Properties

Label 5.32
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 11.18138
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(11.1813819580345604947372703581 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.72940041 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.02650352 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +1.99082579 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.04583519 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.37044605 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.71353454 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.99929756 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.77341138 \pm 1.1 \cdot 10^{-8} \) \(a_{11}= +0.41059224 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.05276389 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.37542475 \pm 1 \cdot 10^{-8} \) \(a_{14}= +2.37004997 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.01185273 \pm 1.1 \cdot 10^{-8} \)
\(a_{16}= +0.97256154 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.49634281 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.72818562 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.72280991 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.89032436 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= -0.03632164 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.71007839 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.41391785 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.04541469 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.64925972 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.05298842 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -2.72831935 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.53225900 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.02049812 \pm 1.1 \cdot 10^{-8} \)
\(a_{31}= -0.42231851 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.03158620 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.01088214 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +2.58777587 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.61288211 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -1.98942736 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.04778596 \pm 1 \cdot 10^{-8} \) \(a_{38}= -1.25002775 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.00995008 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.76631594 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +1.13371232 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.06281466 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.12782499 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.81741762 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.44689946 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= -2.44523012 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.45141104 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.02577630 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.87812239 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.34588008 \pm 1.1 \cdot 10^{-8} \) \(a_{51}= -0.03965835 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.74740527 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.22221673 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.09163819 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.18362243 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= +2.34830664 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.01915701 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -2.64988935 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.67308746 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.02359673 \pm 1.1 \cdot 10^{-8} \)

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