Properties

Label 31.44
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 4.584299
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(4.58429981405929734312685170137 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.86831855 \pm 7.2 \cdot 10^{-6} \) \(a_{3}= +0.17991362 \pm 6.5 \cdot 10^{-6} \)
\(a_{4}= +2.49061419 \pm 7.9 \cdot 10^{-6} \) \(a_{5}= -0.26190705 \pm 6.0 \cdot 10^{-6} \) \(a_{6}= +0.33613595 \pm 8.2 \cdot 10^{-6} \)
\(a_{7}= +1.25324465 \pm 5.9 \cdot 10^{-6} \) \(a_{8}= +2.78494213 \pm 8.2 \cdot 10^{-6} \) \(a_{9}= -0.96763109 \pm 6.1 \cdot 10^{-6} \)
\(a_{10}= -0.48932579 \pm 7.4 \cdot 10^{-6} \) \(a_{11}= +0.56384229 \pm 5.9 \cdot 10^{-6} \) \(a_{12}= +0.44809541 \pm 9.5 \cdot 10^{-6} \)
\(a_{13}= +1.05315657 \pm 6.1 \cdot 10^{-6} \) \(a_{14}= +2.34146022 \pm 6.1 \cdot 10^{-6} \) \(a_{15}= -0.04712064 \pm 6.2 \cdot 10^{-6} \)
\(a_{16}= +2.71254484 \pm 7.3 \cdot 10^{-6} \) \(a_{17}= -0.83187640 \pm 5.6 \cdot 10^{-6} \) \(a_{18}= -1.80784311 \pm 7.9 \cdot 10^{-6} \)
\(a_{19}= -0.79630242 \pm 6.2 \cdot 10^{-6} \) \(a_{20}= -0.65230940 \pm 7.6 \cdot 10^{-6} \) \(a_{21}= +0.22547578 \pm 6.3 \cdot 10^{-6} \)
\(a_{22}= +1.05343701 \pm 6.4 \cdot 10^{-6} \) \(a_{23}= -1.54408494 \pm 5.6 \cdot 10^{-6} \) \(a_{24}= +0.50104901 \pm 9.9 \cdot 10^{-6} \)
\(a_{25}= -0.93140470 \pm 5.7 \cdot 10^{-6} \) \(a_{26}= +1.96763195 \pm 6.2 \cdot 10^{-6} \) \(a_{27}= -0.35400363 \pm 5.4 \cdot 10^{-6} \)
\(a_{28}= +3.12134891 \pm 6.3 \cdot 10^{-6} \) \(a_{29}= -0.64192804 \pm 5.6 \cdot 10^{-6} \) \(a_{30}= -0.08803637 \pm 8.3 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +2.28295570 \pm 7.8 \cdot 10^{-6} \) \(a_{33}= +0.10144291 \pm 6.3 \cdot 10^{-6} \)
\(a_{34}= -1.55421011 \pm 7.7 \cdot 10^{-6} \) \(a_{35}= -0.32823360 \pm 5.4 \cdot 10^{-6} \) \(a_{36}= -2.40999572 \pm 8.5 \cdot 10^{-6} \)
\(a_{37}= +1.80637067 \pm 5.4 \cdot 10^{-6} \) \(a_{38}= -1.48774658 \pm 7.5 \cdot 10^{-6} \) \(a_{39}= +0.18947721 \pm 6.0 \cdot 10^{-6} \)
\(a_{40}= -0.72939596 \pm 7.9 \cdot 10^{-6} \) \(a_{41}= +0.03430816 \pm 5.3 \cdot 10^{-6} \) \(a_{42}= +0.42126058 \pm 7.3 \cdot 10^{-6} \)
\(a_{43}= +0.60428219 \pm 5.1 \cdot 10^{-6} \) \(a_{44}= +1.40431361 \pm 6.2 \cdot 10^{-6} \) \(a_{45}= +0.25342940 \pm 5.9 \cdot 10^{-6} \)
\(a_{46}= -2.88484253 \pm 5.4 \cdot 10^{-6} \) \(a_{47}= -1.49791960 \pm 5.2 \cdot 10^{-6} \) \(a_{48}= +0.48802376 \pm 9.2 \cdot 10^{-6} \)
\(a_{49}= +0.57062216 \pm 5.6 \cdot 10^{-6} \) \(a_{50}= -1.74016067 \pm 7.2 \cdot 10^{-6} \) \(a_{51}= -0.14966589 \pm 6.4 \cdot 10^{-6} \)
\(a_{52}= +2.62300669 \pm 6.3 \cdot 10^{-6} \) \(a_{53}= +0.27538943 \pm 5.6 \cdot 10^{-6} \) \(a_{54}= -0.66139154 \pm 7.1 \cdot 10^{-6} \)
\(a_{55}= -0.14767427 \pm 6.3 \cdot 10^{-6} \) \(a_{56}= +3.49021383 \pm 6.1 \cdot 10^{-6} \) \(a_{57}= -0.14326565 \pm 6.1 \cdot 10^{-6} \)
\(a_{58}= -1.19932605 \pm 6.5 \cdot 10^{-6} \) \(a_{59}= +1.49654056 \pm 6.3 \cdot 10^{-6} \) \(a_{60}= -0.11735934 \pm 9.4 \cdot 10^{-6} \)

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