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: \( 14.7798382665 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.755069868\) \(a_{4}=+0.000000000\) \(a_{5}=+1.530745781\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.826993304\) \(a_{8}=+0.000000000\) \(a_{9}=-0.429869495\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.819300434\) \(a_{12}=+0.000000000\) \(a_{13}=-1.321472421\) \(a_{14}=+0.000000000\) \(a_{15}=+1.155820014\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.465619797\) \(a_{18}=+0.000000000\) \(a_{19}=-0.343126516\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.624437724\) \(a_{22}=+0.000000000\) \(a_{23}=+0.984667085\) \(a_{24}=+0.000000000\) \(a_{25}=+1.343182646\)
\(a_{26}=+0.000000000\) \(a_{27}=-1.079651370\) \(a_{28}=+0.000000000\) \(a_{29}=+0.935240533\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.212334946\) \(a_{32}=+0.000000000\) \(a_{33}=-0.618629065\) \(a_{34}=+0.000000000\) \(a_{35}=-1.265916497\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.601689171\) \(a_{38}=+0.000000000\) \(a_{39}=-0.997803966\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.584565316\) \(a_{42}=+0.000000000\) \(a_{43}=+0.275916083\) \(a_{44}=+0.000000000\) \(a_{45}=-0.658024922\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.274854267\) \(a_{48}=+0.000000000\) \(a_{49}=-0.316150219\) \(a_{50}=+0.000000000\)
\(a_{51}=-1.106897418\) \(a_{52}=+0.000000000\) \(a_{53}=+1.216129598\) \(a_{54}=+0.000000000\) \(a_{55}=-1.256809694\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.266848307\) \(a_{58}=+0.000000000\) \(a_{59}=+1.348582292\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.153328597\) \(a_{62}=+0.000000000\) \(a_{63}=+0.208883494\) \(a_{64}=+0.000000000\) \(a_{65}=-2.400755400\)
\(a_{66}=+0.000000000\)

Showing all 66 available coefficients

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