Properties

Level $8$
Weight $0$
Character 8.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 12.0230258884 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.820610157\) \(a_{4}=+0.000000000\) \(a_{5}=-0.847724750\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.368799563\) \(a_{8}=+0.000000000\) \(a_{9}=+2.314621344\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.445153181\) \(a_{12}=+0.000000000\) \(a_{13}=+0.372469664\) \(a_{14}=+0.000000000\) \(a_{15}=+1.543376290\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.287356269\) \(a_{18}=+0.000000000\) \(a_{19}=+0.795000520\) \(a_{20}=+0.000000000\)
\(a_{21}=-2.492050388\) \(a_{22}=+0.000000000\) \(a_{23}=+0.411899856\) \(a_{24}=+0.000000000\) \(a_{25}=-0.281362749\)
\(a_{26}=+0.000000000\) \(a_{27}=-2.393412971\) \(a_{28}=+0.000000000\) \(a_{29}=-1.468412443\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.448505016\) \(a_{32}=+0.000000000\) \(a_{33}=+0.810450400\) \(a_{34}=+0.000000000\) \(a_{35}=-1.160365274\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.167277891\) \(a_{38}=+0.000000000\) \(a_{39}=-0.678122036\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.467984569\) \(a_{42}=+0.000000000\) \(a_{43}=+1.550247177\) \(a_{44}=+0.000000000\) \(a_{45}=-1.962157766\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.871025049\) \(a_{48}=+0.000000000\) \(a_{49}=+0.873598741\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.523035542\) \(a_{52}=+0.000000000\) \(a_{53}=-1.266660091\) \(a_{54}=+0.000000000\) \(a_{55}=+0.375204224\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.452505295\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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