Properties

Label 5.24
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 10.04582
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(10.0458208250339117398394776953 \pm 5 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.76604997 \pm 1.8 \cdot 10^{-8} \) \(a_{3}= -1.51567547 \pm 1.9 \cdot 10^{-8} \)
\(a_{4}= -0.41316744 \pm 1.5 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -1.16108315 \pm 1.8 \cdot 10^{-8} \)
\(a_{7}= +1.45299570 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.08255688 \pm 1.6 \cdot 10^{-8} \) \(a_{9}= +1.29727213 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.34258796 \pm 2.8 \cdot 10^{-8} \) \(a_{11}= +1.18198387 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= +0.62622775 \pm 1.6 \cdot 10^{-8} \)
\(a_{13}= -0.09958617 \pm 1.2 \cdot 10^{-8} \) \(a_{14}= +1.11306732 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.67783068 \pm 3.0 \cdot 10^{-8} \)
\(a_{16}= -0.41612523 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.99116397 \pm 2.0 \cdot 10^{-8} \) \(a_{18}= +0.99377528 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.12942130 \pm 1.8 \cdot 10^{-8} \) \(a_{20}= -0.18477410 \pm 2.6 \cdot 10^{-8} \) \(a_{21}= -2.20226994 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.90545871 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= -0.40589562 \pm 1 \cdot 10^{-8} \) \(a_{24}= +1.64080490 \pm 1.7 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.07628799 \pm 1.5 \cdot 10^{-8} \) \(a_{27}= -0.45056807 \pm 1.5 \cdot 10^{-8} \)
\(a_{28}= -0.60033052 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.32747491 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.51925217 \pm 4.8 \cdot 10^{-8} \)
\(a_{31}= +0.40756462 \pm 1.9 \cdot 10^{-8} \) \(a_{32}= +0.76378416 \pm 1.9 \cdot 10^{-8} \) \(a_{33}= -1.79150395 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.75928113 \pm 1.9 \cdot 10^{-8} \) \(a_{35}= +0.64979943 \pm 1.8 \cdot 10^{-8} \) \(a_{36}= -0.53599060 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.87533676 \pm 2.4 \cdot 10^{-8} \) \(a_{38}= +0.09914318 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= +0.15094032 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.48413415 \pm 2.7 \cdot 10^{-8} \) \(a_{41}= +0.01388687 \pm 2.0 \cdot 10^{-8} \) \(a_{42}= -1.68704883 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.00022350 \pm 2.0 \cdot 10^{-8} \) \(a_{44}= -0.48835725 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.58015773 \pm 2.0 \cdot 10^{-8} \)
\(a_{46}= -0.31093633 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.08342218 \pm 1.2 \cdot 10^{-8} \) \(a_{48}= +0.63071080 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +1.11119651 \pm 1.6 \cdot 10^{-8} \) \(a_{50}= +0.15320999 \pm 2.8 \cdot 10^{-8} \) \(a_{51}= -1.50228292 \pm 1.9 \cdot 10^{-8} \)
\(a_{52}= +0.04114576 \pm 1.2 \cdot 10^{-8} \) \(a_{53}= +1.08201311 \pm 1.9 \cdot 10^{-8} \) \(a_{54}= -0.34515766 \pm 1.5 \cdot 10^{-8} \)
\(a_{55}= +0.52859925 \pm 2.0 \cdot 10^{-8} \) \(a_{56}= -1.57295049 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.19616069 \pm 2.1 \cdot 10^{-8} \)
\(a_{58}= +0.25086214 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.87004361 \pm 1.5 \cdot 10^{-8} \) \(a_{60}= +0.28005757 \pm 4.6 \cdot 10^{-8} \)

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