Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2548,2,Mod(393,2548)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2548, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2548.393");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 2548.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: | no (minimal twist has level 364) |
Sato-Tate group: |
Embedding invariants
Embedding label | 1569.3 | ||
Root | of defining polynomial | ||
Character | 2548.1569 | ||
Dual form | 2548.2.k.i.393.3 |
-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 | |||||||||
−0.520270 | + | 0.901135i | −0.300378 | + | 0.520270i | −0.976222 | − | 0.216775i | ||
0.675843 | + | 0.737045i | ||||||||
0 | 0 | |||||||||
3.18009 | 1.42218 | 0.711089 | − | 0.703102i | ||||||
0.711089 | + | 0.703102i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.958637 | + | 1.66041i | 0.319546 | + | 0.553470i | |||||
0 | 0 | |||||||||
0.852470 | − | 1.47652i | 0.257029 | − | 0.445188i | −0.708415 | − | 0.705796i | ||
0.965445 | + | 0.260608i | ||||||||
0 | 0 | |||||||||
2.78983 | + | 2.28404i | 0.773760 | + | 0.633479i | |||||
0 | 0 | |||||||||
−1.65451 | + | 2.86569i | −0.427192 | + | 0.739917i | |||||
0 | 0 | |||||||||
−1.40001 | − | 2.42488i | −0.339552 | − | 0.588121i | 0.644797 | − | 0.764354i | ||
−0.984348 | + | 0.176233i | ||||||||
0 | 0 | |||||||||
2.74455 | + | 4.75370i | 0.629643 | + | 1.09057i | 0.987623 | + | 0.156844i | ||
−0.357981 | + | 0.933729i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.73500 | + | 4.73716i | −0.570287 | + | 0.987766i | 0.426249 | + | 0.904606i | ||
−0.996536 | + | 0.0831603i | ||||||||
0 | 0 | |||||||||
5.11296 | 1.02259 | |||||||||
0 | 0 | |||||||||
−5.11663 | −0.984695 | |||||||||
0 | 0 | |||||||||
3.81432 | − | 6.60660i | 0.708302 | − | 1.22682i | −0.257185 | − | 0.966362i | ||
0.965487 | − | 0.260453i | ||||||||
0 | 0 | |||||||||
2.51962 | 0.452537 | 0.226269 | − | 0.974065i | ||||||
0.226269 | + | 0.974065i | ||||||||
0 | 0 | |||||||||
0.887030 | + | 1.53638i | 0.154412 | + | 0.267450i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.95043 | + | 6.84235i | −0.649447 | + | 1.12487i | 0.333808 | + | 0.942641i | ||
−0.983255 | + | 0.182234i | ||||||||
0 | 0 | |||||||||
−3.50970 | + | 1.32569i | −0.562001 | + | 0.212281i | |||||
0 | 0 | |||||||||
4.19364 | − | 7.26359i | 0.654936 | − | 1.13438i | −0.326974 | − | 0.945033i | ||
0.981910 | − | 0.189349i | ||||||||
0 | 0 | |||||||||
5.61467 | + | 9.72490i | 0.856230 | + | 1.48303i | 0.875499 | + | 0.483219i | ||
−0.0192697 | + | 0.999814i | ||||||||
0 | 0 | |||||||||
3.04855 | + | 5.28024i | 0.454451 | + | 0.787132i | |||||
0 | 0 | |||||||||
−6.25007 | −0.911666 | −0.455833 | − | 0.890065i | ||||||
−0.455833 | + | 0.890065i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.91353 | 0.407976 | |||||||||
0 | 0 | |||||||||
−1.84212 | −0.253035 | −0.126517 | − | 0.991964i | ||||||
−0.126517 | + | 0.991964i | ||||||||
0 | 0 | |||||||||
2.71093 | − | 4.69547i | 0.365542 | − | 0.633137i | |||||
0 | 0 | |||||||||
−5.71163 | −0.756524 | |||||||||
0 | 0 | |||||||||
−1.34710 | − | 2.33325i | −0.175378 | − | 0.303764i | 0.764914 | − | 0.644132i | ||
−0.940292 | + | 0.340369i | ||||||||
0 | 0 | |||||||||
−3.38846 | − | 5.86899i | −0.433848 | − | 0.751447i | 0.563353 | − | 0.826217i | ||
−0.997201 | + | 0.0747693i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.87191 | + | 7.26345i | 1.10042 | + | 0.900920i | |||||
0 | 0 | |||||||||
−1.79166 | + | 3.10325i | −0.218887 | + | 0.379123i | −0.954468 | − | 0.298314i | ||
0.735581 | + | 0.677437i | ||||||||
0 | 0 | |||||||||
−2.84588 | − | 4.92921i | −0.342604 | − | 0.593407i | |||||
0 | 0 | |||||||||
−2.00501 | − | 3.47278i | −0.237951 | − | 0.412143i | 0.722175 | − | 0.691710i | ||
−0.960126 | + | 0.279567i | ||||||||
0 | 0 | |||||||||
11.7029 | 1.36972 | 0.684862 | − | 0.728673i | ||||||
0.684862 | + | 0.728673i | ||||||||
0 | 0 | |||||||||
−2.66012 | + | 4.60746i | −0.307164 | + | 0.532024i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
13.2439 | 1.49005 | 0.745027 | − | 0.667034i | ||||||
0.745027 | + | 0.667034i | ||||||||
0 | 0 | |||||||||
−0.213883 | + | 0.370457i | −0.0237648 | + | 0.0411618i | |||||
0 | 0 | |||||||||
−8.55336 | −0.938853 | −0.469426 | − | 0.882972i | ||||||
−0.469426 | + | 0.882972i | ||||||||
0 | 0 | |||||||||
−4.45215 | − | 7.71134i | −0.482903 | − | 0.836413i | |||||
0 | 0 | |||||||||
3.96896 | + | 6.87444i | 0.425517 | + | 0.737017i | |||||
0 | 0 | |||||||||
0.105061 | − | 0.181971i | 0.0111364 | − | 0.0192889i | −0.860403 | − | 0.509613i | ||
0.871540 | + | 0.490325i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.31088 | + | 2.27052i | −0.135932 | + | 0.235442i | |||||
0 | 0 | |||||||||
8.72791 | + | 15.1172i | 0.895464 | + | 1.55099i | |||||
0 | 0 | |||||||||
−6.33077 | − | 10.9652i | −0.642792 | − | 1.11335i | −0.984807 | − | 0.173654i | ||
0.342015 | − | 0.939695i | ||||||||
0 | 0 | |||||||||
3.26884 | 0.328531 | |||||||||
0 | 0 | |||||||||
5.77693 | − | 10.0059i | 0.574826 | − | 0.995628i | −0.421234 | − | 0.906952i | ||
0.996061 | − | 0.0886761i | ||||||||
0 | 0 | |||||||||
12.2027 | 1.20237 | 0.601183 | − | 0.799111i | ||||||
0.601183 | + | 0.799111i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.13656 | − | 1.96858i | 0.109875 | − | 0.190310i | −0.805844 | − | 0.592128i | ||
0.915720 | + | 0.401818i | ||||||||
0 | 0 | |||||||||
−4.85215 | −0.464751 | −0.232376 | − | 0.972626i | ||||||
−0.232376 | + | 0.972626i | ||||||||
0 | 0 | |||||||||
−4.11058 | − | 7.11974i | −0.390159 | − | 0.675776i | |||||
0 | 0 | |||||||||
−0.333301 | − | 0.577294i | −0.0313543 | − | 0.0543072i | 0.849922 | − | 0.526908i | ||
−0.881277 | + | 0.472601i | ||||||||
0 | 0 | |||||||||
−8.69754 | + | 15.0646i | −0.811050 | + | 1.40478i | |||||
0 | 0 | |||||||||
−1.11801 | + | 6.82183i | −0.103360 | + | 0.630678i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.04659 | + | 7.00890i | 0.367872 | + | 0.637172i | |||||
0 | 0 | |||||||||
4.36365 | + | 7.55807i | 0.393457 | + | 0.681488i | |||||
0 | 0 | |||||||||
0.359215 | 0.0321292 | |||||||||
0 | 0 | |||||||||
−9.03831 | + | 15.6548i | −0.802020 | + | 1.38914i | 0.116264 | + | 0.993218i | ||
−0.918284 | + | 0.395922i | ||||||||
0 | 0 | |||||||||
−11.6846 | −1.02877 | |||||||||
0 | 0 | |||||||||
−18.7051 | −1.63427 | −0.817135 | − | 0.576446i | ||||||
−0.817135 | + | 0.576446i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−16.2713 | −1.40041 | |||||||||
0 | 0 | |||||||||
11.2574 | + | 19.4984i | 0.961786 | + | 1.66586i | 0.718012 | + | 0.696031i | ||
0.243775 | + | 0.969832i | ||||||||
0 | 0 | |||||||||
−3.61314 | − | 6.25815i | −0.306463 | − | 0.530809i | 0.671123 | − | 0.741346i | ||
−0.977586 | + | 0.210537i | ||||||||
0 | 0 | |||||||||
3.25173 | − | 5.63215i | 0.273845 | − | 0.474313i | |||||
0 | 0 | |||||||||
5.75068 | − | 2.17217i | 0.480896 | − | 0.181646i | |||||
0 | 0 | |||||||||
12.1299 | − | 21.0096i | 1.00733 | − | 1.74475i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.74931 | + | 6.49399i | 0.307155 | + | 0.532009i | 0.977739 | − | 0.209825i | ||
−0.670584 | + | 0.741834i | ||||||||
0 | 0 | |||||||||
−1.98514 | −0.161549 | −0.0807743 | − | 0.996732i | ||||||
−0.0807743 | + | 0.996732i | ||||||||
0 | 0 | |||||||||
2.68420 | − | 4.64917i | 0.217005 | − | 0.375863i | |||||
0 | 0 | |||||||||
8.01261 | 0.643589 | |||||||||
0 | 0 | |||||||||
−4.02469 | −0.321205 | −0.160603 | − | 0.987019i | ||||||
−0.160603 | + | 0.987019i | ||||||||
0 | 0 | |||||||||
0.958401 | − | 1.66000i | 0.0760061 | − | 0.131646i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.99358 | + | 3.45298i | 0.156149 | + | 0.270458i | 0.933477 | − | 0.358638i | ||
−0.777328 | + | 0.629096i | ||||||||
0 | 0 | |||||||||
2.82083 | + | 4.88583i | 0.219602 | + | 0.380361i | |||||
0 | 0 | |||||||||
1.98915 | − | 3.44532i | 0.153925 | − | 0.266607i | −0.778742 | − | 0.627345i | ||
0.932667 | + | 0.360738i | ||||||||
0 | 0 | |||||||||
2.56631 | + | 12.7442i | 0.197409 | + | 0.980321i | |||||
0 | 0 | |||||||||
−5.26206 | + | 9.11415i | −0.402399 | + | 0.696976i | |||||
0 | 0 | |||||||||
11.3603 | + | 19.6766i | 0.863706 | + | 1.49598i | 0.868326 | + | 0.495993i | ||
−0.00462066 | + | 0.999989i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.80343 | 0.210719 | |||||||||
0 | 0 | |||||||||
2.06510 | − | 3.57686i | 0.154353 | − | 0.267347i | −0.778470 | − | 0.627681i | ||
0.932823 | + | 0.360334i | ||||||||
0 | 0 | |||||||||
−2.63446 | −0.195818 | −0.0979091 | − | 0.995195i | ||||||
−0.0979091 | + | 0.995195i | ||||||||
0 | 0 | |||||||||
7.05167 | 0.521274 | |||||||||
0 | 0 | |||||||||
−12.5627 | + | 21.7593i | −0.923629 | + | 1.59977i | |||||
0 | 0 | |||||||||
−4.77386 | −0.349099 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.34005 | + | 4.05309i | 0.169320 | + | 0.293271i | 0.938181 | − | 0.346145i | ||
−0.768861 | + | 0.639416i | ||||||||
0 | 0 | |||||||||
8.96829 | − | 15.5335i | 0.645551 | − | 1.11813i | −0.338622 | − | 0.940922i | ||
0.984174 | − | 0.177206i | ||||||||
0 | 0 | |||||||||
−11.1611 | + | 4.21583i | −0.799266 | + | 0.301902i | |||||
0 | 0 | |||||||||
11.3526 | − | 19.6632i | 0.808838 | − | 1.40095i | −0.104832 | − | 0.994490i | ||
0.913669 | − | 0.406458i | ||||||||
0 | 0 | |||||||||
−3.97980 | − | 6.89322i | −0.282121 | − | 0.488648i | 0.689786 | − | 0.724013i | ||
−0.971907 | + | 0.235366i | ||||||||
0 | 0 | |||||||||
−1.86430 | − | 3.22906i | −0.131498 | − | 0.227761i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
13.3361 | − | 23.0989i | 0.931436 | − | 1.61329i | |||||
0 | 0 | |||||||||
−10.4875 | −0.728931 | |||||||||
0 | 0 | |||||||||
9.35859 | 0.647347 | |||||||||
0 | 0 | |||||||||
−5.08147 | + | 8.80136i | −0.349823 | + | 0.605911i | −0.986218 | − | 0.165453i | ||
0.636395 | + | 0.771363i | ||||||||
0 | 0 | |||||||||
4.17259 | 0.285901 | |||||||||
0 | 0 | |||||||||
17.8552 | + | 30.9260i | 1.21771 | + | 2.10914i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.08869 | + | 10.5459i | −0.411435 | + | 0.712627i | |||||
0 | 0 | |||||||||
1.63275 | − | 9.96269i | 0.109831 | − | 0.670163i | |||||
0 | 0 | |||||||||
−1.33387 | + | 2.31033i | −0.0893224 | + | 0.154711i | −0.907225 | − | 0.420646i | ||
0.817902 | + | 0.575357i | ||||||||
0 | 0 | |||||||||
4.90147 | + | 8.48960i | 0.326765 | + | 0.565973i | |||||
0 | 0 | |||||||||
−12.5757 | − | 21.7817i | −0.834677 | − | 1.44570i | −0.894293 | − | 0.447482i | ||
0.0596159 | − | 0.998221i | ||||||||
0 | 0 | |||||||||
12.3075 | 0.813301 | 0.406651 | − | 0.913584i | ||||||
0.406651 | + | 0.913584i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−21.1440 | −1.38519 | −0.692594 | − | 0.721327i | ||||||
−0.692594 | + | 0.721327i | ||||||||
0 | 0 | |||||||||
−19.8758 | −1.29655 | |||||||||
0 | 0 | |||||||||
−6.89041 | + | 11.9345i | −0.447580 | + | 0.775231i | |||||
0 | 0 | |||||||||
−27.3984 | −1.77225 | −0.886127 | − | 0.463443i | ||||||
−0.886127 | + | 0.463443i | ||||||||
0 | 0 | |||||||||
8.57805 | + | 14.8576i | 0.552561 | + | 0.957064i | 0.998089 | + | 0.0617955i | ||
−0.445528 | + | 0.895268i | ||||||||
0 | 0 | |||||||||
−7.89749 | − | 13.6789i | −0.506624 | − | 0.877499i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.20082 | + | 19.5307i | −0.203663 | + | 1.24271i | |||||
0 | 0 | |||||||||
4.45006 | − | 7.70773i | 0.282011 | − | 0.488457i | |||||
0 | 0 | |||||||||
13.4469 | + | 23.2907i | 0.848759 | + | 1.47009i | 0.882317 | + | 0.470656i | ||
−0.0335582 | + | 0.999437i | ||||||||
0 | 0 | |||||||||
4.66301 | + | 8.07658i | 0.293161 | + | 0.507770i | |||||
0 | 0 | |||||||||
9.26528 | 0.580214 | |||||||||
0 | 0 | |||||||||
−5.65006 | + | 9.78619i | −0.352441 | + | 0.610446i | −0.986677 | − | 0.162694i | ||
0.634235 | + | 0.773140i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
14.6262 | 0.905340 | |||||||||
0 | 0 | |||||||||
0.498739 | − | 0.863842i | 0.0307536 | − | 0.0532668i | −0.850239 | − | 0.526397i | ||
0.880993 | + | 0.473130i | ||||||||
0 | 0 | |||||||||
−5.85810 | −0.359860 | |||||||||
0 | 0 | |||||||||
0.109320 | + | 0.189348i | 0.00669029 | + | 0.0115879i | |||||
0 | 0 | |||||||||
6.56406 | + | 11.3693i | 0.400218 | + | 0.693198i | 0.993752 | − | 0.111611i | ||
−0.593534 | + | 0.804809i | ||||||||
0 | 0 | |||||||||
3.22120 | − | 5.57928i | 0.195674 | − | 0.338917i | −0.751447 | − | 0.659793i | ||
0.947121 | + | 0.320876i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.35864 | − | 7.54939i | 0.262836 | − | 0.455246i | |||||
0 | 0 | |||||||||
11.9907 | + | 20.7685i | 0.720451 | + | 1.24786i | 0.960819 | + | 0.277175i | ||
−0.240369 | + | 0.970682i | ||||||||
0 | 0 | |||||||||
2.41540 | + | 4.18360i | 0.144606 | + | 0.250466i | |||||
0 | 0 | |||||||||
−10.3602 | −0.618035 | −0.309018 | − | 0.951056i | ||||||
−0.309018 | + | 0.951056i | ||||||||
0 | 0 | |||||||||
14.9565 | − | 25.9054i | 0.889071 | − | 1.53992i | 0.0480964 | − | 0.998843i | ||
0.840975 | − | 0.541074i | ||||||||
0 | 0 | |||||||||
−18.1635 | −1.07591 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.57996 | − | 7.93272i | 0.269409 | − | 0.466631i | |||||
0 | 0 | |||||||||
13.1748 | 0.772323 | |||||||||
0 | 0 | |||||||||
−0.184399 | − | 0.319389i | −0.0107727 | − | 0.0186589i | 0.860589 | − | 0.509300i | ||
−0.871362 | + | 0.490642i | ||||||||
0 | 0 | |||||||||
−4.28391 | − | 7.41995i | −0.249419 | − | 0.432006i | |||||
0 | 0 | |||||||||
−4.36177 | + | 7.55481i | −0.253096 | + | 0.438374i | |||||
0 | 0 | |||||||||
−18.4501 | + | 6.96902i | −1.06699 | + | 0.403029i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.01113 | + | 10.4116i | 0.345331 | + | 0.598130i | |||||
0 | 0 | |||||||||
−10.7756 | − | 18.6639i | −0.617010 | − | 1.06869i | |||||
0 | 0 | |||||||||
13.8684 | 0.791511 | 0.395756 | − | 0.918356i | ||||||
0.395756 | + | 0.918356i | ||||||||
0 | 0 | |||||||||
−6.34869 | + | 10.9963i | −0.361165 | + | 0.625555i | |||||
0 | 0 | |||||||||
1.18119 | 0.0669791 | 0.0334895 | − | 0.999439i | ||||||
0.0334895 | + | 0.999439i | ||||||||
0 | 0 | |||||||||
10.5862 | 0.598368 | 0.299184 | − | 0.954195i | ||||||
0.299184 | + | 0.954195i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.48888 | 0.476783 | 0.238392 | − | 0.971169i | ||||||
0.238392 | + | 0.971169i | ||||||||
0 | 0 | |||||||||
−6.50319 | − | 11.2639i | −0.364109 | − | 0.630655i | |||||
0 | 0 | |||||||||
1.18264 | + | 2.04839i | 0.0660084 | + | 0.114330i | |||||
0 | 0 | |||||||||
7.68478 | − | 13.3104i | 0.427592 | − | 0.740612i | |||||
0 | 0 | |||||||||
14.2643 | + | 11.6782i | 0.791240 | + | 0.647790i | |||||
0 | 0 | |||||||||
2.52443 | − | 4.37244i | 0.139601 | − | 0.241796i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.17210 | − | 3.76219i | −0.119389 | − | 0.206788i | 0.800136 | − | 0.599818i | ||
−0.919526 | + | 0.393030i | ||||||||
0 | 0 | |||||||||
−15.1481 | −0.830112 | |||||||||
0 | 0 | |||||||||
−5.69765 | + | 9.86862i | −0.311296 | + | 0.539180i | |||||
0 | 0 | |||||||||
8.59397 | 0.468143 | 0.234072 | − | 0.972219i | ||||||
0.234072 | + | 0.972219i | ||||||||
0 | 0 | |||||||||
0.693626 | 0.0376726 | |||||||||
0 | 0 | |||||||||
2.14790 | − | 3.72027i | 0.116315 | − | 0.201464i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.05015 | − | 15.6753i | −0.487244 | − | 0.843931i | |||||
0 | 0 | |||||||||
−10.4098 | − | 18.0304i | −0.558829 | − | 0.967920i | −0.997595 | − | 0.0693188i | ||
0.438765 | − | 0.898602i | ||||||||
0 | 0 | |||||||||
0.115786 | − | 0.200546i | 0.00619786 | − | 0.0107350i | −0.862910 | − | 0.505358i | ||
0.869108 | + | 0.494623i | ||||||||
0 | 0 | |||||||||
−14.2745 | − | 11.6866i | −0.761917 | − | 0.623784i | |||||
0 | 0 | |||||||||
−9.09972 | + | 15.7612i | −0.484329 | + | 0.838883i | −0.999838 | − | 0.0180014i | ||
0.515509 | + | 0.856884i | ||||||||
0 | 0 | |||||||||
−6.37611 | − | 11.0437i | −0.338409 | − | 0.586141i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.54298 | 0.239769 | 0.119885 | − | 0.992788i | ||||||
0.119885 | + | 0.992788i | ||||||||
0 | 0 | |||||||||
−5.56510 | + | 9.63904i | −0.292900 | + | 0.507318i | |||||
0 | 0 | |||||||||
−8.42128 | −0.442003 | |||||||||
0 | 0 | |||||||||
37.2163 | 1.94799 | |||||||||
0 | 0 | |||||||||
5.01139 | − | 8.67998i | 0.261592 | − | 0.453091i | −0.705073 | − | 0.709135i | ||
0.966665 | + | 0.256044i | ||||||||
0 | 0 | |||||||||
16.0807 | 0.837128 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.21567 | − | 7.30176i | −0.218279 | − | 0.378071i | 0.736003 | − | 0.676979i | ||
−0.954282 | + | 0.298908i | ||||||||
0 | 0 | |||||||||
−0.186889 | + | 0.323702i | −0.00965092 | + | 0.0167159i | |||||
0 | 0 | |||||||||
25.7311 | − | 9.71923i | 1.32522 | − | 0.500566i | |||||
0 | 0 | |||||||||
−5.15804 | + | 8.93398i | −0.264951 | + | 0.458908i | −0.967551 | − | 0.252677i | ||
0.702600 | + | 0.711585i | ||||||||
0 | 0 | |||||||||
−9.40473 | − | 16.2895i | −0.481819 | − | 0.834535i | |||||
0 | 0 | |||||||||
−1.09813 | − | 1.90201i | −0.0561116 | − | 0.0971881i | 0.836605 | − | 0.547806i | ||
−0.892717 | + | 0.450618i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−10.7649 | + | 18.6453i | −0.547209 | + | 0.947794i | |||||
0 | 0 | |||||||||
−32.7955 | −1.66280 | −0.831398 | − | 0.555677i | ||||||
−0.831398 | + | 0.555677i | ||||||||
0 | 0 | |||||||||
15.3161 | 0.774568 | |||||||||
0 | 0 | |||||||||
9.73170 | − | 16.8558i | 0.490899 | − | 0.850262i | |||||
0 | 0 | |||||||||
42.1167 | 2.11912 | |||||||||
0 | 0 | |||||||||
−2.75848 | − | 4.77782i | −0.138444 | − | 0.239792i | 0.788464 | − | 0.615081i | ||
−0.926908 | + | 0.375289i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.66790 | − | 16.7453i | 0.482792 | − | 0.836220i | −0.517013 | − | 0.855977i | ||
0.999805 | + | 0.0197577i | ||||||||
0 | 0 | |||||||||
7.02931 | + | 5.75492i | 0.350155 | + | 0.286673i | |||||
0 | 0 | |||||||||
−0.680167 | + | 1.17808i | −0.0337978 | + | 0.0585395i | |||||
0 | 0 | |||||||||
6.73525 | + | 11.6658i | 0.333854 | + | 0.578252i | |||||
0 | 0 | |||||||||
−18.0322 | − | 31.2326i | −0.891633 | − | 1.54435i | −0.837918 | − | 0.545797i | ||
−0.0537150 | − | 0.998556i | ||||||||
0 | 0 | |||||||||
−23.4276 | −1.15560 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−27.2004 | −1.33522 | |||||||||
0 | 0 | |||||||||
7.51925 | 0.368219 | |||||||||
0 | 0 | |||||||||
4.22915 | − | 7.32510i | 0.206607 | − | 0.357854i | −0.744036 | − | 0.668139i | ||
0.950644 | + | 0.310285i | ||||||||
0 | 0 | |||||||||
−40.2697 | −1.96262 | −0.981312 | − | 0.192424i | ||||||
−0.981312 | + | 0.192424i | ||||||||
0 | 0 | |||||||||
−5.99155 | − | 10.3777i | −0.291319 | − | 0.504579i | |||||
0 | 0 | |||||||||
−7.15818 | − | 12.3983i | −0.347223 | − | 0.601407i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.03449 | + | 6.31226i | −0.0499458 | + | 0.304759i | |||||
0 | 0 | |||||||||
6.53799 | − | 11.3241i | 0.314924 | − | 0.545464i | −0.664498 | − | 0.747290i | ||
0.979421 | + | 0.201827i | ||||||||
0 | 0 | |||||||||
−9.78438 | − | 16.9470i | −0.470207 | − | 0.814423i | 0.529212 | − | 0.848490i | ||
−0.999420 | + | 0.0340664i | ||||||||
0 | 0 | |||||||||
12.6216 | + | 21.8613i | 0.605161 | + | 1.04817i | |||||
0 | 0 | |||||||||
−30.0254 | −1.43631 | |||||||||
0 | 0 | |||||||||
7.19768 | − | 12.4667i | 0.343527 | − | 0.595006i | −0.641558 | − | 0.767074i | ||
0.985085 | + | 0.172069i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.63764 | 0.410386 | 0.205193 | − | 0.978721i | ||||||
0.205193 | + | 0.978721i | ||||||||
0 | 0 | |||||||||
0.334103 | − | 0.578684i | 0.0158380 | − | 0.0274322i | |||||
0 | 0 | |||||||||
−7.80262 | −0.369051 | |||||||||
0 | 0 | |||||||||
−11.4447 | − | 19.8228i | −0.540110 | − | 0.935498i | −0.998897 | − | 0.0469519i | ||
0.458787 | − | 0.888546i | ||||||||
0 | 0 | |||||||||
−7.14990 | − | 12.3840i | −0.336676 | − | 0.583140i | |||||
0 | 0 | |||||||||
1.03281 | − | 1.78888i | 0.0485257 | − | 0.0840490i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12.9024 | − | 22.3476i | 0.603548 | − | 1.04538i | −0.388732 | − | 0.921351i | ||
0.992279 | − | 0.124024i | ||||||||
0 | 0 | |||||||||
7.16331 | + | 12.4072i | 0.334355 | + | 0.579119i | |||||
0 | 0 | |||||||||
3.84106 | + | 6.65291i | 0.178896 | + | 0.309857i | 0.941503 | − | 0.337005i | ||
−0.762607 | + | 0.646862i | ||||||||
0 | 0 | |||||||||
7.95930 | 0.369900 | 0.184950 | − | 0.982748i | ||||||
0.184950 | + | 0.982748i | ||||||||
0 | 0 | |||||||||
−4.16873 | + | 7.22044i | −0.193320 | + | 0.334840i | |||||
0 | 0 | |||||||||
−21.5156 | −0.995621 | −0.497810 | − | 0.867286i | ||||||
−0.497810 | + | 0.867286i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.09393 | − | 3.62679i | 0.0964831 | − | 0.167114i | |||||
0 | 0 | |||||||||
19.1454 | 0.880305 | |||||||||
0 | 0 | |||||||||
14.0328 | + | 24.3055i | 0.643867 | + | 1.11521i | |||||
0 | 0 | |||||||||
−1.76593 | − | 3.05867i | −0.0808562 | − | 0.140047i | |||||
0 | 0 | |||||||||
16.7505 | − | 29.0126i | 0.765348 | − | 1.32562i | −0.174715 | − | 0.984619i | ||
0.940063 | − | 0.341002i | ||||||||
0 | 0 | |||||||||
−26.6492 | + | 10.0660i | −1.21510 | + | 0.458972i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−20.1324 | − | 34.8703i | −0.914165 | − | 1.58338i | |||||
0 | 0 | |||||||||
−7.62298 | − | 13.2034i | −0.345430 | − | 0.598303i | 0.640001 | − | 0.768374i | ||
−0.985432 | + | 0.170071i | ||||||||
0 | 0 | |||||||||
−4.14880 | −0.187615 | |||||||||
0 | 0 | |||||||||
10.9575 | − | 18.9790i | 0.494507 | − | 0.856510i | −0.505473 | − | 0.862842i | ||
0.999980 | + | 0.00633175i | ||||||||
0 | 0 | |||||||||
−21.3603 | −0.962020 | |||||||||
0 | 0 | |||||||||
10.3952 | 0.467229 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−36.3127 | −1.62558 | −0.812791 | − | 0.582555i | ||||||
−0.812791 | + | 0.582555i | ||||||||
0 | 0 | |||||||||
2.06980 | + | 3.58499i | 0.0924717 | + | 0.160166i | |||||
0 | 0 | |||||||||
−13.2906 | − | 23.0199i | −0.592597 | − | 1.02641i | −0.993881 | − | 0.110454i | ||
0.401285 | − | 0.915953i | ||||||||
0 | 0 | |||||||||
18.3711 | − | 31.8198i | 0.817505 | − | 1.41596i | |||||
0 | 0 | |||||||||
−12.8194 | − | 4.31782i | −0.569329 | − | 0.191761i | |||||
0 | 0 | |||||||||
17.5859 | − | 30.4597i | 0.779483 | − | 1.35010i | −0.152757 | − | 0.988264i | ||
0.932240 | − | 0.361841i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−14.0428 | − | 24.3229i | −0.620006 | − | 1.07388i | |||||
0 | 0 | |||||||||
38.8056 | 1.70998 | |||||||||
0 | 0 | |||||||||
−5.32800 | + | 9.22836i | −0.234325 | + | 0.405863i | |||||
0 | 0 | |||||||||
−23.6417 | −1.03775 | |||||||||
0 | 0 | |||||||||
−7.61490 | −0.333615 | −0.166807 | − | 0.985989i | ||||||
−0.166807 | + | 0.985989i | ||||||||
0 | 0 | |||||||||
19.0037 | − | 32.9154i | 0.830975 | − | 1.43929i | −0.0662915 | − | 0.997800i | ||
0.897266 | − | 0.441490i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.52749 | − | 6.10979i | −0.153660 | − | 0.266146i | |||||
0 | 0 | |||||||||
−3.46046 | − | 5.99369i | −0.150455 | − | 0.260595i | |||||
0 | 0 | |||||||||
2.58277 | − | 4.47349i | 0.112083 | − | 0.194133i | |||||
0 | 0 | |||||||||
28.2899 | − | 10.6858i | 1.22537 | − | 0.462852i | |||||
0 | 0 | |||||||||
3.61436 | − | 6.26026i | 0.156262 | − | 0.270654i | |||||
0 | 0 | |||||||||
2.14882 | + | 3.72187i | 0.0927286 | + | 0.160611i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8.91225 | −0.383168 | −0.191584 | − | 0.981476i | ||||||
−0.191584 | + | 0.981476i | ||||||||
0 | 0 | |||||||||
1.37063 | − | 2.37401i | 0.0588195 | − | 0.101878i | |||||
0 | 0 | |||||||||
−15.4303 | −0.660960 | |||||||||
0 | 0 | |||||||||
−16.7066 | −0.714321 | −0.357161 | − | 0.934043i | ||||||
−0.357161 | + | 0.934043i | ||||||||
0 | 0 | |||||||||
6.49662 | − | 11.2525i | 0.277269 | − | 0.480244i | |||||
0 | 0 | |||||||||
41.8744 | 1.78391 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−13.0720 | − | 22.6414i | −0.554876 | − | 0.961074i | |||||
0 | 0 | |||||||||
18.3262 | − | 31.7419i | 0.776507 | − | 1.34495i | −0.157437 | − | 0.987529i | ||
0.933944 | − | 0.357420i | ||||||||
0 | 0 | |||||||||
−6.54808 | + | 39.9550i | −0.276954 | + | 1.68992i | |||||
0 | 0 | |||||||||
2.48370 | − | 4.30189i | 0.104862 | − | 0.181626i | |||||
0 | 0 | |||||||||
−1.96094 | − | 3.39646i | −0.0826440 | − | 0.143144i | 0.821741 | − | 0.569861i | ||
−0.904385 | + | 0.426718i | ||||||||
0 | 0 | |||||||||
−1.05993 | − | 1.83585i | −0.0445914 | − | 0.0772346i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.00915 | − | 1.74790i | 0.0423058 | − | 0.0732757i | −0.844097 | − | 0.536190i | ||
0.886403 | + | 0.462914i | ||||||||
0 | 0 | |||||||||
5.56366 | 0.232832 | 0.116416 | − | 0.993201i | ||||||
0.116416 | + | 0.993201i | ||||||||
0 | 0 | |||||||||
−4.86984 | −0.203441 | |||||||||
0 | 0 | |||||||||
−13.9839 | + | 24.2209i | −0.583171 | + | 1.01008i | |||||
0 | 0 | |||||||||
1.08138 | 0.0450186 | 0.0225093 | − | 0.999747i | ||||||
0.0225093 | + | 0.999747i | ||||||||
0 | 0 | |||||||||
9.33187 | + | 16.1633i | 0.387819 | + | 0.671723i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.57035 | + | 2.71993i | −0.0650374 | + | 0.112648i | |||||
0 | 0 | |||||||||
−3.55536 | + | 21.6940i | −0.146996 | + | 0.896937i | |||||
0 | 0 | |||||||||
11.3515 | − | 19.6613i | 0.468526 | − | 0.811510i | −0.530827 | − | 0.847480i | ||
0.999353 | + | 0.0359699i | ||||||||
0 | 0 | |||||||||
6.91522 | + | 11.9775i | 0.284937 | + | 0.493525i | |||||
0 | 0 | |||||||||
11.8128 | + | 20.4604i | 0.485915 | + | 0.841629i | |||||
0 | 0 | |||||||||
−22.0550 | −0.905692 | −0.452846 | − | 0.891589i | ||||||
−0.452846 | + | 0.891589i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.28230 | 0.338972 | |||||||||
0 | 0 | |||||||||
6.16283 | 0.251807 | 0.125903 | − | 0.992043i | ||||||
0.125903 | + | 0.992043i | ||||||||
0 | 0 | |||||||||
9.13735 | − | 15.8264i | 0.372720 | − | 0.645571i | −0.617263 | − | 0.786757i | ||
0.989983 | + | 0.141187i | ||||||||
0 | 0 | |||||||||
−6.87023 | −0.279777 | |||||||||
0 | 0 | |||||||||
12.8685 | + | 22.2889i | 0.523179 | + | 0.906173i | |||||
0 | 0 | |||||||||
7.45389 | + | 12.9105i | 0.302544 | + | 0.524022i | 0.976712 | − | 0.214557i | ||
−0.674167 | + | 0.738579i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−17.4366 | − | 14.2754i | −0.705411 | − | 0.577521i | |||||
0 | 0 | |||||||||
−2.32174 | + | 4.02137i | −0.0937742 | + | 0.162422i | −0.909096 | − | 0.416586i | ||
0.815322 | + | 0.579008i | ||||||||
0 | 0 | |||||||||
13.8768 | + | 24.0353i | 0.559566 | + | 0.969197i | |||||
0 | 0 | |||||||||
−5.34393 | − | 9.25597i | −0.215139 | − | 0.372631i | 0.738177 | − | 0.674607i | ||
−0.953315 | + | 0.301976i | ||||||||
0 | 0 | |||||||||
20.5826 | 0.827283 | 0.413642 | − | 0.910440i | ||||||
0.413642 | + | 0.910440i | ||||||||
0 | 0 | |||||||||
13.9940 | − | 24.2383i | 0.561559 | − | 0.972648i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.4225 | −0.976898 | |||||||||
0 | 0 | |||||||||
−4.86900 | + | 8.43335i | −0.194449 | + | 0.336796i | |||||
0 | 0 | |||||||||
22.1225 | 0.882083 | |||||||||
0 | 0 | |||||||||
−21.9750 | − | 38.0619i | −0.874812 | − | 1.51522i | −0.856963 | − | 0.515379i | ||
−0.0178498 | − | 0.999841i | ||||||||
0 | 0 | |||||||||
−5.28748 | − | 9.15818i | −0.210158 | − | 0.364005i | |||||
0 | 0 | |||||||||
−28.7426 | + | 49.7837i | −1.14062 | + | 1.97560i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.84415 | − | 6.65827i | 0.152072 | − | 0.263397i | |||||
0 | 0 | |||||||||
−24.3981 | − | 42.2587i | −0.963666 | − | 1.66912i | −0.713157 | − | 0.701005i | ||
−0.250509 | − | 0.968114i | ||||||||
0 | 0 | |||||||||
2.08350 | + | 3.60873i | 0.0821653 | + | 0.142315i | 0.904180 | − | 0.427152i | ||
−0.822014 | + | 0.569467i | ||||||||
0 | 0 | |||||||||
−37.1580 | −1.46310 | |||||||||
0 | 0 | |||||||||
8.13081 | − | 14.0830i | 0.319655 | − | 0.553659i | −0.660761 | − | 0.750596i | ||
0.980416 | + | 0.196938i | ||||||||
0 | 0 | |||||||||
−4.59346 | −0.180309 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.91378 | + | 6.77886i | −0.153158 | + | 0.265277i | −0.932387 | − | 0.361462i | ||
0.779229 | + | 0.626740i | ||||||||
0 | 0 | |||||||||
−59.4838 | −2.32422 | |||||||||
0 | 0 | |||||||||
11.2189 | + | 19.4316i | 0.437690 | + | 0.758100i | |||||
0 | 0 | |||||||||
20.3114 | + | 35.1805i | 0.791221 | + | 1.37044i | 0.925211 | + | 0.379453i | ||
−0.133990 | + | 0.990983i | ||||||||
0 | 0 | |||||||||
−15.4342 | + | 26.7328i | −0.600320 | + | 1.03979i | 0.392452 | + | 0.919773i | ||
−0.992772 | + | 0.120013i | ||||||||
0 | 0 | |||||||||
8.12825 | + | 6.65462i | 0.315675 | + | 0.258444i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.8644 | + | 36.1381i | 0.807871 | + | 1.39927i | |||||
0 | 0 | |||||||||
−1.38794 | − | 2.40399i | −0.0536610 | − | 0.0929436i | |||||
0 | 0 | |||||||||
−11.5543 | −0.446047 | |||||||||
0 | 0 | |||||||||
−13.5310 | + | 23.4364i | −0.521581 | + | 0.903405i | 0.478104 | + | 0.878303i | ||
−0.999685 | + | 0.0251020i | ||||||||
0 | 0 | |||||||||
−26.1611 | −1.00694 | |||||||||
0 | 0 | |||||||||
−16.8472 | −0.647490 | −0.323745 | − | 0.946144i | ||||||
−0.323745 | + | 0.946144i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
26.1710 | 1.00288 | |||||||||
0 | 0 | |||||||||
−9.89038 | − | 17.1306i | −0.378445 | − | 0.655486i | 0.612391 | − | 0.790555i | ||
−0.990836 | + | 0.135069i | ||||||||
0 | 0 | |||||||||
35.7996 | + | 62.0067i | 1.36783 | + | 2.36915i | |||||
0 | 0 | |||||||||
−6.40322 | + | 11.0907i | −0.244298 | + | 0.423137i | |||||
0 | 0 | |||||||||
−5.13920 | − | 4.20748i | −0.195788 | − | 0.160292i | |||||
0 | 0 | |||||||||
−4.64021 | + | 8.03707i | −0.176522 | + | 0.305745i | −0.940687 | − | 0.339276i | ||
0.764165 | + | 0.645021i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11.4901 | − | 19.9015i | −0.435845 | − | 0.754905i | |||||
0 | 0 | |||||||||
−23.4845 | −0.889539 | |||||||||
0 | 0 | |||||||||
11.0006 | − | 19.0536i | 0.416081 | − | 0.720673i | |||||
0 | 0 | |||||||||
34.6015 | 1.30688 | 0.653441 | − | 0.756977i | ||||||
0.653441 | + | 0.756977i | ||||||||
0 | 0 | |||||||||
−43.3686 | −1.63568 | |||||||||
0 | 0 | |||||||||
10.3408 | − | 17.9107i | 0.389456 | − | 0.674558i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.55823 | + | 13.0912i | 0.283855 | + | 0.491652i | 0.972331 | − | 0.233608i | ||
−0.688476 | + | 0.725260i | ||||||||
0 | 0 | |||||||||
12.6961 | + | 21.9903i | 0.476141 | + | 0.824700i | |||||
0 | 0 | |||||||||
−6.89116 | + | 11.9358i | −0.258076 | + | 0.447001i | |||||
0 | 0 | |||||||||
18.2877 | − | 6.90769i | 0.683920 | − | 0.258333i | |||||
0 | 0 | |||||||||
14.2546 | − | 24.6896i | 0.532346 | − | 0.922051i | |||||
0 | 0 | |||||||||
−10.6380 | − | 18.4255i | −0.396730 | − | 0.687157i | 0.596590 | − | 0.802546i | ||
−0.993320 | + | 0.115389i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−17.8516 | −0.663909 | |||||||||
0 | 0 | |||||||||
19.5025 | − | 33.7793i | 0.724304 | − | 1.25453i | |||||
0 | 0 | |||||||||
−10.5609 | −0.391684 | −0.195842 | − | 0.980635i | ||||||
−0.195842 | + | 0.980635i | ||||||||
0 | 0 | |||||||||
15.1520 | 0.561186 | |||||||||
0 | 0 | |||||||||
15.7212 | − | 27.2299i | 0.581468 | − | 1.00713i | |||||
0 | 0 | |||||||||
−8.81656 | −0.325647 | −0.162824 | − | 0.986655i | ||||||
−0.162824 | + | 0.986655i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.05468 | + | 5.29086i | 0.112521 | + | 0.194891i | |||||
0 | 0 | |||||||||
−14.5384 | + | 25.1812i | −0.534803 | + | 0.926307i | 0.464369 | + | 0.885642i | ||
−0.999173 | + | 0.0406651i | ||||||||
0 | 0 | |||||||||
−15.9345 | − | 13.0456i | −0.585368 | − | 0.479242i | |||||
0 | 0 | |||||||||
−19.3225 | + | 33.4675i | −0.708872 | + | 1.22780i | 0.256404 | + | 0.966570i | ||
−0.965276 | + | 0.261233i | ||||||||
0 | 0 | |||||||||
11.9231 | + | 20.6515i | 0.436830 | + | 0.756611i | |||||
0 | 0 | |||||||||
−8.19957 | − | 14.2021i | −0.300006 | − | 0.519626i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.1942 | − | 34.9775i | 0.736898 | − | 1.27635i | −0.216987 | − | 0.976174i | ||
0.953885 | − | 0.300171i | ||||||||
0 | 0 | |||||||||
−27.9840 | −1.01979 | |||||||||
0 | 0 | |||||||||
−6.31293 | −0.229751 | |||||||||
0 | 0 | |||||||||
11.2192 | − | 19.4322i | 0.407768 | − | 0.706275i | −0.586871 | − | 0.809680i | ||
0.994639 | + | 0.103405i | ||||||||
0 | 0 | |||||||||
−9.70411 | −0.352237 | |||||||||
0 | 0 | |||||||||
−8.58250 | − | 14.8653i | −0.311115 | − | 0.538868i | 0.667489 | − | 0.744620i | ||
−0.978604 | + | 0.205752i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.53599 | − | 14.7848i | 0.308619 | − | 0.534544i | |||||
0 | 0 | |||||||||
1.57105 | − | 9.58622i | 0.0567274 | − | 0.346138i | |||||
0 | 0 | |||||||||
−21.4658 | + | 37.1798i | −0.774076 | + | 1.34074i | 0.161236 | + | 0.986916i | ||
−0.935312 | + | 0.353823i | ||||||||
0 | 0 | |||||||||
−5.87912 | − | 10.1829i | −0.211731 | − | 0.366729i | |||||
0 | 0 | |||||||||
3.36534 | + | 5.82893i | 0.121043 | + | 0.209652i | 0.920179 | − | 0.391498i | ||
−0.799136 | + | 0.601150i | ||||||||
0 | 0 | |||||||||
12.8827 | 0.462761 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
46.0386 | 1.64950 | |||||||||
0 | 0 | |||||||||
−6.83685 | −0.244642 | |||||||||
0 | 0 | |||||||||
−19.5165 | + | 33.8035i | −0.697461 | + | 1.20804i | |||||
0 | 0 | |||||||||
−12.7989 | −0.456811 | |||||||||
0 | 0 | |||||||||
19.1240 | + | 33.1238i | 0.681699 | + | 1.18074i | 0.974462 | + | 0.224552i | ||
−0.292764 | + | 0.956185i | ||||||||
0 | 0 | |||||||||
0.518959 | + | 0.898863i | 0.0184754 | + | 0.0320004i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.95178 | − | 24.1129i | 0.140332 | − | 0.856274i | |||||
0 | 0 | |||||||||
3.04780 | − | 5.27894i | 0.108094 | − | 0.187225i | |||||
0 | 0 | |||||||||
21.3120 | + | 36.9134i | 0.754909 | + | 1.30754i | 0.945420 | + | 0.325855i | ||
−0.190511 | + | 0.981685i | ||||||||
0 | 0 | |||||||||
8.75014 | + | 15.1557i | 0.309558 | + | 0.536170i | |||||
0 | 0 | |||||||||
0.402862 | 0.0142344 | |||||||||
0 | 0 | |||||||||
9.97640 | − | 17.2796i | 0.352059 | − | 0.609785i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−13.6604 | −0.480867 | |||||||||
0 | 0 | |||||||||
18.7448 | − | 32.4670i | 0.659033 | − | 1.14148i | −0.321833 | − | 0.946797i | ||
0.980866 | − | 0.194683i | ||||||||
0 | 0 | |||||||||
25.4069 | 0.892156 | 0.446078 | − | 0.894994i | ||||||
0.446078 | + | 0.894994i | ||||||||
0 | 0 | |||||||||
3.35179 | + | 5.80547i | 0.117552 | + | 0.203607i | |||||
0 | 0 | |||||||||
6.33975 | + | 10.9808i | 0.222072 | + | 0.384640i | |||||
0 | 0 | |||||||||
−30.8195 | + | 53.3809i | −1.07824 | + | 1.86756i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0406154 | − | 0.0703480i | 0.00141749 | − | 0.00245516i | −0.865316 | − | 0.501227i | ||
0.866733 | + | 0.498772i | ||||||||
0 | 0 | |||||||||
0.624767 | + | 1.08213i | 0.0217780 | + | 0.0377206i | 0.876709 | − | 0.481021i | ||
−0.854931 | + | 0.518742i | ||||||||
0 | 0 | |||||||||
4.53535 | + | 7.85545i | 0.157901 | + | 0.273492i | |||||
0 | 0 | |||||||||
32.9535 | 1.14591 | 0.572954 | − | 0.819588i | ||||||
0.572954 | + | 0.819588i | ||||||||
0 | 0 | |||||||||
−8.61206 | + | 14.9165i | −0.299109 | + | 0.518072i | −0.975932 | − | 0.218073i | ||
0.676823 | + | 0.736146i | ||||||||
0 | 0 | |||||||||
−24.9536 | −0.865631 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.32569 | − | 10.9564i | 0.218909 | − | 0.379162i | |||||
0 | 0 | |||||||||
−12.8920 | −0.445611 | |||||||||
0 | 0 | |||||||||
−14.7357 | − | 25.5229i | −0.508731 | − | 0.881149i | −0.999949 | − | 0.0101117i | ||
0.491217 | − | 0.871037i | ||||||||
0 | 0 | |||||||||
−14.5981 | − | 25.2847i | −0.503383 | − | 0.871886i | |||||
0 | 0 | |||||||||
5.39008 | − | 9.33590i | 0.185644 | − | 0.321545i | |||||
0 | 0 | |||||||||
8.16110 | + | 40.5276i | 0.280750 | + | 1.39419i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
15.5628 | + | 26.9556i | 0.534115 | + | 0.925115i | |||||
0 | 0 | |||||||||
−21.6089 | − | 37.4276i | −0.740742 | − | 1.28300i | |||||
0 | 0 | |||||||||
−17.8668 | −0.611747 | −0.305873 | − | 0.952072i | ||||||
−0.305873 | + | 0.952072i | ||||||||
0 | 0 | |||||||||
−16.7338 | + | 28.9838i | −0.572284 | + | 0.991225i | |||||
0 | 0 | |||||||||
−20.1614 | −0.688701 | −0.344351 | − | 0.938841i | ||||||
−0.344351 | + | 0.938841i | ||||||||
0 | 0 | |||||||||
−11.9734 | −0.408526 | −0.204263 | − | 0.978916i | ||||||
−0.204263 | + | 0.978916i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
39.7010 | 1.35144 | 0.675719 | − | 0.737160i | ||||||
0.675719 | + | 0.737160i | ||||||||
0 | 0 | |||||||||
36.1267 | + | 62.5732i | 1.22834 | + | 2.12755i | |||||
0 | 0 | |||||||||
4.76564 | + | 8.25432i | 0.161849 | + | 0.280331i | |||||
0 | 0 | |||||||||
11.2900 | − | 19.5549i | 0.382988 | − | 0.663355i | |||||
0 | 0 | |||||||||
−12.0864 | + | 4.56532i | −0.409532 | + | 0.154690i | |||||
0 | 0 | |||||||||
12.1378 | − | 21.0233i | 0.410803 | − | 0.711532i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
22.8328 | + | 39.5476i | 0.771010 | + | 1.33543i | 0.937010 | + | 0.349302i | ||
−0.166000 | + | 0.986126i | ||||||||
0 | 0 | |||||||||
0.383750 | 0.0129436 | |||||||||
0 | 0 | |||||||||
16.6420 | − | 28.8249i | 0.560685 | − | 0.971134i | −0.436752 | − | 0.899582i | ||
0.997437 | − | 0.0715523i | ||||||||
0 | 0 | |||||||||
32.3115 | 1.08737 | 0.543685 | − | 0.839289i | ||||||
0.543685 | + | 0.839289i | ||||||||
0 | 0 | |||||||||
8.91516 | 0.299680 | |||||||||
0 | 0 | |||||||||
−16.7530 | + | 29.0170i | −0.562509 | + | 0.974295i | 0.434767 | + | 0.900543i | ||
−0.997277 | + | 0.0737520i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.364658 | + | 0.631606i | 0.0122165 | + | 0.0211596i | |||||
0 | 0 | |||||||||
−17.1536 | − | 29.7109i | −0.574024 | − | 0.994239i | |||||
0 | 0 | |||||||||
6.56721 | − | 11.3747i | 0.219517 | − | 0.380215i | |||||
0 | 0 | |||||||||
3.31899 | − | 20.2518i | 0.110818 | − | 0.676187i | |||||
0 | 0 | |||||||||
9.61064 | − | 16.6461i | 0.320533 | − | 0.555179i | |||||
0 | 0 | |||||||||
2.57898 | + | 4.46693i | 0.0859183 | + | 0.148815i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8.37783 | −0.278488 | |||||||||
0 | 0 | |||||||||
19.4451 | − | 33.6798i | 0.645663 | − | 1.11832i | −0.338485 | − | 0.940972i | ||
0.984148 | − | 0.177349i | ||||||||
0 | 0 | |||||||||
22.1519 | 0.734733 | |||||||||
0 | 0 | |||||||||
−41.0133 | −1.35883 | −0.679415 | − | 0.733754i | ||||||
−0.679415 | + | 0.733754i | ||||||||
0 | 0 | |||||||||
−7.29148 | + | 12.6292i | −0.241313 | + | 0.417966i | |||||
0 | 0 | |||||||||
22.4249 | 0.741345 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11.9574 | − | 20.7108i | −0.394438 | − | 0.683186i | 0.598592 | − | 0.801054i | ||
−0.993029 | + | 0.117868i | ||||||||
0 | 0 | |||||||||
−7.21532 | + | 12.4973i | −0.237753 | + | 0.411800i | |||||
0 | 0 | |||||||||
2.33833 | − | 14.2680i | 0.0769671 | − | 0.469637i | |||||
0 | 0 | |||||||||
−20.1984 | + | 34.9846i | −0.664119 | + | 1.15029i | |||||
0 | 0 | |||||||||
11.6979 | + | 20.2614i | 0.384211 | + | 0.665473i | |||||
0 | 0 | |||||||||
−7.74124 | − | 13.4082i | −0.253982 | − | 0.439909i | 0.710637 | − | 0.703559i | ||
−0.964618 | + | 0.263650i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.614538 | + | 1.06441i | −0.0201191 | + | 0.0348472i | |||||
0 | 0 | |||||||||
−15.1813 | −0.496481 | |||||||||
0 | 0 | |||||||||
−38.8172 | −1.26810 | −0.634052 | − | 0.773290i | ||||||
−0.634052 | + | 0.773290i | ||||||||
0 | 0 | |||||||||
−5.50770 | + | 9.53961i | −0.179737 | + | 0.311313i | |||||
0 | 0 | |||||||||
5.28344 | 0.172235 | 0.0861177 | − | 0.996285i | ||||||
0.0861177 | + | 0.996285i | ||||||||
0 | 0 | |||||||||
22.9392 | + | 39.7319i | 0.747003 | + | 1.29385i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.98486 | + | 6.90198i | −0.129491 | + | 0.224284i | −0.923479 | − | 0.383648i | ||
0.793989 | + | 0.607932i | ||||||||
0 | 0 | |||||||||
32.6492 | + | 26.7300i | 1.05984 | + | 0.867691i | |||||
0 | 0 | |||||||||
−4.41651 | + | 7.64963i | −0.143215 | + | 0.248056i | |||||
0 | 0 | |||||||||
−8.48138 | − | 14.6902i | −0.274739 | − | 0.475862i | 0.695330 | − | 0.718690i | ||
−0.970069 | + | 0.242829i | ||||||||
0 | 0 | |||||||||
7.44157 | + | 12.8892i | 0.240804 | + | 0.417084i | |||||
0 | 0 | |||||||||
13.5337 | 0.437482 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.6515 | −0.795210 | |||||||||
0 | 0 | |||||||||
4.35820 | 0.140441 | |||||||||
0 | 0 | |||||||||
28.5199 | − | 49.3980i | 0.918089 | − | 1.59018i | |||||
0 | 0 | |||||||||
21.4177 | 0.688746 | 0.344373 | − | 0.938833i | ||||||
0.344373 | + | 0.938833i | ||||||||
0 | 0 | |||||||||
7.99633 | + | 13.8500i | 0.256879 | + | 0.444927i | |||||
0 | 0 | |||||||||
−8.46512 | − | 14.6620i | −0.271659 | − | 0.470527i | 0.697628 | − | 0.716460i | ||
−0.969287 | + | 0.245933i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−17.9449 | + | 6.77822i | −0.574698 | + | 0.217077i | |||||
0 | 0 | |||||||||
−20.4387 | + | 35.4008i | −0.653891 | + | 1.13257i | 0.328279 | + | 0.944581i | ||
−0.982171 | + | 0.187992i | ||||||||
0 | 0 | |||||||||
−0.179123 | − | 0.310250i | −0.00572479 | − | 0.00991562i | |||||
0 | 0 | |||||||||
−4.65145 | − | 8.05655i | −0.148509 | − | 0.257226i | |||||
0 | 0 | |||||||||
8.53733 | 0.272299 | 0.136149 | − | 0.990688i | ||||||
0.136149 | + | 0.990688i | ||||||||
0 | 0 | |||||||||
36.1022 | − | 62.5308i | 1.15031 | − | 1.99240i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−61.4245 | −1.95319 | |||||||||
0 | 0 | |||||||||
−17.5874 | + | 30.4623i | −0.558682 | + | 0.967666i | 0.438924 | + | 0.898524i | ||
−0.997607 | + | 0.0691423i | ||||||||
0 | 0 | |||||||||
4.52032 | 0.143448 | |||||||||
0 | 0 | |||||||||
−12.6561 | − | 21.9211i | −0.401226 | − | 0.694944i | |||||
0 | 0 | |||||||||
−20.3109 | − | 35.1795i | −0.643252 | − | 1.11414i | −0.984702 | − | 0.174245i | ||
0.341450 | − | 0.939900i | ||||||||
0 | 0 | |||||||||
20.2129 | − | 35.0097i | 0.639507 | − | 1.10766i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2548.2.k.i.1569.3 | 18 | ||
7.2 | even | 3 | 2548.2.i.n.165.3 | 18 | |||
7.3 | odd | 6 | 364.2.l.a.9.3 | yes | 18 | ||
7.4 | even | 3 | 2548.2.l.n.373.7 | 18 | |||
7.5 | odd | 6 | 364.2.i.a.165.7 | ✓ | 18 | ||
7.6 | odd | 2 | 2548.2.k.h.1569.7 | 18 | |||
13.3 | even | 3 | inner | 2548.2.k.i.393.3 | 18 | ||
21.5 | even | 6 | 3276.2.u.k.1621.1 | 18 | |||
21.17 | even | 6 | 3276.2.x.k.2557.1 | 18 | |||
91.3 | odd | 6 | 364.2.i.a.289.7 | yes | 18 | ||
91.16 | even | 3 | 2548.2.l.n.1537.7 | 18 | |||
91.55 | odd | 6 | 2548.2.k.h.393.7 | 18 | |||
91.68 | odd | 6 | 364.2.l.a.81.3 | yes | 18 | ||
91.81 | even | 3 | 2548.2.i.n.1745.3 | 18 | |||
273.68 | even | 6 | 3276.2.x.k.2629.1 | 18 | |||
273.185 | even | 6 | 3276.2.u.k.289.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
364.2.i.a.165.7 | ✓ | 18 | 7.5 | odd | 6 | ||
364.2.i.a.289.7 | yes | 18 | 91.3 | odd | 6 | ||
364.2.l.a.9.3 | yes | 18 | 7.3 | odd | 6 | ||
364.2.l.a.81.3 | yes | 18 | 91.68 | odd | 6 | ||
2548.2.i.n.165.3 | 18 | 7.2 | even | 3 | |||
2548.2.i.n.1745.3 | 18 | 91.81 | even | 3 | |||
2548.2.k.h.393.7 | 18 | 91.55 | odd | 6 | |||
2548.2.k.h.1569.7 | 18 | 7.6 | odd | 2 | |||
2548.2.k.i.393.3 | 18 | 13.3 | even | 3 | inner | ||
2548.2.k.i.1569.3 | 18 | 1.1 | even | 1 | trivial | ||
2548.2.l.n.373.7 | 18 | 7.4 | even | 3 | |||
2548.2.l.n.1537.7 | 18 | 91.16 | even | 3 | |||
3276.2.u.k.289.1 | 18 | 273.185 | even | 6 | |||
3276.2.u.k.1621.1 | 18 | 21.5 | even | 6 | |||
3276.2.x.k.2557.1 | 18 | 21.17 | even | 6 | |||
3276.2.x.k.2629.1 | 18 | 273.68 | even | 6 |