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: \( 12.5844685795 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.707414066\) \(a_{4}=+0.000000000\) \(a_{5}=+0.317865148\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.375845901\) \(a_{8}=+0.000000000\) \(a_{9}=-0.499565339\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.281044293\) \(a_{12}=+0.000000000\) \(a_{13}=-1.287339917\) \(a_{14}=+0.000000000\) \(a_{15}=+0.224862277\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.863327244\) \(a_{18}=+0.000000000\) \(a_{19}=-0.542761164\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.265878677\) \(a_{22}=+0.000000000\) \(a_{23}=-0.212982685\) \(a_{24}=+0.000000000\) \(a_{25}=-0.898961748\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.060813614\) \(a_{28}=+0.000000000\) \(a_{29}=-1.042221214\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.549082368\) \(a_{32}=+0.000000000\) \(a_{33}=-0.198814688\) \(a_{34}=+0.000000000\) \(a_{35}=-0.119468326\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.602407577\) \(a_{38}=+0.000000000\) \(a_{39}=-0.910682382\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.594561051\) \(a_{42}=+0.000000000\) \(a_{43}=-0.851485238\) \(a_{44}=+0.000000000\) \(a_{45}=-0.158792743\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.599000578\) \(a_{48}=+0.000000000\) \(a_{49}=-0.858774055\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.317993226\) \(a_{52}=+0.000000000\) \(a_{53}=-1.130067465\) \(a_{54}=+0.000000000\) \(a_{55}=-0.089702044\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.383184961\) \(a_{58}=+0.000000000\) \(a_{59}=+0.078481229\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.351221949\) \(a_{62}=+0.000000000\) \(a_{63}=+0.079366847\) \(a_{64}=+0.000000000\)

Showing all 64 available coefficients

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