Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 350.j (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: | |
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 70) |
Sato-Tate group: |
Embedding invariants
Embedding label | 249.2 | ||
Root | of defining polynomial | ||
Character | 350.249 | ||
Dual form | 350.2.j.a.149.2 |
-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 .
0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | |||||
−1.73205 | − | 1.00000i | −1.00000 | − | 0.577350i | −0.0917517 | − | 0.995782i | ||
−0.908248 | + | 0.418432i | ||||||||
0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | |||||
0 | 0 | |||||||||
−2.00000 | −0.816497 | |||||||||
1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | |||||
− | 1.00000i | − | 0.353553i | |||||||
0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | |||||
0 | 0 | |||||||||
−1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | ||
0.546259 | + | 0.837616i | ||||||||
−1.73205 | + | 1.00000i | −0.500000 | + | 0.288675i | |||||
− | 5.00000i | − | 1.38675i | −0.720577 | − | 0.693375i | ||||
0.720577 | − | 0.693375i | ||||||||
0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | |||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | |||||
−5.19615 | − | 3.00000i | −1.26025 | − | 0.727607i | −0.287129 | − | 0.957892i | ||
−0.973123 | + | 0.230285i | ||||||||
0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | |||||
−0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | ||
−0.917663 | + | 0.397360i | ||||||||
0 | 0 | |||||||||
−5.00000 | + | 1.73205i | −1.09109 | + | 0.377964i | |||||
3.00000i | 0.639602i | |||||||||
−2.59808 | + | 1.50000i | −0.541736 | + | 0.312772i | −0.745782 | − | 0.666190i | ||
0.204046 | + | 0.978961i | ||||||||
−1.00000 | + | 1.73205i | −0.204124 | + | 0.353553i | |||||
0 | 0 | |||||||||
−2.50000 | − | 4.33013i | −0.490290 | − | 0.849208i | |||||
4.00000i | 0.769800i | |||||||||
−0.866025 | − | 2.50000i | −0.163663 | − | 0.472456i | |||||
6.00000 | 1.11417 | 0.557086 | − | 0.830455i | ||||||
0.557086 | + | 0.830455i | ||||||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | ||
0.987829 | + | 0.155543i | ||||||||
−0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | |||||
5.19615 | − | 3.00000i | 0.904534 | − | 0.522233i | |||||
−6.00000 | −1.02899 | |||||||||
0 | 0 | |||||||||
1.00000 | 0.166667 | |||||||||
9.52628 | − | 5.50000i | 1.56611 | − | 0.904194i | 0.569495 | − | 0.821995i | ||
0.996616 | − | 0.0821995i | ||||||||
−0.866025 | − | 0.500000i | −0.140488 | − | 0.0811107i | |||||
−5.00000 | + | 8.66025i | −0.800641 | + | 1.38675i | |||||
0 | 0 | |||||||||
3.00000 | 0.468521 | 0.234261 | − | 0.972174i | ||||||
0.234261 | + | 0.972174i | ||||||||
−3.46410 | + | 4.00000i | −0.534522 | + | 0.617213i | |||||
10.0000i | 1.52499i | 0.646997 | + | 0.762493i | ||||||
−0.646997 | + | 0.762493i | ||||||||
1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | |||||
0 | 0 | |||||||||
−1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | |||||
2.59808 | − | 1.50000i | 0.378968 | − | 0.218797i | −0.298401 | − | 0.954441i | ||
0.677369 | + | 0.735643i | ||||||||
2.00000i | 0.288675i | |||||||||
−1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.840168 | + | 1.45521i | |||||
−4.33013 | − | 2.50000i | −0.600481 | − | 0.346688i | |||||
2.59808 | + | 1.50000i | 0.356873 | + | 0.206041i | 0.667708 | − | 0.744423i | ||
−0.310835 | + | 0.950464i | ||||||||
2.00000 | + | 3.46410i | 0.272166 | + | 0.471405i | |||||
0 | 0 | |||||||||
−2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | |||||
2.00000i | 0.264906i | |||||||||
5.19615 | − | 3.00000i | 0.682288 | − | 0.393919i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | ||
−0.709113 | + | 0.705095i | ||||||||
− | 4.00000i | − | 0.508001i | |||||||
2.59808 | + | 0.500000i | 0.327327 | + | 0.0629941i | |||||
−1.00000 | −0.125000 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.369274 | − | 0.639602i | |||||
3.46410 | + | 2.00000i | 0.423207 | + | 0.244339i | 0.696449 | − | 0.717607i | ||
−0.273241 | + | 0.961946i | ||||||||
−5.19615 | + | 3.00000i | −0.630126 | + | 0.363803i | |||||
6.00000 | 0.722315 | |||||||||
0 | 0 | |||||||||
12.0000 | 1.42414 | 0.712069 | − | 0.702109i | ||||||
0.712069 | + | 0.702109i | ||||||||
0.866025 | − | 0.500000i | 0.102062 | − | 0.0589256i | |||||
−3.46410 | − | 2.00000i | −0.405442 | − | 0.234082i | 0.283387 | − | 0.959006i | ||
−0.688830 | + | 0.724923i | ||||||||
5.50000 | − | 9.52628i | 0.639362 | − | 1.10741i | |||||
0 | 0 | |||||||||
−1.00000 | −0.114708 | |||||||||
2.59808 | + | 7.50000i | 0.296078 | + | 0.854704i | |||||
10.0000i | 1.13228i | |||||||||
−5.00000 | − | 8.66025i | −0.562544 | − | 0.974355i | −0.997274 | − | 0.0737937i | ||
0.434730 | − | 0.900561i | ||||||||
0 | 0 | |||||||||
5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | |||||
2.59808 | − | 1.50000i | 0.286910 | − | 0.165647i | |||||
12.0000i | 1.31717i | 0.752506 | + | 0.658586i | ||||||
−0.752506 | + | 0.658586i | ||||||||
−1.00000 | + | 5.19615i | −0.109109 | + | 0.566947i | |||||
0 | 0 | |||||||||
5.00000 | + | 8.66025i | 0.539164 | + | 0.933859i | |||||
−10.3923 | − | 6.00000i | −1.11417 | − | 0.643268i | |||||
2.59808 | + | 1.50000i | 0.276956 | + | 0.159901i | |||||
3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | ||
−0.662071 | + | 0.749441i | ||||||||
0 | 0 | |||||||||
−10.0000 | − | 8.66025i | −1.04828 | − | 0.907841i | |||||
3.00000i | 0.312772i | |||||||||
−6.92820 | + | 4.00000i | −0.718421 | + | 0.414781i | |||||
1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | |||||
0 | 0 | |||||||||
1.00000 | + | 1.73205i | 0.102062 | + | 0.176777i | |||||
14.0000i | 1.42148i | 0.703452 | + | 0.710742i | ||||||
−0.703452 | + | 0.710742i | ||||||||
−4.33013 | − | 5.50000i | −0.437409 | − | 0.555584i | |||||
−3.00000 | −0.301511 | |||||||||
0 | 0 | |||||||||
6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | ||
0.993258 | − | 0.115924i | ||||||||
10.3923 | + | 6.00000i | 1.02899 | + | 0.594089i | |||||
3.46410 | − | 2.00000i | 0.341328 | − | 0.197066i | −0.319531 | − | 0.947576i | ||
0.660859 | + | 0.750510i | ||||||||
−5.00000 | −0.490290 | |||||||||
0 | 0 | |||||||||
3.00000 | 0.291386 | |||||||||
−10.3923 | + | 6.00000i | −1.00466 | + | 0.580042i | −0.909624 | − | 0.415432i | ||
−0.0950377 | + | 0.995474i | ||||||||
3.46410 | + | 2.00000i | 0.333333 | + | 0.192450i | |||||
−2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | ||
0.754204 | + | 0.656640i | ||||||||
0 | 0 | |||||||||
−22.0000 | −2.08815 | |||||||||
−2.59808 | − | 0.500000i | −0.245495 | − | 0.0472456i | |||||
− | 12.0000i | − | 1.12887i | −0.825479 | − | 0.564433i | ||||
0.825479 | − | 0.564433i | ||||||||
1.00000 | + | 1.73205i | 0.0936586 | + | 0.162221i | |||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | |||||
4.33013 | − | 2.50000i | 0.400320 | − | 0.231125i | |||||
0 | 0 | |||||||||
−15.0000 | + | 5.19615i | −1.37505 | + | 0.476331i | |||||
0 | 0 | |||||||||
1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | |||||
3.46410 | + | 2.00000i | 0.313625 | + | 0.181071i | |||||
−5.19615 | − | 3.00000i | −0.468521 | − | 0.270501i | |||||
−2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | |||||
0 | 0 | |||||||||
2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | |||||
− | 19.0000i | − | 1.68598i | −0.537931 | − | 0.842989i | ||||
0.537931 | − | 0.842989i | ||||||||
−0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | |||||
10.0000 | − | 17.3205i | 0.880451 | − | 1.52499i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.131056 | − | 0.226995i | 0.793028 | − | 0.609185i | ||
−0.924084 | + | 0.382190i | ||||||||
− | 6.00000i | − | 0.522233i | |||||||
−2.59808 | − | 0.500000i | −0.225282 | − | 0.0433555i | |||||
4.00000 | 0.345547 | |||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | |||||
−10.3923 | − | 6.00000i | −0.887875 | − | 0.512615i | −0.0146279 | − | 0.999893i | ||
−0.873247 | + | 0.487278i | ||||||||
5.19615 | − | 3.00000i | 0.442326 | − | 0.255377i | |||||
4.00000 | 0.339276 | 0.169638 | − | 0.985506i | ||||||
0.169638 | + | 0.985506i | ||||||||
0 | 0 | |||||||||
−6.00000 | −0.505291 | |||||||||
10.3923 | − | 6.00000i | 0.872103 | − | 0.503509i | |||||
12.9904 | + | 7.50000i | 1.08631 | + | 0.627182i | |||||
0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | |||||
0 | 0 | |||||||||
−4.00000 | −0.331042 | |||||||||
−5.19615 | + | 13.0000i | −0.428571 | + | 1.07222i | |||||
− | 11.0000i | − | 0.904194i | |||||||
9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | ||
−0.216394 | + | 0.976306i | ||||||||
0 | 0 | |||||||||
−7.00000 | + | 12.1244i | −0.569652 | + | 0.986666i | 0.426948 | + | 0.904276i | ||
−0.996600 | + | 0.0823900i | ||||||||
−0.866025 | + | 0.500000i | −0.0702439 | + | 0.0405554i | |||||
− | 6.00000i | − | 0.485071i | |||||||
6.00000 | + | 5.19615i | 0.483494 | + | 0.418718i | |||||
0 | 0 | |||||||||
5.00000 | + | 8.66025i | 0.400320 | + | 0.693375i | |||||
−4.33013 | − | 2.50000i | −0.345582 | − | 0.199522i | 0.317156 | − | 0.948373i | ||
−0.662738 | + | 0.748852i | ||||||||
−8.66025 | − | 5.00000i | −0.688973 | − | 0.397779i | |||||
−3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | |||||
0 | 0 | |||||||||
−1.50000 | + | 7.79423i | −0.118217 | + | 0.614271i | |||||
− | 11.0000i | − | 0.864242i | |||||||
3.46410 | − | 2.00000i | 0.271329 | − | 0.156652i | −0.358162 | − | 0.933659i | ||
0.629492 | + | 0.777007i | ||||||||
1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | |||||
9.00000i | 0.696441i | 0.937413 | + | 0.348220i | ||||||
−0.937413 | + | 0.348220i | ||||||||
1.73205 | + | 5.00000i | 0.133631 | + | 0.385758i | |||||
−12.0000 | −0.923077 | |||||||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.0382360 | − | 0.0662266i | |||||
8.66025 | + | 5.00000i | 0.660338 | + | 0.381246i | |||||
−2.59808 | + | 1.50000i | −0.197528 | + | 0.114043i | −0.595502 | − | 0.803354i | ||
0.397974 | + | 0.917397i | ||||||||
−12.0000 | −0.909718 | |||||||||
0 | 0 | |||||||||
3.00000 | 0.226134 | |||||||||
0 | 0 | |||||||||
5.19615 | + | 3.00000i | 0.389468 | + | 0.224860i | |||||
−1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | ||
0.804508 | + | 0.593942i | ||||||||
0 | 0 | |||||||||
2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | ||||||
0.0743294 | + | 0.997234i | ||||||||
−12.9904 | − | 2.50000i | −0.962911 | − | 0.185312i | |||||
− | 8.00000i | − | 0.591377i | |||||||
1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | |||||
0 | 0 | |||||||||
−4.00000 | + | 6.92820i | −0.293294 | + | 0.508001i | |||||
15.5885 | − | 9.00000i | 1.13994 | − | 0.658145i | |||||
− | 3.00000i | − | 0.218797i | |||||||
8.00000 | + | 6.92820i | 0.581914 | + | 0.503953i | |||||
0 | 0 | |||||||||
−6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | ||
−0.997225 | + | 0.0744412i | ||||||||
1.73205 | + | 1.00000i | 0.125000 | + | 0.0721688i | |||||
−3.46410 | − | 2.00000i | −0.249351 | − | 0.143963i | 0.370116 | − | 0.928986i | ||
−0.619467 | + | 0.785022i | ||||||||
7.00000 | + | 12.1244i | 0.502571 | + | 0.870478i | |||||
0 | 0 | |||||||||
−6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | |||||
− | 3.00000i | − | 0.213741i | −0.994273 | − | 0.106871i | ||||
0.994273 | − | 0.106871i | ||||||||
−2.59808 | + | 1.50000i | −0.184637 | + | 0.106600i | |||||
−2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | ||
0.786389 | + | 0.617731i | ||||||||
0 | 0 | |||||||||
−4.00000 | − | 6.92820i | −0.282138 | − | 0.488678i | |||||
− | 12.0000i | − | 0.844317i | |||||||
10.3923 | − | 12.0000i | 0.729397 | − | 0.842235i | |||||
12.0000 | 0.840168 | |||||||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.139347 | − | 0.241355i | |||||
−2.59808 | − | 1.50000i | −0.180579 | − | 0.104257i | |||||
−4.33013 | + | 2.50000i | −0.300240 | + | 0.173344i | |||||
3.00000 | 0.207514 | |||||||||
0 | 0 | |||||||||
−1.00000 | −0.0688428 | −0.0344214 | − | 0.999407i | ||||||
−0.0344214 | + | 0.999407i | ||||||||
2.59808 | − | 1.50000i | 0.178437 | − | 0.103020i | |||||
−20.7846 | − | 12.0000i | −1.42414 | − | 0.822226i | |||||
−6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | |||||
0 | 0 | |||||||||
4.00000 | 0.272166 | |||||||||
−3.46410 | − | 10.0000i | −0.235159 | − | 0.678844i | |||||
4.00000i | 0.270914i | |||||||||
4.00000 | + | 6.92820i | 0.270295 | + | 0.468165i | |||||
0 | 0 | |||||||||
−15.0000 | + | 25.9808i | −1.00901 | + | 1.74766i | |||||
−19.0526 | + | 11.0000i | −1.27872 | + | 0.738272i | |||||
− | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | ||||
0.963458 | − | 0.267860i | ||||||||
−2.50000 | + | 0.866025i | −0.167038 | + | 0.0578638i | |||||
0 | 0 | |||||||||
−6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | |||||
20.7846 | + | 12.0000i | 1.37952 | + | 0.796468i | 0.992102 | − | 0.125435i | ||
0.387421 | + | 0.921903i | ||||||||
1.73205 | + | 1.00000i | 0.114708 | + | 0.0662266i | |||||
−14.0000 | − | 24.2487i | −0.925146 | − | 1.60240i | −0.791326 | − | 0.611394i | ||
−0.133820 | − | 0.991006i | ||||||||
0 | 0 | |||||||||
3.00000 | − | 15.5885i | 0.197386 | − | 1.02565i | |||||
− | 6.00000i | − | 0.393919i | |||||||
5.19615 | − | 3.00000i | 0.340411 | − | 0.196537i | −0.320043 | − | 0.947403i | ||
0.660454 | + | 0.750867i | ||||||||
2.50000 | − | 4.33013i | 0.163430 | − | 0.283069i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.0000i | 1.29914i | |||||||||
−10.3923 | + | 12.0000i | −0.673633 | + | 0.777844i | |||||
−6.00000 | −0.388108 | −0.194054 | − | 0.980991i | ||||||
−0.194054 | + | 0.980991i | ||||||||
0 | 0 | |||||||||
12.5000 | − | 21.6506i | 0.805196 | − | 1.39464i | −0.110963 | − | 0.993825i | ||
0.916159 | − | 0.400815i | ||||||||
1.73205 | + | 1.00000i | 0.111340 | + | 0.0642824i | |||||
−8.66025 | + | 5.00000i | −0.555556 | + | 0.320750i | |||||
4.00000 | 0.256074 | |||||||||
0 | 0 | |||||||||
−6.00000 | −0.382546 | |||||||||
−4.33013 | + | 2.50000i | −0.275519 | + | 0.159071i | |||||
−3.46410 | − | 2.00000i | −0.219971 | − | 0.127000i | |||||
12.0000 | − | 20.7846i | 0.760469 | − | 1.31717i | |||||
0 | 0 | |||||||||
−15.0000 | −0.946792 | −0.473396 | − | 0.880850i | ||||||
−0.473396 | + | 0.880850i | ||||||||
1.73205 | − | 2.00000i | 0.109109 | − | 0.125988i | |||||
− | 9.00000i | − | 0.565825i | |||||||
−9.50000 | − | 16.4545i | −0.596083 | − | 1.03245i | |||||
0 | 0 | |||||||||
−0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | |||||
−10.3923 | + | 6.00000i | −0.648254 | + | 0.374270i | −0.787787 | − | 0.615948i | ||
0.139533 | + | 0.990217i | ||||||||
− | 20.0000i | − | 1.24515i | |||||||
5.50000 | − | 28.5788i | 0.341753 | − | 1.77580i | |||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | |||||
−2.59808 | − | 1.50000i | −0.160510 | − | 0.0926703i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | |||||
0 | 0 | |||||||||
−2.50000 | + | 0.866025i | −0.153285 | + | 0.0530994i | |||||
− | 12.0000i | − | 0.734388i | |||||||
3.46410 | − | 2.00000i | 0.211604 | − | 0.122169i | |||||
−6.00000 | + | 10.3923i | −0.365826 | + | 0.633630i | −0.988908 | − | 0.148527i | ||
0.623082 | + | 0.782157i | ||||||||
0 | 0 | |||||||||
8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | ||
−0.513905 | + | 0.857847i | ||||||||
6.00000i | 0.363803i | |||||||||
8.66025 | + | 25.0000i | 0.524142 | + | 1.51307i | |||||
−12.0000 | −0.724947 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.180579 | − | 0.312772i | |||||
−1.73205 | − | 1.00000i | −0.104069 | − | 0.0600842i | 0.447062 | − | 0.894503i | ||
−0.551131 | + | 0.834419i | ||||||||
3.46410 | − | 2.00000i | 0.207763 | − | 0.119952i | |||||
4.00000 | 0.239474 | |||||||||
0 | 0 | |||||||||
−3.00000 | −0.178965 | −0.0894825 | − | 0.995988i | ||||||
−0.0894825 | + | 0.995988i | ||||||||
−5.19615 | + | 3.00000i | −0.309426 | + | 0.178647i | |||||
22.5167 | + | 13.0000i | 1.33848 | + | 0.772770i | 0.986581 | − | 0.163270i | ||
0.351895 | + | 0.936039i | ||||||||
6.00000 | − | 10.3923i | 0.356034 | − | 0.616670i | |||||
0 | 0 | |||||||||
15.0000 | 0.886969 | |||||||||
5.19615 | − | 6.00000i | 0.306719 | − | 0.354169i | |||||
− | 1.00000i | − | 0.0589256i | |||||||
9.50000 | + | 16.4545i | 0.558824 | + | 0.967911i | |||||
0 | 0 | |||||||||
14.0000 | − | 24.2487i | 0.820695 | − | 1.42148i | |||||
−3.46410 | + | 2.00000i | −0.202721 | + | 0.117041i | |||||
27.0000i | 1.57736i | 0.614806 | + | 0.788678i | ||||||
−0.614806 | + | 0.788678i | ||||||||
2.00000 | + | 13.8564i | 0.116642 | + | 0.808122i | |||||
0 | 0 | |||||||||
−5.50000 | − | 9.52628i | −0.319681 | − | 0.553704i | |||||
−10.3923 | − | 6.00000i | −0.603023 | − | 0.348155i | |||||
15.5885 | + | 9.00000i | 0.903015 | + | 0.521356i | |||||
7.50000 | + | 12.9904i | 0.433736 | + | 0.751253i | |||||
0 | 0 | |||||||||
20.0000 | + | 17.3205i | 1.15278 | + | 0.998337i | |||||
14.0000i | 0.805609i | |||||||||
−20.7846 | + | 12.0000i | −1.19404 | + | 0.689382i | |||||
−0.500000 | + | 0.866025i | −0.0286770 | + | 0.0496700i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.171499 | − | 0.297044i | |||||
2.00000i | 0.114146i | 0.998370 | + | 0.0570730i | ||||||
−0.998370 | + | 0.0570730i | ||||||||
7.79423 | + | 1.50000i | 0.444117 | + | 0.0854704i | |||||
−8.00000 | −0.455104 | |||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | ||
0.644246 | + | 0.764818i | ||||||||
8.66025 | + | 5.00000i | 0.490290 | + | 0.283069i | |||||
−6.92820 | + | 4.00000i | −0.391605 | + | 0.226093i | −0.682855 | − | 0.730554i | ||
0.291250 | + | 0.956647i | ||||||||
−5.00000 | −0.282166 | |||||||||
0 | 0 | |||||||||
−10.0000 | −0.562544 | |||||||||
15.5885 | − | 9.00000i | 0.875535 | − | 0.505490i | 0.00635137 | − | 0.999980i | ||
0.869184 | + | 0.494489i | ||||||||
−5.19615 | − | 3.00000i | −0.291386 | − | 0.168232i | |||||
−9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | |||||
0 | 0 | |||||||||
24.0000 | 1.33955 | |||||||||
2.59808 | + | 7.50000i | 0.144785 | + | 0.417959i | |||||
6.00000i | 0.333849i | |||||||||
−5.50000 | − | 9.52628i | −0.305556 | − | 0.529238i | |||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.110770 | − | 0.191859i | |||||
6.92820 | − | 4.00000i | 0.383131 | − | 0.221201i | |||||
− | 3.00000i | − | 0.165647i | |||||||
1.50000 | − | 7.79423i | 0.0826977 | − | 0.429710i | |||||
0 | 0 | |||||||||
3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | ||
−0.753660 | + | 0.657264i | ||||||||
10.3923 | + | 6.00000i | 0.570352 | + | 0.329293i | |||||
9.52628 | + | 5.50000i | 0.522037 | + | 0.301398i | |||||
4.50000 | + | 7.79423i | 0.246229 | + | 0.426481i | |||||
0 | 0 | |||||||||
4.00000 | + | 3.46410i | 0.218218 | + | 0.188982i | |||||
14.0000i | 0.762629i | 0.924445 | + | 0.381314i | ||||||
−0.924445 | + | 0.381314i | ||||||||
−10.3923 | + | 6.00000i | −0.565267 | + | 0.326357i | |||||
−12.0000 | + | 20.7846i | −0.651751 | + | 1.12887i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.324918 | + | 0.562775i | |||||
− | 1.00000i | − | 0.0540738i | |||||||
−15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | |||||
10.0000 | 0.539164 | |||||||||
0 | 0 | |||||||||
−1.50000 | + | 2.59808i | −0.0806405 | + | 0.139673i | |||||
−20.7846 | − | 12.0000i | −1.11578 | − | 0.644194i | −0.175457 | − | 0.984487i | ||
−0.940319 | + | 0.340293i | ||||||||
−10.3923 | + | 6.00000i | −0.557086 | + | 0.321634i | |||||
10.0000 | 0.535288 | 0.267644 | − | 0.963518i | ||||||
0.267644 | + | 0.963518i | ||||||||
0 | 0 | |||||||||
20.0000 | 1.06752 | |||||||||
2.59808 | − | 1.50000i | 0.138478 | − | 0.0799503i | |||||
10.3923 | + | 6.00000i | 0.553127 | + | 0.319348i | 0.750382 | − | 0.661004i | ||
−0.197256 | + | 0.980352i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.00000 | 0.317999 | |||||||||
31.1769 | + | 6.00000i | 1.65006 | + | 0.317554i | |||||
3.00000i | 0.158555i | |||||||||
3.00000 | + | 5.19615i | 0.158334 | + | 0.274242i | 0.934268 | − | 0.356572i | ||
−0.775934 | + | 0.630814i | ||||||||
0 | 0 | |||||||||
9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | |||||
1.73205 | − | 1.00000i | 0.0910346 | − | 0.0525588i | |||||
− | 4.00000i | − | 0.209946i | |||||||
−12.5000 | + | 4.33013i | −0.655178 | + | 0.226960i | |||||
0 | 0 | |||||||||
−4.00000 | − | 6.92820i | −0.209083 | − | 0.362143i | |||||
0.866025 | + | 0.500000i | 0.0452062 | + | 0.0260998i | 0.522433 | − | 0.852680i | ||
−0.477227 | + | 0.878780i | ||||||||
2.59808 | + | 1.50000i | 0.135434 | + | 0.0781929i | |||||
1.50000 | + | 2.59808i | 0.0780869 | + | 0.135250i | |||||
0 | 0 | |||||||||
7.50000 | − | 2.59808i | 0.389381 | − | 0.134885i | |||||
8.00000i | 0.414781i | |||||||||
29.4449 | − | 17.0000i | 1.52460 | − | 0.880227i | 0.525022 | − | 0.851089i | ||
0.999575 | − | 0.0291379i | ||||||||
9.00000 | − | 15.5885i | 0.465379 | − | 0.806060i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.0773566 | − | 0.133986i | |||||
− | 30.0000i | − | 1.54508i | |||||||
10.3923 | + | 2.00000i | 0.534522 | + | 0.102869i | |||||
25.0000 | 1.28416 | 0.642082 | − | 0.766636i | ||||||
0.642082 | + | 0.766636i | ||||||||
0 | 0 | |||||||||
−19.0000 | + | 32.9090i | −0.973399 | + | 1.68598i | |||||
−10.3923 | − | 6.00000i | −0.531717 | − | 0.306987i | |||||
−12.9904 | + | 7.50000i | −0.663777 | + | 0.383232i | −0.793715 | − | 0.608290i | ||
0.129937 | + | 0.991522i | ||||||||
2.00000 | 0.102062 | |||||||||
0 | 0 | |||||||||
−4.00000 | −0.203595 | |||||||||
−8.66025 | + | 5.00000i | −0.440225 | + | 0.254164i | |||||
12.1244 | + | 7.00000i | 0.615521 | + | 0.355371i | |||||
−12.0000 | + | 20.7846i | −0.608424 | + | 1.05382i | 0.383076 | + | 0.923717i | ||
−0.991500 | + | 0.130105i | ||||||||
0 | 0 | |||||||||
18.0000 | 0.910299 | |||||||||
−6.92820 | + | 1.00000i | −0.349927 | + | 0.0505076i | |||||
6.00000i | 0.302660i | |||||||||
−1.50000 | − | 2.59808i | −0.0755689 | − | 0.130889i | |||||
0 | 0 | |||||||||
−1.50000 | + | 2.59808i | −0.0753778 | + | 0.130558i | |||||
1.73205 | − | 1.00000i | 0.0869291 | − | 0.0501886i | −0.455905 | − | 0.890028i | ||
0.542834 | + | 0.839840i | ||||||||
4.00000i | 0.200502i | |||||||||
4.00000 | + | 3.46410i | 0.200250 | + | 0.173422i | |||||
0 | 0 | |||||||||
−10.5000 | − | 18.1865i | −0.524345 | − | 0.908192i | −0.999598 | − | 0.0283431i | ||
0.475253 | − | 0.879849i | ||||||||
−6.92820 | − | 4.00000i | −0.345547 | − | 0.199502i | |||||
−17.3205 | − | 10.0000i | −0.862796 | − | 0.498135i | |||||
−6.00000 | − | 10.3923i | −0.298511 | − | 0.517036i | |||||
0 | 0 | |||||||||
3.00000 | − | 15.5885i | 0.148888 | − | 0.773642i | |||||
33.0000i | 1.63575i | |||||||||
10.3923 | − | 6.00000i | 0.514496 | − | 0.297044i | |||||
−11.0000 | + | 19.0526i | −0.543915 | + | 0.942088i | 0.454759 | + | 0.890614i | ||
−0.998674 | + | 0.0514740i | ||||||||
0 | 0 | |||||||||
12.0000 | + | 20.7846i | 0.591916 | + | 1.02523i | |||||
− | 4.00000i | − | 0.197066i | |||||||
0 | 0 | |||||||||
−3.00000 | −0.147442 | |||||||||
0 | 0 | |||||||||
−2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | |||||
−6.92820 | − | 4.00000i | −0.339276 | − | 0.195881i | |||||
2.59808 | − | 1.50000i | 0.127076 | − | 0.0733674i | |||||
−15.0000 | −0.732798 | −0.366399 | − | 0.930458i | ||||||
−0.366399 | + | 0.930458i | ||||||||
0 | 0 | |||||||||
−34.0000 | −1.65706 | −0.828529 | − | 0.559946i | ||||||
−0.828529 | + | 0.559946i | ||||||||
−0.866025 | + | 0.500000i | −0.0421575 | + | 0.0243396i | |||||
2.59808 | + | 1.50000i | 0.126323 | + | 0.0729325i | |||||
1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | |||||
0 | 0 | |||||||||
−24.0000 | −1.16280 | |||||||||
10.3923 | + | 2.00000i | 0.502919 | + | 0.0967868i | |||||
12.0000i | 0.580042i | |||||||||
−15.0000 | − | 25.9808i | −0.724207 | − | 1.25436i | |||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
3.46410 | − | 2.00000i | 0.166667 | − | 0.0962250i | |||||
16.0000i | 0.768911i | 0.923144 | + | 0.384455i | ||||||
−0.923144 | + | 0.384455i | ||||||||
−8.00000 | − | 6.92820i | −0.384012 | − | 0.332564i | |||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | |||||
2.59808 | + | 1.50000i | 0.124283 | + | 0.0717547i | |||||
6.92820 | + | 4.00000i | 0.331042 | + | 0.191127i | |||||
−5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | ||
−0.960323 | + | 0.278889i | ||||||||
0 | 0 | |||||||||
5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | |||||
30.0000i | 1.42695i | |||||||||
20.7846 | − | 12.0000i | 0.987507 | − | 0.570137i | 0.0829786 | − | 0.996551i | ||
0.904528 | + | 0.426414i | ||||||||
−11.0000 | + | 19.0526i | −0.522037 | + | 0.904194i | |||||
0 | 0 | |||||||||
−4.00000 | − | 6.92820i | −0.189405 | − | 0.328060i | |||||
− | 36.0000i | − | 1.70274i | |||||||
−1.73205 | + | 2.00000i | −0.0818317 | + | 0.0944911i | |||||
3.00000 | 0.141579 | 0.0707894 | − | 0.997491i | ||||||
0.0707894 | + | 0.997491i | ||||||||
0 | 0 | |||||||||
−4.50000 | + | 7.79423i | −0.211897 | + | 0.367016i | |||||
−10.3923 | − | 6.00000i | −0.488813 | − | 0.282216i | |||||
24.2487 | − | 14.0000i | 1.13930 | − | 0.657777i | |||||
24.0000 | 1.12638 | |||||||||
0 | 0 | |||||||||
2.00000 | 0.0936586 | |||||||||
−19.0526 | + | 11.0000i | −0.891241 | + | 0.514558i | −0.874348 | − | 0.485299i | ||
−0.0168929 | + | 0.999857i | ||||||||
−24.2487 | − | 14.0000i | −1.13307 | − | 0.654177i | |||||
12.0000 | − | 20.7846i | 0.560112 | − | 0.970143i | |||||
0 | 0 | |||||||||
6.00000 | 0.279448 | 0.139724 | − | 0.990190i | ||||||
0.139724 | + | 0.990190i | ||||||||
−5.19615 | − | 15.0000i | −0.241747 | − | 0.697863i | |||||
19.0000i | 0.883005i | 0.897260 | + | 0.441502i | ||||||
−0.897260 | + | 0.441502i | ||||||||
−3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | |||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | |||||
−15.5885 | + | 9.00000i | −0.721348 | + | 0.416470i | −0.815249 | − | 0.579111i | ||
0.0939008 | + | 0.995582i | ||||||||
− | 5.00000i | − | 0.231125i | |||||||
10.0000 | − | 3.46410i | 0.461757 | − | 0.159957i | |||||
0 | 0 | |||||||||
5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | |||||
0 | 0 | |||||||||
−25.9808 | − | 15.0000i | −1.19460 | − | 0.689701i | |||||
10.0000 | + | 17.3205i | 0.459315 | + | 0.795557i | |||||
0 | 0 | |||||||||
−3.00000 | + | 15.5885i | −0.137505 | + | 0.714496i | |||||
3.00000i | 0.137361i | |||||||||
−5.19615 | + | 3.00000i | −0.237666 | + | 0.137217i | |||||
12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | ||
0.998392 | − | 0.0566937i | ||||||||
0 | 0 | |||||||||
−27.5000 | − | 47.6314i | −1.25389 | − | 2.17180i | |||||
− | 25.0000i | − | 1.13872i | |||||||
10.3923 | − | 12.0000i | 0.472866 | − | 0.546019i | |||||
2.00000 | 0.0909091 | |||||||||
0 | 0 | |||||||||
−5.00000 | + | 8.66025i | −0.226805 | + | 0.392837i | |||||
13.8564 | + | 8.00000i | 0.627894 | + | 0.362515i | 0.779936 | − | 0.625859i | ||
−0.152042 | + | 0.988374i | ||||||||
3.46410 | − | 2.00000i | 0.156813 | − | 0.0905357i | |||||
−8.00000 | −0.361773 | |||||||||
0 | 0 | |||||||||
−12.0000 | −0.541552 | −0.270776 | − | 0.962642i | ||||||
−0.270776 | + | 0.962642i | ||||||||
−5.19615 | + | 3.00000i | −0.234261 | + | 0.135250i | |||||
−31.1769 | − | 18.0000i | −1.40414 | − | 0.810679i | |||||
−2.50000 | + | 4.33013i | −0.112480 | + | 0.194822i | |||||
0 | 0 | |||||||||
−4.00000 | −0.179605 | |||||||||
20.7846 | − | 24.0000i | 0.932317 | − | 1.07655i | |||||
− | 24.0000i | − | 1.07547i | |||||||
−14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | ||
0.361478 | − | 0.932381i | ||||||||
0 | 0 | |||||||||
9.00000 | − | 15.5885i | 0.402090 | − | 0.696441i | |||||
−12.9904 | + | 7.50000i | −0.579789 | + | 0.334741i | |||||
− | 24.0000i | − | 1.07011i | −0.844818 | − | 0.535054i | ||||
0.844818 | − | 0.535054i | ||||||||
0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | |||||
0 | 0 | |||||||||
−4.50000 | − | 7.79423i | −0.200049 | − | 0.346496i | |||||
20.7846 | + | 12.0000i | 0.923077 | + | 0.532939i | |||||
−16.4545 | − | 9.50000i | −0.730050 | − | 0.421494i | |||||
3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | ||
−0.791849 | + | 0.610718i | ||||||||
0 | 0 | |||||||||
−10.0000 | + | 3.46410i | −0.442374 | + | 0.153243i | |||||
1.00000i | 0.0441942i | |||||||||
3.46410 | − | 2.00000i | 0.152944 | − | 0.0883022i | |||||
−6.00000 | + | 10.3923i | −0.264649 | + | 0.458385i | |||||
0 | 0 | |||||||||
−10.0000 | − | 17.3205i | −0.440225 | − | 0.762493i | |||||
9.00000i | 0.395820i | |||||||||
−9.52628 | − | 27.5000i | −0.418561 | − | 1.20828i | |||||
6.00000 | 0.263371 | |||||||||
0 | 0 | |||||||||
−16.5000 | + | 28.5788i | −0.722878 | + | 1.25206i | 0.236963 | + | 0.971519i | ||
−0.959841 | + | 0.280543i | ||||||||
5.19615 | + | 3.00000i | 0.227429 | + | 0.131306i | |||||
−17.3205 | + | 10.0000i | −0.757373 | + | 0.437269i | −0.828352 | − | 0.560208i | ||
0.0709788 | + | 0.997478i | ||||||||
−3.00000 | −0.131056 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−20.7846 | + | 12.0000i | −0.905392 | + | 0.522728i | |||||
−5.19615 | − | 3.00000i | −0.226134 | − | 0.130558i | |||||
−7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.73205 | + | 2.00000i | −0.0750939 | + | 0.0867110i | |||||
− | 15.0000i | − | 0.649722i | |||||||
−6.00000 | − | 10.3923i | −0.259645 | − | 0.449719i | |||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.0863868 | − | 0.149626i | |||||
5.19615 | − | 3.00000i | 0.224231 | − | 0.129460i | |||||
12.0000i | 0.517357i | |||||||||
19.5000 | + | 7.79423i | 0.839924 | + | 0.335721i | |||||
0 | 0 | |||||||||
−4.00000 | − | 6.92820i | −0.171973 | − | 0.297867i | 0.767136 | − | 0.641484i | ||
−0.939110 | + | 0.343617i | ||||||||
13.8564 | + | 8.00000i | 0.595184 | + | 0.343629i | |||||
−3.46410 | − | 2.00000i | −0.148659 | − | 0.0858282i | |||||
3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | |||||
0 | 0 | |||||||||
20.0000 | + | 17.3205i | 0.855921 | + | 0.741249i | |||||
− | 28.0000i | − | 1.19719i | −0.801050 | − | 0.598597i | ||||
0.801050 | − | 0.598597i | ||||||||
−10.3923 | + | 6.00000i | −0.443937 | + | 0.256307i | |||||
−2.00000 | + | 3.46410i | −0.0853579 | + | 0.147844i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.127804 | − | 0.221364i | |||||
− | 6.00000i | − | 0.255377i | |||||||
−25.9808 | − | 5.00000i | −1.10481 | − | 0.212622i | |||||
−2.00000 | −0.0849719 | |||||||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | |||||
23.3827 | + | 13.5000i | 0.990756 | + | 0.572013i | 0.905500 | − | 0.424346i | ||
0.0852559 | + | 0.996359i | ||||||||
3.46410 | − | 2.00000i | 0.146647 | − | 0.0846668i | |||||
50.0000 | 2.11477 | |||||||||
0 | 0 | |||||||||
−36.0000 | −1.51992 | |||||||||
−2.59808 | + | 1.50000i | −0.109593 | + | 0.0632737i | |||||
−15.5885 | − | 9.00000i | −0.656975 | − | 0.379305i | 0.134148 | − | 0.990961i | ||
−0.791123 | + | 0.611656i | ||||||||
−3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | |||||
0 | 0 | |||||||||
26.0000 | 1.09286 | |||||||||
−9.52628 | − | 27.5000i | −0.400066 | − | 1.15489i | |||||
− | 12.0000i | − | 0.503509i | |||||||
−1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | ||
−0.895753 | + | 0.444552i | ||||||||
0 | 0 | |||||||||
−10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | ||
0.577301 | + | 0.816532i | ||||||||
12.9904 | − | 7.50000i | 0.543155 | − | 0.313591i | |||||
24.0000i | 1.00261i | |||||||||
1.50000 | − | 7.79423i | 0.0626088 | − | 0.325325i | |||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | |||||
−17.3205 | − | 10.0000i | −0.721062 | − | 0.416305i | 0.0940813 | − | 0.995565i | ||
−0.815144 | + | 0.579259i | ||||||||
16.4545 | + | 9.50000i | 0.684416 | + | 0.395148i | |||||
4.00000 | + | 6.92820i | 0.166234 | + | 0.287926i | |||||
0 | 0 | |||||||||
24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | |||||
− | 28.0000i | − | 1.16064i | |||||||
−7.79423 | + | 4.50000i | −0.322804 | + | 0.186371i | |||||
−2.00000 | + | 3.46410i | −0.0827606 | + | 0.143346i | |||||
0 | 0 | |||||||||
13.5000 | + | 23.3827i | 0.557680 | + | 0.965930i | |||||
12.0000i | 0.495293i | 0.968850 | + | 0.247647i | ||||||
−0.968850 | + | 0.247647i | ||||||||
8.66025 | + | 11.0000i | 0.357143 | + | 0.453632i | |||||
−4.00000 | −0.164817 | |||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.123404 | + | 0.213741i | |||||
−9.52628 | − | 5.50000i | −0.391528 | − | 0.226049i | |||||
31.1769 | − | 18.0000i | 1.28028 | − | 0.739171i | 0.303383 | − | 0.952869i | ||
0.976900 | + | 0.213697i | ||||||||
−12.0000 | −0.492366 | |||||||||
0 | 0 | |||||||||
18.0000 | 0.737309 | |||||||||
6.92820 | − | 4.00000i | 0.283552 | − | 0.163709i | |||||
12.9904 | + | 7.50000i | 0.531216 | + | 0.306698i | |||||
21.0000 | − | 36.3731i | 0.858037 | − | 1.48616i | −0.0157622 | − | 0.999876i | ||
0.873799 | − | 0.486287i | ||||||||
0 | 0 | |||||||||
2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | ||||||
0.0407909 | + | 0.999168i | ||||||||
25.9808 | + | 5.00000i | 1.05890 | + | 0.203785i | |||||
4.00000i | 0.162893i | |||||||||
7.00000 | + | 12.1244i | 0.284826 | + | 0.493333i | |||||
0 | 0 | |||||||||
−12.0000 | + | 20.7846i | −0.487467 | + | 0.844317i | |||||
−16.4545 | + | 9.50000i | −0.667867 | + | 0.385593i | −0.795268 | − | 0.606258i | ||
0.127401 | + | 0.991851i | ||||||||
1.00000i | 0.0405554i | |||||||||
−30.0000 | + | 10.3923i | −1.21566 | + | 0.421117i | |||||
0 | 0 | |||||||||
−7.50000 | − | 12.9904i | −0.303418 | − | 0.525535i | |||||
−5.19615 | − | 3.00000i | −0.210042 | − | 0.121268i | |||||
40.7032 | + | 23.5000i | 1.64399 | + | 0.949156i | 0.979396 | + | 0.201948i | ||
0.664590 | + | 0.747208i | ||||||||
1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | |||||
0 | 0 | |||||||||
7.50000 | − | 2.59808i | 0.302184 | − | 0.104679i | |||||
− | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | ||||
0.992680 | − | 0.120775i | ||||||||
−6.92820 | + | 4.00000i | −0.278693 | + | 0.160904i | |||||
−0.500000 | + | 0.866025i | −0.0200967 | + | 0.0348085i | −0.875899 | − | 0.482495i | ||
0.855802 | + | 0.517303i | ||||||||
0 | 0 | |||||||||
−6.00000 | − | 10.3923i | −0.240772 | − | 0.417029i | |||||
12.0000i | 0.481156i | |||||||||
15.5885 | + | 3.00000i | 0.624538 | + | 0.120192i | |||||
10.0000 | 0.400320 | |||||||||
0 | 0 | |||||||||
−4.00000 | + | 6.92820i | −0.159872 | + | 0.276907i | |||||
−5.19615 | − | 3.00000i | −0.207514 | − | 0.119808i | |||||
−4.33013 | + | 2.50000i | −0.172791 | + | 0.0997609i | |||||
−66.0000 | −2.63159 | |||||||||
0 | 0 | |||||||||
32.0000 | 1.27390 | 0.636950 | − | 0.770905i | ||||||
0.636950 | + | 0.770905i | ||||||||
−8.66025 | + | 5.00000i | −0.344486 | + | 0.198889i | |||||
1.73205 | + | 1.00000i | 0.0688428 | + | 0.0397464i | |||||
9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | |||||
0 | 0 | |||||||||
−6.00000 | −0.237915 | |||||||||
−34.6410 | + | 5.00000i | −1.37253 | + | 0.198107i | |||||
18.0000i | 0.712627i | |||||||||
6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | |||||
0 | 0 | |||||||||
22.5000 | − | 38.9711i | 0.888697 | − | 1.53927i | 0.0472793 | − | 0.998882i | ||
0.841417 | − | 0.540386i | ||||||||
20.7846 | − | 12.0000i | 0.820303 | − | 0.473602i | |||||
− | 38.0000i | − | 1.49857i | −0.662246 | − | 0.749287i | ||||
0.662246 | − | 0.749287i | ||||||||
6.00000 | + | 5.19615i | 0.236433 | + | 0.204757i | |||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.118033 | + | 0.204440i | |||||
18.1865 | + | 10.5000i | 0.714986 | + | 0.412798i | 0.812905 | − | 0.582397i | ||
−0.0979182 | + | 0.995194i | ||||||||
−9.52628 | − | 5.50000i | −0.374228 | − | 0.216060i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.00000 | + | 20.7846i | −0.156772 | + | 0.814613i | |||||
− | 4.00000i | − | 0.156652i | |||||||
−18.1865 | + | 10.5000i | −0.711694 | + | 0.410897i | −0.811688 | − | 0.584091i | ||
0.0999939 | + | 0.994988i | ||||||||
4.00000 | − | 6.92820i | 0.156412 | − | 0.270914i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | |||||
− | 4.00000i | − | 0.156055i | |||||||
−2.59808 | − | 7.50000i | −0.101284 | − | 0.292380i | |||||
−24.0000 | −0.934907 | −0.467454 | − | 0.884018i | ||||||
−0.467454 | + | 0.884018i | ||||||||
0 | 0 | |||||||||
−22.0000 | + | 38.1051i | −0.855701 | + | 1.48212i | 0.0202925 | + | 0.999794i | ||
−0.875993 | + | 0.482323i | ||||||||
6.06218 | + | 3.50000i | 0.235613 | + | 0.136031i | |||||
51.9615 | − | 30.0000i | 2.01802 | − | 1.16510i | |||||
12.0000 | 0.465690 | |||||||||
0 | 0 | |||||||||
11.0000 | 0.426241 | |||||||||
−15.5885 | + | 9.00000i | −0.603587 | + | 0.348481i | |||||
7.79423 | + | 4.50000i | 0.301568 | + | 0.174110i | |||||
−8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | |||||
0 | 0 | |||||||||
−12.0000 | −0.463255 | |||||||||
5.19615 | + | 1.00000i | 0.200446 | + | 0.0385758i | |||||
34.0000i | 1.31060i | 0.755367 | + | 0.655302i | ||||||
−0.755367 | + | 0.655302i | ||||||||
7.00000 | + | 12.1244i | 0.269630 | + | 0.467013i | |||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | |||||
−2.59808 | + | 1.50000i | −0.0998522 | + | 0.0576497i | −0.549095 | − | 0.835760i | ||
0.449242 | + | 0.893410i | ||||||||
24.0000i | 0.921714i | |||||||||
28.0000 | + | 24.2487i | 1.07454 | + | 0.930580i | |||||
0 | 0 | |||||||||
−24.0000 | − | 41.5692i | −0.919682 | − | 1.59294i | |||||
10.3923 | + | 6.00000i | 0.397942 | + | 0.229752i | |||||
−10.3923 | − | 6.00000i | −0.397650 | − | 0.229584i | 0.287819 | − | 0.957685i | ||
−0.685470 | + | 0.728101i | ||||||||
−0.500000 | − | 0.866025i | −0.0191180 | − | 0.0331133i | |||||
0 | 0 | |||||||||
−18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | |||||
56.0000i | 2.13653i | |||||||||
8.66025 | − | 5.00000i | 0.330169 | − | 0.190623i | |||||
7.50000 | − | 12.9904i | 0.285727 | − | 0.494894i | |||||
0 | 0 | |||||||||
−16.0000 | − | 27.7128i | −0.608669 | − | 1.05425i | −0.991460 | − | 0.130410i | ||
0.382791 | − | 0.923835i | ||||||||
3.00000i | 0.114043i | |||||||||
−5.19615 | + | 6.00000i | −0.197386 | + | 0.227921i | |||||
−24.0000 | −0.911028 | |||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.227429 | + | 0.393919i | |||||
−15.5885 | − | 9.00000i | −0.590455 | − | 0.340899i | |||||
8.66025 | − | 5.00000i | 0.327795 | − | 0.189253i | |||||
−12.0000 | −0.453882 | |||||||||
0 | 0 | |||||||||
18.0000 | 0.679851 | 0.339925 | − | 0.940452i | ||||||
0.339925 | + | 0.940452i | ||||||||
17.3205 | − | 10.0000i | 0.653720 | − | 0.377426i | |||||
−9.52628 | − | 5.50000i | −0.359290 | − | 0.207436i | |||||
1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | |||||
0 | 0 | |||||||||
12.0000 | 0.451626 | |||||||||
−10.3923 | − | 30.0000i | −0.390843 | − | 1.12827i | |||||
0 | 0 | |||||||||
7.00000 | + | 12.1244i | 0.262891 | + | 0.455340i | 0.967009 | − | 0.254743i | ||
−0.704118 | + | 0.710083i | ||||||||
0 | 0 | |||||||||
5.00000 | − | 8.66025i | 0.187515 | − | 0.324785i | |||||
5.19615 | − | 3.00000i | 0.194734 | − | 0.112430i | |||||
12.0000i | 0.449404i | |||||||||
30.0000 | − | 10.3923i | 1.12272 | − | 0.388922i | |||||
0 | 0 | |||||||||
1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | |||||
10.3923 | + | 6.00000i | 0.388108 | + | 0.224074i | |||||
5.19615 | + | 3.00000i | 0.193919 | + | 0.111959i | |||||
−18.0000 | − | 31.1769i | −0.671287 | − | 1.16270i | −0.977539 | − | 0.210752i | ||
0.306253 | − | 0.951950i | ||||||||
0 | 0 | |||||||||
2.00000 | − | 10.3923i | 0.0744839 | − | 0.387030i | |||||
− | 18.0000i | − | 0.669891i | |||||||
−43.3013 | + | 25.0000i | −1.61039 | + | 0.929760i | |||||
1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | |||||
0 | 0 | |||||||||
−2.00000 | − | 3.46410i | −0.0742270 | − | 0.128565i | |||||
29.0000i | 1.07555i | 0.843088 | + | 0.537775i | ||||||
−0.843088 | + | 0.537775i | ||||||||
−8.66025 | + | 10.0000i | −0.320970 | + | 0.370625i | |||||
−13.0000 | −0.481481 | |||||||||
0 | 0 | |||||||||
30.0000 | − | 51.9615i | 1.10959 | − | 1.92187i | |||||
−6.92820 | − | 4.00000i | −0.256074 | − | 0.147844i | |||||
−40.7032 | + | 23.5000i | −1.50341 | + | 0.867992i | −0.503415 | + | 0.864045i | ||
−0.999992 | + | 0.00394730i | ||||||||
1.00000 | 0.0369107 | |||||||||
0 | 0 | |||||||||
3.00000 | 0.110581 | |||||||||
−10.3923 | + | 6.00000i | −0.382805 | + | 0.221013i | |||||
2.59808 | + | 1.50000i | 0.0956365 | + | 0.0552158i | |||||
−18.5000 | + | 32.0429i | −0.680534 | + | 1.17872i | 0.294285 | + | 0.955718i | ||
−0.974818 | + | 0.223001i | ||||||||
0 | 0 | |||||||||
10.0000 | 0.367359 | |||||||||
5.19615 | − | 6.00000i | 0.190757 | − | 0.220267i | |||||
− | 9.00000i | − | 0.330178i | −0.986279 | − | 0.165089i | ||||
0.986279 | − | 0.165089i | ||||||||
4.00000 | + | 6.92820i | 0.146647 | + | 0.254000i | |||||
0 | 0 | |||||||||
17.0000 | − | 29.4449i | 0.622414 | − | 1.07805i | |||||
−10.3923 | + | 6.00000i | −0.380235 | + | 0.219529i | |||||
− | 18.0000i | − | 0.658145i | |||||||
−6.00000 | + | 31.1769i | −0.219235 | + | 1.13918i | |||||
0 | 0 | |||||||||
−13.0000 | − | 22.5167i | −0.474377 | − | 0.821645i | 0.525193 | − | 0.850983i | ||
−0.999570 | + | 0.0293387i | ||||||||
−2.59808 | − | 1.50000i | −0.0947421 | − | 0.0546994i | |||||
25.9808 | + | 15.0000i | 0.946792 | + | 0.546630i | |||||
−15.0000 | − | 25.9808i | −0.546268 | − | 0.946164i | |||||
0 | 0 | |||||||||
10.0000 | − | 3.46410i | 0.363696 | − | 0.125988i | |||||
26.0000i | 0.944986i | 0.881334 | + | 0.472493i | ||||||
−0.881334 | + | 0.472493i | ||||||||
21.6506 | − | 12.5000i | 0.786386 | − | 0.454020i | |||||
−9.00000 | + | 15.5885i | −0.326679 | + | 0.565825i | |||||
0 | 0 | |||||||||
25.5000 | + | 44.1673i | 0.924374 | + | 1.60106i | 0.792564 | + | 0.609788i | ||
0.131810 | + | 0.991275i | ||||||||
38.0000i | 1.37659i | |||||||||
3.46410 | + | 10.0000i | 0.125409 | + | 0.362024i | |||||
−12.0000 | −0.434145 | |||||||||
0 | 0 | |||||||||
−7.50000 | + | 12.9904i | −0.270986 | + | 0.469362i | |||||
0 | 0 | |||||||||
1.73205 | − | 1.00000i | 0.0625000 | − | 0.0360844i | |||||
49.0000 | 1.76699 | 0.883493 | − | 0.468445i | ||||||
0.883493 | + | 0.468445i | ||||||||
0 | 0 | |||||||||
24.0000 | 0.864339 | |||||||||
−3.46410 | + | 2.00000i | −0.124676 | + | 0.0719816i | |||||
33.7750 | + | 19.5000i | 1.21480 | + | 0.701366i | 0.963802 | − | 0.266621i | ||
0.251000 | + | 0.967987i | ||||||||
−5.00000 | + | 8.66025i | −0.179721 | + | 0.311286i | |||||
0 | 0 | |||||||||
14.0000 | 0.502571 | |||||||||
−38.1051 | + | 44.0000i | −1.36701 | + | 1.57849i | |||||
24.0000i | 0.860442i | |||||||||
−1.50000 | − | 2.59808i | −0.0537431 | − | 0.0930857i | |||||
0 | 0 | |||||||||
−18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | |||||
15.5885 | − | 9.00000i | 0.557442 | − | 0.321839i | |||||
24.0000i | 0.857690i | |||||||||
−5.50000 | + | 4.33013i | −0.196429 | + | 0.154647i | |||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.107006 | + | 0.185341i | |||||
29.4449 | + | 17.0000i | 1.04960 | + | 0.605985i | 0.922536 | − | 0.385911i | ||
0.127060 | + | 0.991895i | ||||||||
−2.59808 | − | 1.50000i | −0.0925526 | − | 0.0534353i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.0000 | − | 20.7846i | −0.853342 | − | 0.739016i | |||||
3.00000i | 0.106600i | |||||||||
17.3205 | − | 10.0000i | 0.615069 | − | 0.355110i | |||||
1.00000 | − | 1.73205i | 0.0354887 | − | 0.0614682i | |||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | |||||
− | 30.0000i | − | 1.06265i | −0.847167 | − | 0.531327i | ||||
0.847167 | − | 0.531327i | ||||||||
5.19615 | + | 1.00000i | 0.183942 | + | 0.0353996i | |||||
−18.0000 | −0.636794 | |||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.106000 | + | 0.183597i | |||||
−18.1865 | − | 10.5000i | −0.642189 | − | 0.370768i | |||||
10.3923 | − | 6.00000i | 0.366736 | − | 0.211735i | |||||
−8.00000 | −0.282138 | |||||||||
0 | 0 | |||||||||
−20.0000 | −0.704470 | |||||||||
20.7846 | − | 12.0000i | 0.731653 | − | 0.422420i | |||||
−10.3923 | − | 6.00000i | −0.365600 | − | 0.211079i | |||||
19.5000 | − | 33.7750i | 0.685583 | − | 1.18747i | −0.287670 | − | 0.957730i | ||
0.973253 | − | 0.229736i | ||||||||
0 | 0 | |||||||||
47.0000 | 1.65039 | 0.825197 | − | 0.564846i | ||||||
0.825197 | + | 0.564846i | ||||||||
−5.19615 | − | 15.0000i | −0.182349 | − | 0.526397i | |||||
− | 32.0000i | − | 1.12229i | |||||||
16.5000 | + | 28.5788i | 0.578325 | + | 1.00169i | |||||
0 | 0 | |||||||||
6.00000 | − | 10.3923i | 0.210042 | − | 0.363803i | |||||
8.66025 | − | 5.00000i | 0.302984 | − | 0.174928i | |||||
22.0000i | 0.769212i | |||||||||
2.50000 | − | 12.9904i | 0.0873571 | − | 0.453921i | |||||
0 | 0 | |||||||||
9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | ||
−0.665144 | + | 0.746715i | ||||||||
20.7846 | + | 12.0000i | 0.724947 | + | 0.418548i | |||||
38.1051 | + | 22.0000i | 1.32826 | + | 0.766872i | 0.985031 | − | 0.172379i | ||
0.343230 | + | 0.939251i | ||||||||
−2.00000 | − | 3.46410i | −0.0696733 | − | 0.120678i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 54.0000i | − | 1.87776i | −0.344239 | − | 0.938882i | ||||
0.344239 | − | 0.938882i | ||||||||
−2.59808 | + | 1.50000i | −0.0902894 | + | 0.0521286i | |||||
7.00000 | − | 12.1244i | 0.243120 | − | 0.421096i | −0.718481 | − | 0.695546i | ||
0.961601 | + | 0.274450i | ||||||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.0693792 | + | 0.120168i | |||||
5.00000i | 0.173344i | |||||||||
−15.5885 | + | 39.0000i | −0.540108 | + | 1.35127i | |||||
−8.00000 | −0.277017 | |||||||||
0 | 0 | |||||||||
1.50000 | − | 2.59808i | 0.0518786 | − | 0.0898563i | |||||
13.8564 | + | 8.00000i | 0.478947 | + | 0.276520i | |||||
−12.9904 | + | 7.50000i | −0.448745 | + | 0.259083i | |||||
6.00000 | 0.207143 | 0.103572 | − | 0.994622i | ||||||
0.103572 | + | 0.994622i | ||||||||
0 | 0 | |||||||||
7.00000 | 0.241379 | |||||||||
−29.4449 | + | 17.0000i | −1.01474 | + | 0.585859i | |||||
5.19615 | + | 3.00000i | 0.178965 | + | 0.103325i | |||||
−0.500000 | + | 0.866025i | −0.0172107 | + | 0.0298098i | |||||
0 | 0 | |||||||||
3.00000 | 0.103142 | |||||||||
5.19615 | + | 1.00000i | 0.178542 | + | 0.0343604i | |||||
− | 3.00000i | − | 0.103020i | |||||||
−26.0000 | − | 45.0333i | −0.892318 | − | 1.54554i | |||||
0 | 0 | |||||||||
−16.5000 | + | 28.5788i | −0.565613 | + | 0.979670i | |||||
−20.7846 | + | 12.0000i | −0.712069 | + | 0.411113i | |||||
1.00000i | 0.0342393i | 0.999853 | + | 0.0171197i | ||||||
−0.999853 | + | 0.0171197i | ||||||||
10.0000 | − | 3.46410i | 0.342193 | − | 0.118539i | |||||
0 | 0 | |||||||||
6.00000 | + | 10.3923i | 0.205076 | + | 0.355202i | |||||
15.5885 | + | 9.00000i | 0.532492 | + | 0.307434i | 0.742030 | − | 0.670366i | ||
−0.209539 | + | 0.977800i | ||||||||
−25.9808 | − | 15.0000i | −0.886969 | − | 0.512092i | |||||
16.0000 | + | 27.7128i | 0.545913 | + | 0.945549i | 0.998549 | + | 0.0538535i | ||
−0.452636 | + | 0.891695i | ||||||||
0 | 0 | |||||||||
−15.0000 | + | 5.19615i | −0.511199 | + | 0.177084i | |||||
0 | 0 | |||||||||
−33.7750 | + | 19.5000i | −1.14971 | + | 0.663788i | −0.948818 | − | 0.315825i | ||
−0.200897 | + | 0.979612i | ||||||||
2.00000 | − | 3.46410i | 0.0680414 | − | 0.117851i | |||||
0 | 0 | |||||||||
8.00000 | + | 13.8564i | 0.271851 | + | 0.470860i | |||||
− | 38.0000i | − | 1.29055i | |||||||
−10.3923 | − | 2.00000i | −0.352738 | − | 0.0678844i | |||||
30.0000 | 1.01768 | |||||||||
0 | 0 | |||||||||
10.0000 | − | 17.3205i | 0.338837 | − | 0.586883i | |||||
3.46410 | + | 2.00000i | 0.117309 | + | 0.0677285i | |||||
−12.1244 | + | 7.00000i | −0.410347 | + | 0.236914i | |||||
3.00000 | 0.101477 | |||||||||
0 | 0 | |||||||||
8.00000 | 0.270295 | |||||||||
−6.06218 | + | 3.50000i | −0.204705 | + | 0.118187i | −0.598848 | − | 0.800862i | ||
0.394143 | + | 0.919049i | ||||||||
−8.66025 | − | 5.00000i | −0.292269 | − | 0.168742i | |||||
27.0000 | − | 46.7654i | 0.910687 | − | 1.57736i | |||||
0 | 0 | |||||||||
33.0000 | 1.11180 | 0.555899 | − | 0.831250i | ||||||
0.555899 | + | 0.831250i | ||||||||
2.59808 | − | 6.50000i | 0.0874818 | − | 0.218866i | |||||
− | 8.00000i | − | 0.269221i | −0.990899 | − | 0.134611i | ||||
0.990899 | − | 0.134611i | ||||||||
15.0000 | + | 25.9808i | 0.504505 | + | 0.873828i | |||||
0 | 0 | |||||||||
12.0000 | − | 20.7846i | 0.403148 | − | 0.698273i | |||||
20.7846 | − | 12.0000i | 0.697879 | − | 0.402921i | −0.108678 | − | 0.994077i | ||
0.806557 | + | 0.591156i | ||||||||
22.0000i | 0.738272i | |||||||||
−38.0000 | − | 32.9090i | −1.27448 | − | 1.10373i | |||||
0 | 0 | |||||||||
16.5000 | + | 28.5788i | 0.552771 | + | 0.957427i | |||||
−6.92820 | − | 4.00000i | −0.231973 | − | 0.133930i | |||||
−2.59808 | − | 1.50000i | −0.0869413 | − | 0.0501956i | |||||
−18.0000 | − | 31.1769i | −0.602010 | − | 1.04271i | |||||
0 | 0 | |||||||||
−0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | |||||
− | 30.0000i | − | 1.00167i | |||||||
2.59808 | − | 1.50000i | 0.0866989 | − | 0.0500556i | |||||
12.0000 | − | 20.7846i | 0.400222 | − | 0.693206i | |||||
0 | 0 | |||||||||
−9.00000 | − | 15.5885i | −0.299833 | − | 0.519327i | |||||
9.00000i | 0.299667i | |||||||||
−17.3205 | − | 50.0000i | −0.576390 | − | 1.66390i | |||||
−12.0000 | −0.399114 | |||||||||
0 | 0 | |||||||||
14.0000 | − | 24.2487i | 0.465119 | − | 0.805609i | |||||
8.66025 | + | 5.00000i | 0.287559 | + | 0.166022i | 0.636841 | − | 0.770996i | ||
−0.349281 | + | 0.937018i | ||||||||
20.7846 | − | 12.0000i | 0.689761 | − | 0.398234i | |||||
12.0000 | 0.398015 | |||||||||
0 | 0 | |||||||||
−30.0000 | −0.993944 | −0.496972 | − | 0.867766i | ||||||
−0.496972 | + | 0.867766i | ||||||||
1.73205 | − | 1.00000i | 0.0573539 | − | 0.0331133i | |||||
−31.1769 | − | 18.0000i | −1.03181 | − | 0.595713i | |||||
−11.0000 | + | 19.0526i | −0.363848 | + | 0.630203i | |||||
0 | 0 | |||||||||
−28.0000 | −0.925146 | |||||||||
−7.79423 | − | 1.50000i | −0.257388 | − | 0.0495344i | |||||
− | 24.0000i | − | 0.792118i | |||||||
19.0000 | + | 32.9090i | 0.626752 | + | 1.08557i | 0.988199 | + | 0.153174i | ||
−0.361447 | + | 0.932393i | ||||||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.0659022 | − | 0.114146i | |||||
5.19615 | − | 3.00000i | 0.171126 | − | 0.0987997i | |||||
− | 60.0000i | − | 1.97492i | |||||||
−12.0000 | − | 10.3923i | −0.394771 | − | 0.341882i | |||||
0 | 0 | |||||||||
9.50000 | + | 16.4545i | 0.312189 | + | 0.540728i | |||||
3.46410 | + | 2.00000i | 0.113776 | + | 0.0656886i | |||||
−5.19615 | − | 3.00000i | −0.170572 | − | 0.0984798i | |||||
16.5000 | + | 28.5788i | 0.541347 | + | 0.937641i | 0.998827 | + | 0.0484211i | ||
−0.457480 | + | 0.889220i | ||||||||
0 | 0 | |||||||||
−5.50000 | + | 4.33013i | −0.180255 | + | 0.141914i | |||||
− | 6.00000i | − | 0.196537i | |||||||
20.7846 | − | 12.0000i | 0.680458 | − | 0.392862i | |||||
−9.00000 | + | 15.5885i | −0.294489 | + | 0.510070i | |||||
0 | 0 | |||||||||
−2.50000 | − | 4.33013i | −0.0817151 | − | 0.141535i | |||||
2.00000i | 0.0653372i | 0.999466 | + | 0.0326686i | ||||||
−0.999466 | + | 0.0326686i | ||||||||
6.92820 | − | 8.00000i | 0.226214 | − | 0.261209i | |||||
16.0000 | 0.522140 | |||||||||
0 | 0 | |||||||||
−12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | ||
0.601418 | + | 0.798935i | ||||||||
8.66025 | + | 5.00000i | 0.282166 | + | 0.162909i | |||||
−7.79423 | + | 4.50000i | −0.253815 | + | 0.146540i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−30.0000 | −0.975384 | |||||||||
25.9808 | − | 15.0000i | 0.844261 | − | 0.487435i | −0.0144491 | − | 0.999896i | ||
0.858710 | + | 0.512461i | ||||||||
17.3205 | + | 10.0000i | 0.562544 | + | 0.324785i | |||||
−10.0000 | + | 17.3205i | −0.324614 | + | 0.562247i | |||||
0 | 0 | |||||||||
−36.0000 | −1.16738 | |||||||||
5.19615 | + | 15.0000i | 0.168408 | + | 0.486153i | |||||
12.0000i | 0.388718i | 0.980930 | + | 0.194359i | ||||||
−0.980930 | + | 0.194359i | ||||||||
1.50000 | + | 2.59808i | 0.0485643 | + | 0.0841158i | |||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | |||||
31.1769 | − | 18.0000i | 1.00781 | − | 0.581857i | |||||
− | 24.0000i | − | 0.775405i | |||||||
−30.0000 | + | 10.3923i | −0.968751 | + | 0.335585i | |||||
0 | 0 | |||||||||
7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | |||||
−47.6314 | − | 27.5000i | −1.53570 | − | 0.886636i | |||||
−10.3923 | − | 6.00000i | −0.334887 | − | 0.193347i | |||||
−12.5000 | − | 21.6506i | −0.402598 | − | 0.697320i | |||||
0 | 0 | |||||||||
3.00000 | − | 15.5885i | 0.0965234 | − | 0.501550i | |||||
32.0000i | 1.02905i | 0.857475 | + | 0.514525i | ||||||
−0.857475 | + | 0.514525i | ||||||||
1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | |||||
6.00000 | − | 10.3923i | 0.192748 | − | 0.333849i | |||||
0 | 0 | |||||||||
−13.5000 | − | 23.3827i | −0.433236 | − | 0.750386i | 0.563914 | − | 0.825833i | ||
−0.997150 | + | 0.0754473i | ||||||||
10.0000i | 0.320750i | |||||||||
6.92820 | − | 8.00000i | 0.222108 | − | 0.256468i | |||||
16.0000 | 0.512673 | |||||||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.0640184 | − | 0.110883i | |||||
25.9808 | + | 15.0000i | 0.831198 | + | 0.479893i | 0.854263 | − | 0.519841i | ||
−0.0230645 | + | 0.999734i | ||||||||
−6.92820 | + | 4.00000i | −0.221540 | + | 0.127906i | |||||
−18.0000 | −0.575282 | |||||||||
0 | 0 | |||||||||
−4.00000 | −0.127710 | |||||||||
−10.3923 | + | 6.00000i | −0.331632 | + | 0.191468i | |||||
49.3634 | + | 28.5000i | 1.57445 | + | 0.909009i | 0.995613 | + | 0.0935651i | ||
0.578836 | + | 0.815444i | ||||||||
−3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | |||||
0 | 0 | |||||||||
−36.0000 | −1.14647 | |||||||||
−10.3923 | + | 12.0000i | −0.330791 | + | 0.381964i | |||||
5.00000i | 0.159071i | |||||||||
−15.0000 | − | 25.9808i | −0.476972 | − | 0.826140i | |||||
0 | 0 | |||||||||
−10.0000 | + | 17.3205i | −0.317660 | + | 0.550204i | −0.979999 | − | 0.199000i | ||
0.662339 | + | 0.749204i | ||||||||
−3.46410 | + | 2.00000i | −0.109985 | + | 0.0635001i | |||||
− | 14.0000i | − | 0.444277i | |||||||
6.00000 | − | 31.1769i | 0.190308 | − | 0.988872i | |||||
0 | 0 | |||||||||
−12.0000 | − | 20.7846i | −0.380235 | − | 0.658586i | |||||
−12.1244 | − | 7.00000i | −0.383982 | − | 0.221692i | 0.295567 | − | 0.955322i | ||
−0.679549 | + | 0.733630i | ||||||||
−24.2487 | − | 14.0000i | −0.767580 | − | 0.443162i | |||||
22.0000 | + | 38.1051i | 0.696049 | + | 1.20559i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 350.2.j.a.249.2 | 4 | ||
5.2 | odd | 4 | 350.2.e.h.151.1 | 2 | |||
5.3 | odd | 4 | 70.2.e.b.11.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 350.2.j.a.249.1 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.a.149.1 | 4 | ||
7.3 | odd | 6 | 2450.2.c.p.99.2 | 2 | |||
7.4 | even | 3 | 2450.2.c.f.99.2 | 2 | |||
15.8 | even | 4 | 630.2.k.e.361.1 | 2 | |||
20.3 | even | 4 | 560.2.q.d.81.1 | 2 | |||
35.2 | odd | 12 | 350.2.e.h.51.1 | 2 | |||
35.3 | even | 12 | 490.2.a.j.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.f.99.1 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.a.149.2 | 4 | ||
35.13 | even | 4 | 490.2.e.a.361.1 | 2 | |||
35.17 | even | 12 | 2450.2.a.f.1.1 | 1 | |||
35.18 | odd | 12 | 490.2.a.g.1.1 | 1 | |||
35.23 | odd | 12 | 70.2.e.b.51.1 | yes | 2 | ||
35.24 | odd | 6 | 2450.2.c.p.99.1 | 2 | |||
35.32 | odd | 12 | 2450.2.a.p.1.1 | 1 | |||
35.33 | even | 12 | 490.2.e.a.471.1 | 2 | |||
105.23 | even | 12 | 630.2.k.e.541.1 | 2 | |||
105.38 | odd | 12 | 4410.2.a.c.1.1 | 1 | |||
105.53 | even | 12 | 4410.2.a.m.1.1 | 1 | |||
140.3 | odd | 12 | 3920.2.a.g.1.1 | 1 | |||
140.23 | even | 12 | 560.2.q.d.401.1 | 2 | |||
140.123 | even | 12 | 3920.2.a.be.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.e.b.11.1 | ✓ | 2 | 5.3 | odd | 4 | ||
70.2.e.b.51.1 | yes | 2 | 35.23 | odd | 12 | ||
350.2.e.h.51.1 | 2 | 35.2 | odd | 12 | |||
350.2.e.h.151.1 | 2 | 5.2 | odd | 4 | |||
350.2.j.a.149.1 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.a.149.2 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.a.249.1 | 4 | 5.4 | even | 2 | inner | ||
350.2.j.a.249.2 | 4 | 1.1 | even | 1 | trivial | ||
490.2.a.g.1.1 | 1 | 35.18 | odd | 12 | |||
490.2.a.j.1.1 | 1 | 35.3 | even | 12 | |||
490.2.e.a.361.1 | 2 | 35.13 | even | 4 | |||
490.2.e.a.471.1 | 2 | 35.33 | even | 12 | |||
560.2.q.d.81.1 | 2 | 20.3 | even | 4 | |||
560.2.q.d.401.1 | 2 | 140.23 | even | 12 | |||
630.2.k.e.361.1 | 2 | 15.8 | even | 4 | |||
630.2.k.e.541.1 | 2 | 105.23 | even | 12 | |||
2450.2.a.f.1.1 | 1 | 35.17 | even | 12 | |||
2450.2.a.p.1.1 | 1 | 35.32 | odd | 12 | |||
2450.2.c.f.99.1 | 2 | 35.4 | even | 6 | |||
2450.2.c.f.99.2 | 2 | 7.4 | even | 3 | |||
2450.2.c.p.99.1 | 2 | 35.24 | odd | 6 | |||
2450.2.c.p.99.2 | 2 | 7.3 | odd | 6 | |||
3920.2.a.g.1.1 | 1 | 140.3 | odd | 12 | |||
3920.2.a.be.1.1 | 1 | 140.123 | even | 12 | |||
4410.2.a.c.1.1 | 1 | 105.38 | odd | 12 | |||
4410.2.a.m.1.1 | 1 | 105.53 | even | 12 |