Properties

Label 11.162
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 14.82740
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(14.8274044216704387574107898134 \pm 8 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.83574704 \pm 1.1 \cdot 10^{-3} \) \(a_{3}= +0.01781603 \pm 9.7 \cdot 10^{-4} \)
\(a_{4}= +2.36996720 \pm 1.3 \cdot 10^{-3} \) \(a_{5}= -0.23274490 \pm 1.0 \cdot 10^{-3} \) \(a_{6}= -0.03270573 \pm 1.2 \cdot 10^{-3} \)
\(a_{7}= -1.29577121 \pm 1.0 \cdot 10^{-3} \) \(a_{8}= -2.51491324 \pm 1.1 \cdot 10^{-3} \) \(a_{9}= -0.99968259 \pm 1.0 \cdot 10^{-3} \)
\(a_{10}= +0.42726076 \pm 1.2 \cdot 10^{-3} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.04222341 \pm 1.2 \cdot 10^{-3} \)
\(a_{13}= -0.79493299 \pm 8.0 \cdot 10^{-4} \) \(a_{14}= +2.37870817 \pm 8.4 \cdot 10^{-4} \) \(a_{15}= -0.00414659 \pm 7.7 \cdot 10^{-4} \)
\(a_{16}= +2.24677734 \pm 1.0 \cdot 10^{-3} \) \(a_{17}= -1.03699708 \pm 1.0 \cdot 10^{-3} \) \(a_{18}= +1.83516436 \pm 1.1 \cdot 10^{-3} \)
\(a_{19}= +0.93345291 \pm 7.3 \cdot 10^{-4} \) \(a_{20}= -0.55159778 \pm 1.3 \cdot 10^{-3} \) \(a_{21}= -0.02308550 \pm 7.8 \cdot 10^{-4} \)
\(a_{22}= -0.55349856 \pm 1.1 \cdot 10^{-3} \) \(a_{23}= -1.29188712 \pm 9.4 \cdot 10^{-4} \) \(a_{24}= -0.04480577 \pm 1.3 \cdot 10^{-3} \)
\(a_{25}= -0.94582981 \pm 8.4 \cdot 10^{-4} \) \(a_{26}= +1.45929589 \pm 6.2 \cdot 10^{-4} \) \(a_{27}= -0.03562641 \pm 9.3 \cdot 10^{-4} \)
\(a_{28}= -3.07093528 \pm 1.0 \cdot 10^{-3} \) \(a_{29}= -0.22668458 \pm 9.3 \cdot 10^{-4} \) \(a_{30}= +0.00761209 \pm 7.1 \cdot 10^{-4} \)
\(a_{31}= -0.93905401 \pm 9.9 \cdot 10^{-4} \) \(a_{32}= -1.60960161 \pm 8.5 \cdot 10^{-4} \) \(a_{33}= +0.00537174 \pm 9.7 \cdot 10^{-4} \)
\(a_{34}= +1.90366432 \pm 1.2 \cdot 10^{-3} \) \(a_{35}= +0.30158414 \pm 9.6 \cdot 10^{-4} \) \(a_{36}= -2.36921495 \pm 1.1 \cdot 10^{-3} \)
\(a_{37}= -1.59962290 \pm 1.0 \cdot 10^{-3} \) \(a_{38}= -1.71358342 \pm 1.0 \cdot 10^{-3} \) \(a_{39}= -0.01416255 \pm 5.8 \cdot 10^{-4} \)
\(a_{40}= +0.58533323 \pm 9.5 \cdot 10^{-4} \) \(a_{41}= +0.42371092 \pm 6.6 \cdot 10^{-4} \) \(a_{42}= +0.04237914 \pm 8.6 \cdot 10^{-4} \)
\(a_{43}= +0.16705464 \pm 9.6 \cdot 10^{-4} \) \(a_{44}= +0.71457200 \pm 1.3 \cdot 10^{-3} \) \(a_{45}= +0.23267102 \pm 1.0 \cdot 10^{-3} \)
\(a_{46}= +2.37157796 \pm 1.3 \cdot 10^{-3} \) \(a_{47}= -1.96608973 \pm 8.0 \cdot 10^{-4} \) \(a_{48}= +0.04002865 \pm 1.0 \cdot 10^{-3} \)
\(a_{49}= +0.67902304 \pm 8.9 \cdot 10^{-4} \) \(a_{50}= +1.73630428 \pm 1.2 \cdot 10^{-3} \) \(a_{51}= -0.01847517 \pm 9.9 \cdot 10^{-4} \)
\(a_{52}= -1.88396512 \pm 8.4 \cdot 10^{-4} \) \(a_{53}= +0.25747578 \pm 7.7 \cdot 10^{-4} \) \(a_{54}= +0.06540107 \pm 8.0 \cdot 10^{-4} \)
\(a_{55}= -0.07017523 \pm 1.0 \cdot 10^{-3} \) \(a_{56}= +3.25875218 \pm 6.9 \cdot 10^{-4} \) \(a_{57}= +0.01663043 \pm 6.5 \cdot 10^{-4} \)
\(a_{58}= +0.41613555 \pm 9.0 \cdot 10^{-4} \) \(a_{59}= +0.17526237 \pm 1.1 \cdot 10^{-3} \) \(a_{60}= -0.00982728 \pm 6.1 \cdot 10^{-4} \)

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