Properties

Label 11.7
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 3.679698
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(3.67969872505288567870604924332 \pm 2 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.31612440 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.75197276 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.90006536 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.97267433 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.23771694 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.44759746 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.60065703 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.43453697 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.30748609 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.67682463 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.53104165 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.45762089 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.73142459 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.71018302 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.74848338 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.13736774 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.35590905 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.87547047 \pm 1 \cdot 10^{-8} \) \(a_{21}= +1.08855386 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.09531509 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= -0.75855867 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.45167772 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.05390466 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.16787523 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.07873272 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +1.30293233 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.18304605 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.23122116 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.87759272 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.82516321 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.22672832 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.23661386 \pm 1 \cdot 10^{-8} \) \(a_{35}= -1.40804089 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.39111168 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.06579218 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.11251154 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.39932885 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.58424367 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.37607209 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.34411844 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.61352840 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.27137992 \pm 1.2 \cdot 10^{-8} \) \(a_{45}= -0.42266296 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.23979891 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.25635099 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.53403828 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +1.09553842 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.01704058 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.56283911 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.47797220 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.25937273 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.34101374 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.29327234 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= -0.86950959 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.26763391 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.37398973 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.39662561 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.65832994 \pm 1 \cdot 10^{-8} \)

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