Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 637.q (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
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 91) |
Sato-Tate group: |
Embedding invariants
Embedding label | 589.1 | ||
Root | of defining polynomial | ||
Character | 637.589 | ||
Dual form | 637.2.q.c.491.1 |
-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 .
1.50000 | + | 0.866025i | 1.06066 | + | 0.612372i | 0.925615 | − | 0.378467i | ||
0.135045 | + | 0.990839i | ||||||||
0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | −0.684819 | − | 0.728714i | ||
0.973494 | + | 0.228714i | ||||||||
0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | |||||
1.73205i | 0.774597i | 0.921954 | + | 0.387298i | ||||||
−0.921954 | + | 0.387298i | ||||||||
1.50000 | − | 0.866025i | 0.612372 | − | 0.353553i | |||||
0 | 0 | |||||||||
− | 1.73205i | − | 0.612372i | |||||||
1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | |||||
−1.50000 | + | 2.59808i | −0.474342 | + | 0.821584i | |||||
4.50000 | + | 2.59808i | 1.35680 | + | 0.783349i | 0.989191 | − | 0.146631i | ||
0.367610 | + | 0.929980i | ||||||||
1.00000 | 0.288675 | |||||||||
−1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | |||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 0.387298 | + | 0.223607i | |||||
2.50000 | − | 4.33013i | 0.625000 | − | 1.08253i | |||||
−3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | ||
0.230285 | − | 0.973123i | ||||||||
3.46410i | 0.816497i | |||||||||
1.50000 | − | 0.866025i | 0.344124 | − | 0.198680i | −0.317970 | − | 0.948101i | ||
0.662094 | + | 0.749421i | ||||||||
−1.50000 | + | 0.866025i | −0.335410 | + | 0.193649i | |||||
0 | 0 | |||||||||
4.50000 | + | 7.79423i | 0.959403 | + | 1.66174i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
−1.50000 | − | 0.866025i | −0.306186 | − | 0.176777i | |||||
2.00000 | 0.400000 | |||||||||
−4.50000 | + | 4.33013i | −0.882523 | + | 0.849208i | |||||
5.00000 | 0.962250 | |||||||||
0 | 0 | |||||||||
−1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | ||
0.692480 | + | 0.721437i | ||||||||
1.50000 | + | 2.59808i | 0.273861 | + | 0.474342i | |||||
1.73205i | 0.311086i | 0.987829 | + | 0.155543i | ||||||
−0.987829 | + | 0.155543i | ||||||||
4.50000 | − | 2.59808i | 0.795495 | − | 0.459279i | |||||
4.50000 | − | 2.59808i | 0.783349 | − | 0.452267i | |||||
− | 10.3923i | − | 1.78227i | |||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
3.00000 | 0.486664 | |||||||||
2.50000 | + | 2.59808i | 0.400320 | + | 0.416025i | |||||
3.00000 | 0.474342 | |||||||||
−4.50000 | − | 2.59808i | −0.702782 | − | 0.405751i | 0.105601 | − | 0.994409i | ||
−0.808383 | + | 0.588657i | ||||||||
0 | 0 | |||||||||
−5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | ||
0.0522047 | − | 0.998636i | ||||||||
5.19615i | 0.783349i | |||||||||
−3.00000 | + | 1.73205i | −0.447214 | + | 0.258199i | |||||
0 | 0 | |||||||||
8.66025i | 1.26323i | 0.775283 | + | 0.631614i | ||||||
−0.775283 | + | 0.631614i | ||||||||
−2.50000 | − | 4.33013i | −0.360844 | − | 0.625000i | |||||
0 | 0 | |||||||||
3.00000 | + | 1.73205i | 0.424264 | + | 0.244949i | |||||
−6.00000 | −0.840168 | |||||||||
−3.50000 | + | 0.866025i | −0.485363 | + | 0.120096i | |||||
−9.00000 | −1.23625 | −0.618123 | − | 0.786082i | ||||||
−0.618123 | + | 0.786082i | ||||||||
7.50000 | + | 4.33013i | 1.02062 | + | 0.589256i | |||||
−4.50000 | + | 7.79423i | −0.606780 | + | 1.05097i | |||||
0 | 0 | |||||||||
− | 1.73205i | − | 0.229416i | |||||||
−4.50000 | + | 2.59808i | −0.590879 | + | 0.341144i | |||||
3.00000 | − | 1.73205i | 0.390567 | − | 0.225494i | −0.291839 | − | 0.956467i | ||
0.682406 | + | 0.730974i | ||||||||
1.73205i | 0.223607i | |||||||||
−3.50000 | − | 6.06218i | −0.448129 | − | 0.776182i | 0.550135 | − | 0.835076i | ||
−0.998264 | + | 0.0588933i | ||||||||
−1.50000 | + | 2.59808i | −0.190500 | + | 0.329956i | |||||
0 | 0 | |||||||||
−1.00000 | −0.125000 | |||||||||
−6.00000 | − | 1.73205i | −0.744208 | − | 0.214834i | |||||
9.00000 | 1.10782 | |||||||||
−7.50000 | − | 4.33013i | −0.916271 | − | 0.529009i | −0.0338274 | − | 0.999428i | ||
−0.882443 | + | 0.470418i | ||||||||
3.00000 | − | 5.19615i | 0.363803 | − | 0.630126i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.50000 | − | 0.866025i | 0.178017 | − | 0.102778i | −0.408344 | − | 0.912828i | ||
0.586361 | + | 0.810050i | ||||||||
3.00000 | − | 1.73205i | 0.353553 | − | 0.204124i | |||||
− | 8.66025i | − | 1.01361i | −0.862062 | − | 0.506803i | ||||
0.862062 | − | 0.506803i | ||||||||
0 | 0 | |||||||||
1.00000 | − | 1.73205i | 0.115470 | − | 0.200000i | |||||
1.50000 | + | 0.866025i | 0.172062 | + | 0.0993399i | |||||
0 | 0 | |||||||||
1.50000 | + | 6.06218i | 0.169842 | + | 0.686406i | |||||
−5.00000 | −0.562544 | −0.281272 | − | 0.959628i | ||||||
−0.281272 | + | 0.959628i | ||||||||
7.50000 | + | 4.33013i | 0.838525 | + | 0.484123i | |||||
−0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | |||||
−4.50000 | − | 7.79423i | −0.496942 | − | 0.860729i | |||||
− | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | ||||
0.981761 | − | 0.190117i | ||||||||
0 | 0 | |||||||||
9.00000 | − | 5.19615i | 0.976187 | − | 0.563602i | |||||
− | 19.0526i | − | 2.05449i | |||||||
1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | |||||
4.50000 | − | 7.79423i | 0.479702 | − | 0.830868i | |||||
6.00000 | + | 3.46410i | 0.635999 | + | 0.367194i | 0.783072 | − | 0.621932i | ||
−0.147073 | + | 0.989126i | ||||||||
−6.00000 | −0.632456 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.50000 | + | 0.866025i | 0.155543 | + | 0.0898027i | |||||
−7.50000 | + | 12.9904i | −0.773566 | + | 1.33986i | |||||
1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | |||||
− | 5.19615i | − | 0.530330i | |||||||
−4.50000 | + | 2.59808i | −0.456906 | + | 0.263795i | −0.710742 | − | 0.703452i | ||
0.253837 | + | 0.967247i | ||||||||
0 | 0 | |||||||||
10.3923i | 1.04447i | |||||||||
1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | |||||
4.50000 | − | 7.79423i | 0.447767 | − | 0.775555i | −0.550474 | − | 0.834853i | ||
0.998240 | + | 0.0592978i | ||||||||
−9.00000 | − | 5.19615i | −0.891133 | − | 0.514496i | |||||
−13.0000 | −1.28093 | −0.640464 | − | 0.767988i | ||||||
−0.640464 | + | 0.767988i | ||||||||
6.00000 | + | 1.73205i | 0.588348 | + | 0.169842i | |||||
0 | 0 | |||||||||
−13.5000 | − | 7.79423i | −1.31124 | − | 0.757042i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
2.50000 | + | 4.33013i | 0.240563 | + | 0.416667i | |||||
5.19615i | 0.497701i | 0.968542 | + | 0.248851i | ||||||
−0.968542 | + | 0.248851i | ||||||||
−13.5000 | + | 7.79423i | −1.28717 | + | 0.743151i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−7.50000 | − | 12.9904i | −0.705541 | − | 1.22203i | −0.966496 | − | 0.256681i | ||
0.260955 | − | 0.965351i | ||||||||
1.50000 | − | 2.59808i | 0.140488 | − | 0.243332i | |||||
0 | 0 | |||||||||
−3.00000 | −0.278543 | |||||||||
−7.00000 | + | 1.73205i | −0.647150 | + | 0.160128i | |||||
6.00000 | 0.552345 | |||||||||
0 | 0 | |||||||||
1.50000 | − | 2.59808i | 0.136931 | − | 0.237171i | |||||
8.00000 | + | 13.8564i | 0.727273 | + | 1.25967i | |||||
− | 12.1244i | − | 1.09769i | |||||||
−4.50000 | + | 2.59808i | −0.405751 | + | 0.234261i | |||||
−1.50000 | + | 0.866025i | −0.134704 | + | 0.0777714i | |||||
12.1244i | 1.08444i | |||||||||
0 | 0 | |||||||||
−6.50000 | + | 11.2583i | −0.576782 | + | 0.999015i | 0.419064 | + | 0.907957i | ||
−0.995846 | + | 0.0910585i | ||||||||
−10.5000 | − | 6.06218i | −0.928078 | − | 0.535826i | |||||
−11.0000 | −0.968496 | |||||||||
−7.50000 | − | 7.79423i | −0.657794 | − | 0.683599i | |||||
15.0000 | 1.31056 | 0.655278 | − | 0.755388i | ||||||
0.655278 | + | 0.755388i | ||||||||
4.50000 | + | 2.59808i | 0.391675 | + | 0.226134i | |||||
0 | 0 | |||||||||
−7.50000 | − | 12.9904i | −0.647901 | − | 1.12220i | |||||
8.66025i | 0.745356i | |||||||||
−9.00000 | + | 5.19615i | −0.771744 | + | 0.445566i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
6.50000 | + | 11.2583i | 0.551323 | + | 0.954919i | 0.998179 | + | 0.0603135i | ||
−0.446857 | + | 0.894606i | ||||||||
0 | 0 | |||||||||
7.50000 | + | 4.33013i | 0.631614 | + | 0.364662i | |||||
3.00000 | 0.251754 | |||||||||
−13.5000 | + | 12.9904i | −1.12893 | + | 1.08631i | |||||
10.0000 | 0.833333 | |||||||||
−4.50000 | − | 2.59808i | −0.373705 | − | 0.215758i | |||||
7.50000 | − | 12.9904i | 0.620704 | − | 1.07509i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
16.5000 | − | 9.52628i | 1.35173 | − | 0.780423i | 0.363241 | − | 0.931695i | ||
0.988492 | + | 0.151272i | ||||||||
3.00000 | − | 1.73205i | 0.244949 | − | 0.141421i | |||||
− | 12.1244i | − | 0.986666i | −0.869841 | − | 0.493333i | ||||
0.869841 | − | 0.493333i | ||||||||
−1.50000 | − | 2.59808i | −0.121666 | − | 0.210732i | |||||
6.00000 | − | 10.3923i | 0.485071 | − | 0.840168i | |||||
0 | 0 | |||||||||
−3.00000 | −0.240966 | |||||||||
−1.00000 | + | 3.46410i | −0.0800641 | + | 0.277350i | |||||
23.0000 | 1.83560 | 0.917800 | − | 0.397043i | ||||||
0.917800 | + | 0.397043i | ||||||||
−7.50000 | − | 4.33013i | −0.596668 | − | 0.344486i | |||||
−4.50000 | + | 7.79423i | −0.356873 | + | 0.618123i | |||||
4.50000 | + | 7.79423i | 0.355756 | + | 0.616188i | |||||
0 | 0 | |||||||||
−1.50000 | + | 0.866025i | −0.117851 | + | 0.0680414i | |||||
−10.5000 | + | 6.06218i | −0.822423 | + | 0.474826i | −0.851251 | − | 0.524758i | ||
0.0288280 | + | 0.999584i | ||||||||
− | 5.19615i | − | 0.405751i | |||||||
4.50000 | + | 7.79423i | 0.350325 | + | 0.606780i | |||||
3.00000 | − | 5.19615i | 0.232845 | − | 0.403300i | |||||
−1.50000 | − | 0.866025i | −0.116073 | − | 0.0670151i | 0.440839 | − | 0.897586i | ||
−0.556913 | + | 0.830571i | ||||||||
0 | 0 | |||||||||
−11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | |||||
18.0000 | 1.38054 | |||||||||
3.00000 | + | 1.73205i | 0.229416 | + | 0.132453i | |||||
5.50000 | − | 9.52628i | 0.419371 | − | 0.726372i | |||||
−7.50000 | − | 12.9904i | −0.570214 | − | 0.987640i | −0.996544 | − | 0.0830722i | ||
0.426329 | − | 0.904568i | ||||||||
5.19615i | 0.393919i | |||||||||
0 | 0 | |||||||||
22.5000 | − | 12.9904i | 1.69600 | − | 0.979187i | |||||
− | 3.46410i | − | 0.260378i | |||||||
6.00000 | + | 10.3923i | 0.449719 | + | 0.778936i | |||||
−1.50000 | + | 2.59808i | −0.112115 | + | 0.194189i | −0.916623 | − | 0.399753i | ||
0.804508 | + | 0.593942i | ||||||||
−3.00000 | − | 1.73205i | −0.223607 | − | 0.129099i | |||||
2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | ||||||
0.0743294 | + | 0.997234i | ||||||||
0 | 0 | |||||||||
−7.00000 | −0.517455 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.50000 | + | 2.59808i | 0.109985 | + | 0.190500i | |||||
− | 31.1769i | − | 2.27988i | |||||||
−7.50000 | + | 4.33013i | −0.546994 | + | 0.315807i | |||||
0 | 0 | |||||||||
5.19615i | 0.376969i | |||||||||
7.50000 | + | 12.9904i | 0.542681 | + | 0.939951i | 0.998749 | + | 0.0500060i | ||
−0.456068 | + | 0.889945i | ||||||||
−0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | |||||
−1.50000 | − | 0.866025i | −0.107972 | − | 0.0623379i | 0.445041 | − | 0.895510i | ||
−0.553014 | + | 0.833172i | ||||||||
−9.00000 | −0.646162 | |||||||||
−4.50000 | + | 4.33013i | −0.322252 | + | 0.310087i | |||||
0 | 0 | |||||||||
19.5000 | + | 11.2583i | 1.38932 | + | 0.802123i | 0.993238 | − | 0.116094i | ||
0.396079 | + | 0.918216i | ||||||||
−9.00000 | + | 15.5885i | −0.639602 | + | 1.10782i | |||||
−2.00000 | − | 3.46410i | −0.141776 | − | 0.245564i | 0.786389 | − | 0.617731i | ||
−0.928166 | + | 0.372168i | ||||||||
− | 3.46410i | − | 0.244949i | |||||||
−7.50000 | + | 4.33013i | −0.529009 | + | 0.305424i | |||||
13.5000 | − | 7.79423i | 0.949857 | − | 0.548400i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.210042 | − | 0.363803i | |||||
4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | |||||
−19.5000 | − | 11.2583i | −1.35863 | − | 0.784405i | |||||
0 | 0 | |||||||||
12.5000 | + | 12.9904i | 0.866719 | + | 0.900721i | |||||
9.00000 | 0.622543 | |||||||||
0 | 0 | |||||||||
−6.50000 | + | 11.2583i | −0.447478 | + | 0.775055i | −0.998221 | − | 0.0596196i | ||
0.550743 | + | 0.834675i | ||||||||
−4.50000 | − | 7.79423i | −0.309061 | − | 0.535310i | |||||
− | 1.73205i | − | 0.118678i | |||||||
0 | 0 | |||||||||
16.5000 | − | 9.52628i | 1.12529 | − | 0.649687i | |||||
− | 8.66025i | − | 0.589256i | |||||||
0 | 0 | |||||||||
−4.50000 | + | 7.79423i | −0.304778 | + | 0.527892i | |||||
−7.50000 | − | 4.33013i | −0.506803 | − | 0.292603i | |||||
−9.00000 | −0.606780 | |||||||||
21.0000 | − | 5.19615i | 1.41261 | − | 0.349531i | |||||
0 | 0 | |||||||||
4.50000 | + | 2.59808i | 0.301342 | + | 0.173980i | 0.643046 | − | 0.765828i | ||
−0.341703 | + | 0.939808i | ||||||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.133333 | + | 0.230940i | |||||
− | 25.9808i | − | 1.72821i | |||||||
15.0000 | − | 8.66025i | 0.995585 | − | 0.574801i | 0.0886460 | − | 0.996063i | ||
0.906939 | + | 0.421262i | ||||||||
1.50000 | − | 0.866025i | 0.0993399 | − | 0.0573539i | |||||
− | 12.1244i | − | 0.801200i | −0.916253 | − | 0.400600i | ||||
0.916253 | − | 0.400600i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.50000 | + | 2.59808i | 0.295439 | + | 0.170572i | |||||
3.00000 | 0.196537 | 0.0982683 | − | 0.995160i | ||||||
0.0982683 | + | 0.995160i | ||||||||
−12.0000 | − | 3.46410i | −0.784465 | − | 0.226455i | |||||
−15.0000 | −0.978492 | |||||||||
3.00000 | + | 1.73205i | 0.195283 | + | 0.112747i | |||||
−2.50000 | + | 4.33013i | −0.162392 | + | 0.281272i | |||||
0 | 0 | |||||||||
− | 10.3923i | − | 0.672222i | −0.941822 | − | 0.336111i | ||||
0.941822 | − | 0.336111i | ||||||||
7.50000 | − | 4.33013i | 0.484123 | − | 0.279508i | |||||
6.00000 | − | 3.46410i | 0.386494 | − | 0.223142i | −0.294146 | − | 0.955761i | ||
0.680640 | + | 0.732618i | ||||||||
27.7128i | 1.78145i | |||||||||
8.00000 | + | 13.8564i | 0.513200 | + | 0.888889i | |||||
3.50000 | − | 6.06218i | 0.224065 | − | 0.388091i | |||||
0 | 0 | |||||||||
−9.00000 | −0.573819 | |||||||||
1.50000 | + | 6.06218i | 0.0954427 | + | 0.385727i | |||||
3.00000 | 0.190500 | |||||||||
−3.00000 | − | 1.73205i | −0.190117 | − | 0.109764i | |||||
−10.5000 | + | 18.1865i | −0.664078 | + | 1.15022i | |||||
−1.50000 | − | 2.59808i | −0.0946792 | − | 0.163989i | 0.814795 | − | 0.579748i | ||
−0.909475 | + | 0.415759i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−19.5000 | + | 11.2583i | −1.22354 | + | 0.706410i | |||||
− | 10.3923i | − | 0.650791i | |||||||
−9.50000 | − | 16.4545i | −0.593750 | − | 1.02841i | |||||
−15.0000 | + | 25.9808i | −0.935674 | + | 1.62064i | −0.162247 | + | 0.986750i | ||
−0.773427 | + | 0.633885i | ||||||||
−16.5000 | − | 9.52628i | −1.02725 | − | 0.593080i | |||||
0 | 0 | |||||||||
−1.50000 | − | 6.06218i | −0.0930261 | − | 0.375960i | |||||
−6.00000 | −0.371391 | |||||||||
22.5000 | + | 12.9904i | 1.39005 | + | 0.802548i | |||||
−1.50000 | + | 2.59808i | −0.0924940 | + | 0.160204i | −0.908560 | − | 0.417755i | ||
0.816066 | + | 0.577959i | ||||||||
−4.50000 | − | 7.79423i | −0.276956 | − | 0.479702i | |||||
− | 15.5885i | − | 0.957591i | |||||||
0 | 0 | |||||||||
6.00000 | − | 3.46410i | 0.367194 | − | 0.212000i | |||||
− | 8.66025i | − | 0.529009i | |||||||
3.00000 | + | 5.19615i | 0.182913 | + | 0.316815i | 0.942871 | − | 0.333157i | ||
−0.759958 | + | 0.649972i | ||||||||
−7.50000 | + | 12.9904i | −0.456435 | + | 0.790569i | |||||
15.0000 | + | 8.66025i | 0.911185 | + | 0.526073i | 0.880812 | − | 0.473466i | ||
0.0303728 | + | 0.999539i | ||||||||
−30.0000 | −1.81902 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.542720 | + | 0.313340i | |||||
0 | 0 | |||||||||
5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | ||
−0.675810 | + | 0.737075i | ||||||||
22.5167i | 1.35046i | |||||||||
−3.00000 | + | 1.73205i | −0.179605 | + | 0.103695i | |||||
0 | 0 | |||||||||
6.92820i | 0.413302i | 0.978415 | + | 0.206651i | ||||||
−0.978415 | + | 0.206651i | ||||||||
7.50000 | + | 12.9904i | 0.446619 | + | 0.773566i | |||||
−9.50000 | + | 16.4545i | −0.564716 | + | 0.978117i | 0.432360 | + | 0.901701i | ||
−0.997076 | + | 0.0764162i | ||||||||
1.50000 | + | 0.866025i | 0.0890086 | + | 0.0513892i | |||||
3.00000 | 0.177705 | |||||||||
−31.5000 | + | 7.79423i | −1.86263 | + | 0.460882i | |||||
0 | 0 | |||||||||
9.00000 | + | 5.19615i | 0.530330 | + | 0.306186i | |||||
−9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | |||||
−4.50000 | − | 7.79423i | −0.264249 | − | 0.457693i | |||||
5.19615i | 0.304604i | |||||||||
7.50000 | − | 4.33013i | 0.438904 | − | 0.253402i | |||||
−22.5000 | + | 12.9904i | −1.31446 | + | 0.758906i | −0.982832 | − | 0.184503i | ||
−0.331632 | + | 0.943409i | ||||||||
0 | 0 | |||||||||
3.00000 | + | 5.19615i | 0.174667 | + | 0.302532i | |||||
0 | 0 | |||||||||
22.5000 | + | 12.9904i | 1.30558 | + | 0.753778i | |||||
33.0000 | 1.91164 | |||||||||
0 | 0 | |||||||||
2.00000 | 0.115470 | |||||||||
0 | 0 | |||||||||
10.5000 | − | 18.1865i | 0.604207 | − | 1.04652i | |||||
−4.50000 | − | 7.79423i | −0.258518 | − | 0.447767i | |||||
− | 8.66025i | − | 0.496700i | |||||||
10.5000 | − | 6.06218i | 0.601228 | − | 0.347119i | |||||
18.0000 | − | 10.3923i | 1.02899 | − | 0.594089i | |||||
− | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | ||||
0.721923 | − | 0.691974i | ||||||||
0 | 0 | |||||||||
−6.50000 | + | 11.2583i | −0.369772 | + | 0.640464i | |||||
−4.50000 | − | 2.59808i | −0.255583 | − | 0.147561i | |||||
−15.0000 | −0.850572 | −0.425286 | − | 0.905059i | ||||||
−0.425286 | + | 0.905059i | ||||||||
4.50000 | − | 4.33013i | 0.254762 | − | 0.245145i | |||||
19.0000 | 1.07394 | 0.536972 | − | 0.843600i | ||||||
0.536972 | + | 0.843600i | ||||||||
34.5000 | + | 19.9186i | 1.94695 | + | 1.12407i | |||||
0 | 0 | |||||||||
−2.50000 | − | 4.33013i | −0.140636 | − | 0.243589i | |||||
− | 5.19615i | − | 0.291845i | −0.989296 | − | 0.145922i | ||||
0.989296 | − | 0.145922i | ||||||||
−13.5000 | + | 7.79423i | −0.757042 | + | 0.437079i | |||||
−13.5000 | + | 7.79423i | −0.755855 | + | 0.436393i | |||||
− | 1.73205i | − | 0.0968246i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.00000 | − | 5.19615i | −0.500773 | − | 0.289122i | |||||
−1.00000 | −0.0555556 | |||||||||
−2.00000 | + | 6.92820i | −0.110940 | + | 0.384308i | |||||
−21.0000 | −1.16308 | |||||||||
4.50000 | + | 2.59808i | 0.248851 | + | 0.143674i | |||||
−4.50000 | + | 7.79423i | −0.248471 | + | 0.430364i | |||||
0 | 0 | |||||||||
15.5885i | 0.858116i | |||||||||
−28.5000 | + | 16.4545i | −1.56650 | + | 0.904420i | −0.569929 | + | 0.821694i | ||
−0.996572 | + | 0.0827265i | ||||||||
3.00000 | − | 1.73205i | 0.164646 | − | 0.0950586i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | |||||
7.50000 | − | 12.9904i | 0.409769 | − | 0.709740i | |||||
0 | 0 | |||||||||
22.0000 | 1.19842 | 0.599208 | − | 0.800593i | ||||||
0.599208 | + | 0.800593i | ||||||||
−10.5000 | − | 19.9186i | −0.571125 | − | 1.08343i | |||||
−15.0000 | −0.814688 | |||||||||
9.00000 | + | 5.19615i | 0.488094 | + | 0.281801i | |||||
−4.50000 | + | 7.79423i | −0.243689 | + | 0.422081i | |||||
3.00000 | + | 5.19615i | 0.162221 | + | 0.280976i | |||||
0 | 0 | |||||||||
−16.5000 | + | 9.52628i | −0.889620 | + | 0.513623i | |||||
0 | 0 | |||||||||
− | 25.9808i | − | 1.39673i | |||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
−1.50000 | + | 2.59808i | −0.0804084 | + | 0.139272i | |||||
−4.50000 | − | 2.59808i | −0.240879 | − | 0.139072i | 0.374701 | − | 0.927146i | ||
−0.615581 | + | 0.788074i | ||||||||
0 | 0 | |||||||||
−5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | |||||
27.0000 | 1.43910 | |||||||||
−1.50000 | − | 0.866025i | −0.0798369 | − | 0.0460939i | 0.459550 | − | 0.888152i | ||
−0.539387 | + | 0.842058i | ||||||||
3.00000 | − | 5.19615i | 0.159448 | − | 0.276172i | |||||
1.50000 | + | 2.59808i | 0.0796117 | + | 0.137892i | |||||
6.92820i | 0.367194i | |||||||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.237832 | + | 0.137313i | |||||
− | 19.0526i | − | 1.00556i | −0.864416 | − | 0.502778i | ||||
0.864416 | − | 0.502778i | ||||||||
3.00000 | + | 5.19615i | 0.158114 | + | 0.273861i | |||||
−8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | |||||
3.00000 | + | 1.73205i | 0.157676 | + | 0.0910346i | |||||
16.0000 | 0.839782 | |||||||||
0 | 0 | |||||||||
15.0000 | 0.785136 | |||||||||
−10.5000 | − | 6.06218i | −0.548844 | − | 0.316875i | |||||
−11.5000 | + | 19.9186i | −0.600295 | + | 1.03974i | 0.392481 | + | 0.919760i | ||
−0.992776 | + | 0.119982i | ||||||||
0 | 0 | |||||||||
− | 10.3923i | − | 0.541002i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.73205i | 0.0898027i | |||||||||
−9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | ||
−0.999956 | + | 0.00933789i | ||||||||
27.0000 | − | 46.7654i | 1.39614 | − | 2.41818i | |||||
10.5000 | + | 6.06218i | 0.542218 | + | 0.313050i | |||||
15.0000 | 0.773566 | |||||||||
−7.50000 | − | 7.79423i | −0.386270 | − | 0.401423i | |||||
0 | 0 | |||||||||
−1.50000 | − | 0.866025i | −0.0770498 | − | 0.0444847i | 0.460980 | − | 0.887410i | ||
−0.538030 | + | 0.842926i | ||||||||
−1.50000 | + | 2.59808i | −0.0769484 | + | 0.133278i | |||||
6.50000 | + | 11.2583i | 0.333005 | + | 0.576782i | |||||
25.9808i | 1.32929i | |||||||||
13.5000 | − | 7.79423i | 0.689818 | − | 0.398266i | −0.113726 | − | 0.993512i | ||
0.803544 | + | 0.595246i | ||||||||
−10.5000 | + | 6.06218i | −0.535826 | + | 0.309359i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.0763480 | − | 0.132239i | |||||
11.0000 | − | 19.0526i | 0.559161 | − | 0.968496i | |||||
−4.50000 | − | 2.59808i | −0.228453 | − | 0.131897i | |||||
3.00000 | 0.152106 | 0.0760530 | − | 0.997104i | ||||||
0.0760530 | + | 0.997104i | ||||||||
−10.5000 | + | 2.59808i | −0.531688 | + | 0.131559i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.50000 | − | 12.9904i | 0.378325 | − | 0.655278i | |||||
19.5000 | + | 33.7750i | 0.982396 | + | 1.70156i | |||||
− | 8.66025i | − | 0.435745i | |||||||
−9.00000 | + | 5.19615i | −0.452267 | + | 0.261116i | |||||
−31.5000 | + | 18.1865i | −1.58094 | + | 0.912756i | −0.586217 | + | 0.810154i | ||
−0.994722 | + | 0.102602i | ||||||||
− | 6.92820i | − | 0.347279i | |||||||
0 | 0 | |||||||||
5.00000 | − | 8.66025i | 0.250000 | − | 0.433013i | |||||
6.00000 | + | 3.46410i | 0.299626 | + | 0.172989i | 0.642275 | − | 0.766475i | ||
−0.342649 | + | 0.939463i | ||||||||
−15.0000 | −0.748132 | |||||||||
−6.00000 | − | 1.73205i | −0.298881 | − | 0.0862796i | |||||
9.00000 | 0.447767 | |||||||||
−1.50000 | − | 0.866025i | −0.0745356 | − | 0.0430331i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
10.3923i | 0.514496i | |||||||||
−6.00000 | + | 3.46410i | −0.296681 | + | 0.171289i | −0.640951 | − | 0.767582i | ||
0.344270 | + | 0.938871i | ||||||||
13.5000 | − | 7.79423i | 0.666717 | − | 0.384930i | |||||
0 | 0 | |||||||||
−6.50000 | − | 11.2583i | −0.320232 | − | 0.554658i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.00000 | 0.294528 | |||||||||
4.50000 | + | 18.1865i | 0.220631 | + | 0.891668i | |||||
13.0000 | 0.636613 | |||||||||
13.5000 | + | 7.79423i | 0.660307 | + | 0.381228i | |||||
−10.5000 | + | 18.1865i | −0.512959 | + | 0.888470i | 0.486928 | + | 0.873442i | ||
−0.999887 | + | 0.0150285i | ||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−19.5000 | + | 11.2583i | −0.949245 | + | 0.548047i | |||||
−15.0000 | + | 8.66025i | −0.729325 | + | 0.421076i | |||||
15.5885i | 0.757042i | |||||||||
−6.00000 | − | 10.3923i | −0.291043 | − | 0.504101i | |||||
1.50000 | − | 2.59808i | 0.0726752 | − | 0.125877i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.50000 | + | 18.1865i | 0.217262 | + | 0.878054i | |||||
33.0000 | 1.59140 | |||||||||
28.5000 | + | 16.4545i | 1.37280 | + | 0.792585i | 0.991279 | − | 0.131777i | ||
0.381517 | + | 0.924362i | ||||||||
12.5000 | − | 21.6506i | 0.601407 | − | 1.04167i | |||||
−9.50000 | − | 16.4545i | −0.456541 | − | 0.790752i | 0.542234 | − | 0.840227i | ||
−0.998775 | + | 0.0494752i | ||||||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.215758 | + | 0.124568i | |||||
−4.50000 | + | 2.59808i | −0.215511 | + | 0.124425i | |||||
0 | 0 | |||||||||
−7.50000 | − | 12.9904i | −0.358364 | − | 0.620704i | |||||
−4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | ||
0.754642 | + | 0.656136i | ||||||||
13.5000 | + | 7.79423i | 0.643587 | + | 0.371575i | |||||
0 | 0 | |||||||||
36.0000 | + | 10.3923i | 1.71235 | + | 0.494312i | |||||
15.0000 | 0.712672 | 0.356336 | − | 0.934358i | ||||||
0.356336 | + | 0.934358i | ||||||||
0 | 0 | |||||||||
−6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | |||||
4.50000 | + | 7.79423i | 0.213081 | + | 0.369067i | |||||
− | 19.0526i | − | 0.901155i | |||||||
0 | 0 | |||||||||
1.50000 | − | 0.866025i | 0.0707894 | − | 0.0408703i | −0.464188 | − | 0.885737i | ||
0.534977 | + | 0.844867i | ||||||||
6.92820i | 0.326599i | |||||||||
−13.5000 | − | 23.3827i | −0.635690 | − | 1.10105i | |||||
7.50000 | − | 12.9904i | 0.352770 | − | 0.611016i | |||||
−10.5000 | − | 6.06218i | −0.493333 | − | 0.284826i | |||||
30.0000 | 1.40797 | |||||||||
0 | 0 | |||||||||
−3.00000 | −0.140488 | |||||||||
30.0000 | + | 17.3205i | 1.40334 | + | 0.810219i | 0.994734 | − | 0.102491i | ||
0.408607 | + | 0.912710i | ||||||||
10.5000 | − | 18.1865i | 0.490633 | − | 0.849801i | |||||
−15.0000 | − | 25.9808i | −0.700140 | − | 1.21268i | |||||
0 | 0 | |||||||||
25.5000 | − | 14.7224i | 1.18765 | − | 0.685692i | 0.229881 | − | 0.973219i | ||
0.957773 | + | 0.287527i | ||||||||
0 | 0 | |||||||||
24.2487i | 1.12693i | 0.826139 | + | 0.563467i | ||||||
−0.826139 | + | 0.563467i | ||||||||
7.50000 | + | 12.9904i | 0.348179 | + | 0.603063i | |||||
−1.50000 | + | 2.59808i | −0.0695608 | + | 0.120483i | |||||
4.50000 | + | 2.59808i | 0.208458 | + | 0.120354i | |||||
−21.0000 | −0.971764 | −0.485882 | − | 0.874024i | ||||||
−0.485882 | + | 0.874024i | ||||||||
−5.00000 | − | 5.19615i | −0.231125 | − | 0.240192i | |||||
0 | 0 | |||||||||
−22.5000 | − | 12.9904i | −1.03785 | − | 0.599202i | |||||
11.5000 | − | 19.9186i | 0.529892 | − | 0.917800i | |||||
−3.00000 | − | 5.19615i | −0.138086 | − | 0.239172i | |||||
− | 57.1577i | − | 2.62811i | |||||||
−7.50000 | + | 4.33013i | −0.344486 | + | 0.198889i | |||||
3.00000 | − | 1.73205i | 0.137649 | − | 0.0794719i | |||||
0 | 0 | |||||||||
−9.00000 | − | 15.5885i | −0.412082 | − | 0.713746i | |||||
9.00000 | − | 15.5885i | 0.411650 | − | 0.712999i | |||||
−25.5000 | − | 14.7224i | −1.16512 | − | 0.672685i | −0.212598 | − | 0.977140i | ||
−0.952527 | + | 0.304455i | ||||||||
9.00000 | 0.410792 | |||||||||
0 | 0 | |||||||||
12.0000 | 0.546585 | |||||||||
0 | 0 | |||||||||
−8.00000 | + | 13.8564i | −0.363636 | + | 0.629837i | |||||
−4.50000 | − | 7.79423i | −0.204334 | − | 0.353918i | |||||
27.7128i | 1.25708i | |||||||||
21.0000 | − | 12.1244i | 0.951601 | − | 0.549407i | 0.0580230 | − | 0.998315i | ||
0.893578 | + | 0.448908i | ||||||||
−10.5000 | + | 6.06218i | −0.475313 | + | 0.274422i | |||||
12.1244i | 0.548282i | |||||||||
0 | 0 | |||||||||
13.5000 | − | 23.3827i | 0.609246 | − | 1.05525i | −0.382118 | − | 0.924113i | ||
0.991365 | − | 0.131132i | ||||||||
−4.50000 | − | 2.59808i | −0.202876 | − | 0.117130i | |||||
18.0000 | 0.810679 | |||||||||
−3.00000 | + | 10.3923i | −0.134976 | + | 0.467572i | |||||
−18.0000 | −0.809040 | |||||||||
7.50000 | + | 4.33013i | 0.336760 | + | 0.194428i | |||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | |||||
1.73205i | 0.0775372i | 0.999248 | + | 0.0387686i | ||||||
−0.999248 | + | 0.0387686i | ||||||||
−10.5000 | + | 6.06218i | −0.469574 | + | 0.271109i | |||||
−1.50000 | + | 0.866025i | −0.0670151 | + | 0.0386912i | |||||
− | 5.19615i | − | 0.231916i | |||||||
4.50000 | + | 7.79423i | 0.200645 | + | 0.347527i | 0.948736 | − | 0.316068i | ||
−0.748091 | + | 0.663596i | ||||||||
0 | 0 | |||||||||
13.5000 | + | 7.79423i | 0.600742 | + | 0.346839i | |||||
0 | 0 | |||||||||
−11.5000 | + | 6.06218i | −0.510733 | + | 0.269231i | |||||
−13.0000 | −0.576782 | |||||||||
6.00000 | + | 3.46410i | 0.265945 | + | 0.153544i | 0.627044 | − | 0.778984i | ||
−0.361098 | + | 0.932528i | ||||||||
9.00000 | − | 15.5885i | 0.398527 | − | 0.690268i | |||||
0 | 0 | |||||||||
− | 8.66025i | − | 0.382733i | |||||||
7.50000 | − | 4.33013i | 0.331133 | − | 0.191180i | |||||
−45.0000 | + | 25.9808i | −1.98486 | + | 1.14596i | |||||
− | 22.5167i | − | 0.992203i | |||||||
−5.50000 | − | 9.52628i | −0.242124 | − | 0.419371i | |||||
−22.5000 | + | 38.9711i | −0.989549 | + | 1.71395i | |||||
0 | 0 | |||||||||
−15.0000 | −0.658427 | |||||||||
−3.00000 | + | 10.3923i | −0.131559 | + | 0.455733i | |||||
39.0000 | 1.70862 | 0.854311 | − | 0.519763i | ||||||
0.854311 | + | 0.519763i | ||||||||
−9.00000 | − | 5.19615i | −0.393919 | − | 0.227429i | |||||
2.00000 | − | 3.46410i | 0.0874539 | − | 0.151475i | −0.818980 | − | 0.573822i | ||
0.906434 | + | 0.422347i | ||||||||
7.50000 | + | 12.9904i | 0.327639 | + | 0.567487i | |||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.196209 | + | 0.113282i | |||||
9.00000 | − | 5.19615i | 0.392046 | − | 0.226348i | |||||
− | 25.9808i | − | 1.13067i | |||||||
11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | |||||
13.5000 | − | 23.3827i | 0.586403 | − | 1.01568i | |||||
6.00000 | + | 3.46410i | 0.260378 | + | 0.150329i | |||||
0 | 0 | |||||||||
13.5000 | − | 12.9904i | 0.584750 | − | 0.562676i | |||||
12.0000 | 0.519291 | |||||||||
0 | 0 | |||||||||
−7.50000 | + | 12.9904i | −0.323951 | + | 0.561099i | |||||
1.50000 | + | 2.59808i | 0.0647298 | + | 0.112115i | |||||
10.3923i | 0.448044i | |||||||||
0 | 0 | |||||||||
−7.50000 | + | 4.33013i | −0.322749 | + | 0.186339i | |||||
− | 12.1244i | − | 0.521267i | −0.965438 | − | 0.260633i | ||||
0.965438 | − | 0.260633i | ||||||||
15.0000 | + | 25.9808i | 0.644305 | + | 1.11597i | |||||
1.00000 | − | 1.73205i | 0.0429141 | − | 0.0743294i | |||||
−27.0000 | − | 15.5885i | −1.15762 | − | 0.668350i | |||||
−9.00000 | −0.385518 | |||||||||
0 | 0 | |||||||||
−28.0000 | −1.19719 | −0.598597 | − | 0.801050i | ||||||
−0.598597 | + | 0.801050i | ||||||||
0 | 0 | |||||||||
7.00000 | − | 12.1244i | 0.298753 | − | 0.517455i | |||||
9.00000 | + | 15.5885i | 0.383761 | + | 0.664694i | |||||
5.19615i | 0.221364i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
17.3205i | 0.735878i | |||||||||
0 | 0 | |||||||||
−6.50000 | + | 11.2583i | −0.275661 | + | 0.477460i | |||||
−13.5000 | − | 7.79423i | −0.572013 | − | 0.330252i | 0.185940 | − | 0.982561i | ||
−0.757953 | + | 0.652309i | ||||||||
−6.00000 | −0.254000 | |||||||||
38.5000 | − | 9.52628i | 1.62838 | − | 0.402919i | |||||
0 | 0 | |||||||||
−27.0000 | − | 15.5885i | −1.13994 | − | 0.658145i | |||||
−6.00000 | + | 10.3923i | −0.253095 | + | 0.438373i | |||||
18.0000 | + | 31.1769i | 0.758610 | + | 1.31395i | 0.943560 | + | 0.331202i | ||
−0.184950 | + | 0.982748i | ||||||||
8.66025i | 0.364662i | |||||||||
22.5000 | − | 12.9904i | 0.946582 | − | 0.546509i | |||||
−28.5000 | + | 16.4545i | −1.19794 | + | 0.691633i | |||||
0 | 0 | |||||||||
−1.50000 | − | 2.59808i | −0.0629386 | − | 0.109013i | |||||
3.00000 | − | 5.19615i | 0.125767 | − | 0.217834i | −0.796266 | − | 0.604947i | ||
0.922032 | + | 0.387113i | ||||||||
4.50000 | + | 2.59808i | 0.188484 | + | 0.108821i | |||||
−23.0000 | −0.962520 | −0.481260 | − | 0.876578i | ||||||
−0.481260 | + | 0.876578i | ||||||||
−18.0000 | − | 5.19615i | −0.752618 | − | 0.217262i | |||||
15.0000 | 0.626634 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00000 | − | 1.73205i | −0.0416667 | − | 0.0721688i | |||||
− | 15.5885i | − | 0.648956i | −0.945893 | − | 0.324478i | ||||
0.945893 | − | 0.324478i | ||||||||
−28.5000 | + | 16.4545i | −1.18544 | + | 0.684416i | |||||
−1.50000 | + | 0.866025i | −0.0623379 | + | 0.0359908i | |||||
− | 5.19615i | − | 0.215758i | |||||||
0 | 0 | |||||||||
−4.50000 | + | 7.79423i | −0.186531 | + | 0.323081i | |||||
−40.5000 | − | 23.3827i | −1.67734 | − | 0.968412i | |||||
−15.0000 | −0.620704 | |||||||||
−3.00000 | − | 12.1244i | −0.124035 | − | 0.501280i | |||||
−45.0000 | −1.85893 | |||||||||
−13.5000 | − | 7.79423i | −0.557205 | − | 0.321702i | 0.194818 | − | 0.980839i | ||
−0.752023 | + | 0.659137i | ||||||||
0 | 0 | |||||||||
1.50000 | + | 2.59808i | 0.0618064 | + | 0.107052i | |||||
10.3923i | 0.427844i | |||||||||
19.5000 | − | 11.2583i | 0.802123 | − | 0.463106i | |||||
0 | 0 | |||||||||
− | 5.19615i | − | 0.213380i | −0.994292 | − | 0.106690i | ||||
0.994292 | − | 0.106690i | ||||||||
22.5000 | + | 38.9711i | 0.923186 | + | 1.59901i | |||||
0 | 0 | |||||||||
16.5000 | + | 9.52628i | 0.675866 | + | 0.390212i | |||||
−4.00000 | −0.163709 | |||||||||
0 | 0 | |||||||||
9.00000 | 0.367730 | 0.183865 | − | 0.982952i | ||||||
0.183865 | + | 0.982952i | ||||||||
−3.00000 | − | 1.73205i | −0.122474 | − | 0.0707107i | |||||
−9.50000 | + | 16.4545i | −0.387513 | + | 0.671192i | −0.992114 | − | 0.125336i | ||
0.604601 | + | 0.796528i | ||||||||
0 | 0 | |||||||||
− | 17.3205i | − | 0.705346i | |||||||
10.5000 | − | 6.06218i | 0.427239 | − | 0.246667i | |||||
−24.0000 | + | 13.8564i | −0.975739 | + | 0.563343i | |||||
− | 15.5885i | − | 0.633238i | |||||||
21.5000 | + | 37.2391i | 0.872658 | + | 1.51149i | 0.859237 | + | 0.511578i | ||
0.0134214 | + | 0.999910i | ||||||||
4.50000 | − | 7.79423i | 0.182499 | − | 0.316098i | |||||
0 | 0 | |||||||||
21.0000 | 0.850265 | |||||||||
−30.0000 | − | 8.66025i | −1.21367 | − | 0.350356i | |||||
12.0000 | 0.485071 | |||||||||
−31.5000 | − | 18.1865i | −1.27227 | − | 0.734547i | −0.296858 | − | 0.954922i | ||
−0.975415 | + | 0.220375i | ||||||||
21.0000 | − | 36.3731i | 0.847491 | − | 1.46790i | |||||
−4.50000 | − | 7.79423i | −0.181458 | − | 0.314294i | |||||
0 | 0 | |||||||||
37.5000 | − | 21.6506i | 1.50969 | − | 0.871622i | 0.509757 | − | 0.860318i | ||
0.999936 | − | 0.0113033i | ||||||||
−19.5000 | + | 11.2583i | −0.784405 | + | 0.452876i | |||||
− | 19.0526i | − | 0.765787i | −0.923792 | − | 0.382893i | ||||
0.923792 | − | 0.382893i | ||||||||
−1.50000 | − | 2.59808i | −0.0602414 | − | 0.104341i | |||||
0 | 0 | |||||||||
−22.5000 | − | 12.9904i | −0.902168 | − | 0.520867i | |||||
0 | 0 | |||||||||
17.5000 | − | 4.33013i | 0.700561 | − | 0.173344i | |||||
−11.0000 | −0.440000 | |||||||||
28.5000 | + | 16.4545i | 1.13909 | + | 0.657653i | |||||
4.50000 | − | 7.79423i | 0.179713 | − | 0.311272i | |||||
11.5000 | + | 19.9186i | 0.458900 | + | 0.794838i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−40.5000 | + | 23.3827i | −1.61228 | + | 0.930850i | −0.623439 | + | 0.781872i | ||
−0.988841 | + | 0.148978i | ||||||||
8.66025i | 0.344486i | |||||||||
6.50000 | + | 11.2583i | 0.258352 | + | 0.447478i | |||||
4.50000 | − | 7.79423i | 0.178718 | − | 0.309548i | |||||
−19.5000 | − | 11.2583i | −0.773834 | − | 0.446773i | |||||
−9.00000 | −0.356873 | |||||||||
0 | 0 | |||||||||
−27.0000 | −1.06894 | |||||||||
3.00000 | + | 1.73205i | 0.118678 | + | 0.0685189i | |||||
10.5000 | − | 18.1865i | 0.415049 | − | 0.718886i | |||||
−15.0000 | − | 25.9808i | −0.592464 | − | 1.02618i | −0.993899 | − | 0.110291i | ||
0.401435 | − | 0.915888i | ||||||||
0 | 0 | |||||||||
−4.50000 | + | 2.59808i | −0.177463 | + | 0.102458i | −0.586100 | − | 0.810239i | ||
0.408637 | + | 0.912697i | ||||||||
0 | 0 | |||||||||
− | 19.0526i | − | 0.750194i | |||||||
−9.00000 | − | 15.5885i | −0.354100 | − | 0.613320i | |||||
4.50000 | − | 7.79423i | 0.176913 | − | 0.306423i | −0.763908 | − | 0.645325i | ||
0.940822 | + | 0.338902i | ||||||||
1.50000 | + | 0.866025i | 0.0589256 | + | 0.0340207i | |||||
18.0000 | 0.706562 | |||||||||
−9.00000 | + | 8.66025i | −0.353009 | + | 0.339683i | |||||
0 | 0 | |||||||||
−10.5000 | − | 6.06218i | −0.411212 | − | 0.237413i | |||||
15.0000 | − | 25.9808i | 0.586995 | − | 1.01671i | −0.407628 | − | 0.913148i | ||
0.994623 | − | 0.103558i | ||||||||
4.50000 | + | 7.79423i | 0.175964 | + | 0.304778i | |||||
25.9808i | 1.01515i | |||||||||
−22.5000 | + | 12.9904i | −0.878477 | + | 0.507189i | |||||
15.0000 | − | 8.66025i | 0.585206 | − | 0.337869i | |||||
0 | 0 | |||||||||
−7.50000 | − | 12.9904i | −0.292159 | − | 0.506033i | 0.682161 | − | 0.731202i | ||
−0.974320 | + | 0.225168i | ||||||||
−4.50000 | + | 7.79423i | −0.175162 | + | 0.303390i | |||||
−31.5000 | − | 18.1865i | −1.22521 | − | 0.707374i | −0.259184 | − | 0.965828i | ||
−0.966024 | + | 0.258454i | ||||||||
−57.0000 | −2.21537 | |||||||||
6.00000 | − | 20.7846i | 0.233021 | − | 0.807207i | |||||
−6.00000 | −0.232845 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 1.73205i | − | 0.0670151i | |||||||
4.50000 | − | 2.59808i | 0.173980 | − | 0.100447i | |||||
22.5000 | − | 12.9904i | 0.869251 | − | 0.501862i | |||||
− | 36.3731i | − | 1.40417i | |||||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.0192736 | − | 0.0333828i | −0.856228 | − | 0.516599i | ||
0.875501 | + | 0.483216i | ||||||||
33.0000 | + | 19.0526i | 1.27111 | + | 0.733877i | |||||
10.0000 | 0.384900 | |||||||||
0.500000 | − | 12.9904i | 0.0192308 | − | 0.499630i | |||||
27.0000 | 1.03769 | 0.518847 | − | 0.854867i | ||||||
0.518847 | + | 0.854867i | ||||||||
−22.5000 | − | 12.9904i | −0.864107 | − | 0.498893i | |||||
0 | 0 | |||||||||
−9.00000 | − | 15.5885i | −0.345134 | − | 0.597790i | |||||
− | 17.3205i | − | 0.663723i | |||||||
−13.5000 | + | 7.79423i | −0.516942 | + | 0.298456i | |||||
−21.0000 | + | 12.1244i | −0.803543 | + | 0.463926i | −0.844708 | − | 0.535227i | ||
0.0411658 | + | 0.999152i | ||||||||
3.46410i | 0.132453i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−10.5000 | − | 6.06218i | −0.400600 | − | 0.231287i | |||||
−55.0000 | −2.09686 | |||||||||
9.00000 | − | 31.1769i | 0.342873 | − | 1.18775i | |||||
0 | 0 | |||||||||
−27.0000 | − | 15.5885i | −1.02713 | − | 0.593013i | −0.110968 | − | 0.993824i | ||
−0.916161 | + | 0.400811i | ||||||||
7.50000 | − | 12.9904i | 0.285107 | − | 0.493820i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−19.5000 | + | 11.2583i | −0.739677 | + | 0.427053i | |||||
4.50000 | − | 2.59808i | 0.170572 | − | 0.0984798i | |||||
31.1769i | 1.18091i | |||||||||
−4.50000 | − | 7.79423i | −0.170328 | − | 0.295016i | |||||
1.50000 | − | 2.59808i | 0.0567352 | − | 0.0982683i | |||||
0 | 0 | |||||||||
−6.00000 | −0.226617 | −0.113308 | − | 0.993560i | ||||||
−0.113308 | + | 0.993560i | ||||||||
−22.5000 | + | 21.6506i | −0.849208 | + | 0.817151i | |||||
0 | 0 | |||||||||
−4.50000 | − | 2.59808i | −0.169600 | − | 0.0979187i | |||||
−7.50000 | + | 12.9904i | −0.282466 | + | 0.489246i | |||||
−1.50000 | − | 2.59808i | −0.0564532 | − | 0.0977799i | |||||
0 | 0 | |||||||||
3.00000 | − | 1.73205i | 0.112747 | − | 0.0650945i | |||||
10.5000 | − | 6.06218i | 0.394336 | − | 0.227670i | −0.289701 | − | 0.957117i | ||
0.684037 | + | 0.729447i | ||||||||
5.19615i | 0.195008i | |||||||||
−5.00000 | − | 8.66025i | −0.187515 | − | 0.324785i | |||||
6.00000 | − | 10.3923i | 0.224860 | − | 0.389468i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−22.5000 | − | 23.3827i | −0.841452 | − | 0.874463i | |||||
−3.00000 | −0.112115 | |||||||||
−9.00000 | − | 5.19615i | −0.336111 | − | 0.194054i | |||||
16.5000 | − | 28.5788i | 0.615775 | − | 1.06655i | |||||
7.50000 | + | 12.9904i | 0.279703 | + | 0.484459i | 0.971311 | − | 0.237814i | ||
−0.691608 | + | 0.722273i | ||||||||
17.3205i | 0.645497i | |||||||||
0 | 0 | |||||||||
−24.0000 | + | 13.8564i | −0.893188 | + | 0.515682i | |||||
− | 6.92820i | − | 0.257663i | |||||||
1.00000 | + | 1.73205i | 0.0371647 | + | 0.0643712i | |||||
−3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | |||||
24.0000 | + | 13.8564i | 0.890724 | + | 0.514259i | |||||
−32.0000 | −1.18681 | −0.593407 | − | 0.804902i | ||||||
−0.593407 | + | 0.804902i | ||||||||
0 | 0 | |||||||||
13.0000 | 0.481481 | |||||||||
22.5000 | + | 12.9904i | 0.832762 | + | 0.480796i | |||||
−33.0000 | + | 57.1577i | −1.22055 | + | 2.11405i | |||||
−3.50000 | − | 6.06218i | −0.129364 | − | 0.224065i | |||||
50.2295i | 1.85527i | 0.373491 | + | 0.927634i | ||||||
−0.373491 | + | 0.927634i | ||||||||
−34.5000 | + | 19.9186i | −1.27342 | + | 0.735208i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−22.5000 | − | 38.9711i | −0.828798 | − | 1.43552i | |||||
9.00000 | − | 15.5885i | 0.331295 | − | 0.573819i | |||||
34.5000 | + | 19.9186i | 1.26910 | + | 0.732717i | 0.974818 | − | 0.223001i | ||
0.294285 | + | 0.955718i | ||||||||
0 | 0 | |||||||||
6.00000 | + | 1.73205i | 0.220416 | + | 0.0636285i | |||||
0 | 0 | |||||||||
−1.50000 | − | 0.866025i | −0.0550297 | − | 0.0317714i | 0.472233 | − | 0.881474i | ||
−0.527262 | + | 0.849703i | ||||||||
1.50000 | − | 2.59808i | 0.0549927 | − | 0.0952501i | |||||
16.5000 | + | 28.5788i | 0.604513 | + | 1.04705i | |||||
− | 32.9090i | − | 1.20488i | |||||||
6.00000 | − | 3.46410i | 0.219529 | − | 0.126745i | |||||
27.0000 | − | 15.5885i | 0.987218 | − | 0.569970i | |||||
0 | 0 | |||||||||
10.5000 | + | 18.1865i | 0.383406 | + | 0.664078i | |||||
−10.0000 | + | 17.3205i | −0.364905 | + | 0.632034i | −0.988761 | − | 0.149505i | ||
0.623856 | + | 0.781540i | ||||||||
37.5000 | + | 21.6506i | 1.36748 | + | 0.789517i | |||||
−3.00000 | −0.109326 | |||||||||
−4.50000 | − | 18.1865i | −0.163880 | − | 0.662314i | |||||
21.0000 | 0.764268 | |||||||||
0 | 0 | |||||||||
8.50000 | − | 14.7224i | 0.308938 | − | 0.535096i | −0.669193 | − | 0.743089i | ||
0.978130 | + | 0.207993i | ||||||||
−1.50000 | − | 2.59808i | −0.0544825 | − | 0.0943664i | |||||
0 | 0 | |||||||||
4.50000 | − | 2.59808i | 0.163232 | − | 0.0942421i | |||||
−25.5000 | + | 14.7224i | −0.924374 | + | 0.533688i | −0.885028 | − | 0.465538i | ||
−0.0393463 | + | 0.999226i | ||||||||
22.5167i | 0.815693i | |||||||||
0 | 0 | |||||||||
−7.50000 | + | 12.9904i | −0.271340 | + | 0.469975i | |||||
18.0000 | + | 10.3923i | 0.650791 | + | 0.375735i | |||||
27.0000 | 0.975550 | |||||||||
3.00000 | + | 12.1244i | 0.108324 | + | 0.437785i | |||||
−19.0000 | −0.685603 | |||||||||
−16.5000 | − | 9.52628i | −0.595005 | − | 0.343526i | 0.172069 | − | 0.985085i | ||
−0.767074 | + | 0.641558i | ||||||||
0 | 0 | |||||||||
15.0000 | + | 25.9808i | 0.540212 | + | 0.935674i | |||||
− | 1.73205i | − | 0.0623379i | |||||||
12.0000 | − | 6.92820i | 0.431610 | − | 0.249190i | −0.268422 | − | 0.963301i | ||
0.700032 | + | 0.714111i | ||||||||
33.0000 | − | 19.0526i | 1.18616 | − | 0.684830i | |||||
3.46410i | 0.124434i | |||||||||
4.50000 | + | 7.79423i | 0.161541 | + | 0.279797i | |||||
0 | 0 | |||||||||
4.50000 | + | 2.59808i | 0.161333 | + | 0.0931455i | |||||
−9.00000 | −0.322458 | |||||||||
−6.00000 | − | 1.73205i | −0.214834 | − | 0.0620174i | |||||
9.00000 | 0.322045 | |||||||||
0 | 0 | |||||||||
−7.50000 | + | 12.9904i | −0.268028 | + | 0.464238i | |||||
0 | 0 | |||||||||
39.8372i | 1.42185i | |||||||||
22.5000 | − | 12.9904i | 0.802548 | − | 0.463352i | |||||
27.0000 | − | 15.5885i | 0.962446 | − | 0.555668i | 0.0655211 | − | 0.997851i | ||
0.896925 | + | 0.442183i | ||||||||
22.5167i | 0.802123i | |||||||||
1.50000 | + | 2.59808i | 0.0534014 | + | 0.0924940i | |||||
7.50000 | − | 12.9904i | 0.266838 | − | 0.462177i | |||||
0 | 0 | |||||||||
18.0000 | 0.639602 | |||||||||
24.5000 | − | 6.06218i | 0.870021 | − | 0.215274i | |||||
−63.0000 | −2.23579 | |||||||||
−13.5000 | − | 7.79423i | −0.478796 | − | 0.276433i | |||||
2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | |||||
16.5000 | + | 28.5788i | 0.584460 | + | 1.01231i | 0.994943 | + | 0.100446i | ||
−0.410483 | + | 0.911868i | ||||||||
0 | 0 | |||||||||
45.0000 | − | 25.9808i | 1.59199 | − | 0.919133i | |||||
9.00000 | − | 5.19615i | 0.318198 | − | 0.183712i | |||||
13.8564i | 0.489592i | |||||||||
6.00000 | + | 10.3923i | 0.211867 | + | 0.366965i | |||||
22.5000 | − | 38.9711i | 0.794008 | − | 1.37526i | |||||
−7.50000 | − | 4.33013i | −0.264505 | − | 0.152712i | |||||
0 | 0 | |||||||||
−7.50000 | − | 7.79423i | −0.264176 | − | 0.274540i | |||||
6.00000 | 0.211210 | |||||||||
−13.5000 | − | 7.79423i | −0.474928 | − | 0.274200i | |||||
10.5000 | − | 18.1865i | 0.369160 | − | 0.639404i | −0.620274 | − | 0.784385i | ||
0.989434 | + | 0.144981i | ||||||||
−1.50000 | − | 2.59808i | −0.0527046 | − | 0.0912871i | |||||
3.46410i | 0.121641i | 0.998149 | + | 0.0608205i | ||||||
−0.998149 | + | 0.0608205i | ||||||||
0 | 0 | |||||||||
15.0000 | − | 8.66025i | 0.526073 | − | 0.303728i | |||||
0 | 0 | |||||||||
−10.5000 | − | 18.1865i | −0.367799 | − | 0.637046i | |||||
−15.0000 | + | 25.9808i | −0.525105 | + | 0.909509i | |||||
−16.5000 | − | 9.52628i | −0.577262 | − | 0.333282i | |||||
−12.0000 | −0.419570 | |||||||||
0 | 0 | |||||||||
9.00000 | 0.314294 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−16.0000 | − | 27.7128i | −0.557725 | − | 0.966008i | −0.997686 | − | 0.0679910i | ||
0.439961 | − | 0.898017i | ||||||||
22.5167i | 0.784405i | |||||||||
9.00000 | − | 5.19615i | 0.313340 | − | 0.180907i | |||||
0 | 0 | |||||||||
− | 10.3923i | − | 0.361376i | −0.983540 | − | 0.180688i | ||||
0.983540 | − | 0.180688i | ||||||||
0 | 0 | |||||||||
−3.50000 | + | 6.06218i | −0.121560 | + | 0.210548i | −0.920383 | − | 0.391018i | ||
0.798823 | + | 0.601566i | ||||||||
9.00000 | + | 5.19615i | 0.312395 | + | 0.180361i | |||||
10.0000 | 0.346896 | |||||||||
1.00000 | − | 3.46410i | 0.0346688 | − | 0.120096i | |||||
0 | 0 | |||||||||
19.5000 | + | 11.2583i | 0.675230 | + | 0.389844i | |||||
1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | |||||
4.50000 | + | 7.79423i | 0.155636 | + | 0.269569i | |||||
8.66025i | 0.299342i | |||||||||
−31.5000 | + | 18.1865i | −1.08815 | + | 0.628243i | |||||
1.50000 | − | 0.866025i | 0.0517858 | − | 0.0298985i | −0.473884 | − | 0.880587i | ||
0.525669 | + | 0.850689i | ||||||||
0 | 0 | |||||||||
10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | |||||
0 | 0 | |||||||||
6.00000 | + | 3.46410i | 0.206651 | + | 0.119310i | |||||
−13.0000 | −0.447478 | |||||||||
12.0000 | − | 19.0526i | 0.412813 | − | 0.655428i | |||||
−30.0000 | −1.03142 | |||||||||
0 | 0 | |||||||||
−22.5000 | + | 38.9711i | −0.772653 | + | 1.33827i | |||||
9.50000 | + | 16.4545i | 0.326039 | + | 0.564716i | |||||
− | 20.7846i | − | 0.712906i | |||||||
0 | 0 | |||||||||
1.50000 | − | 0.866025i | 0.0513892 | − | 0.0296695i | |||||
− | 41.5692i | − | 1.42330i | −0.702533 | − | 0.711651i | ||||
0.702533 | − | 0.711651i | ||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.102598 | + | 0.177705i | |||||
0 | 0 | |||||||||
−33.0000 | −1.12726 | −0.563629 | − | 0.826028i | ||||||
−0.563629 | + | 0.826028i | ||||||||
−9.00000 | + | 31.1769i | −0.307255 | + | 1.06436i | |||||
−29.0000 | −0.989467 | −0.494734 | − | 0.869045i | ||||||
−0.494734 | + | 0.869045i | ||||||||
16.5000 | + | 9.52628i | 0.562645 | + | 0.324843i | |||||
0 | 0 | |||||||||
28.5000 | + | 49.3634i | 0.970714 | + | 1.68133i | |||||
1.73205i | 0.0589597i | 0.999565 | + | 0.0294798i | ||||||
−0.999565 | + | 0.0294798i | ||||||||
22.5000 | − | 12.9904i | 0.765466 | − | 0.441942i | |||||
22.5000 | − | 12.9904i | 0.765023 | − | 0.441686i | |||||
− | 32.9090i | − | 1.11829i | |||||||
9.50000 | + | 16.4545i | 0.322637 | + | 0.558824i | |||||
0 | 0 | |||||||||
−22.5000 | − | 12.9904i | −0.763260 | − | 0.440668i | |||||
−9.00000 | −0.305129 | |||||||||
22.5000 | − | 21.6506i | 0.762383 | − | 0.733604i | |||||
9.00000 | 0.304778 | |||||||||
−9.00000 | − | 5.19615i | −0.304604 | − | 0.175863i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 8.66025i | − | 0.292603i | |||||||
−1.50000 | + | 0.866025i | −0.0506514 | + | 0.0292436i | −0.525112 | − | 0.851033i | ||
0.474460 | + | 0.880277i | ||||||||
−12.0000 | + | 6.92820i | −0.404980 | + | 0.233816i | |||||
25.9808i | 0.876309i | |||||||||
22.5000 | + | 38.9711i | 0.758475 | + | 1.31372i | |||||
16.5000 | − | 28.5788i | 0.555899 | − | 0.962846i | −0.441934 | − | 0.897048i | ||
0.997833 | − | 0.0657979i | ||||||||
0 | 0 | |||||||||
−44.0000 | −1.48072 | −0.740359 | − | 0.672212i | ||||||
−0.740359 | + | 0.672212i | ||||||||
15.0000 | + | 15.5885i | 0.504505 | + | 0.524297i | |||||
6.00000 | 0.201688 | |||||||||
22.5000 | + | 12.9904i | 0.755902 | + | 0.436420i | |||||
−12.0000 | + | 20.7846i | −0.402921 | + | 0.697879i | −0.994077 | − | 0.108678i | ||
0.591156 | + | 0.806557i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−18.0000 | + | 10.3923i | −0.603361 | + | 0.348351i | |||||
−4.50000 | + | 2.59808i | −0.150756 | + | 0.0870388i | |||||
5.19615i | 0.173980i | |||||||||
7.50000 | + | 12.9904i | 0.250978 | + | 0.434707i | |||||
16.5000 | − | 28.5788i | 0.551843 | − | 0.955819i | |||||
−4.50000 | − | 2.59808i | −0.150418 | − | 0.0868441i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.00000 | 0.100111 | |||||||||
−4.50000 | − | 2.59808i | −0.150083 | − | 0.0866507i | |||||
−2.00000 | + | 3.46410i | −0.0666667 | + | 0.115470i | |||||
27.0000 | + | 46.7654i | 0.899500 | + | 1.55798i | |||||
− | 46.7654i | − | 1.55712i | |||||||
0 | 0 | |||||||||
−22.5000 | + | 12.9904i | −0.748339 | + | 0.432054i | |||||
3.46410i | 0.115151i | |||||||||
−10.5000 | − | 18.1865i | −0.348839 | − | 0.604207i | |||||
14.5000 | − | 25.1147i | 0.481465 | − | 0.833921i | −0.518309 | − | 0.855193i | ||
0.999774 | + | 0.0212722i | ||||||||
15.0000 | + | 8.66025i | 0.497792 | + | 0.287401i | |||||
18.0000 | 0.597022 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−7.50000 | − | 4.33013i | −0.248350 | − | 0.143385i | |||||
9.00000 | − | 15.5885i | 0.297857 | − | 0.515903i | |||||
30.0000 | + | 51.9615i | 0.992312 | + | 1.71873i | |||||
− | 12.1244i | − | 0.400819i | |||||||
10.5000 | − | 6.06218i | 0.346930 | − | 0.200300i | |||||
0 | 0 | |||||||||
− | 51.9615i | − | 1.71499i | |||||||
23.5000 | + | 40.7032i | 0.775193 | + | 1.34267i | 0.934686 | + | 0.355475i | ||
−0.159492 | + | 0.987199i | ||||||||
0 | 0 | |||||||||
−21.0000 | − | 12.1244i | −0.691974 | − | 0.399511i | |||||
51.0000 | 1.67960 | |||||||||
1.50000 | + | 6.06218i | 0.0493731 | + | 0.199539i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−21.0000 | + | 36.3731i | −0.690103 | + | 1.19529i | |||||
−13.0000 | − | 22.5167i | −0.426976 | − | 0.739544i | |||||
15.5885i | 0.511716i | |||||||||
40.5000 | − | 23.3827i | 1.32876 | − | 0.767161i | 0.343654 | − | 0.939096i | ||
0.985108 | + | 0.171935i | ||||||||
−4.50000 | + | 2.59808i | −0.147561 | + | 0.0851943i | |||||
0 | 0 | |||||||||
1.50000 | + | 2.59808i | 0.0491341 | + | 0.0851028i | |||||
−7.50000 | + | 12.9904i | −0.245539 | + | 0.425286i | |||||
−31.5000 | − | 18.1865i | −1.03071 | − | 0.595082i | |||||
54.0000 | 1.76599 | |||||||||
3.00000 | + | 12.1244i | 0.0980581 | + | 0.396297i | |||||
22.0000 | 0.718709 | 0.359354 | − | 0.933201i | ||||||
0.359354 | + | 0.933201i | ||||||||
0 | 0 | |||||||||
9.50000 | − | 16.4545i | 0.310021 | − | 0.536972i | |||||
−7.50000 | − | 12.9904i | −0.244623 | − | 0.423700i | |||||
5.19615i | 0.169390i | 0.996407 | + | 0.0846949i | ||||||
−0.996407 | + | 0.0846949i | ||||||||
34.5000 | − | 19.9186i | 1.12407 | − | 0.648983i | |||||
0 | 0 | |||||||||
− | 17.3205i | − | 0.563735i | |||||||
0 | 0 | |||||||||
49.5000 | − | 85.7365i | 1.60938 | − | 2.78753i | |||||
33.0000 | + | 19.0526i | 1.07236 | + | 0.619125i | 0.928824 | − | 0.370521i | ||
0.143532 | + | 0.989646i | ||||||||
−5.00000 | −0.162392 | |||||||||
30.0000 | + | 8.66025i | 0.973841 | + | 0.281124i | |||||
6.00000 | 0.194666 | |||||||||
−4.50000 | − | 2.59808i | −0.145922 | − | 0.0842484i | |||||
0 | 0 | |||||||||
28.5000 | + | 49.3634i | 0.923206 | + | 1.59904i | 0.794422 | + | 0.607366i | ||
0.128784 | + | 0.991673i | ||||||||
− | 31.1769i | − | 1.00939i | |||||||
−22.5000 | + | 12.9904i | −0.728083 | + | 0.420359i | |||||
9.00000 | − | 5.19615i | 0.291081 | − | 0.168056i | |||||
15.5885i | 0.503903i | |||||||||
−25.5000 | − | 44.1673i | −0.823868 | − | 1.42698i | |||||
0 | 0 | |||||||||
−1.50000 | − | 0.866025i | −0.0484123 | − | 0.0279508i | |||||
28.0000 | 0.903226 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.00000 | + | 3.46410i | 0.193247 | + | 0.111571i | |||||
1.50000 | − | 2.59808i | 0.0482867 | − | 0.0836350i | |||||
0 | 0 | |||||||||
10.3923i | 0.334194i | 0.985940 | + | 0.167097i | ||||||
−0.985940 | + | 0.167097i | ||||||||
24.0000 | − | 13.8564i | 0.771389 | − | 0.445362i | |||||
−9.00000 | + | 5.19615i | −0.289122 | + | 0.166924i | |||||
− | 15.5885i | − | 0.500515i | |||||||
−10.5000 | − | 18.1865i | −0.336961 | − | 0.583634i | 0.646899 | − | 0.762576i | ||
−0.983860 | + | 0.178942i | ||||||||
−8.00000 | + | 13.8564i | −0.256600 | + | 0.444444i | |||||
0 | 0 | |||||||||
42.0000 | 1.34577 | |||||||||
5.00000 | + | 5.19615i | 0.160128 | + | 0.166410i | |||||
−35.0000 | −1.12032 | |||||||||
16.5000 | + | 9.52628i | 0.527882 | + | 0.304773i | 0.740153 | − | 0.672438i | ||
−0.212272 | + | 0.977211i | ||||||||
−10.5000 | + | 18.1865i | −0.335753 | + | 0.581541i | |||||
18.0000 | + | 31.1769i | 0.575282 | + | 0.996419i | |||||
0 | 0 | |||||||||
−9.00000 | + | 5.19615i | −0.287348 | + | 0.165900i | |||||
40.5000 | − | 23.3827i | 1.29241 | − | 0.746171i | |||||
36.3731i | 1.16012i | 0.814574 | + | 0.580060i | ||||||
−0.814574 | + | 0.580060i | ||||||||
4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | |||||
−19.5000 | + | 33.7750i | −0.621322 | + | 1.07616i | |||||
27.0000 | + | 15.5885i | 0.859855 | + | 0.496438i | |||||
0 | 0 | |||||||||
−4.50000 | + | 4.33013i | −0.143164 | + | 0.137760i | |||||
0 | 0 | |||||||||
−27.0000 | − | 15.5885i | −0.858116 | − | 0.495434i | |||||
−29.5000 | + | 51.0955i | −0.937098 | + | 1.62310i | −0.166250 | + | 0.986084i | ||
−0.770849 | + | 0.637018i | ||||||||
4.50000 | + | 7.79423i | 0.142875 | + | 0.247467i | |||||
32.9090i | 1.04433i | |||||||||
0 | 0 | |||||||||
6.00000 | − | 3.46410i | 0.190213 | − | 0.109819i | |||||
− | 3.46410i | − | 0.109764i | |||||||
−1.00000 | − | 1.73205i | −0.0316703 | − | 0.0548546i | 0.849756 | − | 0.527176i | ||
−0.881426 | + | 0.472322i | ||||||||
−1.50000 | + | 2.59808i | −0.0474817 | + | 0.0822407i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.q.c.589.1 | 2 | ||
7.2 | even | 3 | 91.2.k.a.4.1 | ✓ | 2 | ||
7.3 | odd | 6 | 637.2.u.a.30.1 | 2 | |||
7.4 | even | 3 | 91.2.u.a.30.1 | yes | 2 | ||
7.5 | odd | 6 | 637.2.k.b.459.1 | 2 | |||
7.6 | odd | 2 | 637.2.q.b.589.1 | 2 | |||
13.6 | odd | 12 | 8281.2.a.s.1.1 | 2 | |||
13.7 | odd | 12 | 8281.2.a.s.1.2 | 2 | |||
13.10 | even | 6 | inner | 637.2.q.c.491.1 | 2 | ||
21.2 | odd | 6 | 819.2.bm.a.550.1 | 2 | |||
21.11 | odd | 6 | 819.2.do.c.667.1 | 2 | |||
91.6 | even | 12 | 8281.2.a.w.1.1 | 2 | |||
91.10 | odd | 6 | 637.2.k.b.569.1 | 2 | |||
91.20 | even | 12 | 8281.2.a.w.1.2 | 2 | |||
91.23 | even | 6 | 91.2.u.a.88.1 | yes | 2 | ||
91.32 | odd | 12 | 1183.2.e.e.170.2 | 4 | |||
91.46 | odd | 12 | 1183.2.e.e.170.1 | 4 | |||
91.58 | odd | 12 | 1183.2.e.e.508.2 | 4 | |||
91.62 | odd | 6 | 637.2.q.b.491.1 | 2 | |||
91.72 | odd | 12 | 1183.2.e.e.508.1 | 4 | |||
91.75 | odd | 6 | 637.2.u.a.361.1 | 2 | |||
91.88 | even | 6 | 91.2.k.a.23.1 | yes | 2 | ||
273.23 | odd | 6 | 819.2.do.c.361.1 | 2 | |||
273.179 | odd | 6 | 819.2.bm.a.478.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.a.4.1 | ✓ | 2 | 7.2 | even | 3 | ||
91.2.k.a.23.1 | yes | 2 | 91.88 | even | 6 | ||
91.2.u.a.30.1 | yes | 2 | 7.4 | even | 3 | ||
91.2.u.a.88.1 | yes | 2 | 91.23 | even | 6 | ||
637.2.k.b.459.1 | 2 | 7.5 | odd | 6 | |||
637.2.k.b.569.1 | 2 | 91.10 | odd | 6 | |||
637.2.q.b.491.1 | 2 | 91.62 | odd | 6 | |||
637.2.q.b.589.1 | 2 | 7.6 | odd | 2 | |||
637.2.q.c.491.1 | 2 | 13.10 | even | 6 | inner | ||
637.2.q.c.589.1 | 2 | 1.1 | even | 1 | trivial | ||
637.2.u.a.30.1 | 2 | 7.3 | odd | 6 | |||
637.2.u.a.361.1 | 2 | 91.75 | odd | 6 | |||
819.2.bm.a.478.1 | 2 | 273.179 | odd | 6 | |||
819.2.bm.a.550.1 | 2 | 21.2 | odd | 6 | |||
819.2.do.c.361.1 | 2 | 273.23 | odd | 6 | |||
819.2.do.c.667.1 | 2 | 21.11 | odd | 6 | |||
1183.2.e.e.170.1 | 4 | 91.46 | odd | 12 | |||
1183.2.e.e.170.2 | 4 | 91.32 | odd | 12 | |||
1183.2.e.e.508.1 | 4 | 91.72 | odd | 12 | |||
1183.2.e.e.508.2 | 4 | 91.58 | odd | 12 | |||
8281.2.a.s.1.1 | 2 | 13.6 | odd | 12 | |||
8281.2.a.s.1.2 | 2 | 13.7 | odd | 12 | |||
8281.2.a.w.1.1 | 2 | 91.6 | even | 12 | |||
8281.2.a.w.1.2 | 2 | 91.20 | even | 12 |