Properties

Level $12$
Weight $0$
Character 12.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 15.4079280409 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.338299413\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.808563562\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.126204002\) \(a_{12}=+0.000000000\) \(a_{13}=-0.234022093\) \(a_{14}=+0.000000000\) \(a_{15}=+0.195317257\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.554674140\) \(a_{18}=+0.000000000\) \(a_{19}=+1.443349330\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.466824390\) \(a_{22}=+0.000000000\) \(a_{23}=+0.237752074\) \(a_{24}=+0.000000000\) \(a_{25}=-0.885553507\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.637955546\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.824404332\) \(a_{32}=+0.000000000\) \(a_{33}=+0.650214184\) \(a_{34}=+0.000000000\) \(a_{35}=+0.273536578\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.334009135\) \(a_{38}=+0.000000000\) \(a_{39}=-0.135112719\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.952883950\) \(a_{42}=+0.000000000\) \(a_{43}=+0.514975666\) \(a_{44}=+0.000000000\) \(a_{45}=+0.112766471\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.143053018\) \(a_{48}=+0.000000000\) \(a_{49}=-0.346224967\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.320241264\) \(a_{52}=+0.000000000\) \(a_{53}=+1.095574633\) \(a_{54}=+0.000000000\) \(a_{55}=+0.380994152\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.833318124\) \(a_{58}=+0.000000000\) \(a_{59}=+1.814415898\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.086430759\) \(a_{62}=+0.000000000\) \(a_{63}=+0.269521187\) \(a_{64}=+0.000000000\) \(a_{65}=-0.079169537\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.908501075\) \(a_{68}=+0.000000000\) \(a_{69}=+0.137266224\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.381857365\) \(a_{72}=+0.000000000\) \(a_{73}=+1.534745810\) \(a_{74}=+0.000000000\) \(a_{75}=-0.511274556\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.910607519\) \(a_{78}=+0.000000000\) \(a_{79}=+0.586330322\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+1.488688754\) \(a_{84}=+0.000000000\) \(a_{85}=-0.187645936\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.368323806\) \(a_{88}=+0.000000000\) \(a_{89}=-1.712334528\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.189221737\) \(a_{92}=+0.000000000\) \(a_{93}=+0.475970063\) \(a_{94}=+0.000000000\) \(a_{95}=+0.488284231\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.157291685\) \(a_{98}=+0.000000000\) \(a_{99}=+0.375401334\) \(a_{100}=+0.000000000\)

Showing 100 of 210 available coefficients

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