Properties

Label 5.31
Level $5$
Weight $0$
Character 5.1
Symmetry odd
\(R\) 11.15393
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(11.1539349347579065694605247753 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.48828655 \pm 2.3 \cdot 10^{-7} \) \(a_{3}= -0.69640225 \pm 2.5 \cdot 10^{-7} \)
\(a_{4}= +1.21499686 \pm 2.0 \cdot 10^{-7} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -1.03644610 \pm 2.3 \cdot 10^{-7} \)
\(a_{7}= -0.71279555 \pm 9.6 \cdot 10^{-8} \) \(a_{8}= +0.31997694 \pm 2.1 \cdot 10^{-7} \) \(a_{9}= -0.51502391 \pm 1.2 \cdot 10^{-7} \)
\(a_{10}= -0.66558198 \pm 2.4 \cdot 10^{-7} \) \(a_{11}= +0.51774918 \pm 1.2 \cdot 10^{-7} \) \(a_{12}= -0.84612655 \pm 2.1 \cdot 10^{-7} \)
\(a_{13}= -1.48686381 \pm 1.6 \cdot 10^{-7} \) \(a_{14}= -1.06084404 \pm 9.8 \cdot 10^{-8} \) \(a_{15}= +0.31144055 \pm 2.6 \cdot 10^{-7} \)
\(a_{16}= -0.73877948 \pm 1.0 \cdot 10^{-7} \) \(a_{17}= +1.13353925 \pm 2.5 \cdot 10^{-7} \) \(a_{18}= -0.76650316 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= -1.63881495 \pm 2.3 \cdot 10^{-7} \) \(a_{20}= -0.54336312 \pm 2.1 \cdot 10^{-7} \) \(a_{21}= +0.49639242 \pm 1.0 \cdot 10^{-7} \)
\(a_{22}= +0.77055915 \pm 1.3 \cdot 10^{-7} \) \(a_{23}= +0.60856473 \pm 1.0 \cdot 10^{-7} \) \(a_{24}= -0.22283266 \pm 2.2 \cdot 10^{-7} \)
\(a_{25}= +0.2 \) \(a_{26}= -2.21287941 \pm 1.9 \cdot 10^{-7} \) \(a_{27}= +1.05506606 \pm 1.9 \cdot 10^{-7} \)
\(a_{28}= -0.86604436 \pm 7.9 \cdot 10^{-8} \) \(a_{29}= +1.22542299 \pm 1.1 \cdot 10^{-7} \) \(a_{30}= +0.46351279 \pm 4.9 \cdot 10^{-7} \)
\(a_{31}= +0.05438510 \pm 2.4 \cdot 10^{-7} \) \(a_{32}= -1.41949251 \pm 2.5 \cdot 10^{-7} \) \(a_{33}= -0.36056169 \pm 9.3 \cdot 10^{-8} \)
\(a_{34}= +1.68703123 \pm 2.4 \cdot 10^{-7} \) \(a_{35}= +0.31877186 \pm 1.0 \cdot 10^{-7} \) \(a_{36}= -0.62575244 \pm 5.7 \cdot 10^{-8} \)
\(a_{37}= +0.87246569 \pm 3.0 \cdot 10^{-7} \) \(a_{38}= -2.43902625 \pm 1.6 \cdot 10^{-7} \) \(a_{39}= +1.03545530 \pm 1.3 \cdot 10^{-7} \)
\(a_{40}= -0.14309804 \pm 2.2 \cdot 10^{-7} \) \(a_{41}= -0.12814554 \pm 2.6 \cdot 10^{-7} \) \(a_{42}= +0.73877417 \pm 1.0 \cdot 10^{-7} \)
\(a_{43}= -1.16468558 \pm 2.6 \cdot 10^{-7} \) \(a_{44}= +0.62906363 \pm 9.8 \cdot 10^{-8} \) \(a_{45}= +0.23032569 \pm 1.3 \cdot 10^{-7} \)
\(a_{46}= +0.90571871 \pm 1.2 \cdot 10^{-7} \) \(a_{47}= -0.13919694 \pm 1.5 \cdot 10^{-7} \) \(a_{48}= +0.51448769 \pm 1.0 \cdot 10^{-7} \)
\(a_{49}= -0.49192250 \pm 2.1 \cdot 10^{-7} \) \(a_{50}= +0.29765731 \pm 2.4 \cdot 10^{-7} \) \(a_{51}= -0.78939928 \pm 2.5 \cdot 10^{-7} \)
\(a_{52}= -1.80653486 \pm 1.5 \cdot 10^{-7} \) \(a_{53}= -0.73622937 \pm 2.4 \cdot 10^{-7} \) \(a_{54}= +1.57024062 \pm 1.9 \cdot 10^{-7} \)
\(a_{55}= -0.23154447 \pm 1.3 \cdot 10^{-7} \) \(a_{56}= -0.22807814 \pm 8.4 \cdot 10^{-8} \) \(a_{57}= +1.14127441 \pm 2.7 \cdot 10^{-7} \)
\(a_{58}= +1.82378056 \pm 9.1 \cdot 10^{-8} \) \(a_{59}= -0.06746689 \pm 1.9 \cdot 10^{-7} \) \(a_{60}= +0.37839930 \pm 4.6 \cdot 10^{-7} \)

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