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: \( 14.5742766808 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-1.448754403\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.148283625\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.860389957\) \(a_{12}=+0.000000000\) \(a_{13}=-0.646882281\) \(a_{14}=+0.000000000\) \(a_{15}=-0.836438744\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.485909231\) \(a_{18}=+0.000000000\) \(a_{19}=-0.130625224\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.085611591\) \(a_{22}=+0.000000000\) \(a_{23}=-0.525731618\) \(a_{24}=+0.000000000\) \(a_{25}=+1.098889320\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.787221401\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.033026897\) \(a_{32}=+0.000000000\) \(a_{33}=-1.074096643\) \(a_{34}=+0.000000000\) \(a_{35}=+0.214826554\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.809495887\) \(a_{38}=+0.000000000\) \(a_{39}=-0.373477659\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.155636702\) \(a_{42}=+0.000000000\) \(a_{43}=+0.045218081\) \(a_{44}=+0.000000000\) \(a_{45}=-0.482918134\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.176365428\) \(a_{48}=+0.000000000\) \(a_{49}=-0.978011967\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.857890095\) \(a_{52}=+0.000000000\) \(a_{53}=+1.851599340\) \(a_{54}=+0.000000000\) \(a_{55}=+2.695248142\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.075416508\) \(a_{58}=+0.000000000\) \(a_{59}=-0.441485814\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.683435924\) \(a_{62}=+0.000000000\) \(a_{63}=-0.049427875\) \(a_{64}=+0.000000000\) \(a_{65}=+0.937173552\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.791820169\) \(a_{68}=+0.000000000\) \(a_{69}=-0.303531291\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.201503390\) \(a_{72}=+0.000000000\) \(a_{73}=-0.083341578\) \(a_{74}=+0.000000000\) \(a_{75}=+0.634444045\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.275865366\) \(a_{78}=+0.000000000\) \(a_{79}=+0.947200282\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.551555848\) \(a_{84}=+0.000000000\) \(a_{85}=-2.152717541\)
\(a_{86}=+0.000000000\) \(a_{87}=+1.031852757\) \(a_{88}=+0.000000000\) \(a_{89}=+0.535881217\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.095922049\) \(a_{92}=+0.000000000\) \(a_{93}=-0.596418357\) \(a_{94}=+0.000000000\) \(a_{95}=+0.189243869\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.434392826\) \(a_{98}=+0.000000000\) \(a_{99}=-0.620129986\) \(a_{100}=+0.000000000\)

Showing 100 of 198 available coefficients

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