Properties

Label 31.117
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 7.277100
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(7.27710082577246573666707719197 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.17724636 \pm 5.4 \cdot 10^{-7} \) \(a_{3}= +1.50948372 \pm 4.8 \cdot 10^{-7} \)
\(a_{4}= +0.38590900 \pm 5.4 \cdot 10^{-7} \) \(a_{5}= +0.59758622 \pm 4.6 \cdot 10^{-7} \) \(a_{6}= -1.77703423 \pm 5.4 \cdot 10^{-7} \)
\(a_{7}= +1.39635808 \pm 4.7 \cdot 10^{-7} \) \(a_{8}= +0.72293640 \pm 5.2 \cdot 10^{-7} \) \(a_{9}= +1.27854112 \pm 4.6 \cdot 10^{-7} \)
\(a_{10}= -0.70350620 \pm 4.5 \cdot 10^{-7} \) \(a_{11}= +1.46456937 \pm 4.6 \cdot 10^{-7} \) \(a_{12}= +0.58252335 \pm 5.1 \cdot 10^{-7} \)
\(a_{13}= +1.25950715 \pm 3.7 \cdot 10^{-7} \) \(a_{14}= -1.64385748 \pm 6.3 \cdot 10^{-7} \) \(a_{15}= +0.90204667 \pm 4.9 \cdot 10^{-7} \)
\(a_{16}= -1.23698324 \pm 5.5 \cdot 10^{-7} \) \(a_{17}= -1.46843022 \pm 4.3 \cdot 10^{-7} \) \(a_{18}= -1.50515788 \pm 4.0 \cdot 10^{-7} \)
\(a_{19}= +1.06690892 \pm 4.2 \cdot 10^{-7} \) \(a_{20}= +0.23061390 \pm 4.7 \cdot 10^{-7} \) \(a_{21}= +2.10777980 \pm 4.7 \cdot 10^{-7} \)
\(a_{22}= -1.72415896 \pm 5.5 \cdot 10^{-7} \) \(a_{23}= -0.53529546 \pm 3.7 \cdot 10^{-7} \) \(a_{24}= +1.09126072 \pm 5.6 \cdot 10^{-7} \)
\(a_{25}= -0.64289071 \pm 4.9 \cdot 10^{-7} \) \(a_{26}= -1.48275021 \pm 4.2 \cdot 10^{-7} \) \(a_{27}= +0.42045328 \pm 4.8 \cdot 10^{-7} \)
\(a_{28}= +0.53886715 \pm 6.8 \cdot 10^{-7} \) \(a_{29}= +0.31450221 \pm 4.4 \cdot 10^{-7} \) \(a_{30}= -1.06193117 \pm 5.0 \cdot 10^{-7} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.73329763 \pm 5.4 \cdot 10^{-7} \) \(a_{33}= +2.21074362 \pm 5.2 \cdot 10^{-7} \)
\(a_{34}= +1.72870413 \pm 4.6 \cdot 10^{-7} \) \(a_{35}= +0.83444435 \pm 4.8 \cdot 10^{-7} \) \(a_{36}= +0.49340052 \pm 4.1 \cdot 10^{-7} \)
\(a_{37}= -1.69639714 \pm 4.6 \cdot 10^{-7} \) \(a_{38}= -1.25601465 \pm 5.5 \cdot 10^{-7} \) \(a_{39}= +1.90120555 \pm 4.7 \cdot 10^{-7} \)
\(a_{40}= +0.43201683 \pm 4.4 \cdot 10^{-7} \) \(a_{41}= +1.42523321 \pm 3.6 \cdot 10^{-7} \) \(a_{42}= -2.48137611 \pm 6.2 \cdot 10^{-7} \)
\(a_{43}= +0.51419105 \pm 4.7 \cdot 10^{-7} \) \(a_{44}= +0.56519050 \pm 5.8 \cdot 10^{-7} \) \(a_{45}= +0.76403855 \pm 4.7 \cdot 10^{-7} \)
\(a_{46}= +0.63017464 \pm 4.7 \cdot 10^{-7} \) \(a_{47}= -0.01758370 \pm 4.0 \cdot 10^{-7} \) \(a_{48}= -1.86720607 \pm 5.1 \cdot 10^{-7} \)
\(a_{49}= +0.94981590 \pm 4.1 \cdot 10^{-7} \) \(a_{50}= +0.75684075 \pm 4.6 \cdot 10^{-7} \) \(a_{51}= -2.21657151 \pm 4.2 \cdot 10^{-7} \)
\(a_{52}= +0.48605515 \pm 4.1 \cdot 10^{-7} \) \(a_{53}= -1.01870333 \pm 4.6 \cdot 10^{-7} \) \(a_{54}= -0.49497709 \pm 5.1 \cdot 10^{-7} \)
\(a_{55}= +0.87520647 \pm 4.8 \cdot 10^{-7} \) \(a_{56}= +1.00947808 \pm 6.9 \cdot 10^{-7} \) \(a_{57}= +1.61048165 \pm 3.9 \cdot 10^{-7} \)
\(a_{58}= -0.37024658 \pm 5.5 \cdot 10^{-7} \) \(a_{59}= -0.38446066 \pm 3.7 \cdot 10^{-7} \) \(a_{60}= +0.34810793 \pm 4.7 \cdot 10^{-7} \)

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