Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1456,2,Mod(225,1456)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1456, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1456.225");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1456.cc (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 364) |
Sato-Tate group: |
Embedding invariants
Embedding label | 673.7 | ||
Root | of defining polynomial | ||
Character | 1456.673 | ||
Dual form | 1456.2.cc.f.225.7 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
0.888364 | + | 1.53869i | 0.512897 | + | 0.888364i | 0.999888 | + | 0.0149568i | ||
−0.486991 | + | 0.873407i | ||||||||
0 | 0 | |||||||||
− | 3.82804i | − | 1.71195i | −0.517015 | − | 0.855976i | ||||
0.517015 | − | 0.855976i | ||||||||
0 | 0 | |||||||||
0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | |||||
0 | 0 | |||||||||
−0.0783804 | + | 0.135759i | −0.0261268 | + | 0.0452529i | |||||
0 | 0 | |||||||||
3.74735 | − | 2.16353i | 1.12987 | − | 0.652330i | 0.185966 | − | 0.982556i | ||
0.943902 | + | 0.330227i | ||||||||
0 | 0 | |||||||||
−0.930395 | + | 3.48344i | −0.258045 | + | 0.966133i | |||||
0 | 0 | |||||||||
5.89018 | − | 3.40069i | 1.52084 | − | 0.878056i | |||||
0 | 0 | |||||||||
1.45744 | − | 2.52436i | 0.353481 | − | 0.612247i | −0.633376 | − | 0.773844i | ||
0.986857 | + | 0.161597i | ||||||||
0 | 0 | |||||||||
−4.72686 | − | 2.72905i | −1.08442 | − | 0.626088i | −0.152331 | − | 0.988329i | ||
−0.932084 | + | 0.362242i | ||||||||
0 | 0 | |||||||||
1.77673i | 0.387714i | |||||||||
0 | 0 | |||||||||
0.307112 | + | 0.531934i | 0.0640373 | + | 0.110916i | 0.896267 | − | 0.443516i | ||
−0.832229 | + | 0.554432i | ||||||||
0 | 0 | |||||||||
−9.65391 | −1.93078 | |||||||||
0 | 0 | |||||||||
5.05166 | 0.972193 | |||||||||
0 | 0 | |||||||||
−4.62872 | − | 8.01717i | −0.859531 | − | 1.48875i | −0.872377 | − | 0.488834i | ||
0.0128452 | − | 0.999917i | ||||||||
0 | 0 | |||||||||
5.30753i | 0.953261i | 0.879104 | + | 0.476630i | ||||||
−0.879104 | + | 0.476630i | ||||||||
0 | 0 | |||||||||
6.65802 | + | 3.84401i | 1.15901 | + | 0.669156i | |||||
0 | 0 | |||||||||
1.91402 | − | 3.31518i | 0.323529 | − | 0.560368i | |||||
0 | 0 | |||||||||
−0.974022 | + | 0.562352i | −0.160128 | + | 0.0924501i | −0.577923 | − | 0.816091i | ||
0.417795 | + | 0.908542i | ||||||||
0 | 0 | |||||||||
−6.18647 | + | 1.66297i | −0.990628 | + | 0.266289i | |||||
0 | 0 | |||||||||
10.4130 | − | 6.01195i | 1.62624 | − | 0.938909i | 0.641037 | − | 0.767510i | ||
0.985202 | − | 0.171399i | ||||||||
0 | 0 | |||||||||
−0.641552 | + | 1.11120i | −0.0978358 | + | 0.169457i | −0.910789 | − | 0.412873i | ||
0.812953 | + | 0.582330i | ||||||||
0 | 0 | |||||||||
0.519691 | + | 0.300044i | 0.0774709 | + | 0.0447278i | |||||
0 | 0 | |||||||||
− | 5.68074i | − | 0.828620i | −0.910136 | − | 0.414310i | ||||
0.910136 | − | 0.414310i | ||||||||
0 | 0 | |||||||||
0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | |||||
0 | 0 | |||||||||
5.17895 | 0.725197 | |||||||||
0 | 0 | |||||||||
−3.96013 | −0.543966 | −0.271983 | − | 0.962302i | ||||||
−0.271983 | + | 0.962302i | ||||||||
0 | 0 | |||||||||
−8.28210 | − | 14.3450i | −1.11676 | − | 1.93428i | |||||
0 | 0 | |||||||||
− | 9.69757i | − | 1.28447i | |||||||
0 | 0 | |||||||||
6.68359 | + | 3.85877i | 0.870129 | + | 0.502369i | 0.867391 | − | 0.497627i | ||
0.00273800 | + | 0.999996i | ||||||||
0 | 0 | |||||||||
7.17308 | − | 12.4241i | 0.918419 | − | 1.59075i | 0.116601 | − | 0.993179i | ||
0.801817 | − | 0.597569i | ||||||||
0 | 0 | |||||||||
−0.135759 | + | 0.0783804i | −0.0171040 | + | 0.00987500i | |||||
0 | 0 | |||||||||
13.3348 | + | 3.56159i | 1.65397 | + | 0.441761i | |||||
0 | 0 | |||||||||
−0.468974 | + | 0.270762i | −0.0572943 | + | 0.0330789i | −0.528374 | − | 0.849012i | ||
0.471079 | + | 0.882091i | ||||||||
0 | 0 | |||||||||
−0.545654 | + | 0.945101i | −0.0656891 | + | 0.113777i | |||||
0 | 0 | |||||||||
−7.96918 | − | 4.60101i | −0.945768 | − | 0.546040i | −0.0540044 | − | 0.998541i | ||
−0.891764 | + | 0.452501i | ||||||||
0 | 0 | |||||||||
7.36798i | 0.862357i | 0.902267 | + | 0.431179i | ||||||
−0.902267 | + | 0.431179i | ||||||||
0 | 0 | |||||||||
−8.57618 | − | 14.8544i | −0.990293 | − | 1.71524i | |||||
0 | 0 | |||||||||
4.32707 | 0.493115 | |||||||||
0 | 0 | |||||||||
−0.331686 | −0.0373176 | −0.0186588 | − | 0.999826i | ||||||
−0.0186588 | + | 0.999826i | ||||||||
0 | 0 | |||||||||
4.72285 | + | 8.18022i | 0.524762 | + | 0.908914i | |||||
0 | 0 | |||||||||
16.6777i | 1.83061i | 0.402758 | + | 0.915306i | ||||||
−0.402758 | + | 0.915306i | ||||||||
0 | 0 | |||||||||
−9.66335 | − | 5.57914i | −1.04814 | − | 0.605143i | |||||
0 | 0 | |||||||||
8.22397 | − | 14.2443i | 0.881702 | − | 1.52715i | |||||
0 | 0 | |||||||||
2.55836 | − | 1.47707i | 0.271185 | − | 0.156569i | −0.358241 | − | 0.933629i | ||
0.629426 | + | 0.777060i | ||||||||
0 | 0 | |||||||||
−2.54747 | + | 2.55155i | −0.267047 | + | 0.267475i | |||||
0 | 0 | |||||||||
−8.16665 | + | 4.71502i | −0.846842 | + | 0.488925i | |||||
0 | 0 | |||||||||
−10.4469 | + | 18.0946i | −1.07183 | + | 1.85647i | |||||
0 | 0 | |||||||||
8.36220 | + | 4.82792i | 0.849052 | + | 0.490201i | 0.860331 | − | 0.509736i | ||
−0.0112787 | + | 0.999936i | ||||||||
0 | 0 | |||||||||
0.678314i | 0.0681731i | |||||||||
0 | 0 | |||||||||
−3.17528 | − | 5.49975i | −0.315952 | − | 0.547246i | 0.663687 | − | 0.748010i | ||
−0.979639 | + | 0.200765i | ||||||||
0 | 0 | |||||||||
5.07117 | 0.499678 | 0.249839 | − | 0.968287i | ||||||
0.249839 | + | 0.968287i | ||||||||
0 | 0 | |||||||||
6.80139 | 0.663748 | |||||||||
0 | 0 | |||||||||
−2.74289 | − | 4.75083i | −0.265166 | − | 0.459280i | 0.702441 | − | 0.711742i | ||
−0.967607 | + | 0.252461i | ||||||||
0 | 0 | |||||||||
6.80685i | 0.651978i | 0.945374 | + | 0.325989i | ||||||
−0.945374 | + | 0.325989i | ||||||||
0 | 0 | |||||||||
−1.73057 | − | 0.999146i | −0.164259 | − | 0.0948347i | |||||
0 | 0 | |||||||||
3.28384 | − | 5.68778i | 0.308918 | − | 0.535061i | −0.669208 | − | 0.743075i | ||
0.978126 | + | 0.208014i | ||||||||
0 | 0 | |||||||||
2.03626 | − | 1.17564i | 0.189883 | − | 0.109629i | |||||
0 | 0 | |||||||||
−0.399983 | − | 0.399343i | −0.0369785 | − | 0.0369193i | |||||
0 | 0 | |||||||||
2.52436 | − | 1.45744i | 0.231408 | − | 0.133603i | |||||
0 | 0 | |||||||||
3.86175 | − | 6.68874i | 0.351068 | − | 0.608067i | |||||
0 | 0 | |||||||||
18.5011 | + | 10.6816i | 1.66819 | + | 0.963128i | |||||
0 | 0 | |||||||||
17.8154i | 1.59346i | |||||||||
0 | 0 | |||||||||
10.1425 | + | 17.5674i | 0.900003 | + | 1.55885i | 0.827488 | + | 0.561483i | ||
0.0725145 | + | 0.997367i | ||||||||
0 | 0 | |||||||||
−2.27973 | −0.200719 | |||||||||
0 | 0 | |||||||||
−4.92442 | −0.430249 | −0.215124 | − | 0.976587i | ||||||
−0.215124 | + | 0.976587i | ||||||||
0 | 0 | |||||||||
−2.72905 | − | 4.72686i | −0.236639 | − | 0.409871i | |||||
0 | 0 | |||||||||
− | 19.3380i | − | 1.66435i | |||||||
0 | 0 | |||||||||
11.1993 | + | 6.46589i | 0.956817 | + | 0.552419i | 0.895192 | − | 0.445681i | ||
0.0616251 | + | 0.998099i | ||||||||
0 | 0 | |||||||||
7.90466 | − | 13.6913i | 0.670464 | − | 1.16128i | −0.307308 | − | 0.951610i | ||
0.977773 | − | 0.209668i | ||||||||
0 | 0 | |||||||||
8.74090 | − | 5.04656i | 0.736116 | − | 0.424997i | |||||
0 | 0 | |||||||||
4.05003 | + | 15.0666i | 0.338680 | + | 1.25993i | |||||
0 | 0 | |||||||||
−30.6901 | + | 17.7189i | −2.54867 | + | 1.47148i | |||||
0 | 0 | |||||||||
−0.888364 | + | 1.53869i | −0.0732710 | + | 0.126909i | |||||
0 | 0 | |||||||||
13.7967 | + | 7.96552i | 1.13027 | + | 0.652561i | 0.944002 | − | 0.329939i | ||
0.186266 | + | 0.982499i | ||||||||
0 | 0 | |||||||||
6.37358i | 0.518675i | 0.965787 | + | 0.259337i | ||||||
−0.965787 | + | 0.259337i | ||||||||
0 | 0 | |||||||||
0.228469 | + | 0.395721i | 0.0184707 | + | 0.0319921i | |||||
0 | 0 | |||||||||
20.3175 | 1.63194 | |||||||||
0 | 0 | |||||||||
−7.38800 | −0.589627 | −0.294813 | − | 0.955555i | ||||||
−0.294813 | + | 0.955555i | ||||||||
0 | 0 | |||||||||
−3.51804 | − | 6.09342i | −0.278999 | − | 0.483240i | |||||
0 | 0 | |||||||||
0.614224i | 0.0484076i | |||||||||
0 | 0 | |||||||||
0.0758325 | + | 0.0437819i | 0.00593966 | + | 0.00342926i | 0.502967 | − | 0.864306i | ||
−0.497027 | + | 0.867735i | ||||||||
0 | 0 | |||||||||
14.7150 | − | 25.4872i | 1.14556 | − | 1.98417i | |||||
0 | 0 | |||||||||
−16.0309 | + | 9.25542i | −1.24050 | + | 0.716206i | −0.969197 | − | 0.246287i | ||
−0.271308 | + | 0.962493i | ||||||||
0 | 0 | |||||||||
−11.2687 | − | 6.48195i | −0.866826 | − | 0.498612i | |||||
0 | 0 | |||||||||
0.740986 | − | 0.427808i | 0.0566646 | − | 0.0327153i | |||||
0 | 0 | |||||||||
0.205452 | − | 0.355853i | 0.0156202 | − | 0.0270550i | −0.858110 | − | 0.513466i | ||
0.873730 | + | 0.486412i | ||||||||
0 | 0 | |||||||||
−8.36053 | − | 4.82696i | −0.631997 | − | 0.364884i | |||||
0 | 0 | |||||||||
13.7120i | 1.03065i | |||||||||
0 | 0 | |||||||||
−1.07738 | − | 1.86607i | −0.0805268 | − | 0.139477i | 0.822950 | − | 0.568114i | ||
−0.903476 | + | 0.428638i | ||||||||
0 | 0 | |||||||||
6.50124 | 0.483233 | 0.241617 | − | 0.970372i | ||||||
0.241617 | + | 0.970372i | ||||||||
0 | 0 | |||||||||
25.4892 | 1.88422 | |||||||||
0 | 0 | |||||||||
2.15271 | + | 3.72860i | 0.158270 | + | 0.274132i | |||||
0 | 0 | |||||||||
− | 12.6129i | − | 0.922344i | |||||||
0 | 0 | |||||||||
4.37487 | + | 2.52583i | 0.318225 | + | 0.183727i | |||||
0 | 0 | |||||||||
−9.38751 | + | 16.2596i | −0.679256 | + | 1.17651i | 0.295949 | + | 0.955204i | ||
−0.975205 | + | 0.221303i | ||||||||
0 | 0 | |||||||||
−22.1852 | + | 12.8086i | −1.59693 | + | 0.921986i | −0.604851 | + | 0.796339i | ||
−0.992075 | + | 0.125647i | ||||||||
0 | 0 | |||||||||
6.36593 | + | 23.6821i | 0.455874 | + | 1.69591i | |||||
0 | 0 | |||||||||
−0.510570 | + | 0.294778i | −0.0363766 | + | 0.0210021i | −0.518078 | − | 0.855333i | ||
0.481701 | + | 0.876335i | ||||||||
0 | 0 | |||||||||
−8.04513 | + | 13.9346i | −0.570304 | + | 0.987796i | 0.426230 | + | 0.904615i | ||
−0.996534 | + | 0.0831814i | ||||||||
0 | 0 | |||||||||
−0.833240 | − | 0.481071i | −0.0587722 | − | 0.0339321i | |||||
0 | 0 | |||||||||
− | 9.25744i | − | 0.649745i | |||||||
0 | 0 | |||||||||
−23.0140 | − | 39.8614i | −1.60737 | − | 2.78404i | |||||
0 | 0 | |||||||||
−0.0962862 | −0.00669236 | |||||||||
0 | 0 | |||||||||
−23.6176 | −1.63366 | |||||||||
0 | 0 | |||||||||
−5.69247 | − | 9.85965i | −0.391886 | − | 0.678766i | 0.600812 | − | 0.799390i | ||
−0.992698 | + | 0.120624i | ||||||||
0 | 0 | |||||||||
− | 16.3495i | − | 1.12025i | |||||||
0 | 0 | |||||||||
4.25373 | + | 2.45589i | 0.290102 | + | 0.167490i | |||||
0 | 0 | |||||||||
−2.65377 | + | 4.59646i | −0.180149 | + | 0.312028i | |||||
0 | 0 | |||||||||
−11.3370 | + | 6.54545i | −0.766087 | + | 0.442300i | |||||
0 | 0 | |||||||||
7.43746 | + | 7.42556i | 0.500298 | + | 0.499497i | |||||
0 | 0 | |||||||||
2.03182 | − | 1.17307i | 0.136060 | − | 0.0785545i | −0.430425 | − | 0.902626i | ||
0.566485 | + | 0.824072i | ||||||||
0 | 0 | |||||||||
0.756677 | − | 1.31060i | 0.0504452 | − | 0.0873736i | |||||
0 | 0 | |||||||||
7.14587 | + | 4.12567i | 0.474288 | + | 0.273830i | 0.718033 | − | 0.696009i | ||
−0.243745 | + | 0.969839i | ||||||||
0 | 0 | |||||||||
− | 17.2750i | − | 1.14156i | −0.821103 | − | 0.570780i | ||||
0.821103 | − | 0.570780i | ||||||||
0 | 0 | |||||||||
3.84401 | + | 6.65802i | 0.252917 | + | 0.438065i | |||||
0 | 0 | |||||||||
−4.13778 | −0.271075 | −0.135537 | − | 0.990772i | ||||||
−0.135537 | + | 0.990772i | ||||||||
0 | 0 | |||||||||
−21.7461 | −1.41856 | |||||||||
0 | 0 | |||||||||
−0.294658 | − | 0.510363i | −0.0191401 | − | 0.0331516i | |||||
0 | 0 | |||||||||
− | 5.83879i | − | 0.377680i | −0.982008 | − | 0.188840i | ||||
0.982008 | − | 0.188840i | ||||||||
0 | 0 | |||||||||
24.6356 | + | 14.2234i | 1.58692 | + | 0.916207i | 0.993811 | + | 0.111084i | ||
0.593107 | + | 0.805124i | ||||||||
0 | 0 | |||||||||
−0.813733 | + | 1.40943i | −0.0522010 | + | 0.0904148i | |||||
0 | 0 | |||||||||
3.31518 | − | 1.91402i | 0.211799 | − | 0.122282i | |||||
0 | 0 | |||||||||
13.9043 | − | 13.9266i | 0.884712 | − | 0.886131i | |||||
0 | 0 | |||||||||
−25.6618 | + | 14.8158i | −1.62625 | + | 0.938916i | |||||
0 | 0 | |||||||||
6.39001 | − | 11.0678i | 0.403334 | − | 0.698595i | −0.590792 | − | 0.806824i | ||
0.994126 | + | 0.108229i | ||||||||
0 | 0 | |||||||||
2.30171 | + | 1.32889i | 0.144707 | + | 0.0835468i | |||||
0 | 0 | |||||||||
− | 19.8252i | − | 1.24150i | |||||||
0 | 0 | |||||||||
0.335695 | + | 0.581441i | 0.0209401 | + | 0.0362693i | 0.876306 | − | 0.481756i | ||
−0.855365 | + | 0.518025i | ||||||||
0 | 0 | |||||||||
−1.12470 | −0.0698857 | |||||||||
0 | 0 | |||||||||
1.45120 | 0.0898272 | |||||||||
0 | 0 | |||||||||
−9.48512 | − | 16.4287i | −0.584878 | − | 1.01304i | −0.994891 | − | 0.100958i | ||
0.410013 | − | 0.912080i | ||||||||
0 | 0 | |||||||||
15.1596i | 0.931244i | |||||||||
0 | 0 | |||||||||
4.54550 | + | 2.62435i | 0.278180 | + | 0.160607i | |||||
0 | 0 | |||||||||
4.79241 | − | 8.30070i | 0.292198 | − | 0.506102i | −0.682131 | − | 0.731230i | ||
0.974329 | + | 0.225128i | ||||||||
0 | 0 | |||||||||
−9.06856 | + | 5.23574i | −0.550876 | + | 0.318048i | −0.749475 | − | 0.662032i | ||
0.198599 | + | 0.980081i | ||||||||
0 | 0 | |||||||||
−6.18913 | − | 1.65306i | −0.374583 | − | 0.100048i | |||||
0 | 0 | |||||||||
−36.1766 | + | 20.8866i | −2.18153 | + | 1.25951i | |||||
0 | 0 | |||||||||
−9.66856 | + | 16.7464i | −0.580927 | + | 1.00620i | 0.414443 | + | 0.910075i | ||
−0.995370 | + | 0.0961199i | ||||||||
0 | 0 | |||||||||
−0.720544 | − | 0.416006i | −0.0431379 | − | 0.0249057i | |||||
0 | 0 | |||||||||
18.7039i | 1.11578i | 0.829915 | + | 0.557890i | ||||||
−0.829915 | + | 0.557890i | ||||||||
0 | 0 | |||||||||
−0.587956 | − | 1.01837i | −0.0349504 | − | 0.0605358i | 0.848021 | − | 0.529962i | ||
−0.882971 | + | 0.469427i | ||||||||
0 | 0 | |||||||||
−37.1227 | −2.19896 | |||||||||
0 | 0 | |||||||||
12.0239 | 0.709749 | |||||||||
0 | 0 | |||||||||
4.25174 | + | 7.36423i | 0.250102 | + | 0.433190i | |||||
0 | 0 | |||||||||
17.1558i | 1.00569i | |||||||||
0 | 0 | |||||||||
−5.63521 | − | 3.25349i | −0.329213 | − | 0.190071i | 0.326279 | − | 0.945274i | ||
−0.655491 | + | 0.755203i | ||||||||
0 | 0 | |||||||||
14.7715 | − | 25.5851i | 0.860033 | − | 1.48962i | |||||
0 | 0 | |||||||||
18.9303 | − | 10.9294i | 1.09845 | − | 0.634190i | |||||
0 | 0 | |||||||||
−2.13869 | + | 0.574899i | −0.123684 | + | 0.0332472i | |||||
0 | 0 | |||||||||
−1.11120 | + | 0.641552i | −0.0640486 | + | 0.0369785i | |||||
0 | 0 | |||||||||
5.64161 | − | 9.77156i | 0.324102 | − | 0.561361i | |||||
0 | 0 | |||||||||
−47.5601 | − | 27.4589i | −2.72329 | − | 1.57229i | |||||
0 | 0 | |||||||||
− | 27.0573i | − | 1.54424i | −0.635475 | − | 0.772121i | ||||
0.635475 | − | 0.772121i | ||||||||
0 | 0 | |||||||||
4.50505 | + | 7.80297i | 0.256283 | + | 0.443895i | |||||
0 | 0 | |||||||||
−30.9061 | −1.75253 | −0.876263 | − | 0.481834i | ||||||
−0.876263 | + | 0.481834i | ||||||||
0 | 0 | |||||||||
30.0816 | 1.70031 | 0.850157 | − | 0.526530i | ||||||
0.850157 | + | 0.526530i | ||||||||
0 | 0 | |||||||||
0.300044 | + | 0.519691i | 0.0169055 | + | 0.0292812i | |||||
0 | 0 | |||||||||
3.78351i | 0.212503i | 0.994339 | + | 0.106251i | ||||||
−0.994339 | + | 0.106251i | ||||||||
0 | 0 | |||||||||
−34.6908 | − | 20.0288i | −1.94231 | − | 1.12140i | |||||
0 | 0 | |||||||||
4.87338 | − | 8.44093i | 0.272005 | − | 0.471127i | |||||
0 | 0 | |||||||||
−13.7782 | + | 7.95486i | −0.766641 | + | 0.442620i | |||||
0 | 0 | |||||||||
8.98195 | − | 33.6288i | 0.498229 | − | 1.86539i | |||||
0 | 0 | |||||||||
−10.4736 | + | 6.04696i | −0.579194 | + | 0.334398i | |||||
0 | 0 | |||||||||
2.84037 | − | 4.91966i | 0.156595 | − | 0.271230i | |||||
0 | 0 | |||||||||
−20.1396 | − | 11.6276i | −1.10697 | − | 0.639110i | −0.168928 | − | 0.985628i | ||
−0.938043 | + | 0.346518i | ||||||||
0 | 0 | |||||||||
− | 0.176309i | − | 0.00966170i | |||||||
0 | 0 | |||||||||
1.03649 | + | 1.79525i | 0.0566295 | + | 0.0980852i | |||||
0 | 0 | |||||||||
6.51910 | 0.355118 | 0.177559 | − | 0.984110i | ||||||
0.177559 | + | 0.984110i | ||||||||
0 | 0 | |||||||||
11.6690 | 0.633772 | |||||||||
0 | 0 | |||||||||
11.4830 | + | 19.8892i | 0.621840 | + | 1.07706i | |||||
0 | 0 | |||||||||
1.00000i | 0.0539949i | |||||||||
0 | 0 | |||||||||
3.61789 | + | 2.08879i | 0.194780 | + | 0.112457i | |||||
0 | 0 | |||||||||
−6.55696 | + | 11.3570i | −0.351996 | + | 0.609675i | −0.986599 | − | 0.163163i | ||
0.634603 | + | 0.772838i | ||||||||
0 | 0 | |||||||||
8.41298 | − | 4.85724i | 0.450336 | − | 0.260002i | −0.257636 | − | 0.966242i | ||
0.707972 | + | 0.706240i | ||||||||
0 | 0 | |||||||||
−4.70004 | + | 17.5972i | −0.250869 | + | 0.939267i | |||||
0 | 0 | |||||||||
−26.2632 | + | 15.1631i | −1.39785 | + | 0.807049i | −0.994167 | − | 0.107850i | ||
−0.403683 | + | 0.914899i | ||||||||
0 | 0 | |||||||||
−17.6129 | + | 30.5064i | −0.934794 | + | 1.61911i | |||||
0 | 0 | |||||||||
4.48510 | + | 2.58947i | 0.237377 | + | 0.137049i | |||||
0 | 0 | |||||||||
10.5854i | 0.558677i | 0.960193 | + | 0.279339i | ||||||
−0.960193 | + | 0.279339i | ||||||||
0 | 0 | |||||||||
5.39545 | + | 9.34520i | 0.283971 | + | 0.491853i | |||||
0 | 0 | |||||||||
13.7225 | 0.720247 | |||||||||
0 | 0 | |||||||||
28.2050 | 1.47631 | |||||||||
0 | 0 | |||||||||
13.3188 | + | 23.0688i | 0.695234 | + | 1.20418i | 0.970102 | + | 0.242699i | ||
−0.274867 | + | 0.961482i | ||||||||
0 | 0 | |||||||||
1.88488i | 0.0981228i | |||||||||
0 | 0 | |||||||||
−3.42958 | − | 1.98007i | −0.178055 | − | 0.102800i | |||||
0 | 0 | |||||||||
3.07064 | − | 5.31851i | 0.158992 | − | 0.275382i | −0.775514 | − | 0.631331i | ||
0.934505 | + | 0.355949i | ||||||||
0 | 0 | |||||||||
−27.4124 | + | 15.8265i | −1.41557 | + | 0.817278i | |||||
0 | 0 | |||||||||
32.2339 | − | 8.66473i | 1.66013 | − | 0.446256i | |||||
0 | 0 | |||||||||
−20.4175 | + | 11.7880i | −1.04877 | + | 0.605510i | −0.922306 | − | 0.386460i | ||
−0.126469 | + | 0.991971i | ||||||||
0 | 0 | |||||||||
−18.0205 | + | 31.2124i | −0.923217 | + | 1.59906i | |||||
0 | 0 | |||||||||
17.4736 | + | 10.0884i | 0.892860 | + | 0.515493i | 0.874877 | − | 0.484346i | ||
0.0179828 | + | 0.999838i | ||||||||
0 | 0 | |||||||||
− | 16.5642i | − | 0.844189i | |||||||
0 | 0 | |||||||||
−0.100570 | − | 0.174193i | −0.00511227 | − | 0.00885472i | |||||
0 | 0 | |||||||||
−32.8506 | −1.66559 | −0.832795 | − | 0.553581i | ||||||
−0.832795 | + | 0.553581i | ||||||||
0 | 0 | |||||||||
1.79039 | 0.0905438 | |||||||||
0 | 0 | |||||||||
−4.37468 | − | 7.57716i | −0.220673 | − | 0.382217i | |||||
0 | 0 | |||||||||
1.26971i | 0.0638860i | |||||||||
0 | 0 | |||||||||
21.8789 | + | 12.6318i | 1.09807 | + | 0.633970i | 0.935713 | − | 0.352762i | ||
0.162355 | + | 0.986732i | ||||||||
0 | 0 | |||||||||
4.84878 | − | 8.39834i | 0.242743 | − | 0.420443i | |||||
0 | 0 | |||||||||
−25.3059 | + | 14.6104i | −1.26372 | + | 0.729608i | −0.973792 | − | 0.227441i | ||
−0.289926 | + | 0.957049i | ||||||||
0 | 0 | |||||||||
−18.4885 | − | 4.93810i | −0.920977 | − | 0.245984i | |||||
0 | 0 | |||||||||
31.3142 | − | 18.0793i | 1.55602 | − | 0.898367i | |||||
0 | 0 | |||||||||
−2.43333 | + | 4.21466i | −0.120616 | + | 0.208913i | |||||
0 | 0 | |||||||||
23.6697 | + | 13.6657i | 1.17039 | + | 0.675727i | 0.953773 | − | 0.300529i | ||
0.216620 | + | 0.976256i | ||||||||
0 | 0 | |||||||||
22.9763i | 1.13334i | |||||||||
0 | 0 | |||||||||
3.85877 | + | 6.68359i | 0.189878 | + | 0.328878i | |||||
0 | 0 | |||||||||
63.8429 | 3.13392 | |||||||||
0 | 0 | |||||||||
28.0889 | 1.37552 | |||||||||
0 | 0 | |||||||||
10.1693 | + | 17.6137i | 0.496802 | + | 0.860486i | 0.999993 | − | 0.00368888i | ||
−0.503191 | + | 0.864175i | ||||||||
0 | 0 | |||||||||
21.0712i | 1.02695i | 0.858106 | + | 0.513473i | ||||||
−0.858106 | + | 0.513473i | ||||||||
0 | 0 | |||||||||
0.771210 | + | 0.445258i | 0.0374975 | + | 0.0216492i | |||||
0 | 0 | |||||||||
−14.0700 | + | 24.3699i | −0.682495 | + | 1.18212i | |||||
0 | 0 | |||||||||
12.4241 | − | 7.17308i | 0.601246 | − | 0.347130i | |||||
0 | 0 | |||||||||
−19.5850 | + | 19.6164i | −0.945571 | + | 0.947087i | |||||
0 | 0 | |||||||||
25.6632 | − | 14.8167i | 1.23615 | − | 0.713694i | 0.267848 | − | 0.963461i | ||
0.968306 | + | 0.249767i | ||||||||
0 | 0 | |||||||||
−14.2983 | + | 24.7653i | −0.687130 | + | 1.19014i | 0.285632 | + | 0.958339i | ||
−0.972762 | + | 0.231805i | ||||||||
0 | 0 | |||||||||
−54.5279 | − | 31.4817i | −2.61441 | − | 1.50943i | |||||
0 | 0 | |||||||||
− | 3.35250i | − | 0.160372i | |||||||
0 | 0 | |||||||||
10.9124 | + | 18.9009i | 0.520821 | + | 0.902088i | 0.999707 | + | 0.0242113i | ||
−0.478886 | + | 0.877877i | ||||||||
0 | 0 | |||||||||
−0.156761 | −0.00746480 | |||||||||
0 | 0 | |||||||||
6.32956 | 0.300726 | 0.150363 | − | 0.988631i | ||||||
0.150363 | + | 0.988631i | ||||||||
0 | 0 | |||||||||
−5.65428 | − | 9.79350i | −0.268039 | − | 0.464256i | |||||
0 | 0 | |||||||||
28.3051i | 1.33879i | |||||||||
0 | 0 | |||||||||
21.2777 | + | 12.2847i | 1.00415 | + | 0.579749i | 0.909475 | − | 0.415759i | ||
0.0946799 | + | 0.995508i | ||||||||
0 | 0 | |||||||||
26.0141 | − | 45.0578i | 1.22496 | − | 2.12169i | |||||
0 | 0 | |||||||||
−9.80697 | + | 5.66206i | −0.460772 | + | 0.266027i | |||||
0 | 0 | |||||||||
9.76745 | + | 9.75181i | 0.457905 | + | 0.457172i | |||||
0 | 0 | |||||||||
−3.90240 | + | 2.25305i | −0.182547 | + | 0.105393i | −0.588489 | − | 0.808505i | ||
0.405942 | + | 0.913899i | ||||||||
0 | 0 | |||||||||
7.36249 | − | 12.7522i | 0.343652 | − | 0.595222i | |||||
0 | 0 | |||||||||
0.260026 | + | 0.150126i | 0.0121106 | + | 0.00699206i | 0.506043 | − | 0.862508i | ||
−0.493932 | + | 0.869500i | ||||||||
0 | 0 | |||||||||
19.2907i | 0.896514i | 0.893905 | + | 0.448257i | ||||||
−0.893905 | + | 0.448257i | ||||||||
0 | 0 | |||||||||
18.0493 | + | 31.2623i | 0.837016 | + | 1.44975i | |||||
0 | 0 | |||||||||
−13.9509 | −0.645570 | −0.322785 | − | 0.946472i | ||||||
−0.322785 | + | 0.946472i | ||||||||
0 | 0 | |||||||||
−0.541525 | −0.0250053 | |||||||||
0 | 0 | |||||||||
−6.56323 | − | 11.3679i | −0.302418 | − | 0.523803i | |||||
0 | 0 | |||||||||
5.55208i | 0.255285i | |||||||||
0 | 0 | |||||||||
45.6327 | + | 26.3460i | 2.09377 | + | 1.20884i | |||||
0 | 0 | |||||||||
0.310397 | − | 0.537623i | 0.0142121 | − | 0.0246161i | |||||
0 | 0 | |||||||||
23.7743 | − | 13.7261i | 1.08627 | − | 0.627160i | 0.153692 | − | 0.988119i | ||
0.932582 | + | 0.360959i | ||||||||
0 | 0 | |||||||||
−1.05270 | − | 3.91616i | −0.0479988 | − | 0.178561i | |||||
0 | 0 | |||||||||
−0.945101 | + | 0.545654i | −0.0430036 | + | 0.0248281i | |||||
0 | 0 | |||||||||
18.4815 | − | 32.0108i | 0.839200 | − | 1.45354i | |||||
0 | 0 | |||||||||
−12.1206 | − | 6.99785i | −0.549238 | − | 0.317103i | 0.199577 | − | 0.979882i | ||
−0.748815 | + | 0.662780i | ||||||||
0 | 0 | |||||||||
0.155577i | 0.00703543i | |||||||||
0 | 0 | |||||||||
3.76330 | + | 6.51823i | 0.169836 | + | 0.294164i | 0.938362 | − | 0.345654i | ||
−0.768526 | + | 0.639818i | ||||||||
0 | 0 | |||||||||
−26.9843 | −1.21531 | |||||||||
0 | 0 | |||||||||
2.59662 | 0.116709 | |||||||||
0 | 0 | |||||||||
−4.60101 | − | 7.96918i | −0.206384 | − | 0.357467i | |||||
0 | 0 | |||||||||
− | 1.16848i | − | 0.0523083i | −0.999658 | − | 0.0261541i | ||||
0.999658 | − | 0.0261541i | ||||||||
0 | 0 | |||||||||
−28.4825 | − | 16.4444i | −1.27250 | − | 0.734680i | |||||
0 | 0 | |||||||||
−5.30877 | + | 9.19505i | −0.236706 | + | 0.409987i | −0.959767 | − | 0.280797i | ||
0.723061 | + | 0.690784i | ||||||||
0 | 0 | |||||||||
−21.0533 | + | 12.1551i | −0.936859 | + | 0.540896i | |||||
0 | 0 | |||||||||
−0.0370126 | − | 23.0974i | −0.00164379 | − | 1.02579i | |||||
0 | 0 | |||||||||
−21.0450 | + | 12.1503i | −0.932803 | + | 0.538554i | −0.887697 | − | 0.460428i | ||
−0.0451058 | + | 0.998982i | ||||||||
0 | 0 | |||||||||
−3.68399 | + | 6.38086i | −0.162970 | + | 0.282273i | |||||
0 | 0 | |||||||||
−23.8785 | − | 13.7862i | −1.05426 | − | 0.608678i | |||||
0 | 0 | |||||||||
− | 19.4127i | − | 0.855424i | |||||||
0 | 0 | |||||||||
−12.2905 | − | 21.2877i | −0.540534 | − | 0.936232i | |||||
0 | 0 | |||||||||
0.730063 | 0.0320462 | |||||||||
0 | 0 | |||||||||
11.3280 | 0.496289 | 0.248144 | − | 0.968723i | ||||||
0.248144 | + | 0.968723i | ||||||||
0 | 0 | |||||||||
15.1328 | + | 26.2108i | 0.661711 | + | 1.14612i | 0.980166 | + | 0.198180i | ||
−0.318454 | + | 0.947938i | ||||||||
0 | 0 | |||||||||
− | 17.1524i | − | 0.748591i | |||||||
0 | 0 | |||||||||
13.3981 | + | 7.73541i | 0.583631 | + | 0.336960i | |||||
0 | 0 | |||||||||
11.3114 | − | 19.5919i | 0.491798 | − | 0.851820i | |||||
0 | 0 | |||||||||
−1.04772 | + | 0.604904i | −0.0454674 | + | 0.0262506i | |||||
0 | 0 | |||||||||
11.2541 | + | 41.8666i | 0.487468 | + | 1.81344i | |||||
0 | 0 | |||||||||
−18.1864 | + | 10.4999i | −0.786266 | + | 0.453951i | |||||
0 | 0 | |||||||||
1.91420 | − | 3.31550i | 0.0826039 | − | 0.143074i | |||||
0 | 0 | |||||||||
3.74735 | + | 2.16353i | 0.161410 | + | 0.0931899i | |||||
0 | 0 | |||||||||
− | 11.1529i | − | 0.479500i | −0.970835 | − | 0.239750i | ||||
0.970835 | − | 0.239750i | ||||||||
0 | 0 | |||||||||
5.77546 | + | 10.0034i | 0.247849 | + | 0.429287i | |||||
0 | 0 | |||||||||
26.0569 | 1.11616 | |||||||||
0 | 0 | |||||||||
−4.87804 | −0.208570 | −0.104285 | − | 0.994547i | ||||||
−0.104285 | + | 0.994547i | ||||||||
0 | 0 | |||||||||
1.12446 | + | 1.94762i | 0.0479907 | + | 0.0831223i | |||||
0 | 0 | |||||||||
50.5281i | 2.15257i | |||||||||
0 | 0 | |||||||||
−0.287249 | − | 0.165843i | −0.0122151 | − | 0.00705237i | |||||
0 | 0 | |||||||||
−3.82477 | + | 6.62470i | −0.162353 | + | 0.281203i | |||||
0 | 0 | |||||||||
2.62046 | − | 1.51293i | 0.111033 | − | 0.0641047i | −0.443455 | − | 0.896297i | ||
0.554488 | + | 0.832192i | ||||||||
0 | 0 | |||||||||
−3.27391 | − | 3.26867i | −0.138472 | − | 0.138250i | |||||
0 | 0 | |||||||||
19.4073 | − | 11.2048i | 0.819377 | − | 0.473068i | |||||
0 | 0 | |||||||||
13.6591 | − | 23.6583i | 0.575664 | − | 0.997079i | −0.420305 | − | 0.907383i | ||
0.995969 | − | 0.0896963i | ||||||||
0 | 0 | |||||||||
−21.7730 | − | 12.5707i | −0.915999 | − | 0.528852i | |||||
0 | 0 | |||||||||
9.44571i | 0.396682i | |||||||||
0 | 0 | |||||||||
−6.46871 | − | 11.2041i | −0.271183 | − | 0.469702i | 0.697982 | − | 0.716115i | ||
−0.969165 | + | 0.246413i | ||||||||
0 | 0 | |||||||||
−10.6779 | −0.446855 | −0.223427 | − | 0.974721i | ||||||
−0.223427 | + | 0.974721i | ||||||||
0 | 0 | |||||||||
−33.3581 | −1.39355 | |||||||||
0 | 0 | |||||||||
−2.96483 | − | 5.13524i | −0.123642 | − | 0.214154i | |||||
0 | 0 | |||||||||
− | 4.76467i | − | 0.198356i | −0.995070 | − | 0.0991778i | ||||
0.995070 | − | 0.0991778i | ||||||||
0 | 0 | |||||||||
−39.4171 | − | 22.7575i | −1.63812 | − | 0.945767i | |||||
0 | 0 | |||||||||
−8.33884 | + | 14.4433i | −0.345953 | + | 0.599209i | |||||
0 | 0 | |||||||||
−14.8400 | + | 8.56788i | −0.614610 | + | 0.354845i | |||||
0 | 0 | |||||||||
−1.52870 | + | 1.53115i | −0.0632040 | + | 0.0633054i | |||||
0 | 0 | |||||||||
−27.6495 | + | 15.9634i | −1.14122 | + | 0.658881i | −0.946731 | − | 0.322024i | ||
−0.194485 | + | 0.980906i | ||||||||
0 | 0 | |||||||||
14.4845 | − | 25.0879i | 0.596825 | − | 1.03373i | |||||
0 | 0 | |||||||||
−0.907144 | − | 0.523740i | −0.0373149 | − | 0.0215438i | |||||
0 | 0 | |||||||||
− | 1.27362i | − | 0.0523015i | −0.999658 | − | 0.0261508i | ||||
0.999658 | − | 0.0261508i | ||||||||
0 | 0 | |||||||||
−5.57914 | − | 9.66335i | −0.228722 | − | 0.396159i | |||||
0 | 0 | |||||||||
−28.5880 | −1.17003 | |||||||||
0 | 0 | |||||||||
15.1462 | 0.618857 | 0.309428 | − | 0.950923i | ||||||
0.309428 | + | 0.950923i | ||||||||
0 | 0 | |||||||||
−17.1425 | − | 29.6917i | −0.699258 | − | 1.21115i | −0.968724 | − | 0.248141i | ||
0.269466 | − | 0.963010i | ||||||||
0 | 0 | |||||||||
− | 0.0848899i | − | 0.00345698i | |||||||
0 | 0 | |||||||||
−25.6048 | − | 14.7829i | −1.04098 | − | 0.601012i | |||||
0 | 0 | |||||||||
4.73737 | − | 8.20537i | 0.192284 | − | 0.333046i | −0.753723 | − | 0.657192i | ||
0.946007 | + | 0.324147i | ||||||||
0 | 0 | |||||||||
14.2443 | − | 8.22397i | 0.577210 | − | 0.333252i | |||||
0 | 0 | |||||||||
19.7885 | + | 5.28533i | 0.800557 | + | 0.213821i | |||||
0 | 0 | |||||||||
10.0837 | − | 5.82183i | 0.407277 | − | 0.235141i | −0.282342 | − | 0.959314i | ||
0.689619 | + | 0.724172i | ||||||||
0 | 0 | |||||||||
40.8896 | − | 70.8229i | 1.64883 | − | 2.85586i | |||||
0 | 0 | |||||||||
−5.54295 | − | 3.20023i | −0.223151 | − | 0.128836i | 0.384257 | − | 0.923226i | ||
−0.607408 | + | 0.794390i | ||||||||
0 | 0 | |||||||||
11.2065i | 0.450425i | 0.974310 | + | 0.225213i | ||||||
−0.974310 | + | 0.225213i | ||||||||
0 | 0 | |||||||||
1.55143 | + | 2.68715i | 0.0622566 | + | 0.107832i | |||||
0 | 0 | |||||||||
2.95414 | 0.118355 | |||||||||
0 | 0 | |||||||||
19.9284 | 0.797138 | |||||||||
0 | 0 | |||||||||
−20.9810 | − | 36.3402i | −0.837900 | − | 1.45129i | |||||
0 | 0 | |||||||||
3.27837i | 0.130717i | |||||||||
0 | 0 | |||||||||
−39.1148 | − | 22.5830i | −1.55714 | − | 0.899013i | −0.997529 | − | 0.0702554i | ||
−0.559608 | − | 0.828758i | ||||||||
0 | 0 | |||||||||
10.1140 | − | 17.5179i | 0.401994 | − | 0.696274i | |||||
0 | 0 | |||||||||
67.2486 | − | 38.8260i | 2.66868 | − | 1.54076i | |||||
0 | 0 | |||||||||
−3.48195 | + | 0.935975i | −0.137960 | + | 0.0370847i | |||||
0 | 0 | |||||||||
1.24926 | − | 0.721258i | 0.0494198 | − | 0.0285325i | |||||
0 | 0 | |||||||||
−3.57997 | + | 6.20069i | −0.141400 | + | 0.244912i | −0.928024 | − | 0.372520i | ||
0.786624 | + | 0.617432i | ||||||||
0 | 0 | |||||||||
35.9015 | + | 20.7278i | 1.41582 | + | 0.817423i | 0.995928 | − | 0.0901516i | ||
0.419890 | + | 0.907575i | ||||||||
0 | 0 | |||||||||
8.72690i | 0.343621i | |||||||||
0 | 0 | |||||||||
−7.79258 | − | 13.4971i | −0.306358 | − | 0.530627i | 0.671205 | − | 0.741272i | ||
−0.977563 | + | 0.210645i | ||||||||
0 | 0 | |||||||||
33.3943 | 1.31084 | |||||||||
0 | 0 | |||||||||
−9.43004 | −0.369592 | |||||||||
0 | 0 | |||||||||
11.9121 | + | 20.6323i | 0.466156 | + | 0.807406i | 0.999253 | − | 0.0386482i | ||
−0.533097 | + | 0.846054i | ||||||||
0 | 0 | |||||||||
18.8509i | 0.736565i | |||||||||
0 | 0 | |||||||||
−1.00027 | − | 0.577505i | −0.0390242 | − | 0.0225306i | |||||
0 | 0 | |||||||||
2.01861 | − | 3.49634i | 0.0786340 | − | 0.136198i | −0.824027 | − | 0.566551i | ||
0.902661 | + | 0.430353i | ||||||||
0 | 0 | |||||||||
32.2144 | − | 18.5990i | 1.25299 | − | 0.723416i | 0.281290 | − | 0.959623i | ||
0.971703 | + | 0.236207i | ||||||||
0 | 0 | |||||||||
−4.81846 | + | 18.0406i | −0.187134 | + | 0.700637i | |||||
0 | 0 | |||||||||
−18.0946 | + | 10.4469i | −0.701679 | + | 0.405115i | |||||
0 | 0 | |||||||||
2.84307 | − | 4.92434i | 0.110084 | − | 0.190671i | |||||
0 | 0 | |||||||||
3.60998 | + | 2.08422i | 0.139570 | + | 0.0805808i | |||||
0 | 0 | |||||||||
− | 62.0768i | − | 2.39645i | |||||||
0 | 0 | |||||||||
−5.02863 | − | 8.70984i | −0.193839 | − | 0.335740i | 0.752680 | − | 0.658387i | ||
−0.946519 | + | 0.322647i | ||||||||
0 | 0 | |||||||||
−48.7683 | −1.87709 | |||||||||
0 | 0 | |||||||||
−19.8807 | −0.764076 | −0.382038 | − | 0.924147i | ||||||
−0.382038 | + | 0.924147i | ||||||||
0 | 0 | |||||||||
4.82792 | + | 8.36220i | 0.185278 | + | 0.320912i | |||||
0 | 0 | |||||||||
14.6604i | 0.561787i | |||||||||
0 | 0 | |||||||||
17.2194 | + | 9.94161i | 0.658881 | + | 0.380405i | 0.791850 | − | 0.610715i | ||
−0.132970 | + | 0.991120i | ||||||||
0 | 0 | |||||||||
24.7517 | − | 42.8712i | 0.945715 | − | 1.63803i | |||||
0 | 0 | |||||||||
26.5808 | − | 15.3464i | 1.01412 | − | 0.585503i | |||||
0 | 0 | |||||||||
3.68449 | − | 13.7949i | 0.140368 | − | 0.525544i | |||||
0 | 0 | |||||||||
16.5968 | − | 9.58219i | 0.631373 | − | 0.364524i | −0.149910 | − | 0.988700i | ||
0.781284 | + | 0.624176i | ||||||||
0 | 0 | |||||||||
−0.339157 | + | 0.587437i | −0.0128835 | + | 0.0223149i | |||||
0 | 0 | |||||||||
−52.4108 | − | 30.2594i | −1.98805 | − | 1.14780i | |||||
0 | 0 | |||||||||
− | 35.0482i | − | 1.32755i | |||||||
0 | 0 | |||||||||
−3.67585 | − | 6.36676i | −0.139033 | − | 0.240813i | |||||
0 | 0 | |||||||||
18.5012 | 0.698780 | 0.349390 | − | 0.936977i | ||||||
0.349390 | + | 0.936977i | ||||||||
0 | 0 | |||||||||
6.13875 | 0.231527 | |||||||||
0 | 0 | |||||||||
−19.3184 | − | 33.4605i | −0.727575 | − | 1.26020i | |||||
0 | 0 | |||||||||
− | 6.35056i | − | 0.238838i | |||||||
0 | 0 | |||||||||
−20.8032 | − | 12.0107i | −0.781279 | − | 0.451072i | 0.0556043 | − | 0.998453i | ||
−0.836883 | + | 0.547381i | ||||||||
0 | 0 | |||||||||
0.0259977 | − | 0.0450294i | 0.000974990 | − | 0.00168873i | |||||
0 | 0 | |||||||||
−2.82325 | + | 1.63001i | −0.105732 | + | 0.0610442i | |||||
0 | 0 | |||||||||
57.6756 | − | 15.5037i | 2.15695 | − | 0.579805i | |||||
0 | 0 | |||||||||
8.98409 | − | 5.18697i | 0.335517 | − | 0.193711i | |||||
0 | 0 | |||||||||
−12.2149 | + | 21.1568i | −0.455538 | + | 0.789015i | −0.998719 | − | 0.0506008i | ||
0.543181 | + | 0.839616i | ||||||||
0 | 0 | |||||||||
4.39176 | + | 2.53559i | 0.163558 | + | 0.0944302i | |||||
0 | 0 | |||||||||
50.5421i | 1.87968i | |||||||||
0 | 0 | |||||||||
44.6852 | + | 77.3971i | 1.65957 | + | 2.87446i | |||||
0 | 0 | |||||||||
−20.9000 | −0.775138 | −0.387569 | − | 0.921841i | ||||||
−0.387569 | + | 0.921841i | ||||||||
0 | 0 | |||||||||
25.4456 | 0.942428 | |||||||||
0 | 0 | |||||||||
1.87005 | + | 3.23902i | 0.0691662 | + | 0.119799i | |||||
0 | 0 | |||||||||
7.08118i | 0.261549i | 0.991412 | + | 0.130775i | ||||||
−0.991412 | + | 0.130775i | ||||||||
0 | 0 | |||||||||
5.89018 | + | 3.40069i | 0.217262 | + | 0.125437i | |||||
0 | 0 | |||||||||
−1.17161 | + | 2.02928i | −0.0431567 | + | 0.0747496i | |||||
0 | 0 | |||||||||
20.5378 | − | 11.8575i | 0.755496 | − | 0.436186i | −0.0721806 | − | 0.997392i | ||
0.827676 | + | 0.561206i | ||||||||
0 | 0 | |||||||||
33.7809 | + | 9.02256i | 1.24097 | + | 0.331452i | |||||
0 | 0 | |||||||||
36.5813 | − | 21.1202i | 1.34204 | − | 0.774825i | 0.354931 | − | 0.934893i | ||
0.987106 | + | 0.160067i | ||||||||
0 | 0 | |||||||||
30.4923 | − | 52.8143i | 1.11715 | − | 1.93497i | |||||
0 | 0 | |||||||||
−2.26414 | − | 1.30720i | −0.0828406 | − | 0.0478281i | |||||
0 | 0 | |||||||||
− | 5.48579i | − | 0.200446i | |||||||
0 | 0 | |||||||||
−12.0710 | − | 20.9076i | −0.440478 | − | 0.762930i | 0.557247 | − | 0.830347i | ||
−0.997725 | + | 0.0674164i | ||||||||
0 | 0 | |||||||||
22.7066 | 0.827475 | |||||||||
0 | 0 | |||||||||
24.3983 | 0.887947 | |||||||||
0 | 0 | |||||||||
15.9716 | + | 27.6636i | 0.580497 | + | 1.00545i | 0.995420 | + | 0.0955942i | ||
−0.414923 | + | 0.909856i | ||||||||
0 | 0 | |||||||||
4.72216i | 0.171404i | |||||||||
0 | 0 | |||||||||
−36.6083 | − | 21.1358i | −1.32705 | − | 0.766172i | −0.342207 | − | 0.939625i | ||
−0.984842 | + | 0.173452i | ||||||||
0 | 0 | |||||||||
−3.40342 | + | 5.89490i | −0.123212 | + | 0.213410i | |||||
0 | 0 | |||||||||
1.51484 | − | 0.874590i | 0.0547690 | − | 0.0316209i | |||||
0 | 0 | |||||||||
−19.6602 | + | 19.6917i | −0.709888 | + | 0.711026i | |||||
0 | 0 | |||||||||
−2.36768 | + | 1.36698i | −0.0853808 | + | 0.0492946i | −0.542083 | − | 0.840325i | ||
0.456702 | + | 0.889620i | ||||||||
0 | 0 | |||||||||
−0.596439 | + | 1.03306i | −0.0214802 | + | 0.0372048i | |||||
0 | 0 | |||||||||
−16.9343 | − | 9.77703i | −0.609085 | − | 0.351655i | 0.163523 | − | 0.986540i | ||
−0.772607 | + | 0.634884i | ||||||||
0 | 0 | |||||||||
− | 51.2384i | − | 1.84054i | |||||||
0 | 0 | |||||||||
−0.999146 | − | 1.73057i | −0.0358442 | − | 0.0620839i | |||||
0 | 0 | |||||||||
−65.6277 | −2.35136 | |||||||||
0 | 0 | |||||||||
−39.8177 | −1.42479 | |||||||||
0 | 0 | |||||||||
−23.3827 | − | 40.5001i | −0.835630 | − | 1.44735i | |||||
0 | 0 | |||||||||
28.2816i | 1.00941i | |||||||||
0 | 0 | |||||||||
−28.0930 | − | 16.2195i | −1.00141 | − | 0.578163i | −0.0927426 | − | 0.995690i | ||
−0.908664 | + | 0.417528i | ||||||||
0 | 0 | |||||||||
16.8525 | − | 29.1893i | 0.599964 | − | 1.03917i | |||||
0 | 0 | |||||||||
5.68778 | − | 3.28384i | 0.202234 | − | 0.116760i | |||||
0 | 0 | |||||||||
36.6050 | + | 36.5464i | 1.29988 | + | 1.29780i | |||||
0 | 0 | |||||||||
−23.3259 | + | 13.4672i | −0.827284 | + | 0.477632i | |||||
0 | 0 | |||||||||
12.9397 | − | 22.4123i | 0.458349 | − | 0.793883i | −0.540525 | − | 0.841328i | ||
0.998874 | + | 0.0474447i | ||||||||
0 | 0 | |||||||||
−14.3402 | − | 8.27933i | −0.507320 | − | 0.292902i | |||||
0 | 0 | |||||||||
0.463093i | 0.0163626i | |||||||||
0 | 0 | |||||||||
15.9409 | + | 27.6104i | 0.562541 | + | 0.974350i | |||||
0 | 0 | |||||||||
2.35128 | 0.0828716 | |||||||||
0 | 0 | |||||||||
17.0296 | 0.599471 | |||||||||
0 | 0 | |||||||||
−11.2066 | − | 19.4105i | −0.394004 | − | 0.682435i | 0.598969 | − | 0.800772i | ||
−0.992974 | + | 0.118337i | ||||||||
0 | 0 | |||||||||
− | 5.44486i | − | 0.191195i | −0.995420 | − | 0.0955974i | ||||
0.995420 | − | 0.0955974i | ||||||||
0 | 0 | |||||||||
−16.1124 | − | 9.30247i | −0.565085 | − | 0.326252i | |||||
0 | 0 | |||||||||
0.167599 | − | 0.290290i | 0.00587074 | − | 0.0101684i | |||||
0 | 0 | |||||||||
6.06505 | − | 3.50166i | 0.212189 | − | 0.122508i | |||||
0 | 0 | |||||||||
−0.146724 | − | 0.545833i | −0.00512696 | − | 0.0190729i | |||||
0 | 0 | |||||||||
26.6843 | − | 15.4062i | 0.931288 | − | 0.537679i | 0.0440690 | − | 0.999028i | ||
0.887219 | + | 0.461349i | ||||||||
0 | 0 | |||||||||
−0.102850 | + | 0.178141i | −0.00358513 | + | 0.00620962i | −0.867812 | − | 0.496892i | ||
0.864227 | + | 0.503102i | ||||||||
0 | 0 | |||||||||
−64.2759 | − | 37.1097i | −2.23780 | − | 1.29199i | |||||
0 | 0 | |||||||||
9.66411i | 0.336054i | 0.985782 | + | 0.168027i | ||||||
−0.985782 | + | 0.168027i | ||||||||
0 | 0 | |||||||||
15.2667 | + | 26.4427i | 0.530234 | + | 0.918393i | 0.999378 | + | 0.0352709i | ||
−0.469143 | + | 0.883122i | ||||||||
0 | 0 | |||||||||
−34.3568 | −1.19182 | |||||||||
0 | 0 | |||||||||
2.91488 | 0.100995 | |||||||||
0 | 0 | |||||||||
35.4301 | + | 61.3668i | 1.22611 | + | 2.12369i | |||||
0 | 0 | |||||||||
26.8119i | 0.926753i | |||||||||
0 | 0 | |||||||||
33.0722 | + | 19.0942i | 1.14178 | + | 0.659206i | 0.946871 | − | 0.321615i | ||
0.194909 | + | 0.980821i | ||||||||
0 | 0 | |||||||||
−28.3501 | + | 49.1037i | −0.977588 | + | 1.69323i | |||||
0 | 0 | |||||||||
−28.7795 | + | 16.6158i | −0.991218 | + | 0.572280i | |||||
0 | 0 | |||||||||
−24.8132 | + | 43.1372i | −0.853599 | + | 1.48396i | |||||
0 | 0 | |||||||||
6.68874 | − | 3.86175i | 0.229828 | − | 0.132691i | |||||
0 | 0 | |||||||||
1.04464 | − | 1.80937i | 0.0358519 | − | 0.0620973i | |||||
0 | 0 | |||||||||
−0.598268 | − | 0.345410i | −0.0205084 | − | 0.0118405i | |||||
0 | 0 | |||||||||
− | 28.3480i | − | 0.970618i | −0.874343 | − | 0.485309i | ||||
0.874343 | − | 0.485309i | ||||||||
0 | 0 | |||||||||
−1.63767 | − | 2.83653i | −0.0560071 | − | 0.0970071i | |||||
0 | 0 | |||||||||
25.8488 | 0.882978 | 0.441489 | − | 0.897267i | ||||||
0.441489 | + | 0.897267i | ||||||||
0 | 0 | |||||||||
−19.6084 | −0.669029 | −0.334514 | − | 0.942391i | ||||||
−0.334514 | + | 0.942391i | ||||||||
0 | 0 | |||||||||
10.6816 | + | 18.5011i | 0.364028 | + | 0.630515i | |||||
0 | 0 | |||||||||
− | 13.4368i | − | 0.457395i | −0.973498 | − | 0.228697i | ||||
0.973498 | − | 0.228697i | ||||||||
0 | 0 | |||||||||
−1.36222 | − | 0.786477i | −0.0463168 | − | 0.0267410i | |||||
0 | 0 | |||||||||
−7.55418 | + | 13.0842i | −0.256554 | + | 0.444364i | |||||
0 | 0 | |||||||||
−1.24294 | + | 0.717614i | −0.0421640 | + | 0.0243434i | |||||
0 | 0 | |||||||||
−0.506854 | − | 1.88556i | −0.0171741 | − | 0.0638898i | |||||
0 | 0 | |||||||||
−1.31086 | + | 0.756828i | −0.0443660 | + | 0.0256147i | |||||
0 | 0 | |||||||||
−8.90769 | + | 15.4286i | −0.301135 | + | 0.521581i | |||||
0 | 0 | |||||||||
26.1038 | + | 15.0711i | 0.881464 | + | 0.508914i | 0.871141 | − | 0.491033i | ||
0.0103233 | + | 0.999947i | ||||||||
0 | 0 | |||||||||
− | 11.5611i | − | 0.389947i | |||||||
0 | 0 | |||||||||
4.52477 | + | 7.83714i | 0.152443 | + | 0.264040i | 0.932125 | − | 0.362136i | ||
−0.779682 | + | 0.626176i | ||||||||
0 | 0 | |||||||||
−47.3475 | −1.59337 | −0.796685 | − | 0.604395i | ||||||
−0.796685 | + | 0.604395i | ||||||||
0 | 0 | |||||||||
52.4900 | 1.76443 | |||||||||
0 | 0 | |||||||||
18.9895 | + | 32.8908i | 0.637605 | + | 1.10436i | 0.985957 | + | 0.167001i | ||
−0.348352 | + | 0.937364i | ||||||||
0 | 0 | |||||||||
20.2850i | 0.680338i | |||||||||
0 | 0 | |||||||||
35.3964 | + | 20.4361i | 1.18582 | + | 0.684635i | |||||
0 | 0 | |||||||||
−15.5030 | + | 26.8520i | −0.518789 | + | 0.898569i | |||||
0 | 0 | |||||||||
−7.14339 | + | 4.12424i | −0.238777 | + | 0.137858i | |||||
0 | 0 | |||||||||
−2.78453 | − | 2.78007i | −0.0929728 | − | 0.0928239i | |||||
0 | 0 | |||||||||
42.5514 | − | 24.5671i | 1.41917 | − | 0.819358i | |||||
0 | 0 | |||||||||
−5.77165 | + | 9.99680i | −0.192282 | + | 0.333042i | |||||
0 | 0 | |||||||||
−1.97430 | − | 1.13986i | −0.0657007 | − | 0.0379323i | |||||
0 | 0 | |||||||||
− | 24.8870i | − | 0.827272i | |||||||
0 | 0 | |||||||||
−13.9433 | − | 24.1506i | −0.462981 | − | 0.801906i | 0.536127 | − | 0.844137i | ||
−0.999108 | + | 0.0422309i | ||||||||
0 | 0 | |||||||||
0.995519 | 0.0330193 | |||||||||
0 | 0 | |||||||||
26.1435 | 0.866172 | 0.433086 | − | 0.901353i | ||||||
0.433086 | + | 0.901353i | ||||||||
0 | 0 | |||||||||
36.0827 | + | 62.4971i | 1.19416 | + | 2.06835i | |||||
0 | 0 | |||||||||
− | 97.5738i | − | 3.22569i | |||||||
0 | 0 | |||||||||
−4.26467 | − | 2.46221i | −0.140832 | − | 0.0813094i | |||||
0 | 0 | |||||||||
−1.54406 | + | 2.67439i | −0.0509338 | + | 0.0882199i | −0.890368 | − | 0.455241i | ||
0.839434 | + | 0.543461i | ||||||||
0 | 0 | |||||||||
41.6329 | − | 24.0367i | 1.37185 | − | 0.792038i | |||||
0 | 0 | |||||||||
23.4418 | − | 23.4794i | 0.771598 | − | 0.772835i | |||||
0 | 0 | |||||||||
9.40312 | − | 5.42889i | 0.309173 | − | 0.178501i | |||||
0 | 0 | |||||||||
−0.397481 | + | 0.688457i | −0.0130550 | + | 0.0226119i | |||||
0 | 0 | |||||||||
33.4087 | + | 19.2885i | 1.09610 | + | 0.632836i | 0.935195 | − | 0.354133i | ||
0.160910 | + | 0.986969i | ||||||||
0 | 0 | |||||||||
− | 5.45810i | − | 0.178882i | |||||||
0 | 0 | |||||||||
−27.4559 | − | 47.5550i | −0.898865 | − | 1.55688i | |||||
0 | 0 | |||||||||
−48.2826 | −1.57901 | |||||||||
0 | 0 | |||||||||
8.28836 | 0.270769 | 0.135384 | − | 0.990793i | ||||||
0.135384 | + | 0.990793i | ||||||||
0 | 0 | |||||||||
26.7234 | + | 46.2863i | 0.872086 | + | 1.51050i | |||||
0 | 0 | |||||||||
− | 7.72406i | − | 0.251797i | −0.992043 | − | 0.125899i | ||||
0.992043 | − | 0.125899i | ||||||||
0 | 0 | |||||||||
6.39592 | + | 3.69269i | 0.208280 | + | 0.120250i | |||||
0 | 0 | |||||||||
9.66899 | − | 16.7472i | 0.314532 | − | 0.544786i | |||||
0 | 0 | |||||||||
−44.8430 | + | 25.8901i | −1.45720 | + | 0.841316i | −0.998873 | − | 0.0474661i | ||
−0.458330 | + | 0.888782i | ||||||||
0 | 0 | |||||||||
−25.6659 | − | 6.85513i | −0.833152 | − | 0.222527i | |||||
0 | 0 | |||||||||
−5.82165 | + | 3.36113i | −0.188780 | + | 0.108992i | |||||
0 | 0 | |||||||||
24.3912 | − | 42.2468i | 0.790109 | − | 1.36851i | −0.135791 | − | 0.990738i | ||
0.925899 | − | 0.377771i | ||||||||
0 | 0 | |||||||||
62.2426 | + | 35.9358i | 2.01412 | + | 1.16285i | |||||
0 | 0 | |||||||||
− | 71.1713i | − | 2.30064i | |||||||
0 | 0 | |||||||||
6.46589 | + | 11.1993i | 0.208795 | + | 0.361643i | |||||
0 | 0 | |||||||||
2.83011 | 0.0912938 | |||||||||
0 | 0 | |||||||||
0.859956 | 0.0277117 | |||||||||
0 | 0 | |||||||||
49.0320 | + | 84.9259i | 1.57840 | + | 2.73386i | |||||
0 | 0 | |||||||||
− | 3.09186i | − | 0.0994274i | −0.998764 | − | 0.0497137i | ||||
0.998764 | − | 0.0497137i | ||||||||
0 | 0 | |||||||||
−24.4801 | − | 14.1336i | −0.786415 | − | 0.454037i | |||||
0 | 0 | |||||||||
27.2381 | − | 47.1777i | 0.874111 | − | 1.51400i | 0.0164037 | − | 0.999865i | ||
0.857707 | − | 0.514139i | ||||||||
0 | 0 | |||||||||
13.6913 | − | 7.90466i | 0.438922 | − | 0.253412i | |||||
0 | 0 | |||||||||
59.7236 | − | 16.0542i | 1.91269 | − | 0.514146i | |||||
0 | 0 | |||||||||
16.7476 | − | 9.66925i | 0.535804 | − | 0.309347i | −0.207573 | − | 0.978220i | ||
0.743377 | + | 0.668873i | ||||||||
0 | 0 | |||||||||
6.39137 | − | 11.0702i | 0.204269 | − | 0.353804i | |||||
0 | 0 | |||||||||
−0.924090 | − | 0.533524i | −0.0295039 | − | 0.0170341i | |||||
0 | 0 | |||||||||
4.93770i | 0.157488i | 0.996895 | + | 0.0787440i | ||||||
−0.996895 | + | 0.0787440i | ||||||||
0 | 0 | |||||||||
1.12842 | + | 1.95449i | 0.0359545 | + | 0.0622751i | |||||
0 | 0 | |||||||||
10.0931 | 0.321268 | |||||||||
0 | 0 | |||||||||
−0.788114 | −0.0250606 | |||||||||
0 | 0 | |||||||||
24.1717 | + | 41.8666i | 0.767839 | + | 1.32994i | 0.938733 | + | 0.344646i | ||
−0.170894 | + | 0.985289i | ||||||||
0 | 0 | |||||||||
− | 41.3181i | − | 1.31119i | |||||||
0 | 0 | |||||||||
53.3422 | + | 30.7971i | 1.69106 | + | 0.976334i | |||||
0 | 0 | |||||||||
21.6634 | − | 37.5222i | 0.686088 | − | 1.18834i | −0.287005 | − | 0.957929i | ||
0.973094 | − | 0.230411i | ||||||||
0 | 0 | |||||||||
−4.92043 | + | 2.84081i | −0.155675 | + | 0.0898793i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1456.2.cc.f.673.7 | 16 | ||
4.3 | odd | 2 | 364.2.u.a.309.2 | yes | 16 | ||
12.11 | even | 2 | 3276.2.cf.c.1765.7 | 16 | |||
13.4 | even | 6 | inner | 1456.2.cc.f.225.7 | 16 | ||
28.3 | even | 6 | 2548.2.bb.c.569.7 | 16 | |||
28.11 | odd | 6 | 2548.2.bb.d.569.2 | 16 | |||
28.19 | even | 6 | 2548.2.bq.c.361.2 | 16 | |||
28.23 | odd | 6 | 2548.2.bq.e.361.7 | 16 | |||
28.27 | even | 2 | 2548.2.u.c.1765.7 | 16 | |||
52.3 | odd | 6 | 4732.2.g.k.337.13 | 16 | |||
52.11 | even | 12 | 4732.2.a.t.1.7 | 8 | |||
52.15 | even | 12 | 4732.2.a.s.1.7 | 8 | |||
52.23 | odd | 6 | 4732.2.g.k.337.14 | 16 | |||
52.43 | odd | 6 | 364.2.u.a.225.2 | ✓ | 16 | ||
156.95 | even | 6 | 3276.2.cf.c.2773.2 | 16 | |||
364.95 | odd | 6 | 2548.2.bq.e.1941.7 | 16 | |||
364.199 | even | 6 | 2548.2.bq.c.1941.2 | 16 | |||
364.251 | even | 6 | 2548.2.u.c.589.7 | 16 | |||
364.303 | odd | 6 | 2548.2.bb.d.1733.2 | 16 | |||
364.355 | even | 6 | 2548.2.bb.c.1733.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
364.2.u.a.225.2 | ✓ | 16 | 52.43 | odd | 6 | ||
364.2.u.a.309.2 | yes | 16 | 4.3 | odd | 2 | ||
1456.2.cc.f.225.7 | 16 | 13.4 | even | 6 | inner | ||
1456.2.cc.f.673.7 | 16 | 1.1 | even | 1 | trivial | ||
2548.2.u.c.589.7 | 16 | 364.251 | even | 6 | |||
2548.2.u.c.1765.7 | 16 | 28.27 | even | 2 | |||
2548.2.bb.c.569.7 | 16 | 28.3 | even | 6 | |||
2548.2.bb.c.1733.7 | 16 | 364.355 | even | 6 | |||
2548.2.bb.d.569.2 | 16 | 28.11 | odd | 6 | |||
2548.2.bb.d.1733.2 | 16 | 364.303 | odd | 6 | |||
2548.2.bq.c.361.2 | 16 | 28.19 | even | 6 | |||
2548.2.bq.c.1941.2 | 16 | 364.199 | even | 6 | |||
2548.2.bq.e.361.7 | 16 | 28.23 | odd | 6 | |||
2548.2.bq.e.1941.7 | 16 | 364.95 | odd | 6 | |||
3276.2.cf.c.1765.7 | 16 | 12.11 | even | 2 | |||
3276.2.cf.c.2773.2 | 16 | 156.95 | even | 6 | |||
4732.2.a.s.1.7 | 8 | 52.15 | even | 12 | |||
4732.2.a.t.1.7 | 8 | 52.11 | even | 12 | |||
4732.2.g.k.337.13 | 16 | 52.3 | odd | 6 | |||
4732.2.g.k.337.14 | 16 | 52.23 | odd | 6 |