Properties

Label 11.18
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 5.663265
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.66326548840428820607758576913 \pm 5 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.08234733 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.08679552 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.99321892 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.49733502 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.08949471 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.74641102 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.16413626 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.18112451 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.12330154 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.07942587 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.69282341 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.06146496 \pm 1 \cdot 10^{-8} \) \(a_{15}= -1.62729700 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.97970273 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.24372822 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.01491512 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.12472606 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.48718147 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.81119615 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.02482865 \pm 1.3 \cdot 10^{-8} \) \(a_{23}= +1.52957076 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.17838255 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +1.24201217 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.05705216 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.88995022 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.74134954 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.88947615 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.13400357 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.08079573 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.24481216 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.32768118 \pm 1.3 \cdot 10^{-8} \)
\(a_{34}= +0.02007037 \pm 1 \cdot 10^{-8} \) \(a_{35}= +1.11762736 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.17989629 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.46326240 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.09261819 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.75295738 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.24576697 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.86995430 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.06679984 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.08117713 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.29946677 \pm 1.4 \cdot 10^{-8} \) \(a_{45}= +0.27120407 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.12595607 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.02899101 \pm 1 \cdot 10^{-8} \) \(a_{48}= -1.06473655 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.44287059 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.10227639 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.26488273 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.68812532 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.84889823 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.07328503 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.45146350 \pm 1.3 \cdot 10^{-8} \) \(a_{56}= +0.12251311 \pm 1 \cdot 10^{-8} \) \(a_{57}= -1.22234725 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.15559332 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.87909090 \pm 1 \cdot 10^{-8} \) \(a_{60}= +1.61626216 \pm 1 \cdot 10^{-8} \)

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