Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(293,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 504.cc (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
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 | 293.1 | ||
Root | of defining polynomial | ||
Character | 504.293 | ||
Dual form | 504.2.cc.a.461.1 |
-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 .
−1.22474 | + | 0.707107i | −0.866025 | + | 0.500000i | |||||
−1.68014 | − | 0.420861i | −0.970030 | − | 0.242984i | |||||
1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | |||||
3.32070 | + | 1.91721i | 1.48506 | + | 0.857401i | 0.999856 | − | 0.0169992i | ||
0.485206 | + | 0.874400i | ||||||||
2.35534 | − | 0.672592i | 0.961563 | − | 0.274584i | |||||
1.32288 | + | 2.29129i | 0.500000 | + | 0.866025i | |||||
2.82843i | 1.00000i | |||||||||
2.64575 | + | 1.41421i | 0.881917 | + | 0.471405i | |||||
−5.42268 | −1.71480 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
−2.40909 | + | 2.48923i | −0.695446 | + | 0.718579i | |||||
2.27533 | − | 3.94099i | 0.631063 | − | 1.09303i | −0.356272 | − | 0.934382i | ||
0.987335 | − | 0.158651i | ||||||||
−3.24037 | − | 1.87083i | −0.866025 | − | 0.500000i | |||||
−4.77237 | − | 4.61873i | −1.23222 | − | 1.19255i | |||||
−2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−4.24037 | + | 0.138778i | −0.999465 | + | 0.0327103i | |||||
−7.01226 | −1.60872 | −0.804361 | − | 0.594140i | ||||||
−0.804361 | + | 0.594140i | ||||||||
6.64140 | − | 3.83441i | 1.48506 | − | 0.857401i | |||||
−1.25830 | − | 4.40644i | −0.274584 | − | 0.961563i | |||||
0 | 0 | |||||||||
7.74037 | + | 4.46890i | 1.61398 | + | 0.931831i | 0.988436 | + | 0.151642i | ||
0.625543 | + | 0.780189i | ||||||||
1.19038 | − | 4.75216i | 0.242984 | − | 0.970030i | |||||
4.85136 | + | 8.40280i | 0.970272 | + | 1.68056i | |||||
6.43560i | 1.26213i | |||||||||
−3.85005 | − | 3.48957i | −0.740942 | − | 0.671569i | |||||
5.29150 | 1.00000 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
9.11087 | + | 2.28220i | 1.66341 | + | 0.416670i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
4.89898 | + | 2.82843i | 0.866025 | + | 0.500000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
10.1449i | 1.71480i | |||||||||
5.09524 | − | 3.16836i | 0.849207 | − | 0.528060i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
8.58823 | − | 4.95842i | 1.39319 | − | 0.804361i | |||||
−5.48148 | + | 5.66382i | −0.877740 | + | 0.906936i | |||||
−5.42268 | + | 9.39235i | −0.857401 | + | 1.48506i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
4.65692 | + | 4.50700i | 0.718579 | + | 0.695446i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
6.07440 | + | 9.76863i | 0.905519 | + | 1.45622i | |||||
−12.6400 | −1.86366 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
1.90238 | + | 6.66190i | 0.274584 | + | 0.961563i | |||||
−3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | |||||
−11.8834 | − | 6.86086i | −1.68056 | − | 0.970272i | |||||
0 | 0 | |||||||||
−4.55066 | − | 7.88197i | −0.631063 | − | 1.09303i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
7.18283 | + | 1.55144i | 0.977459 | + | 0.211124i | |||||
0 | 0 | |||||||||
−6.48074 | + | 3.74166i | −0.866025 | + | 0.500000i | |||||
11.7816 | + | 2.95119i | 1.56051 | + | 0.390895i | |||||
0 | 0 | |||||||||
4.58621 | + | 2.64785i | 0.597074 | + | 0.344721i | 0.767890 | − | 0.640582i | ||
−0.170816 | + | 0.985303i | ||||||||
−12.7722 | + | 3.64725i | −1.64889 | + | 0.470858i | |||||
3.66740 | + | 6.35212i | 0.469562 | + | 0.813306i | 0.999394 | − | 0.0347968i | ||
−0.529832 | + | 0.848103i | ||||||||
0 | 0 | |||||||||
0.259630 | + | 7.93301i | 0.0327103 | + | 0.999465i | |||||
−8.00000 | −1.00000 | |||||||||
15.1114 | − | 8.72455i | 1.87433 | − | 1.08215i | |||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−11.1241 | − | 10.7660i | −1.33919 | − | 1.29608i | |||||
−7.17353 | − | 12.4249i | −0.857401 | − | 1.48506i | |||||
10.9193i | 1.29588i | 0.761690 | + | 0.647941i | ||||||
−0.761690 | + | 0.647941i | ||||||||
−4.00000 | + | 7.48331i | −0.471405 | + | 0.881917i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
−4.61456 | − | 16.1596i | −0.532843 | − | 1.86595i | |||||
−7.01226 | + | 12.1456i | −0.804361 | + | 1.39319i | |||||
0 | 0 | |||||||||
2.70850 | − | 10.8127i | 0.306677 | − | 1.22430i | |||||
−8.67134 | − | 15.0192i | −0.975603 | − | 1.68979i | −0.677932 | − | 0.735124i | ||
−0.297670 | − | 0.954669i | ||||||||
− | 15.3376i | − | 1.71480i | |||||||
5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | |||||
0 | 0 | |||||||||
15.7330 | − | 9.08345i | 1.72692 | − | 0.997039i | 0.825010 | − | 0.565118i | ||
0.901912 | − | 0.431920i | ||||||||
−8.89047 | − | 2.22699i | −0.970030 | − | 0.242984i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−14.3471 | − | 7.66882i | −1.51231 | − | 0.808365i | |||||
12.0399 | 1.26213 | |||||||||
15.4807 | − | 8.93781i | 1.61398 | − | 0.931831i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−23.2856 | − | 13.4439i | −2.38905 | − | 1.37932i | |||||
−7.04060 | − | 6.81395i | −0.718579 | − | 0.695446i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
− | 9.89949i | − | 1.00000i | |||||||
0 | 0 | |||||||||
19.4054 | 1.94054 | |||||||||
−17.3740 | + | 10.0309i | −1.72877 | + | 0.998109i | −0.833650 | + | 0.552294i | ||
−0.895125 | + | 0.445815i | ||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
11.1468 | + | 6.43560i | 1.09303 | + | 0.631063i | |||||
4.26960 | − | 17.0449i | 0.416670 | − | 1.66341i | |||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−9.89417 | + | 3.17891i | −0.952067 | + | 0.305890i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.29150 | − | 9.16515i | 0.500000 | − | 0.866025i | |||||
−5.78216 | − | 3.33833i | −0.543940 | − | 0.314044i | 0.202735 | − | 0.979234i | ||
−0.746674 | + | 0.665190i | ||||||||
−16.5162 | + | 4.71639i | −1.54689 | + | 0.441730i | |||||
17.1356 | + | 29.6798i | 1.59791 | + | 2.76765i | |||||
0 | 0 | |||||||||
11.5934 | − | 7.20907i | 1.07181 | − | 0.666479i | |||||
−7.48925 | −0.689442 | |||||||||
0 | 0 | |||||||||
13.0637 | − | 13.4983i | 1.19255 | − | 1.23222i | |||||
5.50000 | − | 9.52628i | 0.500000 | − | 0.866025i | |||||
−8.98326 | − | 5.18648i | −0.813306 | − | 0.469562i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
18.0322i | 1.61285i | |||||||||
−5.92746 | − | 9.53232i | −0.528060 | − | 0.849207i | |||||
18.4422 | 1.63648 | 0.818241 | − | 0.574875i | ||||||
0.818241 | + | 0.574875i | ||||||||
9.79796 | − | 5.65685i | 0.866025 | − | 0.500000i | |||||
0 | 0 | |||||||||
−12.3384 | + | 21.3707i | −1.08215 | + | 1.87433i | |||||
−8.39072 | − | 4.84438i | −0.733100 | − | 0.423256i | 0.0864550 | − | 0.996256i | ||
−0.819555 | + | 0.573000i | ||||||||
0 | 0 | |||||||||
−9.27635 | − | 16.0671i | −0.804361 | − | 1.39319i | |||||
0 | 0 | |||||||||
−6.09462 | − | 18.9692i | −0.524541 | − | 1.63261i | |||||
0 | 0 | |||||||||
−12.9615 | + | 7.48331i | −1.10737 | + | 0.639343i | −0.938148 | − | 0.346235i | ||
−0.169226 | + | 0.985577i | ||||||||
21.2369 | + | 5.31968i | 1.80781 | + | 0.452841i | |||||
−1.14233 | + | 1.97858i | −0.0968913 | + | 0.167821i | −0.910396 | − | 0.413737i | ||
0.813505 | + | 0.581558i | ||||||||
17.5715 | + | 10.1449i | 1.48506 | + | 0.857401i | |||||
0 | 0 | |||||||||
−7.72111 | − | 13.3734i | −0.647941 | − | 1.12227i | |||||
0 | 0 | |||||||||
−0.392523 | − | 11.9936i | −0.0327103 | − | 0.999465i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.43183 | − | 8.71230i | 0.695446 | − | 0.718579i | |||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
17.0782 | + | 16.5285i | 1.39443 | + | 1.34954i | |||||
−12.2211 | − | 21.1676i | −0.994540 | − | 1.72259i | −0.587646 | − | 0.809118i | ||
−0.406894 | − | 0.913475i | ||||||||
− | 19.8337i | − | 1.60872i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.32853 | + | 15.1580i | 0.346560 | + | 1.21361i | |||||
3.34486 | − | 5.79347i | 0.266949 | − | 0.462369i | −0.701123 | − | 0.713040i | ||
0.968072 | + | 0.250671i | ||||||||
21.2404 | + | 12.2631i | 1.68979 | + | 0.975603i | |||||
0 | 0 | |||||||||
10.8454 | + | 18.7847i | 0.857401 | + | 1.48506i | |||||
23.6472i | 1.86366i | |||||||||
−11.4152 | − | 5.62962i | −0.896865 | − | 0.442305i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.8459 | + | 22.2498i | −0.997039 | + | 1.72692i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
12.4633 | − | 3.55902i | 0.961563 | − | 0.274584i | |||||
−3.85425 | − | 6.67575i | −0.296481 | − | 0.513520i | |||||
0 | 0 | |||||||||
−18.5527 | − | 9.91683i | −1.41876 | − | 0.758359i | |||||
0 | 0 | |||||||||
−21.3064 | + | 12.3013i | −1.61990 | + | 0.935247i | −0.632950 | + | 0.774193i | ||
−0.986945 | + | 0.161055i | ||||||||
0 | 0 | |||||||||
−12.8355 | + | 22.2317i | −0.970272 | + | 1.68056i | |||||
0 | 0 | |||||||||
−6.59111 | − | 6.37892i | −0.495418 | − | 0.479469i | |||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
22.9942 | − | 0.752548i | 1.71388 | − | 0.0560916i | |||||
3.13802 | 0.233247 | 0.116623 | − | 0.993176i | ||||||
0.116623 | + | 0.993176i | ||||||||
−14.7458 | + | 8.51350i | −1.09303 | + | 0.631063i | |||||
−3.48839 | − | 12.2159i | −0.257869 | − | 0.903027i | |||||
−12.6400 | + | 21.8931i | −0.931831 | + | 1.61398i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.90248 | − | 13.4378i | 0.211124 | − | 0.977459i | |||||
38.0252 | 2.75864 | |||||||||
2.10792 | − | 1.21701i | 0.152524 | − | 0.0880597i | −0.421796 | − | 0.906691i | ||
0.574320 | + | 0.818631i | ||||||||
13.4411 | + | 3.36689i | 0.970030 | + | 0.242984i | |||||
10.2886 | − | 17.8204i | 0.740591 | − | 1.28274i | −0.211636 | − | 0.977349i | ||
0.952227 | − | 0.305392i | ||||||||
0 | 0 | |||||||||
−29.0611 | + | 8.29869i | −2.08111 | + | 0.594282i | |||||
7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−23.7667 | + | 13.7217i | −1.68056 | + | 0.970272i | |||||
0 | 0 | |||||||||
14.1858 | − | 24.5705i | 0.998109 | − | 1.72877i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
14.1591 | + | 22.7701i | 0.984126 | + | 1.58263i | |||||
−18.2026 | −1.26213 | |||||||||
0 | 0 | |||||||||
6.82338 | + | 23.8947i | 0.470858 | + | 1.64889i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
4.59551 | − | 18.3460i | 0.314879 | − | 1.25705i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.87000 | − | 10.8896i | 0.671569 | − | 0.740942i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
14.9666i | 1.00000i | |||||||||
0.952135 | + | 29.0926i | 0.0634757 | + | 1.93951i | |||||
9.44222 | 0.628087 | |||||||||
−12.7602 | + | 7.36712i | −0.846926 | + | 0.488973i | −0.859612 | − | 0.510947i | ||
0.0126866 | + | 0.999920i | ||||||||
16.8932 | − | 17.4551i | 1.11878 | − | 1.15599i | |||||
14.6990 | − | 25.4595i | 0.971339 | − | 1.68241i | 0.279817 | − | 0.960053i | ||
0.691522 | − | 0.722355i | ||||||||
−41.9735 | − | 24.2334i | −2.76765 | − | 1.59791i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 20.1628i | − | 1.32091i | −0.750867 | − | 0.660454i | ||||
0.750867 | − | 0.660454i | ||||||||
−9.10132 | + | 17.0270i | −0.594972 | + | 1.11309i | |||||
0 | 0 | |||||||||
9.17242 | − | 5.29570i | 0.597074 | − | 0.344721i | |||||
8.24808 | + | 28.8838i | 0.535770 | + | 1.87621i | |||||
0 | 0 | |||||||||
−19.2596 | − | 11.1196i | −1.24580 | − | 0.719264i | −0.275533 | − | 0.961292i | ||
−0.970269 | + | 0.242028i | ||||||||
−6.45503 | + | 25.7694i | −0.416670 | + | 1.66341i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
15.5563i | 1.00000i | |||||||||
−5.25127 | − | 14.6773i | −0.336869 | − | 0.941551i | |||||
14.6696 | 0.939125 | |||||||||
−23.2449 | + | 13.4204i | −1.48506 | + | 0.857401i | |||||
0 | 0 | |||||||||
−15.9552 | + | 27.6352i | −1.01521 | + | 1.75839i | |||||
0 | 0 | |||||||||
−30.2566 | + | 8.64007i | −1.91743 | + | 0.547542i | |||||
−12.7507 | − | 22.0848i | −0.806423 | − | 1.39677i | |||||
7.06541i | 0.445965i | 0.974822 | + | 0.222982i | ||||||
−0.974822 | + | 0.222982i | ||||||||
14.0000 | + | 7.48331i | 0.881917 | + | 0.471405i | |||||
0 | 0 | |||||||||
−22.5870 | + | 13.0406i | −1.41724 | + | 0.818241i | |||||
0 | 0 | |||||||||
−8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 34.8982i | − | 2.16429i | |||||||
0 | 0 | |||||||||
13.7020 | 0.846511 | |||||||||
24.1533 | − | 13.9449i | 1.48936 | − | 0.859881i | 0.489432 | − | 0.872041i | ||
0.999926 | + | 0.0121601i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
22.7223 | + | 13.1187i | 1.39319 | + | 0.804361i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 20.5179i | − | 1.25100i | −0.780225 | − | 0.625498i | ||||
0.780225 | − | 0.625498i | ||||||||
20.8776 | + | 18.9228i | 1.27057 | + | 1.15161i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
−20.2288 | − | 5.06713i | −1.22430 | − | 0.306677i | |||||
10.5830 | − | 18.3303i | 0.639343 | − | 1.10737i | |||||
0 | 0 | |||||||||
−29.7714 | + | 8.50154i | −1.79203 | + | 0.511733i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
− | 3.23100i | − | 0.193783i | |||||||
0 | 0 | |||||||||
−28.6941 | −1.71480 | |||||||||
28.9807 | − | 16.7320i | 1.72885 | − | 0.998150i | 0.834021 | − | 0.551733i | ||
0.894825 | − | 0.446417i | ||||||||
0 | 0 | |||||||||
3.82867 | − | 6.63145i | 0.227591 | − | 0.394199i | −0.729503 | − | 0.683978i | ||
0.957094 | + | 0.289779i | ||||||||
18.9128 | + | 10.9193i | 1.12227 | + | 0.647941i | |||||
33.4651 | + | 32.3877i | 1.98230 | + | 1.91848i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8.96148 | + | 14.4115i | 0.528060 | + | 0.849207i | |||||
−17.0000 | −1.00000 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
16.9789 | + | 9.80280i | 0.991921 | + | 0.572686i | 0.905848 | − | 0.423603i | ||
0.0860728 | + | 0.996289i | ||||||||
−4.16632 | + | 16.6326i | −0.242984 | + | 0.970030i | |||||
10.1530 | + | 17.5854i | 0.591128 | + | 1.02386i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
35.2238 | − | 20.3365i | 2.03704 | − | 1.17609i | |||||
−32.6039 | − | 8.16700i | −1.88239 | − | 0.471522i | |||||
0 | 0 | |||||||||
29.9355 | + | 17.2833i | 1.72259 | + | 0.994540i | |||||
33.4123 | − | 9.54124i | 1.91949 | − | 0.548130i | |||||
14.0245 | + | 24.2912i | 0.804361 | + | 1.39319i | |||||
28.1246i | 1.61041i | |||||||||
0 | 0 | |||||||||
34.8207 | 1.98732 | 0.993662 | − | 0.112409i | ||||||
0.993662 | + | 0.112409i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
−16.0197 | − | 15.5040i | −0.906936 | − | 0.877740i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
9.46070i | 0.533898i | |||||||||
−14.3471 | + | 26.8409i | −0.808365 | + | 1.51231i | |||||
−34.6854 | −1.95121 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−26.5656 | − | 15.3376i | −1.48506 | − | 0.857401i | |||||
0 | 0 | |||||||||
−16.7211 | − | 28.9618i | −0.931831 | − | 1.61398i | |||||
0 | 0 | |||||||||
17.9615 | − | 1.17694i | 0.997860 | − | 0.0653855i | |||||
44.1538 | 2.44921 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
− | 36.3338i | − | 1.99408i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.7477 | + | 13.1718i | −0.695446 | + | 0.718579i | |||||
−13.2288 | + | 22.9129i | −0.720616 | + | 1.24814i | 0.240137 | + | 0.970739i | ||
−0.960753 | + | 0.277405i | ||||||||
9.44094 | + | 5.45073i | 0.513520 | + | 0.296481i | |||||
8.30987 | + | 8.04235i | 0.451330 | + | 0.436801i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
29.7346 | − | 0.973147i | 1.60786 | − | 0.0526217i | |||||
−18.5203 | −1.00000 | |||||||||
0 | 0 | |||||||||
−16.2992 | − | 57.0779i | −0.877520 | − | 3.07297i | |||||
17.3966 | − | 30.1318i | 0.935247 | − | 1.61990i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
−14.3152 | − | 24.7947i | −0.766277 | − | 1.32723i | −0.939569 | − | 0.342361i | ||
0.173291 | − | 0.984871i | ||||||||
− | 36.3042i | − | 1.94054i | |||||||
−22.5125 | + | 7.23306i | −1.20163 | + | 0.386072i | |||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
12.5830 | + | 3.15194i | 0.668779 | + | 0.167524i | |||||
−20.9345 | + | 36.2597i | −1.11109 | + | 1.92447i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
13.5121i | 0.713143i | 0.934268 | + | 0.356572i | ||||||
−0.934268 | + | 0.356572i | ||||||||
−27.6299 | + | 17.1810i | −1.45622 | + | 0.905519i | |||||
30.1718 | 1.58799 | |||||||||
−3.84327 | + | 2.21891i | −0.201998 | + | 0.116623i | |||||
−13.2500 | + | 13.6908i | −0.695446 | + | 0.718579i | |||||
12.0399 | − | 20.8537i | 0.631063 | − | 1.09303i | |||||
0 | 0 | |||||||||
12.9103 | + | 12.4947i | 0.674835 | + | 0.653110i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
− | 35.7512i | − | 1.86366i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
7.58904 | − | 30.2966i | 0.391896 | − | 1.56451i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.94719 | + | 18.5103i | 0.305890 | + | 0.952067i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−46.5712 | + | 26.8879i | −2.38905 | + | 1.37932i | |||||
−30.9855 | − | 7.76162i | −1.58744 | − | 0.397640i | |||||
−1.72111 | + | 2.98105i | −0.0880597 | + | 0.152524i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
−18.8427 | + | 5.38073i | −0.961563 | + | 0.274584i | |||||
0 | 0 | |||||||||
29.1006i | 1.48118i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
29.7243 | − | 30.7131i | 1.50515 | − | 1.55522i | |||||
0 | 0 | |||||||||
−17.1464 | − | 9.89949i | −0.866025 | − | 0.500000i | |||||
12.0588 | + | 11.6706i | 0.608285 | + | 0.588703i | |||||
0 | 0 | |||||||||
− | 66.4990i | − | 3.34593i | |||||||
0 | 0 | |||||||||
−37.7318 | −1.89370 | −0.946852 | − | 0.321668i | ||||||
−0.946852 | + | 0.321668i | ||||||||
0 | 0 | |||||||||
8.82355 | + | 30.8991i | 0.441730 | + | 1.54689i | |||||
19.4054 | − | 33.6112i | 0.970272 | − | 1.68056i | |||||
−27.8276 | − | 16.0663i | −1.38964 | − | 0.802310i | −0.396368 | − | 0.918092i | ||
−0.993275 | + | 0.115782i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
40.1235i | 1.99622i | |||||||||
2.25644 | + | 34.4359i | 0.112123 | + | 1.71113i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
24.9266 | − | 7.11804i | 1.22954 | − | 0.351107i | |||||
0 | 0 | |||||||||
14.0111i | 0.689442i | |||||||||
−33.4422 | − | 17.8756i | −1.64360 | − | 0.878539i | |||||
69.6594 | 3.41945 | |||||||||
22.2936 | − | 12.8712i | 1.09303 | − | 0.631063i | |||||
2.75198 | − | 2.84352i | 0.134765 | − | 0.139248i | |||||
0 | 0 | |||||||||
−7.16397 | − | 4.13612i | −0.349983 | − | 0.202063i | 0.314695 | − | 0.949193i | ||
−0.664678 | + | 0.747130i | ||||||||
−25.2530 | − | 24.4400i | −1.23222 | − | 1.19255i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.34423 | + | 25.7187i | 0.355829 | + | 1.24607i | |||||
−9.70302 | + | 16.8061i | −0.469562 | + | 0.813306i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 37.4166i | − | 1.80229i | −0.433515 | − | 0.901146i | ||||
0.433515 | − | 0.901146i | ||||||||
−4.38814 | + | 20.3161i | −0.211124 | + | 0.977459i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−54.2775 | − | 31.3371i | −2.59644 | − | 1.49906i | |||||
0 | 0 | |||||||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−17.8333 | + | 11.0893i | −0.849207 | + | 0.528060i | |||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−10.5830 | − | 18.3303i | −0.500000 | − | 0.866025i | |||||
11.0141i | 0.519789i | 0.965637 | + | 0.259895i | ||||||
−0.965637 | + | 0.259895i | ||||||||
−21.7377 | − | 34.9577i | −1.02472 | − | 1.64792i | |||||
0 | 0 | |||||||||
−11.5643 | + | 6.67666i | −0.543940 | + | 0.314044i | |||||
11.6246 | + | 40.7079i | 0.546170 | + | 1.91263i | |||||
10.4187 | − | 18.0457i | 0.488973 | − | 0.846926i | |||||
39.9809 | + | 23.0830i | 1.87433 | + | 1.08215i | |||||
−8.34723 | + | 33.3234i | −0.390895 | + | 1.56051i | |||||
−19.6940 | − | 34.1111i | −0.921249 | − | 1.59565i | −0.797486 | − | 0.603338i | ||
−0.123763 | − | 0.992312i | ||||||||
41.5751i | 1.94268i | |||||||||
0 | 0 | |||||||||
68.5425 | 3.19581 | |||||||||
34.5504 | − | 19.9477i | 1.60917 | − | 0.929057i | 0.619619 | − | 0.784903i | ||
0.989555 | − | 0.144154i | ||||||||
0 | 0 | |||||||||
21.3113 | − | 36.9123i | 0.990421 | − | 1.71546i | 0.375628 | − | 0.926770i | ||
0.614792 | − | 0.788689i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
14.2572 | + | 24.6943i | 0.660454 | + | 1.14394i | |||||
41.6295i | 1.92638i | 0.268814 | + | 0.963192i | ||||||
−0.268814 | + | 0.963192i | ||||||||
−0.893119 | − | 27.2893i | −0.0412845 | − | 1.26145i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8.05809 | + | 8.32613i | −0.371297 | + | 0.383648i | |||||
−7.48925 | + | 12.9718i | −0.344721 | + | 0.597074i | |||||
0 | 0 | |||||||||
−30.5257 | − | 29.5431i | −1.40209 | − | 1.35696i | |||||
−34.0190 | − | 58.9226i | −1.56090 | − | 2.70356i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
31.4508 | 1.43853 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
−10.3160 | − | 36.1254i | −0.470858 | − | 1.64889i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.95220 | − | 39.7307i | 0.452841 | − | 1.80781i | |||||
−11.0000 | − | 19.0526i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
16.8099 | + | 14.2628i | 0.762513 | + | 0.646973i | |||||
0.442222 | 0.0200390 | 0.0100195 | − | 0.999950i | ||||||
0.0100195 | + | 0.999950i | ||||||||
−17.9665 | + | 10.3730i | −0.813306 | + | 0.469562i | |||||
0 | 0 | |||||||||
18.9794 | − | 32.8732i | 0.857401 | − | 1.48506i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 45.1281i | − | 2.03041i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−25.0193 | + | 14.4449i | −1.12227 | + | 0.647941i | |||||
30.9471 | − | 31.9765i | 1.38677 | − | 1.43290i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
31.2326 | + | 18.0322i | 1.39677 | + | 0.806423i | |||||
0 | 0 | |||||||||
−4.99600 | − | 8.65333i | −0.222982 | − | 0.386217i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−22.4379 | + | 0.734344i | −0.999465 | + | 0.0327103i | |||||
−76.9250 | −3.42312 | |||||||||
0 | 0 | |||||||||
3.66612 | + | 12.8383i | 0.162818 | + | 0.570170i | |||||
18.4422 | − | 31.9429i | 0.818241 | − | 1.41724i | |||||
−32.4532 | − | 18.7369i | −1.43846 | − | 0.830497i | −0.440719 | − | 0.897645i | ||
−0.997743 | + | 0.0671482i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 22.6274i | − | 1.00000i | |||||||
26.9975 | + | 24.4698i | 1.19197 | + | 1.08037i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
40.9749 | − | 11.7008i | 1.79860 | − | 0.513609i | |||||
24.6768 | + | 42.7414i | 1.08215 | + | 1.87433i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
−45.6661 | −1.99684 | −0.998419 | − | 0.0562050i | ||||||
−0.998419 | + | 0.0562050i | ||||||||
−16.7814 | + | 9.68876i | −0.733100 | + | 0.423256i | |||||
30.9219 | − | 31.9505i | 1.34954 | − | 1.39443i | |||||
−19.7211 | + | 34.1580i | −0.859881 | + | 1.48936i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
28.4422 | + | 49.2634i | 1.23662 | + | 2.14189i | |||||
0 | 0 | |||||||||
8.38935 | + | 13.4914i | 0.364067 | + | 0.585479i | |||||
−37.1054 | −1.60872 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
14.5083 | + | 25.1292i | 0.625498 | + | 1.08339i | |||||
0 | 0 | |||||||||
−38.9502 | − | 8.41297i | −1.67615 | − | 0.362037i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
−5.27231 | − | 1.32067i | −0.226257 | − | 0.0566754i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
28.3581 | − | 8.09794i | 1.21361 | − | 0.346560i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
29.9333i | 1.27869i | |||||||||
0.719769 | + | 21.9926i | 0.0307190 | + | 0.938622i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
30.4509 | − | 31.4638i | 1.29608 | − | 1.33919i | |||||
22.9422 | − | 39.7371i | 0.975603 | − | 1.68979i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.28466 | + | 3.95715i | 0.0968913 | + | 0.167821i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
35.1430 | − | 20.2898i | 1.48506 | − | 0.857401i | |||||
0 | 0 | |||||||||
−23.6627 | + | 40.9850i | −0.998150 | + | 1.72885i | |||||
13.8054 | + | 7.97053i | 0.581827 | + | 0.335918i | 0.761859 | − | 0.647743i | ||
−0.180032 | + | 0.983661i | ||||||||
0 | 0 | |||||||||
−12.8005 | − | 22.1712i | −0.538522 | − | 0.932748i | |||||
10.8291i | 0.455181i | |||||||||
−10.5320 | + | 21.3559i | −0.442305 | + | 0.896865i | |||||
−30.8844 | −1.29588 | |||||||||
−2.44949 | + | 1.41421i | −0.102688 | + | 0.0592869i | −0.550464 | − | 0.834859i | ||
0.447777 | + | 0.894146i | ||||||||
−63.8878 | − | 16.0034i | −2.67596 | − | 0.670307i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−4.05380 | + | 1.15760i | −0.169350 | + | 0.0483596i | |||||
0 | 0 | |||||||||
86.7210i | 3.61652i | |||||||||
−21.1660 | − | 11.3137i | −0.881917 | − | 0.471405i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
20.8207 | − | 12.0208i | 0.866025 | − | 0.500000i | |||||
−24.7862 | + | 25.6107i | −1.03008 | + | 1.06434i | |||||
0 | 0 | |||||||||
41.6256 | + | 24.0326i | 1.72692 | + | 0.997039i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
52.3193 | − | 1.71229i | 2.16314 | − | 0.0707947i | |||||
−27.7265 | −1.14537 | |||||||||
7.99569 | − | 4.61631i | 0.330017 | − | 0.190536i | −0.325831 | − | 0.945428i | ||
0.655849 | + | 0.754892i | ||||||||
−6.65832 | − | 23.3167i | −0.274584 | − | 0.961563i | |||||
0 | 0 | |||||||||
−24.8696 | − | 14.3584i | −1.02386 | − | 0.591128i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−28.7601 | + | 49.8140i | −1.17609 | + | 2.03704i | |||||
9.79796 | + | 5.65685i | 0.400334 | + | 0.231133i | 0.686628 | − | 0.727009i | ||
−0.286294 | + | 0.958142i | ||||||||
45.7064 | − | 13.0519i | 1.86595 | − | 0.532843i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−48.8844 | −1.98908 | |||||||||
36.5277 | − | 21.0893i | 1.48506 | − | 0.857401i | |||||
−34.1749 | + | 35.3117i | −1.38826 | + | 1.43444i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
−34.3529 | − | 19.8337i | −1.39319 | − | 0.804361i | |||||
0 | 0 | |||||||||
−19.8871 | − | 34.4455i | −0.805206 | − | 1.39466i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
−42.6465 | + | 24.6220i | −1.72107 | + | 0.993662i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12.2474 | − | 7.07107i | −0.493064 | − | 0.284670i | 0.232781 | − | 0.972529i | ||
−0.725845 | + | 0.687859i | ||||||||
0 | 0 | |||||||||
24.8654 | + | 43.0682i | 0.999427 | + | 1.73106i | 0.529034 | + | 0.848601i | ||
0.470393 | + | 0.882457i | ||||||||
0 | 0 | |||||||||
−14.2062 | − | 44.2161i | −0.570076 | − | 1.77433i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
30.5830 | + | 7.66079i | 1.22430 | + | 0.306677i | |||||
−10.3146 | + | 17.8654i | −0.412583 | + | 0.714615i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.68972 | − | 11.5869i | −0.266949 | − | 0.462369i | |||||
0 | 0 | |||||||||
−1.40789 | − | 43.0181i | −0.0560916 | − | 1.71388i | |||||
−10.8736 | −0.432872 | −0.216436 | − | 0.976297i | ||||||
−0.216436 | + | 0.976297i | ||||||||
42.4807 | − | 24.5263i | 1.68979 | − | 0.975603i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
61.2411 | + | 35.3575i | 2.43028 | + | 1.40312i | |||||
0 | 0 | |||||||||
15.9273 | + | 27.5869i | 0.631063 | + | 1.09303i | |||||
0 | 0 | |||||||||
−15.4422 | + | 28.8898i | −0.610885 | + | 1.14286i | |||||
43.3814 | 1.71480 | |||||||||
−8.91478 | + | 5.14695i | −0.352113 | + | 0.203292i | −0.665615 | − | 0.746295i | ||
0.313503 | + | 0.949587i | ||||||||
0 | 0 | |||||||||
7.63202 | − | 13.2190i | 0.300978 | − | 0.521308i | −0.675380 | − | 0.737470i | ||
0.976358 | + | 0.216161i | ||||||||
40.9582 | + | 23.6472i | 1.61398 | + | 0.931831i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−21.1660 | + | 14.1421i | −0.831479 | + | 0.555556i | |||||
0 | 0 | |||||||||
−54.0771 | + | 31.2214i | −2.12108 | + | 1.22460i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
−18.5754 | − | 32.1735i | −0.725799 | − | 1.25712i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
−25.5444 | + | 44.2442i | −0.993561 | + | 1.72090i | −0.398664 | + | 0.917097i | ||
−0.594898 | + | 0.803801i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
25.6919 | + | 44.4997i | 0.997039 | + | 1.72692i | |||||
− | 71.1387i | − | 2.75864i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.29888 | − | 25.1461i | 0.242984 | − | 0.970030i | |||||
25.9422 | + | 44.9332i | 0.999999 | + | 1.73205i | 0.501113 | + | 0.865382i | ||
0.498886 | + | 0.866668i | ||||||||
− | 37.4166i | − | 1.44123i | |||||||
10.6442 | − | 49.2804i | 0.409696 | − | 1.89680i | |||||
−15.4170 | −0.592961 | |||||||||
−8.18524 | + | 4.72575i | −0.314584 | + | 0.181625i | −0.648976 | − | 0.760809i | ||
0.334392 | + | 0.942434i | ||||||||
−15.8643 | − | 3.97387i | −0.609264 | − | 0.152615i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
24.5395 | − | 7.00752i | 0.940356 | − | 0.268529i | |||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
−35.7292 | + | 22.2174i | −1.36614 | + | 0.849503i | |||||
−57.3882 | −2.19269 | |||||||||
22.6826 | − | 13.0958i | 0.866025 | − | 0.500000i | |||||
−35.4113 | + | 36.5892i | −1.35103 | + | 1.39597i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
60.3226 | + | 58.3806i | 2.29644 | + | 2.22251i | |||||
15.1257 | + | 26.1985i | 0.575409 | + | 0.996637i | 0.995997 | + | 0.0893857i | ||
−0.420588 | + | 0.907252i | ||||||||
49.2050i | 1.87049i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−7.58667 | + | 4.38017i | −0.287779 | + | 0.166149i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
35.0650 | + | 20.2448i | 1.32723 | + | 0.766277i | |||||
−8.48574 | + | 33.8763i | −0.320960 | + | 1.28132i | |||||
25.6710 | + | 44.4634i | 0.970272 | + | 1.68056i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
22.4575 | − | 24.7774i | 0.847604 | − | 0.935162i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−45.9672 | − | 26.5392i | −1.72877 | − | 0.998109i | |||||
−17.6397 | + | 5.03721i | −0.662942 | + | 0.189310i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
− | 59.2118i | − | 2.22218i | |||||||
−1.70185 | − | 52.0002i | −0.0638244 | − | 1.95016i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
27.6791 | + | 26.7881i | 1.03370 | + | 1.00042i | |||||
−9.55452 | − | 16.5489i | −0.356572 | − | 0.617600i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
21.6907 | − | 40.5796i | 0.808365 | − | 1.51231i | |||||
0 | 0 | |||||||||
−36.9527 | + | 21.3347i | −1.37524 | + | 0.793994i | |||||
0 | 0 | |||||||||
3.13802 | − | 5.43520i | 0.116623 | − | 0.201998i | |||||
0 | 0 | |||||||||
6.54707 | − | 26.1369i | 0.242984 | − | 0.970030i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
34.0540i | 1.26213i | |||||||||
2.64575 | + | 26.8701i | 0.0979908 | + | 0.995187i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.6470 | − | 6.17387i | −0.910979 | − | 0.228193i | |||||
25.0267 | − | 43.3475i | 0.924383 | − | 1.60108i | 0.131832 | − | 0.991272i | ||
0.792551 | − | 0.609806i | ||||||||
0 | 0 | |||||||||
44.7029 | − | 12.7654i | 1.64889 | − | 0.470858i | |||||
25.2799 | + | 43.7861i | 0.931831 | + | 1.61398i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
38.4376 | − | 39.7162i | 1.41204 | − | 1.45901i | |||||
0 | 0 | |||||||||
−6.48074 | − | 3.74166i | −0.237755 | − | 0.137268i | 0.376389 | − | 0.926462i | ||
−0.614145 | + | 0.789193i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
54.4716 | − | 1.78273i | 1.99301 | − | 0.0652268i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12.1283 | + | 42.4718i | 0.442862 | + | 1.55085i | |||||
2.77889 | − | 4.81318i | 0.101403 | − | 0.175635i | −0.810860 | − | 0.585240i | ||
0.912263 | + | 0.409605i | ||||||||
0 | 0 | |||||||||
2.97356 | − | 11.8709i | 0.108363 | − | 0.432599i | |||||
0 | 0 | |||||||||
− | 93.7216i | − | 3.41088i | |||||||
−20.3725 | − | 18.4651i | −0.740942 | − | 0.671569i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
38.0252 | − | 65.8616i | 1.37932 | − | 2.38905i | |||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
43.4377 | − | 12.4041i | 1.57358 | − | 0.449353i | |||||
0 | 0 | |||||||||
− | 4.86804i | − | 0.176119i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.8703 | − | 12.0495i | 0.753582 | − | 0.435081i | |||||
19.2728 | − | 19.9138i | 0.695446 | − | 0.718579i | |||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−20.5772 | − | 35.6408i | −0.740591 | − | 1.28274i | |||||
40.8077i | 1.46775i | 0.679285 | + | 0.733875i | ||||||
−0.679285 | + | 0.733875i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−14.6873 | + | 58.6339i | −0.525890 | + | 2.09943i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
28.0000 | 1.00000 | |||||||||
22.2146 | − | 12.8256i | 0.792871 | − | 0.457764i | |||||
−23.0213 | − | 5.76664i | −0.821142 | − | 0.205689i | |||||
−22.6105 | + | 39.1626i | −0.805978 | + | 1.39600i | 0.109650 | + | 0.993970i | ||
−0.915629 | + | 0.402025i | ||||||||
0 | 0 | |||||||||
−46.4499 | + | 13.2643i | −1.65366 | + | 0.472220i | |||||
47.0219 | + | 81.4443i | 1.67296 | + | 2.89766i | |||||
− | 17.6648i | − | 0.628087i | |||||||
0 | 0 | |||||||||
33.3782 | 1.18529 | |||||||||
46.2118 | − | 26.6804i | 1.64000 | − | 0.946852i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
18.1640 | + | 10.4870i | 0.643403 | + | 0.371469i | 0.785924 | − | 0.618323i | ||
−0.142521 | + | 0.989792i | ||||||||
−32.6555 | − | 31.6043i | −1.15599 | − | 1.11878i | |||||
0 | 0 | |||||||||
54.8869i | 1.94054i | |||||||||
0 | 0 | |||||||||
45.4422 | 1.60462 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−45.3366 | + | 78.5253i | −1.59791 | + | 2.76765i | |||||
0 | 0 | |||||||||
−8.63518 | + | 34.4729i | −0.303973 | + | 1.21350i | |||||
−28.3716 | − | 49.1410i | −0.998109 | − | 1.72877i | |||||
31.1127i | 1.09386i | 0.837177 | + | 0.546932i | ||||||
−0.837177 | + | 0.546932i | ||||||||
−27.1134 | − | 40.5796i | −0.952667 | − | 1.42582i | |||||
−48.4452 | −1.70114 | −0.850570 | − | 0.525861i | ||||||
−0.850570 | + | 0.525861i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
31.8546 | + | 17.0270i | 1.11309 | + | 0.594972i | |||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
−25.4955 | + | 26.3435i | −0.889256 | + | 0.918836i | |||||
−13.2288 | + | 22.9129i | −0.461125 | + | 0.798693i | −0.999017 | − | 0.0443211i | ||
0.537892 | + | 0.843014i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9.90735 | − | 17.1600i | −0.344721 | − | 0.597074i | |||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
53.5982 | − | 1.75415i | 1.86266 | − | 0.0609609i | |||||
1.32653 | 0.0460723 | 0.0230361 | − | 0.999735i | ||||||
0.0230361 | + | 0.999735i | ||||||||
−85.3150 | + | 49.2566i | −2.96133 | + | 1.70972i | |||||
0 | 0 | |||||||||
−18.2026 | + | 31.5279i | −0.631063 | + | 1.09303i | |||||
0 | 0 | |||||||||
−1.35980 | + | 5.42854i | −0.0470861 | + | 0.187975i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
11.6987 | 0.404125 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
48.2102 | + | 12.0762i | 1.66341 | + | 0.416670i | |||||
14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
−55.7336 | + | 15.9153i | −1.91957 | + | 0.548153i | |||||
0 | 0 | |||||||||
− | 29.5576i | − | 1.01681i | |||||||
0 | 0 | |||||||||
29.1033 | 1.00000 | |||||||||
0 | 0 | |||||||||
−9.22362 | + | 9.53043i | −0.316554 | + | 0.327084i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−27.1806 | − | 26.3056i | −0.931193 | − | 0.901216i | |||||
−17.8370 | − | 30.8947i | −0.610729 | − | 1.05781i | −0.991118 | − | 0.132987i | ||
0.380389 | − | 0.924827i | ||||||||
− | 27.4443i | − | 0.939125i | |||||||
−42.5953 | − | 68.5002i | −1.45673 | − | 2.34266i | |||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
27.1612 | − | 47.0446i | 0.926728 | − | 1.60514i | 0.137969 | − | 0.990437i | ||
0.788759 | − | 0.614703i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
26.4575 | + | 45.8258i | 0.901146 | + | 1.56083i | |||||
− | 14.5365i | − | 0.494830i | −0.968910 | − | 0.247415i | ||||
0.968910 | − | 0.247415i | ||||||||
−8.99131 | − | 27.9849i | −0.305890 | − | 0.952067i | |||||
−94.3362 | −3.20753 | |||||||||
0 | 0 | |||||||||
28.5624 | + | 7.15464i | 0.970030 | + | 0.242984i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
88.6348 | 2.99812 | |||||||||
−41.3169 | + | 23.8543i | −1.39677 | + | 0.806423i | |||||
0 | 0 | |||||||||
0 | 0 | 0.500000 | − | 0.866025i | ||||||
−0.500000 | + | 0.866025i | ||||||||
0 | 0 | |||||||||
−24.4014 | − | 23.6159i | −0.823039 | − | 0.796544i | |||||
0 | 0 | |||||||||
0 | 0 | − | 1.00000i | |||||||
1.00000i | ||||||||||
14.0000 | − | 26.1916i | 0.471405 | − | 0.881917i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
−9.65737 | − | 33.8190i | −0.324629 | − | 1.13681i | |||||
0 | 0 | |||||||||
0 | 0 | −0.866025 | − | 0.500000i | ||||||
0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
24.3968 | + | 42.2564i | 0.818241 | + | 1.41724i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
25.9230 | + | 14.9666i | 0.866025 | + | 0.500000i | |||||
−67.7398 | + | 19.3438i | −2.26177 | + | 0.645871i | |||||
−7.78817 | − | 13.4895i | −0.259895 | − | 0.450151i | |||||
0 | 0 | |||||||||
51.3420 | + | 27.4434i | 1.71140 | + | 0.914781i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.44222 | − | 16.3544i | 0.314044 | − | 0.543940i | |||||
10.4204 | + | 6.01622i | 0.346386 | + | 0.199986i | |||||
−43.0220 | − | 41.6370i | −1.42931 | − | 1.38330i | |||||
0 | 0 | −0.500000 | − | 0.866025i | ||||||
0.500000 | + | 0.866025i | ||||||||
29.4685i | 0.977946i | |||||||||
−60.1530 | + | 1.96867i | −1.99515 | + | 0.0652968i | |||||
−65.2886 | −2.16429 | |||||||||
−0.182592 | + | 0.105420i | −0.00604956 | + | 0.00349271i | −0.503022 | − | 0.864274i | ||
0.496972 | + | 0.867766i | ||||||||
−13.3400 | − | 46.7150i | −0.441730 | − | 1.54689i | |||||
0 | 0 | |||||||||
48.2404 | + | 27.8516i | 1.59565 | + | 0.921249i | |||||
11.8366 | − | 47.2534i | 0.391305 | − | 1.56215i | |||||
−29.3981 | − | 50.9189i | −0.971339 | − | 1.68241i | |||||
− | 25.6341i | − | 0.846511i | |||||||
0 | 0 | |||||||||
−14.4063 | −0.475221 | −0.237610 | − | 0.971361i | ||||||
−0.237610 | + | 0.971361i | ||||||||
−83.9471 | + | 48.4669i | −2.76765 | + | 1.59791i | |||||
−58.5038 | − | 14.6547i | −1.92776 | − | 0.482889i | |||||
−28.2103 | + | 48.8617i | −0.929057 | + | 1.60917i | |||||
43.0328 | + | 24.8450i | 1.41644 | + | 0.817783i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
60.2775i | 1.98084i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
24.5429 | − | 42.5096i | 0.804361 | − | 1.39319i | |||||
−34.9230 | − | 20.1628i | −1.14394 | − | 0.660454i | |||||
0 | 0 | |||||||||
−29.4365 | − | 50.9855i | −0.963192 | − | 1.66830i | |||||
0 | 0 | |||||||||
20.3903 | + | 32.7910i | 0.666479 | + | 1.07181i | |||||
0 | 0 | 1.00000 | ||||||||
−1.00000 | ||||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−35.4825 | − | 20.4859i | −1.15670 | − | 0.667820i | −0.206187 | − | 0.978513i | ||
−0.950510 | + | 0.310693i | ||||||||
3.98164 | − | 15.8953i | 0.129729 | − | 0.517897i | |||||
0 | 0 | |||||||||
− | 21.1828i | − | 0.689442i | |||||||
35.4014 | − | 39.0584i | 1.15161 | − | 1.27057i | |||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
58.2763 | + | 14.5977i | 1.89273 | + | 0.474113i | |||||
0 | 0 | |||||||||
83.3292 | + | 48.1101i | 2.70356 | + | 1.56090i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
29.9333i | 0.969633i | 0.874616 | + | 0.484817i | ||||||
−0.874616 | + | 0.484817i | ||||||||
0 | 0 | |||||||||
9.33303 | 0.302010 | |||||||||
−38.5193 | + | 22.2391i | −1.24580 | + | 0.719264i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−34.2929 | − | 19.7990i | −1.10737 | − | 0.639343i | |||||
38.1789 | + | 36.9499i | 1.23222 | + | 1.19255i | |||||
−15.5000 | − | 26.8468i | −0.500000 | − | 0.866025i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
68.3308 | − | 39.4508i | 2.19965 | − | 1.26997i | |||||
15.9049 | + | 55.6972i | 0.511733 | + | 1.79203i | |||||
−24.2211 | + | 41.9522i | −0.778898 | + | 1.34909i | 0.153679 | + | 0.988121i | ||
−0.932577 | + | 0.360971i | ||||||||
26.9444 | + | 15.5563i | 0.866025 | + | 0.500000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
31.2787i | 1.00378i | 0.864931 | + | 0.501891i | ||||||
−0.864931 | + | 0.501891i | ||||||||
−30.6732 | − | 5.58187i | −0.983842 | − | 0.179039i | |||||
−6.04465 | −0.193783 | |||||||||
−0.541609 | + | 0.312698i | −0.0173543 | + | 0.0100195i | |||||
−74.1846 | − | 18.5826i | −2.37581 | − | 0.595120i | |||||
14.6696 | − | 25.4085i | 0.469562 | − | 0.813306i | |||||
51.8459 | + | 29.9333i | 1.65870 | + | 0.957650i | 0.973317 | + | 0.229465i | ||
0.685381 | + | 0.728184i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
53.6818i | 1.71480i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | 0.866025 | − | 0.500000i | ||||||
−0.866025 | + | 0.500000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
31.9104 | + | 55.2704i | 1.01521 | + | 1.75839i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−37.0405 | −1.17663 | −0.588315 | − | 0.808632i | ||||||
−0.588315 | + | 0.808632i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
20.4281 | − | 35.3826i | 0.647941 | − | 1.12227i | |||||
0 | 0 | |||||||||
−15.2915 | + | 61.0460i | −0.484530 | + | 1.93432i | |||||
30.9671 | + | 53.6365i | 0.980737 | + | 1.69869i | 0.659533 | + | 0.751675i | ||
0.321203 | + | 0.947010i | ||||||||
0 | 0 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.cc.a.293.1 | ✓ | 16 | |
7.6 | odd | 2 | inner | 504.2.cc.a.293.4 | yes | 16 | |
8.5 | even | 2 | inner | 504.2.cc.a.293.4 | yes | 16 | |
9.2 | odd | 6 | inner | 504.2.cc.a.461.1 | yes | 16 | |
56.13 | odd | 2 | CM | 504.2.cc.a.293.1 | ✓ | 16 | |
63.20 | even | 6 | inner | 504.2.cc.a.461.4 | yes | 16 | |
72.29 | odd | 6 | inner | 504.2.cc.a.461.4 | yes | 16 | |
504.461 | even | 6 | inner | 504.2.cc.a.461.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.cc.a.293.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
504.2.cc.a.293.1 | ✓ | 16 | 56.13 | odd | 2 | CM | |
504.2.cc.a.293.4 | yes | 16 | 7.6 | odd | 2 | inner | |
504.2.cc.a.293.4 | yes | 16 | 8.5 | even | 2 | inner | |
504.2.cc.a.461.1 | yes | 16 | 9.2 | odd | 6 | inner | |
504.2.cc.a.461.1 | yes | 16 | 504.461 | even | 6 | inner | |
504.2.cc.a.461.4 | yes | 16 | 63.20 | even | 6 | inner | |
504.2.cc.a.461.4 | yes | 16 | 72.29 | odd | 6 | inner |