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: \( 10.0894530628 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.110208130\) \(a_{3}=+0.000000000\) \(a_{4}=-0.987854168\) \(a_{5}=-1.211005416\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.359576759\) \(a_{8}=+0.219077691\) \(a_{9}=+0.000000000\) \(a_{10}=+0.133462643\)
\(a_{11}=-1.109006968\) \(a_{12}=+0.000000000\) \(a_{13}=-0.685022985\) \(a_{14}=+0.039628282\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.963710025\) \(a_{17}=+1.661644162\) \(a_{18}=+0.000000000\) \(a_{19}=-0.928089520\) \(a_{20}=+1.196296748\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.122221584\) \(a_{23}=+1.515904480\) \(a_{24}=+0.000000000\) \(a_{25}=+0.466534118\)
\(a_{26}=+0.075495102\) \(a_{27}=+0.000000000\) \(a_{28}=+0.355209401\) \(a_{29}=+0.943887381\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.175826346\) \(a_{32}=-0.325286372\) \(a_{33}=+0.000000000\) \(a_{34}=-0.183126696\) \(a_{35}=+0.435449402\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.502349172\) \(a_{38}=+0.102283008\) \(a_{39}=+0.000000000\) \(a_{40}=-0.265304285\)
\(a_{41}=-0.648727076\) \(a_{42}=+0.000000000\) \(a_{43}=-0.451976273\) \(a_{44}=+1.095537437\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.167065778\) \(a_{47}=-0.743106054\) \(a_{48}=+0.000000000\) \(a_{49}=-0.870709545\) \(a_{50}=-0.051405902\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.676676659\) \(a_{53}=+0.426728414\) \(a_{54}=+0.000000000\) \(a_{55}=+1.342881369\)
\(a_{56}=-0.078571736\) \(a_{57}=+0.000000000\) \(a_{58}=-0.104617881\) \(a_{59}=-0.339870540\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.779983575\) \(a_{62}=+0.132854101\) \(a_{63}=+0.000000000\) \(a_{64}=-0.936465852\) \(a_{65}=+0.840601932\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.289382650\) \(a_{68}=-1.607559209\) \(a_{69}=+0.000000000\) \(a_{70}=-0.143008047\)

Showing all 70 available coefficients

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