Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1216.s (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 31.3 | ||
Root | of defining polynomial | ||
Character | 1216.31 | ||
Dual form | 1216.2.s.g.863.3 |
-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 | |||||||||
−0.121621 | + | 0.0702177i | −0.0702177 | + | 0.0405402i | −0.534698 | − | 0.845043i | ||
0.464480 | + | 0.885584i | ||||||||
0 | 0 | |||||||||
−1.50000 | + | 0.866025i | −0.670820 | + | 0.387298i | −0.796387 | − | 0.604787i | ||
0.125567 | + | 0.992085i | ||||||||
0 | 0 | |||||||||
2.00000i | 0.755929i | 0.925820 | + | 0.377964i | ||||||
−0.925820 | + | 0.377964i | ||||||||
0 | 0 | |||||||||
−1.49014 | + | 2.58100i | −0.496713 | + | 0.860332i | |||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
2.13057 | − | 3.69026i | 0.590915 | − | 1.02349i | −0.403194 | − | 0.915114i | ||
0.994109 | − | 0.108380i | ||||||||
0 | 0 | |||||||||
0.121621 | − | 0.210653i | 0.0314023 | − | 0.0543904i | |||||
0 | 0 | |||||||||
1.99014 | + | 3.44702i | 0.482680 | + | 0.836026i | 0.999802 | − | 0.0198857i | ||
−0.517123 | + | 0.855911i | ||||||||
0 | 0 | |||||||||
4.31305 | − | 0.630574i | 0.989481 | − | 0.144664i | |||||
0 | 0 | |||||||||
−0.140435 | − | 0.243241i | −0.0306455 | − | 0.0530796i | |||||
0 | 0 | |||||||||
−6.40996 | − | 3.70079i | −1.33657 | − | 0.771668i | −0.350272 | − | 0.936648i | ||
−0.986297 | + | 0.164980i | ||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | |||||
0 | 0 | |||||||||
− | 0.839843i | − | 0.161628i | |||||||
0 | 0 | |||||||||
−1.99014 | + | 3.44702i | −0.369560 | + | 0.640096i | −0.989497 | − | 0.144556i | ||
0.619937 | + | 0.784651i | ||||||||
0 | 0 | |||||||||
−8.62609 | −1.54929 | −0.774646 | − | 0.632395i | ||||||
−0.774646 | + | 0.632395i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.73205 | − | 3.00000i | −0.292770 | − | 0.507093i | |||||
0 | 0 | |||||||||
−7.26115 | −1.19373 | −0.596863 | − | 0.802343i | ||||||
−0.596863 | + | 0.802343i | ||||||||
0 | 0 | |||||||||
0.598416i | 0.0958232i | |||||||||
0 | 0 | |||||||||
−6.39172 | + | 3.69026i | −0.998219 | + | 0.576322i | −0.907721 | − | 0.419574i | ||
−0.0904984 | + | 0.995897i | ||||||||
0 | 0 | |||||||||
−6.16672 | − | 10.6811i | −0.940416 | − | 1.62885i | −0.764680 | − | 0.644411i | ||
−0.175736 | − | 0.984437i | ||||||||
0 | 0 | |||||||||
− | 5.16199i | − | 0.769504i | |||||||
0 | 0 | |||||||||
0.364862 | + | 0.210653i | 0.0532206 | + | 0.0307269i | 0.526374 | − | 0.850253i | ||
−0.473154 | + | 0.880980i | ||||||||
0 | 0 | |||||||||
3.00000 | 0.428571 | |||||||||
0 | 0 | |||||||||
−0.484084 | − | 0.279486i | −0.0677853 | − | 0.0391359i | |||||
0 | 0 | |||||||||
−5.48028 | + | 9.49212i | −0.752774 | + | 1.30384i | 0.193699 | + | 0.981061i | ||
−0.946473 | + | 0.322782i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.480278 | + | 0.379543i | −0.0636144 | + | 0.0502717i | |||||
0 | 0 | |||||||||
1.21381 | − | 0.700792i | 0.158024 | − | 0.0912353i | −0.418903 | − | 0.908031i | ||
0.576927 | + | 0.816796i | ||||||||
0 | 0 | |||||||||
1.92131 | + | 1.10927i | 0.245998 | + | 0.142027i | 0.617930 | − | 0.786233i | ||
−0.371932 | + | 0.928260i | ||||||||
0 | 0 | |||||||||
−5.16199 | − | 2.98028i | −0.650350 | − | 0.375480i | |||||
0 | 0 | |||||||||
7.38053i | 0.915442i | |||||||||
0 | 0 | |||||||||
1.81951 | + | 1.05050i | 0.222289 | + | 0.128338i | 0.607010 | − | 0.794695i | ||
−0.384721 | + | 0.923033i | ||||||||
0 | 0 | |||||||||
1.03944 | 0.125134 | |||||||||
0 | 0 | |||||||||
−0.970566 | − | 1.68107i | −0.115185 | − | 0.199506i | 0.802669 | − | 0.596425i | ||
−0.917854 | + | 0.396919i | ||||||||
0 | 0 | |||||||||
2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | ||
−0.681822 | + | 0.731519i | ||||||||
0 | 0 | |||||||||
− | 0.280871i | − | 0.0324322i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.70262 | + | 4.68107i | 0.304068 | + | 0.526662i | 0.977053 | − | 0.212994i | ||
−0.672985 | + | 0.739656i | ||||||||
0 | 0 | |||||||||
−4.41145 | − | 7.64085i | −0.490161 | − | 0.848983i | |||||
0 | 0 | |||||||||
−8.62609 | −0.946837 | −0.473418 | − | 0.880838i | ||||||
−0.473418 | + | 0.880838i | ||||||||
0 | 0 | |||||||||
−5.97042 | − | 3.44702i | −0.647583 | − | 0.373882i | |||||
0 | 0 | |||||||||
− | 0.558972i | − | 0.0599281i | |||||||
0 | 0 | |||||||||
14.5491 | + | 8.39993i | 1.54220 | + | 0.890391i | 0.998699 | + | 0.0509840i | ||
0.543503 | + | 0.839407i | ||||||||
0 | 0 | |||||||||
7.38053 | + | 4.26115i | 0.773689 | + | 0.446690i | |||||
0 | 0 | |||||||||
1.04911 | − | 0.605704i | 0.108788 | − | 0.0628086i | |||||
0 | 0 | |||||||||
−5.92348 | + | 4.68107i | −0.607736 | + | 0.480268i | |||||
0 | 0 | |||||||||
−6.39172 | + | 3.69026i | −0.648981 | + | 0.374689i | −0.788066 | − | 0.615591i | ||
0.139085 | + | 0.990280i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.0295831 | + | 0.0170798i | 0.00294363 | + | 0.00169951i | 0.501471 | − | 0.865174i | ||
−0.498527 | + | 0.866874i | ||||||||
0 | 0 | |||||||||
−3.95058 | −0.389263 | −0.194631 | − | 0.980876i | ||||||
−0.194631 | + | 0.980876i | ||||||||
0 | 0 | |||||||||
0.421306 | + | 0.243241i | 0.0411153 | + | 0.0237379i | |||||
0 | 0 | |||||||||
7.96056i | 0.769576i | 0.923005 | + | 0.384788i | ||||||
−0.923005 | + | 0.384788i | ||||||||
0 | 0 | |||||||||
−7.70927 | − | 13.3528i | −0.738414 | − | 1.27897i | −0.953209 | − | 0.302311i | ||
0.214795 | − | 0.976659i | ||||||||
0 | 0 | |||||||||
0.883105 | − | 0.509861i | 0.0838206 | − | 0.0483939i | |||||
0 | 0 | |||||||||
13.0632i | 1.22888i | 0.788964 | + | 0.614439i | ||||||
−0.788964 | + | 0.614439i | ||||||||
0 | 0 | |||||||||
12.8199 | 1.19546 | |||||||||
0 | 0 | |||||||||
6.34970 | + | 10.9980i | 0.587030 | + | 1.01677i | |||||
0 | 0 | |||||||||
−6.89404 | + | 3.98028i | −0.631976 | + | 0.364871i | |||||
0 | 0 | |||||||||
−11.0000 | −1.00000 | |||||||||
0 | 0 | |||||||||
0.518243 | − | 0.897624i | 0.0467284 | − | 0.0809360i | |||||
0 | 0 | |||||||||
− | 12.1244i | − | 1.08444i | |||||||
0 | 0 | |||||||||
6.40996 | − | 11.1024i | 0.568792 | − | 0.985177i | −0.427894 | − | 0.903829i | ||
0.996686 | − | 0.0813476i | ||||||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 0.132068 | + | 0.0762493i | |||||
0 | 0 | |||||||||
−8.99096 | − | 15.5728i | −0.785543 | − | 1.36060i | −0.928674 | − | 0.370897i | ||
0.143130 | − | 0.989704i | ||||||||
0 | 0 | |||||||||
1.26115 | + | 8.62609i | 0.109355 | + | 0.747977i | |||||
0 | 0 | |||||||||
0.727325 | + | 1.25976i | 0.0625982 | + | 0.108423i | |||||
0 | 0 | |||||||||
7.99014 | − | 13.8393i | 0.682644 | − | 1.18237i | −0.291527 | − | 0.956562i | ||
0.974171 | − | 0.225811i | ||||||||
0 | 0 | |||||||||
−2.45938 | + | 4.25976i | −0.208602 | + | 0.361308i | −0.951274 | − | 0.308346i | ||
0.742673 | + | 0.669655i | ||||||||
0 | 0 | |||||||||
−0.0591663 | −0.00498270 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 6.89404i | − | 0.572519i | |||||||
0 | 0 | |||||||||
−0.364862 | + | 0.210653i | −0.0300933 | + | 0.0173744i | |||||
0 | 0 | |||||||||
0.0295831 | − | 0.0170798i | 0.00242355 | − | 0.00139923i | −0.498788 | − | 0.866724i | ||
0.501211 | + | 0.865325i | ||||||||
0 | 0 | |||||||||
9.90582 | 0.806124 | 0.403062 | − | 0.915173i | ||||||
0.403062 | + | 0.915173i | ||||||||
0 | 0 | |||||||||
−11.8623 | −0.959013 | |||||||||
0 | 0 | |||||||||
12.9391 | − | 7.47042i | 1.03930 | − | 0.600038i | |||||
0 | 0 | |||||||||
16.8621 | − | 9.73536i | 1.34575 | − | 0.776966i | 0.358102 | − | 0.933683i | ||
0.987644 | + | 0.156716i | ||||||||
0 | 0 | |||||||||
− | 1.53925i | − | 0.122070i | |||||||
0 | 0 | |||||||||
7.40158 | − | 12.8199i | 0.583327 | − | 1.01035i | |||||
0 | 0 | |||||||||
2.97762 | 0.233225 | 0.116613 | − | 0.993177i | ||||||
0.116613 | + | 0.993177i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.121621 | − | 0.210653i | 0.00941128 | − | 0.0163008i | −0.861281 | − | 0.508128i | ||
0.870693 | + | 0.491827i | ||||||||
0 | 0 | |||||||||
−2.57869 | − | 4.46643i | −0.198361 | − | 0.343571i | |||||
0 | 0 | |||||||||
−4.79953 | + | 12.0716i | −0.367029 | + | 0.923139i | |||||
0 | 0 | |||||||||
1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | ||
−0.803354 | + | 0.595502i | ||||||||
0 | 0 | |||||||||
−3.46410 | − | 2.00000i | −0.261861 | − | 0.151186i | |||||
0 | 0 | |||||||||
−0.0984160 | + | 0.170461i | −0.00739740 | + | 0.0128127i | |||||
0 | 0 | |||||||||
11.1574i | 0.833942i | 0.908920 | + | 0.416971i | ||||||
−0.908920 | + | 0.416971i | ||||||||
0 | 0 | |||||||||
−5.76115 | + | 9.97860i | −0.428223 | + | 0.741704i | −0.996715 | − | 0.0809848i | ||
0.568493 | + | 0.822688i | ||||||||
0 | 0 | |||||||||
−0.311561 | −0.0230312 | |||||||||
0 | 0 | |||||||||
10.8917 | − | 6.28834i | 0.800775 | − | 0.462328i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.67969 | 0.122179 | |||||||||
0 | 0 | |||||||||
13.1179i | 0.949181i | 0.880207 | + | 0.474591i | ||||||
−0.880207 | + | 0.474591i | ||||||||
0 | 0 | |||||||||
2.34261 | − | 1.35251i | 0.168625 | − | 0.0973556i | −0.413312 | − | 0.910589i | ||
0.581937 | + | 0.813234i | ||||||||
0 | 0 | |||||||||
−0.518243 | − | 0.897624i | −0.0371122 | − | 0.0642802i | |||||
0 | 0 | |||||||||
12.0902i | 0.861391i | 0.902497 | + | 0.430695i | ||||||
−0.902497 | + | 0.430695i | ||||||||
0 | 0 | |||||||||
−0.637465 | − | 0.368041i | −0.0451887 | − | 0.0260897i | 0.477235 | − | 0.878775i | ||
−0.522424 | + | 0.852686i | ||||||||
0 | 0 | |||||||||
−0.295053 | −0.0208115 | |||||||||
0 | 0 | |||||||||
−6.89404 | − | 3.98028i | −0.483867 | − | 0.279361i | |||||
0 | 0 | |||||||||
6.39172 | − | 11.0708i | 0.446417 | − | 0.773217i | |||||
0 | 0 | |||||||||
19.1035 | − | 11.0294i | 1.32778 | − | 0.766596i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−18.1377 | + | 10.4718i | −1.24865 | + | 0.720909i | −0.970840 | − | 0.239727i | ||
−0.277810 | + | 0.960636i | ||||||||
0 | 0 | |||||||||
0.236082 | + | 0.136302i | 0.0161760 | + | 0.00933925i | |||||
0 | 0 | |||||||||
18.5002 | + | 10.6811i | 1.26170 | + | 0.728443i | |||||
0 | 0 | |||||||||
− | 17.2522i | − | 1.17115i | |||||||
0 | 0 | |||||||||
−0.608103 | − | 0.351088i | −0.0410918 | − | 0.0237244i | |||||
0 | 0 | |||||||||
16.9606 | 1.14089 | |||||||||
0 | 0 | |||||||||
5.52685 | + | 9.57279i | 0.370106 | + | 0.641042i | 0.989581 | − | 0.143974i | ||
−0.619476 | + | 0.785016i | ||||||||
0 | 0 | |||||||||
−2.98028 | − | 5.16199i | −0.198685 | − | 0.344133i | |||||
0 | 0 | |||||||||
19.9606i | 1.32483i | 0.749138 | + | 0.662414i | ||||||
−0.749138 | + | 0.662414i | ||||||||
0 | 0 | |||||||||
11.1172i | 0.734647i | 0.930093 | + | 0.367324i | ||||||
−0.930093 | + | 0.367324i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.39172 | + | 11.0708i | 0.418736 | + | 0.725271i | 0.995813 | − | 0.0914183i | ||
−0.577077 | + | 0.816690i | ||||||||
0 | 0 | |||||||||
−0.729724 | −0.0476019 | |||||||||
0 | 0 | |||||||||
−0.657388 | − | 0.379543i | −0.0427019 | − | 0.0246540i | |||||
0 | 0 | |||||||||
17.7440i | 1.14776i | 0.818938 | + | 0.573882i | ||||||
−0.818938 | + | 0.573882i | ||||||||
0 | 0 | |||||||||
−3.81303 | − | 2.20145i | −0.245619 | − | 0.141808i | 0.372138 | − | 0.928178i | ||
−0.617756 | + | 0.786369i | ||||||||
0 | 0 | |||||||||
3.25502 | + | 1.87929i | 0.208810 | + | 0.120556i | |||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.287494 | + | 0.165985i | |||||
0 | 0 | |||||||||
6.86228 | − | 17.2598i | 0.436637 | − | 1.09821i | |||||
0 | 0 | |||||||||
1.04911 | − | 0.605704i | 0.0664847 | − | 0.0383850i | |||||
0 | 0 | |||||||||
8.14201 | − | 14.1024i | 0.513919 | − | 0.890134i | −0.485950 | − | 0.873986i | ||
0.999870 | − | 0.0161477i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.968168 | 0.0606290 | |||||||||
0 | 0 | |||||||||
−13.0787 | − | 7.55099i | −0.815827 | − | 0.471018i | 0.0331486 | − | 0.999450i | ||
−0.848975 | + | 0.528433i | ||||||||
0 | 0 | |||||||||
− | 14.5223i | − | 0.902372i | |||||||
0 | 0 | |||||||||
−5.93117 | − | 10.2731i | −0.367130 | − | 0.635888i | |||||
0 | 0 | |||||||||
10.0274 | − | 5.78935i | 0.618319 | − | 0.356986i | −0.157895 | − | 0.987456i | ||
0.776214 | + | 0.630469i | ||||||||
0 | 0 | |||||||||
− | 18.9842i | − | 1.16619i | |||||||
0 | 0 | |||||||||
−2.35930 | −0.144387 | |||||||||
0 | 0 | |||||||||
9.39172 | + | 16.2669i | 0.572623 | + | 0.991813i | 0.996295 | + | 0.0859972i | ||
−0.423672 | + | 0.905816i | ||||||||
0 | 0 | |||||||||
24.5111 | − | 14.1515i | 1.48894 | − | 0.859642i | 0.489023 | − | 0.872271i | ||
0.999920 | + | 0.0126295i | ||||||||
0 | 0 | |||||||||
−1.19683 | −0.0724356 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.15734i | 0.189706i | 0.995491 | + | 0.0948530i | ||||||
−0.995491 | + | 0.0948530i | ||||||||
0 | 0 | |||||||||
12.8541 | − | 22.2639i | 0.769554 | − | 1.33291i | |||||
0 | 0 | |||||||||
−5.34261 | − | 3.08456i | −0.318714 | − | 0.184009i | 0.332105 | − | 0.943242i | ||
−0.650819 | + | 0.759233i | ||||||||
0 | 0 | |||||||||
7.25891 | + | 12.5728i | 0.431497 | + | 0.747375i | 0.997002 | − | 0.0773697i | ||
−0.565505 | + | 0.824745i | ||||||||
0 | 0 | |||||||||
0.391723 | − | 0.985247i | 0.0232037 | − | 0.0583610i | |||||
0 | 0 | |||||||||
−7.38053 | − | 12.7834i | −0.435659 | − | 0.754583i | |||||
0 | 0 | |||||||||
0.578694 | − | 1.00233i | 0.0340408 | − | 0.0589604i | |||||
0 | 0 | |||||||||
0.518243 | − | 0.897624i | 0.0303800 | − | 0.0526196i | |||||
0 | 0 | |||||||||
−30.5866 | −1.78689 | −0.893445 | − | 0.449174i | ||||||
−0.893445 | + | 0.449174i | ||||||||
0 | 0 | |||||||||
−1.21381 | + | 2.10238i | −0.0706706 | + | 0.122405i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−27.3138 | + | 15.7696i | −1.57960 | + | 0.911981i | |||||
0 | 0 | |||||||||
21.3621 | − | 12.3334i | 1.23129 | − | 0.710888i | |||||
0 | 0 | |||||||||
−0.00479723 | −0.000275593 | |||||||||
0 | 0 | |||||||||
−3.84261 | −0.220027 | |||||||||
0 | 0 | |||||||||
14.8611 | − | 8.58008i | 0.848170 | − | 0.489691i | −0.0118632 | − | 0.999930i | ||
0.860033 | + | 0.510239i | ||||||||
0 | 0 | |||||||||
0.480472 | − | 0.277401i | 0.0273331 | − | 0.0157808i | |||||
0 | 0 | |||||||||
29.7440i | 1.68663i | 0.537421 | + | 0.843314i | ||||||
−0.537421 | + | 0.843314i | ||||||||
0 | 0 | |||||||||
5.81303 | − | 10.0685i | 0.328572 | − | 0.569103i | −0.653657 | − | 0.756791i | ||
0.982229 | + | 0.187688i | ||||||||
0 | 0 | |||||||||
10.3240 | 0.581691 | |||||||||
0 | 0 | |||||||||
8.41145 | − | 14.5691i | 0.472434 | − | 0.818279i | −0.527069 | − | 0.849823i | ||
0.999502 | + | 0.0315434i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.558972 | − | 0.968168i | −0.0311988 | − | 0.0540378i | |||||
0 | 0 | |||||||||
10.7572 | + | 13.6122i | 0.598545 | + | 0.757405i | |||||
0 | 0 | |||||||||
4.26115 | + | 7.38053i | 0.236366 | + | 0.409398i | |||||
0 | 0 | |||||||||
1.87521 | + | 1.08265i | 0.103699 | + | 0.0598709i | |||||
0 | 0 | |||||||||
−0.421306 | + | 0.729724i | −0.0232274 | + | 0.0402310i | |||||
0 | 0 | |||||||||
33.3594i | 1.83360i | 0.399350 | + | 0.916798i | ||||||
−0.399350 | + | 0.916798i | ||||||||
0 | 0 | |||||||||
10.8201 | − | 18.7410i | 0.592939 | − | 1.02700i | |||||
0 | 0 | |||||||||
−3.63902 | −0.198821 | |||||||||
0 | 0 | |||||||||
−11.5491 | + | 6.66788i | −0.629120 | + | 0.363223i | −0.780411 | − | 0.625267i | ||
0.151291 | + | 0.988489i | ||||||||
0 | 0 | |||||||||
−0.917265 | − | 1.58875i | −0.0498190 | − | 0.0862890i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.0000i | 1.07990i | |||||||||
0 | 0 | |||||||||
−1.55917 | + | 0.900185i | −0.0839427 | + | 0.0484643i | |||||
0 | 0 | |||||||||
−3.98235 | − | 6.89762i | −0.213783 | − | 0.370284i | 0.739112 | − | 0.673582i | ||
−0.952896 | + | 0.303299i | ||||||||
0 | 0 | |||||||||
6.13496i | 0.328397i | 0.986427 | + | 0.164198i | ||||||
−0.986427 | + | 0.164198i | ||||||||
0 | 0 | |||||||||
−3.09924 | − | 1.78935i | −0.165425 | − | 0.0955083i | |||||
0 | 0 | |||||||||
12.9803 | 0.690870 | 0.345435 | − | 0.938443i | ||||||
0.345435 | + | 0.938443i | ||||||||
0 | 0 | |||||||||
2.91170 | + | 1.68107i | 0.154537 | + | 0.0892219i | |||||
0 | 0 | |||||||||
0.558972 | − | 0.968168i | 0.0295839 | − | 0.0512409i | |||||
0 | 0 | |||||||||
−23.4746 | + | 13.5531i | −1.23894 | + | 0.715304i | −0.968878 | − | 0.247539i | ||
−0.270064 | + | 0.962842i | ||||||||
0 | 0 | |||||||||
18.2048 | − | 5.43939i | 0.958145 | − | 0.286284i | |||||
0 | 0 | |||||||||
1.33783 | − | 0.772395i | 0.0702177 | − | 0.0405402i | |||||
0 | 0 | |||||||||
−7.50000 | − | 4.33013i | −0.392568 | − | 0.226649i | |||||
0 | 0 | |||||||||
3.82896 | + | 2.21065i | 0.199870 | + | 0.115395i | 0.596595 | − | 0.802542i | ||
−0.396725 | + | 0.917938i | ||||||||
0 | 0 | |||||||||
− | 21.9960i | − | 1.14507i | |||||||
0 | 0 | |||||||||
−18.9842 | − | 10.9606i | −0.985613 | − | 0.569044i | |||||
0 | 0 | |||||||||
13.6797 | 0.708307 | 0.354154 | − | 0.935187i | ||||||
0.354154 | + | 0.935187i | ||||||||
0 | 0 | |||||||||
0.851344 | + | 1.47457i | 0.0439632 | + | 0.0761465i | |||||
0 | 0 | |||||||||
8.48028 | + | 14.6883i | 0.436757 | + | 0.756485i | |||||
0 | 0 | |||||||||
− | 23.0446i | − | 1.18372i | −0.806040 | − | 0.591861i | ||||
0.806040 | − | 0.591861i | ||||||||
0 | 0 | |||||||||
1.80037i | 0.0922358i | |||||||||
0 | 0 | |||||||||
3.98235 | + | 6.89762i | 0.203488 | + | 0.352452i | 0.949650 | − | 0.313313i | ||
−0.746162 | + | 0.665765i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
36.7571 | 1.86847 | |||||||||
0 | 0 | |||||||||
17.7048 | + | 10.2218i | 0.897667 | + | 0.518268i | 0.876442 | − | 0.481507i | ||
0.0212242 | + | 0.999775i | ||||||||
0 | 0 | |||||||||
− | 29.4604i | − | 1.48987i | |||||||
0 | 0 | |||||||||
2.18697 | + | 1.26265i | 0.110318 | + | 0.0636922i | |||||
0 | 0 | |||||||||
−8.10785 | − | 4.68107i | −0.407950 | − | 0.235530i | |||||
0 | 0 | |||||||||
13.0787 | − | 7.55099i | 0.656401 | − | 0.378973i | −0.134503 | − | 0.990913i | ||
0.790904 | + | 0.611940i | ||||||||
0 | 0 | |||||||||
−0.759086 | − | 0.960556i | −0.0380018 | − | 0.0480879i | |||||
0 | 0 | |||||||||
26.9113 | − | 15.5372i | 1.34388 | − | 0.775892i | 0.356509 | − | 0.934292i | ||
0.987375 | + | 0.158400i | ||||||||
0 | 0 | |||||||||
−18.3785 | + | 31.8326i | −0.915500 | + | 1.58569i | |||||
0 | 0 | |||||||||
13.2343 | + | 7.64085i | 0.657619 | + | 0.379677i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.13786 | + | 0.656944i | 0.0562636 | + | 0.0324838i | 0.527868 | − | 0.849326i | ||
−0.471604 | + | 0.881810i | ||||||||
0 | 0 | |||||||||
2.24420i | 0.110698i | |||||||||
0 | 0 | |||||||||
1.40158 | + | 2.42761i | 0.0689674 | + | 0.119455i | |||||
0 | 0 | |||||||||
12.9391 | − | 7.47042i | 0.635157 | − | 0.366708i | |||||
0 | 0 | |||||||||
− | 0.690767i | − | 0.0338270i | |||||||
0 | 0 | |||||||||
15.2475 | 0.744891 | 0.372445 | − | 0.928054i | ||||||
0.372445 | + | 0.928054i | ||||||||
0 | 0 | |||||||||
6.23885 | + | 10.8060i | 0.304063 | + | 0.526653i | 0.977052 | − | 0.213000i | ||
−0.672989 | + | 0.739652i | ||||||||
0 | 0 | |||||||||
−1.08739 | + | 0.627805i | −0.0528707 | + | 0.0305249i | |||||
0 | 0 | |||||||||
−7.96056 | −0.386144 | |||||||||
0 | 0 | |||||||||
−2.21853 | + | 3.84261i | −0.107362 | + | 0.185957i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.8175 | + | 22.2006i | −0.617398 | + | 1.06937i | 0.372560 | + | 0.928008i | ||
−0.989959 | + | 0.141357i | ||||||||
0 | 0 | |||||||||
−2.76392 | − | 1.59575i | −0.132825 | − | 0.0766868i | 0.432115 | − | 0.901819i | ||
−0.564940 | + | 0.825132i | ||||||||
0 | 0 | |||||||||
0.484084 | + | 0.838458i | 0.0232100 | + | 0.0402010i | |||||
0 | 0 | |||||||||
−29.9801 | − | 11.9197i | −1.43414 | − | 0.570198i | |||||
0 | 0 | |||||||||
−1.24797 | − | 2.16154i | −0.0595622 | − | 0.103165i | 0.834707 | − | 0.550695i | ||
−0.894269 | + | 0.447530i | ||||||||
0 | 0 | |||||||||
−4.47042 | + | 7.74299i | −0.212877 | + | 0.368714i | |||||
0 | 0 | |||||||||
14.3063 | − | 24.7793i | 0.679714 | − | 1.17730i | −0.295353 | − | 0.955388i | ||
0.975067 | − | 0.221911i | ||||||||
0 | 0 | |||||||||
−29.0982 | −1.37939 | |||||||||
0 | 0 | |||||||||
−0.00239861 | + | 0.00415452i | −0.000113450 | + | 0.000196502i | |||||
0 | 0 | |||||||||
5.58016i | 0.263344i | 0.991293 | + | 0.131672i | ||||||
−0.991293 | + | 0.131672i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.20475 | + | 0.695564i | −0.0566042 | + | 0.0326804i | |||||
0 | 0 | |||||||||
−14.7611 | −0.692009 | |||||||||
0 | 0 | |||||||||
−38.7243 | −1.81145 | −0.905723 | − | 0.423871i | ||||||
−0.905723 | + | 0.423871i | ||||||||
0 | 0 | |||||||||
2.89496 | − | 1.67140i | 0.135125 | − | 0.0780144i | |||||
0 | 0 | |||||||||
−13.1752 | + | 7.60669i | −0.613629 | + | 0.354279i | −0.774384 | − | 0.632716i | ||
0.160756 | + | 0.986994i | ||||||||
0 | 0 | |||||||||
− | 11.7834i | − | 0.547623i | −0.961783 | − | 0.273812i | ||||
0.961783 | − | 0.273812i | ||||||||
0 | 0 | |||||||||
−1.04911 | + | 1.81711i | −0.0486513 | + | 0.0842666i | |||||
0 | 0 | |||||||||
−36.0321 | −1.66737 | −0.833684 | − | 0.552241i | ||||||
−0.833684 | + | 0.552241i | ||||||||
0 | 0 | |||||||||
−2.10099 | + | 3.63902i | −0.0970148 | + | 0.168034i | |||||
0 | 0 | |||||||||
−1.36719 | + | 2.36804i | −0.0629967 | + | 0.109114i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.22086 | + | 8.10099i | −0.147783 | + | 0.371699i | |||||
0 | 0 | |||||||||
−16.3328 | − | 28.2892i | −0.747825 | − | 1.29527i | |||||
0 | 0 | |||||||||
9.29772 | + | 5.36804i | 0.424824 | + | 0.245272i | 0.697139 | − | 0.716936i | ||
−0.272315 | + | 0.962208i | ||||||||
0 | 0 | |||||||||
−15.4704 | + | 26.7955i | −0.705390 | + | 1.22177i | |||||
0 | 0 | |||||||||
2.07889i | 0.0945927i | |||||||||
0 | 0 | |||||||||
6.39172 | − | 11.0708i | 0.290233 | − | 0.502699i | |||||
0 | 0 | |||||||||
28.5491 | 1.29368 | 0.646842 | − | 0.762624i | ||||||
0.646842 | + | 0.762624i | ||||||||
0 | 0 | |||||||||
−0.362140 | + | 0.209082i | −0.0163765 | + | 0.00945499i | |||||
0 | 0 | |||||||||
−17.6171 | − | 30.5136i | −0.795046 | − | 1.37706i | −0.922810 | − | 0.385256i | ||
0.127763 | − | 0.991805i | ||||||||
0 | 0 | |||||||||
−15.8426 | −0.713515 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.36214 | − | 1.94113i | 0.150813 | − | 0.0870717i | |||||
0 | 0 | |||||||||
−6.16672 | − | 10.6811i | −0.276060 | − | 0.478150i | 0.694342 | − | 0.719645i | ||
−0.970402 | + | 0.241495i | ||||||||
0 | 0 | |||||||||
0.0341597i | 0.00152614i | |||||||||
0 | 0 | |||||||||
−20.1980 | − | 11.6613i | −0.900586 | − | 0.519954i | −0.0231960 | − | 0.999731i | ||
−0.877390 | + | 0.479777i | ||||||||
0 | 0 | |||||||||
−0.0591663 | −0.00263286 | |||||||||
0 | 0 | |||||||||
0.627245 | + | 0.362140i | 0.0278569 | + | 0.0160832i | |||||
0 | 0 | |||||||||
−17.5491 | + | 30.3960i | −0.777851 | + | 1.34728i | 0.155328 | + | 0.987863i | ||
−0.933178 | + | 0.359414i | ||||||||
0 | 0 | |||||||||
−8.66025 | + | 5.00000i | −0.383107 | + | 0.221187i | |||||
0 | 0 | |||||||||
−0.529583 | − | 3.62228i | −0.0233817 | − | 0.159928i | |||||
0 | 0 | |||||||||
5.92588 | − | 3.42131i | 0.261125 | − | 0.150761i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.364862 | − | 0.210653i | −0.0160157 | − | 0.00924664i | |||||
0 | 0 | |||||||||
29.5221i | 1.29339i | 0.762750 | + | 0.646693i | ||||||
−0.762750 | + | 0.646693i | ||||||||
0 | 0 | |||||||||
1.19227 | + | 0.688356i | 0.0521342 | + | 0.0300997i | 0.525841 | − | 0.850583i | ||
−0.473706 | + | 0.880683i | ||||||||
0 | 0 | |||||||||
0.561741 | 0.0245164 | |||||||||
0 | 0 | |||||||||
−17.1671 | − | 29.7343i | −0.747812 | − | 1.29525i | |||||
0 | 0 | |||||||||
15.8917 | + | 27.5253i | 0.690944 | + | 1.19675i | |||||
0 | 0 | |||||||||
4.17711i | 0.181271i | |||||||||
0 | 0 | |||||||||
31.4495i | 1.36223i | |||||||||
0 | 0 | |||||||||
−6.89404 | − | 11.9408i | −0.298055 | − | 0.516247i | |||||
0 | 0 | |||||||||
−0.783446 | − | 1.35697i | −0.0338082 | − | 0.0585575i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−0.450889 | − | 0.260321i | −0.0193852 | − | 0.0111921i | 0.490276 | − | 0.871567i | ||
−0.509661 | + | 0.860375i | ||||||||
0 | 0 | |||||||||
− | 1.61814i | − | 0.0694410i | |||||||
0 | 0 | |||||||||
23.1278 | + | 13.3528i | 0.990686 | + | 0.571973i | |||||
0 | 0 | |||||||||
9.66498 | + | 5.58008i | 0.413245 | + | 0.238587i | 0.692183 | − | 0.721722i | ||
−0.278938 | + | 0.960309i | ||||||||
0 | 0 | |||||||||
−5.72603 | + | 3.30592i | −0.244381 | + | 0.141093i | |||||
0 | 0 | |||||||||
−6.40996 | + | 16.1221i | −0.273073 | + | 0.686824i | |||||
0 | 0 | |||||||||
−9.36214 | + | 5.40523i | −0.398119 | + | 0.229854i | |||||
0 | 0 | |||||||||
−0.883105 | + | 1.52958i | −0.0374857 | + | 0.0649272i | |||||
0 | 0 | |||||||||
27.1769 | + | 15.6906i | 1.15152 | + | 0.664832i | 0.949258 | − | 0.314499i | ||
0.202265 | + | 0.979331i | ||||||||
0 | 0 | |||||||||
−52.5546 | −2.22282 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 42.7243i | − | 1.80061i | −0.435256 | − | 0.900307i | ||||
0.435256 | − | 0.900307i | ||||||||
0 | 0 | |||||||||
−11.3130 | − | 19.5947i | −0.475943 | − | 0.824357i | |||||
0 | 0 | |||||||||
15.2817 | − | 8.82289i | 0.641771 | − | 0.370527i | |||||
0 | 0 | |||||||||
19.8547i | 0.832353i | 0.909284 | + | 0.416177i | ||||||
−0.909284 | + | 0.416177i | ||||||||
0 | 0 | |||||||||
39.0098 | 1.63251 | 0.816254 | − | 0.577693i | ||||||
0.816254 | + | 0.577693i | ||||||||
0 | 0 | |||||||||
−0.921112 | − | 1.59541i | −0.0384800 | − | 0.0666493i | |||||
0 | 0 | |||||||||
12.8199 | − | 7.40158i | 0.534628 | − | 0.308667i | |||||
0 | 0 | |||||||||
−12.0982 | −0.503656 | −0.251828 | − | 0.967772i | ||||||
−0.251828 | + | 0.967772i | ||||||||
0 | 0 | |||||||||
−0.189940 | + | 0.328986i | −0.00789363 | + | 0.0136722i | |||||
0 | 0 | |||||||||
− | 17.2522i | − | 0.715741i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−19.0491 | − | 10.9980i | −0.787584 | − | 0.454712i | |||||
0 | 0 | |||||||||
6.56334 | + | 11.3680i | 0.270898 | + | 0.469209i | 0.969092 | − | 0.246699i | ||
−0.698194 | + | 0.715909i | ||||||||
0 | 0 | |||||||||
−37.2048 | + | 5.43939i | −1.53300 | + | 0.224126i | |||||
0 | 0 | |||||||||
−0.848946 | − | 1.47042i | −0.0349210 | − | 0.0604849i | |||||
0 | 0 | |||||||||
−3.39172 | + | 5.87464i | −0.139281 | + | 0.241242i | −0.927225 | − | 0.374505i | ||
0.787943 | + | 0.615748i | ||||||||
0 | 0 | |||||||||
6.89404 | − | 11.9408i | 0.282628 | − | 0.489526i | |||||
0 | 0 | |||||||||
0.103372 | 0.00423073 | |||||||||
0 | 0 | |||||||||
−11.1196 | + | 19.2598i | −0.454336 | + | 0.786933i | −0.998650 | − | 0.0519490i | ||
0.544314 | + | 0.838882i | ||||||||
0 | 0 | |||||||||
25.9466i | 1.05838i | 0.848502 | + | 0.529192i | ||||||
−0.848502 | + | 0.529192i | ||||||||
0 | 0 | |||||||||
−5.42265 | + | 3.13077i | −0.220827 | + | 0.127495i | |||||
0 | 0 | |||||||||
16.5000 | − | 9.52628i | 0.670820 | − | 0.387298i | |||||
0 | 0 | |||||||||
−12.8834 | −0.522923 | −0.261461 | − | 0.965214i | ||||||
−0.261461 | + | 0.965214i | ||||||||
0 | 0 | |||||||||
1.11794 | 0.0453014 | |||||||||
0 | 0 | |||||||||
1.55473 | − | 0.897624i | 0.0628977 | − | 0.0363140i | |||||
0 | 0 | |||||||||
26.9704 | − | 15.5714i | 1.08932 | − | 0.628922i | 0.155928 | − | 0.987768i | ||
0.933397 | + | 0.358846i | ||||||||
0 | 0 | |||||||||
1.79525i | 0.0723914i | |||||||||
0 | 0 | |||||||||
−8.54911 | + | 14.8075i | −0.344174 | + | 0.596127i | −0.985203 | − | 0.171389i | ||
0.641029 | + | 0.767517i | ||||||||
0 | 0 | |||||||||
−42.4055 | −1.70442 | −0.852211 | − | 0.523198i | ||||||
−0.852211 | + | 0.523198i | ||||||||
0 | 0 | |||||||||
−3.10808 | + | 5.38336i | −0.124723 | + | 0.216027i | |||||
0 | 0 | |||||||||
−16.7999 | + | 29.0982i | −0.673072 | + | 1.16580i | |||||
0 | 0 | |||||||||
5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−14.4507 | − | 25.0293i | −0.576187 | − | 0.997985i | |||||
0 | 0 | |||||||||
−29.4346 | − | 16.9941i | −1.17177 | − | 0.676524i | −0.217677 | − | 0.976021i | ||
−0.954097 | + | 0.299496i | ||||||||
0 | 0 | |||||||||
1.47061 | − | 2.54717i | 0.0584516 | − | 0.101241i | |||||
0 | 0 | |||||||||
22.2048i | 0.881169i | |||||||||
0 | 0 | |||||||||
6.39172 | − | 11.0708i | 0.253249 | − | 0.438641i | |||||
0 | 0 | |||||||||
5.78511 | 0.228856 | |||||||||
0 | 0 | |||||||||
25.8621 | − | 14.9315i | 1.02149 | − | 0.589759i | 0.106957 | − | 0.994264i | ||
0.914536 | + | 0.404504i | ||||||||
0 | 0 | |||||||||
−22.7233 | − | 39.3580i | −0.896121 | − | 1.55213i | −0.832411 | − | 0.554159i | ||
−0.0637103 | − | 0.997968i | ||||||||
0 | 0 | |||||||||
−3.00000 | −0.118125 | |||||||||
0 | 0 | |||||||||
2.35422i | 0.0925539i | 0.998929 | + | 0.0462770i | ||||||
−0.998929 | + | 0.0462770i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.21141 | + | 2.09822i | 0.0474789 | + | 0.0822358i | |||||
0 | 0 | |||||||||
27.9513i | 1.09382i | 0.837192 | + | 0.546909i | ||||||
−0.837192 | + | 0.546909i | ||||||||
0 | 0 | |||||||||
26.9729 | + | 15.5728i | 1.05392 | + | 0.608479i | |||||
0 | 0 | |||||||||
−14.9014 | −0.581359 | |||||||||
0 | 0 | |||||||||
−16.9215 | − | 9.76962i | −0.659168 | − | 0.380571i | 0.132792 | − | 0.991144i | ||
−0.791960 | + | 0.610573i | ||||||||
0 | 0 | |||||||||
−1.29073 | + | 2.23561i | −0.0502036 | + | 0.0869553i | −0.890035 | − | 0.455892i | ||
0.839832 | + | 0.542847i | ||||||||
0 | 0 | |||||||||
−2.06275 | + | 1.19093i | −0.0801107 | + | 0.0462519i | |||||
0 | 0 | |||||||||
−9.36214 | − | 11.8470i | −0.363048 | − | 0.459405i | |||||
0 | 0 | |||||||||
25.5134 | − | 14.7302i | 0.987884 | − | 0.570355i | |||||
0 | 0 | |||||||||
−1.34436 | − | 0.776166i | −0.0519759 | − | 0.0300083i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 36.8254i | − | 1.41951i | −0.704446 | − | 0.709757i | ||||
0.704446 | − | 0.709757i | ||||||||
0 | 0 | |||||||||
1.45465 | + | 0.839843i | 0.0559895 | + | 0.0323256i | |||||
0 | 0 | |||||||||
−31.8229 | −1.22305 | −0.611527 | − | 0.791224i | ||||||
−0.611527 | + | 0.791224i | ||||||||
0 | 0 | |||||||||
−7.38053 | − | 12.7834i | −0.283239 | − | 0.490584i | |||||
0 | 0 | |||||||||
−1.40158 | − | 2.42761i | −0.0537088 | − | 0.0930264i | |||||
0 | 0 | |||||||||
27.7834i | 1.06310i | 0.847026 | + | 0.531552i | ||||||
−0.847026 | + | 0.531552i | ||||||||
0 | 0 | |||||||||
27.6787i | 1.05755i | |||||||||
0 | 0 | |||||||||
−0.780626 | − | 1.35208i | −0.0297827 | − | 0.0515852i | |||||
0 | 0 | |||||||||
23.3523 | + | 40.4473i | 0.889651 | + | 1.54092i | |||||
0 | 0 | |||||||||
20.7846 | 0.790684 | 0.395342 | − | 0.918534i | ||||||
0.395342 | + | 0.918534i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 8.51953i | − | 0.323164i | |||||||
0 | 0 | |||||||||
−25.4408 | − | 14.6883i | −0.963640 | − | 0.556358i | |||||
0 | 0 | |||||||||
−1.55473 | − | 0.897624i | −0.0588053 | − | 0.0339513i | |||||
0 | 0 | |||||||||
−23.4391 | + | 13.5326i | −0.885282 | + | 0.511118i | −0.872396 | − | 0.488799i | ||
−0.0128857 | + | 0.999917i | ||||||||
0 | 0 | |||||||||
−31.3177 | + | 4.57869i | −1.18117 | + | 0.172689i | |||||
0 | 0 | |||||||||
0.0887494 | − | 0.0512395i | 0.00334250 | − | 0.00192979i | |||||
0 | 0 | |||||||||
−0.0341597 | + | 0.0591663i | −0.00128471 | + | 0.00222518i | |||||
0 | 0 | |||||||||
10.8621 | + | 6.27126i | 0.407936 | + | 0.235522i | 0.689903 | − | 0.723902i | ||
−0.281966 | + | 0.959424i | ||||||||
0 | 0 | |||||||||
−16.1091 | −0.604138 | |||||||||
0 | 0 | |||||||||
55.2929 | + | 31.9234i | 2.07074 | + | 1.19554i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.24594 | − | 2.15804i | −0.0465306 | − | 0.0805933i | |||||
0 | 0 | |||||||||
−14.1529 | + | 8.17121i | −0.527816 | + | 0.304735i | −0.740127 | − | 0.672468i | ||
0.212311 | + | 0.977202i | ||||||||
0 | 0 | |||||||||
− | 7.90117i | − | 0.294255i | |||||||
0 | 0 | |||||||||
0.618324 | 0.0229957 | |||||||||
0 | 0 | |||||||||
−3.98028 | − | 6.89404i | −0.147824 | − | 0.256038i | |||||
0 | 0 | |||||||||
−34.6308 | + | 19.9941i | −1.28439 | + | 0.741540i | −0.977647 | − | 0.210254i | ||
−0.306738 | + | 0.951794i | ||||||||
0 | 0 | |||||||||
25.9408 | 0.960772 | |||||||||
0 | 0 | |||||||||
24.5453 | − | 42.5136i | 0.907839 | − | 1.57242i | |||||
0 | 0 | |||||||||
− | 6.55312i | − | 0.242045i | −0.992650 | − | 0.121023i | ||||
0.992650 | − | 0.121023i | ||||||||
0 | 0 | |||||||||
0.364862 | − | 0.631959i | 0.0134581 | − | 0.0233102i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.66846 | + | 4.62190i | 0.0981608 | + | 0.170019i | 0.910923 | − | 0.412576i | ||
−0.812763 | + | 0.582595i | ||||||||
0 | 0 | |||||||||
0.377346 | + | 2.58100i | 0.0138621 | + | 0.0948153i | |||||
0 | 0 | |||||||||
10.2707 | + | 17.7893i | 0.376795 | + | 0.652628i | 0.990594 | − | 0.136834i | ||
−0.613799 | + | 0.789462i | ||||||||
0 | 0 | |||||||||
−0.0295831 | + | 0.0512395i | −0.00108384 | + | 0.00187727i | |||||
0 | 0 | |||||||||
12.8541 | − | 22.2639i | 0.470306 | − | 0.814594i | |||||
0 | 0 | |||||||||
−15.9211 | −0.581745 | |||||||||
0 | 0 | |||||||||
15.5225 | − | 26.8858i | 0.566425 | − | 0.981078i | −0.430490 | − | 0.902595i | ||
0.996916 | − | 0.0784823i | ||||||||
0 | 0 | |||||||||
2.28685i | 0.0833375i | |||||||||
0 | 0 | |||||||||
−14.8587 | + | 8.57869i | −0.540765 | + | 0.312211i | |||||
0 | 0 | |||||||||
44.1651 | − | 25.4987i | 1.60521 | − | 0.926767i | 0.614786 | − | 0.788694i | ||
0.990422 | − | 0.138074i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
13.7046 | 0.496790 | 0.248395 | − | 0.968659i | ||||||
0.248395 | + | 0.968659i | ||||||||
0 | 0 | |||||||||
26.7057 | − | 15.4185i | 0.966811 | − | 0.558188i | |||||
0 | 0 | |||||||||
17.7935 | − | 10.2731i | 0.643325 | − | 0.371424i | |||||
0 | 0 | |||||||||
− | 5.97236i | − | 0.215649i | |||||||
0 | 0 | |||||||||
−21.8621 | + | 37.8663i | −0.788369 | + | 1.36550i | 0.138597 | + | 0.990349i | ||
−0.926966 | + | 0.375146i | ||||||||
0 | 0 | |||||||||
2.12085 | 0.0763806 | |||||||||
0 | 0 | |||||||||
21.4606 | − | 37.1708i | 0.771883 | − | 1.33694i | −0.164648 | − | 0.986352i | ||
0.936530 | − | 0.350587i | ||||||||
0 | 0 | |||||||||
8.62609 | − | 14.9408i | 0.309858 | − | 0.536691i | |||||
0 | 0 | |||||||||
1.01972 | + | 1.76621i | 0.0365823 | + | 0.0633624i | |||||
0 | 0 | |||||||||
−25.2408 | + | 19.9467i | −0.904346 | + | 0.714666i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.89496 | + | 1.67140i | 0.103457 | + | 0.0597311i | |||||
0 | 0 | |||||||||
−16.8621 | + | 29.2061i | −0.601836 | + | 1.04241i | |||||
0 | 0 | |||||||||
25.6797i | 0.915382i | 0.889111 | + | 0.457691i | ||||||
−0.889111 | + | 0.457691i | ||||||||
0 | 0 | |||||||||
−0.813029 | + | 1.40821i | −0.0289446 | + | 0.0501335i | |||||
0 | 0 | |||||||||
−26.1263 | −0.928945 | |||||||||
0 | 0 | |||||||||
8.18697 | − | 4.72675i | 0.290728 | − | 0.167852i | |||||
0 | 0 | |||||||||
1.33303 | + | 2.30887i | 0.0472777 | + | 0.0818873i | |||||
0 | 0 | |||||||||
−1.70456 | −0.0603785 | −0.0301893 | − | 0.999544i | ||||||
−0.0301893 | + | 0.999544i | ||||||||
0 | 0 | |||||||||
1.67692i | 0.0593250i | |||||||||
0 | 0 | |||||||||
−43.3604 | + | 25.0341i | −1.53206 | + | 0.884538i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
25.6398i | 0.903686i | |||||||||
0 | 0 | |||||||||
−2.28445 | − | 1.31893i | −0.0804166 | − | 0.0464285i | |||||
0 | 0 | |||||||||
4.17711 | 0.146859 | 0.0734297 | − | 0.997300i | ||||||
0.0734297 | + | 0.997300i | ||||||||
0 | 0 | |||||||||
−42.6590 | − | 24.6292i | −1.49796 | − | 0.864848i | −0.497963 | − | 0.867198i | ||
−0.999997 | + | 0.00235039i | ||||||||
0 | 0 | |||||||||
−1.98737 | + | 3.44222i | −0.0697001 | + | 0.120724i | |||||
0 | 0 | |||||||||
−4.46643 | + | 2.57869i | −0.156452 | + | 0.0903277i | |||||
0 | 0 | |||||||||
−33.3326 | − | 42.1794i | −1.16616 | − | 1.47567i | |||||
0 | 0 | |||||||||
−21.9960 | + | 12.6994i | −0.768603 | + | 0.443753i | |||||
0 | 0 | |||||||||
−43.1752 | − | 24.9272i | −1.50682 | − | 0.869965i | −0.999969 | − | 0.00793394i | ||
−0.506855 | − | 0.862031i | ||||||||
0 | 0 | |||||||||
24.6136 | + | 14.2107i | 0.857975 | + | 0.495352i | 0.863334 | − | 0.504633i | ||
−0.00535850 | + | 0.999986i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
32.0498 | + | 18.5040i | 1.11448 | + | 0.643446i | 0.939986 | − | 0.341212i | ||
0.174494 | + | 0.984658i | ||||||||
0 | 0 | |||||||||
−23.0446 | −0.800372 | −0.400186 | − | 0.916434i | ||||||
−0.400186 | + | 0.916434i | ||||||||
0 | 0 | |||||||||
−0.221701 | − | 0.383997i | −0.00769072 | − | 0.0133207i | |||||
0 | 0 | |||||||||
5.97042 | + | 10.3411i | 0.206863 | + | 0.358297i | |||||
0 | 0 | |||||||||
0.421306i | 0.0145799i | |||||||||
0 | 0 | |||||||||
7.24456i | 0.250409i | |||||||||
0 | 0 | |||||||||
24.5453 | + | 42.5136i | 0.847396 | + | 1.46773i | 0.883524 | + | 0.468386i | ||
−0.0361276 | + | 0.999347i | ||||||||
0 | 0 | |||||||||
6.57869 | + | 11.3946i | 0.226852 | + | 0.392918i | |||||
0 | 0 | |||||||||
0.866362 | 0.0298391 | |||||||||
0 | 0 | |||||||||
7.73608 | + | 4.46643i | 0.266129 | + | 0.153650i | |||||
0 | 0 | |||||||||
− | 22.0000i | − | 0.755929i | |||||||
0 | 0 | |||||||||
−1.76566 | − | 1.01941i | −0.0605975 | − | 0.0349860i | |||||
0 | 0 | |||||||||
46.5437 | + | 26.8720i | 1.59550 | + | 0.921160i | |||||
0 | 0 | |||||||||
7.92131 | − | 4.57337i | 0.271220 | − | 0.156589i | −0.358222 | − | 0.933637i | ||
0.629442 | + | 0.777047i | ||||||||
0 | 0 | |||||||||
−3.25502 | − | 22.2639i | −0.111319 | − | 0.761410i | |||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.153717 | + | 0.0887486i | −0.574886 | − | 0.818234i | ||
0.421168 | + | 0.906982i | ||||||||
0 | 0 | |||||||||
1.85367 | − | 3.21065i | 0.0632465 | − | 0.109546i | −0.832668 | − | 0.553772i | ||
0.895915 | + | 0.444226i | ||||||||
0 | 0 | |||||||||
1.79525 | + | 1.03649i | 0.0611819 | + | 0.0353234i | |||||
0 | 0 | |||||||||
2.67086 | 0.0909170 | 0.0454585 | − | 0.998966i | ||||||
0.0454585 | + | 0.998966i | ||||||||
0 | 0 | |||||||||
−4.50000 | − | 2.59808i | −0.153005 | − | 0.0883372i | |||||
0 | 0 | |||||||||
0.162538i | 0.00552009i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.75321 | − | 4.47632i | 0.262707 | − | 0.151674i | |||||
0 | 0 | |||||||||
− | 21.9960i | − | 0.744452i | |||||||
0 | 0 | |||||||||
24.2487 | 0.819756 | |||||||||
0 | 0 | |||||||||
7.71204 | + | 13.3576i | 0.260417 | + | 0.451056i | 0.966353 | − | 0.257220i | ||
−0.705936 | + | 0.708276i | ||||||||
0 | 0 | |||||||||
3.71996 | − | 2.14772i | 0.125471 | − | 0.0724408i | |||||
0 | 0 | |||||||||
−11.4687 | −0.386389 | −0.193195 | − | 0.981160i | ||||||
−0.193195 | + | 0.981160i | ||||||||
0 | 0 | |||||||||
−19.9890 | + | 34.6219i | −0.672682 | + | 1.16512i | 0.304458 | + | 0.952526i | ||
−0.977141 | + | 0.212594i | ||||||||
0 | 0 | |||||||||
− | 0.340923i | − | 0.0114600i | |||||||
0 | 0 | |||||||||
29.2549 | − | 50.6710i | 0.982284 | − | 1.70137i | 0.328851 | − | 0.944382i | ||
0.653433 | − | 0.756984i | ||||||||
0 | 0 | |||||||||
22.2048 | + | 12.8199i | 0.744723 | + | 0.429966i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.70650 | + | 0.678484i | 0.0571058 | + | 0.0227046i | |||||
0 | 0 | |||||||||
−9.66258 | − | 16.7361i | −0.322984 | − | 0.559426i | |||||
0 | 0 | |||||||||
2.21461 | − | 3.83582i | 0.0739438 | − | 0.128074i | |||||
0 | 0 | |||||||||
17.1671 | − | 29.7343i | 0.572556 | − | 0.991696i | |||||
0 | 0 | |||||||||
−43.6261 | −1.45339 | |||||||||
0 | 0 | |||||||||
−1.73205 | + | 3.00000i | −0.0576390 | + | 0.0998337i | |||||
0 | 0 | |||||||||
− | 19.9572i | − | 0.663400i | |||||||
0 | 0 | |||||||||
−45.9356 | + | 26.5209i | −1.52527 | + | 0.880612i | −0.525714 | + | 0.850661i | ||
−0.999551 | + | 0.0299511i | ||||||||
0 | 0 | |||||||||
−0.0881660 | + | 0.0509027i | −0.00292428 | + | 0.00168833i | |||||
0 | 0 | |||||||||
−30.6904 | −1.01682 | −0.508410 | − | 0.861115i | ||||||
−0.508410 | + | 0.861115i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.467341 | − | 0.269819i | 0.0154498 | − | 0.00891995i | |||||
0 | 0 | |||||||||
31.1456 | − | 17.9819i | 1.02852 | − | 0.593815i | |||||
0 | 0 | |||||||||
32.8426i | 1.08338i | 0.840579 | + | 0.541689i | ||||||
−0.840579 | + | 0.541689i | ||||||||
0 | 0 | |||||||||
−1.20495 | + | 2.08703i | −0.0397043 | + | 0.0687699i | |||||
0 | 0 | |||||||||
−8.27145 | −0.272258 | |||||||||
0 | 0 | |||||||||
7.26115 | − | 12.5767i | 0.238745 | − | 0.413519i | |||||
0 | 0 | |||||||||
5.88692 | − | 10.1964i | 0.193352 | − | 0.334895i | |||||
0 | 0 | |||||||||
−6.88186 | − | 11.9197i | −0.225787 | − | 0.391074i | 0.730769 | − | 0.682625i | ||
−0.956555 | + | 0.291551i | ||||||||
0 | 0 | |||||||||
12.9391 | − | 1.89172i | 0.424063 | − | 0.0619987i | |||||
0 | 0 | |||||||||
−2.08855 | − | 3.61748i | −0.0683762 | − | 0.118431i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
21.2243 | − | 36.7615i | 0.693367 | − | 1.20095i | −0.277361 | − | 0.960766i | ||
0.970728 | − | 0.240181i | ||||||||
0 | 0 | |||||||||
1.63271i | 0.0532815i | |||||||||
0 | 0 | |||||||||
−28.2440 | + | 48.9200i | −0.920728 | + | 1.59475i | −0.122437 | + | 0.992476i | ||
−0.798291 | + | 0.602272i | ||||||||
0 | 0 | |||||||||
54.6276 | 1.77892 | |||||||||
0 | 0 | |||||||||
−2.51953 | + | 1.45465i | −0.0819602 | + | 0.0473198i | |||||
0 | 0 | |||||||||
−19.5366 | − | 33.8385i | −0.634856 | − | 1.09960i | −0.986546 | − | 0.163486i | ||
0.351690 | − | 0.936116i | ||||||||
0 | 0 | |||||||||
21.3057 | 0.691614 | |||||||||
0 | 0 | |||||||||
2.36253i | 0.0766102i | |||||||||
0 | 0 | |||||||||
−15.1769 | + | 8.76240i | −0.491629 | + | 0.283842i | −0.725250 | − | 0.688486i | ||
0.233621 | + | 0.972328i | ||||||||
0 | 0 | |||||||||
−11.3605 | − | 19.6769i | −0.367616 | − | 0.636730i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
27.6787 | + | 15.9803i | 0.893790 | + | 0.516030i | |||||
0 | 0 | |||||||||
43.4095 | 1.40031 | |||||||||
0 | 0 | |||||||||
−20.5462 | − | 11.8623i | −0.662091 | − | 0.382258i | |||||
0 | 0 | |||||||||
−2.34261 | + | 4.05752i | −0.0754114 | + | 0.130616i | |||||
0 | 0 | |||||||||
18.1251 | − | 10.4645i | 0.582863 | − | 0.336516i | −0.179407 | − | 0.983775i | ||
0.762270 | + | 0.647259i | ||||||||
0 | 0 | |||||||||
−2.26411 | − | 0.900185i | −0.0727338 | − | 0.0289181i | |||||
0 | 0 | |||||||||
−41.3715 | + | 23.8858i | −1.32767 | + | 0.766533i | −0.984939 | − | 0.172900i | ||
−0.342734 | + | 0.939433i | ||||||||
0 | 0 | |||||||||
−8.51953 | − | 4.91875i | −0.273124 | − | 0.157688i | |||||
0 | 0 | |||||||||
−1.03649 | − | 0.598416i | −0.0331941 | − | 0.0191646i | |||||
0 | 0 | |||||||||
− | 48.1223i | − | 1.53957i | −0.638303 | − | 0.769785i | ||||
0.638303 | − | 0.769785i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
45.9515 | 1.46712 | |||||||||
0 | 0 | |||||||||
−18.9866 | − | 32.8858i | −0.605580 | − | 1.04889i | −0.991960 | − | 0.126555i | ||
0.386380 | − | 0.922340i | ||||||||
0 | 0 | |||||||||
−10.4704 | − | 18.1353i | −0.333615 | − | 0.577839i | |||||
0 | 0 | |||||||||
− | 0.118333i | − | 0.00376657i | |||||||
0 | 0 | |||||||||
91.2870i | 2.90276i | |||||||||
0 | 0 | |||||||||
22.4166 | + | 38.8267i | 0.712086 | + | 1.23337i | 0.964073 | + | 0.265639i | ||
−0.251987 | + | 0.967731i | ||||||||
0 | 0 | |||||||||
−2.34242 | − | 4.05719i | −0.0743344 | − | 0.128751i | |||||
0 | 0 | |||||||||
1.27493 | 0.0404180 | |||||||||
0 | 0 | |||||||||
−12.6574 | − | 7.30775i | −0.400863 | − | 0.231439i | 0.285993 | − | 0.958232i | ||
−0.686856 | + | 0.726793i | ||||||||
0 | 0 | |||||||||
6.09822i | 0.192939i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1216.2.s.g.31.3 | ✓ | 12 | |
4.3 | odd | 2 | inner | 1216.2.s.g.31.4 | yes | 12 | |
8.3 | odd | 2 | 1216.2.s.h.31.3 | yes | 12 | ||
8.5 | even | 2 | 1216.2.s.h.31.4 | yes | 12 | ||
19.8 | odd | 6 | 1216.2.s.h.863.3 | yes | 12 | ||
76.27 | even | 6 | 1216.2.s.h.863.4 | yes | 12 | ||
152.27 | even | 6 | inner | 1216.2.s.g.863.3 | yes | 12 | |
152.141 | odd | 6 | inner | 1216.2.s.g.863.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.g.31.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1216.2.s.g.31.4 | yes | 12 | 4.3 | odd | 2 | inner | |
1216.2.s.g.863.3 | yes | 12 | 152.27 | even | 6 | inner | |
1216.2.s.g.863.4 | yes | 12 | 152.141 | odd | 6 | inner | |
1216.2.s.h.31.3 | yes | 12 | 8.3 | odd | 2 | ||
1216.2.s.h.31.4 | yes | 12 | 8.5 | even | 2 | ||
1216.2.s.h.863.3 | yes | 12 | 19.8 | odd | 6 | ||
1216.2.s.h.863.4 | yes | 12 | 76.27 | even | 6 |