Properties

Label 11.43
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 8.142021
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(8.14202179524998289176347244901 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.59270770 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.85525842 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +1.53671783 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.28038333 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.36217668 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +1.13968858 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.85483463 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.26853303 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.44656869 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +1.31429087 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.59811165 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.81519079 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.23980021 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.17521614 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.28555021 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.42769463 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.74176402 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.43087006 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.97472826 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.48021944 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -0.62636712 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.73110451 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.92138519 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.95261703 \pm 1 \cdot 10^{-8} \) \(a_{27}= -1.08492356 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +1.75137977 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.94672410 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.38193163 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.12689637 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.13390272 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.25787012 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.45479802 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.31954968 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.41265950 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.23957119 \pm 1 \cdot 10^{-8} \) \(a_{38}= +2.77412097 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.51154002 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.23968138 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.11054708 \pm 1 \cdot 10^{-8} \) \(a_{42}= +1.55245721 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -1.82463327 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.46333786 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.07529219 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.99761974 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.09465477 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.14985508 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.29889006 \pm 1 \cdot 10^{-8} \) \(a_{50}= -1.46749729 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.24421922 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.91912883 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.56517750 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.72796611 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.08453876 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +0.97424526 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.48965834 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +1.50785476 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.48456164 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.36850525 \pm 1 \cdot 10^{-8} \)

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