Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 15.1417241517 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.292118328\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.561417624\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.913665632\)
\(a_{11}=-0.983894704\) \(a_{12}=-0.288675135\) \(a_{13}=+1.133168855\) \(a_{14}=-0.396982209\) \(a_{15}=+0.746004864\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.457378090\) \(a_{18}=+0.235702260\) \(a_{19}=-1.244075220\) \(a_{20}=-0.646059164\)
\(a_{21}=+0.324134616\) \(a_{22}=-0.695718617\) \(a_{23}=+0.523897900\) \(a_{24}=-0.204124145\) \(a_{25}=+0.669569773\)
\(a_{26}=+0.801271381\) \(a_{27}=-0.192450090\) \(a_{28}=-0.280708812\) \(a_{29}=+1.701447267\) \(a_{30}=+0.527505098\)
\(a_{31}=+0.102536899\) \(a_{32}=+0.176776695\) \(a_{33}=+0.568051872\) \(a_{34}=+1.030521931\) \(a_{35}=+0.725418002\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.004386952\) \(a_{38}=-0.879694024\) \(a_{39}=-0.654235343\) \(a_{40}=-0.456832816\)
\(a_{41}=+1.131937916\) \(a_{42}=+0.229197785\) \(a_{43}=+1.172414292\) \(a_{44}=-0.491947352\) \(a_{45}=-0.430706109\)
\(a_{46}=+0.370451758\) \(a_{47}=+0.959169248\) \(a_{48}=-0.144337567\) \(a_{49}=-0.684810251\) \(a_{50}=+0.473457327\)
\(a_{51}=-0.841417633\) \(a_{52}=+0.566584427\) \(a_{53}=-1.720848600\) \(a_{54}=-0.136082763\) \(a_{55}=+1.271308379\)
\(a_{56}=-0.198491105\) \(a_{57}=+0.718267163\) \(a_{58}=+1.203104900\) \(a_{59}=-0.229051990\) \(a_{60}=+0.373002432\)
\(a_{61}=-1.151015250\) \(a_{62}=+0.072504537\) \(a_{63}=-0.187139208\) \(a_{64}=+0.125000000\) \(a_{65}=-1.464188246\)
\(a_{66}=+0.401673331\) \(a_{67}=-0.184088000\) \(a_{68}=+0.728689045\) \(a_{69}=-0.302472594\) \(a_{70}=+0.512947988\)
\(a_{71}=-0.778455000\) \(a_{72}=+0.117851130\) \(a_{73}=+1.344072998\) \(a_{74}=+0.710208824\) \(a_{75}=-0.386576289\)
\(a_{76}=-0.622037610\) \(a_{77}=+0.552375827\) \(a_{78}=-0.462614248\) \(a_{79}=-0.956440002\) \(a_{80}=-0.323029582\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.800400976\) \(a_{83}=+0.771100044\) \(a_{84}=+0.162067308\) \(a_{85}=-1.883104941\)
\(a_{86}=+0.829022096\) \(a_{87}=-0.982331038\) \(a_{88}=-0.347859308\) \(a_{89}=+1.445999146\) \(a_{90}=-0.304555211\)
\(a_{91}=-0.636180966\) \(a_{92}=+0.261948950\) \(a_{93}=-0.059199706\) \(a_{94}=+0.678235080\) \(a_{95}=+1.607492392\)
\(a_{96}=-0.102062073\)

Showing all 96 available coefficients

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