Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(111,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 170.k (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 121.3 | ||
Root | of defining polynomial | ||
Character | 170.121 | ||
Dual form | 170.2.k.b.111.3 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | |||||
1.36338 | − | 0.564729i | 0.787145 | − | 0.326046i | 0.0473502 | − | 0.998878i | ||
0.739795 | + | 0.672832i | ||||||||
1.00000i | 0.500000i | |||||||||
0.382683 | + | 0.923880i | 0.171141 | + | 0.413171i | |||||
1.36338 | + | 0.564729i | 0.556596 | + | 0.230550i | |||||
1.35785 | − | 3.27815i | 0.513221 | − | 1.23902i | −0.428779 | − | 0.903410i | ||
0.941999 | − | 0.335615i | ||||||||
−0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | |||||
−0.581445 | + | 0.581445i | −0.193815 | + | 0.193815i | |||||
−0.382683 | + | 0.923880i | −0.121015 | + | 0.292156i | |||||
−4.35013 | − | 1.80188i | −1.31161 | − | 0.543288i | −0.386258 | − | 0.922391i | ||
−0.925354 | + | 0.379103i | ||||||||
0.564729 | + | 1.36338i | 0.163023 | + | 0.393573i | |||||
5.47699i | 1.51904i | 0.650481 | + | 0.759522i | ||||||
−0.650481 | + | 0.759522i | ||||||||
3.27815 | − | 1.35785i | 0.876123 | − | 0.362902i | |||||
1.04348 | + | 1.04348i | 0.269426 | + | 0.269426i | |||||
−1.00000 | −0.250000 | |||||||||
2.52894 | − | 3.25645i | 0.613358 | − | 0.789805i | |||||
−0.822287 | −0.193815 | |||||||||
0.857748 | + | 0.857748i | 0.196781 | + | 0.196781i | 0.798619 | − | 0.601838i | ||
−0.601838 | + | 0.798619i | ||||||||
−0.923880 | + | 0.382683i | −0.206586 | + | 0.0855706i | |||||
− | 5.23617i | − | 1.14263i | |||||||
−1.80188 | − | 4.35013i | −0.384162 | − | 0.927450i | |||||
−5.28485 | − | 2.18906i | −1.10197 | − | 0.456450i | −0.243803 | − | 0.969825i | ||
−0.858165 | + | 0.513375i | ||||||||
−0.564729 | + | 1.36338i | −0.115275 | + | 0.278298i | |||||
−0.707107 | + | 0.707107i | −0.141421 | + | 0.141421i | |||||
−3.87282 | + | 3.87282i | −0.759522 | + | 0.759522i | |||||
−2.15856 | + | 5.21121i | −0.415414 | + | 1.00290i | |||||
3.27815 | + | 1.35785i | 0.619512 | + | 0.256610i | |||||
−1.77710 | − | 4.29029i | −0.329999 | − | 0.796687i | −0.998591 | − | 0.0530586i | ||
0.668593 | − | 0.743629i | ||||||||
1.47571i | 0.269426i | |||||||||
6.72892 | − | 2.78721i | 1.20855 | − | 0.500598i | 0.314798 | − | 0.949159i | ||
0.893752 | + | 0.448561i | ||||||||
−0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | |||||
−6.94843 | −1.20957 | |||||||||
4.09089 | − | 0.514430i | 0.701581 | − | 0.0882239i | |||||
3.54824 | 0.599763 | |||||||||
−0.581445 | − | 0.581445i | −0.0969075 | − | 0.0969075i | |||||
−8.58444 | + | 3.55579i | −1.41127 | + | 0.584569i | −0.952652 | − | 0.304063i | ||
−0.458622 | + | 0.888631i | ||||||||
1.21304i | 0.196781i | |||||||||
3.09302 | + | 7.46720i | 0.495279 | + | 1.19571i | |||||
−0.923880 | − | 0.382683i | −0.146078 | − | 0.0605076i | |||||
0.0547598 | − | 0.132202i | 0.00855205 | − | 0.0206465i | −0.919546 | − | 0.392983i | ||
0.928098 | + | 0.372336i | ||||||||
3.70253 | − | 3.70253i | 0.571313 | − | 0.571313i | |||||
−0.587013 | + | 0.587013i | −0.0895186 | + | 0.0895186i | −0.750448 | − | 0.660929i | ||
0.660929 | + | 0.750448i | ||||||||
1.80188 | − | 4.35013i | 0.271644 | − | 0.655806i | |||||
−0.759695 | − | 0.314676i | −0.113249 | − | 0.0469091i | |||||
−2.18906 | − | 5.28485i | −0.322759 | − | 0.779209i | |||||
− | 5.85635i | − | 0.854236i | −0.904196 | − | 0.427118i | ||||
0.904196 | − | 0.427118i | ||||||||
−1.36338 | + | 0.564729i | −0.196786 | + | 0.0815116i | |||||
−3.95275 | − | 3.95275i | −0.564679 | − | 0.564679i | |||||
−1.00000 | −0.141421 | |||||||||
1.60888 | − | 5.86793i | 0.225288 | − | 0.821675i | |||||
−5.47699 | −0.759522 | |||||||||
6.54226 | + | 6.54226i | 0.898648 | + | 0.898648i | 0.995317 | − | 0.0966687i | ||
−0.0966687 | + | 0.995317i | ||||||||
−5.21121 | + | 2.15856i | −0.709156 | + | 0.293742i | |||||
− | 4.70854i | − | 0.634900i | |||||||
1.35785 | + | 3.27815i | 0.181451 | + | 0.438061i | |||||
1.65383 | + | 0.685038i | 0.219055 | + | 0.0907355i | |||||
1.77710 | − | 4.29029i | 0.233344 | − | 0.563343i | |||||
−3.33507 | + | 3.33507i | −0.434189 | + | 0.434189i | −0.890051 | − | 0.455861i | ||
0.455861 | + | 0.890051i | ||||||||
−1.04348 | + | 1.04348i | −0.134713 | + | 0.134713i | |||||
4.76261 | − | 11.4980i | 0.609790 | − | 1.47216i | −0.253439 | − | 0.967351i | ||
0.863229 | − | 0.504812i | ||||||||
6.72892 | + | 2.78721i | 0.854574 | + | 0.353976i | |||||
1.11655 | + | 2.69558i | 0.140672 | + | 0.339611i | |||||
− | 1.00000i | − | 0.125000i | |||||||
−5.06008 | + | 2.09595i | −0.627626 | + | 0.259971i | |||||
−4.91328 | − | 4.91328i | −0.604783 | − | 0.604783i | |||||
8.66703 | 1.05885 | 0.529423 | − | 0.848358i | ||||||
0.529423 | + | 0.848358i | ||||||||
3.25645 | + | 2.52894i | 0.394903 | + | 0.306679i | |||||
−8.44146 | −1.01623 | |||||||||
2.50899 | + | 2.50899i | 0.299881 | + | 0.299881i | |||||
4.75235 | − | 1.96849i | 0.564000 | − | 0.233617i | −0.0824206 | − | 0.996598i | ||
0.646421 | + | 0.762981i | ||||||||
− | 0.822287i | − | 0.0969075i | |||||||
6.17351 | + | 14.9042i | 0.722555 | + | 1.74440i | 0.665939 | + | 0.746006i | ||
0.0566159 | + | 0.998396i | ||||||||
−8.58444 | − | 3.55579i | −0.997921 | − | 0.413353i | |||||
−0.564729 | + | 1.36338i | −0.0652093 | + | 0.157429i | |||||
−0.857748 | + | 0.857748i | −0.0983905 | + | 0.0983905i | |||||
−11.8137 | + | 11.8137i | −1.34629 | + | 1.34629i | |||||
−3.09302 | + | 7.46720i | −0.350215 | + | 0.845494i | |||||
9.34587 | + | 3.87118i | 1.05149 | + | 0.435542i | 0.840424 | − | 0.541929i | ||
0.211068 | + | 0.977471i | ||||||||
−0.382683 | − | 0.923880i | −0.0427853 | − | 0.103293i | |||||
5.85698i | 0.650776i | |||||||||
0.132202 | − | 0.0547598i | 0.0145993 | − | 0.00604721i | |||||
2.40841 | + | 2.40841i | 0.264358 | + | 0.264358i | 0.826822 | − | 0.562464i | ||
−0.562464 | + | 0.826822i | ||||||||
5.23617 | 0.571313 | |||||||||
3.97635 | + | 1.09024i | 0.431296 | + | 0.118254i | |||||
−0.830161 | −0.0895186 | |||||||||
−4.84570 | − | 4.84570i | −0.519514 | − | 0.519514i | |||||
4.35013 | − | 1.80188i | 0.463725 | − | 0.192081i | |||||
2.24175i | 0.237625i | 0.992917 | + | 0.118813i | ||||||
−0.992917 | + | 0.118813i | ||||||||
−0.314676 | − | 0.759695i | −0.0331697 | − | 0.0800788i | |||||
17.9544 | + | 7.43696i | 1.88213 | + | 0.779605i | |||||
2.18906 | − | 5.28485i | 0.228225 | − | 0.550984i | |||||
7.60004 | − | 7.60004i | 0.788087 | − | 0.788087i | |||||
4.14106 | − | 4.14106i | 0.427118 | − | 0.427118i | |||||
−0.464210 | + | 1.12070i | −0.0476269 | + | 0.114982i | |||||
−1.36338 | − | 0.564729i | −0.139149 | − | 0.0576374i | |||||
1.66675 | + | 4.02389i | 0.169233 | + | 0.408564i | 0.985628 | − | 0.168929i | ||
−0.816395 | + | 0.577493i | ||||||||
− | 5.59004i | − | 0.564679i | |||||||
3.57705 | − | 1.48166i | 0.359507 | − | 0.148913i | |||||
−0.707107 | − | 0.707107i | −0.0707107 | − | 0.0707107i | |||||
−10.7393 | −1.06860 | −0.534301 | − | 0.845294i | ||||||
−0.534301 | + | 0.845294i | ||||||||
5.28690 | − | 3.01160i | 0.523482 | − | 0.298193i | |||||
−7.43306 | −0.732401 | −0.366200 | − | 0.930536i | ||||||
−0.366200 | + | 0.930536i | ||||||||
−3.87282 | − | 3.87282i | −0.379761 | − | 0.379761i | |||||
4.83759 | − | 2.00380i | 0.472101 | − | 0.195550i | |||||
9.25215i | 0.898648i | |||||||||
6.01999 | + | 14.5335i | 0.581974 | + | 1.40501i | 0.891020 | + | 0.453963i | ||
−0.309046 | + | 0.951047i | ||||||||
−5.21121 | − | 2.15856i | −0.501449 | − | 0.207707i | |||||
2.46089 | − | 5.94112i | 0.235711 | − | 0.569056i | −0.761120 | − | 0.648611i | ||
0.996830 | + | 0.0795553i | ||||||||
3.32944 | − | 3.32944i | 0.317450 | − | 0.317450i | |||||
−9.69577 | + | 9.69577i | −0.920281 | + | 0.920281i | |||||
−1.35785 | + | 3.27815i | −0.128305 | + | 0.309756i | |||||
−8.90782 | − | 3.68974i | −0.837978 | − | 0.347102i | −0.0779218 | − | 0.996959i | ||
−0.760056 | + | 0.649858i | ||||||||
0.685038 | + | 1.65383i | 0.0641597 | + | 0.154895i | |||||
− | 5.72028i | − | 0.533419i | |||||||
4.29029 | − | 1.77710i | 0.398344 | − | 0.164999i | |||||
−3.18457 | − | 3.18457i | −0.294414 | − | 0.294414i | |||||
−4.71650 | −0.434189 | |||||||||
−7.24121 | − | 12.7120i | −0.663800 | − | 1.16531i | |||||
−1.47571 | −0.134713 | |||||||||
7.89864 | + | 7.89864i | 0.718058 | + | 0.718058i | |||||
11.4980 | − | 4.76261i | 1.04098 | − | 0.431187i | |||||
− | 0.211165i | − | 0.0190401i | |||||||
2.78721 | + | 6.72892i | 0.250299 | + | 0.604275i | |||||
−0.923880 | − | 0.382683i | −0.0826343 | − | 0.0342282i | |||||
−1.11655 | + | 2.69558i | −0.0994699 | + | 0.240142i | |||||
2.26692 | − | 2.26692i | 0.201157 | − | 0.201157i | −0.599339 | − | 0.800496i | ||
0.800496 | + | 0.599339i | ||||||||
0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | |||||
−0.468816 | + | 1.13182i | −0.0412769 | + | 0.0996513i | |||||
−5.06008 | − | 2.09595i | −0.443798 | − | 0.183827i | |||||
−1.36747 | − | 3.30136i | −0.119476 | − | 0.288441i | 0.852815 | − | 0.522213i | ||
−0.972292 | + | 0.233771i | ||||||||
− | 6.94843i | − | 0.604783i | |||||||
3.97653 | − | 1.64713i | 0.344808 | − | 0.142824i | |||||
6.12852 | + | 6.12852i | 0.529423 | + | 0.529423i | |||||
−5.64058 | −0.485464 | |||||||||
0.514430 | + | 4.09089i | 0.0441120 | + | 0.350791i | |||||
3.30950 | 0.282750 | 0.141375 | − | 0.989956i | ||||||
0.141375 | + | 0.989956i | ||||||||
−5.96902 | − | 5.96902i | −0.508116 | − | 0.508116i | |||||
−1.66295 | + | 0.688816i | −0.141049 | + | 0.0584246i | −0.452092 | − | 0.891972i | ||
0.311042 | + | 0.950396i | ||||||||
3.54824i | 0.299881i | |||||||||
−3.30725 | − | 7.98440i | −0.278520 | − | 0.672408i | |||||
4.75235 | + | 1.96849i | 0.398808 | + | 0.165192i | |||||
9.86889 | − | 23.8256i | 0.825278 | − | 1.99240i | |||||
0.581445 | − | 0.581445i | 0.0484538 | − | 0.0484538i | |||||
3.28365 | − | 3.28365i | 0.272692 | − | 0.272692i | |||||
−6.17351 | + | 14.9042i | −0.510924 | + | 1.23348i | |||||
−7.62132 | − | 3.15686i | −0.628596 | − | 0.260373i | |||||
−3.55579 | − | 8.58444i | −0.292284 | − | 0.705637i | |||||
− | 4.16768i | − | 0.341430i | −0.985320 | − | 0.170715i | ||||
0.985320 | − | 0.170715i | ||||||||
−1.36338 | + | 0.564729i | −0.111319 | + | 0.0461099i | |||||
−3.24744 | − | 3.24744i | −0.264273 | − | 0.264273i | 0.562514 | − | 0.826788i | ||
−0.826788 | + | 0.562514i | ||||||||
−1.21304 | −0.0983905 | |||||||||
0.423009 | + | 3.36389i | 0.0341982 | + | 0.271954i | |||||
−16.7071 | −1.34629 | |||||||||
5.15010 | + | 5.15010i | 0.413666 | + | 0.413666i | |||||
−7.46720 | + | 3.09302i | −0.597854 | + | 0.247639i | |||||
− | 15.5482i | − | 1.24088i | −0.784253 | − | 0.620442i | ||||
0.784253 | − | 0.620442i | ||||||||
3.87118 | + | 9.34587i | 0.307975 | + | 0.743517i | |||||
12.6142 | + | 5.22495i | 1.00037 | + | 0.414366i | |||||
0.382683 | − | 0.923880i | 0.0302538 | − | 0.0730391i | |||||
−14.3521 | + | 14.3521i | −1.13111 | + | 1.13111i | |||||
−4.14151 | + | 4.14151i | −0.325388 | + | 0.325388i | |||||
3.87956 | − | 9.36608i | 0.303870 | − | 0.733608i | −0.696008 | − | 0.718034i | ||
0.999879 | − | 0.0155742i | ||||||||
0.132202 | + | 0.0547598i | 0.0103232 | + | 0.00427602i | |||||
−2.65905 | − | 6.41951i | −0.207007 | − | 0.499758i | |||||
3.40601i | 0.264358i | |||||||||
−11.5038 | + | 4.76501i | −0.890187 | + | 0.368728i | −0.780439 | − | 0.625232i | ||
−0.109748 | + | 0.993959i | ||||||||
3.70253 | + | 3.70253i | 0.285657 | + | 0.285657i | |||||
−16.9974 | −1.30750 | |||||||||
2.04079 | + | 3.58262i | 0.156521 | + | 0.274775i | |||||
−0.997467 | −0.0762782 | |||||||||
−0.587013 | − | 0.587013i | −0.0447593 | − | 0.0447593i | |||||
−3.27672 | + | 1.35726i | −0.249125 | + | 0.103191i | −0.503752 | − | 0.863849i | ||
0.254627 | + | 0.967039i | ||||||||
− | 6.85286i | − | 0.519514i | |||||||
1.35785 | + | 3.27815i | 0.102644 | + | 0.247805i | |||||
4.35013 | + | 1.80188i | 0.327903 | + | 0.135822i | |||||
−2.66354 | + | 6.43037i | −0.200204 | + | 0.483336i | |||||
−1.58516 | + | 1.58516i | −0.118813 | + | 0.118813i | |||||
−9.26485 | + | 9.26485i | −0.692487 | + | 0.692487i | −0.962779 | − | 0.270291i | ||
0.270291 | + | 0.962779i | ||||||||
0.314676 | − | 0.759695i | 0.0234545 | − | 0.0566243i | |||||
1.68821 | + | 0.699281i | 0.125484 | + | 0.0519772i | 0.444542 | − | 0.895758i | ||
−0.319058 | + | 0.947735i | ||||||||
7.43696 | + | 17.9544i | 0.551264 | + | 1.33087i | |||||
− | 18.3656i | − | 1.35763i | |||||||
5.28485 | − | 2.18906i | 0.389604 | − | 0.161379i | |||||
−6.57025 | − | 6.57025i | −0.483054 | − | 0.483054i | |||||
10.7481 | 0.788087 | |||||||||
−16.8689 | + | 9.60913i | −1.23358 | + | 0.702689i | |||||
5.85635 | 0.427118 | |||||||||
14.1521 | + | 14.1521i | 1.02942 | + | 1.02942i | |||||
−1.12070 | + | 0.464210i | −0.0813043 | + | 0.0336773i | |||||
− | 16.8319i | − | 1.21791i | −0.793205 | − | 0.608955i | ||||
0.793205 | − | 0.608955i | ||||||||
−0.564729 | − | 1.36338i | −0.0407558 | − | 0.0983932i | |||||
−5.38504 | − | 2.23056i | −0.387624 | − | 0.160559i | 0.180356 | − | 0.983601i | ||
−0.567980 | + | 0.823042i | ||||||||
−1.66675 | + | 4.02389i | −0.119666 | + | 0.288899i | |||||
−5.71515 | + | 5.71515i | −0.409270 | + | 0.409270i | |||||
3.95275 | − | 3.95275i | 0.282340 | − | 0.282340i | |||||
1.34760 | − | 3.25339i | 0.0960123 | − | 0.231794i | −0.868575 | − | 0.495557i | ||
0.964587 | + | 0.263763i | ||||||||
3.57705 | + | 1.48166i | 0.254210 | + | 0.105297i | |||||
−6.42910 | − | 15.5212i | −0.455747 | − | 1.10027i | −0.970103 | − | 0.242694i | ||
0.514356 | − | 0.857577i | ||||||||
− | 1.00000i | − | 0.0707107i | |||||||
11.8164 | − | 4.89452i | 0.833466 | − | 0.345233i | |||||
−7.59384 | − | 7.59384i | −0.534301 | − | 0.534301i | |||||
−16.4773 | −1.15648 | |||||||||
5.86793 | + | 1.60888i | 0.410837 | + | 0.112644i | |||||
0.143094 | 0.00999414 | |||||||||
−5.25597 | − | 5.25597i | −0.366200 | − | 0.366200i | |||||
4.34567 | − | 1.80003i | 0.302045 | − | 0.125111i | |||||
− | 5.47699i | − | 0.379761i | |||||||
−2.18575 | − | 5.27687i | −0.151192 | − | 0.365009i | |||||
4.83759 | + | 2.00380i | 0.333826 | + | 0.138275i | |||||
−8.73280 | + | 21.0828i | −0.601191 | + | 1.45140i | 0.271166 | + | 0.962533i | ||
−0.872357 | + | 0.488870i | ||||||||
−6.54226 | + | 6.54226i | −0.449324 | + | 0.449324i | |||||
5.36758 | − | 5.36758i | 0.367780 | − | 0.367780i | |||||
−6.01999 | + | 14.5335i | −0.411518 | + | 0.993492i | |||||
−0.766969 | − | 0.317689i | −0.0523068 | − | 0.0216662i | |||||
−2.15856 | − | 5.21121i | −0.146871 | − | 0.354578i | |||||
− | 25.8431i | − | 1.75434i | |||||||
5.94112 | − | 2.46089i | 0.402383 | − | 0.166673i | |||||
16.8336 | + | 16.8336i | 1.13751 | + | 1.13751i | |||||
4.70854 | 0.317450 | |||||||||
17.8356 | + | 13.8510i | 1.19975 | + | 0.931717i | |||||
−13.7119 | −0.920281 | |||||||||
−6.41246 | − | 6.41246i | −0.429410 | − | 0.429410i | 0.459017 | − | 0.888427i | ||
−0.888427 | + | 0.459017i | ||||||||
−3.27815 | + | 1.35785i | −0.219031 | + | 0.0907255i | |||||
− | 0.822287i | − | 0.0548192i | |||||||
−3.68974 | − | 8.90782i | −0.245438 | − | 0.592540i | |||||
14.5491 | + | 6.02643i | 0.965658 | + | 0.399988i | 0.809094 | − | 0.587679i | ||
0.156564 | + | 0.987668i | ||||||||
−0.685038 | + | 1.65383i | −0.0453678 | + | 0.109527i | |||||
14.2262 | − | 14.2262i | 0.940092 | − | 0.940092i | −0.0582124 | − | 0.998304i | ||
0.998304 | + | 0.0582124i | ||||||||
4.04485 | − | 4.04485i | 0.266710 | − | 0.266710i | |||||
−9.43496 | + | 22.7780i | −0.620775 | + | 1.49868i | |||||
4.29029 | + | 1.77710i | 0.281672 | + | 0.116672i | |||||
−7.37613 | − | 17.8076i | −0.483227 | − | 1.16661i | −0.958068 | − | 0.286541i | ||
0.474841 | − | 0.880071i | ||||||||
− | 4.50366i | − | 0.294414i | |||||||
5.41056 | − | 2.24113i | 0.352946 | − | 0.146195i | |||||
−3.33507 | − | 3.33507i | −0.217095 | − | 0.217095i | |||||
14.9281 | 0.969684 | |||||||||
3.86845 | − | 14.1091i | 0.250755 | − | 0.914555i | |||||
14.2040 | 0.918778 | 0.459389 | − | 0.888235i | ||||||
0.459389 | + | 0.888235i | ||||||||
−1.04348 | − | 1.04348i | −0.0673565 | − | 0.0673565i | |||||
−4.22633 | + | 1.75060i | −0.272242 | + | 0.112766i | −0.514628 | − | 0.857414i | ||
0.242386 | + | 0.970180i | ||||||||
11.1704i | 0.718058i | |||||||||
−3.16806 | − | 7.64838i | −0.203231 | − | 0.490644i | |||||
11.4980 | + | 4.76261i | 0.736082 | + | 0.304895i | |||||
2.13922 | − | 5.16452i | 0.136669 | − | 0.329949i | |||||
0.149316 | − | 0.149316i | 0.00952007 | − | 0.00952007i | |||||
−4.69788 | + | 4.69788i | −0.298919 | + | 0.298919i | |||||
−2.78721 | + | 6.72892i | −0.176988 | + | 0.427287i | |||||
4.64367 | + | 1.92347i | 0.294281 | + | 0.121895i | |||||
−0.382683 | − | 0.923880i | −0.0242030 | − | 0.0584313i | |||||
− | 9.00712i | − | 0.568524i | −0.958747 | − | 0.284262i | ||||
0.958747 | − | 0.284262i | ||||||||
−2.69558 | + | 1.11655i | −0.169806 | + | 0.0703358i | |||||
19.0453 | + | 19.0453i | 1.19737 | + | 1.19737i | |||||
3.20591 | 0.201157 | |||||||||
6.03695 | − | 0.759148i | 0.378049 | − | 0.0475397i | |||||
1.00000 | 0.0625000 | |||||||||
20.2643 | + | 20.2643i | 1.26405 | + | 1.26405i | 0.949112 | + | 0.314938i | ||
0.314938 | + | 0.949112i | ||||||||
−1.13182 | + | 0.468816i | −0.0704641 | + | 0.0291872i | |||||
32.9693i | 2.04862i | |||||||||
−2.09595 | − | 5.06008i | −0.129986 | − | 0.313813i | |||||
3.52785 | + | 1.46129i | 0.218369 | + | 0.0904513i | |||||
1.36747 | − | 3.30136i | 0.0844825 | − | 0.203959i | |||||
−4.27498 | + | 4.27498i | −0.263606 | + | 0.263606i | −0.826517 | − | 0.562911i | ||
0.562911 | + | 0.826517i | ||||||||
4.91328 | − | 4.91328i | 0.302392 | − | 0.302392i | |||||
−3.54064 | + | 8.54787i | −0.217500 | + | 0.525091i | |||||
3.97653 | + | 1.64713i | 0.243816 | + | 0.100992i | |||||
1.26598 | + | 3.05635i | 0.0774769 | + | 0.187046i | |||||
8.66703i | 0.529423i | |||||||||
−15.6073 | + | 6.46477i | −0.951596 | + | 0.394164i | −0.803830 | − | 0.594858i | ||
−0.147765 | + | 0.989022i | ||||||||
−3.98849 | − | 3.98849i | −0.242732 | − | 0.242732i | |||||
−22.9305 | −1.39293 | −0.696463 | − | 0.717593i | ||||||
−0.696463 | + | 0.717593i | ||||||||
−2.52894 | + | 3.25645i | −0.153339 | + | 0.197451i | |||||
28.6785 | 1.73570 | |||||||||
2.34017 | + | 2.34017i | 0.141375 | + | 0.141375i | |||||
4.35013 | − | 1.80188i | 0.262322 | − | 0.108658i | |||||
− | 8.44146i | − | 0.508116i | |||||||
7.65435 | + | 18.4792i | 0.459905 | + | 1.11031i | 0.968435 | + | 0.249265i | ||
−0.508530 | + | 0.861044i | ||||||||
−1.66295 | − | 0.688816i | −0.0997370 | − | 0.0413124i | |||||
−2.29189 | + | 5.53311i | −0.137212 | + | 0.331259i | |||||
−2.50899 | + | 2.50899i | −0.149941 | + | 0.149941i | |||||
16.4633 | − | 16.4633i | 0.982118 | − | 0.982118i | −0.0177247 | − | 0.999843i | ||
0.999843 | + | 0.0177247i | ||||||||
3.30725 | − | 7.98440i | 0.196944 | − | 0.475464i | |||||
−23.2363 | − | 9.62478i | −1.38125 | − | 0.572134i | −0.436437 | − | 0.899735i | ||
−0.944816 | + | 0.327601i | ||||||||
1.96849 | + | 4.75235i | 0.116808 | + | 0.282000i | |||||
1.79009i | 0.106036i | |||||||||
23.8256 | − | 9.86889i | 1.40884 | − | 0.583560i | |||||
−0.359022 | − | 0.359022i | −0.0211924 | − | 0.0211924i | |||||
0.822287 | 0.0484538 | |||||||||
−4.20895 | − | 16.4707i | −0.247585 | − | 0.968866i | |||||
4.64378 | 0.272692 | |||||||||
4.54481 | + | 4.54481i | 0.266422 | + | 0.266422i | |||||
−14.9042 | + | 6.17351i | −0.872201 | + | 0.361278i | |||||
25.5251i | 1.49119i | 0.666399 | + | 0.745595i | ||||||
−0.666399 | + | 0.745595i | ||||||||
−3.15686 | − | 7.62132i | −0.184112 | − | 0.444485i | |||||
−4.35748 | − | 1.80493i | −0.253702 | − | 0.105087i | |||||
3.55579 | − | 8.58444i | 0.206676 | − | 0.498961i | |||||
18.7800 | − | 18.7800i | 1.08972 | − | 1.08972i | |||||
2.94700 | − | 2.94700i | 0.170715 | − | 0.170715i | |||||
11.9894 | − | 28.9451i | 0.693368 | − | 1.67394i | |||||
−1.36338 | − | 0.564729i | −0.0787145 | − | 0.0326046i | |||||
1.12724 | + | 2.72139i | 0.0649729 | + | 0.156858i | |||||
− | 4.59258i | − | 0.264273i | |||||||
−14.6417 | + | 6.06480i | −0.841145 | + | 0.348414i | |||||
−0.857748 | − | 0.857748i | −0.0491952 | − | 0.0491952i | |||||
12.4453 | 0.712616 | |||||||||
−2.07951 | + | 2.67774i | −0.118878 | + | 0.153076i | |||||
−14.2382 | −0.812616 | −0.406308 | − | 0.913736i | ||||||
−0.406308 | + | 0.913736i | ||||||||
−11.8137 | − | 11.8137i | −0.673147 | − | 0.673147i | |||||
−10.1341 | + | 4.19766i | −0.576506 | + | 0.238797i | |||||
7.28334i | 0.413666i | |||||||||
−4.65012 | − | 11.2264i | −0.263684 | − | 0.636590i | 0.735477 | − | 0.677550i | ||
−0.999161 | + | 0.0409602i | ||||||||
−7.46720 | − | 3.09302i | −0.422747 | − | 0.175108i | |||||
−8.33854 | + | 20.1310i | −0.471322 | + | 1.13787i | 0.492257 | + | 0.870450i | ||
−0.963579 | + | 0.267422i | ||||||||
10.9943 | − | 10.9943i | 0.620442 | − | 0.620442i | |||||
−2.06311 | + | 2.06311i | −0.116243 | + | 0.116243i | |||||
−3.87118 | + | 9.34587i | −0.217771 | + | 0.525746i | |||||
9.47130 | + | 3.92314i | 0.531961 | + | 0.220346i | 0.632462 | − | 0.774591i | ||
−0.100501 | + | 0.994937i | ||||||||
5.22495 | + | 12.6142i | 0.293001 | + | 0.707367i | |||||
21.8654i | 1.22423i | |||||||||
0.923880 | − | 0.382683i | 0.0516464 | − | 0.0213927i | |||||
16.4150 | + | 16.4150i | 0.916197 | + | 0.916197i | |||||
−20.2970 | −1.13111 | |||||||||
4.96241 | − | 0.624023i | 0.276116 | − | 0.0347216i | |||||
−5.85698 | −0.325388 | |||||||||
−3.87282 | − | 3.87282i | −0.214825 | − | 0.214825i | |||||
9.36608 | − | 3.87956i | 0.518739 | − | 0.214869i | |||||
− | 9.48972i | − | 0.524783i | |||||||
0.0547598 | + | 0.132202i | 0.00302360 | + | 0.00729963i | |||||
−19.1980 | − | 7.95207i | −1.05842 | − | 0.438412i | |||||
2.65905 | − | 6.41951i | 0.146376 | − | 0.353383i | |||||
−0.209438 | + | 0.209438i | −0.0115117 | + | 0.0115117i | −0.712839 | − | 0.701327i | ||
0.701327 | + | 0.712839i | ||||||||
−2.40841 | + | 2.40841i | −0.132179 | + | 0.132179i | |||||
2.92388 | − | 7.05888i | 0.160228 | − | 0.386824i | |||||
−11.5038 | − | 4.76501i | −0.629457 | − | 0.260730i | |||||
3.31673 | + | 8.00729i | 0.181212 | + | 0.437485i | |||||
5.23617i | 0.285657i | |||||||||
−12.9824 | + | 5.37748i | −0.707196 | + | 0.292930i | −0.707144 | − | 0.707070i | ||
−5.22341e−5 | 1.00000i | |||||||||
−12.0190 | − | 12.0190i | −0.653748 | − | 0.653748i | |||||
−14.2284 | −0.772782 | |||||||||
−1.09024 | + | 3.97635i | −0.0591268 | + | 0.215648i | |||||
−34.2939 | −1.85712 | |||||||||
−0.705316 | − | 0.705316i | −0.0381391 | − | 0.0381391i | |||||
4.62206 | − | 1.91452i | 0.249568 | − | 0.103374i | |||||
− | 0.830161i | − | 0.0447593i | |||||||
−3.23041 | − | 7.79889i | −0.173919 | − | 0.419878i | |||||
−3.27672 | − | 1.35726i | −0.176158 | − | 0.0729669i | |||||
−4.26669 | + | 10.3007i | −0.229048 | + | 0.552971i | −0.996062 | − | 0.0886594i | ||
0.767014 | + | 0.641631i | ||||||||
4.84570 | − | 4.84570i | 0.259757 | − | 0.259757i | |||||
−1.77671 | + | 1.77671i | −0.0951051 | + | 0.0951051i | −0.753059 | − | 0.657953i | ||
0.657953 | + | 0.753059i | ||||||||
−1.35785 | + | 3.27815i | −0.0725804 | + | 0.175225i | |||||
−28.5418 | − | 11.8224i | −1.52345 | − | 0.631033i | |||||
1.80188 | + | 4.35013i | 0.0960406 | + | 0.231862i | |||||
− | 10.0823i | − | 0.536629i | −0.963331 | − | 0.268314i | ||||
0.963331 | − | 0.268314i | ||||||||
−6.43037 | + | 2.66354i | −0.341770 | + | 0.141566i | |||||
3.63729 | + | 3.63729i | 0.193047 | + | 0.193047i | |||||
−2.24175 | −0.118813 | |||||||||
−17.0513 | − | 13.2420i | −0.902452 | − | 0.700838i | |||||
−13.1025 | −0.692487 | |||||||||
−17.4429 | − | 17.4429i | −0.920599 | − | 0.920599i | 0.0764723 | − | 0.997072i | ||
−0.997072 | + | 0.0764723i | ||||||||
0.759695 | − | 0.314676i | 0.0400394 | − | 0.0165849i | |||||
− | 17.5285i | − | 0.922555i | |||||||
0.699281 | + | 1.68821i | 0.0367534 | + | 0.0887306i | |||||
15.2294 | + | 6.30823i | 0.799337 | + | 0.331096i | |||||
−7.43696 | + | 17.9544i | −0.389803 | + | 0.941067i | |||||
−11.4072 | + | 11.4072i | −0.597078 | + | 0.597078i | |||||
12.9865 | − | 12.9865i | 0.678813 | − | 0.678813i | |||||
11.3939 | − | 27.5072i | 0.594755 | − | 1.43587i | −0.284108 | − | 0.958792i | ||
0.878863 | − | 0.477073i | ||||||||
5.28485 | + | 2.18906i | 0.275492 | + | 0.114112i | |||||
0.0450283 | + | 0.108708i | 0.00234408 | + | 0.00565911i | |||||
− | 9.29174i | − | 0.483054i | |||||||
30.3299 | − | 12.5631i | 1.57465 | − | 0.652242i | |||||
7.60004 | + | 7.60004i | 0.394043 | + | 0.394043i | |||||
20.8039 | 1.07718 | 0.538592 | − | 0.842567i | ||||||
0.538592 | + | 0.842567i | ||||||||
−18.7228 | − | 5.13346i | −0.968134 | − | 0.265445i | |||||
−1.47571 | −0.0762052 | |||||||||
4.14106 | + | 4.14106i | 0.213559 | + | 0.213559i | |||||
23.4979 | − | 9.73315i | 1.21020 | − | 0.501283i | |||||
20.0142i | 1.02942i | |||||||||
3.99706 | + | 9.64974i | 0.205315 | + | 0.495674i | 0.992674 | − | 0.120820i | ||
−0.787359 | + | 0.616494i | ||||||||
−1.12070 | − | 0.464210i | −0.0574908 | − | 0.0238135i | |||||
1.81047 | − | 4.37087i | 0.0927533 | − | 0.223926i | |||||
11.9019 | − | 11.9019i | 0.608955 | − | 0.608955i | |||||
−14.2495 | + | 14.2495i | −0.728113 | + | 0.728113i | −0.970244 | − | 0.242130i | ||
0.242130 | + | 0.970244i | ||||||||
0.564729 | − | 1.36338i | 0.0288187 | − | 0.0695745i | |||||
−15.4353 | − | 6.39351i | −0.786656 | − | 0.325844i | |||||
−2.23056 | − | 5.38504i | −0.113532 | − | 0.274091i | |||||
− | 0.682631i | − | 0.0347001i | |||||||
−4.02389 | + | 1.66675i | −0.204282 | + | 0.0846164i | |||||
−13.9058 | − | 13.9058i | −0.705051 | − | 0.705051i | 0.260440 | − | 0.965490i | ||
−0.965490 | + | 0.260440i | ||||||||
−8.08244 | −0.409270 | |||||||||
−20.4936 | + | 11.6739i | −1.03641 | + | 0.590373i | |||||
5.59004 | 0.282340 | |||||||||
−3.72875 | − | 3.72875i | −0.188090 | − | 0.188090i | |||||
3.25339 | − | 1.34760i | 0.163903 | − | 0.0678909i | |||||
10.1159i | 0.508986i | |||||||||
1.48166 | + | 3.57705i | 0.0744564 | + | 0.179754i | |||||
−22.1250 | − | 9.16446i | −1.11042 | − | 0.459951i | −0.249338 | − | 0.968416i | ||
−0.861083 | + | 0.508465i | ||||||||
6.42910 | − | 15.5212i | 0.322262 | − | 0.778009i | |||||
4.49132 | − | 4.49132i | 0.224847 | − | 0.224847i | |||||
0.707107 | − | 0.707107i | 0.0353553 | − | 0.0353553i | |||||
−8.81734 | + | 21.2869i | −0.440317 | + | 1.06302i | 0.535521 | + | 0.844522i | ||
−0.975838 | + | 0.218497i | ||||||||
11.8164 | + | 4.89452i | 0.589350 | + | 0.244117i | |||||
15.2655 | + | 36.8543i | 0.760431 | + | 1.83584i | |||||
− | 10.7393i | − | 0.534301i | |||||||
−5.41114 | + | 2.24137i | −0.268882 | + | 0.111375i | |||||
−11.6512 | − | 11.6512i | −0.578239 | − | 0.578239i | |||||
43.7505 | 2.16863 | |||||||||
3.01160 | + | 5.28690i | 0.149097 | + | 0.261741i | |||||
12.7488 | 0.630389 | 0.315195 | − | 0.949027i | ||||||
0.315195 | + | 0.949027i | ||||||||
0.101183 | + | 0.101183i | 0.00499707 | + | 0.00499707i | |||||
4.51209 | − | 1.86897i | 0.222565 | − | 0.0921895i | |||||
− | 7.43306i | − | 0.366200i | |||||||
6.40432 | + | 15.4614i | 0.315136 | + | 0.760806i | |||||
4.34567 | + | 1.80003i | 0.213578 | + | 0.0884669i | |||||
−1.30342 | + | 3.14674i | −0.0639826 | + | 0.154468i | |||||
3.87282 | − | 3.87282i | 0.189881 | − | 0.189881i | |||||
−1.87823 | + | 1.87823i | −0.0919773 | + | 0.0919773i | |||||
2.18575 | − | 5.27687i | 0.106909 | − | 0.258100i | |||||
25.2883 | + | 10.4748i | 1.23541 | + | 0.511725i | 0.902279 | − | 0.431153i | ||
0.333136 | + | 0.942879i | ||||||||
2.00380 | + | 4.83759i | 0.0977752 | + | 0.236050i | |||||
33.6813i | 1.64153i | 0.571268 | + | 0.820764i | ||||||
−0.571268 | + | 0.820764i | ||||||||
−21.0828 | + | 8.73280i | −1.02630 | + | 0.425106i | |||||
3.40514 | + | 3.40514i | 0.165564 | + | 0.165564i | |||||
−9.25215 | −0.449324 | |||||||||
0.514430 | + | 4.09089i | 0.0249535 | + | 0.198437i | |||||
7.59090 | 0.367780 | |||||||||
−31.2251 | − | 31.2251i | −1.51109 | − | 1.51109i | |||||
−14.5335 | + | 6.01999i | −0.702505 | + | 0.290987i | |||||
− | 38.0565i | − | 1.83739i | |||||||
−0.317689 | − | 0.766969i | −0.0153203 | − | 0.0369865i | |||||
−16.7963 | − | 6.95725i | −0.809049 | − | 0.335119i | −0.0604746 | − | 0.998170i | ||
−0.748575 | + | 0.663051i | ||||||||
2.15856 | − | 5.21121i | 0.103854 | − | 0.250725i | |||||
−5.73034 | + | 5.73034i | −0.275382 | + | 0.275382i | −0.831262 | − | 0.555880i | ||
0.555880 | + | 0.831262i | ||||||||
18.2738 | − | 18.2738i | 0.877170 | − | 0.877170i | |||||
2.62248 | − | 6.33122i | 0.125738 | − | 0.303559i | |||||
5.94112 | + | 2.46089i | 0.284528 | + | 0.117855i | |||||
−2.65541 | − | 6.41073i | −0.127026 | − | 0.306667i | |||||
23.8064i | 1.13751i | |||||||||
22.1522 | − | 9.17574i | 1.05727 | − | 0.437934i | 0.214786 | − | 0.976661i | ||
0.842480 | + | 0.538727i | ||||||||
3.32944 | + | 3.32944i | 0.158725 | + | 0.158725i | |||||
4.59662 | 0.218887 | |||||||||
2.81753 | + | 22.4058i | 0.134016 | + | 1.06573i | |||||
0.244075 | 0.0115964 | 0.00579819 | − | 0.999983i | ||||||
0.00579819 | + | 0.999983i | ||||||||
−9.69577 | − | 9.69577i | −0.460141 | − | 0.460141i | |||||
−2.07111 | + | 0.857882i | −0.0981800 | + | 0.0406675i | |||||
− | 9.06859i | − | 0.429410i | |||||||
−2.35361 | − | 5.68212i | −0.111322 | − | 0.268755i | |||||
−3.27815 | − | 1.35785i | −0.154878 | − | 0.0641526i | |||||
−0.0315454 | + | 0.0761574i | −0.00148872 | + | 0.00359409i | −0.924622 | − | 0.380886i | ||
0.923133 | + | 0.384480i | ||||||||
0.581445 | − | 0.581445i | 0.0274096 | − | 0.0274096i | |||||
−0.476424 | + | 0.476424i | −0.0224339 | + | 0.0224339i | |||||
3.68974 | − | 8.90782i | 0.173551 | − | 0.418989i | |||||
−6.26141 | − | 2.59356i | −0.294187 | − | 0.121856i | |||||
6.02643 | + | 14.5491i | 0.282835 | + | 0.682823i | |||||
19.4337i | 0.911066i | |||||||||
−1.65383 | + | 0.685038i | −0.0774476 | + | 0.0320799i | |||||
17.2461 | + | 17.2461i | 0.806737 | + | 0.806737i | 0.984139 | − | 0.177402i | ||
−0.177402 | + | 0.984139i | ||||||||
20.1188 | 0.940092 | |||||||||
11.5112 | + | 20.2081i | 0.537297 | + | 0.943232i | |||||
5.72028 | 0.266710 | |||||||||
20.5839 | + | 20.5839i | 0.958687 | + | 0.958687i | 0.999180 | − | 0.0404924i | ||
−0.0404924 | + | 0.999180i | ||||||||
−22.7780 | + | 9.43496i | −1.05973 | + | 0.438954i | |||||
27.9762i | 1.30016i | 0.759865 | + | 0.650081i | ||||||
−0.759865 | + | 0.650081i | ||||||||
1.77710 | + | 4.29029i | 0.0824997 | + | 0.199172i | |||||
9.92992 | + | 4.11311i | 0.460489 | + | 0.190741i | |||||
7.37613 | − | 17.8076i | 0.341693 | − | 0.824919i | |||||
22.1173 | − | 22.1173i | 1.02347 | − | 1.02347i | 0.0237504 | − | 0.999718i | ||
0.999718 | − | 0.0237504i | ||||||||
3.18457 | − | 3.18457i | 0.147207 | − | 0.147207i | |||||
11.7686 | − | 28.4118i | 0.543422 | − | 1.31194i | |||||
5.41056 | + | 2.24113i | 0.249570 | + | 0.103375i | |||||
−8.78053 | − | 21.1981i | −0.404586 | − | 0.976756i | |||||
− | 4.71650i | − | 0.217095i | |||||||
3.61131 | − | 1.49585i | 0.166048 | − | 0.0687793i | |||||
10.5558 | + | 10.5558i | 0.484842 | + | 0.484842i | |||||
−1.21304 | −0.0556581 | |||||||||
12.7120 | − | 7.24121i | 0.582655 | − | 0.331900i | |||||
−7.60792 | −0.348343 | |||||||||
10.0437 | + | 10.0437i | 0.459389 | + | 0.459389i | |||||
−11.1564 | + | 4.62112i | −0.509748 | + | 0.211144i | −0.622707 | − | 0.782455i | ||
0.112959 | + | 0.993600i | ||||||||
− | 1.47571i | − | 0.0673565i | |||||||
−19.4751 | − | 47.0169i | −0.887986 | − | 2.14379i | |||||
−4.22633 | − | 1.75060i | −0.192504 | − | 0.0797378i | |||||
−11.4623 | + | 27.6724i | −0.521552 | + | 1.25914i | |||||
−7.89864 | + | 7.89864i | −0.359029 | + | 0.359029i | |||||
−3.07975 | + | 3.07975i | −0.139844 | + | 0.139844i | |||||
3.16806 | − | 7.64838i | 0.143706 | − | 0.346937i | |||||
4.63377 | + | 1.91937i | 0.209976 | + | 0.0869749i | 0.485192 | − | 0.874407i | ||
−0.275217 | + | 0.961382i | ||||||||
4.76261 | + | 11.4980i | 0.215593 | + | 0.520488i | |||||
− | 14.9604i | − | 0.676532i | |||||||
5.16452 | − | 2.13922i | 0.233309 | − | 0.0966399i | |||||
−18.6988 | − | 18.6988i | −0.843865 | − | 0.843865i | 0.145494 | − | 0.989359i | ||
−0.989359 | + | 0.145494i | ||||||||
0.211165 | 0.00952007 | |||||||||
−18.4653 | − | 5.06285i | −0.831635 | − | 0.228019i | |||||
−6.64381 | −0.298919 | |||||||||
2.73776 | + | 2.73776i | 0.123053 | + | 0.123053i | |||||
−6.72892 | + | 2.78721i | −0.302138 | + | 0.125150i | |||||
− | 18.2518i | − | 0.818707i | |||||||
1.92347 | + | 4.64367i | 0.0861929 | + | 0.208088i | |||||
−27.6595 | − | 11.4569i | −1.23821 | − | 0.512882i | −0.335053 | − | 0.942199i | ||
−0.903154 | + | 0.429317i | ||||||||
0.382683 | − | 0.923880i | 0.0171141 | − | 0.0413171i | |||||
−12.9930 | + | 12.9930i | −0.580484 | + | 0.580484i | |||||
6.36899 | − | 6.36899i | 0.284262 | − | 0.284262i | |||||
13.0499 | − | 31.5052i | 0.581865 | − | 1.40475i | −0.309255 | − | 0.950979i | ||
0.891120 | − | 0.453768i | ||||||||
−2.69558 | − | 1.11655i | −0.120071 | − | 0.0497349i | |||||
−4.10976 | − | 9.92183i | −0.182882 | − | 0.441516i | |||||
26.9342i | 1.19737i | |||||||||
−23.1739 | + | 9.59895i | −1.02919 | + | 0.426304i | |||||
2.26692 | + | 2.26692i | 0.100578 | + | 0.100578i | |||||
28.0939 | 1.24524 | 0.622620 | − | 0.782525i | ||||||
0.622620 | + | 0.782525i | ||||||||
4.80557 | + | 3.73197i | 0.212794 | + | 0.165255i | |||||
57.2409 | 2.53219 | |||||||||
0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | |||||
−6.32141 | + | 2.61841i | −0.279097 | + | 0.115606i | |||||
28.6580i | 1.26405i | |||||||||
−2.84451 | − | 6.86725i | −0.125344 | − | 0.302607i | |||||
−1.13182 | − | 0.468816i | −0.0498257 | − | 0.0206385i | |||||
−10.5524 | + | 25.4758i | −0.464096 | + | 1.12043i | |||||
−23.3129 | + | 23.3129i | −1.02431 | + | 1.02431i | |||||
−3.70092 | + | 3.70092i | −0.162452 | + | 0.162452i | |||||
2.09595 | − | 5.06008i | 0.0919137 | − | 0.221899i | |||||
17.6215 | + | 7.29907i | 0.772013 | + | 0.319778i | 0.733687 | − | 0.679487i | ||
0.0383252 | + | 0.999265i | ||||||||
1.46129 | + | 3.52785i | 0.0639587 | + | 0.154410i | |||||
6.69653i | 0.292819i | 0.989224 | + | 0.146409i | ||||||
−0.989224 | + | 0.146409i | ||||||||
3.30136 | − | 1.36747i | 0.144221 | − | 0.0597381i | |||||
3.70253 | + | 3.70253i | 0.161592 | + | 0.161592i | |||||
−6.04573 | −0.263606 | |||||||||
7.94061 | − | 28.9611i | 0.345899 | − | 1.26157i | |||||
6.94843 | 0.302392 | |||||||||
6.87423 | + | 6.87423i | 0.298879 | + | 0.298879i | |||||
−8.54787 | + | 3.54064i | −0.371296 | + | 0.153796i | |||||
− | 3.87832i | − | 0.168305i | |||||||
1.64713 | + | 3.97653i | 0.0714122 | + | 0.172404i | |||||
0.724069 | + | 0.299919i | 0.0313629 | + | 0.0129909i | |||||
−1.26598 | + | 3.05635i | −0.0547844 | + | 0.132261i | |||||
−11.1235 | + | 11.1235i | −0.480910 | + | 0.480910i | |||||
−6.12852 | + | 6.12852i | −0.264712 | + | 0.264712i | |||||
−7.39935 | + | 17.8636i | −0.319305 | + | 0.770871i | |||||
−15.6073 | − | 6.46477i | −0.672880 | − | 0.278716i | |||||
10.0726 | + | 24.3174i | 0.433857 | + | 1.04742i | |||||
− | 5.64058i | − | 0.242732i | |||||||
−6.32639 | + | 2.62047i | −0.271993 | + | 0.112663i | −0.514511 | − | 0.857484i | ||
0.242518 | + | 0.970147i | ||||||||
−16.2143 | − | 16.2143i | −0.696463 | − | 0.696463i | |||||
2.69657 | 0.115721 | |||||||||
−4.09089 | + | 0.514430i | −0.175395 | + | 0.0220560i | |||||
6.43062 | 0.275458 | |||||||||
20.2787 | + | 20.2787i | 0.867850 | + | 0.867850i | |||||
−3.26202 | + | 1.35117i | −0.139474 | + | 0.0577719i | −0.451329 | − | 0.892358i | ||
0.311855 | + | 0.950130i | ||||||||
3.30950i | 0.141375i | |||||||||
3.91624 | + | 9.45463i | 0.167141 | + | 0.403514i | |||||
4.35013 | + | 1.80188i | 0.185490 | + | 0.0768325i | |||||
2.15569 | − | 5.20429i | 0.0918355 | − | 0.221710i | |||||
5.96902 | − | 5.96902i | 0.254058 | − | 0.254058i | |||||
25.3806 | − | 25.3806i | 1.07929 | − | 1.07929i | |||||
−7.65435 | + | 18.4792i | −0.325202 | + | 0.785108i | |||||
−12.6681 | − | 5.24731i | −0.537732 | − | 0.222736i | |||||
−0.688816 | − | 1.66295i | −0.0292123 | − | 0.0705247i | |||||
45.7591i | 1.93888i | 0.245338 | + | 0.969438i | ||||||
−0.245338 | + | 0.969438i | ||||||||
−5.53311 | + | 2.29189i | −0.234235 | + | 0.0970234i | |||||
−3.21506 | − | 3.21506i | −0.135983 | − | 0.135983i | |||||
−3.54824 | −0.149941 | |||||||||
−17.5721 | + | 22.6272i | −0.741897 | + | 0.955322i | |||||
23.2826 | 0.982118 | |||||||||
−7.05601 | − | 7.05601i | −0.297375 | − | 0.297375i | 0.542610 | − | 0.839985i | ||
−0.839985 | + | 0.542610i | ||||||||
7.98440 | − | 3.30725i | 0.336204 | − | 0.139260i | |||||
− | 9.64176i | − | 0.405632i | |||||||
−9.62478 | − | 23.2363i | −0.404560 | − | 0.976693i | |||||
19.2001 | + | 7.95293i | 0.806327 | + | 0.333992i | |||||
−1.96849 | + | 4.75235i | −0.0825959 | + | 0.199404i | |||||
−9.56020 | + | 9.56020i | −0.400784 | + | 0.400784i | −0.878509 | − | 0.477725i | ||
0.477725 | + | 0.878509i | ||||||||
−1.26579 | + | 1.26579i | −0.0530179 | + | 0.0530179i | |||||
6.49469 | − | 15.6796i | 0.271794 | − | 0.656169i | −0.727766 | − | 0.685826i | ||
0.999560 | + | 0.0296562i | ||||||||
23.8256 | + | 9.86889i | 0.996199 | + | 0.412639i | |||||
−9.50543 | − | 22.9481i | −0.397095 | − | 0.958673i | |||||
− | 0.507734i | − | 0.0211924i | |||||||
5.28485 | − | 2.18906i | 0.220394 | − | 0.0912900i | |||||
0.581445 | + | 0.581445i | 0.0242269 | + | 0.0242269i | |||||
−9.67374 | −0.402723 | −0.201361 | − | 0.979517i | ||||||
−0.201361 | + | 0.979517i | ||||||||
8.67039 | − | 14.6227i | 0.360641 | − | 0.608226i | |||||
−8.60150 | −0.357466 | |||||||||
3.28365 | + | 3.28365i | 0.136346 | + | 0.136346i | |||||
11.1654 | − | 4.62487i | 0.463220 | − | 0.191872i | |||||
6.42734i | 0.266422i | |||||||||
−16.6713 | − | 40.2480i | −0.690453 | − | 1.66690i | |||||
−14.9042 | − | 6.17351i | −0.616739 | − | 0.255462i | |||||
1.72348 | − | 4.16084i | 0.0712570 | − | 0.172030i | |||||
−18.0489 | + | 18.0489i | −0.745595 | + | 0.745595i | |||||
3.24694 | − | 3.24694i | 0.134015 | − | 0.134015i | −0.636917 | − | 0.770932i | ||
0.770932 | + | 0.636917i | ||||||||
3.15686 | − | 7.62132i | 0.130187 | − | 0.314298i | |||||
8.16245 | + | 3.38100i | 0.336328 | + | 0.139312i | |||||
−1.80493 | − | 4.35748i | −0.0743077 | − | 0.179395i | |||||
− | 5.19661i | − | 0.213760i | |||||||
8.58444 | − | 3.55579i | 0.352818 | − | 0.146142i | |||||
−0.550724 | − | 0.550724i | −0.0226155 | − | 0.0226155i | 0.695709 | − | 0.718324i | ||
−0.718324 | + | 0.695709i | ||||||||
26.5589 | 1.08972 | |||||||||
8.97329 | − | 11.5547i | 0.367869 | − | 0.473696i | |||||
4.16768 | 0.170715 | |||||||||
−17.5306 | − | 17.5306i | −0.717478 | − | 0.717478i | |||||
28.9451 | − | 11.9894i | 1.18365 | − | 0.490285i | |||||
− | 10.4846i | − | 0.428391i | −0.976791 | − | 0.214196i | ||||
0.976791 | − | 0.214196i | ||||||||
−0.564729 | − | 1.36338i | −0.0230550 | − | 0.0556596i | |||||
−14.1755 | − | 5.87170i | −0.578233 | − | 0.239512i | 0.0743464 | − | 0.997232i | ||
−0.652579 | + | 0.757721i | ||||||||
−1.12724 | + | 2.72139i | −0.0459428 | + | 0.110916i | |||||
−5.03940 | + | 5.03940i | −0.205220 | + | 0.205220i | |||||
3.24744 | − | 3.24744i | 0.132137 | − | 0.132137i | |||||
−4.27471 | + | 10.3201i | −0.173792 | + | 0.419571i | |||||
−14.6417 | − | 6.06480i | −0.594779 | − | 0.246366i | |||||
8.27458 | + | 19.9766i | 0.335855 | + | 0.810825i | 0.998105 | + | 0.0615418i | ||
−0.662250 | + | 0.749283i | ||||||||
− | 1.21304i | − | 0.0491952i | |||||||
−22.4647 | + | 9.30519i | −0.910316 | + | 0.377065i | |||||
8.80016 | + | 8.80016i | 0.356308 | + | 0.356308i | |||||
32.0752 | 1.29762 | |||||||||
−3.36389 | + | 0.423009i | −0.135977 | + | 0.0170991i | |||||
−18.6071 | −0.751535 | −0.375768 | − | 0.926714i | ||||||
−0.375768 | + | 0.926714i | ||||||||
−10.0679 | − | 10.0679i | −0.406308 | − | 0.406308i | |||||
0.195091 | − | 0.0808095i | 0.00786684 | − | 0.00325855i | |||||
− | 16.7071i | − | 0.673147i | |||||||
2.18286 | + | 5.26989i | 0.0878787 | + | 0.212158i | 0.961709 | − | 0.274074i | ||
−0.873830 | + | 0.486231i | ||||||||
−10.1341 | − | 4.19766i | −0.407651 | − | 0.168855i | |||||
11.1868 | − | 27.0073i | 0.449635 | − | 1.08552i | −0.522823 | − | 0.852441i | ||
0.972459 | − | 0.233075i | ||||||||
−5.15010 | + | 5.15010i | −0.206833 | + | 0.206833i | |||||
22.8153 | − | 22.8153i | 0.915546 | − | 0.915546i | |||||
4.65012 | − | 11.2264i | 0.186453 | − | 0.450137i | |||||
7.34881 | + | 3.04397i | 0.294424 | + | 0.121954i | |||||
−3.09302 | − | 7.46720i | −0.123820 | − | 0.298927i | |||||
− | 1.00000i | − | 0.0400000i | |||||||
−20.1310 | + | 8.33854i | −0.804597 | + | 0.333275i | |||||
−5.96000 | − | 5.96000i | −0.238020 | − | 0.238020i | |||||
15.5482 | 0.620442 | |||||||||
−10.1303 | + | 36.9472i | −0.403920 | + | 1.47318i | |||||
−2.91768 | −0.116243 | |||||||||
30.9574 | + | 30.9574i | 1.23239 | + | 1.23239i | 0.963042 | + | 0.269351i | ||
0.269351 | + | 0.963042i | ||||||||
−9.34587 | + | 3.87118i | −0.371759 | + | 0.153987i | |||||
33.6755i | 1.33848i | |||||||||
3.92314 | + | 9.47130i | 0.155808 | + | 0.376153i | |||||
2.96188 | + | 1.22685i | 0.117539 | + | 0.0486861i | |||||
−5.22495 | + | 12.6142i | −0.207183 | + | 0.500184i | |||||
21.6492 | − | 21.6492i | 0.857773 | − | 0.857773i | |||||
−15.4612 | + | 15.4612i | −0.612115 | + | 0.612115i | |||||
−1.61866 | + | 3.90780i | −0.0640333 | + | 0.154590i | |||||
0.923880 | + | 0.382683i | 0.0365195 | + | 0.0151269i | |||||
−16.6913 | − | 40.2963i | −0.659265 | − | 1.59161i | −0.798941 | − | 0.601410i | ||
0.139676 | − | 0.990197i | ||||||||
23.2143i | 0.916197i | |||||||||
−5.12401 | + | 2.12244i | −0.202071 | + | 0.0837007i | −0.481424 | − | 0.876488i | ||
0.279353 | + | 0.960189i | ||||||||
−14.3521 | − | 14.3521i | −0.565553 | − | 0.565553i | |||||
−1.22508 | −0.0482373 | |||||||||
3.95020 | + | 3.06770i | 0.155419 | + | 0.120697i | |||||
−25.3893 | −0.998155 | −0.499078 | − | 0.866557i | ||||||
−0.499078 | + | 0.866557i | ||||||||
−4.14151 | − | 4.14151i | −0.162694 | − | 0.162694i | |||||
20.5174 | − | 8.49858i | 0.805378 | − | 0.333598i | |||||
− | 5.47699i | − | 0.214825i | |||||||
−14.5943 | − | 35.2338i | −0.571996 | − | 1.38092i | |||||
9.36608 | + | 3.87956i | 0.366804 | + | 0.151935i | |||||
15.0457 | − | 36.3236i | 0.588784 | − | 1.42145i | −0.295882 | − | 0.955225i | ||
0.884666 | − | 0.466226i | ||||||||
6.71024 | − | 6.71024i | 0.262391 | − | 0.262391i | |||||
2.52675 | − | 2.52675i | 0.0987284 | − | 0.0987284i | |||||
−0.0547598 | + | 0.132202i | −0.00213801 | + | 0.00516162i | |||||
−12.2555 | − | 5.07640i | −0.478133 | − | 0.198049i | |||||
−7.95207 | − | 19.1980i | −0.310004 | − | 0.748415i | |||||
39.5179i | 1.53940i | 0.638408 | + | 0.769698i | ||||||
−0.638408 | + | 0.769698i | ||||||||
6.41951 | − | 2.65905i | 0.249879 | − | 0.103503i | |||||
−2.21986 | − | 2.21986i | −0.0863427 | − | 0.0863427i | 0.662616 | − | 0.748959i | ||
−0.748959 | + | 0.662616i | ||||||||
−0.296190 | −0.0115117 | |||||||||
32.1386 | + | 8.81183i | 1.24816 | + | 0.342223i | |||||
−3.40601 | −0.132179 | |||||||||
3.04350 | + | 3.04350i | 0.118022 | + | 0.118022i | |||||
7.05888 | − | 2.92388i | 0.273526 | − | 0.113298i | |||||
26.5637i | 1.02855i | |||||||||
−4.76501 | − | 11.5038i | −0.184364 | − | 0.445093i | |||||
−12.3639 | − | 5.12129i | −0.478016 | − | 0.198001i | |||||
−3.31673 | + | 8.00729i | −0.128136 | + | 0.309349i | |||||
−41.4359 | + | 41.4359i | −1.59962 | + | 1.59962i | |||||
−3.70253 | + | 3.70253i | −0.142828 | + | 0.142828i | |||||
−8.91195 | + | 21.5153i | −0.343530 | + | 0.829355i | 0.653823 | + | 0.756647i | ||
−0.997353 | + | 0.0727079i | ||||||||
−12.9824 | − | 5.37748i | −0.500063 | − | 0.207133i | |||||
−2.15856 | − | 5.21121i | −0.0830829 | − | 0.200580i | |||||
− | 16.9974i | − | 0.653748i | |||||||
−38.1349 | + | 15.7960i | −1.46564 | + | 0.607089i | −0.965861 | − | 0.259062i | ||
−0.499782 | + | 0.866151i | ||||||||
−10.0610 | − | 10.0610i | −0.386391 | − | 0.386391i | |||||
15.4541 | 0.593075 | |||||||||
−3.58262 | + | 2.04079i | −0.137387 | + | 0.0782606i | |||||
23.2392 | 0.890528 | |||||||||
−24.2494 | − | 24.2494i | −0.928559 | − | 0.928559i | |||||
5.77636 | − | 2.39265i | 0.221026 | − | 0.0915521i | −0.269423 | − | 0.963022i | ||
0.490449 | + | 0.871470i | ||||||||
− | 0.997467i | − | 0.0381391i | |||||||
1.26649 | + | 3.05758i | 0.0483901 | + | 0.116824i | |||||
4.62206 | + | 1.91452i | 0.176471 | + | 0.0730968i | |||||
11.3617 | − | 27.4295i | 0.433476 | − | 1.04650i | |||||
0.587013 | − | 0.587013i | 0.0223796 | − | 0.0223796i | |||||
−35.8319 | + | 35.8319i | −1.36509 | + | 1.36509i | |||||
3.23041 | − | 7.79889i | 0.122980 | − | 0.296899i | |||||
−29.6992 | − | 12.3018i | −1.12981 | − | 0.467983i | −0.262094 | − | 0.965042i | ||
−0.867716 | + | 0.497060i | ||||||||
−1.35726 | − | 3.27672i | −0.0515954 | − | 0.124562i | |||||
− | 13.7380i | − | 0.521864i | |||||||
−10.3007 | + | 4.26669i | −0.391010 | + | 0.161961i | |||||
−1.27277 | − | 1.27277i | −0.0482788 | − | 0.0482788i | |||||
6.85286 | 0.259757 | |||||||||
−0.292025 | − | 0.512653i | −0.0110612 | − | 0.0194181i | |||||
−2.51265 | −0.0951051 | |||||||||
−20.1129 | − | 20.1129i | −0.760739 | − | 0.760739i | |||||
−3.27815 | + | 1.35785i | −0.123902 | + | 0.0513221i | |||||
− | 12.7609i | − | 0.481972i | −0.970529 | − | 0.240986i | ||||
0.970529 | − | 0.240986i | ||||||||
−11.8224 | − | 28.5418i | −0.446208 | − | 1.07724i | |||||
−10.4133 | − | 4.31332i | −0.392744 | − | 0.162680i | |||||
−1.80188 | + | 4.35013i | −0.0679109 | + | 0.163952i | |||||
6.11100 | − | 6.11100i | 0.230153 | − | 0.230153i | |||||
7.12929 | − | 7.12929i | 0.268314 | − | 0.268314i | |||||
−14.5824 | + | 35.2051i | −0.548429 | + | 1.32402i | |||||
−6.43037 | − | 2.66354i | −0.241668 | − | 0.100102i | |||||
12.8274 | + | 30.9681i | 0.481744 | + | 1.16303i | 0.958780 | + | 0.284149i | ||
−0.477036 | + | 0.878884i | ||||||||
5.14391i | 0.193047i | |||||||||
−7.68499 | + | 3.18323i | −0.288210 | + | 0.119380i | |||||
−1.58516 | − | 1.58516i | −0.0594063 | − | 0.0594063i | |||||
−41.6627 | −1.56028 | |||||||||
−2.69364 | − | 21.4206i | −0.100807 | − | 0.801645i | |||||
25.7886 | 0.964441 | |||||||||
−9.26485 | − | 9.26485i | −0.346244 | − | 0.346244i | |||||
19.3653 | − | 8.02139i | 0.723212 | − | 0.299564i | |||||
− | 24.6679i | − | 0.920599i | |||||||
−10.9707 | − | 26.4857i | −0.409140 | − | 0.987750i | −0.985365 | − | 0.170459i | ||
0.576225 | − | 0.817291i | ||||||||
0.759695 | + | 0.314676i | 0.0283121 | + | 0.0117273i | |||||
−10.0930 | + | 24.3667i | −0.375883 | + | 0.907463i | |||||
12.3945 | − | 12.3945i | 0.461277 | − | 0.461277i | |||||
−4.77346 | + | 4.77346i | −0.177527 | + | 0.177527i | |||||
−0.699281 | + | 1.68821i | −0.0259886 | + | 0.0627420i | |||||
4.29029 | + | 1.77710i | 0.159337 | + | 0.0659998i | |||||
6.30823 | + | 15.2294i | 0.234120 | + | 0.565216i | |||||
21.0302i | 0.779966i | 0.920822 | + | 0.389983i | ||||||
−0.920822 | + | 0.389983i | ||||||||
−17.9544 | + | 7.43696i | −0.665435 | + | 0.275632i | |||||
−21.0631 | − | 21.0631i | −0.780113 | − | 0.780113i | |||||
−16.1322 | −0.597078 | |||||||||
0.427059 | + | 3.39610i | 0.0157954 | + | 0.125609i | |||||
18.3656 | 0.678813 | |||||||||
−6.38248 | − | 6.38248i | −0.235742 | − | 0.235742i | 0.579342 | − | 0.815084i | ||
−0.815084 | + | 0.579342i | ||||||||
27.5072 | − | 11.3939i | 1.01531 | − | 0.420555i | |||||
− | 8.24926i | − | 0.304279i | |||||||
2.18906 | + | 5.28485i | 0.0806897 | + | 0.194802i | |||||
−37.7027 | − | 15.6170i | −1.38880 | − | 0.575258i | |||||
−0.0450283 | + | 0.108708i | −0.00165751 | + | 0.00400160i | |||||
10.1850 | − | 10.1850i | 0.374662 | − | 0.374662i | −0.494510 | − | 0.869172i | ||
0.869172 | + | 0.494510i | ||||||||
6.57025 | − | 6.57025i | 0.241527 | − | 0.241527i | |||||
−3.75195 | + | 9.05801i | −0.137831 | + | 0.332754i | |||||
30.3299 | + | 12.5631i | 1.11345 | + | 0.461205i | |||||
12.6717 | + | 30.5921i | 0.464879 | + | 1.12232i | 0.966370 | + | 0.257154i | ||
−0.501492 | + | 0.865162i | ||||||||
10.7481i | 0.394043i | |||||||||
3.85044 | − | 1.59490i | 0.141069 | − | 0.0584327i | |||||
14.7106 | + | 14.7106i | 0.538592 | + | 0.538592i | |||||
−2.80072 | −0.102473 | |||||||||
−9.60913 | − | 16.8689i | −0.351344 | − | 0.616789i | |||||
55.8174 | 2.03952 | |||||||||
−1.04348 | − | 1.04348i | −0.0381026 | − | 0.0381026i | |||||
−5.92242 | + | 2.45315i | −0.216112 | + | 0.0895166i | −0.488113 | − | 0.872780i | ||
0.272001 | + | 0.962297i | ||||||||
5.85635i | 0.213559i | |||||||||
−5.08658 | − | 12.2801i | −0.185365 | − | 0.447511i | |||||
23.4979 | + | 9.73315i | 0.855743 | + | 0.354460i | |||||
1.75750 | − | 4.24299i | 0.0639621 | − | 0.154418i | |||||
−14.1521 | + | 14.1521i | −0.514708 | + | 0.514708i | |||||
34.6660 | − | 34.6660i | 1.25996 | − | 1.25996i | 0.308847 | − | 0.951112i | ||
0.951112 | − | 0.308847i | ||||||||
−3.99706 | + | 9.64974i | −0.145180 | + | 0.350495i | |||||
36.7214 | + | 15.2105i | 1.33290 | + | 0.552107i | |||||
−0.464210 | − | 1.12070i | −0.0168387 | − | 0.0406521i | |||||
42.6819i | 1.54722i | 0.633662 | + | 0.773610i | ||||||
−0.633662 | + | 0.773610i | ||||||||
4.37087 | − | 1.81047i | 0.158340 | − | 0.0655865i | |||||
−16.1344 | − | 16.1344i | −0.584103 | − | 0.584103i | |||||
16.8319 | 0.608955 | |||||||||
−2.94595 | + | 1.67811i | −0.106511 | + | 0.0606723i | |||||
−20.1518 | −0.728113 | |||||||||
−18.2662 | − | 18.2662i | −0.659553 | − | 0.659553i | |||||
1.36338 | − | 0.564729i | 0.0491966 | − | 0.0203779i | |||||
14.6429i | 0.528035i | 0.964518 | + | 0.264018i | ||||||
−0.964518 | + | 0.264018i | ||||||||
−6.39351 | − | 15.4353i | −0.230406 | − | 0.556250i | |||||
39.0716 | + | 16.1840i | 1.40713 | + | 0.582853i | |||||
2.23056 | − | 5.38504i | 0.0802795 | − | 0.193812i | |||||
10.5010 | − | 10.5010i | 0.377696 | − | 0.377696i | −0.492575 | − | 0.870270i | ||
0.870270 | + | 0.492575i | ||||||||
0.482693 | − | 0.482693i | 0.0173500 | − | 0.0173500i | |||||
−2.78721 | + | 6.72892i | −0.100120 | + | 0.241710i | |||||
−4.02389 | − | 1.66675i | −0.144449 | − | 0.0598328i | |||||
18.6187 | + | 44.9496i | 0.667944 | + | 1.61256i | |||||
− | 19.6657i | − | 0.705051i | |||||||
0.160366 | − | 0.0664258i | 0.00574571 | − | 0.00237995i | |||||
−5.71515 | − | 5.71515i | −0.204635 | − | 0.204635i | |||||
−24.2203 | −0.866670 | |||||||||
−22.7458 | − | 6.23650i | −0.813390 | − | 0.223017i | |||||
26.1936 | 0.936083 | |||||||||
3.95275 | + | 3.95275i | 0.141170 | + | 0.141170i | |||||
14.3647 | − | 5.95005i | 0.512698 | − | 0.212366i | |||||
− | 5.27324i | − | 0.188090i | |||||||
8.22589 | + | 19.8591i | 0.293221 | + | 0.707899i | 1.00000 | 0.000464022i | |||
−0.706779 | + | 0.707435i | ||||||||
3.25339 | + | 1.34760i | 0.115897 | + | 0.0480061i | |||||
−3.41420 | + | 8.24261i | −0.121549 | + | 0.293445i | |||||
−7.15302 | + | 7.15302i | −0.254493 | + | 0.254493i | |||||
−24.1911 | + | 24.1911i | −0.860135 | + | 0.860135i | |||||
−1.48166 | + | 3.57705i | −0.0526486 | + | 0.127105i | |||||
62.9743 | + | 26.0848i | 2.23628 | + | 0.926298i | |||||
−9.16446 | − | 22.1250i | −0.325235 | − | 0.785186i | |||||
13.6535i | 0.484238i | |||||||||
15.5212 | − | 6.42910i | 0.550135 | − | 0.227874i | |||||
14.8934 | + | 14.8934i | 0.527550 | + | 0.527550i | 0.919841 | − | 0.392291i | ||
−0.392291 | + | 0.919841i | ||||||||
6.35168 | 0.224847 | |||||||||
−19.0709 | − | 14.8103i | −0.674680 | − | 0.523952i | |||||
1.00000 | 0.0353553 | |||||||||
−1.30346 | − | 1.30346i | −0.0460554 | − | 0.0460554i | |||||
−21.2869 | + | 8.81734i | −0.751668 | + | 0.311351i | |||||
− | 75.9590i | − | 2.68053i | |||||||
4.89452 | + | 11.8164i | 0.172617 | + | 0.416733i | |||||
−18.7519 | − | 7.76731i | −0.660919 | − | 0.273762i | |||||
−15.2655 | + | 36.8543i | −0.537706 | + | 1.29814i | |||||
−17.6278 | + | 17.6278i | −0.620529 | + | 0.620529i | |||||
7.59384 | − | 7.59384i | 0.267150 | − | 0.267150i | |||||
−6.98690 | + | 16.8679i | −0.245646 | + | 0.593042i | −0.997825 | − | 0.0659166i | ||
0.752179 | + | 0.658959i | ||||||||
−5.41114 | − | 2.24137i | −0.190128 | − | 0.0787537i | |||||
−5.56638 | − | 13.4384i | −0.195462 | − | 0.471887i | 0.795512 | − | 0.605937i | ||
−0.990975 | + | 0.134050i | ||||||||
− | 16.4773i | − | 0.578239i | |||||||
−31.2628 | + | 12.9495i | −1.09644 | + | 0.454158i | |||||
30.9363 | + | 30.9363i | 1.08432 | + | 1.08432i | |||||
10.1378 | 0.355111 | |||||||||
−1.60888 | + | 5.86793i | −0.0563221 | + | 0.205419i | |||||
−1.00702 | −0.0352311 | |||||||||
9.01479 | + | 9.01479i | 0.315195 | + | 0.315195i | |||||
−14.7637 | + | 6.11532i | −0.515885 | + | 0.213686i | |||||
0.143094i | 0.00499707i | |||||||||
15.6230 | + | 37.7172i | 0.545246 | + | 1.31634i | 0.920979 | + | 0.389613i | ||
−0.375733 | + | 0.926728i | ||||||||
4.51209 | + | 1.86897i | 0.157377 | + | 0.0651878i | |||||
0.697439 | − | 1.68377i | 0.0243112 | − | 0.0586925i | −0.911258 | − | 0.411837i | ||
0.935569 | + | 0.353144i | ||||||||
5.25597 | − | 5.25597i | 0.183100 | − | 0.183100i | |||||
4.91328 | − | 4.91328i | 0.171059 | − | 0.171059i | |||||
−6.40432 | + | 15.4614i | −0.222835 | + | 0.537971i | |||||
42.9008 | + | 17.7701i | 1.49181 | + | 0.617927i | 0.971709 | − | 0.236180i | ||
0.520098 | + | 0.854107i | ||||||||
1.80003 | + | 4.34567i | 0.0625555 | + | 0.151022i | |||||
− | 34.9749i | − | 1.21473i | −0.794424 | − | 0.607364i | ||||
0.794424 | − | 0.607364i | ||||||||
−3.14674 | + | 1.30342i | −0.109225 | + | 0.0452425i | |||||
20.8715 | + | 20.8715i | 0.724025 | + | 0.724025i | |||||
5.47699 | 0.189881 | |||||||||
−22.8682 | + | 2.87568i | −0.792337 | + | 0.0996365i | |||||
−2.65622 | −0.0919773 | |||||||||
−8.80459 | − | 8.80459i | −0.304695 | − | 0.304695i | |||||
5.27687 | − | 2.18575i | 0.182504 | − | 0.0755958i | |||||
41.0822i | 1.42001i | |||||||||
10.4748 | + | 25.2883i | 0.361845 | + | 0.873570i | |||||
39.6860 | + | 16.4385i | 1.37011 | + | 0.567520i | 0.941819 | − | 0.336120i | ||
0.428294 | + | 0.903639i | ||||||||
−2.00380 | + | 4.83759i | −0.0691375 | + | 0.166913i | |||||
5.25756 | − | 5.25756i | 0.181295 | − | 0.181295i | |||||
−23.8163 | + | 23.8163i | −0.820764 | + | 0.820764i | |||||
13.1484 | − | 31.7430i | 0.452854 | − | 1.09329i | |||||
−21.0828 | − | 8.73280i | −0.725701 | − | 0.300595i | |||||
−6.50464 | − | 15.7036i | −0.223766 | − | 0.540220i | |||||
4.81560i | 0.165564i | |||||||||
36.6181 | − | 15.1677i | 1.25821 | − | 0.521169i | |||||
−6.54226 | − | 6.54226i | −0.224662 | − | 0.224662i | |||||
−37.1152 | −1.27379 | |||||||||
−2.52894 | + | 3.25645i | −0.0867419 | + | 0.111695i | |||||
53.1513 | 1.82200 | |||||||||
5.36758 | + | 5.36758i | 0.183890 | + | 0.183890i | |||||
−8.59031 | + | 3.55822i | −0.294127 | + | 0.121831i | −0.524867 | − | 0.851184i | ||
0.230741 | + | 0.973015i | ||||||||
− | 44.1590i | − | 1.51109i | |||||||
−0.381714 | − | 0.921539i | −0.0130543 | − | 0.0315160i | |||||
−14.5335 | − | 6.01999i | −0.496746 | − | 0.205759i | |||||
−11.8527 | + | 28.6150i | −0.404881 | + | 0.977469i | 0.581582 | + | 0.813488i | ||
−0.986463 | + | 0.163982i | ||||||||
26.9100 | − | 26.9100i | 0.918693 | − | 0.918693i | |||||
13.1008 | − | 13.1008i | 0.446994 | − | 0.446994i | −0.447360 | − | 0.894354i | ||
0.894354 | + | 0.447360i | ||||||||
0.317689 | − | 0.766969i | 0.0108331 | − | 0.0261534i | |||||
−0.692232 | − | 0.286732i | −0.0235912 | − | 0.00977179i | |||||
−6.95725 | − | 16.7963i | −0.236965 | − | 0.572084i | |||||
− | 18.5377i | − | 0.631030i | −0.948921 | − | 0.315515i | ||||
0.948921 | − | 0.315515i | ||||||||
5.21121 | − | 2.15856i | 0.177289 | − | 0.0734356i | |||||
−2.50790 | − | 2.50790i | −0.0852710 | − | 0.0852710i | |||||
−8.10392 | −0.275382 | |||||||||
−15.0399 | − | 20.0789i | −0.510781 | − | 0.681914i | |||||
25.8431 | 0.877170 | |||||||||
−33.6803 | − | 33.6803i | −1.14253 | − | 1.14253i | |||||
6.33122 | − | 2.62248i | 0.214648 | − | 0.0889103i | |||||
47.4693i | 1.60843i | |||||||||
2.46089 | + | 5.94112i | 0.0833363 | + | 0.201192i | |||||
−3.30880 | − | 1.37055i | −0.111986 | − | 0.0463860i | |||||
2.65541 | − | 6.41073i | 0.0898207 | − | 0.216846i | |||||
−2.50899 | + | 2.50899i | −0.0848193 | + | 0.0848193i | |||||
−16.8336 | + | 16.8336i | −0.568756 | + | 0.568756i | |||||
16.3998 | − | 39.5926i | 0.553781 | − | 1.33695i | −0.360837 | − | 0.932629i | ||
0.914619 | − | 0.404318i | ||||||||
22.1522 | + | 9.17574i | 0.747600 | + | 0.309666i | |||||
14.4147 | + | 34.8003i | 0.486197 | + | 1.17378i | |||||
4.70854i | 0.158725i | |||||||||
37.7646 | − | 15.6426i | 1.27232 | − | 0.527014i | 0.358653 | − | 0.933471i | ||
0.913670 | + | 0.406457i | ||||||||
3.25030 | + | 3.25030i | 0.109443 | + | 0.109443i | |||||
52.3174 | 1.76062 | 0.880310 | − | 0.474398i | ||||||
0.880310 | + | 0.474398i | ||||||||
−13.8510 | + | 17.8356i | −0.465859 | + | 0.599875i | |||||
−6.96018 | −0.233964 | |||||||||
0.172587 | + | 0.172587i | 0.00579819 | + | 0.00579819i | |||||
−13.9607 | + | 5.78272i | −0.468755 | + | 0.194165i | −0.604542 | − | 0.796573i | ||
0.135787 | + | 0.990738i | ||||||||
− | 13.7119i | − | 0.460141i | |||||||
−4.35317 | − | 10.5095i | −0.146000 | − | 0.352476i | |||||
−2.07111 | − | 0.857882i | −0.0694238 | − | 0.0287563i | |||||
10.5536 | − | 25.4786i | 0.353558 | − | 0.853565i | |||||
6.41246 | − | 6.41246i | 0.214705 | − | 0.214705i | |||||
5.02327 | − | 5.02327i | 0.168097 | − | 0.168097i | |||||
2.35361 | − | 5.68212i | 0.0787165 | − | 0.190038i | |||||
−12.1051 | − | 5.01410i | −0.404629 | − | 0.167603i | |||||
−1.35785 | − | 3.27815i | −0.0453627 | − | 0.109515i | |||||
− | 46.2338i | − | 1.54370i | |||||||
−0.0761574 | + | 0.0315454i | −0.00254140 | + | 0.00105268i | |||||
−23.9159 | − | 23.9159i | −0.797640 | − | 0.797640i | |||||
0.822287 | 0.0274096 | |||||||||
37.8495 | − | 4.75958i | 1.26095 | − | 0.158565i | |||||
−0.673765 | −0.0224339 | |||||||||
3.07370 | + | 3.07370i | 0.102286 | + | 0.102286i | |||||
8.90782 | − | 3.68974i | 0.296270 | − | 0.122719i | |||||
1.82731i | 0.0607418i | |||||||||
−2.59356 | − | 6.26141i | −0.0861653 | − | 0.208022i | |||||
−23.1561 | − | 9.59155i | −0.768884 | − | 0.318482i | −0.0364638 | − | 0.999335i | ||
−0.732420 | + | 0.680853i | ||||||||
−6.02643 | + | 14.5491i | −0.199994 | + | 0.482829i | |||||
6.24432 | − | 6.24432i | 0.207111 | − | 0.207111i | |||||
−13.7417 | + | 13.7417i | −0.455533 | + | 0.455533i | |||||
−1.10387 | + | 2.66499i | −0.0365730 | + | 0.0882950i | −0.941111 | − | 0.338099i | ||
0.904538 | + | 0.426394i | ||||||||
−1.65383 | − | 0.685038i | −0.0547637 | − | 0.0226839i | |||||
−6.13723 | − | 14.8166i | −0.203113 | − | 0.490357i | |||||
24.3896i | 0.806737i | |||||||||
16.9676 | − | 7.02822i | 0.560933 | − | 0.232346i | |||||
14.2262 | + | 14.2262i | 0.470046 | + | 0.470046i | |||||
−12.6792 | −0.418703 | |||||||||
−6.14961 | + | 22.4289i | −0.202967 | + | 0.740265i | |||||
−48.0746 | −1.58584 | −0.792918 | − | 0.609328i | ||||||
−0.792918 | + | 0.609328i | ||||||||
4.04485 | + | 4.04485i | 0.133355 | + | 0.133355i | |||||
−19.4120 | + | 8.04071i | −0.639647 | + | 0.264950i | |||||
29.1100i | 0.958687i | |||||||||
10.7814 | + | 26.0286i | 0.354874 | + | 0.856741i | |||||
−22.7780 | − | 9.43496i | −0.749341 | − | 0.310387i | |||||
3.55579 | − | 8.58444i | 0.116914 | − | 0.282255i | |||||
−19.7821 | + | 19.7821i | −0.650081 | + | 0.650081i | |||||
4.32191 | − | 4.32191i | 0.141950 | − | 0.141950i | |||||
−1.77710 | + | 4.29029i | −0.0583361 | + | 0.140836i | |||||
25.3430 | + | 10.4974i | 0.831478 | + | 0.344409i | 0.757487 | − | 0.652850i | ||
0.0739901 | + | 0.997259i | ||||||||
4.11311 | + | 9.92992i | 0.134874 | + | 0.325615i | |||||
− | 6.78094i | − | 0.222236i | |||||||
17.8076 | − | 7.37613i | 0.583306 | − | 0.241613i | |||||
−12.6797 | − | 12.6797i | −0.415116 | − | 0.415116i | |||||
31.2786 | 1.02347 | |||||||||
−15.3331 | − | 11.9076i | −0.501447 | − | 0.389420i | |||||
4.50366 | 0.147207 | |||||||||
−10.3762 | − | 10.3762i | −0.338975 | − | 0.338975i | 0.517007 | − | 0.855981i | ||
−0.855981 | + | 0.517007i | ||||||||
28.4118 | − | 11.7686i | 0.927679 | − | 0.384257i | |||||
32.1552i | 1.04934i | |||||||||
2.24113 | + | 5.41056i | 0.0730975 | + | 0.176473i | |||||
22.8397 | + | 9.46050i | 0.744552 | + | 0.308404i | 0.722517 | − | 0.691354i | ||
0.0220356 | + | 0.999757i | ||||||||
8.78053 | − | 21.1981i | 0.286085 | − | 0.690671i | |||||
−0.578795 | + | 0.578795i | −0.0188482 | + | 0.0188482i | |||||
3.33507 | − | 3.33507i | 0.108547 | − | 0.108547i | |||||
−7.65908 | + | 18.4907i | −0.249150 | + | 0.601501i | |||||
3.61131 | + | 1.49585i | 0.117414 | + | 0.0486343i | |||||
−2.49335 | − | 6.01947i | −0.0810228 | − | 0.195606i | 0.878177 | − | 0.478336i | ||
−0.959200 | + | 0.282730i | ||||||||
14.9281i | 0.484842i | |||||||||
−81.6301 | + | 33.8123i | −2.64982 | + | 1.09759i | |||||
−0.857748 | − | 0.857748i | −0.0278290 | − | 0.0278290i | |||||
15.1285 | 0.490574 | |||||||||
14.1091 | + | 3.86845i | 0.457277 | + | 0.125377i | |||||
13.6944 | 0.443607 | 0.221803 | − | 0.975091i | ||||||
0.221803 | + | 0.975091i | ||||||||
−5.37961 | − | 5.37961i | −0.174171 | − | 0.174171i | |||||
15.5506 | − | 6.44127i | 0.503206 | − | 0.208435i | |||||
14.2040i | 0.459389i | |||||||||
12.3480 | + | 29.8108i | 0.399155 | + | 0.963646i | |||||
−11.1564 | − | 4.62112i | −0.360446 | − | 0.149302i | |||||
4.49382 | − | 10.8490i | 0.145113 | − | 0.350334i | |||||
1.04348 | − | 1.04348i | 0.0336783 | − | 0.0336783i | |||||
15.5896 | − | 15.5896i | 0.502889 | − | 0.502889i | |||||
19.4751 | − | 47.0169i | 0.627901 | − | 1.51589i | |||||
−11.9507 | − | 4.95016i | −0.385107 | − | 0.159517i | |||||
−1.75060 | − | 4.22633i | −0.0563832 | − | 0.136121i | |||||
− | 5.82873i | − | 0.187633i | |||||||
−27.6724 | + | 11.4623i | −0.890344 | + | 0.368793i | |||||
11.5376 | + | 11.5376i | 0.371026 | + | 0.371026i | 0.867851 | − | 0.496825i | ||
−0.496825 | + | 0.867851i | ||||||||
−11.1704 | −0.359029 | |||||||||
6.41322 | − | 3.65319i | 0.206022 | − | 0.117357i | |||||
−4.35543 | −0.139844 | |||||||||
−19.0136 | − | 19.0136i | −0.610176 | − | 0.610176i | 0.332816 | − | 0.942992i | ||
−0.942992 | + | 0.332816i | ||||||||
7.64838 | − | 3.16806i | 0.245322 | − | 0.101616i | |||||
6.38671i | 0.204748i | |||||||||
1.91937 | + | 4.63377i | 0.0615005 | + | 0.148475i | |||||
−7.46720 | − | 3.09302i | −0.239142 | − | 0.0990558i | |||||
−4.76261 | + | 11.4980i | −0.152448 | + | 0.368041i | |||||
−14.1423 | + | 14.1423i | −0.452451 | + | 0.452451i | −0.896167 | − | 0.443716i | ||
0.443716 | + | 0.896167i | ||||||||
10.5786 | − | 10.5786i | 0.338266 | − | 0.338266i | |||||
4.03937 | − | 9.75191i | 0.129099 | − | 0.311672i | |||||
5.16452 | + | 2.13922i | 0.164975 | + | 0.0683347i | |||||
2.02356 | + | 4.88531i | 0.0646073 | + | 0.155976i | |||||
− | 26.4441i | − | 0.843865i | |||||||
−26.6406 | + | 11.0349i | −0.849704 | + | 0.351959i | −0.764672 | − | 0.644419i | ||
−0.0850316 | + | 0.996378i | ||||||||
0.149316 | + | 0.149316i | 0.00476003 | + | 0.00476003i | |||||
3.52144 | 0.112202 | |||||||||
−9.47696 | − | 16.6369i | −0.301808 | − | 0.529827i | |||||
−30.6648 | −0.976072 | |||||||||
−4.69788 | − | 4.69788i | −0.149460 | − | 0.149460i | |||||
4.38728 | − | 1.81727i | 0.139507 | − | 0.0577858i | |||||
3.87177i | 0.123053i | |||||||||
−10.2929 | − | 24.8494i | −0.326966 | − | 0.789366i | −0.998815 | − | 0.0486775i | ||
0.671848 | − | 0.740689i | ||||||||
−6.72892 | − | 2.78721i | −0.213644 | − | 0.0884941i | |||||
−0.167267 | + | 0.403818i | −0.00530805 | + | 0.0128148i | |||||
12.9060 | − | 12.9060i | 0.409353 | − | 0.409353i | |||||
11.8794 | − | 11.8794i | 0.376603 | − | 0.376603i | |||||
−1.92347 | + | 4.64367i | −0.0609476 | + | 0.147140i | |||||
28.1434 | + | 11.6574i | 0.891310 | + | 0.369193i | 0.780872 | − | 0.624690i | ||
0.110437 | + | 0.993883i | ||||||||
−11.4569 | − | 27.6595i | −0.362663 | − | 0.875545i | |||||
− | 52.4108i | − | 1.65820i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 170.2.k.b.121.3 | yes | 16 | |
5.2 | odd | 4 | 850.2.o.g.699.2 | 16 | |||
5.3 | odd | 4 | 850.2.o.j.699.3 | 16 | |||
5.4 | even | 2 | 850.2.l.e.801.2 | 16 | |||
17.3 | odd | 16 | 2890.2.a.bi.1.7 | 8 | |||
17.5 | odd | 16 | 2890.2.b.r.2311.12 | 16 | |||
17.9 | even | 8 | inner | 170.2.k.b.111.3 | ✓ | 16 | |
17.12 | odd | 16 | 2890.2.b.r.2311.5 | 16 | |||
17.14 | odd | 16 | 2890.2.a.bj.1.2 | 8 | |||
85.9 | even | 8 | 850.2.l.e.451.2 | 16 | |||
85.43 | odd | 8 | 850.2.o.g.349.2 | 16 | |||
85.77 | odd | 8 | 850.2.o.j.349.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.k.b.111.3 | ✓ | 16 | 17.9 | even | 8 | inner | |
170.2.k.b.121.3 | yes | 16 | 1.1 | even | 1 | trivial | |
850.2.l.e.451.2 | 16 | 85.9 | even | 8 | |||
850.2.l.e.801.2 | 16 | 5.4 | even | 2 | |||
850.2.o.g.349.2 | 16 | 85.43 | odd | 8 | |||
850.2.o.g.699.2 | 16 | 5.2 | odd | 4 | |||
850.2.o.j.349.3 | 16 | 85.77 | odd | 8 | |||
850.2.o.j.699.3 | 16 | 5.3 | odd | 4 | |||
2890.2.a.bi.1.7 | 8 | 17.3 | odd | 16 | |||
2890.2.a.bj.1.2 | 8 | 17.14 | odd | 16 | |||
2890.2.b.r.2311.5 | 16 | 17.12 | odd | 16 | |||
2890.2.b.r.2311.12 | 16 | 17.5 | odd | 16 |