Properties

Label 11.85
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 10.98990
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(10.9899047920475420421886097926 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.37799891 \pm 5.7 \cdot 10^{-7} \) \(a_{3}= -1.76401178 \pm 4.7 \cdot 10^{-7} \)
\(a_{4}= +0.89888100 \pm 6.7 \cdot 10^{-7} \) \(a_{5}= +0.56444728 \pm 4.9 \cdot 10^{-7} \) \(a_{6}= -2.43080631 \pm 5.8 \cdot 10^{-7} \)
\(a_{7}= +1.09281904 \pm 4.9 \cdot 10^{-7} \) \(a_{8}= -0.13934188 \pm 5.6 \cdot 10^{-7} \) \(a_{9}= +2.11173757 \pm 5.3 \cdot 10^{-7} \)
\(a_{10}= +0.77780773 \pm 6.0 \cdot 10^{-7} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -1.58563667 \pm 6.2 \cdot 10^{-7} \)
\(a_{13}= -0.16360491 \pm 3.9 \cdot 10^{-7} \) \(a_{14}= +1.50590345 \pm 4.1 \cdot 10^{-7} \) \(a_{15}= -0.99569165 \pm 3.7 \cdot 10^{-7} \)
\(a_{16}= -1.09089395 \pm 4.9 \cdot 10^{-7} \) \(a_{17}= -1.15982407 \pm 4.8 \cdot 10^{-7} \) \(a_{18}= +2.90997207 \pm 5.4 \cdot 10^{-7} \)
\(a_{19}= -1.18160512 \pm 3.5 \cdot 10^{-7} \) \(a_{20}= +0.50737093 \pm 6.5 \cdot 10^{-7} \) \(a_{21}= -1.92774566 \pm 3.8 \cdot 10^{-7} \)
\(a_{22}= -0.41548230 \pm 5.8 \cdot 10^{-7} \) \(a_{23}= +0.91885496 \pm 4.6 \cdot 10^{-7} \) \(a_{24}= +0.24580071 \pm 6.6 \cdot 10^{-7} \)
\(a_{25}= -0.68139927 \pm 4.0 \cdot 10^{-7} \) \(a_{26}= -0.22544738 \pm 3.0 \cdot 10^{-7} \) \(a_{27}= -1.96111817 \pm 4.5 \cdot 10^{-7} \)
\(a_{28}= +0.98231427 \pm 4.9 \cdot 10^{-7} \) \(a_{29}= -1.56124203 \pm 4.5 \cdot 10^{-7} \) \(a_{30}= -1.37206201 \pm 3.4 \cdot 10^{-7} \)
\(a_{31}= +0.87680398 \pm 4.8 \cdot 10^{-7} \) \(a_{32}= -1.36390880 \pm 4.1 \cdot 10^{-7} \) \(a_{33}= +0.53186956 \pm 4.8 \cdot 10^{-7} \)
\(a_{34}= -1.59823630 \pm 5.8 \cdot 10^{-7} \) \(a_{35}= +0.61683873 \pm 4.7 \cdot 10^{-7} \) \(a_{36}= +1.89820077 \pm 5.6 \cdot 10^{-7} \)
\(a_{37}= +0.24178608 \pm 4.9 \cdot 10^{-7} \) \(a_{38}= -1.62825057 \pm 4.8 \cdot 10^{-7} \) \(a_{39}= +0.28860098 \pm 2.8 \cdot 10^{-7} \)
\(a_{40}= -0.07865114 \pm 4.6 \cdot 10^{-7} \) \(a_{41}= +0.45191683 \pm 3.2 \cdot 10^{-7} \) \(a_{42}= -2.65643142 \pm 4.2 \cdot 10^{-7} \)
\(a_{43}= -1.95279426 \pm 4.6 \cdot 10^{-7} \) \(a_{44}= -0.27102282 \pm 6.8 \cdot 10^{-7} \) \(a_{45}= +1.19196452 \pm 5.2 \cdot 10^{-7} \)
\(a_{46}= +1.26618114 \pm 6.6 \cdot 10^{-7} \) \(a_{47}= -0.70127837 \pm 3.9 \cdot 10^{-7} \) \(a_{48}= +1.92434978 \pm 5.1 \cdot 10^{-7} \)
\(a_{49}= +0.19425346 \pm 4.3 \cdot 10^{-7} \) \(a_{50}= -0.93896745 \pm 6.2 \cdot 10^{-7} \) \(a_{51}= +2.04594332 \pm 4.8 \cdot 10^{-7} \)
\(a_{52}= -0.14706134 \pm 4.1 \cdot 10^{-7} \) \(a_{53}= +0.09587727 \pm 3.7 \cdot 10^{-7} \) \(a_{54}= -2.70241871 \pm 3.9 \cdot 10^{-7} \)
\(a_{55}= -0.17018726 \pm 5.0 \cdot 10^{-7} \) \(a_{56}= -0.15227546 \pm 3.3 \cdot 10^{-7} \) \(a_{57}= +2.08436536 \pm 3.1 \cdot 10^{-7} \)
\(a_{58}= -2.15138982 \pm 4.4 \cdot 10^{-7} \) \(a_{59}= -1.18938312 \pm 5.5 \cdot 10^{-7} \) \(a_{60}= -0.89500830 \pm 3.0 \cdot 10^{-7} \)

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