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: \( 9.00120580965 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.712515309\) \(a_{4}=+0.000000000\) \(a_{5}=-1.189711412\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.018617569\) \(a_{8}=+0.000000000\) \(a_{9}=-0.492321935\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.192141915\) \(a_{12}=+0.000000000\) \(a_{13}=-1.441511007\) \(a_{14}=+0.000000000\) \(a_{15}=-0.847687594\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.565320974\) \(a_{18}=+0.000000000\) \(a_{19}=+0.426323976\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.725780612\) \(a_{22}=+0.000000000\) \(a_{23}=-1.722769019\) \(a_{24}=+0.000000000\) \(a_{25}=+0.415413244\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.063302224\) \(a_{28}=+0.000000000\) \(a_{29}=+1.052986760\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.715558450\) \(a_{32}=+0.000000000\) \(a_{33}=-0.136904056\) \(a_{34}=+0.000000000\) \(a_{35}=-1.211860947\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.920496002\) \(a_{38}=+0.000000000\) \(a_{39}=-1.027098660\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.040798000\) \(a_{42}=+0.000000000\) \(a_{43}=+0.181449994\) \(a_{44}=+0.000000000\) \(a_{45}=+0.585721024\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.134500504\) \(a_{48}=+0.000000000\) \(a_{49}=+0.037581752\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.115315157\) \(a_{52}=+0.000000000\) \(a_{53}=-1.149993896\) \(a_{54}=+0.000000000\) \(a_{55}=+0.228593429\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.303762360\) \(a_{58}=+0.000000000\) \(a_{59}=+0.000000000\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.000000000\) \(a_{62}=+0.000000000\) \(a_{63}=-0.501487773\) \(a_{64}=+0.000000000\) \(a_{65}=+1.714982096\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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