Properties

Level $9$
Weight $0$
Character 9.1
Symmetry odd
Fricke sign $+1$

Related objects

Downloads

Learn more about

Maass form invariants

Level: \( 9 = 3^{2} \)
Weight: \( 0 \)
Character: 9.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 14.7326818427 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.483752808\) \(a_{3}=+0.000000000\) \(a_{4}=+1.201522394\) \(a_{5}=-1.297013269\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.586593337\) \(a_{8}=-0.299009418\) \(a_{9}=+0.000000000\) \(a_{10}=+1.924447080\)
\(a_{11}=-1.579850677\) \(a_{12}=+0.000000000\) \(a_{13}=-0.618568547\) \(a_{14}=-0.870359510\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.757866331\) \(a_{17}=+1.057043395\) \(a_{18}=+0.000000000\) \(a_{19}=+1.787922333\) \(a_{20}=-1.558390488\)
\(a_{21}=+0.000000000\) \(a_{22}=+2.344107878\) \(a_{23}=+0.018299016\) \(a_{24}=+0.000000000\) \(a_{25}=+0.682243420\)
\(a_{26}=+0.917802819\) \(a_{27}=+0.000000000\) \(a_{28}=+0.704805030\) \(a_{29}=+0.254847276\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.531145307\) \(a_{32}=+1.423495714\) \(a_{33}=+0.000000000\) \(a_{34}=-1.568391106\) \(a_{35}=-0.760819339\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.640396941\) \(a_{38}=-2.652834777\) \(a_{39}=+0.000000000\) \(a_{40}=+0.387819173\)
\(a_{41}=+0.560796534\) \(a_{42}=+0.000000000\) \(a_{43}=+0.107248578\) \(a_{44}=-1.898225978\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.027151056\) \(a_{47}=-1.651679155\) \(a_{48}=+0.000000000\) \(a_{49}=-0.655906968\) \(a_{50}=-1.012282993\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.743216128\) \(a_{53}=-0.043502758\) \(a_{54}=+0.000000000\) \(a_{55}=+2.049126787\)
\(a_{56}=-0.175459494\) \(a_{57}=+0.000000000\) \(a_{58}=-0.377963856\) \(a_{59}=-0.035578256\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.060195965\) \(a_{62}=-2.272841707\) \(a_{63}=+0.000000000\) \(a_{64}=-1.351933728\) \(a_{65}=+0.798691293\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.243867284\) \(a_{68}=+1.257359157\) \(a_{69}=+0.000000000\) \(a_{70}=+1.152450824\)
\(a_{71}=-0.317454362\) \(a_{72}=+0.000000000\) \(a_{73}=-1.413544593\) \(a_{74}=-1.062412985\) \(a_{75}=+0.000000000\)
\(a_{76}=+2.323908682\) \(a_{77}=-1.287626382\)

Showing all 77 available coefficients

Rows: Cols: