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: \( 14.4676129234 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.432612118\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.911742594\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.305902962\)
\(a_{11}=+1.048731586\) \(a_{12}=-0.288675135\) \(a_{13}=-1.572300853\) \(a_{14}=-0.644699371\) \(a_{15}=-0.249768723\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.677935087\) \(a_{18}=+0.235702260\) \(a_{19}=-0.902890919\) \(a_{20}=+0.216306059\)
\(a_{21}=+0.526394832\) \(a_{22}=+0.741565216\) \(a_{23}=-1.085307869\) \(a_{24}=-0.204124145\) \(a_{25}=-0.812846755\)
\(a_{26}=-1.111784595\) \(a_{27}=-0.192450090\) \(a_{28}=-0.455871297\) \(a_{29}=-0.671404576\) \(a_{30}=-0.176613158\)
\(a_{31}=-0.884189931\) \(a_{32}=+0.176776695\) \(a_{33}=-0.605485463\) \(a_{34}=+0.479372497\) \(a_{35}=-0.394430898\)
\(a_{36}=+0.166666675\) \(a_{37}=-1.782790477\) \(a_{38}=-0.638440291\) \(a_{39}=+0.907768321\) \(a_{40}=+0.152951481\)
\(a_{41}=-0.261657580\) \(a_{42}=+0.372217355\) \(a_{43}=-0.111258809\) \(a_{44}=+0.524365793\) \(a_{45}=+0.144204039\)
\(a_{46}=-0.767428554\) \(a_{47}=+0.175860047\) \(a_{48}=-0.144337567\) \(a_{49}=-0.168725442\) \(a_{50}=-0.574769453\)
\(a_{51}=-0.391406005\) \(a_{52}=-0.786150427\) \(a_{53}=+1.769360458\) \(a_{54}=-0.136082763\) \(a_{55}=+0.453693993\)
\(a_{56}=-0.322349685\) \(a_{57}=+0.521284315\) \(a_{58}=-0.474754729\) \(a_{59}=+1.718539264\) \(a_{60}=-0.124884361\)
\(a_{61}=-1.588769576\) \(a_{62}=-0.625216696\) \(a_{63}=-0.303914198\) \(a_{64}=+0.125000000\) \(a_{65}=-0.680196403\)
\(a_{66}=-0.428142877\) \(a_{67}=+1.455438871\) \(a_{68}=+0.338967543\) \(a_{69}=+0.626602790\) \(a_{70}=-0.278904760\)
\(a_{71}=-0.286301127\) \(a_{72}=+0.117851131\) \(a_{73}=+1.438706678\) \(a_{74}=-1.260623235\) \(a_{75}=+0.469297293\)
\(a_{76}=-0.451445460\) \(a_{77}=-0.956173256\) \(a_{78}=+0.641889134\) \(a_{79}=-0.358577724\) \(a_{80}=+0.108153046\)
\(a_{81}=+0.111111115\) \(a_{82}=-0.185019849\) \(a_{83}=-0.571391613\) \(a_{84}=+0.263197416\) \(a_{85}=+0.293282934\)
\(a_{86}=-0.078671858\) \(a_{87}=+0.387635613\) \(a_{88}=+0.370782608\) \(a_{89}=-1.276416216\) \(a_{90}=+0.101967654\)
\(a_{91}=+1.433533658\) \(a_{92}=-0.542653935\) \(a_{93}=+0.510487295\) \(a_{94}=+0.124351832\) \(a_{95}=-0.390601553\)
\(a_{96}=-0.102062073\) \(a_{97}=+0.931848694\) \(a_{98}=-0.119306905\) \(a_{99}=+0.349577195\) \(a_{100}=-0.406423378\)

Showing 100 of 1000 available coefficients

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