Properties

Label 19.14
Level $19$
Weight $0$
Character 19.1
Symmetry even
\(R\) 3.642456
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(3.64245616517541303534964000819 \pm 5 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.26451544 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.34475820 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.93003158 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.12900832 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.09119387 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.32496391 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.51052315 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.88114178 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.03412469 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.54064054 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.32063602 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.48272118 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.08595797 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.04447668 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.79499033 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.03183673 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.23307561 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.22941573 \pm 1.0 \cdot 10^{-8} \) \(a_{20}= -0.11998181 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.11203398 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.14300777 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.52674100 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.17600705 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.98335685 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.12768720 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.64853906 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.30222670 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.00075540 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.01176477 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.39921868 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.72081037 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.18639026 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.00842131 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.04192305 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.81948968 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.13315641 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.06068400 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.16642209 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.06586174 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.86857719 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.02963472 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.95466358 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.50281278 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.11367462 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.40384657 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.30959843 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.27407944 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.89439845 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.26011307 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.01097597 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.44894594 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.17386465 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.17154860 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.06974713 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.16590160 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.07909296 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.00019982 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.86332267 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.04136471 \pm 1 \cdot 10^{-8} \)

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