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: \( 11.1309636349 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.296766888\) \(a_{3}=+0.000000000\) \(a_{4}=+0.681604362\) \(a_{5}=+0.943052219\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.286523838\) \(a_{8}=+0.412884920\) \(a_{9}=+0.000000000\) \(a_{10}=-1.222918892\)
\(a_{11}=+0.768679723\) \(a_{12}=+0.000000000\) \(a_{13}=-1.658730973\) \(a_{14}=-1.668321514\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.217019856\) \(a_{17}=+0.422908373\) \(a_{18}=+0.000000000\) \(a_{19}=+0.750245825\) \(a_{20}=+0.642788506\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.996798413\) \(a_{23}=+1.576669861\) \(a_{24}=+0.000000000\) \(a_{25}=-0.110652512\)
\(a_{26}=+2.150987402\) \(a_{27}=+0.000000000\) \(a_{28}=+0.876900261\) \(a_{29}=-0.466013591\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.175270429\) \(a_{32}=+1.165306130\) \(a_{33}=+0.000000000\) \(a_{34}=-0.548413572\) \(a_{35}=+1.213259154\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.385124892\) \(a_{38}=-0.972893987\) \(a_{39}=+0.000000000\) \(a_{40}=+0.389372044\)
\(a_{41}=+0.069001155\) \(a_{42}=+0.000000000\) \(a_{43}=+1.768950502\) \(a_{44}=+0.523934086\) \(a_{45}=+0.000000000\)
\(a_{46}=-2.044574126\) \(a_{47}=+0.388001423\) \(a_{48}=+0.000000000\) \(a_{49}=+0.655138315\) \(a_{50}=+0.143458588\)
\(a_{51}=+0.000000000\) \(a_{52}=-1.130623470\) \(a_{53}=-1.531578139\) \(a_{54}=+0.000000000\) \(a_{55}=+0.724771916\)
\(a_{56}=+0.530595521\) \(a_{57}=+0.000000000\) \(a_{58}=+0.603741731\) \(a_{59}=+1.165154623\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.536301014\) \(a_{62}=+0.219395268\) \(a_{63}=+0.000000000\) \(a_{64}=-0.301163872\) \(a_{65}=-1.590780650\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.556373332\) \(a_{68}=+0.205480105\) \(a_{69}=+0.000000000\) \(a_{70}=-1.664465889\)

Showing all 70 available coefficients

Rows: Cols: