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: \( 8.48412118212 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.982188116\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.595879918\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.467957856\) \(a_{12}=+0.000000000\) \(a_{13}=+1.613519553\) \(a_{14}=+0.000000000\) \(a_{15}=+0.567066573\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.890378125\) \(a_{18}=+0.000000000\) \(a_{19}=-1.648744707\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.344031431\) \(a_{22}=+0.000000000\) \(a_{23}=+0.888581203\) \(a_{24}=+0.000000000\) \(a_{25}=-0.035306504\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.314484104\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.705865899\) \(a_{32}=+0.000000000\) \(a_{33}=+0.270175594\) \(a_{34}=+0.000000000\) \(a_{35}=+0.585266175\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.222524139\) \(a_{38}=+0.000000000\) \(a_{39}=+0.931565948\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.683487626\) \(a_{42}=+0.000000000\) \(a_{43}=+1.710174785\) \(a_{44}=+0.000000000\) \(a_{45}=+0.327396039\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.570912202\) \(a_{48}=+0.000000000\) \(a_{49}=-0.644927123\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.514060050\) \(a_{52}=+0.000000000\) \(a_{53}=+1.432019553\) \(a_{54}=+0.000000000\) \(a_{55}=+0.459622645\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.951903200\) \(a_{58}=+0.000000000\) \(a_{59}=-1.113596581\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.447595849\) \(a_{62}=+0.000000000\) \(a_{63}=+0.198626639\) \(a_{64}=+0.000000000\) \(a_{65}=+1.584779730\)
\(a_{66}=+0.000000000\) \(a_{67}=-1.711269255\) \(a_{68}=+0.000000000\) \(a_{69}=+0.513022597\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.682101072\) \(a_{72}=+0.000000000\) \(a_{73}=+1.876810743\) \(a_{74}=+0.000000000\) \(a_{75}=-0.020384220\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.278846689\) \(a_{78}=+0.000000000\) \(a_{79}=-0.970610722\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.795613659\) \(a_{84}=+0.000000000\) \(a_{85}=-0.874518813\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.181567482\) \(a_{88}=+0.000000000\) \(a_{89}=-1.382255454\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.961463899\) \(a_{92}=+0.000000000\) \(a_{93}=+0.407531867\) \(a_{94}=+0.000000000\) \(a_{95}=-1.619377458\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.733343580\) \(a_{98}=+0.000000000\) \(a_{99}=+0.155985952\) \(a_{100}=+0.000000000\)

Showing 100 of 330 available coefficients

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