Properties

Label 5.30
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 11.09312
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(11.0931280004854038979726892996 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.31821009 \pm 3.9 \cdot 10^{-7} \) \(a_{3}= -0.14985869 \pm 4.2 \cdot 10^{-7} \)
\(a_{4}= -0.89874234 \pm 3.4 \cdot 10^{-7} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.04768655 \pm 4.0 \cdot 10^{-7} \)
\(a_{7}= -1.39569714 \pm 1.6 \cdot 10^{-7} \) \(a_{8}= +0.60419897 \pm 3.6 \cdot 10^{-7} \) \(a_{9}= -0.97754237 \pm 2.0 \cdot 10^{-7} \)
\(a_{10}= -0.14230788 \pm 4.0 \cdot 10^{-7} \) \(a_{11}= +0.94349242 \pm 2.1 \cdot 10^{-7} \) \(a_{12}= +0.13468435 \pm 3.5 \cdot 10^{-7} \)
\(a_{13}= +1.57536981 \pm 2.7 \cdot 10^{-7} \) \(a_{14}= +0.44412491 \pm 1.6 \cdot 10^{-7} \) \(a_{15}= -0.06701884 \pm 4.3 \cdot 10^{-7} \)
\(a_{16}= +0.70648014 \pm 1.7 \cdot 10^{-7} \) \(a_{17}= -0.27827180 \pm 4.3 \cdot 10^{-7} \) \(a_{18}= +0.31106384 \pm 1.8 \cdot 10^{-7} \)
\(a_{19}= +1.35632093 \pm 4.0 \cdot 10^{-7} \) \(a_{20}= -0.40192979 \pm 3.5 \cdot 10^{-7} \) \(a_{21}= +0.20915734 \pm 1.8 \cdot 10^{-7} \)
\(a_{22}= -0.30022881 \pm 2.3 \cdot 10^{-7} \) \(a_{23}= -0.14379336 \pm 1.7 \cdot 10^{-7} \) \(a_{24}= -0.09054447 \pm 3.8 \cdot 10^{-7} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.50129857 \pm 3.3 \cdot 10^{-7} \) \(a_{27}= +0.29635191 \pm 3.2 \cdot 10^{-7} \)
\(a_{28}= +1.25437211 \pm 1.3 \cdot 10^{-7} \) \(a_{29}= -0.25170097 \pm 1.9 \cdot 10^{-7} \) \(a_{30}= +0.02132607 \pm 8.3 \cdot 10^{-7} \)
\(a_{31}= -0.24790308 \pm 4.2 \cdot 10^{-7} \) \(a_{32}= -0.82900807 \pm 4.2 \cdot 10^{-7} \) \(a_{33}= -0.14139054 \pm 1.5 \cdot 10^{-7} \)
\(a_{34}= +0.08854889 \pm 4.1 \cdot 10^{-7} \) \(a_{35}= -0.62417473 \pm 1.7 \cdot 10^{-7} \) \(a_{36}= +0.87855872 \pm 9.7 \cdot 10^{-8} \)
\(a_{37}= +1.01274664 \pm 5.2 \cdot 10^{-7} \) \(a_{38}= -0.43159500 \pm 2.8 \cdot 10^{-7} \) \(a_{39}= -0.23608286 \pm 2.2 \cdot 10^{-7} \)
\(a_{40}= +0.27020599 \pm 3.7 \cdot 10^{-7} \) \(a_{41}= +0.51964696 \pm 4.4 \cdot 10^{-7} \) \(a_{42}= -0.06655598 \pm 1.7 \cdot 10^{-7} \)
\(a_{43}= -0.68912000 \pm 4.4 \cdot 10^{-7} \) \(a_{44}= -0.84795659 \pm 1.6 \cdot 10^{-7} \) \(a_{45}= -0.43717024 \pm 2.1 \cdot 10^{-7} \)
\(a_{46}= +0.04575650 \pm 2.0 \cdot 10^{-7} \) \(a_{47}= +0.83793176 \pm 2.6 \cdot 10^{-7} \) \(a_{48}= -0.10587219 \pm 1.7 \cdot 10^{-7} \)
\(a_{49}= +0.94797049 \pm 3.5 \cdot 10^{-7} \) \(a_{50}= -0.06364202 \pm 4.0 \cdot 10^{-7} \) \(a_{51}= +0.04170145 \pm 4.2 \cdot 10^{-7} \)
\(a_{52}= -1.41585155 \pm 2.6 \cdot 10^{-7} \) \(a_{53}= +1.55839449 \pm 4.1 \cdot 10^{-7} \) \(a_{54}= -0.09430217 \pm 3.3 \cdot 10^{-7} \)
\(a_{55}= +0.42194264 \pm 2.3 \cdot 10^{-7} \) \(a_{56}= -0.84327876 \pm 1.4 \cdot 10^{-7} \) \(a_{57}= -0.20325648 \pm 4.7 \cdot 10^{-7} \)
\(a_{58}= +0.08009379 \pm 1.5 \cdot 10^{-7} \) \(a_{59}= -0.49169326 \pm 3.3 \cdot 10^{-7} \) \(a_{60}= +0.06023267 \pm 7.8 \cdot 10^{-7} \)

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