Properties

Label 13.194
Level $13$
Weight $0$
Character 13.1
Symmetry even
\(R\) 14.67181
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(14.6718170691001421911597173815 \pm 3 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.85454918 \pm 6.8 \cdot 10^{-6} \) \(a_{3}= +1.18939602 \pm 5.2 \cdot 10^{-6} \)
\(a_{4}= -0.26974569 \pm 7.3 \cdot 10^{-6} \) \(a_{5}= +0.75803629 \pm 5.7 \cdot 10^{-6} \) \(a_{6}= -1.01639740 \pm 6.6 \cdot 10^{-6} \)
\(a_{7}= -0.88638633 \pm 5.2 \cdot 10^{-6} \) \(a_{8}= +1.08506015 \pm 6.7 \cdot 10^{-6} \) \(a_{9}= +0.41466289 \pm 4.6 \cdot 10^{-6} \)
\(a_{10}= -0.64777929 \pm 5.2 \cdot 10^{-6} \) \(a_{11}= +0.37806249 \pm 3.9 \cdot 10^{-6} \) \(a_{12}= -0.32083445 \pm 6.5 \cdot 10^{-6} \)
\(a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +0.75746072 \pm 7.4 \cdot 10^{-6} \) \(a_{15}= +0.90160535 \pm 4.2 \cdot 10^{-6} \)
\(a_{16}= -0.65749157 \pm 4.7 \cdot 10^{-6} \) \(a_{17}= +0.37829645 \pm 5.1 \cdot 10^{-6} \) \(a_{18}= -0.35434983 \pm 5.4 \cdot 10^{-6} \)
\(a_{19}= -1.82298932 \pm 5.5 \cdot 10^{-6} \) \(a_{20}= -0.20447702 \pm 6.3 \cdot 10^{-6} \) \(a_{21}= -1.05426437 \pm 4.2 \cdot 10^{-6} \)
\(a_{22}= -0.32307300 \pm 3.7 \cdot 10^{-6} \) \(a_{23}= -0.06393740 \pm 3.7 \cdot 10^{-6} \) \(a_{24}= +1.29056622 \pm 6.1 \cdot 10^{-6} \)
\(a_{25}= -0.42538098 \pm 6.3 \cdot 10^{-6} \) \(a_{26}= -0.23700930 \pm 6.8 \cdot 10^{-6} \) \(a_{27}= -0.69619763 \pm 5.6 \cdot 10^{-6} \)
\(a_{28}= +0.23909889 \pm 8.0 \cdot 10^{-6} \) \(a_{29}= +0.06231457 \pm 4.9 \cdot 10^{-6} \) \(a_{30}= -0.77046611 \pm 3.5 \cdot 10^{-6} \)
\(a_{31}= +1.72167118 \pm 3.8 \cdot 10^{-6} \) \(a_{32}= -0.52320126 \pm 5.1 \cdot 10^{-6} \) \(a_{33}= +0.44966603 \pm 4.6 \cdot 10^{-6} \)
\(a_{34}= -0.32327292 \pm 6.5 \cdot 10^{-6} \) \(a_{35}= -0.67191301 \pm 4.7 \cdot 10^{-6} \) \(a_{36}= -0.11185353 \pm 4.5 \cdot 10^{-6} \)
\(a_{37}= +1.57690600 \pm 4.5 \cdot 10^{-6} \) \(a_{38}= +1.55783404 \pm 7.4 \cdot 10^{-6} \) \(a_{39}= +0.32987910 \pm 5.2 \cdot 10^{-6} \)
\(a_{40}= +0.82251497 \pm 6.1 \cdot 10^{-6} \) \(a_{41}= -1.00557767 \pm 7.6 \cdot 10^{-6} \) \(a_{42}= +0.90092076 \pm 6.1 \cdot 10^{-6} \)
\(a_{43}= -0.03451455 \pm 4.3 \cdot 10^{-6} \) \(a_{44}= -0.10198073 \pm 3.0 \cdot 10^{-6} \) \(a_{45}= +0.31432952 \pm 3.9 \cdot 10^{-6} \)
\(a_{46}= +0.05463765 \pm 4.4 \cdot 10^{-6} \) \(a_{47}= +0.00747220 \pm 4.0 \cdot 10^{-6} \) \(a_{48}= -0.78201786 \pm 4.2 \cdot 10^{-6} \)
\(a_{49}= -0.21431927 \pm 3.9 \cdot 10^{-6} \) \(a_{50}= +0.36350897 \pm 5.1 \cdot 10^{-6} \) \(a_{51}= +0.44994429 \pm 5.5 \cdot 10^{-6} \)
\(a_{52}= -0.07481399 \pm 7.3 \cdot 10^{-6} \) \(a_{53}= +0.41581193 \pm 5.4 \cdot 10^{-6} \) \(a_{54}= +0.59493512 \pm 5.9 \cdot 10^{-6} \)
\(a_{55}= +0.28658509 \pm 3.6 \cdot 10^{-6} \) \(a_{56}= -0.96178248 \pm 6.3 \cdot 10^{-6} \) \(a_{57}= -2.16825624 \pm 3.1 \cdot 10^{-6} \)
\(a_{58}= -0.05325087 \pm 7.9 \cdot 10^{-6} \) \(a_{59}= -1.56038292 \pm 4.5 \cdot 10^{-6} \) \(a_{60}= -0.24320416 \pm 4.1 \cdot 10^{-6} \)

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