Properties

Label 5.38
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 12.12077
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(12.1207735458662596310782812941 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.86250554 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.24430311 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.46892689 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +2.31752144 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.37429656 \pm 1 \cdot 10^{-8} \) \(a_{8}= +2.73588447 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.54829023 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.83293780 \pm 1.2 \cdot 10^{-8} \) \(a_{11}= -0.66447859 \pm 1 \cdot 10^{-8} \) \(a_{12}= +3.07209340 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -1.12221953 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.69712942 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.55646927 \pm 1.2 \cdot 10^{-8} \)
\(a_{16}= +2.62667309 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.55828246 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.02119359 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.53869025 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.10413767 \pm 1.2 \cdot 10^{-8} \) \(a_{21}= +0.46573838 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -1.23759505 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.11774247 \pm 1 \cdot 10^{-8} \) \(a_{24}= +3.40426955 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -2.09014009 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.56206387 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.92411084 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.57335873 \pm 1 \cdot 10^{-8} \) \(a_{30}= -1.03642709 \pm 1.4 \cdot 10^{-8} \)
\(a_{31}= -0.39813933 \pm 1 \cdot 10^{-8} \) \(a_{32}= +2.15630871 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.82681277 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.03980418 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.16739051 \pm 1.3 \cdot 10^{-8} \) \(a_{36}= +1.35368849 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.29128183 \pm 1 \cdot 10^{-8} \) \(a_{38}= +2.86581912 \pm 1 \cdot 10^{-8} \) \(a_{39}= -1.39638125 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -1.22352473 \pm 1.3 \cdot 10^{-8} \) \(a_{41}= +0.06993954 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.86744030 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.12491591 \pm 1 \cdot 10^{-8} \) \(a_{44}= -1.64054905 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.24520284 \pm 1.1 \cdot 10^{-8} \)
\(a_{46}= -0.21929601 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.42554400 \pm 1 \cdot 10^{-8} \) \(a_{48}= +3.26837749 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.85990208 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.37250111 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= -0.69467260 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -2.77067797 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.41010604 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.04684708 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.29716386 \pm 1.3 \cdot 10^{-8} \) \(a_{56}= +1.02403215 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.91459706 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +1.06788380 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.48036131 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.37388194 \pm 1.4 \cdot 10^{-8} \)

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