Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1100,2,Mod(221,1100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1100, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 6, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1100.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 1100.q (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 221.9 | ||
Character | 1100.221 | ||
Dual form | 1100.2.q.b.881.9 |
-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 | |||||||||
0.921658 | + | 0.669624i | 0.532120 | + | 0.386608i | 0.821150 | − | 0.570712i | ||
−0.289030 | + | 0.957320i | ||||||||
0 | 0 | |||||||||
−1.47725 | + | 1.67861i | −0.660644 | + | 0.750699i | |||||
0 | 0 | |||||||||
−4.58549 | −1.73315 | −0.866577 | − | 0.499044i | ||||||
−0.866577 | + | 0.499044i | ||||||||
0 | 0 | |||||||||
−0.525993 | − | 1.61884i | −0.175331 | − | 0.539614i | |||||
0 | 0 | |||||||||
−0.309017 | + | 0.951057i | −0.0931721 | + | 0.286754i | |||||
0 | 0 | |||||||||
0.545520 | + | 1.67894i | 0.151300 | + | 0.465654i | 0.997767 | − | 0.0667872i | ||
−0.846467 | + | 0.532441i | ||||||||
0 | 0 | |||||||||
−2.48556 | + | 0.557910i | −0.641768 | + | 0.144052i | |||||
0 | 0 | |||||||||
5.64523 | − | 4.10150i | 1.36917 | − | 0.994759i | 0.371367 | − | 0.928486i | ||
0.997802 | − | 0.0662726i | ||||||||
0 | 0 | |||||||||
0.225177 | − | 0.163601i | 0.0516592 | − | 0.0375326i | −0.561656 | − | 0.827371i | ||
0.613315 | + | 0.789838i | ||||||||
0 | 0 | |||||||||
−4.22626 | − | 3.07056i | −0.922245 | − | 0.670050i | |||||
0 | 0 | |||||||||
0.433073 | − | 1.33286i | 0.0903020 | − | 0.277921i | −0.895699 | − | 0.444661i | ||
0.986001 | + | 0.166740i | ||||||||
0 | 0 | |||||||||
−0.635492 | − | 4.95945i | −0.127098 | − | 0.991890i | |||||
0 | 0 | |||||||||
1.65535 | − | 5.09466i | 0.318573 | − | 0.980467i | |||||
0 | 0 | |||||||||
−4.48401 | − | 3.25782i | −0.832659 | − | 0.604962i | 0.0876513 | − | 0.996151i | ||
−0.920310 | + | 0.391189i | ||||||||
0 | 0 | |||||||||
−1.75233 | + | 1.27315i | −0.314728 | + | 0.228664i | −0.733923 | − | 0.679233i | ||
0.419194 | + | 0.907897i | ||||||||
0 | 0 | |||||||||
−0.921658 | + | 0.669624i | −0.160440 | + | 0.116567i | |||||
0 | 0 | |||||||||
6.77390 | − | 7.69727i | 1.14500 | − | 1.30108i | |||||
0 | 0 | |||||||||
−3.20398 | − | 9.86084i | −0.526731 | − | 1.62111i | −0.760867 | − | 0.648908i | ||
0.234135 | − | 0.972204i | ||||||||
0 | 0 | |||||||||
−0.621474 | + | 1.91270i | −0.0995155 | + | 0.306277i | |||||
0 | 0 | |||||||||
−0.479808 | − | 1.47670i | −0.0749334 | − | 0.230621i | 0.906574 | − | 0.422048i | ||
−0.981507 | + | 0.191427i | ||||||||
0 | 0 | |||||||||
−10.0846 | −1.53789 | −0.768944 | − | 0.639316i | ||||||
−0.768944 | + | 0.639316i | ||||||||
0 | 0 | |||||||||
3.49443 | + | 1.50849i | 0.520919 | + | 0.224872i | |||||
0 | 0 | |||||||||
−8.19224 | − | 5.95201i | −1.19496 | − | 0.868190i | −0.201181 | − | 0.979554i | ||
−0.993780 | + | 0.111364i | ||||||||
0 | 0 | |||||||||
14.0267 | 2.00382 | |||||||||
0 | 0 | |||||||||
7.94943 | 1.11314 | |||||||||
0 | 0 | |||||||||
−8.31392 | − | 6.04042i | −1.14201 | − | 0.829715i | −0.154608 | − | 0.987976i | ||
−0.987397 | + | 0.158260i | ||||||||
0 | 0 | |||||||||
−1.13996 | − | 1.92366i | −0.153713 | − | 0.259387i | |||||
0 | 0 | |||||||||
0.317087 | 0.0419992 | |||||||||
0 | 0 | |||||||||
1.65927 | + | 5.10671i | 0.216019 | + | 0.664837i | 0.999080 | + | 0.0428920i | ||
−0.783061 | + | 0.621945i | ||||||||
0 | 0 | |||||||||
−0.419275 | + | 1.29039i | −0.0536826 | + | 0.165218i | −0.974303 | − | 0.225240i | ||
0.920621 | + | 0.390458i | ||||||||
0 | 0 | |||||||||
2.41194 | + | 7.42318i | 0.303876 | + | 0.935233i | |||||
0 | 0 | |||||||||
−3.62416 | − | 1.56449i | −0.449521 | − | 0.194051i | |||||
0 | 0 | |||||||||
7.20492 | − | 5.23468i | 0.880221 | − | 0.639518i | −0.0530889 | − | 0.998590i | ||
0.933310 | + | 0.359072i | ||||||||
0 | 0 | |||||||||
1.29166 | − | 0.938447i | 0.155498 | − | 0.112976i | |||||
0 | 0 | |||||||||
11.8891 | + | 8.63790i | 1.41097 | + | 1.02513i | 0.993180 | + | 0.116587i | ||
0.417791 | + | 0.908543i | ||||||||
0 | 0 | |||||||||
−2.82642 | + | 8.69883i | −0.330808 | + | 1.01812i | 0.637943 | + | 0.770084i | ||
−0.968750 | + | 0.248038i | ||||||||
0 | 0 | |||||||||
2.73526 | − | 4.99646i | 0.315841 | − | 0.576941i | |||||
0 | 0 | |||||||||
1.41700 | − | 4.36106i | 0.161482 | − | 0.496989i | |||||
0 | 0 | |||||||||
−2.03346 | − | 1.47739i | −0.228782 | − | 0.166220i | 0.467489 | − | 0.883999i | ||
−0.696271 | + | 0.717779i | ||||||||
0 | 0 | |||||||||
0.805971 | − | 0.585572i | 0.0895523 | − | 0.0650636i | |||||
0 | 0 | |||||||||
2.57741 | − | 1.87260i | 0.282908 | − | 0.205545i | −0.437277 | − | 0.899327i | ||
0.720185 | + | 0.693782i | ||||||||
0 | 0 | |||||||||
−1.45455 | + | 15.5351i | −0.157768 | + | 1.68502i | |||||
0 | 0 | |||||||||
−1.95121 | − | 6.00519i | −0.209191 | − | 0.643824i | |||||
0 | 0 | |||||||||
−3.18037 | + | 9.78818i | −0.337119 | + | 1.03754i | 0.628550 | + | 0.777769i | ||
−0.965669 | + | 0.259776i | ||||||||
0 | 0 | |||||||||
−2.50148 | − | 7.69876i | −0.262226 | − | 0.807049i | |||||
0 | 0 | |||||||||
−2.46758 | −0.255876 | |||||||||
0 | 0 | |||||||||
−0.0580193 | + | 0.619664i | −0.00595265 | + | 0.0635762i | |||||
0 | 0 | |||||||||
13.8642 | + | 10.0729i | 1.40770 | + | 1.02275i | 0.993652 | + | 0.112497i | ||
0.414047 | + | 0.910256i | ||||||||
0 | 0 | |||||||||
1.70215 | 0.171073 | |||||||||
0 | 0 | |||||||||
−10.6373 | −1.05845 | −0.529224 | − | 0.848482i | ||||||
−0.529224 | + | 0.848482i | ||||||||
0 | 0 | |||||||||
2.75387 | + | 2.00080i | 0.271346 | + | 0.197145i | 0.715134 | − | 0.698987i | ||
−0.443788 | + | 0.896132i | ||||||||
0 | 0 | |||||||||
11.3975 | − | 2.55829i | 1.11228 | − | 0.249664i | |||||
0 | 0 | |||||||||
−17.5843 | −1.69994 | −0.849968 | − | 0.526834i | ||||||
−0.849968 | + | 0.526834i | ||||||||
0 | 0 | |||||||||
−4.60659 | − | 14.1776i | −0.441231 | − | 1.35797i | −0.886564 | − | 0.462605i | ||
0.445333 | − | 0.895365i | ||||||||
0 | 0 | |||||||||
3.65008 | − | 11.2338i | 0.346450 | − | 1.06626i | |||||
0 | 0 | |||||||||
1.52667 | + | 4.69861i | 0.143617 | + | 0.442008i | 0.996831 | − | 0.0795537i | ||
−0.853213 | + | 0.521562i | ||||||||
0 | 0 | |||||||||
1.59761 | + | 2.69593i | 0.148978 | + | 0.251396i | |||||
0 | 0 | |||||||||
2.43099 | − | 1.76622i | 0.224746 | − | 0.163287i | |||||
0 | 0 | |||||||||
−25.8861 | + | 18.8074i | −2.37298 | + | 1.72407i | |||||
0 | 0 | |||||||||
−0.809017 | − | 0.587785i | −0.0735470 | − | 0.0534350i | |||||
0 | 0 | |||||||||
0.546613 | − | 1.68230i | 0.0492864 | − | 0.151688i | |||||
0 | 0 | |||||||||
9.26378 | + | 6.25958i | 0.828578 | + | 0.559874i | |||||
0 | 0 | |||||||||
−3.84281 | + | 11.8270i | −0.340994 | + | 1.04947i | 0.622699 | + | 0.782462i | ||
−0.963693 | + | 0.267011i | ||||||||
0 | 0 | |||||||||
−9.29456 | − | 6.75289i | −0.818340 | − | 0.594559i | |||||
0 | 0 | |||||||||
−0.0419436 | + | 0.0304738i | −0.00366463 | + | 0.00266251i | −0.589616 | − | 0.807684i | ||
0.585951 | + | 0.810346i | ||||||||
0 | 0 | |||||||||
−1.03255 | + | 0.750190i | −0.0895332 | + | 0.0650497i | |||||
0 | 0 | |||||||||
6.10660 | + | 10.3048i | 0.525573 | + | 0.886893i | |||||
0 | 0 | |||||||||
−5.54272 | − | 17.0587i | −0.473546 | − | 1.45743i | −0.847908 | − | 0.530143i | ||
0.374362 | − | 0.927283i | ||||||||
0 | 0 | |||||||||
−4.53157 | + | 13.9467i | −0.384362 | + | 1.18295i | 0.552579 | + | 0.833460i | ||
−0.936942 | + | 0.349486i | ||||||||
0 | 0 | |||||||||
−3.56484 | − | 10.9714i | −0.300213 | − | 0.923962i | |||||
0 | 0 | |||||||||
−1.76534 | −0.147625 | |||||||||
0 | 0 | |||||||||
12.0926 | − | 2.71432i | 1.00424 | − | 0.225412i | |||||
0 | 0 | |||||||||
12.9279 | + | 9.39264i | 1.06627 | + | 0.774692i | |||||
0 | 0 | |||||||||
6.79887 | 0.556985 | 0.278492 | − | 0.960438i | ||||||
0.278492 | + | 0.960438i | ||||||||
0 | 0 | |||||||||
2.83345 | 0.230583 | 0.115291 | − | 0.993332i | ||||||
0.115291 | + | 0.993332i | ||||||||
0 | 0 | |||||||||
−9.60902 | − | 6.98136i | −0.776843 | − | 0.564410i | |||||
0 | 0 | |||||||||
0.451508 | − | 4.82224i | 0.0362660 | − | 0.387332i | |||||
0 | 0 | |||||||||
−3.72445 | −0.297244 | −0.148622 | − | 0.988894i | ||||||
−0.148622 | + | 0.988894i | ||||||||
0 | 0 | |||||||||
−3.61779 | − | 11.1344i | −0.286909 | − | 0.883016i | |||||
0 | 0 | |||||||||
−1.98585 | + | 6.11183i | −0.156507 | + | 0.481680i | |||||
0 | 0 | |||||||||
−7.65663 | − | 23.5647i | −0.599713 | − | 1.84573i | −0.529706 | − | 0.848181i | ||
−0.0700069 | − | 0.997547i | ||||||||
0 | 0 | |||||||||
0.237475 | − | 2.53631i | 0.0184874 | − | 0.197451i | |||||
0 | 0 | |||||||||
−13.3087 | + | 9.66933i | −1.02986 | + | 0.748235i | −0.968280 | − | 0.249867i | ||
−0.0615774 | + | 0.998102i | ||||||||
0 | 0 | |||||||||
7.99598 | − | 5.80942i | 0.615075 | − | 0.446878i | |||||
0 | 0 | |||||||||
−0.383285 | − | 0.278473i | −0.0293105 | − | 0.0212954i | |||||
0 | 0 | |||||||||
3.87771 | − | 11.9343i | 0.294816 | − | 0.907352i | −0.688467 | − | 0.725268i | ||
0.983283 | − | 0.182084i | ||||||||
0 | 0 | |||||||||
2.91404 | + | 22.7415i | 0.220281 | + | 1.71910i | |||||
0 | 0 | |||||||||
−1.89029 | + | 5.81773i | −0.142083 | + | 0.437287i | |||||
0 | 0 | |||||||||
−3.89837 | − | 2.83233i | −0.291378 | − | 0.211698i | 0.432487 | − | 0.901640i | ||
−0.723865 | + | 0.689942i | ||||||||
0 | 0 | |||||||||
17.6958 | − | 12.8567i | 1.31532 | − | 0.955633i | 0.315338 | − | 0.948979i | ||
0.999978 | − | 0.00665351i | ||||||||
0 | 0 | |||||||||
−1.25051 | + | 0.908547i | −0.0924401 | + | 0.0671617i | |||||
0 | 0 | |||||||||
21.2856 | + | 9.18863i | 1.56495 | + | 0.675562i | |||||
0 | 0 | |||||||||
2.15628 | + | 6.63636i | 0.157683 | + | 0.485299i | |||||
0 | 0 | |||||||||
−7.59062 | + | 23.3615i | −0.552136 | + | 1.69930i | |||||
0 | 0 | |||||||||
−0.110617 | − | 0.340443i | −0.00800394 | − | 0.0246336i | 0.946975 | − | 0.321308i | ||
−0.954979 | + | 0.296674i | ||||||||
0 | 0 | |||||||||
−8.83535 | −0.635983 | −0.317991 | − | 0.948094i | ||||||
−0.317991 | + | 0.948094i | ||||||||
0 | 0 | |||||||||
−2.29262 | − | 3.86874i | −0.164178 | − | 0.277047i | |||||
0 | 0 | |||||||||
−18.0192 | − | 13.0917i | −1.28381 | − | 0.932746i | −0.284154 | − | 0.958779i | ||
−0.999661 | + | 0.0260325i | ||||||||
0 | 0 | |||||||||
−2.73266 | −0.193713 | −0.0968564 | − | 0.995298i | ||||||
−0.0968564 | + | 0.995298i | ||||||||
0 | 0 | |||||||||
10.1457 | 0.715625 | |||||||||
0 | 0 | |||||||||
20.5614 | + | 14.9387i | 1.44313 | + | 1.04849i | |||||
0 | 0 | |||||||||
3.18760 | + | 1.37603i | 0.222632 | + | 0.0961062i | |||||
0 | 0 | |||||||||
−2.38549 | −0.165803 | |||||||||
0 | 0 | |||||||||
0.0860100 | + | 0.264711i | 0.00594943 | + | 0.0183105i | |||||
0 | 0 | |||||||||
4.73541 | − | 14.5741i | 0.325999 | − | 1.00332i | −0.644989 | − | 0.764192i | ||
0.970988 | − | 0.239129i | ||||||||
0 | 0 | |||||||||
5.17350 | + | 15.9224i | 0.354482 | + | 1.09098i | |||||
0 | 0 | |||||||||
14.8974 | − | 16.9282i | 1.01600 | − | 1.15449i | |||||
0 | 0 | |||||||||
8.03531 | − | 5.83800i | 0.545473 | − | 0.396309i | |||||
0 | 0 | |||||||||
−8.42994 | + | 6.12471i | −0.569643 | + | 0.413870i | |||||
0 | 0 | |||||||||
9.96574 | + | 7.24054i | 0.670369 | + | 0.487051i | |||||
0 | 0 | |||||||||
−4.53228 | + | 13.9489i | −0.303504 | + | 0.934090i | 0.676727 | + | 0.736234i | ||
−0.980231 | + | 0.197856i | ||||||||
0 | 0 | |||||||||
−7.69430 | + | 3.63740i | −0.512953 | + | 0.242493i | |||||
0 | 0 | |||||||||
0.260500 | − | 0.801738i | 0.0172900 | − | 0.0532132i | −0.942039 | − | 0.335503i | ||
0.959329 | + | 0.282289i | ||||||||
0 | 0 | |||||||||
6.76463 | + | 4.91479i | 0.447019 | + | 0.324778i | 0.788418 | − | 0.615140i | ||
−0.341399 | + | 0.939919i | ||||||||
0 | 0 | |||||||||
4.22626 | − | 3.07056i | 0.278067 | − | 0.202028i | |||||
0 | 0 | |||||||||
4.34638 | − | 3.15783i | 0.284741 | − | 0.206876i | −0.436242 | − | 0.899829i | ||
0.720982 | + | 0.692953i | ||||||||
0 | 0 | |||||||||
22.0931 | − | 4.95903i | 1.44119 | − | 0.323492i | |||||
0 | 0 | |||||||||
−0.884854 | − | 2.72330i | −0.0574775 | − | 0.176897i | |||||
0 | 0 | |||||||||
−6.49070 | + | 19.9763i | −0.419849 | + | 1.29216i | 0.487993 | + | 0.872848i | ||
−0.907841 | + | 0.419314i | ||||||||
0 | 0 | |||||||||
−4.00121 | − | 12.3145i | −0.257740 | − | 0.793244i | −0.993277 | − | 0.115759i | ||
0.735537 | − | 0.677485i | ||||||||
0 | 0 | |||||||||
−14.9356 | −0.958118 | |||||||||
0 | 0 | |||||||||
−20.7209 | + | 23.5455i | −1.32381 | + | 1.50427i | |||||
0 | 0 | |||||||||
0.397514 | + | 0.288811i | 0.0252932 | + | 0.0183766i | |||||
0 | 0 | |||||||||
3.62943 | 0.230006 | |||||||||
0 | 0 | |||||||||
−22.4497 | −1.41701 | −0.708507 | − | 0.705704i | ||||||
−0.708507 | + | 0.705704i | ||||||||
0 | 0 | |||||||||
1.13380 | + | 0.823754i | 0.0712814 | + | 0.0517890i | |||||
0 | 0 | |||||||||
−11.7433 | + | 13.3440i | −0.735391 | + | 0.835635i | |||||
0 | 0 | |||||||||
−7.47518 | −0.466289 | −0.233144 | − | 0.972442i | ||||||
−0.233144 | + | 0.972442i | ||||||||
0 | 0 | |||||||||
14.6918 | + | 45.2168i | 0.912906 | + | 2.80964i | |||||
0 | 0 | |||||||||
−2.91534 | + | 8.97248i | −0.180455 | + | 0.555383i | |||||
0 | 0 | |||||||||
9.89291 | + | 30.4472i | 0.610023 | + | 1.87746i | 0.457645 | + | 0.889135i | ||
0.152378 | + | 0.988322i | ||||||||
0 | 0 | |||||||||
22.4212 | − | 5.03269i | 1.37733 | − | 0.309156i | |||||
0 | 0 | |||||||||
−9.48561 | + | 6.89170i | −0.580510 | + | 0.421765i | |||||
0 | 0 | |||||||||
−11.7758 | + | 8.55564i | −0.717985 | + | 0.521647i | −0.885740 | − | 0.464182i | ||
0.167755 | + | 0.985829i | ||||||||
0 | 0 | |||||||||
−4.98543 | − | 3.62213i | −0.302843 | − | 0.220028i | 0.425976 | − | 0.904734i | ||
−0.728820 | + | 0.684706i | ||||||||
0 | 0 | |||||||||
2.84977 | − | 8.77068i | 0.172476 | − | 0.530825i | |||||
0 | 0 | |||||||||
4.91310 | + | 0.928165i | 0.296271 | + | 0.0559705i | |||||
0 | 0 | |||||||||
3.74157 | − | 11.5154i | 0.224809 | − | 0.691891i | −0.773502 | − | 0.633794i | ||
0.998311 | − | 0.0580970i | ||||||||
0 | 0 | |||||||||
2.98274 | + | 2.16708i | 0.178572 | + | 0.129740i | |||||
0 | 0 | |||||||||
−14.9792 | + | 10.8830i | −0.893582 | + | 0.649226i | −0.936810 | − | 0.349840i | ||
0.0432272 | + | 0.999065i | ||||||||
0 | 0 | |||||||||
−8.00704 | + | 5.81746i | −0.475969 | + | 0.345812i | −0.799763 | − | 0.600316i | ||
0.323794 | + | 0.946128i | ||||||||
0 | 0 | |||||||||
−0.468416 | + | 0.532267i | −0.0277465 | + | 0.0315288i | |||||
0 | 0 | |||||||||
2.20016 | + | 6.77139i | 0.129871 | + | 0.399702i | |||||
0 | 0 | |||||||||
9.79301 | − | 30.1398i | 0.576059 | − | 1.77293i | |||||
0 | 0 | |||||||||
6.03299 | + | 18.5676i | 0.353660 | + | 1.08845i | |||||
0 | 0 | |||||||||
−21.8732 | −1.27784 | −0.638922 | − | 0.769272i | ||||||
−0.638922 | + | 0.769272i | ||||||||
0 | 0 | |||||||||
−11.0233 | − | 4.75859i | −0.641804 | − | 0.277056i | |||||
0 | 0 | |||||||||
4.33378 | + | 3.14867i | 0.251471 | + | 0.182704i | |||||
0 | 0 | |||||||||
2.47404 | 0.143078 | |||||||||
0 | 0 | |||||||||
46.2429 | 2.66540 | |||||||||
0 | 0 | |||||||||
−9.80393 | − | 7.12297i | −0.563221 | − | 0.409204i | |||||
0 | 0 | |||||||||
−1.54670 | − | 2.61003i | −0.0885640 | − | 0.149450i | |||||
0 | 0 | |||||||||
13.7714 | 0.785973 | 0.392987 | − | 0.919544i | ||||||
0.392987 | + | 0.919544i | ||||||||
0 | 0 | |||||||||
1.19834 | + | 3.68811i | 0.0681711 | + | 0.209809i | |||||
0 | 0 | |||||||||
8.35233 | − | 25.7058i | 0.473617 | − | 1.45764i | −0.374196 | − | 0.927350i | ||
0.847813 | − | 0.530295i | ||||||||
0 | 0 | |||||||||
−7.32139 | − | 22.5329i | −0.413829 | − | 1.27364i | −0.913294 | − | 0.407301i | ||
0.499464 | − | 0.866334i | ||||||||
0 | 0 | |||||||||
−16.0237 | − | 6.91715i | −0.902832 | − | 0.389737i | |||||
0 | 0 | |||||||||
10.5954 | − | 7.69801i | 0.595097 | − | 0.432363i | −0.249038 | − | 0.968494i | ||
0.844135 | + | 0.536130i | ||||||||
0 | 0 | |||||||||
4.48401 | − | 3.25782i | 0.251056 | − | 0.182403i | |||||
0 | 0 | |||||||||
−16.2067 | − | 11.7749i | −0.904569 | − | 0.657208i | |||||
0 | 0 | |||||||||
0.600167 | − | 1.84713i | 0.0333942 | − | 0.102777i | |||||
0 | 0 | |||||||||
7.97994 | − | 3.77243i | 0.442647 | − | 0.209257i | |||||
0 | 0 | |||||||||
5.24798 | − | 16.1516i | 0.290214 | − | 0.893186i | |||||
0 | 0 | |||||||||
37.5655 | + | 27.2929i | 2.07105 | + | 1.50471i | |||||
0 | 0 | |||||||||
1.33122 | − | 0.967189i | 0.0731705 | − | 0.0531615i | −0.550599 | − | 0.834770i | ||
0.623769 | + | 0.781609i | ||||||||
0 | 0 | |||||||||
−14.2779 | + | 10.3735i | −0.782422 | + | 0.568463i | |||||
0 | 0 | |||||||||
−1.85642 | + | 19.8272i | −0.101427 | + | 1.08328i | |||||
0 | 0 | |||||||||
−6.94397 | − | 21.3714i | −0.378262 | − | 1.16417i | −0.941251 | − | 0.337707i | ||
0.562989 | − | 0.826465i | ||||||||
0 | 0 | |||||||||
−1.73923 | + | 5.35281i | −0.0944622 | + | 0.290725i | |||||
0 | 0 | |||||||||
−0.669332 | − | 2.05999i | −0.0362464 | − | 0.111555i | |||||
0 | 0 | |||||||||
−32.2211 | −1.73977 | |||||||||
0 | 0 | |||||||||
−0.332810 | + | 3.55452i | −0.0179179 | + | 0.191369i | |||||
0 | 0 | |||||||||
5.08911 | + | 3.69745i | 0.273198 | + | 0.198490i | 0.715945 | − | 0.698157i | ||
−0.442747 | + | 0.896646i | ||||||||
0 | 0 | |||||||||
29.5658 | 1.58262 | 0.791310 | − | 0.611415i | ||||||
0.791310 | + | 0.611415i | ||||||||
0 | 0 | |||||||||
9.45665 | 0.504759 | |||||||||
0 | 0 | |||||||||
12.4799 | + | 9.06715i | 0.664236 | + | 0.482596i | 0.868091 | − | 0.496405i | ||
−0.203855 | + | 0.979001i | ||||||||
0 | 0 | |||||||||
−32.0628 | + | 7.19683i | −1.70171 | + | 0.381968i | |||||
0 | 0 | |||||||||
−36.4520 | −1.92925 | |||||||||
0 | 0 | |||||||||
4.02855 | + | 12.3986i | 0.212619 | + | 0.654374i | 0.999314 | + | 0.0370321i | ||
−0.786695 | + | 0.617342i | ||||||||
0 | 0 | |||||||||
−5.84738 | + | 17.9964i | −0.307757 | + | 0.947179i | |||||
0 | 0 | |||||||||
−0.352042 | − | 1.08347i | −0.0184774 | − | 0.0568676i | |||||
0 | 0 | |||||||||
−10.4267 | − | 17.5948i | −0.545757 | − | 0.920953i | |||||
0 | 0 | |||||||||
10.7106 | − | 7.78171i | 0.559089 | − | 0.406202i | −0.272036 | − | 0.962287i | ||
0.831126 | + | 0.556085i | ||||||||
0 | 0 | |||||||||
−2.13816 | + | 1.55347i | −0.111308 | + | 0.0808702i | |||||
0 | 0 | |||||||||
38.1234 | + | 27.6983i | 1.97927 | + | 1.43802i | |||||
0 | 0 | |||||||||
−1.39598 | + | 4.29638i | −0.0722811 | + | 0.222458i | −0.980670 | − | 0.195667i | ||
0.908389 | + | 0.418126i | ||||||||
0 | 0 | |||||||||
4.34648 | + | 11.9724i | 0.224451 | + | 0.618254i | |||||
0 | 0 | |||||||||
3.02357 | − | 9.30558i | 0.155722 | − | 0.479262i | |||||
0 | 0 | |||||||||
−6.97127 | − | 5.06492i | −0.358090 | − | 0.260168i | 0.394165 | − | 0.919040i | ||
−0.752255 | + | 0.658872i | ||||||||
0 | 0 | |||||||||
−11.4614 | + | 8.32718i | −0.587184 | + | 0.426614i | |||||
0 | 0 | |||||||||
4.31988 | − | 3.13857i | 0.220735 | − | 0.160374i | −0.471922 | − | 0.881640i | ||
0.692658 | + | 0.721267i | ||||||||
0 | 0 | |||||||||
5.22729 | + | 8.82095i | 0.266408 | + | 0.449557i | |||||
0 | 0 | |||||||||
5.30444 | + | 16.3254i | 0.269640 | + | 0.829865i | |||||
0 | 0 | |||||||||
4.92524 | − | 15.1583i | 0.249720 | − | 0.768559i | −0.745104 | − | 0.666948i | ||
0.994824 | − | 0.101611i | ||||||||
0 | 0 | |||||||||
−3.02193 | − | 9.30055i | −0.152826 | − | 0.470349i | |||||
0 | 0 | |||||||||
−0.0590637 | −0.00297937 | |||||||||
0 | 0 | |||||||||
5.48389 | − | 1.23092i | 0.275924 | − | 0.0619342i | |||||
0 | 0 | |||||||||
−8.58441 | − | 6.23694i | −0.430839 | − | 0.313023i | 0.351145 | − | 0.936321i | ||
−0.781984 | + | 0.623298i | ||||||||
0 | 0 | |||||||||
−1.45400 | −0.0727911 | |||||||||
0 | 0 | |||||||||
2.39723 | 0.119712 | 0.0598561 | − | 0.998207i | ||||||
0.0598561 | + | 0.998207i | ||||||||
0 | 0 | |||||||||
−3.09347 | − | 2.24753i | −0.154097 | − | 0.111958i | |||||
0 | 0 | |||||||||
−0.207667 | + | 2.21795i | −0.0103191 | + | 0.110211i | |||||
0 | 0 | |||||||||
10.3683 | 0.513938 | |||||||||
0 | 0 | |||||||||
3.81628 | + | 11.7453i | 0.188703 | + | 0.580768i | 0.999992 | − | 0.00387685i | ||
−0.811290 | + | 0.584644i | ||||||||
0 | 0 | |||||||||
6.31444 | − | 19.4339i | 0.311469 | − | 0.958602i | |||||
0 | 0 | |||||||||
−7.60857 | − | 23.4168i | −0.374393 | − | 1.15226i | |||||
0 | 0 | |||||||||
−0.664098 | + | 7.09277i | −0.0325993 | + | 0.348171i | |||||
0 | 0 | |||||||||
−13.5156 | + | 9.81967i | −0.661863 | + | 0.480871i | |||||
0 | 0 | |||||||||
−11.9035 | + | 8.64837i | −0.581522 | + | 0.422500i | −0.839272 | − | 0.543711i | ||
0.257751 | + | 0.966211i | ||||||||
0 | 0 | |||||||||
25.6588 | + | 18.6422i | 1.25054 | + | 0.908567i | 0.998253 | − | 0.0590866i | ||
0.252282 | + | 0.967654i | ||||||||
0 | 0 | |||||||||
−5.32630 | + | 16.3927i | −0.258973 | + | 0.797038i | |||||
0 | 0 | |||||||||
−23.9287 | − | 25.3907i | −1.16071 | − | 1.23163i | |||||
0 | 0 | |||||||||
1.92258 | − | 5.91710i | 0.0930402 | − | 0.286348i | |||||
0 | 0 | |||||||||
−1.62704 | − | 1.18211i | −0.0785543 | − | 0.0570730i | |||||
0 | 0 | |||||||||
−4.27343 | + | 3.10483i | −0.205844 | + | 0.149554i | −0.685931 | − | 0.727666i | ||
0.480087 | + | 0.877221i | ||||||||
0 | 0 | |||||||||
22.2601 | − | 16.1729i | 1.06975 | − | 0.777221i | 0.0938847 | − | 0.995583i | ||
0.975868 | + | 0.218362i | ||||||||
0 | 0 | |||||||||
12.9628 | + | 5.59582i | 0.621519 | + | 0.268299i | |||||
0 | 0 | |||||||||
−0.120539 | − | 0.370981i | −0.00576616 | − | 0.0177464i | |||||
0 | 0 | |||||||||
10.8600 | − | 33.4237i | 0.518320 | − | 1.59523i | −0.258838 | − | 0.965921i | ||
0.777159 | − | 0.629305i | ||||||||
0 | 0 | |||||||||
−7.37797 | − | 22.7071i | −0.351332 | − | 1.08129i | |||||
0 | 0 | |||||||||
−19.1930 | −0.911889 | −0.455944 | − | 0.890008i | ||||||
−0.455944 | + | 0.890008i | ||||||||
0 | 0 | |||||||||
−11.7324 | − | 19.7982i | −0.556168 | − | 0.938523i | |||||
0 | 0 | |||||||||
6.26623 | + | 4.55268i | 0.296383 | + | 0.215335i | |||||
0 | 0 | |||||||||
4.97256 | 0.234670 | 0.117335 | − | 0.993092i | ||||||
0.117335 | + | 0.993092i | ||||||||
0 | 0 | |||||||||
1.55269 | 0.0731134 | |||||||||
0 | 0 | |||||||||
2.61147 | + | 1.89735i | 0.122698 | + | 0.0891451i | |||||
0 | 0 | |||||||||
16.6185 | + | 7.17394i | 0.779090 | + | 0.336319i | |||||
0 | 0 | |||||||||
32.8864 | 1.53836 | 0.769181 | − | 0.639031i | ||||||
0.769181 | + | 0.639031i | ||||||||
0 | 0 | |||||||||
−11.5509 | − | 35.5499i | −0.539148 | − | 1.65933i | |||||
0 | 0 | |||||||||
2.33973 | − | 7.20094i | 0.108972 | − | 0.335381i | −0.881670 | − | 0.471866i | ||
0.990642 | + | 0.136485i | ||||||||
0 | 0 | |||||||||
5.06969 | + | 15.6029i | 0.235608 | + | 0.725128i | 0.997040 | + | 0.0768831i | ||
−0.761432 | + | 0.648245i | ||||||||
0 | 0 | |||||||||
3.64522 | − | 4.14212i | 0.169043 | − | 0.192086i | |||||
0 | 0 | |||||||||
6.05684 | − | 4.40055i | 0.280277 | − | 0.203633i | −0.438761 | − | 0.898604i | ||
0.719038 | + | 0.694971i | ||||||||
0 | 0 | |||||||||
−33.0381 | + | 24.0036i | −1.52556 | + | 1.10838i | |||||
0 | 0 | |||||||||
−3.43267 | − | 2.49398i | −0.158169 | − | 0.114917i | |||||
0 | 0 | |||||||||
3.11631 | − | 9.59103i | 0.143288 | − | 0.440996i | |||||
0 | 0 | |||||||||
−0.954468 | − | 1.01279i | −0.0437940 | − | 0.0464699i | |||||
0 | 0 | |||||||||
−5.40541 | + | 16.6361i | −0.247497 | + | 0.761717i | |||||
0 | 0 | |||||||||
13.7560 | + | 9.99436i | 0.628530 | + | 0.456654i | 0.855891 | − | 0.517157i | ||
−0.227361 | + | 0.973811i | ||||||||
0 | 0 | |||||||||
14.8079 | − | 10.7586i | 0.675183 | − | 0.490549i | |||||
0 | 0 | |||||||||
−5.92291 | + | 4.30324i | −0.269502 | + | 0.195804i | |||||
0 | 0 | |||||||||
−37.3895 | + | 8.39247i | −1.69777 | + | 0.381082i | |||||
0 | 0 | |||||||||
0.709421 | + | 2.18337i | 0.0321470 | + | 0.0989381i | 0.965843 | − | 0.259130i | ||
−0.933696 | + | 0.358068i | ||||||||
0 | 0 | |||||||||
8.72268 | − | 26.8456i | 0.394453 | − | 1.21400i | |||||
0 | 0 | |||||||||
−0.814069 | − | 2.50545i | −0.0367384 | − | 0.113069i | 0.931006 | − | 0.365005i | ||
−0.967744 | + | 0.251936i | ||||||||
0 | 0 | |||||||||
−38.6752 | −1.74184 | |||||||||
0 | 0 | |||||||||
−2.51449 | + | 2.85725i | −0.113018 | + | 0.128424i | |||||
0 | 0 | |||||||||
−54.5172 | − | 39.6090i | −2.44543 | − | 1.77671i | |||||
0 | 0 | |||||||||
−13.3532 | −0.597773 | −0.298887 | − | 0.954289i | ||||||
−0.298887 | + | 0.954289i | ||||||||
0 | 0 | |||||||||
−18.7409 | −0.837281 | |||||||||
0 | 0 | |||||||||
−5.51952 | − | 4.01016i | −0.246103 | − | 0.178804i | 0.457895 | − | 0.889006i | ||
−0.703998 | + | 0.710202i | ||||||||
0 | 0 | |||||||||
15.7139 | − | 17.8559i | 0.699258 | − | 0.794576i | |||||
0 | 0 | |||||||||
11.2597 | 0.500060 | |||||||||
0 | 0 | |||||||||
3.74714 | + | 11.5325i | 0.166089 | + | 0.511170i | 0.999115 | − | 0.0420645i | ||
−0.833026 | + | 0.553234i | ||||||||
0 | 0 | |||||||||
12.9605 | − | 39.8884i | 0.573340 | − | 1.76456i | |||||
0 | 0 | |||||||||
−0.460742 | − | 1.41802i | −0.0203422 | − | 0.0626070i | |||||
0 | 0 | |||||||||
−7.42671 | + | 1.66701i | −0.327260 | + | 0.0734570i | |||||
0 | 0 | |||||||||
8.19224 | − | 5.95201i | 0.360294 | − | 0.261769i | |||||
0 | 0 | |||||||||
11.5654 | − | 8.40279i | 0.507667 | − | 0.368841i | |||||
0 | 0 | |||||||||
13.6406 | + | 9.91051i | 0.597607 | + | 0.434187i | 0.845029 | − | 0.534721i | ||
−0.247421 | + | 0.968908i | ||||||||
0 | 0 | |||||||||
6.52443 | − | 20.0801i | 0.285294 | − | 0.878043i | −0.701017 | − | 0.713145i | ||
0.986311 | − | 0.164899i | ||||||||
0 | 0 | |||||||||
−12.5425 | + | 22.9112i | −0.547400 | + | 0.999928i | |||||
0 | 0 | |||||||||
−4.67052 | + | 14.3744i | −0.203451 | + | 0.626158i | |||||
0 | 0 | |||||||||
17.0184 | + | 12.3646i | 0.739931 | + | 0.537592i | |||||
0 | 0 | |||||||||
7.39418 | − | 5.37219i | 0.320880 | − | 0.233133i | |||||
0 | 0 | |||||||||
2.21754 | − | 1.61114i | 0.0960523 | − | 0.0697861i | |||||
0 | 0 | |||||||||
25.9763 | − | 29.5172i | 1.12305 | − | 1.27614i | |||||
0 | 0 | |||||||||
−1.69637 | − | 5.22088i | −0.0732037 | − | 0.225298i | |||||
0 | 0 | |||||||||
−4.33450 | + | 13.3402i | −0.186700 | + | 0.574604i | |||||
0 | 0 | |||||||||
5.55390 | + | 17.0931i | 0.238781 | + | 0.734891i | 0.996597 | + | 0.0824238i | ||
−0.757817 | + | 0.652468i | ||||||||
0 | 0 | |||||||||
24.9186 | 1.06936 | |||||||||
0 | 0 | |||||||||
30.6038 | + | 13.2111i | 1.31092 | + | 0.565903i | |||||
0 | 0 | |||||||||
−20.8191 | − | 15.1259i | −0.890159 | − | 0.646739i | 0.0457603 | − | 0.998952i | ||
−0.935920 | + | 0.352214i | ||||||||
0 | 0 | |||||||||
2.30948 | 0.0985662 | |||||||||
0 | 0 | |||||||||
−1.54268 | −0.0657202 | |||||||||
0 | 0 | |||||||||
9.32440 | + | 6.77457i | 0.396514 | + | 0.288084i | |||||
0 | 0 | |||||||||
13.4651 | + | 22.7221i | 0.571563 | + | 0.964501i | |||||
0 | 0 | |||||||||
−8.80469 | −0.373067 | −0.186533 | − | 0.982449i | ||||||
−0.186533 | + | 0.982449i | ||||||||
0 | 0 | |||||||||
−5.50136 | − | 16.9314i | −0.232683 | − | 0.716123i | |||||
0 | 0 | |||||||||
−2.45651 | + | 7.56035i | −0.103714 | + | 0.319198i | |||||
0 | 0 | |||||||||
−5.16793 | − | 15.9053i | −0.217802 | − | 0.670326i | −0.998943 | − | 0.0459712i | ||
0.781140 | − | 0.624355i | ||||||||
0 | 0 | |||||||||
−10.1424 | − | 4.37831i | −0.426695 | − | 0.184197i | |||||
0 | 0 | |||||||||
−3.69577 | + | 2.68514i | −0.155208 | + | 0.112765i | |||||
0 | 0 | |||||||||
1.65776 | − | 1.20443i | 0.0694967 | − | 0.0504923i | −0.552494 | − | 0.833517i | ||
0.621991 | + | 0.783024i | ||||||||
0 | 0 | |||||||||
−31.0693 | − | 22.5731i | −1.30021 | − | 0.944657i | −0.300251 | − | 0.953860i | ||
−0.999958 | + | 0.00920359i | ||||||||
0 | 0 | |||||||||
0.126018 | − | 0.387843i | 0.00526448 | − | 0.0162024i | |||||
0 | 0 | |||||||||
−6.88548 | − | 1.30078i | −0.287144 | − | 0.0542463i | |||||
0 | 0 | |||||||||
−2.90734 | + | 8.94789i | −0.121034 | + | 0.372505i | −0.993158 | − | 0.116781i | ||
0.872123 | + | 0.489286i | ||||||||
0 | 0 | |||||||||
−8.14318 | − | 5.91636i | −0.338419 | − | 0.245876i | |||||
0 | 0 | |||||||||
−11.8187 | + | 8.58679i | −0.490323 | + | 0.356240i | |||||
0 | 0 | |||||||||
8.31392 | − | 6.04042i | 0.344328 | − | 0.250169i | |||||
0 | 0 | |||||||||
−0.626372 | + | 6.68984i | −0.0258973 | + | 0.276591i | |||||
0 | 0 | |||||||||
−10.7447 | − | 33.0687i | −0.443480 | − | 1.36489i | −0.884142 | − | 0.467217i | ||
0.440663 | − | 0.897673i | ||||||||
0 | 0 | |||||||||
−0.186298 | + | 0.573366i | −0.00767627 | + | 0.0236251i | |||||
0 | 0 | |||||||||
−7.84102 | − | 24.1322i | −0.322536 | − | 0.992665i | |||||
0 | 0 | |||||||||
−40.7019 | −1.67143 | −0.835713 | − | 0.549166i | ||||||
−0.835713 | + | 0.549166i | ||||||||
0 | 0 | |||||||||
6.66984 | − | 71.2360i | 0.273437 | − | 2.92039i | |||||
0 | 0 | |||||||||
−2.51858 | − | 1.82985i | −0.103078 | − | 0.0748909i | |||||
0 | 0 | |||||||||
−6.80611 | −0.278090 | −0.139045 | − | 0.990286i | ||||||
−0.139045 | + | 0.990286i | ||||||||
0 | 0 | |||||||||
−12.3566 | −0.504036 | −0.252018 | − | 0.967722i | ||||||
−0.252018 | + | 0.967722i | ||||||||
0 | 0 | |||||||||
−12.2639 | − | 8.91021i | −0.499423 | − | 0.362852i | |||||
0 | 0 | |||||||||
2.18178 | − | 0.489724i | 0.0887020 | − | 0.0199101i | |||||
0 | 0 | |||||||||
−7.11226 | −0.288678 | −0.144339 | − | 0.989528i | ||||||
−0.144339 | + | 0.989528i | ||||||||
0 | 0 | |||||||||
8.94724 | + | 27.5368i | 0.362561 | + | 1.11585i | |||||
0 | 0 | |||||||||
5.52403 | − | 17.0012i | 0.223478 | − | 0.687795i | |||||
0 | 0 | |||||||||
8.05789 | + | 24.7996i | 0.325455 | + | 1.00165i | 0.971235 | + | 0.238124i | ||
−0.645779 | + | 0.763524i | ||||||||
0 | 0 | |||||||||
2.01645 | + | 3.40272i | 0.0813113 | + | 0.137211i | |||||
0 | 0 | |||||||||
−18.3156 | + | 13.3071i | −0.737359 | + | 0.535723i | −0.891883 | − | 0.452266i | ||
0.154524 | + | 0.987989i | ||||||||
0 | 0 | |||||||||
−0.445488 | + | 0.323666i | −0.0179057 | + | 0.0130092i | −0.596702 | − | 0.802463i | ||
0.578796 | + | 0.815472i | ||||||||
0 | 0 | |||||||||
−6.07359 | − | 4.41272i | −0.243725 | − | 0.177076i | |||||
0 | 0 | |||||||||
14.5836 | − | 44.8836i | 0.584278 | − | 1.79822i | |||||
0 | 0 | |||||||||
−24.1923 | + | 6.30338i | −0.967692 | + | 0.252135i | |||||
0 | 0 | |||||||||
−0.0979853 | + | 0.301568i | −0.00391316 | + | 0.0120435i | |||||
0 | 0 | |||||||||
−58.5314 | − | 42.5256i | −2.33380 | − | 1.69560i | |||||
0 | 0 | |||||||||
2.23979 | − | 1.62730i | 0.0891646 | − | 0.0647819i | −0.542310 | − | 0.840179i | ||
0.631474 | + | 0.775397i | ||||||||
0 | 0 | |||||||||
14.1236 | − | 10.2614i | 0.561362 | − | 0.407853i | |||||
0 | 0 | |||||||||
−14.1761 | − | 23.9219i | −0.562562 | − | 0.949312i | |||||
0 | 0 | |||||||||
7.65187 | + | 23.5500i | 0.303178 | + | 0.933087i | |||||
0 | 0 | |||||||||
7.72983 | − | 23.7900i | 0.305787 | − | 0.941117i | |||||
0 | 0 | |||||||||
−0.307565 | − | 0.946588i | −0.0121481 | − | 0.0373880i | 0.944799 | − | 0.327651i | ||
−0.956947 | + | 0.290263i | ||||||||
0 | 0 | |||||||||
15.0690 | 0.594264 | 0.297132 | − | 0.954836i | ||||||
0.297132 | + | 0.954836i | ||||||||
0 | 0 | |||||||||
25.0658 | − | 5.62630i | 0.986967 | − | 0.221535i | |||||
0 | 0 | |||||||||
32.4314 | + | 23.5628i | 1.27501 | + | 0.926348i | 0.999390 | − | 0.0349197i | ||
0.275618 | + | 0.961267i | ||||||||
0 | 0 | |||||||||
−5.36951 | −0.210772 | |||||||||
0 | 0 | |||||||||
11.3151 | 0.443473 | |||||||||
0 | 0 | |||||||||
6.17534 | + | 4.48664i | 0.241660 | + | 0.175576i | 0.702022 | − | 0.712155i | ||
−0.460363 | + | 0.887731i | ||||||||
0 | 0 | |||||||||
0.0108072 | − | 0.115425i | 0.000422273 | − | 0.00451001i | |||||
0 | 0 | |||||||||
15.5687 | 0.607393 | |||||||||
0 | 0 | |||||||||
9.38662 | + | 28.8891i | 0.365651 | + | 1.12536i | 0.949572 | + | 0.313548i | ||
−0.583922 | + | 0.811810i | ||||||||
0 | 0 | |||||||||
0.602895 | − | 1.85552i | 0.0234499 | − | 0.0721714i | −0.938647 | − | 0.344880i | ||
0.962097 | + | 0.272709i | ||||||||
0 | 0 | |||||||||
4.33657 | + | 13.3466i | 0.168419 | + | 0.518339i | |||||
0 | 0 | |||||||||
0.266047 | − | 2.84146i | 0.0103169 | − | 0.110187i | |||||
0 | 0 | |||||||||
−6.28413 | + | 4.56569i | −0.243322 | + | 0.176784i | |||||
0 | 0 | |||||||||
−13.5178 | + | 9.82123i | −0.522627 | + | 0.379711i | |||||
0 | 0 | |||||||||
−1.09768 | − | 0.797508i | −0.0423753 | − | 0.0307874i | |||||
0 | 0 | |||||||||
−5.86346 | + | 18.0459i | −0.226020 | + | 0.695617i | 0.772167 | + | 0.635420i | ||
−0.998186 | + | 0.0601973i | ||||||||
0 | 0 | |||||||||
−26.3187 | − | 4.97203i | −1.01301 | − | 0.191374i | |||||
0 | 0 | |||||||||
8.84693 | − | 27.2280i | 0.340015 | − | 1.04646i | −0.624184 | − | 0.781278i | ||
0.964199 | − | 0.265181i | ||||||||
0 | 0 | |||||||||
−63.5743 | − | 46.1894i | −2.43976 | − | 1.77259i | |||||
0 | 0 | |||||||||
0.776955 | − | 0.564491i | 0.0297730 | − | 0.0216313i | |||||
0 | 0 | |||||||||
−3.99716 | + | 2.90411i | −0.152947 | + | 0.111123i | −0.661627 | − | 0.749833i | ||
0.508680 | + | 0.860956i | ||||||||
0 | 0 | |||||||||
36.8230 | + | 15.8958i | 1.40693 | + | 0.607349i | |||||
0 | 0 | |||||||||
2.94361 | + | 9.05951i | 0.112306 | + | 0.345642i | |||||
0 | 0 | |||||||||
5.60608 | − | 17.2537i | 0.213575 | − | 0.657315i | |||||
0 | 0 | |||||||||
12.1626 | + | 37.4325i | 0.462685 | + | 1.42400i | 0.861870 | + | 0.507129i | ||
−0.399185 | + | 0.916871i | ||||||||
0 | 0 | |||||||||
−7.80520 | −0.296495 | |||||||||
0 | 0 | |||||||||
−16.7169 | − | 28.2095i | −0.634110 | − | 1.07005i | |||||
0 | 0 | |||||||||
−8.76529 | − | 6.36836i | −0.332009 | − | 0.241219i | |||||
0 | 0 | |||||||||
6.12043 | 0.231496 | |||||||||
0 | 0 | |||||||||
2.25152 | 0.0850387 | 0.0425194 | − | 0.999096i | ||||||
0.0425194 | + | 0.999096i | ||||||||
0 | 0 | |||||||||
−2.33470 | − | 1.69626i | −0.0880550 | − | 0.0639757i | |||||
0 | 0 | |||||||||
23.6830 | + | 10.2235i | 0.891952 | + | 0.385040i | |||||
0 | 0 | |||||||||
48.7772 | 1.83445 | |||||||||
0 | 0 | |||||||||
7.33541 | + | 22.5761i | 0.275487 | + | 0.847863i | 0.989090 | + | 0.147312i | ||
−0.713603 | + | 0.700551i | ||||||||
0 | 0 | |||||||||
−1.32208 | + | 4.06894i | −0.0495818 | + | 0.152597i | |||||
0 | 0 | |||||||||
0.938038 | + | 2.88698i | 0.0351298 | + | 0.108118i | |||||
0 | 0 | |||||||||
2.60784 | − | 2.96333i | 0.0975277 | − | 0.110822i | |||||
0 | 0 | |||||||||
−19.3588 | + | 14.0650i | −0.722969 | + | 0.525268i | |||||
0 | 0 | |||||||||
24.5662 | − | 17.8484i | 0.916163 | − | 0.665631i | −0.0264030 | − | 0.999651i | ||
0.942566 | + | 0.334020i | ||||||||
0 | 0 | |||||||||
−12.6278 | − | 9.17466i | −0.470285 | − | 0.341682i | |||||
0 | 0 | |||||||||
4.55830 | − | 14.0290i | 0.169525 | − | 0.521745i | |||||
0 | 0 | |||||||||
−13.3075 | + | 24.3085i | −0.494226 | + | 0.902796i | |||||
0 | 0 | |||||||||
1.43839 | − | 4.42691i | 0.0533470 | − | 0.164185i | −0.920833 | − | 0.389956i | ||
0.974180 | + | 0.225771i | ||||||||
0 | 0 | |||||||||
−16.1834 | − | 11.7579i | −0.599386 | − | 0.435479i | |||||
0 | 0 | |||||||||
−56.9299 | + | 41.3620i | −2.10563 | + | 1.52983i | |||||
0 | 0 | |||||||||
30.9322 | − | 22.4735i | 1.14251 | − | 0.830079i | 0.155039 | − | 0.987908i | ||
0.987466 | + | 0.157830i | ||||||||
0 | 0 | |||||||||
−34.8642 | + | 7.82566i | −1.28599 | + | 0.288654i | |||||
0 | 0 | |||||||||
2.75203 | + | 8.46989i | 0.101372 | + | 0.311992i | |||||
0 | 0 | |||||||||
−5.73319 | + | 17.6450i | −0.210899 | + | 0.649080i | 0.788520 | + | 0.615008i | ||
−0.999419 | + | 0.0340716i | ||||||||
0 | 0 | |||||||||
0.172977 | + | 0.532370i | 0.00635449 | + | 0.0195571i | |||||
0 | 0 | |||||||||
28.1558 | 1.03294 | 0.516469 | − | 0.856306i | ||||||
0.516469 | + | 0.856306i | ||||||||
0 | 0 | |||||||||
−10.0436 | + | 11.4127i | −0.367969 | + | 0.418128i | |||||
0 | 0 | |||||||||
−4.38714 | − | 3.18745i | −0.160517 | − | 0.116623i | |||||
0 | 0 | |||||||||
80.6326 | 2.94625 | |||||||||
0 | 0 | |||||||||
−1.68076 | −0.0613319 | −0.0306660 | − | 0.999530i | ||||||
−0.0306660 | + | 0.999530i | ||||||||
0 | 0 | |||||||||
−20.6910 | − | 15.0329i | −0.754020 | − | 0.547828i | |||||
0 | 0 | |||||||||
−4.18570 | + | 4.75627i | −0.152333 | + | 0.173098i | |||||
0 | 0 | |||||||||
11.4300 | 0.415430 | 0.207715 | − | 0.978189i | ||||||
0.207715 | + | 0.978189i | ||||||||
0 | 0 | |||||||||
0.493371 | + | 1.51844i | 0.0179082 | + | 0.0551159i | |||||
0 | 0 | |||||||||
−6.66007 | + | 20.4976i | −0.241427 | + | 0.743037i | 0.754776 | + | 0.655982i | ||
−0.996204 | + | 0.0870547i | ||||||||
0 | 0 | |||||||||
21.1235 | + | 65.0114i | 0.764722 | + | 2.35357i | |||||
0 | 0 | |||||||||
25.9139 | − | 5.81665i | 0.936919 | − | 0.210302i | |||||
0 | 0 | |||||||||
−7.66868 | + | 5.57162i | −0.276900 | + | 0.201180i | |||||
0 | 0 | |||||||||
10.7228 | − | 7.79053i | 0.386672 | − | 0.280934i | −0.377418 | − | 0.926043i | ||
0.764091 | + | 0.645109i | ||||||||
0 | 0 | |||||||||
−6.88956 | − | 5.00556i | −0.248121 | − | 0.180271i | |||||
0 | 0 | |||||||||
2.52496 | − | 7.77103i | 0.0908165 | − | 0.279505i | −0.895324 | − | 0.445415i | ||
0.986141 | + | 0.165910i | ||||||||
0 | 0 | |||||||||
7.42769 | + | 7.88154i | 0.266811 | + | 0.283113i | |||||
0 | 0 | |||||||||
−16.7374 | + | 51.5125i | −0.600451 | + | 1.84800i | |||||
0 | 0 | |||||||||
−0.349631 | − | 0.254021i | −0.0125268 | − | 0.00910126i | |||||
0 | 0 | |||||||||
−11.8891 | + | 8.63790i | −0.425424 | + | 0.309089i | |||||
0 | 0 | |||||||||
−24.0201 | + | 17.4516i | −0.858409 | + | 0.623670i | |||||
0 | 0 | |||||||||
5.50193 | − | 6.25192i | 0.196372 | − | 0.223141i | |||||
0 | 0 | |||||||||
14.5311 | + | 44.7220i | 0.517976 | + | 1.59417i | 0.777800 | + | 0.628511i | ||
−0.259824 | + | 0.965656i | ||||||||
0 | 0 | |||||||||
−11.2703 | + | 34.6865i | −0.401234 | + | 1.23487i | |||||
0 | 0 | |||||||||
−7.00054 | − | 21.5455i | −0.248911 | − | 0.766068i | |||||
0 | 0 | |||||||||
−2.39522 | −0.0850566 | |||||||||
0 | 0 | |||||||||
24.0347 | + | 10.3754i | 0.852424 | + | 0.367977i | |||||
0 | 0 | |||||||||
34.8436 | + | 25.3154i | 1.23422 | + | 0.896716i | 0.997199 | − | 0.0747878i | ||
0.237024 | + | 0.971504i | ||||||||
0 | 0 | |||||||||
−70.6592 | −2.49974 | |||||||||
0 | 0 | |||||||||
17.5184 | 0.618981 | |||||||||
0 | 0 | |||||||||
−7.39967 | − | 5.37617i | −0.261129 | − | 0.189721i | |||||
0 | 0 | |||||||||
−7.32581 | − | 12.3622i | −0.258201 | − | 0.435709i | |||||
0 | 0 | |||||||||
−16.5824 | −0.583727 | |||||||||
0 | 0 | |||||||||
7.56461 | + | 23.2815i | 0.265958 | + | 0.818534i | 0.991471 | + | 0.130326i | ||
−0.725514 | + | 0.688208i | ||||||||
0 | 0 | |||||||||
−9.79588 | + | 30.1486i | −0.343980 | + | 1.05866i | 0.618148 | + | 0.786062i | ||
−0.962128 | + | 0.272599i | ||||||||
0 | 0 | |||||||||
−2.16940 | − | 6.67672i | −0.0760841 | − | 0.234163i | |||||
0 | 0 | |||||||||
50.8667 | + | 21.9583i | 1.78178 | + | 0.769165i | |||||
0 | 0 | |||||||||
−2.27082 | + | 1.64985i | −0.0794460 | + | 0.0577209i | |||||
0 | 0 | |||||||||
−11.1473 | + | 8.09899i | −0.389518 | + | 0.283002i | |||||
0 | 0 | |||||||||
−8.15139 | − | 5.92233i | −0.284485 | − | 0.206691i | 0.436386 | − | 0.899760i | ||
−0.720871 | + | 0.693069i | ||||||||
0 | 0 | |||||||||
2.79584 | − | 8.60472i | 0.0974569 | − | 0.299942i | −0.890429 | − | 0.455122i | ||
0.987886 | + | 0.155180i | ||||||||
0 | 0 | |||||||||
3.90667 | + | 4.14538i | 0.136013 | + | 0.144324i | |||||
0 | 0 | |||||||||
11.1649 | − | 34.3619i | 0.388240 | − | 1.19488i | −0.545862 | − | 0.837875i | ||
0.934102 | − | 0.357006i | ||||||||
0 | 0 | |||||||||
16.9324 | + | 12.3021i | 0.588085 | + | 0.427269i | 0.841630 | − | 0.540055i | ||
−0.253545 | + | 0.967324i | ||||||||
0 | 0 | |||||||||
11.1594 | − | 8.10778i | 0.387115 | − | 0.281256i | |||||
0 | 0 | |||||||||
79.1841 | − | 57.5306i | 2.74357 | − | 1.99332i | |||||
0 | 0 | |||||||||
3.42913 | − | 36.6241i | 0.118670 | − | 1.26743i | |||||
0 | 0 | |||||||||
3.58550 | + | 11.0350i | 0.123933 | + | 0.381427i | |||||
0 | 0 | |||||||||
16.3818 | − | 50.4181i | 0.565564 | − | 1.74063i | −0.100706 | − | 0.994916i | ||
0.666270 | − | 0.745710i | ||||||||
0 | 0 | |||||||||
0.531419 | + | 1.63554i | 0.0183248 | + | 0.0563979i | |||||
0 | 0 | |||||||||
−21.0932 | −0.726488 | |||||||||
0 | 0 | |||||||||
−2.06025 | + | 22.0041i | −0.0708747 | + | 0.756964i | |||||
0 | 0 | |||||||||
3.70974 | + | 2.69528i | 0.127468 | + | 0.0926111i | |||||
0 | 0 | |||||||||
−11.2753 | −0.386966 | |||||||||
0 | 0 | |||||||||
−14.5307 | −0.498106 | |||||||||
0 | 0 | |||||||||
24.2281 | + | 17.6027i | 0.829553 | + | 0.602705i | 0.919433 | − | 0.393247i | ||
−0.0898799 | + | 0.995953i | ||||||||
0 | 0 | |||||||||
1.03365 | − | 0.232015i | 0.0353502 | − | 0.00793475i | |||||
0 | 0 | |||||||||
−45.4353 | −1.55204 | −0.776020 | − | 0.630708i | ||||||
−0.776020 | + | 0.630708i | ||||||||
0 | 0 | |||||||||
−6.39177 | − | 19.6719i | −0.218084 | − | 0.671195i | −0.998920 | − | 0.0464586i | ||
0.780836 | − | 0.624736i | ||||||||
0 | 0 | |||||||||
−2.50649 | + | 7.71418i | −0.0854209 | + | 0.262899i | |||||
0 | 0 | |||||||||
9.67666 | + | 29.7817i | 0.329397 | + | 1.01378i | 0.969416 | + | 0.245422i | ||
−0.640019 | + | 0.768359i | ||||||||
0 | 0 | |||||||||
14.3048 | + | 24.1391i | 0.486379 | + | 0.820755i | |||||
0 | 0 | |||||||||
29.2081 | − | 21.2209i | 0.991960 | − | 0.720701i | |||||
0 | 0 | |||||||||
2.03346 | − | 1.47739i | 0.0689803 | − | 0.0501171i | |||||
0 | 0 | |||||||||
12.7191 | + | 9.24099i | 0.430972 | + | 0.313119i | |||||
0 | 0 | |||||||||
9.01401 | − | 27.7423i | 0.305078 | − | 0.938934i | |||||
0 | 0 | |||||||||
−42.4790 | − | 28.7033i | −1.43605 | − | 0.970347i | |||||
0 | 0 | |||||||||
3.55277 | − | 10.9343i | 0.119968 | − | 0.369225i | −0.872982 | − | 0.487752i | ||
0.992951 | + | 0.118527i | ||||||||
0 | 0 | |||||||||
−20.1596 | − | 14.6468i | −0.679966 | − | 0.494024i | |||||
0 | 0 | |||||||||
14.9835 | − | 10.8862i | 0.504809 | − | 0.366765i | −0.306042 | − | 0.952018i | ||
0.810851 | + | 0.585253i | ||||||||
0 | 0 | |||||||||
14.4200 | − | 10.4767i | 0.485271 | − | 0.352570i | −0.318092 | − | 0.948060i | ||
0.803363 | + | 0.595490i | ||||||||
0 | 0 | |||||||||
−6.97329 | − | 11.7673i | −0.234405 | − | 0.395553i | |||||
0 | 0 | |||||||||
−4.86199 | − | 14.9637i | −0.163250 | − | 0.502431i | 0.835653 | − | 0.549257i | ||
−0.998903 | + | 0.0468263i | ||||||||
0 | 0 | |||||||||
17.6212 | − | 54.2324i | 0.590996 | − | 1.81890i | |||||
0 | 0 | |||||||||
0.307854 | + | 0.947476i | 0.0103135 | + | 0.0317416i | |||||
0 | 0 | |||||||||
−2.81846 | −0.0943161 | |||||||||
0 | 0 | |||||||||
10.5132 | − | 2.35981i | 0.351419 | − | 0.0788798i | |||||
0 | 0 | |||||||||
2.28022 | + | 1.65668i | 0.0761344 | + | 0.0553149i | |||||
0 | 0 | |||||||||
12.0052 | 0.400394 | |||||||||
0 | 0 | |||||||||
−71.7087 | −2.38896 | |||||||||
0 | 0 | |||||||||
42.6201 | + | 30.9653i | 1.41831 | + | 1.03046i | |||||
0 | 0 | |||||||||
−4.55950 | + | 48.6969i | −0.151563 | + | 1.61874i | |||||
0 | 0 | |||||||||
41.9377 | 1.39252 | 0.696260 | − | 0.717790i | ||||||
0.696260 | + | 0.717790i | ||||||||
0 | 0 | |||||||||
5.59514 | + | 17.2201i | 0.185579 | + | 0.571153i | |||||
0 | 0 | |||||||||
−1.31596 | + | 4.05011i | −0.0435997 | + | 0.134186i | −0.970487 | − | 0.241154i | ||
0.926887 | + | 0.375340i | ||||||||
0 | 0 | |||||||||
0.984484 | + | 3.02993i | 0.0325817 | + | 0.100276i | |||||
0 | 0 | |||||||||
0.322206 | − | 3.44127i | 0.0106518 | − | 0.113765i | |||||
0 | 0 | |||||||||
0.192332 | − | 0.139738i | 0.00635137 | − | 0.00461454i | |||||
0 | 0 | |||||||||
18.0413 | − | 13.1078i | 0.595129 | − | 0.432386i | −0.249018 | − | 0.968499i | ||
0.844146 | + | 0.536113i | ||||||||
0 | 0 | |||||||||
12.6925 | + | 9.22164i | 0.418232 | + | 0.303863i | |||||
0 | 0 | |||||||||
−8.01679 | + | 24.6731i | −0.263876 | + | 0.812126i | |||||
0 | 0 | |||||||||
−46.8683 | + | 22.1565i | −1.54102 | + | 0.728500i | |||||
0 | 0 | |||||||||
1.79046 | − | 5.51048i | 0.0588065 | − | 0.180988i | |||||
0 | 0 | |||||||||
−8.98659 | − | 6.52914i | −0.294841 | − | 0.214214i | 0.430524 | − | 0.902579i | ||
−0.725365 | + | 0.688365i | ||||||||
0 | 0 | |||||||||
3.15850 | − | 2.29478i | 0.103516 | − | 0.0752085i | |||||
0 | 0 | |||||||||
24.9112 | − | 18.0991i | 0.815557 | − | 0.592537i | |||||
0 | 0 | |||||||||
−14.3253 | − | 6.18396i | −0.468486 | − | 0.202237i | |||||
0 | 0 | |||||||||
−1.55456 | − | 4.78445i | −0.0507854 | − | 0.156301i | 0.922447 | − | 0.386123i | ||
−0.973233 | + | 0.229821i | ||||||||
0 | 0 | |||||||||
8.34076 | − | 25.6702i | 0.272190 | − | 0.837716i | |||||
0 | 0 | |||||||||
0.681989 | + | 2.09894i | 0.0222322 | + | 0.0684236i | 0.961557 | − | 0.274605i | ||
−0.939325 | + | 0.343029i | ||||||||
0 | 0 | |||||||||
−2.17603 | −0.0708612 | |||||||||
0 | 0 | |||||||||
−28.0018 | − | 47.2524i | −0.910898 | − | 1.53712i | |||||
0 | 0 | |||||||||
−5.33110 | − | 3.87327i | −0.173238 | − | 0.125864i | 0.497788 | − | 0.867299i | ||
−0.671025 | + | 0.741434i | ||||||||
0 | 0 | |||||||||
−16.1467 | −0.524143 | |||||||||
0 | 0 | |||||||||
14.9201 | 0.483818 | |||||||||
0 | 0 | |||||||||
28.2142 | + | 20.4988i | 0.913948 | + | 0.664022i | 0.942010 | − | 0.335584i | ||
−0.0280620 | + | 0.999606i | ||||||||
0 | 0 | |||||||||
0.734880 | + | 0.317235i | 0.0237802 | + | 0.0102655i | |||||
0 | 0 | |||||||||
6.31424 | 0.204110 | |||||||||
0 | 0 | |||||||||
25.4161 | + | 78.2227i | 0.820729 | + | 2.52594i | |||||
0 | 0 | |||||||||
−8.12975 | + | 25.0208i | −0.262250 | + | 0.807123i | |||||
0 | 0 | |||||||||
9.24921 | + | 28.4661i | 0.298052 | + | 0.917309i | |||||
0 | 0 | |||||||||
13.0520 | − | 14.8312i | 0.420158 | − | 0.477432i | |||||
0 | 0 | |||||||||
−10.4451 | + | 7.58878i | −0.335891 | + | 0.244039i | −0.742926 | − | 0.669374i | ||
0.407035 | + | 0.913412i | ||||||||
0 | 0 | |||||||||
1.79003 | − | 1.30053i | 0.0575040 | − | 0.0417791i | |||||
0 | 0 | |||||||||
−35.8313 | − | 26.0330i | −1.14988 | − | 0.835437i | −0.161416 | − | 0.986887i | ||
−0.988465 | + | 0.151449i | ||||||||
0 | 0 | |||||||||
20.7795 | − | 63.9526i | 0.666159 | − | 2.05023i | |||||
0 | 0 | |||||||||
9.88089 | + | 1.86666i | 0.316442 | + | 0.0597811i | |||||
0 | 0 | |||||||||
−12.8772 | + | 39.6321i | −0.411980 | + | 1.26794i | 0.502945 | + | 0.864318i | ||
−0.914925 | + | 0.403624i | ||||||||
0 | 0 | |||||||||
−8.32632 | − | 6.04943i | −0.266110 | − | 0.193341i | |||||
0 | 0 | |||||||||
−20.5283 | + | 14.9147i | −0.655418 | + | 0.476189i | |||||
0 | 0 | |||||||||
−12.4536 | + | 9.04806i | −0.397208 | + | 0.288588i | −0.768403 | − | 0.639967i | ||
0.371195 | + | 0.928555i | ||||||||
0 | 0 | |||||||||
48.5947 | − | 10.9076i | 1.54836 | − | 0.347545i | |||||
0 | 0 | |||||||||
16.3465 | + | 50.3095i | 0.520316 | + | 1.60137i | |||||
0 | 0 | |||||||||
−4.36737 | + | 13.4414i | −0.138874 | + | 0.427411i | |||||
0 | 0 | |||||||||
−6.62847 | − | 20.4003i | −0.210560 | − | 0.648038i | −0.999439 | − | 0.0334889i | ||
0.788879 | − | 0.614549i | ||||||||
0 | 0 | |||||||||
1.87458 | 0.0594881 | |||||||||
0 | 0 | |||||||||
4.03680 | − | 4.58708i | 0.127975 | − | 0.145420i | |||||
0 | 0 | |||||||||
2.25047 | + | 1.63506i | 0.0712730 | + | 0.0517829i | 0.622851 | − | 0.782340i | ||
−0.551578 | + | 0.834123i | ||||||||
0 | 0 | |||||||||
−55.5413 | −1.75725 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1100.2.q.b.221.9 | ✓ | 52 | |
25.6 | even | 5 | inner | 1100.2.q.b.881.9 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1100.2.q.b.221.9 | ✓ | 52 | 1.1 | even | 1 | trivial | |
1100.2.q.b.881.9 | yes | 52 | 25.6 | even | 5 | inner |