Properties

Level $8$
Weight $0$
Character 8.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 10.5388080579 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.953390949\) \(a_{4}=+0.000000000\) \(a_{5}=+0.123561950\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.647194542\) \(a_{8}=+0.000000000\) \(a_{9}=-0.091045698\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.898510026\) \(a_{12}=+0.000000000\) \(a_{13}=-0.347842839\) \(a_{14}=+0.000000000\) \(a_{15}=+0.117802845\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.006880414\) \(a_{18}=+0.000000000\) \(a_{19}=-1.719137869\) \(a_{20}=+0.000000000\)
\(a_{21}=-1.570420368\) \(a_{22}=+0.000000000\) \(a_{23}=+1.216743398\) \(a_{24}=+0.000000000\) \(a_{25}=-0.984732444\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.040193094\) \(a_{28}=+0.000000000\) \(a_{29}=+0.199799872\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.987599784\) \(a_{32}=+0.000000000\) \(a_{33}=+0.856631325\) \(a_{34}=+0.000000000\) \(a_{35}=-0.203530555\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.638603516\) \(a_{38}=+0.000000000\) \(a_{39}=-0.331629833\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.400924016\) \(a_{42}=+0.000000000\) \(a_{43}=-1.906443344\) \(a_{44}=+0.000000000\) \(a_{45}=-0.011230484\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.613348266\) \(a_{48}=+0.000000000\) \(a_{49}=+1.713466504\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.959213305\) \(a_{52}=+0.000000000\) \(a_{53}=+0.573066861\) \(a_{54}=+0.000000000\) \(a_{55}=+0.116834836\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.627294184\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

Rows: Cols: