Properties

Label 13.91
Level $13$
Weight $0$
Character 13.1
Symmetry even
\(R\) 10.31744
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(10.3174493943770964696347589092 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.98531349 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.01469006 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.02915733 \pm 1.0 \cdot 10^{-8} \) \(a_{5}= -1.65020586 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.99978780 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.89403345 \pm 1 \cdot 10^{-8} \) \(a_{8}= +1.01404260 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.02959591 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +1.62597010 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.81774040 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.02958565 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +1.86621671 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -1.67444748 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.96999252 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.90300182 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.02916125 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.46664169 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.04811559 \pm 1 \cdot 10^{-8} \) \(a_{21}= -1.92185691 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.80573065 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.20150784 \pm 1 \cdot 10^{-8} \) \(a_{24}= +1.02893894 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +1.72317938 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.27327679 \pm 2.0 \cdot 10^{-8} \) \(a_{27}= -0.98465938 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.05522495 \pm 1.1 \cdot 10^{-8} \) \(a_{29}= +0.16420408 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.64985569 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.84137374 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.05829588 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.82975306 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.88973988 \pm 1 \cdot 10^{-8} \) \(a_{35}= +3.12554510 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.00086294 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.30551891 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.45978835 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -0.28142439 \pm 1.7 \cdot 10^{-8} \)
\(a_{40}= -1.67337904 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.32230748 \pm 1.0 \cdot 10^{-8} \) \(a_{42}= +1.89363154 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.94007302 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.02384312 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.04883935 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.19854839 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.43012565 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.98424177 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +2.58736272 \pm 1 \cdot 10^{-8} \) \(a_{50}= -1.69787189 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.91626697 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.00808679 \pm 2.0 \cdot 10^{-8} \) \(a_{53}= +1.27584131 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.97019817 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +1.34944001 \pm 1 \cdot 10^{-8} \) \(a_{56}= -1.92063060 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.47349668 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.16179249 \pm 1.1 \cdot 10^{-8} \) \(a_{59}= -0.46770093 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.04882241 \pm 1 \cdot 10^{-8} \)

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