Properties

Label 13.157
Level $13$
Weight $0$
Character 13.1
Symmetry odd
\(R\) 13.35820
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(13.3582067458369704833518679994 \pm 4 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.80423950 \pm 1.5 \cdot 10^{-4} \) \(a_{3}= +0.67317451 \pm 1.4 \cdot 10^{-4} \)
\(a_{4}= -0.35319882 \pm 1.3 \cdot 10^{-4} \) \(a_{5}= +0.27788527 \pm 1.3 \cdot 10^{-4} \) \(a_{6}= -0.54139354 \pm 1.6 \cdot 10^{-4} \)
\(a_{7}= -1.26715774 \pm 1.3 \cdot 10^{-4} \) \(a_{8}= +1.08829595 \pm 1.1 \cdot 10^{-4} \) \(a_{9}= -0.54683607 \pm 1.4 \cdot 10^{-4} \)
\(a_{10}= -0.22348632 \pm 1.4 \cdot 10^{-4} \) \(a_{11}= -1.29891987 \pm 1.2 \cdot 10^{-4} \) \(a_{12}= -0.23776444 \pm 1.4 \cdot 10^{-4} \)
\(a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +1.01909832 \pm 1.4 \cdot 10^{-4} \) \(a_{15}= +0.18706528 \pm 1.5 \cdot 10^{-4} \)
\(a_{16}= -0.52205177 \pm 1.2 \cdot 10^{-4} \) \(a_{17}= -0.09971520 \pm 1.3 \cdot 10^{-4} \) \(a_{18}= +0.43978717 \pm 1.6 \cdot 10^{-4} \)
\(a_{19}= +0.98390521 \pm 1.1 \cdot 10^{-4} \) \(a_{20}= -0.09814875 \pm 1.3 \cdot 10^{-4} \) \(a_{21}= -0.85301830 \pm 1.1 \cdot 10^{-4} \)
\(a_{22}= +1.04464267 \pm 1.3 \cdot 10^{-4} \) \(a_{23}= -0.60576610 \pm 1.1 \cdot 10^{-4} \) \(a_{24}= +0.73261310 \pm 1.1 \cdot 10^{-4} \)
\(a_{25}= -0.92277977 \pm 1.0 \cdot 10^{-4} \) \(a_{26}= -0.22305591 \pm 1.5 \cdot 10^{-4} \) \(a_{27}= -1.04129062 \pm 1.1 \cdot 10^{-4} \)
\(a_{28}= +0.44755862 \pm 1.2 \cdot 10^{-4} \) \(a_{29}= +0.80154077 \pm 1.0 \cdot 10^{-4} \) \(a_{30}= -0.15044529 \pm 1.9 \cdot 10^{-4} \)
\(a_{31}= -1.57670479 \pm 1.4 \cdot 10^{-4} \) \(a_{32}= -0.66844129 \pm 1.5 \cdot 10^{-4} \) \(a_{33}= -0.87439975 \pm 1.0 \cdot 10^{-4} \)
\(a_{34}= +0.08019490 \pm 1.4 \cdot 10^{-4} \) \(a_{35}= -0.35212448 \pm 1.0 \cdot 10^{-4} \) \(a_{36}= +0.19314186 \pm 1.3 \cdot 10^{-4} \)
\(a_{37}= +0.14023588 \pm 1.6 \cdot 10^{-4} \) \(a_{38}= -0.79129544 \pm 1.0 \cdot 10^{-4} \) \(a_{39}= +0.18670502 \pm 1.4 \cdot 10^{-4} \)
\(a_{40}= +0.30242142 \pm 1.1 \cdot 10^{-4} \) \(a_{41}= -1.04120720 \pm 1.2 \cdot 10^{-4} \) \(a_{42}= +0.68603101 \pm 9.6 \cdot 10^{-5} \)
\(a_{43}= +1.13507617 \pm 1.3 \cdot 10^{-4} \) \(a_{44}= +0.45877696 \pm 1.2 \cdot 10^{-4} \) \(a_{45}= -0.15195769 \pm 1.4 \cdot 10^{-4} \)
\(a_{46}= +0.48718103 \pm 1.4 \cdot 10^{-4} \) \(a_{47}= +1.29695332 \pm 1.3 \cdot 10^{-4} \) \(a_{48}= -0.35143195 \pm 1.3 \cdot 10^{-4} \)
\(a_{49}= +0.60568875 \pm 1.2 \cdot 10^{-4} \) \(a_{50}= +0.74213595 \pm 1.2 \cdot 10^{-4} \) \(a_{51}= -0.06712573 \pm 1.5 \cdot 10^{-4} \)
\(a_{52}= -0.09795973 \pm 1.3 \cdot 10^{-4} \) \(a_{53}= +0.92117423 \pm 1.0 \cdot 10^{-4} \) \(a_{54}= +0.83744705 \pm 1.3 \cdot 10^{-4} \)
\(a_{55}= -0.36095070 \pm 8.9 \cdot 10^{-5} \) \(a_{56}= -1.37904264 \pm 1.0 \cdot 10^{-4} \) \(a_{57}= +0.66233991 \pm 1.0 \cdot 10^{-4} \)
\(a_{58}= -0.64463075 \pm 9.8 \cdot 10^{-5} \) \(a_{59}= +1.84432955 \pm 1.2 \cdot 10^{-4} \) \(a_{60}= -0.06607124 \pm 1.5 \cdot 10^{-4} \)

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