Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [396,2,Mod(287,396)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(396, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("396.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 396.c (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: | |
Coefficient field: | 10.0.5236158660608.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 287.2 | ||
Root | of defining polynomial | ||
Character | 396.287 | ||
Dual form | 396.2.c.a.287.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−1.40857 | + | 0.126175i | −0.996012 | + | 0.0892191i | |||||
0 | 0 | |||||||||
1.96816 | − | 0.355453i | 0.984080 | − | 0.177727i | |||||
0.450958i | 0.201674i | 0.994903 | + | 0.100837i | ||||||
−0.994903 | + | 0.100837i | ||||||||
0 | 0 | |||||||||
− | 4.60354i | − | 1.73997i | −0.493074 | − | 0.869987i | ||||
0.493074 | − | 0.869987i | ||||||||
−2.72745 | + | 0.749014i | −0.964299 | + | 0.264816i | |||||
0 | 0 | |||||||||
−0.0568995 | − | 0.635207i | −0.0179932 | − | 0.200870i | |||||
−1.00000 | −0.301511 | |||||||||
0 | 0 | |||||||||
−5.39122 | −1.49525 | −0.747627 | − | 0.664118i | ||||||
−0.747627 | + | 0.664118i | ||||||||
0.580851 | + | 6.48443i | 0.155239 | + | 1.73304i | |||||
0 | 0 | |||||||||
3.74731 | − | 1.39918i | 0.936827 | − | 0.349794i | |||||
− | 5.39826i | − | 1.30927i | −0.755945 | − | 0.654635i | ||||
0.755945 | − | 0.654635i | ||||||||
0 | 0 | |||||||||
4.38126i | 1.00513i | 0.864539 | + | 0.502565i | ||||||
−0.864539 | + | 0.502565i | ||||||||
0.160294 | + | 0.887557i | 0.0358429 | + | 0.198464i | |||||
0 | 0 | |||||||||
1.40857 | − | 0.126175i | 0.300309 | − | 0.0269006i | |||||
−6.03971 | −1.25937 | −0.629684 | − | 0.776852i | ||||||
−0.629684 | + | 0.776852i | ||||||||
0 | 0 | |||||||||
4.79664 | 0.959327 | |||||||||
7.59393 | − | 0.680236i | 1.48929 | − | 0.133405i | |||||
0 | 0 | |||||||||
−1.63634 | − | 9.06050i | −0.309240 | − | 1.71227i | |||||
− | 3.31081i | − | 0.614803i | −0.951580 | − | 0.307401i | ||||
0.951580 | − | 0.307401i | ||||||||
0 | 0 | |||||||||
− | 4.57881i | − | 0.822378i | −0.911550 | − | 0.411189i | ||||
0.911550 | − | 0.411189i | ||||||||
−5.10182 | + | 2.44366i | −0.901882 | + | 0.431982i | |||||
0 | 0 | |||||||||
0.681125 | + | 7.60385i | 0.116812 | + | 1.30405i | |||||
2.07600 | 0.350908 | |||||||||
0 | 0 | |||||||||
−6.27205 | −1.03112 | −0.515559 | − | 0.856854i | ||||||
−0.515559 | + | 0.856854i | ||||||||
−0.552805 | − | 6.17133i | −0.0896769 | − | 1.00112i | |||||
0 | 0 | |||||||||
−0.337774 | − | 1.22996i | −0.0534067 | − | 0.194474i | |||||
− | 11.2722i | − | 1.76042i | −0.474580 | − | 0.880212i | ||||
0.474580 | − | 0.880212i | ||||||||
0 | 0 | |||||||||
− | 0.650922i | − | 0.0992646i | −0.998768 | − | 0.0496323i | ||||
0.998768 | − | 0.0496323i | ||||||||
−1.96816 | + | 0.355453i | −0.296711 | + | 0.0535866i | |||||
0 | 0 | |||||||||
8.50738 | − | 0.762060i | 1.25435 | − | 0.112360i | |||||
5.79062 | 0.844649 | 0.422325 | − | 0.906445i | ||||||
0.422325 | + | 0.906445i | ||||||||
0 | 0 | |||||||||
−14.1926 | −2.02751 | |||||||||
−6.75642 | + | 0.605215i | −0.955502 | + | 0.0855903i | |||||
0 | 0 | |||||||||
−10.6108 | + | 1.91633i | −1.47145 | + | 0.265746i | |||||
− | 1.46036i | − | 0.200595i | −0.994957 | − | 0.100298i | ||||
0.994957 | − | 0.100298i | ||||||||
0 | 0 | |||||||||
− | 0.450958i | − | 0.0608071i | |||||||
3.44812 | + | 12.5559i | 0.460774 | + | 1.67786i | |||||
0 | 0 | |||||||||
0.417741 | + | 4.66353i | 0.0548521 | + | 0.612351i | |||||
4.71375 | 0.613678 | 0.306839 | − | 0.951761i | ||||||
0.306839 | + | 0.951761i | ||||||||
0 | 0 | |||||||||
1.28023 | 0.163917 | 0.0819586 | − | 0.996636i | ||||||
0.0819586 | + | 0.996636i | ||||||||
0.577730 | + | 6.44958i | 0.0733718 | + | 0.819098i | |||||
0 | 0 | |||||||||
6.87796 | − | 4.08580i | 0.859744 | − | 0.510724i | |||||
− | 2.43121i | − | 0.301555i | |||||||
0 | 0 | |||||||||
− | 6.54628i | − | 0.799756i | −0.916568 | − | 0.399878i | ||||
0.916568 | − | 0.399878i | ||||||||
−1.91883 | − | 10.6246i | −0.232692 | − | 1.28843i | |||||
0 | 0 | |||||||||
−2.92420 | + | 0.261939i | −0.349509 | + | 0.0313077i | |||||
4.27806 | 0.507712 | 0.253856 | − | 0.967242i | ||||||
0.253856 | + | 0.967242i | ||||||||
0 | 0 | |||||||||
9.86189 | 1.15425 | 0.577124 | − | 0.816657i | ||||||
0.577124 | + | 0.816657i | ||||||||
8.83464 | − | 0.791374i | 1.02701 | − | 0.0919954i | |||||
0 | 0 | |||||||||
1.55733 | + | 8.62303i | 0.178638 | + | 0.989129i | |||||
4.60354i | 0.524622i | |||||||||
0 | 0 | |||||||||
8.84129i | 0.994723i | 0.867543 | + | 0.497362i | ||||||
−0.867543 | + | 0.497362i | ||||||||
0.630970 | + | 1.68988i | 0.0705446 | + | 0.188934i | |||||
0 | 0 | |||||||||
1.42227 | + | 15.8777i | 0.157063 | + | 1.75340i | |||||
−0.627004 | −0.0688226 | −0.0344113 | − | 0.999408i | ||||||
−0.0344113 | + | 0.999408i | ||||||||
0 | 0 | |||||||||
2.43439 | 0.264046 | |||||||||
0.0821299 | + | 0.916871i | 0.00885630 | + | 0.0988688i | |||||
0 | 0 | |||||||||
2.72745 | − | 0.749014i | 0.290747 | − | 0.0798452i | |||||
10.6365i | 1.12747i | 0.825957 | + | 0.563733i | ||||||
−0.825957 | + | 0.563733i | ||||||||
0 | 0 | |||||||||
24.8187i | 2.60171i | |||||||||
−11.8871 | + | 2.14684i | −1.23932 | + | 0.223823i | |||||
0 | 0 | |||||||||
−8.15652 | + | 0.730631i | −0.841281 | + | 0.0753588i | |||||
−1.97576 | −0.202709 | |||||||||
0 | 0 | |||||||||
1.59931 | 0.162386 | 0.0811928 | − | 0.996698i | ||||||
0.0811928 | + | 0.996698i | ||||||||
19.9913 | − | 1.79075i | 2.01943 | − | 0.180893i | |||||
0 | 0 | |||||||||
9.44055 | − | 1.70498i | 0.944055 | − | 0.170498i | |||||
5.90296i | 0.587367i | 0.955903 | + | 0.293683i | ||||||
−0.955903 | + | 0.293683i | ||||||||
0 | 0 | |||||||||
7.11963i | 0.701518i | 0.936466 | + | 0.350759i | ||||||
−0.936466 | + | 0.350759i | ||||||||
14.7043 | − | 4.03810i | 1.44187 | − | 0.395968i | |||||
0 | 0 | |||||||||
0.184260 | + | 2.05702i | 0.0178969 | + | 0.199795i | |||||
12.9205 | 1.24908 | 0.624538 | − | 0.780994i | ||||||
0.624538 | + | 0.780994i | ||||||||
0 | 0 | |||||||||
−7.40196 | −0.708980 | −0.354490 | − | 0.935060i | ||||||
−0.354490 | + | 0.935060i | ||||||||
0.0568995 | + | 0.635207i | 0.00542516 | + | 0.0605646i | |||||
0 | 0 | |||||||||
−6.44117 | − | 17.2509i | −0.608633 | − | 1.63005i | |||||
13.2201i | 1.24365i | 0.783158 | + | 0.621823i | ||||||
−0.783158 | + | 0.621823i | ||||||||
0 | 0 | |||||||||
− | 2.72366i | − | 0.253982i | |||||||
−1.17684 | − | 6.51621i | −0.109267 | − | 0.605015i | |||||
0 | 0 | |||||||||
−6.63967 | + | 0.594757i | −0.611231 | + | 0.0547518i | |||||
−24.8511 | −2.27810 | |||||||||
0 | 0 | |||||||||
1.00000 | 0.0909091 | |||||||||
−1.80330 | + | 0.161533i | −0.163263 | + | 0.0146245i | |||||
0 | 0 | |||||||||
−1.62755 | − | 9.01182i | −0.146158 | − | 0.809285i | |||||
4.41787i | 0.395146i | |||||||||
0 | 0 | |||||||||
− | 14.9079i | − | 1.32286i | −0.750008 | − | 0.661429i | ||||
0.750008 | − | 0.661429i | ||||||||
−9.17258 | + | 6.62297i | −0.810749 | + | 0.585393i | |||||
0 | 0 | |||||||||
0.306758 | + | 3.42454i | 0.0269044 | + | 0.300352i | |||||
−5.69955 | −0.497972 | −0.248986 | − | 0.968507i | ||||||
−0.248986 | + | 0.968507i | ||||||||
0 | 0 | |||||||||
20.1693 | 1.74890 | |||||||||
0.825976 | + | 9.22092i | 0.0713535 | + | 0.796566i | |||||
0 | 0 | |||||||||
4.04337 | + | 14.7235i | 0.346716 | + | 1.26253i | |||||
− | 3.67780i | − | 0.314215i | −0.987581 | − | 0.157108i | ||||
0.987581 | − | 0.157108i | ||||||||
0 | 0 | |||||||||
11.3998i | 0.966917i | 0.875367 | + | 0.483459i | ||||||
−0.875367 | + | 0.483459i | ||||||||
4.08590 | − | 0.737921i | 0.345322 | − | 0.0623657i | |||||
0 | 0 | |||||||||
−6.02596 | + | 0.539783i | −0.505687 | + | 0.0452976i | |||||
5.39122 | 0.450836 | |||||||||
0 | 0 | |||||||||
1.49304 | 0.123990 | |||||||||
−13.8912 | + | 1.24432i | −1.14964 | + | 0.102981i | |||||
0 | 0 | |||||||||
−12.3444 | + | 2.22942i | −1.01470 | + | 0.183257i | |||||
− | 19.7575i | − | 1.61860i | −0.587397 | − | 0.809299i | ||||
0.587397 | − | 0.809299i | ||||||||
0 | 0 | |||||||||
− | 4.51126i | − | 0.367121i | −0.983008 | − | 0.183560i | ||||
0.983008 | − | 0.183560i | ||||||||
−3.28163 | − | 11.9497i | −0.266175 | − | 0.969247i | |||||
0 | 0 | |||||||||
−0.580851 | − | 6.48443i | −0.0468063 | − | 0.522530i | |||||
2.06485 | 0.165853 | |||||||||
0 | 0 | |||||||||
−2.46466 | −0.196701 | −0.0983507 | − | 0.995152i | ||||||
−0.0983507 | + | 0.995152i | ||||||||
−1.11555 | − | 12.4536i | −0.0887483 | − | 0.990756i | |||||
0 | 0 | |||||||||
−1.10199 | − | 2.30070i | −0.0871197 | − | 0.181887i | |||||
27.8041i | 2.19127i | |||||||||
0 | 0 | |||||||||
− | 22.2074i | − | 1.73941i | −0.493568 | − | 0.869707i | ||||
0.493568 | − | 0.869707i | ||||||||
−4.00674 | − | 22.1855i | −0.312874 | − | 1.73240i | |||||
0 | 0 | |||||||||
0.883181 | − | 0.0791121i | 0.0685482 | − | 0.00614029i | |||||
11.8748 | 0.918898 | 0.459449 | − | 0.888204i | ||||||
0.459449 | + | 0.888204i | ||||||||
0 | 0 | |||||||||
16.0652 | 1.23579 | |||||||||
−3.42901 | + | 0.307158i | −0.262993 | + | 0.0235580i | |||||
0 | 0 | |||||||||
−0.231372 | − | 1.28112i | −0.0176420 | − | 0.0976843i | |||||
12.9026i | 0.980968i | 0.871450 | + | 0.490484i | ||||||
−0.871450 | + | 0.490484i | ||||||||
0 | 0 | |||||||||
− | 22.0815i | − | 1.66921i | |||||||
−3.74731 | + | 1.39918i | −0.282464 | + | 0.105467i | |||||
0 | 0 | |||||||||
−1.34206 | − | 14.9823i | −0.100591 | − | 1.12297i | |||||
14.2207 | 1.06290 | 0.531452 | − | 0.847088i | ||||||
0.531452 | + | 0.847088i | ||||||||
0 | 0 | |||||||||
15.1818 | 1.12846 | 0.564229 | − | 0.825619i | ||||||
0.564229 | + | 0.825619i | ||||||||
−3.13149 | − | 34.9590i | −0.232122 | − | 2.59133i | |||||
0 | 0 | |||||||||
16.4730 | − | 4.52383i | 1.21441 | − | 0.333501i | |||||
− | 2.82843i | − | 0.207950i | |||||||
0 | 0 | |||||||||
5.39826i | 0.394760i | |||||||||
11.3969 | − | 2.05830i | 0.831202 | − | 0.150117i | |||||
0 | 0 | |||||||||
2.78301 | − | 0.249292i | 0.201901 | − | 0.0180855i | |||||
−13.7056 | −0.991700 | −0.495850 | − | 0.868408i | ||||||
−0.495850 | + | 0.868408i | ||||||||
0 | 0 | |||||||||
−15.7345 | −1.13260 | −0.566298 | − | 0.824200i | ||||||
−0.566298 | + | 0.824200i | ||||||||
−2.25275 | + | 0.201793i | −0.161738 | + | 0.0144879i | |||||
0 | 0 | |||||||||
−27.9333 | + | 5.04480i | −1.99523 | + | 0.360343i | |||||
− | 12.5112i | − | 0.891386i | −0.895186 | − | 0.445693i | ||||
0.895186 | − | 0.445693i | ||||||||
0 | 0 | |||||||||
− | 11.9736i | − | 0.848783i | −0.905479 | − | 0.424391i | ||||
0.905479 | − | 0.424391i | ||||||||
−13.0826 | + | 3.59275i | −0.925078 | + | 0.254046i | |||||
0 | 0 | |||||||||
−0.744805 | − | 8.31476i | −0.0524043 | − | 0.585024i | |||||
−15.2415 | −1.06974 | |||||||||
0 | 0 | |||||||||
5.08329 | 0.355033 | |||||||||
−0.898319 | − | 10.0285i | −0.0625888 | − | 0.698721i | |||||
0 | 0 | |||||||||
−20.2025 | + | 7.54327i | −1.40079 | + | 0.523032i | |||||
− | 4.38126i | − | 0.303058i | |||||||
0 | 0 | |||||||||
22.8088i | 1.57022i | 0.619354 | + | 0.785112i | ||||||
−0.619354 | + | 0.785112i | ||||||||
−0.519088 | − | 2.87421i | −0.0356511 | − | 0.197402i | |||||
0 | 0 | |||||||||
−18.1995 | + | 1.63025i | −1.24409 | + | 0.111441i | |||||
0.293538 | 0.0200191 | |||||||||
0 | 0 | |||||||||
−21.0787 | −1.43092 | |||||||||
10.4262 | − | 0.933942i | 0.706152 | − | 0.0632545i | |||||
0 | 0 | |||||||||
−0.160294 | − | 0.887557i | −0.0108070 | − | 0.0598391i | |||||
29.1032i | 1.95769i | |||||||||
0 | 0 | |||||||||
7.05369i | 0.472350i | 0.971710 | + | 0.236175i | ||||||
−0.971710 | + | 0.236175i | ||||||||
11.2495 | + | 23.4864i | 0.751638 | + | 1.56925i | |||||
0 | 0 | |||||||||
−1.66805 | − | 18.6215i | −0.110957 | − | 1.23869i | |||||
−17.1425 | −1.13779 | −0.568894 | − | 0.822411i | ||||||
−0.568894 | + | 0.822411i | ||||||||
0 | 0 | |||||||||
−0.206790 | −0.0136650 | −0.00683252 | − | 0.999977i | ||||||
−0.00683252 | + | 0.999977i | ||||||||
0.343657 | + | 3.83647i | 0.0226601 | + | 0.252969i | |||||
0 | 0 | |||||||||
2.47985 | + | 9.03008i | 0.162810 | + | 0.592854i | |||||
− | 7.61451i | − | 0.498843i | −0.968395 | − | 0.249421i | ||||
0.968395 | − | 0.249421i | ||||||||
0 | 0 | |||||||||
2.61133i | 0.170344i | |||||||||
9.27742 | − | 1.67552i | 0.603909 | − | 0.109067i | |||||
0 | 0 | |||||||||
35.0046 | − | 3.13559i | 2.26901 | − | 0.203250i | |||||
−11.7859 | −0.762366 | −0.381183 | − | 0.924500i | ||||||
−0.381183 | + | 0.924500i | ||||||||
0 | 0 | |||||||||
5.78630 | 0.372728 | 0.186364 | − | 0.982481i | ||||||
0.186364 | + | 0.982481i | ||||||||
−1.40857 | + | 0.126175i | −0.0905465 | + | 0.00811083i | |||||
0 | 0 | |||||||||
2.51970 | − | 0.455063i | 0.161308 | − | 0.0291324i | |||||
− | 6.40026i | − | 0.408897i | |||||||
0 | 0 | |||||||||
− | 23.6203i | − | 1.50293i | |||||||
3.42959 | + | 12.4885i | 0.217779 | + | 0.793018i | |||||
0 | 0 | |||||||||
−0.557424 | − | 6.22289i | −0.0352546 | − | 0.393570i | |||||
22.0592 | 1.39237 | 0.696183 | − | 0.717865i | ||||||
0.696183 | + | 0.717865i | ||||||||
0 | 0 | |||||||||
6.03971 | 0.379714 | |||||||||
1.88100 | + | 20.9988i | 0.118024 | + | 1.31758i | |||||
0 | 0 | |||||||||
12.0846 | − | 10.4863i | 0.755288 | − | 0.655393i | |||||
8.51467i | 0.531130i | 0.964093 | + | 0.265565i | ||||||
−0.964093 | + | 0.265565i | ||||||||
0 | 0 | |||||||||
28.8736i | 1.79412i | |||||||||
−0.864182 | − | 4.78501i | −0.0535943 | − | 0.296754i | |||||
0 | 0 | |||||||||
8.02824 | − | 0.719140i | 0.495986 | − | 0.0444286i | |||||
−5.07086 | −0.312682 | −0.156341 | − | 0.987703i | ||||||
−0.156341 | + | 0.987703i | ||||||||
0 | 0 | |||||||||
0.658559 | 0.0404550 | |||||||||
−28.4100 | + | 2.54486i | −1.74193 | + | 0.156035i | |||||
0 | 0 | |||||||||
−2.32690 | − | 12.8841i | −0.142138 | − | 0.787024i | |||||
− | 25.5790i | − | 1.55958i | −0.626040 | − | 0.779791i | ||||
0.626040 | − | 0.779791i | ||||||||
0 | 0 | |||||||||
− | 29.2394i | − | 1.77617i | −0.459682 | − | 0.888084i | ||||
0.459682 | − | 0.888084i | ||||||||
−7.55312 | − | 20.2289i | −0.457975 | − | 1.22656i | |||||
0 | 0 | |||||||||
0.464045 | + | 5.18045i | 0.0280340 | + | 0.312962i | |||||
−4.79664 | −0.289248 | |||||||||
0 | 0 | |||||||||
32.1011 | 1.92877 | 0.964383 | − | 0.264508i | ||||||
0.964383 | + | 0.264508i | ||||||||
−1.43837 | − | 16.0574i | −0.0862675 | − | 0.963061i | |||||
0 | 0 | |||||||||
−5.66219 | + | 1.55495i | −0.338381 | + | 0.0929263i | |||||
19.4654i | 1.16121i | 0.814186 | + | 0.580604i | ||||||
−0.814186 | + | 0.580604i | ||||||||
0 | 0 | |||||||||
14.3357i | 0.852169i | 0.904683 | + | 0.426084i | ||||||
−0.904683 | + | 0.426084i | ||||||||
8.41990 | − | 1.52065i | 0.499629 | − | 0.0902339i | |||||
0 | 0 | |||||||||
−7.59393 | + | 0.680236i | −0.449038 | + | 0.0402232i | |||||
−51.8921 | −3.06309 | |||||||||
0 | 0 | |||||||||
−12.1412 | −0.714190 | |||||||||
−2.10305 | + | 0.188384i | −0.123496 | + | 0.0110623i | |||||
0 | 0 | |||||||||
19.4098 | − | 3.50544i | 1.13587 | − | 0.205140i | |||||
21.2956i | 1.24410i | 0.782976 | + | 0.622052i | ||||||
−0.782976 | + | 0.622052i | ||||||||
0 | 0 | |||||||||
2.12570i | 0.123763i | |||||||||
17.1067 | − | 4.69785i | 0.994306 | − | 0.273057i | |||||
0 | 0 | |||||||||
2.49290 | + | 27.8299i | 0.144410 | + | 1.61214i | |||||
32.5614 | 1.88308 | |||||||||
0 | 0 | |||||||||
−2.99654 | −0.172718 | |||||||||
0.569207 | + | 6.35444i | 0.0327542 | + | 0.365657i | |||||
0 | 0 | |||||||||
6.13016 | + | 16.4179i | 0.351589 | + | 0.941633i | |||||
0.577331i | 0.0330579i | |||||||||
0 | 0 | |||||||||
− | 2.34785i | − | 0.133999i | −0.997753 | − | 0.0669993i | ||||
0.997753 | − | 0.0669993i | ||||||||
1.63634 | + | 9.06050i | 0.0932393 | + | 0.516270i | |||||
0 | 0 | |||||||||
−2.90849 | + | 0.260532i | −0.165191 | + | 0.0147972i | |||||
12.9742 | 0.735697 | 0.367848 | − | 0.929886i | ||||||
0.367848 | + | 0.929886i | ||||||||
0 | 0 | |||||||||
8.66454 | 0.489749 | 0.244874 | − | 0.969555i | ||||||
0.244874 | + | 0.969555i | ||||||||
3.47166 | − | 0.310978i | 0.195917 | − | 0.0175495i | |||||
0 | 0 | |||||||||
3.14267 | + | 17.4011i | 0.176789 | + | 0.978887i | |||||
− | 7.51714i | − | 0.422205i | −0.977464 | − | 0.211102i | ||||
0.977464 | − | 0.211102i | ||||||||
0 | 0 | |||||||||
3.31081i | 0.185370i | |||||||||
1.84252 | + | 3.10167i | 0.103000 | + | 0.173388i | |||||
0 | 0 | |||||||||
−3.50817 | − | 39.1641i | −0.195503 | − | 2.18253i | |||||
23.6512 | 1.31599 | |||||||||
0 | 0 | |||||||||
−25.8597 | −1.43444 | |||||||||
2.80201 | + | 31.2807i | 0.155189 | + | 1.73248i | |||||
0 | 0 | |||||||||
8.44305 | + | 30.7444i | 0.466189 | + | 1.69758i | |||||
− | 26.6574i | − | 1.46967i | |||||||
0 | 0 | |||||||||
− | 26.1423i | − | 1.43691i | −0.695572 | − | 0.718456i | ||||
0.695572 | − | 0.718456i | ||||||||
−1.23404 | + | 0.222871i | −0.0677270 | + | 0.0122316i | |||||
0 | 0 | |||||||||
−16.7265 | + | 1.49830i | −0.915234 | + | 0.0819833i | |||||
2.95210 | 0.161290 | |||||||||
0 | 0 | |||||||||
7.72064 | 0.420570 | 0.210285 | − | 0.977640i | ||||||
0.210285 | + | 0.977640i | ||||||||
−22.6291 | + | 2.02703i | −1.23086 | + | 0.110256i | |||||
0 | 0 | |||||||||
4.79126 | − | 0.865311i | 0.259843 | − | 0.0469281i | |||||
4.57881i | 0.247956i | |||||||||
0 | 0 | |||||||||
33.1114i | 1.78785i | |||||||||
0.487550 | + | 1.77536i | 0.0262869 | + | 0.0957208i | |||||
0 | 0 | |||||||||
−1.62799 | − | 18.1743i | −0.0875211 | − | 0.977056i | |||||
30.6201 | 1.64377 | 0.821886 | − | 0.569651i | ||||||
0.821886 | + | 0.569651i | ||||||||
0 | 0 | |||||||||
−19.2853 | −1.03232 | −0.516161 | − | 0.856492i | ||||||
−0.516161 | + | 0.856492i | ||||||||
2.78613 | + | 31.1034i | 0.148925 | + | 1.66255i | |||||
0 | 0 | |||||||||
5.10182 | − | 2.44366i | 0.271928 | − | 0.130248i | |||||
− | 24.5083i | − | 1.30444i | −0.758028 | − | 0.652222i | ||||
0.758028 | − | 0.652222i | ||||||||
0 | 0 | |||||||||
1.92922i | 0.102393i | |||||||||
3.78077 | + | 20.9343i | 0.200381 | + | 1.10952i | |||||
0 | 0 | |||||||||
−20.0309 | + | 1.79429i | −1.05867 | + | 0.0948313i | |||||
21.6374 | 1.14198 | 0.570990 | − | 0.820957i | ||||||
0.570990 | + | 0.820957i | ||||||||
0 | 0 | |||||||||
−0.195476 | −0.0102882 | |||||||||
−21.3847 | + | 1.91557i | −1.12396 | + | 0.100680i | |||||
0 | 0 | |||||||||
8.82188 | + | 48.8471i | 0.462392 | + | 2.56029i | |||||
4.44730i | 0.232782i | |||||||||
0 | 0 | |||||||||
− | 11.3739i | − | 0.593710i | −0.954923 | − | 0.296855i | ||||
0.954923 | − | 0.296855i | ||||||||
−22.6327 | + | 8.45063i | −1.17981 | + | 0.440520i | |||||
0 | 0 | |||||||||
0.356876 | + | 3.98405i | 0.0185531 | + | 0.207121i | |||||
−6.72281 | −0.349031 | |||||||||
0 | 0 | |||||||||
−22.0678 | −1.14263 | −0.571313 | − | 0.820732i | ||||||
−0.571313 | + | 0.820732i | ||||||||
−0.681125 | − | 7.60385i | −0.0352201 | − | 0.393186i | |||||
0 | 0 | |||||||||
−15.7936 | + | 4.33726i | −0.814494 | + | 0.223677i | |||||
17.8493i | 0.919287i | |||||||||
0 | 0 | |||||||||
11.5928i | 0.595480i | 0.954647 | + | 0.297740i | ||||||
−0.954647 | + | 0.297740i | ||||||||
−3.88862 | + | 0.702292i | −0.199482 | + | 0.0360268i | |||||
0 | 0 | |||||||||
19.3053 | − | 1.72930i | 0.987745 | − | 0.0884785i | |||||
−8.35063 | −0.426697 | −0.213349 | − | 0.976976i | ||||||
−0.213349 | + | 0.976976i | ||||||||
0 | 0 | |||||||||
−2.07600 | −0.105803 | |||||||||
22.1632 | − | 1.98530i | 1.12808 | − | 0.101049i | |||||
0 | 0 | |||||||||
3.14770 | − | 0.568481i | 0.159800 | − | 0.0288602i | |||||
− | 21.1897i | − | 1.07436i | −0.843467 | − | 0.537181i | ||||
0.843467 | − | 0.537181i | ||||||||
0 | 0 | |||||||||
32.6040i | 1.64885i | |||||||||
38.7096 | − | 10.6304i | 1.95513 | − | 0.536919i | |||||
0 | 0 | |||||||||
1.57860 | + | 17.6230i | 0.0795287 | + | 0.887831i | |||||
−3.98705 | −0.200610 | |||||||||
0 | 0 | |||||||||
−5.63389 | −0.282757 | −0.141378 | − | 0.989956i | ||||||
−0.141378 | + | 0.989956i | ||||||||
1.51076 | + | 16.8656i | 0.0757276 | + | 0.845398i | |||||
0 | 0 | |||||||||
17.9745 | − | 6.71134i | 0.898723 | − | 0.335567i | |||||
− | 27.1670i | − | 1.35665i | −0.734761 | − | 0.678327i | ||||
0.734761 | − | 0.678327i | ||||||||
0 | 0 | |||||||||
24.6853i | 1.22966i | |||||||||
2.09823 | + | 11.6180i | 0.104391 | + | 0.578016i | |||||
0 | 0 | |||||||||
21.4687 | − | 1.92309i | 1.06548 | − | 0.0954413i | |||||
6.27205 | 0.310894 | |||||||||
0 | 0 | |||||||||
−35.1236 | −1.73675 | −0.868374 | − | 0.495909i | ||||||
−0.868374 | + | 0.495909i | ||||||||
−7.16019 | + | 0.641384i | −0.353617 | + | 0.0316757i | |||||
0 | 0 | |||||||||
2.53070 | + | 14.0126i | 0.124678 | + | 0.690350i | |||||
− | 21.7000i | − | 1.06778i | |||||||
0 | 0 | |||||||||
− | 0.282752i | − | 0.0138798i | |||||||
27.5050 | − | 13.1743i | 1.34854 | − | 0.645923i | |||||
0 | 0 | |||||||||
0.552805 | + | 6.17133i | 0.0270386 | + | 0.301850i | |||||
5.90419 | 0.288439 | 0.144219 | − | 0.989546i | ||||||
0.144219 | + | 0.989546i | ||||||||
0 | 0 | |||||||||
−4.05579 | −0.197667 | −0.0988336 | − | 0.995104i | ||||||
−0.0988336 | + | 0.995104i | ||||||||
−2.87790 | − | 32.1279i | −0.140094 | − | 1.56396i | |||||
0 | 0 | |||||||||
1.09383 | + | 3.98305i | 0.0531210 | + | 0.193434i | |||||
− | 25.8935i | − | 1.25602i | |||||||
0 | 0 | |||||||||
− | 5.89361i | − | 0.285212i | |||||||
25.4297 | − | 4.59265i | 1.22919 | − | 0.221994i | |||||
0 | 0 | |||||||||
−0.413470 | + | 0.0370371i | −0.0199393 | + | 0.00178609i | |||||
−12.5967 | −0.606763 | −0.303382 | − | 0.952869i | ||||||
−0.303382 | + | 0.952869i | ||||||||
0 | 0 | |||||||||
7.12665 | 0.342485 | 0.171242 | − | 0.985229i | ||||||
0.171242 | + | 0.985229i | ||||||||
29.6909 | − | 2.65960i | 1.42521 | − | 0.127665i | |||||
0 | 0 | |||||||||
−14.5682 | + | 2.63105i | −0.697693 | + | 0.126004i | |||||
− | 26.4616i | − | 1.26583i | |||||||
0 | 0 | |||||||||
− | 14.7602i | − | 0.704466i | −0.935912 | − | 0.352233i | ||||
0.935912 | − | 0.352233i | ||||||||
0.337774 | + | 1.22996i | 0.0161027 | + | 0.0586362i | |||||
0 | 0 | |||||||||
−3.67209 | − | 40.9940i | −0.174664 | − | 1.94989i | |||||
0.00946572 | 0.000449730 | 0.000224865 | − | 1.00000i | ||||||
0.000224865 | 1.00000i | |||||||||
0 | 0 | |||||||||
−4.79661 | −0.227381 | |||||||||
−0.889999 | − | 9.93565i | −0.0421427 | − | 0.470467i | |||||
0 | 0 | |||||||||
−18.8091 | − | 31.6629i | −0.888648 | − | 1.49593i | |||||
3.11056i | 0.146796i | 0.997303 | + | 0.0733982i | ||||||
−0.997303 | + | 0.0733982i | ||||||||
0 | 0 | |||||||||
11.2722i | 0.530788i | |||||||||
4.69914 | + | 26.0193i | 0.221029 | + | 1.22385i | |||||
0 | 0 | |||||||||
24.1465 | − | 2.16295i | 1.13325 | − | 0.101512i | |||||
−11.1922 | −0.524697 | |||||||||
0 | 0 | |||||||||
7.09532 | 0.331905 | 0.165953 | − | 0.986134i | ||||||
0.165953 | + | 0.986134i | ||||||||
0.291278 | − | 0.0260916i | 0.0136105 | − | 0.00121918i | |||||
0 | 0 | |||||||||
−0.968132 | − | 5.36059i | −0.0451394 | − | 0.249939i | |||||
30.5522i | 1.42296i | 0.702708 | + | 0.711478i | ||||||
−0.702708 | + | 0.711478i | ||||||||
0 | 0 | |||||||||
− | 25.8995i | − | 1.20365i | −0.798628 | − | 0.601825i | ||||
0.798628 | − | 0.601825i | ||||||||
−4.63241 | − | 12.4066i | −0.215054 | − | 0.575963i | |||||
0 | 0 | |||||||||
0.960759 | + | 10.7256i | 0.0445063 | + | 0.496854i | |||||
−30.1266 | −1.39409 | −0.697047 | − | 0.717026i | ||||||
−0.697047 | + | 0.717026i | ||||||||
0 | 0 | |||||||||
−30.1361 | −1.39156 | |||||||||
−0.329484 | − | 3.67825i | −0.0151979 | − | 0.169665i | |||||
0 | 0 | |||||||||
−12.8565 | + | 3.53067i | −0.591769 | + | 0.162512i | |||||
0.650922i | 0.0299294i | |||||||||
0 | 0 | |||||||||
21.0153i | 0.964250i | |||||||||
−48.9110 | + | 8.83341i | −2.24183 | + | 0.404879i | |||||
0 | 0 | |||||||||
16.6013 | − | 1.48708i | 0.759326 | − | 0.0680176i | |||||
35.2644 | 1.61127 | 0.805636 | − | 0.592411i | ||||||
0.805636 | + | 0.592411i | ||||||||
0 | 0 | |||||||||
33.8140 | 1.54178 | |||||||||
−8.15043 | + | 0.730085i | −0.371242 | + | 0.0332545i | |||||
0 | 0 | |||||||||
1.96816 | − | 0.355453i | 0.0894618 | − | 0.0161570i | |||||
0.721223i | 0.0327490i | |||||||||
0 | 0 | |||||||||
8.15092i | 0.369354i | 0.982799 | + | 0.184677i | ||||||
−0.982799 | + | 0.184677i | ||||||||
−3.49177 | + | 0.958913i | −0.158065 | + | 0.0434080i | |||||
0 | 0 | |||||||||
0.807551 | + | 9.01523i | 0.0364814 | + | 0.407267i | |||||
−35.0295 | −1.58086 | −0.790430 | − | 0.612553i | ||||||
−0.790430 | + | 0.612553i | ||||||||
0 | 0 | |||||||||
−17.8726 | −0.804943 | |||||||||
2.98029 | + | 33.2710i | 0.134090 | + | 1.49693i | |||||
0 | 0 | |||||||||
−6.40656 | − | 17.1582i | −0.287663 | − | 0.770425i | |||||
− | 19.6942i | − | 0.883406i | |||||||
0 | 0 | |||||||||
− | 25.0804i | − | 1.12275i | −0.827560 | − | 0.561377i | ||||
0.827560 | − | 0.561377i | ||||||||
1.57035 | + | 8.69507i | 0.0702280 | + | 0.388855i | |||||
0 | 0 | |||||||||
−31.0720 | + | 2.78332i | −1.38681 | + | 0.124226i | |||||
18.9025 | 0.842820 | 0.421410 | − | 0.906870i | ||||||
0.421410 | + | 0.906870i | ||||||||
0 | 0 | |||||||||
−2.66199 | −0.118457 | |||||||||
−8.50738 | + | 0.762060i | −0.378199 | + | 0.0338777i | |||||
0 | 0 | |||||||||
−5.29904 | − | 29.3410i | −0.235107 | − | 1.30180i | |||||
− | 10.9702i | − | 0.486247i | −0.969995 | − | 0.243124i | ||||
0.969995 | − | 0.243124i | ||||||||
0 | 0 | |||||||||
− | 45.3996i | − | 2.00836i | |||||||
−15.6990 | + | 16.2955i | −0.693802 | + | 0.720165i | |||||
0 | 0 | |||||||||
−1.07434 | − | 11.9935i | −0.0473870 | − | 0.529012i | |||||
−3.21065 | −0.141478 | |||||||||
0 | 0 | |||||||||
−5.79062 | −0.254671 | |||||||||
−3.64312 | − | 40.6706i | −0.160070 | − | 1.78696i | |||||
0 | 0 | |||||||||
1.82101 | + | 6.63100i | 0.0798566 | + | 0.290789i | |||||
− | 6.21862i | − | 0.272443i | −0.990678 | − | 0.136221i | ||||
0.990678 | − | 0.136221i | ||||||||
0 | 0 | |||||||||
8.06214i | 0.352533i | 0.984343 | + | 0.176266i | ||||||
−0.984343 | + | 0.176266i | ||||||||
−11.2176 | + | 2.02592i | −0.490044 | + | 0.0885029i | |||||
0 | 0 | |||||||||
7.14268 | − | 0.639815i | 0.311435 | − | 0.0278972i | |||||
−24.7176 | −1.07672 | |||||||||
0 | 0 | |||||||||
13.4782 | 0.586007 | |||||||||
−0.927629 | + | 0.0830936i | −0.0402936 | + | 0.00360935i | |||||
0 | 0 | |||||||||
39.6965 | − | 7.16925i | 1.72106 | − | 0.310826i | |||||
60.7710i | 2.63228i | |||||||||
0 | 0 | |||||||||
5.82662i | 0.251907i | |||||||||
4.90326 | + | 17.8547i | 0.211789 | + | 0.771204i | |||||
0 | 0 | |||||||||
3.22743 | + | 36.0300i | 0.139144 | + | 1.55336i | |||||
14.1926 | 0.611318 | |||||||||
0 | 0 | |||||||||
−15.5904 | −0.670284 | −0.335142 | − | 0.942168i | ||||||
−0.335142 | + | 0.942168i | ||||||||
3.68928 | + | 41.1859i | 0.158468 | + | 1.76908i | |||||
0 | 0 | |||||||||
13.1915 | + | 27.5409i | 0.565582 | + | 1.18081i | |||||
− | 3.33797i | − | 0.142983i | |||||||
0 | 0 | |||||||||
− | 35.1984i | − | 1.50497i | −0.658607 | − | 0.752487i | ||||
0.658607 | − | 0.752487i | ||||||||
−1.30728 | − | 7.23849i | −0.0558444 | − | 0.309213i | |||||
0 | 0 | |||||||||
6.75642 | − | 0.605215i | 0.288095 | − | 0.0258064i | |||||
14.5055 | 0.617957 | |||||||||
0 | 0 | |||||||||
40.7013 | 1.73079 | |||||||||
−45.2167 | + | 4.05035i | −1.92107 | + | 0.172083i | |||||
0 | 0 | |||||||||
4.05209 | + | 22.4366i | 0.171847 | + | 0.951524i | |||||
− | 34.1280i | − | 1.44605i | −0.690823 | − | 0.723024i | ||||
0.690823 | − | 0.723024i | ||||||||
0 | 0 | |||||||||
3.50926i | 0.148426i | |||||||||
7.77942 | − | 2.90469i | 0.328740 | − | 0.122746i | |||||
0 | 0 | |||||||||
−2.45604 | − | 27.4184i | −0.103602 | − | 1.15658i | |||||
45.8757 | 1.93343 | 0.966716 | − | 0.255853i | ||||||
0.966716 | + | 0.255853i | ||||||||
0 | 0 | |||||||||
−5.96172 | −0.250812 | |||||||||
−1.80880 | − | 20.1929i | −0.0760297 | − | 0.848770i | |||||
0 | 0 | |||||||||
−11.6682 | + | 3.20433i | −0.489586 | + | 0.134451i | |||||
6.58959i | 0.276250i | 0.990415 | + | 0.138125i | ||||||
−0.990415 | + | 0.138125i | ||||||||
0 | 0 | |||||||||
− | 4.44412i | − | 0.185981i | −0.995667 | − | 0.0929904i | ||||
0.995667 | − | 0.0929904i | ||||||||
10.6108 | − | 1.91633i | 0.443659 | − | 0.0801256i | |||||
0 | 0 | |||||||||
73.0939 | − | 6.54748i | 3.05088 | − | 0.273286i | |||||
−28.9703 | −1.20815 | |||||||||
0 | 0 | |||||||||
−26.8917 | −1.11952 | −0.559759 | − | 0.828656i | ||||||
−0.559759 | + | 0.828656i | ||||||||
17.1018 | − | 1.53192i | 0.711342 | − | 0.0637194i | |||||
0 | 0 | |||||||||
2.93854 | − | 0.530705i | 0.122016 | − | 0.0220363i | |||||
2.88644i | 0.119750i | |||||||||
0 | 0 | |||||||||
1.46036i | 0.0604818i | |||||||||
−26.8978 | + | 7.38670i | −1.11304 | + | 0.305664i | |||||
0 | 0 | |||||||||
−2.68697 | − | 29.9965i | −0.110998 | − | 1.23914i | |||||
−18.6184 | −0.768464 | −0.384232 | − | 0.923237i | ||||||
−0.384232 | + | 0.923237i | ||||||||
0 | 0 | |||||||||
20.0610 | 0.826597 | |||||||||
−0.268210 | − | 2.99421i | −0.0110420 | − | 0.123270i | |||||
0 | 0 | |||||||||
−23.5033 | + | 8.77570i | −0.965979 | + | 0.360679i | |||||
24.8200i | 1.01924i | 0.860401 | + | 0.509618i | ||||||
−0.860401 | + | 0.509618i | ||||||||
0 | 0 | |||||||||
− | 11.2068i | − | 0.459434i | |||||||
−7.02286 | − | 38.8859i | −0.287668 | − | 1.59283i | |||||
0 | 0 | |||||||||
−45.8652 | + | 4.10843i | −1.87557 | + | 0.168006i | |||||
−4.54608 | −0.185748 | −0.0928739 | − | 0.995678i | ||||||
−0.0928739 | + | 0.995678i | ||||||||
0 | 0 | |||||||||
10.5497 | 0.430332 | 0.215166 | − | 0.976577i | ||||||
0.215166 | + | 0.976577i | ||||||||
4.22085 | − | 0.378088i | 0.172029 | − | 0.0154097i | |||||
0 | 0 | |||||||||
−1.60354 | − | 8.87887i | −0.0652471 | − | 0.361276i | |||||
0.450958i | 0.0183340i | |||||||||
0 | 0 | |||||||||
− | 4.75119i | − | 0.192845i | −0.995340 | − | 0.0964225i | ||||
0.995340 | − | 0.0964225i | ||||||||
−10.7063 | − | 22.3524i | −0.434199 | − | 0.906510i | |||||
0 | 0 | |||||||||
−0.0728447 | − | 0.813214i | −0.00294939 | − | 0.0329261i | |||||
−31.2185 | −1.26297 | |||||||||
0 | 0 | |||||||||
24.6283 | 0.994726 | 0.497363 | − | 0.867543i | ||||||
0.497363 | + | 0.867543i | ||||||||
0.296239 | + | 3.30712i | 0.0119552 | + | 0.133464i | |||||
0 | 0 | |||||||||
−3.44812 | − | 12.5559i | −0.138929 | − | 0.505893i | |||||
14.0774i | 0.566736i | 0.959011 | + | 0.283368i | ||||||
−0.959011 | + | 0.283368i | ||||||||
0 | 0 | |||||||||
16.9924i | 0.682980i | 0.939885 | + | 0.341490i | ||||||
−0.939885 | + | 0.341490i | ||||||||
4.06395 | − | 0.733956i | 0.163212 | − | 0.0294764i | |||||
0 | 0 | |||||||||
−18.2751 | + | 1.63701i | −0.732763 | + | 0.0656382i | |||||
48.9655 | 1.96176 | |||||||||
0 | 0 | |||||||||
21.9909 | 0.879637 | |||||||||
−12.2046 | + | 1.09325i | −0.487796 | + | 0.0436949i | |||||
0 | 0 | |||||||||
−4.85085 | + | 0.876072i | −0.193570 | + | 0.0349591i | |||||
33.8581i | 1.35001i | |||||||||
0 | 0 | |||||||||
11.2451i | 0.447659i | 0.974628 | + | 0.223829i | ||||||
−0.974628 | + | 0.223829i | ||||||||
−6.62225 | − | 24.1142i | −0.263419 | − | 0.959211i | |||||
0 | 0 | |||||||||
0.948474 | + | 10.5884i | 0.0376687 | + | 0.420521i | |||||
6.72281 | 0.266787 | |||||||||
0 | 0 | |||||||||
76.5153 | 3.03165 | |||||||||
−0.417741 | − | 4.66353i | −0.0165385 | − | 0.184631i | |||||
0 | 0 | |||||||||
−2.98668 | − | 4.13645i | −0.118059 | − | 0.163507i | |||||
− | 17.6143i | − | 0.695722i | −0.937546 | − | 0.347861i | ||||
0.937546 | − | 0.347861i | ||||||||
0 | 0 | |||||||||
− | 6.03887i | − | 0.238150i | −0.992885 | − | 0.119075i | ||||
0.992885 | − | 0.119075i | ||||||||
9.88304 | + | 54.7229i | 0.389446 | + | 2.15638i | |||||
0 | 0 | |||||||||
−33.3145 | + | 2.98419i | −1.31074 | + | 0.117411i | |||||
−48.1430 | −1.89270 | −0.946349 | − | 0.323146i | ||||||
−0.946349 | + | 0.323146i | ||||||||
0 | 0 | |||||||||
−4.71375 | −0.185031 | |||||||||
36.4253 | − | 3.26285i | 1.42872 | − | 0.127979i | |||||
0 | 0 | |||||||||
−7.89368 | − | 43.7076i | −0.309140 | − | 1.71172i | |||||
20.5620i | 0.804655i | 0.915496 | + | 0.402328i | ||||||
−0.915496 | + | 0.402328i | ||||||||
0 | 0 | |||||||||
− | 2.57026i | − | 0.100428i | |||||||
−15.7718 | − | 42.2404i | −0.615786 | − | 1.64921i | |||||
0 | 0 | |||||||||
3.36349 | + | 37.5489i | 0.131122 | + | 1.46381i | |||||
−33.8196 | −1.31742 | −0.658712 | − | 0.752395i | ||||||
−0.658712 | + | 0.752395i | ||||||||
0 | 0 | |||||||||
−18.7893 | −0.730821 | −0.365410 | − | 0.930847i | ||||||
−0.365410 | + | 0.930847i | ||||||||
3.29850 | + | 36.8234i | 0.128200 | + | 1.43118i | |||||
0 | 0 | |||||||||
1.71012 | − | 0.469635i | 0.0663656 | − | 0.0182254i | |||||
9.09551i | 0.352709i | |||||||||
0 | 0 | |||||||||
19.9964i | 0.774263i | |||||||||
23.3715 | − | 4.22093i | 0.904270 | − | 0.163313i | |||||
0 | 0 | |||||||||
−4.15825 | + | 0.372480i | −0.160647 | + | 0.0143902i | |||||
−1.28023 | −0.0494229 | |||||||||
0 | 0 | |||||||||
−10.8744 | −0.419178 | −0.209589 | − | 0.977790i | ||||||
−0.209589 | + | 0.977790i | ||||||||
−10.8751 | + | 0.974150i | −0.418893 | + | 0.0375228i | |||||
0 | 0 | |||||||||
31.6189 | − | 5.71043i | 1.21611 | − | 0.219632i | |||||
49.5233i | 1.90333i | 0.307133 | + | 0.951667i | ||||||
−0.307133 | + | 0.951667i | ||||||||
0 | 0 | |||||||||
− | 7.36250i | − | 0.282547i | |||||||
−6.63967 | + | 1.82339i | −0.254620 | + | 0.0699238i | |||||
0 | 0 | |||||||||
−0.577730 | − | 6.44958i | −0.0221224 | − | 0.246967i | |||||
−8.75966 | −0.335179 | −0.167590 | − | 0.985857i | ||||||
−0.167590 | + | 0.985857i | ||||||||
0 | 0 | |||||||||
1.65853 | 0.0633692 | |||||||||
−4.17782 | − | 46.6398i | −0.159510 | − | 1.78072i | |||||
0 | 0 | |||||||||
−0.910755 | − | 2.43920i | −0.0347222 | − | 0.0929937i | |||||
7.87310i | 0.299941i | |||||||||
0 | 0 | |||||||||
− | 9.60042i | − | 0.365217i | −0.983186 | − | 0.182609i | ||||
0.983186 | − | 0.182609i | ||||||||
4.58628 | + | 25.3944i | 0.174344 | + | 0.965351i | |||||
0 | 0 | |||||||||
−43.1307 | + | 3.86349i | −1.63722 | + | 0.146656i | |||||
−5.14082 | −0.195002 | |||||||||
0 | 0 | |||||||||
−60.8504 | −2.30487 | |||||||||
27.1648 | − | 2.43333i | 1.02820 | − | 0.0921027i | |||||
0 | 0 | |||||||||
−7.84894 | − | 43.4600i | −0.296662 | − | 1.64263i | |||||
− | 28.5860i | − | 1.07968i | −0.841769 | − | 0.539839i | ||||
0.841769 | − | 0.539839i | ||||||||
0 | 0 | |||||||||
− | 27.4795i | − | 1.03641i | |||||||
−6.87796 | + | 4.08580i | −0.259223 | + | 0.153989i | |||||
0 | 0 | |||||||||
3.09233 | + | 34.5217i | 0.116381 | + | 1.29924i | |||||
27.1745 | 1.02200 | |||||||||
0 | 0 | |||||||||
−6.19988 | −0.232841 | −0.116421 | − | 0.993200i | ||||||
−0.116421 | + | 0.993200i | ||||||||
−0.243419 | − | 2.71745i | −0.00913537 | − | 0.101984i | |||||
0 | 0 | |||||||||
−7.96688 | − | 29.0105i | −0.298572 | − | 1.08721i | |||||
27.6547i | 1.03568i | |||||||||
0 | 0 | |||||||||
2.43121i | 0.0909221i | |||||||||
27.9886 | − | 5.05479i | 1.04598 | − | 0.188906i | |||||
0 | 0 | |||||||||
−30.4779 | + | 2.73010i | −1.13743 | + | 0.101886i | |||||
−16.1753 | −0.603238 | −0.301619 | − | 0.953428i | ||||||
−0.301619 | + | 0.953428i | ||||||||
0 | 0 | |||||||||
32.7755 | 1.22062 | |||||||||
0.275342 | − | 0.0246641i | 0.0102472 | − | 0.000917903i | |||||
0 | 0 | |||||||||
29.8803 | − | 5.39643i | 1.11049 | − | 0.200557i | |||||
− | 15.8808i | − | 0.589797i | |||||||
0 | 0 | |||||||||
14.8038i | 0.549042i | 0.961581 | + | 0.274521i | ||||||
−0.961581 | + | 0.274521i | ||||||||
−18.5895 | − | 67.6917i | −0.688975 | − | 2.50882i | |||||
0 | 0 | |||||||||
−0.561137 | − | 6.26434i | −0.0207686 | − | 0.231854i | |||||
−3.51385 | −0.129964 | |||||||||
0 | 0 | |||||||||
4.58421 | 0.169322 | 0.0846609 | − | 0.996410i | ||||||
0.0846609 | + | 0.996410i | ||||||||
1.43509 | + | 16.0209i | 0.0529703 | + | 0.591343i | |||||
0 | 0 | |||||||||
30.8135 | − | 14.7590i | 1.13580 | − | 0.544024i | |||||
6.54628i | 0.241135i | |||||||||
0 | 0 | |||||||||
− | 1.28355i | − | 0.0472163i | −0.999721 | − | 0.0236081i | ||||
0.999721 | − | 0.0236081i | ||||||||
−1.00537 | − | 5.56680i | −0.0369583 | − | 0.204640i | |||||
0 | 0 | |||||||||
9.46957 | − | 0.848249i | 0.347639 | − | 0.0311402i | |||||
−23.9767 | −0.879620 | −0.439810 | − | 0.898091i | ||||||
−0.439810 | + | 0.898091i | ||||||||
0 | 0 | |||||||||
8.90980 | 0.326430 | |||||||||
31.0841 | − | 2.78440i | 1.13807 | − | 0.101944i | |||||
0 | 0 | |||||||||
1.91883 | + | 10.6246i | 0.0701593 | + | 0.388475i | |||||
− | 59.4802i | − | 2.17336i | |||||||
0 | 0 | |||||||||
37.2322i | 1.35862i | 0.733850 | + | 0.679312i | ||||||
−0.733850 | + | 0.679312i | ||||||||
21.6992 | − | 8.10211i | 0.791290 | − | 0.295453i | |||||
0 | 0 | |||||||||
−2.25213 | − | 25.1421i | −0.0820179 | − | 0.915621i | |||||
2.03439 | 0.0740389 | |||||||||
0 | 0 | |||||||||
33.0955 | 1.20288 | 0.601438 | − | 0.798919i | ||||||
0.601438 | + | 0.798919i | ||||||||
−1.46272 | − | 16.3293i | −0.0531282 | − | 0.593106i | |||||
0 | 0 | |||||||||
5.38880 | − | 1.47988i | 0.195472 | − | 0.0536807i | |||||
14.2090i | 0.515077i | 0.966268 | + | 0.257538i | ||||||
−0.966268 | + | 0.257538i | ||||||||
0 | 0 | |||||||||
34.0752i | 1.23361i | |||||||||
−26.9747 | + | 4.87169i | −0.975912 | + | 0.176251i | |||||
0 | 0 | |||||||||
11.7625 | − | 1.05364i | 0.424996 | − | 0.0380696i | |||||
−25.4129 | −0.917605 | |||||||||
0 | 0 | |||||||||
−29.1166 | −1.04997 | −0.524985 | − | 0.851111i | ||||||
−0.524985 | + | 0.851111i | ||||||||
2.92420 | − | 0.261939i | 0.105381 | − | 0.00943963i | |||||
0 | 0 | |||||||||
−30.9681 | + | 5.59289i | −1.11457 | + | 0.201292i | |||||
− | 6.64019i | − | 0.238831i | −0.992844 | − | 0.119416i | ||||
0.992844 | − | 0.119416i | ||||||||
0 | 0 | |||||||||
− | 21.9629i | − | 0.788929i | |||||||
−4.36205 | + | 1.19791i | −0.156588 | + | 0.0430024i | |||||
0 | 0 | |||||||||
2.67361 | + | 29.8473i | 0.0958537 | + | 1.07008i | |||||
49.3866 | 1.76946 | |||||||||
0 | 0 | |||||||||
−4.27806 | −0.153081 | |||||||||
−4.11380 | − | 45.9251i | −0.147109 | − | 1.64228i | |||||
0 | 0 | |||||||||
−53.1840 | + | 19.8579i | −1.89943 | + | 0.709212i | |||||
− | 1.11146i | − | 0.0396696i | |||||||
0 | 0 | |||||||||
− | 5.12622i | − | 0.182730i | −0.995817 | − | 0.0913651i | ||||
0.995817 | − | 0.0913651i | ||||||||
−4.44715 | − | 24.6240i | −0.158423 | − | 0.877195i | |||||
0 | 0 | |||||||||
5.61605 | − | 0.503065i | 0.199810 | − | 0.0178983i | |||||
60.8594 | 2.16391 | |||||||||
0 | 0 | |||||||||
−6.90202 | −0.245098 | |||||||||
7.93574 | − | 0.710855i | 0.281629 | − | 0.0252273i | |||||
0 | 0 | |||||||||
−4.25604 | − | 23.5659i | −0.150851 | − | 0.835270i | |||||
25.6924i | 0.910072i | 0.890473 | + | 0.455036i | ||||||
−0.890473 | + | 0.455036i | ||||||||
0 | 0 | |||||||||
− | 31.2593i | − | 1.10587i | |||||||
−24.4716 | + | 11.7213i | −0.865200 | + | 0.414412i | |||||
0 | 0 | |||||||||
3.42779 | + | 38.2667i | 0.121039 | + | 1.35124i | |||||
−9.86189 | −0.348019 | |||||||||
0 | 0 | |||||||||
−12.5385 | −0.441923 | |||||||||
−3.11467 | − | 34.7711i | −0.109709 | − | 1.22476i | |||||
0 | 0 | |||||||||
−4.42140 | − | 16.1000i | −0.155544 | − | 0.566397i | |||||
11.1617i | 0.392424i | 0.980561 | + | 0.196212i | ||||||
−0.980561 | + | 0.196212i | ||||||||
0 | 0 | |||||||||
25.6391i | 0.900309i | 0.892951 | + | 0.450154i | ||||||
−0.892951 | + | 0.450154i | ||||||||
−29.9976 | + | 5.41763i | −1.05271 | + | 0.190121i | |||||
0 | 0 | |||||||||
−8.83464 | + | 0.791374i | −0.309654 | + | 0.0277377i | |||||
10.0146 | 0.350795 | |||||||||
0 | 0 | |||||||||
2.85186 | 0.0997739 | |||||||||
49.4741 | − | 4.43171i | 1.72982 | − | 0.154951i | |||||
0 | 0 | |||||||||
10.0047 | − | 1.80687i | 0.349380 | − | 0.0630987i | |||||
− | 32.3388i | − | 1.12863i | −0.825559 | − | 0.564316i | ||||
0.825559 | − | 0.564316i | ||||||||
0 | 0 | |||||||||
10.1239i | 0.352896i | 0.984310 | + | 0.176448i | ||||||
−0.984310 | + | 0.176448i | ||||||||
−5.33271 | − | 19.4184i | −0.185774 | − | 0.676473i | |||||
0 | 0 | |||||||||
2.73799 | + | 30.5660i | 0.0952668 | + | 1.06353i | |||||
5.77199 | 0.200712 | 0.100356 | − | 0.994952i | ||||||
0.100356 | + | 0.994952i | ||||||||
0 | 0 | |||||||||
46.2848 | 1.60754 | 0.803769 | − | 0.594942i | ||||||
0.803769 | + | 0.594942i | ||||||||
0.0356762 | + | 0.398277i | 0.00123834 | + | 0.0138244i | |||||
0 | 0 | |||||||||
−37.0806 | + | 22.0274i | −1.28554 | + | 0.763663i | |||||
76.6153i | 2.65456i | |||||||||
0 | 0 | |||||||||
5.35503i | 0.185318i | |||||||||
−1.55733 | − | 8.62303i | −0.0538615 | − | 0.298234i | |||||
0 | 0 | |||||||||
−8.31649 | + | 0.744961i | −0.287288 | + | 0.0257342i | |||||
48.0233 | 1.65795 | 0.828975 | − | 0.559286i | ||||||
0.828975 | + | 0.559286i | ||||||||
0 | 0 | |||||||||
18.0385 | 0.622018 | |||||||||
5.71288 | − | 0.511739i | 0.196879 | − | 0.0176357i | |||||
0 | 0 | |||||||||
8.10746 | + | 44.8914i | 0.279070 | + | 1.54523i | |||||
7.24474i | 0.249227i | |||||||||
0 | 0 | |||||||||
− | 4.60354i | − | 0.158180i | |||||||
−2.04330 | − | 5.47240i | −0.0701671 | − | 0.187923i | |||||
0 | 0 | |||||||||
3.26711 | + | 36.4729i | 0.112061 | + | 1.25101i | |||||
37.8814 | 1.29856 | |||||||||
0 | 0 | |||||||||
33.6945 | 1.15368 | 0.576839 | − | 0.816858i | ||||||
0.576839 | + | 0.816858i | ||||||||
0.743625 | + | 8.30158i | 0.0254463 | + | 0.284074i | |||||
0 | 0 | |||||||||
−35.2401 | + | 9.67767i | −1.20448 | + | 0.330776i | |||||
27.0979i | 0.925646i | 0.886451 | + | 0.462823i | ||||||
−0.886451 | + | 0.462823i | ||||||||
0 | 0 | |||||||||
3.07528i | 0.104927i | 0.998623 | + | 0.0524636i | ||||||
−0.998623 | + | 0.0524636i | ||||||||
0.577730 | − | 0.104339i | 0.0197004 | − | 0.00355793i | |||||
0 | 0 | |||||||||
17.7434 | − | 1.58939i | 0.604343 | − | 0.0541348i | |||||
−4.36829 | −0.148698 | −0.0743492 | − | 0.997232i | ||||||
−0.0743492 | + | 0.997232i | ||||||||
0 | 0 | |||||||||
−5.81854 | −0.197836 | |||||||||
−10.0384 | + | 0.899204i | −0.341119 | + | 0.0305562i | |||||
0 | 0 | |||||||||
−41.4863 | + | 7.49249i | −1.40814 | + | 0.254312i | |||||
− | 8.84129i | − | 0.299920i | |||||||
0 | 0 | |||||||||
35.2924i | 1.19584i | |||||||||
20.1885 | − | 5.54418i | 0.683668 | − | 0.187749i | |||||
0 | 0 | |||||||||
3.33879 | + | 37.2731i | 0.112936 | + | 1.26078i | |||||
20.3378 | 0.687544 | |||||||||
0 | 0 | |||||||||
5.50220 | 0.185796 | 0.0928981 | − | 0.995676i | ||||||
0.0928981 | + | 0.995676i | ||||||||
1.86237 | + | 20.7908i | 0.0628518 | + | 0.701656i | |||||
0 | 0 | |||||||||
−0.630970 | − | 1.68988i | −0.0212700 | − | 0.0569657i | |||||
− | 24.1682i | − | 0.814247i | −0.913373 | − | 0.407124i | ||||
0.913373 | − | 0.407124i | ||||||||
0 | 0 | |||||||||
− | 51.0030i | − | 1.71639i | −0.513326 | − | 0.858194i | ||||
0.513326 | − | 0.858194i | ||||||||
10.3448 | + | 57.2798i | 0.347934 | + | 1.92653i | |||||
0 | 0 | |||||||||
−0.0133332 | + | 0.00119434i | −0.000447936 | + | 4.01245e-5i | |||||
−27.1324 | −0.911015 | −0.455508 | − | 0.890232i | ||||||
−0.455508 | + | 0.890232i | ||||||||
0 | 0 | |||||||||
−68.6289 | −2.30174 | |||||||||
6.75638 | − | 0.605211i | 0.226474 | − | 0.0202867i | |||||
0 | 0 | |||||||||
2.50726 | + | 13.8828i | 0.0839492 | + | 0.464830i | |||||
25.3703i | 0.848983i | |||||||||
0 | 0 | |||||||||
6.41293i | 0.214361i | |||||||||
30.4891 | + | 42.2264i | 1.01857 | + | 1.41068i | |||||
0 | 0 | |||||||||
−0.392475 | − | 4.38145i | −0.0130970 | − | 0.146211i | |||||
−15.1596 | −0.505600 | |||||||||
0 | 0 | |||||||||
−7.88339 | −0.262634 | |||||||||
−1.42227 | − | 15.8777i | −0.0473564 | − | 0.528671i | |||||
0 | 0 | |||||||||
−9.90207 | − | 36.0572i | −0.329338 | − | 1.19925i | |||||
6.84637i | 0.227581i | |||||||||
0 | 0 | |||||||||
53.1849i | 1.76598i | 0.469396 | + | 0.882988i | ||||||
−0.469396 | + | 0.882988i | ||||||||
−33.7392 | + | 6.09336i | −1.11967 | + | 0.202215i | |||||
0 | 0 | |||||||||
15.7650 | − | 1.41217i | 0.522605 | − | 0.0468130i | |||||
29.2194 | 0.968082 | 0.484041 | − | 0.875045i | ||||||
0.484041 | + | 0.875045i | ||||||||
0 | 0 | |||||||||
0.627004 | 0.0207508 | |||||||||
−9.99428 | + | 0.895251i | −0.330581 | + | 0.0296123i | |||||
0 | 0 | |||||||||
−0.406995 | + | 0.0735040i | −0.0134475 | + | 0.00242864i | |||||
26.2381i | 0.866459i | |||||||||
0 | 0 | |||||||||
37.4675i | 1.23594i | 0.786202 | + | 0.617969i | ||||||
−0.786202 | + | 0.617969i | ||||||||
2.04006 | + | 7.42863i | 0.0672587 | + | 0.244915i | |||||
0 | 0 | |||||||||
−3.85492 | − | 43.0350i | −0.126955 | − | 1.41728i | |||||
−23.0639 | −0.759159 | |||||||||
0 | 0 | |||||||||
−30.0847 | −0.989180 | |||||||||
3.26786 | + | 36.4813i | 0.107389 | + | 1.19885i | |||||
0 | 0 | |||||||||
8.09050 | + | 16.8912i | 0.265584 | + | 0.554480i | |||||
− | 7.31585i | − | 0.240025i | −0.992772 | − | 0.120013i | ||||
0.992772 | − | 0.120013i | ||||||||
0 | 0 | |||||||||
− | 62.1815i | − | 2.03792i | |||||||
−2.70660 | − | 14.9866i | −0.0886576 | − | 0.490901i | |||||
0 | 0 | |||||||||
42.4356 | − | 3.80122i | 1.38853 | − | 0.124380i | |||||
−2.43439 | −0.0796130 | |||||||||
0 | 0 | |||||||||
35.3106 | 1.15355 | 0.576774 | − | 0.816904i | ||||||
0.576774 | + | 0.816904i | ||||||||
42.4489 | − | 3.80242i | 1.38601 | − | 0.124153i | |||||
0 | 0 | |||||||||
0.928204 | + | 5.13951i | 0.0302747 | + | 0.167632i | |||||
3.59895i | 0.117323i | 0.998278 | + | 0.0586613i | ||||||
−0.998278 | + | 0.0586613i | ||||||||
0 | 0 | |||||||||
68.0810i | 2.21702i | |||||||||
17.6639 | − | 6.59537i | 0.574910 | − | 0.214661i | |||||
0 | 0 | |||||||||
−0.0821299 | − | 0.916871i | −0.00267027 | − | 0.0298101i | |||||
−43.7091 | −1.42036 | −0.710178 | − | 0.704022i | ||||||
−0.710178 | + | 0.704022i | ||||||||
0 | 0 | |||||||||
−53.1676 | −1.72589 | |||||||||
−2.65161 | − | 29.6016i | −0.0860295 | − | 0.960404i | |||||
0 | 0 | |||||||||
67.7802 | − | 18.6138i | 2.19677 | − | 0.603278i | |||||
7.81428i | 0.253129i | 0.991958 | + | 0.126565i | ||||||
−0.991958 | + | 0.126565i | ||||||||
0 | 0 | |||||||||
− | 6.18063i | − | 0.200000i | |||||||
−23.1965 | + | 4.18933i | −0.750229 | + | 0.135493i | |||||
0 | 0 | |||||||||
−49.6725 | + | 4.44948i | −1.60485 | + | 0.143756i | |||||
−16.9309 | −0.546727 | |||||||||
0 | 0 | |||||||||
10.0345 | 0.323695 | |||||||||
−47.6295 | + | 4.26647i | −1.53564 | + | 0.137557i | |||||
0 | 0 | |||||||||
11.3884 | − | 2.05676i | 0.366794 | − | 0.0662437i | |||||
− | 7.09561i | − | 0.228416i | |||||||
0 | 0 | |||||||||
40.7961i | 1.31191i | 0.754798 | + | 0.655957i | ||||||
−0.754798 | + | 0.655957i | ||||||||
−2.72745 | + | 0.749014i | −0.0876635 | + | 0.0240742i | |||||
0 | 0 | |||||||||
−0.0910001 | − | 1.01590i | −0.00292184 | − | 0.0326184i | |||||
−17.8775 | −0.573717 | −0.286859 | − | 0.957973i | ||||||
−0.286859 | + | 0.957973i | ||||||||
0 | 0 | |||||||||
52.4794 | 1.68241 | |||||||||
−1.02844 | − | 11.4812i | −0.0329534 | − | 0.367881i | |||||
0 | 0 | |||||||||
4.79743 | − | 1.79127i | 0.153562 | − | 0.0573373i | |||||
− | 26.9702i | − | 0.862854i | −0.902148 | − | 0.431427i | ||||
0.902148 | − | 0.431427i | ||||||||
0 | 0 | |||||||||
− | 10.6365i | − | 0.339944i | |||||||
−2.27499 | − | 12.5967i | −0.0726719 | − | 0.402388i | |||||
0 | 0 | |||||||||
49.3416 | − | 4.41984i | 1.57455 | − | 0.141043i | |||||
21.5536 | 0.687452 | 0.343726 | − | 0.939070i | ||||||
0.343726 | + | 0.939070i | ||||||||
0 | 0 | |||||||||
5.64202 | 0.179770 | |||||||||
25.1749 | − | 2.25508i | 0.801733 | − | 0.0718163i | |||||
0 | 0 | |||||||||
−8.39593 | − | 46.4886i | −0.267110 | − | 1.47900i | |||||
3.93138i | 0.125011i | |||||||||
0 | 0 | |||||||||
− | 0.996115i | − | 0.0316426i | −0.999875 | − | 0.0158213i | ||||
0.999875 | − | 0.0158213i | ||||||||
11.1890 | + | 23.3602i | 0.355252 | + | 0.741688i | |||||
0 | 0 | |||||||||
2.48491 | + | 27.7408i | 0.0788167 | + | 0.879883i | |||||
5.39957 | 0.171178 | |||||||||
0 | 0 | |||||||||
−17.8333 | −0.564787 | −0.282394 | − | 0.959299i | ||||||
−0.282394 | + | 0.959299i | ||||||||
3.16452 | + | 35.3276i | 0.100171 | + | 1.11828i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 396.2.c.a.287.2 | yes | 10 | |
3.2 | odd | 2 | 396.2.c.b.287.9 | yes | 10 | ||
4.3 | odd | 2 | 396.2.c.b.287.10 | yes | 10 | ||
8.3 | odd | 2 | 6336.2.d.g.3455.5 | 10 | |||
8.5 | even | 2 | 6336.2.d.h.3455.5 | 10 | |||
12.11 | even | 2 | inner | 396.2.c.a.287.1 | ✓ | 10 | |
24.5 | odd | 2 | 6336.2.d.g.3455.6 | 10 | |||
24.11 | even | 2 | 6336.2.d.h.3455.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
396.2.c.a.287.1 | ✓ | 10 | 12.11 | even | 2 | inner | |
396.2.c.a.287.2 | yes | 10 | 1.1 | even | 1 | trivial | |
396.2.c.b.287.9 | yes | 10 | 3.2 | odd | 2 | ||
396.2.c.b.287.10 | yes | 10 | 4.3 | odd | 2 | ||
6336.2.d.g.3455.5 | 10 | 8.3 | odd | 2 | |||
6336.2.d.g.3455.6 | 10 | 24.5 | odd | 2 | |||
6336.2.d.h.3455.5 | 10 | 8.5 | even | 2 | |||
6336.2.d.h.3455.6 | 10 | 24.11 | even | 2 |