Properties

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

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 10.0894530628 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.110208130\) \(a_{3}=+0.000000000\) \(a_{4}=-0.987854168\) \(a_{5}=+1.211005416\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.359576759\) \(a_{8}=-0.219077691\) \(a_{9}=+0.000000000\) \(a_{10}=+0.133462643\)
\(a_{11}=+1.109006968\) \(a_{12}=+0.000000000\) \(a_{13}=-0.685022985\) \(a_{14}=-0.039628282\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.963710025\) \(a_{17}=-1.661644162\) \(a_{18}=+0.000000000\) \(a_{19}=-0.928089520\) \(a_{20}=-1.196296748\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.122221584\) \(a_{23}=-1.515904480\) \(a_{24}=+0.000000000\) \(a_{25}=+0.466534118\)
\(a_{26}=-0.075495102\) \(a_{27}=+0.000000000\) \(a_{28}=+0.355209400\) \(a_{29}=-0.943887381\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.175826346\) \(a_{32}=+0.325286371\) \(a_{33}=+0.000000000\) \(a_{34}=-0.183126697\) \(a_{35}=-0.435449403\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.502349170\) \(a_{38}=-0.102283006\) \(a_{39}=+0.000000000\) \(a_{40}=-0.265304280\)
\(a_{41}=+0.648727127\) \(a_{42}=+0.000000000\) \(a_{43}=-0.451976166\) \(a_{44}=-1.095536983\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.167064906\) \(a_{47}=+0.743108796\) \(a_{48}=+0.000000000\) \(a_{49}=-0.870703877\) \(a_{50}=+0.051419061\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.676706814\) \(a_{53}=-0.426670494\) \(a_{54}=+0.000000000\) \(a_{55}=+1.343023823\)
\(a_{56}=+0.078819011\) \(a_{57}=+0.000000000\) \(a_{58}=-0.104003369\) \(a_{59}=+0.340755488\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.777852617\) \(a_{62}=-0.130284185\) \(a_{63}=+0.000000000\) \(a_{64}=-0.930413000\) \(a_{65}=-0.831384225\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.304966452\) \(a_{68}=+1.640181255\) \(a_{69}=+0.000000000\) \(a_{70}=-0.093161959\)
\(a_{71}=-1.229128599\)

Showing all 71 available coefficients

Rows: Cols: