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: \( 10.4711201375 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.698026059\) \(a_{3}=+0.000000000\) \(a_{4}=+1.883292496\) \(a_{5}=-1.636998807\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.168039008\) \(a_{8}=-1.499853676\) \(a_{9}=+0.000000000\) \(a_{10}=+2.779666632\)
\(a_{11}=+0.907521447\) \(a_{12}=+0.000000000\) \(a_{13}=+1.198916938\) \(a_{14}=+0.285334615\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.663498131\) \(a_{17}=-0.209938508\) \(a_{18}=+0.000000000\) \(a_{19}=+0.690216367\) \(a_{20}=-3.082947569\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.540995066\) \(a_{23}=+0.507404645\) \(a_{24}=+0.000000000\) \(a_{25}=+1.679765093\)
\(a_{26}=-2.035792202\) \(a_{27}=+0.000000000\) \(a_{28}=-0.316466603\) \(a_{29}=-0.701136250\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.657672652\) \(a_{32}=+0.373216560\) \(a_{33}=+0.000000000\) \(a_{34}=+0.356481058\) \(a_{35}=+0.275079660\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.074860688\) \(a_{38}=-1.172005331\) \(a_{39}=+0.000000000\) \(a_{40}=+2.455258547\)
\(a_{41}=-0.565262018\) \(a_{42}=+0.000000000\) \(a_{43}=-0.941963359\) \(a_{44}=+1.709130486\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.861591952\) \(a_{47}=+0.486343922\) \(a_{48}=+0.000000000\) \(a_{49}=-0.971794114\) \(a_{50}=-2.852244098\)
\(a_{51}=+0.000000000\) \(a_{52}=+2.257749885\) \(a_{53}=+1.475126832\) \(a_{54}=+0.000000000\) \(a_{55}=-1.486437737\)
\(a_{56}=+0.252269200\) \(a_{57}=+0.000000000\) \(a_{58}=+1.186651991\) \(a_{59}=-0.019518200\) \(a_{60}=+0.000000000\)

Showing all 60 available coefficients

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