Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1785,2,Mod(1429,1785)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1785, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1785.1429");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1785.g (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: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 1429.8 | ||
Character | 1785.1429 | ||
Dual form | 1785.2.g.f.1429.21 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
− | 1.69985i | − | 1.20198i | −0.799258 | − | 0.600988i | ||||
0.799258 | − | 0.600988i | ||||||||
− | 1.00000i | − | 0.577350i | |||||||
−0.889490 | −0.444745 | |||||||||
1.47723 | − | 1.67863i | 0.660638 | − | 0.750705i | |||||
−1.69985 | −0.693961 | |||||||||
− | 1.00000i | − | 0.377964i | |||||||
− | 1.88770i | − | 0.667403i | |||||||
−1.00000 | −0.333333 | |||||||||
−2.85341 | − | 2.51107i | −0.902328 | − | 0.794071i | |||||
−1.31823 | −0.397461 | −0.198731 | − | 0.980054i | ||||||
−0.198731 | + | 0.980054i | ||||||||
0.889490i | 0.256774i | |||||||||
− | 4.26284i | − | 1.18230i | −0.806562 | − | 0.591149i | ||||
0.806562 | − | 0.591149i | ||||||||
−1.69985 | −0.454304 | |||||||||
−1.67863 | − | 1.47723i | −0.433419 | − | 0.381420i | |||||
−4.98779 | −1.24695 | |||||||||
− | 1.00000i | − | 0.242536i | |||||||
1.69985i | 0.400659i | |||||||||
5.21905 | 1.19733 | 0.598666 | − | 0.800999i | ||||||
0.598666 | + | 0.800999i | ||||||||
−1.31398 | + | 1.49312i | −0.293816 | + | 0.333872i | |||||
−1.00000 | −0.218218 | |||||||||
2.24079i | 0.477739i | |||||||||
2.71209i | 0.565509i | 0.959192 | + | 0.282754i | ||||||
−0.959192 | + | 0.282754i | ||||||||
−1.88770 | −0.385325 | |||||||||
−0.635573 | − | 4.95944i | −0.127115 | − | 0.991888i | |||||
−7.24619 | −1.42109 | |||||||||
1.00000i | 0.192450i | |||||||||
0.889490i | 0.168098i | |||||||||
0.948665 | 0.176163 | 0.0880814 | − | 0.996113i | ||||||
0.0880814 | + | 0.996113i | ||||||||
−2.51107 | + | 2.85341i | −0.458457 | + | 0.520960i | |||||
−2.19047 | −0.393420 | −0.196710 | − | 0.980462i | ||||||
−0.196710 | + | 0.980462i | ||||||||
4.70309i | 0.831397i | |||||||||
1.31823i | 0.229474i | |||||||||
−1.69985 | −0.291522 | |||||||||
−1.67863 | − | 1.47723i | −0.283740 | − | 0.249698i | |||||
0.889490 | 0.148248 | |||||||||
3.64278i | 0.598870i | 0.954117 | + | 0.299435i | ||||||
−0.954117 | + | 0.299435i | ||||||||
− | 8.87160i | − | 1.43916i | |||||||
−4.26284 | −0.682601 | |||||||||
−3.16874 | − | 2.78857i | −0.501022 | − | 0.440912i | |||||
10.0648 | 1.57185 | 0.785925 | − | 0.618321i | ||||||
0.785925 | + | 0.618321i | ||||||||
1.69985i | 0.262293i | |||||||||
− | 1.43751i | − | 0.219218i | −0.993975 | − | 0.109609i | ||||
0.993975 | − | 0.109609i | ||||||||
1.17255 | 0.176769 | |||||||||
−1.47723 | + | 1.67863i | −0.220213 | + | 0.250235i | |||||
4.61014 | 0.679728 | |||||||||
3.21978i | 0.469654i | 0.972037 | + | 0.234827i | ||||||
−0.972037 | + | 0.234827i | ||||||||
4.98779i | 0.719925i | |||||||||
−1.00000 | −0.142857 | |||||||||
−8.43031 | + | 1.08038i | −1.19223 | + | 0.152789i | |||||
−1.00000 | −0.140028 | |||||||||
3.79175i | 0.525822i | |||||||||
14.1176i | 1.93920i | 0.244701 | + | 0.969599i | ||||||
−0.244701 | + | 0.969599i | ||||||||
1.69985 | 0.231320 | |||||||||
−1.94733 | + | 2.21282i | −0.262578 | + | 0.298376i | |||||
−1.88770 | −0.252255 | |||||||||
− | 5.21905i | − | 0.691280i | |||||||
− | 1.61259i | − | 0.211743i | |||||||
−14.0099 | −1.82394 | −0.911968 | − | 0.410262i | ||||||
−0.911968 | + | 0.410262i | ||||||||
1.49312 | + | 1.31398i | 0.192761 | + | 0.169635i | |||||
8.36086 | 1.07050 | 0.535249 | − | 0.844694i | ||||||
0.535249 | + | 0.844694i | ||||||||
3.72347i | 0.472881i | |||||||||
1.00000i | 0.125988i | |||||||||
−1.98102 | −0.247628 | |||||||||
−7.15571 | − | 6.29720i | −0.887557 | − | 0.781072i | |||||
2.24079 | 0.275823 | |||||||||
− | 13.6284i | − | 1.66497i | −0.554049 | − | 0.832484i | ||||
0.554049 | − | 0.832484i | ||||||||
0.889490i | 0.107867i | |||||||||
2.71209 | 0.326497 | |||||||||
−2.51107 | + | 2.85341i | −0.300131 | + | 0.341048i | |||||
−6.66687 | −0.791212 | −0.395606 | − | 0.918420i | ||||||
−0.395606 | + | 0.918420i | ||||||||
1.88770i | 0.222468i | |||||||||
− | 13.0816i | − | 1.53109i | −0.643383 | − | 0.765544i | ||||
0.643383 | − | 0.765544i | ||||||||
6.19219 | 0.719827 | |||||||||
−4.95944 | + | 0.635573i | −0.572667 | + | 0.0733896i | |||||
−4.64229 | −0.532508 | |||||||||
1.31823i | 0.150226i | |||||||||
7.24619i | 0.820469i | |||||||||
9.12564 | 1.02672 | 0.513358 | − | 0.858175i | ||||||
0.513358 | + | 0.858175i | ||||||||
−7.36812 | + | 8.37263i | −0.823781 | + | 0.936089i | |||||
1.00000 | 0.111111 | |||||||||
− | 17.1086i | − | 1.88933i | |||||||
6.08519i | 0.667936i | 0.942584 | + | 0.333968i | ||||||
−0.942584 | + | 0.333968i | ||||||||
0.889490 | 0.0970514 | |||||||||
−1.67863 | − | 1.47723i | −0.182073 | − | 0.160228i | |||||
−2.44355 | −0.263494 | |||||||||
− | 0.948665i | − | 0.101708i | |||||||
2.48842i | 0.265267i | |||||||||
−0.0400448 | −0.00424474 | −0.00212237 | − | 0.999998i | ||||||
−0.00212237 | + | 0.999998i | ||||||||
2.85341 | + | 2.51107i | 0.300776 | + | 0.264690i | |||||
−4.26284 | −0.446867 | |||||||||
− | 2.41237i | − | 0.251507i | |||||||
2.19047i | 0.227141i | |||||||||
5.47315 | 0.564512 | |||||||||
7.70974 | − | 8.76083i | 0.791003 | − | 0.898842i | |||||
4.70309 | 0.480007 | |||||||||
7.33549i | 0.744806i | 0.928071 | + | 0.372403i | ||||||
−0.928071 | + | 0.372403i | ||||||||
1.69985i | 0.171711i | |||||||||
1.31823 | 0.132487 | |||||||||
0.565336 | + | 4.41137i | 0.0565336 | + | 0.441137i | |||||
−2.66094 | −0.264774 | −0.132387 | − | 0.991198i | ||||||
−0.132387 | + | 0.991198i | ||||||||
1.69985i | 0.168310i | |||||||||
8.62526i | 0.849872i | 0.905223 | + | 0.424936i | ||||||
−0.905223 | + | 0.424936i | ||||||||
−8.04696 | −0.789069 | |||||||||
−1.47723 | + | 1.67863i | −0.144163 | + | 0.163817i | |||||
23.9978 | 2.33087 | |||||||||
− | 19.2943i | − | 1.86525i | −0.360852 | − | 0.932623i | ||||
0.360852 | − | 0.932623i | ||||||||
− | 0.889490i | − | 0.0855913i | |||||||
−4.03341 | −0.386331 | −0.193166 | − | 0.981166i | ||||||
−0.193166 | + | 0.981166i | ||||||||
3.76146 | + | 3.31017i | 0.358641 | + | 0.315612i | |||||
3.64278 | 0.345758 | |||||||||
4.98779i | 0.471302i | |||||||||
18.5353i | 1.74366i | 0.489810 | + | 0.871829i | ||||||
−0.489810 | + | 0.871829i | ||||||||
−8.87160 | −0.830902 | |||||||||
4.55258 | + | 4.00638i | 0.424530 | + | 0.373597i | |||||
−0.843829 | −0.0783475 | |||||||||
4.26284i | 0.394100i | |||||||||
23.8148i | 2.19233i | |||||||||
−1.00000 | −0.0916698 | |||||||||
−2.78857 | + | 3.16874i | −0.254560 | + | 0.289265i | |||||
−9.26227 | −0.842024 | |||||||||
− | 14.2122i | − | 1.28671i | |||||||
− | 10.0648i | − | 0.907509i | |||||||
1.94840 | 0.174972 | |||||||||
−9.26394 | − | 6.25935i | −0.828592 | − | 0.559854i | |||||
1.69985 | 0.151435 | |||||||||
− | 7.03516i | − | 0.624269i | −0.950038 | − | 0.312135i | ||||
0.950038 | − | 0.312135i | ||||||||
12.7736i | 1.12904i | |||||||||
−1.43751 | −0.126565 | |||||||||
−10.7043 | + | 12.1636i | −0.938829 | + | 1.06682i | |||||
−2.49412 | −0.217913 | −0.108956 | − | 0.994047i | ||||||
−0.108956 | + | 0.994047i | ||||||||
− | 1.17255i | − | 0.102058i | |||||||
− | 5.21905i | − | 0.452549i | |||||||
−23.1662 | −2.00125 | |||||||||
1.67863 | + | 1.47723i | 0.144473 | + | 0.127140i | |||||
−1.88770 | −0.161869 | |||||||||
4.36841i | 0.373218i | 0.982434 | + | 0.186609i | ||||||
−0.982434 | + | 0.186609i | ||||||||
− | 4.61014i | − | 0.392441i | |||||||
11.3585 | 0.963413 | 0.481707 | − | 0.876333i | ||||||
0.481707 | + | 0.876333i | ||||||||
1.49312 | + | 1.31398i | 0.126192 | + | 0.111052i | |||||
3.21978 | 0.271155 | |||||||||
11.3327i | 0.951018i | |||||||||
5.61940i | 0.469918i | |||||||||
4.98779 | 0.415649 | |||||||||
1.40140 | − | 1.59245i | 0.116380 | − | 0.132246i | |||||
−22.2368 | −1.84033 | |||||||||
1.00000i | 0.0824786i | |||||||||
− | 3.24022i | − | 0.266345i | |||||||
15.8707 | 1.30018 | 0.650090 | − | 0.759858i | ||||||
0.650090 | + | 0.759858i | ||||||||
1.08038 | + | 8.43031i | 0.0882125 | + | 0.688332i | |||||
10.9078 | 0.887667 | 0.443833 | − | 0.896109i | ||||||
0.443833 | + | 0.896109i | ||||||||
− | 9.85200i | − | 0.799103i | |||||||
1.00000i | 0.0808452i | |||||||||
2.24079 | 0.180568 | |||||||||
−3.23583 | + | 3.67698i | −0.259908 | + | 0.295342i | |||||
3.79175 | 0.303583 | |||||||||
5.06290i | 0.404063i | 0.979379 | + | 0.202032i | ||||||
−0.979379 | + | 0.202032i | ||||||||
− | 15.5122i | − | 1.23409i | |||||||
14.1176 | 1.11960 | |||||||||
7.89473 | + | 6.94756i | 0.624134 | + | 0.549253i | |||||
2.71209 | 0.213742 | |||||||||
− | 1.69985i | − | 0.133553i | |||||||
13.9637i | 1.09372i | 0.837224 | + | 0.546860i | ||||||
−0.837224 | + | 0.546860i | ||||||||
−8.95250 | −0.699073 | |||||||||
2.21282 | + | 1.94733i | 0.172267 | + | 0.151600i | |||||
10.3439 | 0.802843 | |||||||||
20.0975i | 1.55519i | 0.628766 | + | 0.777595i | ||||||
−0.628766 | + | 0.777595i | ||||||||
1.88770i | 0.145639i | |||||||||
−5.17180 | −0.397830 | |||||||||
−2.51107 | + | 2.85341i | −0.192590 | + | 0.218847i | |||||
−5.21905 | −0.399111 | |||||||||
1.27865i | 0.0974960i | |||||||||
− | 9.66834i | − | 0.735071i | −0.930010 | − | 0.367535i | ||||
0.930010 | − | 0.367535i | ||||||||
−1.61259 | −0.122250 | |||||||||
−4.95944 | + | 0.635573i | −0.374898 | + | 0.0480448i | |||||
6.57505 | 0.495613 | |||||||||
14.0099i | 1.05305i | |||||||||
0.0680701i | 0.00510207i | |||||||||
−2.03325 | −0.151972 | −0.0759859 | − | 0.997109i | ||||||
−0.0759859 | + | 0.997109i | ||||||||
1.31398 | − | 1.49312i | 0.0979385 | − | 0.111291i | |||||
22.0739 | 1.64074 | 0.820369 | − | 0.571835i | ||||||
0.820369 | + | 0.571835i | ||||||||
7.24619i | 0.537123i | |||||||||
− | 8.36086i | − | 0.618052i | |||||||
5.11960 | 0.377422 | |||||||||
6.11487 | + | 5.38124i | 0.449574 | + | 0.395636i | |||||
3.72347 | 0.273018 | |||||||||
1.31823i | 0.0963985i | |||||||||
− | 2.86397i | − | 0.208876i | |||||||
1.00000 | 0.0727393 | |||||||||
−14.8921 | − | 13.1054i | −1.08039 | − | 0.950766i | |||||
18.4256 | 1.33323 | 0.666614 | − | 0.745403i | ||||||
0.666614 | + | 0.745403i | ||||||||
1.98102i | 0.142968i | |||||||||
− | 20.9313i | − | 1.50666i | −0.657640 | − | 0.753332i | ||||
0.657640 | − | 0.753332i | ||||||||
12.4692 | 0.895239 | |||||||||
−6.29720 | + | 7.15571i | −0.450952 | + | 0.512431i | |||||
0.889490 | 0.0635350 | |||||||||
− | 16.7970i | − | 1.19674i | −0.801221 | − | 0.598368i | ||||
0.801221 | − | 0.598368i | ||||||||
− | 2.24079i | − | 0.159246i | |||||||
−17.0325 | −1.20740 | −0.603700 | − | 0.797211i | ||||||
−0.603700 | + | 0.797211i | ||||||||
−9.36193 | + | 1.19977i | −0.661989 | + | 0.0848366i | |||||
−13.6284 | −0.961270 | |||||||||
4.52320i | 0.318252i | |||||||||
− | 0.948665i | − | 0.0665832i | |||||||
0.889490 | 0.0622768 | |||||||||
14.8680 | − | 16.8950i | 1.03842 | − | 1.18000i | |||||
14.6616 | 1.02152 | |||||||||
− | 2.71209i | − | 0.188503i | |||||||
21.2621i | 1.47426i | |||||||||
−6.87991 | −0.475893 | |||||||||
2.85341 | + | 2.51107i | 0.196904 | + | 0.173280i | |||||
−10.1723 | −0.700293 | −0.350147 | − | 0.936695i | ||||||
−0.350147 | + | 0.936695i | ||||||||
− | 12.5574i | − | 0.862449i | |||||||
6.66687i | 0.456807i | |||||||||
−32.7974 | −2.24198 | |||||||||
−2.41304 | − | 2.12353i | −0.164568 | − | 0.144824i | |||||
1.88770 | 0.128442 | |||||||||
2.19047i | 0.148699i | |||||||||
6.85620i | 0.464361i | |||||||||
−13.0816 | −0.883974 | |||||||||
1.73213 | − | 1.96828i | 0.116780 | − | 0.132701i | |||||
−4.26284 | −0.286750 | |||||||||
− | 6.19219i | − | 0.415592i | |||||||
2.54258i | 0.170264i | 0.996370 | + | 0.0851320i | ||||||
−0.996370 | + | 0.0851320i | ||||||||
4.70309 | 0.314239 | |||||||||
0.635573 | + | 4.95944i | 0.0423715 | + | 0.330629i | |||||
31.5073 | 2.09583 | |||||||||
− | 10.5749i | − | 0.701883i | −0.936397 | − | 0.350942i | ||||
0.936397 | − | 0.350942i | ||||||||
4.64229i | 0.307443i | |||||||||
16.7374 | 1.10604 | 0.553020 | − | 0.833168i | ||||||
0.553020 | + | 0.833168i | ||||||||
6.81024 | − | 7.73870i | 0.449054 | − | 0.510275i | |||||
1.31823 | 0.0867332 | |||||||||
− | 1.79080i | − | 0.117571i | |||||||
− | 5.57246i | − | 0.365064i | −0.983200 | − | 0.182532i | ||||
0.983200 | − | 0.182532i | ||||||||
7.24619 | 0.473698 | |||||||||
5.40481 | + | 4.75637i | 0.352571 | + | 0.310271i | |||||
12.4617 | 0.811187 | |||||||||
− | 9.12564i | − | 0.592774i | |||||||
1.69985i | 0.110185i | |||||||||
−12.4766 | −0.807041 | −0.403521 | − | 0.914971i | ||||||
−0.403521 | + | 0.914971i | ||||||||
8.37263 | + | 7.36812i | 0.540451 | + | 0.475610i | |||||
10.1786 | 0.655659 | 0.327829 | − | 0.944737i | ||||||
0.327829 | + | 0.944737i | ||||||||
15.7445i | 1.01209i | |||||||||
− | 1.00000i | − | 0.0641500i | |||||||
−7.43690 | −0.476099 | |||||||||
−1.47723 | + | 1.67863i | −0.0943769 | + | 0.107244i | |||||
−17.1086 | −1.09080 | |||||||||
− | 22.2480i | − | 1.41560i | |||||||
4.13495i | 0.262569i | |||||||||
6.08519 | 0.385633 | |||||||||
−10.6400 | + | 15.7473i | −0.672930 | + | 0.995947i | |||||
−5.67410 | −0.358146 | −0.179073 | − | 0.983836i | ||||||
−0.179073 | + | 0.983836i | ||||||||
− | 0.889490i | − | 0.0560326i | |||||||
− | 3.57515i | − | 0.224768i | |||||||
−11.9587 | −0.750356 | |||||||||
−1.47723 | + | 1.67863i | −0.0925078 | + | 0.105120i | |||||
17.7512 | 1.10945 | |||||||||
− | 18.9299i | − | 1.18082i | −0.807105 | − | 0.590408i | ||||
0.807105 | − | 0.590408i | ||||||||
2.44355i | 0.152129i | |||||||||
3.64278 | 0.226352 | |||||||||
6.36494 | + | 5.60130i | 0.394737 | + | 0.347378i | |||||
−0.948665 | −0.0587209 | |||||||||
4.23963i | 0.261926i | |||||||||
4.50632i | 0.277872i | 0.990301 | + | 0.138936i | ||||||
−0.990301 | + | 0.138936i | ||||||||
2.48842 | 0.153152 | |||||||||
23.6981 | + | 20.8549i | 1.45576 | + | 1.28111i | |||||
−8.87160 | −0.543953 | |||||||||
0.0400448i | 0.00245070i | |||||||||
12.1223i | 0.740487i | |||||||||
6.65868 | 0.405987 | 0.202993 | − | 0.979180i | ||||||
0.202993 | + | 0.979180i | ||||||||
2.51107 | − | 2.85341i | 0.152819 | − | 0.173653i | |||||
6.91612 | 0.420124 | 0.210062 | − | 0.977688i | ||||||
0.210062 | + | 0.977688i | ||||||||
4.98779i | 0.302429i | |||||||||
4.26284i | 0.257999i | |||||||||
7.42564 | 0.448599 | |||||||||
0.837831 | + | 6.53768i | 0.0505231 | + | 0.394237i | |||||
−2.41237 | −0.145208 | |||||||||
− | 8.39750i | − | 0.504557i | −0.967655 | − | 0.252278i | ||||
0.967655 | − | 0.252278i | ||||||||
− | 19.3077i | − | 1.15800i | |||||||
2.19047 | 0.131140 | |||||||||
−2.78857 | + | 3.16874i | −0.166649 | + | 0.189369i | |||||
5.79215 | 0.345531 | 0.172765 | − | 0.984963i | ||||||
0.172765 | + | 0.984963i | ||||||||
− | 5.47315i | − | 0.325921i | |||||||
25.7255i | 1.52922i | 0.644493 | + | 0.764610i | ||||||
−0.644493 | + | 0.764610i | ||||||||
5.93012 | 0.351888 | |||||||||
−8.76083 | − | 7.70974i | −0.518947 | − | 0.456686i | |||||
9.55214 | 0.564830 | |||||||||
− | 10.0648i | − | 0.594104i | |||||||
− | 4.70309i | − | 0.277132i | |||||||
−1.00000 | −0.0588235 | |||||||||
−2.70693 | − | 2.38217i | −0.158957 | − | 0.139886i | |||||
7.33549 | 0.430014 | |||||||||
11.6360i | 0.680944i | |||||||||
− | 3.51413i | − | 0.205298i | −0.994718 | − | 0.102649i | ||||
0.994718 | − | 0.102649i | ||||||||
1.69985 | 0.0991373 | |||||||||
−20.6959 | + | 23.5174i | −1.20496 | + | 1.36924i | |||||
6.87648 | 0.399687 | |||||||||
− | 1.31823i | − | 0.0764915i | |||||||
− | 26.9778i | − | 1.56278i | |||||||
11.5612 | 0.668600 | |||||||||
4.41137 | − | 0.565336i | 0.254691 | − | 0.0326397i | |||||
−1.43751 | −0.0828565 | |||||||||
− | 18.5417i | − | 1.06695i | |||||||
2.66094i | 0.152867i | |||||||||
−26.0315 | −1.49301 | |||||||||
12.3509 | − | 14.0348i | 0.707212 | − | 0.803628i | |||||
1.69985 | 0.0971740 | |||||||||
15.6901i | 0.895481i | 0.894163 | + | 0.447741i | ||||||
−0.894163 | + | 0.447741i | ||||||||
− | 1.17255i | − | 0.0668124i | |||||||
8.62526 | 0.490674 | |||||||||
6.25031 | + | 5.50043i | 0.354994 | + | 0.312403i | |||||
−33.0126 | −1.87197 | −0.935987 | − | 0.352035i | ||||||
−0.935987 | + | 0.352035i | ||||||||
8.04696i | 0.455569i | |||||||||
1.96627i | 0.111140i | 0.998455 | + | 0.0555702i | ||||||
−0.998455 | + | 0.0555702i | ||||||||
8.60617 | 0.485674 | |||||||||
1.67863 | + | 1.47723i | 0.0945799 | + | 0.0832326i | |||||
−8.11717 | −0.456627 | |||||||||
− | 29.0692i | − | 1.63269i | −0.577564 | − | 0.816345i | ||||
0.577564 | − | 0.816345i | ||||||||
− | 23.9978i | − | 1.34573i | |||||||
−1.25056 | −0.0700179 | |||||||||
−2.92643 | + | 3.32540i | −0.163593 | + | 0.185895i | |||||
−19.2943 | −1.07690 | |||||||||
− | 4.61014i | − | 0.256913i | |||||||
− | 5.21905i | − | 0.290396i | |||||||
−0.889490 | −0.0494161 | |||||||||
−21.1413 | + | 2.70934i | −1.17271 | + | 0.150287i | |||||
23.7362 | 1.31462 | |||||||||
4.03341i | 0.223048i | |||||||||
− | 18.9992i | − | 1.04906i | |||||||
3.21978 | 0.177512 | |||||||||
3.31017 | − | 3.76146i | 0.182219 | − | 0.207061i | |||||
29.7790 | 1.63680 | 0.818401 | − | 0.574647i | ||||||
0.818401 | + | 0.574647i | ||||||||
− | 5.41272i | − | 0.297061i | |||||||
− | 3.64278i | − | 0.199623i | |||||||
34.1627 | 1.86930 | |||||||||
−22.8769 | − | 20.1322i | −1.24990 | − | 1.09994i | |||||
4.98779 | 0.272106 | |||||||||
− | 31.8660i | − | 1.73585i | −0.496694 | − | 0.867925i | ||||
0.496694 | − | 0.867925i | ||||||||
8.79128i | 0.478182i | |||||||||
18.5353 | 1.00670 | |||||||||
1.49312 | + | 1.31398i | 0.0809759 | + | 0.0712608i | |||||
2.88754 | 0.156369 | |||||||||
8.87160i | 0.479721i | |||||||||
1.00000i | 0.0539949i | |||||||||
−2.71358 | −0.146306 | |||||||||
4.00638 | − | 4.55258i | 0.215696 | − | 0.245103i | |||||
−16.4347 | −0.883537 | |||||||||
− | 1.62114i | − | 0.0870273i | −0.999053 | − | 0.0435136i | ||||
0.999053 | − | 0.0435136i | ||||||||
0.843829i | 0.0452340i | |||||||||
−24.2326 | −1.29714 | −0.648572 | − | 0.761153i | ||||||
−0.648572 | + | 0.761153i | ||||||||
1.08038 | + | 8.43031i | 0.0577487 | + | 0.450619i | |||||
4.26284 | 0.227534 | |||||||||
− | 6.19976i | − | 0.330448i | |||||||
− | 13.1172i | − | 0.698159i | −0.937093 | − | 0.349080i | ||||
0.937093 | − | 0.349080i | ||||||||
23.8148 | 1.26574 | |||||||||
−9.84851 | + | 11.1912i | −0.522705 | + | 0.593967i | |||||
0.0356195 | 0.00188783 | |||||||||
1.00000i | 0.0529256i | |||||||||
3.45621i | 0.182666i | |||||||||
0.584856 | 0.0308675 | 0.0154338 | − | 0.999881i | ||||||
0.0154338 | + | 0.999881i | ||||||||
3.16874 | + | 2.78857i | 0.167007 | + | 0.146971i | |||||
8.23847 | 0.433604 | |||||||||
− | 37.5223i | − | 1.97213i | |||||||
9.26227i | 0.486143i | |||||||||
3.79175 | 0.198742 | |||||||||
−21.9592 | − | 19.3246i | −1.14940 | − | 1.01150i | |||||
−14.2122 | −0.742884 | |||||||||
− | 20.0167i | − | 1.04486i | −0.852682 | − | 0.522431i | ||||
0.852682 | − | 0.522431i | ||||||||
− | 13.5273i | − | 0.705160i | |||||||
−10.0648 | −0.523950 | |||||||||
9.14730 | − | 10.3944i | 0.475545 | − | 0.540377i | |||||
14.1176 | 0.732948 | |||||||||
− | 1.94840i | − | 0.101020i | |||||||
− | 18.8646i | − | 0.976774i | −0.872627 | − | 0.488387i | ||||
0.872627 | − | 0.488387i | ||||||||
2.24079 | 0.115869 | |||||||||
−6.25935 | + | 9.26394i | −0.323232 | + | 0.478388i | |||||
6.07798 | 0.313448 | |||||||||
− | 4.04401i | − | 0.208277i | |||||||
− | 1.69985i | − | 0.0874309i | |||||||
20.4953 | 1.05277 | 0.526385 | − | 0.850246i | ||||||
0.526385 | + | 0.850246i | ||||||||
−6.85774 | + | 7.79268i | −0.351795 | + | 0.399756i | |||||
−7.03516 | −0.360422 | |||||||||
− | 31.3207i | − | 1.60251i | |||||||
13.8741i | 0.708935i | 0.935068 | + | 0.354468i | ||||||
−0.935068 | + | 0.354468i | ||||||||
12.7736 | 0.651851 | |||||||||
2.21282 | + | 1.94733i | 0.112776 | + | 0.0992452i | |||||
−35.5800 | −1.81097 | |||||||||
1.43751i | 0.0730726i | |||||||||
− | 6.52485i | − | 0.331249i | |||||||
35.8144 | 1.81586 | 0.907931 | − | 0.419120i | ||||||
0.907931 | + | 0.419120i | ||||||||
12.1636 | + | 10.7043i | 0.615930 | + | 0.542033i | |||||
2.71209 | 0.137156 | |||||||||
1.88770i | 0.0953432i | |||||||||
2.49412i | 0.125812i | |||||||||
−28.5524 | −1.43845 | |||||||||
13.4807 | − | 15.3185i | 0.678287 | − | 0.770760i | |||||
−1.17255 | −0.0589230 | |||||||||
− | 16.1355i | − | 0.809820i | −0.914357 | − | 0.404910i | ||||
0.914357 | − | 0.404910i | ||||||||
28.9527i | 1.45127i | |||||||||
−5.21905 | −0.261279 | |||||||||
3.17010 | + | 24.7366i | 0.158505 | + | 1.23683i | |||||
−10.5679 | −0.527736 | −0.263868 | − | 0.964559i | ||||||
−0.263868 | + | 0.964559i | ||||||||
23.1662i | 1.15542i | |||||||||
9.33761i | 0.465140i | |||||||||
2.36688 | 0.117757 | |||||||||
1.47723 | − | 1.67863i | 0.0734042 | − | 0.0834116i | |||||
−1.61259 | −0.0800314 | |||||||||
− | 4.80203i | − | 0.238028i | |||||||
1.88770i | 0.0934551i | |||||||||
−16.7929 | −0.830353 | −0.415177 | − | 0.909741i | ||||||
−0.415177 | + | 0.909741i | ||||||||
−28.7189 | − | 25.2733i | −1.41833 | − | 1.24816i | |||||
4.36841 | 0.215478 | |||||||||
− | 7.67208i | − | 0.377976i | |||||||
14.0099i | 0.689383i | |||||||||
−4.61014 | −0.226576 | |||||||||
10.2148 | + | 8.98923i | 0.501423 | + | 0.441264i | |||||
20.0485 | 0.982960 | |||||||||
− | 11.3585i | − | 0.556227i | |||||||
11.6948i | 0.572012i | |||||||||
−15.1395 | −0.739612 | −0.369806 | − | 0.929109i | ||||||
−0.369806 | + | 0.929109i | ||||||||
1.31398 | − | 1.49312i | 0.0641158 | − | 0.0728569i | |||||
17.1786 | 0.837236 | 0.418618 | − | 0.908162i | ||||||
0.418618 | + | 0.908162i | ||||||||
17.2915i | 0.841735i | |||||||||
− | 3.21978i | − | 0.156551i | |||||||
26.6497 | 1.29423 | |||||||||
−4.95944 | + | 0.635573i | −0.240568 | + | 0.0308298i | |||||
11.3327 | 0.549070 | |||||||||
− | 8.36086i | − | 0.404610i | |||||||
17.1621i | 0.829559i | |||||||||
5.61940 | 0.271307 | |||||||||
−3.60968 | + | 4.10180i | −0.174074 | + | 0.197806i | |||||
−34.0312 | −1.63922 | −0.819612 | − | 0.572919i | ||||||
−0.819612 | + | 0.572919i | ||||||||
− | 4.98779i | − | 0.239975i | |||||||
− | 16.0610i | − | 0.771842i | −0.922532 | − | 0.385921i | ||||
0.922532 | − | 0.385921i | ||||||||
3.72347 | 0.178732 | |||||||||
−1.59245 | − | 1.40140i | −0.0763523 | − | 0.0671919i | |||||
3.58768 | 0.171819 | |||||||||
14.1545i | 0.677102i | |||||||||
22.2368i | 1.06252i | |||||||||
−10.1471 | −0.484293 | −0.242147 | − | 0.970240i | ||||||
−0.242147 | + | 0.970240i | ||||||||
4.17713 | + | 3.67598i | 0.199137 | + | 0.175245i | |||||
1.00000 | 0.0476190 | |||||||||
7.24619i | 0.344666i | |||||||||
20.6208i | 0.979726i | 0.871799 | + | 0.489863i | ||||||
−0.871799 | + | 0.489863i | ||||||||
−3.24022 | −0.153774 | |||||||||
−0.0591554 | + | 0.0672202i | −0.00280424 | + | 0.00318654i | |||||
4.32201 | 0.204653 | |||||||||
− | 15.8707i | − | 0.750659i | |||||||
1.98102i | 0.0935946i | |||||||||
−16.1240 | −0.760940 | −0.380470 | − | 0.924793i | ||||||
−0.380470 | + | 0.924793i | ||||||||
8.43031 | − | 1.08038i | 0.397408 | − | 0.0509295i | |||||
−13.2677 | −0.624750 | |||||||||
− | 16.4870i | − | 0.775484i | |||||||
− | 10.9078i | − | 0.512495i | |||||||
−17.9758 | −0.843646 | |||||||||
−6.29720 | + | 7.15571i | −0.295217 | + | 0.335465i | |||||
−9.85200 | −0.461362 | |||||||||
− | 8.92593i | − | 0.417538i | −0.977965 | − | 0.208769i | ||||
0.977965 | − | 0.208769i | ||||||||
− | 28.4511i | − | 1.32943i | |||||||
1.00000 | 0.0466760 | |||||||||
−4.04947 | − | 3.56364i | −0.188808 | − | 0.166155i | |||||
−15.6712 | −0.729881 | −0.364941 | − | 0.931031i | ||||||
−0.364941 | + | 0.931031i | ||||||||
− | 2.24079i | − | 0.104251i | |||||||
− | 20.0753i | − | 0.932980i | −0.884526 | − | 0.466490i | ||||
0.884526 | − | 0.466490i | ||||||||
−4.73174 | −0.219666 | |||||||||
3.67698 | + | 3.23583i | 0.170516 | + | 0.150058i | |||||
−9.47234 | −0.438798 | |||||||||
20.2971i | 0.939239i | 0.882869 | + | 0.469619i | ||||||
−0.882869 | + | 0.469619i | ||||||||
− | 3.79175i | − | 0.175274i | |||||||
−13.6284 | −0.629299 | |||||||||
8.08511 | − | 9.18737i | 0.372938 | − | 0.423782i | |||||
5.06290 | 0.233286 | |||||||||
26.4465i | 1.21730i | |||||||||
1.89496i | 0.0871306i | |||||||||
−15.5122 | −0.712500 | |||||||||
−3.31709 | − | 25.8836i | −0.152198 | − | 1.18762i | |||||
0.889490 | 0.0407697 | |||||||||
− | 14.1176i | − | 0.646399i | |||||||
21.2083i | 0.970044i | |||||||||
40.7298 | 1.86099 | 0.930496 | − | 0.366301i | ||||||
0.930496 | + | 0.366301i | ||||||||
6.94756 | − | 7.89473i | 0.317111 | − | 0.360344i | |||||
15.5286 | 0.708043 | |||||||||
− | 17.3020i | − | 0.788086i | |||||||
− | 2.71209i | − | 0.123404i | |||||||
8.23870 | 0.374486 | |||||||||
12.3135 | + | 10.8362i | 0.559129 | + | 0.492047i | |||||
−1.69985 | −0.0771068 | |||||||||
− | 28.7836i | − | 1.30431i | −0.758085 | − | 0.652156i | ||||
0.758085 | − | 0.652156i | ||||||||
− | 15.7828i | − | 0.714453i | |||||||
13.9637 | 0.631459 | |||||||||
2.85341 | + | 2.51107i | 0.128904 | + | 0.113439i | |||||
−5.30798 | −0.239546 | −0.119773 | − | 0.992801i | ||||||
−0.119773 | + | 0.992801i | ||||||||
8.95250i | 0.403610i | |||||||||
− | 0.948665i | − | 0.0427257i | |||||||
−37.8182 | −1.70152 | |||||||||
1.94733 | − | 2.21282i | 0.0875260 | − | 0.0994587i | |||||
10.9256 | 0.490574 | |||||||||
6.66687i | 0.299050i | |||||||||
− | 10.3439i | − | 0.463522i | |||||||
−11.5574 | −0.517378 | −0.258689 | − | 0.965961i | ||||||
−0.258689 | + | 0.965961i | ||||||||
8.24018 | + | 5.56763i | 0.368512 | + | 0.248992i | |||||
20.0975 | 0.897889 | |||||||||
9.64512i | 0.430483i | |||||||||
− | 9.99769i | − | 0.445775i | −0.974844 | − | 0.222888i | ||||
0.974844 | − | 0.222888i | ||||||||
1.88770 | 0.0840848 | |||||||||
−3.93083 | + | 4.46673i | −0.174920 | + | 0.198767i | |||||
−6.07722 | −0.270166 | |||||||||
5.17180i | 0.229688i | |||||||||
6.25770i | 0.277641i | |||||||||
31.2809 | 1.38650 | 0.693250 | − | 0.720697i | ||||||
0.693250 | + | 0.720697i | ||||||||
2.85341 | + | 2.51107i | 0.126351 | + | 0.111192i | |||||
−13.0816 | −0.578697 | |||||||||
− | 4.62713i | − | 0.204492i | |||||||
5.21905i | 0.230427i | |||||||||
−32.1780 | −1.41931 | |||||||||
14.4786 | + | 12.7415i | 0.638002 | + | 0.561458i | |||||
1.27865 | 0.0562894 | |||||||||
− | 4.24442i | − | 0.186669i | |||||||
− | 6.19219i | − | 0.272069i | |||||||
−9.66834 | −0.424393 | |||||||||
−11.8872 | + | 13.5078i | −0.521289 | + | 0.592358i | |||||
−5.52167 | −0.241909 | −0.120954 | − | 0.992658i | ||||||
−0.120954 | + | 0.992658i | ||||||||
1.61259i | 0.0705811i | |||||||||
32.7457i | 1.43187i | 0.698167 | + | 0.715935i | ||||||
−0.698167 | + | 0.715935i | ||||||||
2.21850 | 0.0969155 | |||||||||
0.635573 | + | 4.95944i | 0.0277387 | + | 0.216448i | |||||
7.66007 | 0.333995 | |||||||||
2.19047i | 0.0954183i | |||||||||
− | 6.57505i | − | 0.286142i | |||||||
15.6446 | 0.680200 | |||||||||
35.4502 | − | 40.2833i | 1.53986 | − | 1.74979i | |||||
14.0099 | 0.607978 | |||||||||
4.64229i | 0.201269i | |||||||||
− | 42.9044i | − | 1.85840i | |||||||
0.0680701 | 0.00294568 | |||||||||
−32.3879 | − | 28.5021i | −1.40025 | − | 1.23225i | |||||
−25.7262 | −1.11120 | |||||||||
2.03325i | 0.0877410i | |||||||||
− | 11.3187i | − | 0.487986i | |||||||
1.31823 | 0.0567802 | |||||||||
−1.49312 | − | 1.31398i | −0.0642537 | − | 0.0565448i | |||||
10.3254 | 0.443923 | 0.221961 | − | 0.975055i | ||||||
0.221961 | + | 0.975055i | ||||||||
− | 11.7564i | − | 0.504979i | |||||||
− | 22.0739i | − | 0.947280i | |||||||
4.70309 | 0.201643 | |||||||||
−5.95829 | + | 6.77060i | −0.255225 | + | 0.290020i | |||||
7.24619 | 0.310108 | |||||||||
− | 14.0894i | − | 0.602417i | −0.953558 | − | 0.301209i | ||||
0.953558 | − | 0.301209i | ||||||||
− | 3.88566i | − | 0.165987i | |||||||
−8.36086 | −0.356833 | |||||||||
11.1131 | − | 1.42419i | 0.473863 | − | 0.0607276i | |||||
4.95113 | 0.210925 | |||||||||
− | 5.11960i | − | 0.217905i | |||||||
− | 9.12564i | − | 0.388062i | |||||||
−14.2745 | −0.606465 | |||||||||
5.38124 | − | 6.11487i | 0.228421 | − | 0.259562i | |||||
−10.1033 | −0.428473 | |||||||||
− | 11.2428i | − | 0.476374i | −0.971219 | − | 0.238187i | ||||
0.971219 | − | 0.238187i | ||||||||
− | 3.72347i | − | 0.157627i | |||||||
−6.12786 | −0.259181 | |||||||||
8.37263 | + | 7.36812i | 0.353808 | + | 0.311360i | |||||
1.31823 | 0.0556557 | |||||||||
− | 9.84579i | − | 0.415320i | |||||||
22.1961i | 0.935455i | 0.883873 | + | 0.467727i | ||||||
−0.883873 | + | 0.467727i | ||||||||
−2.86397 | −0.120595 | |||||||||
31.1139 | + | 27.3810i | 1.30897 | + | 1.15193i | |||||
43.7294 | 1.83808 | |||||||||
− | 1.00000i | − | 0.0419961i | |||||||
12.5851i | 0.528057i | |||||||||
−12.0342 | −0.504500 | −0.252250 | − | 0.967662i | ||||||
−0.252250 | + | 0.967662i | ||||||||
−13.1054 | + | 14.8921i | −0.548925 | + | 0.623762i | |||||
−0.950397 | −0.0397729 | −0.0198864 | − | 0.999802i | ||||||
−0.0198864 | + | 0.999802i | ||||||||
− | 4.99841i | − | 0.208994i | |||||||
− | 18.4256i | − | 0.769739i | |||||||
−17.1086 | −0.714098 | |||||||||
13.4504 | − | 1.72373i | 0.560921 | − | 0.0718844i | |||||
1.98102 | 0.0825427 | |||||||||
11.5643i | 0.481430i | 0.970596 | + | 0.240715i | ||||||
−0.970596 | + | 0.240715i | ||||||||
1.69985i | 0.0707044i | |||||||||
−20.9313 | −0.869873 | |||||||||
−1.24653 | + | 1.41647i | −0.0517594 | + | 0.0588158i | |||||
6.08519 | 0.252456 | |||||||||
− | 12.4692i | − | 0.516866i | |||||||
− | 18.6102i | − | 0.770756i | |||||||
−24.6942 | −1.02185 | |||||||||
7.15571 | + | 6.29720i | 0.295852 | + | 0.260357i | |||||
−5.97350 | −0.246763 | |||||||||
− | 5.90911i | − | 0.243895i | −0.992537 | − | 0.121947i | ||||
0.992537 | − | 0.121947i | ||||||||
− | 0.889490i | − | 0.0366820i | |||||||
−11.4322 | −0.471054 | |||||||||
39.9761 | + | 35.1799i | 1.64579 | + | 1.44833i | |||||
−16.7970 | −0.690936 | |||||||||
− | 18.1694i | − | 0.746759i | |||||||
42.4543i | 1.74339i | 0.490051 | + | 0.871694i | ||||||
−0.490051 | + | 0.871694i | ||||||||
−2.24079 | −0.0919409 | |||||||||
−1.47723 | + | 1.67863i | −0.0605606 | + | 0.0688170i | |||||
−14.1168 | −0.578249 | |||||||||
17.0325i | 0.697093i | |||||||||
− | 19.6523i | − | 0.803641i | |||||||
27.1576 | 1.10963 | 0.554815 | − | 0.831974i | ||||||
0.554815 | + | 0.831974i | ||||||||
1.19977 | + | 9.36193i | 0.0489804 | + | 0.382199i | |||||
25.5859 | 1.04367 | 0.521836 | − | 0.853046i | ||||||
0.521836 | + | 0.853046i | ||||||||
2.44355i | 0.0995915i | |||||||||
13.6284i | 0.554990i | |||||||||
−9.70241 | −0.394786 | |||||||||
−13.6825 | + | 15.5479i | −0.556273 | + | 0.632112i | |||||
4.52320 | 0.183743 | |||||||||
23.6758i | 0.960970i | 0.877003 | + | 0.480485i | ||||||
−0.877003 | + | 0.480485i | ||||||||
24.5457i | 0.995458i | |||||||||
−0.948665 | −0.0384419 | |||||||||
−23.8570 | − | 20.9947i | −0.965941 | − | 0.850052i | |||||
13.7254 | 0.555271 | |||||||||
− | 0.889490i | − | 0.0359555i | |||||||
− | 34.1771i | − | 1.38040i | −0.723619 | − | 0.690199i | ||||
0.723619 | − | 0.690199i | ||||||||
26.6708 | 1.07635 | |||||||||
−16.8950 | − | 14.8680i | −0.681271 | − | 0.599535i | |||||
2.48842 | 0.100261 | |||||||||
− | 39.7875i | − | 1.60178i | −0.598810 | − | 0.800891i | ||||
0.598810 | − | 0.800891i | ||||||||
− | 14.6616i | − | 0.589778i | |||||||
41.5801 | 1.67125 | 0.835623 | − | 0.549303i | ||||||
0.835623 | + | 0.549303i | ||||||||
2.87824 | − | 3.27064i | 0.115593 | − | 0.131352i | |||||
−2.71209 | −0.108832 | |||||||||
56.1165i | 2.25007i | |||||||||
0.0400448i | 0.00160436i | |||||||||
21.2621 | 0.851167 | |||||||||
−24.1921 | + | 6.30417i | −0.967684 | + | 0.252167i | |||||
3.34237 | 0.133588 | |||||||||
6.87991i | 0.274757i | |||||||||
− | 4.50340i | − | 0.179705i | |||||||
3.64278 | 0.145247 | |||||||||
2.51107 | − | 2.85341i | 0.100044 | − | 0.113683i | |||||
−28.5787 | −1.13770 | −0.568849 | − | 0.822442i | ||||||
−0.568849 | + | 0.822442i | ||||||||
− | 17.2265i | − | 0.685232i | |||||||
10.1723i | 0.404315i | |||||||||
−49.4133 | −1.96245 | |||||||||
−11.8094 | − | 10.3926i | −0.468642 | − | 0.412416i | |||||
−12.5574 | −0.497935 | |||||||||
4.26284i | 0.168900i | |||||||||
2.12576i | 0.0841598i | |||||||||
6.66687 | 0.263737 | |||||||||
21.4421 | + | 18.8696i | 0.847575 | + | 0.745887i | |||||
13.0074 | 0.513760 | 0.256880 | − | 0.966443i | ||||||
0.256880 | + | 0.966443i | ||||||||
32.7974i | 1.29441i | |||||||||
− | 0.285527i | − | 0.0112601i | −0.999984 | − | 0.00563003i | ||||
0.999984 | − | 0.00563003i | ||||||||
−2.41237 | −0.0950608 | |||||||||
−2.12353 | + | 2.41304i | −0.0836139 | + | 0.0950132i | |||||
−8.87160 | −0.349048 | |||||||||
− | 14.0337i | − | 0.551722i | −0.961198 | − | 0.275861i | ||||
0.961198 | − | 0.275861i | ||||||||
− | 1.88770i | − | 0.0741559i | |||||||
18.4683 | 0.724944 | |||||||||
4.60548 | + | 35.9370i | 0.180642 | + | 1.40957i | |||||
2.19047 | 0.0858512 | |||||||||
− | 12.4206i | − | 0.486427i | |||||||
23.1312i | 0.905193i | 0.891715 | + | 0.452597i | ||||||
−0.891715 | + | 0.452597i | ||||||||
6.85620 | 0.268099 | |||||||||
−3.68440 | + | 4.18670i | −0.143961 | + | 0.163588i | |||||
−50.2009 | −1.96001 | |||||||||
13.0816i | 0.510363i | |||||||||
− | 5.47315i | − | 0.213366i | |||||||
20.8210 | 0.811072 | 0.405536 | − | 0.914079i | ||||||
0.405536 | + | 0.914079i | ||||||||
−1.96828 | − | 1.73213i | −0.0766151 | − | 0.0674232i | |||||
−20.3681 | −0.792229 | −0.396114 | − | 0.918201i | ||||||
−0.396114 | + | 0.918201i | ||||||||
− | 50.6198i | − | 1.96740i | |||||||
4.26284i | 0.165555i | |||||||||
11.4870 | 0.445782 | |||||||||
−8.76083 | − | 7.70974i | −0.339731 | − | 0.298971i | |||||
−6.19219 | −0.239942 | |||||||||
2.57286i | 0.0996216i | |||||||||
− | 17.8765i | − | 0.691663i | |||||||
2.54258 | 0.0983019 | |||||||||
−34.2218 | + | 38.8873i | −1.32210 | + | 1.50235i | |||||
−11.0215 | −0.425482 | |||||||||
− | 4.70309i | − | 0.181426i | |||||||
11.0671i | 0.426604i | 0.976986 | + | 0.213302i | ||||||
−0.976986 | + | 0.213302i | ||||||||
−54.1674 | −2.08645 | |||||||||
4.95944 | − | 0.635573i | 0.190889 | − | 0.0244632i | |||||
4.60026 | 0.176933 | |||||||||
− | 1.98385i | − | 0.0762456i | −0.999273 | − | 0.0381228i | ||||
0.999273 | − | 0.0381228i | ||||||||
− | 31.5073i | − | 1.21003i | |||||||
7.33549 | 0.281510 | |||||||||
−2.78857 | + | 3.16874i | −0.106937 | + | 0.121516i | |||||
−10.5749 | −0.405232 | |||||||||
− | 4.90839i | − | 0.187952i | |||||||
45.6910i | 1.74832i | 0.485641 | + | 0.874158i | ||||||
−0.485641 | + | 0.874158i | ||||||||
4.64229 | 0.177503 | |||||||||
7.33293 | + | 6.45315i | 0.280177 | + | 0.246562i | |||||
1.69985 | 0.0649006 | |||||||||
− | 16.7374i | − | 0.638573i | |||||||
7.16998i | 0.273353i | |||||||||
60.1809 | 2.29271 | |||||||||
−7.73870 | − | 6.81024i | −0.294607 | − | 0.259262i | |||||
0.629981 | 0.0239656 | 0.0119828 | − | 0.999928i | ||||||
0.0119828 | + | 0.999928i | ||||||||
8.59990i | 0.326919i | |||||||||
− | 1.31823i | − | 0.0500754i | |||||||
−2.75569 | −0.104605 | |||||||||
16.7791 | − | 19.0666i | 0.636467 | − | 0.723239i | |||||
−1.79080 | −0.0678799 | |||||||||
− | 10.0648i | − | 0.381230i | |||||||
41.1919i | 1.55913i | |||||||||
−5.57246 | −0.210770 | |||||||||
4.41137 | − | 0.565336i | 0.166734 | − | 0.0213677i | |||||
10.2343 | 0.386545 | 0.193272 | − | 0.981145i | ||||||
0.193272 | + | 0.981145i | ||||||||
− | 7.24619i | − | 0.273490i | |||||||
19.0119i | 0.717046i | |||||||||
2.61145 | 0.0984226 | |||||||||
4.75637 | − | 5.40481i | 0.179135 | − | 0.203557i | |||||
−22.2973 | −0.839170 | |||||||||
2.66094i | 0.100075i | |||||||||
− | 12.4617i | − | 0.468339i | |||||||
−7.85615 | −0.295044 | −0.147522 | − | 0.989059i | ||||||
−0.147522 | + | 0.989059i | ||||||||
19.0233 | + | 16.7410i | 0.713933 | + | 0.628278i | |||||
−9.12564 | −0.342238 | |||||||||
0.0755925i | 0.00283295i | |||||||||
− | 5.94074i | − | 0.222482i | |||||||
1.69985 | 0.0636153 | |||||||||
9.43288 | + | 8.30116i | 0.352770 | + | 0.310446i | |||||
1.80855 | 0.0675888 | |||||||||
12.4766i | 0.465945i | |||||||||
− | 0.994168i | − | 0.0371020i | |||||||
−0.739304 | −0.0275714 | −0.0137857 | − | 0.999905i | ||||||
−0.0137857 | + | 0.999905i | ||||||||
7.36812 | − | 8.37263i | 0.274594 | − | 0.312030i | |||||
8.62526 | 0.321221 | |||||||||
− | 14.0042i | − | 0.521181i | |||||||
− | 10.1786i | − | 0.378545i | |||||||
−19.6345 | −0.729710 | |||||||||
−0.602946 | − | 4.70485i | −0.0223928 | − | 0.174734i | |||||
15.7445 | 0.584332 | |||||||||
34.2680i | 1.27093i | 0.772129 | + | 0.635465i | ||||||
−0.772129 | + | 0.635465i | ||||||||
8.04696i | 0.298240i | |||||||||
−1.00000 | −0.0370370 | |||||||||
−32.8489 | + | 37.3273i | −1.21579 | + | 1.38154i | |||||
−1.43751 | −0.0531681 | |||||||||
7.43690i | 0.274876i | |||||||||
32.0094i | 1.18229i | 0.806564 | + | 0.591147i | ||||||
−0.806564 | + | 0.591147i | ||||||||
−34.0253 | −1.25590 | |||||||||
1.67863 | + | 1.47723i | 0.0619171 | + | 0.0544885i | |||||
−12.7552 | −0.470162 | |||||||||
17.9653i | 0.661761i | |||||||||
17.1086i | 0.629775i | |||||||||
−37.4413 | −1.37730 | −0.688650 | − | 0.725094i | ||||||
−0.688650 | + | 0.725094i | ||||||||
−5.43912 | − | 4.78656i | −0.199946 | − | 0.175957i | |||||
−22.2480 | −0.817299 | |||||||||
− | 23.9978i | − | 0.880985i | |||||||
49.8815i | 1.82997i | 0.403484 | + | 0.914987i | ||||||
−0.403484 | + | 0.914987i | ||||||||
4.13495 | 0.151595 | |||||||||
23.4447 | − | 26.6410i | 0.858948 | − | 0.976050i | |||||
−32.0671 | −1.17406 | |||||||||
− | 6.08519i | − | 0.222645i | |||||||
− | 1.17255i | − | 0.0428728i | |||||||
−19.2943 | −0.704997 | |||||||||
15.7473 | + | 10.6400i | 0.575010 | + | 0.388516i | |||||
27.9959 | 1.02158 | 0.510792 | − | 0.859704i | ||||||
0.510792 | + | 0.859704i | ||||||||
− | 16.0596i | − | 0.585633i | |||||||
5.67410i | 0.206776i | |||||||||
−6.87421 | −0.250344 | |||||||||
16.1134 | − | 18.3102i | 0.586427 | − | 0.666376i | |||||
−0.889490 | −0.0323505 | |||||||||
39.6490i | 1.44107i | 0.693419 | + | 0.720534i | ||||||
−0.693419 | + | 0.720534i | ||||||||
− | 34.8389i | − | 1.26540i | |||||||
−3.57515 | −0.129770 | |||||||||
−16.5378 | − | 14.5537i | −0.599890 | − | 0.527918i | |||||
25.0189 | 0.906933 | 0.453467 | − | 0.891273i | ||||||
0.453467 | + | 0.891273i | ||||||||
11.9587i | 0.433218i | |||||||||
4.03341i | 0.146019i | |||||||||
−16.3894 | −0.592947 | |||||||||
1.67863 | + | 1.47723i | 0.0606909 | + | 0.0534094i | |||||
23.5840 | 0.852123 | |||||||||
59.7220i | 2.15644i | |||||||||
− | 17.7512i | − | 0.640541i | |||||||
39.9051 | 1.43901 | 0.719507 | − | 0.694486i | ||||||
0.719507 | + | 0.694486i | ||||||||
3.31017 | − | 3.76146i | 0.119290 | − | 0.135553i | |||||
−18.9299 | −0.681744 | |||||||||
18.6182i | 0.670082i | |||||||||
31.4649i | 1.13171i | 0.824503 | + | 0.565857i | ||||||
−0.824503 | + | 0.565857i | ||||||||
2.44355 | 0.0878314 | |||||||||
1.39220 | + | 10.8635i | 0.0500094 | + | 0.390228i | |||||
13.8472 | 0.497086 | |||||||||
− | 3.64278i | − | 0.130684i | |||||||
− | 60.8791i | − | 2.18262i | |||||||
52.5285 | 1.88203 | |||||||||
5.60130 | − | 6.36494i | 0.200559 | − | 0.227901i | |||||
8.78847 | 0.314476 | |||||||||
− | 4.61014i | − | 0.164858i | |||||||
0.948665i | 0.0339025i | |||||||||
4.98779 | 0.178135 | |||||||||
8.49872 | + | 7.47908i | 0.303332 | + | 0.266940i | |||||
4.23963 | 0.151223 | |||||||||
3.16406i | 0.112787i | 0.998409 | + | 0.0563933i | ||||||
−0.998409 | + | 0.0563933i | ||||||||
14.9408i | 0.532243i | |||||||||
4.50632 | 0.160429 | |||||||||
−26.0392 | − | 22.9152i | −0.926434 | − | 0.815284i | |||||
18.5353 | 0.659041 | |||||||||
− | 2.48842i | − | 0.0884223i | |||||||
− | 35.6410i | − | 1.26565i | |||||||
−27.4280 | −0.973384 | |||||||||
20.8549 | − | 23.6981i | 0.739648 | − | 0.840486i | |||||
15.1502 | 0.536986 | |||||||||
53.2495i | 1.88619i | 0.332519 | + | 0.943097i | ||||||
−0.332519 | + | 0.943097i | ||||||||
8.87160i | 0.314051i | |||||||||
3.21978 | 0.113908 | |||||||||
23.3247 | − | 2.98916i | 0.824653 | − | 0.105683i | |||||
0.0400448 | 0.00141491 | |||||||||
17.9639i | 0.634326i | |||||||||
17.2446i | 0.608549i | |||||||||
12.1223 | 0.427520 | |||||||||
4.00638 | − | 4.55258i | 0.141206 | − | 0.160457i | |||||
15.8725 | 0.559087 | |||||||||
− | 6.65868i | − | 0.234396i | |||||||
5.02306i | 0.176711i | |||||||||
−44.4117 | −1.56143 | −0.780716 | − | 0.624886i | ||||||
−0.780716 | + | 0.624886i | ||||||||
−2.85341 | − | 2.51107i | −0.100259 | − | 0.0882301i | |||||
12.0589 | 0.423445 | 0.211723 | − | 0.977330i | ||||||
0.211723 | + | 0.977330i | ||||||||
0.843829i | 0.0296126i | |||||||||
− | 6.91612i | − | 0.242559i | |||||||
−8.16273 | −0.286103 | |||||||||
23.4398 | + | 20.6276i | 0.821060 | + | 0.722553i | |||||
4.98779 | 0.174607 | |||||||||
− | 7.50242i | − | 0.262476i | |||||||
28.5453i | 0.998064i | |||||||||
4.26284 | 0.148956 | |||||||||
−13.2249 | + | 15.0279i | −0.461834 | + | 0.524797i | |||||
34.5235 | 1.20488 | 0.602440 | − | 0.798165i | ||||||
0.602440 | + | 0.798165i | ||||||||
− | 7.42564i | − | 0.258999i | |||||||
7.07375i | 0.246576i | 0.992371 | + | 0.123288i | ||||||
−0.992371 | + | 0.123288i | ||||||||
16.2819 | 0.567207 | |||||||||
6.53768 | − | 0.837831i | 0.227613 | − | 0.0291695i | |||||
23.8148 | 0.828621 | |||||||||
− | 26.2151i | − | 0.911589i | −0.890085 | − | 0.455795i | ||||
0.890085 | − | 0.455795i | ||||||||
2.41237i | 0.0838358i | |||||||||
−21.0062 | −0.729577 | −0.364788 | − | 0.931090i | ||||||
−0.364788 | + | 0.931090i | ||||||||
15.2803 | − | 17.3636i | 0.530389 | − | 0.602698i | |||||
−8.39750 | −0.291306 | |||||||||
8.44479i | 0.292770i | |||||||||
1.00000i | 0.0346479i | |||||||||
−19.3077 | −0.668571 | |||||||||
33.7362 | + | 29.6886i | 1.16749 | + | 1.02742i | |||||
6.11961 | 0.211651 | |||||||||
− | 2.19047i | − | 0.0757137i | |||||||
25.7348i | 0.888995i | |||||||||
33.1058 | 1.14294 | 0.571469 | − | 0.820624i | ||||||
0.571469 | + | 0.820624i | ||||||||
3.16874 | + | 2.78857i | 0.109332 | + | 0.0962148i | |||||
−28.1000 | −0.968967 | |||||||||
− | 29.2011i | − | 1.00634i | |||||||
− | 5.79215i | − | 0.199492i | |||||||
9.04821 | 0.311452 | |||||||||
−7.63994 | + | 8.68151i | −0.262822 | + | 0.298653i | |||||
−5.47315 | −0.188171 | |||||||||
9.26227i | 0.318255i | |||||||||
− | 70.4154i | − | 2.41808i | |||||||
25.7255 | 0.882895 | |||||||||
1.08038 | + | 8.43031i | 0.0370567 | + | 0.289157i | |||||
−9.87954 | −0.338666 | |||||||||
− | 5.93012i | − | 0.203163i | |||||||
− | 30.3394i | − | 1.03880i | −0.854531 | − | 0.519401i | ||||
0.854531 | − | 0.519401i | ||||||||
−14.2122 | −0.486332 | |||||||||
−7.70974 | + | 8.76083i | −0.263668 | + | 0.299614i | |||||
−36.4218 | −1.24487 | |||||||||
21.2155i | 0.724708i | 0.932041 | + | 0.362354i | ||||||
−0.932041 | + | 0.362354i | ||||||||
− | 9.55214i | − | 0.326105i | |||||||
9.64903 | 0.329221 | 0.164610 | − | 0.986359i | ||||||
0.164610 | + | 0.986359i | ||||||||
2.14637 | + | 1.88886i | 0.0731907 | + | 0.0644096i | |||||
−10.0648 | −0.343006 | |||||||||
57.8479i | 1.97031i | |||||||||
− | 15.2145i | − | 0.517906i | −0.965890 | − | 0.258953i | ||||
0.965890 | − | 0.258953i | ||||||||
−4.70309 | −0.160002 | |||||||||
−16.2295 | − | 14.2824i | −0.551821 | − | 0.485616i | |||||
−27.3013 | −0.927735 | |||||||||
1.00000i | 0.0339618i | |||||||||
− | 1.94840i | − | 0.0661330i | |||||||
−12.0297 | −0.408080 | |||||||||
−2.38217 | + | 2.70693i | −0.0807630 | + | 0.0917737i | |||||
−58.0955 | −1.96849 | |||||||||
7.61388i | 0.257838i | |||||||||
− | 7.33549i | − | 0.248269i | |||||||
24.0605 | 0.813860 | |||||||||
−6.25935 | + | 9.26394i | −0.211605 | + | 0.313178i | |||||
11.6360 | 0.393143 | |||||||||
− | 53.5867i | − | 1.80949i | −0.425949 | − | 0.904747i | ||||
0.425949 | − | 0.904747i | ||||||||
17.2485i | 0.582109i | |||||||||
−3.51413 | −0.118529 | |||||||||
9.71288 | − | 11.0371i | 0.327421 | − | 0.372059i | |||||
−24.1273 | −0.812870 | −0.406435 | − | 0.913680i | ||||||
−0.406435 | + | 0.913680i | ||||||||
− | 1.69985i | − | 0.0572369i | |||||||
− | 41.1894i | − | 1.38614i | −0.720873 | − | 0.693068i | ||||
0.720873 | − | 0.693068i | ||||||||
3.79175 | 0.127531 | |||||||||
23.5174 | + | 20.6959i | 0.790529 | + | 0.695685i | |||||
35.0523 | 1.17761 | |||||||||
13.5093i | 0.453599i | 0.973942 | + | 0.226799i | ||||||
−0.973942 | + | 0.226799i | ||||||||
− | 6.87648i | − | 0.230760i | |||||||
−7.03516 | −0.235952 | |||||||||
0.114264 | + | 0.100555i | 0.00383015 | + | 0.00337062i | |||||
−1.31823 | −0.0441624 | |||||||||
− | 2.26160i | − | 0.0757241i | |||||||
16.8042i | 0.562331i | |||||||||
−26.9778 | −0.902274 | |||||||||
−3.00357 | + | 3.41306i | −0.100398 | + | 0.114086i | |||||
12.7736 | 0.426737 | |||||||||
− | 11.5612i | − | 0.386017i | |||||||
27.4084i | 0.914631i | |||||||||
−2.07802 | −0.0693059 | |||||||||
−0.565336 | − | 4.41137i | −0.0188445 | − | 0.147046i | |||||
14.1176 | 0.470324 | |||||||||
22.5530i | 0.750934i | |||||||||
1.43751i | 0.0478372i | |||||||||
34.9892 | 1.16372 | |||||||||
32.6082 | − | 37.0538i | 1.08393 | − | 1.23171i | |||||
−18.5417 | −0.616006 | |||||||||
47.6075i | 1.58078i | 0.612603 | + | 0.790391i | ||||||
−0.612603 | + | 0.790391i | ||||||||
9.40630i | 0.312159i | |||||||||
2.66094 | 0.0882579 | |||||||||
12.1636 | + | 10.7043i | 0.403221 | + | 0.354844i | |||||
22.5367 | 0.746674 | 0.373337 | − | 0.927696i | ||||||
0.373337 | + | 0.927696i | ||||||||
26.0315i | 0.861989i | |||||||||
− | 8.02168i | − | 0.265479i | |||||||
−15.1727 | −0.501870 | |||||||||
−14.0348 | − | 12.3509i | −0.463975 | − | 0.408309i | |||||
−14.8878 | −0.491906 | |||||||||
2.49412i | 0.0823632i | |||||||||
− | 1.69985i | − | 0.0561034i | |||||||
−21.8566 | −0.720982 | −0.360491 | − | 0.932763i | ||||||
−0.360491 | + | 0.932763i | ||||||||
7.56284 | − | 8.59390i | 0.249339 | − | 0.283333i | |||||
15.6901 | 0.517006 | |||||||||
26.6387i | 0.877299i | |||||||||
28.4198i | 0.935449i | |||||||||
−1.17255 | −0.0385742 | |||||||||
18.0662 | − | 2.31525i | 0.594012 | − | 0.0761251i | |||||
−34.1251 | −1.12142 | |||||||||
− | 8.62526i | − | 0.283291i | |||||||
4.46166i | 0.146461i | |||||||||
34.2174 | 1.12264 | 0.561318 | − | 0.827600i | ||||||
0.561318 | + | 0.827600i | ||||||||
5.50043 | − | 6.25031i | 0.180366 | − | 0.204956i | |||||
−5.21905 | −0.171047 | |||||||||
4.95665i | 0.162360i | |||||||||
33.0126i | 1.08078i | |||||||||
34.5021 | 1.12894 | |||||||||
2.21282 | + | 1.94733i | 0.0723668 | + | 0.0636846i | |||||
8.04696 | 0.263023 | |||||||||
31.9632i | 1.04419i | 0.852887 | + | 0.522095i | ||||||
−0.852887 | + | 0.522095i | ||||||||
23.1662i | 0.756402i | |||||||||
1.96627 | 0.0641669 | |||||||||
−4.80753 | − | 4.23074i | −0.156804 | − | 0.137992i | |||||
−7.31089 | −0.238328 | −0.119164 | − | 0.992875i | ||||||
−0.119164 | + | 0.992875i | ||||||||
− | 8.60617i | − | 0.280404i | |||||||
27.2965i | 0.888896i | |||||||||
69.8785 | 2.27435 | |||||||||
1.47723 | − | 1.67863i | 0.0480544 | − | 0.0546057i | |||||
3.22116 | 0.104729 | |||||||||
− | 19.7154i | − | 0.640664i | −0.947305 | − | 0.320332i | ||||
0.947305 | − | 0.320332i | ||||||||
8.11717i | 0.263633i | |||||||||
−55.7649 | −1.81020 | |||||||||
−43.9982 | + | 5.63855i | −1.42749 | + | 0.182939i | |||||
−29.0692 | −0.942635 | |||||||||
1.88770i | 0.0611807i | |||||||||
36.8324i | 1.19312i | 0.802569 | + | 0.596560i | ||||||
−0.802569 | + | 0.596560i | ||||||||
−23.9978 | −0.776956 | |||||||||
27.2188 | − | 30.9297i | 0.880781 | − | 1.00086i | |||||
11.0978 | 0.358928 | |||||||||
1.25056i | 0.0404248i | |||||||||
− | 69.2346i | − | 2.23687i | |||||||
4.36841 | 0.141063 | |||||||||
3.32540 | + | 2.92643i | 0.107327 | + | 0.0944502i | |||||
−26.2018 | −0.845221 | |||||||||
− | 26.3963i | − | 0.851051i | |||||||
19.2943i | 0.621749i | |||||||||
−9.05373 | −0.291601 | |||||||||
−35.1358 | − | 30.9203i | −1.13106 | − | 0.995360i | |||||
−4.61014 | −0.148329 | |||||||||
− | 24.8807i | − | 0.800109i | −0.916491 | − | 0.400054i | ||||
0.916491 | − | 0.400054i | ||||||||
17.4844i | 0.561969i | |||||||||
−5.21905 | −0.167660 | |||||||||
18.4199 | − | 20.9312i | 0.591429 | − | 0.672060i | |||||
−37.8289 | −1.21399 | −0.606993 | − | 0.794707i | ||||||
−0.606993 | + | 0.794707i | ||||||||
0.889490i | 0.0285304i | |||||||||
− | 11.3585i | − | 0.364136i | |||||||
−48.9279 | −1.56775 | |||||||||
2.70934 | + | 21.1413i | 0.0867685 | + | 0.677063i | |||||
−41.7022 | −1.33485 | |||||||||
59.8958i | 1.91624i | 0.286374 | + | 0.958118i | ||||||
−0.286374 | + | 0.958118i | ||||||||
− | 23.7362i | − | 0.758999i | |||||||
0.0527883 | 0.00168712 | |||||||||
1.31398 | − | 1.49312i | 0.0419737 | − | 0.0476960i | |||||
4.03341 | 0.128777 | |||||||||
9.02276i | 0.287928i | |||||||||
− | 40.5495i | − | 1.29333i | −0.762775 | − | 0.646664i | ||||
0.762775 | − | 0.646664i | ||||||||
−18.9992 | −0.605674 | |||||||||
−28.1959 | − | 24.8131i | −0.898396 | − | 0.790610i | |||||
−1.61259 | −0.0513553 | |||||||||
− | 3.21978i | − | 0.102487i | |||||||
19.7894i | 0.629583i | |||||||||
3.89864 | 0.123970 | |||||||||
−3.76146 | − | 3.31017i | −0.119547 | − | 0.105204i | |||||
−38.2772 | −1.21591 | −0.607957 | − | 0.793970i | ||||||
−0.607957 | + | 0.793970i | ||||||||
− | 10.3020i | − | 0.327088i | |||||||
− | 29.7790i | − | 0.945008i | |||||||
11.3327 | 0.359451 | |||||||||
−25.1609 | + | 28.5912i | −0.797655 | + | 0.906401i | |||||
−5.41272 | −0.171508 | |||||||||
− | 27.4621i | − | 0.869732i | −0.900495 | − | 0.434866i | ||||
0.900495 | − | 0.434866i | ||||||||
19.6458i | 0.621876i | |||||||||
−3.64278 | −0.115253 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1785.2.g.f.1429.8 | ✓ | 28 | |
5.2 | odd | 4 | 8925.2.a.cw.1.10 | 14 | |||
5.3 | odd | 4 | 8925.2.a.cv.1.5 | 14 | |||
5.4 | even | 2 | inner | 1785.2.g.f.1429.21 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1785.2.g.f.1429.8 | ✓ | 28 | 1.1 | even | 1 | trivial | |
1785.2.g.f.1429.21 | yes | 28 | 5.4 | even | 2 | inner | |
8925.2.a.cv.1.5 | 14 | 5.3 | odd | 4 | |||
8925.2.a.cw.1.10 | 14 | 5.2 | odd | 4 |