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: \( 13.6349664437 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-1.002947328\) \(a_{4}=+0.000000000\) \(a_{5}=+0.424731601\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.662483549\) \(a_{8}=+0.000000000\) \(a_{9}=+0.005903343\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.489606850\) \(a_{12}=+0.000000000\) \(a_{13}=+0.738459626\) \(a_{14}=+0.000000000\) \(a_{15}=-0.425983425\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.880921115\) \(a_{18}=+0.000000000\) \(a_{19}=+1.632134074\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.664436105\) \(a_{22}=+0.000000000\) \(a_{23}=+0.011815949\) \(a_{24}=+0.000000000\) \(a_{25}=-0.819603068\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.997026582\) \(a_{28}=+0.000000000\) \(a_{29}=-1.195895925\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.546306883\) \(a_{32}=+0.000000000\) \(a_{33}=-1.493997328\) \(a_{34}=+0.000000000\) \(a_{35}=-0.281378156\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.680773167\) \(a_{38}=+0.000000000\) \(a_{39}=-0.740640236\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.532287386\) \(a_{42}=+0.000000000\) \(a_{43}=-0.986638617\) \(a_{44}=+0.000000000\) \(a_{45}=+0.002442283\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.278581728\) \(a_{48}=+0.000000000\) \(a_{49}=-0.561501732\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.882149326\) \(a_{52}=+0.000000000\) \(a_{53}=+0.874026057\) \(a_{54}=+0.000000000\) \(a_{55}=+0.625143863\)
\(a_{56}=+0.000000000\) \(a_{57}=-1.644560502\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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