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: \( 14.1179069025 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.321785678\) \(a_{3}=+0.000000000\) \(a_{4}=+0.747117378\) \(a_{5}=-0.287699156\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.570658424\) \(a_{8}=-0.334256628\) \(a_{9}=+0.000000000\) \(a_{10}=-0.380276624\)
\(a_{11}=-1.369510364\) \(a_{12}=+0.000000000\) \(a_{13}=+1.542792336\) \(a_{14}=+0.754288131\) \(a_{15}=+0.000000000\)
\(a_{16}=-1.188933002\) \(a_{17}=-0.852523045\) \(a_{18}=+0.000000000\) \(a_{19}=-1.344615903\) \(a_{20}=-0.214945039\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.810199185\) \(a_{23}=-0.120763339\) \(a_{24}=+0.000000000\) \(a_{25}=-0.917229196\)
\(a_{26}=+2.039240814\) \(a_{27}=+0.000000000\) \(a_{28}=+0.426348825\) \(a_{29}=-0.076011150\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.417485685\) \(a_{32}=-1.237257985\) \(a_{33}=+0.000000000\) \(a_{34}=-1.126852750\) \(a_{35}=-0.164177947\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.229951710\) \(a_{38}=-1.777294040\) \(a_{39}=+0.000000000\) \(a_{40}=+0.096165346\)
\(a_{41}=-1.865224500\) \(a_{42}=+0.000000000\) \(a_{43}=-0.482975421\) \(a_{44}=-1.023184955\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.159623446\) \(a_{47}=+0.390517640\) \(a_{48}=+0.000000000\) \(a_{49}=-0.674349655\) \(a_{50}=-1.212379268\)
\(a_{51}=+0.000000000\) \(a_{52}=+1.152642749\) \(a_{53}=-1.125692265\) \(a_{54}=+0.000000000\) \(a_{55}=+0.393984822\)
\(a_{56}=-0.190710813\) \(a_{57}=+0.000000000\) \(a_{58}=-0.100567123\) \(a_{59}=+1.150686610\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.177018033\) \(a_{62}=-0.550965901\) \(a_{63}=+0.000000000\) \(a_{64}=-0.448617078\) \(a_{65}=-0.440607019\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.134474537\) \(a_{68}=-0.621400276\) \(a_{69}=+0.000000000\) \(a_{70}=-0.257905694\)

Showing all 70 available coefficients

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