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: \( 15.9256262912 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.350488789\) \(a_{3}=+0.000000000\) \(a_{4}=+0.823819969\) \(a_{5}=-1.935581415\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.565816384\) \(a_{8}=-0.237929157\) \(a_{9}=+0.000000000\) \(a_{10}=-2.613981001\)
\(a_{11}=+0.680290908\) \(a_{12}=+0.000000000\) \(a_{13}=-0.130932716\) \(a_{14}=+0.764128683\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.145140628\) \(a_{17}=+1.041516442\) \(a_{18}=+0.000000000\) \(a_{19}=-0.522302604\) \(a_{20}=-1.594570621\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.918725244\) \(a_{23}=+1.376912743\) \(a_{24}=+0.000000000\) \(a_{25}=+2.746475415\)
\(a_{26}=-0.176823165\) \(a_{27}=+0.000000000\) \(a_{28}=+0.466130836\) \(a_{29}=+0.964008203\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.849381023\) \(a_{32}=-1.308570422\) \(a_{33}=+0.000000000\) \(a_{34}=+1.406556279\) \(a_{35}=-1.095183677\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.709933680\) \(a_{38}=-0.705363811\) \(a_{39}=+0.000000000\) \(a_{40}=+0.460531254\)
\(a_{41}=+1.469293910\) \(a_{42}=+0.000000000\) \(a_{43}=-0.997396086\) \(a_{44}=+0.560437277\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.859505174\) \(a_{47}=-0.267201561\) \(a_{48}=+0.000000000\) \(a_{49}=-0.679852148\) \(a_{50}=+3.709085197\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.107866694\) \(a_{53}=+0.746478925\) \(a_{54}=+0.000000000\) \(a_{55}=-1.316766364\)
\(a_{56}=-0.134602363\) \(a_{57}=+0.000000000\) \(a_{58}=+1.301837787\) \(a_{59}=+1.128565194\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.557107276\) \(a_{62}=+1.147486251\) \(a_{63}=+0.000000000\) \(a_{64}=-0.622874112\) \(a_{65}=+0.255095457\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.709679735\) \(a_{68}=+0.863575741\) \(a_{69}=+0.000000000\) \(a_{70}=-1.488317035\)

Showing all 70 available coefficients

Rows: Cols: