Properties

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

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 11.1309636349 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.296766888\) \(a_{3}=+0.000000000\) \(a_{4}=+0.681604362\) \(a_{5}=-0.943052219\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.286523838\) \(a_{8}=-0.412884920\) \(a_{9}=+0.000000000\) \(a_{10}=-1.222918892\)
\(a_{11}=-0.768679723\) \(a_{12}=+0.000000000\) \(a_{13}=-1.658730973\) \(a_{14}=+1.668321514\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.217019856\) \(a_{17}=-0.422908373\) \(a_{18}=+0.000000000\) \(a_{19}=+0.750245825\) \(a_{20}=-0.642788506\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.996798413\) \(a_{23}=-1.576669861\) \(a_{24}=+0.000000000\) \(a_{25}=-0.110652512\)
\(a_{26}=-2.150987402\) \(a_{27}=+0.000000000\) \(a_{28}=+0.876900261\) \(a_{29}=+0.466013591\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.175270429\) \(a_{32}=-1.165306131\) \(a_{33}=+0.000000000\) \(a_{34}=-0.548413572\) \(a_{35}=-1.213259164\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.385124894\) \(a_{38}=+0.972893920\) \(a_{39}=+0.000000000\) \(a_{40}=+0.389372016\)
\(a_{41}=-0.069001544\) \(a_{42}=+0.000000000\) \(a_{43}=+1.768950292\) \(a_{44}=-0.523936254\) \(a_{45}=+0.000000000\)
\(a_{46}=-2.044575019\) \(a_{47}=-0.388012189\) \(a_{48}=+0.000000000\) \(a_{49}=+0.655134534\) \(a_{50}=-0.143505761\)
\(a_{51}=+0.000000000\) \(a_{52}=-1.130637974\) \(a_{53}=+1.531380499\) \(a_{54}=+0.000000000\) \(a_{55}=+0.724759769\)
\(a_{56}=-0.531333065\) \(a_{57}=+0.000000000\) \(a_{58}=+0.603818612\) \(a_{59}=-1.167587086\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.537003027\) \(a_{62}=-0.226606465\) \(a_{63}=+0.000000000\) \(a_{64}=-0.296837960\) \(a_{65}=+1.572181334\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.532980516\) \(a_{68}=-0.244781266\) \(a_{69}=+0.000000000\) \(a_{70}=-1.579994502\)

Showing all 70 available coefficients

Rows: Cols: