Properties

Level $21$
Weight $0$
Character 21.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.36432553144 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.874508883\) \(a_{3}=-0.577350270\) \(a_{4}=+2.513783551\) \(a_{5}=-0.927355073\)
\(a_{6}=+1.082248206\) \(a_{7}=+0.377964473\) \(a_{8}=-2.837600712\) \(a_{9}=+0.333333334\) \(a_{10}=+1.738335315\)
\(a_{11}=+1.204600159\) \(a_{12}=-1.451333610\) \(a_{13}=-0.294486510\) \(a_{14}=-0.708497762\) \(a_{15}=+0.535408699\)
\(a_{16}=+2.805324190\) \(a_{17}=+0.242030239\) \(a_{18}=-0.624836294\) \(a_{19}=+0.526573544\) \(a_{20}=-2.331169920\)
\(a_{21}=-0.218217892\) \(a_{22}=-2.258033699\) \(a_{23}=+0.913816626\) \(a_{24}=+1.638289537\) \(a_{25}=-0.140012573\)
\(a_{26}=+0.552017576\) \(a_{27}=-0.192450092\) \(a_{28}=+0.950120876\) \(a_{29}=+0.890666505\) \(a_{30}=-1.003628361\)
\(a_{31}=+0.763823906\) \(a_{32}=-2.421004408\) \(a_{33}=-0.695476222\) \(a_{34}=-0.453687821\) \(a_{35}=-0.350507272\)
\(a_{36}=+0.837927844\) \(a_{37}=+0.918164717\) \(a_{38}=-0.987066773\) \(a_{39}=+0.170021878\) \(a_{40}=+2.631463410\)
\(a_{41}=+0.733434667\) \(a_{42}=+0.409051350\) \(a_{43}=-1.033256252\) \(a_{44}=+3.028104112\) \(a_{45}=-0.309118358\)
\(a_{46}=-1.712957451\) \(a_{47}=-1.824652915\) \(a_{48}=-1.619654717\) \(a_{49}=+0.142857144\) \(a_{50}=+0.262454755\)
\(a_{51}=-0.139736245\) \(a_{52}=-0.740275372\) \(a_{53}=+1.687639443\) \(a_{54}=+0.360749432\) \(a_{55}=-1.117092051\)
\(a_{56}=-1.072512241\) \(a_{57}=-0.304017394\) \(a_{58}=-1.669562336\) \(a_{59}=+0.840909555\) \(a_{60}=+1.345901725\)
\(a_{61}=+0.323420911\) \(a_{62}=-1.431794673\) \(a_{63}=+0.125987975\) \(a_{64}=+1.732869928\) \(a_{65}=+0.273093662\)
\(a_{66}=+1.303676665\) \(a_{67}=+1.159503510\) \(a_{68}=+0.608411270\) \(a_{69}=-0.527592393\) \(a_{70}=+0.657029350\)
\(a_{71}=+0.166452102\) \(a_{72}=-0.945866985\) \(a_{73}=+0.638651873\) \(a_{74}=-1.721107912\) \(a_{75}=+0.080836435\)
\(a_{76}=+1.323691947\) \(a_{77}=+0.455296056\) \(a_{78}=-0.318707594\) \(a_{79}=+0.423647143\) \(a_{80}=-2.601531522\)
\(a_{81}=+0.111111195\) \(a_{82}=-1.374829882\) \(a_{83}=-0.270760614\) \(a_{84}=-0.548552540\) \(a_{85}=-0.224447910\)
\(a_{86}=+1.936848135\) \(a_{87}=-0.514226590\) \(a_{88}=-3.418174289\) \(a_{89}=-0.961979081\) \(a_{90}=+0.579445133\)
\(a_{91}=-0.111305558\) \(a_{92}=+2.297137200\) \(a_{93}=-0.440993763\) \(a_{94}=+3.420328212\) \(a_{95}=-0.488320867\)
\(a_{96}=+1.397767402\) \(a_{97}=+0.806849047\) \(a_{98}=-0.267786850\) \(a_{99}=+0.401533211\) \(a_{100}=-0.351961487\)

Showing 100 of 1500 available coefficients

Rows: Cols: