Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(81,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 560.q (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 35) |
Sato-Tate group: |
Embedding invariants
Embedding label | 81.1 | ||
Root | of defining polynomial | ||
Character | 560.81 | ||
Dual form | 560.2.q.k.401.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
−0.207107 | + | 0.358719i | −0.119573 | + | 0.207107i | −0.919599 | − | 0.392859i | ||
0.800025 | + | 0.599966i | ||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | |||||
0 | 0 | |||||||||
−2.62132 | − | 0.358719i | −0.990766 | − | 0.135583i | |||||
0 | 0 | |||||||||
1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | |||||
0 | 0 | |||||||||
−0.414214 | + | 0.717439i | −0.124890 | + | 0.216316i | −0.921690 | − | 0.387927i | ||
0.796800 | + | 0.604243i | ||||||||
0 | 0 | |||||||||
−4.82843 | −1.33916 | −0.669582 | − | 0.742738i | ||||||
−0.669582 | + | 0.742738i | ||||||||
0 | 0 | |||||||||
0.414214 | 0.106949 | |||||||||
0 | 0 | |||||||||
−2.41421 | + | 4.18154i | −0.585533 | + | 1.01417i | 0.409276 | + | 0.912411i | ||
−0.994809 | + | 0.101762i | ||||||||
0 | 0 | |||||||||
1.41421 | + | 2.44949i | 0.324443 | + | 0.561951i | 0.981399 | − | 0.191977i | ||
−0.656957 | + | 0.753928i | ||||||||
0 | 0 | |||||||||
0.671573 | − | 0.866025i | 0.146549 | − | 0.188982i | |||||
0 | 0 | |||||||||
0.207107 | + | 0.358719i | 0.0431847 | + | 0.0747982i | 0.886810 | − | 0.462134i | ||
−0.843625 | + | 0.536933i | ||||||||
0 | 0 | |||||||||
−0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | |||||
0 | 0 | |||||||||
−2.41421 | −0.464616 | |||||||||
0 | 0 | |||||||||
−1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | ||||||
−0.0928477 | + | 0.995680i | ||||||||
0 | 0 | |||||||||
−3.00000 | + | 5.19615i | −0.538816 | + | 0.933257i | 0.460152 | + | 0.887840i | ||
−0.998968 | + | 0.0454165i | ||||||||
0 | 0 | |||||||||
−0.171573 | − | 0.297173i | −0.0298670 | − | 0.0517312i | |||||
0 | 0 | |||||||||
1.00000 | + | 2.44949i | 0.169031 | + | 0.414039i | |||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | |||||
0 | 0 | |||||||||
−7.82843 | −1.22259 | −0.611297 | − | 0.791401i | ||||||
−0.611297 | + | 0.791401i | ||||||||
0 | 0 | |||||||||
−3.58579 | −0.546827 | −0.273414 | − | 0.961897i | ||||||
−0.273414 | + | 0.961897i | ||||||||
0 | 0 | |||||||||
1.41421 | − | 2.44949i | 0.210819 | − | 0.365148i | |||||
0 | 0 | |||||||||
1.00000 | + | 1.73205i | 0.145865 | + | 0.252646i | 0.929695 | − | 0.368329i | ||
−0.783830 | + | 0.620975i | ||||||||
0 | 0 | |||||||||
6.74264 | + | 1.88064i | 0.963234 | + | 0.268662i | |||||
0 | 0 | |||||||||
−1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | |||||
0 | 0 | |||||||||
0.585786 | − | 1.01461i | 0.0804640 | − | 0.139368i | −0.822985 | − | 0.568063i | ||
0.903449 | + | 0.428695i | ||||||||
0 | 0 | |||||||||
0.828427 | 0.111705 | |||||||||
0 | 0 | |||||||||
−1.17157 | −0.155179 | |||||||||
0 | 0 | |||||||||
2.24264 | − | 3.88437i | 0.291967 | − | 0.505702i | −0.682308 | − | 0.731065i | ||
0.974275 | + | 0.225363i | ||||||||
0 | 0 | |||||||||
−2.74264 | − | 4.75039i | −0.351159 | − | 0.608226i | 0.635294 | − | 0.772271i | ||
−0.986453 | + | 0.164045i | ||||||||
0 | 0 | |||||||||
−2.82843 | − | 6.92820i | −0.356348 | − | 0.872872i | |||||
0 | 0 | |||||||||
2.41421 | + | 4.18154i | 0.299446 | + | 0.518656i | |||||
0 | 0 | |||||||||
4.79289 | − | 8.30153i | 0.585545 | − | 1.01419i | −0.409262 | − | 0.912417i | ||
0.994807 | − | 0.101777i | ||||||||
0 | 0 | |||||||||
−0.171573 | −0.0206549 | |||||||||
0 | 0 | |||||||||
−4.48528 | −0.532305 | −0.266152 | − | 0.963931i | ||||||
−0.266152 | + | 0.963931i | ||||||||
0 | 0 | |||||||||
0.414214 | − | 0.717439i | 0.0484800 | − | 0.0839699i | −0.840767 | − | 0.541397i | ||
0.889247 | + | 0.457427i | ||||||||
0 | 0 | |||||||||
−0.207107 | − | 0.358719i | −0.0239146 | − | 0.0414214i | |||||
0 | 0 | |||||||||
1.34315 | − | 1.73205i | 0.153066 | − | 0.197386i | |||||
0 | 0 | |||||||||
7.41421 | + | 12.8418i | 0.834164 | + | 1.44481i | 0.894709 | + | 0.446649i | ||
−0.0605449 | + | 0.998165i | ||||||||
0 | 0 | |||||||||
−3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | |||||
0 | 0 | |||||||||
−13.7279 | −1.50684 | −0.753418 | − | 0.657542i | ||||||
−0.753418 | + | 0.657542i | ||||||||
0 | 0 | |||||||||
4.82843 | 0.523716 | |||||||||
0 | 0 | |||||||||
0.207107 | − | 0.358719i | 0.0222042 | − | 0.0384588i | |||||
0 | 0 | |||||||||
4.32843 | + | 7.49706i | 0.458812 | + | 0.794686i | 0.998898 | − | 0.0469234i | ||
−0.540086 | + | 0.841610i | ||||||||
0 | 0 | |||||||||
12.6569 | + | 1.73205i | 1.32680 | + | 0.181568i | |||||
0 | 0 | |||||||||
−1.24264 | − | 2.15232i | −0.128856 | − | 0.223185i | |||||
0 | 0 | |||||||||
1.41421 | − | 2.44949i | 0.145095 | − | 0.251312i | |||||
0 | 0 | |||||||||
11.6569 | 1.18357 | 0.591787 | − | 0.806094i | ||||||
0.591787 | + | 0.806094i | ||||||||
0 | 0 | |||||||||
−2.34315 | −0.235495 | |||||||||
0 | 0 | |||||||||
5.15685 | − | 8.93193i | 0.513126 | − | 0.888761i | −0.486758 | − | 0.873537i | ||
0.999884 | − | 0.0152237i | ||||||||
0 | 0 | |||||||||
−1.20711 | − | 2.09077i | −0.118940 | − | 0.206010i | 0.800408 | − | 0.599456i | ||
−0.919348 | + | 0.393446i | ||||||||
0 | 0 | |||||||||
−1.08579 | − | 0.148586i | −0.105962 | − | 0.0145006i | |||||
0 | 0 | |||||||||
5.62132 | + | 9.73641i | 0.543434 | + | 0.941255i | 0.998704 | + | 0.0509012i | ||
−0.455270 | + | 0.890353i | ||||||||
0 | 0 | |||||||||
6.74264 | − | 11.6786i | 0.645828 | − | 1.11861i | −0.338282 | − | 0.941045i | ||
0.984110 | − | 0.177562i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.48528 | −0.421940 | −0.210970 | − | 0.977493i | ||||||
−0.210970 | + | 0.977493i | ||||||||
0 | 0 | |||||||||
0.207107 | − | 0.358719i | 0.0193128 | − | 0.0334508i | |||||
0 | 0 | |||||||||
−6.82843 | − | 11.8272i | −0.631288 | − | 1.09342i | |||||
0 | 0 | |||||||||
7.82843 | − | 10.0951i | 0.717631 | − | 0.925419i | |||||
0 | 0 | |||||||||
5.15685 | + | 8.93193i | 0.468805 | + | 0.811994i | |||||
0 | 0 | |||||||||
1.62132 | − | 2.80821i | 0.146190 | − | 0.253208i | |||||
0 | 0 | |||||||||
1.00000 | 0.0894427 | |||||||||
0 | 0 | |||||||||
9.31371 | 0.826458 | 0.413229 | − | 0.910627i | ||||||
0.413229 | + | 0.910627i | ||||||||
0 | 0 | |||||||||
0.742641 | − | 1.28629i | 0.0653859 | − | 0.113252i | |||||
0 | 0 | |||||||||
−9.65685 | − | 16.7262i | −0.843723 | − | 1.46137i | −0.886725 | − | 0.462297i | ||
0.0430021 | − | 0.999075i | ||||||||
0 | 0 | |||||||||
−2.82843 | − | 6.92820i | −0.245256 | − | 0.600751i | |||||
0 | 0 | |||||||||
1.20711 | + | 2.09077i | 0.103891 | + | 0.179945i | |||||
0 | 0 | |||||||||
4.82843 | − | 8.36308i | 0.412520 | − | 0.714506i | −0.582644 | − | 0.812727i | ||
0.995165 | + | 0.0982211i | ||||||||
0 | 0 | |||||||||
16.1421 | 1.36916 | 0.684579 | − | 0.728939i | ||||||
0.684579 | + | 0.728939i | ||||||||
0 | 0 | |||||||||
−0.828427 | −0.0697661 | |||||||||
0 | 0 | |||||||||
2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | |||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.0415227 | + | 0.0719195i | |||||
0 | 0 | |||||||||
−2.07107 | + | 2.02922i | −0.170819 | + | 0.167368i | |||||
0 | 0 | |||||||||
1.08579 | + | 1.88064i | 0.0889511 | + | 0.154068i | 0.907068 | − | 0.420984i | ||
−0.818117 | + | 0.575052i | ||||||||
0 | 0 | |||||||||
5.82843 | − | 10.0951i | 0.474311 | − | 0.821530i | −0.525257 | − | 0.850944i | ||
0.999567 | + | 0.0294137i | ||||||||
0 | 0 | |||||||||
−13.6569 | −1.10409 | |||||||||
0 | 0 | |||||||||
6.00000 | 0.481932 | |||||||||
0 | 0 | |||||||||
−8.65685 | + | 14.9941i | −0.690892 | + | 1.19666i | 0.280654 | + | 0.959809i | ||
−0.971546 | + | 0.236851i | ||||||||
0 | 0 | |||||||||
0.242641 | + | 0.420266i | 0.0192427 | + | 0.0333293i | |||||
0 | 0 | |||||||||
−0.414214 | − | 1.01461i | −0.0326446 | − | 0.0799626i | |||||
0 | 0 | |||||||||
6.17157 | + | 10.6895i | 0.483395 | + | 0.837265i | 0.999818 | − | 0.0190689i | ||
−0.516423 | + | 0.856333i | ||||||||
0 | 0 | |||||||||
−0.171573 | + | 0.297173i | −0.0133569 | + | 0.0231349i | |||||
0 | 0 | |||||||||
−22.4142 | −1.73446 | −0.867232 | − | 0.497904i | ||||||
−0.867232 | + | 0.497904i | ||||||||
0 | 0 | |||||||||
10.3137 | 0.793362 | |||||||||
0 | 0 | |||||||||
−4.00000 | + | 6.92820i | −0.305888 | + | 0.529813i | |||||
0 | 0 | |||||||||
−1.65685 | − | 2.86976i | −0.125968 | − | 0.218183i | 0.796143 | − | 0.605109i | ||
−0.922111 | + | 0.386925i | ||||||||
0 | 0 | |||||||||
1.62132 | − | 2.09077i | 0.122560 | − | 0.158047i | |||||
0 | 0 | |||||||||
0.928932 | + | 1.60896i | 0.0698228 | + | 0.120937i | |||||
0 | 0 | |||||||||
−5.00000 | + | 8.66025i | −0.373718 | + | 0.647298i | −0.990134 | − | 0.140122i | ||
0.616417 | + | 0.787420i | ||||||||
0 | 0 | |||||||||
2.65685 | 0.197482 | 0.0987412 | − | 0.995113i | ||||||
0.0987412 | + | 0.995113i | ||||||||
0 | 0 | |||||||||
2.27208 | 0.167957 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.00000 | − | 3.46410i | −0.146254 | − | 0.253320i | |||||
0 | 0 | |||||||||
6.32843 | + | 0.866025i | 0.460325 | + | 0.0629941i | |||||
0 | 0 | |||||||||
−6.41421 | − | 11.1097i | −0.464116 | − | 0.803873i | 0.535045 | − | 0.844824i | ||
−0.999161 | + | 0.0409507i | ||||||||
0 | 0 | |||||||||
1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | ||
0.899770 | + | 0.436365i | ||||||||
0 | 0 | |||||||||
−2.00000 | −0.143223 | |||||||||
0 | 0 | |||||||||
−12.3431 | −0.879413 | −0.439706 | − | 0.898142i | ||||||
−0.439706 | + | 0.898142i | ||||||||
0 | 0 | |||||||||
−4.82843 | + | 8.36308i | −0.342278 | + | 0.592843i | −0.984855 | − | 0.173378i | ||
0.642577 | + | 0.766221i | ||||||||
0 | 0 | |||||||||
1.98528 | + | 3.43861i | 0.140031 | + | 0.242541i | |||||
0 | 0 | |||||||||
2.62132 | + | 0.358719i | 0.183981 | + | 0.0251772i | |||||
0 | 0 | |||||||||
3.91421 | + | 6.77962i | 0.273381 | + | 0.473509i | |||||
0 | 0 | |||||||||
−0.585786 | + | 1.01461i | −0.0407150 | + | 0.0705204i | |||||
0 | 0 | |||||||||
−2.34315 | −0.162079 | |||||||||
0 | 0 | |||||||||
−20.4853 | −1.41026 | −0.705132 | − | 0.709076i | ||||||
−0.705132 | + | 0.709076i | ||||||||
0 | 0 | |||||||||
0.928932 | − | 1.60896i | 0.0636494 | − | 0.110244i | |||||
0 | 0 | |||||||||
1.79289 | + | 3.10538i | 0.122274 | + | 0.211785i | |||||
0 | 0 | |||||||||
9.72792 | − | 12.5446i | 0.660374 | − | 0.851584i | |||||
0 | 0 | |||||||||
0.171573 | + | 0.297173i | 0.0115938 | + | 0.0200811i | |||||
0 | 0 | |||||||||
11.6569 | − | 20.1903i | 0.784125 | − | 1.35814i | |||||
0 | 0 | |||||||||
−0.343146 | −0.0229787 | −0.0114894 | − | 0.999934i | ||||||
−0.0114894 | + | 0.999934i | ||||||||
0 | 0 | |||||||||
−2.82843 | −0.188562 | |||||||||
0 | 0 | |||||||||
−3.48528 | + | 6.03668i | −0.231326 | + | 0.400669i | −0.958199 | − | 0.286104i | ||
0.726872 | + | 0.686773i | ||||||||
0 | 0 | |||||||||
5.82843 | + | 10.0951i | 0.385153 | + | 0.667105i | 0.991790 | − | 0.127874i | ||
−0.606637 | + | 0.794979i | ||||||||
0 | 0 | |||||||||
0.343146 | + | 0.840532i | 0.0225773 | + | 0.0553029i | |||||
0 | 0 | |||||||||
8.41421 | + | 14.5738i | 0.551233 | + | 0.954764i | 0.998186 | + | 0.0602067i | ||
−0.446952 | + | 0.894558i | ||||||||
0 | 0 | |||||||||
1.00000 | − | 1.73205i | 0.0652328 | − | 0.112987i | |||||
0 | 0 | |||||||||
−6.14214 | −0.398975 | |||||||||
0 | 0 | |||||||||
21.3137 | 1.37867 | 0.689335 | − | 0.724443i | ||||||
0.689335 | + | 0.724443i | ||||||||
0 | 0 | |||||||||
−13.8284 | + | 23.9515i | −0.890767 | + | 1.54285i | −0.0518100 | + | 0.998657i | ||
−0.838957 | + | 0.544197i | ||||||||
0 | 0 | |||||||||
−5.17157 | − | 8.95743i | −0.331757 | − | 0.574619i | |||||
0 | 0 | |||||||||
−1.74264 | − | 6.77962i | −0.111333 | − | 0.433134i | |||||
0 | 0 | |||||||||
−6.82843 | − | 11.8272i | −0.434482 | − | 0.752546i | |||||
0 | 0 | |||||||||
2.84315 | − | 4.92447i | 0.180177 | − | 0.312076i | |||||
0 | 0 | |||||||||
9.31371 | 0.587876 | 0.293938 | − | 0.955824i | ||||||
0.293938 | + | 0.955824i | ||||||||
0 | 0 | |||||||||
−0.343146 | −0.0215734 | |||||||||
0 | 0 | |||||||||
−1.00000 | + | 1.73205i | −0.0626224 | + | 0.108465i | |||||
0 | 0 | |||||||||
−3.17157 | − | 5.49333i | −0.197837 | − | 0.342664i | 0.749990 | − | 0.661450i | ||
−0.947827 | + | 0.318785i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.41421 | − | 2.44949i | −0.0875376 | − | 0.151620i | |||||
0 | 0 | |||||||||
−14.5208 | + | 25.1508i | −0.895392 | + | 1.55086i | −0.0620729 | + | 0.998072i | ||
−0.833319 | + | 0.552793i | ||||||||
0 | 0 | |||||||||
−1.17157 | −0.0719691 | |||||||||
0 | 0 | |||||||||
−3.58579 | −0.219447 | |||||||||
0 | 0 | |||||||||
−10.2279 | + | 17.7153i | −0.623607 | + | 1.08012i | 0.365201 | + | 0.930929i | ||
−0.988808 | + | 0.149191i | ||||||||
0 | 0 | |||||||||
8.24264 | + | 14.2767i | 0.500705 | + | 0.867246i | 1.00000 | 0.000813982i | |||
−0.499295 | + | 0.866432i | ||||||||
0 | 0 | |||||||||
−3.24264 | + | 4.18154i | −0.196254 | + | 0.253078i | |||||
0 | 0 | |||||||||
−0.414214 | − | 0.717439i | −0.0249780 | − | 0.0432632i | |||||
0 | 0 | |||||||||
−8.07107 | + | 13.9795i | −0.484943 | + | 0.839947i | −0.999850 | − | 0.0172994i | ||
0.514907 | + | 0.857246i | ||||||||
0 | 0 | |||||||||
−16.9706 | −1.01600 | |||||||||
0 | 0 | |||||||||
−30.2843 | −1.80661 | −0.903304 | − | 0.429001i | ||||||
−0.903304 | + | 0.429001i | ||||||||
0 | 0 | |||||||||
7.00000 | − | 12.1244i | 0.416107 | − | 0.720718i | −0.579437 | − | 0.815017i | ||
0.995544 | + | 0.0942988i | ||||||||
0 | 0 | |||||||||
0.585786 | + | 1.01461i | 0.0346990 | + | 0.0601004i | |||||
0 | 0 | |||||||||
20.5208 | + | 2.80821i | 1.21131 | + | 0.165763i | |||||
0 | 0 | |||||||||
−3.15685 | − | 5.46783i | −0.185697 | − | 0.321637i | |||||
0 | 0 | |||||||||
−2.41421 | + | 4.18154i | −0.141524 | + | 0.245126i | |||||
0 | 0 | |||||||||
−16.0000 | −0.934730 | −0.467365 | − | 0.884064i | ||||||
−0.467365 | + | 0.884064i | ||||||||
0 | 0 | |||||||||
−4.48528 | −0.261143 | |||||||||
0 | 0 | |||||||||
1.00000 | − | 1.73205i | 0.0580259 | − | 0.100504i | |||||
0 | 0 | |||||||||
−1.00000 | − | 1.73205i | −0.0578315 | − | 0.100167i | |||||
0 | 0 | |||||||||
9.39949 | + | 1.28629i | 0.541778 | + | 0.0741406i | |||||
0 | 0 | |||||||||
2.13604 | + | 3.69973i | 0.122712 | + | 0.212544i | |||||
0 | 0 | |||||||||
−2.74264 | + | 4.75039i | −0.157043 | + | 0.272007i | |||||
0 | 0 | |||||||||
4.75736 | 0.271517 | 0.135758 | − | 0.990742i | ||||||
0.135758 | + | 0.990742i | ||||||||
0 | 0 | |||||||||
1.00000 | 0.0568880 | |||||||||
0 | 0 | |||||||||
−6.58579 | + | 11.4069i | −0.373446 | + | 0.646827i | −0.990093 | − | 0.140413i | ||
0.616647 | + | 0.787239i | ||||||||
0 | 0 | |||||||||
3.17157 | + | 5.49333i | 0.179268 | + | 0.310501i | 0.941630 | − | 0.336650i | ||
−0.762362 | + | 0.647151i | ||||||||
0 | 0 | |||||||||
−4.58579 | + | 5.91359i | −0.258380 | + | 0.333193i | |||||
0 | 0 | |||||||||
6.89949 | + | 11.9503i | 0.387514 | + | 0.671194i | 0.992115 | − | 0.125335i | ||
−0.604600 | + | 0.796529i | ||||||||
0 | 0 | |||||||||
0.414214 | − | 0.717439i | 0.0231915 | − | 0.0401689i | |||||
0 | 0 | |||||||||
−4.65685 | −0.259920 | |||||||||
0 | 0 | |||||||||
−13.6569 | −0.759888 | |||||||||
0 | 0 | |||||||||
2.41421 | − | 4.18154i | 0.133916 | − | 0.231950i | |||||
0 | 0 | |||||||||
2.79289 | + | 4.83743i | 0.154447 | + | 0.267511i | |||||
0 | 0 | |||||||||
−2.00000 | − | 4.89898i | −0.110264 | − | 0.270089i | |||||
0 | 0 | |||||||||
11.4853 | + | 19.8931i | 0.631288 | + | 1.09342i | 0.987289 | + | 0.158937i | ||
−0.356001 | + | 0.934486i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.58579 | −0.523727 | |||||||||
0 | 0 | |||||||||
9.17157 | 0.499607 | 0.249804 | − | 0.968296i | ||||||
0.249804 | + | 0.968296i | ||||||||
0 | 0 | |||||||||
0.928932 | − | 1.60896i | 0.0504527 | − | 0.0873866i | |||||
0 | 0 | |||||||||
−2.48528 | − | 4.30463i | −0.134586 | − | 0.233109i | |||||
0 | 0 | |||||||||
−17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | |||||
0 | 0 | |||||||||
0.0857864 | + | 0.148586i | 0.00461859 | + | 0.00799963i | |||||
0 | 0 | |||||||||
3.96447 | − | 6.86666i | 0.212824 | − | 0.368621i | −0.739773 | − | 0.672856i | ||
0.952597 | + | 0.304235i | ||||||||
0 | 0 | |||||||||
−15.3431 | −0.821300 | −0.410650 | − | 0.911793i | ||||||
−0.410650 | + | 0.911793i | ||||||||
0 | 0 | |||||||||
11.6569 | 0.622197 | |||||||||
0 | 0 | |||||||||
13.4142 | − | 23.2341i | 0.713967 | − | 1.23663i | −0.249390 | − | 0.968403i | ||
0.963357 | − | 0.268223i | ||||||||
0 | 0 | |||||||||
2.24264 | + | 3.88437i | 0.119027 | + | 0.206161i | |||||
0 | 0 | |||||||||
2.00000 | + | 4.89898i | 0.105851 | + | 0.259281i | |||||
0 | 0 | |||||||||
−5.00000 | − | 8.66025i | −0.263890 | − | 0.457071i | 0.703382 | − | 0.710812i | ||
−0.967272 | + | 0.253741i | ||||||||
0 | 0 | |||||||||
5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | |||||
0 | 0 | |||||||||
−4.27208 | −0.224226 | |||||||||
0 | 0 | |||||||||
−0.828427 | −0.0433619 | |||||||||
0 | 0 | |||||||||
−1.37868 | + | 2.38794i | −0.0719665 | + | 0.124650i | −0.899763 | − | 0.436379i | ||
0.827797 | + | 0.561028i | ||||||||
0 | 0 | |||||||||
−11.0711 | − | 19.1757i | −0.576337 | − | 0.998245i | |||||
0 | 0 | |||||||||
−1.89949 | + | 2.44949i | −0.0986169 | + | 0.127171i | |||||
0 | 0 | |||||||||
10.4853 | + | 18.1610i | 0.542907 | + | 0.940343i | 0.998735 | + | 0.0502752i | ||
−0.455828 | + | 0.890068i | ||||||||
0 | 0 | |||||||||
−0.207107 | + | 0.358719i | −0.0106949 | + | 0.0185242i | |||||
0 | 0 | |||||||||
4.82843 | 0.248677 | |||||||||
0 | 0 | |||||||||
−26.8284 | −1.37808 | −0.689042 | − | 0.724722i | ||||||
−0.689042 | + | 0.724722i | ||||||||
0 | 0 | |||||||||
−1.92893 | + | 3.34101i | −0.0988222 | + | 0.171165i | |||||
0 | 0 | |||||||||
−1.44975 | − | 2.51104i | −0.0740786 | − | 0.128308i | 0.826607 | − | 0.562780i | ||
−0.900685 | + | 0.434472i | ||||||||
0 | 0 | |||||||||
−2.17157 | − | 0.297173i | −0.110674 | − | 0.0151453i | |||||
0 | 0 | |||||||||
−5.07107 | − | 8.78335i | −0.257777 | − | 0.446483i | |||||
0 | 0 | |||||||||
−11.8284 | + | 20.4874i | −0.599725 | + | 1.03875i | 0.393136 | + | 0.919480i | ||
−0.992861 | + | 0.119274i | ||||||||
0 | 0 | |||||||||
−2.00000 | −0.101144 | |||||||||
0 | 0 | |||||||||
8.00000 | 0.403547 | |||||||||
0 | 0 | |||||||||
7.41421 | − | 12.8418i | 0.373050 | − | 0.646141i | |||||
0 | 0 | |||||||||
8.31371 | + | 14.3998i | 0.417253 | + | 0.722704i | 0.995662 | − | 0.0930434i | ||
−0.578409 | + | 0.815747i | ||||||||
0 | 0 | |||||||||
3.07107 | + | 0.420266i | 0.153746 | + | 0.0210396i | |||||
0 | 0 | |||||||||
−15.1569 | − | 26.2524i | −0.756897 | − | 1.31098i | −0.944426 | − | 0.328725i | ||
0.187528 | − | 0.982259i | ||||||||
0 | 0 | |||||||||
14.4853 | − | 25.0892i | 0.721563 | − | 1.24978i | |||||
0 | 0 | |||||||||
7.48528 | 0.371947 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.39949 | − | 12.8163i | 0.365881 | − | 0.633725i | −0.623036 | − | 0.782193i | ||
0.988917 | + | 0.148468i | ||||||||
0 | 0 | |||||||||
2.00000 | + | 3.46410i | 0.0986527 | + | 0.170872i | |||||
0 | 0 | |||||||||
−7.27208 | + | 9.37769i | −0.357836 | + | 0.461446i | |||||
0 | 0 | |||||||||
6.86396 | + | 11.8887i | 0.336939 | + | 0.583595i | |||||
0 | 0 | |||||||||
−3.34315 | + | 5.79050i | −0.163715 | + | 0.283562i | |||||
0 | 0 | |||||||||
0.686292 | 0.0335275 | 0.0167638 | − | 0.999859i | ||||||
0.0167638 | + | 0.999859i | ||||||||
0 | 0 | |||||||||
13.4853 | 0.657232 | 0.328616 | − | 0.944464i | ||||||
0.328616 | + | 0.944464i | ||||||||
0 | 0 | |||||||||
−2.82843 | + | 4.89898i | −0.137523 | + | 0.238197i | |||||
0 | 0 | |||||||||
−2.41421 | − | 4.18154i | −0.117107 | − | 0.202835i | |||||
0 | 0 | |||||||||
5.48528 | + | 13.4361i | 0.265451 | + | 0.650220i | |||||
0 | 0 | |||||||||
0.828427 | + | 1.43488i | 0.0399968 | + | 0.0692766i | |||||
0 | 0 | |||||||||
8.89949 | − | 15.4144i | 0.428674 | − | 0.742484i | −0.568082 | − | 0.822972i | ||
0.996756 | + | 0.0804875i | ||||||||
0 | 0 | |||||||||
7.79899 | 0.374796 | 0.187398 | − | 0.982284i | ||||||
0.187398 | + | 0.982284i | ||||||||
0 | 0 | |||||||||
−0.414214 | −0.0198600 | |||||||||
0 | 0 | |||||||||
−0.585786 | + | 1.01461i | −0.0280220 | + | 0.0485355i | |||||
0 | 0 | |||||||||
−16.9706 | − | 29.3939i | −0.809961 | − | 1.40289i | −0.912890 | − | 0.408205i | ||
0.102930 | − | 0.994689i | ||||||||
0 | 0 | |||||||||
4.92893 | + | 19.1757i | 0.234711 | + | 0.913126i | |||||
0 | 0 | |||||||||
15.1066 | + | 26.1654i | 0.717736 | + | 1.24316i | 0.961895 | + | 0.273420i | ||
−0.244158 | + | 0.969735i | ||||||||
0 | 0 | |||||||||
4.32843 | − | 7.49706i | 0.205187 | − | 0.355395i | |||||
0 | 0 | |||||||||
−0.899495 | −0.0425447 | |||||||||
0 | 0 | |||||||||
3.82843 | 0.180675 | 0.0903373 | − | 0.995911i | ||||||
0.0903373 | + | 0.995911i | ||||||||
0 | 0 | |||||||||
3.24264 | − | 5.61642i | 0.152690 | − | 0.264467i | |||||
0 | 0 | |||||||||
2.41421 | + | 4.18154i | 0.113430 | + | 0.196466i | |||||
0 | 0 | |||||||||
−4.82843 | − | 11.8272i | −0.226360 | − | 0.554467i | |||||
0 | 0 | |||||||||
−12.1421 | − | 21.0308i | −0.567985 | − | 0.983779i | −0.996765 | − | 0.0803702i | ||
0.428780 | − | 0.903409i | ||||||||
0 | 0 | |||||||||
5.82843 | − | 10.0951i | 0.272048 | − | 0.471200i | |||||
0 | 0 | |||||||||
41.3137 | 1.92417 | 0.962086 | − | 0.272748i | ||||||
0.962086 | + | 0.272748i | ||||||||
0 | 0 | |||||||||
37.0416 | 1.72147 | 0.860735 | − | 0.509053i | ||||||
0.860735 | + | 0.509053i | ||||||||
0 | 0 | |||||||||
−1.24264 | + | 2.15232i | −0.0576261 | + | 0.0998113i | |||||
0 | 0 | |||||||||
−1.55025 | − | 2.68512i | −0.0717371 | − | 0.124252i | 0.827926 | − | 0.560838i | ||
−0.899663 | + | 0.436586i | ||||||||
0 | 0 | |||||||||
−15.5416 | + | 20.0417i | −0.717646 | + | 0.925439i | |||||
0 | 0 | |||||||||
−3.58579 | − | 6.21076i | −0.165224 | − | 0.286177i | |||||
0 | 0 | |||||||||
1.48528 | − | 2.57258i | 0.0682933 | − | 0.118287i | |||||
0 | 0 | |||||||||
−2.82843 | −0.129777 | |||||||||
0 | 0 | |||||||||
3.31371 | 0.151724 | |||||||||
0 | 0 | |||||||||
−17.8284 | + | 30.8797i | −0.814602 | + | 1.41093i | 0.0950120 | + | 0.995476i | ||
−0.909614 | + | 0.415455i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.449747 | + | 0.0615465i | 0.0204642 | + | 0.00280046i | |||||
0 | 0 | |||||||||
−5.82843 | − | 10.0951i | −0.264655 | − | 0.458396i | |||||
0 | 0 | |||||||||
2.17157 | − | 3.76127i | 0.0984034 | − | 0.170440i | −0.812621 | − | 0.582793i | ||
0.911024 | + | 0.412353i | ||||||||
0 | 0 | |||||||||
−5.11270 | −0.231204 | |||||||||
0 | 0 | |||||||||
−9.31371 | −0.420322 | −0.210161 | − | 0.977667i | ||||||
−0.210161 | + | 0.977667i | ||||||||
0 | 0 | |||||||||
2.41421 | − | 4.18154i | 0.108731 | − | 0.188327i | |||||
0 | 0 | |||||||||
1.17157 | + | 2.02922i | 0.0526583 | + | 0.0912068i | |||||
0 | 0 | |||||||||
11.7574 | + | 1.60896i | 0.527390 | + | 0.0721716i | |||||
0 | 0 | |||||||||
−0.414214 | − | 0.717439i | −0.0185427 | − | 0.0321170i | 0.856605 | − | 0.515973i | ||
−0.875148 | + | 0.483856i | ||||||||
0 | 0 | |||||||||
4.64214 | − | 8.04041i | 0.207395 | − | 0.359219i | |||||
0 | 0 | |||||||||
15.8701 | 0.707611 | 0.353805 | − | 0.935319i | ||||||
0.353805 | + | 0.935319i | ||||||||
0 | 0 | |||||||||
−10.3137 | −0.458954 | |||||||||
0 | 0 | |||||||||
−2.13604 | + | 3.69973i | −0.0948648 | + | 0.164311i | |||||
0 | 0 | |||||||||
−6.67157 | − | 11.5555i | −0.295712 | − | 0.512189i | 0.679438 | − | 0.733733i | ||
−0.975150 | + | 0.221544i | ||||||||
0 | 0 | |||||||||
−1.34315 | + | 1.73205i | −0.0594173 | + | 0.0766214i | |||||
0 | 0 | |||||||||
−3.41421 | − | 5.91359i | −0.150741 | − | 0.261091i | |||||
0 | 0 | |||||||||
−1.20711 | + | 2.09077i | −0.0531915 | + | 0.0921303i | |||||
0 | 0 | |||||||||
−1.65685 | −0.0728684 | |||||||||
0 | 0 | |||||||||
1.37258 | 0.0602497 | |||||||||
0 | 0 | |||||||||
−7.48528 | + | 12.9649i | −0.327936 | + | 0.568002i | −0.982102 | − | 0.188349i | ||
0.654166 | + | 0.756351i | ||||||||
0 | 0 | |||||||||
17.8284 | + | 30.8797i | 0.779583 | + | 1.35028i | 0.932182 | + | 0.361989i | ||
−0.152600 | + | 0.988288i | ||||||||
0 | 0 | |||||||||
0.414214 | + | 1.01461i | 0.0180778 | + | 0.0442813i | |||||
0 | 0 | |||||||||
−14.4853 | − | 25.0892i | −0.630989 | − | 1.09290i | |||||
0 | 0 | |||||||||
11.4142 | − | 19.7700i | 0.496270 | − | 0.859565i | |||||
0 | 0 | |||||||||
12.6863 | 0.550538 | |||||||||
0 | 0 | |||||||||
37.7990 | 1.63726 | |||||||||
0 | 0 | |||||||||
5.62132 | − | 9.73641i | 0.243031 | − | 0.420942i | |||||
0 | 0 | |||||||||
−2.07107 | − | 3.58719i | −0.0893732 | − | 0.154799i | |||||
0 | 0 | |||||||||
−4.14214 | + | 4.05845i | −0.178414 | + | 0.174810i | |||||
0 | 0 | |||||||||
−3.67157 | − | 6.35935i | −0.157853 | − | 0.273410i | 0.776241 | − | 0.630436i | ||
−0.934094 | + | 0.357026i | ||||||||
0 | 0 | |||||||||
−0.550253 | + | 0.953065i | −0.0236136 | + | 0.0408999i | |||||
0 | 0 | |||||||||
−13.4853 | −0.577646 | |||||||||
0 | 0 | |||||||||
−24.8995 | −1.06463 | −0.532313 | − | 0.846548i | ||||||
−0.532313 | + | 0.846548i | ||||||||
0 | 0 | |||||||||
7.75736 | − | 13.4361i | 0.331076 | − | 0.573441i | |||||
0 | 0 | |||||||||
−1.41421 | − | 2.44949i | −0.0602475 | − | 0.104352i | |||||
0 | 0 | |||||||||
−14.8284 | − | 36.3221i | −0.630569 | − | 1.54457i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11.1421 | + | 19.2987i | −0.472107 | + | 0.817714i | −0.999491 | − | 0.0319135i | ||
0.527383 | + | 0.849628i | ||||||||
0 | 0 | |||||||||
17.3137 | 0.732292 | |||||||||
0 | 0 | |||||||||
1.65685 | 0.0699524 | |||||||||
0 | 0 | |||||||||
20.8640 | − | 36.1374i | 0.879311 | − | 1.52301i | 0.0272129 | − | 0.999630i | ||
0.852098 | − | 0.523382i | ||||||||
0 | 0 | |||||||||
2.24264 | + | 3.88437i | 0.0943486 | + | 0.163417i | |||||
0 | 0 | |||||||||
12.1360 | − | 15.6500i | 0.509666 | − | 0.657238i | |||||
0 | 0 | |||||||||
−3.82843 | − | 6.63103i | −0.160496 | − | 0.277987i | 0.774551 | − | 0.632512i | ||
−0.935047 | + | 0.354525i | ||||||||
0 | 0 | |||||||||
4.58579 | − | 7.94282i | 0.191909 | − | 0.332396i | −0.753974 | − | 0.656905i | ||
0.945883 | + | 0.324508i | ||||||||
0 | 0 | |||||||||
5.31371 | 0.221983 | |||||||||
0 | 0 | |||||||||
−0.414214 | −0.0172739 | |||||||||
0 | 0 | |||||||||
21.9706 | − | 38.0541i | 0.914646 | − | 1.58421i | 0.107228 | − | 0.994234i | ||
0.807418 | − | 0.589980i | ||||||||
0 | 0 | |||||||||
0.414214 | + | 0.717439i | 0.0172141 | + | 0.0298157i | |||||
0 | 0 | |||||||||
35.9853 | + | 4.92447i | 1.49292 | + | 0.204302i | |||||
0 | 0 | |||||||||
0.485281 | + | 0.840532i | 0.0200983 | + | 0.0348113i | |||||
0 | 0 | |||||||||
−6.82843 | + | 11.8272i | −0.282321 | + | 0.488994i | |||||
0 | 0 | |||||||||
34.2843 | 1.41506 | 0.707532 | − | 0.706682i | ||||||
0.707532 | + | 0.706682i | ||||||||
0 | 0 | |||||||||
−16.9706 | −0.699260 | |||||||||
0 | 0 | |||||||||
2.55635 | − | 4.42773i | 0.105154 | − | 0.182132i | |||||
0 | 0 | |||||||||
−2.10051 | − | 3.63818i | −0.0862574 | − | 0.149402i | 0.819669 | − | 0.572838i | ||
−0.905926 | + | 0.423435i | ||||||||
0 | 0 | |||||||||
−12.6569 | − | 1.73205i | −0.518880 | − | 0.0710072i | |||||
0 | 0 | |||||||||
−2.00000 | − | 3.46410i | −0.0818546 | − | 0.141776i | |||||
0 | 0 | |||||||||
3.17157 | − | 5.49333i | 0.129587 | − | 0.224451i | −0.793930 | − | 0.608010i | ||
0.923517 | + | 0.383558i | ||||||||
0 | 0 | |||||||||
19.6569 | 0.801820 | 0.400910 | − | 0.916117i | ||||||
0.400910 | + | 0.916117i | ||||||||
0 | 0 | |||||||||
27.1127 | 1.10411 | |||||||||
0 | 0 | |||||||||
5.15685 | − | 8.93193i | 0.209656 | − | 0.363135i | |||||
0 | 0 | |||||||||
19.1066 | + | 33.0936i | 0.775513 | + | 1.34323i | 0.934506 | + | 0.355948i | ||
−0.158993 | + | 0.987280i | ||||||||
0 | 0 | |||||||||
−0.671573 | + | 0.866025i | −0.0272135 | + | 0.0350931i | |||||
0 | 0 | |||||||||
−4.82843 | − | 8.36308i | −0.195337 | − | 0.338334i | |||||
0 | 0 | |||||||||
−17.7279 | + | 30.7057i | −0.716024 | + | 1.24019i | 0.246539 | + | 0.969133i | ||
−0.962563 | + | 0.271057i | ||||||||
0 | 0 | |||||||||
−3.24264 | −0.130756 | |||||||||
0 | 0 | |||||||||
11.3137 | 0.455473 | 0.227736 | − | 0.973723i | ||||||
0.227736 | + | 0.973723i | ||||||||
0 | 0 | |||||||||
12.7574 | − | 22.0964i | 0.512762 | − | 0.888129i | −0.487129 | − | 0.873330i | ||
0.999890 | − | 0.0147990i | ||||||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | |||||
0 | 0 | |||||||||
−8.65685 | − | 21.2049i | −0.346830 | − | 0.849555i | |||||
0 | 0 | |||||||||
−0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | |||||
0 | 0 | |||||||||
0.485281 | − | 0.840532i | 0.0193803 | − | 0.0335676i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.1421 | 0.801846 | 0.400923 | − | 0.916112i | ||||||
0.400923 | + | 0.916112i | ||||||||
0 | 0 | |||||||||
4.24264 | − | 7.34847i | 0.168630 | − | 0.292075i | |||||
0 | 0 | |||||||||
−4.65685 | − | 8.06591i | −0.184802 | − | 0.320086i | |||||
0 | 0 | |||||||||
−32.5563 | − | 9.08052i | −1.28993 | − | 0.359783i | |||||
0 | 0 | |||||||||
−6.34315 | − | 10.9867i | −0.250931 | − | 0.434625i | |||||
0 | 0 | |||||||||
−15.7426 | + | 27.2671i | −0.621797 | + | 1.07698i | 0.367354 | + | 0.930081i | ||
−0.989151 | + | 0.146903i | ||||||||
0 | 0 | |||||||||
−26.2843 | −1.03655 | −0.518275 | − | 0.855214i | ||||||
−0.518275 | + | 0.855214i | ||||||||
0 | 0 | |||||||||
−1.48528 | −0.0584829 | |||||||||
0 | 0 | |||||||||
−15.5208 | + | 26.8828i | −0.610186 | + | 1.05687i | 0.381022 | + | 0.924566i | ||
−0.991209 | + | 0.132308i | ||||||||
0 | 0 | |||||||||
1.85786 | + | 3.21792i | 0.0729276 | + | 0.126314i | |||||
0 | 0 | |||||||||
2.48528 | + | 6.08767i | 0.0974059 | + | 0.238595i | |||||
0 | 0 | |||||||||
9.58579 | + | 16.6031i | 0.375121 | + | 0.649728i | 0.990345 | − | 0.138624i | ||
−0.615224 | + | 0.788352i | ||||||||
0 | 0 | |||||||||
−9.65685 | + | 16.7262i | −0.377325 | + | 0.653545i | |||||
0 | 0 | |||||||||
2.34315 | 0.0914148 | |||||||||
0 | 0 | |||||||||
−21.1716 | −0.824727 | −0.412364 | − | 0.911019i | ||||||
−0.412364 | + | 0.911019i | ||||||||
0 | 0 | |||||||||
−15.9142 | + | 27.5642i | −0.618991 | + | 1.07212i | 0.370679 | + | 0.928761i | ||
−0.989670 | + | 0.143363i | ||||||||
0 | 0 | |||||||||
4.82843 | + | 8.36308i | 0.187521 | + | 0.324795i | |||||
0 | 0 | |||||||||
−4.58579 | + | 5.91359i | −0.177829 | + | 0.229319i | |||||
0 | 0 | |||||||||
−0.207107 | − | 0.358719i | −0.00801921 | − | 0.0138897i | |||||
0 | 0 | |||||||||
0.0710678 | − | 0.123093i | 0.00274764 | − | 0.00475905i | |||||
0 | 0 | |||||||||
4.54416 | 0.175425 | |||||||||
0 | 0 | |||||||||
29.6569 | 1.14319 | 0.571594 | − | 0.820537i | ||||||
0.571594 | + | 0.820537i | ||||||||
0 | 0 | |||||||||
1.20711 | − | 2.09077i | 0.0464616 | − | 0.0804738i | |||||
0 | 0 | |||||||||
14.0711 | + | 24.3718i | 0.540795 | + | 0.936685i | 0.998859 | + | 0.0477651i | ||
−0.458064 | + | 0.888919i | ||||||||
0 | 0 | |||||||||
−30.5563 | − | 4.18154i | −1.17265 | − | 0.160473i | |||||
0 | 0 | |||||||||
−1.44365 | − | 2.50048i | −0.0553208 | − | 0.0958185i | |||||
0 | 0 | |||||||||
−17.3787 | + | 30.1008i | −0.664977 | + | 1.15177i | 0.314315 | + | 0.949319i | ||
−0.979292 | + | 0.202455i | ||||||||
0 | 0 | |||||||||
−9.65685 | −0.368969 | |||||||||
0 | 0 | |||||||||
−4.82843 | −0.184216 | |||||||||
0 | 0 | |||||||||
−2.82843 | + | 4.89898i | −0.107754 | + | 0.186636i | |||||
0 | 0 | |||||||||
0.414214 | + | 0.717439i | 0.0157574 | + | 0.0272927i | 0.873797 | − | 0.486292i | ||
−0.858039 | + | 0.513584i | ||||||||
0 | 0 | |||||||||
6.14214 | + | 0.840532i | 0.233320 | + | 0.0319292i | |||||
0 | 0 | |||||||||
−8.07107 | − | 13.9795i | −0.306153 | − | 0.530273i | |||||
0 | 0 | |||||||||
18.8995 | − | 32.7349i | 0.715869 | − | 1.23992i | |||||
0 | 0 | |||||||||
−6.97056 | −0.263651 | |||||||||
0 | 0 | |||||||||
−3.20101 | −0.120900 | −0.0604502 | − | 0.998171i | ||||||
−0.0604502 | + | 0.998171i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0.414214 | + | 0.717439i | 0.0156002 | + | 0.0270203i | |||||
0 | 0 | |||||||||
−16.7218 | + | 21.5636i | −0.628889 | + | 0.810982i | |||||
0 | 0 | |||||||||
−7.84315 | − | 13.5847i | −0.294556 | − | 0.510185i | 0.680326 | − | 0.732910i | ||
−0.974881 | + | 0.222725i | ||||||||
0 | 0 | |||||||||
−20.9706 | + | 36.3221i | −0.786458 | + | 1.36218i | |||||
0 | 0 | |||||||||
−2.48528 | −0.0930745 | |||||||||
0 | 0 | |||||||||
−4.00000 | −0.149592 | |||||||||
0 | 0 | |||||||||
−4.41421 | + | 7.64564i | −0.164852 | + | 0.285532i | |||||
0 | 0 | |||||||||
10.5563 | + | 18.2841i | 0.393685 | + | 0.681883i | 0.992932 | − | 0.118681i | ||
−0.599247 | + | 0.800564i | ||||||||
0 | 0 | |||||||||
2.41421 | + | 5.91359i | 0.0899100 | + | 0.220234i | |||||
0 | 0 | |||||||||
−5.72792 | − | 9.92105i | −0.213024 | − | 0.368968i | |||||
0 | 0 | |||||||||
0.500000 | − | 0.866025i | 0.0185695 | − | 0.0321634i | |||||
0 | 0 | |||||||||
37.5858 | 1.39398 | 0.696990 | − | 0.717081i | ||||||
0.696990 | + | 0.717081i | ||||||||
0 | 0 | |||||||||
−18.1716 | −0.673021 | |||||||||
0 | 0 | |||||||||
8.65685 | − | 14.9941i | 0.320185 | − | 0.554577i | |||||
0 | 0 | |||||||||
11.0000 | + | 19.0526i | 0.406294 | + | 0.703722i | 0.994471 | − | 0.105010i | ||
−0.588177 | + | 0.808732i | ||||||||
0 | 0 | |||||||||
2.79289 | + | 0.778985i | 0.103017 | + | 0.0287333i | |||||
0 | 0 | |||||||||
3.97056 | + | 6.87722i | 0.146258 | + | 0.253326i | |||||
0 | 0 | |||||||||
−10.5563 | + | 18.2841i | −0.388322 | + | 0.672593i | −0.992224 | − | 0.124466i | ||
0.603902 | + | 0.797058i | ||||||||
0 | 0 | |||||||||
5.65685 | 0.207810 | |||||||||
0 | 0 | |||||||||
16.0711 | 0.589590 | 0.294795 | − | 0.955560i | ||||||
0.294795 | + | 0.955560i | ||||||||
0 | 0 | |||||||||
1.08579 | − | 1.88064i | 0.0397801 | − | 0.0689012i | |||||
0 | 0 | |||||||||
−19.4142 | − | 33.6264i | −0.710329 | − | 1.23033i | |||||
0 | 0 | |||||||||
−11.2426 | − | 27.5387i | −0.410797 | − | 1.00624i | |||||
0 | 0 | |||||||||
−15.1716 | − | 26.2779i | −0.553619 | − | 0.958895i | −0.998010 | − | 0.0630625i | ||
0.444391 | − | 0.895833i | ||||||||
0 | 0 | |||||||||
−1.92893 | + | 3.34101i | −0.0702942 | + | 0.121753i | |||||
0 | 0 | |||||||||
−11.6569 | −0.424236 | |||||||||
0 | 0 | |||||||||
−31.4558 | −1.14328 | −0.571641 | − | 0.820504i | ||||||
−0.571641 | + | 0.820504i | ||||||||
0 | 0 | |||||||||
0.0710678 | − | 0.123093i | 0.00257960 | − | 0.00446800i | |||||
0 | 0 | |||||||||
−4.65685 | − | 8.06591i | −0.168811 | − | 0.292389i | 0.769191 | − | 0.639019i | ||
−0.938002 | + | 0.346630i | ||||||||
0 | 0 | |||||||||
−21.8640 | + | 28.1946i | −0.791529 | + | 1.02071i | |||||
0 | 0 | |||||||||
6.82843 | + | 11.8272i | 0.246882 | + | 0.427613i | |||||
0 | 0 | |||||||||
−10.8284 | + | 18.7554i | −0.390992 | + | 0.677218i | |||||
0 | 0 | |||||||||
−0.627417 | −0.0226252 | −0.0113126 | − | 0.999936i | ||||||
−0.0113126 | + | 0.999936i | ||||||||
0 | 0 | |||||||||
2.62742 | 0.0946241 | |||||||||
0 | 0 | |||||||||
18.5563 | − | 32.1405i | 0.667425 | − | 1.15601i | −0.311196 | − | 0.950346i | ||
0.978622 | − | 0.205669i | ||||||||
0 | 0 | |||||||||
−3.00000 | − | 5.19615i | −0.107763 | − | 0.186651i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11.0711 | − | 19.1757i | −0.396662 | − | 0.687039i | |||||
0 | 0 | |||||||||
1.85786 | − | 3.21792i | 0.0664796 | − | 0.115146i | |||||
0 | 0 | |||||||||
2.41421 | 0.0862770 | |||||||||
0 | 0 | |||||||||
17.3137 | 0.617953 | |||||||||
0 | 0 | |||||||||
1.27817 | − | 2.21386i | 0.0455620 | − | 0.0789157i | −0.842345 | − | 0.538939i | ||
0.887907 | + | 0.460023i | ||||||||
0 | 0 | |||||||||
−6.01472 | − | 10.4178i | −0.214130 | − | 0.370883i | |||||
0 | 0 | |||||||||
11.7574 | + | 1.60896i | 0.418044 | + | 0.0572080i | |||||
0 | 0 | |||||||||
13.2426 | + | 22.9369i | 0.470260 | + | 0.814514i | |||||
0 | 0 | |||||||||
0.242641 | − | 0.420266i | 0.00860558 | − | 0.0149053i | |||||
0 | 0 | |||||||||
−8.00000 | −0.283375 | −0.141687 | − | 0.989911i | ||||||
−0.141687 | + | 0.989911i | ||||||||
0 | 0 | |||||||||
−9.65685 | −0.341635 | |||||||||
0 | 0 | |||||||||
−12.2426 | + | 21.2049i | −0.432572 | + | 0.749237i | |||||
0 | 0 | |||||||||
0.343146 | + | 0.594346i | 0.0121094 | + | 0.0209740i | |||||
0 | 0 | |||||||||
−0.671573 | + | 0.866025i | −0.0236698 | + | 0.0305234i | |||||
0 | 0 | |||||||||
−4.23654 | − | 7.33791i | −0.149133 | − | 0.258307i | |||||
0 | 0 | |||||||||
−17.8137 | + | 30.8542i | −0.626297 | + | 1.08478i | 0.361992 | + | 0.932181i | ||
−0.988289 | + | 0.152596i | ||||||||
0 | 0 | |||||||||
20.6274 | 0.724327 | 0.362163 | − | 0.932115i | ||||||
0.362163 | + | 0.932115i | ||||||||
0 | 0 | |||||||||
−6.82843 | −0.239483 | |||||||||
0 | 0 | |||||||||
6.17157 | − | 10.6895i | 0.216181 | − | 0.374436i | |||||
0 | 0 | |||||||||
−5.07107 | − | 8.78335i | −0.177414 | − | 0.307290i | |||||
0 | 0 | |||||||||
13.6569 | + | 33.4523i | 0.477209 | + | 1.16892i | |||||
0 | 0 | |||||||||
−23.9706 | − | 41.5182i | −0.836578 | − | 1.44900i | −0.892739 | − | 0.450575i | ||
0.0561604 | − | 0.998422i | ||||||||
0 | 0 | |||||||||
1.03553 | − | 1.79360i | 0.0360964 | − | 0.0625209i | −0.847413 | − | 0.530935i | ||
0.883509 | + | 0.468414i | ||||||||
0 | 0 | |||||||||
0.343146 | 0.0119468 | |||||||||
0 | 0 | |||||||||
26.2132 | 0.911522 | 0.455761 | − | 0.890102i | ||||||
0.455761 | + | 0.890102i | ||||||||
0 | 0 | |||||||||
−14.6569 | + | 25.3864i | −0.509054 | + | 0.881707i | 0.490891 | + | 0.871221i | ||
−0.999945 | + | 0.0104859i | ||||||||
0 | 0 | |||||||||
−3.34315 | − | 5.79050i | −0.115972 | − | 0.200870i | |||||
0 | 0 | |||||||||
−24.1421 | + | 23.6544i | −0.836475 | + | 0.819575i | |||||
0 | 0 | |||||||||
11.2071 | + | 19.4113i | 0.387838 | + | 0.671755i | |||||
0 | 0 | |||||||||
7.24264 | − | 12.5446i | 0.250342 | − | 0.433606i | |||||
0 | 0 | |||||||||
−15.1716 | −0.523781 | −0.261890 | − | 0.965098i | ||||||
−0.261890 | + | 0.965098i | ||||||||
0 | 0 | |||||||||
−28.0000 | −0.965517 | |||||||||
0 | 0 | |||||||||
6.27208 | − | 10.8636i | 0.216022 | − | 0.374161i | |||||
0 | 0 | |||||||||
−5.15685 | − | 8.93193i | −0.177401 | − | 0.307268i | |||||
0 | 0 | |||||||||
−10.3137 | − | 25.2633i | −0.354383 | − | 0.868058i | |||||
0 | 0 | |||||||||
2.89949 | + | 5.02207i | 0.0995104 | + | 0.172357i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.54416 | 0.0871102 | 0.0435551 | − | 0.999051i | ||||||
0.0435551 | + | 0.999051i | ||||||||
0 | 0 | |||||||||
8.00000 | 0.273594 | |||||||||
0 | 0 | |||||||||
−17.1421 | + | 29.6910i | −0.585564 | + | 1.01423i | 0.409241 | + | 0.912426i | ||
−0.994805 | + | 0.101800i | ||||||||
0 | 0 | |||||||||
0.686292 | + | 1.18869i | 0.0234160 | + | 0.0405576i | 0.877496 | − | 0.479584i | ||
−0.854080 | + | 0.520142i | ||||||||
0 | 0 | |||||||||
−5.25736 | + | 6.77962i | −0.179170 | + | 0.231049i | |||||
0 | 0 | |||||||||
7.27817 | + | 12.6062i | 0.247752 | + | 0.429119i | 0.962902 | − | 0.269852i | ||
−0.715150 | + | 0.698971i | ||||||||
0 | 0 | |||||||||
−1.65685 | + | 2.86976i | −0.0563347 | + | 0.0975746i | |||||
0 | 0 | |||||||||
2.61522 | 0.0888177 | |||||||||
0 | 0 | |||||||||
−12.2843 | −0.416715 | |||||||||
0 | 0 | |||||||||
−23.1421 | + | 40.0834i | −0.784141 | + | 1.35817i | |||||
0 | 0 | |||||||||
16.4853 | + | 28.5533i | 0.557942 | + | 0.966384i | |||||
0 | 0 | |||||||||
−2.62132 | − | 0.358719i | −0.0886168 | − | 0.0121269i | |||||
0 | 0 | |||||||||
−12.5858 | − | 21.7992i | −0.424992 | − | 0.736107i | 0.571428 | − | 0.820652i | ||
−0.996420 | + | 0.0845449i | ||||||||
0 | 0 | |||||||||
3.31371 | − | 5.73951i | 0.111769 | − | 0.193589i | |||||
0 | 0 | |||||||||
1.82843 | 0.0616013 | 0.0308006 | − | 0.999526i | ||||||
0.0308006 | + | 0.999526i | ||||||||
0 | 0 | |||||||||
−18.2843 | −0.615315 | −0.307657 | − | 0.951497i | ||||||
−0.307657 | + | 0.951497i | ||||||||
0 | 0 | |||||||||
0.928932 | − | 1.60896i | 0.0312257 | − | 0.0540845i | |||||
0 | 0 | |||||||||
14.9645 | + | 25.9192i | 0.502458 | + | 0.870282i | 0.999996 | + | 0.00284012i | ||
−0.497538 | + | 0.867442i | ||||||||
0 | 0 | |||||||||
−24.4142 | − | 3.34101i | −0.818826 | − | 0.112054i | |||||
0 | 0 | |||||||||
−3.10051 | − | 5.37023i | −0.103871 | − | 0.179910i | |||||
0 | 0 | |||||||||
−2.82843 | + | 4.89898i | −0.0946497 | + | 0.163938i | |||||
0 | 0 | |||||||||
10.0000 | 0.334263 | |||||||||
0 | 0 | |||||||||
0.828427 | 0.0276604 | |||||||||
0 | 0 | |||||||||
3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | |||||
0 | 0 | |||||||||
2.82843 | + | 4.89898i | 0.0942286 | + | 0.163209i | |||||
0 | 0 | |||||||||
−2.40812 | + | 3.10538i | −0.0801371 | + | 0.103341i | |||||
0 | 0 | |||||||||
−1.32843 | − | 2.30090i | −0.0441584 | − | 0.0764846i | |||||
0 | 0 | |||||||||
−7.10660 | + | 12.3090i | −0.235971 | + | 0.408713i | −0.959554 | − | 0.281523i | ||
0.723584 | + | 0.690237i | ||||||||
0 | 0 | |||||||||
29.1716 | 0.967560 | |||||||||
0 | 0 | |||||||||
10.2010 | 0.337975 | 0.168987 | − | 0.985618i | ||||||
0.168987 | + | 0.985618i | ||||||||
0 | 0 | |||||||||
5.68629 | − | 9.84895i | 0.188189 | − | 0.325953i | |||||
0 | 0 | |||||||||
−1.13604 | − | 1.96768i | −0.0375563 | − | 0.0650494i | |||||
0 | 0 | |||||||||
19.3137 | + | 47.3087i | 0.637795 | + | 1.56227i | |||||
0 | 0 | |||||||||
−21.5563 | − | 37.3367i | −0.711078 | − | 1.23162i | −0.964453 | − | 0.264256i | ||
0.253374 | − | 0.967368i | ||||||||
0 | 0 | |||||||||
−0.985281 | + | 1.70656i | −0.0324661 | + | 0.0562330i | |||||
0 | 0 | |||||||||
21.6569 | 0.712844 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.41421 | − | 5.91359i | 0.112137 | − | 0.194228i | |||||
0 | 0 | |||||||||
−2.74264 | − | 4.75039i | −0.0899831 | − | 0.155855i | 0.817521 | − | 0.575899i | ||
−0.907504 | + | 0.420044i | ||||||||
0 | 0 | |||||||||
4.92893 | + | 19.1757i | 0.161539 | + | 0.628457i | |||||
0 | 0 | |||||||||
−2.72792 | − | 4.72490i | −0.0893082 | − | 0.154686i | |||||
0 | 0 | |||||||||
−2.00000 | + | 3.46410i | −0.0654070 | + | 0.113288i | |||||
0 | 0 | |||||||||
34.6274 | 1.13123 | 0.565614 | − | 0.824670i | ||||||
0.565614 | + | 0.824670i | ||||||||
0 | 0 | |||||||||
−2.62742 | −0.0857425 | |||||||||
0 | 0 | |||||||||
23.1421 | − | 40.0834i | 0.754412 | − | 1.30668i | −0.191254 | − | 0.981541i | ||
0.945666 | − | 0.325139i | ||||||||
0 | 0 | |||||||||
−1.62132 | − | 2.80821i | −0.0527975 | − | 0.0914479i | |||||
0 | 0 | |||||||||
−2.41421 | − | 5.91359i | −0.0785344 | − | 0.192369i | |||||
0 | 0 | |||||||||
16.5919 | + | 28.7380i | 0.539164 | + | 0.933859i | 0.998949 | + | 0.0458290i | ||
−0.459786 | + | 0.888030i | ||||||||
0 | 0 | |||||||||
−2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | |||||
0 | 0 | |||||||||
−5.71573 | −0.185345 | |||||||||
0 | 0 | |||||||||
−13.6569 | −0.442389 | −0.221194 | − | 0.975230i | ||||||
−0.221194 | + | 0.975230i | ||||||||
0 | 0 | |||||||||
−6.41421 | + | 11.1097i | −0.207559 | + | 0.359503i | |||||
0 | 0 | |||||||||
0.171573 | + | 0.297173i | 0.00554616 | + | 0.00960624i | |||||
0 | 0 | |||||||||
−15.6569 | + | 20.1903i | −0.505586 | + | 0.651978i | |||||
0 | 0 | |||||||||
−2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | |||||
0 | 0 | |||||||||
−15.8995 | + | 27.5387i | −0.512354 | + | 0.887423i | |||||
0 | 0 | |||||||||
−2.00000 | −0.0643823 | |||||||||
0 | 0 | |||||||||
−37.5269 | −1.20678 | −0.603392 | − | 0.797445i | ||||||
−0.603392 | + | 0.797445i | ||||||||
0 | 0 | |||||||||
2.82843 | − | 4.89898i | 0.0908622 | − | 0.157378i | |||||
0 | 0 | |||||||||
−12.0000 | − | 20.7846i | −0.385098 | − | 0.667010i | 0.606685 | − | 0.794943i | ||
−0.991783 | + | 0.127933i | ||||||||
0 | 0 | |||||||||
−42.3137 | − | 5.79050i | −1.35652 | − | 0.185635i | |||||
0 | 0 | |||||||||
1.00000 | + | 1.73205i | 0.0320256 | + | 0.0554700i | |||||
0 | 0 | |||||||||
0.656854 | − | 1.13770i | 0.0210146 | − | 0.0363984i | −0.855327 | − | 0.518089i | ||
0.876341 | + | 0.481690i | ||||||||
0 | 0 | |||||||||
−7.17157 | −0.229204 | |||||||||
0 | 0 | |||||||||
38.1421 | 1.21778 | |||||||||
0 | 0 | |||||||||
14.1066 | − | 24.4334i | 0.449931 | − | 0.779303i | −0.548450 | − | 0.836183i | ||
0.998381 | + | 0.0568803i | ||||||||
0 | 0 | |||||||||
6.17157 | + | 10.6895i | 0.196643 | + | 0.340595i | |||||
0 | 0 | |||||||||
2.17157 | + | 0.297173i | 0.0691219 | + | 0.00945912i | |||||
0 | 0 | |||||||||
−0.742641 | − | 1.28629i | −0.0236146 | − | 0.0409017i | |||||
0 | 0 | |||||||||
−2.17157 | + | 3.76127i | −0.0689823 | + | 0.119481i | −0.898454 | − | 0.439069i | ||
0.829471 | + | 0.558549i | ||||||||
0 | 0 | |||||||||
−9.51472 | −0.301940 | |||||||||
0 | 0 | |||||||||
9.65685 | 0.306143 | |||||||||
0 | 0 | |||||||||
−16.7279 | + | 28.9736i | −0.529779 | + | 0.917603i | 0.469618 | + | 0.882870i | ||
−0.999397 | + | 0.0347337i | ||||||||
0 | 0 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 560.2.q.k.81.1 | 4 | ||
4.3 | odd | 2 | 35.2.e.a.11.1 | ✓ | 4 | ||
7.2 | even | 3 | inner | 560.2.q.k.401.1 | 4 | ||
7.3 | odd | 6 | 3920.2.a.bv.1.1 | 2 | |||
7.4 | even | 3 | 3920.2.a.bq.1.2 | 2 | |||
12.11 | even | 2 | 315.2.j.e.46.2 | 4 | |||
20.3 | even | 4 | 175.2.k.a.74.1 | 8 | |||
20.7 | even | 4 | 175.2.k.a.74.4 | 8 | |||
20.19 | odd | 2 | 175.2.e.c.151.2 | 4 | |||
28.3 | even | 6 | 245.2.a.g.1.2 | 2 | |||
28.11 | odd | 6 | 245.2.a.h.1.2 | 2 | |||
28.19 | even | 6 | 245.2.e.e.226.1 | 4 | |||
28.23 | odd | 6 | 35.2.e.a.16.1 | yes | 4 | ||
28.27 | even | 2 | 245.2.e.e.116.1 | 4 | |||
84.11 | even | 6 | 2205.2.a.n.1.1 | 2 | |||
84.23 | even | 6 | 315.2.j.e.226.2 | 4 | |||
84.59 | odd | 6 | 2205.2.a.q.1.1 | 2 | |||
140.3 | odd | 12 | 1225.2.b.h.99.1 | 4 | |||
140.23 | even | 12 | 175.2.k.a.149.4 | 8 | |||
140.39 | odd | 6 | 1225.2.a.k.1.1 | 2 | |||
140.59 | even | 6 | 1225.2.a.m.1.1 | 2 | |||
140.67 | even | 12 | 1225.2.b.g.99.4 | 4 | |||
140.79 | odd | 6 | 175.2.e.c.51.2 | 4 | |||
140.87 | odd | 12 | 1225.2.b.h.99.4 | 4 | |||
140.107 | even | 12 | 175.2.k.a.149.1 | 8 | |||
140.123 | even | 12 | 1225.2.b.g.99.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.1 | ✓ | 4 | 4.3 | odd | 2 | ||
35.2.e.a.16.1 | yes | 4 | 28.23 | odd | 6 | ||
175.2.e.c.51.2 | 4 | 140.79 | odd | 6 | |||
175.2.e.c.151.2 | 4 | 20.19 | odd | 2 | |||
175.2.k.a.74.1 | 8 | 20.3 | even | 4 | |||
175.2.k.a.74.4 | 8 | 20.7 | even | 4 | |||
175.2.k.a.149.1 | 8 | 140.107 | even | 12 | |||
175.2.k.a.149.4 | 8 | 140.23 | even | 12 | |||
245.2.a.g.1.2 | 2 | 28.3 | even | 6 | |||
245.2.a.h.1.2 | 2 | 28.11 | odd | 6 | |||
245.2.e.e.116.1 | 4 | 28.27 | even | 2 | |||
245.2.e.e.226.1 | 4 | 28.19 | even | 6 | |||
315.2.j.e.46.2 | 4 | 12.11 | even | 2 | |||
315.2.j.e.226.2 | 4 | 84.23 | even | 6 | |||
560.2.q.k.81.1 | 4 | 1.1 | even | 1 | trivial | ||
560.2.q.k.401.1 | 4 | 7.2 | even | 3 | inner | ||
1225.2.a.k.1.1 | 2 | 140.39 | odd | 6 | |||
1225.2.a.m.1.1 | 2 | 140.59 | even | 6 | |||
1225.2.b.g.99.1 | 4 | 140.123 | even | 12 | |||
1225.2.b.g.99.4 | 4 | 140.67 | even | 12 | |||
1225.2.b.h.99.1 | 4 | 140.3 | odd | 12 | |||
1225.2.b.h.99.4 | 4 | 140.87 | odd | 12 | |||
2205.2.a.n.1.1 | 2 | 84.11 | even | 6 | |||
2205.2.a.q.1.1 | 2 | 84.59 | odd | 6 | |||
3920.2.a.bq.1.2 | 2 | 7.4 | even | 3 | |||
3920.2.a.bv.1.1 | 2 | 7.3 | odd | 6 |