Properties

Label 5.43
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 12.85545
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(12.8554583745688571317287512642 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.34107983 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.83325140 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.79849510 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -2.45853646 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.26643107 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.27023415 \pm 1 \cdot 10^{-8} \) \(a_{9}= +2.36081068 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.59974913 \pm 1.6 \cdot 10^{-8} \) \(a_{11}= +0.39369449 \pm 1 \cdot 10^{-8} \) \(a_{12}= -1.46384226 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.45101490 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.35730534 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.81985495 \pm 1.5 \cdot 10^{-8} \)
\(a_{16}= -1.16090067 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.00559672 \pm 1 \cdot 10^{-8} \) \(a_{18}= +3.16603558 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.89093530 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.35709787 \pm 1.6 \cdot 10^{-8} \) \(a_{21}= -0.48843514 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.52797574 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.23720464 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.49540714 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +1.94592682 \pm 1 \cdot 10^{-8} \) \(a_{27}= -2.49470807 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.21274391 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.62235679 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.09949093 \pm 2.0 \cdot 10^{-8} \)
\(a_{31}= +0.18724929 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.28662632 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.72174097 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.00750564 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.11915160 \pm 1.6 \cdot 10^{-8} \) \(a_{36}= +1.88509577 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.09280769 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.19481536 \pm 1 \cdot 10^{-8} \) \(a_{39}= -2.66007510 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.12085239 \pm 1.7 \cdot 10^{-8} \) \(a_{41}= +1.70760798 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.65503051 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.84433376 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.31436312 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.05578663 \pm 1.3 \cdot 10^{-8} \)
\(a_{46}= +0.31811035 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.12484987 \pm 1 \cdot 10^{-8} \) \(a_{48}= +2.12822278 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.92901448 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.26821597 \pm 1.6 \cdot 10^{-8} \) \(a_{51}= +0.01026019 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +1.15862829 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.97296659 \pm 1 \cdot 10^{-8} \) \(a_{54}= -3.34560267 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.17606553 \pm 1.7 \cdot 10^{-8} \) \(a_{56}= -0.07199878 \pm 1 \cdot 10^{-8} \) \(a_{57}= -1.63330838 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.83463013 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.75657928 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.65465016 \pm 2.0 \cdot 10^{-8} \)

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