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: \( 15.9256262912 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.350488789\) \(a_{3}=+0.000000000\) \(a_{4}=+0.823819969\) \(a_{5}=+1.935581415\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.565816384\) \(a_{8}=+0.237929157\) \(a_{9}=+0.000000000\) \(a_{10}=-2.613981001\)
\(a_{11}=-0.680290908\) \(a_{12}=+0.000000000\) \(a_{13}=-0.130932716\) \(a_{14}=-0.764128683\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.145140628\) \(a_{17}=-1.041516442\) \(a_{18}=+0.000000000\) \(a_{19}=-0.522302605\) \(a_{20}=+1.594570621\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.918725244\) \(a_{23}=-1.376912743\) \(a_{24}=+0.000000000\) \(a_{25}=+2.746475415\)
\(a_{26}=+0.176823165\) \(a_{27}=+0.000000000\) \(a_{28}=+0.466130836\) \(a_{29}=-0.964008204\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.849381025\) \(a_{32}=+1.308570420\) \(a_{33}=+0.000000000\) \(a_{34}=+1.406556284\) \(a_{35}=+1.095183671\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.709933673\) \(a_{38}=+0.705363808\) \(a_{39}=+0.000000000\) \(a_{40}=+0.460531213\)
\(a_{41}=-1.469293797\) \(a_{42}=+0.000000000\) \(a_{43}=-0.997396578\) \(a_{44}=-0.560436267\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.859501877\) \(a_{47}=+0.267207712\) \(a_{48}=+0.000000000\) \(a_{49}=-0.679869663\) \(a_{50}=-3.709053831\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.107948126\) \(a_{53}=-0.746337750\) \(a_{54}=+0.000000000\) \(a_{55}=-1.317107622\)
\(a_{56}=+0.135181572\) \(a_{57}=+0.000000000\) \(a_{58}=+1.300541620\) \(a_{59}=-1.126383774\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.552450602\) \(a_{62}=-1.139711789\) \(a_{63}=+0.000000000\) \(a_{64}=-0.638612587\) \(a_{65}=-0.228957436\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.658408838\) \(a_{68}=-0.780929055\) \(a_{69}=+0.000000000\) \(a_{70}=-1.641281724\)

Showing all 70 available coefficients

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