Properties

Label 31.103
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 6.839394
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(6.83939446352366643334478225066 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.48381404 \pm 9.9 \cdot 10^{-6} \) \(a_{3}= +0.88584932 \pm 8.9 \cdot 10^{-6} \)
\(a_{4}= -0.76592398 \pm 1.0 \cdot 10^{-5} \) \(a_{5}= -1.74746121 \pm 8.3 \cdot 10^{-6} \) \(a_{6}= -0.42858634 \pm 1.1 \cdot 10^{-5} \)
\(a_{7}= -1.10407322 \pm 8.1 \cdot 10^{-6} \) \(a_{8}= +0.85437881 \pm 1.1 \cdot 10^{-5} \) \(a_{9}= -0.21527098 \pm 8.4 \cdot 10^{-6} \)
\(a_{10}= +0.84544626 \pm 1.0 \cdot 10^{-5} \) \(a_{11}= -1.37948571 \pm 8.1 \cdot 10^{-6} \) \(a_{12}= -0.67849323 \pm 1.3 \cdot 10^{-5} \)
\(a_{13}= +0.75014060 \pm 8.4 \cdot 10^{-6} \) \(a_{14}= +0.53416613 \pm 8.4 \cdot 10^{-6} \) \(a_{15}= -1.54798732 \pm 8.6 \cdot 10^{-6} \)
\(a_{16}= +0.35256351 \pm 1.0 \cdot 10^{-5} \) \(a_{17}= -1.73435203 \pm 7.7 \cdot 10^{-6} \) \(a_{18}= +0.10415112 \pm 1.0 \cdot 10^{-5} \)
\(a_{19}= +0.31239364 \pm 8.6 \cdot 10^{-6} \) \(a_{20}= +1.33842244 \pm 1.0 \cdot 10^{-5} \) \(a_{21}= -0.97804251 \pm 8.7 \cdot 10^{-6} \)
\(a_{22}= +0.66741455 \pm 8.8 \cdot 10^{-6} \) \(a_{23}= -0.54185362 \pm 7.8 \cdot 10^{-6} \) \(a_{24}= +0.75685089 \pm 1.3 \cdot 10^{-5} \)
\(a_{25}= +2.05362067 \pm 7.9 \cdot 10^{-6} \) \(a_{26}= -0.36292855 \pm 8.6 \cdot 10^{-6} \) \(a_{27}= -1.07654697 \pm 7.5 \cdot 10^{-6} \)
\(a_{28}= +0.84563615 \pm 8.7 \cdot 10^{-6} \) \(a_{29}= +0.67473695 \pm 7.7 \cdot 10^{-6} \) \(a_{30}= +0.74893800 \pm 1.1 \cdot 10^{-5} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -1.02495399 \pm 1.0 \cdot 10^{-5} \) \(a_{33}= -1.22201648 \pm 8.7 \cdot 10^{-6} \)
\(a_{34}= +0.83910386 \pm 1.0 \cdot 10^{-5} \) \(a_{35}= +1.92932513 \pm 7.5 \cdot 10^{-6} \) \(a_{36}= +0.16488121 \pm 1.1 \cdot 10^{-5} \)
\(a_{37}= -0.91901463 \pm 7.4 \cdot 10^{-6} \) \(a_{38}= -0.15114043 \pm 1.0 \cdot 10^{-5} \) \(a_{39}= +0.66451154 \pm 8.3 \cdot 10^{-6} \)
\(a_{40}= -1.49299383 \pm 1.0 \cdot 10^{-5} \) \(a_{41}= +1.10108896 \pm 7.4 \cdot 10^{-6} \) \(a_{42}= +0.47319070 \pm 1.0 \cdot 10^{-5} \)
\(a_{43}= +1.72533377 \pm 7.0 \cdot 10^{-6} \) \(a_{44}= +1.05658118 \pm 8.6 \cdot 10^{-6} \) \(a_{45}= +0.37617769 \pm 8.2 \cdot 10^{-6} \)
\(a_{46}= +0.26215639 \pm 7.4 \cdot 10^{-6} \) \(a_{47}= +0.25108968 \pm 7.2 \cdot 10^{-6} \) \(a_{48}= +0.31231815 \pm 1.2 \cdot 10^{-5} \)
\(a_{49}= +0.21897768 \pm 7.7 \cdot 10^{-6} \) \(a_{50}= -0.99357051 \pm 9.9 \cdot 10^{-6} \) \(a_{51}= -1.53637456 \pm 8.8 \cdot 10^{-6} \)
\(a_{52}= -0.57455067 \pm 8.7 \cdot 10^{-6} \) \(a_{53}= -1.38425802 \pm 7.7 \cdot 10^{-6} \) \(a_{54}= +0.52084854 \pm 9.8 \cdot 10^{-6} \)
\(a_{55}= +2.41059777 \pm 8.7 \cdot 10^{-6} \) \(a_{56}= -0.94329677 \pm 8.4 \cdot 10^{-6} \) \(a_{57}= +0.27673369 \pm 8.4 \cdot 10^{-6} \)
\(a_{58}= -0.32644721 \pm 9.0 \cdot 10^{-6} \) \(a_{59}= +0.34448759 \pm 8.7 \cdot 10^{-6} \) \(a_{60}= +1.18564060 \pm 1.2 \cdot 10^{-5} \)

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