Properties

Label 31.109
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 7.017098
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(7.01709847951352824735727578143 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.83874834 \pm 8.5 \cdot 10^{-6} \) \(a_{3}= -0.87799741 \pm 7.6 \cdot 10^{-6} \)
\(a_{4}= +2.38099546 \pm 9.3 \cdot 10^{-6} \) \(a_{5}= -1.09520120 \pm 7.1 \cdot 10^{-6} \) \(a_{6}= +1.61441628 \pm 9.7 \cdot 10^{-6} \)
\(a_{7}= -1.35439401 \pm 6.9 \cdot 10^{-6} \) \(a_{8}= -2.53930311 \pm 9.7 \cdot 10^{-6} \) \(a_{9}= -0.22912054 \pm 7.2 \cdot 10^{-6} \)
\(a_{10}= +2.01379939 \pm 8.7 \cdot 10^{-6} \) \(a_{11}= -0.36331278 \pm 6.9 \cdot 10^{-6} \) \(a_{12}= -2.09050785 \pm 1.1 \cdot 10^{-5} \)
\(a_{13}= +0.82593063 \pm 7.2 \cdot 10^{-6} \) \(a_{14}= +2.49038974 \pm 7.2 \cdot 10^{-6} \) \(a_{15}= +0.96158382 \pm 7.3 \cdot 10^{-6} \)
\(a_{16}= +2.28814392 \pm 8.6 \cdot 10^{-6} \) \(a_{17}= +1.26912908 \pm 6.6 \cdot 10^{-6} \) \(a_{18}= +0.42129502 \pm 9.3 \cdot 10^{-6} \)
\(a_{19}= -1.44746219 \pm 7.3 \cdot 10^{-6} \) \(a_{20}= -2.60766909 \pm 9.0 \cdot 10^{-6} \) \(a_{21}= +1.18915444 \pm 7.5 \cdot 10^{-6} \)
\(a_{22}= +0.66804078 \pm 7.5 \cdot 10^{-6} \) \(a_{23}= +0.93500199 \pm 6.6 \cdot 10^{-6} \) \(a_{24}= +2.22950156 \pm 1.1 \cdot 10^{-5} \)
\(a_{25}= +0.19946568 \pm 6.7 \cdot 10^{-6} \) \(a_{26}= -1.51867858 \pm 7.4 \cdot 10^{-6} \) \(a_{27}= +1.07916466 \pm 6.4 \cdot 10^{-6} \)
\(a_{28}= -3.22480599 \pm 7.4 \cdot 10^{-6} \) \(a_{29}= +1.88656536 \pm 6.6 \cdot 10^{-6} \) \(a_{30}= -1.76811066 \pm 9.8 \cdot 10^{-6} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -1.66801772 \pm 9.3 \cdot 10^{-6} \) \(a_{33}= +0.31898768 \pm 7.4 \cdot 10^{-6} \)
\(a_{34}= -2.33360899 \pm 9.1 \cdot 10^{-6} \) \(a_{35}= +1.48333395 \pm 6.4 \cdot 10^{-6} \) \(a_{36}= -0.54553497 \pm 1.0 \cdot 10^{-5} \)
\(a_{37}= +0.75141883 \pm 6.4 \cdot 10^{-6} \) \(a_{38}= +2.66151869 \pm 8.8 \cdot 10^{-6} \) \(a_{39}= -0.72516496 \pm 7.1 \cdot 10^{-6} \)
\(a_{40}= +2.78104782 \pm 9.3 \cdot 10^{-6} \) \(a_{41}= -0.30171553 \pm 6.3 \cdot 10^{-6} \) \(a_{42}= -2.18655575 \pm 8.6 \cdot 10^{-6} \)
\(a_{43}= -1.02960034 \pm 6.0 \cdot 10^{-6} \) \(a_{44}= -0.86504609 \pm 7.4 \cdot 10^{-6} \) \(a_{45}= +0.25093310 \pm 7.0 \cdot 10^{-6} \)
\(a_{46}= -1.71923335 \pm 6.4 \cdot 10^{-6} \) \(a_{47}= -0.74132489 \pm 6.2 \cdot 10^{-6} \) \(a_{48}= -2.00898444 \pm 1.0 \cdot 10^{-5} \)
\(a_{49}= +0.83438314 \pm 6.6 \cdot 10^{-6} \) \(a_{50}= -0.36676718 \pm 8.5 \cdot 10^{-6} \) \(a_{51}= -1.11429205 \pm 7.5 \cdot 10^{-6} \)
\(a_{52}= +1.96653709 \pm 7.5 \cdot 10^{-6} \) \(a_{53}= +0.25275683 \pm 6.6 \cdot 10^{-6} \) \(a_{54}= -1.98431222 \pm 8.4 \cdot 10^{-6} \)
\(a_{55}= +0.39790060 \pm 7.5 \cdot 10^{-6} \) \(a_{56}= +3.43921692 \pm 7.2 \cdot 10^{-6} \) \(a_{57}= +1.27086805 \pm 7.2 \cdot 10^{-6} \)
\(a_{58}= -3.46891892 \pm 7.7 \cdot 10^{-6} \) \(a_{59}= +0.07110043 \pm 7.5 \cdot 10^{-6} \) \(a_{60}= +2.28952671 \pm 1.1 \cdot 10^{-5} \)

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