Properties

Label 23.16
Level $23$
Weight $0$
Character 23.1
Symmetry odd
\(R\) 3.524543
Fricke sign $+1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(3.52454363827765669937957334759 \pm 10 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.35025558 \pm 2.7 \cdot 10^{-7} \) \(a_{3}= +1.20836683 \pm 2.5 \cdot 10^{-7} \)
\(a_{4}= -0.87732103 \pm 2.9 \cdot 10^{-7} \) \(a_{5}= -1.07017002 \pm 2.0 \cdot 10^{-7} \) \(a_{6}= -0.42323723 \pm 3.3 \cdot 10^{-7} \)
\(a_{7}= -1.52369010 \pm 2.0 \cdot 10^{-7} \) \(a_{8}= +0.65754217 \pm 2.6 \cdot 10^{-7} \) \(a_{9}= +0.46015038 \pm 2.2 \cdot 10^{-7} \)
\(a_{10}= +0.37483302 \pm 2.2 \cdot 10^{-7} \) \(a_{11}= +1.13275866 \pm 2.3 \cdot 10^{-7} \) \(a_{12}= -1.06012562 \pm 3.5 \cdot 10^{-7} \)
\(a_{13}= -1.08860264 \pm 1.8 \cdot 10^{-7} \) \(a_{14}= +0.53368096 \pm 2.3 \cdot 10^{-7} \) \(a_{15}= -1.29315795 \pm 2.3 \cdot 10^{-7} \)
\(a_{16}= +0.64701321 \pm 2.4 \cdot 10^{-7} \) \(a_{17}= -0.47608018 \pm 2.2 \cdot 10^{-7} \) \(a_{18}= -0.16117024 \pm 2.9 \cdot 10^{-7} \)
\(a_{19}= +0.99295676 \pm 1.8 \cdot 10^{-7} \) \(a_{20}= +0.93888266 \pm 2.6 \cdot 10^{-7} \) \(a_{21}= -1.84117657 \pm 2.3 \cdot 10^{-7} \)
\(a_{22}= -0.39675504 \pm 2.3 \cdot 10^{-7} \) \(a_{23}= -0.20851441 \pm 1.0 \cdot 10^{-8} \) \(a_{24}= +0.79455214 \pm 2.9 \cdot 10^{-7} \)
\(a_{25}= +0.14526388 \pm 2.0 \cdot 10^{-7} \) \(a_{26}= +0.38128915 \pm 2.2 \cdot 10^{-7} \) \(a_{27}= -0.65233637 \pm 1.9 \cdot 10^{-7} \)
\(a_{28}= +1.33676536 \pm 2.7 \cdot 10^{-7} \) \(a_{29}= -0.94917996 \pm 1.9 \cdot 10^{-7} \) \(a_{30}= +0.45293579 \pm 2.8 \cdot 10^{-7} \)
\(a_{31}= +0.34826645 \pm 1.9 \cdot 10^{-7} \) \(a_{32}= -0.88416216 \pm 2.6 \cdot 10^{-7} \) \(a_{33}= +1.36878798 \pm 2.0 \cdot 10^{-7} \)
\(a_{34}= +0.16674974 \pm 2.6 \cdot 10^{-7} \) \(a_{35}= +1.63060747 \pm 2.2 \cdot 10^{-7} \) \(a_{36}= -0.40369961 \pm 3.0 \cdot 10^{-7} \)
\(a_{37}= -1.53801214 \pm 2.0 \cdot 10^{-7} \) \(a_{38}= -0.34778865 \pm 2.1 \cdot 10^{-7} \) \(a_{39}= -1.31543132 \pm 2.2 \cdot 10^{-7} \)
\(a_{40}= -0.70368192 \pm 2.4 \cdot 10^{-7} \) \(a_{41}= -1.07602831 \pm 2.3 \cdot 10^{-7} \) \(a_{42}= +0.64488237 \pm 2.9 \cdot 10^{-7} \)
\(a_{43}= +1.65311699 \pm 2.3 \cdot 10^{-7} \) \(a_{44}= -0.99379299 \pm 2.5 \cdot 10^{-7} \) \(a_{45}= -0.49243915 \pm 2.3 \cdot 10^{-7} \)
\(a_{46}= +0.07303334 \pm 2.8 \cdot 10^{-7} \) \(a_{47}= -0.10876275 \pm 2.2 \cdot 10^{-7} \) \(a_{48}= +0.78182930 \pm 2.5 \cdot 10^{-7} \)
\(a_{49}= +1.32163152 \pm 1.7 \cdot 10^{-7} \) \(a_{50}= -0.05087948 \pm 2.2 \cdot 10^{-7} \) \(a_{51}= -0.57527950 \pm 2.2 \cdot 10^{-7} \)
\(a_{52}= +0.95505399 \pm 2.7 \cdot 10^{-7} \) \(a_{53}= -0.32152298 \pm 2.0 \cdot 10^{-7} \) \(a_{54}= +0.22848445 \pm 2.2 \cdot 10^{-7} \)
\(a_{55}= -1.21224436 \pm 1.7 \cdot 10^{-7} \) \(a_{56}= -1.00189050 \pm 2.5 \cdot 10^{-7} \) \(a_{57}= +1.19985601 \pm 2.1 \cdot 10^{-7} \)
\(a_{58}= +0.33245558 \pm 2.5 \cdot 10^{-7} \) \(a_{59}= +0.34001749 \pm 2.0 \cdot 10^{-7} \) \(a_{60}= +1.13451466 \pm 3.0 \cdot 10^{-7} \)

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