Properties

Label 19.18
Level $19$
Weight $0$
Character 19.1
Symmetry even
\(R\) 4.088788
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(4.08878884698417969959541780302 \pm 4 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.56712359 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.73248702 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.67837084 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.06933261 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.98253425 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.24557535 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.95184369 \pm 1 \cdot 10^{-8} \) \(a_{9}= +2.00151129 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.60644374 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.14349247 \pm 1 \cdot 10^{-8} \) \(a_{12}= -1.17526868 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -1.44826767 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.13927157 \pm 1 \cdot 10^{-8} \) \(a_{15}= +1.85260486 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.13855783 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.81445294 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.13510426 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.22941573 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= -0.72540406 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.42545610 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.64850155 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.77066278 \pm 1 \cdot 10^{-8} \) \(a_{24}= +1.64905684 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.14347222 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.82134675 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.73510531 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.16659116 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.32881930 \pm 1 \cdot 10^{-8} \) \(a_{30}= -1.05065591 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.25032930 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.03042310 \pm 1 \cdot 10^{-8} \) \(a_{33}= +1.98108586 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.46189547 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.26260173 \pm 1 \cdot 10^{-8} \) \(a_{36}= -1.35776689 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.88641219 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.13010707 \pm 1.1 \cdot 10^{-8} \) \(a_{39}= -2.50910494 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.01783749 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.47089870 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.24128619 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.84178976 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.77571194 \pm 1 \cdot 10^{-8} \) \(a_{45}= +2.14028128 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.43706104 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.19197255 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.24004965 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.93969275 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.08136648 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.41102915 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.98246255 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.76414226 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.98401915 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +1.22277378 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.23374935 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.39745978 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= +0.18648118 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.77144019 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.25675312 \pm 1 \cdot 10^{-8} \)

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