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: \( 12.3544320764 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.153759105\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.630802425\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.108724106\)
\(a_{11}=-1.390109578\) \(a_{12}=-0.288675135\) \(a_{13}=-1.193116027\) \(a_{14}=+0.446044672\) \(a_{15}=-0.088772860\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.590844704\) \(a_{18}=-0.235702260\) \(a_{19}=+1.393612701\) \(a_{20}=+0.076879552\)
\(a_{21}=+0.364193950\) \(a_{22}=+0.982955909\) \(a_{23}=+1.171968791\) \(a_{24}=+0.204124145\) \(a_{25}=-0.976358138\)
\(a_{26}=+0.843660433\) \(a_{27}=-0.192450090\) \(a_{28}=-0.315401212\) \(a_{29}=+0.777427282\) \(a_{30}=+0.062771892\)
\(a_{31}=+0.541132196\) \(a_{32}=-0.176776697\) \(a_{33}=+0.802580143\) \(a_{34}=-0.417790297\) \(a_{35}=-0.096991616\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.942251779\) \(a_{38}=-0.985432992\) \(a_{39}=+0.688845859\) \(a_{40}=-0.054362053\)
\(a_{41}=+1.059913105\) \(a_{42}=-0.257524012\) \(a_{43}=+1.782980979\) \(a_{44}=-0.695054789\) \(a_{45}=+0.051253035\)
\(a_{46}=-0.828707080\) \(a_{47}=-0.478952423\) \(a_{48}=-0.144337567\) \(a_{49}=-0.602088301\) \(a_{50}=+0.690389460\)
\(a_{51}=-0.341124349\) \(a_{52}=-0.596558013\) \(a_{53}=+1.644024707\) \(a_{54}=+0.136082763\) \(a_{55}=-0.213742004\)
\(a_{56}=+0.223022336\) \(a_{57}=-0.804602668\) \(a_{58}=-0.549724103\) \(a_{59}=+1.768260886\) \(a_{60}=-0.044386430\)
\(a_{61}=-0.285040311\) \(a_{62}=-0.382638245\) \(a_{63}=-0.210267475\) \(a_{64}=+0.125000000\) \(a_{65}=-0.183452452\)
\(a_{66}=-0.567509859\) \(a_{67}=-0.052690245\) \(a_{68}=+0.295422352\) \(a_{69}=-0.676636497\) \(a_{70}=+0.068583429\)
\(a_{71}=+1.226052428\) \(a_{72}=-0.117851131\) \(a_{73}=-1.016739939\) \(a_{74}=+0.666272623\) \(a_{75}=+0.563700633\)
\(a_{76}=+0.696806351\) \(a_{77}=+0.876884497\) \(a_{78}=-0.487087568\) \(a_{79}=-1.163024874\) \(a_{80}=+0.038439776\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.749471744\) \(a_{83}=-0.073418481\) \(a_{84}=+0.182096975\) \(a_{85}=+0.090847753\)
\(a_{86}=-1.260757941\) \(a_{87}=-0.448847850\) \(a_{88}=+0.491477955\) \(a_{89}=+0.649717701\) \(a_{90}=-0.036241369\)
\(a_{91}=+0.752620483\) \(a_{92}=+0.585984396\) \(a_{93}=-0.312422819\) \(a_{94}=+0.338670506\) \(a_{95}=+0.214280641\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.178916301\) \(a_{98}=+0.425740720\) \(a_{99}=-0.463369859\) \(a_{100}=-0.488179069\)

Showing 100 of 1000 available coefficients

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