Properties

Label 13.42
Level $13$
Weight $0$
Character 13.1
Symmetry even
\(R\) 7.266725
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(7.26672532739623709080258495332 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.87204905 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.00906733 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.50456764 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.53380582 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.01697448 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.29987619 \pm 1 \cdot 10^{-8} \) \(a_{8}= -2.81662442 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.99991778 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +2.87135973 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.40578733 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.02270973 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +0.56138295 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.01390752 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +2.76829143 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.29609404 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.87189514 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.57987337 \pm 1 \cdot 10^{-8} \) \(a_{20}= -3.84152043 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.00271908 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +2.63170283 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.35332279 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.02553925 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +1.35256030 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.51921299 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +0.01813391 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.75106021 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.58967746 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.02603556 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +1.07637975 \pm 1 \cdot 10^{-8} \) \(a_{32}= -2.36575292 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.01274673 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.55430257 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.45995185 \pm 1 \cdot 10^{-8} \) \(a_{36}= -2.50436173 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.21714047 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.08555140 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.00251482 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +4.32015494 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.55157820 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.00509024 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.23183534 \pm 1 \cdot 10^{-8} \) \(a_{44}= -3.52088946 \pm 1 \cdot 10^{-8} \) \(a_{45}= +1.53367972 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.66143759 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.12022168 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.02510100 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.91007427 \pm 1 \cdot 10^{-8} \) \(a_{50}= -2.53205922 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.00268478 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.69464208 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= +0.97715152 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.03394757 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +2.15620479 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.84463861 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.00525790 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.10390513 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.86374070 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.03483232 \pm 1 \cdot 10^{-8} \)

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