Properties

Label 5.49
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 13.64739
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.6473942984543737641050917837 \pm 10 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.11088028 \pm 1.2 \cdot 10^{-5} \) \(a_{3}= -0.17425754 \pm 1.3 \cdot 10^{-5} \)
\(a_{4}= +0.23405500 \pm 1.0 \cdot 10^{-5} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.19357926 \pm 1.2 \cdot 10^{-5} \)
\(a_{7}= +1.83541165 \pm 5.0 \cdot 10^{-6} \) \(a_{8}= -0.85087320 \pm 1.1 \cdot 10^{-5} \) \(a_{9}= -0.96963431 \pm 6.4 \cdot 10^{-6} \)
\(a_{10}= -0.49680076 \pm 1.2 \cdot 10^{-5} \) \(a_{11}= -0.75542845 \pm 6.8 \cdot 10^{-6} \) \(a_{12}= -0.04078585 \pm 1.1 \cdot 10^{-5} \)
\(a_{13}= -1.05671932 \pm 8.6 \cdot 10^{-6} \) \(a_{14}= +2.03892261 \pm 5.1 \cdot 10^{-6} \) \(a_{15}= +0.07793034 \pm 1.3 \cdot 10^{-5} \)
\(a_{16}= -1.17927326 \pm 5.4 \cdot 10^{-6} \) \(a_{17}= -0.33370103 \pm 1.3 \cdot 10^{-5} \) \(a_{18}= -1.07714764 \pm 5.7 \cdot 10^{-6} \)
\(a_{19}= -0.19896072 \pm 1.2 \cdot 10^{-5} \) \(a_{20}= -0.10467258 \pm 1.0 \cdot 10^{-5} \) \(a_{21}= -0.31983432 \pm 5.6 \cdot 10^{-6} \)
\(a_{22}= -0.83919057 \pm 7.2 \cdot 10^{-6} \) \(a_{23}= -1.52474887 \pm 5.2 \cdot 10^{-6} \) \(a_{24}= +0.14827107 \pm 1.1 \cdot 10^{-5} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.17388866 \pm 1.0 \cdot 10^{-5} \) \(a_{27}= +0.34322363 \pm 1.0 \cdot 10^{-5} \)
\(a_{28}= +0.42958727 \pm 4.1 \cdot 10^{-6} \) \(a_{29}= -0.92616787 \pm 6.1 \cdot 10^{-6} \) \(a_{30}= +0.08657128 \pm 2.5 \cdot 10^{-5} \)
\(a_{31}= +0.57848674 \pm 1.3 \cdot 10^{-5} \) \(a_{32}= -0.45915821 \pm 1.3 \cdot 10^{-5} \) \(a_{33}= +0.13163910 \pm 4.9 \cdot 10^{-6} \)
\(a_{34}= -0.37070189 \pm 1.2 \cdot 10^{-5} \) \(a_{35}= -0.82082104 \pm 5.0 \cdot 10^{-6} \) \(a_{36}= -0.22694776 \pm 3.0 \cdot 10^{-6} \)
\(a_{37}= +1.12637488 \pm 1.6 \cdot 10^{-5} \) \(a_{38}= -0.22102154 \pm 8.8 \cdot 10^{-6} \) \(a_{39}= +0.18414131 \pm 6.8 \cdot 10^{-6} \)
\(a_{40}= +0.38052206 \pm 1.1 \cdot 10^{-5} \) \(a_{41}= +0.52233007 \pm 1.3 \cdot 10^{-5} \) \(a_{42}= -0.35529764 \pm 5.2 \cdot 10^{-6} \)
\(a_{43}= -0.57389719 \pm 1.3 \cdot 10^{-5} \) \(a_{44}= -0.17681181 \pm 5.1 \cdot 10^{-6} \) \(a_{45}= +0.43363365 \pm 6.4 \cdot 10^{-6} \)
\(a_{46}= -1.69381346 \pm 6.3 \cdot 10^{-6} \) \(a_{47}= -0.46539521 \pm 8.1 \cdot 10^{-6} \) \(a_{48}= +0.20549726 \pm 5.5 \cdot 10^{-6} \)
\(a_{49}= +2.36873593 \pm 1.1 \cdot 10^{-5} \) \(a_{50}= +0.22217606 \pm 1.2 \cdot 10^{-5} \) \(a_{51}= +0.05814992 \pm 1.3 \cdot 10^{-5} \)
\(a_{52}= -0.24733044 \pm 8.2 \cdot 10^{-6} \) \(a_{53}= -0.48902105 \pm 1.2 \cdot 10^{-5} \) \(a_{54}= +0.38128036 \pm 1.0 \cdot 10^{-5} \)
\(a_{55}= +0.33783787 \pm 6.8 \cdot 10^{-6} \) \(a_{56}= -1.56170258 \pm 4.4 \cdot 10^{-6} \) \(a_{57}= +0.03467041 \pm 1.4 \cdot 10^{-5} \)
\(a_{58}= -1.02886162 \pm 4.8 \cdot 10^{-6} \) \(a_{59}= +0.27014848 \pm 1.0 \cdot 10^{-5} \) \(a_{60}= +0.01823999 \pm 2.3 \cdot 10^{-5} \)

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