Properties

Label 5.61
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 14.98678
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(14.9867895143026282497687488554 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.96060755 \pm 3.3 \cdot 10^{-4} \) \(a_{3}= -0.23968016 \pm 3.6 \cdot 10^{-4} \)
\(a_{4}= -0.07723313 \pm 2.9 \cdot 10^{-4} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.23023857 \pm 3.4 \cdot 10^{-4} \)
\(a_{7}= +0.94632982 \pm 1.3 \cdot 10^{-4} \) \(a_{8}= -1.03479828 \pm 3.1 \cdot 10^{-4} \) \(a_{9}= -0.94255342 \pm 1.7 \cdot 10^{-4} \)
\(a_{10}= +0.42959676 \pm 3.3 \cdot 10^{-4} \) \(a_{11}= +0.83684963 \pm 1.8 \cdot 10^{-4} \) \(a_{12}= +0.01851125 \pm 3.0 \cdot 10^{-4} \)
\(a_{13}= +1.29993484 \pm 2.3 \cdot 10^{-4} \) \(a_{14}= +0.90905157 \pm 1.4 \cdot 10^{-4} \) \(a_{15}= -0.10718823 \pm 3.6 \cdot 10^{-4} \)
\(a_{16}= -0.91680191 \pm 1.4 \cdot 10^{-4} \) \(a_{17}= -0.12407729 \pm 3.7 \cdot 10^{-4} \) \(a_{18}= -0.90542393 \pm 1.5 \cdot 10^{-4} \)
\(a_{19}= +1.47712782 \pm 3.4 \cdot 10^{-4} \) \(a_{20}= -0.03453971 \pm 2.9 \cdot 10^{-4} \) \(a_{21}= -0.22681648 \pm 1.5 \cdot 10^{-4} \)
\(a_{22}= +0.80388407 \pm 1.9 \cdot 10^{-4} \) \(a_{23}= +0.85717918 \pm 1.4 \cdot 10^{-4} \) \(a_{24}= +0.24802062 \pm 3.2 \cdot 10^{-4} \)
\(a_{25}= +0.2 \) \(a_{26}= +1.24872723 \pm 2.8 \cdot 10^{-4} \) \(a_{27}= +0.46559151 \pm 2.7 \cdot 10^{-4} \)
\(a_{28}= -0.07308802 \pm 1.1 \cdot 10^{-4} \) \(a_{29}= +1.50225644 \pm 1.6 \cdot 10^{-4} \) \(a_{30}= -0.10296582 \pm 6.9 \cdot 10^{-4} \)
\(a_{31}= -0.03240728 \pm 3.5 \cdot 10^{-4} \) \(a_{32}= +0.15411145 \pm 3.6 \cdot 10^{-4} \) \(a_{33}= -0.20057625 \pm 1.3 \cdot 10^{-4} \)
\(a_{34}= -0.11918958 \pm 3.5 \cdot 10^{-4} \) \(a_{35}= +0.42321156 \pm 1.3 \cdot 10^{-4} \) \(a_{36}= +0.07279636 \pm 8.2 \cdot 10^{-5} \)
\(a_{37}= +0.28178048 \pm 4.4 \cdot 10^{-4} \) \(a_{38}= +1.41894013 \pm 2.4 \cdot 10^{-4} \) \(a_{39}= -0.31156859 \pm 1.8 \cdot 10^{-4} \)
\(a_{40}= -0.46277586 \pm 3.1 \cdot 10^{-4} \) \(a_{41}= -0.47520235 \pm 3.7 \cdot 10^{-4} \) \(a_{42}= -0.21788163 \pm 1.4 \cdot 10^{-4} \)
\(a_{43}= -0.32897076 \pm 3.7 \cdot 10^{-4} \) \(a_{44}= -0.06463252 \pm 1.4 \cdot 10^{-4} \) \(a_{45}= -0.42152270 \pm 1.7 \cdot 10^{-4} \)
\(a_{46}= +0.82341279 \pm 1.7 \cdot 10^{-4} \) \(a_{47}= +0.89230822 \pm 2.2 \cdot 10^{-4} \) \(a_{48}= +0.21973923 \pm 1.5 \cdot 10^{-4} \)
\(a_{49}= -0.10445987 \pm 3.0 \cdot 10^{-4} \) \(a_{50}= +0.19212151 \pm 3.3 \cdot 10^{-4} \) \(a_{51}= +0.02973886 \pm 3.6 \cdot 10^{-4} \)
\(a_{52}= -0.10039804 \pm 2.2 \cdot 10^{-4} \) \(a_{53}= -1.82846460 \pm 3.5 \cdot 10^{-4} \) \(a_{54}= +0.44725072 \pm 2.8 \cdot 10^{-4} \)
\(a_{55}= +0.37425053 \pm 1.8 \cdot 10^{-4} \) \(a_{56}= -0.97926048 \pm 1.2 \cdot 10^{-4} \) \(a_{57}= -0.35403823 \pm 3.9 \cdot 10^{-4} \)
\(a_{58}= +1.44307888 \pm 1.3 \cdot 10^{-4} \) \(a_{59}= +1.37176601 \pm 2.8 \cdot 10^{-4} \) \(a_{60}= +0.00827848 \pm 6.5 \cdot 10^{-4} \)

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