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: \( 9.43936207844 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-0.770254330\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.713468513\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.510844475\) \(a_{12}=+0.000000000\) \(a_{13}=-1.231142837\) \(a_{14}=+0.000000000\) \(a_{15}=-0.444706545\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.593907496\) \(a_{18}=+0.000000000\) \(a_{19}=+1.379474323\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.411921238\) \(a_{22}=+0.000000000\) \(a_{23}=+1.736536212\) \(a_{24}=+0.000000000\) \(a_{25}=-0.406708268\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.914284830\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.560099293\) \(a_{32}=+0.000000000\) \(a_{33}=+0.294936195\) \(a_{34}=+0.000000000\) \(a_{35}=-0.549552212\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.411770138\) \(a_{38}=+0.000000000\) \(a_{39}=-0.710800649\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.615533667\) \(a_{42}=+0.000000000\) \(a_{43}=+0.784633459\) \(a_{44}=+0.000000000\) \(a_{45}=-0.256751445\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.662817033\) \(a_{48}=+0.000000000\) \(a_{49}=-0.490962731\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.342892656\) \(a_{52}=+0.000000000\) \(a_{53}=-0.596603598\) \(a_{54}=+0.000000000\) \(a_{55}=-0.393480168\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.796439872\) \(a_{58}=+0.000000000\) \(a_{59}=-0.597807633\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.319789906\) \(a_{62}=+0.000000000\) \(a_{63}=+0.237822838\) \(a_{64}=+0.000000000\) \(a_{65}=+0.948293101\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.003234199\) \(a_{68}=+0.000000000\) \(a_{69}=+1.002589647\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.825623129\) \(a_{72}=+0.000000000\) \(a_{73}=-0.508164429\) \(a_{74}=+0.000000000\) \(a_{75}=-0.234813135\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.364471454\) \(a_{78}=+0.000000000\) \(a_{79}=-1.701604303\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.489760189\) \(a_{84}=+0.000000000\) \(a_{85}=-0.457459820\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.527862592\) \(a_{88}=+0.000000000\) \(a_{89}=+0.611063262\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.878381649\) \(a_{92}=+0.000000000\) \(a_{93}=+0.900723745\) \(a_{94}=+0.000000000\) \(a_{95}=-1.062546070\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.791334404\) \(a_{98}=+0.000000000\) \(a_{99}=+0.170281493\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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