Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 16.2115601963 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.005991715\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.339161077\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.004236783\)
\(a_{11}=+0.889788488\) \(a_{12}=+0.288675135\) \(a_{13}=-0.230988178\) \(a_{14}=-0.239823097\) \(a_{15}=+0.003459319\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.972931203\) \(a_{18}=+0.235702260\) \(a_{19}=+0.461943938\) \(a_{20}=+0.002995858\)
\(a_{21}=-0.195814739\) \(a_{22}=+0.629175473\) \(a_{23}=-0.643454452\) \(a_{24}=+0.204124145\) \(a_{25}=-0.999964099\)
\(a_{26}=-0.163333307\) \(a_{27}=+0.192450090\) \(a_{28}=-0.169580538\) \(a_{29}=+0.328887613\) \(a_{30}=+0.002446108\)
\(a_{31}=+1.264586232\) \(a_{32}=+0.176776695\) \(a_{33}=+0.513719623\) \(a_{34}=+1.395073032\) \(a_{35}=-0.002032157\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.529010010\) \(a_{38}=+0.326643691\) \(a_{39}=-0.133361087\) \(a_{40}=+0.002118391\)
\(a_{41}=+1.633714598\) \(a_{42}=-0.138461930\) \(a_{43}=+1.152064665\) \(a_{44}=+0.444894244\) \(a_{45}=+0.001997238\)
\(a_{46}=-0.454991007\) \(a_{47}=-0.089558485\) \(a_{48}=+0.144337567\) \(a_{49}=-0.884969764\) \(a_{50}=-0.707081396\)
\(a_{51}=+1.139072361\) \(a_{52}=-0.115494089\) \(a_{53}=+1.545847291\) \(a_{54}=+0.136082763\) \(a_{55}=+0.005331359\)
\(a_{56}=-0.119911549\) \(a_{57}=+0.266703457\) \(a_{58}=+0.232558661\) \(a_{59}=-1.601408995\) \(a_{60}=+0.001729659\)
\(a_{61}=-0.594745260\) \(a_{62}=+0.894197500\) \(a_{63}=-0.113053692\) \(a_{64}=+0.125000000\) \(a_{65}=-0.001384015\)
\(a_{66}=+0.363254629\) \(a_{67}=-0.890833720\) \(a_{68}=+0.986465601\) \(a_{69}=-0.371498601\) \(a_{70}=-0.001436952\)
\(a_{71}=+1.398381300\) \(a_{72}=+0.117851130\) \(a_{73}=-1.193200500\) \(a_{74}=+0.374066566\) \(a_{75}=-0.577329542\)
\(a_{76}=+0.230971969\) \(a_{77}=-0.301781621\) \(a_{78}=-0.094300529\) \(a_{79}=-0.656413000\) \(a_{80}=+0.001497929\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.155210671\) \(a_{83}=-0.843900025\) \(a_{84}=-0.097907369\) \(a_{85}=+0.011821242\)
\(a_{86}=+0.814632737\) \(a_{87}=+0.189883352\) \(a_{88}=+0.314587737\) \(a_{89}=-0.531899989\) \(a_{90}=+0.001412261\)
\(a_{91}=+0.078342199\) \(a_{92}=-0.321727226\) \(a_{93}=+0.730109201\) \(a_{94}=-0.063327412\) \(a_{95}=+0.002767837\)
\(a_{96}=+0.102062073\) \(a_{97}=-0.610000610\) \(a_{98}=-0.625768121\) \(a_{99}=+0.296596163\) \(a_{100}=-0.499982050\)

Showing 100 of 106 available coefficients

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