Properties

Label 19.16
Level $19$
Weight $0$
Character 19.1
Symmetry odd
\(R\) 3.840448
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.84044805111431923274515994417 \pm 4 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.97374773 \pm 1.0 \cdot 10^{-7} \) \(a_{3}= -0.17706866 \pm 9.8 \cdot 10^{-8} \)
\(a_{4}= -0.05181537 \pm 1.0 \cdot 10^{-7} \) \(a_{5}= +1.50521148 \pm 8.0 \cdot 10^{-8} \) \(a_{6}= +0.17242021 \pm 1.1 \cdot 10^{-7} \)
\(a_{7}= -0.16909248 \pm 9.5 \cdot 10^{-8} \) \(a_{8}= +1.02420282 \pm 1.1 \cdot 10^{-7} \) \(a_{9}= -0.96864669 \pm 8.6 \cdot 10^{-8} \)
\(a_{10}= -1.46569626 \pm 9.0 \cdot 10^{-8} \) \(a_{11}= +1.54539415 \pm 8.6 \cdot 10^{-8} \) \(a_{12}= +0.00917488 \pm 1.1 \cdot 10^{-7} \)
\(a_{13}= +1.32982933 \pm 8.1 \cdot 10^{-8} \) \(a_{14}= +0.16465342 \pm 1.0 \cdot 10^{-7} \) \(a_{15}= -0.26652578 \pm 8.5 \cdot 10^{-8} \)
\(a_{16}= -0.94549980 \pm 1.0 \cdot 10^{-7} \) \(a_{17}= +0.06231457 \pm 8.1 \cdot 10^{-8} \) \(a_{18}= +0.94321751 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= +0.22941573 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= -0.07799308 \pm 1.0 \cdot 10^{-7} \) \(a_{21}= +0.02994098 \pm 1.0 \cdot 10^{-7} \)
\(a_{22}= -1.50482404 \pm 8.6 \cdot 10^{-8} \) \(a_{23}= +0.37696171 \pm 9.0 \cdot 10^{-8} \) \(a_{24}= -0.18135422 \pm 1.2 \cdot 10^{-7} \)
\(a_{25}= +1.26566161 \pm 6.8 \cdot 10^{-8} \) \(a_{26}= -1.29491829 \pm 9.2 \cdot 10^{-8} \) \(a_{27}= +0.34858563 \pm 7.9 \cdot 10^{-8} \)
\(a_{28}= +0.00876159 \pm 9.1 \cdot 10^{-8} \) \(a_{29}= -1.16401010 \pm 6.5 \cdot 10^{-8} \) \(a_{30}= +0.25952887 \pm 9.6 \cdot 10^{-8} \)
\(a_{31}= +1.44284161 \pm 8.4 \cdot 10^{-8} \) \(a_{32}= -0.10352454 \pm 9.7 \cdot 10^{-8} \) \(a_{33}= -0.27364087 \pm 1.0 \cdot 10^{-7} \)
\(a_{34}= -0.06067867 \pm 1.0 \cdot 10^{-7} \) \(a_{35}= -0.25451994 \pm 6.9 \cdot 10^{-8} \) \(a_{36}= +0.05019078 \pm 1.1 \cdot 10^{-7} \)
\(a_{37}= +0.75374362 \pm 8.0 \cdot 10^{-8} \) \(a_{38}= -0.22339305 \pm 1.1 \cdot 10^{-7} \) \(a_{39}= -0.23547110 \pm 7.1 \cdot 10^{-8} \)
\(a_{40}= +1.54164185 \pm 1.1 \cdot 10^{-7} \) \(a_{41}= +0.96309164 \pm 6.5 \cdot 10^{-8} \) \(a_{42}= -0.02915496 \pm 1.2 \cdot 10^{-7} \)
\(a_{43}= -0.63414666 \pm 6.8 \cdot 10^{-8} \) \(a_{44}= -0.08007516 \pm 7.5 \cdot 10^{-8} \) \(a_{45}= -1.45801812 \pm 7.6 \cdot 10^{-8} \)
\(a_{46}= -0.36706561 \pm 9.1 \cdot 10^{-8} \) \(a_{47}= -0.05809019 \pm 8.3 \cdot 10^{-8} \) \(a_{48}= +0.16741838 \pm 8.3 \cdot 10^{-8} \)
\(a_{49}= -0.97140773 \pm 9.4 \cdot 10^{-8} \) \(a_{50}= -1.23243511 \pm 8.4 \cdot 10^{-8} \) \(a_{51}= -0.01103396 \pm 7.2 \cdot 10^{-8} \)
\(a_{52}= -0.06890559 \pm 9.8 \cdot 10^{-8} \) \(a_{53}= -0.09857959 \pm 8.6 \cdot 10^{-8} \) \(a_{54}= -0.33943447 \pm 9.3 \cdot 10^{-8} \)
\(a_{55}= +2.32614502 \pm 7.8 \cdot 10^{-8} \) \(a_{56}= -0.17318500 \pm 9.8 \cdot 10^{-8} \) \(a_{57}= -0.04062234 \pm 1.0 \cdot 10^{-7} \)
\(a_{58}= +1.13345219 \pm 8.2 \cdot 10^{-8} \) \(a_{59}= +0.34180750 \pm 8.3 \cdot 10^{-8} \) \(a_{60}= +0.01381013 \pm 1.0 \cdot 10^{-7} \)

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