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: \( 12.6229848659 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.214093609\) \(a_{3}=+0.000000000\) \(a_{4}=+0.474023291\) \(a_{5}=+0.788328886\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.072804678\) \(a_{8}=-0.638584961\) \(a_{9}=+0.000000000\) \(a_{10}=+0.957105062\)
\(a_{11}=+0.391440317\) \(a_{12}=+0.000000000\) \(a_{13}=-1.299294535\) \(a_{14}=-1.302485303\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.249325211\) \(a_{17}=+1.028528544\) \(a_{18}=+0.000000000\) \(a_{19}=-1.788819764\) \(a_{20}=+0.373686253\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.475245188\) \(a_{23}=+0.947477458\) \(a_{24}=+0.000000000\) \(a_{25}=-0.378537568\)
\(a_{26}=-1.577465191\) \(a_{27}=+0.000000000\) \(a_{28}=-0.508534405\) \(a_{29}=-1.607552894\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.118395136\) \(a_{32}=-0.878212786\) \(a_{33}=+0.000000000\) \(a_{34}=+1.248729919\) \(a_{35}=-0.845722902\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.775426826\) \(a_{38}=-2.171794629\) \(a_{39}=+0.000000000\) \(a_{40}=-0.503415026\)
\(a_{41}=+0.549279184\) \(a_{42}=+0.000000000\) \(a_{43}=-0.239827624\) \(a_{44}=+0.185551762\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.150324568\) \(a_{47}=-1.077691579\) \(a_{48}=+0.000000000\) \(a_{49}=+0.150896420\) \(a_{50}=-0.459562272\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.615980325\) \(a_{53}=+0.295740884\) \(a_{54}=+0.000000000\) \(a_{55}=+0.308146004\)
\(a_{56}=+0.685783420\) \(a_{57}=+0.000000000\) \(a_{58}=-1.953596014\) \(a_{59}=-0.382142262\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.734219187\) \(a_{62}=-0.131718222\) \(a_{63}=+0.000000000\) \(a_{64}=+0.165507419\) \(a_{65}=-0.985053693\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.797523628\) \(a_{68}=+0.604137813\) \(a_{69}=+0.000000000\) \(a_{70}=-1.048042216\)

Showing all 70 available coefficients

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