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: \( 13.9432420039 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.593407973\) \(a_{3}=+0.000000000\) \(a_{4}=-0.647866978\) \(a_{5}=-1.228188653\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.404304688\) \(a_{8}=-0.977857403\) \(a_{9}=+0.000000000\) \(a_{10}=-0.728816938\)
\(a_{11}=-0.364705683\) \(a_{12}=+0.000000000\) \(a_{13}=-0.367007661\) \(a_{14}=-0.833325598\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.067598599\) \(a_{17}=+0.640172649\) \(a_{18}=+0.000000000\) \(a_{19}=+1.553720495\) \(a_{20}=+0.795702871\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.216419260\) \(a_{23}=-1.570513425\) \(a_{24}=+0.000000000\) \(a_{25}=+0.508447366\)
\(a_{26}=-0.217785272\) \(a_{27}=+0.000000000\) \(a_{28}=+0.909802634\) \(a_{29}=-0.666952201\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.064812402\) \(a_{32}=+1.017970951\) \(a_{33}=+0.000000000\) \(a_{34}=+0.379883555\) \(a_{35}=+1.724751085\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.145109301\) \(a_{38}=+0.921990138\) \(a_{39}=+0.000000000\) \(a_{40}=+1.200993385\)
\(a_{41}=+1.625991836\) \(a_{42}=+0.000000000\) \(a_{43}=-0.973381712\) \(a_{44}=+0.236280929\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.931955071\) \(a_{47}=+1.721740358\) \(a_{48}=+0.000000000\) \(a_{49}=+0.972072566\) \(a_{50}=+0.301720196\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.237778733\) \(a_{53}=-0.904389683\) \(a_{54}=+0.000000000\) \(a_{55}=+0.447940824\)
\(a_{56}=+1.373267023\) \(a_{57}=+0.000000000\) \(a_{58}=-0.395739610\) \(a_{59}=+0.342611496\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.065046500\) \(a_{62}=-0.630501158\) \(a_{63}=+0.000000000\) \(a_{64}=+0.539985819\) \(a_{65}=+0.454039875\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.521197593\) \(a_{68}=-0.398901980\) \(a_{69}=+0.000000000\) \(a_{70}=+1.067197289\)

Showing all 70 available coefficients

Rows: Cols: