Properties

Label 19.15
Level $19$
Weight $0$
Character 19.1
Symmetry odd
\(R\) 3.776887
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.77688712054364208404997087332 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.78603007 \pm 5.3 \cdot 10^{-8} \) \(a_{3}= -1.34553914 \pm 5.2 \cdot 10^{-8} \)
\(a_{4}= +2.18990339 \pm 5.3 \cdot 10^{-8} \) \(a_{5}= -1.56215608 \pm 4.3 \cdot 10^{-8} \) \(a_{6}= +2.40317336 \pm 5.9 \cdot 10^{-8} \)
\(a_{7}= -0.69574874 \pm 5.1 \cdot 10^{-8} \) \(a_{8}= -2.12520324 \pm 6.1 \cdot 10^{-8} \) \(a_{9}= +0.81047558 \pm 4.6 \cdot 10^{-8} \)
\(a_{10}= +2.79005772 \pm 4.8 \cdot 10^{-8} \) \(a_{11}= -0.40610348 \pm 4.6 \cdot 10^{-8} \) \(a_{12}= -2.94660073 \pm 5.9 \cdot 10^{-8} \)
\(a_{13}= -0.03189416 \pm 4.3 \cdot 10^{-8} \) \(a_{14}= +1.24262817 \pm 5.6 \cdot 10^{-8} \) \(a_{15}= +2.10194215 \pm 4.6 \cdot 10^{-8} \)
\(a_{16}= +1.60577348 \pm 5.8 \cdot 10^{-8} \) \(a_{17}= -0.69306348 \pm 4.3 \cdot 10^{-8} \) \(a_{18}= -1.44753376 \pm 5.6 \cdot 10^{-8} \)
\(a_{19}= +0.22941573 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= -3.42097089 \pm 5.5 \cdot 10^{-8} \) \(a_{21}= +0.93615716 \pm 5.7 \cdot 10^{-8} \)
\(a_{22}= +0.72531302 \pm 4.6 \cdot 10^{-8} \) \(a_{23}= -1.62803505 \pm 4.8 \cdot 10^{-8} \) \(a_{24}= +2.85954414 \pm 6.4 \cdot 10^{-8} \)
\(a_{25}= +1.44033161 \pm 3.6 \cdot 10^{-8} \) \(a_{26}= +0.05696393 \pm 4.9 \cdot 10^{-8} \) \(a_{27}= +0.25501252 \pm 4.2 \cdot 10^{-8} \)
\(a_{28}= -1.52362253 \pm 4.8 \cdot 10^{-8} \) \(a_{29}= +0.62556522 \pm 3.4 \cdot 10^{-8} \) \(a_{30}= -3.75413187 \pm 5.1 \cdot 10^{-8} \)
\(a_{31}= +0.41611287 \pm 4.5 \cdot 10^{-8} \) \(a_{32}= -0.74275648 \pm 5.2 \cdot 10^{-8} \) \(a_{33}= +0.54642812 \pm 5.4 \cdot 10^{-8} \)
\(a_{34}= +1.23783221 \pm 5.4 \cdot 10^{-8} \) \(a_{35}= +1.08686813 \pm 3.7 \cdot 10^{-8} \) \(a_{36}= +1.77486323 \pm 6.0 \cdot 10^{-8} \)
\(a_{37}= -0.90304818 \pm 4.2 \cdot 10^{-8} \) \(a_{38}= -0.40974340 \pm 6.4 \cdot 10^{-8} \) \(a_{39}= +0.04291484 \pm 3.8 \cdot 10^{-8} \)
\(a_{40}= +3.31989915 \pm 6.4 \cdot 10^{-8} \) \(a_{41}= -0.90116425 \pm 3.4 \cdot 10^{-8} \) \(a_{42}= -1.67200484 \pm 6.7 \cdot 10^{-8} \)
\(a_{43}= -0.21990856 \pm 3.6 \cdot 10^{-8} \) \(a_{44}= -0.88932738 \pm 4.0 \cdot 10^{-8} \) \(a_{45}= -1.26608936 \pm 4.1 \cdot 10^{-8} \)
\(a_{46}= +2.90771954 \pm 4.9 \cdot 10^{-8} \) \(a_{47}= +0.44462400 \pm 4.4 \cdot 10^{-8} \) \(a_{48}= -2.16063107 \pm 4.4 \cdot 10^{-8} \)
\(a_{49}= -0.51593369 \pm 5.0 \cdot 10^{-8} \) \(a_{50}= -2.57247556 \pm 4.5 \cdot 10^{-8} \) \(a_{51}= +0.93254404 \pm 3.8 \cdot 10^{-8} \)
\(a_{52}= -0.06984513 \pm 5.2 \cdot 10^{-8} \) \(a_{53}= -0.79955463 \pm 4.6 \cdot 10^{-8} \) \(a_{54}= -0.45546003 \pm 4.9 \cdot 10^{-8} \)
\(a_{55}= +0.63439701 \pm 4.2 \cdot 10^{-8} \) \(a_{56}= +1.47860748 \pm 5.2 \cdot 10^{-8} \) \(a_{57}= -0.30868785 \pm 6.3 \cdot 10^{-8} \)
\(a_{58}= -1.11727829 \pm 4.4 \cdot 10^{-8} \) \(a_{59}= +1.59324929 \pm 4.4 \cdot 10^{-8} \) \(a_{60}= +4.60305024 \pm 5.6 \cdot 10^{-8} \)

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