Properties

Label 11.17
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 5.384281
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(5.38428160735382821947017382169 \pm 5 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.04837166 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.99269547 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.99766018 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.64658783 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.04801832 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.21567779 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.09663013 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.01455570 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.03127652 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.99037274 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.20612247 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.05880435 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.64186481 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.99298602 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.39720632 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.00070408 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -1.28606393 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.64507493 \pm 1 \cdot 10^{-8} \) \(a_{21}= -1.20679783 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.01458460 \pm 1.2 \cdot 10^{-8} \) \(a_{23}= +0.53742958 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.09592429 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.58192418 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.00997049 \pm 1 \cdot 10^{-8} \) \(a_{27}= -1.00714485 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +1.21283332 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.22172316 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.03104806 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +1.36756444 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.14466251 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.29930895 \pm 1.2 \cdot 10^{-8} \)
\(a_{34}= -0.06758518 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.78604246 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.01452165 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.26212096 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.06220904 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.20461684 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.06247987 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.91453189 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.05837481 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.07923596 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.30080586 \pm 1.3 \cdot 10^{-8} \) \(a_{45}= +0.00941154 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.02599636 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.42752196 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.98573273 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.47787248 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.02814864 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.38700038 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.20564018 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.18787841 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.04871726 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.19495357 \pm 1.2 \cdot 10^{-8} \) \(a_{56}= -0.11747110 \pm 1 \cdot 10^{-8} \) \(a_{57}= -1.27666983 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.01072512 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.12715837 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.64036296 \pm 1 \cdot 10^{-8} \)

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