Properties

Label 11.38
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 7.599266
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(7.59926619692645837952332821359 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.87766224 \pm 2.3 \cdot 10^{-8} \) \(a_{3}= +1.16124289 \pm 1.9 \cdot 10^{-8} \)
\(a_{4}= -0.22970900 \pm 2.7 \cdot 10^{-8} \) \(a_{5}= -1.92995095 \pm 2.0 \cdot 10^{-8} \) \(a_{6}= +1.01917903 \pm 2.3 \cdot 10^{-8} \)
\(a_{7}= -0.08110149 \pm 2.0 \cdot 10^{-8} \) \(a_{8}= -1.07926915 \pm 2.3 \cdot 10^{-8} \) \(a_{9}= +0.34848504 \pm 2.1 \cdot 10^{-8} \)
\(a_{10}= -1.69384507 \pm 2.4 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.26674794 \pm 2.5 \cdot 10^{-8} \)
\(a_{13}= +0.69505004 \pm 1.5 \cdot 10^{-8} \) \(a_{14}= -0.07117971 \pm 1.6 \cdot 10^{-8} \) \(a_{15}= -2.24114181 \pm 1.5 \cdot 10^{-8} \)
\(a_{16}= -0.71752478 \pm 2.0 \cdot 10^{-8} \) \(a_{17}= -0.54788802 \pm 1.9 \cdot 10^{-8} \) \(a_{18}= +0.30585216 \pm 2.2 \cdot 10^{-8} \)
\(a_{19}= +0.25455234 \pm 1.4 \cdot 10^{-8} \) \(a_{20}= +0.44332710 \pm 2.6 \cdot 10^{-8} \) \(a_{21}= -0.09417852 \pm 1.5 \cdot 10^{-8} \)
\(a_{22}= -0.26462512 \pm 3.4 \cdot 10^{-8} \) \(a_{23}= -1.28028189 \pm 1.8 \cdot 10^{-8} \) \(a_{24}= -1.25329362 \pm 2.6 \cdot 10^{-8} \)
\(a_{25}= +2.72471067 \pm 1.6 \cdot 10^{-8} \) \(a_{26}= +0.61001917 \pm 1.2 \cdot 10^{-8} \) \(a_{27}= -0.75656711 \pm 1.8 \cdot 10^{-8} \)
\(a_{28}= +0.01862974 \pm 2.0 \cdot 10^{-8} \) \(a_{29}= -0.49018473 \pm 1.8 \cdot 10^{-8} \) \(a_{30}= -1.96696554 \pm 1.4 \cdot 10^{-8} \)
\(a_{31}= +1.19909892 \pm 1.9 \cdot 10^{-8} \) \(a_{32}= +0.44952475 \pm 1.6 \cdot 10^{-8} \) \(a_{33}= -0.35012790 \pm 2.9 \cdot 10^{-8} \)
\(a_{34}= -0.48086063 \pm 2.3 \cdot 10^{-8} \) \(a_{35}= +0.15652189 \pm 1.9 \cdot 10^{-8} \) \(a_{36}= -0.08005015 \pm 2.2 \cdot 10^{-8} \)
\(a_{37}= +0.26849749 \pm 1.9 \cdot 10^{-8} \) \(a_{38}= +0.22341098 \pm 1.9 \cdot 10^{-8} \) \(a_{39}= +0.80712192 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= +2.08293652 \pm 1.8 \cdot 10^{-8} \) \(a_{41}= -1.85859339 \pm 1.3 \cdot 10^{-8} \) \(a_{42}= -0.08265693 \pm 1.7 \cdot 10^{-8} \)
\(a_{43}= +0.20634587 \pm 1.9 \cdot 10^{-8} \) \(a_{44}= +0.06925987 \pm 3.7 \cdot 10^{-8} \) \(a_{45}= -0.67255904 \pm 2.1 \cdot 10^{-8} \)
\(a_{46}= -1.12365507 \pm 2.6 \cdot 10^{-8} \) \(a_{47}= +0.09776346 \pm 1.6 \cdot 10^{-8} \) \(a_{48}= -0.83322055 \pm 2.0 \cdot 10^{-8} \)
\(a_{49}= -0.99342255 \pm 1.7 \cdot 10^{-8} \) \(a_{50}= +2.39137566 \pm 2.5 \cdot 10^{-8} \) \(a_{51}= -0.63623107 \pm 1.9 \cdot 10^{-8} \)
\(a_{52}= -0.15965925 \pm 1.6 \cdot 10^{-8} \) \(a_{53}= +1.22319198 \pm 1.5 \cdot 10^{-8} \) \(a_{54}= -0.66401038 \pm 1.5 \cdot 10^{-8} \)
\(a_{55}= +0.58190211 \pm 3.0 \cdot 10^{-8} \) \(a_{56}= +0.08753033 \pm 1.3 \cdot 10^{-8} \) \(a_{57}= +0.29559710 \pm 1.2 \cdot 10^{-8} \)
\(a_{58}= -0.43021663 \pm 1.8 \cdot 10^{-8} \) \(a_{59}= +0.27735127 \pm 2.2 \cdot 10^{-8} \) \(a_{60}= +0.51481044 \pm 1.2 \cdot 10^{-8} \)

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