Properties

Label 31.14
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 2.743830
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(2.74383051117742682961922288538 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.93805790 \pm 3.7 \cdot 10^{-6} \) \(a_{3}= -1.46985244 \pm 3.3 \cdot 10^{-6} \)
\(a_{4}= +2.75606841 \pm 4.1 \cdot 10^{-6} \) \(a_{5}= -0.87556323 \pm 3.1 \cdot 10^{-6} \) \(a_{6}= +2.84865913 \pm 4.2 \cdot 10^{-6} \)
\(a_{7}= -0.34607547 \pm 3.0 \cdot 10^{-6} \) \(a_{8}= -3.40336225 \pm 4.2 \cdot 10^{-6} \) \(a_{9}= +1.16046621 \pm 3.1 \cdot 10^{-6} \)
\(a_{10}= +1.69689223 \pm 3.8 \cdot 10^{-6} \) \(a_{11}= -0.06758227 \pm 3.0 \cdot 10^{-6} \) \(a_{12}= -4.05101389 \pm 4.9 \cdot 10^{-6} \)
\(a_{13}= +0.57586461 \pm 3.1 \cdot 10^{-6} \) \(a_{14}= +0.67071431 \pm 3.1 \cdot 10^{-6} \) \(a_{15}= +1.28694875 \pm 3.2 \cdot 10^{-6} \)
\(a_{16}= +3.83984467 \pm 3.7 \cdot 10^{-6} \) \(a_{17}= -0.96448744 \pm 2.9 \cdot 10^{-6} \) \(a_{18}= -2.24905069 \pm 4.1 \cdot 10^{-6} \)
\(a_{19}= +0.32995325 \pm 3.2 \cdot 10^{-6} \) \(a_{20}= -2.41311215 \pm 3.9 \cdot 10^{-6} \) \(a_{21}= +0.50867988 \pm 3.3 \cdot 10^{-6} \)
\(a_{22}= +0.13097835 \pm 3.3 \cdot 10^{-6} \) \(a_{23}= +0.80531790 \pm 2.9 \cdot 10^{-6} \) \(a_{24}= +5.00244031 \pm 5.1 \cdot 10^{-6} \)
\(a_{25}= -0.23338903 \pm 2.9 \cdot 10^{-6} \) \(a_{26}= -1.11605896 \pm 3.2 \cdot 10^{-6} \) \(a_{27}= -0.23586165 \pm 2.8 \cdot 10^{-6} \)
\(a_{28}= -0.95380768 \pm 3.2 \cdot 10^{-6} \) \(a_{29}= -0.21904025 \pm 2.9 \cdot 10^{-6} \) \(a_{30}= -2.49418119 \pm 4.3 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -4.03847903 \pm 4.0 \cdot 10^{-6} \) \(a_{33}= +0.09933596 \pm 3.2 \cdot 10^{-6} \)
\(a_{34}= +1.86923249 \pm 3.9 \cdot 10^{-6} \) \(a_{35}= +0.30301096 \pm 2.8 \cdot 10^{-6} \) \(a_{36}= +3.19832425 \pm 4.4 \cdot 10^{-6} \)
\(a_{37}= -0.69258205 \pm 2.8 \cdot 10^{-6} \) \(a_{38}= -0.63946850 \pm 3.8 \cdot 10^{-6} \) \(a_{39}= -0.84643601 \pm 3.1 \cdot 10^{-6} \)
\(a_{40}= +2.97985884 \pm 4.0 \cdot 10^{-6} \) \(a_{41}= +1.82896747 \pm 2.7 \cdot 10^{-6} \) \(a_{42}= -0.98585106 \pm 3.8 \cdot 10^{-6} \)
\(a_{43}= +0.83349597 \pm 2.6 \cdot 10^{-6} \) \(a_{44}= -0.18626136 \pm 3.2 \cdot 10^{-6} \) \(a_{45}= -1.01606154 \pm 3.1 \cdot 10^{-6} \)
\(a_{46}= -1.56075271 \pm 2.8 \cdot 10^{-6} \) \(a_{47}= +1.80188824 \pm 2.7 \cdot 10^{-6} \) \(a_{48}= -5.64400507 \pm 4.7 \cdot 10^{-6} \)
\(a_{49}= -0.88023177 \pm 2.9 \cdot 10^{-6} \) \(a_{50}= +0.45232146 \pm 3.7 \cdot 10^{-6} \) \(a_{51}= +1.41765421 \pm 3.3 \cdot 10^{-6} \)
\(a_{52}= +1.58712227 \pm 3.2 \cdot 10^{-6} \) \(a_{53}= -0.71860022 \pm 2.9 \cdot 10^{-6} \) \(a_{54}= +0.45711352 \pm 3.6 \cdot 10^{-6} \)
\(a_{55}= +0.05917255 \pm 3.3 \cdot 10^{-6} \) \(a_{56}= +1.17782020 \pm 3.1 \cdot 10^{-6} \) \(a_{57}= -0.48498259 \pm 3.1 \cdot 10^{-6} \)
\(a_{58}= +0.42451268 \pm 3.3 \cdot 10^{-6} \) \(a_{59}= +0.11840461 \pm 3.3 \cdot 10^{-6} \) \(a_{60}= +3.54691880 \pm 4.8 \cdot 10^{-6} \)

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