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: \( 2.88439837461 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-1.716257436\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.574391957\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.385921195\) \(a_{12}=+0.000000000\) \(a_{13}=-0.225674098\) \(a_{14}=+0.000000000\) \(a_{15}=+0.990881693\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.899623327\) \(a_{18}=+0.000000000\) \(a_{19}=-0.504730077\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.331625351\) \(a_{22}=+0.000000000\) \(a_{23}=+0.921599160\) \(a_{24}=+0.000000000\) \(a_{25}=+1.945539588\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.586503204\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.194969440\) \(a_{32}=+0.000000000\) \(a_{33}=+0.222811706\) \(a_{34}=+0.000000000\) \(a_{35}=-0.985804468\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.168017732\) \(a_{38}=+0.000000000\) \(a_{39}=+0.130293001\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.108192924\) \(a_{42}=+0.000000000\) \(a_{43}=-1.525612964\) \(a_{44}=+0.000000000\) \(a_{45}=-0.572085812\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.208260034\) \(a_{48}=+0.000000000\) \(a_{49}=-0.670073879\) \(a_{50}=+0.000000000\)
\(a_{51}=+1.096748039\) \(a_{52}=+0.000000000\) \(a_{53}=+0.414967551\) \(a_{54}=+0.000000000\) \(a_{55}=+0.662340120\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.291406045\) \(a_{58}=+0.000000000\) \(a_{59}=-0.510013743\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.130550213\) \(a_{62}=+0.000000000\) \(a_{63}=+0.191463989\) \(a_{64}=+0.000000000\) \(a_{65}=+0.387314854\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.808092100\) \(a_{68}=+0.000000000\) \(a_{69}=-0.532085543\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.619415733\) \(a_{72}=+0.000000000\) \(a_{73}=-1.022309498\) \(a_{74}=+0.000000000\) \(a_{75}=-1.123257806\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.221670014\) \(a_{78}=+0.000000000\) \(a_{79}=-1.031181732\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111105\) \(a_{82}=+0.000000000\) \(a_{83}=-0.460067862\) \(a_{84}=+0.000000000\) \(a_{85}=+3.260242316\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.338617927\) \(a_{88}=+0.000000000\) \(a_{89}=-0.796846579\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.129627398\) \(a_{92}=+0.000000000\) \(a_{93}=-0.112566284\) \(a_{94}=+0.000000000\) \(a_{95}=+0.866240378\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.381819387\) \(a_{98}=+0.000000000\) \(a_{99}=-0.128640352\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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