Properties

Label 19.10
Level $19$
Weight $0$
Character 19.1
Symmetry even
\(R\) 3.105384
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(3.10538415095337785570786485475 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.12305616 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.64749996 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.26125513 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.57537523 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.85023498 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.99123091 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.82965197 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.71425613 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -1.76923485 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.07441573 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.43041782 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.55699525 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.11320798 \pm 1 \cdot 10^{-8} \) \(a_{15}= -2.59543063 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.19300089 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.04636277 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.92520590 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.22941573 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= -0.41157486 \pm 1 \cdot 10^{-8} \) \(a_{21}= +1.63305289 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.08357305 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.32045373 \pm 1 \cdot 10^{-8} \) \(a_{24}= -1.36685160 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +1.48180711 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.62553694 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.17673694 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.25896416 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.45799581 \pm 1 \cdot 10^{-8} \) \(a_{30}= -2.91481435 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.25937800 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.51015502 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.12259992 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.05206799 \pm 1 \cdot 10^{-8} \) \(a_{35}= -1.56156063 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.44785821 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.50499437 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.25764675 \pm 1.1 \cdot 10^{-8} \) \(a_{39}= +0.91764965 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.30701317 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.54366853 \pm 1 \cdot 10^{-8} \) \(a_{42}= +1.83401011 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.50049456 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.01944149 \pm 1 \cdot 10^{-8} \) \(a_{45}= -2.70059664 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.35988754 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.95174571 \pm 1 \cdot 10^{-8} \) \(a_{48}= -1.96546892 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.01746128 \pm 1 \cdot 10^{-8} \) \(a_{50}= +1.66415260 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.07638265 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.14551787 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.69134126 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.32154167 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.11723270 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.82237668 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.37796241 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= -0.51435502 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.18747985 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.67806957 \pm 1 \cdot 10^{-8} \)

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