Properties

Label 11.80
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 10.66941
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(10.6694194813172660517110241767 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.83015314 \pm 1.1 \cdot 10^{-6} \) \(a_{3}= -0.06787432 \pm 9.0 \cdot 10^{-7} \)
\(a_{4}= +2.34946053 \pm 1.2 \cdot 10^{-6} \) \(a_{5}= -0.97667227 \pm 9.4 \cdot 10^{-7} \) \(a_{6}= -0.12422041 \pm 1.1 \cdot 10^{-6} \)
\(a_{7}= -1.64023254 \pm 9.4 \cdot 10^{-7} \) \(a_{8}= +2.46971943 \pm 1.0 \cdot 10^{-6} \) \(a_{9}= -0.99539308 \pm 1.0 \cdot 10^{-6} \)
\(a_{10}= -1.78745983 \pm 1.1 \cdot 10^{-6} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.15946804 \pm 1.1 \cdot 10^{-6} \)
\(a_{13}= -0.38330067 \pm 7.4 \cdot 10^{-7} \) \(a_{14}= -3.00187674 \pm 7.8 \cdot 10^{-7} \) \(a_{15}= +0.06629097 \pm 7.1 \cdot 10^{-7} \)
\(a_{16}= +2.17050425 \pm 9.5 \cdot 10^{-7} \) \(a_{17}= -0.73225768 \pm 9.3 \cdot 10^{-7} \) \(a_{18}= -1.82172177 \pm 1.0 \cdot 10^{-6} \)
\(a_{19}= +1.70042108 \pm 6.7 \cdot 10^{-7} \) \(a_{20}= -2.29465296 \pm 1.2 \cdot 10^{-6} \) \(a_{21}= +0.11132967 \pm 7.2 \cdot 10^{-7} \)
\(a_{22}= -0.55181194 \pm 1.1 \cdot 10^{-6} \) \(a_{23}= +0.51786692 \pm 8.7 \cdot 10^{-7} \) \(a_{24}= -0.16763054 \pm 1.2 \cdot 10^{-6} \)
\(a_{25}= -0.04611127 \pm 7.7 \cdot 10^{-7} \) \(a_{26}= -0.70149892 \pm 5.8 \cdot 10^{-7} \) \(a_{27}= +0.13543596 \pm 8.6 \cdot 10^{-7} \)
\(a_{28}= -3.85366161 \pm 9.4 \cdot 10^{-7} \) \(a_{29}= -0.41268375 \pm 8.6 \cdot 10^{-7} \) \(a_{30}= +0.12132263 \pm 6.6 \cdot 10^{-7} \)
\(a_{31}= +0.10945521 \pm 9.2 \cdot 10^{-7} \) \(a_{32}= +1.50263574 \pm 7.8 \cdot 10^{-7} \) \(a_{33}= +0.02046488 \pm 9.1 \cdot 10^{-7} \)
\(a_{34}= -1.34014370 \pm 1.1 \cdot 10^{-6} \) \(a_{35}= +1.60196964 \pm 8.9 \cdot 10^{-7} \) \(a_{36}= -2.33863674 \pm 1.0 \cdot 10^{-6} \)
\(a_{37}= -0.86847304 \pm 9.3 \cdot 10^{-7} \) \(a_{38}= +3.11203098 \pm 9.2 \cdot 10^{-7} \) \(a_{39}= +0.02601627 \pm 5.4 \cdot 10^{-7} \)
\(a_{40}= -2.41210649 \pm 8.8 \cdot 10^{-7} \) \(a_{41}= -1.78003002 \pm 6.1 \cdot 10^{-7} \) \(a_{42}= +0.20375035 \pm 8.0 \cdot 10^{-7} \)
\(a_{43}= +0.04571231 \pm 8.9 \cdot 10^{-7} \) \(a_{44}= -0.70838900 \pm 1.2 \cdot 10^{-6} \) \(a_{45}= +0.97217282 \pm 9.8 \cdot 10^{-7} \)
\(a_{46}= +0.94777577 \pm 1.2 \cdot 10^{-6} \) \(a_{47}= -0.17497620 \pm 7.4 \cdot 10^{-7} \) \(a_{48}= -0.14732151 \pm 9.7 \cdot 10^{-7} \)
\(a_{49}= +1.69036279 \pm 8.2 \cdot 10^{-7} \) \(a_{50}= -0.08439068 \pm 1.1 \cdot 10^{-6} \) \(a_{51}= +0.04970150 \pm 9.1 \cdot 10^{-7} \)
\(a_{52}= -0.90054978 \pm 7.8 \cdot 10^{-7} \) \(a_{53}= +1.14584089 \pm 7.2 \cdot 10^{-7} \) \(a_{54}= +0.24786854 \pm 7.4 \cdot 10^{-7} \)
\(a_{55}= +0.29447777 \pm 9.5 \cdot 10^{-7} \) \(a_{56}= -4.05091417 \pm 6.4 \cdot 10^{-7} \) \(a_{57}= -0.11541493 \pm 6.0 \cdot 10^{-7} \)
\(a_{58}= -0.75527446 \pm 8.4 \cdot 10^{-7} \) \(a_{59}= +0.82636531 \pm 1.0 \cdot 10^{-6} \) \(a_{60}= +0.15574802 \pm 5.7 \cdot 10^{-7} \)

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