Properties

Label 11.6
Level $11$
Weight $0$
Character 11.1
Symmetry odd
\(R\) 3.481888
Fricke sign $-1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.4818884750665173941266632489 \pm 2 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.78779815 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.77685909 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.37937408 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.87997698 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.39980630 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.16528745 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.08666834 \pm 1 \cdot 10^{-8} \) \(a_{9}= +2.15722822 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.69324423 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -0.67409428 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.19513764 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.13021315 \pm 1 \cdot 10^{-8} \) \(a_{15}= -1.56359509 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.47670123 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.87582024 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.69946040 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.58752847 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.33384045 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.29369251 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.23753008 \pm 1.1 \cdot 10^{-8} \) \(a_{23}= -0.93256543 \pm 1 \cdot 10^{-8} \) \(a_{24}= -1.93085652 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.22564052 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.15372907 \pm 1 \cdot 10^{-8} \) \(a_{27}= +2.05623149 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.06270578 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.14485670 \pm 1 \cdot 10^{-8} \) \(a_{30}= -1.23179731 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.09498420 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.71112400 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.53574317 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.68996957 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.14544915 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.81839647 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.30436550 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.46285384 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.34673210 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.95624312 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.05957179 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.23137042 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.99392739 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.11438559 \pm 1.1 \cdot 10^{-8} \) \(a_{45}= -1.89831117 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.73467332 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.53734706 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.84703091 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.97268006 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.17775919 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.55620916 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.07403016 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.57203934 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.61989536 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.26532304 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= +0.17961264 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.04395530 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.11411784 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.19551901 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.59318745 \pm 1 \cdot 10^{-8} \)

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