Properties

Label 5.10
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 6.823526
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(6.82352699542004840638783053459 \pm 8 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.50239859 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.44420778 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +1.25720152 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +2.16977574 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.01867775 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.38641921 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.08573612 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.67189308 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.27403754 \pm 1 \cdot 10^{-8} \) \(a_{12}= -1.81566022 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.60090893 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.53046002 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.64586935 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.67664585 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.16850492 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.63120841 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.04373142 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.56223761 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +1.47118233 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.41171361 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.85617233 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.55806963 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.90280472 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.12382077 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -1.28068322 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.02771347 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.97035321 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -0.46294828 \pm 1 \cdot 10^{-8} \) \(a_{32}= +1.40301098 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.39576715 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.75556014 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.45556654 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +1.36498910 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.61665958 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.06570202 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.86783735 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.17281192 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -0.49940161 \pm 1 \cdot 10^{-8} \) \(a_{42}= -2.21030226 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -1.26831230 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.34452041 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.48555595 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +1.28631210 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.82916469 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.97721721 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.03770436 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.30047972 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -1.68756390 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.75546362 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.94964223 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.18602815 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.12255331 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +0.39363665 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.06315725 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.54403527 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.12799937 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.81198794 \pm 1.0 \cdot 10^{-8} \)

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