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: \( 10.2659151168 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.071270968\) \(a_{4}=+0.000000000\) \(a_{5}=+1.064147386\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.387714511\) \(a_{8}=+0.000000000\) \(a_{9}=+0.147621488\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.197788596\) \(a_{12}=+0.000000000\) \(a_{13}=+0.292213777\) \(a_{14}=+0.000000000\) \(a_{15}=+1.139990201\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.536372950\) \(a_{18}=+0.000000000\) \(a_{19}=-0.496736247\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.486618268\) \(a_{22}=+0.000000000\) \(a_{23}=+1.523306229\) \(a_{24}=+0.000000000\) \(a_{25}=+0.132409656\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.913128365\) \(a_{28}=+0.000000000\) \(a_{29}=+0.175986038\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.155895411\) \(a_{32}=+0.000000000\) \(a_{33}=-1.283156482\) \(a_{34}=+0.000000000\) \(a_{35}=+1.476731745\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.001446518\) \(a_{38}=+0.000000000\) \(a_{39}=+0.313031012\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.821486968\) \(a_{42}=+0.000000000\) \(a_{43}=+0.346482015\) \(a_{44}=+0.000000000\) \(a_{45}=+0.156884090\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.221315207\) \(a_{48}=+0.000000000\) \(a_{49}=+0.924281542\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.642235524\) \(a_{52}=+0.000000000\) \(a_{53}=-1.127119976\) \(a_{54}=+0.000000000\) \(a_{55}=-1.294891033\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.576533866\) \(a_{58}=+0.000000000\)

Showing all 58 available coefficients

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