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: \( 11.7057493189 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.668509687\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.072066132\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.472707733\)
\(a_{11}=+1.679854115\) \(a_{12}=+0.288675135\) \(a_{13}=-0.943900033\) \(a_{14}=+0.050958450\) \(a_{15}=-0.385964248\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.256858646\) \(a_{18}=-0.235702260\) \(a_{19}=-1.081231786\) \(a_{20}=-0.334254844\)
\(a_{21}=-0.041607401\) \(a_{22}=-1.187836236\) \(a_{23}=+0.425574459\) \(a_{24}=-0.204124145\) \(a_{25}=-0.553094798\)
\(a_{26}=+0.667438114\) \(a_{27}=+0.192450090\) \(a_{28}=-0.036033066\) \(a_{29}=-1.158290436\) \(a_{30}=+0.272917937\)
\(a_{31}=-1.101928725\) \(a_{32}=-0.176776689\) \(a_{33}=+0.969864226\) \(a_{34}=+0.888733271\) \(a_{35}=+0.048176907\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.819187017\) \(a_{38}=+0.764546328\) \(a_{39}=-0.544960938\) \(a_{40}=+0.236353867\)
\(a_{41}=-1.727463233\) \(a_{42}=+0.029420875\) \(a_{43}=+0.246157732\) \(a_{44}=+0.839927058\) \(a_{45}=-0.222836562\)
\(a_{46}=-0.300926586\) \(a_{47}=+1.815327558\) \(a_{48}=+0.144337567\) \(a_{49}=-0.994806473\) \(a_{50}=+0.391097082\)
\(a_{51}=-0.725647677\) \(a_{52}=-0.471950017\) \(a_{53}=+1.023155431\) \(a_{54}=-0.136082763\) \(a_{55}=-1.122998749\)
\(a_{56}=+0.025479225\) \(a_{57}=-0.624249463\) \(a_{58}=+0.819035022\) \(a_{59}=+0.319305641\) \(a_{60}=-0.192982124\)
\(a_{61}=+0.075488963\) \(a_{62}=+0.779181273\) \(a_{63}=-0.024022044\) \(a_{64}=+0.125000000\) \(a_{65}=+0.631006316\)
\(a_{66}=-0.685797570\) \(a_{67}=-0.392935218\) \(a_{68}=-0.628429323\) \(a_{69}=+0.245705529\) \(a_{70}=-0.034066220\)
\(a_{71}=+1.154396176\) \(a_{72}=-0.117851131\) \(a_{73}=-1.518368518\) \(a_{74}=+0.579252702\) \(a_{75}=-0.319329435\)
\(a_{76}=-0.540615910\) \(a_{77}=-0.121060588\) \(a_{78}=+0.385345575\) \(a_{79}=+0.152934540\) \(a_{80}=-0.167127422\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.221500967\) \(a_{83}=+0.683266055\) \(a_{84}=-0.020803700\) \(a_{85}=+0.840222180\)
\(a_{86}=-0.174059802\) \(a_{87}=-0.668739295\) \(a_{88}=-0.593918118\) \(a_{89}=-1.303752449\) \(a_{90}=+0.157569244\)
\(a_{91}=+0.068023224\) \(a_{92}=+0.212787230\) \(a_{93}=-0.636198845\) \(a_{94}=-1.283630426\) \(a_{95}=+0.722813923\)
\(a_{96}=-0.102062073\) \(a_{97}=+0.725986072\) \(a_{98}=+0.703434403\) \(a_{99}=+0.559951372\) \(a_{100}=-0.276547399\)

Showing 100 of 1000 available coefficients

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