Properties

Label 11.89
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 11.26124
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(11.2612425027035251260082390096 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.72164439 \pm 4.6 \cdot 10^{-6} \) \(a_{3}= -1.72027069 \pm 3.8 \cdot 10^{-6} \)
\(a_{4}= -0.47922938 \pm 5.4 \cdot 10^{-6} \) \(a_{5}= -0.98168527 \pm 3.9 \cdot 10^{-6} \) \(a_{6}= +1.24142368 \pm 4.7 \cdot 10^{-6} \)
\(a_{7}= -1.50765960 \pm 3.9 \cdot 10^{-6} \) \(a_{8}= +1.06747758 \pm 4.5 \cdot 10^{-6} \) \(a_{9}= +1.95933124 \pm 4.2 \cdot 10^{-6} \)
\(a_{10}= +0.70842766 \pm 4.8 \cdot 10^{-6} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.82440426 \pm 5.0 \cdot 10^{-6} \)
\(a_{13}= -0.52388168 \pm 3.1 \cdot 10^{-6} \) \(a_{14}= +1.08799409 \pm 3.3 \cdot 10^{-6} \) \(a_{15}= +1.68876439 \pm 3.0 \cdot 10^{-6} \)
\(a_{16}= -0.29110982 \pm 4.0 \cdot 10^{-6} \) \(a_{17}= +1.90860392 \pm 3.9 \cdot 10^{-6} \) \(a_{18}= -1.41394039 \pm 4.3 \cdot 10^{-6} \)
\(a_{19}= -0.25340204 \pm 2.8 \cdot 10^{-6} \) \(a_{20}= +0.47045242 \pm 5.2 \cdot 10^{-6} \) \(a_{21}= +2.59358262 \pm 3.0 \cdot 10^{-6} \)
\(a_{22}= +0.21758397 \pm 4.6 \cdot 10^{-6} \) \(a_{23}= -0.42825166 \pm 3.7 \cdot 10^{-6} \) \(a_{24}= -1.83635039 \pm 5.3 \cdot 10^{-6} \)
\(a_{25}= -0.03629403 \pm 3.2 \cdot 10^{-6} \) \(a_{26}= +0.37805628 \pm 2.4 \cdot 10^{-6} \) \(a_{27}= -1.65030942 \pm 3.6 \cdot 10^{-6} \)
\(a_{28}= +0.72251478 \pm 4.0 \cdot 10^{-6} \) \(a_{29}= +0.25659394 \pm 3.6 \cdot 10^{-6} \) \(a_{30}= -1.21868734 \pm 2.7 \cdot 10^{-6} \)
\(a_{31}= -1.16637508 \pm 3.8 \cdot 10^{-6} \) \(a_{32}= -0.85739981 \pm 3.3 \cdot 10^{-6} \) \(a_{33}= +0.51868113 \pm 3.8 \cdot 10^{-6} \)
\(a_{34}= -1.37733330 \pm 4.7 \cdot 10^{-6} \) \(a_{35}= +1.48004722 \pm 3.7 \cdot 10^{-6} \) \(a_{36}= -0.93896910 \pm 4.5 \cdot 10^{-6} \)
\(a_{37}= -0.20216591 \pm 3.9 \cdot 10^{-6} \) \(a_{38}= +0.18286616 \pm 3.9 \cdot 10^{-6} \) \(a_{39}= +0.90121830 \pm 2.3 \cdot 10^{-6} \)
\(a_{40}= -1.04792701 \pm 3.7 \cdot 10^{-6} \) \(a_{41}= +0.24774315 \pm 2.6 \cdot 10^{-6} \) \(a_{42}= -1.87164434 \pm 3.3 \cdot 10^{-6} \)
\(a_{43}= +0.05793280 \pm 3.7 \cdot 10^{-6} \) \(a_{44}= +0.14449309 \pm 5.4 \cdot 10^{-6} \) \(a_{45}= -1.92344662 \pm 4.1 \cdot 10^{-6} \)
\(a_{46}= +0.30904540 \pm 5.3 \cdot 10^{-6} \) \(a_{47}= +1.39770660 \pm 3.1 \cdot 10^{-6} \) \(a_{48}= +0.50078769 \pm 4.1 \cdot 10^{-6} \)
\(a_{49}= +1.27303748 \pm 3.4 \cdot 10^{-6} \) \(a_{50}= +0.02619139 \pm 5.0 \cdot 10^{-6} \) \(a_{51}= -3.28331538 \pm 3.8 \cdot 10^{-6} \)
\(a_{52}= +0.25105949 \pm 3.3 \cdot 10^{-6} \) \(a_{53}= +1.33820657 \pm 3.0 \cdot 10^{-6} \) \(a_{54}= +1.19093653 \pm 3.1 \cdot 10^{-6} \)
\(a_{55}= +0.29598925 \pm 3.9 \cdot 10^{-6} \) \(a_{56}= -1.60939282 \pm 2.7 \cdot 10^{-6} \) \(a_{57}= +0.43592010 \pm 2.5 \cdot 10^{-6} \)
\(a_{58}= -0.18516958 \pm 3.5 \cdot 10^{-6} \) \(a_{59}= -0.06959452 \pm 4.4 \cdot 10^{-6} \) \(a_{60}= -0.80930551 \pm 2.4 \cdot 10^{-6} \)

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