Properties

Label 5.53
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 14.03425
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(14.0342548178518598562834278234 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.53474823 \pm 4.7 \cdot 10^{-6} \) \(a_{3}= +1.80268776 \pm 5.1 \cdot 10^{-6} \)
\(a_{4}= +1.35545214 \pm 4.1 \cdot 10^{-6} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +2.76667185 \pm 4.8 \cdot 10^{-6} \)
\(a_{7}= -0.46705075 \pm 1.9 \cdot 10^{-6} \) \(a_{8}= +0.54552955 \pm 4.4 \cdot 10^{-6} \) \(a_{9}= +2.24968314 \pm 2.5 \cdot 10^{-6} \)
\(a_{10}= +0.68636028 \pm 4.7 \cdot 10^{-6} \) \(a_{11}= +0.73916855 \pm 2.6 \cdot 10^{-6} \) \(a_{12}= +2.44345698 \pm 4.3 \cdot 10^{-6} \)
\(a_{13}= -0.71617956 \pm 3.3 \cdot 10^{-6} \) \(a_{14}= -0.71680531 \pm 2.0 \cdot 10^{-6} \) \(a_{15}= +0.80618647 \pm 5.1 \cdot 10^{-6} \)
\(a_{16}= -0.51820163 \pm 2.1 \cdot 10^{-6} \) \(a_{17}= -1.27938300 \pm 5.2 \cdot 10^{-6} \) \(a_{18}= +3.45269723 \pm 2.2 \cdot 10^{-6} \)
\(a_{19}= -0.49486548 \pm 4.9 \cdot 10^{-6} \) \(a_{20}= +0.60617663 \pm 4.1 \cdot 10^{-6} \) \(a_{21}= -0.84194666 \pm 2.1 \cdot 10^{-6} \)
\(a_{22}= +1.13443763 \pm 2.8 \cdot 10^{-6} \) \(a_{23}= +1.28901318 \pm 2.0 \cdot 10^{-6} \) \(a_{24}= +0.98341944 \pm 4.6 \cdot 10^{-6} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.09915532 \pm 4.0 \cdot 10^{-6} \) \(a_{27}= +2.25278850 \pm 3.9 \cdot 10^{-6} \)
\(a_{28}= -0.63306493 \pm 1.6 \cdot 10^{-6} \) \(a_{29}= -0.99104796 \pm 2.4 \cdot 10^{-6} \) \(a_{30}= +1.23729327 \pm 9.9 \cdot 10^{-6} \)
\(a_{31}= +0.90597356 \pm 5.1 \cdot 10^{-6} \) \(a_{32}= -1.34083859 \pm 5.1 \cdot 10^{-6} \) \(a_{33}= +1.33249009 \pm 1.9 \cdot 10^{-6} \)
\(a_{34}= -1.96353081 \pm 5.0 \cdot 10^{-6} \) \(a_{35}= -0.20887144 \pm 1.9 \cdot 10^{-6} \) \(a_{36}= +3.04933784 \pm 1.1 \cdot 10^{-6} \)
\(a_{37}= +0.22283092 \pm 6.3 \cdot 10^{-6} \) \(a_{38}= -0.75949393 \pm 3.4 \cdot 10^{-6} \) \(a_{39}= -1.29104813 \pm 2.6 \cdot 10^{-6} \)
\(a_{40}= +0.24396823 \pm 4.4 \cdot 10^{-6} \) \(a_{41}= +0.05756213 \pm 5.4 \cdot 10^{-6} \) \(a_{42}= -1.29217615 \pm 2.0 \cdot 10^{-6} \)
\(a_{43}= -0.40814263 \pm 5.3 \cdot 10^{-6} \) \(a_{44}= +1.00190760 \pm 2.0 \cdot 10^{-6} \) \(a_{45}= +1.00608889 \pm 2.5 \cdot 10^{-6} \)
\(a_{46}= +1.97831071 \pm 2.4 \cdot 10^{-6} \) \(a_{47}= -0.10966020 \pm 3.1 \cdot 10^{-6} \) \(a_{48}= -0.93415574 \pm 2.1 \cdot 10^{-6} \)
\(a_{49}= -0.78186360 \pm 4.3 \cdot 10^{-6} \) \(a_{50}= +0.30694965 \pm 4.7 \cdot 10^{-6} \) \(a_{51}= -2.30632808 \pm 5.1 \cdot 10^{-6} \)
\(a_{52}= -0.97074712 \pm 3.2 \cdot 10^{-6} \) \(a_{53}= +0.25023030 \pm 5.0 \cdot 10^{-6} \) \(a_{54}= +3.45746318 \pm 4.0 \cdot 10^{-6} \)
\(a_{55}= +0.33056623 \pm 2.6 \cdot 10^{-6} \) \(a_{56}= -0.25478998 \pm 1.7 \cdot 10^{-6} \) \(a_{57}= -0.89208795 \pm 5.6 \cdot 10^{-6} \)
\(a_{58}= -1.52100911 \pm 1.8 \cdot 10^{-6} \) \(a_{59}= +0.99922716 \pm 4.0 \cdot 10^{-6} \) \(a_{60}= +1.09274718 \pm 9.3 \cdot 10^{-6} \)

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