Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [592,2,Mod(33,592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(592, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("592.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 592.bc (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | no (minimal twist has level 296) |
Sato-Tate group: |
Embedding invariants
Embedding label | 49.4 | ||
Character | 592.49 | ||
Dual form | 592.2.bc.g.145.4 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
0.714590 | + | 0.599612i | 0.412569 | + | 0.346186i | 0.825328 | − | 0.564654i | ||
−0.412759 | + | 0.910840i | ||||||||
0 | 0 | |||||||||
−2.46699 | + | 0.897912i | −1.10327 | + | 0.401558i | −0.828522 | − | 0.559957i | ||
−0.274751 | + | 0.961515i | ||||||||
0 | 0 | |||||||||
−3.18160 | + | 1.15801i | −1.20253 | + | 0.437686i | −0.864107 | − | 0.503308i | ||
−0.338424 | + | 0.940994i | ||||||||
0 | 0 | |||||||||
−0.369841 | − | 2.09747i | −0.123280 | − | 0.699157i | |||||
0 | 0 | |||||||||
0.622664 | + | 1.07848i | 0.187740 | + | 0.325175i | 0.944496 | − | 0.328522i | ||
−0.756756 | + | 0.653697i | ||||||||
0 | 0 | |||||||||
0.564386 | − | 3.20079i | 0.156532 | − | 0.887740i | −0.800839 | − | 0.598880i | ||
0.957371 | − | 0.288860i | ||||||||
0 | 0 | |||||||||
−2.30129 | − | 0.837600i | −0.594190 | − | 0.216267i | |||||
0 | 0 | |||||||||
−1.30849 | − | 7.42080i | −0.317355 | − | 1.79981i | −0.558700 | − | 0.829370i | ||
0.241345 | − | 0.970439i | ||||||||
0 | 0 | |||||||||
−0.803967 | − | 0.674609i | −0.184443 | − | 0.154766i | 0.545891 | − | 0.837856i | ||
−0.730334 | + | 0.683090i | ||||||||
0 | 0 | |||||||||
−2.96789 | − | 1.08022i | −0.647647 | − | 0.235724i | |||||
0 | 0 | |||||||||
0.113710 | − | 0.196952i | 0.0237102 | − | 0.0410673i | −0.853927 | − | 0.520393i | ||
0.877637 | + | 0.479326i | ||||||||
0 | 0 | |||||||||
1.44959 | − | 1.21635i | 0.289917 | − | 0.243269i | |||||
0 | 0 | |||||||||
2.39263 | − | 4.14416i | 0.460462 | − | 0.797543i | |||||
0 | 0 | |||||||||
−2.96136 | − | 5.12922i | −0.549910 | − | 0.952472i | −0.998280 | − | 0.0586242i | ||
0.448370 | − | 0.893848i | ||||||||
0 | 0 | |||||||||
−7.32779 | −1.31611 | −0.658055 | − | 0.752970i | ||||||
−0.658055 | + | 0.752970i | ||||||||
0 | 0 | |||||||||
−0.201724 | + | 1.14403i | −0.0351156 | + | 0.199150i | |||||
0 | 0 | |||||||||
6.80919 | − | 5.71359i | 1.15096 | − | 0.965773i | |||||
0 | 0 | |||||||||
−1.52734 | + | 5.88789i | −0.251093 | + | 0.967963i | |||||
0 | 0 | |||||||||
2.32254 | − | 1.94884i | 0.371904 | − | 0.312064i | |||||
0 | 0 | |||||||||
−1.30197 | + | 7.38387i | −0.203334 | + | 1.15317i | 0.696705 | + | 0.717358i | ||
−0.900039 | + | 0.435809i | ||||||||
0 | 0 | |||||||||
−3.93777 | −0.600505 | −0.300253 | − | 0.953860i | ||||||
−0.300253 | + | 0.953860i | ||||||||
0 | 0 | |||||||||
2.79574 | + | 4.84236i | 0.416764 | + | 0.721856i | |||||
0 | 0 | |||||||||
−3.87141 | + | 6.70548i | −0.564703 | + | 0.978095i | 0.432374 | + | 0.901694i | ||
−0.997077 | + | 0.0764005i | ||||||||
0 | 0 | |||||||||
3.41928 | − | 2.86912i | 0.488468 | − | 0.409874i | |||||
0 | 0 | |||||||||
3.51457 | − | 6.08742i | 0.492138 | − | 0.852409i | |||||
0 | 0 | |||||||||
7.65285 | + | 2.78541i | 1.05120 | + | 0.382606i | 0.809116 | − | 0.587650i | ||
0.242085 | + | 0.970255i | ||||||||
0 | 0 | |||||||||
−2.50449 | − | 2.10152i | −0.337706 | − | 0.283369i | |||||
0 | 0 | |||||||||
−0.170003 | − | 0.964137i | −0.0225175 | − | 0.127703i | |||||
0 | 0 | |||||||||
8.89397 | + | 3.23714i | 1.15790 | + | 0.421440i | 0.848345 | − | 0.529443i | ||
0.309551 | + | 0.950883i | ||||||||
0 | 0 | |||||||||
0.453786 | − | 2.57355i | 0.0581014 | − | 0.329509i | −0.941878 | − | 0.335955i | ||
0.999979 | + | 0.00644632i | ||||||||
0 | 0 | |||||||||
3.60557 | + | 6.24503i | 0.454259 | + | 0.786800i | |||||
0 | 0 | |||||||||
1.48169 | + | 8.40310i | 0.183781 | + | 1.04228i | |||||
0 | 0 | |||||||||
−6.57694 | + | 2.39381i | −0.803501 | + | 0.292450i | −0.710936 | − | 0.703256i | ||
−0.0925645 | + | 0.995707i | ||||||||
0 | 0 | |||||||||
0.199351 | − | 0.0725578i | 0.0239990 | − | 0.00873493i | |||||
0 | 0 | |||||||||
−10.6575 | − | 8.94266i | −1.26481 | − | 1.06130i | −0.995153 | − | 0.0983415i | ||
−0.269654 | − | 0.962957i | ||||||||
0 | 0 | |||||||||
−12.7621 | −1.49369 | −0.746843 | − | 0.665000i | ||||||
−0.746843 | + | 0.665000i | ||||||||
0 | 0 | |||||||||
1.76520 | 0.203827 | |||||||||
0 | 0 | |||||||||
−3.22996 | − | 2.71026i | −0.368088 | − | 0.308863i | |||||
0 | 0 | |||||||||
6.77570 | − | 2.46615i | 0.762326 | − | 0.277464i | 0.0685433 | − | 0.997648i | ||
0.693783 | + | 0.720184i | ||||||||
0 | 0 | |||||||||
−1.80951 | + | 0.658608i | −0.201057 | + | 0.0731787i | |||||
0 | 0 | |||||||||
−2.24007 | − | 12.7041i | −0.245880 | − | 1.39445i | −0.818441 | − | 0.574591i | ||
0.572561 | − | 0.819862i | ||||||||
0 | 0 | |||||||||
9.89126 | + | 17.1322i | 1.07286 | + | 1.85824i | |||||
0 | 0 | |||||||||
0.959387 | − | 5.44095i | 0.102857 | − | 0.583332i | |||||
0 | 0 | |||||||||
−2.47099 | − | 0.899365i | −0.261924 | − | 0.0953325i | 0.207720 | − | 0.978188i | ||
−0.469644 | + | 0.882856i | ||||||||
0 | 0 | |||||||||
1.91089 | + | 10.8372i | 0.200316 | + | 1.13605i | |||||
0 | 0 | |||||||||
−5.23636 | − | 4.39383i | −0.542985 | − | 0.455619i | |||||
0 | 0 | |||||||||
2.58912 | + | 0.942363i | 0.265638 | + | 0.0966844i | |||||
0 | 0 | |||||||||
−1.63655 | + | 2.83459i | −0.166167 | + | 0.287809i | −0.937069 | − | 0.349144i | ||
0.770902 | + | 0.636953i | ||||||||
0 | 0 | |||||||||
2.03180 | − | 1.70489i | 0.204204 | − | 0.171347i | |||||
0 | 0 | |||||||||
2.31341 | − | 4.00694i | 0.230193 | − | 0.398706i | −0.727672 | − | 0.685925i | ||
0.957865 | + | 0.287220i | ||||||||
0 | 0 | |||||||||
5.85346 | + | 10.1385i | 0.576759 | + | 0.998976i | 0.995848 | + | 0.0910308i | ||
−0.419089 | + | 0.907945i | ||||||||
0 | 0 | |||||||||
8.29172 | 0.809189 | |||||||||
0 | 0 | |||||||||
2.25971 | − | 12.8155i | 0.218455 | − | 1.23892i | −0.656355 | − | 0.754452i | ||
0.874810 | − | 0.484467i | ||||||||
0 | 0 | |||||||||
−0.104826 | + | 0.0879597i | −0.0100405 | + | 0.00842501i | −0.647794 | − | 0.761815i | ||
0.637754 | + | 0.770240i | ||||||||
0 | 0 | |||||||||
−4.62187 | + | 3.29162i | −0.438688 | + | 0.312426i | |||||
0 | 0 | |||||||||
5.70275 | − | 4.78518i | 0.536470 | − | 0.450152i | −0.333859 | − | 0.942623i | ||
0.870329 | + | 0.492471i | ||||||||
0 | 0 | |||||||||
−0.103677 | + | 0.587981i | −0.00966792 | + | 0.0548295i | |||||
0 | 0 | |||||||||
−6.92230 | −0.639966 | |||||||||
0 | 0 | |||||||||
12.7564 | + | 22.0948i | 1.16938 | + | 2.02543i | |||||
0 | 0 | |||||||||
4.72458 | − | 8.18321i | 0.429507 | − | 0.743928i | |||||
0 | 0 | |||||||||
−5.35783 | + | 4.49576i | −0.483100 | + | 0.405369i | |||||
0 | 0 | |||||||||
4.07935 | − | 7.06564i | 0.364868 | − | 0.631970i | |||||
0 | 0 | |||||||||
−19.1828 | − | 6.98197i | −1.70220 | − | 0.619550i | −0.706127 | − | 0.708085i | ||
−0.996073 | + | 0.0885354i | ||||||||
0 | 0 | |||||||||
−2.81389 | − | 2.36114i | −0.247750 | − | 0.207887i | |||||
0 | 0 | |||||||||
1.65466 | + | 9.38404i | 0.144568 | + | 0.819887i | 0.967713 | + | 0.252055i | ||
−0.823145 | + | 0.567832i | ||||||||
0 | 0 | |||||||||
3.33910 | + | 1.21533i | 0.289537 | + | 0.105383i | |||||
0 | 0 | |||||||||
−2.18151 | + | 12.3720i | −0.187755 | + | 1.06481i | |||||
0 | 0 | |||||||||
4.74114 | + | 8.21190i | 0.405063 | + | 0.701590i | 0.994329 | − | 0.106349i | ||
−0.589266 | + | 0.807939i | ||||||||
0 | 0 | |||||||||
3.23003 | + | 18.3184i | 0.273968 | + | 1.55375i | 0.742222 | + | 0.670154i | ||
−0.468255 | + | 0.883593i | ||||||||
0 | 0 | |||||||||
−6.78716 | + | 2.47032i | −0.571582 | + | 0.208039i | |||||
0 | 0 | |||||||||
3.80343 | − | 1.38433i | 0.318059 | − | 0.115764i | |||||
0 | 0 | |||||||||
11.9112 | + | 9.99471i | 0.989174 | + | 0.830016i | |||||
0 | 0 | |||||||||
4.16374 | 0.343419 | |||||||||
0 | 0 | |||||||||
8.02290 | 0.657261 | 0.328631 | − | 0.944458i | ||||||
0.328631 | + | 0.944458i | ||||||||
0 | 0 | |||||||||
2.04800 | + | 1.71848i | 0.166664 | + | 0.139848i | 0.722305 | − | 0.691575i | ||
−0.555641 | + | 0.831422i | ||||||||
0 | 0 | |||||||||
−15.0810 | + | 5.48903i | −1.21922 | + | 0.443762i | |||||
0 | 0 | |||||||||
18.0776 | − | 6.57971i | 1.45203 | − | 0.528495i | |||||
0 | 0 | |||||||||
−1.40926 | − | 7.99229i | −0.112471 | − | 0.637854i | −0.987971 | − | 0.154637i | ||
0.875501 | − | 0.483217i | ||||||||
0 | 0 | |||||||||
3.79848 | + | 6.57917i | 0.301239 | + | 0.521762i | |||||
0 | 0 | |||||||||
−0.133709 | + | 0.758299i | −0.0105377 | + | 0.0597623i | |||||
0 | 0 | |||||||||
−8.54919 | − | 3.11165i | −0.669624 | − | 0.243723i | −0.0152382 | − | 0.999884i | ||
−0.654386 | + | 0.756161i | ||||||||
0 | 0 | |||||||||
−0.529589 | − | 3.00345i | −0.0412284 | − | 0.233818i | |||||
0 | 0 | |||||||||
−15.5178 | − | 13.0210i | −1.20081 | − | 1.00760i | −0.999607 | − | 0.0280460i | ||
−0.201200 | − | 0.979550i | ||||||||
0 | 0 | |||||||||
2.28947 | + | 0.833299i | 0.176113 | + | 0.0640999i | |||||
0 | 0 | |||||||||
−1.11763 | + | 1.93579i | −0.0854674 | + | 0.148034i | |||||
0 | 0 | |||||||||
14.4874 | − | 12.1563i | 1.10145 | − | 0.924229i | 0.103931 | − | 0.994584i | ||
0.997522 | + | 0.0703555i | ||||||||
0 | 0 | |||||||||
−3.20346 | + | 5.54856i | −0.242159 | + | 0.419432i | |||||
0 | 0 | |||||||||
4.41451 | + | 7.64616i | 0.331815 | + | 0.574721i | |||||
0 | 0 | |||||||||
13.4598 | 1.00604 | 0.503018 | − | 0.864276i | ||||||
0.503018 | + | 0.864276i | ||||||||
0 | 0 | |||||||||
−2.34928 | + | 13.3234i | −0.174621 | + | 0.990323i | 0.763960 | + | 0.645263i | ||
−0.938581 | + | 0.345060i | ||||||||
0 | 0 | |||||||||
1.86740 | − | 1.56694i | 0.138042 | − | 0.115831i | |||||
0 | 0 | |||||||||
−1.51888 | − | 15.8968i | −0.111670 | − | 1.16876i | |||||
0 | 0 | |||||||||
7.18848 | − | 6.03185i | 0.525673 | − | 0.441092i | |||||
0 | 0 | |||||||||
−2.81343 | + | 15.9557i | −0.204647 | + | 1.16061i | |||||
0 | 0 | |||||||||
2.36093 | 0.170831 | 0.0854155 | − | 0.996345i | ||||||
0.0854155 | + | 0.996345i | ||||||||
0 | 0 | |||||||||
4.63768 | + | 8.03270i | 0.333827 | + | 0.578206i | 0.983259 | − | 0.182214i | ||
−0.649431 | + | 0.760420i | ||||||||
0 | 0 | |||||||||
−3.97980 | + | 6.89321i | −0.284999 | + | 0.493633i | |||||
0 | 0 | |||||||||
−1.05645 | + | 0.886469i | −0.0752691 | + | 0.0631583i | −0.679646 | − | 0.733540i | ||
0.604377 | + | 0.796699i | ||||||||
0 | 0 | |||||||||
−1.97499 | + | 3.42079i | −0.140003 | + | 0.242493i | −0.927498 | − | 0.373829i | ||
0.787494 | + | 0.616322i | ||||||||
0 | 0 | |||||||||
−6.13517 | − | 2.23302i | −0.432742 | − | 0.157505i | |||||
0 | 0 | |||||||||
15.3615 | + | 12.8898i | 1.07817 | + | 0.904690i | |||||
0 | 0 | |||||||||
−3.41810 | − | 19.3850i | −0.238730 | − | 1.35391i | |||||
0 | 0 | |||||||||
−0.455155 | − | 0.165663i | −0.0316355 | − | 0.0115144i | |||||
0 | 0 | |||||||||
0.226954 | − | 1.28712i | 0.0156987 | − | 0.0890320i | |||||
0 | 0 | |||||||||
10.4164 | + | 18.0417i | 0.717095 | + | 1.24204i | 0.962146 | + | 0.272534i | ||
−0.245051 | + | 0.969510i | ||||||||
0 | 0 | |||||||||
−2.25358 | − | 12.7807i | −0.154413 | − | 0.875717i | |||||
0 | 0 | |||||||||
9.71446 | − | 3.53578i | 0.662521 | − | 0.241138i | |||||
0 | 0 | |||||||||
23.3141 | − | 8.48563i | 1.58266 | − | 0.576042i | |||||
0 | 0 | |||||||||
−9.11964 | − | 7.65229i | −0.616248 | − | 0.517094i | |||||
0 | 0 | |||||||||
−24.4909 | −1.64744 | |||||||||
0 | 0 | |||||||||
−24.9633 | −1.67166 | −0.835832 | − | 0.548985i | ||||||
−0.835832 | + | 0.548985i | ||||||||
0 | 0 | |||||||||
−3.08737 | − | 2.59061i | −0.205824 | − | 0.172707i | |||||
0 | 0 | |||||||||
−0.996856 | + | 0.362826i | −0.0661637 | + | 0.0240816i | −0.374890 | − | 0.927069i | ||
0.308726 | + | 0.951151i | ||||||||
0 | 0 | |||||||||
5.99574 | − | 2.18227i | 0.396210 | − | 0.144209i | −0.136228 | − | 0.990677i | ||
0.532438 | + | 0.846469i | ||||||||
0 | 0 | |||||||||
−0.682993 | − | 3.87345i | −0.0449376 | − | 0.254854i | |||||
0 | 0 | |||||||||
4.79443 | + | 8.30419i | 0.314093 | + | 0.544026i | 0.979244 | − | 0.202683i | ||
−0.665151 | + | 0.746709i | ||||||||
0 | 0 | |||||||||
3.52981 | − | 20.0186i | 0.230260 | − | 1.30587i | |||||
0 | 0 | |||||||||
6.32059 | + | 2.30051i | 0.410566 | + | 0.149434i | |||||
0 | 0 | |||||||||
−2.28199 | − | 12.9418i | −0.147610 | − | 0.837138i | −0.965234 | − | 0.261386i | ||
0.817624 | − | 0.575752i | ||||||||
0 | 0 | |||||||||
−3.56189 | − | 2.98878i | −0.229441 | − | 0.192524i | 0.520818 | − | 0.853668i | ||
−0.750259 | + | 0.661143i | ||||||||
0 | 0 | |||||||||
−15.1780 | − | 5.52434i | −0.973668 | − | 0.354386i | |||||
0 | 0 | |||||||||
−5.85912 | + | 10.1483i | −0.374326 | + | 0.648351i | |||||
0 | 0 | |||||||||
−2.61303 | + | 2.19259i | −0.166263 | + | 0.139511i | |||||
0 | 0 | |||||||||
6.01678 | − | 10.4214i | 0.381298 | − | 0.660427i | |||||
0 | 0 | |||||||||
−8.89316 | − | 15.4034i | −0.561331 | − | 0.972254i | −0.997381 | − | 0.0723317i | ||
0.436049 | − | 0.899923i | ||||||||
0 | 0 | |||||||||
0.283213 | 0.0178054 | |||||||||
0 | 0 | |||||||||
−3.20446 | + | 18.1734i | −0.200671 | + | 1.13806i | |||||
0 | 0 | |||||||||
−13.3966 | + | 11.2411i | −0.835660 | + | 0.701202i | −0.956583 | − | 0.291460i | ||
0.120923 | + | 0.992662i | ||||||||
0 | 0 | |||||||||
−1.95885 | − | 20.5016i | −0.121717 | − | 1.27391i | |||||
0 | 0 | |||||||||
−9.66316 | + | 8.10835i | −0.598134 | + | 0.501894i | |||||
0 | 0 | |||||||||
1.37219 | − | 7.78206i | 0.0846127 | − | 0.479862i | −0.912827 | − | 0.408347i | ||
0.997439 | − | 0.0715154i | ||||||||
0 | 0 | |||||||||
−21.3806 | −1.31340 | |||||||||
0 | 0 | |||||||||
−1.22647 | − | 2.12431i | −0.0750588 | − | 0.130006i | |||||
0 | 0 | |||||||||
3.22251 | − | 5.58155i | 0.196480 | − | 0.340313i | −0.750905 | − | 0.660410i | ||
0.947385 | + | 0.320097i | ||||||||
0 | 0 | |||||||||
13.8349 | − | 11.6089i | 0.840410 | − | 0.705187i | −0.117246 | − | 0.993103i | ||
0.957656 | + | 0.287915i | ||||||||
0 | 0 | |||||||||
−5.13261 | + | 8.88994i | −0.310640 | + | 0.538044i | |||||
0 | 0 | |||||||||
2.21442 | + | 0.805982i | 0.133534 | + | 0.0486025i | |||||
0 | 0 | |||||||||
20.4091 | + | 17.1252i | 1.22626 | + | 1.02896i | 0.998473 | + | 0.0552461i | ||
0.227790 | + | 0.973710i | ||||||||
0 | 0 | |||||||||
2.71011 | + | 15.3698i | 0.162250 | + | 0.920166i | |||||
0 | 0 | |||||||||
3.47714 | + | 1.26558i | 0.207429 | + | 0.0754979i | 0.443645 | − | 0.896203i | ||
−0.236216 | + | 0.971701i | ||||||||
0 | 0 | |||||||||
3.63239 | − | 20.6003i | 0.215923 | − | 1.22456i | −0.663375 | − | 0.748287i | ||
0.879298 | − | 0.476272i | ||||||||
0 | 0 | |||||||||
1.28511 | + | 2.22587i | 0.0761232 | + | 0.131849i | |||||
0 | 0 | |||||||||
−4.40821 | − | 25.0002i | −0.260208 | − | 1.47572i | |||||
0 | 0 | |||||||||
−37.3814 | + | 13.6057i | −2.19891 | + | 0.800336i | |||||
0 | 0 | |||||||||
−2.86912 | + | 1.04427i | −0.168191 | + | 0.0612164i | |||||
0 | 0 | |||||||||
−19.2124 | − | 16.1211i | −1.12240 | − | 0.941805i | −0.123676 | − | 0.992323i | ||
−0.998723 | + | 0.0505175i | ||||||||
0 | 0 | |||||||||
−24.8480 | −1.44671 | |||||||||
0 | 0 | |||||||||
5.95921 | 0.345789 | |||||||||
0 | 0 | |||||||||
−0.566225 | − | 0.475120i | −0.0327457 | − | 0.0274769i | |||||
0 | 0 | |||||||||
12.5284 | − | 4.55997i | 0.722126 | − | 0.262832i | |||||
0 | 0 | |||||||||
4.05575 | − | 1.47617i | 0.232997 | − | 0.0848039i | |||||
0 | 0 | |||||||||
1.19133 | + | 6.75639i | 0.0682155 | + | 0.386870i | |||||
0 | 0 | |||||||||
−10.9498 | − | 18.9656i | −0.624939 | − | 1.08243i | −0.988553 | − | 0.150876i | ||
0.363614 | − | 0.931550i | ||||||||
0 | 0 | |||||||||
−1.89634 | + | 10.7547i | −0.107879 | + | 0.611812i | |||||
0 | 0 | |||||||||
−0.490564 | − | 0.178551i | −0.0278173 | − | 0.0101247i | 0.328074 | − | 0.944652i | ||
−0.355891 | + | 0.934527i | ||||||||
0 | 0 | |||||||||
−4.67797 | − | 26.5301i | −0.264415 | − | 1.49957i | −0.770696 | − | 0.637202i | ||
0.506282 | − | 0.862368i | ||||||||
0 | 0 | |||||||||
−14.5024 | − | 12.1690i | −0.817118 | − | 0.685643i | |||||
0 | 0 | |||||||||
12.9323 | + | 4.70698i | 0.726352 | + | 0.264370i | 0.678620 | − | 0.734490i | ||
0.0477320 | + | 0.998860i | ||||||||
0 | 0 | |||||||||
3.68786 | − | 6.38756i | 0.206480 | − | 0.357635i | |||||
0 | 0 | |||||||||
9.29909 | − | 7.80286i | 0.519024 | − | 0.435513i | |||||
0 | 0 | |||||||||
−3.95416 | + | 6.84880i | −0.220015 | + | 0.381077i | |||||
0 | 0 | |||||||||
−3.07515 | − | 5.32631i | −0.170578 | − | 0.295451i | |||||
0 | 0 | |||||||||
−0.127649 | −0.00705903 | |||||||||
0 | 0 | |||||||||
4.55228 | − | 25.8173i | 0.250975 | − | 1.42335i | |||||
0 | 0 | |||||||||
−15.5503 | + | 13.0482i | −0.854719 | + | 0.717194i | −0.960824 | − | 0.277161i | ||
0.106105 | + | 0.994355i | ||||||||
0 | 0 | |||||||||
12.9145 | + | 1.02596i | 0.707713 | + | 0.0562224i | |||||
0 | 0 | |||||||||
14.0758 | − | 11.8110i | 0.769045 | − | 0.645305i | |||||
0 | 0 | |||||||||
−5.77178 | + | 32.7334i | −0.314409 | + | 1.78310i | 0.261107 | + | 0.965310i | ||
−0.575516 | + | 0.817791i | ||||||||
0 | 0 | |||||||||
6.94438 | 0.377167 | |||||||||
0 | 0 | |||||||||
−4.56275 | − | 7.90291i | −0.247087 | − | 0.427966i | |||||
0 | 0 | |||||||||
4.29394 | − | 7.43732i | 0.231851 | − | 0.401577i | |||||
0 | 0 | |||||||||
−0.426647 | + | 0.357999i | −0.0229699 | + | 0.0192740i | |||||
0 | 0 | |||||||||
−11.2032 | + | 19.4045i | −0.601418 | + | 1.04169i | 0.391188 | + | 0.920311i | ||
−0.992607 | + | 0.121377i | ||||||||
0 | 0 | |||||||||
−28.6222 | − | 10.4176i | −1.53211 | − | 0.557644i | −0.567975 | − | 0.823046i | ||
−0.964138 | + | 0.265402i | ||||||||
0 | 0 | |||||||||
−11.9142 | − | 9.99721i | −0.635934 | − | 0.533612i | |||||
0 | 0 | |||||||||
−3.47525 | − | 19.7091i | −0.184969 | − | 1.04901i | −0.925995 | − | 0.377536i | ||
0.741026 | − | 0.671476i | ||||||||
0 | 0 | |||||||||
34.3216 | + | 12.4920i | 1.82160 | + | 0.663008i | |||||
0 | 0 | |||||||||
−4.13268 | + | 23.4376i | −0.218725 | + | 1.24045i | |||||
0 | 0 | |||||||||
12.6779 | + | 21.9587i | 0.669113 | + | 1.15894i | 0.978152 | + | 0.207889i | ||
−0.309039 | + | 0.951049i | ||||||||
0 | 0 | |||||||||
−3.10805 | − | 17.6266i | −0.163582 | − | 0.927717i | |||||
0 | 0 | |||||||||
8.28289 | − | 3.01473i | 0.434739 | − | 0.158232i | |||||
0 | 0 | |||||||||
31.4839 | − | 11.4592i | 1.64794 | − | 0.599802i | |||||
0 | 0 | |||||||||
3.13156 | + | 2.62769i | 0.163466 | + | 0.137164i | 0.720852 | − | 0.693090i | ||
−0.557385 | + | 0.830254i | ||||||||
0 | 0 | |||||||||
15.9690 | 0.831311 | |||||||||
0 | 0 | |||||||||
−27.5738 | −1.43156 | |||||||||
0 | 0 | |||||||||
−7.03559 | − | 5.90356i | −0.364289 | − | 0.305675i | 0.442208 | − | 0.896912i | ||
−0.806498 | + | 0.591237i | ||||||||
0 | 0 | |||||||||
7.15171 | − | 2.60301i | 0.369313 | − | 0.134419i | |||||
0 | 0 | |||||||||
−18.0889 | + | 6.58383i | −0.931626 | + | 0.339084i | |||||
0 | 0 | |||||||||
0.949204 | + | 5.38320i | 0.0487573 | + | 0.276516i | 0.999433 | − | 0.0336702i | ||
−0.950676 | + | 0.310187i | ||||||||
0 | 0 | |||||||||
−9.52137 | − | 16.4915i | −0.487795 | − | 0.844885i | |||||
0 | 0 | |||||||||
5.04396 | − | 28.6057i | 0.257734 | − | 1.46168i | −0.531222 | − | 0.847233i | ||
0.788956 | − | 0.614450i | ||||||||
0 | 0 | |||||||||
10.4019 | + | 3.78597i | 0.530128 | + | 0.192951i | |||||
0 | 0 | |||||||||
1.45635 | + | 8.25936i | 0.0740304 | + | 0.419847i | |||||
0 | 0 | |||||||||
15.6096 | + | 13.0980i | 0.791438 | + | 0.664095i | 0.946101 | − | 0.323872i | ||
−0.154663 | + | 0.987967i | ||||||||
0 | 0 | |||||||||
−1.61033 | − | 0.586112i | −0.0814379 | − | 0.0296410i | |||||
0 | 0 | |||||||||
−4.44438 | + | 7.69789i | −0.224189 | + | 0.388307i | |||||
0 | 0 | |||||||||
−14.5012 | + | 12.1680i | −0.729636 | + | 0.612237i | |||||
0 | 0 | |||||||||
−3.84463 | + | 6.65910i | −0.192957 | + | 0.334211i | −0.946229 | − | 0.323498i | ||
0.753272 | + | 0.657709i | ||||||||
0 | 0 | |||||||||
1.65736 | + | 2.87063i | 0.0829718 | + | 0.143711i | |||||
0 | 0 | |||||||||
14.7251 | 0.735338 | 0.367669 | − | 0.929957i | ||||||
0.367669 | + | 0.929957i | ||||||||
0 | 0 | |||||||||
−4.13570 | + | 23.4547i | −0.206014 | + | 1.16836i | |||||
0 | 0 | |||||||||
3.87268 | − | 3.24956i | 0.192435 | − | 0.161472i | |||||
0 | 0 | |||||||||
−7.30102 | + | 2.01896i | −0.361898 | + | 0.100076i | |||||
0 | 0 | |||||||||
2.63421 | − | 2.21037i | 0.130253 | − | 0.109296i | −0.575334 | − | 0.817919i | ||
0.705587 | + | 0.708623i | ||||||||
0 | 0 | |||||||||
−1.53598 | + | 8.71099i | −0.0757644 | + | 0.429681i | |||||
0 | 0 | |||||||||
−32.0457 | −1.57686 | |||||||||
0 | 0 | |||||||||
16.9334 | + | 29.3295i | 0.831226 | + | 1.43973i | |||||
0 | 0 | |||||||||
−8.67579 | + | 15.0269i | −0.424855 | + | 0.735871i | |||||
0 | 0 | |||||||||
−23.9931 | + | 20.1326i | −1.17214 | + | 0.983541i | −0.999999 | − | 0.00153152i | ||
−0.172140 | + | 0.985073i | ||||||||
0 | 0 | |||||||||
−0.199850 | + | 0.346151i | −0.00974011 | + | 0.0168704i | −0.870854 | − | 0.491541i | ||
0.861114 | + | 0.508411i | ||||||||
0 | 0 | |||||||||
15.4963 | + | 5.64021i | 0.753458 | + | 0.274236i | |||||
0 | 0 | |||||||||
−10.9230 | − | 9.16552i | −0.529845 | − | 0.444593i | |||||
0 | 0 | |||||||||
1.53642 | + | 8.71349i | 0.0743527 | + | 0.421675i | |||||
0 | 0 | |||||||||
3.54795 | + | 1.29135i | 0.171297 | + | 0.0623470i | |||||
0 | 0 | |||||||||
0.839936 | − | 4.76352i | 0.0404583 | − | 0.229450i | −0.957873 | − | 0.287191i | ||
0.998332 | + | 0.0577406i | ||||||||
0 | 0 | |||||||||
−4.89095 | − | 8.47137i | −0.235044 | − | 0.407108i | 0.724241 | − | 0.689546i | ||
−0.959285 | + | 0.282438i | ||||||||
0 | 0 | |||||||||
2.51870 | + | 14.2842i | 0.120762 | + | 0.684877i | |||||
0 | 0 | |||||||||
−0.224285 | + | 0.0816330i | −0.0107290 | + | 0.00390504i | |||||
0 | 0 | |||||||||
37.0174 | − | 13.4732i | 1.76674 | − | 0.643042i | 0.766744 | − | 0.641952i | ||
0.999999 | − | 0.00108969i | ||||||||
0 | 0 | |||||||||
−7.28247 | − | 6.11072i | −0.346784 | − | 0.290987i | |||||
0 | 0 | |||||||||
15.2550 | 0.724788 | 0.362394 | − | 0.932025i | ||||||
0.362394 | + | 0.932025i | ||||||||
0 | 0 | |||||||||
6.90345 | 0.327255 | |||||||||
0 | 0 | |||||||||
5.73308 | + | 4.81063i | 0.271165 | + | 0.227535i | |||||
0 | 0 | |||||||||
30.8222 | − | 11.2184i | 1.45459 | − | 0.529428i | 0.510721 | − | 0.859746i | ||
0.943869 | + | 0.330319i | ||||||||
0 | 0 | |||||||||
−8.77408 | + | 3.19350i | −0.413155 | + | 0.150376i | |||||
0 | 0 | |||||||||
0.433062 | + | 2.45601i | 0.0203470 | + | 0.115394i | |||||
0 | 0 | |||||||||
−14.4450 | − | 25.0195i | −0.677192 | − | 1.17293i | |||||
0 | 0 | |||||||||
6.46679 | − | 36.6750i | 0.302504 | − | 1.71558i | −0.332525 | − | 0.943095i | ||
0.635028 | − | 0.772489i | ||||||||
0 | 0 | |||||||||
−33.8837 | − | 12.3327i | −1.58156 | − | 0.575639i | |||||
0 | 0 | |||||||||
4.75723 | + | 26.9796i | 0.221566 | + | 1.25657i | 0.869141 | + | 0.494564i | ||
−0.647575 | + | 0.762002i | ||||||||
0 | 0 | |||||||||
−0.676688 | − | 0.567808i | −0.0314483 | − | 0.0263883i | 0.626928 | − | 0.779077i | ||
−0.658376 | + | 0.752689i | ||||||||
0 | 0 | |||||||||
16.8633 | + | 6.13775i | 0.782019 | + | 0.284632i | |||||
0 | 0 | |||||||||
1.83634 | − | 3.18064i | 0.0849758 | − | 0.147182i | −0.820405 | − | 0.571783i | ||
0.905381 | + | 0.424600i | ||||||||
0 | 0 | |||||||||
18.1531 | − | 15.2323i | 0.838234 | − | 0.703362i | |||||
0 | 0 | |||||||||
3.78523 | − | 6.55621i | 0.174414 | − | 0.302094i | |||||
0 | 0 | |||||||||
−2.45191 | − | 4.24683i | −0.112739 | − | 0.195269i | |||||
0 | 0 | |||||||||
−1.98598 | −0.0911229 | |||||||||
0 | 0 | |||||||||
3.01198 | − | 17.0818i | 0.137909 | − | 0.782121i | |||||
0 | 0 | |||||||||
18.2228 | − | 15.2908i | 0.832623 | − | 0.698654i | −0.123268 | − | 0.992373i | ||
0.955892 | + | 0.293720i | ||||||||
0 | 0 | |||||||||
17.9839 | + | 8.21173i | 0.819995 | + | 0.374423i | |||||
0 | 0 | |||||||||
−0.550232 | + | 0.461700i | −0.0250364 | + | 0.0210081i | |||||
0 | 0 | |||||||||
1.49215 | − | 8.46240i | 0.0677550 | − | 0.384258i | |||||
0 | 0 | |||||||||
15.7470 | 0.713565 | 0.356782 | − | 0.934188i | ||||||
0.356782 | + | 0.934188i | ||||||||
0 | 0 | |||||||||
−4.24338 | − | 7.34975i | −0.191892 | − | 0.332367i | |||||
0 | 0 | |||||||||
−0.943381 | + | 1.63398i | −0.0425742 | + | 0.0737406i | −0.886527 | − | 0.462676i | ||
0.843953 | + | 0.536417i | ||||||||
0 | 0 | |||||||||
−34.1880 | + | 28.6872i | −1.53975 | + | 1.29200i | |||||
0 | 0 | |||||||||
−3.48161 | + | 6.03032i | −0.156487 | + | 0.271043i | |||||
0 | 0 | |||||||||
44.2634 | + | 16.1106i | 1.98548 | + | 0.722657i | |||||
0 | 0 | |||||||||
27.1748 | + | 22.8023i | 1.21651 | + | 1.02077i | 0.999000 | + | 0.0447151i | ||
0.217510 | + | 0.976058i | ||||||||
0 | 0 | |||||||||
−3.28133 | − | 18.6094i | −0.146599 | − | 0.831405i | |||||
0 | 0 | |||||||||
−30.7970 | − | 11.2092i | −1.37317 | − | 0.499793i | −0.453070 | − | 0.891475i | ||
−0.920101 | + | 0.391682i | ||||||||
0 | 0 | |||||||||
−2.10928 | + | 11.9623i | −0.0938618 | + | 0.532317i | |||||
0 | 0 | |||||||||
1.13638 | + | 1.96826i | 0.0504682 | + | 0.0874136i | |||||
0 | 0 | |||||||||
−4.56507 | − | 25.8898i | −0.202343 | − | 1.14755i | −0.901566 | − | 0.432642i | ||
0.699222 | − | 0.714904i | ||||||||
0 | 0 | |||||||||
40.6038 | − | 14.7786i | 1.79620 | − | 0.653765i | |||||
0 | 0 | |||||||||
−4.71928 | + | 1.71768i | −0.208361 | + | 0.0758373i | |||||
0 | 0 | |||||||||
−23.5439 | − | 19.7557i | −1.03747 | − | 0.870540i | |||||
0 | 0 | |||||||||
−9.64235 | −0.424070 | |||||||||
0 | 0 | |||||||||
17.6416 | 0.774380 | |||||||||
0 | 0 | |||||||||
−20.9631 | − | 17.5902i | −0.918412 | − | 0.770639i | 0.0552886 | − | 0.998470i | ||
−0.973701 | + | 0.227831i | ||||||||
0 | 0 | |||||||||
−37.7012 | + | 13.7221i | −1.64856 | + | 0.600026i | −0.988505 | − | 0.151191i | ||
−0.660054 | + | 0.751218i | ||||||||
0 | 0 | |||||||||
−5.61615 | + | 2.04411i | −0.245109 | + | 0.0892123i | |||||
0 | 0 | |||||||||
9.58832 | + | 54.3781i | 0.417674 | + | 2.36875i | |||||
0 | 0 | |||||||||
11.4741 | + | 19.8738i | 0.498876 | + | 0.864078i | |||||
0 | 0 | |||||||||
3.50045 | − | 19.8521i | 0.151907 | − | 0.861506i | |||||
0 | 0 | |||||||||
22.8994 | + | 8.33470i | 0.991883 | + | 0.361016i | |||||
0 | 0 | |||||||||
5.93247 | + | 33.6447i | 0.256483 | + | 1.45459i | |||||
0 | 0 | |||||||||
9.61827 | + | 8.07069i | 0.415059 | + | 0.348276i | |||||
0 | 0 | |||||||||
5.22336 | + | 1.90115i | 0.224986 | + | 0.0818882i | |||||
0 | 0 | |||||||||
−13.2494 | + | 22.9486i | −0.569635 | + | 0.986636i | 0.426967 | + | 0.904267i | ||
−0.996602 | + | 0.0823693i | ||||||||
0 | 0 | |||||||||
−9.66766 | + | 8.11213i | −0.414879 | + | 0.348125i | |||||
0 | 0 | |||||||||
0.179626 | − | 0.311121i | 0.00769431 | − | 0.0133269i | |||||
0 | 0 | |||||||||
−14.8012 | − | 25.6364i | −0.632853 | − | 1.09613i | −0.986966 | − | 0.160931i | ||
0.354113 | − | 0.935203i | ||||||||
0 | 0 | |||||||||
−5.56577 | −0.237541 | |||||||||
0 | 0 | |||||||||
−1.07938 | + | 6.12148i | −0.0459832 | + | 0.260784i | |||||
0 | 0 | |||||||||
−18.7017 | + | 15.6926i | −0.795279 | + | 0.667319i | |||||
0 | 0 | |||||||||
8.44654 | − | 12.2704i | 0.358535 | − | 0.520851i | |||||
0 | 0 | |||||||||
1.56151 | − | 1.31026i | 0.0661633 | − | 0.0555176i | −0.609106 | − | 0.793089i | ||
0.675270 | + | 0.737571i | ||||||||
0 | 0 | |||||||||
−2.22242 | + | 12.6040i | −0.0939985 | + | 0.533092i | |||||
0 | 0 | |||||||||
8.75358 | 0.369576 | |||||||||
0 | 0 | |||||||||
21.5625 | + | 37.3473i | 0.908751 | + | 1.57400i | 0.815802 | + | 0.578332i | ||
0.0929493 | + | 0.995671i | ||||||||
0 | 0 | |||||||||
−9.77198 | + | 16.9256i | −0.411110 | + | 0.712064i | |||||
0 | 0 | |||||||||
4.99446 | − | 4.19085i | 0.209748 | − | 0.175999i | |||||
0 | 0 | |||||||||
2.16570 | − | 3.75110i | 0.0907908 | − | 0.157254i | −0.817053 | − | 0.576562i | ||
0.907844 | + | 0.419308i | ||||||||
0 | 0 | |||||||||
−25.9464 | − | 9.44371i | −1.08582 | − | 0.395207i | −0.263751 | − | 0.964591i | ||
−0.822072 | + | 0.569384i | ||||||||
0 | 0 | |||||||||
1.68710 | + | 1.41564i | 0.0704795 | + | 0.0591393i | |||||
0 | 0 | |||||||||
−0.0747291 | − | 0.423810i | −0.00311642 | − | 0.0176741i | |||||
0 | 0 | |||||||||
−28.6487 | − | 10.4273i | −1.19266 | − | 0.434093i | −0.332004 | − | 0.943278i | ||
−0.860657 | + | 0.509185i | ||||||||
0 | 0 | |||||||||
−1.50246 | + | 8.52089i | −0.0624402 | + | 0.354116i | |||||
0 | 0 | |||||||||
21.8384 | + | 37.8252i | 0.906010 | + | 1.56925i | |||||
0 | 0 | |||||||||
1.76113 | + | 9.98786i | 0.0729385 | + | 0.413655i | |||||
0 | 0 | |||||||||
17.0773 | − | 6.21561i | 0.706058 | − | 0.256984i | |||||
0 | 0 | |||||||||
−3.46775 | + | 1.26216i | −0.143129 | + | 0.0520948i | −0.412591 | − | 0.910916i | ||
0.269462 | + | 0.963011i | ||||||||
0 | 0 | |||||||||
5.89130 | + | 4.94339i | 0.242747 | + | 0.203689i | |||||
0 | 0 | |||||||||
−1.28647 | −0.0529182 | |||||||||
0 | 0 | |||||||||
−0.261315 | −0.0107309 | −0.00536546 | − | 0.999986i | ||||||
−0.00536546 | + | 0.999986i | ||||||||
0 | 0 | |||||||||
−51.3092 | − | 43.0535i | −2.10347 | − | 1.76502i | |||||
0 | 0 | |||||||||
−3.46245 | + | 1.26023i | −0.141709 | + | 0.0515778i | |||||
0 | 0 | |||||||||
8.61184 | − | 3.13445i | 0.351870 | − | 0.128070i | −0.160037 | − | 0.987111i | ||
0.511907 | + | 0.859041i | ||||||||
0 | 0 | |||||||||
1.02400 | + | 5.80742i | 0.0417700 | + | 0.236890i | 0.998544 | − | 0.0539429i | ||
−0.956774 | + | 0.290832i | ||||||||
0 | 0 | |||||||||
7.45336 | + | 12.9096i | 0.303524 | + | 0.525720i | |||||
0 | 0 | |||||||||
−4.30770 | + | 24.4302i | −0.175133 | + | 0.993228i | |||||
0 | 0 | |||||||||
28.7256 | + | 10.4552i | 1.16593 | + | 0.424365i | 0.851214 | − | 0.524819i | ||
0.314721 | + | 0.949184i | ||||||||
0 | 0 | |||||||||
3.24828 | + | 18.4219i | 0.131627 | + | 0.746494i | |||||
0 | 0 | |||||||||
19.2779 | + | 16.1761i | 0.779899 | + | 0.654413i | |||||
0 | 0 | |||||||||
−1.91751 | − | 0.697915i | −0.0774473 | − | 0.0281885i | 0.303006 | − | 0.952989i | ||
−0.380453 | + | 0.924800i | ||||||||
0 | 0 | |||||||||
9.18095 | − | 15.9019i | 0.370211 | − | 0.641225i | |||||
0 | 0 | |||||||||
6.14266 | − | 5.15431i | 0.247294 | − | 0.207505i | −0.510712 | − | 0.859752i | ||
0.758006 | + | 0.652247i | ||||||||
0 | 0 | |||||||||
−5.81923 | + | 10.0792i | −0.233895 | + | 0.405118i | −0.958951 | − | 0.283572i | ||
0.725056 | + | 0.688690i | ||||||||
0 | 0 | |||||||||
−0.544133 | − | 0.942466i | −0.0218353 | − | 0.0378199i | |||||
0 | 0 | |||||||||
8.90316 | 0.356697 | |||||||||
0 | 0 | |||||||||
−5.36238 | + | 30.4116i | −0.214495 | + | 1.21646i | |||||
0 | 0 | |||||||||
0.933953 | − | 0.783679i | 0.0372985 | − | 0.0312971i | |||||
0 | 0 | |||||||||
45.6914 | + | 3.62983i | 1.82183 | + | 0.144731i | |||||
0 | 0 | |||||||||
23.8402 | − | 20.0043i | 0.949063 | − | 0.796358i | −0.0300766 | − | 0.999548i | ||
0.979139 | + | 0.203189i | ||||||||
0 | 0 | |||||||||
−3.37459 | + | 19.1382i | −0.134128 | + | 0.760677i | |||||
0 | 0 | |||||||||
53.5931 | 2.12678 | |||||||||
0 | 0 | |||||||||
−7.25365 | − | 12.5637i | −0.287400 | − | 0.497791i | |||||
0 | 0 | |||||||||
−14.8154 | + | 25.6610i | −0.586088 | + | 1.01514i | |||||
0 | 0 | |||||||||
−25.2141 | + | 21.1571i | −0.995897 | + | 0.835657i | −0.986411 | − | 0.164298i | ||
−0.00948626 | + | 0.999955i | ||||||||
0 | 0 | |||||||||
5.30025 | − | 9.18031i | 0.209022 | − | 0.362036i | −0.742385 | − | 0.669974i | ||
0.951407 | + | 0.307937i | ||||||||
0 | 0 | |||||||||
9.06195 | + | 3.29828i | 0.356814 | + | 0.129870i | |||||
0 | 0 | |||||||||
−31.5917 | − | 26.5086i | −1.24200 | − | 1.04216i | −0.997365 | − | 0.0725450i | ||
−0.244634 | − | 0.969616i | ||||||||
0 | 0 | |||||||||
2.04674 | + | 11.6077i | 0.0803417 | + | 0.455641i | |||||
0 | 0 | |||||||||
21.7481 | + | 7.91566i | 0.852375 | + | 0.310239i | |||||
0 | 0 | |||||||||
7.29955 | − | 41.3978i | 0.285653 | − | 1.62002i | −0.417289 | − | 0.908774i | ||
0.702943 | − | 0.711247i | ||||||||
0 | 0 | |||||||||
−12.5081 | − | 21.6646i | −0.488731 | − | 0.846506i | |||||
0 | 0 | |||||||||
4.71993 | + | 26.7680i | 0.184142 | + | 1.04432i | |||||
0 | 0 | |||||||||
19.7147 | − | 7.17557i | 0.767977 | − | 0.279521i | 0.0718269 | − | 0.997417i | ||
0.696150 | + | 0.717896i | ||||||||
0 | 0 | |||||||||
11.7123 | − | 4.26293i | 0.455556 | − | 0.165809i | −0.104042 | − | 0.994573i | ||
0.559598 | + | 0.828764i | ||||||||
0 | 0 | |||||||||
−17.5010 | − | 14.6851i | −0.679681 | − | 0.570320i | |||||
0 | 0 | |||||||||
−9.32881 | −0.361756 | |||||||||
0 | 0 | |||||||||
−1.34695 | −0.0521540 | |||||||||
0 | 0 | |||||||||
−17.8385 | − | 14.9683i | −0.689676 | − | 0.578707i | |||||
0 | 0 | |||||||||
3.05809 | − | 1.11305i | 0.118056 | − | 0.0429690i | |||||
0 | 0 | |||||||||
−44.2357 | + | 16.1005i | −1.70516 | + | 0.620628i | −0.996397 | − | 0.0848166i | ||
−0.708765 | + | 0.705445i | ||||||||
0 | 0 | |||||||||
−1.57241 | − | 8.91758i | −0.0605221 | − | 0.343238i | |||||
0 | 0 | |||||||||
16.6746 | + | 28.8812i | 0.640856 | + | 1.10999i | 0.985242 | + | 0.171166i | ||
−0.344387 | + | 0.938828i | ||||||||
0 | 0 | |||||||||
1.92437 | − | 10.9137i | 0.0738507 | − | 0.418828i | |||||
0 | 0 | |||||||||
−0.929898 | − | 0.338455i | −0.0356338 | − | 0.0129696i | |||||
0 | 0 | |||||||||
1.03627 | + | 5.87697i | 0.0396517 | + | 0.224876i | 0.998194 | − | 0.0600747i | ||
−0.958542 | + | 0.284951i | ||||||||
0 | 0 | |||||||||
−19.0699 | − | 16.0016i | −0.728625 | − | 0.611389i | |||||
0 | 0 | |||||||||
5.59301 | + | 2.03569i | 0.213387 | + | 0.0776664i | |||||
0 | 0 | |||||||||
13.2347 | − | 22.9231i | 0.504201 | − | 0.873302i | |||||
0 | 0 | |||||||||
−7.73164 | + | 6.48761i | −0.294125 | + | 0.246800i | −0.777894 | − | 0.628395i | ||
0.483769 | + | 0.875196i | ||||||||
0 | 0 | |||||||||
−4.49011 | + | 7.77710i | −0.170565 | + | 0.295428i | |||||
0 | 0 | |||||||||
−24.4168 | − | 42.2911i | −0.926181 | − | 1.60419i | |||||
0 | 0 | |||||||||
56.4978 | 2.14001 | |||||||||
0 | 0 | |||||||||
−1.55324 | + | 8.80889i | −0.0587491 | + | 0.333183i | |||||
0 | 0 | |||||||||
−18.3592 | + | 15.4052i | −0.693416 | + | 0.581845i | −0.919892 | − | 0.392172i | ||
0.226476 | + | 0.974017i | ||||||||
0 | 0 | |||||||||
5.19995 | − | 3.70332i | 0.196120 | − | 0.139673i | |||||
0 | 0 | |||||||||
14.5257 | − | 12.1885i | 0.547071 | − | 0.459047i | |||||
0 | 0 | |||||||||
−2.72027 | + | 15.4274i | −0.102306 | + | 0.580208i | |||||
0 | 0 | |||||||||
3.33993 | 0.125434 | 0.0627168 | − | 0.998031i | ||||||
0.0627168 | + | 0.998031i | ||||||||
0 | 0 | |||||||||
−7.67862 | − | 13.2998i | −0.287971 | − | 0.498780i | |||||
0 | 0 | |||||||||
−0.833244 | + | 1.44322i | −0.0312052 | + | 0.0540491i | |||||
0 | 0 | |||||||||
−8.14002 | + | 6.83029i | −0.304419 | + | 0.255438i | |||||
0 | 0 | |||||||||
6.12939 | − | 10.6164i | 0.228906 | − | 0.396477i | |||||
0 | 0 | |||||||||
−29.0244 | − | 10.5640i | −1.08243 | − | 0.393972i | −0.261617 | − | 0.965172i | ||
−0.820811 | + | 0.571200i | ||||||||
0 | 0 | |||||||||
−30.3638 | − | 25.4783i | −1.13081 | − | 0.948861i | |||||
0 | 0 | |||||||||
−0.753181 | − | 4.27150i | −0.0280111 | − | 0.158859i | |||||
0 | 0 | |||||||||
−10.5317 | − | 3.83321i | −0.391136 | − | 0.142362i | |||||
0 | 0 | |||||||||
−0.0553353 | + | 0.313822i | −0.00205227 | + | 0.0116390i | −0.985817 | − | 0.167826i | ||
0.983764 | + | 0.179465i | ||||||||
0 | 0 | |||||||||
−4.64512 | − | 8.04558i | −0.172041 | − | 0.297984i | |||||
0 | 0 | |||||||||
5.15253 | + | 29.2214i | 0.190573 | + | 1.08079i | |||||
0 | 0 | |||||||||
30.2544 | − | 11.0117i | 1.11747 | − | 0.406726i | 0.283742 | − | 0.958901i | ||
0.833728 | + | 0.552175i | ||||||||
0 | 0 | |||||||||
−10.2719 | + | 3.73867i | −0.378885 | + | 0.137903i | |||||
0 | 0 | |||||||||
−6.67691 | − | 5.60259i | −0.245947 | − | 0.206374i | |||||
0 | 0 | |||||||||
31.0155 | 1.14092 | 0.570461 | − | 0.821325i | ||||||
0.570461 | + | 0.821325i | ||||||||
0 | 0 | |||||||||
−3.18195 | −0.116892 | |||||||||
0 | 0 | |||||||||
−2.11789 | − | 1.77712i | −0.0776980 | − | 0.0651964i | 0.603111 | − | 0.797657i | ||
−0.680809 | + | 0.732461i | ||||||||
0 | 0 | |||||||||
−19.7924 | + | 7.20386i | −0.725139 | + | 0.263929i | |||||
0 | 0 | |||||||||
−25.8179 | + | 9.39696i | −0.944629 | + | 0.343817i | |||||
0 | 0 | |||||||||
7.65091 | + | 43.3905i | 0.279558 | + | 1.58545i | |||||
0 | 0 | |||||||||
−14.0482 | − | 24.3323i | −0.512628 | − | 0.887897i | −0.999893 | − | 0.0146429i | ||
0.487265 | − | 0.873254i | ||||||||
0 | 0 | |||||||||
2.88111 | − | 16.3396i | 0.104993 | − | 0.595447i | |||||
0 | 0 | |||||||||
−6.59545 | − | 2.40055i | −0.240033 | − | 0.0873649i | |||||
0 | 0 | |||||||||
−5.72565 | − | 32.4718i | −0.208102 | − | 1.18021i | −0.892483 | − | 0.451082i | ||
0.684380 | − | 0.729125i | ||||||||
0 | 0 | |||||||||
0.202381 | + | 0.169818i | 0.00734597 | + | 0.00616400i | |||||
0 | 0 | |||||||||
5.00448 | + | 1.82148i | 0.181412 | + | 0.0660286i | 0.431129 | − | 0.902290i | ||
−0.249717 | + | 0.968319i | ||||||||
0 | 0 | |||||||||
0.231657 | − | 0.401242i | 0.00838655 | − | 0.0145259i | |||||
0 | 0 | |||||||||
32.2760 | − | 27.0828i | 1.16694 | − | 0.979180i | |||||
0 | 0 | |||||||||
15.3810 | − | 26.6407i | 0.555377 | − | 0.961942i | |||||
0 | 0 | |||||||||
−17.9353 | − | 31.0648i | −0.646762 | − | 1.12022i | −0.983892 | − | 0.178766i | ||
0.337130 | − | 0.941458i | ||||||||
0 | 0 | |||||||||
−16.3134 | −0.587513 | |||||||||
0 | 0 | |||||||||
0.584521 | − | 3.31498i | 0.0210238 | − | 0.119232i | −0.972490 | − | 0.232946i | ||
0.993514 | + | 0.113714i | ||||||||
0 | 0 | |||||||||
−10.6223 | + | 8.91313i | −0.381563 | + | 0.320169i | |||||
0 | 0 | |||||||||
10.8932 | − | 15.8248i | 0.390792 | − | 0.567710i | |||||
0 | 0 | |||||||||
6.02797 | − | 5.05806i | 0.215974 | − | 0.181224i | |||||
0 | 0 | |||||||||
3.00852 | − | 17.0622i | 0.107653 | − | 0.610532i | |||||
0 | 0 | |||||||||
−28.3417 | −1.01285 | |||||||||
0 | 0 | |||||||||
10.6530 | + | 18.4515i | 0.380222 | + | 0.658563i | |||||
0 | 0 | |||||||||
20.2776 | − | 35.1219i | 0.722820 | − | 1.25196i | −0.237045 | − | 0.971499i | ||
0.959865 | − | 0.280462i | ||||||||
0 | 0 | |||||||||
5.64677 | − | 4.73820i | 0.201030 | − | 0.168684i | |||||
0 | 0 | |||||||||
−12.6026 | + | 21.8283i | −0.448097 | + | 0.776127i | |||||
0 | 0 | |||||||||
−7.98128 | − | 2.90495i | −0.283424 | − | 0.103158i | |||||
0 | 0 | |||||||||
−15.2783 | − | 12.8201i | −0.541867 | − | 0.454681i | |||||
0 | 0 | |||||||||
−7.10571 | − | 40.2985i | −0.251697 | − | 1.42745i | −0.804410 | − | 0.594075i | ||
0.552713 | − | 0.833372i | ||||||||
0 | 0 | |||||||||
54.8257 | + | 19.9549i | 1.93960 | + | 0.705955i | |||||
0 | 0 | |||||||||
−0.972521 | + | 5.51544i | −0.0343623 | + | 0.194878i | |||||
0 | 0 | |||||||||
−7.94647 | − | 13.7637i | −0.280425 | − | 0.485710i | |||||
0 | 0 | |||||||||
−0.351028 | − | 1.99078i | −0.0123721 | − | 0.0701657i | |||||
0 | 0 | |||||||||
5.64954 | − | 2.05626i | 0.198873 | − | 0.0723839i | |||||
0 | 0 | |||||||||
−43.8247 | + | 15.9509i | −1.54079 | + | 0.560803i | −0.966235 | − | 0.257661i | ||
−0.574558 | + | 0.818464i | ||||||||
0 | 0 | |||||||||
−19.0963 | − | 16.0237i | −0.670562 | − | 0.562668i | 0.242670 | − | 0.970109i | ||
−0.913232 | + | 0.407441i | ||||||||
0 | 0 | |||||||||
16.8471 | 0.590853 | |||||||||
0 | 0 | |||||||||
23.8848 | 0.836647 | |||||||||
0 | 0 | |||||||||
3.16584 | + | 2.65646i | 0.110759 | + | 0.0929377i | |||||
0 | 0 | |||||||||
22.0240 | − | 8.01607i | 0.769580 | − | 0.280104i | |||||
0 | 0 | |||||||||
−32.2949 | + | 11.7544i | −1.12710 | + | 0.410231i | −0.837238 | − | 0.546838i | ||
−0.289861 | + | 0.957069i | ||||||||
0 | 0 | |||||||||
3.74718 | + | 21.2513i | 0.130619 | + | 0.740774i | 0.977811 | + | 0.209488i | ||
−0.847193 | + | 0.531286i | ||||||||
0 | 0 | |||||||||
1.09912 | + | 1.90374i | 0.0382666 | + | 0.0662796i | |||||
0 | 0 | |||||||||
4.05290 | − | 22.9852i | 0.140933 | − | 0.799272i | −0.829610 | − | 0.558344i | ||
0.970543 | − | 0.240928i | ||||||||
0 | 0 | |||||||||
17.5307 | + | 6.38067i | 0.608868 | + | 0.221610i | 0.628008 | − | 0.778207i | ||
−0.0191401 | + | 0.999817i | ||||||||
0 | 0 | |||||||||
4.31561 | + | 24.4751i | 0.149707 | + | 0.849030i | |||||
0 | 0 | |||||||||
−25.7652 | − | 21.6196i | −0.892712 | − | 0.749074i | |||||
0 | 0 | |||||||||
49.9741 | + | 18.1891i | 1.72943 | + | 0.629460i | |||||
0 | 0 | |||||||||
−17.5327 | + | 30.3675i | −0.606018 | + | 1.04965i | |||||
0 | 0 | |||||||||
−19.0280 | + | 15.9664i | −0.656919 | + | 0.551220i | −0.909161 | − | 0.416444i | ||
0.252243 | + | 0.967664i | ||||||||
0 | 0 | |||||||||
−3.03927 | + | 5.26417i | −0.104802 | + | 0.181523i | |||||
0 | 0 | |||||||||
1.72587 | + | 2.98930i | 0.0594423 | + | 0.102957i | |||||
0 | 0 | |||||||||
−6.39634 | −0.220041 | |||||||||
0 | 0 | |||||||||
−5.55550 | + | 31.5068i | −0.190889 | + | 1.08259i | |||||
0 | 0 | |||||||||
14.9478 | − | 12.5427i | 0.513009 | − | 0.430465i | |||||
0 | 0 | |||||||||
0.985957 | + | 0.970325i | 0.0337982 | + | 0.0332623i | |||||
0 | 0 | |||||||||
−27.6465 | + | 23.1982i | −0.946599 | + | 0.794291i | −0.978722 | − | 0.205193i | ||
0.0321226 | + | 0.999484i | ||||||||
0 | 0 | |||||||||
1.01902 | − | 5.77913i | 0.0348496 | − | 0.197642i | |||||
0 | 0 | |||||||||
−23.1215 | −0.789814 | −0.394907 | − | 0.918721i | ||||||
−0.394907 | + | 0.918721i | ||||||||
0 | 0 | |||||||||
−17.2312 | − | 29.8454i | −0.587922 | − | 1.01831i | −0.994504 | − | 0.104697i | ||
0.406582 | − | 0.913614i | ||||||||
0 | 0 | |||||||||
11.8404 | − | 20.5081i | 0.403518 | − | 0.698914i | |||||
0 | 0 | |||||||||
−28.1125 | + | 23.5892i | −0.956960 | + | 0.802985i | −0.980456 | − | 0.196739i | ||
0.0234960 | + | 0.999724i | ||||||||
0 | 0 | |||||||||
−24.8249 | + | 42.9980i | −0.844071 | + | 1.46197i | |||||
0 | 0 | |||||||||
−34.8705 | − | 12.6918i | −1.18426 | − | 0.431037i | |||||
0 | 0 | |||||||||
6.87870 | + | 5.77191i | 0.233344 | + | 0.195799i | |||||
0 | 0 | |||||||||
3.95015 | + | 22.4024i | 0.133846 | + | 0.759078i | |||||
0 | 0 | |||||||||
6.55073 | + | 2.38427i | 0.221709 | + | 0.0806954i | |||||
0 | 0 | |||||||||
−4.79679 | + | 27.2040i | −0.162161 | + | 0.919662i | |||||
0 | 0 | |||||||||
−7.04975 | − | 12.2105i | −0.238053 | − | 0.412320i | 0.722102 | − | 0.691786i | ||
−0.960156 | + | 0.279466i | ||||||||
0 | 0 | |||||||||
−4.06257 | − | 23.0400i | −0.137027 | − | 0.777119i | |||||
0 | 0 | |||||||||
34.2171 | − | 12.4540i | 1.15280 | − | 0.419587i | 0.306283 | − | 0.951940i | ||
0.846522 | + | 0.532354i | ||||||||
0 | 0 | |||||||||
−3.95749 | + | 1.44041i | −0.133180 | + | 0.0484736i | −0.407750 | − | 0.913093i | ||
0.274570 | + | 0.961567i | ||||||||
0 | 0 | |||||||||
−17.7562 | − | 14.8992i | −0.596867 | − | 0.500830i | |||||
0 | 0 | |||||||||
10.5188 | 0.353188 | 0.176594 | − | 0.984284i | ||||||
0.176594 | + | 0.984284i | ||||||||
0 | 0 | |||||||||
69.1172 | 2.31812 | |||||||||
0 | 0 | |||||||||
−1.83702 | − | 1.54144i | −0.0615423 | − | 0.0516402i | |||||
0 | 0 | |||||||||
7.63606 | − | 2.77930i | 0.255531 | − | 0.0930057i | |||||
0 | 0 | |||||||||
−33.2054 | + | 12.0858i | −1.10993 | + | 0.403982i | |||||
0 | 0 | |||||||||
−0.119732 | − | 0.679031i | −0.00399772 | − | 0.0226722i | |||||
0 | 0 | |||||||||
21.7002 | + | 37.5858i | 0.723742 | + | 1.25356i | |||||
0 | 0 | |||||||||
10.6563 | − | 60.4350i | 0.355013 | − | 2.01338i | |||||
0 | 0 | |||||||||
11.6869 | + | 4.25368i | 0.388916 | + | 0.141554i | |||||
0 | 0 | |||||||||
−6.16761 | − | 34.9783i | −0.205018 | − | 1.16272i | |||||
0 | 0 | |||||||||
23.4994 | + | 19.7184i | 0.780286 | + | 0.654738i | 0.943321 | − | 0.331883i | ||
−0.163035 | + | 0.986620i | ||||||||
0 | 0 | |||||||||
−9.26003 | − | 3.37038i | −0.307136 | − | 0.111788i | |||||
0 | 0 | |||||||||
−6.03455 | + | 10.4521i | −0.199934 | + | 0.346295i | −0.948507 | − | 0.316757i | ||
0.748573 | + | 0.663052i | ||||||||
0 | 0 | |||||||||
12.3063 | − | 10.3262i | 0.407280 | − | 0.341749i | |||||
0 | 0 | |||||||||
−3.19990 | + | 5.54238i | −0.105785 | + | 0.183226i | |||||
0 | 0 | |||||||||
−16.1312 | − | 27.9401i | −0.532701 | − | 0.922664i | |||||
0 | 0 | |||||||||
3.94293 | 0.130065 | 0.0650327 | − | 0.997883i | ||||||
0.0650327 | + | 0.997883i | ||||||||
0 | 0 | |||||||||
3.54740 | − | 20.1183i | 0.116891 | − | 0.662920i | |||||
0 | 0 | |||||||||
−34.6385 | + | 29.0652i | −1.14014 | + | 0.956691i | |||||
0 | 0 | |||||||||
4.94771 | + | 10.3928i | 0.162680 | + | 0.341712i | |||||
0 | 0 | |||||||||
19.1003 | − | 16.0271i | 0.627338 | − | 0.526399i | |||||
0 | 0 | |||||||||
−7.19718 | + | 40.8172i | −0.236132 | + | 1.33917i | 0.604085 | + | 0.796920i | ||
−0.840217 | + | 0.542250i | ||||||||
0 | 0 | |||||||||
−4.68452 | −0.153529 | |||||||||
0 | 0 | |||||||||
−0.243491 | − | 0.421738i | −0.00797153 | − | 0.0138071i | |||||
0 | 0 | |||||||||
−12.3179 | + | 21.3351i | −0.402837 | + | 0.697734i | |||||
0 | 0 | |||||||||
−2.45023 | + | 2.05599i | −0.0800455 | + | 0.0671662i | −0.681932 | − | 0.731415i | ||
0.601887 | + | 0.798581i | ||||||||
0 | 0 | |||||||||
12.5649 | − | 21.7631i | 0.410041 | − | 0.710213i | |||||
0 | 0 | |||||||||
−4.69883 | − | 1.71023i | −0.153177 | − | 0.0557520i | 0.264294 | − | 0.964442i | ||
−0.417471 | + | 0.908690i | ||||||||
0 | 0 | |||||||||
1.30622 | + | 1.09605i | 0.0425363 | + | 0.0356922i | |||||
0 | 0 | |||||||||
−7.38614 | − | 41.8889i | −0.240271 | − | 1.36265i | |||||
0 | 0 | |||||||||
−19.3880 | − | 7.05667i | −0.630026 | − | 0.229311i | 0.00721636 | − | 0.999974i | ||
−0.637243 | + | 0.770663i | ||||||||
0 | 0 | |||||||||
−7.20273 | + | 40.8487i | −0.233810 | + | 1.32600i | |||||
0 | 0 | |||||||||
6.41895 | + | 11.1179i | 0.208149 | + | 0.360524i | |||||
0 | 0 | |||||||||
0.215365 | + | 1.22139i | 0.00697635 | + | 0.0395648i | 0.988097 | − | 0.153831i | ||
−0.981121 | + | 0.193396i | ||||||||
0 | 0 | |||||||||
−5.82440 | + | 2.11991i | −0.188473 | + | 0.0685986i | |||||
0 | 0 | |||||||||
6.46536 | − | 2.35320i | 0.208996 | − | 0.0760681i | |||||
0 | 0 | |||||||||
−24.5939 | − | 20.6367i | −0.794177 | − | 0.666394i | |||||
0 | 0 | |||||||||
22.6964 | 0.732143 | |||||||||
0 | 0 | |||||||||
−27.7158 | −0.893130 | |||||||||
0 | 0 | |||||||||
−18.6538 | − | 15.6524i | −0.600486 | − | 0.503868i | |||||
0 | 0 | |||||||||
30.3246 | − | 11.0373i | 0.975173 | − | 0.354934i | 0.195212 | − | 0.980761i | ||
0.779962 | + | 0.625827i | ||||||||
0 | 0 | |||||||||
−6.93222 | + | 2.52312i | −0.222695 | + | 0.0810544i | |||||
0 | 0 | |||||||||
3.97330 | + | 22.5337i | 0.127509 | + | 0.723141i | 0.979786 | + | 0.200050i | ||
−0.852276 | + | 0.523092i | ||||||||
0 | 0 | |||||||||
−31.4895 | − | 54.5414i | −1.00951 | − | 1.74852i | |||||
0 | 0 | |||||||||
0.996252 | − | 5.65002i | 0.0319056 | − | 0.180946i | |||||
0 | 0 | |||||||||
−45.0795 | − | 16.4076i | −1.44222 | − | 0.524926i | −0.501815 | − | 0.864975i | ||
−0.940408 | + | 0.340049i | ||||||||
0 | 0 | |||||||||
−0.568641 | − | 3.22492i | −0.0181738 | − | 0.103069i | |||||
0 | 0 | |||||||||
0.223262 | + | 0.187339i | 0.00712820 | + | 0.00598127i | |||||
0 | 0 | |||||||||
−23.6561 | − | 8.61011i | −0.754512 | − | 0.274620i | −0.0640089 | − | 0.997949i | ||
−0.690503 | + | 0.723329i | ||||||||
0 | 0 | |||||||||
1.81029 | − | 3.13551i | 0.0576806 | − | 0.0999058i | |||||
0 | 0 | |||||||||
18.7334 | − | 15.7192i | 0.596290 | − | 0.500346i | |||||
0 | 0 | |||||||||
−0.447765 | + | 0.775552i | −0.0142381 | + | 0.0246611i | |||||
0 | 0 | |||||||||
−5.92932 | − | 10.2699i | −0.188351 | − | 0.326234i | 0.756350 | − | 0.654168i | ||
−0.944701 | + | 0.327934i | ||||||||
0 | 0 | |||||||||
−18.9359 | −0.600913 | |||||||||
0 | 0 | |||||||||
1.80073 | − | 10.2124i | 0.0570868 | − | 0.323756i | |||||
0 | 0 | |||||||||
−9.84239 | + | 8.25875i | −0.311712 | + | 0.261557i | −0.785199 | − | 0.619243i | ||
0.473487 | + | 0.880801i | ||||||||
0 | 0 | |||||||||
20.7460 | + | 20.4171i | 0.656374 | + | 0.645967i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 592.2.bc.g.49.4 | 30 | ||
4.3 | odd | 2 | 296.2.u.b.49.2 | ✓ | 30 | ||
37.34 | even | 9 | inner | 592.2.bc.g.145.4 | 30 | ||
148.71 | odd | 18 | 296.2.u.b.145.2 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
296.2.u.b.49.2 | ✓ | 30 | 4.3 | odd | 2 | ||
296.2.u.b.145.2 | yes | 30 | 148.71 | odd | 18 | ||
592.2.bc.g.49.4 | 30 | 1.1 | even | 1 | trivial | ||
592.2.bc.g.145.4 | 30 | 37.34 | even | 9 | inner |