Properties

Label 13.175
Level $13$
Weight $0$
Character 13.1
Symmetry odd
\(R\) 13.99015
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(13.990151114539748168779049836 \pm 6 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.98255203 \pm 1.6 \cdot 10^{-3} \) \(a_{3}= -1.45695237 \pm 1.5 \cdot 10^{-3} \)
\(a_{4}= -0.03459151 \pm 1.4 \cdot 10^{-3} \) \(a_{5}= -1.49462642 \pm 1.3 \cdot 10^{-3} \) \(a_{6}= +1.43153151 \pm 1.7 \cdot 10^{-3} \)
\(a_{7}= +1.71204737 \pm 1.4 \cdot 10^{-3} \) \(a_{8}= +1.01653999 \pm 1.2 \cdot 10^{-3} \) \(a_{9}= +1.12271021 \pm 1.5 \cdot 10^{-3} \)
\(a_{10}= +1.46854822 \pm 1.5 \cdot 10^{-3} \) \(a_{11}= -0.83527788 \pm 1.3 \cdot 10^{-3} \) \(a_{12}= +0.05039818 \pm 1.5 \cdot 10^{-3} \)
\(a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= -1.68217561 \pm 1.5 \cdot 10^{-3} \) \(a_{15}= +2.17759950 \pm 1.6 \cdot 10^{-3} \)
\(a_{16}= -0.96421192 \pm 1.2 \cdot 10^{-3} \) \(a_{17}= -1.15806476 \pm 1.4 \cdot 10^{-3} \) \(a_{18}= -1.10312119 \pm 1.7 \cdot 10^{-3} \)
\(a_{19}= +1.00443703 \pm 1.1 \cdot 10^{-3} \) \(a_{20}= +0.05170139 \pm 1.4 \cdot 10^{-3} \) \(a_{21}= -2.49437147 \pm 1.2 \cdot 10^{-3} \)
\(a_{22}= +0.82070397 \pm 1.4 \cdot 10^{-3} \) \(a_{23}= -0.93441880 \pm 1.1 \cdot 10^{-3} \) \(a_{24}= -1.48105034 \pm 1.1 \cdot 10^{-3} \)
\(a_{25}= +1.23390814 \pm 1.0 \cdot 10^{-3} \) \(a_{26}= -0.27251090 \pm 1.6 \cdot 10^{-3} \) \(a_{27}= -0.17878293 \pm 1.2 \cdot 10^{-3} \)
\(a_{28}= -0.05922231 \pm 1.3 \cdot 10^{-3} \) \(a_{29}= +0.02523085 \pm 1.0 \cdot 10^{-3} \) \(a_{30}= -2.13960481 \pm 2.0 \cdot 10^{-3} \)
\(a_{31}= -0.96065549 \pm 1.5 \cdot 10^{-3} \) \(a_{32}= -0.06915161 \pm 1.6 \cdot 10^{-3} \) \(a_{33}= +1.21696008 \pm 1.1 \cdot 10^{-3} \)
\(a_{34}= +1.13785888 \pm 1.5 \cdot 10^{-3} \) \(a_{35}= -2.55887123 \pm 1.1 \cdot 10^{-3} \) \(a_{36}= -0.03883624 \pm 1.4 \cdot 10^{-3} \)
\(a_{37}= -0.16346245 \pm 1.7 \cdot 10^{-3} \) \(a_{38}= -0.98691164 \pm 1.1 \cdot 10^{-3} \) \(a_{39}= -0.40408588 \pm 1.5 \cdot 10^{-3} \)
\(a_{40}= -1.51934752 \pm 1.2 \cdot 10^{-3} \) \(a_{41}= -0.85362131 \pm 1.2 \cdot 10^{-3} \) \(a_{42}= +2.45084974 \pm 1.0 \cdot 10^{-3} \)
\(a_{43}= +0.31238335 \pm 1.4 \cdot 10^{-3} \) \(a_{44}= +0.02889352 \pm 1.3 \cdot 10^{-3} \) \(a_{45}= -1.67803234 \pm 1.5 \cdot 10^{-3} \)
\(a_{46}= +0.91811508 \pm 1.5 \cdot 10^{-3} \) \(a_{47}= -0.51211644 \pm 1.4 \cdot 10^{-3} \) \(a_{48}= +1.40481084 \pm 1.4 \cdot 10^{-3} \)
\(a_{49}= +1.93110618 \pm 1.2 \cdot 10^{-3} \) \(a_{50}= -1.21237894 \pm 1.2 \cdot 10^{-3} \) \(a_{51}= +1.68724519 \pm 1.6 \cdot 10^{-3} \)
\(a_{52}= -0.00959396 \pm 1.4 \cdot 10^{-3} \) \(a_{53}= -1.27738153 \pm 1.0 \cdot 10^{-3} \) \(a_{54}= +0.17566353 \pm 1.4 \cdot 10^{-3} \)
\(a_{55}= +1.24842838 \pm 9.4 \cdot 10^{-4} \) \(a_{56}= +1.74036461 \pm 1.0 \cdot 10^{-3} \) \(a_{57}= -1.46341691 \pm 1.1 \cdot 10^{-3} \)
\(a_{58}= -0.02479062 \pm 1.0 \cdot 10^{-3} \) \(a_{59}= +1.25718691 \pm 1.3 \cdot 10^{-3} \) \(a_{60}= -0.07532646 \pm 1.6 \cdot 10^{-3} \)

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