Properties

Label 7.76
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 13.58384
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.5838479949470338728978508051 \pm 9 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.50413279 \pm 1.7 \cdot 10^{-5} \) \(a_{3}= -1.59984529 \pm 1.1 \cdot 10^{-5} \)
\(a_{4}= -0.74585013 \pm 1.0 \cdot 10^{-5} \) \(a_{5}= -0.74880727 \pm 1.2 \cdot 10^{-5} \) \(a_{6}= +0.80653446 \pm 1.3 \cdot 10^{-5} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.88014029 \pm 1.1 \cdot 10^{-5} \) \(a_{9}= +1.55950494 \pm 1.1 \cdot 10^{-5} \)
\(a_{10}= +0.37749829 \pm 1.2 \cdot 10^{-5} \) \(a_{11}= +0.77264687 \pm 1.0 \cdot 10^{-5} \) \(a_{12}= +1.19324482 \pm 9.2 \cdot 10^{-6} \)
\(a_{13}= -1.03465630 \pm 1.2 \cdot 10^{-5} \) \(a_{14}= +0.19054428 \pm 1.7 \cdot 10^{-5} \) \(a_{15}= +1.19797578 \pm 9.8 \cdot 10^{-6} \)
\(a_{16}= +0.30214255 \pm 1.4 \cdot 10^{-5} \) \(a_{17}= +0.26125351 \pm 9.7 \cdot 10^{-6} \) \(a_{18}= -0.78619757 \pm 1.0 \cdot 10^{-5} \)
\(a_{19}= +1.66610425 \pm 1.2 \cdot 10^{-5} \) \(a_{20}= +0.55849800 \pm 8.1 \cdot 10^{-6} \) \(a_{21}= +0.60468468 \pm 1.1 \cdot 10^{-5} \)
\(a_{22}= -0.38951662 \pm 1.0 \cdot 10^{-5} \) \(a_{23}= -0.49190565 \pm 1.5 \cdot 10^{-5} \) \(a_{24}= -1.40808830 \pm 7.6 \cdot 10^{-6} \)
\(a_{25}= -0.43928768 \pm 1.1 \cdot 10^{-5} \) \(a_{26}= +0.52160417 \pm 1.5 \cdot 10^{-5} \) \(a_{27}= -0.89512134 \pm 1.2 \cdot 10^{-5} \)
\(a_{28}= +0.28190485 \pm 1.0 \cdot 10^{-5} \) \(a_{29}= -1.59284143 \pm 1.1 \cdot 10^{-5} \) \(a_{30}= -0.60393887 \pm 1.1 \cdot 10^{-5} \)
\(a_{31}= +1.24938873 \pm 9.5 \cdot 10^{-6} \) \(a_{32}= -1.03246026 \pm 1.5 \cdot 10^{-5} \) \(a_{33}= -1.23611545 \pm 8.8 \cdot 10^{-6} \)
\(a_{34}= -0.13170646 \pm 1.1 \cdot 10^{-5} \) \(a_{35}= +0.28302254 \pm 1.2 \cdot 10^{-5} \) \(a_{36}= -1.16315697 \pm 6.2 \cdot 10^{-6} \)
\(a_{37}= -0.24395273 \pm 1.1 \cdot 10^{-5} \) \(a_{38}= -0.83993778 \pm 1.2 \cdot 10^{-5} \) \(a_{39}= +1.65529001 \pm 9.6 \cdot 10^{-6} \)
\(a_{40}= -0.65905545 \pm 1.2 \cdot 10^{-5} \) \(a_{41}= +1.09004208 \pm 1.5 \cdot 10^{-5} \) \(a_{42}= -0.30484137 \pm 2.9 \cdot 10^{-5} \)
\(a_{43}= +0.31120157 \pm 9.3 \cdot 10^{-6} \) \(a_{44}= -0.57627877 \pm 7.9 \cdot 10^{-6} \) \(a_{45}= -1.16776863 \pm 9.9 \cdot 10^{-6} \)
\(a_{46}= +0.24798577 \pm 1.8 \cdot 10^{-5} \) \(a_{47}= -0.50251645 \pm 1.4 \cdot 10^{-5} \) \(a_{48}= -0.48338134 \pm 1.1 \cdot 10^{-5} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.22145932 \pm 1.4 \cdot 10^{-5} \) \(a_{51}= -0.41796520 \pm 7.1 \cdot 10^{-6} \)
\(a_{52}= +0.77169854 \pm 8.4 \cdot 10^{-6} \) \(a_{53}= +1.89865232 \pm 9.7 \cdot 10^{-6} \) \(a_{54}= +0.45126002 \pm 1.6 \cdot 10^{-5} \)
\(a_{55}= -0.57856359 \pm 1.0 \cdot 10^{-5} \) \(a_{56}= -0.33266176 \pm 1.1 \cdot 10^{-5} \) \(a_{57}= -2.66550903 \pm 6.1 \cdot 10^{-6} \)
\(a_{58}= +0.80300359 \pm 1.2 \cdot 10^{-5} \) \(a_{59}= +0.99455189 \pm 1.9 \cdot 10^{-5} \) \(a_{60}= -0.89351039 \pm 7.9 \cdot 10^{-6} \)

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