Properties

Label 13.160
Level $13$
Weight $0$
Character 13.1
Symmetry even
\(R\) 13.41580
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(13.4158009597210121854598159867 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.88031464 \pm 2.6 \cdot 10^{-6} \) \(a_{3}= -1.61741644 \pm 1.9 \cdot 10^{-6} \)
\(a_{4}= +2.53558313 \pm 2.8 \cdot 10^{-6} \) \(a_{5}= -0.24019175 \pm 2.1 \cdot 10^{-6} \) \(a_{6}= -3.04125181 \pm 2.5 \cdot 10^{-6} \)
\(a_{7}= -0.68390253 \pm 1.9 \cdot 10^{-6} \) \(a_{8}= +2.88737944 \pm 2.5 \cdot 10^{-6} \) \(a_{9}= +1.61603596 \pm 1.7 \cdot 10^{-6} \)
\(a_{10}= -0.45163606 \pm 2.0 \cdot 10^{-6} \) \(a_{11}= +1.18549539 \pm 1.4 \cdot 10^{-6} \) \(a_{12}= -4.10109385 \pm 2.5 \cdot 10^{-6} \)
\(a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= -1.28595195 \pm 2.8 \cdot 10^{-6} \) \(a_{15}= +0.38849009 \pm 1.6 \cdot 10^{-6} \)
\(a_{16}= +2.89359869 \pm 1.8 \cdot 10^{-6} \) \(a_{17}= -1.12199695 \pm 1.9 \cdot 10^{-6} \) \(a_{18}= +3.03865606 \pm 2.0 \cdot 10^{-6} \)
\(a_{19}= -1.83018630 \pm 2.1 \cdot 10^{-6} \) \(a_{20}= -0.60902615 \pm 2.4 \cdot 10^{-6} \) \(a_{21}= +1.10615521 \pm 1.6 \cdot 10^{-6} \)
\(a_{22}= +2.22910433 \pm 1.4 \cdot 10^{-6} \) \(a_{23}= -0.64541876 \pm 1.4 \cdot 10^{-6} \) \(a_{24}= -4.67009499 \pm 2.3 \cdot 10^{-6} \)
\(a_{25}= -0.94230792 \pm 2.4 \cdot 10^{-6} \) \(a_{26}= +0.52150545 \pm 2.6 \cdot 10^{-6} \) \(a_{27}= -0.99638669 \pm 2.1 \cdot 10^{-6} \)
\(a_{28}= -1.73409173 \pm 3.0 \cdot 10^{-6} \) \(a_{29}= +0.87752768 \pm 1.8 \cdot 10^{-6} \) \(a_{30}= +0.73048360 \pm 1.3 \cdot 10^{-6} \)
\(a_{31}= -0.60009031 \pm 1.4 \cdot 10^{-6} \) \(a_{32}= +2.55349652 \pm 1.9 \cdot 10^{-6} \) \(a_{33}= -1.91743974 \pm 1.7 \cdot 10^{-6} \)
\(a_{34}= -2.10970728 \pm 2.4 \cdot 10^{-6} \) \(a_{35}= +0.16426775 \pm 1.8 \cdot 10^{-6} \) \(a_{36}= +4.09759351 \pm 1.7 \cdot 10^{-6} \)
\(a_{37}= -0.64629534 \pm 1.7 \cdot 10^{-6} \) \(a_{38}= -3.44132608 \pm 2.8 \cdot 10^{-6} \) \(a_{39}= -0.44859061 \pm 2.0 \cdot 10^{-6} \)
\(a_{40}= -0.69352472 \pm 2.3 \cdot 10^{-6} \) \(a_{41}= -1.17413876 \pm 2.9 \cdot 10^{-6} \) \(a_{42}= +2.07991982 \pm 2.3 \cdot 10^{-6} \)
\(a_{43}= +0.27150214 \pm 1.6 \cdot 10^{-6} \) \(a_{44}= +3.00592211 \pm 1.1 \cdot 10^{-6} \) \(a_{45}= -0.38815850 \pm 1.5 \cdot 10^{-6} \)
\(a_{46}= -1.21359034 \pm 1.7 \cdot 10^{-6} \) \(a_{47}= +0.30525552 \pm 1.5 \cdot 10^{-6} \) \(a_{48}= -4.68015410 \pm 1.6 \cdot 10^{-6} \)
\(a_{49}= -0.53227732 \pm 1.5 \cdot 10^{-6} \) \(a_{50}= -1.77183538 \pm 1.9 \cdot 10^{-6} \) \(a_{51}= +1.81473631 \pm 2.1 \cdot 10^{-6} \)
\(a_{52}= +0.70324423 \pm 2.8 \cdot 10^{-6} \) \(a_{53}= -0.91096385 \pm 2.1 \cdot 10^{-6} \) \(a_{54}= -1.87352047 \pm 2.2 \cdot 10^{-6} \)
\(a_{55}= -0.28474621 \pm 1.4 \cdot 10^{-6} \) \(a_{56}= -1.97468612 \pm 2.4 \cdot 10^{-6} \) \(a_{57}= +2.96017341 \pm 1.1 \cdot 10^{-6} \)
\(a_{58}= +1.65002814 \pm 3.0 \cdot 10^{-6} \) \(a_{59}= -1.37046961 \pm 1.7 \cdot 10^{-6} \) \(a_{60}= +0.98504891 \pm 1.5 \cdot 10^{-6} \)

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