Properties

Label 11.155
Level $11$
Weight $0$
Character 11.1
Symmetry even
\(R\) 14.61952
Fricke sign $+1$

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Maass form invariants

Level: \( 11 \)
Weight: \( 0 \)
Character: 11.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(14.6195267863392865081993436122 \pm 4 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.92269644 \pm 8.7 \cdot 10^{-7} \) \(a_{3}= +1.51571954 \pm 9.3 \cdot 10^{-7} \)
\(a_{4}= +2.69676159 \pm 6.5 \cdot 10^{-7} \) \(a_{5}= -0.56817807 \pm 6.9 \cdot 10^{-7} \) \(a_{6}= +2.91426856 \pm 9.9 \cdot 10^{-7} \)
\(a_{7}= +0.87209295 \pm 5.4 \cdot 10^{-7} \) \(a_{8}= +3.26235745 \pm 8.8 \cdot 10^{-7} \) \(a_{9}= +1.29740572 \pm 9.3 \cdot 10^{-7} \)
\(a_{10}= -1.09243395 \pm 8.0 \cdot 10^{-7} \) \(a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +4.08753423 \pm 6.1 \cdot 10^{-7} \)
\(a_{13}= +0.12065055 \pm 7.7 \cdot 10^{-7} \) \(a_{14}= +1.67677000 \pm 6.2 \cdot 10^{-7} \) \(a_{15}= -0.86119860 \pm 7.6 \cdot 10^{-7} \)
\(a_{16}= +3.57576146 \pm 9.1 \cdot 10^{-7} \) \(a_{17}= -1.83239465 \pm 6.8 \cdot 10^{-7} \) \(a_{18}= +2.49451736 \pm 9.6 \cdot 10^{-7} \)
\(a_{19}= -0.28643798 \pm 7.3 \cdot 10^{-7} \) \(a_{20}= -1.53224079 \pm 8.5 \cdot 10^{-7} \) \(a_{21}= +1.32184832 \pm 7.5 \cdot 10^{-7} \)
\(a_{22}= -0.57971479 \pm 8.9 \cdot 10^{-7} \) \(a_{23}= +1.46712420 \pm 6.9 \cdot 10^{-7} \) \(a_{24}= +4.94481894 \pm 9.2 \cdot 10^{-7} \)
\(a_{25}= -0.67717368 \pm 6.1 \cdot 10^{-7} \) \(a_{26}= +0.23197438 \pm 8.4 \cdot 10^{-7} \) \(a_{27}= +0.45078367 \pm 6.0 \cdot 10^{-7} \)
\(a_{28}= +2.35182676 \pm 4.3 \cdot 10^{-7} \) \(a_{29}= +0.72900718 \pm 8.3 \cdot 10^{-7} \) \(a_{30}= -1.65582348 \pm 8.0 \cdot 10^{-7} \)
\(a_{31}= -0.49381992 \pm 6.5 \cdot 10^{-7} \) \(a_{32}= +3.61274637 \pm 5.8 \cdot 10^{-7} \) \(a_{33}= -0.45700664 \pm 9.4 \cdot 10^{-7} \)
\(a_{34}= -3.52313867 \pm 6.5 \cdot 10^{-7} \) \(a_{35}= -0.49550409 \pm 4.6 \cdot 10^{-7} \) \(a_{36}= +3.49879392 \pm 4.4 \cdot 10^{-7} \)
\(a_{37}= +0.80736911 \pm 6.9 \cdot 10^{-7} \) \(a_{38}= -0.55073328 \pm 7.1 \cdot 10^{-7} \) \(a_{39}= +0.18287239 \pm 6.8 \cdot 10^{-7} \)
\(a_{40}= -1.85359996 \pm 9.1 \cdot 10^{-7} \) \(a_{41}= -1.26331962 \pm 8.0 \cdot 10^{-7} \) \(a_{42}= +2.54151305 \pm 8.3 \cdot 10^{-7} \)
\(a_{43}= -0.76037262 \pm 6.7 \cdot 10^{-7} \) \(a_{44}= -0.81310421 \pm 6.6 \cdot 10^{-7} \) \(a_{45}= -0.73715748 \pm 7.0 \cdot 10^{-7} \)
\(a_{46}= +2.82083448 \pm 7.9 \cdot 10^{-7} \) \(a_{47}= -0.28942525 \pm 8.3 \cdot 10^{-7} \) \(a_{48}= +5.41985152 \pm 1.0 \cdot 10^{-6} \)
\(a_{49}= -0.23945389 \pm 5.6 \cdot 10^{-7} \) \(a_{50}= -1.30199943 \pm 6.8 \cdot 10^{-7} \) \(a_{51}= -2.77739638 \pm 7.7 \cdot 10^{-7} \)
\(a_{52}= +0.32536576 \pm 3.8 \cdot 10^{-7} \) \(a_{53}= +0.58139249 \pm 8.5 \cdot 10^{-7} \) \(a_{54}= +0.86672015 \pm 7.1 \cdot 10^{-7} \)
\(a_{55}= +0.17131213 \pm 7.0 \cdot 10^{-7} \) \(a_{56}= +2.84507893 \pm 5.7 \cdot 10^{-7} \) \(a_{57}= -0.43415964 \pm 9.4 \cdot 10^{-7} \)
\(a_{58}= +1.40165950 \pm 8.7 \cdot 10^{-7} \) \(a_{59}= +0.29069674 \pm 1.0 \cdot 10^{-6} \) \(a_{60}= -2.32244730 \pm 7.9 \cdot 10^{-7} \)

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