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: \( 15.1846732396 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.260188399\)
\(a_{6}=+0.000000000\) \(a_{7}=+1.188664566\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.283029898\) \(a_{12}=+0.000000000\) \(a_{13}=+1.730560416\) \(a_{14}=+0.000000000\) \(a_{15}=-0.727570111\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.405216655\) \(a_{18}=+0.000000000\) \(a_{19}=-0.467128527\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.686275807\) \(a_{22}=+0.000000000\) \(a_{23}=-1.316804942\) \(a_{24}=+0.000000000\) \(a_{25}=+0.588074801\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.248010194\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.045352036\) \(a_{32}=+0.000000000\) \(a_{33}=-0.740757657\) \(a_{34}=+0.000000000\) \(a_{35}=+1.497941296\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.718574255\) \(a_{38}=+0.000000000\) \(a_{39}=-0.999139522\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.685997488\) \(a_{42}=+0.000000000\) \(a_{43}=-1.628358088\) \(a_{44}=+0.000000000\) \(a_{45}=+0.420062800\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.890228805\) \(a_{48}=+0.000000000\) \(a_{49}=+0.412923450\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.811302214\) \(a_{52}=+0.000000000\) \(a_{53}=+1.156951797\) \(a_{54}=+0.000000000\) \(a_{55}=+1.616859393\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.269696781\) \(a_{58}=+0.000000000\) \(a_{59}=-0.166944326\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.322109704\) \(a_{62}=+0.000000000\) \(a_{63}=+0.396221522\) \(a_{64}=+0.000000000\) \(a_{65}=+2.180832161\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.490391102\) \(a_{68}=+0.000000000\) \(a_{69}=+0.760257688\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.153841798\) \(a_{72}=+0.000000000\) \(a_{73}=-0.470202684\) \(a_{74}=+0.000000000\) \(a_{75}=-0.339525145\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.525092176\) \(a_{78}=+0.000000000\) \(a_{79}=-0.822370657\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.541338868\) \(a_{84}=+0.000000000\) \(a_{85}=+1.770837727\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.143188752\) \(a_{88}=+0.000000000\) \(a_{89}=-0.353075927\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.057055846\) \(a_{92}=+0.000000000\) \(a_{93}=-0.603534279\) \(a_{94}=+0.000000000\) \(a_{95}=-0.588669951\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.763598258\) \(a_{98}=+0.000000000\) \(a_{99}=+0.427676633\) \(a_{100}=+0.000000000\)

Showing 100 of 196 available coefficients

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