Properties

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

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Maass form invariants

Level: \( 8 = 2^{3} \)
Weight: \( 0 \)
Character: 8.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 12.4023495483 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.054249209\) \(a_{4}=+0.000000000\) \(a_{5}=-1.829489488\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.563020489\) \(a_{8}=+0.000000000\) \(a_{9}=-0.997057023\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.202366436\) \(a_{12}=+0.000000000\) \(a_{13}=-0.522412414\) \(a_{14}=+0.000000000\) \(a_{15}=+0.099248358\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.908520708\) \(a_{18}=+0.000000000\) \(a_{19}=-0.387877231\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.030543416\) \(a_{22}=+0.000000000\) \(a_{23}=+0.909490860\) \(a_{24}=+0.000000000\) \(a_{25}=+2.347031785\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.108338753\) \(a_{28}=+0.000000000\) \(a_{29}=-0.125862965\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.814703972\) \(a_{32}=+0.000000000\) \(a_{33}=-0.065227554\) \(a_{34}=+0.000000000\) \(a_{35}=+1.030040001\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.684695629\) \(a_{38}=+0.000000000\) \(a_{39}=+0.028345002\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.705162461\) \(a_{42}=+0.000000000\) \(a_{43}=-1.154330682\) \(a_{44}=+0.000000000\) \(a_{45}=+1.824304171\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.466437984\) \(a_{48}=+0.000000000\) \(a_{49}=-0.681942090\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.050115831\) \(a_{52}=+0.000000000\) \(a_{53}=+1.868287022\) \(a_{54}=+0.000000000\) \(a_{55}=-2.232095321\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.094901844\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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