Properties

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

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 5.35269680215 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-1.147179797\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.340504007\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.092999678\) \(a_{12}=+0.000000000\) \(a_{13}=-0.288055268\) \(a_{14}=+0.000000000\) \(a_{15}=-0.662324565\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.239104954\) \(a_{18}=+0.000000000\) \(a_{19}=+1.802364387\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.773940349\) \(a_{22}=+0.000000000\) \(a_{23}=-1.240579836\) \(a_{24}=+0.000000000\) \(a_{25}=+0.316021487\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-1.179930335\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.508847979\) \(a_{32}=+0.000000000\) \(a_{33}=-0.631043659\) \(a_{34}=+0.000000000\) \(a_{35}=+1.537799115\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.270586255\) \(a_{38}=+0.000000000\) \(a_{39}=-0.166308785\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.546344415\) \(a_{42}=+0.000000000\) \(a_{43}=-0.811847325\) \(a_{44}=+0.000000000\) \(a_{45}=-0.382393264\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.183505385\) \(a_{48}=+0.000000000\) \(a_{49}=+0.796950992\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.138047310\) \(a_{52}=+0.000000000\) \(a_{53}=-0.103054547\) \(a_{54}=+0.000000000\) \(a_{55}=+1.253867149\)
\(a_{56}=+0.000000000\) \(a_{57}=+1.040595564\) \(a_{58}=+0.000000000\) \(a_{59}=-0.783263584\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.193666747\) \(a_{62}=+0.000000000\) \(a_{63}=-0.446834669\) \(a_{64}=+0.000000000\) \(a_{65}=+0.330451183\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.727558458\) \(a_{68}=+0.000000000\) \(a_{69}=-0.716249102\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.538797746\) \(a_{72}=+0.000000000\) \(a_{73}=-1.353666356\) \(a_{74}=+0.000000000\) \(a_{75}=+0.182455095\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.465170425\) \(a_{78}=+0.000000000\) \(a_{79}=+0.778521156\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111149\) \(a_{82}=+0.000000000\) \(a_{83}=+1.390271755\) \(a_{84}=+0.000000000\) \(a_{85}=-0.274296272\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.681231743\) \(a_{88}=+0.000000000\) \(a_{89}=-0.870144372\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.386139240\) \(a_{92}=+0.000000000\) \(a_{93}=+0.871133787\) \(a_{94}=+0.000000000\) \(a_{95}=-2.067636012\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.023326323\) \(a_{98}=+0.000000000\) \(a_{99}=-0.364333226\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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