Properties

Label 11.160
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 14.81037
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(14.8103795352232879036592441547 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.09443521 \pm 1.7 \cdot 10^{-3} \) \(a_{3}= +1.79041375 \pm 1.4 \cdot 10^{-3} \)
\(a_{4}= -0.99108199 \pm 2.0 \cdot 10^{-3} \) \(a_{5}= +0.77363586 \pm 1.5 \cdot 10^{-3} \) \(a_{6}= +0.16907809 \pm 1.7 \cdot 10^{-3} \)
\(a_{7}= +0.37351923 \pm 1.5 \cdot 10^{-3} \) \(a_{8}= -0.18802824 \pm 1.7 \cdot 10^{-3} \) \(a_{9}= +2.20558139 \pm 1.6 \cdot 10^{-3} \)
\(a_{10}= +0.07305846 \pm 1.8 \cdot 10^{-3} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -1.77444682 \pm 1.8 \cdot 10^{-3} \)
\(a_{13}= -0.66755367 \pm 1.1 \cdot 10^{-3} \) \(a_{14}= +0.03527337 \pm 1.2 \cdot 10^{-3} \) \(a_{15}= +1.38512828 \pm 1.1 \cdot 10^{-3} \)
\(a_{16}= +0.97332551 \pm 1.5 \cdot 10^{-3} \) \(a_{17}= -0.69440097 \pm 1.4 \cdot 10^{-3} \) \(a_{18}= +0.20828453 \pm 1.6 \cdot 10^{-3} \)
\(a_{19}= +1.68472998 \pm 1.0 \cdot 10^{-3} \) \(a_{20}= -0.76673657 \pm 1.9 \cdot 10^{-3} \) \(a_{21}= +0.66875397 \pm 1.1 \cdot 10^{-3} \)
\(a_{22}= +0.02847329 \pm 1.7 \cdot 10^{-3} \) \(a_{23}= +1.52025048 \pm 1.3 \cdot 10^{-3} \) \(a_{24}= -0.33664834 \pm 2.0 \cdot 10^{-3} \)
\(a_{25}= -0.40148755 \pm 1.2 \cdot 10^{-3} \) \(a_{26}= -0.06304057 \pm 9.2 \cdot 10^{-4} \) \(a_{27}= +2.15848949 \pm 1.3 \cdot 10^{-3} \)
\(a_{28}= -0.37018818 \pm 1.5 \cdot 10^{-3} \) \(a_{29}= +0.36185300 \pm 1.3 \cdot 10^{-3} \) \(a_{30}= +0.13080487 \pm 1.0 \cdot 10^{-3} \)
\(a_{31}= -1.40355306 \pm 1.4 \cdot 10^{-3} \) \(a_{32}= +0.27994443 \pm 1.2 \cdot 10^{-3} \) \(a_{33}= +0.53983006 \pm 1.4 \cdot 10^{-3} \)
\(a_{34}= -0.06557590 \pm 1.7 \cdot 10^{-3} \) \(a_{35}= +0.28896787 \pm 1.4 \cdot 10^{-3} \) \(a_{36}= -2.18591200 \pm 1.7 \cdot 10^{-3} \)
\(a_{37}= +0.28504196 \pm 1.4 \cdot 10^{-3} \) \(a_{38}= +0.15909782 \pm 1.4 \cdot 10^{-3} \) \(a_{39}= -1.19519726 \pm 8.6 \cdot 10^{-4} \)
\(a_{40}= -0.14546539 \pm 1.4 \cdot 10^{-3} \) \(a_{41}= +0.18037046 \pm 9.8 \cdot 10^{-4} \) \(a_{42}= +0.06315392 \pm 1.2 \cdot 10^{-3} \)
\(a_{43}= +1.25014492 \pm 1.4 \cdot 10^{-3} \) \(a_{44}= -0.29882246 \pm 2.0 \cdot 10^{-3} \) \(a_{45}= +1.70631686 \pm 1.5 \cdot 10^{-3} \)
\(a_{46}= +0.14356517 \pm 2.0 \cdot 10^{-3} \) \(a_{47}= -0.45293810 \pm 1.1 \cdot 10^{-3} \) \(a_{48}= +1.74265537 \pm 1.5 \cdot 10^{-3} \)
\(a_{49}= -0.86048338 \pm 1.3 \cdot 10^{-3} \) \(a_{50}= -0.03791456 \pm 1.8 \cdot 10^{-3} \) \(a_{51}= -1.24326504 \pm 1.4 \cdot 10^{-3} \)
\(a_{52}= +0.66160042 \pm 1.2 \cdot 10^{-3} \) \(a_{53}= +1.39335227 \pm 1.1 \cdot 10^{-3} \) \(a_{54}= +0.20383740 \pm 1.1 \cdot 10^{-3} \)
\(a_{55}= +0.23325999 \pm 1.5 \cdot 10^{-3} \) \(a_{56}= -0.07023216 \pm 1.0 \cdot 10^{-3} \) \(a_{57}= +3.01636372 \pm 9.6 \cdot 10^{-4} \)
\(a_{58}= +0.03417166 \pm 1.3 \cdot 10^{-3} \) \(a_{59}= +0.49375585 \pm 1.6 \cdot 10^{-3} \) \(a_{60}= -1.37277570 \pm 9.1 \cdot 10^{-4} \)

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