Properties

Level $9$
Weight $0$
Character 9.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 14.7326818427 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.483752808\) \(a_{3}=+0.000000000\) \(a_{4}=+1.201522394\) \(a_{5}=+1.297013269\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.586593337\) \(a_{8}=+0.299009418\) \(a_{9}=+0.000000000\) \(a_{10}=+1.924447080\)
\(a_{11}=+1.579850677\) \(a_{12}=+0.000000000\) \(a_{13}=-0.618568547\) \(a_{14}=+0.870359510\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.757866331\) \(a_{17}=-1.057043395\) \(a_{18}=+0.000000000\) \(a_{19}=+1.787922333\) \(a_{20}=+1.558390488\)
\(a_{21}=+0.000000000\) \(a_{22}=+2.344107878\) \(a_{23}=-0.018299016\) \(a_{24}=+0.000000000\) \(a_{25}=+0.682243420\)
\(a_{26}=-0.917802819\) \(a_{27}=+0.000000000\) \(a_{28}=+0.704805030\) \(a_{29}=-0.254847276\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.531145308\) \(a_{32}=-1.423495714\) \(a_{33}=+0.000000000\) \(a_{34}=-1.568391105\) \(a_{35}=+0.760819340\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.640396944\) \(a_{38}=+2.652834780\) \(a_{39}=+0.000000000\) \(a_{40}=+0.387819178\)
\(a_{41}=-0.560796523\) \(a_{42}=+0.000000000\) \(a_{43}=+0.107248552\) \(a_{44}=+1.898226003\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.027151426\) \(a_{47}=+1.651679157\) \(a_{48}=+0.000000000\) \(a_{49}=-0.655909541\) \(a_{50}=+1.012283035\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.743231107\) \(a_{53}=+0.043504361\) \(a_{54}=+0.000000000\) \(a_{55}=+2.049050953\)
\(a_{56}=+0.175475683\) \(a_{57}=+0.000000000\) \(a_{58}=-0.378300256\) \(a_{59}=+0.035685964\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.061574030\) \(a_{62}=+2.273473251\) \(a_{63}=+0.000000000\) \(a_{64}=-1.357103217\) \(a_{65}=-0.795890107\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.226492703\) \(a_{68}=-1.247332987\) \(a_{69}=+0.000000000\) \(a_{70}=+1.101787411\)

Showing all 70 available coefficients

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