Properties

Label 11.131
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 13.46378
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(13.4637893382526451096086714008 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.17423596 \pm 1.5 \cdot 10^{-7} \) \(a_{3}= -0.13743090 \pm 1.6 \cdot 10^{-7} \)
\(a_{4}= +0.37883010 \pm 1.1 \cdot 10^{-7} \) \(a_{5}= -0.32132566 \pm 1.2 \cdot 10^{-7} \) \(a_{6}= +0.16137630 \pm 1.7 \cdot 10^{-7} \)
\(a_{7}= -0.60231504 \pm 9.5 \cdot 10^{-8} \) \(a_{8}= +0.72940004 \pm 1.5 \cdot 10^{-7} \) \(a_{9}= -0.98111275 \pm 1.6 \cdot 10^{-7} \)
\(a_{10}= +0.37731214 \pm 1.4 \cdot 10^{-7} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.05206296 \pm 1.0 \cdot 10^{-7} \)
\(a_{13}= +0.89969709 \pm 1.3 \cdot 10^{-7} \) \(a_{14}= +0.70725998 \pm 1.0 \cdot 10^{-7} \) \(a_{15}= +0.04416007 \pm 1.3 \cdot 10^{-7} \)
\(a_{16}= -1.23531785 \pm 1.6 \cdot 10^{-7} \) \(a_{17}= -0.40030830 \pm 1.1 \cdot 10^{-7} \) \(a_{18}= +1.15205787 \pm 1.6 \cdot 10^{-7} \)
\(a_{19}= -1.02579385 \pm 1.2 \cdot 10^{-7} \) \(a_{20}= -0.12172783 \pm 1.4 \cdot 10^{-7} \) \(a_{21}= +0.08277670 \pm 1.3 \cdot 10^{-7} \)
\(a_{22}= +0.35404546 \pm 1.6 \cdot 10^{-7} \) \(a_{23}= -1.50816262 \pm 1.2 \cdot 10^{-7} \) \(a_{24}= -0.10024210 \pm 1.6 \cdot 10^{-7} \)
\(a_{25}= -0.89674982 \pm 1.0 \cdot 10^{-7} \) \(a_{26}= -1.05645667 \pm 1.4 \cdot 10^{-7} \) \(a_{27}= +0.27226611 \pm 1.0 \cdot 10^{-7} \)
\(a_{28}= -0.22817506 \pm 7.6 \cdot 10^{-8} \) \(a_{29}= -1.24812960 \pm 1.4 \cdot 10^{-7} \) \(a_{30}= -0.05185435 \pm 1.4 \cdot 10^{-7} \)
\(a_{31}= -1.15178777 \pm 1.1 \cdot 10^{-7} \) \(a_{32}= +0.72115461 \pm 1.0 \cdot 10^{-7} \) \(a_{33}= +0.04143698 \pm 1.7 \cdot 10^{-7} \)
\(a_{34}= +0.47005641 \pm 1.1 \cdot 10^{-7} \) \(a_{35}= +0.19353928 \pm 8.1 \cdot 10^{-8} \) \(a_{36}= -0.37167504 \pm 7.7 \cdot 10^{-8} \)
\(a_{37}= -0.00309026 \pm 1.2 \cdot 10^{-7} \) \(a_{38}= +1.20452403 \pm 1.2 \cdot 10^{-7} \) \(a_{39}= -0.12364618 \pm 1.2 \cdot 10^{-7} \)
\(a_{40}= -0.23437495 \pm 1.6 \cdot 10^{-7} \) \(a_{41}= +0.50626780 \pm 1.4 \cdot 10^{-7} \) \(a_{42}= -0.09719937 \pm 1.4 \cdot 10^{-7} \)
\(a_{43}= +1.41103813 \pm 1.1 \cdot 10^{-7} \) \(a_{44}= -0.11422157 \pm 1.2 \cdot 10^{-7} \) \(a_{45}= +0.31525670 \pm 1.2 \cdot 10^{-7} \)
\(a_{46}= +1.77093879 \pm 1.3 \cdot 10^{-7} \) \(a_{47}= +0.85264322 \pm 1.4 \cdot 10^{-7} \) \(a_{48}= +0.16977084 \pm 1.8 \cdot 10^{-7} \)
\(a_{49}= -0.63721660 \pm 9.9 \cdot 10^{-8} \) \(a_{50}= +1.05299589 \pm 1.2 \cdot 10^{-7} \) \(a_{51}= +0.05501473 \pm 1.3 \cdot 10^{-7} \)
\(a_{52}= +0.34083233 \pm 6.7 \cdot 10^{-8} \) \(a_{53}= -0.74661814 \pm 1.4 \cdot 10^{-7} \) \(a_{54}= -0.31970465 \pm 1.2 \cdot 10^{-7} \)
\(a_{55}= +0.09688333 \pm 1.3 \cdot 10^{-7} \) \(a_{56}= -0.43932861 \pm 1.0 \cdot 10^{-7} \) \(a_{57}= +0.14097577 \pm 1.6 \cdot 10^{-7} \)
\(a_{58}= +1.46559866 \pm 1.5 \cdot 10^{-7} \) \(a_{59}= -0.29293821 \pm 1.8 \cdot 10^{-7} \) \(a_{60}= +0.01672917 \pm 1.3 \cdot 10^{-7} \)

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