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: \( 8.69834295647 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.904692330\) \(a_{3}=+0.000000000\) \(a_{4}=-0.181531788\) \(a_{5}=+0.262583542\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.463780858\) \(a_{8}=-1.068922746\) \(a_{9}=+0.000000000\) \(a_{10}=+0.237557316\)
\(a_{11}=+1.130816556\) \(a_{12}=+0.000000000\) \(a_{13}=+0.814031368\) \(a_{14}=+1.324271315\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.785514421\) \(a_{17}=+1.726209628\) \(a_{18}=+0.000000000\) \(a_{19}=+0.107928103\) \(a_{20}=-0.047667260\)
\(a_{21}=+0.000000000\) \(a_{22}=+1.023041065\) \(a_{23}=+0.511253430\) \(a_{24}=+0.000000000\) \(a_{25}=-0.931049883\)
\(a_{26}=+0.736447935\) \(a_{27}=+0.000000000\) \(a_{28}=-0.265722757\) \(a_{29}=-0.909301900\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.083934300\) \(a_{32}=+0.358273874\) \(a_{33}=+0.000000000\) \(a_{34}=+1.561688610\) \(a_{35}=+0.384364762\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.808109999\) \(a_{38}=+0.097641727\) \(a_{39}=+0.000000000\) \(a_{40}=-0.280681521\)
\(a_{41}=-0.715490700\) \(a_{42}=+0.000000000\) \(a_{43}=-0.902300000\) \(a_{44}=-0.205279152\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.462527057\) \(a_{47}=+1.363006592\) \(a_{48}=+0.000000000\) \(a_{49}=+1.142654400\) \(a_{50}=-0.842313688\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.147772570\) \(a_{53}=+0.489990234\) \(a_{54}=+0.000000000\) \(a_{55}=+0.296933817\)
\(a_{56}=-1.564668655\) \(a_{57}=+0.000000000\) \(a_{58}=-0.822638454\) \(a_{59}=+1.500000000\) \(a_{60}=+0.000000000\)

Showing all 60 available coefficients

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