Properties

Label 11.78
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 10.64451
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(10.6445164140206035384864299726 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.49534078 \pm 1.4 \cdot 10^{-6} \) \(a_{3}= +0.66208937 \pm 1.2 \cdot 10^{-6} \)
\(a_{4}= +1.23604404 \pm 1.7 \cdot 10^{-6} \) \(a_{5}= +0.95933433 \pm 1.2 \cdot 10^{-6} \) \(a_{6}= -0.99004923 \pm 1.5 \cdot 10^{-6} \)
\(a_{7}= -1.08290117 \pm 1.2 \cdot 10^{-6} \) \(a_{8}= -0.35296628 \pm 1.4 \cdot 10^{-6} \) \(a_{9}= -0.56163767 \pm 1.3 \cdot 10^{-6} \)
\(a_{10}= -1.43453174 \pm 1.5 \cdot 10^{-6} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.81837162 \pm 1.6 \cdot 10^{-6} \)
\(a_{13}= +1.08092793 \pm 1.0 \cdot 10^{-6} \) \(a_{14}= +1.61930627 \pm 1.0 \cdot 10^{-6} \) \(a_{15}= +0.63516506 \pm 9.6 \cdot 10^{-7} \)
\(a_{16}= -0.70823917 \pm 1.2 \cdot 10^{-6} \) \(a_{17}= +0.91039712 \pm 1.2 \cdot 10^{-6} \) \(a_{18}= +0.83983971 \pm 1.3 \cdot 10^{-6} \)
\(a_{19}= -0.43665861 \pm 9.1 \cdot 10^{-7} \) \(a_{20}= +1.18577948 \pm 1.6 \cdot 10^{-6} \) \(a_{21}= -0.71697735 \pm 9.7 \cdot 10^{-7} \)
\(a_{22}= +0.45086221 \pm 1.4 \cdot 10^{-6} \) \(a_{23}= -0.71041971 \pm 1.1 \cdot 10^{-6} \) \(a_{24}= -0.23369522 \pm 1.6 \cdot 10^{-6} \)
\(a_{25}= -0.07967765 \pm 1.0 \cdot 10^{-6} \) \(a_{26}= -1.61635561 \pm 7.8 \cdot 10^{-7} \) \(a_{27}= -1.03394370 \pm 1.1 \cdot 10^{-6} \)
\(a_{28}= -1.33851353 \pm 1.2 \cdot 10^{-6} \) \(a_{29}= +1.15519343 \pm 1.1 \cdot 10^{-6} \) \(a_{30}= -0.94978821 \pm 8.8 \cdot 10^{-7} \)
\(a_{31}= +0.65552397 \pm 1.2 \cdot 10^{-6} \) \(a_{32}= +1.41202519 \pm 1.0 \cdot 10^{-6} \) \(a_{33}= -0.19962746 \pm 1.2 \cdot 10^{-6} \)
\(a_{34}= -1.36135394 \pm 1.5 \cdot 10^{-6} \) \(a_{35}= -1.03886427 \pm 1.2 \cdot 10^{-6} \) \(a_{36}= -0.69420889 \pm 1.4 \cdot 10^{-6} \)
\(a_{37}= -1.03522985 \pm 1.2 \cdot 10^{-6} \) \(a_{38}= +0.65295342 \pm 1.2 \cdot 10^{-6} \) \(a_{39}= +0.71567089 \pm 7.3 \cdot 10^{-7} \)
\(a_{40}= -0.33861267 \pm 1.1 \cdot 10^{-6} \) \(a_{41}= +0.72937665 \pm 8.3 \cdot 10^{-7} \) \(a_{42}= +1.07212547 \pm 1.0 \cdot 10^{-6} \)
\(a_{43}= -1.95358952 \pm 1.2 \cdot 10^{-6} \) \(a_{44}= -0.37268130 \pm 1.7 \cdot 10^{-6} \) \(a_{45}= -0.53879830 \pm 1.3 \cdot 10^{-6} \)
\(a_{46}= +1.06231956 \pm 1.6 \cdot 10^{-6} \) \(a_{47}= -0.65726940 \pm 1.0 \cdot 10^{-6} \) \(a_{48}= -0.46891762 \pm 1.3 \cdot 10^{-6} \)
\(a_{49}= +0.17267494 \pm 1.1 \cdot 10^{-6} \) \(a_{50}= +0.11914523 \pm 1.5 \cdot 10^{-6} \) \(a_{51}= +0.60276426 \pm 1.2 \cdot 10^{-6} \)
\(a_{52}= +1.33607453 \pm 1.0 \cdot 10^{-6} \) \(a_{53}= -1.46285801 \pm 9.7 \cdot 10^{-7} \) \(a_{54}= +1.54609817 \pm 1.0 \cdot 10^{-6} \)
\(a_{55}= -0.28925018 \pm 1.2 \cdot 10^{-6} \) \(a_{56}= +0.38222760 \pm 8.6 \cdot 10^{-7} \) \(a_{57}= -0.28910702 \pm 8.1 \cdot 10^{-7} \)
\(a_{58}= -1.72740784 \pm 1.1 \cdot 10^{-6} \) \(a_{59}= -0.43967476 \pm 1.4 \cdot 10^{-6} \) \(a_{60}= +0.78509199 \pm 7.6 \cdot 10^{-7} \)

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