Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [702,2,Mod(161,702)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(702, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("702.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 702.j (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 593.4 | ||
Character | 702.593 | ||
Dual form | 702.2.j.b.161.4 |
-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 .
−0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | |||||
0 | 0 | |||||||||
− | 1.00000i | − | 0.500000i | |||||||
0.730953 | − | 0.730953i | 0.326892 | − | 0.326892i | −0.524511 | − | 0.851403i | ||
0.851403 | + | 0.524511i | ||||||||
0 | 0 | |||||||||
−2.49696 | + | 2.49696i | −0.943761 | + | 0.943761i | −0.998501 | − | 0.0547394i | ||
0.0547394 | + | 0.998501i | ||||||||
0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | |||||
0 | 0 | |||||||||
1.03372i | 0.326892i | |||||||||
1.95374 | + | 1.95374i | 0.589075 | + | 0.589075i | 0.937381 | − | 0.348306i | ||
−0.348306 | + | 0.937381i | ||||||||
0 | 0 | |||||||||
−3.21489 | + | 1.63232i | −0.891651 | + | 0.452723i | |||||
− | 3.53123i | − | 0.943761i | |||||||
0 | 0 | |||||||||
−1.00000 | −0.250000 | |||||||||
5.44078 | 1.31958 | 0.659791 | − | 0.751449i | ||||||
0.659791 | + | 0.751449i | ||||||||
0 | 0 | |||||||||
−5.99076 | − | 5.99076i | −1.37438 | − | 1.37438i | −0.853840 | − | 0.520536i | ||
−0.520536 | − | 0.853840i | ||||||||
−0.730953 | − | 0.730953i | −0.163446 | − | 0.163446i | |||||
0 | 0 | |||||||||
−2.76300 | −0.589075 | |||||||||
−5.11422 | −1.06639 | −0.533194 | − | 0.845993i | ||||||
−0.533194 | + | 0.845993i | ||||||||
0 | 0 | |||||||||
3.93142i | 0.786283i | |||||||||
1.11905 | − | 3.42750i | 0.219464 | − | 0.672187i | |||||
0 | 0 | |||||||||
2.49696 | + | 2.49696i | 0.471881 | + | 0.471881i | |||||
8.51991i | 1.58211i | 0.611746 | + | 0.791054i | ||||||
−0.611746 | + | 0.791054i | ||||||||
0 | 0 | |||||||||
3.53068 | + | 3.53068i | 0.634129 | + | 0.634129i | 0.949101 | − | 0.314972i | ||
−0.314972 | + | 0.949101i | ||||||||
0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | |||||
0 | 0 | |||||||||
−3.84721 | + | 3.84721i | −0.659791 | + | 0.659791i | |||||
3.65032i | 0.617016i | |||||||||
0 | 0 | |||||||||
−7.78749 | + | 7.78749i | −1.28026 | + | 1.28026i | −0.339734 | + | 0.940521i | ||
−0.940521 | + | 0.339734i | ||||||||
8.47222 | 1.37438 | |||||||||
0 | 0 | |||||||||
1.03372 | 0.163446 | |||||||||
1.06181 | − | 1.06181i | 0.165827 | − | 0.165827i | −0.619315 | − | 0.785142i | ||
0.785142 | + | 0.619315i | ||||||||
0 | 0 | |||||||||
3.79673i | 0.578996i | 0.957179 | + | 0.289498i | ||||||
−0.957179 | + | 0.289498i | ||||||||
1.95374 | − | 1.95374i | 0.294537 | − | 0.294537i | |||||
0 | 0 | |||||||||
3.61630 | − | 3.61630i | 0.533194 | − | 0.533194i | |||||
−7.80931 | − | 7.80931i | −1.13910 | − | 1.13910i | −0.988611 | − | 0.150493i | ||
−0.150493 | − | 0.988611i | ||||||||
0 | 0 | |||||||||
− | 5.46960i | − | 0.781371i | |||||||
−2.77993 | − | 2.77993i | −0.393142 | − | 0.393142i | |||||
0 | 0 | |||||||||
1.63232 | + | 3.21489i | 0.226362 | + | 0.445826i | |||||
11.7290i | 1.61111i | 0.592522 | + | 0.805554i | ||||||
−0.592522 | + | 0.805554i | ||||||||
0 | 0 | |||||||||
2.85618 | 0.385128 | |||||||||
−3.53123 | −0.471881 | |||||||||
0 | 0 | |||||||||
−6.02449 | − | 6.02449i | −0.791054 | − | 0.791054i | |||||
−1.86185 | − | 1.86185i | −0.242393 | − | 0.242393i | 0.575447 | − | 0.817839i | ||
−0.817839 | + | 0.575447i | ||||||||
0 | 0 | |||||||||
6.42979 | 0.823250 | 0.411625 | − | 0.911353i | ||||||
0.411625 | + | 0.911353i | ||||||||
−4.99314 | −0.634129 | |||||||||
0 | 0 | |||||||||
1.00000i | 0.125000i | |||||||||
−1.15679 | + | 3.54308i | −0.143482 | + | 0.439465i | |||||
0 | 0 | |||||||||
0.887018 | + | 0.887018i | 0.108367 | + | 0.108367i | 0.759211 | − | 0.650845i | ||
−0.650845 | + | 0.759211i | ||||||||
− | 5.44078i | − | 0.659791i | |||||||
0 | 0 | |||||||||
−2.58116 | − | 2.58116i | −0.308508 | − | 0.308508i | |||||
−3.17883 | + | 3.17883i | −0.377258 | + | 0.377258i | −0.870112 | − | 0.492854i | ||
0.492854 | + | 0.870112i | ||||||||
0 | 0 | |||||||||
−2.31653 | + | 2.31653i | −0.271129 | + | 0.271129i | −0.829555 | − | 0.558425i | ||
0.558425 | + | 0.829555i | ||||||||
− | 11.0132i | − | 1.28026i | |||||||
0 | 0 | |||||||||
−5.99076 | + | 5.99076i | −0.687188 | + | 0.687188i | |||||
−9.75681 | −1.11189 | |||||||||
0 | 0 | |||||||||
−5.29836 | −0.596112 | −0.298056 | − | 0.954548i | ||||||
−0.298056 | + | 0.954548i | ||||||||
−0.730953 | + | 0.730953i | −0.0817230 | + | 0.0817230i | |||||
0 | 0 | |||||||||
1.50163i | 0.165827i | |||||||||
4.77771 | − | 4.77771i | 0.524422 | − | 0.524422i | −0.394482 | − | 0.918904i | ||
0.918904 | + | 0.394482i | ||||||||
0 | 0 | |||||||||
3.97695 | − | 3.97695i | 0.431361 | − | 0.431361i | |||||
−2.68469 | − | 2.68469i | −0.289498 | − | 0.289498i | |||||
0 | 0 | |||||||||
2.76300i | 0.294537i | |||||||||
0.144930 | + | 0.144930i | 0.0153625 | + | 0.0153625i | 0.714746 | − | 0.699384i | ||
−0.699384 | + | 0.714746i | ||||||||
0 | 0 | |||||||||
3.95163 | − | 12.1033i | 0.414243 | − | 1.26877i | |||||
5.11422i | 0.533194i | |||||||||
0 | 0 | |||||||||
11.0440 | 1.13910 | |||||||||
−8.75793 | −0.898545 | |||||||||
0 | 0 | |||||||||
−4.66500 | − | 4.66500i | −0.473659 | − | 0.473659i | 0.429438 | − | 0.903097i | ||
−0.903097 | + | 0.429438i | ||||||||
3.86759 | + | 3.86759i | 0.390685 | + | 0.390685i | |||||
0 | 0 | |||||||||
3.93142 | 0.393142 | |||||||||
16.6680 | 1.65853 | 0.829266 | − | 0.558855i | ||||||
0.829266 | + | 0.558855i | ||||||||
0 | 0 | |||||||||
− | 1.83045i | − | 0.180360i | −0.995925 | − | 0.0901799i | ||||
0.995925 | − | 0.0901799i | ||||||||
−3.42750 | − | 1.11905i | −0.336094 | − | 0.109732i | |||||
0 | 0 | |||||||||
−8.29369 | − | 8.29369i | −0.805554 | − | 0.805554i | |||||
9.43019i | 0.911651i | 0.890069 | + | 0.455825i | ||||||
−0.890069 | + | 0.455825i | ||||||||
0 | 0 | |||||||||
−6.65317 | − | 6.65317i | −0.637259 | − | 0.637259i | 0.312620 | − | 0.949878i | ||
−0.949878 | + | 0.312620i | ||||||||
−2.01963 | + | 2.01963i | −0.192564 | + | 0.192564i | |||||
0 | 0 | |||||||||
2.49696 | − | 2.49696i | 0.235940 | − | 0.235940i | |||||
− | 13.5909i | − | 1.27852i | −0.768989 | − | 0.639262i | ||||
0.768989 | − | 0.639262i | ||||||||
0 | 0 | |||||||||
−3.73825 | + | 3.73825i | −0.348594 | + | 0.348594i | |||||
8.51991 | 0.791054 | |||||||||
0 | 0 | |||||||||
2.63306 | 0.242393 | |||||||||
−13.5854 | + | 13.5854i | −1.24537 | + | 1.24537i | |||||
0 | 0 | |||||||||
− | 3.36580i | − | 0.305982i | |||||||
−4.54655 | + | 4.54655i | −0.411625 | + | 0.411625i | |||||
0 | 0 | |||||||||
3.53068 | − | 3.53068i | 0.317065 | − | 0.317065i | |||||
6.52844 | + | 6.52844i | 0.583922 | + | 0.583922i | |||||
0 | 0 | |||||||||
11.0838i | 0.983531i | 0.870728 | + | 0.491766i | ||||||
−0.870728 | + | 0.491766i | ||||||||
−0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | |||||
0 | 0 | |||||||||
−1.68736 | − | 3.32331i | −0.147992 | − | 0.291474i | |||||
− | 12.1356i | − | 1.06029i | −0.847906 | − | 0.530146i | ||||
0.847906 | − | 0.530146i | ||||||||
0 | 0 | |||||||||
29.9174 | 2.59416 | |||||||||
−1.25443 | −0.108367 | |||||||||
0 | 0 | |||||||||
3.84721 | + | 3.84721i | 0.329896 | + | 0.329896i | |||||
9.00744 | + | 9.00744i | 0.769558 | + | 0.769558i | 0.978029 | − | 0.208471i | ||
−0.208471 | + | 0.978029i | ||||||||
0 | 0 | |||||||||
3.26746 | 0.277142 | 0.138571 | − | 0.990352i | ||||||
0.138571 | + | 0.990352i | ||||||||
3.65032 | 0.308508 | |||||||||
0 | 0 | |||||||||
− | 4.49554i | − | 0.377258i | |||||||
−9.47019 | − | 3.09194i | −0.791937 | − | 0.258561i | |||||
0 | 0 | |||||||||
6.22765 | + | 6.22765i | 0.517178 | + | 0.517178i | |||||
− | 3.27607i | − | 0.271129i | |||||||
0 | 0 | |||||||||
7.78749 | + | 7.78749i | 0.640128 | + | 0.640128i | |||||
10.6695 | − | 10.6695i | 0.874082 | − | 0.874082i | −0.118832 | − | 0.992914i | ||
0.992914 | + | 0.118832i | ||||||||
0 | 0 | |||||||||
10.4284 | − | 10.4284i | 0.848649 | − | 0.848649i | −0.141316 | − | 0.989965i | ||
0.989965 | + | 0.141316i | ||||||||
− | 8.47222i | − | 0.687188i | |||||||
0 | 0 | |||||||||
6.89911 | − | 6.89911i | 0.555946 | − | 0.555946i | |||||
5.16152 | 0.414583 | |||||||||
0 | 0 | |||||||||
9.82931 | 0.784465 | 0.392232 | − | 0.919866i | ||||||
0.392232 | + | 0.919866i | ||||||||
3.74650 | − | 3.74650i | 0.298056 | − | 0.298056i | |||||
0 | 0 | |||||||||
− | 1.03372i | − | 0.0817230i | |||||||
12.7700 | − | 12.7700i | 1.00642 | − | 1.00642i | |||||
0 | 0 | |||||||||
−0.658684 | + | 0.658684i | −0.0515921 | + | 0.0515921i | −0.732432 | − | 0.680840i | ||
0.680840 | + | 0.732432i | ||||||||
−1.06181 | − | 1.06181i | −0.0829136 | − | 0.0829136i | |||||
0 | 0 | |||||||||
6.75670i | 0.524422i | |||||||||
12.5357 | + | 12.5357i | 0.970041 | + | 0.970041i | 0.999564 | − | 0.0295232i | ||
−0.0295232 | + | 0.999564i | ||||||||
0 | 0 | |||||||||
7.67108 | − | 10.4955i | 0.590083 | − | 0.807342i | |||||
5.62426i | 0.431361i | |||||||||
0 | 0 | |||||||||
3.79673 | 0.289498 | |||||||||
−3.87945 | −0.294949 | −0.147475 | − | 0.989066i | ||||||
−0.147475 | + | 0.989066i | ||||||||
0 | 0 | |||||||||
−9.81658 | − | 9.81658i | −0.742064 | − | 0.742064i | |||||
−1.95374 | − | 1.95374i | −0.147269 | − | 0.147269i | |||||
0 | 0 | |||||||||
−0.204962 | −0.0153625 | |||||||||
−5.10968 | −0.381916 | −0.190958 | − | 0.981598i | ||||||
−0.190958 | + | 0.981598i | ||||||||
0 | 0 | |||||||||
− | 4.01356i | − | 0.298326i | −0.988813 | − | 0.149163i | ||||
0.988813 | − | 0.149163i | ||||||||
5.76409 | + | 11.3525i | 0.427263 | + | 0.841506i | |||||
0 | 0 | |||||||||
−3.61630 | − | 3.61630i | −0.266597 | − | 0.266597i | |||||
11.3846i | 0.837011i | |||||||||
0 | 0 | |||||||||
10.6299 | + | 10.6299i | 0.777332 | + | 0.777332i | |||||
−7.80931 | + | 7.80931i | −0.569552 | + | 0.569552i | |||||
0 | 0 | |||||||||
6.19279 | − | 6.19279i | 0.449272 | − | 0.449272i | |||||
22.1476i | 1.60254i | 0.598302 | + | 0.801271i | ||||||
−0.598302 | + | 0.801271i | ||||||||
0 | 0 | |||||||||
−2.20149 | + | 2.20149i | −0.158467 | + | 0.158467i | −0.781887 | − | 0.623420i | ||
0.623420 | + | 0.781887i | ||||||||
6.59730 | 0.473659 | |||||||||
0 | 0 | |||||||||
−5.46960 | −0.390685 | |||||||||
2.43748 | − | 2.43748i | 0.173663 | − | 0.173663i | −0.614923 | − | 0.788587i | ||
0.788587 | + | 0.614923i | ||||||||
0 | 0 | |||||||||
− | 8.47213i | − | 0.600573i | −0.953849 | − | 0.300287i | ||||
0.953849 | − | 0.300287i | ||||||||
−2.77993 | + | 2.77993i | −0.196571 | + | 0.196571i | |||||
0 | 0 | |||||||||
−11.7861 | + | 11.7861i | −0.829266 | + | 0.829266i | |||||
−21.2739 | − | 21.2739i | −1.49313 | − | 1.49313i | |||||
0 | 0 | |||||||||
− | 1.55227i | − | 0.108415i | |||||||
1.29432 | + | 1.29432i | 0.0901799 | + | 0.0901799i | |||||
0 | 0 | |||||||||
3.21489 | − | 1.63232i | 0.222913 | − | 0.113181i | |||||
− | 23.4088i | − | 1.61922i | |||||||
0 | 0 | |||||||||
4.56205 | 0.314064 | 0.157032 | − | 0.987594i | ||||||
0.157032 | + | 0.987594i | ||||||||
11.7290 | 0.805554 | |||||||||
0 | 0 | |||||||||
−6.66815 | − | 6.66815i | −0.455825 | − | 0.455825i | |||||
2.77523 | + | 2.77523i | 0.189269 | + | 0.189269i | |||||
0 | 0 | |||||||||
−17.6319 | −1.19693 | |||||||||
9.40901 | 0.637259 | |||||||||
0 | 0 | |||||||||
− | 2.85618i | − | 0.192564i | |||||||
−17.4915 | + | 8.88107i | −1.17661 | + | 0.597406i | |||||
0 | 0 | |||||||||
2.22483 | + | 2.22483i | 0.148985 | + | 0.148985i | 0.777665 | − | 0.628679i | ||
−0.628679 | + | 0.777665i | ||||||||
3.53123i | 0.235940i | |||||||||
0 | 0 | |||||||||
9.61022 | + | 9.61022i | 0.639262 | + | 0.639262i | |||||
1.28867 | − | 1.28867i | 0.0855323 | − | 0.0855323i | −0.663046 | − | 0.748578i | ||
0.748578 | + | 0.663046i | ||||||||
0 | 0 | |||||||||
−9.06136 | + | 9.06136i | −0.598792 | + | 0.598792i | −0.939991 | − | 0.341199i | ||
0.341199 | + | 0.939991i | ||||||||
− | 5.28669i | − | 0.348594i | |||||||
0 | 0 | |||||||||
−6.02449 | + | 6.02449i | −0.395527 | + | 0.395527i | |||||
5.22631 | 0.342387 | 0.171193 | − | 0.985237i | ||||||
0.171193 | + | 0.985237i | ||||||||
0 | 0 | |||||||||
−11.4165 | −0.744728 | |||||||||
−1.86185 | + | 1.86185i | −0.121196 | + | 0.121196i | |||||
0 | 0 | |||||||||
− | 19.2126i | − | 1.24537i | |||||||
7.28487 | − | 7.28487i | 0.471219 | − | 0.471219i | −0.431090 | − | 0.902309i | ||
0.902309 | + | 0.431090i | ||||||||
0 | 0 | |||||||||
−18.8070 | + | 18.8070i | −1.21147 | + | 1.21147i | −0.240923 | + | 0.970544i | ||
−0.970544 | + | 0.240923i | ||||||||
2.37998 | + | 2.37998i | 0.152991 | + | 0.152991i | |||||
0 | 0 | |||||||||
− | 6.42979i | − | 0.411625i | |||||||
−3.99802 | − | 3.99802i | −0.255424 | − | 0.255424i | |||||
0 | 0 | |||||||||
29.0385 | + | 9.48085i | 1.84768 | + | 0.603252i | |||||
4.99314i | 0.317065i | |||||||||
0 | 0 | |||||||||
−9.23261 | −0.583922 | |||||||||
14.2652 | 0.900408 | 0.450204 | − | 0.892926i | ||||||
0.450204 | + | 0.892926i | ||||||||
0 | 0 | |||||||||
−9.99186 | − | 9.99186i | −0.628183 | − | 0.628183i | |||||
−7.83746 | − | 7.83746i | −0.491766 | − | 0.491766i | |||||
0 | 0 | |||||||||
1.00000 | 0.0625000 | |||||||||
7.06194 | 0.440512 | 0.220256 | − | 0.975442i | ||||||
0.220256 | + | 0.975442i | ||||||||
0 | 0 | |||||||||
− | 38.8901i | − | 2.41651i | |||||||
3.54308 | + | 1.15679i | 0.219733 | + | 0.0717410i | |||||
0 | 0 | |||||||||
8.58116 | + | 8.58116i | 0.530146 | + | 0.530146i | |||||
− | 24.5931i | − | 1.51648i | −0.651977 | − | 0.758239i | ||||
0.651977 | − | 0.758239i | ||||||||
0 | 0 | |||||||||
8.57338 | + | 8.57338i | 0.526658 | + | 0.526658i | |||||
−21.1548 | + | 21.1548i | −1.29708 | + | 1.29708i | |||||
0 | 0 | |||||||||
0.887018 | − | 0.887018i | 0.0541833 | − | 0.0541833i | |||||
− | 13.0138i | − | 0.793464i | −0.917934 | − | 0.396732i | ||||
0.917934 | − | 0.396732i | ||||||||
0 | 0 | |||||||||
2.41921 | − | 2.41921i | 0.146956 | − | 0.146956i | −0.629801 | − | 0.776757i | ||
0.776757 | + | 0.629801i | ||||||||
−5.44078 | −0.329896 | |||||||||
0 | 0 | |||||||||
−12.7384 | −0.769558 | |||||||||
−7.68096 | + | 7.68096i | −0.463180 | + | 0.463180i | |||||
0 | 0 | |||||||||
− | 25.0593i | − | 1.50567i | −0.658211 | − | 0.752833i | ||||
0.658211 | − | 0.752833i | ||||||||
−2.31044 | + | 2.31044i | −0.138571 | + | 0.138571i | |||||
0 | 0 | |||||||||
−2.58116 | + | 2.58116i | −0.154254 | + | 0.154254i | |||||
−9.20333 | − | 9.20333i | −0.549024 | − | 0.549024i | 0.377134 | − | 0.926159i | ||
−0.926159 | + | 0.377134i | ||||||||
0 | 0 | |||||||||
31.0477i | 1.84559i | 0.385289 | + | 0.922796i | ||||||
−0.385289 | + | 0.922796i | ||||||||
3.17883 | + | 3.17883i | 0.188629 | + | 0.188629i | |||||
0 | 0 | |||||||||
8.88277 | − | 4.51010i | 0.525249 | − | 0.266688i | |||||
5.30260i | 0.313002i | |||||||||
0 | 0 | |||||||||
12.6021 | 0.741298 | |||||||||
−8.80723 | −0.517178 | |||||||||
0 | 0 | |||||||||
2.31653 | + | 2.31653i | 0.135565 | + | 0.135565i | |||||
19.8206 | + | 19.8206i | 1.15793 | + | 1.15793i | 0.984920 | + | 0.173009i | ||
0.173009 | + | 0.984920i | ||||||||
0 | 0 | |||||||||
−2.72185 | −0.158473 | |||||||||
−11.0132 | −0.640128 | |||||||||
0 | 0 | |||||||||
15.0890i | 0.874082i | |||||||||
16.4417 | − | 8.34803i | 0.950847 | − | 0.482779i | |||||
0 | 0 | |||||||||
−9.48027 | − | 9.48027i | −0.546434 | − | 0.546434i | |||||
14.7479i | 0.848649i | |||||||||
0 | 0 | |||||||||
5.99076 | + | 5.99076i | 0.343594 | + | 0.343594i | |||||
4.69987 | − | 4.69987i | 0.269114 | − | 0.269114i | |||||
0 | 0 | |||||||||
−12.6972 | + | 12.6972i | −0.724668 | + | 0.724668i | −0.969552 | − | 0.244885i | ||
0.244885 | + | 0.969552i | ||||||||
9.75681i | 0.555946i | |||||||||
0 | 0 | |||||||||
−3.64975 | + | 3.64975i | −0.207292 | + | 0.207292i | |||||
−12.3667 | −0.701250 | −0.350625 | − | 0.936516i | ||||||
−0.350625 | + | 0.936516i | ||||||||
0 | 0 | |||||||||
−10.4672 | −0.591639 | −0.295820 | − | 0.955244i | ||||||
−0.295820 | + | 0.955244i | ||||||||
−6.95037 | + | 6.95037i | −0.392232 | + | 0.392232i | |||||
0 | 0 | |||||||||
5.29836i | 0.298056i | |||||||||
−10.8423 | + | 10.8423i | −0.608967 | + | 0.608967i | −0.942676 | − | 0.333709i | ||
0.333709 | + | 0.942676i | ||||||||
0 | 0 | |||||||||
−16.6457 | + | 16.6457i | −0.931980 | + | 0.931980i | |||||
0.730953 | + | 0.730953i | 0.0408615 | + | 0.0408615i | |||||
0 | 0 | |||||||||
18.0595i | 1.00642i | |||||||||
−32.5944 | − | 32.5944i | −1.81360 | − | 1.81360i | |||||
0 | 0 | |||||||||
−6.41732 | − | 12.6391i | −0.355969 | − | 0.701090i | |||||
− | 0.931520i | − | 0.0515921i | |||||||
0 | 0 | |||||||||
1.50163 | 0.0829136 | |||||||||
38.9990 | 2.15009 | |||||||||
0 | 0 | |||||||||
19.4823 | + | 19.4823i | 1.07084 | + | 1.07084i | 0.997291 | + | 0.0735518i | ||
0.0735518 | + | 0.997291i | ||||||||
−4.77771 | − | 4.77771i | −0.262211 | − | 0.262211i | |||||
0 | 0 | |||||||||
−17.7281 | −0.970041 | |||||||||
1.29674 | 0.0708483 | |||||||||
0 | 0 | |||||||||
− | 22.0991i | − | 1.20381i | −0.798566 | − | 0.601907i | ||||
0.798566 | − | 0.601907i | ||||||||
1.99713 | + | 12.8457i | 0.108629 | + | 0.698713i | |||||
0 | 0 | |||||||||
−3.97695 | − | 3.97695i | −0.215680 | − | 0.215680i | |||||
13.7961i | 0.747099i | |||||||||
0 | 0 | |||||||||
−3.82136 | − | 3.82136i | −0.206334 | − | 0.206334i | |||||
−2.68469 | + | 2.68469i | −0.144749 | + | 0.144749i | |||||
0 | 0 | |||||||||
2.74319 | − | 2.74319i | 0.147475 | − | 0.147475i | |||||
− | 2.56427i | − | 0.137657i | −0.997629 | − | 0.0688285i | ||||
0.997629 | − | 0.0688285i | ||||||||
0 | 0 | |||||||||
−25.9102 | + | 25.9102i | −1.38694 | + | 1.38694i | −0.555276 | + | 0.831666i | ||
−0.831666 | + | 0.555276i | ||||||||
13.8827 | 0.742064 | |||||||||
0 | 0 | |||||||||
2.76300 | 0.147269 | |||||||||
4.90973 | − | 4.90973i | 0.261319 | − | 0.261319i | −0.564271 | − | 0.825590i | ||
0.825590 | + | 0.564271i | ||||||||
0 | 0 | |||||||||
4.64715i | 0.246645i | |||||||||
0.144930 | − | 0.144930i | 0.00768126 | − | 0.00768126i | |||||
0 | 0 | |||||||||
3.61309 | − | 3.61309i | 0.190958 | − | 0.190958i | |||||
−17.3664 | − | 17.3664i | −0.916563 | − | 0.916563i | 0.0802151 | − | 0.996778i | ||
−0.996778 | + | 0.0802151i | ||||||||
0 | 0 | |||||||||
52.7785i | 2.77782i | |||||||||
2.83802 | + | 2.83802i | 0.149163 | + | 0.149163i | |||||
0 | 0 | |||||||||
−12.1033 | − | 3.95163i | −0.634384 | − | 0.207122i | |||||
3.38655i | 0.177260i | |||||||||
0 | 0 | |||||||||
3.21535 | 0.167840 | 0.0839199 | − | 0.996473i | ||||||
0.0839199 | + | 0.996473i | ||||||||
5.11422 | 0.266597 | |||||||||
0 | 0 | |||||||||
−8.05011 | − | 8.05011i | −0.418505 | − | 0.418505i | |||||
−29.2869 | − | 29.2869i | −1.52050 | − | 1.52050i | |||||
0 | 0 | |||||||||
23.0464 | 1.19330 | 0.596648 | − | 0.802503i | ||||||
0.596648 | + | 0.802503i | ||||||||
−15.0329 | −0.777332 | |||||||||
0 | 0 | |||||||||
− | 11.0440i | − | 0.569552i | |||||||
−13.9072 | − | 27.3906i | −0.716257 | − | 1.41069i | |||||
0 | 0 | |||||||||
−12.6790 | − | 12.6790i | −0.651276 | − | 0.651276i | 0.302024 | − | 0.953300i | ||
−0.953300 | + | 0.302024i | ||||||||
8.75793i | 0.449272i | |||||||||
0 | 0 | |||||||||
−15.6607 | − | 15.6607i | −0.801271 | − | 0.801271i | |||||
2.64413 | − | 2.64413i | 0.135109 | − | 0.135109i | −0.636318 | − | 0.771427i | ||
0.771427 | + | 0.636318i | ||||||||
0 | 0 | |||||||||
−7.13177 | + | 7.13177i | −0.363469 | + | 0.363469i | |||||
− | 3.11337i | − | 0.158467i | |||||||
0 | 0 | |||||||||
−4.66500 | + | 4.66500i | −0.236829 | + | 0.236829i | |||||
22.7276 | 1.15234 | 0.576169 | − | 0.817331i | ||||||
0.576169 | + | 0.817331i | ||||||||
0 | 0 | |||||||||
−27.8253 | −1.40719 | |||||||||
3.86759 | − | 3.86759i | 0.195343 | − | 0.195343i | |||||
0 | 0 | |||||||||
3.44712i | 0.173663i | |||||||||
−3.87285 | + | 3.87285i | −0.194864 | + | 0.194864i | |||||
0 | 0 | |||||||||
−5.15592 | + | 5.15592i | −0.258768 | + | 0.258768i | −0.824553 | − | 0.565785i | ||
0.565785 | + | 0.824553i | ||||||||
5.99070 | + | 5.99070i | 0.300287 | + | 0.300287i | |||||
0 | 0 | |||||||||
− | 3.93142i | − | 0.196571i | |||||||
−13.8525 | − | 13.8525i | −0.691763 | − | 0.691763i | 0.270857 | − | 0.962620i | ||
−0.962620 | + | 0.270857i | ||||||||
0 | 0 | |||||||||
−17.1140 | − | 5.58757i | −0.852507 | − | 0.278337i | |||||
− | 16.6680i | − | 0.829266i | |||||||
0 | 0 | |||||||||
30.0858 | 1.49313 | |||||||||
−30.4295 | −1.50833 | |||||||||
0 | 0 | |||||||||
−11.1285 | − | 11.1285i | −0.550269 | − | 0.550269i | 0.376249 | − | 0.926519i | ||
−0.926519 | + | 0.376249i | ||||||||
1.09762 | + | 1.09762i | 0.0542076 | + | 0.0542076i | |||||
0 | 0 | |||||||||
−1.83045 | −0.0901799 | |||||||||
9.29794 | 0.457522 | |||||||||
0 | 0 | |||||||||
− | 6.98456i | − | 0.342859i | |||||||
−1.11905 | + | 3.42750i | −0.0548660 | + | 0.168047i | |||||
0 | 0 | |||||||||
16.5525 | + | 16.5525i | 0.809610 | + | 0.809610i | |||||
28.7408i | 1.40408i | 0.712137 | + | 0.702041i | ||||||
−0.712137 | + | 0.702041i | ||||||||
0 | 0 | |||||||||
15.4602 | + | 15.4602i | 0.753484 | + | 0.753484i | 0.975128 | − | 0.221643i | ||
−0.221643 | + | 0.975128i | ||||||||
−3.22585 | + | 3.22585i | −0.157032 | + | 0.157032i | |||||
0 | 0 | |||||||||
−8.29369 | + | 8.29369i | −0.402777 | + | 0.402777i | |||||
21.3900i | 1.03757i | |||||||||
0 | 0 | |||||||||
−16.0549 | + | 16.0549i | −0.776951 | + | 0.776951i | |||||
9.43019 | 0.455825 | |||||||||
0 | 0 | |||||||||
−3.92477 | −0.189269 | |||||||||
−3.04773 | + | 3.04773i | −0.146804 | + | 0.146804i | −0.776689 | − | 0.629885i | ||
0.629885 | + | 0.776689i | ||||||||
0 | 0 | |||||||||
10.5849i | 0.508676i | 0.967115 | + | 0.254338i | ||||||
−0.967115 | + | 0.254338i | ||||||||
12.4677 | − | 12.4677i | 0.598466 | − | 0.598466i | |||||
0 | 0 | |||||||||
−6.65317 | + | 6.65317i | −0.318629 | + | 0.318629i | |||||
30.6381 | + | 30.6381i | 1.46562 | + | 1.46562i | |||||
0 | 0 | |||||||||
0.756908i | 0.0361252i | 0.999837 | + | 0.0180626i | ||||||
−0.999837 | + | 0.0180626i | ||||||||
2.01963 | + | 2.01963i | 0.0962819 | + | 0.0962819i | |||||
0 | 0 | |||||||||
6.08851 | − | 18.6482i | 0.289601 | − | 0.887006i | |||||
36.7332i | 1.74525i | 0.488393 | + | 0.872624i | ||||||
−0.488393 | + | 0.872624i | ||||||||
0 | 0 | |||||||||
0.211874 | 0.0100438 | |||||||||
−3.14638 | −0.148985 | |||||||||
0 | 0 | |||||||||
−2.49696 | − | 2.49696i | −0.117970 | − | 0.117970i | |||||
16.5702 | + | 16.5702i | 0.781996 | + | 0.781996i | 0.980167 | − | 0.198172i | ||
−0.198172 | + | 0.980167i | ||||||||
0 | 0 | |||||||||
4.14901 | 0.195369 | |||||||||
−13.5909 | −0.639262 | |||||||||
0 | 0 | |||||||||
1.82246i | 0.0855323i | |||||||||
−5.95847 | − | 11.7354i | −0.279337 | − | 0.550163i | |||||
0 | 0 | |||||||||
−0.692812 | − | 0.692812i | −0.0324084 | − | 0.0324084i | 0.690717 | − | 0.723125i | ||
−0.723125 | + | 0.690717i | ||||||||
− | 12.8147i | − | 0.598792i | |||||||
0 | 0 | |||||||||
3.73825 | + | 3.73825i | 0.174297 | + | 0.174297i | |||||
8.54391 | − | 8.54391i | 0.397930 | − | 0.397930i | −0.479573 | − | 0.877502i | ||
0.877502 | + | 0.479573i | ||||||||
0 | 0 | |||||||||
−10.8803 | + | 10.8803i | −0.505650 | + | 0.505650i | −0.913188 | − | 0.407538i | ||
0.407538 | + | 0.913188i | ||||||||
− | 8.51991i | − | 0.395527i | |||||||
0 | 0 | |||||||||
−3.69556 | + | 3.69556i | −0.171193 | + | 0.171193i | |||||
−18.8587 | −0.872678 | −0.436339 | − | 0.899782i | ||||||
−0.436339 | + | 0.899782i | ||||||||
0 | 0 | |||||||||
−4.42970 | −0.204544 | |||||||||
8.07266 | − | 8.07266i | 0.372364 | − | 0.372364i | |||||
0 | 0 | |||||||||
− | 2.63306i | − | 0.121196i | |||||||
−7.41782 | + | 7.41782i | −0.341072 | + | 0.341072i | |||||
0 | 0 | |||||||||
23.5522 | − | 23.5522i | 1.08065 | − | 1.08065i | |||||
13.5854 | + | 13.5854i | 0.622685 | + | 0.622685i | |||||
0 | 0 | |||||||||
10.3024i | 0.471219i | |||||||||
−10.5691 | − | 10.5691i | −0.482915 | − | 0.482915i | 0.423146 | − | 0.906061i | ||
−0.906061 | + | 0.423146i | ||||||||
0 | 0 | |||||||||
12.3243 | − | 37.7476i | 0.561940 | − | 1.72114i | |||||
− | 26.5972i | − | 1.21147i | |||||||
0 | 0 | |||||||||
−3.36580 | −0.152991 | |||||||||
−6.81979 | −0.309671 | |||||||||
0 | 0 | |||||||||
−20.2191 | − | 20.2191i | −0.916214 | − | 0.916214i | 0.0805378 | − | 0.996752i | ||
−0.996752 | + | 0.0805378i | ||||||||
4.54655 | + | 4.54655i | 0.205812 | + | 0.205812i | |||||
0 | 0 | |||||||||
5.65405 | 0.255424 | |||||||||
28.8492 | 1.30195 | 0.650973 | − | 0.759101i | ||||||
0.650973 | + | 0.759101i | ||||||||
0 | 0 | |||||||||
46.3549i | 2.08772i | |||||||||
−27.2373 | + | 13.8293i | −1.22546 | + | 0.622212i | |||||
0 | 0 | |||||||||
−3.53068 | − | 3.53068i | −0.158532 | − | 0.158532i | |||||
− | 15.8748i | − | 0.712082i | |||||||
0 | 0 | |||||||||
10.5258 | + | 10.5258i | 0.471199 | + | 0.471199i | 0.902303 | − | 0.431103i | ||
−0.431103 | + | 0.902303i | ||||||||
6.52844 | − | 6.52844i | 0.291961 | − | 0.291961i | |||||
0 | 0 | |||||||||
−10.0870 | + | 10.0870i | −0.450204 | + | 0.450204i | |||||
− | 8.87705i | − | 0.395808i | −0.980221 | − | 0.197904i | ||||
0.980221 | − | 0.197904i | ||||||||
0 | 0 | |||||||||
12.1835 | − | 12.1835i | 0.542161 | − | 0.542161i | |||||
14.1306 | 0.628183 | |||||||||
0 | 0 | |||||||||
11.0838 | 0.491766 | |||||||||
17.5845 | − | 17.5845i | 0.779418 | − | 0.779418i | −0.200314 | − | 0.979732i | ||
0.979732 | + | 0.200314i | ||||||||
0 | 0 | |||||||||
− | 11.5686i | − | 0.511763i | |||||||
−0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | |||||
0 | 0 | |||||||||
−4.99355 | + | 4.99355i | −0.220256 | + | 0.220256i | |||||
−1.33797 | − | 1.33797i | −0.0589582 | − | 0.0589582i | |||||
0 | 0 | |||||||||
− | 30.5147i | − | 1.34204i | |||||||
27.4994 | + | 27.4994i | 1.20826 | + | 1.20826i | |||||
0 | 0 | |||||||||
−3.32331 | + | 1.68736i | −0.145737 | + | 0.0739958i | |||||
7.10124i | 0.311111i | 0.987827 | + | 0.155556i | ||||||
−0.987827 | + | 0.155556i | ||||||||
0 | 0 | |||||||||
28.9433 | 1.26560 | 0.632801 | − | 0.774314i | ||||||
0.632801 | + | 0.774314i | ||||||||
−12.1356 | −0.530146 | |||||||||
0 | 0 | |||||||||
17.3900 | + | 17.3900i | 0.758239 | + | 0.758239i | |||||
19.2096 | + | 19.2096i | 0.836785 | + | 0.836785i | |||||
0 | 0 | |||||||||
3.15525 | 0.137185 | |||||||||
−12.1246 | −0.526658 | |||||||||
0 | 0 | |||||||||
− | 29.9174i | − | 1.29708i | |||||||
−1.68040 | + | 5.14683i | −0.0727862 | + | 0.222934i | |||||
0 | 0 | |||||||||
6.89302 | + | 6.89302i | 0.298011 | + | 0.298011i | |||||
1.25443i | 0.0541833i | |||||||||
0 | 0 | |||||||||
9.20213 | + | 9.20213i | 0.396732 | + | 0.396732i | |||||
10.6862 | − | 10.6862i | 0.460286 | − | 0.460286i | |||||
0 | 0 | |||||||||
9.21585 | − | 9.21585i | 0.396221 | − | 0.396221i | −0.480677 | − | 0.876898i | ||
0.876898 | + | 0.480677i | ||||||||
3.42128i | 0.146956i | |||||||||
0 | 0 | |||||||||
3.84721 | − | 3.84721i | 0.164948 | − | 0.164948i | |||||
−9.72631 | −0.416629 | |||||||||
0 | 0 | |||||||||
−8.53557 | −0.364955 | −0.182477 | − | 0.983210i | ||||||
−0.182477 | + | 0.983210i | ||||||||
9.00744 | − | 9.00744i | 0.384779 | − | 0.384779i | |||||
0 | 0 | |||||||||
− | 10.8625i | − | 0.463180i | |||||||
51.0408 | − | 51.0408i | 2.17441 | − | 2.17441i | |||||
0 | 0 | |||||||||
13.2298 | − | 13.2298i | 0.562587 | − | 0.562587i | |||||
17.7196 | + | 17.7196i | 0.752833 | + | 0.752833i | |||||
0 | 0 | |||||||||
− | 3.26746i | − | 0.138571i | |||||||
10.9056 | + | 10.9056i | 0.462083 | + | 0.462083i | 0.899338 | − | 0.437255i | ||
−0.437255 | + | 0.899338i | ||||||||
0 | 0 | |||||||||
−6.19746 | − | 12.2061i | −0.262125 | − | 0.516262i | |||||
− | 3.65032i | − | 0.154254i | |||||||
0 | 0 | |||||||||
13.0155 | 0.549024 | |||||||||
−6.06531 | −0.255622 | −0.127811 | − | 0.991799i | ||||||
−0.127811 | + | 0.991799i | ||||||||
0 | 0 | |||||||||
−9.93430 | − | 9.93430i | −0.417939 | − | 0.417939i | |||||
−21.9540 | − | 21.9540i | −0.922796 | − | 0.922796i | |||||
0 | 0 | |||||||||
−4.49554 | −0.188629 | |||||||||
14.3081 | 0.599827 | 0.299913 | − | 0.953966i | ||||||
0.299913 | + | 0.953966i | ||||||||
0 | 0 | |||||||||
5.93459i | 0.248355i | 0.992260 | + | 0.124177i | ||||||
−0.992260 | + | 0.124177i | ||||||||
−3.09194 | + | 9.47019i | −0.129281 | + | 0.395968i | |||||
0 | 0 | |||||||||
−3.74950 | − | 3.74950i | −0.156501 | − | 0.156501i | |||||
− | 20.1061i | − | 0.838484i | |||||||
0 | 0 | |||||||||
20.4971 | + | 20.4971i | 0.853304 | + | 0.853304i | 0.990539 | − | 0.137235i | ||
−0.137235 | + | 0.990539i | ||||||||
−8.91100 | + | 8.91100i | −0.370649 | + | 0.370649i | |||||
0 | 0 | |||||||||
6.22765 | − | 6.22765i | 0.258589 | − | 0.258589i | |||||
23.8595i | 0.989858i | |||||||||
0 | 0 | |||||||||
−22.9155 | + | 22.9155i | −0.949063 | + | 0.949063i | |||||
−3.27607 | −0.135565 | |||||||||
0 | 0 | |||||||||
−28.0305 | −1.15793 | |||||||||
−27.9522 | + | 27.9522i | −1.15371 | + | 1.15371i | −0.167907 | + | 0.985803i | ||
−0.985803 | + | 0.167907i | ||||||||
0 | 0 | |||||||||
− | 42.3030i | − | 1.74306i | |||||||
1.92464 | − | 1.92464i | 0.0792363 | − | 0.0792363i | |||||
0 | 0 | |||||||||
7.78749 | − | 7.78749i | 0.320064 | − | 0.320064i | |||||
−21.8876 | − | 21.8876i | −0.898816 | − | 0.898816i | 0.0965155 | − | 0.995331i | ||
−0.995331 | + | 0.0965155i | ||||||||
0 | 0 | |||||||||
19.8606i | 0.814203i | |||||||||
−10.6695 | − | 10.6695i | −0.437041 | − | 0.437041i | |||||
0 | 0 | |||||||||
−5.72307 | + | 17.5290i | −0.234034 | + | 0.716813i | |||||
30.4677i | 1.24488i | 0.782668 | + | 0.622439i | ||||||
−0.782668 | + | 0.622439i | ||||||||
0 | 0 | |||||||||
10.5012 | 0.428354 | 0.214177 | − | 0.976795i | ||||||
0.214177 | + | 0.976795i | ||||||||
13.4071 | 0.546434 | |||||||||
0 | 0 | |||||||||
−10.4284 | − | 10.4284i | −0.424325 | − | 0.424325i | |||||
−2.46024 | − | 2.46024i | −0.100023 | − | 0.100023i | |||||
0 | 0 | |||||||||
16.5851 | 0.673168 | 0.336584 | − | 0.941653i | ||||||
0.336584 | + | 0.941653i | ||||||||
−8.47222 | −0.343594 | |||||||||
0 | 0 | |||||||||
6.64662i | 0.269114i | |||||||||
37.8534 | + | 12.3588i | 1.53138 | + | 0.499985i | |||||
0 | 0 | |||||||||
13.3912 | + | 13.3912i | 0.540866 | + | 0.540866i | 0.923783 | − | 0.382917i | ||
−0.382917 | + | 0.923783i | ||||||||
− | 17.9566i | − | 0.724668i | |||||||
0 | 0 | |||||||||
−6.89911 | − | 6.89911i | −0.277973 | − | 0.277973i | |||||
−5.96507 | + | 5.96507i | −0.240145 | + | 0.240145i | −0.816910 | − | 0.576765i | ||
0.576765 | + | 0.816910i | ||||||||
0 | 0 | |||||||||
8.99098 | − | 8.99098i | 0.361378 | − | 0.361378i | −0.502942 | − | 0.864320i | ||
0.864320 | + | 0.502942i | ||||||||
− | 5.16152i | − | 0.207292i | |||||||
0 | 0 | |||||||||
8.74456 | − | 8.74456i | 0.350625 | − | 0.350625i | |||||
−0.723767 | −0.0289971 | |||||||||
0 | 0 | |||||||||
−10.1131 | −0.404525 | |||||||||
7.40140 | − | 7.40140i | 0.295820 | − | 0.295820i | |||||
0 | 0 | |||||||||
− | 9.82931i | − | 0.392232i | |||||||
−42.3700 | + | 42.3700i | −1.68940 | + | 1.68940i | |||||
0 | 0 | |||||||||
13.1946 | − | 13.1946i | 0.525267 | − | 0.525267i | −0.393890 | − | 0.919157i | ||
0.919157 | + | 0.393890i | ||||||||
−3.74650 | − | 3.74650i | −0.149028 | − | 0.149028i | |||||
0 | 0 | |||||||||
− | 15.3334i | − | 0.608967i | |||||||
8.10176 | + | 8.10176i | 0.321509 | + | 0.321509i | |||||
0 | 0 | |||||||||
8.92811 | + | 17.5842i | 0.353745 | + | 0.696710i | |||||
− | 23.5406i | − | 0.931980i | |||||||
0 | 0 | |||||||||
−1.03372 | −0.0408615 | |||||||||
−2.95203 | −0.116598 | −0.0582992 | − | 0.998299i | ||||||
−0.0582992 | + | 0.998299i | ||||||||
0 | 0 | |||||||||
−23.5471 | − | 23.5471i | −0.928607 | − | 0.928607i | 0.0690092 | − | 0.997616i | ||
−0.997616 | + | 0.0690092i | ||||||||
−12.7700 | − | 12.7700i | −0.503208 | − | 0.503208i | |||||
0 | 0 | |||||||||
46.0955 | 1.81360 | |||||||||
21.5988 | 0.849138 | 0.424569 | − | 0.905396i | ||||||
0.424569 | + | 0.905396i | ||||||||
0 | 0 | |||||||||
− | 7.27516i | − | 0.285575i | |||||||
13.4749 | + | 4.39945i | 0.528529 | + | 0.172561i | |||||
0 | 0 | |||||||||
0.658684 | + | 0.658684i | 0.0257961 | + | 0.0257961i | |||||
5.01350i | 0.196194i | 0.995177 | + | 0.0980968i | ||||||
−0.995177 | + | 0.0980968i | ||||||||
0 | 0 | |||||||||
−8.87055 | − | 8.87055i | −0.346601 | − | 0.346601i | |||||
−1.06181 | + | 1.06181i | −0.0414568 | + | 0.0414568i | |||||
0 | 0 | |||||||||
−27.5765 | + | 27.5765i | −1.07504 | + | 1.07504i | |||||
21.4750i | 0.836546i | 0.908321 | + | 0.418273i | ||||||
−0.908321 | + | 0.418273i | ||||||||
0 | 0 | |||||||||
−7.22887 | + | 7.22887i | −0.281171 | + | 0.281171i | −0.833576 | − | 0.552405i | ||
0.552405 | + | 0.833576i | ||||||||
−27.5521 | −1.07084 | |||||||||
0 | 0 | |||||||||
6.75670 | 0.262211 | |||||||||
21.8682 | − | 21.8682i | 0.848012 | − | 0.848012i | |||||
0 | 0 | |||||||||
− | 43.5727i | − | 1.68714i | |||||||
12.5357 | − | 12.5357i | 0.485020 | − | 0.485020i | |||||
0 | 0 | |||||||||
−0.916932 | + | 0.916932i | −0.0354242 | + | 0.0354242i | |||||
12.5621 | + | 12.5621i | 0.484956 | + | 0.484956i | |||||
0 | 0 | |||||||||
− | 18.2056i | − | 0.701774i | −0.936418 | − | 0.350887i | ||||
0.936418 | − | 0.350887i | ||||||||
15.6264 | + | 15.6264i | 0.601907 | + | 0.601907i | |||||
0 | 0 | |||||||||
−10.4955 | − | 7.67108i | −0.403671 | − | 0.295042i | |||||
14.3760i | 0.552515i | 0.961084 | + | 0.276257i | ||||||
−0.961084 | + | 0.276257i | ||||||||
0 | 0 | |||||||||
23.2966 | 0.894042 | |||||||||
5.62426 | 0.215680 | |||||||||
0 | 0 | |||||||||
−9.75529 | − | 9.75529i | −0.373549 | − | 0.373549i | |||||
11.7572 | + | 11.7572i | 0.449877 | + | 0.449877i | 0.895313 | − | 0.445437i | ||
−0.445437 | + | 0.895313i | ||||||||
0 | 0 | |||||||||
13.1680 | 0.503125 | |||||||||
5.40421 | 0.206334 | |||||||||
0 | 0 | |||||||||
− | 3.79673i | − | 0.144749i | |||||||
−19.1455 | − | 37.7076i | −0.729386 | − | 1.43655i | |||||
0 | 0 | |||||||||
14.9559 | + | 14.9559i | 0.568948 | + | 0.568948i | 0.931834 | − | 0.362886i | ||
−0.362886 | + | 0.931834i | ||||||||
3.87945i | 0.147475i | |||||||||
0 | 0 | |||||||||
1.81321 | + | 1.81321i | 0.0688285 | + | 0.0688285i | |||||
2.38836 | − | 2.38836i | 0.0905956 | − | 0.0905956i | |||||
0 | 0 | |||||||||
5.77708 | − | 5.77708i | 0.218823 | − | 0.218823i | |||||
− | 36.6426i | − | 1.38694i | |||||||
0 | 0 | |||||||||
−9.81658 | + | 9.81658i | −0.371032 | + | 0.371032i | |||||
−45.3798 | −1.71397 | −0.856985 | − | 0.515342i | ||||||
−0.856985 | + | 0.515342i | ||||||||
0 | 0 | |||||||||
93.3061 | 3.51910 | |||||||||
−1.95374 | + | 1.95374i | −0.0736343 | + | 0.0736343i | |||||
0 | 0 | |||||||||
6.94341i | 0.261319i | |||||||||
−41.6194 | + | 41.6194i | −1.56526 | + | 1.56526i | |||||
0 | 0 | |||||||||
−24.8489 | + | 24.8489i | −0.933218 | + | 0.933218i | −0.997906 | − | 0.0646873i | ||
0.0646873 | + | 0.997906i | ||||||||
−3.28603 | − | 3.28603i | −0.123323 | − | 0.123323i | |||||
0 | 0 | |||||||||
0.204962i | 0.00768126i | |||||||||
−18.0567 | − | 18.0567i | −0.676228 | − | 0.676228i | |||||
0 | 0 | |||||||||
−9.18232 | + | 4.66219i | −0.343399 | + | 0.174356i | |||||
5.10968i | 0.190958i | |||||||||
0 | 0 | |||||||||
24.5598 | 0.916563 | |||||||||
−34.3801 | −1.28216 | −0.641081 | − | 0.767473i | ||||||
−0.641081 | + | 0.767473i | ||||||||
0 | 0 | |||||||||
4.57056 | + | 4.57056i | 0.170217 | + | 0.170217i | |||||
−37.3200 | − | 37.3200i | −1.38891 | − | 1.38891i | |||||
0 | 0 | |||||||||
−4.01356 | −0.149163 | |||||||||
−33.4953 | −1.24398 | |||||||||
0 | 0 | |||||||||
− | 7.44017i | − | 0.275941i | −0.990436 | − | 0.137970i | ||||
0.990436 | − | 0.137970i | ||||||||
11.3525 | − | 5.76409i | 0.420753 | − | 0.213631i | |||||
0 | 0 | |||||||||
−2.39465 | − | 2.39465i | −0.0886300 | − | 0.0886300i | |||||
20.6572i | 0.764032i | |||||||||
0 | 0 | |||||||||
36.0059 | + | 36.0059i | 1.32991 | + | 1.32991i | 0.905446 | + | 0.424460i | ||
0.424460 | + | 0.905446i | ||||||||
−2.27359 | + | 2.27359i | −0.0839199 | + | 0.0839199i | |||||
0 | 0 | |||||||||
−3.61630 | + | 3.61630i | −0.133299 | + | 0.133299i | |||||
3.46601i | 0.127672i | |||||||||
0 | 0 | |||||||||
17.8745 | − | 17.8745i | 0.657525 | − | 0.657525i | −0.297269 | − | 0.954794i | ||
0.954794 | + | 0.297269i | ||||||||
11.3846 | 0.418505 | |||||||||
0 | 0 | |||||||||
41.4180 | 1.52050 | |||||||||
6.18249 | − | 6.18249i | 0.226814 | − | 0.226814i | −0.584547 | − | 0.811360i | ||
0.811360 | + | 0.584547i | ||||||||
0 | 0 | |||||||||
− | 15.5979i | − | 0.571461i | |||||||
−16.2962 | + | 16.2962i | −0.596648 | + | 0.596648i | |||||
0 | 0 | |||||||||
10.6299 | − | 10.6299i | 0.388666 | − | 0.388666i | |||||
−23.5468 | − | 23.5468i | −0.860381 | − | 0.860381i | |||||
0 | 0 | |||||||||
18.2839i | 0.667189i | 0.942717 | + | 0.333594i | ||||||
−0.942717 | + | 0.333594i | ||||||||
7.80931 | + | 7.80931i | 0.284776 | + | 0.284776i | |||||
0 | 0 | |||||||||
29.2020 | + | 9.53421i | 1.06347 | + | 0.347216i | |||||
− | 15.2453i | − | 0.554833i | |||||||
0 | 0 | |||||||||
−7.47864 | −0.271816 | −0.135908 | − | 0.990721i | ||||||
−0.135908 | + | 0.990721i | ||||||||
17.9308 | 0.651276 | |||||||||
0 | 0 | |||||||||
−6.19279 | − | 6.19279i | −0.224636 | − | 0.224636i | |||||
2.80360 | + | 2.80360i | 0.101630 | + | 0.101630i | 0.756094 | − | 0.654463i | ||
−0.654463 | + | 0.756094i | ||||||||
0 | 0 | |||||||||
33.2254 | 1.20284 | |||||||||
22.1476 | 0.801271 | |||||||||
0 | 0 | |||||||||
3.73937i | 0.135109i | |||||||||
9.02480 | + | 2.94653i | 0.325867 | + | 0.106393i | |||||
0 | 0 | |||||||||
−0.486296 | − | 0.486296i | −0.0175363 | − | 0.0175363i | 0.698284 | − | 0.715821i | ||
−0.715821 | + | 0.698284i | ||||||||
− | 10.0858i | − | 0.363469i | |||||||
0 | 0 | |||||||||
2.20149 | + | 2.20149i | 0.0792333 | + | 0.0792333i | |||||
−15.2154 | + | 15.2154i | −0.547261 | + | 0.547261i | −0.925648 | − | 0.378387i | ||
0.378387 | + | 0.925648i | ||||||||
0 | 0 | |||||||||
−13.8806 | + | 13.8806i | −0.498605 | + | 0.498605i | |||||
− | 6.59730i | − | 0.236829i | |||||||
0 | 0 | |||||||||
−16.0709 | + | 16.0709i | −0.576169 | + | 0.576169i | |||||
−12.7221 | −0.455818 | |||||||||
0 | 0 | |||||||||
−12.4212 | −0.444466 | |||||||||
19.6755 | − | 19.6755i | 0.703594 | − | 0.703594i | |||||
0 | 0 | |||||||||
5.46960i | 0.195343i | |||||||||
7.18476 | − | 7.18476i | 0.256435 | − | 0.256435i | |||||
0 | 0 | |||||||||
0.495643 | − | 0.495643i | 0.0176678 | − | 0.0176678i | −0.698218 | − | 0.715885i | ||
0.715885 | + | 0.698218i | ||||||||
−2.43748 | − | 2.43748i | −0.0868317 | − | 0.0868317i | |||||
0 | 0 | |||||||||
− | 5.47703i | − | 0.194864i | |||||||
33.9359 | + | 33.9359i | 1.20662 | + | 1.20662i | |||||
0 | 0 | |||||||||
−20.6711 | + | 10.4955i | −0.734052 | + | 0.372704i | |||||
− | 7.29157i | − | 0.258768i | |||||||
0 | 0 | |||||||||
−8.47213 | −0.300287 | |||||||||
17.9090 | 0.634369 | 0.317185 | − | 0.948364i | ||||||
0.317185 | + | 0.948364i | ||||||||
0 | 0 | |||||||||
−42.4887 | − | 42.4887i | −1.50314 | − | 1.50314i | |||||
2.77993 | + | 2.77993i | 0.0982854 | + | 0.0982854i | |||||
0 | 0 | |||||||||
19.5904 | 0.691763 | |||||||||
−9.05179 | −0.319431 | |||||||||
0 | 0 | |||||||||
− | 18.6685i | − | 0.657979i | |||||||
16.0524 | − | 8.15038i | 0.565422 | − | 0.287085i | |||||
0 | 0 | |||||||||
11.7861 | + | 11.7861i | 0.414633 | + | 0.414633i | |||||
− | 27.2029i | − | 0.956402i | −0.878250 | − | 0.478201i | ||||
0.878250 | − | 0.478201i | ||||||||
0 | 0 | |||||||||
−31.6498 | − | 31.6498i | −1.11138 | − | 1.11138i | −0.992965 | − | 0.118412i | ||
−0.118412 | − | 0.992965i | ||||||||
−21.2739 | + | 21.2739i | −0.746566 | + | 0.746566i | |||||
0 | 0 | |||||||||
21.5169 | − | 21.5169i | 0.754166 | − | 0.754166i | |||||
0.962934i | 0.0337301i | |||||||||
0 | 0 | |||||||||
22.7453 | − | 22.7453i | 0.795757 | − | 0.795757i | |||||
15.7381 | 0.550269 | |||||||||
0 | 0 | |||||||||
−1.55227 | −0.0542076 | |||||||||
−32.8949 | + | 32.8949i | −1.14804 | + | 1.14804i | −0.161104 | + | 0.986937i | ||
−0.986937 | + | 0.161104i | ||||||||
0 | 0 | |||||||||
6.29469i | 0.219419i | 0.993964 | + | 0.109710i | ||||||
−0.993964 | + | 0.109710i | ||||||||
1.29432 | − | 1.29432i | 0.0450899 | − | 0.0450899i | |||||
0 | 0 | |||||||||
−6.57464 | + | 6.57464i | −0.228761 | + | 0.228761i | |||||
23.3955 | + | 23.3955i | 0.813543 | + | 0.813543i | 0.985163 | − | 0.171620i | ||
−0.171620 | + | 0.985163i | ||||||||
0 | 0 | |||||||||
− | 3.14079i | − | 0.109084i | −0.998511 | − | 0.0545421i | ||||
0.998511 | − | 0.0545421i | ||||||||
4.93883 | + | 4.93883i | 0.171429 | + | 0.171429i | |||||
0 | 0 | |||||||||
−1.63232 | − | 3.21489i | −0.0565904 | − | 0.111456i | |||||
− | 29.7589i | − | 1.03108i | |||||||
0 | 0 | |||||||||
18.3260 | 0.634197 | |||||||||
−23.4088 | −0.809610 | |||||||||
0 | 0 | |||||||||
−20.3228 | − | 20.3228i | −0.702041 | − | 0.702041i | |||||
28.0370 | + | 28.0370i | 0.967944 | + | 0.967944i | 0.999502 | − | 0.0315577i | ||
−0.0315577 | + | 0.999502i | ||||||||
0 | 0 | |||||||||
−43.5889 | −1.50307 | |||||||||
−21.8640 | −0.753484 | |||||||||
0 | 0 | |||||||||
− | 4.56205i | − | 0.157032i | |||||||
−2.06448 | − | 13.2789i | −0.0710202 | − | 0.456807i | |||||
0 | 0 | |||||||||
8.40427 | + | 8.40427i | 0.288774 | + | 0.288774i | |||||
− | 11.7290i | − | 0.402777i | |||||||
0 | 0 | |||||||||
−15.1250 | − | 15.1250i | −0.518783 | − | 0.518783i | |||||
39.8270 | − | 39.8270i | 1.36525 | − | 1.36525i | |||||
0 | 0 | |||||||||
−5.31816 | + | 5.31816i | −0.182090 | + | 0.182090i | −0.792266 | − | 0.610176i | ||
0.610176 | + | 0.792266i | ||||||||
− | 22.7051i | − | 0.776951i | |||||||
0 | 0 | |||||||||
−6.66815 | + | 6.66815i | −0.227913 | + | 0.227913i | |||||
13.1601 | 0.449540 | 0.224770 | − | 0.974412i | ||||||
0.224770 | + | 0.974412i | ||||||||
0 | 0 | |||||||||
−39.9763 | −1.36397 | −0.681987 | − | 0.731365i | ||||||
−0.681987 | + | 0.731365i | ||||||||
2.77523 | − | 2.77523i | 0.0946345 | − | 0.0946345i | |||||
0 | 0 | |||||||||
− | 4.31015i | − | 0.146804i | |||||||
−19.5420 | + | 19.5420i | −0.665217 | + | 0.665217i | −0.956605 | − | 0.291388i | ||
0.291388 | + | 0.956605i | ||||||||
0 | 0 | |||||||||
−2.83570 | + | 2.83570i | −0.0964166 | + | 0.0964166i | |||||
−7.48462 | − | 7.48462i | −0.254338 | − | 0.254338i | |||||
0 | 0 | |||||||||
17.6319i | 0.598466i | |||||||||
−10.3516 | − | 10.3516i | −0.351154 | − | 0.351154i | |||||
0 | 0 | |||||||||
−4.29957 | − | 1.40377i | −0.145685 | − | 0.0475651i | |||||
− | 9.40901i | − | 0.318629i | |||||||
0 | 0 | |||||||||
−43.3288 | −1.46562 | |||||||||
−32.6025 | −1.10217 | |||||||||
0 | 0 | |||||||||
10.6502 | + | 10.6502i | 0.359633 | + | 0.359633i | 0.863678 | − | 0.504045i | ||
−0.504045 | + | 0.863678i | ||||||||
−0.535215 | − | 0.535215i | −0.0180626 | − | 0.0180626i | |||||
0 | 0 | |||||||||
−2.85618 | −0.0962819 | |||||||||
−5.09673 | −0.171713 | −0.0858567 | − | 0.996307i | ||||||
−0.0858567 | + | 0.996307i | ||||||||
0 | 0 | |||||||||
43.6345i | 1.46842i | 0.678924 | + | 0.734209i | ||||||
−0.678924 | + | 0.734209i | ||||||||
8.88107 | + | 17.4915i | 0.298703 | + | 0.588304i | |||||
0 | 0 | |||||||||
−25.9743 | − | 25.9743i | −0.872624 | − | 0.872624i | |||||
− | 53.9013i | − | 1.80983i | −0.425593 | − | 0.904915i | ||||
0.425593 | − | 0.904915i | ||||||||
0 | 0 | |||||||||
−27.6759 | − | 27.6759i | −0.928219 | − | 0.928219i | |||||
−0.149817 | + | 0.149817i | −0.00502189 | + | 0.00502189i | |||||
0 | 0 | |||||||||
2.22483 | − | 2.22483i | 0.0744927 | − | 0.0744927i | |||||
93.5674i | 3.13111i | |||||||||
0 | 0 | |||||||||
−3.73494 | + | 3.73494i | −0.124845 | + | 0.124845i | |||||
3.53123 | 0.117970 | |||||||||
0 | 0 | |||||||||
−23.4338 | −0.781996 | |||||||||
−30.0811 | + | 30.0811i | −1.00326 | + | 1.00326i | |||||
0 | 0 | |||||||||
63.8151i | 2.12599i | |||||||||
−2.93379 | + | 2.93379i | −0.0976846 | + | 0.0976846i | |||||
0 | 0 | |||||||||
9.61022 | − | 9.61022i | 0.319631 | − | 0.319631i | |||||
−2.93372 | − | 2.93372i | −0.0975203 | − | 0.0975203i | |||||
0 | 0 | |||||||||
7.07627i | 0.234964i | 0.993075 | + | 0.117482i | ||||||
−0.993075 | + | 0.117482i | ||||||||
−1.28867 | − | 1.28867i | −0.0427661 | − | 0.0427661i | |||||
0 | 0 | |||||||||
12.5114 | + | 4.08489i | 0.414750 | + | 0.135413i | |||||
20.6283i | 0.683447i | 0.939801 | + | 0.341723i | ||||||
−0.939801 | + | 0.341723i | ||||||||
0 | 0 | |||||||||
18.6688 | 0.617847 | |||||||||
0.979785 | 0.0324084 | |||||||||
0 | 0 | |||||||||
9.06136 | + | 9.06136i | 0.299396 | + | 0.299396i | |||||
30.3021 | + | 30.3021i | 1.00066 | + | 1.00066i | |||||
0 | 0 | |||||||||
−27.6811 | −0.913115 | −0.456558 | − | 0.889694i | ||||||
−0.456558 | + | 0.889694i | ||||||||
−5.28669 | −0.174297 | |||||||||
0 | 0 | |||||||||
12.0829i | 0.397930i | |||||||||
5.03074 | − | 15.4085i | 0.165589 | − | 0.507176i | |||||
0 | 0 | |||||||||
−30.6159 | − | 30.6159i | −1.00664 | − | 1.00664i | |||||
− | 15.3871i | − | 0.505650i | |||||||
0 | 0 | |||||||||
6.02449 | + | 6.02449i | 0.197763 | + | 0.197763i | |||||
19.1542 | − | 19.1542i | 0.628430 | − | 0.628430i | −0.319243 | − | 0.947673i | ||
0.947673 | + | 0.319243i | ||||||||
0 | 0 | |||||||||
−32.7671 | + | 32.7671i | −1.07390 | + | 1.07390i | |||||
− | 5.22631i | − | 0.171193i | |||||||
0 | 0 | |||||||||
13.3351 | − | 13.3351i | 0.436339 | − | 0.436339i | |||||
15.5399 | 0.508208 | |||||||||
0 | 0 | |||||||||
−14.2237 | −0.464668 | −0.232334 | − | 0.972636i | ||||||
−0.232334 | + | 0.972636i | ||||||||
3.13227 | − | 3.13227i | 0.102272 | − | 0.102272i | |||||
0 | 0 | |||||||||
11.4165i | 0.372364i | |||||||||
−25.7864 | + | 25.7864i | −0.840613 | + | 0.840613i | −0.988939 | − | 0.148325i | ||
0.148325 | + | 0.988939i | ||||||||
0 | 0 | |||||||||
−5.43034 | + | 5.43034i | −0.176836 | + | 0.176836i | |||||
1.86185 | + | 1.86185i | 0.0605982 | + | 0.0605982i | |||||
0 | 0 | |||||||||
− | 10.4904i | − | 0.341072i | |||||||
−5.61473 | − | 5.61473i | −0.182454 | − | 0.182454i | 0.609970 | − | 0.792424i | ||
−0.792424 | + | 0.609970i | ||||||||
0 | 0 | |||||||||
3.66609 | − | 11.2287i | 0.119006 | − | 0.364499i | |||||
33.3078i | 1.08065i | |||||||||
0 | 0 | |||||||||
−19.2126 | −0.622685 | |||||||||
35.0177 | 1.13434 | 0.567168 | − | 0.823602i | ||||||
0.567168 | + | 0.823602i | ||||||||
0 | 0 | |||||||||
16.1888 | + | 16.1888i | 0.523858 | + | 0.523858i | |||||
−7.28487 | − | 7.28487i | −0.235609 | − | 0.235609i | |||||
0 | 0 | |||||||||
14.9470 | 0.482915 | |||||||||
−44.9824 | −1.45256 | |||||||||
0 | 0 | |||||||||
− | 6.06858i | − | 0.195761i | |||||||
17.9770 | + | 35.4062i | 0.579602 | + | 1.14154i | |||||
0 | 0 | |||||||||
18.8070 | + | 18.8070i | 0.605734 | + | 0.605734i | |||||
3.21837i | 0.103603i | |||||||||
0 | 0 | |||||||||
28.4024 | + | 28.4024i | 0.913361 | + | 0.913361i | 0.996535 | − | 0.0831742i | ||
−0.0831742 | + | 0.996535i | ||||||||
2.37998 | − | 2.37998i | 0.0764955 | − | 0.0764955i | |||||
0 | 0 | |||||||||
4.82232 | − | 4.82232i | 0.154835 | − | 0.154835i | |||||
− | 18.0510i | − | 0.579283i | −0.957135 | − | 0.289642i | ||||
0.957135 | − | 0.289642i | ||||||||
0 | 0 | |||||||||
−8.15871 | + | 8.15871i | −0.261556 | + | 0.261556i | |||||
28.5941 | 0.916214 | |||||||||
0 | 0 | |||||||||
−6.42979 | −0.205812 | |||||||||
8.94926 | − | 8.94926i | 0.286312 | − | 0.286312i | −0.549308 | − | 0.835620i | ||
0.835620 | + | 0.549308i | ||||||||
0 | 0 | |||||||||
0.566310i | 0.0180994i | |||||||||
−3.99802 | + | 3.99802i | −0.127712 | + | 0.127712i | |||||
0 | 0 | |||||||||
−20.3995 | + | 20.3995i | −0.650973 | + | 0.650973i | |||||
27.8757 | + | 27.8757i | 0.889098 | + | 0.889098i | 0.994436 | − | 0.105338i | ||
−0.105338 | + | 0.994436i | ||||||||
0 | 0 | |||||||||
− | 3.56337i | − | 0.113538i | |||||||
−32.7779 | − | 32.7779i | −1.04386 | − | 1.04386i | |||||
0 | 0 | |||||||||
9.48085 | − | 29.0385i | 0.301626 | − | 0.923838i | |||||
− | 19.4173i | − | 0.617434i | |||||||
0 | 0 | |||||||||
10.8811 | 0.345649 | 0.172825 | − | 0.984953i | ||||||
0.172825 | + | 0.984953i | ||||||||
4.99314 | 0.158532 | |||||||||
0 | 0 | |||||||||
11.2252 | + | 11.2252i | 0.356041 | + | 0.356041i | |||||
−6.19272 | − | 6.19272i | −0.196323 | − | 0.196323i | |||||
0 | 0 | |||||||||
−10.4383 | −0.330585 | −0.165292 | − | 0.986245i | ||||||
−0.165292 | + | 0.986245i | ||||||||
−14.8857 | −0.471199 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 702.2.j.b.593.4 | yes | 24 | |
3.2 | odd | 2 | inner | 702.2.j.b.593.9 | yes | 24 | |
13.5 | odd | 4 | inner | 702.2.j.b.161.9 | yes | 24 | |
39.5 | even | 4 | inner | 702.2.j.b.161.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
702.2.j.b.161.4 | ✓ | 24 | 39.5 | even | 4 | inner | |
702.2.j.b.161.9 | yes | 24 | 13.5 | odd | 4 | inner | |
702.2.j.b.593.4 | yes | 24 | 1.1 | even | 1 | trivial | |
702.2.j.b.593.9 | yes | 24 | 3.2 | odd | 2 | inner |