871i | −0.653340 | − | 0.175062i | |||||
0 | 0 | |||||||||
− | 21.5280i | − | 1.66588i | −0.553361 | − | 0.832942i | ||||
0.553361 | − | 0.832942i | ||||||||
0 | 0 | |||||||||
6.18963i | 0.476126i | |||||||||
0 | 0 | |||||||||
5.86798 | + | 1.57232i | 0.448736 | + | 0.120238i | |||||
0 | 0 | |||||||||
5.18431 | + | 19.3481i | 0.394156 | + | 1.47101i | 0.823213 | + | 0.567733i | ||
−0.429057 | + | 0.903278i | ||||||||
0 | 0 | |||||||||
−4.56434 | − | 6.17274i | −0.345032 | − | 0.466615i | |||||
0 | 0 | |||||||||
−3.71531 | + | 6.43510i | −0.279260 | + | 0.483692i | |||||
0 | 0 | |||||||||
6.57967 | + | 1.76302i | 0.491787 | + | 0.131774i | 0.496186 | − | 0.868216i | ||
−0.00439858 | + | 0.999990i | ||||||||
0 | 0 | |||||||||
−6.32019 | − | 6.32019i | −0.469776 | − | 0.469776i | 0.432066 | − | 0.901842i | ||
−0.901842 | + | 0.432066i | ||||||||
0 | 0 | |||||||||
5.51821 | 0.407917 | |||||||||
0 | 0 | |||||||||
−3.01121 | − | 5.21558i | −0.221389 | − | 0.383457i | |||||
0 | 0 | |||||||||
9.35112 | + | 34.8989i | 0.683822 | + | 2.55206i | |||||
0 | 0 | |||||||||
10.8649 | + | 8.64836i | 0.790305 | + | 0.629076i | |||||
0 | 0 | |||||||||
−11.5374 | − | 6.66112i | −0.834817 | − | 0.481982i | 0.0206820 | − | 0.999786i | ||
−0.855499 | + | 0.517804i | ||||||||
0 | 0 | |||||||||
5.25772 | + | 9.10664i | 0.378459 | + | 0.655511i | 0.990838 | − | 0.135054i | ||
−0.612379 | + | 0.790564i | ||||||||
0 | 0 | |||||||||
−2.91773 | − | 2.91773i | −0.208943 | − | 0.208943i | |||||
0 | 0 | |||||||||
14.0642 | − | 14.0642i | 1.00203 | − | 1.00203i | 0.00203129 | − | 0.999998i | ||
0.999998 | − | 0.00203129i | ||||||||
0 | 0 | |||||||||
20.9503 | − | 12.0957i | 1.48513 | − | 0.857439i | 0.485272 | − | 0.874363i | ||
0.999857 | + | 0.0169240i | ||||||||
0 | 0 | |||||||||
3.50206 | − | 6.06575i | 0.247017 | − | 0.427845i | |||||
0 | 0 | |||||||||
5.36565 | − | 6.74085i | 0.376595 | − | 0.473115i | |||||
0 | 0 | |||||||||
0.634110 | − | 0.169909i | 0.0442882 | − | 0.0118670i | |||||
0 | 0 | |||||||||
0.802472 | − | 0.463307i | 0.0557757 | − | 0.0322021i | |||||
0 | 0 | |||||||||
18.4574i | 1.27673i | |||||||||
0 | 0 | |||||||||
−8.81296 | + | 8.81296i | −0.606709 | + | 0.606709i | −0.942085 | − | 0.335375i | ||
0.335375 | + | 0.942085i | ||||||||
0 | 0 | |||||||||
−1.82179 | + | 6.79902i | −0.124827 | + | 0.465861i | |||||
0 | 0 | |||||||||
6.04700 | + | 3.49124i | 0.412402 | + | 0.238101i | |||||
0 | 0 | |||||||||
−16.1523 | + | 11.9436i | −1.09649 | + | 0.810785i | |||||
0 | 0 | |||||||||
15.6883 | − | 4.20368i | 1.06012 | − | 0.284058i | |||||
0 | 0 | |||||||||
−4.44106 | + | 16.5743i | −0.298738 | + | 1.11490i | |||||
0 | 0 | |||||||||
5.44902 | 0.364893 | 0.182447 | − | 0.983216i | ||||||
0.182447 | + | 0.983216i | ||||||||
0 | 0 | |||||||||
−5.24780 | −0.349853 | |||||||||
0 | 0 | |||||||||
−0.389502 | + | 1.45364i | −0.0258521 | + | 0.0964815i | −0.977647 | − | 0.210255i | ||
0.951794 | + | 0.306737i | ||||||||
0 | 0 | |||||||||
4.77902 | − | 1.28054i | 0.315807 | − | 0.0846202i | −0.0974340 | − | 0.995242i | ||
0.413241 | + | 0.910622i | ||||||||
0 | 0 | |||||||||
−6.33263 | + | 14.5505i | −0.416656 | + | 0.957354i | |||||
0 | 0 | |||||||||
−10.7652 | − | 6.21528i | −0.705251 | − | 0.407177i | 0.104049 | − | 0.994572i | ||
−0.809300 | + | 0.587395i | ||||||||
0 | 0 | |||||||||
−1.28574 | + | 4.79843i | −0.0838721 | + | 0.313015i | |||||
0 | 0 | |||||||||
2.97474 | − | 2.97474i | 0.193230 | − | 0.193230i | |||||
0 | 0 | |||||||||
7.34038i | 0.474810i | 0.971411 | + | 0.237405i | ||||||
−0.971411 | + | 0.237405i | ||||||||
0 | 0 | |||||||||
−8.98405 | + | 5.18694i | −0.578713 | + | 0.334120i | −0.760622 | − | 0.649195i | ||
0.181909 | + | 0.983315i | ||||||||
0 | 0 | |||||||||
14.8897 | − | 3.98968i | 0.955173 | − | 0.255938i | |||||
0 | 0 | |||||||||
8.95636 | − | 4.75438i | 0.572201 | − | 0.303746i | |||||
0 | 0 | |||||||||
−4.38292 | + | 7.59144i | −0.278879 | + | 0.483032i | |||||
0 | 0 | |||||||||
−3.26257 | + | 1.88365i | −0.206757 | + | 0.119371i | |||||
0 | 0 | |||||||||
0.401720 | − | 0.401720i | 0.0253563 | − | 0.0253563i | −0.694315 | − | 0.719671i | ||
0.719671 | + | 0.694315i | ||||||||
0 | 0 | |||||||||
1.99072 | + | 1.99072i | 0.125156 | + | 0.125156i | |||||
0 | 0 | |||||||||
5.19817 | + | 9.00349i | 0.325522 | + | 0.563820i | |||||
0 | 0 | |||||||||
7.92211 | + | 4.57383i | 0.494168 | + | 0.285308i | 0.726302 | − | 0.687376i | ||
−0.232134 | + | 0.972684i | ||||||||
0 | 0 | |||||||||
−10.2356 | + | 4.02791i | −0.636012 | + | 0.250282i | |||||
0 | 0 | |||||||||
−1.52430 | − | 5.68877i | −0.0943519 | − | 0.352126i | |||||
0 | 0 | |||||||||
2.29116 | + | 3.96841i | 0.141279 | + | 0.244703i | 0.927979 | − | 0.372634i | ||
−0.786699 | + | 0.617336i | ||||||||
0 | 0 | |||||||||
2.05795 | 0.126419 | |||||||||
0 | 0 | |||||||||
−5.88661 | − | 5.88661i | −0.360254 | − | 0.360254i | |||||
0 | 0 | |||||||||
−9.22279 | − | 2.47124i | −0.562323 | − | 0.150674i | −0.0335497 | − | 0.999437i | ||
−0.528773 | + | 0.848763i | ||||||||
0 | 0 | |||||||||
−3.64178 | + | 6.30775i | −0.221223 | + | 0.383169i | −0.955179 | − | 0.296027i | ||
0.733957 | + | 0.679196i | ||||||||
0 | 0 | |||||||||
−6.05976 | + | 4.48080i | −0.366754 | + | 0.271190i | |||||
0 | 0 | |||||||||
−4.12667 | − | 15.4009i | −0.248848 | − | 0.928712i | |||||
0 | 0 | |||||||||
31.2724 | + | 8.37942i | 1.87898 | + | 0.503470i | 0.999627 | + | 0.0272931i | ||
0.879349 | + | 0.476177i | ||||||||
0 | 0 | |||||||||
13.7320i | 0.822115i | |||||||||
0 | 0 | |||||||||
− | 4.09880i | − | 0.244514i | −0.992498 | − | 0.122257i | ||||
0.992498 | − | 0.122257i | ||||||||
0 | 0 | |||||||||
−13.1954 | − | 3.53570i | −0.784387 | − | 0.210176i | −0.155669 | − | 0.987809i | ||
−0.628718 | + | 0.777633i | ||||||||
0 | 0 | |||||||||
1.37461 | + | 5.13012i | 0.0814249 | + | 0.303882i | |||||
0 | 0 | |||||||||
−0.135329 | − | 1.19136i | −0.00798819 | − | 0.0703239i | |||||
0 | 0 | |||||||||
13.1162 | − | 22.7180i | 0.771543 | − | 1.33635i | |||||
0 | 0 | |||||||||
−11.8245 | − | 3.16838i | −0.693167 | − | 0.185733i | |||||
0 | 0 | |||||||||
−16.6941 | − | 16.6941i | −0.975280 | − | 0.975280i | 0.0244213 | − | 0.999702i | ||
−0.999702 | + | 0.0244213i | ||||||||
0 | 0 | |||||||||
9.86128 | 0.574146 | |||||||||
0 | 0 | |||||||||
14.4206 | + | 24.9771i | 0.836766 | + | 1.44932i | |||||
0 | 0 | |||||||||
0.346054 | + | 1.29149i | 0.0200128 | + | 0.0746889i | |||||
0 | 0 | |||||||||
7.94240 | − | 9.97801i | 0.457792 | − | 0.575123i | |||||
0 | 0 | |||||||||
−18.3878 | − | 10.6162i | −1.05635 | − | 0.609886i | |||||
0 | 0 | |||||||||
−3.66164 | − | 6.34215i | −0.209665 | − | 0.363151i | |||||
0 | 0 | |||||||||
16.7590 | + | 16.7590i | 0.956484 | + | 0.956484i | 0.999092 | − | 0.0426074i | ||
−0.0426074 | + | 0.999092i | ||||||||
0 | 0 | |||||||||
−5.48135 | + | 5.48135i | −0.311823 | + | 0.311823i | |||||
0 | 0 | |||||||||
18.6053 | − | 10.7418i | 1.05501 | − | 0.609111i | 0.130963 | − | 0.991387i | ||
0.924048 | + | 0.382277i | ||||||||
0 | 0 | |||||||||
10.4249 | − | 18.0565i | 0.589253 | − | 1.02062i | −0.405078 | − | 0.914282i | ||
0.994331 | − | 0.106334i | ||||||||
0 | 0 | |||||||||
1.02687 | − | 6.85501i | 0.0578576 | − | 0.386236i | |||||
0 | 0 | |||||||||
14.3981 | − | 3.85795i | 0.808676 | − | 0.216684i | 0.169287 | − | 0.985567i | ||
0.639390 | + | 0.768883i | ||||||||
0 | 0 | |||||||||
15.4964 | − | 8.94686i | 0.867633 | − | 0.500928i | |||||
0 | 0 | |||||||||
− | 13.0891i | − | 0.730565i | |||||||
0 | 0 | |||||||||
15.6170 | − | 15.6170i | 0.868955 | − | 0.868955i | |||||
0 | 0 | |||||||||
1.95985 | − | 7.31425i | 0.108713 | − | 0.405722i | |||||
0 | 0 | |||||||||
−9.80980 | − | 5.66369i | −0.542483 | − | 0.313203i | |||||
0 | 0 | |||||||||
8.31948 | + | 3.62078i | 0.458668 | + | 0.199620i | |||||
0 | 0 | |||||||||
−2.89002 | + | 0.774378i | −0.158850 | + | 0.0425637i | −0.337367 | − | 0.941373i | ||
0.178518 | + | 0.983937i | ||||||||
0 | 0 | |||||||||
−1.94609 | + | 7.26290i | −0.106645 | + | 0.398005i | |||||
0 | 0 | |||||||||
−9.29528 | −0.507855 | |||||||||
0 | 0 | |||||||||
−20.5605 | −1.12000 | −0.560000 | − | 0.828493i | ||||||
−0.560000 | + | 0.828493i | ||||||||
0 | 0 | |||||||||
−3.80257 | + | 14.1914i | −0.206527 | + | 0.770771i | |||||
0 | 0 | |||||||||
−40.3000 | + | 10.7983i | −2.18237 | + | 0.584763i | |||||
0 | 0 | |||||||||
−6.16439 | − | 17.4643i | −0.332846 | − | 0.942981i | |||||
0 | 0 | |||||||||
0.701566 | + | 0.405049i | 0.0377711 | + | 0.0218071i | |||||
0 | 0 | |||||||||
1.55085 | − | 5.78787i | 0.0832542 | − | 0.310709i | −0.911724 | − | 0.410804i | ||
0.994978 | + | 0.100095i | ||||||||
0 | 0 | |||||||||
3.15549 | − | 3.15549i | 0.168909 | − | 0.168909i | −0.617590 | − | 0.786500i | ||
0.786500 | + | 0.617590i | ||||||||
0 | 0 | |||||||||
13.6973i | 0.731108i | |||||||||
0 | 0 | |||||||||
6.03486 | − | 3.48423i | 0.321203 | − | 0.185447i | −0.330726 | − | 0.943727i | ||
0.651929 | + | 0.758280i | ||||||||
0 | 0 | |||||||||
9.02307 | − | 2.41773i | 0.478895 | − | 0.128320i | |||||
0 | 0 | |||||||||
17.6695 | − | 6.95325i | 0.935168 | − | 0.368005i | |||||
0 | 0 | |||||||||
−18.6187 | + | 32.2485i | −0.982656 | + | 1.70201i | −0.330735 | + | 0.943724i | ||
−0.651921 | + | 0.758287i | ||||||||
0 | 0 | |||||||||
−6.68329 | + | 3.85860i | −0.351752 | + | 0.203084i | |||||
0 | 0 | |||||||||
−14.8146 | + | 14.8146i | −0.777566 | + | 0.777566i | |||||
0 | 0 | |||||||||
−15.2415 | − | 15.2415i | −0.797774 | − | 0.797774i | |||||
0 | 0 | |||||||||
13.0391 | + | 22.5844i | 0.680637 | + | 1.17890i | 0.974787 | + | 0.223138i | ||
−0.294150 | + | 0.955759i | ||||||||
0 | 0 | |||||||||
−0.709816 | − | 0.409813i | −0.0369516 | − | 0.0213340i | |||||
0 | 0 | |||||||||
0.556840 | − | 3.71726i | 0.0289097 | − | 0.192991i | |||||
0 | 0 | |||||||||
9.46676 | + | 35.3304i | 0.490170 | + | 1.82934i | 0.555555 | + | 0.831480i | ||
−0.0653850 | + | 0.997860i | ||||||||
0 | 0 | |||||||||
−6.24686 | − | 10.8199i | −0.322586 | − | 0.558736i | |||||
0 | 0 | |||||||||
8.49813 | 0.437676 | |||||||||
0 | 0 | |||||||||
0.261074 | + | 0.261074i | 0.0134105 | + | 0.0134105i | 0.713780 | − | 0.700370i | ||
−0.700370 | + | 0.713780i | ||||||||
0 | 0 | |||||||||
−14.4819 | − | 3.88041i | −0.741929 | − | 0.198799i | |||||
0 | 0 | |||||||||
8.76848 | − | 15.1875i | 0.448048 | − | 0.776043i | −0.550211 | − | 0.835026i | ||
0.998259 | + | 0.0589834i | ||||||||
0 | 0 | |||||||||
20.9252 | − | 2.37692i | 1.06645 | − | 0.121139i | |||||
0 | 0 | |||||||||
−2.25632 | − | 8.42070i | −0.114695 | − | 0.428048i | |||||
0 | 0 | |||||||||
−21.5199 | − | 5.76625i | −1.09110 | − | 0.292361i | −0.331967 | − | 0.943291i | ||
−0.759137 | + | 0.650930i | ||||||||
0 | 0 | |||||||||
− | 3.36874i | − | 0.170365i | |||||||
0 | 0 | |||||||||
3.18058i | 0.160439i | |||||||||
0 | 0 | |||||||||
−5.39281 | − | 1.44500i | −0.271342 | − | 0.0727058i | |||||
0 | 0 | |||||||||
−6.12529 | − | 22.8599i | −0.307419 | − | 1.14730i | −0.930843 | − | 0.365420i | ||
0.623424 | − | 0.781884i | ||||||||
0 | 0 | |||||||||
9.63844 | − | 1.09484i | 0.482526 | − | 0.0548108i | |||||
0 | 0 | |||||||||
−3.87231 | + | 6.70703i | −0.193374 | + | 0.334933i | −0.946366 | − | 0.323096i | ||
0.752992 | + | 0.658029i | ||||||||
0 | 0 | |||||||||
−19.1394 | − | 5.12838i | −0.953400 | − | 0.255463i | |||||
0 | 0 | |||||||||
0.310707 | + | 0.310707i | 0.0154392 | + | 0.0154392i | |||||
0 | 0 | |||||||||
−22.8451 | −1.13239 | |||||||||
0 | 0 | |||||||||
−15.9651 | − | 27.6524i | −0.789425 | − | 1.36732i | −0.926320 | − | 0.376739i | ||
0.136894 | − | 0.990586i | ||||||||
0 | 0 | |||||||||
−2.04109 | − | 7.61745i | −0.100680 | − | 0.375741i | |||||
0 | 0 | |||||||||
2.66827 | − | 17.8124i | 0.131297 | − | 0.876489i | |||||
0 | 0 | |||||||||
4.32981 | + | 2.49981i | 0.212542 | + | 0.122711i | |||||
0 | 0 | |||||||||
0.547209 | + | 0.947793i | 0.0267969 | + | 0.0464136i | |||||
0 | 0 | |||||||||
−6.96449 | − | 6.96449i | −0.340238 | − | 0.340238i | 0.516219 | − | 0.856457i | ||
−0.856457 | + | 0.516219i | ||||||||
0 | 0 | |||||||||
6.31935 | − | 6.31935i | 0.307986 | − | 0.307986i | −0.536142 | − | 0.844128i | ||
0.844128 | + | 0.536142i | ||||||||
0 | 0 | |||||||||
5.37132 | − | 3.10113i | 0.261162 | − | 0.150782i | |||||
0 | 0 | |||||||||
−9.53929 | + | 16.5225i | −0.462724 | + | 0.801461i | |||||
0 | 0 | |||||||||
−12.4466 | + | 4.89795i | −0.602331 | + | 0.237028i | |||||
0 | 0 | |||||||||
−15.1191 | + | 4.05114i | −0.729955 | + | 0.195591i | |||||
0 | 0 | |||||||||
−5.61569 | + | 3.24222i | −0.270498 | + | 0.156172i | −0.629114 | − | 0.777313i | ||
0.358616 | + | 0.933485i | ||||||||
0 | 0 | |||||||||
− | 17.1718i | − | 0.825223i | −0.910907 | − | 0.412612i | ||||
0.910907 | − | 0.412612i | ||||||||
0 | 0 | |||||||||
3.64081 | − | 3.64081i | 0.174564 | − | 0.174564i | |||||
0 | 0 | |||||||||
0.445418 | − | 1.66232i | 0.0213072 | − | 0.0795196i | |||||
0 | 0 | |||||||||
−27.1054 | − | 15.6493i | −1.29367 | − | 0.746900i | −0.314366 | − | 0.949302i | ||
−0.979302 | + | 0.202402i | ||||||||
0 | 0 | |||||||||
−12.1043 | − | 3.70966i | −0.576396 | − | 0.176650i | |||||
0 | 0 | |||||||||
11.7094 | − | 3.13752i | 0.556330 | − | 0.149068i | 0.0303104 | − | 0.999541i | ||
0.526020 | + | 0.850472i | ||||||||
0 | 0 | |||||||||
−2.85946 | + | 10.6717i | −0.135552 | + | 0.505885i | |||||
0 | 0 | |||||||||
10.3914 | 0.491495 | |||||||||
0 | 0 | |||||||||
33.4968 | 1.58081 | 0.790406 | − | 0.612583i | ||||||
0.790406 | + | 0.612583i | ||||||||
0 | 0 | |||||||||
0.644522 | − | 2.40539i | 0.0303494 | − | 0.113265i | |||||
0 | 0 | |||||||||
−7.48729 | + | 2.00621i | −0.351783 | + | 0.0942601i | |||||
0 | 0 | |||||||||
9.17085 | + | 3.99130i | 0.429936 | + | 0.187115i | |||||
0 | 0 | |||||||||
−2.60908 | − | 1.50635i | −0.122047 | − | 0.0704641i | 0.437733 | − | 0.899105i | ||
−0.559781 | + | 0.828641i | ||||||||
0 | 0 | |||||||||
8.93205 | − | 33.3349i | 0.416912 | − | 1.55594i | |||||
0 | 0 | |||||||||
−20.6763 | + | 20.6763i | −0.962993 | + | 0.962993i | −0.999339 | − | 0.0363467i | ||
0.0363467 | + | 0.999339i | ||||||||
0 | 0 | |||||||||
11.6775i | 0.542697i | 0.962481 | + | 0.271349i | ||||||
−0.962481 | + | 0.271349i | ||||||||
0 | 0 | |||||||||
−10.3969 | + | 6.00266i | −0.482145 | + | 0.278367i | |||||
0 | 0 | |||||||||
−9.80739 | + | 2.62788i | −0.453832 | + | 0.121604i | −0.478492 | − | 0.878092i | ||
0.0246599 | + | 0.999696i | ||||||||
0 | 0 | |||||||||
−2.51512 | + | 16.7900i | −0.116137 | + | 0.775290i | |||||
0 | 0 | |||||||||
4.78986 | − | 8.29629i | 0.220705 | − | 0.382273i | |||||
0 | 0 | |||||||||
22.9383 | − | 13.2434i | 1.05470 | − | 0.608933i | |||||
0 | 0 | |||||||||
−6.89183 | + | 6.89183i | −0.316219 | + | 0.316219i | |||||
0 | 0 | |||||||||
−1.81683 | − | 1.81683i | −0.0831870 | − | 0.0831870i | |||||
0 | 0 | |||||||||
−5.72312 | − | 9.91273i | −0.261496 | − | 0.452924i | 0.705144 | − | 0.709064i | ||
−0.966640 | + | 0.256140i | ||||||||
0 | 0 | |||||||||
−9.39606 | − | 5.42482i | −0.428424 | − | 0.247350i | |||||
0 | 0 | |||||||||
0.921468 | − | 1.15764i | 0.0419283 | − | 0.0526743i | |||||
0 | 0 | |||||||||
4.20479 | + | 15.6925i | 0.190930 | + | 0.712560i | |||||
0 | 0 | |||||||||
−4.85037 | − | 8.40108i | −0.219791 | − | 0.380689i | 0.734953 | − | 0.678118i | ||
−0.954744 | + | 0.297429i | ||||||||
0 | 0 | |||||||||
13.8618 | 0.626851 | |||||||||
0 | 0 | |||||||||
11.4667 | + | 11.4667i | 0.517483 | + | 0.517483i | 0.916809 | − | 0.399326i | ||
−0.399326 | + | 0.916809i | ||||||||
0 | 0 | |||||||||
−20.6817 | − | 5.54166i | −0.931459 | − | 0.249584i | |||||
0 | 0 | |||||||||
7.19798 | − | 12.4673i | 0.323525 | − | 0.560362i | |||||
0 | 0 | |||||||||
−1.92566 | − | 16.9525i | −0.0863776 | − | 0.760424i | |||||
0 | 0 | |||||||||
−4.93931 | − | 18.4338i | −0.221114 | − | 0.825209i | −0.983924 | − | 0.178586i | ||
0.762810 | − | 0.646623i | ||||||||
0 | 0 | |||||||||
−22.6976 | − | 6.08181i | −1.01405 | − | 0.271715i | |||||
0 | 0 | |||||||||
22.4043i | 0.998960i | 0.866325 | + | 0.499480i | ||||||
−0.866325 | + | 0.499480i | ||||||||
0 | 0 | |||||||||
28.1779i | 1.25390i | |||||||||
0 | 0 | |||||||||
6.52593 | + | 1.74862i | 0.289827 | + | 0.0776588i | |||||
0 | 0 | |||||||||
−3.91534 | − | 14.6122i | −0.173544 | − | 0.647676i | −0.996795 | − | 0.0799982i | ||
0.823251 | − | 0.567678i | ||||||||
0 | 0 | |||||||||
−31.6546 | + | 23.4065i | −1.40032 | + | 1.03544i | |||||
0 | 0 | |||||||||
8.81512 | − | 15.2682i | 0.389197 | − | 0.674109i | |||||
0 | 0 | |||||||||
9.93698 | + | 2.66261i | 0.437876 | + | 0.117328i | |||||
0 | 0 | |||||||||
13.3248 | + | 13.3248i | 0.586025 | + | 0.586025i | |||||
0 | 0 | |||||||||
21.8639 | 0.959721 | |||||||||
0 | 0 | |||||||||
3.63800 | + | 6.30121i | 0.159384 | + | 0.276061i | 0.934647 | − | 0.355578i | ||
−0.775263 | + | 0.631639i | ||||||||
0 | 0 | |||||||||
−4.66897 | − | 17.4249i | −0.204160 | − | 0.761936i | −0.989704 | − | 0.143130i | ||
0.785544 | − | 0.618806i | ||||||||
0 | 0 | |||||||||
−7.79758 | + | 3.06849i | −0.340314 | + | 0.133920i | |||||
0 | 0 | |||||||||
43.2349 | + | 24.9617i | 1.88334 | + | 1.08735i | |||||
0 | 0 | |||||||||
11.3688 | + | 19.6913i | 0.494294 | + | 0.856141i | |||||
0 | 0 | |||||||||
−8.70588 | − | 8.70588i | −0.377803 | − | 0.377803i | |||||
0 | 0 | |||||||||
0.836275 | − | 0.836275i | 0.0362231 | − | 0.0362231i | |||||
0 | 0 | |||||||||
−15.0435 | + | 8.68540i | −0.650389 | + | 0.375502i | |||||
0 | 0 | |||||||||
3.71761 | − | 6.43909i | 0.160427 | − | 0.277867i | |||||
0 | 0 | |||||||||
1.36852 | − | 38.4402i | 0.0589463 | − | 1.65574i | |||||
0 | 0 | |||||||||
−2.61709 | + | 0.701247i | −0.112518 | + | 0.0301490i | −0.314638 | − | 0.949212i | ||
0.202121 | + | 0.979361i | ||||||||
0 | 0 | |||||||||
−8.44907 | + | 4.87808i | −0.362585 | + | 0.209338i | |||||
0 | 0 | |||||||||
15.0327i | 0.643931i | |||||||||
0 | 0 | |||||||||
20.4366 | − | 20.4366i | 0.873807 | − | 0.873807i | −0.119078 | − | 0.992885i | ||
0.992885 | + | 0.119078i | ||||||||
0 | 0 | |||||||||
−2.36645 | + | 8.83170i | −0.100998 | + | 0.376928i | |||||
0 | 0 | |||||||||
−9.47278 | − | 5.46911i | −0.403554 | − | 0.232992i | |||||
0 | 0 | |||||||||
−4.06928 | + | 9.35002i | −0.173043 | + | 0.397603i | |||||
0 | 0 | |||||||||
−6.34964 | + | 1.70138i | −0.269527 | + | 0.0722196i | |||||
0 | 0 | |||||||||
1.22222 | − | 4.56137i | 0.0517869 | − | 0.193271i | −0.935186 | − | 0.354156i | ||
0.986973 | + | 0.160885i | ||||||||
0 | 0 | |||||||||
12.5792 | 0.532044 | |||||||||
0 | 0 | |||||||||
39.4367 | 1.66502 | |||||||||
0 | 0 | |||||||||
1.89945 | − | 7.08884i | 0.0800522 | − | 0.298759i | −0.914279 | − | 0.405085i | ||
0.994331 | + | 0.106326i | ||||||||
0 | 0 | |||||||||
18.8336 | − | 5.04645i | 0.792335 | − | 0.212306i | |||||
0 | 0 | |||||||||
0.645300 | − | 0.477158i | 0.0271001 | − | 0.0200387i | |||||
0 | 0 | |||||||||
10.8006 | + | 6.23575i | 0.452787 | + | 0.261416i | 0.709006 | − | 0.705202i | ||
−0.256220 | + | 0.966619i | ||||||||
0 | 0 | |||||||||
−9.94080 | + | 37.0996i | −0.416010 | + | 1.55257i | 0.366795 | + | 0.930302i | ||
−0.782805 | + | 0.622267i | ||||||||
0 | 0 | |||||||||
−10.2824 | + | 10.2824i | −0.429555 | + | 0.429555i | |||||
0 | 0 | |||||||||
1.48663i | 0.0619969i | |||||||||
0 | 0 | |||||||||
−16.4040 | + | 9.47084i | −0.682906 | + | 0.394276i | −0.800949 | − | 0.598732i | ||
0.118043 | + | 0.993009i | ||||||||
0 | 0 | |||||||||
11.0868 | − | 2.97069i | 0.460750 | − | 0.123458i | |||||
0 | 0 | |||||||||
5.68696 | − | 7.14450i | 0.235935 | − | 0.296404i | |||||
0 | 0 | |||||||||
3.90324 | − | 6.76062i | 0.161656 | − | 0.279996i | |||||
0 | 0 | |||||||||
5.92098 | − | 3.41848i | 0.244803 | − | 0.141337i | |||||
0 | 0 | |||||||||
−7.54134 | + | 7.54134i | −0.311264 | + | 0.311264i | −0.845399 | − | 0.534135i | ||
0.534135 | + | 0.845399i | ||||||||
0 | 0 | |||||||||
18.0340 | + | 18.0340i | 0.743078 | + | 0.743078i | |||||
0 | 0 | |||||||||
−10.8551 | − | 18.8015i | −0.446517 | − | 0.773391i | |||||
0 | 0 | |||||||||
−10.2804 | − | 5.93539i | −0.422165 | − | 0.243737i | 0.273838 | − | 0.961776i | ||
−0.696003 | + | 0.718039i | ||||||||
0 | 0 | |||||||||
−19.7162 | − | 15.6939i | −0.808284 | − | 0.643387i | |||||
0 | 0 | |||||||||
−6.83423 | − | 25.5057i | −0.279706 | − | 1.04388i | |||||
0 | 0 | |||||||||
10.9170 | + | 18.9089i | 0.446058 | + | 0.772595i | 0.998125 | − | 0.0612043i | ||
−0.552067 | + | 0.833800i | ||||||||
0 | 0 | |||||||||
−37.4893 | −1.52922 | −0.764610 | − | 0.644493i | ||||||
−0.764610 | + | 0.644493i | ||||||||
0 | 0 | |||||||||
8.20620 | + | 8.20620i | 0.334182 | + | 0.334182i | |||||
0 | 0 | |||||||||
26.8570 | + | 7.19631i | 1.09189 | + | 0.292572i | |||||
0 | 0 | |||||||||
2.33958 | − | 4.05227i | 0.0949605 | − | 0.164476i | −0.814632 | − | 0.579979i | ||
0.909592 | + | 0.415502i | ||||||||
0 | 0 | |||||||||
−5.59125 | − | 7.56151i | −0.226569 | − | 0.306408i | |||||
0 | 0 | |||||||||
2.31630 | + | 8.64456i | 0.0937075 | + | 0.349721i | |||||
0 | 0 | |||||||||
−4.89703 | − | 1.31216i | −0.197789 | − | 0.0529975i | 0.158564 | − | 0.987349i | ||
−0.356354 | + | 0.934351i | ||||||||
0 | 0 | |||||||||
− | 0.716563i | − | 0.0288946i | |||||||
0 | 0 | |||||||||
16.4696i | 0.663041i | 0.943448 | + | 0.331520i | ||||||
−0.943448 | + | 0.331520i | ||||||||
0 | 0 | |||||||||
−14.6852 | − | 3.93490i | −0.590249 | − | 0.158157i | −0.0486822 | − | 0.998814i | ||
−0.541567 | + | 0.840657i | ||||||||
0 | 0 | |||||||||
−0.696000 | − | 2.59751i | −0.0279295 | − | 0.104234i | |||||
0 | 0 | |||||||||
18.5024 | + | 8.05257i | 0.741285 | + | 0.322619i | |||||
0 | 0 | |||||||||
−1.03623 | + | 1.79481i | −0.0414493 | + | 0.0717922i | |||||
0 | 0 | |||||||||
19.4602 | + | 5.21435i | 0.777167 | + | 0.208241i | |||||
0 | 0 | |||||||||
19.3295 | + | 19.3295i | 0.770717 | + | 0.770717i | |||||
0 | 0 | |||||||||
6.82302 | 0.271620 | 0.135810 | − | 0.990735i | ||||||
0.135810 | + | 0.990735i | ||||||||
0 | 0 | |||||||||
6.80206 | + | 11.7815i | 0.270357 | + | 0.468273i | |||||
0 | 0 | |||||||||
5.14974 | + | 19.2191i | 0.204361 | + | 0.762686i | |||||
0 | 0 | |||||||||
9.69092 | − | 15.4853i | 0.383968 | − | 0.613549i | |||||
0 | 0 | |||||||||
−10.1003 | − | 5.83143i | −0.399563 | − | 0.230688i | |||||
0 | 0 | |||||||||
−16.5379 | − | 28.6446i | −0.653210 | − | 1.13139i | −0.982339 | − | 0.187108i | ||
0.329130 | − | 0.944285i | ||||||||
0 | 0 | |||||||||
14.7445 | + | 14.7445i | 0.581464 | + | 0.581464i | 0.935306 | − | 0.353841i | ||
−0.353841 | + | 0.935306i | ||||||||
0 | 0 | |||||||||
5.38925 | − | 5.38925i | 0.212201 | − | 0.212201i | |||||
0 | 0 | |||||||||
−9.62533 | + | 5.55719i | −0.378411 | + | 0.218476i | −0.677127 | − | 0.735867i | ||
0.298716 | + | 0.954342i | ||||||||
0 | 0 | |||||||||
18.7035 | − | 32.3955i | 0.734178 | − | 1.27163i | |||||
0 | 0 | |||||||||
8.02937 | + | 20.4041i | 0.314696 | + | 0.799699i | |||||
0 | 0 | |||||||||
16.2451 | − | 4.35285i | 0.635718 | − | 0.170340i | 0.0734551 | − | 0.997299i | ||
0.562263 | + | 0.826958i | ||||||||
0 | 0 | |||||||||
3.65548 | − | 2.11049i | 0.142831 | − | 0.0824638i | |||||
0 | 0 | |||||||||
26.9114i | 1.04991i | |||||||||
0 | 0 | |||||||||
−32.5839 | + | 32.5839i | −1.26929 | + | 1.26929i | −0.322834 | + | 0.946455i | ||
−0.946455 | + | 0.322834i | ||||||||
0 | 0 | |||||||||
4.53812 | − | 16.9365i | 0.176512 | − | 0.658753i | −0.819777 | − | 0.572683i | ||
0.996289 | − | 0.0860697i | ||||||||
0 | 0 | |||||||||
16.2201 | + | 9.36470i | 0.629938 | + | 0.363695i | |||||
0 | 0 | |||||||||
−7.65398 | − | 10.3511i | −0.296809 | − | 0.401399i | |||||
0 | 0 | |||||||||
−1.61155 | + | 0.431815i | −0.0623996 | + | 0.0167199i | |||||
0 | 0 | |||||||||
1.53939 | − | 5.74507i | 0.0595162 | − | 0.222117i | |||||
0 | 0 | |||||||||
−27.7796 | −1.07242 | |||||||||
0 | 0 | |||||||||
11.0728 | 0.426827 | 0.213413 | − | 0.976962i | ||||||
0.213413 | + | 0.976962i | ||||||||
0 | 0 | |||||||||
−3.94173 | + | 14.7107i | −0.151717 | + | 0.566217i | |||||
0 | 0 | |||||||||
5.69655 | − | 1.52639i | 0.218936 | − | 0.0586638i | −0.147684 | − | 0.989035i | ||
0.366620 | + | 0.930371i | ||||||||
0 | 0 | |||||||||
29.4830 | − | 3.34902i | 1.13145 | − | 0.128523i | |||||
0 | 0 | |||||||||
1.42258 | + | 0.821328i | 0.0545135 | + | 0.0314734i | |||||
0 | 0 | |||||||||
0.824476 | − | 3.07699i | 0.0315477 | − | 0.117738i | −0.948356 | − | 0.317207i | ||
0.979904 | + | 0.199469i | ||||||||
0 | 0 | |||||||||
−7.40047 | + | 7.40047i | −0.282757 | + | 0.282757i | |||||
0 | 0 | |||||||||
− | 5.40044i | − | 0.206040i | |||||||
0 | 0 | |||||||||
3.21077 | − | 1.85374i | 0.122321 | − | 0.0706218i | |||||
0 | 0 | |||||||||
20.4319 | − | 5.47470i | 0.777265 | − | 0.208267i | 0.151686 | − | 0.988429i | ||
0.625578 | + | 0.780161i | ||||||||
0 | 0 | |||||||||
−20.5719 | − | 16.3751i | −0.781462 | − | 0.622037i | |||||
0 | 0 | |||||||||
0.726208 | − | 1.25783i | 0.0275466 | − | 0.0477122i | |||||
0 | 0 | |||||||||
−2.58056 | + | 1.48989i | −0.0977458 | + | 0.0564336i | |||||
0 | 0 | |||||||||
−9.59422 | + | 9.59422i | −0.362887 | + | 0.362887i | |||||
0 | 0 | |||||||||
19.0687 | + | 19.0687i | 0.720214 | + | 0.720214i | 0.968649 | − | 0.248435i | ||
−0.248435 | + | 0.968649i | ||||||||
0 | 0 | |||||||||
6.98246 | + | 12.0940i | 0.263348 | + | 0.456133i | |||||
0 | 0 | |||||||||
4.69591 | + | 2.71118i | 0.176858 | + | 0.102109i | |||||
0 | 0 | |||||||||
50.8975 | + | 7.62437i | 1.91420 | + | 0.286744i | |||||
0 | 0 | |||||||||
−9.03837 | − | 33.7317i | −0.339443 | − | 1.26682i | −0.898971 | − | 0.438008i | ||
0.559528 | − | 0.828812i | ||||||||
0 | 0 | |||||||||
3.48527 | + | 6.03666i | 0.130708 | + | 0.226392i | |||||
0 | 0 | |||||||||
3.89011 | 0.145686 | |||||||||
0 | 0 | |||||||||
14.6884 | + | 14.6884i | 0.549315 | + | 0.549315i | |||||
0 | 0 | |||||||||
7.73920 | + | 2.07371i | 0.289026 | + | 0.0774442i | |||||
0 | 0 | |||||||||
−25.7551 | + | 44.6092i | −0.960505 | + | 1.66364i | −0.239268 | + | 0.970953i | ||
−0.721236 | + | 0.692689i | ||||||||
0 | 0 | |||||||||
7.49820 | − | 17.2287i | 0.279248 | − | 0.641629i | |||||
0 | 0 | |||||||||
2.93070 | + | 10.9375i | 0.108994 | + | 0.406771i | |||||
0 | 0 | |||||||||
9.12690 | + | 2.44555i | 0.338965 | + | 0.0908253i | |||||
0 | 0 | |||||||||
10.3415i | 0.383546i | 0.981439 | + | 0.191773i | ||||||
−0.981439 | + | 0.191773i | ||||||||
0 | 0 | |||||||||
− | 17.7358i | − | 0.656881i | |||||||
0 | 0 | |||||||||
−30.6138 | − | 8.20293i | −1.13229 | − | 0.303396i | |||||
0 | 0 | |||||||||
5.21156 | + | 19.4498i | 0.192493 | + | 0.718395i | 0.992901 | + | 0.118940i | ||
−0.800408 | + | 0.599455i | ||||||||
0 | 0 | |||||||||
−2.48245 | − | 10.7861i | −0.0915666 | − | 0.397852i | |||||
0 | 0 | |||||||||
−17.6300 | + | 30.5361i | −0.649411 | + | 1.12481i | |||||
0 | 0 | |||||||||
−29.5182 | − | 7.90938i | −1.08584 | − | 0.290951i | −0.328856 | − | 0.944380i | ||
−0.756988 | + | 0.653429i | ||||||||
0 | 0 | |||||||||
6.76569 | + | 6.76569i | 0.248544 | + | 0.248544i | |||||
0 | 0 | |||||||||
36.5659 | 1.34147 | 0.670735 | − | 0.741697i | ||||||
0.670735 | + | 0.741697i | ||||||||
0 | 0 | |||||||||
−6.89526 | − | 11.9429i | −0.252623 | − | 0.437556i | |||||
0 | 0 | |||||||||
−1.61558 | − | 6.02943i | −0.0591110 | − | 0.220605i | |||||
0 | 0 | |||||||||
11.6179 | + | 29.5232i | 0.424509 | + | 1.07875i | |||||
0 | 0 | |||||||||
−30.5955 | − | 17.6643i | −1.11644 | − | 0.644580i | −0.175954 | − | 0.984398i | ||
−0.940491 | + | 0.339819i | ||||||||
0 | 0 | |||||||||
−0.310057 | − | 0.537034i | −0.0112991 | − | 0.0195706i | |||||
0 | 0 | |||||||||
7.27401 | + | 7.27401i | 0.264728 | + | 0.264728i | |||||
0 | 0 | |||||||||
−1.06021 | + | 1.06021i | −0.0385339 | + | 0.0385339i | −0.726111 | − | 0.687577i | ||
0.687577 | + | 0.726111i | ||||||||
0 | 0 | |||||||||
2.66127 | − | 1.53649i | 0.0965981 | − | 0.0557709i | |||||
0 | 0 | |||||||||
−15.2003 | + | 26.3277i | −0.551010 | + | 0.954378i | 0.447192 | + | 0.894438i | ||
−0.998202 | + | 0.0599396i | ||||||||
0 | 0 | |||||||||
27.1535 | + | 4.06755i | 0.983023 | + | 0.147255i | |||||
0 | 0 | |||||||||
−16.6390 | + | 4.45840i | −0.601584 | + | 0.161194i | |||||
0 | 0 | |||||||||
15.3853 | − | 8.88274i | 0.555533 | − | 0.320737i | |||||
0 | 0 | |||||||||
38.0523i | 1.37220i | 0.727507 | + | 0.686101i | ||||||
−0.727507 | + | 0.686101i | ||||||||
0 | 0 | |||||||||
7.06039 | − | 7.06039i | 0.254274 | − | 0.254274i | |||||
0 | 0 | |||||||||
−4.02680 | + | 15.0282i | −0.144834 | + | 0.540528i | 0.854929 | + | 0.518746i | ||
−0.999763 | + | 0.0217825i | ||||||||
0 | 0 | |||||||||
−19.0796 | − | 11.0156i | −0.685361 | − | 0.395693i | |||||
0 | 0 | |||||||||
1.35511 | + | 11.9297i | 0.0486142 | + | 0.427975i | |||||
0 | 0 | |||||||||
−1.47039 | + | 0.393989i | −0.0526820 | + | 0.0141161i | |||||
0 | 0 | |||||||||
9.17123 | − | 34.2275i | 0.328172 | − | 1.22476i | |||||
0 | 0 | |||||||||
−17.0918 | −0.610812 | |||||||||
0 | 0 | |||||||||
−12.7134 | −0.453760 | |||||||||
0 | 0 | |||||||||
−4.32518 | + | 16.1418i | −0.154176 | + | 0.575393i | 0.844998 | + | 0.534769i | ||
−0.999175 | + | 0.0406241i | ||||||||
0 | 0 | |||||||||
4.83129 | − | 1.29454i | 0.171998 | − | 0.0460868i | |||||
0 | 0 | |||||||||
−4.01937 | − | 35.3845i | −0.142912 | − | 1.25813i | |||||
0 | 0 | |||||||||
−11.4256 | − | 6.59659i | −0.405736 | − | 0.234252i | |||||
0 | 0 | |||||||||
0.581386 | − | 2.16976i | 0.0206196 | − | 0.0769535i | |||||
0 | 0 | |||||||||
−6.46029 | + | 6.46029i | −0.228835 | + | 0.228835i | −0.812206 | − | 0.583371i | ||
0.583371 | + | 0.812206i | ||||||||
0 | 0 | |||||||||
− | 22.5486i | − | 0.797710i | |||||||
0 | 0 | |||||||||
11.9457 | − | 6.89688i | 0.422082 | − | 0.243689i | |||||
0 | 0 | |||||||||
−78.9780 | + | 21.1621i | −2.78707 | + | 0.746794i | |||||
0 | 0 | |||||||||
−1.94194 | − | 0.290899i | −0.0684442 | − | 0.0102528i | |||||
0 | 0 | |||||||||
−5.21101 | + | 9.02573i | −0.183436 | + | 0.317721i | |||||
0 | 0 | |||||||||
−24.9554 | + | 14.4080i | −0.877386 | + | 0.506559i | −0.869796 | − | 0.493412i | ||
−0.00759061 | + | 0.999971i | ||||||||
0 | 0 | |||||||||
32.3761 | − | 32.3761i | 1.13688 | − | 1.13688i | 0.147873 | − | 0.989006i | ||
0.989006 | − | 0.147873i | ||||||||
0 | 0 | |||||||||
5.62163 | + | 5.62163i | 0.197159 | + | 0.197159i | |||||
0 | 0 | |||||||||
−9.19808 | − | 15.9315i | −0.322195 | − | 0.558058i | |||||
0 | 0 | |||||||||
−14.0219 | − | 8.09555i | −0.490564 | − | 0.283227i | |||||
0 | 0 | |||||||||
−4.57268 | − | 11.6200i | −0.159782 | − | 0.406036i | |||||
0 | 0 | |||||||||
7.00094 | + | 26.1279i | 0.244334 | + | 0.911869i | 0.973717 | + | 0.227762i | ||
−0.729382 | + | 0.684106i | ||||||||
0 | 0 | |||||||||
12.1699 | + | 21.0790i | 0.424218 | + | 0.734767i | 0.996347 | − | 0.0853968i | ||
−0.572129 | + | 0.820163i | ||||||||
0 | 0 | |||||||||
−17.4035 | −0.605913 | |||||||||
0 | 0 | |||||||||
31.7583 | + | 31.7583i | 1.10435 | + | 1.10435i | 0.993880 | + | 0.110466i | ||
0.110466 | + | 0.993880i | ||||||||
0 | 0 | |||||||||
39.6910 | + | 10.6352i | 1.37853 | + | 0.369375i | 0.870586 | − | 0.492017i | ||
0.507941 | + | 0.861392i | ||||||||
0 | 0 | |||||||||
17.6694 | − | 30.6042i | 0.612944 | − | 1.06165i | |||||
0 | 0 | |||||||||
−33.6826 | + | 31.3668i | −1.16703 | + | 1.08679i | |||||
0 | 0 | |||||||||
8.07125 | + | 30.1223i | 0.279317 | + | 1.04243i | |||||
0 | 0 | |||||||||
38.4939 | + | 10.3144i | 1.33054 | + | 0.356518i | |||||
0 | 0 | |||||||||
12.4384i | 0.429423i | 0.976678 | + | 0.214711i | ||||||
−0.976678 | + | 0.214711i | ||||||||
0 | 0 | |||||||||
− | 18.3958i | − | 0.634339i | |||||||
0 | 0 | |||||||||
−4.32149 | − | 1.15794i | −0.148840 | − | 0.0398816i | |||||
0 | 0 | |||||||||
−2.32061 | − | 8.66065i | −0.0798316 | − | 0.297935i | |||||
0 | 0 | |||||||||
20.2656 | − | 46.5645i | 0.696335 | − | 1.59997i | |||||
0 | 0 | |||||||||
−7.45561 | + | 12.9135i | −0.255876 | + | 0.443190i | |||||
0 | 0 | |||||||||
2.05748 | + | 0.551301i | 0.0705297 | + | 0.0188984i | |||||
0 | 0 | |||||||||
−11.8456 | − | 11.8456i | −0.405585 | − | 0.405585i | 0.474611 | − | 0.880196i | ||
−0.880196 | + | 0.474611i | ||||||||
0 | 0 | |||||||||
−8.80008 | −0.300956 | |||||||||
0 | 0 | |||||||||
7.54656 | + | 13.0710i | 0.257786 | + | 0.446498i | 0.965648 | − | 0.259852i | ||
−0.707863 | + | 0.706350i | ||||||||
0 | 0 | |||||||||
−11.8045 | − | 44.0551i | −0.402765 | − | 1.50314i | −0.808141 | − | 0.588990i | ||
0.405375 | − | 0.914150i | ||||||||
0 | 0 | |||||||||
−1.29432 | − | 0.193888i | −0.0441104 | − | 0.00660767i | |||||
0 | 0 | |||||||||
23.4497 | + | 13.5387i | 0.798237 | + | 0.460862i | 0.842854 | − | 0.538142i | ||
−0.0446175 | + | 0.999004i | ||||||||
0 | 0 | |||||||||
−14.5080 | − | 25.1285i | −0.493286 | − | 0.854396i | |||||
0 | 0 | |||||||||
−20.2469 | − | 20.2469i | −0.687619 | − | 0.687619i | |||||
0 | 0 | |||||||||
−14.9754 | + | 14.9754i | −0.508004 | + | 0.508004i | |||||
0 | 0 | |||||||||
−14.5023 | + | 8.37290i | −0.491391 | + | 0.283705i | |||||
0 | 0 | |||||||||
10.1418 | − | 17.5660i | 0.343246 | − | 0.594520i | |||||
0 | 0 | |||||||||
23.6938 | + | 18.8600i | 0.800995 | + | 0.637585i | |||||
0 | 0 | |||||||||
−8.80425 | + | 2.35909i | −0.297298 | + | 0.0796609i | −0.404385 | − | 0.914589i | ||
0.107087 | + | 0.994250i | ||||||||
0 | 0 | |||||||||
−22.3173 | + | 12.8849i | −0.752745 | + | 0.434598i | |||||
0 | 0 | |||||||||
− | 0.723819i | − | 0.0243861i | −0.999926 | − | 0.0121930i | ||||
0.999926 | − | 0.0121930i | ||||||||
0 | 0 | |||||||||
21.2381 | − | 21.2381i | 0.714718 | − | 0.714718i | −0.252800 | − | 0.967518i | ||
0.967518 | + | 0.252800i | ||||||||
0 | 0 | |||||||||
2.78588 | − | 10.3971i | 0.0936464 | − | 0.349493i | |||||
0 | 0 | |||||||||
−17.5247 | − | 10.1179i | −0.588422 | − | 0.339726i | 0.176051 | − | 0.984381i | ||
−0.764473 | + | 0.644655i | ||||||||
0 | 0 | |||||||||
36.1088 | − | 4.10164i | 1.21105 | − | 0.137565i | |||||
0 | 0 | |||||||||
1.61002 | − | 0.431403i | 0.0539377 | − | 0.0144526i | |||||
0 | 0 | |||||||||
2.98139 | − | 11.1267i | 0.0997683 | − | 0.372340i | |||||
0 | 0 | |||||||||
−9.86738 | −0.329830 | |||||||||
0 | 0 | |||||||||
1.45942 | 0.0487288 | |||||||||
0 | 0 | |||||||||
6.39931 | − | 23.8825i | 0.213429 | − | 0.796528i | |||||
0 | 0 | |||||||||
−9.02281 | + | 2.41766i | −0.300594 | + | 0.0805438i | |||||
0 | 0 | |||||||||
−8.27634 | − | 11.1928i | −0.275419 | − | 0.372473i | |||||
0 | 0 | |||||||||
11.2129 | + | 6.47376i | 0.372729 | + | 0.215195i | |||||
0 | 0 | |||||||||
−3.46515 | + | 12.9321i | −0.115058 | + | 0.429404i | −0.999291 | − | 0.0376423i | ||
0.884233 | + | 0.467046i | ||||||||
0 | 0 | |||||||||
24.8764 | − | 24.8764i | 0.825099 | − | 0.825099i | |||||
0 | 0 | |||||||||
− | 34.5549i | − | 1.14485i | −0.819955 | − | 0.572427i | ||||
0.819955 | − | 0.572427i | ||||||||
0 | 0 | |||||||||
16.4244 | − | 9.48262i | 0.543568 | − | 0.313829i | |||||
0 | 0 | |||||||||
−7.72117 | + | 2.06888i | −0.255254 | + | 0.0683951i | |||||
0 | 0 | |||||||||
−2.82307 | − | 7.17393i | −0.0932260 | − | 0.236904i | |||||
0 | 0 | |||||||||
26.7589 | − | 46.3478i | 0.882695 | − | 1.52887i | 0.0343626 | − | 0.999409i | ||
0.848333 | − | 0.529464i | ||||||||
0 | 0 | |||||||||
22.4040 | − | 12.9350i | 0.738238 | − | 0.426222i | |||||
0 | 0 | |||||||||
11.8998 | − | 11.8998i | 0.391686 | − | 0.391686i | |||||
0 | 0 | |||||||||
−8.53014 | − | 8.53014i | −0.280469 | − | 0.280469i | |||||
0 | 0 | |||||||||
−6.42208 | − | 11.1234i | −0.210929 | − | 0.365339i | |||||
0 | 0 | |||||||||
−0.0427340 | − | 0.0246725i | −0.00140206 | − | 0.000809477i | 0.499299 | − | 0.866430i | ||
−0.500701 | + | 0.865620i | ||||||||
0 | 0 | |||||||||
−20.7682 | + | 11.0245i | −0.680649 | + | 0.361314i | |||||
0 | 0 | |||||||||
−6.06927 | − | 22.6508i | −0.198699 | − | 0.741554i | |||||
0 | 0 | |||||||||
−26.1685 | − | 45.3252i | −0.855802 | − | 1.48229i | |||||
0 | 0 | |||||||||
−0.977039 | −0.0319185 | −0.0159592 | − | 0.999873i | ||||||
−0.0159592 | + | 0.999873i | ||||||||
0 | 0 | |||||||||
−16.0925 | − | 16.0925i | −0.525157 | − | 0.525157i | |||||
0 | 0 | |||||||||
−37.6344 | − | 10.0841i | −1.22685 | − | 0.328733i | −0.413496 | − | 0.910506i | ||
−0.813351 | + | 0.581773i | ||||||||
0 | 0 | |||||||||
−0.116095 | + | 0.201082i | −0.00378056 | + | 0.00654812i | |||||
0 | 0 | |||||||||
−18.4448 | − | 8.02748i | −0.600010 | − | 0.261134i | |||||
0 | 0 | |||||||||
5.93312 | + | 22.1427i | 0.192801 | + | 0.719541i | 0.992825 | + | 0.119574i | ||
−0.800025 | + | 0.599967i | ||||||||
0 | 0 | |||||||||
−37.5084 | − | 10.0504i | −1.21757 | − | 0.326248i | |||||
0 | 0 | |||||||||
− | 16.2702i | − | 0.527599i | |||||||
0 | 0 | |||||||||
− | 34.2308i | − | 1.10884i | −0.832235 | − | 0.554422i | ||||
0.832235 | − | 0.554422i | ||||||||
0 | 0 | |||||||||
18.6407 | + | 4.99477i | 0.603200 | + | 0.161627i | |||||
0 | 0 | |||||||||
−5.05511 | − | 18.8659i | −0.163408 | − | 0.609849i | |||||
0 | 0 | |||||||||
11.3650 | + | 15.3698i | 0.366995 | + | 0.496318i | |||||
0 | 0 | |||||||||
−13.3248 | + | 23.0793i | −0.429834 | + | 0.744494i | |||||
0 | 0 | |||||||||
20.9487 | + | 5.61320i | 0.675064 | + | 0.180883i | |||||
0 | 0 | |||||||||
−10.7710 | − | 10.7710i | −0.346729 | − | 0.346729i | |||||
0 | 0 | |||||||||
−21.2761 | −0.684193 | −0.342096 | − | 0.939665i | ||||||
−0.342096 | + | 0.939665i | ||||||||
0 | 0 | |||||||||
−12.0536 | − | 20.8775i | −0.387218 | − | 0.670680i | |||||
0 | 0 | |||||||||
−7.74616 | − | 28.9091i | −0.248586 | − | 0.927736i | −0.971547 | − | 0.236847i | ||
0.722961 | − | 0.690889i | ||||||||
0 | 0 | |||||||||
−2.07551 | − | 1.65209i | −0.0665379 | − | 0.0529635i | |||||
0 | 0 | |||||||||
−7.15798 | − | 4.13266i | −0.229239 | − | 0.132351i | |||||
0 | 0 | |||||||||
1.50722 | + | 2.61058i | 0.0482201 | + | 0.0835197i | 0.889128 | − | 0.457659i | ||
−0.840908 | + | 0.541178i | ||||||||
0 | 0 | |||||||||
29.6342 | + | 29.6342i | 0.947115 | + | 0.947115i | |||||
0 | 0 | |||||||||
13.2714 | − | 13.2714i | 0.423724 | − | 0.423724i | |||||
0 | 0 | |||||||||
−35.2886 | + | 20.3739i | −1.12553 | + | 0.649826i | −0.942807 | − | 0.333339i | ||
−0.182724 | + | 0.983164i | ||||||||
0 | 0 | |||||||||
−14.4059 | + | 24.9517i | −0.459010 | + | 0.795029i | |||||
0 | 0 | |||||||||
6.16781 | − | 7.74860i | 0.196324 | − | 0.246641i | |||||
0 | 0 | |||||||||
−2.38547 | + | 0.639186i | −0.0758536 | + | 0.0203249i | |||||
0 | 0 | |||||||||
21.1944 | − | 12.2366i | 0.673262 | − | 0.388708i | −0.124049 | − | 0.992276i | ||
0.797312 | + | 0.603568i | ||||||||
0 | 0 | |||||||||
3.26581i | 0.103637i | |||||||||
0 | 0 | |||||||||
−24.7792 | + | 24.7792i | −0.785552 | + | 0.785552i | |||||
0 | 0 | |||||||||
−11.1506 | + | 41.6146i | −0.353143 | + | 1.31795i | 0.529662 | + | 0.848209i | ||
−0.882805 | + | 0.469740i | ||||||||
0 | 0 | |||||||||
18.8978 | + | 10.9106i | 0.597899 | + | 0.345197i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 448.2.z.a.47.10 | 56 | ||
4.3 | odd | 2 | 112.2.v.a.19.12 | yes | 56 | ||
7.3 | odd | 6 | inner | 448.2.z.a.367.10 | 56 | ||
8.3 | odd | 2 | 896.2.z.b.607.10 | 56 | |||
8.5 | even | 2 | 896.2.z.a.607.5 | 56 | |||
16.3 | odd | 4 | 896.2.z.a.159.5 | 56 | |||
16.5 | even | 4 | 112.2.v.a.75.3 | yes | 56 | ||
16.11 | odd | 4 | inner | 448.2.z.a.271.10 | 56 | ||
16.13 | even | 4 | 896.2.z.b.159.10 | 56 | |||
28.3 | even | 6 | 112.2.v.a.3.3 | ✓ | 56 | ||
28.11 | odd | 6 | 784.2.w.f.227.3 | 56 | |||
28.19 | even | 6 | 784.2.j.a.195.14 | 56 | |||
28.23 | odd | 6 | 784.2.j.a.195.13 | 56 | |||
28.27 | even | 2 | 784.2.w.f.19.12 | 56 | |||
56.3 | even | 6 | 896.2.z.b.479.10 | 56 | |||
56.45 | odd | 6 | 896.2.z.a.479.5 | 56 | |||
112.3 | even | 12 | 896.2.z.a.31.5 | 56 | |||
112.5 | odd | 12 | 784.2.j.a.587.13 | 56 | |||
112.37 | even | 12 | 784.2.j.a.587.14 | 56 | |||
112.45 | odd | 12 | 896.2.z.b.31.10 | 56 | |||
112.53 | even | 12 | 784.2.w.f.619.12 | 56 | |||
112.59 | even | 12 | inner | 448.2.z.a.143.10 | 56 | ||
112.69 | odd | 4 | 784.2.w.f.411.3 | 56 | |||
112.101 | odd | 12 | 112.2.v.a.59.12 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.v.a.3.3 | ✓ | 56 | 28.3 | even | 6 | ||
112.2.v.a.19.12 | yes | 56 | 4.3 | odd | 2 | ||
112.2.v.a.59.12 | yes | 56 | 112.101 | odd | 12 | ||
112.2.v.a.75.3 | yes | 56 | 16.5 | even | 4 | ||
448.2.z.a.47.10 | 56 | 1.1 | even | 1 | trivial | ||
448.2.z.a.143.10 | 56 | 112.59 | even | 12 | inner | ||
448.2.z.a.271.10 | 56 | 16.11 | odd | 4 | inner | ||
448.2.z.a.367.10 | 56 | 7.3 | odd | 6 | inner | ||
784.2.j.a.195.13 | 56 | 28.23 | odd | 6 | |||
784.2.j.a.195.14 | 56 | 28.19 | even | 6 | |||
784.2.j.a.587.13 | 56 | 112.5 | odd | 12 | |||
784.2.j.a.587.14 | 56 | 112.37 | even | 12 | |||
784.2.w.f.19.12 | 56 | 28.27 | even | 2 | |||
784.2.w.f.227.3 | 56 | 28.11 | odd | 6 | |||
784.2.w.f.411.3 | 56 | 112.69 | odd | 4 | |||
784.2.w.f.619.12 | 56 | 112.53 | even | 12 | |||
896.2.z.a.31.5 | 56 | 112.3 | even | 12 | |||
896.2.z.a.159.5 | 56 | 16.3 | odd | 4 | |||
896.2.z.a.479.5 | 56 | 56.45 | odd | 6 | |||
896.2.z.a.607.5 | 56 | 8.5 | even | 2 | |||
896.2.z.b.31.10 | 56 | 112.45 | odd | 12 | |||
896.2.z.b.159.10 | 56 | 16.13 | even | 4 | |||
896.2.z.b.479.10 | 56 | 56.3 | even | 6 | |||
896.2.z.b.607.10 | 56 | 8.3 | odd | 2 |