Properties

Label 11.105
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 12.03811
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(12.0381132141352239525395110625 \pm 9 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.59997244 \pm 5.6 \cdot 10^{-8} \) \(a_{3}= +1.10777899 \pm 5.9 \cdot 10^{-8} \)
\(a_{4}= +1.55991181 \pm 4.1 \cdot 10^{-8} \) \(a_{5}= -1.60982448 \pm 4.4 \cdot 10^{-8} \) \(a_{6}= -1.77241585 \pm 6.3 \cdot 10^{-8} \)
\(a_{7}= -1.40334508 \pm 3.4 \cdot 10^{-8} \) \(a_{8}= -0.89584347 \pm 5.6 \cdot 10^{-8} \) \(a_{9}= +0.22717428 \pm 5.9 \cdot 10^{-8} \)
\(a_{10}= +2.57567481 \pm 5.0 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.72803752 \pm 3.9 \cdot 10^{-8} \)
\(a_{13}= -1.25099817 \pm 4.9 \cdot 10^{-8} \) \(a_{14}= +2.24531346 \pm 3.9 \cdot 10^{-8} \) \(a_{15}= -1.78332973 \pm 4.8 \cdot 10^{-8} \)
\(a_{16}= -0.12658695 \pm 5.8 \cdot 10^{-8} \) \(a_{17}= +0.30046479 \pm 4.3 \cdot 10^{-8} \) \(a_{18}= -0.36347259 \pm 6.1 \cdot 10^{-8} \)
\(a_{19}= -0.15933351 \pm 4.6 \cdot 10^{-8} \) \(a_{20}= -2.51118423 \pm 5.4 \cdot 10^{-8} \) \(a_{21}= -1.55459619 \pm 4.7 \cdot 10^{-8} \)
\(a_{22}= +0.48240984 \pm 6.6 \cdot 10^{-8} \) \(a_{23}= -0.95239662 \pm 4.4 \cdot 10^{-8} \) \(a_{24}= -0.99239657 \pm 5.9 \cdot 10^{-8} \)
\(a_{25}= +1.59153487 \pm 3.9 \cdot 10^{-8} \) \(a_{26}= +2.00156260 \pm 5.4 \cdot 10^{-8} \) \(a_{27}= -0.85612009 \pm 3.8 \cdot 10^{-8} \)
\(a_{28}= -2.18909457 \pm 2.7 \cdot 10^{-8} \) \(a_{29}= -1.66981115 \pm 5.3 \cdot 10^{-8} \) \(a_{30}= +2.85327843 \pm 5.1 \cdot 10^{-8} \)
\(a_{31}= +0.69839334 \pm 4.1 \cdot 10^{-8} \) \(a_{32}= +1.09837910 \pm 3.7 \cdot 10^{-8} \) \(a_{33}= -0.33400793 \pm 6.9 \cdot 10^{-8} \)
\(a_{34}= -0.48073538 \pm 4.1 \cdot 10^{-8} \) \(a_{35}= +2.25913927 \pm 2.9 \cdot 10^{-8} \) \(a_{36}= +0.35437184 \pm 2.8 \cdot 10^{-8} \)
\(a_{37}= -0.41081440 \pm 4.3 \cdot 10^{-8} \) \(a_{38}= +0.25492923 \pm 4.5 \cdot 10^{-8} \) \(a_{39}= -1.38582949 \pm 4.3 \cdot 10^{-8} \)
\(a_{40}= +1.44215075 \pm 5.8 \cdot 10^{-8} \) \(a_{41}= +0.44541762 \pm 5.1 \cdot 10^{-8} \) \(a_{42}= +2.48731106 \pm 5.3 \cdot 10^{-8} \)
\(a_{43}= -0.83075544 \pm 4.2 \cdot 10^{-8} \) \(a_{44}= -0.47033111 \pm 5.2 \cdot 10^{-8} \) \(a_{45}= -0.36571072 \pm 4.4 \cdot 10^{-8} \)
\(a_{46}= +1.52380834 \pm 5.0 \cdot 10^{-8} \) \(a_{47}= -0.02187978 \pm 5.3 \cdot 10^{-8} \) \(a_{48}= -0.14023036 \pm 6.6 \cdot 10^{-8} \)
\(a_{49}= +0.96937742 \pm 3.6 \cdot 10^{-8} \) \(a_{50}= -2.54641193 \pm 4.3 \cdot 10^{-8} \) \(a_{51}= +0.33284858 \pm 4.9 \cdot 10^{-8} \)
\(a_{52}= -1.95144683 \pm 2.4 \cdot 10^{-8} \) \(a_{53}= +0.89471091 \pm 5.4 \cdot 10^{-8} \) \(a_{54}= +1.36976855 \pm 4.5 \cdot 10^{-8} \)
\(a_{55}= +0.48538034 \pm 5.4 \cdot 10^{-8} \) \(a_{56}= +1.25717753 \pm 3.6 \cdot 10^{-8} \) \(a_{57}= -0.17650631 \pm 6.0 \cdot 10^{-8} \)
\(a_{58}= +2.67165182 \pm 5.5 \cdot 10^{-8} \) \(a_{59}= +1.22808960 \pm 6.6 \cdot 10^{-8} \) \(a_{60}= -2.78183712 \pm 5.0 \cdot 10^{-8} \)

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