Properties

Level $9$
Weight $0$
Character 9.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 13.9432420039 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.593407973\) \(a_{3}=+0.000000000\) \(a_{4}=-0.647866978\) \(a_{5}=+1.228188653\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.404304688\) \(a_{8}=+0.977857403\) \(a_{9}=+0.000000000\) \(a_{10}=-0.728816938\)
\(a_{11}=+0.364705683\) \(a_{12}=+0.000000000\) \(a_{13}=-0.367007661\) \(a_{14}=+0.833325598\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.067598599\) \(a_{17}=-0.640172649\) \(a_{18}=+0.000000000\) \(a_{19}=+1.553720495\) \(a_{20}=-0.795702871\)
\(a_{21}=+0.000000000\) \(a_{22}=-0.216419260\) \(a_{23}=+1.570513425\) \(a_{24}=+0.000000000\) \(a_{25}=+0.508447366\)
\(a_{26}=+0.217785272\) \(a_{27}=+0.000000000\) \(a_{28}=+0.909802634\) \(a_{29}=+0.666952201\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.064812402\) \(a_{32}=-1.017970951\) \(a_{33}=+0.000000000\) \(a_{34}=+0.379883554\) \(a_{35}=-1.724751086\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.145109312\) \(a_{38}=-0.921990146\) \(a_{39}=+0.000000000\) \(a_{40}=+1.200993329\)
\(a_{41}=-1.625991862\) \(a_{42}=+0.000000000\) \(a_{43}=-0.973381974\) \(a_{44}=-0.236280902\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.931956108\) \(a_{47}=-1.721739875\) \(a_{48}=+0.000000000\) \(a_{49}=+0.972068468\) \(a_{50}=-0.301716313\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.237759950\) \(a_{53}=+0.904413874\) \(a_{54}=+0.000000000\) \(a_{55}=+0.447901428\)
\(a_{56}=-1.373132268\) \(a_{57}=+0.000000000\) \(a_{58}=-0.395717090\) \(a_{59}=-0.341849836\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.065479976\) \(a_{62}=+0.633831919\) \(a_{63}=+0.000000000\) \(a_{64}=+0.538596716\) \(a_{65}=-0.441995150\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.512840287\) \(a_{68}=+0.435052135\) \(a_{69}=+0.000000000\) \(a_{70}=+1.075188183\)

Showing all 70 available coefficients

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