Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(127,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 960.w (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 |
Coefficient field: | 8.0.1698758656.6 |
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 480) |
Sato-Tate group: |
Embedding invariants
Embedding label | 127.1 | ||
Root | of defining polynomial | ||
Character | 960.127 | ||
Dual form | 960.2.w.f.703.1 |
-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 | |||||||||
−0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | |||||
0 | 0 | |||||||||
−2.23483 | + | 0.0743018i | −0.999448 | + | 0.0332288i | |||||
0 | 0 | |||||||||
3.16053 | − | 3.16053i | 1.19457 | − | 1.19457i | 0.218799 | − | 0.975770i | ||
0.975770 | − | 0.218799i | ||||||||
0 | 0 | |||||||||
1.00000i | 0.333333i | |||||||||
0 | 0 | |||||||||
4.46967i | 1.34766i | 0.738889 | + | 0.673828i | ||||||
−0.738889 | + | 0.673828i | ||||||||
0 | 0 | |||||||||
2.51929 | − | 2.51929i | 0.698726 | − | 0.698726i | −0.265410 | − | 0.964136i | ||
0.964136 | + | 0.265410i | ||||||||
0 | 0 | |||||||||
1.63280 | + | 1.52773i | 0.421588 | + | 0.394457i | |||||
0 | 0 | |||||||||
−2.30913 | − | 2.30913i | −0.560047 | − | 0.560047i | 0.369273 | − | 0.929321i | ||
−0.929321 | + | 0.369273i | ||||||||
0 | 0 | |||||||||
2.61827 | 0.600672 | 0.300336 | − | 0.953833i | ||||||
0.300336 | + | 0.953833i | ||||||||
0 | 0 | |||||||||
−4.46967 | −0.975361 | |||||||||
0 | 0 | |||||||||
−1.64124 | − | 1.64124i | −0.342222 | − | 0.342222i | 0.514980 | − | 0.857202i | ||
−0.857202 | + | 0.514980i | ||||||||
0 | 0 | |||||||||
4.98896 | − | 0.332104i | 0.997792 | − | 0.0664208i | |||||
0 | 0 | |||||||||
0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | |||||
0 | 0 | |||||||||
− | 8.17246i | − | 1.51759i | −0.651331 | − | 0.758794i | ||||
0.651331 | − | 0.758794i | ||||||||
0 | 0 | |||||||||
4.00000i | 0.718421i | 0.933257 | + | 0.359211i | ||||||
−0.933257 | + | 0.359211i | ||||||||
0 | 0 | |||||||||
3.16053 | − | 3.16053i | 0.550178 | − | 0.550178i | |||||
0 | 0 | |||||||||
−6.82843 | + | 7.29809i | −1.15421 | + | 1.23360i | |||||
0 | 0 | |||||||||
−5.80177 | − | 5.80177i | −0.953805 | − | 0.953805i | 0.0451739 | − | 0.998979i | ||
−0.998979 | + | 0.0451739i | ||||||||
0 | 0 | |||||||||
−3.56282 | −0.570507 | |||||||||
0 | 0 | |||||||||
−2.61827 | −0.408905 | −0.204453 | − | 0.978876i | ||||||
−0.204453 | + | 0.978876i | ||||||||
0 | 0 | |||||||||
−5.14949 | − | 5.14949i | −0.785290 | − | 0.785290i | 0.195428 | − | 0.980718i | ||
−0.980718 | + | 0.195428i | ||||||||
0 | 0 | |||||||||
−0.0743018 | − | 2.23483i | −0.0110763 | − | 0.333149i | |||||
0 | 0 | |||||||||
−0.679824 | + | 0.679824i | −0.0991625 | + | 0.0991625i | −0.754948 | − | 0.655785i | ||
0.655785 | + | 0.754948i | ||||||||
0 | 0 | |||||||||
− | 12.9779i | − | 1.85399i | |||||||
0 | 0 | |||||||||
3.26561i | 0.457277i | |||||||||
0 | 0 | |||||||||
7.81739 | − | 7.81739i | 1.07380 | − | 1.07380i | 0.0767501 | − | 0.997050i | ||
0.997050 | − | 0.0767501i | ||||||||
0 | 0 | |||||||||
−0.332104 | − | 9.98896i | −0.0447809 | − | 1.34691i | |||||
0 | 0 | |||||||||
−1.85140 | − | 1.85140i | −0.245223 | − | 0.245223i | |||||
0 | 0 | |||||||||
4.88998 | 0.636621 | 0.318311 | − | 0.947986i | ||||||
0.318311 | + | 0.947986i | ||||||||
0 | 0 | |||||||||
−12.2751 | −1.57167 | −0.785834 | − | 0.618437i | ||||||
−0.785834 | + | 0.618437i | ||||||||
0 | 0 | |||||||||
3.16053 | + | 3.16053i | 0.398190 | + | 0.398190i | |||||
0 | 0 | |||||||||
−5.44301 | + | 5.81739i | −0.675122 | + | 0.721558i | |||||
0 | 0 | |||||||||
9.44670 | − | 9.44670i | 1.15410 | − | 1.15410i | 0.168375 | − | 0.985723i | ||
0.985723 | − | 0.168375i | ||||||||
0 | 0 | |||||||||
2.32106i | 0.279423i | |||||||||
0 | 0 | |||||||||
− | 5.65685i | − | 0.671345i | −0.941979 | − | 0.335673i | ||||
0.941979 | − | 0.335673i | ||||||||
0 | 0 | |||||||||
−5.61827 | + | 5.61827i | −0.657569 | + | 0.657569i | −0.954804 | − | 0.297235i | ||
0.297235 | + | 0.954804i | ||||||||
0 | 0 | |||||||||
−3.76256 | − | 3.29289i | −0.434463 | − | 0.380231i | |||||
0 | 0 | |||||||||
14.1265 | + | 14.1265i | 1.60987 | + | 1.60987i | |||||
0 | 0 | |||||||||
3.57969 | 0.402746 | 0.201373 | − | 0.979515i | ||||||
0.201373 | + | 0.979515i | ||||||||
0 | 0 | |||||||||
−1.00000 | −0.111111 | |||||||||
0 | 0 | |||||||||
1.34403 | + | 1.34403i | 0.147527 | + | 0.147527i | 0.777012 | − | 0.629486i | ||
−0.629486 | + | 0.777012i | ||||||||
0 | 0 | |||||||||
5.33210 | + | 4.98896i | 0.578348 | + | 0.541129i | |||||
0 | 0 | |||||||||
−5.77880 | + | 5.77880i | −0.619553 | + | 0.619553i | |||||
0 | 0 | |||||||||
− | 17.6348i | − | 1.86928i | −0.355593 | − | 0.934641i | ||||
0.355593 | − | 0.934641i | ||||||||
0 | 0 | |||||||||
− | 15.9246i | − | 1.66935i | |||||||
0 | 0 | |||||||||
2.82843 | − | 2.82843i | 0.293294 | − | 0.293294i | |||||
0 | 0 | |||||||||
−5.85140 | + | 0.194542i | −0.600341 | + | 0.0199596i | |||||
0 | 0 | |||||||||
−1.32106 | − | 1.32106i | −0.134134 | − | 0.134134i | 0.636852 | − | 0.770986i | ||
−0.770986 | + | 0.636852i | ||||||||
0 | 0 | |||||||||
−4.46967 | −0.449218 | |||||||||
0 | 0 | |||||||||
1.47702 | 0.146969 | 0.0734845 | − | 0.997296i | ||||||
0.0734845 | + | 0.997296i | ||||||||
0 | 0 | |||||||||
9.11459 | + | 9.11459i | 0.898088 | + | 0.898088i | 0.995267 | − | 0.0971794i | ||
−0.0971794 | + | 0.995267i | ||||||||
0 | 0 | |||||||||
9.98896 | − | 0.332104i | 0.974823 | − | 0.0324101i | |||||
0 | 0 | |||||||||
2.06155 | − | 2.06155i | 0.199298 | − | 0.199298i | −0.600401 | − | 0.799699i | ||
0.799699 | + | 0.600401i | ||||||||
0 | 0 | |||||||||
9.70279i | 0.929359i | 0.885479 | + | 0.464679i | ||||||
−0.885479 | + | 0.464679i | ||||||||
0 | 0 | |||||||||
8.20494i | 0.778779i | |||||||||
0 | 0 | |||||||||
−4.63020 | + | 4.63020i | −0.435572 | + | 0.435572i | −0.890519 | − | 0.454946i | ||
0.454946 | + | 0.890519i | ||||||||
0 | 0 | |||||||||
3.78984 | + | 3.54595i | 0.353405 | + | 0.330661i | |||||
0 | 0 | |||||||||
2.51929 | + | 2.51929i | 0.232909 | + | 0.232909i | |||||
0 | 0 | |||||||||
−14.5962 | −1.33803 | |||||||||
0 | 0 | |||||||||
−8.97792 | −0.816174 | |||||||||
0 | 0 | |||||||||
1.85140 | + | 1.85140i | 0.166935 | + | 0.166935i | |||||
0 | 0 | |||||||||
−11.1248 | + | 1.11289i | −0.995034 | + | 0.0995396i | |||||
0 | 0 | |||||||||
−10.1991 | + | 10.1991i | −0.905025 | + | 0.905025i | −0.995865 | − | 0.0908403i | ||
0.0908403 | + | 0.995865i | ||||||||
0 | 0 | |||||||||
7.28248i | 0.641186i | |||||||||
0 | 0 | |||||||||
12.4697i | 1.08948i | 0.838605 | + | 0.544740i | ||||||
−0.838605 | + | 0.544740i | ||||||||
0 | 0 | |||||||||
8.27512 | − | 8.27512i | 0.717544 | − | 0.717544i | |||||
0 | 0 | |||||||||
−1.52773 | + | 1.63280i | −0.131486 | + | 0.140529i | |||||
0 | 0 | |||||||||
4.63020 | + | 4.63020i | 0.395584 | + | 0.395584i | 0.876672 | − | 0.481088i | ||
−0.481088 | + | 0.876672i | ||||||||
0 | 0 | |||||||||
−3.00735 | −0.255080 | −0.127540 | − | 0.991833i | ||||||
−0.127540 | + | 0.991833i | ||||||||
0 | 0 | |||||||||
0.961416 | 0.0809658 | |||||||||
0 | 0 | |||||||||
11.2604 | + | 11.2604i | 0.941642 | + | 0.941642i | |||||
0 | 0 | |||||||||
0.607228 | + | 18.2641i | 0.0504276 | + | 1.51675i | |||||
0 | 0 | |||||||||
−9.17677 | + | 9.17677i | −0.756887 | + | 0.756887i | |||||
0 | 0 | |||||||||
− | 0.148604i | − | 0.0121741i | −0.999981 | − | 0.00608704i | ||||
0.999981 | − | 0.00608704i | ||||||||
0 | 0 | |||||||||
− | 20.6200i | − | 1.67804i | −0.544104 | − | 0.839018i | ||||
0.544104 | − | 0.839018i | ||||||||
0 | 0 | |||||||||
2.30913 | − | 2.30913i | 0.186682 | − | 0.186682i | |||||
0 | 0 | |||||||||
−0.297207 | − | 8.93933i | −0.0238723 | − | 0.718024i | |||||
0 | 0 | |||||||||
9.77969 | + | 9.77969i | 0.780504 | + | 0.780504i | 0.979916 | − | 0.199412i | ||
−0.199412 | + | 0.979916i | ||||||||
0 | 0 | |||||||||
−11.0555 | −0.876754 | |||||||||
0 | 0 | |||||||||
−10.3744 | −0.817615 | |||||||||
0 | 0 | |||||||||
10.4081 | + | 10.4081i | 0.815226 | + | 0.815226i | 0.985412 | − | 0.170186i | ||
−0.170186 | + | 0.985412i | ||||||||
0 | 0 | |||||||||
−6.82843 | + | 7.29809i | −0.531592 | + | 0.568156i | |||||
0 | 0 | |||||||||
6.06155 | − | 6.06155i | 0.469057 | − | 0.469057i | −0.432552 | − | 0.901609i | ||
0.901609 | + | 0.432552i | ||||||||
0 | 0 | |||||||||
0.306334i | 0.0235641i | |||||||||
0 | 0 | |||||||||
2.61827i | 0.200224i | |||||||||
0 | 0 | |||||||||
−0.355074 | + | 0.355074i | −0.0269957 | + | 0.0269957i | −0.720476 | − | 0.693480i | ||
0.693480 | + | 0.720476i | ||||||||
0 | 0 | |||||||||
14.7181 | − | 16.8174i | 1.11259 | − | 1.27127i | |||||
0 | 0 | |||||||||
−3.45774 | − | 3.45774i | −0.259900 | − | 0.259900i | |||||
0 | 0 | |||||||||
15.7521 | 1.17737 | 0.588685 | − | 0.808362i | ||||||
0.588685 | + | 0.808362i | ||||||||
0 | 0 | |||||||||
−7.77996 | −0.578280 | −0.289140 | − | 0.957287i | ||||||
−0.289140 | + | 0.957287i | ||||||||
0 | 0 | |||||||||
8.67982 | + | 8.67982i | 0.641631 | + | 0.641631i | |||||
0 | 0 | |||||||||
13.3971 | + | 12.5349i | 0.984972 | + | 0.921585i | |||||
0 | 0 | |||||||||
10.3211 | − | 10.3211i | 0.754751 | − | 0.754751i | |||||
0 | 0 | |||||||||
− | 4.46967i | − | 0.325120i | |||||||
0 | 0 | |||||||||
9.35965i | 0.677240i | 0.940923 | + | 0.338620i | ||||||
−0.940923 | + | 0.338620i | ||||||||
0 | 0 | |||||||||
17.1759 | − | 17.1759i | 1.23635 | − | 1.23635i | 0.274863 | − | 0.961483i | ||
0.961483 | − | 0.274863i | ||||||||
0 | 0 | |||||||||
7.96230 | − | 0.264724i | 0.570192 | − | 0.0189573i | |||||
0 | 0 | |||||||||
−1.83947 | − | 1.83947i | −0.131057 | − | 0.131057i | 0.638536 | − | 0.769592i | ||
−0.769592 | + | 0.638536i | ||||||||
0 | 0 | |||||||||
0.442397 | 0.0313607 | 0.0156804 | − | 0.999877i | ||||||
0.0156804 | + | 0.999877i | ||||||||
0 | 0 | |||||||||
−13.3596 | −0.942317 | |||||||||
0 | 0 | |||||||||
−25.8293 | − | 25.8293i | −1.81286 | − | 1.81286i | |||||
0 | 0 | |||||||||
5.85140 | − | 0.194542i | 0.408679 | − | 0.0135874i | |||||
0 | 0 | |||||||||
1.64124 | − | 1.64124i | 0.114074 | − | 0.114074i | |||||
0 | 0 | |||||||||
11.7028i | 0.809499i | |||||||||
0 | 0 | |||||||||
5.30633i | 0.365303i | 0.983178 | + | 0.182652i | ||||||
−0.983178 | + | 0.182652i | ||||||||
0 | 0 | |||||||||
−4.00000 | + | 4.00000i | −0.274075 | + | 0.274075i | |||||
0 | 0 | |||||||||
11.8909 | + | 11.1256i | 0.810950 | + | 0.758762i | |||||
0 | 0 | |||||||||
12.6421 | + | 12.6421i | 0.858203 | + | 0.858203i | |||||
0 | 0 | |||||||||
7.94543 | 0.536903 | |||||||||
0 | 0 | |||||||||
−11.6348 | −0.782639 | |||||||||
0 | 0 | |||||||||
−5.48159 | − | 5.48159i | −0.367075 | − | 0.367075i | 0.499335 | − | 0.866409i | ||
−0.866409 | + | 0.499335i | ||||||||
0 | 0 | |||||||||
0.332104 | + | 4.98896i | 0.0221403 | + | 0.332597i | |||||
0 | 0 | |||||||||
−9.51649 | + | 9.51649i | −0.631632 | + | 0.631632i | −0.948477 | − | 0.316845i | ||
0.316845 | + | 0.948477i | ||||||||
0 | 0 | |||||||||
5.25862i | 0.347500i | 0.984790 | + | 0.173750i | ||||||
−0.984790 | + | 0.173750i | ||||||||
0 | 0 | |||||||||
− | 19.9779i | − | 1.31445i | |||||||
0 | 0 | |||||||||
2.92740 | − | 2.92740i | 0.191781 | − | 0.191781i | −0.604684 | − | 0.796465i | ||
0.796465 | + | 0.604684i | ||||||||
0 | 0 | |||||||||
1.46878 | − | 1.56980i | 0.0958126 | − | 0.102403i | |||||
0 | 0 | |||||||||
−2.53122 | − | 2.53122i | −0.164420 | − | 0.164420i | |||||
0 | 0 | |||||||||
12.6421 | 0.817751 | 0.408876 | − | 0.912590i | ||||||
0.408876 | + | 0.912590i | ||||||||
0 | 0 | |||||||||
14.5650 | 0.938211 | 0.469106 | − | 0.883142i | ||||||
0.469106 | + | 0.883142i | ||||||||
0 | 0 | |||||||||
0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | |||||
0 | 0 | |||||||||
0.964283 | + | 29.0035i | 0.0616058 | + | 1.85296i | |||||
0 | 0 | |||||||||
6.59619 | − | 6.59619i | 0.419705 | − | 0.419705i | |||||
0 | 0 | |||||||||
− | 1.90075i | − | 0.120455i | |||||||
0 | 0 | |||||||||
18.5468i | 1.17067i | 0.810793 | + | 0.585333i | ||||||
−0.810793 | + | 0.585333i | ||||||||
0 | 0 | |||||||||
7.33579 | − | 7.33579i | 0.461197 | − | 0.461197i | |||||
0 | 0 | |||||||||
−0.242641 | − | 7.29809i | −0.0151947 | − | 0.457024i | |||||
0 | 0 | |||||||||
13.2485 | + | 13.2485i | 0.826417 | + | 0.826417i | 0.987019 | − | 0.160602i | ||
−0.160602 | + | 0.987019i | ||||||||
0 | 0 | |||||||||
−36.6734 | −2.27877 | |||||||||
0 | 0 | |||||||||
8.17246 | 0.505863 | |||||||||
0 | 0 | |||||||||
−22.5806 | − | 22.5806i | −1.39238 | − | 1.39238i | −0.819967 | − | 0.572411i | ||
−0.572411 | − | 0.819967i | ||||||||
0 | 0 | |||||||||
−16.8897 | + | 18.0514i | −1.03753 | + | 1.10889i | |||||
0 | 0 | |||||||||
−12.4697 | + | 12.4697i | −0.763131 | + | 0.763131i | |||||
0 | 0 | |||||||||
− | 6.82019i | − | 0.415834i | −0.978146 | − | 0.207917i | ||||
0.978146 | − | 0.207917i | ||||||||
0 | 0 | |||||||||
2.74138i | 0.166527i | 0.996528 | + | 0.0832634i | ||||||
−0.996528 | + | 0.0832634i | ||||||||
0 | 0 | |||||||||
−11.2604 | + | 11.2604i | −0.681510 | + | 0.681510i | |||||
0 | 0 | |||||||||
1.48440 | + | 22.2990i | 0.0895124 | + | 1.34468i | |||||
0 | 0 | |||||||||
7.75583 | + | 7.75583i | 0.466003 | + | 0.466003i | 0.900617 | − | 0.434614i | ||
−0.434614 | + | 0.900617i | ||||||||
0 | 0 | |||||||||
−4.00000 | −0.239474 | |||||||||
0 | 0 | |||||||||
4.54110 | 0.270899 | 0.135450 | − | 0.990784i | ||||||
0.135450 | + | 0.990784i | ||||||||
0 | 0 | |||||||||
7.91295 | + | 7.91295i | 0.470376 | + | 0.470376i | 0.902036 | − | 0.431660i | ||
−0.431660 | + | 0.902036i | ||||||||
0 | 0 | |||||||||
4.27512 | + | 4.00000i | 0.253236 | + | 0.236940i | |||||
0 | 0 | |||||||||
−8.27512 | + | 8.27512i | −0.488465 | + | 0.488465i | |||||
0 | 0 | |||||||||
− | 6.33579i | − | 0.372694i | |||||||
0 | 0 | |||||||||
1.86826i | 0.109520i | |||||||||
0 | 0 | |||||||||
−15.0999 | + | 15.0999i | −0.882143 | + | 0.882143i | −0.993752 | − | 0.111609i | ||
0.111609 | + | 0.993752i | ||||||||
0 | 0 | |||||||||
−10.9283 | + | 0.363334i | −0.636270 | + | 0.0211541i | |||||
0 | 0 | |||||||||
3.16053 | + | 3.16053i | 0.183393 | + | 0.183393i | |||||
0 | 0 | |||||||||
−8.26952 | −0.478239 | |||||||||
0 | 0 | |||||||||
−32.5502 | −1.87617 | |||||||||
0 | 0 | |||||||||
−1.04441 | − | 1.04441i | −0.0599999 | − | 0.0599999i | |||||
0 | 0 | |||||||||
27.4329 | − | 0.912064i | 1.57080 | − | 0.0522246i | |||||
0 | 0 | |||||||||
4.43197 | − | 4.43197i | 0.252946 | − | 0.252946i | −0.569232 | − | 0.822177i | ||
0.822177 | + | 0.569232i | ||||||||
0 | 0 | |||||||||
− | 12.8900i | − | 0.733285i | |||||||
0 | 0 | |||||||||
23.5355i | 1.33458i | 0.744799 | + | 0.667288i | ||||||
−0.744799 | + | 0.667288i | ||||||||
0 | 0 | |||||||||
−18.6035 | + | 18.6035i | −1.05153 | + | 1.05153i | −0.0529364 | + | 0.998598i | ||
−0.998598 | + | 0.0529364i | ||||||||
0 | 0 | |||||||||
−7.29809 | − | 6.82843i | −0.411201 | − | 0.384738i | |||||
0 | 0 | |||||||||
−7.56953 | − | 7.56953i | −0.425147 | − | 0.425147i | 0.461824 | − | 0.886971i | ||
−0.886971 | + | 0.461824i | ||||||||
0 | 0 | |||||||||
36.5282 | 2.04518 | |||||||||
0 | 0 | |||||||||
−2.91548 | −0.162726 | |||||||||
0 | 0 | |||||||||
−6.04594 | − | 6.04594i | −0.336405 | − | 0.336405i | |||||
0 | 0 | |||||||||
11.7320 | − | 13.4053i | 0.650773 | − | 0.743593i | |||||
0 | 0 | |||||||||
6.86091 | − | 6.86091i | 0.379409 | − | 0.379409i | |||||
0 | 0 | |||||||||
4.29721i | 0.236913i | |||||||||
0 | 0 | |||||||||
− | 13.8020i | − | 0.758629i | −0.925268 | − | 0.379314i | ||||
0.925268 | − | 0.379314i | ||||||||
0 | 0 | |||||||||
5.80177 | − | 5.80177i | 0.317935 | − | 0.317935i | |||||
0 | 0 | |||||||||
−20.4099 | + | 21.8137i | −1.11511 | + | 1.19181i | |||||
0 | 0 | |||||||||
10.9541 | + | 10.9541i | 0.596706 | + | 0.596706i | 0.939434 | − | 0.342729i | ||
−0.342729 | + | 0.939434i | ||||||||
0 | 0 | |||||||||
6.54809 | 0.355643 | |||||||||
0 | 0 | |||||||||
−17.8787 | −0.968184 | |||||||||
0 | 0 | |||||||||
−18.8934 | − | 18.8934i | −1.02015 | − | 1.02015i | |||||
0 | 0 | |||||||||
−0.172459 | − | 5.18719i | −0.00928489 | − | 0.279269i | |||||
0 | 0 | |||||||||
13.3934 | − | 13.3934i | 0.718995 | − | 0.718995i | −0.249405 | − | 0.968399i | ||
0.968399 | + | 0.249405i | ||||||||
0 | 0 | |||||||||
21.6035i | 1.15641i | 0.815891 | + | 0.578206i | ||||||
−0.815891 | + | 0.578206i | ||||||||
0 | 0 | |||||||||
− | 3.56282i | − | 0.190169i | |||||||
0 | 0 | |||||||||
25.9678 | − | 25.9678i | 1.38212 | − | 1.38212i | 0.541286 | − | 0.840839i | ||
0.840839 | − | 0.541286i | ||||||||
0 | 0 | |||||||||
0.420314 | + | 12.6421i | 0.0223080 | + | 0.670974i | |||||
0 | 0 | |||||||||
10.3211 | + | 10.3211i | 0.546249 | + | 0.546249i | |||||
0 | 0 | |||||||||
8.93933 | 0.471800 | 0.235900 | − | 0.971777i | ||||||
0.235900 | + | 0.971777i | ||||||||
0 | 0 | |||||||||
−12.1447 | −0.639193 | |||||||||
0 | 0 | |||||||||
6.34835 | + | 6.34835i | 0.333202 | + | 0.333202i | |||||
0 | 0 | |||||||||
12.1384 | − | 12.9733i | 0.635355 | − | 0.679056i | |||||
0 | 0 | |||||||||
−13.7788 | + | 13.7788i | −0.719248 | + | 0.719248i | −0.968451 | − | 0.249204i | ||
0.249204 | + | 0.968451i | ||||||||
0 | 0 | |||||||||
− | 2.61827i | − | 0.136302i | |||||||
0 | 0 | |||||||||
− | 49.4142i | − | 2.56546i | |||||||
0 | 0 | |||||||||
12.4439 | − | 12.4439i | 0.644321 | − | 0.644321i | −0.307294 | − | 0.951615i | ||
0.951615 | + | 0.307294i | ||||||||
0 | 0 | |||||||||
8.65336 | + | 7.07950i | 0.446858 | + | 0.365584i | |||||
0 | 0 | |||||||||
−20.5888 | − | 20.5888i | −1.06038 | − | 1.06038i | |||||
0 | 0 | |||||||||
34.9190 | 1.79367 | 0.896835 | − | 0.442366i | ||||||
0.896835 | + | 0.442366i | ||||||||
0 | 0 | |||||||||
14.4237 | 0.738950 | |||||||||
0 | 0 | |||||||||
−5.69455 | − | 5.69455i | −0.290978 | − | 0.290978i | 0.546489 | − | 0.837467i | ||
−0.837467 | + | 0.546489i | ||||||||
0 | 0 | |||||||||
−32.6200 | − | 30.5208i | −1.66247 | − | 1.55548i | |||||
0 | 0 | |||||||||
5.14949 | − | 5.14949i | 0.261763 | − | 0.261763i | |||||
0 | 0 | |||||||||
− | 8.44581i | − | 0.428220i | −0.976810 | − | 0.214110i | ||||
0.976810 | − | 0.214110i | ||||||||
0 | 0 | |||||||||
7.57969i | 0.383321i | |||||||||
0 | 0 | |||||||||
8.81739 | − | 8.81739i | 0.444778 | − | 0.444778i | |||||
0 | 0 | |||||||||
−8.00000 | + | 0.265977i | −0.402524 | + | 0.0133828i | |||||
0 | 0 | |||||||||
−18.0769 | − | 18.0769i | −0.907253 | − | 0.907253i | 0.0887965 | − | 0.996050i | ||
−0.996050 | + | 0.0887965i | ||||||||
0 | 0 | |||||||||
−11.7028 | −0.585872 | |||||||||
0 | 0 | |||||||||
−31.8787 | −1.59194 | −0.795972 | − | 0.605333i | ||||||
−0.795972 | + | 0.605333i | ||||||||
0 | 0 | |||||||||
10.0772 | + | 10.0772i | 0.501980 | + | 0.501980i | |||||
0 | 0 | |||||||||
2.23483 | − | 0.0743018i | 0.111050 | − | 0.00369209i | |||||
0 | 0 | |||||||||
25.9320 | − | 25.9320i | 1.28540 | − | 1.28540i | |||||
0 | 0 | |||||||||
− | 27.3063i | − | 1.35021i | −0.737721 | − | 0.675106i | ||||
0.737721 | − | 0.675106i | ||||||||
0 | 0 | |||||||||
− | 6.54809i | − | 0.322993i | |||||||
0 | 0 | |||||||||
15.4549 | − | 15.4549i | 0.760488 | − | 0.760488i | |||||
0 | 0 | |||||||||
−3.10355 | − | 2.90382i | −0.152347 | − | 0.142543i | |||||
0 | 0 | |||||||||
2.12652 | + | 2.12652i | 0.104136 | + | 0.104136i | |||||
0 | 0 | |||||||||
16.1412 | 0.788551 | 0.394275 | − | 0.918992i | ||||||
0.394275 | + | 0.918992i | ||||||||
0 | 0 | |||||||||
20.6200 | 1.00496 | 0.502480 | − | 0.864589i | ||||||
0.502480 | + | 0.864589i | ||||||||
0 | 0 | |||||||||
−0.679824 | − | 0.679824i | −0.0330542 | − | 0.0330542i | |||||
0 | 0 | |||||||||
−12.2871 | − | 10.7533i | −0.596010 | − | 0.521612i | |||||
0 | 0 | |||||||||
−38.7959 | + | 38.7959i | −1.87747 | + | 1.87747i | |||||
0 | 0 | |||||||||
− | 15.9246i | − | 0.768847i | |||||||
0 | 0 | |||||||||
2.54848i | 0.122756i | 0.998115 | + | 0.0613779i | ||||||
−0.998115 | + | 0.0613779i | ||||||||
0 | 0 | |||||||||
6.77996 | − | 6.77996i | 0.325824 | − | 0.325824i | −0.525172 | − | 0.850996i | ||
0.850996 | + | 0.525172i | ||||||||
0 | 0 | |||||||||
12.4853 | − | 13.3440i | 0.598623 | − | 0.639797i | |||||
0 | 0 | |||||||||
−4.29721 | − | 4.29721i | −0.205563 | − | 0.205563i | |||||
0 | 0 | |||||||||
−15.0698 | −0.719243 | −0.359622 | − | 0.933098i | ||||||
−0.359622 | + | 0.933098i | ||||||||
0 | 0 | |||||||||
12.9779 | 0.617996 | |||||||||
0 | 0 | |||||||||
−9.69059 | − | 9.69059i | −0.460414 | − | 0.460414i | 0.438377 | − | 0.898791i | ||
−0.898791 | + | 0.438377i | ||||||||
0 | 0 | |||||||||
1.31030 | + | 39.4108i | 0.0621139 | + | 1.86825i | |||||
0 | 0 | |||||||||
−0.105079 | + | 0.105079i | −0.00497005 | + | 0.00497005i | |||||
0 | 0 | |||||||||
20.1759i | 0.952158i | 0.879402 | + | 0.476079i | ||||||
−0.879402 | + | 0.476079i | ||||||||
0 | 0 | |||||||||
− | 11.7028i | − | 0.551063i | |||||||
0 | 0 | |||||||||
−14.5806 | + | 14.5806i | −0.685055 | + | 0.685055i | |||||
0 | 0 | |||||||||
1.18323 | + | 35.5888i | 0.0554705 | + | 1.66843i | |||||
0 | 0 | |||||||||
−0.579686 | − | 0.579686i | −0.0271165 | − | 0.0271165i | 0.693419 | − | 0.720535i | ||
−0.720535 | + | 0.693419i | ||||||||
0 | 0 | |||||||||
−3.26561 | −0.152426 | |||||||||
0 | 0 | |||||||||
4.40164 | 0.205005 | 0.102503 | − | 0.994733i | ||||||
0.102503 | + | 0.994733i | ||||||||
0 | 0 | |||||||||
0.786155 | + | 0.786155i | 0.0365357 | + | 0.0365357i | 0.725139 | − | 0.688603i | ||
−0.688603 | + | 0.725139i | ||||||||
0 | 0 | |||||||||
−6.11091 | + | 6.53122i | −0.283386 | + | 0.302878i | |||||
0 | 0 | |||||||||
19.6430 | − | 19.6430i | 0.908970 | − | 0.908970i | −0.0872190 | − | 0.996189i | ||
0.996189 | + | 0.0872190i | ||||||||
0 | 0 | |||||||||
− | 59.7132i | − | 2.75730i | |||||||
0 | 0 | |||||||||
− | 13.8306i | − | 0.637279i | |||||||
0 | 0 | |||||||||
23.0165 | − | 23.0165i | 1.05830 | − | 1.05830i | |||||
0 | 0 | |||||||||
13.0624 | − | 0.869539i | 0.599346 | − | 0.0398972i | |||||
0 | 0 | |||||||||
7.81739 | + | 7.81739i | 0.357933 | + | 0.357933i | |||||
0 | 0 | |||||||||
30.6274 | 1.39940 | 0.699701 | − | 0.714436i | ||||||
0.699701 | + | 0.714436i | ||||||||
0 | 0 | |||||||||
−29.2327 | −1.33290 | |||||||||
0 | 0 | |||||||||
7.33579 | + | 7.33579i | 0.333790 | + | 0.333790i | |||||
0 | 0 | |||||||||
3.05051 | + | 2.85420i | 0.138517 | + | 0.129602i | |||||
0 | 0 | |||||||||
−24.7641 | + | 24.7641i | −1.12217 | + | 1.12217i | −0.130752 | + | 0.991415i | ||
−0.991415 | + | 0.130752i | ||||||||
0 | 0 | |||||||||
− | 14.7193i | − | 0.665629i | |||||||
0 | 0 | |||||||||
23.3318i | 1.05295i | 0.850190 | + | 0.526475i | ||||||
−0.850190 | + | 0.526475i | ||||||||
0 | 0 | |||||||||
−18.8713 | + | 18.8713i | −0.849921 | + | 0.849921i | |||||
0 | 0 | |||||||||
9.98896 | − | 0.332104i | 0.448970 | − | 0.0149270i | |||||
0 | 0 | |||||||||
−17.8787 | − | 17.8787i | −0.801968 | − | 0.801968i | |||||
0 | 0 | |||||||||
−40.4051 | −1.80878 | −0.904389 | − | 0.426708i | ||||||
−0.904389 | + | 0.426708i | ||||||||
0 | 0 | |||||||||
−8.57233 | −0.382984 | |||||||||
0 | 0 | |||||||||
−0.160805 | − | 0.160805i | −0.00716996 | − | 0.00716996i | 0.703513 | − | 0.710683i | ||
−0.710683 | + | 0.703513i | ||||||||
0 | 0 | |||||||||
−3.30089 | + | 0.109745i | −0.146888 | + | 0.00488360i | |||||
0 | 0 | |||||||||
0.216611 | − | 0.216611i | 0.00962002 | − | 0.00962002i | |||||
0 | 0 | |||||||||
− | 11.4862i | − | 0.509115i | −0.967058 | − | 0.254558i | ||||
0.967058 | − | 0.254558i | ||||||||
0 | 0 | |||||||||
35.5134i | 1.57102i | |||||||||
0 | 0 | |||||||||
1.85140 | − | 1.85140i | 0.0817411 | − | 0.0817411i | |||||
0 | 0 | |||||||||
−21.0468 | − | 19.6924i | −0.927434 | − | 0.867749i | |||||
0 | 0 | |||||||||
−3.03858 | − | 3.03858i | −0.133637 | − | 0.133637i | |||||
0 | 0 | |||||||||
0.502150 | 0.0220419 | |||||||||
0 | 0 | |||||||||
16.3744 | 0.717374 | 0.358687 | − | 0.933458i | ||||||
0.358687 | + | 0.933458i | ||||||||
0 | 0 | |||||||||
5.02638 | + | 5.02638i | 0.219788 | + | 0.219788i | 0.808409 | − | 0.588621i | ||
−0.588621 | + | 0.808409i | ||||||||
0 | 0 | |||||||||
−22.2990 | + | 1.48440i | −0.973207 | + | 0.0647843i | |||||
0 | 0 | |||||||||
9.23654 | − | 9.23654i | 0.402350 | − | 0.402350i | |||||
0 | 0 | |||||||||
− | 17.6127i | − | 0.765768i | |||||||
0 | 0 | |||||||||
4.88998i | 0.212207i | |||||||||
0 | 0 | |||||||||
−6.59619 | + | 6.59619i | −0.285713 | + | 0.285713i | |||||
0 | 0 | |||||||||
−4.45405 | + | 4.76041i | −0.192565 | + | 0.205810i | |||||
0 | 0 | |||||||||
−11.1384 | − | 11.1384i | −0.480660 | − | 0.480660i | |||||
0 | 0 | |||||||||
58.0070 | 2.49854 | |||||||||
0 | 0 | |||||||||
32.3302 | 1.38998 | 0.694992 | − | 0.719017i | ||||||
0.694992 | + | 0.719017i | ||||||||
0 | 0 | |||||||||
5.50126 | + | 5.50126i | 0.236082 | + | 0.236082i | |||||
0 | 0 | |||||||||
−0.720935 | − | 21.6841i | −0.0308815 | − | 0.928846i | |||||
0 | 0 | |||||||||
−8.01165 | + | 8.01165i | −0.342554 | + | 0.342554i | −0.857327 | − | 0.514773i | ||
0.514773 | + | 0.857327i | ||||||||
0 | 0 | |||||||||
− | 12.2751i | − | 0.523890i | |||||||
0 | 0 | |||||||||
− | 21.3977i | − | 0.911573i | |||||||
0 | 0 | |||||||||
11.3137 | − | 11.3137i | 0.481108 | − | 0.481108i | |||||
0 | 0 | |||||||||
−0.609642 | − | 18.3367i | −0.0258779 | − | 0.778349i | |||||
0 | 0 | |||||||||
−0.138448 | − | 0.138448i | −0.00586624 | − | 0.00586624i | 0.704168 | − | 0.710034i | ||
−0.710034 | + | 0.704168i | ||||||||
0 | 0 | |||||||||
−25.9461 | −1.09740 | |||||||||
0 | 0 | |||||||||
−14.5962 | −0.616251 | |||||||||
0 | 0 | |||||||||
14.7843 | + | 14.7843i | 0.623082 | + | 0.623082i | 0.946318 | − | 0.323236i | ||
−0.323236 | + | 0.946318i | ||||||||
0 | 0 | |||||||||
10.0037 | − | 10.6918i | 0.420858 | − | 0.449805i | |||||
0 | 0 | |||||||||
−3.16053 | + | 3.16053i | −0.132730 | + | 0.132730i | |||||
0 | 0 | |||||||||
29.9558i | 1.25581i | 0.778288 | + | 0.627907i | ||||||
−0.778288 | + | 0.627907i | ||||||||
0 | 0 | |||||||||
8.52134i | 0.356607i | 0.983976 | + | 0.178303i | ||||||
−0.983976 | + | 0.178303i | ||||||||
0 | 0 | |||||||||
6.61827 | − | 6.61827i | 0.276482 | − | 0.276482i | |||||
0 | 0 | |||||||||
−8.73314 | − | 7.64301i | −0.364197 | − | 0.318736i | |||||
0 | 0 | |||||||||
10.9779 | + | 10.9779i | 0.457017 | + | 0.457017i | 0.897675 | − | 0.440658i | ||
−0.440658 | + | 0.897675i | ||||||||
0 | 0 | |||||||||
−24.2904 | −1.00947 | |||||||||
0 | 0 | |||||||||
8.49571 | 0.352461 | |||||||||
0 | 0 | |||||||||
34.9411 | + | 34.9411i | 1.44711 | + | 1.44711i | |||||
0 | 0 | |||||||||
−5.81739 | − | 5.44301i | −0.240519 | − | 0.225041i | |||||
0 | 0 | |||||||||
−18.0174 | + | 18.0174i | −0.743657 | + | 0.743657i | −0.973280 | − | 0.229623i | ||
0.229623 | + | 0.973280i | ||||||||
0 | 0 | |||||||||
10.4731i | 0.431536i | |||||||||
0 | 0 | |||||||||
2.60140i | 0.107007i | |||||||||
0 | 0 | |||||||||
−25.8906 | + | 25.8906i | −1.06320 | + | 1.06320i | −0.0653359 | + | 0.997863i | ||
−0.997863 | + | 0.0653359i | ||||||||
0 | 0 | |||||||||
32.6200 | − | 1.08452i | 1.33729 | − | 0.0444611i | |||||
0 | 0 | |||||||||
−0.312822 | − | 0.312822i | −0.0128030 | − | 0.0128030i | |||||
0 | 0 | |||||||||
−8.89517 | −0.363447 | −0.181723 | − | 0.983350i | ||||||
−0.181723 | + | 0.983350i | ||||||||
0 | 0 | |||||||||
35.3393 | 1.44152 | 0.720761 | − | 0.693184i | ||||||
0.720761 | + | 0.693184i | ||||||||
0 | 0 | |||||||||
9.44670 | + | 9.44670i | 0.384699 | + | 0.384699i | |||||
0 | 0 | |||||||||
20.0641 | − | 0.667075i | 0.815724 | − | 0.0271205i | |||||
0 | 0 | |||||||||
4.90926 | − | 4.90926i | 0.199261 | − | 0.199261i | −0.600422 | − | 0.799683i | ||
0.799683 | + | 0.600422i | ||||||||
0 | 0 | |||||||||
36.5282i | 1.48020i | |||||||||
0 | 0 | |||||||||
3.42535i | 0.138575i | |||||||||
0 | 0 | |||||||||
−1.87894 | + | 1.87894i | −0.0758896 | + | 0.0758896i | −0.744033 | − | 0.668143i | ||
0.668143 | + | 0.744033i | ||||||||
0 | 0 | |||||||||
−4.27512 | − | 4.00000i | −0.172390 | − | 0.161296i | |||||
0 | 0 | |||||||||
−5.07260 | − | 5.07260i | −0.204215 | − | 0.204215i | 0.597588 | − | 0.801803i | ||
−0.801803 | + | 0.597588i | ||||||||
0 | 0 | |||||||||
−46.2769 | −1.86003 | −0.930013 | − | 0.367527i | ||||||
−0.930013 | + | 0.367527i | ||||||||
0 | 0 | |||||||||
−2.32106 | −0.0931410 | |||||||||
0 | 0 | |||||||||
−55.7352 | − | 55.7352i | −2.23299 | − | 2.23299i | |||||
0 | 0 | |||||||||
24.7794 | − | 3.31371i | 0.991177 | − | 0.132548i | |||||
0 | 0 | |||||||||
8.27512 | − | 8.27512i | 0.330477 | − | 0.330477i | |||||
0 | 0 | |||||||||
26.7941i | 1.06835i | |||||||||
0 | 0 | |||||||||
36.6457i | 1.45884i | 0.684066 | + | 0.729421i | ||||||
−0.684066 | + | 0.729421i | ||||||||
0 | 0 | |||||||||
3.75214 | − | 3.75214i | 0.149134 | − | 0.149134i | |||||
0 | 0 | |||||||||
22.0355 | − | 23.5511i | 0.874453 | − | 0.934598i | |||||
0 | 0 | |||||||||
−32.6952 | − | 32.6952i | −1.29543 | − | 1.29543i | |||||
0 | 0 | |||||||||
5.65685 | 0.223782 | |||||||||
0 | 0 | |||||||||
−12.1520 | −0.479976 | −0.239988 | − | 0.970776i | ||||||
−0.239988 | + | 0.970776i | ||||||||
0 | 0 | |||||||||
6.53122 | + | 6.53122i | 0.257566 | + | 0.257566i | 0.824064 | − | 0.566497i | ||
−0.566497 | + | 0.824064i | ||||||||
0 | 0 | |||||||||
−0.541101 | − | 16.2751i | −0.0213058 | − | 0.640832i | |||||
0 | 0 | |||||||||
17.6192 | − | 17.6192i | 0.692681 | − | 0.692681i | −0.270140 | − | 0.962821i | ||
0.962821 | + | 0.270140i | ||||||||
0 | 0 | |||||||||
21.8566i | 0.857946i | |||||||||
0 | 0 | |||||||||
− | 17.8787i | − | 0.700720i | |||||||
0 | 0 | |||||||||
−0.727677 | + | 0.727677i | −0.0284762 | + | 0.0284762i | −0.721202 | − | 0.692725i | ||
0.692725 | + | 0.721202i | ||||||||
0 | 0 | |||||||||
−0.926519 | − | 27.8676i | −0.0362021 | − | 1.08888i | |||||
0 | 0 | |||||||||
−5.61827 | − | 5.61827i | −0.219190 | − | 0.219190i | |||||
0 | 0 | |||||||||
−44.9004 | −1.74907 | −0.874535 | − | 0.484963i | ||||||
−0.874535 | + | 0.484963i | ||||||||
0 | 0 | |||||||||
−14.9320 | −0.580786 | −0.290393 | − | 0.956907i | ||||||
−0.290393 | + | 0.956907i | ||||||||
0 | 0 | |||||||||
8.22703 | + | 8.22703i | 0.319511 | + | 0.319511i | |||||
0 | 0 | |||||||||
−17.8787 | + | 19.1084i | −0.693305 | + | 0.740991i | |||||
0 | 0 | |||||||||
−13.4130 | + | 13.4130i | −0.519352 | + | 0.519352i | |||||
0 | 0 | |||||||||
7.75214i | 0.299715i | |||||||||
0 | 0 | |||||||||
− | 54.8657i | − | 2.11807i | |||||||
0 | 0 | |||||||||
2.55583 | − | 2.55583i | 0.0985200 | − | 0.0985200i | −0.656129 | − | 0.754649i | ||
0.754649 | + | 0.656129i | ||||||||
0 | 0 | |||||||||
3.29289 | − | 3.76256i | 0.126744 | − | 0.144821i | |||||
0 | 0 | |||||||||
−17.7147 | − | 17.7147i | −0.680832 | − | 0.680832i | 0.279356 | − | 0.960188i | ||
−0.960188 | + | 0.279356i | ||||||||
0 | 0 | |||||||||
−8.35052 | −0.320464 | |||||||||
0 | 0 | |||||||||
13.4584 | 0.515725 | |||||||||
0 | 0 | |||||||||
11.3968 | + | 11.3968i | 0.436086 | + | 0.436086i | 0.890693 | − | 0.454606i | ||
−0.454606 | + | 0.890693i | ||||||||
0 | 0 | |||||||||
−10.6918 | − | 10.0037i | −0.408511 | − | 0.382221i | |||||
0 | 0 | |||||||||
3.71841 | − | 3.71841i | 0.141866 | − | 0.141866i | |||||
0 | 0 | |||||||||
− | 39.3886i | − | 1.50058i | |||||||
0 | 0 | |||||||||
− | 6.94671i | − | 0.264265i | −0.991232 | − | 0.132133i | ||||
0.991232 | − | 0.132133i | ||||||||
0 | 0 | |||||||||
−14.1265 | + | 14.1265i | −0.536622 | + | 0.536622i | |||||
0 | 0 | |||||||||
6.72093 | − | 0.223452i | 0.254940 | − | 0.00847601i | |||||
0 | 0 | |||||||||
6.04594 | + | 6.04594i | 0.229006 | + | 0.229006i | |||||
0 | 0 | |||||||||
−4.13998 | −0.156588 | |||||||||
0 | 0 | |||||||||
9.70621 | 0.366598 | 0.183299 | − | 0.983057i | ||||||
0.183299 | + | 0.983057i | ||||||||
0 | 0 | |||||||||
−15.1906 | − | 15.1906i | −0.572924 | − | 0.572924i | |||||
0 | 0 | |||||||||
−2.14860 | + | 0.0714349i | −0.0809211 | + | 0.00269039i | |||||
0 | 0 | |||||||||
4.66817 | − | 4.66817i | 0.175565 | − | 0.175565i | |||||
0 | 0 | |||||||||
10.7414i | 0.403401i | 0.979447 | + | 0.201700i | ||||||
−0.979447 | + | 0.201700i | ||||||||
0 | 0 | |||||||||
3.57969i | 0.134249i | |||||||||
0 | 0 | |||||||||
6.56496 | − | 6.56496i | 0.245860 | − | 0.245860i | |||||
0 | 0 | |||||||||
−26.0018 | − | 24.3284i | −0.972411 | − | 0.909832i | |||||
0 | 0 | |||||||||
−8.93933 | − | 8.93933i | −0.333845 | − | 0.333845i | |||||
0 | 0 | |||||||||
43.8640 | 1.63585 | 0.817925 | − | 0.575325i | ||||||
0.817925 | + | 0.575325i | ||||||||
0 | 0 | |||||||||
57.6139 | 2.14565 | |||||||||
0 | 0 | |||||||||
−10.2990 | − | 10.2990i | −0.383023 | − | 0.383023i | |||||
0 | 0 | |||||||||
−2.71411 | − | 40.7721i | −0.100799 | − | 1.51424i | |||||
0 | 0 | |||||||||
9.95522 | − | 9.95522i | 0.369219 | − | 0.369219i | −0.497974 | − | 0.867192i | ||
0.867192 | + | 0.497974i | ||||||||
0 | 0 | |||||||||
− | 1.00000i | − | 0.0370370i | |||||||
0 | 0 | |||||||||
23.7817i | 0.879599i | |||||||||
0 | 0 | |||||||||
−16.9924 | + | 16.9924i | −0.627628 | + | 0.627628i | −0.947471 | − | 0.319843i | ||
0.319843 | + | 0.947471i | ||||||||
0 | 0 | |||||||||
19.8267 | − | 21.1904i | 0.731319 | − | 0.781620i | |||||
0 | 0 | |||||||||
42.2236 | + | 42.2236i | 1.55533 | + | 1.55533i | |||||
0 | 0 | |||||||||
−27.9025 | −1.02641 | −0.513205 | − | 0.858266i | ||||||
−0.513205 | + | 0.858266i | ||||||||
0 | 0 | |||||||||
−9.32842 | −0.342688 | |||||||||
0 | 0 | |||||||||
20.2907 | + | 20.2907i | 0.744395 | + | 0.744395i | 0.973420 | − | 0.229025i | ||
−0.229025 | + | 0.973420i | ||||||||
0 | 0 | |||||||||
0.0110415 | + | 0.332104i | 0.000404530 | + | 0.0121674i | |||||
0 | 0 | |||||||||
−1.34403 | + | 1.34403i | −0.0491756 | + | 0.0491756i | |||||
0 | 0 | |||||||||
− | 13.0312i | − | 0.476150i | |||||||
0 | 0 | |||||||||
− | 1.97054i | − | 0.0719061i | −0.999353 | − | 0.0359531i | ||||
0.999353 | − | 0.0359531i | ||||||||
0 | 0 | |||||||||
13.1146 | − | 13.1146i | 0.477922 | − | 0.477922i | |||||
0 | 0 | |||||||||
1.53211 | + | 46.0824i | 0.0557591 | + | 1.67711i | |||||
0 | 0 | |||||||||
−9.13933 | − | 9.13933i | −0.332175 | − | 0.332175i | 0.521237 | − | 0.853412i | ||
−0.853412 | + | 0.521237i | ||||||||
0 | 0 | |||||||||
−10.3744 | −0.376566 | |||||||||
0 | 0 | |||||||||
−23.7800 | −0.862023 | −0.431011 | − | 0.902346i | ||||||
−0.431011 | + | 0.902346i | ||||||||
0 | 0 | |||||||||
30.6660 | + | 30.6660i | 1.11018 | + | 1.11018i | |||||
0 | 0 | |||||||||
−4.98896 | + | 5.33210i | −0.180376 | + | 0.192783i | |||||
0 | 0 | |||||||||
12.3193 | − | 12.3193i | 0.444824 | − | 0.444824i | |||||
0 | 0 | |||||||||
− | 17.7022i | − | 0.638359i | −0.947694 | − | 0.319180i | ||||
0.947694 | − | 0.319180i | ||||||||
0 | 0 | |||||||||
− | 18.7362i | − | 0.674766i | |||||||
0 | 0 | |||||||||
−9.30178 | + | 9.30178i | −0.334562 | + | 0.334562i | −0.854316 | − | 0.519754i | ||
0.519754 | + | 0.854316i | ||||||||
0 | 0 | |||||||||
1.32842 | + | 19.9558i | 0.0477181 | + | 0.716835i | |||||
0 | 0 | |||||||||
25.9320 | + | 25.9320i | 0.930305 | + | 0.930305i | |||||
0 | 0 | |||||||||
−6.85534 | −0.245618 | |||||||||
0 | 0 | |||||||||
25.2843 | 0.904742 | |||||||||
0 | 0 | |||||||||
−5.77880 | − | 5.77880i | −0.206518 | − | 0.206518i | |||||
0 | 0 | |||||||||
−22.5826 | − | 21.1293i | −0.806008 | − | 0.754138i | |||||
0 | 0 | |||||||||
18.1642 | − | 18.1642i | 0.647484 | − | 0.647484i | −0.304900 | − | 0.952384i | ||
0.952384 | + | 0.304900i | ||||||||
0 | 0 | |||||||||
31.9338i | 1.13687i | |||||||||
0 | 0 | |||||||||
29.2678i | 1.04064i | |||||||||
0 | 0 | |||||||||
−30.9246 | + | 30.9246i | −1.09817 | + | 1.09817i | |||||
0 | 0 | |||||||||
24.7071 | − | 0.821440i | 0.876270 | − | 0.0291335i | |||||
0 | 0 | |||||||||
4.75098 | + | 4.75098i | 0.168289 | + | 0.168289i | 0.786227 | − | 0.617938i | ||
−0.617938 | + | 0.786227i | ||||||||
0 | 0 | |||||||||
3.13961 | 0.111071 | |||||||||
0 | 0 | |||||||||
17.6348 | 0.623094 | |||||||||
0 | 0 | |||||||||
−25.1118 | − | 25.1118i | −0.886176 | − | 0.886176i | |||||
0 | 0 | |||||||||
23.1850 | − | 0.770835i | 0.817164 | − | 0.0271684i | |||||
0 | 0 | |||||||||
−4.82260 | + | 4.82260i | −0.169764 | + | 0.169764i | |||||
0 | 0 | |||||||||
37.7891i | 1.32859i | 0.747469 | + | 0.664297i | ||||||
−0.747469 | + | 0.664297i | ||||||||
0 | 0 | |||||||||
44.4215i | 1.55985i | 0.625872 | + | 0.779926i | ||||||
−0.625872 | + | 0.779926i | ||||||||
0 | 0 | |||||||||
1.93845 | − | 1.93845i | 0.0679843 | − | 0.0679843i | |||||
0 | 0 | |||||||||
−24.0337 | − | 22.4871i | −0.841865 | − | 0.787687i | |||||
0 | 0 | |||||||||
−13.4828 | − | 13.4828i | −0.471702 | − | 0.471702i | |||||
0 | 0 | |||||||||
15.9246 | 0.556451 | |||||||||
0 | 0 | |||||||||
29.3648 | 1.02484 | 0.512420 | − | 0.858735i | ||||||
0.512420 | + | 0.858735i | ||||||||
0 | 0 | |||||||||
22.7402 | + | 22.7402i | 0.792674 | + | 0.792674i | 0.981928 | − | 0.189254i | ||
−0.189254 | + | 0.981928i | ||||||||
0 | 0 | |||||||||
14.7181 | − | 16.8174i | 0.512420 | − | 0.585506i | |||||
0 | 0 | |||||||||
−1.50001 | + | 1.50001i | −0.0521605 | + | 0.0521605i | −0.732706 | − | 0.680545i | ||
0.680545 | + | 0.732706i | ||||||||
0 | 0 | |||||||||
29.0642i | 1.00944i | 0.863283 | + | 0.504721i | ||||||
−0.863283 | + | 0.504721i | ||||||||
0 | 0 | |||||||||
− | 10.9684i | − | 0.380490i | |||||||
0 | 0 | |||||||||
−29.9678 | + | 29.9678i | −1.03832 | + | 1.03832i | |||||
0 | 0 | |||||||||
−13.0962 | + | 13.9969i | −0.453212 | + | 0.484384i | |||||
0 | 0 | |||||||||
2.82843 | + | 2.82843i | 0.0977647 | + | 0.0977647i | |||||
0 | 0 | |||||||||
−38.3779 | −1.32495 | −0.662476 | − | 0.749083i | ||||||
−0.662476 | + | 0.749083i | ||||||||
0 | 0 | |||||||||
−37.7891 | −1.30307 | |||||||||
0 | 0 | |||||||||
−3.21104 | − | 3.21104i | −0.110594 | − | 0.110594i | |||||
0 | 0 | |||||||||
−0.0227612 | − | 0.684605i | −0.000783008 | − | 0.0235511i | |||||
0 | 0 | |||||||||
−28.3750 | + | 28.3750i | −0.974976 | + | 0.974976i | |||||
0 | 0 | |||||||||
− | 11.1906i | − | 0.384060i | |||||||
0 | 0 | |||||||||
19.0442i | 0.652826i | |||||||||
0 | 0 | |||||||||
−28.1467 | + | 28.1467i | −0.963724 | + | 0.963724i | −0.999365 | − | 0.0356404i | ||
0.0356404 | + | 0.999365i | ||||||||
0 | 0 | |||||||||
−0.194542 | − | 5.85140i | −0.00665320 | − | 0.200114i | |||||
0 | 0 | |||||||||
−13.5990 | − | 13.5990i | −0.464533 | − | 0.464533i | 0.435605 | − | 0.900138i | ||
−0.900138 | + | 0.435605i | ||||||||
0 | 0 | |||||||||
−14.9155 | −0.508910 | −0.254455 | − | 0.967085i | ||||||
−0.254455 | + | 0.967085i | ||||||||
0 | 0 | |||||||||
11.7028 | 0.398830 | |||||||||
0 | 0 | |||||||||
8.95495 | + | 8.95495i | 0.304830 | + | 0.304830i | 0.842900 | − | 0.538070i | ||
−0.538070 | + | 0.842900i | ||||||||
0 | 0 | |||||||||
0.767147 | − | 0.819913i | 0.0260838 | − | 0.0278779i | |||||
0 | 0 | |||||||||
−4.48008 | + | 4.48008i | −0.152152 | + | 0.152152i | |||||
0 | 0 | |||||||||
16.0000i | 0.542763i | |||||||||
0 | 0 | |||||||||
− | 47.5980i | − | 1.61280i | |||||||
0 | 0 | |||||||||
1.32106 | − | 1.32106i | 0.0447112 | − | 0.0447112i | |||||
0 | 0 | |||||||||
−31.6430 | + | 38.6776i | −1.06973 | + | 1.30754i | |||||
0 | 0 | |||||||||
37.8274 | + | 37.8274i | 1.27734 | + | 1.27734i | 0.942151 | + | 0.335190i | ||
0.335190 | + | 0.942151i | ||||||||
0 | 0 | |||||||||
21.3544 | 0.720267 | |||||||||
0 | 0 | |||||||||
23.7119 | 0.798876 | 0.399438 | − | 0.916760i | ||||||
0.399438 | + | 0.916760i | ||||||||
0 | 0 | |||||||||
−9.39338 | − | 9.39338i | −0.316113 | − | 0.316113i | 0.531159 | − | 0.847272i | ||
−0.847272 | + | 0.531159i | ||||||||
0 | 0 | |||||||||
7.98438 | + | 7.47055i | 0.268392 | + | 0.251120i | |||||
0 | 0 | |||||||||
−0.825014 | + | 0.825014i | −0.0277013 | + | 0.0277013i | −0.720822 | − | 0.693120i | ||
0.693120 | + | 0.720822i | ||||||||
0 | 0 | |||||||||
64.4693i | 2.16223i | |||||||||
0 | 0 | |||||||||
− | 4.46967i | − | 0.149739i | |||||||
0 | 0 | |||||||||
−1.77996 | + | 1.77996i | −0.0595641 | + | 0.0595641i | |||||
0 | 0 | |||||||||
−35.2034 | + | 1.17041i | −1.17672 | + | 0.0391226i | |||||
0 | 0 | |||||||||
5.84744 | + | 5.84744i | 0.195240 | + | 0.195240i | |||||
0 | 0 | |||||||||
32.6898 | 1.09027 | |||||||||
0 | 0 | |||||||||
−36.1028 | −1.20276 | |||||||||
0 | 0 | |||||||||
23.0165 | + | 23.0165i | 0.765941 | + | 0.765941i | |||||
0 | 0 | |||||||||
17.3869 | − | 0.578065i | 0.577961 | − | 0.0192155i | |||||
0 | 0 | |||||||||
−1.59189 | + | 1.59189i | −0.0528578 | + | 0.0528578i | −0.733042 | − | 0.680184i | ||
0.680184 | + | 0.733042i | ||||||||
0 | 0 | |||||||||
1.47702i | 0.0489897i | |||||||||
0 | 0 | |||||||||
55.3926i | 1.83524i | 0.397458 | + | 0.917620i | ||||||
−0.397458 | + | 0.917620i | ||||||||
0 | 0 | |||||||||
−6.00737 | + | 6.00737i | −0.198815 | + | 0.198815i | |||||
0 | 0 | |||||||||
−20.0429 | − | 18.7530i | −0.662597 | − | 0.619956i | |||||
0 | 0 | |||||||||
39.4108 | + | 39.4108i | 1.30146 | + | 1.30146i | |||||
0 | 0 | |||||||||
4.31369 | 0.142295 | 0.0711477 | − | 0.997466i | ||||||
0.0711477 | + | 0.997466i | ||||||||
0 | 0 | |||||||||
−6.26775 | −0.206529 | |||||||||
0 | 0 | |||||||||
−14.2513 | − | 14.2513i | −0.469086 | − | 0.469086i | |||||
0 | 0 | |||||||||
−30.8716 | − | 27.0180i | −1.01505 | − | 0.888346i | |||||
0 | 0 | |||||||||
−9.11459 | + | 9.11459i | −0.299363 | + | 0.299363i | |||||
0 | 0 | |||||||||
19.9774i | 0.655436i | 0.944776 | + | 0.327718i | ||||||
−0.944776 | + | 0.327718i | ||||||||
0 | 0 | |||||||||
− | 33.9797i | − | 1.11364i | |||||||
0 | 0 | |||||||||
16.6421 | − | 16.6421i | 0.544839 | − | 0.544839i | |||||
0 | 0 | |||||||||
−22.2990 | + | 23.8327i | −0.729255 | + | 0.779414i | |||||
0 | 0 | |||||||||
−8.97792 | − | 8.97792i | −0.293296 | − | 0.293296i | 0.545085 | − | 0.838381i | ||
−0.838381 | + | 0.545085i | ||||||||
0 | 0 | |||||||||
26.3094 | 0.858574 | |||||||||
0 | 0 | |||||||||
37.9831 | 1.23821 | 0.619107 | − | 0.785307i | ||||||
0.619107 | + | 0.785307i | ||||||||
0 | 0 | |||||||||
4.29721 | + | 4.29721i | 0.139936 | + | 0.139936i | |||||
0 | 0 | |||||||||
0.332104 | + | 9.98896i | 0.0108034 | + | 0.324941i | |||||
0 | 0 | |||||||||
39.0815 | − | 39.0815i | 1.26998 | − | 1.26998i | 0.323878 | − | 0.946099i | ||
0.946099 | − | 0.323878i | ||||||||
0 | 0 | |||||||||
28.3081i | 0.918921i | |||||||||
0 | 0 | |||||||||
10.7049i | 0.347131i | |||||||||
0 | 0 | |||||||||
−1.27232 | + | 1.27232i | −0.0412146 | + | 0.0412146i | −0.727414 | − | 0.686199i | ||
0.686199 | + | 0.727414i | ||||||||
0 | 0 | |||||||||
−0.695439 | − | 20.9172i | −0.0225039 | − | 0.676866i | |||||
0 | 0 | |||||||||
−25.8293 | − | 25.8293i | −0.834943 | − | 0.834943i | |||||
0 | 0 | |||||||||
29.2678 | 0.945106 | |||||||||
0 | 0 | |||||||||
15.0000 | 0.483871 | |||||||||
0 | 0 | |||||||||
2.06155 | + | 2.06155i | 0.0664326 | + | 0.0664326i | |||||
0 | 0 | |||||||||
−37.1090 | + | 39.6614i | −1.19458 | + | 1.27675i | |||||
0 | 0 | |||||||||
1.67778 | − | 1.67778i | 0.0539537 | − | 0.0539537i | −0.679615 | − | 0.733569i | ||
0.733569 | + | 0.679615i | ||||||||
0 | 0 | |||||||||
8.55025i | 0.274674i | |||||||||
0 | 0 | |||||||||
15.9887i | 0.513102i | 0.966531 | + | 0.256551i | ||||||
−0.966531 | + | 0.256551i | ||||||||
0 | 0 | |||||||||
−9.50484 | + | 9.50484i | −0.304711 | + | 0.304711i | |||||
0 | 0 | |||||||||
−17.7747 | + | 1.18323i | −0.569247 | + | 0.0378936i | |||||
0 | 0 | |||||||||
16.7754 | + | 16.7754i | 0.536692 | + | 0.536692i | 0.922556 | − | 0.385864i | ||
−0.385864 | + | 0.922556i | ||||||||
0 | 0 | |||||||||
78.8215 | 2.51915 | |||||||||
0 | 0 | |||||||||
−9.70279 | −0.309786 | |||||||||
0 | 0 | |||||||||
−34.3367 | − | 34.3367i | −1.09517 | − | 1.09517i | −0.994967 | − | 0.100203i | ||
−0.100203 | − | 0.994967i | ||||||||
0 | 0 | |||||||||
4.24758 | + | 3.97423i | 0.135339 | + | 0.126629i | |||||
0 | 0 | |||||||||
3.03858 | − | 3.03858i | 0.0967192 | − | 0.0967192i | |||||
0 | 0 | |||||||||
16.9031i | 0.537487i | |||||||||
0 | 0 | |||||||||
− | 26.7414i | − | 0.849468i | −0.905318 | − | 0.424734i | ||||
0.905318 | − | 0.424734i | ||||||||
0 | 0 | |||||||||
−9.75952 | + | 9.75952i | −0.309709 | + | 0.309709i | |||||
0 | 0 | |||||||||
−0.988685 | + | 0.0328709i | −0.0313434 | + | 0.00104208i | |||||
0 | 0 | |||||||||
9.80177 | + | 9.80177i | 0.310425 | + | 0.310425i | 0.845074 | − | 0.534649i | ||
−0.534649 | + | 0.845074i | ||||||||
0 | 0 | |||||||||
−8.20494 | −0.259593 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 960.2.w.f.127.1 | 8 | ||
4.3 | odd | 2 | 960.2.w.e.127.3 | 8 | |||
5.3 | odd | 4 | 960.2.w.e.703.3 | 8 | |||
8.3 | odd | 2 | 480.2.w.c.127.2 | ✓ | 8 | ||
8.5 | even | 2 | 480.2.w.d.127.4 | yes | 8 | ||
20.3 | even | 4 | inner | 960.2.w.f.703.1 | 8 | ||
24.5 | odd | 2 | 1440.2.x.r.127.1 | 8 | |||
24.11 | even | 2 | 1440.2.x.q.127.1 | 8 | |||
40.3 | even | 4 | 480.2.w.d.223.4 | yes | 8 | ||
40.13 | odd | 4 | 480.2.w.c.223.2 | yes | 8 | ||
40.19 | odd | 2 | 2400.2.w.j.607.4 | 8 | |||
40.27 | even | 4 | 2400.2.w.i.2143.1 | 8 | |||
40.29 | even | 2 | 2400.2.w.i.607.1 | 8 | |||
40.37 | odd | 4 | 2400.2.w.j.2143.4 | 8 | |||
120.53 | even | 4 | 1440.2.x.q.703.1 | 8 | |||
120.83 | odd | 4 | 1440.2.x.r.703.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.2.w.c.127.2 | ✓ | 8 | 8.3 | odd | 2 | ||
480.2.w.c.223.2 | yes | 8 | 40.13 | odd | 4 | ||
480.2.w.d.127.4 | yes | 8 | 8.5 | even | 2 | ||
480.2.w.d.223.4 | yes | 8 | 40.3 | even | 4 | ||
960.2.w.e.127.3 | 8 | 4.3 | odd | 2 | |||
960.2.w.e.703.3 | 8 | 5.3 | odd | 4 | |||
960.2.w.f.127.1 | 8 | 1.1 | even | 1 | trivial | ||
960.2.w.f.703.1 | 8 | 20.3 | even | 4 | inner | ||
1440.2.x.q.127.1 | 8 | 24.11 | even | 2 | |||
1440.2.x.q.703.1 | 8 | 120.53 | even | 4 | |||
1440.2.x.r.127.1 | 8 | 24.5 | odd | 2 | |||
1440.2.x.r.703.1 | 8 | 120.83 | odd | 4 | |||
2400.2.w.i.607.1 | 8 | 40.29 | even | 2 | |||
2400.2.w.i.2143.1 | 8 | 40.27 | even | 4 | |||
2400.2.w.j.607.4 | 8 | 40.19 | odd | 2 | |||
2400.2.w.j.2143.4 | 8 | 40.37 | odd | 4 |