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: \( 14.1179069025 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.321785678\) \(a_{3}=+0.000000000\) \(a_{4}=+0.747117378\) \(a_{5}=+0.287699156\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.570658424\) \(a_{8}=+0.334256628\) \(a_{9}=+0.000000000\) \(a_{10}=-0.380276624\)
\(a_{11}=+1.369510364\) \(a_{12}=+0.000000000\) \(a_{13}=+1.542792336\) \(a_{14}=-0.754288131\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.188933002\) \(a_{17}=+0.852523045\) \(a_{18}=+0.000000000\) \(a_{19}=-1.344615903\) \(a_{20}=+0.214945039\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.810199185\) \(a_{23}=+0.120763339\) \(a_{24}=+0.000000000\) \(a_{25}=-0.917229196\)
\(a_{26}=-2.039240814\) \(a_{27}=+0.000000000\) \(a_{28}=+0.426348825\) \(a_{29}=+0.076011150\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.417485685\) \(a_{32}=+1.237257985\) \(a_{33}=+0.000000000\) \(a_{34}=-1.126852750\) \(a_{35}=+0.164177947\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.229951710\) \(a_{38}=+1.777294043\) \(a_{39}=+0.000000000\) \(a_{40}=+0.096165353\)
\(a_{41}=+1.865224521\) \(a_{42}=+0.000000000\) \(a_{43}=-0.482975382\) \(a_{44}=+1.023184967\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.159623231\) \(a_{47}=-0.390517494\) \(a_{48}=+0.000000000\) \(a_{49}=-0.674348322\) \(a_{50}=+1.212379345\)
\(a_{51}=+0.000000000\) \(a_{52}=+1.152646851\) \(a_{53}=+1.125703683\) \(a_{54}=+0.000000000\) \(a_{55}=+0.394010998\)
\(a_{56}=+0.190764763\) \(a_{57}=+0.000000000\) \(a_{58}=-0.100435565\) \(a_{59}=-1.150526303\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.176325343\) \(a_{62}=+0.551298751\) \(a_{63}=+0.000000000\) \(a_{64}=-0.444630927\) \(a_{65}=+0.444834276\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.148605676\) \(a_{68}=+0.639835850\) \(a_{69}=+0.000000000\) \(a_{70}=-0.242493959\)

Showing all 70 available coefficients

Rows: Cols: