Properties

Label 31.121
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 7.418592
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(7.41859279571831036075752032494 \pm 6 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.05350453 \pm 2.2 \cdot 10^{-5} \) \(a_{3}= -0.93111119 \pm 2.0 \cdot 10^{-5} \)
\(a_{4}= -0.99713727 \pm 2.4 \cdot 10^{-5} \) \(a_{5}= +0.92089816 \pm 1.8 \cdot 10^{-5} \) \(a_{6}= -0.04981866 \pm 2.5 \cdot 10^{-5} \)
\(a_{7}= -1.03086691 \pm 1.8 \cdot 10^{-5} \) \(a_{8}= -0.10685589 \pm 2.5 \cdot 10^{-5} \) \(a_{9}= -0.13303195 \pm 1.9 \cdot 10^{-5} \)
\(a_{10}= +0.04927222 \pm 2.3 \cdot 10^{-5} \) \(a_{11}= -0.91194557 \pm 1.8 \cdot 10^{-5} \) \(a_{12}= +0.92844566 \pm 2.9 \cdot 10^{-5} \)
\(a_{13}= -1.08265489 \pm 1.9 \cdot 10^{-5} \) \(a_{14}= -0.05515605 \pm 1.9 \cdot 10^{-5} \) \(a_{15}= -0.85745858 \pm 1.9 \cdot 10^{-5} \)
\(a_{16}= +0.99141999 \pm 2.2 \cdot 10^{-5} \) \(a_{17}= -1.40500109 \pm 1.7 \cdot 10^{-5} \) \(a_{18}= -0.00711781 \pm 2.4 \cdot 10^{-5} \)
\(a_{19}= -1.59507034 \pm 1.9 \cdot 10^{-5} \) \(a_{20}= -0.91826188 \pm 2.3 \cdot 10^{-5} \) \(a_{21}= +0.95985172 \pm 1.9 \cdot 10^{-5} \)
\(a_{22}= -0.04879322 \pm 2.0 \cdot 10^{-5} \) \(a_{23}= +1.09686155 \pm 1.7 \cdot 10^{-5} \) \(a_{24}= +0.09949471 \pm 3.0 \cdot 10^{-5} \)
\(a_{25}= -0.15194657 \pm 1.7 \cdot 10^{-5} \) \(a_{26}= -0.05792694 \pm 1.9 \cdot 10^{-5} \) \(a_{27}= +1.05497873 \pm 1.7 \cdot 10^{-5} \)
\(a_{28}= +1.02791581 \pm 1.9 \cdot 10^{-5} \) \(a_{29}= -0.88712747 \pm 1.7 \cdot 10^{-5} \) \(a_{30}= -0.04587792 \pm 2.5 \cdot 10^{-5} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.15990135 \pm 2.4 \cdot 10^{-5} \) \(a_{33}= +0.84912272 \pm 1.9 \cdot 10^{-5} \)
\(a_{34}= -0.07517392 \pm 2.4 \cdot 10^{-5} \) \(a_{35}= -0.94932345 \pm 1.7 \cdot 10^{-5} \) \(a_{36}= +0.13265112 \pm 2.6 \cdot 10^{-5} \)
\(a_{37}= +1.74912004 \pm 1.7 \cdot 10^{-5} \) \(a_{38}= -0.08534349 \pm 2.3 \cdot 10^{-5} \) \(a_{39}= +1.00807208 \pm 1.8 \cdot 10^{-5} \)
\(a_{40}= -0.09840339 \pm 2.4 \cdot 10^{-5} \) \(a_{41}= +0.57754304 \pm 1.6 \cdot 10^{-5} \) \(a_{42}= +0.05135641 \pm 2.2 \cdot 10^{-5} \)
\(a_{43}= -0.94263673 \pm 1.6 \cdot 10^{-5} \) \(a_{44}= +0.90933491 \pm 1.9 \cdot 10^{-5} \) \(a_{45}= -0.12250888 \pm 1.8 \cdot 10^{-5} \)
\(a_{46}= +0.05868706 \pm 1.6 \cdot 10^{-5} \) \(a_{47}= +1.51304593 \pm 1.6 \cdot 10^{-5} \) \(a_{48}= -0.92312225 \pm 2.8 \cdot 10^{-5} \)
\(a_{49}= +0.06268659 \pm 1.7 \cdot 10^{-5} \) \(a_{50}= -0.00812983 \pm 2.2 \cdot 10^{-5} \) \(a_{51}= +1.30821223 \pm 2.0 \cdot 10^{-5} \)
\(a_{52}= +1.07955553 \pm 1.9 \cdot 10^{-5} \) \(a_{53}= -0.37931548 \pm 1.7 \cdot 10^{-5} \) \(a_{54}= +0.05644614 \pm 2.2 \cdot 10^{-5} \)
\(a_{55}= -0.83980900 \pm 1.9 \cdot 10^{-5} \) \(a_{56}= +0.11015420 \pm 1.9 \cdot 10^{-5} \) \(a_{57}= +1.48518784 \pm 1.9 \cdot 10^{-5} \)
\(a_{58}= -0.04746534 \pm 2.0 \cdot 10^{-5} \) \(a_{59}= +0.00219525 \pm 1.9 \cdot 10^{-5} \) \(a_{60}= +0.85500391 \pm 2.9 \cdot 10^{-5} \)

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