Properties

Label 5.36
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 11.87084
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(11.8708494299610709121935764783 \pm 7 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.90216504 \pm 2.2 \cdot 10^{-7} \) \(a_{3}= +1.11027136 \pm 2.4 \cdot 10^{-7} \)
\(a_{4}= -0.18609823 \pm 1.9 \cdot 10^{-7} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -1.00164802 \pm 2.2 \cdot 10^{-7} \)
\(a_{7}= +0.29262002 \pm 9.2 \cdot 10^{-8} \) \(a_{8}= +1.07005636 \pm 2.0 \cdot 10^{-7} \) \(a_{9}= +0.23270250 \pm 1.1 \cdot 10^{-7} \)
\(a_{10}= +0.40346047 \pm 2.3 \cdot 10^{-7} \) \(a_{11}= +1.12649795 \pm 1.2 \cdot 10^{-7} \) \(a_{12}= -0.20661954 \pm 2.0 \cdot 10^{-7} \)
\(a_{13}= -1.47610410 \pm 1.5 \cdot 10^{-7} \) \(a_{14}= -0.26399156 \pm 9.4 \cdot 10^{-8} \) \(a_{15}= -0.49652845 \pm 2.5 \cdot 10^{-7} \)
\(a_{16}= -0.77926922 \pm 9.8 \cdot 10^{-8} \) \(a_{17}= -0.30300272 \pm 2.4 \cdot 10^{-7} \) \(a_{18}= -0.20993606 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= -0.85351717 \pm 2.2 \cdot 10^{-7} \) \(a_{20}= +0.08322566 \pm 2.0 \cdot 10^{-7} \) \(a_{21}= +0.32488763 \pm 1.0 \cdot 10^{-7} \)
\(a_{22}= -1.01628707 \pm 1.3 \cdot 10^{-7} \) \(a_{23}= -1.28676882 \pm 9.6 \cdot 10^{-8} \) \(a_{24}= +1.18805294 \pm 2.1 \cdot 10^{-7} \)
\(a_{25}= +0.2 \) \(a_{26}= +1.33168953 \pm 1.8 \cdot 10^{-7} \) \(a_{27}= -0.85190844 \pm 1.8 \cdot 10^{-7} \)
\(a_{28}= -0.05445607 \pm 7.6 \cdot 10^{-8} \) \(a_{29}= -1.82849360 \pm 1.1 \cdot 10^{-7} \) \(a_{30}= +0.44795061 \pm 4.7 \cdot 10^{-7} \)
\(a_{31}= +0.26130441 \pm 2.3 \cdot 10^{-7} \) \(a_{32}= -0.36702692 \pm 2.4 \cdot 10^{-7} \) \(a_{33}= +1.25071842 \pm 8.9 \cdot 10^{-8} \)
\(a_{34}= +0.27335846 \pm 2.3 \cdot 10^{-7} \) \(a_{35}= -0.13086365 \pm 1.0 \cdot 10^{-7} \) \(a_{36}= -0.04330552 \pm 5.4 \cdot 10^{-8} \)
\(a_{37}= -0.33958279 \pm 2.9 \cdot 10^{-7} \) \(a_{38}= +0.77001336 \pm 1.6 \cdot 10^{-7} \) \(a_{39}= -1.63887612 \pm 1.2 \cdot 10^{-7} \)
\(a_{40}= -0.47854375 \pm 2.1 \cdot 10^{-7} \) \(a_{41}= +1.10074038 \pm 2.5 \cdot 10^{-7} \) \(a_{42}= -0.29310227 \pm 9.6 \cdot 10^{-8} \)
\(a_{43}= +0.06663303 \pm 2.5 \cdot 10^{-7} \) \(a_{44}= -0.20963928 \pm 9.4 \cdot 10^{-8} \) \(a_{45}= -0.10406772 \pm 1.2 \cdot 10^{-7} \)
\(a_{46}= +1.16087785 \pm 1.1 \cdot 10^{-7} \) \(a_{47}= +1.26014065 \pm 1.4 \cdot 10^{-7} \) \(a_{48}= -0.86520030 \pm 1.0 \cdot 10^{-7} \)
\(a_{49}= -0.91437352 \pm 2.0 \cdot 10^{-7} \) \(a_{50}= -0.18043301 \pm 2.3 \cdot 10^{-7} \) \(a_{51}= -0.33641524 \pm 2.4 \cdot 10^{-7} \)
\(a_{52}= +0.27470036 \pm 1.4 \cdot 10^{-7} \) \(a_{53}= -0.40773311 \pm 2.3 \cdot 10^{-7} \) \(a_{54}= +0.76856201 \pm 1.9 \cdot 10^{-7} \)
\(a_{55}= -0.50378520 \pm 1.3 \cdot 10^{-7} \) \(a_{56}= +0.31311992 \pm 8.0 \cdot 10^{-8} \) \(a_{57}= -0.94763568 \pm 2.6 \cdot 10^{-7} \)
\(a_{58}= +1.64960301 \pm 8.7 \cdot 10^{-8} \) \(a_{59}= -1.06795050 \pm 1.8 \cdot 10^{-7} \) \(a_{60}= +0.09240307 \pm 4.4 \cdot 10^{-7} \)

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