Properties

Label 13.186
Level $13$
Weight $0$
Character 13.1
Symmetry odd
\(R\) 14.45835
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(14.4583560141038604331992208333 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.63993643 \pm 5.9 \cdot 10^{-3} \) \(a_{3}= -1.02336159 \pm 5.7 \cdot 10^{-3} \)
\(a_{4}= -0.59048137 \pm 5.4 \cdot 10^{-3} \) \(a_{5}= +0.55557033 \pm 5.1 \cdot 10^{-3} \) \(a_{6}= +0.65488636 \pm 6.6 \cdot 10^{-3} \)
\(a_{7}= -0.76492561 \pm 5.2 \cdot 10^{-3} \) \(a_{8}= +1.01780697 \pm 4.5 \cdot 10^{-3} \) \(a_{9}= +0.04726894 \pm 5.6 \cdot 10^{-3} \)
\(a_{10}= -0.35552970 \pm 5.8 \cdot 10^{-3} \) \(a_{11}= -1.72927124 \pm 4.8 \cdot 10^{-3} \) \(a_{12}= +0.60427595 \pm 5.8 \cdot 10^{-3} \)
\(a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +0.48950376 \pm 5.7 \cdot 10^{-3} \) \(a_{15}= -0.56854934 \pm 6.2 \cdot 10^{-3} \)
\(a_{16}= -0.06085039 \pm 4.7 \cdot 10^{-3} \) \(a_{17}= +1.06973512 \pm 5.2 \cdot 10^{-3} \) \(a_{18}= -0.03024912 \pm 6.4 \cdot 10^{-3} \)
\(a_{19}= +0.01906219 \pm 4.3 \cdot 10^{-3} \) \(a_{20}= -0.32805393 \pm 5.3 \cdot 10^{-3} \) \(a_{21}= +0.78279548 \pm 4.5 \cdot 10^{-3} \)
\(a_{22}= +1.10662367 \pm 5.3 \cdot 10^{-3} \) \(a_{23}= +1.87897865 \pm 4.3 \cdot 10^{-3} \) \(a_{24}= -1.04158456 \pm 4.4 \cdot 10^{-3} \)
\(a_{25}= -0.69134160 \pm 3.9 \cdot 10^{-3} \) \(a_{26}= +0.17748643 \pm 5.9 \cdot 10^{-3} \) \(a_{27}= +0.97498837 \pm 4.6 \cdot 10^{-3} \)
\(a_{28}= +0.45167432 \pm 4.9 \cdot 10^{-3} \) \(a_{29}= -0.67032694 \pm 3.9 \cdot 10^{-3} \) \(a_{30}= +0.36383544 \pm 7.5 \cdot 10^{-3} \)
\(a_{31}= +0.83009116 \pm 5.6 \cdot 10^{-3} \) \(a_{32}= -0.97886658 \pm 6.0 \cdot 10^{-3} \) \(a_{33}= +1.76966977 \pm 4.2 \cdot 10^{-3} \)
\(a_{34}= -0.68456248 \pm 5.7 \cdot 10^{-3} \) \(a_{35}= -0.42496997 \pm 4.2 \cdot 10^{-3} \) \(a_{36}= -0.02791143 \pm 5.2 \cdot 10^{-3} \)
\(a_{37}= +1.35864801 \pm 6.5 \cdot 10^{-3} \) \(a_{38}= -0.01219859 \pm 4.1 \cdot 10^{-3} \) \(a_{39}= +0.28382944 \pm 5.7 \cdot 10^{-3} \)
\(a_{40}= +0.56546336 \pm 4.5 \cdot 10^{-3} \) \(a_{41}= +1.16657830 \pm 4.7 \cdot 10^{-3} \) \(a_{42}= -0.50093935 \pm 3.7 \cdot 10^{-3} \)
\(a_{43}= +0.81083656 \pm 5.2 \cdot 10^{-3} \) \(a_{44}= +1.02110244 \pm 5.0 \cdot 10^{-3} \) \(a_{45}= +0.02626122 \pm 5.6 \cdot 10^{-3} \)
\(a_{46}= -1.20242689 \pm 5.6 \cdot 10^{-3} \) \(a_{47}= -0.44118848 \pm 5.4 \cdot 10^{-3} \) \(a_{48}= +0.06227195 \pm 5.3 \cdot 10^{-3} \)
\(a_{49}= -0.41488882 \pm 4.7 \cdot 10^{-3} \) \(a_{50}= +0.44241468 \pm 4.7 \cdot 10^{-3} \) \(a_{51}= -1.09472584 \pm 6.1 \cdot 10^{-3} \)
\(a_{52}= +0.16377006 \pm 5.4 \cdot 10^{-3} \) \(a_{53}= -0.03535638 \pm 4.0 \cdot 10^{-3} \) \(a_{54}= -0.62393058 \pm 5.4 \cdot 10^{-3} \)
\(a_{55}= -0.96073180 \pm 3.4 \cdot 10^{-3} \) \(a_{56}= -0.77854661 \pm 3.9 \cdot 10^{-3} \) \(a_{57}= -0.01950752 \pm 4.1 \cdot 10^{-3} \)
\(a_{58}= +0.42896663 \pm 3.8 \cdot 10^{-3} \) \(a_{59}= +0.24168906 \pm 4.8 \cdot 10^{-3} \) \(a_{60}= +0.33571779 \pm 6.2 \cdot 10^{-3} \)

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