Properties

Label 31.24
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 3.478988
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.47898831142711573223006071544 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.72791016 \pm 9.3 \cdot 10^{-7} \) \(a_{3}= -1.32422091 \pm 8.4 \cdot 10^{-7} \)
\(a_{4}= -0.47014679 \pm 1.0 \cdot 10^{-6} \) \(a_{5}= +0.79843234 \pm 7.8 \cdot 10^{-7} \) \(a_{6}= +0.96391386 \pm 1.0 \cdot 10^{-6} \)
\(a_{7}= -1.08230912 \pm 7.6 \cdot 10^{-7} \) \(a_{8}= +1.07013479 \pm 1.0 \cdot 10^{-6} \) \(a_{9}= +0.75356103 \pm 7.9 \cdot 10^{-7} \)
\(a_{10}= -0.58118701 \pm 9.5 \cdot 10^{-7} \) \(a_{11}= +1.02328670 \pm 7.6 \cdot 10^{-7} \) \(a_{12}= +0.62257821 \pm 1.2 \cdot 10^{-6} \)
\(a_{13}= -1.75405630 \pm 8.0 \cdot 10^{-7} \) \(a_{14}= +0.78782381 \pm 7.9 \cdot 10^{-7} \) \(a_{15}= -1.05730080 \pm 8.1 \cdot 10^{-7} \)
\(a_{16}= -0.30881520 \pm 9.5 \cdot 10^{-7} \) \(a_{17}= +0.58426123 \pm 7.2 \cdot 10^{-7} \) \(a_{18}= -0.54852473 \pm 1.0 \cdot 10^{-6} \)
\(a_{19}= +1.49729922 \pm 8.1 \cdot 10^{-7} \) \(a_{20}= -0.37538040 \pm 9.9 \cdot 10^{-7} \) \(a_{21}= +1.43321637 \pm 8.2 \cdot 10^{-7} \)
\(a_{22}= -0.74486079 \pm 8.3 \cdot 10^{-7} \) \(a_{23}= +1.01158468 \pm 7.3 \cdot 10^{-7} \) \(a_{24}= -1.41709487 \pm 1.2 \cdot 10^{-6} \)
\(a_{25}= -0.36250580 \pm 7.4 \cdot 10^{-7} \) \(a_{26}= +1.27679541 \pm 8.1 \cdot 10^{-7} \) \(a_{27}= +0.32633964 \pm 7.0 \cdot 10^{-7} \)
\(a_{28}= +0.50884416 \pm 8.2 \cdot 10^{-7} \) \(a_{29}= -0.44026424 \pm 7.2 \cdot 10^{-7} \) \(a_{30}= +0.76962000 \pm 1.0 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -0.84534507 \pm 1.0 \cdot 10^{-6} \) \(a_{33}= -1.35505765 \pm 8.2 \cdot 10^{-7} \)
\(a_{34}= -0.42528969 \pm 1.0 \cdot 10^{-6} \) \(a_{35}= -0.86415060 \pm 7.1 \cdot 10^{-7} \) \(a_{36}= -0.35428430 \pm 1.1 \cdot 10^{-6} \)
\(a_{37}= +0.60062855 \pm 7.0 \cdot 10^{-7} \) \(a_{38}= -1.08989932 \pm 9.7 \cdot 10^{-7} \) \(a_{39}= +2.32275804 \pm 7.8 \cdot 10^{-7} \)
\(a_{40}= +0.85443022 \pm 1.0 \cdot 10^{-6} \) \(a_{41}= +0.01108401 \pm 6.9 \cdot 10^{-7} \) \(a_{42}= -1.04325276 \pm 9.5 \cdot 10^{-7} \)
\(a_{43}= -0.16195906 \pm 6.6 \cdot 10^{-7} \) \(a_{44}= -0.48109496 \pm 8.1 \cdot 10^{-7} \) \(a_{45}= +0.60166749 \pm 7.7 \cdot 10^{-7} \)
\(a_{46}= -0.73634277 \pm 7.0 \cdot 10^{-7} \) \(a_{47}= +0.19649383 \pm 6.8 \cdot 10^{-7} \) \(a_{48}= +0.40893955 \pm 1.1 \cdot 10^{-6} \)
\(a_{49}= +0.17139303 \pm 7.3 \cdot 10^{-7} \) \(a_{50}= +0.26387166 \pm 9.3 \cdot 10^{-7} \) \(a_{51}= -0.77369094 \pm 8.3 \cdot 10^{-7} \)
\(a_{52}= +0.82466394 \pm 8.2 \cdot 10^{-7} \) \(a_{53}= +0.56987592 \pm 7.3 \cdot 10^{-7} \) \(a_{54}= -0.23754594 \pm 9.2 \cdot 10^{-7} \)
\(a_{55}= +0.81702520 \pm 8.2 \cdot 10^{-7} \) \(a_{56}= -1.15821664 \pm 7.9 \cdot 10^{-7} \) \(a_{57}= -1.98275494 \pm 7.9 \cdot 10^{-7} \)
\(a_{58}= +0.32047282 \pm 8.4 \cdot 10^{-7} \) \(a_{59}= +1.35832910 \pm 8.2 \cdot 10^{-7} \) \(a_{60}= +0.49708658 \pm 1.2 \cdot 10^{-6} \)

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