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: \( 8.69834295647 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.904692330\) \(a_{3}=+0.000000000\) \(a_{4}=-0.181531788\) \(a_{5}=-0.262583542\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.463780858\) \(a_{8}=+1.068922746\) \(a_{9}=+0.000000000\) \(a_{10}=+0.237557316\)
\(a_{11}=-1.130816556\) \(a_{12}=+0.000000000\) \(a_{13}=+0.814031368\) \(a_{14}=-1.324271315\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.785514421\) \(a_{17}=-1.726209628\) \(a_{18}=+0.000000000\) \(a_{19}=+0.107928103\) \(a_{20}=+0.047667260\)
\(a_{21}=+0.000000000\) \(a_{22}=+1.023041065\) \(a_{23}=-0.511253436\) \(a_{24}=+0.000000000\) \(a_{25}=-0.931049883\)
\(a_{26}=-0.736447935\) \(a_{27}=+0.000000000\) \(a_{28}=-0.265722757\) \(a_{29}=+0.909301895\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.083934282\) \(a_{32}=-0.358273874\) \(a_{33}=+0.000000000\) \(a_{34}=+1.561688610\) \(a_{35}=-0.384364763\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.808108867\) \(a_{38}=-0.097641726\) \(a_{39}=+0.000000000\) \(a_{40}=-0.280681521\)
\(a_{41}=+0.715491881\) \(a_{42}=+0.000000000\) \(a_{43}=-0.902316526\) \(a_{44}=+0.205279152\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.462527062\) \(a_{47}=-1.363114164\) \(a_{48}=+0.000000000\) \(a_{49}=+1.142654400\) \(a_{50}=+0.842313688\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.147772570\) \(a_{53}=-0.486717982\) \(a_{54}=+0.000000000\) \(a_{55}=+0.296933817\)
\(a_{56}=+1.564668655\) \(a_{57}=+0.000000000\) \(a_{58}=-0.822638450\) \(a_{59}=-1.427276229\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.465684932\) \(a_{62}=+0.075934701\) \(a_{63}=+0.000000000\) \(a_{64}=+1.109642048\) \(a_{65}=-0.213751240\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.224861744\) \(a_{68}=+0.313361921\) \(a_{69}=+0.000000000\) \(a_{70}=+0.347731852\)
\(a_{71}=+0.431260395\) \(a_{72}=+0.000000000\) \(a_{73}=+0.917734305\) \(a_{74}=+0.731089893\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.019592382\) \(a_{77}=-1.655267630\) \(a_{78}=+0.000000000\) \(a_{79}=-1.251779033\) \(a_{80}=+0.206263157\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.647300020\) \(a_{83}=-0.144605986\) \(a_{84}=+0.000000000\) \(a_{85}=+0.453274228\)
\(a_{86}=+0.816318840\) \(a_{87}=+0.000000000\) \(a_{88}=-1.208755539\) \(a_{89}=+0.082547376\) \(a_{90}=+0.000000000\)
\(a_{91}=+1.191563534\) \(a_{92}=+0.092808750\) \(a_{93}=+0.000000000\) \(a_{94}=+1.233198929\) \(a_{95}=-0.028340144\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.001554884\) \(a_{98}=-1.033750671\) \(a_{99}=+0.000000000\) \(a_{100}=+0.169015151\)

Showing 100 of 1500 available coefficients

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