Properties

Label 5.28
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 10.63115
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(10.631153086564503430411822531 \pm 10 \cdot 10^{-11}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -0.81166960 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.00486297 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.34119246 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.00394712 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +1.42360112 \pm 1 \cdot 10^{-8} \) \(a_{8}= +1.08860515 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.99997635 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.36298968 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.57357140 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.00165921 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.81441857 \pm 1 \cdot 10^{-8} \) \(a_{14}= -1.15549376 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.00217479 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.54239525 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.31097435 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.81165041 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.57750416 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.15258591 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +0.00692293 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.46555047 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.24308126 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.00529385 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.66103879 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.00972582 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.48572197 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.45670957 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.00176521 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -1.60184005 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.64835941 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.00278926 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.25240842 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.63665378 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.34118439 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.10194376 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.46874257 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.00396049 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.48683902 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.46544734 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.00561913 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.62106549 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.19569823 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.44720302 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +1.00897127 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.19074173 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.00263765 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +1.02664016 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.16233392 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.00151226 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.27787347 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.17316185 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.00789416 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.25650893 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +1.54973951 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.00280838 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.18236688 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.15427601 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.00074202 \pm 1.0 \cdot 10^{-8} \)

Displaying $a_n$ with $n$ up to: 60 180 1000