Properties

Level $9$
Weight $0$
Character 9.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 13.0773211701 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.265379104\) \(a_{3}=+0.000000000\) \(a_{4}=-0.929573931\) \(a_{5}=+1.543951357\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.545386103\) \(a_{8}=-0.512068600\) \(a_{9}=+0.000000000\) \(a_{10}=+0.409732427\)
\(a_{11}=-1.128807354\) \(a_{12}=+0.000000000\) \(a_{13}=-0.252585403\) \(a_{14}=+0.410113179\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.793681625\) \(a_{17}=+0.690149265\) \(a_{18}=+0.000000000\) \(a_{19}=+0.051167265\) \(a_{20}=-1.435216933\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.299561884\) \(a_{23}=-0.421812100\) \(a_{24}=+0.000000000\) \(a_{25}=+1.383785792\)
\(a_{26}=-0.067030888\) \(a_{27}=+0.000000000\) \(a_{28}=-1.436550635\) \(a_{29}=+1.670159734\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.448042289\) \(a_{32}=+0.722695119\) \(a_{33}=+0.000000000\) \(a_{34}=+0.183151196\) \(a_{35}=+2.386000973\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.611507817\) \(a_{38}=+0.013578731\) \(a_{39}=+0.000000000\) \(a_{40}=-0.790608937\)
\(a_{41}=+1.100583460\) \(a_{42}=+0.000000000\) \(a_{43}=-0.359006226\) \(a_{44}=+1.049309990\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.111938593\) \(a_{47}=-0.419313631\) \(a_{48}=+0.000000000\) \(a_{49}=+1.388226080\) \(a_{50}=+0.367226506\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.234835520\) \(a_{53}=+0.664036900\) \(a_{54}=+0.000000000\) \(a_{55}=-1.742681465\)
\(a_{56}=-0.791377653\) \(a_{57}=+0.000000000\) \(a_{58}=+0.443872859\) \(a_{59}=+0.723263325\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.085798540\) \(a_{62}=+0.117794234\) \(a_{63}=+0.000000000\) \(a_{64}=-0.590670576\) \(a_{65}=-0.393667270\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.560918008\) \(a_{68}=-0.654665384\) \(a_{69}=+0.000000000\) \(a_{70}=+0.726987936\)

Showing all 70 available coefficients

Rows: Cols: