Properties

Label 5.118
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 20.35933
Fricke sign not computed rigorously

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: \(20.3593370401821489713520622198 \pm 9 \cdot 10^{-4}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.69363499 \pm 1.0 \) \(a_{3}= -1.32008305 \pm 1.1 \)
\(a_{4}= -0.51887050 \pm 9.3 \cdot 10^{-1} \) \(a_{5}= \pm0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.91565579 \pm 1.0 \)
\(a_{7}= +1.77749939 \pm 4.4 \cdot 10^{-1} \) \(a_{8}= +1.05354172 \pm 9.9 \cdot 10^{-1} \) \(a_{9}= +0.74261926 \pm 5.6 \cdot 10^{-1} \)
\(a_{10}= \pm0.31020300 \pm 4.7 \cdot 10^{-1} \) \(a_{11}= +0.93132069 \pm 5.9 \cdot 10^{-1} \) \(a_{12}= +0.68495215 \pm 9.6 \cdot 10^{-1} \)
\(a_{13}= -0.92870586 \pm 7.5 \cdot 10^{-1} \) \(a_{14}= -1.23293577 \pm 4.5 \cdot 10^{-1} \) \(a_{15}= \pm0.59035909 \pm 5.1 \cdot 10^{-1} \)
\(a_{16}= -0.21190290 \pm 4.7 \cdot 10^{-1} \) \(a_{17}= -0.61833714 \pm 1.1 \) \(a_{18}= -0.51510671 \pm 5.0 \cdot 10^{-1} \)
\(a_{19}= +1.23571786 \pm 1.1 \) \(a_{20}= \pm0.23204594 \pm 4.1 \cdot 10^{-1} \) \(a_{21}= -2.34644682 \pm 4.9 \cdot 10^{-1} \)
\(a_{22}= -0.64599661 \pm 6.3 \cdot 10^{-1} \) \(a_{23}= +0.63406692 \pm 4.6 \cdot 10^{-1} \) \(a_{24}= -1.39076258 \pm 1.0 \)
\(a_{25}= \pm0.2 \) \(a_{26}= +0.64418288 \pm 9.0 \cdot 10^{-1} \) \(a_{27}= +0.33976395 \pm 8.8 \cdot 10^{-1} \)
\(a_{28}= -0.92229200 \pm 3.6 \cdot 10^{-1} \) \(a_{29}= +0.12937389 \pm 5.4 \cdot 10^{-1} \) \(a_{30}= \pm0.40949372 \pm 4.9 \cdot 10^{-1} \)
\(a_{31}= -0.34874821 \pm 1.1 \) \(a_{32}= -0.90655846 \pm 1.1 \) \(a_{33}= -1.22942065 \pm 4.3 \cdot 10^{-1} \)
\(a_{34}= +0.42890028 \pm 1.1 \) \(a_{35}= \pm0.79492189 \pm 1.9 \cdot 10^{-1} \) \(a_{36}= -0.38532323 \pm 2.6 \cdot 10^{-1} \)
\(a_{37}= -1.61123588 \pm 1.4 \) \(a_{38}= -0.85713715 \pm 7.7 \cdot 10^{-1} \) \(a_{39}= +1.22596887 \pm 6.0 \cdot 10^{-1} \)
\(a_{40}= \pm0.47115818 \pm 4.4 \cdot 10^{-1} \) \(a_{41}= -0.59111522 \pm 1.2 \) \(a_{42}= +1.62757762 \pm 4.6 \cdot 10^{-1} \)
\(a_{43}= +1.87689094 \pm 1.2 \) \(a_{44}= -0.48323483 \pm 4.5 \cdot 10^{-1} \) \(a_{45}= \pm0.33210943 \pm 2.5 \cdot 10^{-1} \)
\(a_{46}= -0.43981100 \pm 5.5 \cdot 10^{-1} \) \(a_{47}= +0.16771543 \pm 7.1 \cdot 10^{-1} \) \(a_{48}= +0.27972943 \pm 4.8 \cdot 10^{-1} \)
\(a_{49}= +2.15950409 \pm 9.7 \cdot 10^{-1} \) \(a_{50}= \pm0.13872700 \pm 2.1 \cdot 10^{-1} \) \(a_{51}= +0.81625638 \pm 1.1 \)
\(a_{52}= +0.48187808 \pm 7.1 \cdot 10^{-1} \) \(a_{53}= +0.38788274 \pm 1.1 \) \(a_{54}= -0.23567216 \pm 9.1 \cdot 10^{-1} \)
\(a_{55}= \pm0.41649927 \pm 2.6 \cdot 10^{-1} \) \(a_{56}= +1.87266977 \pm 3.8 \cdot 10^{-1} \) \(a_{57}= -1.63125021 \pm 1.2 \)
\(a_{58}= -0.08973826 \pm 4.2 \cdot 10^{-1} \) \(a_{59}= +0.34344337 \pm 9.1 \cdot 10^{-1} \) \(a_{60}= \pm0.30631992 \pm 4.3 \cdot 10^{-1} \)

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