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: \( 15.7351247464 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.803672486\) \(a_{3}=+0.000000000\) \(a_{4}=+2.253234438\) \(a_{5}=+0.062476577\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.552476209\) \(a_{8}=+2.260424475\) \(a_{9}=+0.000000000\) \(a_{10}=+0.112687282\)
\(a_{11}=-1.533693387\) \(a_{12}=+0.000000000\) \(a_{13}=-1.164292624\) \(a_{14}=-2.800158624\) \(a_{15}=+0.000000000\)
\(a_{16}=+1.823830996\) \(a_{17}=-0.252146651\) \(a_{18}=+0.000000000\) \(a_{19}=+0.387096178\) \(a_{20}=+0.140774374\)
\(a_{21}=+0.000000000\) \(a_{22}=-2.766280565\) \(a_{23}=+0.223999303\) \(a_{24}=+0.000000000\) \(a_{25}=-0.996096677\)
\(a_{26}=-2.100002572\) \(a_{27}=+0.000000000\) \(a_{28}=-3.498092858\) \(a_{29}=+1.381821812\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.336349202\) \(a_{32}=+1.029169312\) \(a_{33}=+0.000000000\) \(a_{34}=-0.454789977\) \(a_{35}=-0.096993398\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.852944807\) \(a_{38}=+0.698194727\) \(a_{39}=+0.000000000\) \(a_{40}=+0.141223580\)
\(a_{41}=+0.521357065\) \(a_{42}=+0.000000000\) \(a_{43}=-0.367547620\) \(a_{44}=-3.455770754\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.404021349\) \(a_{47}=-0.074167159\) \(a_{48}=+0.000000000\) \(a_{49}=+1.410182281\) \(a_{50}=-1.796631959\)
\(a_{51}=+0.000000000\) \(a_{52}=-2.623424679\) \(a_{53}=+0.749749672\) \(a_{54}=+0.000000000\) \(a_{55}=-0.095822322\)
\(a_{56}=-3.509247120\) \(a_{57}=+0.000000000\) \(a_{58}=+2.492333724\) \(a_{59}=-0.435728680\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.208544415\) \(a_{62}=+0.606925689\) \(a_{63}=+0.000000000\) \(a_{64}=+0.031516727\) \(a_{65}=-0.071305466\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.165849685\) \(a_{68}=-0.561668607\) \(a_{69}=+0.000000000\) \(a_{70}=-0.195592818\)
\(a_{71}=-0.817966336\) \(a_{72}=+0.000000000\) \(a_{73}=-1.427114623\) \(a_{74}=-1.445727336\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.674987568\) \(a_{77}=+2.644402734\) \(a_{78}=+0.000000000\)

Showing all 78 available coefficients

Rows: Cols: