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: \( 12.6229848659 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.214093609\) \(a_{3}=+0.000000000\) \(a_{4}=+0.474023291\) \(a_{5}=-0.788328886\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.072804678\) \(a_{8}=+0.638584961\) \(a_{9}=+0.000000000\) \(a_{10}=+0.957105062\)
\(a_{11}=-0.391440317\) \(a_{12}=+0.000000000\) \(a_{13}=-1.299294535\) \(a_{14}=+1.302485303\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.249325211\) \(a_{17}=-1.028528544\) \(a_{18}=+0.000000000\) \(a_{19}=-1.788819764\) \(a_{20}=-0.373686253\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.475245188\) \(a_{23}=-0.947477458\) \(a_{24}=+0.000000000\) \(a_{25}=-0.378537568\)
\(a_{26}=+1.577465191\) \(a_{27}=+0.000000000\) \(a_{28}=-0.508534404\) \(a_{29}=+1.607552897\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.118395132\) \(a_{32}=+0.878212793\) \(a_{33}=+0.000000000\) \(a_{34}=+1.248729932\) \(a_{35}=+0.845722920\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.775426795\) \(a_{38}=+2.171794665\) \(a_{39}=+0.000000000\) \(a_{40}=-0.503414943\)
\(a_{41}=-0.549279092\) \(a_{42}=+0.000000000\) \(a_{43}=-0.239827251\) \(a_{44}=-0.185551220\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.150327241\) \(a_{47}=+1.077695913\) \(a_{48}=+0.000000000\) \(a_{49}=+0.150915322\) \(a_{50}=+0.459589215\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.615866272\) \(a_{53}=-0.295579070\) \(a_{54}=+0.000000000\) \(a_{55}=+0.308699130\)
\(a_{56}=-0.684994940\) \(a_{57}=+0.000000000\) \(a_{58}=-1.951176556\) \(a_{59}=+0.385473772\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.742555672\) \(a_{62}=+0.144160067\) \(a_{63}=+0.000000000\) \(a_{64}=+0.187671884\) \(a_{65}=+1.020798422\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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