Properties

Level $24$
Weight $0$
Character 24.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 24 = 2^{3} \cdot 3 \)
Weight: \( 0 \)
Character: 24.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 7.9395222316 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.239761044\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.188447497\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.495629443\) \(a_{12}=+0.000000000\) \(a_{13}=-0.447381199\) \(a_{14}=+0.000000000\) \(a_{15}=-0.715776373\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.868633181\) \(a_{18}=+0.000000000\) \(a_{19}=+1.063423771\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.108800213\) \(a_{22}=+0.000000000\) \(a_{23}=+0.755206330\) \(a_{24}=+0.000000000\) \(a_{25}=+0.537007447\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.920217577\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.212741299\) \(a_{32}=+0.000000000\) \(a_{33}=-0.286151792\) \(a_{34}=+0.000000000\) \(a_{35}=+0.233629866\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.893585653\) \(a_{38}=+0.000000000\) \(a_{39}=+0.258295655\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.846071031\) \(a_{42}=+0.000000000\) \(a_{43}=+1.171302818\) \(a_{44}=+0.000000000\) \(a_{45}=+0.413253681\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.302799379\) \(a_{48}=+0.000000000\) \(a_{49}=-0.964487541\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.078855870\) \(a_{52}=+0.000000000\) \(a_{53}=-1.398705606\) \(a_{54}=+0.000000000\) \(a_{55}=+0.614462075\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.613968000\) \(a_{58}=+0.000000000\) \(a_{59}=+1.467937116\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.412493522\) \(a_{62}=+0.000000000\) \(a_{63}=+0.062815832\) \(a_{64}=+0.000000000\) \(a_{65}=-0.554645782\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.881401420\) \(a_{68}=+0.000000000\) \(a_{69}=-0.436018578\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.076333979\) \(a_{72}=+0.000000000\) \(a_{73}=-0.053855719\) \(a_{74}=+0.000000000\) \(a_{75}=-0.310041394\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.093400128\) \(a_{78}=+0.000000000\) \(a_{79}=-0.385022306\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+0.052874089\) \(a_{84}=+0.000000000\) \(a_{85}=-2.316658624\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.531287866\) \(a_{88}=+0.000000000\) \(a_{89}=+1.863561136\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.084307867\) \(a_{92}=+0.000000000\) \(a_{93}=-0.700176515\) \(a_{94}=+0.000000000\) \(a_{95}=+1.318391365\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.212587673\) \(a_{98}=+0.000000000\) \(a_{99}=+0.165209814\) \(a_{100}=+0.000000000\)

Showing 100 of 306 available coefficients

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