Properties

Label 11.5
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 3.283472
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(3.283472435176575939419780285 \pm 2 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.13131099 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.22440636 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.27986456 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.58912233 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.25387338 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.34562008 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.81469714 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.94964179 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.66648057 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.06280339 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.56671434 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.39100380 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.13220280 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.20154039 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.31110338 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.07434019 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.60733675 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.16487446 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.07755934 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.34110310 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +1.70468915 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.18282322 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.65293488 \pm 1 \cdot 10^{-8} \) \(a_{26}= +1.77244116 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.43751201 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.09672681 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.36209325 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.14956248 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.58720283 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.54461870 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.06766106 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.35195468 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.20361251 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.26577108 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.10781508 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.68708674 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.35158066 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.47995628 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.20945871 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.08774374 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.18000122 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.08438234 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.55945518 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.92853357 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.72812046 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.26963330 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.88054676 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.73867241 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.06981358 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.43846782 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.54531721 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.49496215 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.17762707 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.28157569 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.13629023 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.54095107 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.53170771 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.03699888 \pm 1 \cdot 10^{-8} \)

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