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: \( 16.8886860039 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.595708682\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.282507162\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.128336430\)
\(a_{11}=+1.541327549\) \(a_{12}=-0.288675135\) \(a_{13}=-0.424036861\) \(a_{14}=+0.906869511\) \(a_{15}=+0.921282837\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.879759609\) \(a_{18}=+0.235702260\) \(a_{19}=-1.143589855\) \(a_{20}=-0.797854341\)
\(a_{21}=-0.740455855\) \(a_{22}=+1.089883162\) \(a_{23}=-1.281796318\) \(a_{24}=-0.204124145\) \(a_{25}=+1.546286198\)
\(a_{26}=-0.299839340\) \(a_{27}=-0.192450090\) \(a_{28}=+0.641253581\) \(a_{29}=+0.076940400\) \(a_{30}=+0.651445342\)
\(a_{31}=-0.372260115\) \(a_{32}=+0.176776695\) \(a_{33}=-0.889885875\) \(a_{34}=-0.622083985\) \(a_{35}=-2.046507814\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.613466465\) \(a_{38}=-0.808640141\) \(a_{39}=+0.244817796\) \(a_{40}=-0.564168215\)
\(a_{41}=-1.187940268\) \(a_{42}=-0.523581357\) \(a_{43}=-0.804910434\) \(a_{44}=+0.770663775\) \(a_{45}=-0.531902894\)
\(a_{46}=-0.906366869\) \(a_{47}=-1.261876293\) \(a_{48}=-0.144337567\) \(a_{49}=+0.644824622\) \(a_{50}=+1.093389456\)
\(a_{51}=+0.507929447\) \(a_{52}=-0.212018431\) \(a_{53}=-0.301092418\) \(a_{54}=-0.136082763\) \(a_{55}=-2.459509752\)
\(a_{56}=+0.453434756\) \(a_{57}=+0.660251910\) \(a_{58}=+0.054405078\) \(a_{59}=-0.995231829\) \(a_{60}=+0.460641419\)
\(a_{61}=+0.690218870\) \(a_{62}=-0.263227651\) \(a_{63}=+0.427502387\) \(a_{64}=+0.125000000\) \(a_{65}=+0.676639301\)
\(a_{66}=-0.629244337\) \(a_{67}=-0.004799370\) \(a_{68}=-0.439879804\) \(a_{69}=+0.740045449\) \(a_{70}=-1.447099553\)
\(a_{71}=-0.001037440\) \(a_{72}=+0.117851130\) \(a_{73}=+0.248810580\) \(a_{74}=+0.433786297\) \(a_{75}=-0.892748753\)
\(a_{76}=-0.571794927\) \(a_{77}=+1.976763621\) \(a_{78}=+0.173112324\) \(a_{79}=-0.768964000\) \(a_{80}=-0.398927171\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.840000619\) \(a_{83}=+1.486639977\) \(a_{84}=-0.370227928\) \(a_{85}=+1.403840046\)
\(a_{86}=-0.569157626\) \(a_{87}=-0.044421560\) \(a_{88}=+0.544941581\) \(a_{89}=-1.285100000\) \(a_{90}=-0.376112143\)
\(a_{91}=-0.543830312\) \(a_{92}=-0.640898159\) \(a_{93}=+0.214924477\) \(a_{94}=-0.892281284\) \(a_{95}=+1.824836260\)
\(a_{96}=-0.102062073\)

Showing all 96 available coefficients

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