Properties

Level $33$
Weight $0$
Character 33.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 33 = 3 \cdot 11 \)
Weight: \( 0 \)
Character: 33.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 3.3337141434 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.691280728\) \(a_{3}=+0.577350269\) \(a_{4}=+1.860430502\) \(a_{5}=-0.821382625\)
\(a_{6}=-0.976461384\) \(a_{7}=+0.334266589\) \(a_{8}=-1.455229526\) \(a_{9}=+0.333333333\) \(a_{10}=+1.389188604\)
\(a_{11}=+0.301511345\) \(a_{12}=+1.074120051\) \(a_{13}=+1.355513030\) \(a_{14}=-0.565338641\) \(a_{15}=-0.474225480\)
\(a_{16}=+0.600771151\) \(a_{17}=-0.826233864\) \(a_{18}=-0.563760243\) \(a_{19}=+1.800824885\) \(a_{20}=-1.528125289\)
\(a_{21}=+0.192988905\) \(a_{22}=-0.509940326\) \(a_{23}=+1.253836280\) \(a_{24}=-0.840177159\) \(a_{25}=-0.325330584\)
\(a_{26}=-2.292553065\) \(a_{27}=+0.192450090\) \(a_{28}=+0.621879758\) \(a_{29}=+1.290981128\) \(a_{30}=+0.802048415\)
\(a_{31}=-0.183176597\) \(a_{32}=+0.439156857\) \(a_{33}=+0.174077656\) \(a_{34}=+1.397393411\) \(a_{35}=-0.274560769\)
\(a_{36}=+0.620143501\) \(a_{37}=-1.250729589\) \(a_{38}=-3.045700423\) \(a_{39}=+0.782605813\) \(a_{40}=+1.195300248\)
\(a_{41}=-0.464022582\) \(a_{42}=-0.326398416\) \(a_{43}=+1.298701481\) \(a_{44}=+0.560940902\) \(a_{45}=-0.273794208\)
\(a_{46}=-2.120589136\) \(a_{47}=+1.055097490\) \(a_{48}=+0.346855385\) \(a_{49}=-0.888265847\) \(a_{50}=+0.550225346\)
\(a_{51}=-0.477026344\) \(a_{52}=+2.521837787\) \(a_{53}=+1.016807022\) \(a_{54}=-0.325487128\) \(a_{55}=-0.247656180\)
\(a_{56}=-0.486434610\) \(a_{57}=+1.039706732\) \(a_{58}=-2.183411502\) \(a_{59}=+0.416927423\) \(a_{60}=-0.882263547\)
\(a_{61}=-0.628441154\) \(a_{62}=+0.309803049\) \(a_{63}=+0.111422196\) \(a_{64}=-1.343508679\) \(a_{65}=-1.113394851\)
\(a_{66}=-0.294414185\) \(a_{67}=+0.378293567\) \(a_{68}=-1.537150682\) \(a_{69}=+0.723902713\) \(a_{70}=+0.464359337\)
\(a_{71}=-0.578933902\) \(a_{72}=-0.485076509\) \(a_{73}=+1.168209255\) \(a_{74}=+2.115334851\) \(a_{75}=-0.187829700\)
\(a_{76}=+3.350309545\) \(a_{77}=+0.100785169\) \(a_{78}=-1.323606129\) \(a_{79}=-0.417580405\) \(a_{80}=-0.493462985\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.784792450\) \(a_{83}=+0.408464010\) \(a_{84}=+0.359042446\) \(a_{85}=+0.678654140\)
\(a_{86}=-2.196468787\) \(a_{87}=+0.745348301\) \(a_{88}=-0.438768211\) \(a_{89}=-0.954191167\) \(a_{90}=+0.463062868\)
\(a_{91}=+0.453102717\) \(a_{92}=+2.332675259\) \(a_{93}=-0.105757058\) \(a_{94}=-1.784466051\) \(a_{95}=-1.479166271\)
\(a_{96}=+0.253547330\) \(a_{97}=+1.825459155\) \(a_{98}=+1.502306909\) \(a_{99}=+0.100503782\) \(a_{100}=-0.605254941\)

Showing 100 of 306 available coefficients

Rows: Cols: