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: \( 15.7351247464 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.803672486\) \(a_{3}=+0.000000000\) \(a_{4}=+2.253234438\) \(a_{5}=-0.062476577\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.552476209\) \(a_{8}=-2.260424475\) \(a_{9}=+0.000000000\) \(a_{10}=+0.112687282\)
\(a_{11}=+1.533693387\) \(a_{12}=+0.000000000\) \(a_{13}=-1.164292624\) \(a_{14}=+2.800158624\) \(a_{15}=+0.000000000\)
\(a_{16}=+1.823830996\) \(a_{17}=+0.252146651\) \(a_{18}=+0.000000000\) \(a_{19}=+0.387096178\) \(a_{20}=-0.140774374\)
\(a_{21}=+0.000000000\) \(a_{22}=-2.766280565\) \(a_{23}=-0.223999303\) \(a_{24}=+0.000000000\) \(a_{25}=-0.996096677\)
\(a_{26}=+2.100002572\) \(a_{27}=+0.000000000\) \(a_{28}=-3.498092858\) \(a_{29}=-1.381821812\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.336349203\) \(a_{32}=-1.029169312\) \(a_{33}=+0.000000000\) \(a_{34}=-0.454789977\) \(a_{35}=+0.096993399\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.852944805\) \(a_{38}=-0.698194724\) \(a_{39}=+0.000000000\) \(a_{40}=+0.141223584\)
\(a_{41}=-0.521357057\) \(a_{42}=+0.000000000\) \(a_{43}=-0.367547595\) \(a_{44}=+3.455770776\) \(a_{45}=+0.000000000\)
\(a_{46}=+0.404021471\) \(a_{47}=+0.074167241\) \(a_{48}=+0.000000000\) \(a_{49}=+1.410182871\) \(a_{50}=+1.796632236\)
\(a_{51}=+0.000000000\) \(a_{52}=-2.623421893\) \(a_{53}=-0.749749085\) \(a_{54}=+0.000000000\) \(a_{55}=-0.095810640\)
\(a_{56}=+3.509246975\) \(a_{57}=+0.000000000\) \(a_{58}=+2.492386363\) \(a_{59}=+0.435721128\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.208304940\) \(a_{62}=-0.606983225\) \(a_{63}=+0.000000000\) \(a_{64}=+0.032619009\) \(a_{65}=+0.071185818\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.170476587\) \(a_{68}=+0.561684814\) \(a_{69}=+0.000000000\) \(a_{70}=-0.178842377\)

Showing all 70 available coefficients

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