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: \( 13.0773211701 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.265379104\) \(a_{3}=+0.000000000\) \(a_{4}=-0.929573931\) \(a_{5}=-1.543951357\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.545386103\) \(a_{8}=+0.512068600\) \(a_{9}=+0.000000000\) \(a_{10}=+0.409732427\)
\(a_{11}=+1.128807354\) \(a_{12}=+0.000000000\) \(a_{13}=-0.252585403\) \(a_{14}=-0.410113179\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.793681625\) \(a_{17}=-0.690149265\) \(a_{18}=+0.000000000\) \(a_{19}=+0.051167265\) \(a_{20}=+1.435216933\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.299561884\) \(a_{23}=+0.421812100\) \(a_{24}=+0.000000000\) \(a_{25}=+1.383785792\)
\(a_{26}=+0.067030888\) \(a_{27}=+0.000000000\) \(a_{28}=-1.436550635\) \(a_{29}=-1.670159734\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.448042288\) \(a_{32}=-0.722695118\) \(a_{33}=+0.000000000\) \(a_{34}=+0.183151193\) \(a_{35}=-2.386000969\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.611507801\) \(a_{38}=-0.013578717\) \(a_{39}=+0.000000000\) \(a_{40}=-0.790609020\)
\(a_{41}=-1.100583404\) \(a_{42}=+0.000000000\) \(a_{43}=-0.359006645\) \(a_{44}=-1.049309773\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.111940387\) \(a_{47}=+0.419314802\) \(a_{48}=+0.000000000\) \(a_{49}=+1.388216108\) \(a_{50}=-0.367223866\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.234786772\) \(a_{53}=-0.664033964\) \(a_{54}=+0.000000000\) \(a_{55}=-1.742854352\)
\(a_{56}=+0.791415145\) \(a_{57}=+0.000000000\) \(a_{58}=+0.443073597\) \(a_{59}=-0.723264652\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.082473883\) \(a_{62}=-0.118186078\) \(a_{63}=+0.000000000\) \(a_{64}=-0.603721985\) \(a_{65}=+0.393102782\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.523231054\) \(a_{68}=+0.636665264\) \(a_{69}=+0.000000000\) \(a_{70}=+0.654533402\)

Showing all 70 available coefficients

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