Properties

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

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Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 11.728024516 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.627908079\) \(a_{3}=+0.000000000\) \(a_{4}=-0.605731445\) \(a_{5}=-0.337954619\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.422016282\) \(a_{8}=-1.008251746\) \(a_{9}=+0.000000000\) \(a_{10}=-0.212204436\)
\(a_{11}=+0.651460357\) \(a_{12}=+0.000000000\) \(a_{13}=+1.426865361\) \(a_{14}=-0.264987433\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.027357972\) \(a_{17}=-1.261451510\) \(a_{18}=+0.000000000\) \(a_{19}=+0.613740611\) \(a_{20}=+0.204709740\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.409057221\) \(a_{23}=+1.623594130\) \(a_{24}=+0.000000000\) \(a_{25}=-0.885786675\)
\(a_{26}=+0.895940287\) \(a_{27}=+0.000000000\) \(a_{28}=+0.255628532\) \(a_{29}=+1.740581407\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.055845250\) \(a_{32}=+0.991073458\) \(a_{33}=+0.000000000\) \(a_{34}=-0.792075600\) \(a_{35}=+0.142622372\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.573890622\) \(a_{38}=+0.385372807\) \(a_{39}=+0.000000000\) \(a_{40}=+0.340743108\)
\(a_{41}=+0.833601151\) \(a_{42}=+0.000000000\) \(a_{43}=+0.216108083\) \(a_{44}=-0.394606641\) \(a_{45}=+0.000000000\)
\(a_{46}=+1.019462827\) \(a_{47}=+0.249276411\) \(a_{48}=+0.000000000\) \(a_{49}=-0.821922731\) \(a_{50}=-0.556121337\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.864369420\) \(a_{53}=+0.783899953\) \(a_{54}=+0.000000000\) \(a_{55}=-0.220375328\)
\(a_{56}=+0.426590177\) \(a_{57}=+0.000000000\) \(a_{58}=+1.092458140\) \(a_{59}=-1.229615533\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.144904013\) \(a_{62}=+0.674487652\) \(a_{63}=+0.000000000\) \(a_{64}=+0.653132197\) \(a_{65}=-0.451043156\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.933974115\) \(a_{68}=+0.831669391\) \(a_{69}=+0.000000000\) \(a_{70}=+0.186772293\)

Showing all 70 available coefficients

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