Properties

Label 11.152
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 14.42998
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(14.4299835020959630049341856446 \pm 6 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.67699455 \pm 6.9 \cdot 10^{-7} \) \(a_{3}= -1.19532106 \pm 7.3 \cdot 10^{-7} \)
\(a_{4}= -0.54167837 \pm 5.1 \cdot 10^{-7} \) \(a_{5}= +1.40703518 \pm 5.4 \cdot 10^{-7} \) \(a_{6}= -0.80922585 \pm 7.8 \cdot 10^{-7} \)
\(a_{7}= +0.23829628 \pm 4.2 \cdot 10^{-7} \) \(a_{8}= -1.04370786 \pm 6.9 \cdot 10^{-7} \) \(a_{9}= +0.42879244 \pm 7.4 \cdot 10^{-7} \)
\(a_{10}= +0.95255515 \pm 6.3 \cdot 10^{-7} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.64747957 \pm 4.8 \cdot 10^{-7} \)
\(a_{13}= +0.48285625 \pm 6.1 \cdot 10^{-7} \) \(a_{14}= +0.16132528 \pm 4.9 \cdot 10^{-7} \) \(a_{15}= -1.68185878 \pm 6.0 \cdot 10^{-7} \)
\(a_{16}= -0.16490617 \pm 7.2 \cdot 10^{-7} \) \(a_{17}= -1.14464083 \pm 5.4 \cdot 10^{-7} \) \(a_{18}= +0.29029015 \pm 7.6 \cdot 10^{-7} \)
\(a_{19}= -1.14023863 \pm 5.7 \cdot 10^{-7} \) \(a_{20}= -0.76216053 \pm 6.7 \cdot 10^{-7} \) \(a_{21}= -0.28484056 \pm 5.9 \cdot 10^{-7} \)
\(a_{22}= -0.20412154 \pm 7.0 \cdot 10^{-7} \) \(a_{23}= +0.53931985 \pm 5.5 \cdot 10^{-7} \) \(a_{24}= +1.24756599 \pm 7.3 \cdot 10^{-7} \)
\(a_{25}= +0.97974799 \pm 4.8 \cdot 10^{-7} \) \(a_{26}= +0.32689105 \pm 6.7 \cdot 10^{-7} \) \(a_{27}= +0.68277643 \pm 4.7 \cdot 10^{-7} \)
\(a_{28}= -0.12907994 \pm 3.4 \cdot 10^{-7} \) \(a_{29}= -0.75389948 \pm 6.6 \cdot 10^{-7} \) \(a_{30}= -1.13860924 \pm 6.4 \cdot 10^{-7} \)
\(a_{31}= -0.28691113 \pm 5.1 \cdot 10^{-7} \) \(a_{32}= +0.93206729 \pm 4.6 \cdot 10^{-7} \) \(a_{33}= +0.36040286 \pm 7.4 \cdot 10^{-7} \)
\(a_{34}= -0.77491561 \pm 5.2 \cdot 10^{-7} \) \(a_{35}= +0.33529125 \pm 3.6 \cdot 10^{-7} \) \(a_{36}= -0.23226759 \pm 3.5 \cdot 10^{-7} \)
\(a_{37}= +1.16075973 \pm 5.4 \cdot 10^{-7} \) \(a_{38}= -0.77193535 \pm 5.6 \cdot 10^{-7} \) \(a_{39}= -0.57716825 \pm 5.4 \cdot 10^{-7} \)
\(a_{40}= -1.46853368 \pm 7.2 \cdot 10^{-7} \) \(a_{41}= +0.76632156 \pm 6.3 \cdot 10^{-7} \) \(a_{42}= -0.19283551 \pm 6.6 \cdot 10^{-7} \)
\(a_{43}= +1.81313126 \pm 5.3 \cdot 10^{-7} \) \(a_{44}= +0.16332217 \pm 5.2 \cdot 10^{-7} \) \(a_{45}= +0.60332605 \pm 5.5 \cdot 10^{-7} \)
\(a_{46}= +0.36511660 \pm 6.2 \cdot 10^{-7} \) \(a_{47}= +1.00597444 \pm 6.5 \cdot 10^{-7} \) \(a_{48}= +0.19711581 \pm 8.3 \cdot 10^{-7} \)
\(a_{49}= -0.94321488 \pm 4.4 \cdot 10^{-7} \) \(a_{50}= +0.66328406 \pm 5.4 \cdot 10^{-7} \) \(a_{51}= +1.36821330 \pm 6.1 \cdot 10^{-7} \)
\(a_{52}= -0.26155279 \pm 3.0 \cdot 10^{-7} \) \(a_{53}= +1.42510208 \pm 6.7 \cdot 10^{-7} \) \(a_{54}= +0.46223592 \pm 5.6 \cdot 10^{-7} \)
\(a_{55}= -0.42423707 \pm 5.5 \cdot 10^{-7} \) \(a_{56}= -0.24871170 \pm 4.5 \cdot 10^{-7} \) \(a_{57}= +1.36295125 \pm 7.4 \cdot 10^{-7} \)
\(a_{58}= -0.51038584 \pm 6.9 \cdot 10^{-7} \) \(a_{59}= +0.52172759 \pm 8.3 \cdot 10^{-7} \) \(a_{60}= +0.91102653 \pm 6.2 \cdot 10^{-7} \)

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