Properties

Label 31.42
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 4.561472
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(4.56147272190425031369425246533 \pm 9 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.60303055 \pm 6.1 \cdot 10^{-8} \) \(a_{3}= +0.45446526 \pm 5.4 \cdot 10^{-8} \)
\(a_{4}= -0.63635415 \pm 6.1 \cdot 10^{-8} \) \(a_{5}= +0.84530077 \pm 5.2 \cdot 10^{-8} \) \(a_{6}= +0.27405643 \pm 6.1 \cdot 10^{-8} \)
\(a_{7}= -1.49729790 \pm 5.3 \cdot 10^{-8} \) \(a_{8}= -0.98677155 \pm 5.9 \cdot 10^{-8} \) \(a_{9}= -0.79346133 \pm 5.2 \cdot 10^{-8} \)
\(a_{10}= +0.50974219 \pm 5.0 \cdot 10^{-8} \) \(a_{11}= +0.96654384 \pm 5.2 \cdot 10^{-8} \) \(a_{12}= -0.28920085 \pm 5.8 \cdot 10^{-8} \)
\(a_{13}= -1.30585237 \pm 4.2 \cdot 10^{-8} \) \(a_{14}= -0.90291638 \pm 7.1 \cdot 10^{-8} \) \(a_{15}= +0.38415983 \pm 5.6 \cdot 10^{-8} \)
\(a_{16}= +0.04130076 \pm 6.3 \cdot 10^{-8} \) \(a_{17}= -1.34782974 \pm 4.9 \cdot 10^{-8} \) \(a_{18}= -0.47848143 \pm 4.6 \cdot 10^{-8} \)
\(a_{19}= +0.40130482 \pm 4.8 \cdot 10^{-8} \) \(a_{20}= -0.53791066 \pm 5.3 \cdot 10^{-8} \) \(a_{21}= -0.68046987 \pm 5.3 \cdot 10^{-8} \)
\(a_{22}= +0.58285547 \pm 6.2 \cdot 10^{-8} \) \(a_{23}= +0.33431889 \pm 4.2 \cdot 10^{-8} \) \(a_{24}= -0.44845338 \pm 6.3 \cdot 10^{-8} \)
\(a_{25}= -0.28546660 \pm 5.6 \cdot 10^{-8} \) \(a_{26}= -0.78746888 \pm 4.7 \cdot 10^{-8} \) \(a_{27}= -0.81506586 \pm 5.4 \cdot 10^{-8} \)
\(a_{28}= +0.95281173 \pm 7.6 \cdot 10^{-8} \) \(a_{29}= +1.19314019 \pm 5.0 \cdot 10^{-8} \) \(a_{30}= +0.23166012 \pm 5.7 \cdot 10^{-8} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +1.01167717 \pm 6.1 \cdot 10^{-8} \) \(a_{33}= +0.43926059 \pm 5.9 \cdot 10^{-8} \)
\(a_{34}= -0.81278251 \pm 5.2 \cdot 10^{-8} \) \(a_{35}= -1.26566707 \pm 5.5 \cdot 10^{-8} \) \(a_{36}= +0.50492241 \pm 4.6 \cdot 10^{-8} \)
\(a_{37}= +1.03292118 \pm 5.2 \cdot 10^{-8} \) \(a_{38}= +0.24199907 \pm 6.2 \cdot 10^{-8} \) \(a_{39}= -0.59346453 \pm 5.3 \cdot 10^{-8} \)
\(a_{40}= -0.83411876 \pm 4.9 \cdot 10^{-8} \) \(a_{41}= -1.83785036 \pm 4.0 \cdot 10^{-8} \) \(a_{42}= -0.41034412 \pm 7.0 \cdot 10^{-8} \)
\(a_{43}= +1.28174198 \pm 5.3 \cdot 10^{-8} \) \(a_{44}= -0.61506418 \pm 6.5 \cdot 10^{-8} \) \(a_{45}= -0.67071348 \pm 5.4 \cdot 10^{-8} \)
\(a_{46}= +0.20160451 \pm 5.3 \cdot 10^{-8} \) \(a_{47}= -0.94443330 \pm 4.6 \cdot 10^{-8} \) \(a_{48}= +0.01876976 \pm 5.7 \cdot 10^{-8} \)
\(a_{49}= +1.24190100 \pm 4.6 \cdot 10^{-8} \) \(a_{50}= -0.17214508 \pm 5.2 \cdot 10^{-8} \) \(a_{51}= -0.61254179 \pm 4.7 \cdot 10^{-8} \)
\(a_{52}= +0.83098458 \pm 4.6 \cdot 10^{-8} \) \(a_{53}= +0.69832631 \pm 5.2 \cdot 10^{-8} \) \(a_{54}= -0.49150962 \pm 5.8 \cdot 10^{-8} \)
\(a_{55}= +0.81702026 \pm 5.4 \cdot 10^{-8} \) \(a_{56}= +1.47749097 \pm 7.8 \cdot 10^{-8} \) \(a_{57}= +0.18237910 \pm 4.4 \cdot 10^{-8} \)
\(a_{58}= +0.71949999 \pm 6.2 \cdot 10^{-8} \) \(a_{59}= -1.20918560 \pm 4.2 \cdot 10^{-8} \) \(a_{60}= -0.24446170 \pm 5.3 \cdot 10^{-8} \)

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