Properties

Level $4$
Weight $0$
Character 4.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 4 = 2^{2} \)
Weight: \( 0 \)
Character: 4.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 23.4326487652 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+1.412246614\) \(a_{4}=+0.000000000\) \(a_{5}=-1.399745486\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.496095485\) \(a_{8}=+0.000000000\) \(a_{9}=+0.994440498\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.002100802\) \(a_{12}=+0.000000000\) \(a_{13}=+1.770677924\) \(a_{14}=+0.000000000\) \(a_{15}=-1.976785823\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.753696094\) \(a_{18}=+0.000000000\) \(a_{19}=-1.268809842\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.700609168\) \(a_{22}=+0.000000000\) \(a_{23}=-0.306229975\) \(a_{24}=+0.000000000\) \(a_{25}=+0.959287441\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.007851282\) \(a_{28}=+0.000000000\) \(a_{29}=-0.429366602\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.913451028\) \(a_{32}=+0.000000000\) \(a_{33}=+1.415255282\) \(a_{34}=+0.000000000\) \(a_{35}=+0.694688540\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.732140547\) \(a_{38}=+0.000000000\) \(a_{39}=+2.511876323\) \(a_{40}=+0.000000000\)

Showing all 40 available coefficients

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