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: \( 15.0055700413 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.075835997\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.210722435\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.227214185\) \(a_{12}=+0.000000000\) \(a_{13}=-0.602740811\) \(a_{14}=+0.000000000\) \(a_{15}=-0.621134202\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.211015033\) \(a_{18}=+0.000000000\) \(a_{19}=+0.162408593\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.121660654\) \(a_{22}=+0.000000000\) \(a_{23}=+1.826266454\) \(a_{24}=+0.000000000\) \(a_{25}=+0.157423093\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-1.189885570\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.632443266\) \(a_{32}=+0.000000000\) \(a_{33}=+0.708532440\) \(a_{34}=+0.000000000\) \(a_{35}=+0.226702780\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.206757526\) \(a_{38}=+0.000000000\) \(a_{39}=+0.347992570\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.141086912\) \(a_{42}=+0.000000000\) \(a_{43}=+1.387068116\) \(a_{44}=+0.000000000\) \(a_{45}=+0.358611999\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.402437682\) \(a_{48}=+0.000000000\) \(a_{49}=-0.955596056\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.121829586\) \(a_{52}=+0.000000000\) \(a_{53}=-0.726667176\) \(a_{54}=+0.000000000\) \(a_{55}=-1.320281196\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.093766645\) \(a_{58}=+0.000000000\) \(a_{59}=-1.869147885\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.401046356\) \(a_{62}=+0.000000000\) \(a_{63}=+0.070240812\) \(a_{64}=+0.000000000\) \(a_{65}=-0.648450262\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.506912332\) \(a_{68}=+0.000000000\) \(a_{69}=-1.054395429\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.742162788\) \(a_{72}=+0.000000000\) \(a_{73}=-1.627371716\) \(a_{74}=+0.000000000\) \(a_{75}=-0.090888265\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.258601561\) \(a_{78}=+0.000000000\) \(a_{79}=-0.939099196\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.044727133\) \(a_{84}=+0.000000000\) \(a_{85}=+0.227017568\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.686980754\) \(a_{88}=+0.000000000\) \(a_{89}=-0.082431233\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.127011011\) \(a_{92}=+0.000000000\) \(a_{93}=+0.365141290\) \(a_{94}=+0.000000000\) \(a_{95}=+0.174725010\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.426205814\) \(a_{98}=+0.000000000\) \(a_{99}=-0.409071395\) \(a_{100}=+0.000000000\)

Showing 100 of 196 available coefficients

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