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: \( 11.3130895989 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.140543474\)
\(a_{6}=+0.408248290\) \(a_{7}=+1.150748942\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.099379243\)
\(a_{11}=-0.990038367\) \(a_{12}=+0.288675135\) \(a_{13}=+1.122738584\) \(a_{14}=+0.813702381\) \(a_{15}=-0.081142812\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.588014056\) \(a_{18}=+0.235702260\) \(a_{19}=+1.903553307\) \(a_{20}=-0.070271737\)
\(a_{21}=+0.664385212\) \(a_{22}=-0.700062843\) \(a_{23}=+0.354552014\) \(a_{24}=+0.204124145\) \(a_{25}=-0.980247532\)
\(a_{26}=+0.793896067\) \(a_{27}=+0.192450090\) \(a_{28}=+0.575374472\) \(a_{29}=+0.818298102\) \(a_{30}=-0.057376635\)
\(a_{31}=-1.199634159\) \(a_{32}=+0.176776709\) \(a_{33}=-0.571598918\) \(a_{34}=+0.415788726\) \(a_{35}=-0.161730254\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.832567644\) \(a_{38}=+1.346015452\) \(a_{39}=+0.648213424\) \(a_{40}=-0.049689622\)
\(a_{41}=-1.522616846\) \(a_{42}=+0.469791288\) \(a_{43}=+0.976963085\) \(a_{44}=-0.495019184\) \(a_{45}=-0.046847825\)
\(a_{46}=+0.250706133\) \(a_{47}=-1.229918193\) \(a_{48}=+0.144337567\) \(a_{49}=+0.324223128\) \(a_{50}=-0.693139677\)
\(a_{51}=+0.339490073\) \(a_{52}=+0.561369292\) \(a_{53}=-0.159751218\) \(a_{54}=+0.136082763\) \(a_{55}=+0.139143431\)
\(a_{56}=+0.406851190\) \(a_{57}=+1.099017014\) \(a_{58}=+0.578624139\) \(a_{59}=-1.478349621\) \(a_{60}=-0.040571406\)
\(a_{61}=-1.280306314\) \(a_{62}=-0.848269459\) \(a_{63}=+0.383582981\) \(a_{64}=+0.125000000\) \(a_{65}=-0.157793581\)
\(a_{66}=-0.404181471\) \(a_{67}=+1.548880125\) \(a_{68}=+0.294007027\) \(a_{69}=+0.204700699\) \(a_{70}=-0.114360559\)
\(a_{71}=+0.529357534\) \(a_{72}=+0.117851126\) \(a_{73}=+0.050529394\) \(a_{74}=-0.588714229\) \(a_{75}=-0.565946162\)
\(a_{76}=+0.951776656\) \(a_{77}=-1.139285628\) \(a_{78}=+0.458356108\) \(a_{79}=-0.437187416\) \(a_{80}=-0.035135868\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.076652697\) \(a_{83}=+0.038912626\) \(a_{84}=+0.332192606\) \(a_{85}=-0.082641538\)
\(a_{86}=+0.690817222\) \(a_{87}=+0.472444631\) \(a_{88}=-0.350031422\) \(a_{89}=+0.245918918\) \(a_{90}=-0.033126414\)
\(a_{91}=+1.291990239\) \(a_{92}=+0.177276007\) \(a_{93}=-0.692609113\) \(a_{94}=-0.869683495\) \(a_{95}=-0.267531995\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.904585337\) \(a_{98}=+0.229260373\) \(a_{99}=-0.330012789\) \(a_{100}=-0.490123766\)

Showing 100 of 1000 available coefficients

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